Advances in Intelligent Systems and Computing 749

Surajit Chattopadhyay · Tamal Roy 
Samarjit Sengupta
Christian Berger-Vachon Editors

Modelling and Simulation

in Science, Technology
and Engineering
Mathematics
Proceedings of the International
Conference on Modelling and
Simulation (MS-17)
Advances in Intelligent Systems and Computing

Volume 749

Series editor
Janusz Kacprzyk, Polish Academy of Sciences, Warsaw, Poland
e-mail: kacprzyk@ibspan.waw.pl
The series “Advances in Intelligent Systems and Computing” contains publications on theory,
applications, and design methods of Intelligent Systems and Intelligent Computing. Virtually all
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e-mail: nikhil@isical.ac.in
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e-mail: rbellop@uclv.edu.cu
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e-mail: escorchado@usal.es
Hani Hagras, University of Essex, Colchester, UK
e-mail: hani@essex.ac.uk
László T. Kóczy, Széchenyi István University, Győr, Hungary
e-mail: koczy@sze.hu
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e-mail: vladik@utep.edu
Chin-Teng Lin, National Chiao Tung University, Hsinchu, Taiwan
e-mail: ctlin@mail.nctu.edu.tw
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e-mail: Jie.Lu@uts.edu.au
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e-mail: Ngoc-Thanh.Nguyen@pwr.edu.pl
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e-mail: jwang@mae.cuhk.edu.hk

More information about this series at http://www.springer.com/series/11156

Surajit Chattopadhyay Tamal Roy
•

Samarjit Sengupta Christian Berger-Vachon

•

Editors

Modelling and Simulation

in Science, Technology
and Engineering Mathematics
Proceedings of the International Conference
on Modelling and Simulation (MS-17)

123
Editors
Surajit Chattopadhyay Samarjit Sengupta
Department of Electrical Engineering University of Calcutta
Ghani Khan Choudhury Institute of Kolkata, West Bengal, India
Engineering and Technology
Malda, West Bengal, India Christian Berger-Vachon
University of Lyon
Tamal Roy Lyon, France
Department of Electrical Engineering
MCKV Institute of Engineering
Howrah, West Bengal, India

ISSN 2194-5357 ISSN 2194-5365 (electronic)

Advances in Intelligent Systems and Computing
ISBN 978-3-319-74807-8 ISBN 978-3-319-74808-5 (eBook)
https://doi.org/10.1007/978-3-319-74808-5

Library of Congress Control Number: 2018954605

© Springer Nature Switzerland AG 2019

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Preface

Application of modelling and simulation in science and technology has undergone a

change during the last few decades. During this period, newer ideas have been
prescribed, and phenomenal changes have taken place in different directions in
R&D activities. In view of this, it becomes important to discuss on the issues of
Modelling and Simulation in Science, Technology and Engineering Mathematics.
With this motivation, the book entitled Modelling and Simulation in Science,
Technology and Engineering Mathematics has been edited.
This book contains the research papers presented in International Conference on
Modelling and Simulation (MS-17) organized by Association for the Advancement
of Modelling and Simulation Techniques in Enterprises (AMSE) in collaboration
with The Institution of Engineering and Technology (IET-UK), Kolkata Local
Network, on 4–5 November 2017, in Kolkata.

Papers have been divided into following tracks:

• Fuzzy, Optical and Opto Electronic Control of Oscillations
• Power System
• Energy
• Control Techniques
• Neuro Fuzzy, Control System and Optimization
• Computation Technique
• Modelling and Simulation in General Application
Editors of this book would like to acknowledge the support received from authors
of the chapters and reviewers for their valuable contribution.

v
vi Preface

We express our sincere thanks to the members of Springer for their support in
publishing the book.
We are sure that this book will give ample scope to the readers to gather
knowledge and information on the above subject matters.

Malda, India Surajit Chattopadhyay

Howrah, India Tamal Roy
Kolkata, India Samarjit Sengupta
Lyon, France Christian Berger-Vachon
Contents

Part I Fuzzy, Optical and Opto Electronics Control of Oscillations

Studies of Optical Properties of RF Magnetron Sputtered
Deposited Zinc Oxide Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
S. K. Nandi
Effect of Transmission Delay in a Modified Hybrid Long
Loop Phase Lock Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Arindum Mukherjee, Shuvajit Roy and B. N. Biswas
Comparative Study of Single Loop OEO Using Static
and Dynamic Band Pass Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Shantanu Mandal, Kousik Bishayee, C. K. Sarkar, Arindum Mukherjee
and B. N. Biswas
A Study on the Effect of an External Periodic Signal in a Chaotic
Optoelectronic Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Dia Ghosh, Arindum Mukherjee, Nikhil Ranjan Das
and Baidya Nath Biswas
Computation of Current Density in Double Well Resonant
Tunneling Diode Using Self-consistency Technique . . . . . . . . . . . . . . . . 37
Biswarup Karmakar, Rupali Lodh, Pradipta Biswas, Subhro Ghosal
and Arpan Deyasi
Computation of Electrical Parameters for Single-Gate High-K
Nanoscale MOSFET with Cylindrical Geometry . . . . . . . . . . . . . . . . . . 47
Suporna Bhowmick, Debarati Chakraborty and Arpan Deyasi

Part II Power System

Fault Diagnosis in Isolated Renewable Energy Conversion System
Using Skewness and Kurtosis Assessment . . . . . . . . . . . . . . . . . . . . . . . 57
Debopoma Kar Ray, Surajit Chattopadhyay and Samarjit Sengupta

vii
viii Contents

FFT Based Harmonic Assessment of Line to Ground Fault

in 14 Bus Microgrid System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Sagnik Datta, Surajit Chattopadhyay and Arabinda Das
Harmonics Assessment Based Symmetrical Fault Diagnosis
in PV Array Based Microgrid System . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Tapash Kr. Das, Surajit Chattopadhyay and Arabinda Das
Optimal Design of KVAr Based SVC for Improvement of Stability in
Electrical Power System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Sayantan Adhikary and Sandip Chanda
An Improved Reactive Power Compensation Scheme for Unbalanced
Four Wire System with Low Harmonic Injection Using SVC . . . . . . . . 119
Sankar Das, Debashis Chatterjee and Swapan K. Goswami
A Comprehensive Review on Distribution System . . . . . . . . . . . . . . . . . 133
Anirban Chowdhury, Ranjit Roy, Kamal Krishna Mandal and S. Mandal
Solution of Multi-objective Combined Economic Emission Load
Dispatch Using Krill Herd Algorithm with Constraints . . . . . . . . . . . . . 145
D. Maity, M. Chatterjee, S. Banerjee and C. K. Chanda
Classification of Crossover Faults and Determining Their
Location in a Double Circuit Power Transmission System
with Multiple Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
Nabamita Roy
Optimal Value of Excitation of Self-excited Induction
Generators by Simulated Annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
Writwik Balow, Arabinda Das, Amarnath Sanyal and Raju Basak
Different Setting of Unified Power Flow Controller (UPFC)
and Its Effect on Performance of Distance Relay . . . . . . . . . . . . . . . . . . 179
Rajib Sadhu and P. S. Bhowmik
Assessment of Discrimination Between Fault and Inrush Condition
of Power Transformer by Radar Analysis and Wavelet Transform
Based Kurtosis and Skewness Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 191
Sushil Paul, Shantanu Kr Das, Aveek Chattopadhyaya
and Surajit Chattopadhyay
SCADA Based Real Time Reactive Power Compensation Scheme
for Assessment and Improvement of Voltage Stability
in Power System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
Kabir Chakraborty and Arghyadeep Majumder
Contents ix

Part III Energy

Solar Photovoltaic Power Supply to Utility Grid and Its
Synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
Sonalika Dutta, Soumya Kanti Bandyopadhyay
and Tapas Kumar Sengupta
Optimum Sizing and Economic Analysis of Renewable Energy
System Integration into a Micro-Grid for an Academic
Institution—A Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
Nithya Saiprasad, Akhtar Kalam and Aladin Zayegh
Modelling and Simulation of Solar Cell Under Variable Irradiance
and Load Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
Payel Ghosh and Palash Kumar Kundu
Power Management of Non-conventional Energy Sources Connected
to Local Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
Siddhartha Singh and Biswarup Basak
Smart Coordination Approach for Power Management
with PEV Based on Real Time Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . 269
Purbasha Singha, Debanjan Ghosh, Sayan Koley, Rishiraj Sarkar
and Sawan Sen
Fault Analysis in Grid Connected Solar Photovoltaic System . . . . . . . . . 283
Nirjhar Saha, Atanu Maji, Subhra Mukherjee and Niladri Mukherjee
Sub-harmonics Based String Fault Assessment in Solar
PV Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
Tapash Kr. Das, Ayan Banik, Surajit Chattopadhyay and Arabinda Das

Part IV Control Techniques

Design of Bacterial Foraging Optimization Algorithm Based
Adaptive Sliding Mode Controller for Inverted Pendulum . . . . . . . . . . . 305
Rajeev Ranjan Pathak and Anindita Sengupta
Design of Sliding Mode Excitation Controller to Improve
Transient Stability of a Power System . . . . . . . . . . . . . . . . . . . . . . . . . . 315
Asim Halder, Debasish Mondal and Manas kr. Bera
Modelling of an Optimum Fuzzy Logic Controller Using Genetic
Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
Piyali Ganguly, Akhtar Kalam and Aladin Zayegh
Evolutionary Smith Predictor for Control of Time-Delay
Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
Neelbrata Roy, Anindita Sengupta and Ashoke Sutradhar
x Contents

On-line Adaptation of Parameter Uncertainties of a Practical Plant

Employing L1 Adaptive Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
Roshni Maiti, Kaushik Das Sharma and Gautam Sarkar
Two-Degree-of-Freedom Control of Non-minimum Phase
Mechanical System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
Mita Pal, Gautam Sarkar, Ranjit Kumar Barai and Tamal Roy
LFT Modeling of Differentially Driven Wheeled Mobile Robot . . . . . . . 379
Tamal Roy, Ranjit Kumar Barai and Rajeeb Dey

Part V Neuro Fuzzy, Control System and Optimization

Automatic Electronic Excitation Control
in a Modern Alternator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
Avik Ghosh, Sourish Sanyal, Arabinda Das and Amaranth Sanyal
Analysis of Linear Time Invariant and Time Varying Dynamic
Systems via Taylor Series Using a New Recursive Algorithm . . . . . . . . 407
Suchismita Ghosh
Severity and Location Detection of Three Phase Induction
Motor Stator Fault Using Sample Shifting Technique
and Adaptive Neuro Fuzzy Inference System . . . . . . . . . . . . . . . . . . . . . 423
S. Samanta, J. N. Bera and G. Sarkar
Level Adjustment of Hydrofoil Sea-Craft Under
Wave Disturbance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
Sohorab Hossain, Sourish Sanyal and Amarnath Sanyal

Part VI Computation Technique

Law of Time and Mathematical Axioms . . . . . . . . . . . . . . . . . . . . . . . . 449
Hiran Das Mahar
Analysis of Resources for the Safety and Comfort
of Railway Passenger Using Analytical Hierarchy Process . . . . . . . . . . . 459
Gopal Marik
Electrocardiogram Signal Analysis for Diagnosis of Congestive
Heart Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473
Santanu Chattopadhyay, Gautam Sarkar and Arabinda Das
Condition Assessment of Structure Through Non Destructive
Testing—A Case Study on Two Identical Buildings
of Different Age . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
Bhaskar Chandrakar, M. K. Gupta and N. P. Dewangan
Contents xi

A Real Time Health Monitoring and Human Tracking System

Using Arduino . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495
P. L. Lekshmy Lal, Arjun Uday, V. J. Abhijith and Parvathy R. L. Nair
Study of Arrhythmia Using Wavelet Transformation Based Statistical
Parameter Computation of Electrocardiogram Signal . . . . . . . . . . . . . . 501
Santanu Chattopadhyay, Gautam Sarkar and Arabinda Das

Part VII Modelling and Simulation in General Application

Analysis of Retinal OCT Images for the Early Diagnosis of
Alzheimer’s Disease . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509
C. S. Sandeep, A. Sukesh Kumar, K. Mahadevan and P. Manoj
Real Time Diagnosis of Rural Cardiac Patients Through
Telemedicine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521
R. Ramu and A. Sukesh Kumar
A Comparative Analysis of a Healthy Retina and Retina
of a Stroke Patient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531
R. S. Jeena and A. Sukesh Kumar
Square Root Quadrature Information Filters for Multiple
Sensor Fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539
Aritro Dey, Smita Sadhu and Tapan Kumar Ghoshal
Cost Effective, Water Controlled Automated Gardening System . . . . . . 549
Piyali Mukherjee
Ear Based Biometric Analysis for Human Identification . . . . . . . . . . . . 555
Samik Chakraborty, Anumita Mitra, Sanhita Biswas and Saurabh Pal
An Integrated Model for Early Detection and Monitoring
of Diabetic Foot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567
K. S. Suresh and A. Sukesh Kumar
Real Time Periodic Assessment of Retina of Diabetic Patients
for Early Detection of Diabetic Retinopathy . . . . . . . . . . . . . . . . . . . . . . 575
P. G. Prageeth, A. Sukesh Kumar and K. Mahadevan
Product Recommendation for E-Commerce Data Using
Association Rule and Apriori Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 585
Soma Bandyopadhyay, S. S. Thakur and J. K. Mandal
A Comparative Analysis Between EDR and Respiration Signal:
A Pilot Study with Normal Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595
Surita Sarkar, Saurabh Pal and Parthasarathi Bhattacharyya
xii Contents

Uncertainty in Fission Product Transient Release Under

Accident Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605
Subrata Bera, U. K. Paul, D. Datta and A. J. Gaikwad
Statistical Aggregation of Extreme Value Analysis Models . . . . . . . . . . . 615
Subrata Bera, Dhanesh B. Nagrale, U. K. Paul, D. Datta and A. J. Gaikwad
Electroosmotic Effects on Rough Wall Micro-channel Flow . . . . . . . . . . 623
Nisat Nowroz Anika and L. Djenidi
Comparative Study on Fuzzy Based Linearization Technique
Between MATLAB and LABVIEW Platform . . . . . . . . . . . . . . . . . . . . 631
Joyanta Kumar Roy and Bansari Deb Majumder
Automated Identification of Myocardial Infarction Using
a Single Vectorcardiographic Feature . . . . . . . . . . . . . . . . . . . . . . . . . . 641
Deboleena Sadhukhan, Jayita Datta, Saurabh Pal and Madhuchhanda Mitra
Content Extraction Studies for Multilingual Unstructured
Web Documents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653
Kolla Bhanu Prakash and M. A. Dorai Rangaswamy
Potentiality of Retina for Disease Diagnosis Through Retinal
Image Processing Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665
P. G. Prageeth, A. Sukesh Kumar, C. S. Sandeep and R. S. Jeena
Generalized LFT Modeling of an Uncertain MIMO System . . . . . . . . . 677
Tamal Roy, Ranjit Kumar Barai and Rajeeb Dey
About the Editors

Surajit Chattopadhyay has obtained B.Sc. in physics honours from Ramakrishna

Mission Vidyamandir (Belur Math), University of Calcutta, in 1998, and then
B.Tech., M.Tech. and Ph.D. (Technology) in electrical engineering from the
Department of Applied Physics of University of Calcutta in 2001, 2003 and 2010,
respectively. He has obtained CEng from Engineering Council, UK, in 2013. He
has authored/coauthored around 100 papers published in international and national
journals and conferences and 4 books (also with Springer). Seven papers have been
selected as “Best Paper” in international level. He has visited many countries for
technical interaction like in Lyon (France), Kuala Lumpur (Malaysia), Dhaka
(Bangladesh), London and Stevenage (UK) and Negombo (Sri Lanka) and pre-
sented his work in different international forums. Presently, he is Dean (Research
and Consultancy) and Associate Professor of Electrical Engineering in Ghani Khan
Choudhury Institute of Engineering and Technology (under Ministry of HRD,
Government of India). He served as Honourable Secretary of the Institution of
Engineering and Technology (UK), Kolkata Local Network, from 2013 to 2016 and
now Executive Committee Member of the Network. His fields of interest include
electric power quality, fault diagnosis, power system protection, signal analysis,
robotics application and UAV.

Tamal Roy received his Bachelor of Technology in electrical engineering and

Master of Technology in mechatronics engineering from West Bengal University of
Technology, Kolkata, in 2005 and 2008, respectively. In 2008, he joined the
Department of Electrical Engineering at Hooghly Engineering and Technology
College as a Lecturer. Since 2011, he has been working as an Assistant Professor in
the Department of Electrical Engineering, MCKV Institute of Engineering. He was
awarded his Ph.D. in 2016 in robust control-oriented LFT modelling of nonlinear
MIMO system from Jadavpur University. His current research interests include
modelling and the robust control of the nonlinear systems, model reference adaptive
control.

xiii
xiv About the Editors

Samarjit Sengupta holds a B.Sc., B.Tech., M.Tech. and Ph.D. from the
University of Calcutta, Kolkata, India. He is currently a Professor of electrical
engineering in the Department of Applied Physics at the University of Calcutta. He
has published 130 journal papers and eight books on various topics of electrical
engineering. His main research interests include power quality instrumentation,
power system stability, and security and power system protection. He is a Fellow of
IET and IETE, as well as a Senior Member of IEEE. He is former Chairman of IET
(UK) Kolkata Network.

Christian Berger-Vachon was born in Lyon, France, in 1944. He received the

B.E. in electrical engineering from the University of Lyon, France, in 1965; an
engineering degree in Lyon (INSA 1967); a Ph.D. in sciences from the University
of Lyon, in 1975; and a MD in 1980.
In 1974, he joined the Department of Electrical Engineering, University of Lyon,
as a Lecturer, and in 1989, he was named Professor. He was given the title of
Emeritus Professor in 2013 and since then allowed to continue his research activity
in the University.
His current research interests include signal processing in electrical machines
and in hearing aid devices, and also the construction of models in close connection
with the patients’ behaviour. He is also involved in sports mechanics and in sports
medicine.
He is the General Secretary of AMSE, an international association concerned
with the edition of scientific journals and with the organization of scientific con-
ferences throughout the world. He is the Vice-Chairman of IFRATH, a French
Association concerned with the use of assistive devices for handicapped people. He
was the recipient of the “Academic Palms” awarded by the French Government for
his academic career in 2014.
 Part I
Fuzzy, Optical and Opto Electronics
Control of Oscillations
Studies of Optical Properties of RF
Magnetron Sputtered Deposited Zinc
Oxide Films

S. K. Nandi

1 Introduction

Zinc oxide (ZnO) is of great interest as a suitable material for high temperature,
high power electronic devices either as the active material or as a suitable substrate
for epitaxial growth of group III-nitride compounds. With its large, direct band gap
≈3·4 eV, a low-power threshold (~160 µJ cm−2 ) for optical pumping at room temper-
ature and wurtzite crystal structure, ZnO is similar to GaN. Due to its relatively close
match in lattice constants, it may be used as a substrate for GaN and AlN epitaxy. As
a consequence, there is renewed interest in the properties of ZnO relevant for micro-
electronic device applications. ZnO thin films have been prepared by a wide variety
of techniques, including sputtering, spray-pyrolysis, and electro deposition [1] etc.
In particular, the r.f. sputter method has advantages over other processes because
of its simplicity [2]. We investigate the optical properties of r.f. magnetron Sputter
ZnO/Si films by photoluminescence (PL) measurements, Structure and composition
of the ZnO/Si films have been investigated by X-ray diffraction (XRD), atomic force
microscopy (AFM), scanning electron microscopy (SEM) and X-ray photoelectron
spectroscopy (XPS) for chemical composition.

2 Experiment and Results

The undoped ZnO (100 nm) thin film deposited on Si (100) at 450 °C using 13.56 MHz
r.f. magnetron sputtering system with a base pressure of 1.0 × 10−6 Torr., working
pressure of 1.0 × 10−2 Torr., used gas of Argon, substrate temperature of 450 °C

S. K. Nandi (B)
Department of Physics, Rishi Bankim Chandra College, 24-Parganas (North),
Naihati 743165, West Bengal, India
e-mail: susantanandi@gmail.com
© Springer Nature Switzerland AG 2019 3
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_1
4 S. K. Nandi

with RF power of 100 W. In the XRD pattern (Fig. 1) a major peak of preferential
orientation along (103) and minor one related to (002) of the undoped ZnO films
were observed. It indicates that ZnO films are polycrystalline structures.
Figure 2 shows the atomic force micrograph of ZnO film. The scan was taken on a
5 µm × 5 µm area. The statistical information of the topography of the ZnO films as
observed from the height histogram of the AFM image are: Rms surface roughness
(Zrms) and average roughness (Zav) were found to be 50.9 and 30.4 Å, respectively.
A scanning electron microscopy (SEM) image of the cross-sectional view of
ZnO/Si film (Fig. 3) shows columnar growth which indicates an orientation parallel
c-axis (002) with thickness 100 nm.
Figure 4 shows core levels of Zn 2p of the ZnO films measured by X-ray photo-
electron spectroscopy (PHI-5800). The as-grown ZnO thin film of the peaks of Zn 2p
are found to be at 1044·8 eV and 1021·7 eV for Zn 2p1/2 and Zn 2p3/2 , respectively,
with a separation of 23·1 eV between the two peaks which is due to the Zn 2p state.
To investigate the optical properties of the films, photoluminescence (PL) mea-
surements were performed Under the 325 nm excitation, the emission PL spectra of
a ZnO film at different temperatures are shown in Fig. 5. From the emission spectra,

Fig. 1 X-ray diffraction

pattern of the as-grown ZnO
thin film at 450 °C and r.f.
power 100 W

Fig. 2 Two-dimensional AFM image of ZnO Film with scan area of 5 µm × 5 µm

Studies of Optical Properties of RF Magnetron … 5

Fig. 3 SEM view of the rf sputtered ZnO film deposited on Si

Fig. 4 XPS core-level of O

1 s and Zn 2p of the
as-grown ZnO thin film

it is clearly found that there is two emission bands peaked at 380 nm (UV band)
and 502 nm (green band) for all. The origin of the 380 and 502 nm bands has been
ascribed to the band edge radiative recombination and intrinsic defects (mostly O
vacancy) of ZnO, respectively in many reports [3]. From Fig. 6, it can be found that
the intensity of 380 and 502 nm emission decreases when the sample temperature is
increased. When the temperatures are higher than 100 K, the 502 nm emission dis-
appears [4]. Meanwhile, the intensity of 380 nm increases as the sample temperature
increases, until it reaches 200 K.
Afterwards, the intensity of 380 nm decreases when the sample temperature con-
tinues increasing. The integrated intensities of 380 and 502 nm emission peaks at
different temperatures are shown in Fig. 6, which were calculated from the area under
the curves of related emission peaks in Fig. 5.
6 S. K. Nandi

Fig. 5 Emission PL spectra

of ZnO films at different
temperatures

Fig. 6 Integrated intensities

of 380 and 502 nm emission
peaks at different
temperatures

3 Conclusion

The r.f. magnetron sputter ZnO/Si films has been studied. Physical and chemical
characterizations of the films were investigated using AFM, SEM, XRD and XPS.
Due to its attractive properties ZnO films may have attracted much interest of potential
commercial application in Photo voltaic Solar cell and optoelectronic devices, such
as light-emitting diodes, laser diodes and UV photo detectors.
Studies of Optical Properties of RF Magnetron … 7

References

1. A. Moustaghfir, E. Tomasella, S. Ben Amor, M. Jacquet, J. Cellier, T. Sauvage, Structural and

optical studies of ZnO thin films deposited by r.f. magnetron sputtering: influence of annealing.
Surf. Coatings Technol. 174–175, 193–196 (2003)
2. A.E. Rakhshani, Characterization and device applications of p-type ZnO films prepared by
thermal oxidation of sputter-deposited zinc oxynitride. J. Alloy. Compd. 695, 124–132 (2017)
3. W. Water, S.Y. Chu, Physical and structural properties of ZnO sputtered films. Mater. Lett. 55,
67–72 (2002)
4. S. Tanaka, K. Takahashi, T. Sekiguchi, K. Sumino, J. Tanaka, Cathodoluminescence from frac-
tured surfaces of ZnO varistors. J. Appl. Phys. 77, 4021–4023 (1995)
Effect of Transmission Delay
in a Modified Hybrid Long Loop Phase
Lock Loop

Arindum Mukherjee, Shuvajit Roy and B. N. Biswas

1 Introduction

In an ordinary phase lock loop (PLL), it is a common observation that any attempt
made to improve the noise squelching property of the loop inevitably leads to lower
the capture capability [3, 4]. The earlier works of Biswas et al. [1, 2] overcomes
this restriction by using a hybrid long loop (HLL) whereby the limitations imposed
on circuit on the capture capability of a conventional phase lock-loop is overcome,
and the system response linearity also increases. This paper presents the effect of
transmission delay arising due to an IF filter in the loop and hence an attempt has
been made here to mitigate this deleterious effect with the help of injection syn-
chronization. Moreover an additional control by incorporating a phase modulator in
the loop has been included which will increase the lock range of the loop beyond
90°, thereby reducing the probability of cycle slipping phenomenon. The loop will
be now referred to as the modified hybrid long loop PLL (MHLL) because of the
presence of this extra phase modulator in the circuit.
Consider the proposed circuit shown in Fig. 1, it consists of an analog mixer, a sinu-
soidal phase detector (PD), two voltage controlled oscillators (VCO1 and VCO2),
 filters (F 1 (p) and F 2 (p)), a phase modulator (PH. MOD) and an ampli-
two low-pass
fier K in j to control the gain of the injection synchronized path to the VCO1. In
addition to these components, a broadband IF filter is inserted which controls the

A. Mukherjee (B)
Central Institute of Technology, Assam, India
e-mail: a.mukherjee@cit.ac.in
S. Roy
Institute of Radio Physics and Electronics, Kolkata, India
e-mail: roy.shuvajit007@gmail.com
B. N. Biswas
Chairman Education Division, SKFGI, Mankundu, West Bengal, India
e-mail: baidyanathbiswas@gmail.com
© Springer Nature Switzerland AG 2019 9
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_2
10 A. Mukherjee et al.

Broad-band Narrow-band
Mixer IF IF PD

Input
e − s×τ
φ (t )
OSC LPF
π
2 VCO 1 F1 ( p )
K inj
PH. MOD

2 × cos (ω2t + θ 2 ( t ) + ϕm ( t ) )

ϕm (t ) = Kϕ sin ⎡⎣φ ( t − τ ) ⎤⎦
VCO 2 LPF
F2 ( p )

Fig. 1 Modified hybrid long loop PLL

noise bandwidth for the system. The detailed analysis of the noise bandwidth will
be reported in a future communication. Finally, the presence of a narrowband tuned
circuit introduces transmission delay (τ ) in the loop. Output from the mixer feeds
simultaneously the PD and the π/2-phase shifter. For harmonic synchronization of
VCO1, this output is injected into the oscillator circuit of the VCO1. The PD output
is then delivered through the low-pass filters to the reactance modulators of the two
VCO’s in order to control the instantaneous frequencies of the VCO’s. Thus the error
signal from the PD output and the RF signal from the output of the mixer control the
instantaneous frequency of VCO1. It is worthwhile to mention here that the low-pass
filters are employed to attenuate out the disturbances accompanying the reference
signal. With the introduction of the low-pass filters, the capture region of the PLL will
be reduced significantly relative to the zone of synchronism (maximum frequency
error in the steady state). Again, it is known that for direct synchronization, the cap-
ture region and the synchronization region are same. Moreover, the linearity of the
proposed system increases as the effective phase error becomes small at the input to
the PD, which may be further observed by noting that the heterodyne output of the
mixer feeds the PD.

2 Theoretical Analysis

Let us assume the input to be of the form A sin[ωi t + θi (t)], and the two VCO
outputs are chosen as, VCO1: 2 cos[ω1 t + θ1 (t)] and VCO2: 2 cos[ω2 t + θ2 (t)]. The
phase-detector output is given by

A × sin[(ωi − ω1 − ω2 )t + θi (t) − θ1 (t) − θ2 (t) − ϕm (t)]

 A × sin[ × t + θi (t) − θ1 (t) − θ2 (t) − ϕm (t)], (1)
Effect of Transmission Delay in a Modified Hybrid … 11

where   (ωi − ω1 − ω2 ) is the open loop phase error. Again, since the filter trans-
fer functions are ‘F 1 (p)’ and ‘F 2 (p)’ respectively, ‘p’ being the Heaviside operator,
and recognising that the output of the LPF modulates the instantaneous phase of the
VCO, one gets
dθ2
 A × β2 × F2 ( p) × sin[φ(t − τ )] (2)
dt
and
 
dθ1 ω0
 × K in j × A sin[φ(t)] + {β1 × F1 ( p) × A sin[φ(t − τ )]} (3)
dt 2Q

the instantaneous phase equation is given by

 
dφ ω0
− × K in j × A sin[φ(t)]
dt 2Q
− [β1 × F1 ( p) + β2 × F2 ( p)] × A sin[φ(t − τ )]
dφ(t − τ ) dθi
− K ϕ × cos[φ(t − τ )] × + (4)
dt dt
This equation is solved numerically to study the variation of phase detector output
voltage and its spectrum in absence and presence of delay. It is to be noted that ‘ω0 ’
is the centre frequency of the narrowband IF filter, ‘β’ is the VCO sensitivity and the
low-pass filters are chosen as first order with time constant ‘T’.

3 Results and Discussions

It will be reported in a later communication,

  that injection synchronization reduces
the effect of transmission delay τ  2×Q ω0
introduced by the narrowband IF filter.
It will be also shown that the additional phase control arrangement has more pro-
nounced effect in reducing the third harmonic distortion as compared to the injection
synchronized component. The phase detector output in absence and presence of delay
are shown in Figs. 2 and 4 respectively. The presences of third harmonic distortion
are shown in Figs. 3 and 5 respectively. A numerical experiment has been performed
to study the effect of third harmonic distortion (THD) with transmission delay and is
shown in Fig. 6 and in Table 1. With the increase in delay, the 3rd harmonic distortion
decreases.
12 A. Mukherjee et al.

Fig. 2 Phase detector Phase detector voltage without delay

voltage in absence of delay 1

Phase detector voltage

0.5

− 0.5

−1
15 16 17 18 19 20
Time

Fig. 3 Spectrum of phase Magnitude response in absence of delay

detector output in absence of
Magnitude response of phase det voltage

delay

80

60

40

20

0
0 1 2 3 4 5
Frequency in Hz

Fig. 4 Phase detector Phase detector voltage in presence of delay

voltage in presence of delay 1
Phase detector voltage

0.5

− 0.5

−1
10 11 12 13 14 15
Time
Effect of Transmission Delay in a Modified Hybrid … 13

Magnitude response in presence of delay

Magnitude response of phase det voltage

80

60

40

20

0
0 1 2 3 4 5
Frequency in Hz

Fig. 5 Spectrum of phase detector output in presence of delay

Fig. 6 Third harmonic distortion with delay; red dots are experimental data and blue curve is curve
fitting
14 A. Mukherjee et al.

Table 1 Ratio of 3rd harmonic to fundamental frequency

Without delay THD % Delay (s) THD (%)
2.5997/69.178  4.24 0.031 2.5677/69.226  3.71
0.244 2.6618/69.121  3.85
0.549 2.6131/68.434  3.82
0.763 2.4359/68.552  3.55
0.854 2.4625/68.796  3.57
Injection strength  1.5 V; VCO1 sensitivity  6 Hz/V; VCO2 sensitivity  2 Hz/V; Filter time
constants  0.1 s; Modulating signal frequency  1 Hz; IF filter centre frequency  10 Hz; Initial
detuning  0

4 Conclusion

A modified HLL is analysed with particular emphasis on the effect of transmission

delay in the loop. The presence of third harmonic distortion is reported and its
variation with delay is studied. Phase detector output and the corresponding spectrum
are also studied in absence and presence of delay. In a future communication, it will
be reported that injection synchronization reduces the effect of transmission delay
and the phase modulator reduces the loop noise bandwidth.

Acknowledgements The authors are thankful to BoG, Central Institute of Technology and Mr B
Guha Mallick, the Chairman of the Supreme Knowledge Group of Institutions, for successfully
carrying out this work.

References

1. B.N. Biswas, Combination injection locking with indirect synchronization technique. IEEE
Trans. Commun. Technol. (Corres.) 21, 73 (1967)
2. B.N. Biswas, P. Banerjee, Range extension of a phase-locked loop. IEEE Trans. Commn. COM-
21, 293–296 (1972)
3. B.N. Biswas, Phase Lock Theories And Application (Oxford & IBH, New Delhi, 1988)
4. F.M. Gardner, in Phase Lock Techniques, 3rd edn. (Wiley, Hoboken, 2005)
Comparative Study of Single Loop OEO
Using Static and Dynamic Band Pass
Filter

Shantanu Mandal, Kousik Bishayee, C. K. Sarkar,

Arindum Mukherjee and B. N. Biswas

1 Introduction

Traditional method of microwave or mm-wave signal generation was realized by

means of oscillators based on diodes like Gunn, IMPATT, TRAPATT etc. or using
transistors. To achieve the desired frequency range, several stages of frequency mul-
tiplication using electronic circuitry needs to be done. Microwave or mm-wave signal
can also be generated by beating of two laser beams or by optical injection locking
method [1, 2]. These approaches were good and useful for most of traditional appli-
cations. However, for many emerging applications of recent days such as in radar,
wireless communications, GPS, software defined radio etc., this traditional method
fails to produce satisfactory results. Those systems were not only complicated and
costly, but also lack of spectral purity, low phase noise and frequency-tunability,
which are essential in these modern applications.
Optoelectronic Oscillator (OEO) is the most advanced method for extracting high
purity and extremely low phase noise microwave signal proposed by Nakazawa et al.

S. Mandal (B) · K. Bishayee

Department of ECE, University Institute of Technology,
The University of Burdwan, Burdwan, WB, India
e-mail: mshantanu2253@gmail.com
C. K. Sarkar
Department of Electronics and Telecommunication Engineering,
Jadavpur University, Kolkata, WB, India
A. Mukherjee
Department of ECE, Central Institute of Technology, Kokrajhar, Assam, India
B. N. Biswas
Sir J. C. Bose School of Engineering, SKFGI, Mankundu, WB, India

© Springer Nature Switzerland AG 2019 15

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_3
16 S. Mandal et al.

DC Bias
Optical Output

Laser MZM
Source
Optical Photo
Coupler Diode
Long S.M.F.

RF Amplifier

Band Pass Filter

Electrical Output Microwave

Coupler

Fig. 1 Conventional single loop optoelectronics oscillator (OEO)

[3] in 1984. The construction, operation and benefits of OEO have been reported
elaborately by Yeo and Meleki [4–6].

In single loop OEO (Fig. 1), a highly coherent laser beam is fed to an electro-optic
modulator (MZM), the output of which is passed through a long optical fiber and
detected with a photo detector. The optical fiber used here as a microwave resonator,
which provides low loss and an extremely high Q factor. The output of the photo
detector is amplified by an RF amplifier and filtered by a sharp cut off band pass
filter and fed back to the electric port of the electro-optic modulator. This PLL
configuration supports self-sustained oscillations, at a frequency determined by the
fiber delay length, the bias setting of the modulator, and the band pass characteristics
of the filter [4–7].

Therefore, in this paper the behavioral pattern of a single loop OEO with a Static
RF filter and Dynamic Band Pass filter has been compared. Dynamic Band Pass filter
used here is a tuned circuit whose center frequency can be changed with external
dc control voltage [8–10]. Steady state amplitude and frequency of the OEO with
different type of filter has been derived theoretically. Then the amplitude and fre-
quency variation of the OEO with fiber delay for two different type of filter has
been measured. Finally the tracking capability of the OEO with two type of filter
is compared for external injection signal of different amplitudes and frequency has
been derived theoretically and measured practically. Both theoretical analysis and
practical findings are found in good agreement.
Comparative Study of Single Loop OEO Using Static … 17

2 System Equation of OEO

Let us assume the RF input to the modulating grid of the MZM to be Vin (t) 
V (t)e j[ω1 t+θ(t)] where, V (t) is the oscillation amplitude with a frequency ω1 and
initial phase θ . The optical power from the electro-optic modulator output port can
be obtained
  
1 Vin (t) + VB
P  α P0 1 − η × sin π (1)
2 Vπ

where α is the fraction of insertion loss of the modulator, Vπ is the half-wave voltage,
VB is the bias voltage, P0 is the input optical power, Vin (t) is the input RF voltage to
the MZ modulator and η determines the extinction ratio of the modulator. If ρ is the
sensitivity of the photo detector and R is the output impedance of the photo detector
then the output of the MZ modulator can be written as
   
π VB π V (t − τ )
V0 (t)  −2ηV ph cos J1 sin[ω(t − τ )]
Vπ Vπ
N [V (t − τ )]
 exp(−sτ )Vin (t) (2)
V (t)

where, τ is the time delay of the long optical fiber in the loop, V ph  Rαρ P0
2
and
   
π VB π V (t − τ )
N (V (t − τ ))  −2ηV ph cos J1 (3)
Vπ Vπ

Without loss of any generality, we can assume that VB  Vπ ; η  1 and π V ph 

Vπ and Vπ  π then,

N (V (t − τ ))  2J1 [V (t − τ )] (4)

If the gain of the second order tuned circuit is G 1 , gain of the RF amplifier is G 2 ,
frequency detuning is ω then, the transfer function can be written as
G1
G(s)     (5)
ω0 1+ ω
ω
s 0
1+ Q ω0
+ s

where, ‘Q’ is the quality factor of the tank circuit.

The closed loop equation can be written as
⎡ ⎧  2 ⎫⎤
⎪
⎨ ω 1+ ω ⎪
⎬
Vin Vin ⎢ s 0 ω0 ⎥
V0 (t)   ⎣1 + Q + ⎦ (6)
G 2 G(s) G2G1 ⎪
⎩ ω0 s ⎪
⎭
18 S. Mandal et al.

where Vin (t)  V (t) exp[ j(ω0 t + θ (t)] and G  G 1 G 2 .

The Eq. (6) can be written as with the help of complex frequency [6]
⎡  ⎤
 
  1 + Q 1 dV
+ j ω + dθ
2J1 [V (t − τ )] −sτ 1⎢ ω0 V (t) dt 1 dt ⎥
e  ⎢ ⎣  2   ⎥
⎦ (7)
V (t) G
+Qω0 1 + ω ω0
1
jω1
+ ω12 V1 ddtV + j dθ
dt
1

Equating the real and imaginary part of Eq. (7) and considering ω1 ≈ ω0 we can
get
dV ω0
  2 [2G J1 [V (t − τ )] cos(ω0 τ ) − V (t)] (8)
dt ω
Q 1 + ω0
 2 
ω
ω0 1 + ω0 − 1
dθ 2ω0 G J1 [V (t − τ )] sin(ω0 τ )
  2 −  2
 (9)
dt V (t)
1 + ω
ω0
+1 Q 1 + ω ω0
+1

Now in steady state, considering ddtV  0, the free running amplitude of the
oscillation is obtained exactly same as using a static band pass filter [11, 12] given
by
 
√ 1
V (t)  2 2 1− (10)
G cos(ω0 τ )

The normalized free running frequency is obtained as

  
ωf 1 ω 2 tan(ω0 τ )
1+   2  1+ −1− (11)
ω0 ω ω0 Q
1 + 1 + ω0

Whereas the normalized free running frequency using a static band pass filter
obtained earlier [11] is given by
ωf tan(ω0 τ )
1− (12)
ω0 2Q

Growth of amplitude of oscillation of OEO using static and dynamic BPF is

obtained by numerically solving the coupled non-linear delay differential Eqs. (8)
and (9) using Wolfram Mathematica 11.1® as shown in Fig. 2. This variation in
response is due to the detuning effect of the dynamic filter which has the noticeable
difference in the damping factor of the oscillators during the initiation of oscillation.
Comparative Study of Single Loop OEO Using Static … 19

Growth of oscillation in OEO using Static and Dynamic filter

3.0

2.5

2.0
RFOutput

1.5

1.0

0.5
Dynamic
Static
0.0
0.0000 0.0001 0.0002 0.0003 0.0004
Time

Fig. 2 Growth of amplitude of oscillation of OEO using static and dynamic BPF

Further, when an external synchronization signal is injected into the OEO, it is

most important to see the zone over which the sync signal is in lock with the OEO free
running signal. In steady state, the non-linear term N [VV(t−τ
(t)
)]
 2J1 [VV (t)
(t−τ )]
 2J1V[V ]
can be considered as constant (‘C’). Therefore, the normalized lock range of OEO
can be written as [11–13].
 
GE 2

 ω1 − GC sin(ω0 τ ) − − (GC cos ω0 τ − 1)2 (13)
V
 
where, ω1  2Q ω0
× ω
Here the variation of lock range with different fiber delay as well as with different
detuning values using static and dynamic filter has been compared experimentally.

3 Experimental Results and Discussion

The experimental validations of the theoretical expressions are obtained using

MATLAB® Simulink® environment. The designed experimental setup of the OEO
is shown in Fig. 3. Here, the conventional static BPF of earlier work is replaced with
the proposed dynamic BPF as shown in the Fig. 3.
The frequency response of the static and dynamic band pass filter is shown in
Fig. 4 which shows exactly same type of response in both cases. But in dynamic
filter, the center frequency is varying nearly the same amount as frequency detuning
( w), which is ideal for a dynamic BPF and is the prime goal of using dynamic filter
here.
20 S. Mandal et al.

Fig. 3 Simulation block diagram of OEO using dynamic filter

Frequency Response of Static and Dynamik BPF

1

0.9

0.8
Normalized Amplitude

0.7

0.6 Center freq shift due to change

of freq. detuning

0.5
static
Detuning 0.05 MHz
Detuning 0.1 MHz
0.4 Data fit 1
Data fit 2
Data fit 3

11.85 11.9 11.95 12 12.05 12.1 12.15 12.2 12.25

Frequency in MHz

Fig. 4 Frequency response of single loop OEO using static and dynamic filter

The previous observation becomes more prominent when the center frequency
variation along with different detuning ( w) has been measured. Plot of center
frequency variation with detuning, considering RF amplifier gain of 3.0 and quality
factor (Q) value of 76.9 (Fig. 5), shows completely linear variation.
Next, the experimental variation of normalized amplitude and frequency of the
single loop OEO with optical fiber delay is compared for static and dynamic BPF as
shown in Figs. 6 and 7. The corresponding experimental data is given in the Tables 1
and 2 respectively where, different frequency detuning of the dynamic filter has been
considered. Visualizing the nature of the curves it can be concluded that the use of
dynamic filter in OEO reduces its amplitude as well as the frequency variation with
delay considerably.
Comparative Study of Single Loop OEO Using Static … 21

Variation of Normalized Frequency with Frequency Detuning

1.2

1.18

1.16
Normalized Frequency

1.14

1.12

1.1

1.08

1.06

1.04
0.5 1 1.5 2 2.5
Frequency Detuning in MHz

Fig. 5 Frequency Detuning with center frequency shift of dynamic filter

Varition of Normalized Amplitude With fiber Delay

1

0.95

0.9
Normalized Amplitude

0.85

0.8

0.75

0.7

0.65 Static
Detuning 0.5 MHz
0.6 Detuning 1.5 MHz
Detuning 2.5 MHz
Data fit 1
0.55 Data fit 2
Data fit 3
0.5 Data fit 4

1 2 3 4 5 6 7 8 9 10
Fiber Delay in nsec

Fig. 6 Experimental variation of normalized amplitude with fiber delay

Finally, the modified single loop OEO is synchronized with the externally injected
signal. The dynamic filter adjusts its center frequency in such a way that the center
frequency becomes equal to the instantaneous frequency of the injected signal. Once
22 S. Mandal et al.

Variation of Normalized Frequency With Fiber Delay

1 Static
Detuning 0.5 MHz
Detuning 1.5 MHz
Detuning 2.5 MHz
0.999 Data fit 1
Data fit 4
Normalized Frequency

Data fit 2
Data fit 3
0.998

0.997

0.996

0.995

0.994
1 2 3 4 5 6 7 8
Fiber Delay in nsec

Fig. 7 Experimental variation of normalized frequency with fiber delay

Table 1 Experimental data for normalized amplitude with fiber dela

Fiber delay in Normalized Normalized Normalized Normalized
nsec amplitude of amplitude of amplitude of amplitude of
static BPF dynamic BPF dynamic BPF dynamic BPF
with W  with W  with W 
2.5 MHz 1.5 MHz 0.5 MHz
1 1 1 1 1
3 0.972 0.989 0.987 0.986
5 0.916 0.961 0.963 0.962
7 0.813 0.919 0.92 0.931
9 0.641 0.841 0.851 0.878
10 0.493 0.785 0.8 0.839

synchronized, the variation of normalized lock range of OEO with fiber delay as well
as injection signal amplitude is shown in Figs. 8 and 9 respectively. The nature of
the graph shows the exact resemblance with of static and dynamic filter. That means
with the use of such a dynamic filter, variable frequency OEO of similar nature to
static one, can be obtained.
Comparative Study of Single Loop OEO Using Static … 23

Table 2 Experimental data for normalized frequency with fiber delay

Fiber delay in Normalized Normalized Normalized Normalized
nsec frequency of frequency of frequency of frequency of
static BPF dynamic BPF dynamic BPF dynamic BPF
with W  with W  with W 
2.5 MHz 1.5 MHz 0.5 MHz
1 1 1 1 1
3 0.999 0.999 0.999 0.998
5 0.997 0.997 0.999 0.998
7 0.997 0.996 0.997 0.996
9 0.995 0.994 0.995 0.994

Variation of Normalized Locking Range with Fiber Delay

1
Static
Detuning 0.5 KHz
0.9 Detuning 5 KHz
Data fit 1
Data fit 2
0.8 Data fit 3
Normalized Locking Range

0.7

0.6

0.5

0.4

0.3

0.2

0.1
1 2 3 4 5 6 7 8 9 10
Fiber Delay in Microsec

Fig. 8 Experimental variation of lock range with fiber delay

4 Conclusion

This paper considers the effect of synchronizing capability when a conventional

RF static band-pass filter is replaced by a dynamic filter in a single loop OEO.
System governing equations are derived when the synchronization signal is in the
form of angle modulation and an expression for locking range of the OEO has been
calculated. In a future communication, the dynamic tracking capability of this filter
will be reported.
24 S. Mandal et al.

Variation of Normalized Locking Range With Injection Amplitude

1

0.9

0.8
Normalized Locking Range

0.7

0.6

0.5

0.4

0.3

0.2
Static
Dynamic
0.1 Data fit 1
Data fit 2

0.1 0.2 0.3 0.4 0.5 0.6 0.7

Injection Amplitude

Fig. 9 Experimental variation of lock range with injection amplitude

Acknowledgements The authors are thankful to the management of University Institute of Tech-
nology, The University of Burdwan, Burdwan, West Bengal and Central Institute of Technology,
Assam for giving an opportunity to carry out this work and also the management of Sir J C Bose
School of Engineering for carrying out the work on Sir J C Bose Creativity Centre of Supreme
Knowledge Foundation Group of Institution, Mankundu, Hooghly.

References

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links based on remote heterodyne detection. IEEE Trans. Microwave Theory Tech. 46(5),
458–468 (1998)
2. L. Goldberg, H.F. Taylor, J.F. Weller, D.M. Bloom, Microwave signal generation with injection
locked laser diodes. Electron. Lett. 19(13), 491–493 (1983)
3. M. Nakazawa, T. Nakashima, M. Tokuda, An Optoelectronic self-oscillatory circuit with an
optical fibre delayed feedback and its injection locking technique. J. Lightwave Technol. LT
2(5), 719–730 (1984)
4. X.S. Yao, L. Maleki, Optoelectronic microwave oscillator. J. Opt. Soc. Am. B 13(8), 1725–1735
(1996)
5. X.S. Yao, L. Maleki, L. Devis, Coupled Optoelectronic Oscillators for Generating Both RF
Signal and Optical Pulses. J. Lightwave Technol. 18(1), 73–78 (2000)
6. B.N. Biswas, S. Chatterjee, S Pal, Laser induced microwave oscillator. Int. J. Electron.
Commun. Eng. Technol. (IJACET), ISSN 0976–6464(Print), ISSN 0976–6472(Online), 3(1),
(2012), © IAEME
7. I. Gonorovsky, Radio Circuit and Signals (Mir Publisher, Moscow, 1974)
Comparative Study of Single Loop OEO Using Static … 25

8. A. Mukherjee, D. Ghosh, N.R. Das, B.N. Biswas, On a single loop optoelectronic oscillator
using variable centre frequency dynamic filter. IJECT 6(1), Spl-1, Jan-March-2015, ISSN:
2230–7109 (Online) ISSN: 2230-9543(Print)
9. A. Mukherjee, D. Ghosh, B.N. Biswas, On the effect of combining an external synchronizing
signal feeding the Mach-Zehnder modulator in an optoelectronic oscillator. Optik Int. J. Light
Electron. Optics 127, 3576–3581 (2015)
10. A. Mukherjee, D. Ghosh, N.R. Das, B.N. Biswas, Harmonic distortion and power relations in a
single loop optoelectronic oscillator. Optik Int. J. Light Electron. Optics 127, 973–980 (2015)
11. K. Bishayee, S. Mandal, A. Mukherjee, S. Pal, B.N. Biswas, Locking phenomenon in a sin-
gle loop OEO. IJECT 5(2), Spl-1, Jan–March-2014, ISSN : 2230–7109 (Online) | ISSN:
2230–9543(Print)
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modulated signal in a single loop optoelectronic oscillator. Optik Int. J. Light Electron. Optics
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A Study on the Effect of an External
Periodic Signal in a Chaotic
Optoelectronic Oscillator

Dia Ghosh, Arindum Mukherjee, Nikhil Ranjan Das

and Baidya Nath Biswas

1 Introduction

Over the last few years OEO has seen wide spread application in the field of RADAR,
fiber optic communication system, long distance digital communication system, in
view of the fact that it has the ability to produce high frequency signal with ultra high
spectral purity. This oscillator was first introduced by Neyer and Voges [1]. Posterior
to their pioneering work, Yao and Maleki introduced this oscillator as a high quality
microwave oscillator [2]. The OEO contains a continuous wave laser source. The
optical signal generated from the laser is fed to a Mach-Zehnder modulator (MZM),
which is acting as an intensity modulator. The intensity modulated optical signal
is passed through an optical fiber delay line and applied to the photo detector. The
detected RF signal is then filtered by a band pass filter (BPF). The output of the BPF
is fed to the electrical port of the MZM. Generation of high spectrally pure signal is

D. Ghosh (B)
Department of Electronics and Communication Engineering,
Siliguri Institute of Technology, Siliguri 734009, West Bengal, India
e-mail: dia.slg42@gmail.com
A. Mukherjee
Department of Electronics and Communication Engineering,
Central Institute of Technology, Kokrajhar 783370, Assam, India
e-mail: arindum78@gmail.com
N. R. Das
Institute of Radio Physics and Electronics,
Calcutta University, 92 A.P.C. Road, Kolkata 700009, West Bengal, India
e-mail: nrd@ieee.org
B. N. Biswas
Education Division, SKF Group of Institutions,
Mankundu, Hooghly 712139, West Bengal, India
e-mail: baidyanathbiswas@gmail.com

© Springer Nature Switzerland AG 2019 27

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_4
28 D. Ghosh et al.

possible due to the long low loss optical fiber delay line in its feedback loop. The long
delay line results in a high quality factor and spectral purity. The presence of optical
fiber delay line facilitates OEO as a candidate of electro-optical system with delayed
feedback. Therefore the study on the complex dynamics of OEO is an important
aspect, both from academic and engineering application point of view. Considering
the feedback gain as a control parameter Chembo et al. described the generation of
chaotic breathers in an OEO [3]. Other schemes for chaotic signal generation and
stability analysis in an OEO was also being contemplated [4–9]. By controlling both
feedback delay and loop gain the complex dynamics and synchronization property
of an OEO was reported [10, 11] but the OEO in this report was implemented using
discrete time DSP technology. The oscillator was designed with a laser, electro-optic
modulator and a photo-detector but for delay and filtering purpose the DSP board
was used. In [12], it has been reported by the present authors that with the variation
of loop delay the system loses its stability and following a period doubling route it
produces chaotic oscillation.
In the present work we report a study on the complex dynamics of an OEO under
the influence of a synchronizing signal. In OEO in order to obtain high spectral purity
of the signal a long feedback loop delay is required. But long feedback loop delay
produces additional cavity modes. These adjacent cavity modes can even produce
unwanted chaotic oscillation. It has been shown that by controlling amplitude of
the external signal the chaotic oscillation at the output of the free running oscillator
can be destroyed and period −1 oscillation can be produced. Although the method
of chaos quenching is not new [13, 14], as far as the knowledge of the authors is
concerned, the effect of sync signal to control the chaotic dynamics of the OEO is
addressed nowhere.
The paper is organized in the following way: Sect. 2 describes the basic configu-
ration of the oscillator and derivation of the system equation. In Sect. 3 the numerical
study is presented. The simulation study is described in Sect. 4. Finally the paper
concludes.

2 Derivation of System Equation

Figure 1 shows the basic configuration of an SLOEO. It consists of a continuous wave

laser source which is fed into a Mach-Zehnder modulator (MZM), the MZM acts
as an intensity modulator of the optical signal. The optical output of the modulator
is detected by a photo detector after passing through a long optical delay line. This
signal is then passed through an electrical band pass filter (BPF). The output from
the BPF is fed back to the electrical port of the MZM. The BPF implemented here
using a single tuned circuit.
Let us consider the RF input to the MZM is Vin (t)  V (t)e j(ω0 t+θ(t)) where V (t)
is the amplitude of the signal with free-running frequency ω0 and the initial phase of
θ (t). The output power of the MZM can be expressed as [15].
A Study on the Effect of an External Periodic … 29

Fig. 1 Basic configuration of a single loop optoelectronic oscillator

  
1 Vin (t) + VB
P(t)  α P0 1 − η Sin π (1)
2 Vπ

where P0 is the input optical power, α is the fraction of insertion loss of the modulator,
η is the extinction ratio of the modulator, V B is the bias voltage of the modulator, and
Vπ is the half wave voltage of the modulator. Therefore the photo-detector output can
be expressed as V0 (t)  ρ R P(t − τ ), where ρ is the sensitivity and R is the output
impedance of the photo-detector and τ is the time delay resulting from the physical
length of the optical fiber in the feed-back loop. Considering all these arguments it
can be shown that [15, 16].
⎡


⎤
π VB π V (t−τ ) ∞
π V (t−τ )
⎢ 1 − η sin Vπ J0 Vπ + 2 J2m Vπ cos[2 m ω(t − τ )] ⎥
⎢ m1 ⎥
V0 (t)  V ph ⎢
⎢

⎥
⎥
⎣ π VB 
∞
π V (t−τ ) ⎦
−2η cos Vπ × 2 J2m+1 Vπ sin[(2m + 1)ω(t − τ )]
m0

It is to be noted that with the growth of oscillation amplitude the effective Q value
of the tuned circuit becomes narrow and the smaller components of the spectrum are
rejected. The highest component of the spectrum only sustains at the output of the
oscillator. Thus the output of the MZM is seen to be
   
π VB π V (t − τ ) N (V (t − τ ))
V0 (t)  −2ηV ph cos J1 sin[ω(t − τ )]  exp (−sτ )Vin (t)
Vπ Vπ V (t)

α Rρ P0
where N (V (t − τ ))  −2ηV ph cos π VB
Vπ
J1 π VV(t−τ
π
)
and V ph  2
,
30 D. Ghosh et al.

now for simplicity let us consider η  1; VB  Vπ ; π V ph  Vπ ; Vπ  π and

N (V (t − τ ))  2J1 (V (t − τ )). Here J 1 is the Bessel function of the first kind for
order zero.
When the input signal V in (t) passes through the SLOEO the output voltage can
be expressed as

V0 (t)  β(s) · Vin (t) (2)

 
N (V (t − τ )) −s τ
β(s)  G(s)e (3)
V

here G(s) is the transfer function of the single tuned circuit and can be written as
G(s)  gm Z (s), gm is the gain of the tuned circuit.
Using (2) and (3) it can be shown that
 
1 J1 (V (t − τ )) −s τ
 2gm e (4)
Z (s) V
V ∼ 
 2J1 (V (t − τ ))e−sτ gm (5)
Z (s)
  
V dV 1  
+C + V dt  2J1 V (t − τ )e−sτ gm (6)
R dt L

To realize the transient behavior, we consider the operation of the system near
resonance
 
1 1 ∼
+ jωC +  G + 2C( jω − jω0 ) (7)
R jωL

and
1 dV dθ
jω  · + jω0 + j (8)
V (t) dt dt

using (7), (8) in (6) and equating the real and imaginary part the time varying ampli-
tude and phase of an SLOEO can be written as.
dV ω0
 [G 1 2J1 [V (t − τ )]Cos (ω0 τ ) − V (t)]
dt 2Q

dθ ω0 G 1 2J1 [V (t − τ )]
− Sin (ω0 τ )] (9)
dt 2Q V

where G 1  gm R is gain at resonance.

Considering the following normalized quantities (9) can be rewritten as
A Study on the Effect of an External Periodic … 31

ω0 t τ
t  , τ  , b  2G 1 ,
2Q RC
V (t) V (t − τ )
v  , v(t  − τ  ) 
Vmax Vmax
dv   
 −v + b J1 v(t − τ  ) Cos (ω0 τ  )
dt   
dθ b J1 v(t  − τ  )
− Sin (ω0 τ  ) (10)
dt  v

Now let us consider a synchronizing signal having a form of S(t)  Ee j(ω1 t+ψ(t))
is injected in the free running oscillator, here E is the amplitude and ψ(t) is the
phase of the injected signal. The phase difference between the free running signal
and the injected signal is φ(t)  ψ(t) − θ (t). Thus it is not difficult to show that the
closed loop amplitude and phase equation of the synchronized oscillator will take
the following form.
dv   
 −v + b J1 v t  − τ  Cos(ω0 τ  ) + G1 e Cos(φ(t  ))
dt    
dφ 2Q b J1 v t  − τ  G1 e
 + Sin (ω0 τ  ) − Sin(φ(t  )) (11)
dt  ω0 v v

here   ω1 − ω0 and e is the normalized amplitude of the sync signal.

3 Numerical Analysis

Equation (10) is the free running system equation of the oscillator. This equation
is solved numerically using Mathematica version 10 considering G 1  3.55, b 
2G 1  7.1. In our previous work [12] it has been shown that with the variation of
feedback loop delay τ  the system produces chaotic oscillation following a period
doubling sequence. Figure 2 depicts phase plane plot of the oscillator. In this figure
the hyper chaotic oscillation for τ   3.3 is shown.
The chaotic dynamics is quantified using Lyapunov exponent spectrum, following
the technique proposed by Farmer [17]. The spectrum of Lyapunov exponent also
ensures the existence of chaotic oscillation beyond τ   2.3(Fig. 3). Now at τ   3.3
keeping all other parameter values unchanged the external sync signal is injected into
the oscillator. The injected signal frequency is same as the free running oscillation
frequency. It has been observed using (11) that with suitable control of the sync signal
amplitude the chaotic state of the free running oscillator disappears and period −1
oscillation is produced. Figure 4 shows the phase plane plot of the driven oscillator
for e  2.26 and e  2.31.
32 D. Ghosh et al.

Fig. 2 Numerically obtained phase plane plot of free running oscillator (v, v(t  − τ  ) space)

Fig. 3 Lyapunov exponent (λ) with feedback delay

A Study on the Effect of an External Periodic … 33

Fig. 4 Numerically obtained phase plane plot of the driven oscillator (v, v(t  − τ  ) space)

4 Simulation Study Using MATLAB Simulink Software

The oscillator under study is realized using MATLABTM 9.0 Simulink software.
Figure 5 represents block diagram of the simulation set-up. In general OEO can
generate high frequency signal in microwave and mm wave range. However it is
difficult to carry out the simulation study in such a high frequency range. To overcome
this difficulty the frequency of laser source is chosen as 500 M rad/s and the output
signal amplitude of the laser is set at 1.4 V. To design the BPF we have taken C  1nF,
L  0.2 µH, R  3 k, with these parameters the operating frequency becomes f 
11.22 MHz, RF gain G1 is set to 3.55. It can be shown that the fiber delay τ  10 µs
τ
(τ   RC  3.33) produces the chaotic oscillation at the output of the oscillator
(Fig. 6). The amplitude of the chaotic oscillation is 5 V. Now we have applied an
external RF signal into the oscillator. The operating frequency of the sync signal is
kept fixed at f s  11.22 MHz and the amplitude E is varied. The output spectrum
of the driven oscillator is shown in Fig. 7. It can be seen from the figure that at
E  2.15 V the chaotic oscillation completely disappears but some other adjacent
oscillating modes are present. These additional cavity modes are produced due the
large feedback loop delay. Now as E is increased further the effect of the side modes
are reduced and at E  2.55 V the effect of all side modes are disappeared and single
frequency oscillation at 11.22 MHz is achieved.
34 D. Ghosh et al.

Fig. 5 Schematic representation of simulation set-up

Spectrum of RF Output

1
Normalized Amplitude

0.8

0.6

0.4

0.2

0
1.09 1.1 1.11 1.12 1.13 1.14 1.15 1.16
7
Frequency (Hz) x 10

Fig. 6 Chaotic oscillation with C  1 nF, L  0.2 µH, R  3 k, τ  10 µs

5 Conclusion

In this literature we have studied the dynamics of an SLOEO under the influence of an
external sync signal. It has been demonstrated through the numerical and simulation
study that the application of the injected signal destroys the chaotic oscillation and
suitable control of the injected signal amplitude can produce period −1 oscillation.
Optoelectronic oscillator can efficiently produce high frequency signal with high
spectral purity. Generation of high spectrally pure signal is possible due to the long
low loss optical fiber delay line in its feedback loop. However long feedback loop
delay may produce unwanted chaotic oscillation. The proposed technique can be
efficiently used to remove chaotic oscillation and produce single frequency oscillation
in an OEO.
A Study on the Effect of an External Periodic … 35

Spectrum of RF Output Spectrum of RF Output

Normalized Amplitude
Normalized Amplitude

1 1

0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2

0 0
1.06 1.08 1.1 1.12 1.14 1.16 1.18 1.06 1.08 1.1 1.12 1.14 1.16 1.18
Frequency (Hz) x 10
7
Frequency (Hz) x 107

(a) E = 2.15 Volt (b) E = 2.55 Volt

Fig. 7 RF spectrum of the oscillator obtained from the simulation study with τ = 10 µs and with
different values of E, keeping all other parameters unchanged

Acknowledgements The authors are thankful to the management of Siliguri Institute of technology,
Siliguri, West Bengal, India, Central Institute of Technology, Assam, India for giving an opportunity
to carry out this work. The authors also acknowledge the support from the management of Sir J
C Bose School of Engineering to conduct the work at Sir J C Bose Creativity Centre of Supreme
Knowledge Foundation Group of Institution, Mankundu, Hooghly, West Bengal, India.

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URSI—APRASC’2016, Seoul, Korea, August, 2016
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(2012)
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modulated signal in a single loop optoelectronic oscillator. Optik Int. J. Light Electron. Opt.
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Computation of Current Density
in Double Well Resonant Tunneling
Diode Using Self-consistency Technique

Biswarup Karmakar, Rupali Lodh, Pradipta Biswas,

Subhro Ghosal and Arpan Deyasi

1 Introduction

Resonant tunneling devices are found the interest of both theoretical [1] and exper-
imental researchers [2] for the post decade owing to its novel electronic properties
[3], its less complex mechanism supported by the controlled microelectronic growth
techniques with various combination of semiconducting materials [4]. Electrical
and optical properties of these heterostructure devices can be computed from the
knowledge of quantum transport processes, and precise estimation of transmission
coefficient is essential for the device with incorporation of physical parameters [5,
6]. Easki and Tsu first proposed a semiconductor symmetric double barrier structure
[7] where electronic transport proceeds via resonant tunneling mechanism. This pio-
neering work makes the road for future research using quantum-confined devices.
They showed that a series of energy levels and associated subbands are produced
due to the confinement of carriers along one direction of otherwise bulk structures.
Computation for transmission coefficient carried out [8, 9] and later Scandella [10]
was without effect of material parameters, which was later realized [11, 12]; who
computed resonant tunneling probability in semiconductor double barrier structure
for different material parameters. They showed that computation of thermal prob-
ability is essential to calculate current from quantum devices. Thermal probability
was also computed [13] for thin barrier considering the GaAs/Alx Ga1−x As material
composition. Influence of the electron interference effects on the inhomogeneous
spatial distribution of the probability current density for the electron waves in semi-
conductor 2D nanostructures was theoretically investigated [14]. Researchers also

B. Karmakar · R. Lodh · P. Biswas · S. Ghosal

Department of Electronic Science, A.P.C College, Kolkata 700131, India
A. Deyasi (B)
Department of Electronics and Communication Engineering, RCC Institute
of Information Technology, Kolkata 700015, India
e-mail: deyasi_arpan@yahoo.co.in
© Springer Nature Switzerland AG 2019 37
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_5
38 B. Karmakar et al.

proposed [15] a transition layer model used to calculate resonant tunneling in a

double-barrier quantum well system. Modified TBDQW structures are used [16] to
design long wavelength semiconductor lasers with low threshold current and small
beam divergence.
Recently, photoluminescence spectroscopy of the RTD based THz devices is
experimentally measured [17] along with free electron concentration at contact lay-
ers. Very high peak current is recently achieved by using novel material as contact
[18] in order to improve its candidature to fit into THz range. Triple barrier structure
is used for high PVCR [19]; and low cost device is also proposed for high frequency
applications [20]. This structure is also able to exhibit microwave generation and
detection [21]. In this paper, current density and corresponding peak are calculated
for double well resonant tunneling device for different structural parameters, and
self-consistency technique is adopted for accurate estimation. Material composition
so also modified within type-I limit, and two different sets of dimension are consid-
ered for comparative performance estimation related with peak value. Results are
significant for application of the device at low bias ranges.

2 Mathematical Modeling

Considering envelope function approximation, electron motion can be written by

using time-independent Schrödinger equation
 
2 ∂ 1 ∂
− ∗ ψ(z) + V (z)ψ(z) − qξ (z)z  E(z)ψ(z) (1)
2m ∂z m * (z) ∂z

where V(z) is the Hartee-Fock potential represents electrostatic interaction in the

quantum device, ζ(z) is the applied field along the direction of wave propagation.
This potential function can be obtained by solving Poisson’s equation

d 2 V (z) q2
 [N D (z) − n(z)] (2)
dz 2 εr ε0

where n(z) is confined electron concentration, ND (z) is the total density of ionized
donors.
Thermal equilibrium probability is calculated assuming the physical probable
range of wave vector as
dk
P (3)
2π 2 ln[1 + exp(E F − 2 (n k − 1)dk + kmin )2 ]

where dk denotes the range of ‘k’ values, k is the minimum value of wavevector,
E F is the Fermi energy. Tunneling current density is theoretically defined as the
Computation of Current Density in Double Well Resonant … 39

Fig. 1 Current density variation with applied voltage using a without self consistency technique;
b with self consistency technique

probability of finding the electron in a region of space due to the flow of wavevector,
either form left or right of the structure. This is defined as
 
  ∂ψ ∂ψ 
Jz  ψ − ψ (4)
2m ∗ ∂z ∂z

In practice, it is calculated from the knowledge of Fermi function as

∞
2q
Jz  [ f (E, μ L ) − f (E, μ R )]T (E)d E (5)
h
UL

3 Results and Discussions

Using Eq. (3), current density is computed for double well RTD using self-
consistency method. Figure 1 shows the peak current density variation with applied
voltage using (A) without using self-consistency technique and (B) using self-
consistency technique. From the plot, it is observed that in case of using without
self-consistency technique only one maximum peak is obtained and with further
increase in applied voltage peak current density decreases and peak is broadened.
Effect of different material compositions on peak tunneling current density is
observed and analyzed from Fig. 2 which shows the current density profile as a
function of applied voltage of DBQW structure. From the plot, it is observed that
40 B. Karmakar et al.

Fig. 2 Current density variation with applied voltage for different material compositions of barrier
widths with self consistency technique (for y  0.1)

maximum peaks are found for Al mole fraction 0.2 and 0.4 at 0.08 V; and for x 
0.1, it is 0.13 V. So, among three set of Al mole fraction maximum tunneling current
density is achieved for 0.2 which is 4.416 × 105 amp.m−2 at 0.08 V and the current
densities are comparatively low for mole fraction 0.4 and 0.1. This is so because
when any two Eigenenergy state of DBQW structure matched with each other, the
maximum transmission probability occurs i.e. the quantum tunneling phenomenon
is happened and maximum value of peak current density is achieved. Then further
variation of voltage multiple peaks are achieved but their peak current densities are
lower than maximum peak .because the carrier concentration is lowered for such
energy state.
Figure 3 shows the current density profile with applied voltage for three different
well widths. The peak current density becomes maximum 10.1 × 105 amp.m−2 at
0.03 V for well width equals to 8 nm, otherwise it remains less than 105 amp.m−2 for
well widths 4 and 12 nm respectively. This behavior can be well explained following
the reason mentioned in the first paragraph of this section. So, among the three well
width dimensions, for a particular well width, the transmission probability is maxi-
mum; and henceforth, maximum peak current density is achieved. But for other well
dimensions, transmission probability is lowered and current density is consequently
reduced.
Effect of different middle barrier width on peak tunneling current density is
observed and analyzed from Fig. 4. From the result, it is observed that the maximum
value of current density is 14.14 × 104 amp.m−2 at 0.03 V for barrier width 100 nm
and hence peak current density is comparatively lower for 70 nm which is 4.753 × 104
Computation of Current Density in Double Well Resonant … 41

Fig. 3 Current density variation with applied voltage for different well widths with self-consistency
technique

amp.m−2 and for 40 nm which is 4.091 × 104 amp.m−2 both at 0.07 V. For a particu-
lar barrier width dimension, the eigenenergy states of DBQW are matched perfectly
to each other and maximum transmission probability achieved and the peak current
density becomes maximum. But changing the barrier width, transmission probability
decreases and corresponding peak current density also decrease.
Effect of different temperature on peak tunneling current density is represented
from Fig. 5. It is seen from the figure that at 0.13 V, current density becomes maximum
which is 2.414 × 105 amp.m−2 for temperature 700 K. Peak current densities for 500
and 300 K are 1.725 × 105 and 1.035 × 105 amp.m−2 respectively both at 0.13 V
which is comparatively lower than the peak current density achieved at temperature
700 K. Hence peak current density increases with higher temperature.
Figure 6 shows the variation of peak tunneling current density as a function of
material composition for two different set of barrier width. For L.B.W  30 nm,
R.B.W  40 nm peak current density increases with increasing the Al mole fraction
up to the limit 0.15 and at 0.17 the peak current density attains maximum value which
is 9.77 × 105 amp.m−2 . Then further increase of mole fraction peak current density
decreases. This is because for this barrier dimensions the quantum encirclement
decreases for very high and very low value of Al mole fraction x and hence peak
current density also decrease.
For L.B.W  70 nm, R.B.W  80 nm, the peak current density remain constant
from mole fraction 0.5 to 0.1. After 0.1 the peak current density slowly increase up to
0.3, then increases rapidly. For higher barrier dimension set quantum encirclement
42 B. Karmakar et al.

Fig. 4 Current density variation with applied voltage for different middle barrier widths with self-
consistency technique

Fig. 5 Current density variation with applied voltage for different temperature with self-consistency
technique

increases with increase the Al mole fraction from lower value to higher and the
current density also increases.
For L.B.W as 30 nm and R.B.W as 40 nm, peak current density remain constant
from well width range 1–9 nm except the range from 4 to 6 nm. In this range peak
Computation of Current Density in Double Well Resonant … 43

Fig. 6 Variation of peak tunneling current density as a function of material composition for two
different set of barrier width

current density first decrease from 4 to 5 nm then it increase from 5 to 6 nm. After
9 nm, peak current density increases rapidly. For this set of barrier width the peak
current density is low up to certain limit and nears about show a constant peak current
density except the region 4–6 nm and after 6 nm its again show a constant peak
current density. In region 4–6 nm there is a dip showing in Fig. 7. In this region first
tunneling probability reduced such that the peak current density decreases from 5.5 ×
104 amp.m−2 to less than 2 × 104 amp.m−2 from 4 to 5 nm and minimum 1.714 × 104
amp.m−2 at 5 nm then the tunneling probability increases slightly and the peak current
density reach 4.681 × 104 amp.m−2 at 6 nm. After 9 nm the quantum confinement
increases which increase the tunneling probability and the current density increases
rapidly.

4 Conclusion

Double well resonant tunneling diode is analytically simulated for different con-
stituent layer widths, and also for different operating temperatures. Peak current
densities are obtained at particular bias values, which speak for eigenstates align-
ment between adjacent quantum wells. Self-consistency technique is incorporated
for simulation purpose which provides accurate result regarding the position of the
peaks, optimum structural parameters in order to obtain that magnitude, and the junc-
tion temperature to obtain measurable current at the applied bias range. It may also
44 B. Karmakar et al.

Fig. 7 Variation of peak tunneling current density as a function of well width for the dipping section
for L.B.W  30 nm, R.B.W  40 nm

be noted that current increases with increase in temperature. Two different dimen-
sion set are used for simulation in order to reveal the external influence on electrical
properties of the device. Different dimensions of contact regions also help to analyze
fluctuations in peak current profile. Thus the device can be operated at those biasing
points, where peaks are appeared.

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Computation of Current Density in Double Well Resonant … 45

8. L.A. Chanda, L.F. Eastman, Quantum mechanical reflection at triangular planar-doped’ poten-
tial barriers for transistors. J. Appl. Phys. 53, 9165–9169 (1982)
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Ga1−x Alx As Heterostructures. Phys. Rev. B 39, 10246–10250 (1989)
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resonant tunneling diodes for microwave signal generation and detection. European Microwave
Integrated Circuits Conference (EuMIC), 2013
Computation of Electrical Parameters
for Single-Gate High-K Nanoscale
MOSFET with Cylindrical Geometry

Suporna Bhowmick, Debarati Chakraborty and Arpan Deyasi

1 Introduction

Research on nanoscale MOSFET has been initiated a decade ago due to the shrinking
gate size [1] with the increasing demand of incorporating more no. of transistors
inside the reduced floor area; and this technological improvement is associated with
the additional generated complexity in terms of short channel effect [2]. As gate
length goes beyond 100 nm, quantum wire is formed in the otherwise bulk channel;
and owing to different geometries of the channel, solution of Schrödinger’s equation
with various boundary conditions becomes more difficult to solve for calculating
electrical parameters. This computational problem is solved by adopting Green’s
function formalism [3], and dissipative effects is considered at both source and drain
ends under ballistic limit [4] for near accurate performance estimation. This technique
helps to cop up with the ITRS roadmap [1] from theoretical stand-point as predicted
in 2007.
Measurement of tunneling current in nano-dimensional MOSFET is the subject
of interest [5, 6] as it governs the performance of the device when applied bias is sig-
nificantly low. The reduction of subthreshold current [7] in short-channel MOSFET
is one of the major tasks as depicted in the last decade, and thus gate control plays
a major part in this context. This leads to a series of novel proposals as double-gate
MOSFET [8, 9], triple-gate MOSFET [10], GAA MOSFET [11] etc. Also high-K
dielectrics provide another much-needed breakthrough in context of reduction of
subthreshold current [12]. But the interesting fact is that most of the theoretical
results available in literatures related with reduction of short-channel effect deals
with rectangular structure, which is ideal, and very difficult to reproduce experimen-
tally. In the present paper, electrical parameters in the single-gate nano-dimensional

S. Bhowmick · D. Chakraborty · A. Deyasi (B)

Department of Electronics and Communication Engineering, RCC Institute
of Information Technology, Kolkata 700015, India
e-mail: deyasi_arpan@yahoo.co.in
© Springer Nature Switzerland AG 2019 47
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_6
48 S. Bhowmick et al.

MOSFET is calculated using green’s function technique; where cylindrical channel

geometry is considered. Though a few reports are already available for Cartesian
coordinate system, but rarely manuscripts are written considering cylindrical sys-
tem. Results are calculated considering high-K dielectric, and are compared with
that obtained for low-k material.

2 Mathematical Modeling

For computation of drain current, first self-consistent solution of Schrödinger and

Poisson equations is to be calculated. Considering the geometry of the structure,
Schrödinger equation is given in the following form
⎡  2  ⎤
2 ∂ 1 ∂
−
⎢ 2m r* (θ,z) ∂r 2 + r ∂r ⎥
⎢ ⎥
⎢ 2  1 ∂  1  ∂  ⎥
⎢− − ⎥ψ(x, y, z)  Eψ(x, y, z) (1)
⎢ 2 r ∂θ m θ* (r,z) ∂θ
2
⎥
⎢   ⎥
⎣ 2 ∂ 1 ∂
⎦
2 ∂z m * (r,θ) ∂z
+ V (x, y, z)
z

Potential can be computed from Poisson’s equation if electron density in the

channel is known

∇ 2 ψ(r, θ, z)  −n 3D,m /ε (2)

where ψ(z) is the potential that should be determined using self-consistency tech-
nique. Self energies at source and drain ends are given by [3].
  2 

E [ p, q]  − 2
amn (r )|r 0 exp ( jkm,1 a)δ p,(m−1)R+1 δq,(m−1)R+1 (3)
S/D S/D
2a

Retarded Green’s function is given by [3]

 
G(E)  [E I − H − (E) − (E)]−1 (4)
S D

Finally, drain current is obtained in the form

kB T  1 + exp[(μ S − E i0 )/k B T ]
I DS  G 0 gi In (5)
q i
1 + exp[(μ D − E i0 )/k B T ]

where E i0 represents the minimum energy of ith subband, gi is the spin degeneracy.
After calculating drain current, quantum capacitance and subthreshold swing are
obtained as
Computation of Electrical Parameters for Single-Gate … 49
  
d|Q| d(μ − μ0 )
CQ  q / q− (6)
d VG d VG
 
1 d(μs − μ0 ) −1
S (7)
k B T In (10) d VG

DIBL is measured by

VthD D − Vthlow
D− (8)
V D D − VDlow

3 Results and Discussions

Using Eq. (5), drain current is first calculated as function of both drain voltage and
gate voltage. The result is obtained for high-K dielectric, and simultaneously the
performance enhancement is measured by comparing with that obtained for con-
ventional low-K dielectric material. Figure 1 shows the drain current variation as
a function of drain voltage for two different VGS . The lowest magnitude of VGS is
considered as 0.5 V due to the fact that less than the value, the difference of result
due to various dielectrics becomes insignificant. It may be observed that replacing
SiO2 by HfO2 , drain current is significantly increased. The saturation value for low-K
dielectric is very close to subthreshold region, and thus lowering gate bias may cause
a serious problem when applied for digital circuits. The present result shows how
significantly the performance is improved for high-K dielectric. Similar distinguish-
able difference is also observed when transfer characteristics are plotted, as depicted
in Fig. 2.
Figure 3 shows the variation of channel transconductance for different channel
diameter. It is seen form the plot that with increasing channel dimension, transcon-
ductance decreases. With higher dimension, the variation becomes almost linear.
Figure 4 shows the variation of quantum capacitance. It is observed that capacitance
increases rapidly at lower gate bias, but becomes almost saturated when gate voltage
reaches close to 1 V.
Sub threshold swing and DIBL are plotted in Figs. 5 and 6 respectively. For
circuit application, it is always desirable to reduce the sub threshold swing, which is
achieved by increasing the dielectric constant of the insulating material surrounded
the channel. In Fig. 5, it is seen that at larger channel thickness, SS remains very
low when HfO2 is used instead of SiO2 , where the rate of increment with channel
dimension is very large. This measurement is very difficult for rectangular channel,
as simultaneous tuning of two different confinements leads various results, which
is one major disadvantage form fabrication stand-point. The similar nature is also
observed in DIBL plot.
50 S. Bhowmick et al.

Fig. 1 Static characteristics for two different gate biases with both high-K and low-K dielectrics

Fig. 2 Transfer characteristics with both high-K and low-K dielectrics

Computation of Electrical Parameters for Single-Gate … 51

Fig. 3 Transconductance with gate voltage for different channel diameter

Fig. 4 Quantum capacitance with gate voltage for different channel diameter
52 S. Bhowmick et al.

Fig. 5 Sub threshold swing with channel thickness for different dielectrics

Fig. 6 DIBL with channel thickness for different dielectrics

Computation of Electrical Parameters for Single-Gate … 53

4 Conclusion

Electrical performance parameters of cylindrical single-gate MOSFET is analyti-

cally calculated in presence of low and high-K dielectrics. Result speaks in favor of
higher dielectric constant of the insulating material which substantially reduces sub-
threshold swing and DIBL. Drain current is also considerably increased compared to
subthreshold leakage current level even at very low gate bias. Appropriate tailoring
of channel diameter effectively controls the device transconductance and quantum
capacitance, which are essentially useful for practical implementation of the device
in analog and digital circuits respectively.

References

1. http://www.itrs2.net/
2. Y. Taur, T.H. Ning, Fundamentals of modern VLSI devices (Cambridge University Press, Cam-
bridge, U.K., 1998)
3. A. Rahman, J. Guo, S. Datta, M. Lundstrom, Theory of ballistic nanotransistors. IEEE Trans.
Electron Devices 50, 1853–1864 (2003)
4. R. Venugopal, Z. Ren, S. Datta, M. Lundstrom, Simulating quantum transport in nanoscale
transistors: real versus mode-space approaches. J. Appl. Phys. 92, 3730–3739 (2002)
5. M. Bella, S. Latreche, Analyze of DGMOS tunneling current through nanoscale gate oxide.
Nanosci. Nanotechnol. 6(1A), 117–121 (2016)
6. M. Chanda, S. De, C.K. Sarkar, Modeling of parameters for nano-scale surrounding-gate MOS-
FET considering quantum mechanical effect. Int. J. Numer. Model. Electron. Netw. Dev. Fields
Spec. Issue Model. High Freq. Silicon Transistors 27, 883–895 (2014)
7. Y. Swami, S. Rai, Modeling and analysis of sub-surface leakage current in nano-MOSFET
under cutoff regime. Superlattices Microstruct. 102, 259–272 (2017)
8. F. Djeffal, Z. Dibi, M.L. Hafiane, D. Arar, Design and simulation of a nanoelectronic DG MOS-
FET current source using artificial neural networks. Mater. Sci. Eng., C 27(5–8), 1111–1116
(2007)
9. B. Baral, A.K. Das, D. De, A. Sarkar, An analytical model of triple-material double-gate metal-
oxide-semiconductor field-effect transistor to suppress short-channel effects. Int. J. Numer.
Model. Electron. Netw. Dev. Fields 29(1), 47–62 (2016)
10. P.R. Kumar, S. Mahapatra, Analytical modeling of quantum threshold voltage for triple gate
MOSFET. Solid State Electron. 54(12), 1586–1591 (2010)
11. B. Jena, B.S. Ramkrishna, S. Dash, G.P. Mishra, Conical surrounding gate MOSFET: a possi-
bility in gate-all-around family. Adv. Nat. Sci. Nanosci. Nanotechnol. 7, 015009 (2016)
12. N.B. Atan, I.B. Ahmad, B.B.Y. Majlis, in Effects of high-K dielectrics with metal gate for elec-
trical characteristics of 18 nm NMOS device, IEEE International Conference on Semiconductor
Electronics (2014)
 Part II
Power System
Fault Diagnosis in Isolated Renewable
Energy Conversion System Using
Skewness and Kurtosis Assessment

Debopoma Kar Ray, Surajit Chattopadhyay

and Samarjit Sengupta

1 Introduction

Renewable energy technology is of great concern in recent days due to the ever-
increasing use of fossil fuels and the risk persisting with the rapid depletion of the
conventional resources [1] . However, the present trend of developments of non-
conventional sources indicates that these will serve as supplements for conventional
sources for the coming days. Due to this, it has been of great concern for identifying
the various non-linearity in the renewable energy systems and for the condition mon-
itoring of the grid connected and standalone renewable energy networks. Throughout
the world, wind energy has become a principle energy source in the world’s energy
market in more than 70 countries across the universe. A current-source inverter-
based standalone WECS (Wind Energy Conversion System) [2] nullifies dump load
to avoid surplus power generation. A wind farm associated hybrid energy storage
system (HESS) smooth out ripples for reducing impact on the grids [3], wherein a
cutoff frequency method optimizes the system, to find the rated power and capacity of
HESS. A condition monitoring technique has been seen for an early fault detection to
prevent sudden breakdown [4]. Grid-interconnected wind energy system installed in
Jordan [5] analysis depicts more percentage error in the estimation of the cost as well
as energy extracted per year. A Discrete Wavelet Transform (DWT) based algorithm

D. K. Ray (B)
EE Department, Faculty, MCKV Institute of Engineering, Howrah, India
e-mail: debopoma86@gmail.com
S. Chattopadhyay
EE Department, Faculty, Ghani Khan Choudhury Institute
of Engineering and Technology, Malda, India
e-mail: surajitchattopadhyay@gmail.com
S. Sengupta
Applied Physics Department, Ex-Faculty, University of Calcutta, Kolkata, India
e-mail: samarsgp@rediffmail.com
© Springer Nature Switzerland AG 2019 57
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_7
58 D. K. Ray et al.

minimizes wind power forecasting errors in WECS [6]. A two-stage optimal power
flow iterative algorithm is able to calculate the minimum storage size of a plant dur-
ing congestion [7]. Baseline principal component analysis (PCA) model can be used
for online fault detection in wind turbine [8]. A Fault detection estimator can be used
for fault detection at specified location [9]. Various condition monitoring techniques
has been seen for increasing the accuracy of wind turbine operation [10]. A SCADA
based clustering algorithm and principal components analysis is effective for wind
turbine gearbox failure [11]. Various 3 phase induction motor fault diagnosis can
be done using Skewness and Kurtosis analysis of the current signatures at different
faults occurring in the system [12]. None of studies reviewed so far, deals with the
unsymmetrical fault identification in load and source sides of either stand alone or
grid interconnected wind energy conversion system, monitoring the Skewness and
Kurtosis of the current signatures of the network at normal and in presence of double
line (LL), single line to ground (LG) and double line to ground (LLG) faults in the
system.
In this paper an attempt has been made for determining the various unsymmetrical
faults occurring in a stand-alone wind energy conversion system at generator and
load buses of the network, monitoring the Skewness and Kurtosis of the discrete
wavelet transform decomposition levels of the bus current signature at normal and in
presence of LL, LG, LLG faults in the network. The generator and load bus currents
have been acquired at normal and in presence of LL, LG, LLG faults in source
and load sides of the network, considered one at a time. These currents have been
assessed using Multi-Resolution Analysis of Discrete Wavelet Transform (MRA of
DWT). The wavelet decomposition levels obtained from this analysis were analyzed
using statistical Skewness and Kurtosis value monitoring technique. Monitoring the
Skewness and Kurtosis value of DWT level coefficients, changes obtained at fault
from normal has been recorded and corresponding features have been extracted for
exact identification of the various faults occurring in the system.

2 Wind Energy Conversion System Under Analysis

A stand alone wind energy conversion system (WECS) has been modeled and used
for the analysis purpose. Figure 1 depicts the block diagram of the system and Table 1
shows the network ratings.
In the above Table 1 p.u. voltage  440 V and 1 p.u. power  300 kVA.

3 Theoretical Backgrounds

In this analysis MRA of DWT statistical monitoring has been done. A discrete wavelet
transform is given by the expression [13]:
Fault Diagnosis in Isolated Renewable Energy Conversion … 59

Fig. 1 Block diagram of stand-alone WECS

∞
1
DW T (m, n)   m f (t) g(a0−m t − nb0 ) d(t) (1)
a0
−∞

The wavelet representation is discrete in DWT is discrete and represent the cor-
relation between the original signal and wavelets for different combinations m and
n. The digital signal to be analyzed is then decomposed into successive scales. After
decomposing the signal into successive levels, the approximate and detailed coef-
ficients obtained has been analyzed and Skewness and Kurtosis values have been
calculated.
Skewness [13] defines, how much a distribution is symmetrical/asymmetrical over
a sample mean and positive skewness refers to the spreading of data to the right of
the mean.
Kurtosis [13] defines how much a distribution is having extension towards right
or left of a sample mean.
60 D. K. Ray et al.

Table 1 System specifications

Equipments Specifications
Wind turbine 4 blades, shaft speed-10 m/s
Asynchronous generator 300 kVA, 440 V, 50 Hz, stator resistance and inductance (p.u.):
0.016, 0.06, rotor resistance and inductance (p.u.): 0.015, 0.06,
mutual inductance (p.u.): 3.5
Synchronous condenser 300 kVA, 440 V, 50 Hz, stator resistance: 0.017 , reactances
(p.u.): Xd  3.23, Xd -0.21, Xd  0.15, Xd  2.79, Xq  0.37,
Xl  0.09
Var compensator 440 V, 50 Hz, 75 KVar
Step up transformer 440 V/33 kV
Step down transformer 33 kV/11 kV
Distribution transformer 11 kV/440 V
Relay Operating time  10 ms, % voltage sag  63% of supply voltage
Circuit breaker Breaker resistance  0.001 , transition time  0.2 s
Load 25, 10 kW

4 Determination of MRA of DWT Coefficients at Normal

and Fault

The current signatures of the generator and load buses of the network at normal
and at fault have been acquired and assessed using MRA of DWT. The wavelet
decomposition and the approximate and detailed coefficients for each decomposition
level have been presented in Figs. 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15. In
this analysis Daubechies 20 mother wavelet has been used.
The Figs. 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15 have been observed and
it has been inferred that, the features for each case study are distinctively different.
But specific identification cannot be done from this monitoring technique. Thus for
more specific analysis, the various wavelet decomposition levels have been assessed
calculating the statistical Skewness and Kurtosis value, which has been provided in
succeeding section.

Fig. 2 Source current wavelet decomposition and approximate and detailed coefficients at normal
condition
Fault Diagnosis in Isolated Renewable Energy Conversion … 61

Fig. 3 Load current wavelet decomposition and approximate and detailed coefficients at normal
condition

Fig. 4 Source current wavelet decomposition and approximate and detailed coefficients at LG fault
in generator bus

Fig. 5 Source current wavelet decomposition and approximate and detailed coefficients at LL fault
in generator bus

Fig. 6 Source current wavelet decomposition and approximate and detailed coefficients at LLG
fault in generator bus
62 D. K. Ray et al.

Fig. 7 Load current wavelet decomposition and approximate and detailed coefficients at LG fault
in generator bus

Fig. 8 Load current wavelet decomposition and approximate and detailed coefficients at LL fault
in generator bus

Fig. 9 Load current wavelet decomposition and approximate and detailed coefficients at LLG fault
in generator bus

Fig. 10 Source current wavelet decomposition and approximate and detailed coefficients at LG
fault in load bus
Fault Diagnosis in Isolated Renewable Energy Conversion … 63

Fig. 11 Source current wavelet decomposition and approximate and detailed coefficients at LL
fault in load bus

Fig. 12 Source current wavelet decomposition and approximate and detailed coefficients at LLG
fault in load bus

Fig. 13 Load current wavelet decomposition and approximate and detailed coefficients at LG fault
in load bus

Fig. 14 Load current wavelet decomposition and approximate and detailed coefficients at LL fault
in load bus
64 D. K. Ray et al.

Fig. 15 Load current wavelet decomposition and approximate and detailed coefficients at LLG
fault in load bus

5 Determination of Skewness and Kurtosis Values

at Normal and Fault

The calculated Skewness and Kurtosis values for normal and at fault in generator
and load buses of the network were presented in matrix form in Tables 2, 3, 4 and 5.
In each of the matrices, the Skewness and Kurtosis coefficients can be demonstrated
as:
⎛ ⎞
Sa1 Sd1 K a1 K d1
⎜ Sa2 Sd2 K a2 K d2 ⎟
⎜ ⎟
⎜ ⎟
(S K ) M x N  ⎜ Sa3 Sd3 K a3 K d3 ⎟
⎜ ⎟
⎝ Sa4 Sd4 K a4 K d4 ⎠
Sa5 Sd5 K a5 K d5

(S K ) M x N denote the Skewness and Kurtosis matrix for M rows and N

columns

Table 2 Skewness and Kurtosis matrix for source side and load side current DWT decomposition
levels at healthy condition
Case study (S K ) M x N
⎛ ⎞
−0.01339 −0.17514 1.495922 99.79288
⎜ ⎟
⎜ −0.03295 −1.32368 1.492209 56.12955 ⎟
⎜ ⎟
For source side current ⎜ −0.06995 0.242319 1.489988 35.51113 ⎟
⎜ ⎟
⎜ ⎟
⎝ −0.14407 0.171094 1.486702 24.42911 ⎠
−0.31513 −0.10621 1.580086 3.469751
⎛ ⎞
−0.00145 −0.6324 1.502547 103.3608
⎜ ⎟
⎜ 0.001528 2.518314 1.504211 135.469 ⎟
⎜ ⎟
For load side current ⎜ 0.007446 0.716615 1.506871 99.88604 ⎟
⎜ ⎟
⎜ ⎟
⎝ 0.020698 1.285346 1.50683 35.7106 ⎠
0.04426 −0.07544 1.543202 6.345082
Fault Diagnosis in Isolated Renewable Energy Conversion … 65

Table 3 Skewness and Kurtosis matrix for source side and load side current DWT decomposition
levels at LG fault in generator and load buses, considered one at a time
Case study (S K ) M x N generator bus f ault (S K ) M x N load bus f ault
⎛ ⎞ ⎛ ⎞
0.004051 −0.31478 1.498862 15.29745 −0.00221 0.226096 1.973001 16.09459
⎜ ⎟ ⎜ ⎟
⎜ 0.013732 35.58154 ⎟ ⎜ −0.005 0.276028 1.972289 11.87682 ⎟
⎜ 0.887511 1.502256 ⎟ ⎜ ⎟
⎜ ⎟ ⎜ ⎟
For source side current ⎜ 0.032777 0.445972 1.546337 20.73361 ⎟ ⎜ −0.01059 0.170794 1.9694 16.54555 ⎟
⎜ ⎟ ⎜ ⎟
⎜ ⎟ ⎜ ⎟
⎜ 0.072961 −0.02592 1.54543 2.373368 ⎟ ⎜ −0.01734 0.60522 1.960292 40.44648 ⎟
⎝ ⎠ ⎝ ⎠
0.119334 −0.00456 1.529321 3.051837 −0.05017 −0.07076 1.972842 44.31766
⎛ ⎞ ⎛ ⎞
0.019569 −0.05502 1.587121 9.0657 0.002851 −0.01353 1.496464 15.34837
⎜ ⎟ ⎜ ⎟
⎜ 0.025333 −0.0356 1.588903 6.804406 ⎟ ⎜ 0.00752 −0.07094 1.495122 6.461887 ⎟
⎜ ⎟ ⎜ ⎟
⎜ ⎟ ⎜ ⎟
For load side current ⎜ 0.036437 0.104321 1.602708 5.568114 ⎟ ⎜ 0.016793 −0.09026 1.49299 9.549587 ⎟
⎜ ⎟ ⎜ ⎟
⎜ ⎟ ⎜ ⎟
⎜ 0.044845 −0.03039 1.50174 2.908291 ⎟ ⎜ 0.035813 −0.05297 1.496044 30.60578 ⎟
⎝ ⎠ ⎝ ⎠
0.112922 −0.01862 1.589668 5.139542 0.074567 −0.29069 1.494198 43.0236

Table 4 Skewness and Kurtosis matrix for source side and load side current DWT decomposition
levels at LL fault in generator and load buses, considered one at a time
Case study (S K ) M x N generator bus f ault (S K ) M x N load bus f ault

⎛ ⎞ ⎛ ⎞
0.00891 −0.17975 1.731736 17.57612 0.00891 −0.17975 1.731736 17.57612
⎜ ⎟ ⎜ ⎟
⎜ 0.019178 0.016043 1.754151 10.52569 ⎟ ⎜ 0.019178 0.016043 1.754151 10.52569 ⎟
⎜ ⎟ ⎜ ⎟
⎜ ⎟ ⎜ ⎟
For source side current ⎜ 0.03673 0.170514 1.791537 8.758571 ⎟ ⎜ 0.03673 0.170514 1.791537 8.758571 ⎟
⎜ ⎟ ⎜ ⎟
⎜ ⎟ ⎜ ⎟
⎝ 0.061719 0.625364 1.840528 42.78958 ⎠ ⎝ 0.061719 0.625364 1.840528 42.78958 ⎠
0.083803 −0.55682 1.862598 54.79014 0.083803 −0.55682 1.862598 54.79014
⎛ ⎞ ⎛ ⎞
−0.03514 −0.13522 1.847466 225.1158 0.001318 −0.28492 1.501157 119.2922
⎜ ⎟ ⎜ ⎟
⎜ −0.07652 −0.73658 1.955504 121.8549 ⎟ ⎜ 0.000043 −2.78988 1.502868 199.5778 ⎟
⎜ ⎟ ⎜ ⎟
⎜ ⎟ ⎜ ⎟
For load side current ⎜ −0.14812 −0.42996 2.131499 76.75545 ⎟ ⎜ −0.00244 0.243855 1.506193 95.43031 ⎟
⎜ ⎟ ⎜ ⎟
⎜ ⎟ ⎜ ⎟
⎜ −0.25532 −0.51682 2.369899 72.38661 ⎟ ⎜ −0.0078 −1.20755 1.512086 46.56893 ⎟
⎝ ⎠ ⎝ ⎠
−0.35902 0.278571 2.496105 70.70538 −0.02874 0.141903 1.540432 40.20908

Table 5 Skewness and Kurtosis matrix for source side and load side current DWT decomposition
levels at LLG fault in generator and load buses, considered one at a time
Case study (S K ) M x N generator bus f ault (S K ) M x N load bus f ault

⎛ ⎞ ⎛ ⎞
0.002516 0.038965 1.606521 15.6858 0.016009 4.371866 1.660812 287.9464
⎜ ⎟ ⎜ ⎟
⎜ 0.002713 −0.13023 1.60732 7.428806 ⎟ ⎜ 0.034012 −1.76333 1.708085 118.3351 ⎟
⎜ ⎟ ⎜ ⎟
⎜ ⎟ ⎜ ⎟
For source side current ⎜ 0.00319 0.264675 1.608419 9.356144 ⎟ ⎜ 0.06608 0.003883 1.789696 80.40759 ⎟
⎜ ⎟ ⎜ ⎟
⎜ ⎟ ⎜ ⎟
⎝ 0.005379 0.086461 1.607178 53.28107 ⎠ ⎝ 0.117219 0.093933 1.922053 60.74021 ⎠
−0.00538 −0.18838 1.61077 42.75261 0.163501 0.125944 1.992691 55.86645

⎛ ⎞ ⎛ ⎞
0.003112 0.010786 1.499355 15.34421 −0.00497 2.537022 1.500994 181.2674
⎜ ⎟ ⎜ ⎟
⎜ 0.008699 0.375878 1.498318 17.91369 ⎟ ⎜ −0.00856 −0.4281 1.501842 51.58309 ⎟
⎜ ⎟ ⎜ ⎟
⎜ ⎟ ⎜ ⎟
For load side current ⎜ 0.01975 0.24549 1.496731 27.4928 ⎟ ⎜ −0.01564 −1.19686 1.503619 108.3703 ⎟
⎜ ⎟ ⎜ ⎟
⎜ ⎟ ⎜ ⎟
⎝ 0.041983 0.063178 1.493616 41.66792 ⎠ ⎜ −0.02965 0.890177 1.508668 43.55096 ⎟
⎝ ⎠
0.084355 0.360648 1.489268 46.23959 −0.06337 −0.21793 1.520679 45.34609
66 D. K. Ray et al.

Sa1 − − − −Sa5 denote the Skewness values for approximation coefficients for
5 decomposition levels
Sd1 − − − −Sd5 denote the Skewness values for detailed coefficients for 5
decomposition levels
K a1 − − − −K a5 denote the Kurtosis values for approximation coefficients for
5 decomposition levels
K d1 − − − −K d5 denote the Kurtosis values for detailed coefficients for 5
decomposition levels.

Monitoring the Skewness and Kurtosis matrices of Tables 2, 3, 4 and 5, it has

been inferred that for LL, LG and LLG faults in generator bus, prediction can be
fruitfully done, monitoring the load side current and for the inception of these faults
in load bus, fault analysis can be done monitoring the source current. Features have
been extracted from these matrices and has been presented in succeeding section for
more specific identification of these faults in the system.

6 Feature Extraction

Analysis on the Skewness and Kurtosis coefficients from Tables 2, 3, 4 and 5 depicts
significant change in the generator and load bus current’s MRA of DWT decomposi-
tion levels, which has been consolidated to develop a pictographic feature extraction
from the Skewness and Kurtosis matrices. The feature extraction from the above
tables is presented in Tables 6 and 7.
Monitoring Tables 6 and 7, it is clear that for LG, LL and LLG faults in source
and load buses of the network, the Skewness and Kurtosis signatures are distinctly
different and if these patterns can be monitored, the type of faults in the network can
be identified and the location of these faults in the system can be ascertained.

7 Conclusion

Identification and localization of various faults in a system is of utmost importance

in successful running of a power utility system. The motivation of this work was
thus to determine the presence of LG, LL and LLG faults in the system as well
as to determine the zone of inception of these faults in the system, monitoring the
Skewness and Kurtosis signatures of the MRA of DWT decomposition level of the
source and load side currents at normal and at fault. The features extracted, from
the patterns generated, distinctively determine the occurrence of these faults in the
system. Also monitoring the load and source side spectrums, the faulty zone can be
identified. This analysis can be extended for the identification of other type of faults
in simulated as well as real time systems, which may occur in large scale or may be
incipient in nature.
Table 6 Feature extraction from source and load side currents at normal and fault in generator bus
Case study Feature extraction from Skewness monitoring Feature extraction from Kurtosis monitoring

Source side Approximate values

Detailed values
Fault Diagnosis in Isolated Renewable Energy Conversion …

(continued)
67
Table 6 (continued)
68

Case study Feature extraction from Skewness monitoring Feature extraction from Kurtosis monitoring

Load side Approximate values

Detailed values
D. K. Ray et al.
Table 7 Feature extraction from source and load side currents at normal and fault in load bus
Case study Feature extraction from Skewness monitoring Feature extraction from Kurtosis monitoring

Source side Approximate values

Detailed values
Fault Diagnosis in Isolated Renewable Energy Conversion …

(continued)
69
Table 7 (continued)
70

Case study Feature extraction from Skewness monitoring Feature extraction from Kurtosis monitoring

Load side Approximate values

Detailed values
D. K. Ray et al.
Fault Diagnosis in Isolated Renewable Energy Conversion … 71

References

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detection of wind turbines and related algorithms: a review. Renew. Sustain. Energy Rev.
13(1), 1–39 (2009)
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distribution networks. Power and energy Society General Meeting (PESGM), (2016). https://
doi.org/10.1109/pesgm.2016.7741202
8. F. Pozo, Y. Vidal, L. Acho, in Wind turbine fault detection through principal component analysis
and multivariate statistical inference. 8th European workshop on Structural Health Monitoring
(EWSHM) (2016)
9. X. Zhang, Q. Zhang, S. Zhao, R. Ferrari, M. M. Polycarpou, T. Parisini, in Fault Detection and
Isolation of the Wind Turbine Benchmark: an Estimation-based Approach. 18th IFAC World
Congress, pp. 8295–8300 (2011)
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International Journal of Renewable Energy Research, vol. 6, Nº 1, 2016
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(2011)
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MATLAB® , Mathworks
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approach through Current Signature Analysis. (Springer, Berlin). https://doi.org/10.1007/978-
981-10-0624-1
FFT Based Harmonic Assessment of Line
to Ground Fault in 14 Bus Microgrid
System

Sagnik Datta, Surajit Chattopadhyay and Arabinda Das

1 Introduction

A microgrid is a small-scale power grid which operates independently or in con-

junction with the main electrical grid of that area. Microgrid effectively cuts down
the dependency on the main electrical grid and also improves the overall reliability
of the electrical power system. Recently rapid development of “green energy” and
storage devices are taking place throughout the world. Microgrids implemented in
line with the concept of distributed generation are emerging as an effective form of
power management. Alike the conventional power grid, effective fault identification
and isolation is of paramount importance in microgrid system. In order to do so, the
location of the fault has to be precisely found out.
A lot of research works have been going on in this regard. Hooshyar et al. [1]
has carried out fault type classification in Microgrids including photovoltaic DGs.
Short-circuit fault analysis on microgrid has been done by Bayindir et al. [2]. DC
short circuit fault analysis has been done and protection of ring type DC microgrid
has been developed by Yu et al. [3]. A short-circuit current calculation method has
been introduced by Lai et al. [4] for low-voltage DC microgrid. Suppression strategy
has been introduced by Zha et al. [5] for short-circuit current in loop-type DC micro-
grid. Petrea et al. [6] presented factors influencing a micro-grid recovery process
following a short-circuit. Park et al. [7] developed DC Ring-Bus Microgrid Fault

S. Datta (B)
SKF Group of Institution, Hooghly, West Bengal, India
e-mail: sagnik.ee@gmail.com
S. Chattopadhyay
Ghani Khan Choudhury Institute of Engineering and Technology, Malda, India
e-mail: surajitchattopadhyay@gmail.com
A. Das
Jadavpur University, Kolkata, India
e-mail: arbinda.das@ju.in
© Springer Nature Switzerland AG 2019 73
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_8
74 S. Datta et al.

Protection and Identification of Fault Location. Fault detection and isolation have
been done by Park et al. [8] in Low-Voltage DC-Bus Microgrid System. Modeling
and real-time simulation of an AC microgrid have been done by Sahoo et al. [9] with
solar photovoltaic system. Modeling and reliability assessment have been carried
out by Quevedo et al. [10] of microgrids including renewable distributed generation.
Reliability assessment of a microgrid distribution system has also been carried out
Tuffaha and AlMuhaini [11] with PV and storage. Photovoltaic power generation
system low voltage ride has been analysed by Jin et al. [12] through control during
asymmetric fault. Integrated Fault Location and Power-Quality Analysis have been
done by Bíscaro et al. [13] in Electric Power Distribution Systems. Analysis of two
fault locators considering operation variations of the power distribution systems has
been done by Ramírez-Ramírez et al. [14]. Ehrenbenberger [15] has introduced fault
analysis of Smart Grid Power System employing Simultaneous Faults Method. Zhu
and Zhang [16] introduced a novel control strategy of DC microgrid under unbal-
anced grid voltage. FFT and wavelet decomposition based harmonics assessments
have been observed using current signature analysis for fault diagnosis [17–20].
This paper aims to reveal a harmonics assessment based technique of fault location
identification for Line to ground (LG) faults occurring at different load buses of a 14
bus microgrid system which is working in conjunction with main electrical grid. Fast
Fourier Transform (FFT) based total harmonic distortion (THD) analysis of outgoing
currents from the different generator buses are examined when LG fault occurs at
different load buses.

2 Microgrid Modelling

Single line diagram of the IEEE standard 14 bus microgridsystem is shown in Fig. 1.
In Fig. 1, it can be seen that there are four sources connected to the system. Bulk
power generator is present at generator bus G13, PV cell at G12, diesel generator
1(DG 1) at G8 and diesel generator 2 (DG 2) at G3. Five different kinds of loads
are present. A non-linear load is present at bus B10, furnace at B6, battery charging
system at B1, linear load at B2 and linear load 1 at B3.
section lines are joining
one bus to the other and these sections are 1 km in length.

3 Fault Simulation

LG faults are made to occur at different load buses and THD values of outgoing
currents from the different generator buses are measured. At first, the entire system
is kept healthy and the THD values of outgoing currents from the different generator
buses are recorded. Afterwards LG fault is made to occur on one specific load bus
while leaving the other load buses healthy and THD values of outgoing currents
from all the different generator buses are monitored. Like this all the load buses
FFT Based Harmonic Assessment of Line to Ground … 75

Fig. 1 Single line diagram of IEEE standard 14 bus microgrid system

are considered separately and in all cases distortion in outgoing currents from the
different generator buses are assessed through the THD values of those currents. THD
values are obtained by FFT analysis of the above mentioned current waveforms. Total
simulation time is set at 0.8 s. Fault duration is kept within 0.2–0.4 s. 40 cycles of the
outgoing currents from the different generator buses are considered for FFT analysis
with start time of 0.15 s and maximum sampling frequency of 1000 Hz.

4 Harmonic Assessment and Results

Results obtained from the FFT analysis are provided in the Tables 1, 2, 3, 4 and 5.
Data provided in the following tables present harmonic contents of outgoing currents
from different generator buses, when LG fault occurs at different load buses.

5 Observation

Based on the results given above, THD values of outgoing currents from one specific
generator bus for LG fault at different load buses is ascertained. This process is
 76

Table 1 Harmonic content at different generator bus outgoing currents for LG fault in B10 (non-linear load)
Gen. bus Fund. (%) Values are in % of fundamental Total THD
(in %)
DC 2nd order 3rd order 5th order 7th order 9th order 11th order
component
G13 100% 0.32 0.01 0.03 0.02 0.00 0.00 0.00 0.37
(Bulk Gen)
G12 100% 21.93 0.45 1.14 0.87 0.44 0.24 0.08 15.8
(PV)
G8 100% 1.84 0.27 0.32 0.14 0.01 0.04 0.02 4.4
(DG 1)
G3 100% 1.5 0.2 0.25 0.11 0.01 0.01 0.01 3.38
(DG 2)
S. Datta et al.
Table 2 Harmonic content at different generator bus outgoing currents for LG fault in B6 (furnace)
Gen. bus Fund. (%) Values are in % of Fundamental Total THD
(in %)
DC 2nd order 3rd order 5th order 7th order 9th order 11th order
component
G13 (Bulk 100 0.35 0.04 0.01 0.01 0.01 0.00 0.00 0.43
Gen)
FFT Based Harmonic Assessment of Line to Ground …

G12 (PV) 100 55.51 3.22 3.55 0.78 0.32 0.27 0.10 48.7
G8 (DG 1) 100 7.58 0.41 0.45 0.08 0.02 0.02 0.02 6.08
G3 (DG 2) 100 7.1 0.5 0.56 0.05 0.02 0.02 0.01 7.53
77
 78

Table 3 Harmonic content at different generator bus outgoing currents for LG fault in B1 (battery storage)
Gen. bus Fund. (%) Values are in % of fundamental Total THD
(in %)
DC 2nd order 3rd order 5th order 7th order 9th order 11th order
component
G13 (Bulk 100 0.37 0.01 0.04 0.03 0.01 0.01 0.00 0.53
Gen)
G12 (PV) 100 21.16 0.25 1.42 1.19 0.68 0.39 0.08 20.28
G8 (DG 1) 100 0.47 0.24 0.27 0.21 0.06 0.04 0.04 4.26
G3 (DG 2) 100 0.35 0.2 0.25 0.19 0.06 0.04 0.02 3.8
S. Datta et al.
Table 4 Harmonic content at different generator bus outgoing currents for LG fault in B2 (linear load)
Gen. bus Fund. (%) Values are in % of fundamental Total THD
(in %)
DC 2nd order 3rd order 5th order 7th order 9th order 11th order
component
G13 (Bulk 100 0.37 0.01 0.04 0.03 0.01 0.01 0.00 0.53
Gen)
FFT Based Harmonic Assessment of Line to Ground …

G12 (PV) 100 21.16 0.25 1.42 1.19 0.68 0.39 0.08 20.28
G8 (DG 1) 100 0.47 0.24 0.27 0.21 0.06 0.04 0.04 4.26
G3 (DG 2) 100 0.35 0.2 0.25 0.19 0.06 0.04 0.02 3.8
79
 80

Table 5 Harmonic content at different generator bus outgoing currents for LG fault in B3 (linear load 1)
Gen. bus Fund. Values are in % of Fundamental Total THD
(in %)
DC 2nd order 3rd order 5th order 7th order 9th order 11th order
component
G13 (Bulk 100% 0.37 0.01 0.04 0.03 0.01 0.01 0.00 0.53
Gen)
G12 (PV) 100% 21.16 0.25 1.40 1.19 0.68 0.38 0.08 20.28
G8 (DG 1) 100% 0.46 0.24 0.27 0.21 0.06 0.04 0.04 4.26
G3 (DG 2) 100% 0.35 0.2 0.25 0.19 0.06 0.04 0.02 3.8
S. Datta et al.
FFT Based Harmonic Assessment of Line to Ground … 81

Table 6 THD values of Site of fault THD values (in %)

outgoing current of bulk
generator bus (G13) B10 (non linear load) 0.37
B6 (furnace) 0.43
B1 (battery storage) 0.53
B2 (linear load) 0.53
B3 (linear load 1) 0.53

0.6
0.5
0.4
THD Values

0.3
0.2
0.1
0
B10 (Non linear B6 (Furnace) B1 (BaƩery B2 (Linear load) B3 (Linear load 1)
load) storage)
Place of occurrence of LG fault

Fig. 2 THD values of outgoing current of bulk generator bus (G13) for LG fault in the load buses

repeated for all the generator buses. One by one those values have been presented as
follows:
a. Bulk Generator Bus (G13)
THD values of outgoing currents from bulk generator bus (G13) for LG fault at
different load buses have been considered and given in Table 6.
As seen from Fig. 2, THD values of the outgoing current of Bulk Generator Bus
(G13) are much lower in comparison with the other Generator buses as shown in
Tables 8 and 9.
b. PV Cell Bus (G12)
THD values of outgoing currents from PV cell bus (G12) for LG fault at different
load buses have been considered and given in Table 7.
From Fig. 3, it has been observed that THD values of the outgoing current of
PV Cell Bus (G12) are much higher in comparison with the other Generator buses
as shown in Tables 7 and 9. When LG fault occurs at the bus (B6) connected with
the furnace, outgoing current waveform of PV Cell Bus (G12) gets considerably
distorted and contains high values of THD as shown in Fig. 2.
82 S. Datta et al.

Table 7 THD values of Site of fault THD values (in %)

outgoing current of PV cell
bus (G12) B10 (non linear load) 15.8
B6 (furnace) 48.7
B1 (battery storage) 20.3
B2 (linear load) 20.3
B3 (linear load 1) 20.3

60
50
THD Values

40
30
20
10
0
B10 (Non linear B6 (Furnace) B1 (BaƩery B2 (Linear load) B3 (Linear load
load) storage) 1)
Place of occurrence of LG fault

Fig. 3 THD values of outgoing current of PV cell bus (G12) for LG fault in the load buses

Table 8 THD values of Site of fault THD values (in %)

outgoing current of ‘diesel
generator 1’ bus (G8) B10 (non linear load) 4.4
B6 (furnace) 6.08
B1 (battery storage) 4.3
B2 (linear load) 4.3
B3 (linear load 1) 4.3

c. ‘Diesel Generator 1’ Bus (G8)

THD values of outgoing currents from ‘Diesel Generator 1’ bus for LG fault at
different load buses have been considered and given in Table 8.
Figure 4, shows that THD value of the outgoing current of ‘Diesel Generator 1’
(G8) is the highest for LG fault in Bus 10, where Non-linear load is connected.
d. ‘Diesel Generator 2’ Bus (G8)
THD values of outgoing currents from ‘Diesel Generator 2’ bus for LG fault at
different load buses have been considered and given in Table 9.
FFT Based Harmonic Assessment of Line to Ground … 83

5
THD Values

0
B10 (Non linear B6 (Furnace) B1 (BaƩery B2 (Linear load) B3 (Linear load 1)
load) storage)
Place of occurrence of LG fault

Fig. 4 THD values of outgoing current of ‘diesel generator 1’ (G8) for LG fault in the load buses

Table 9 THD values of Site of fault THD values (in %)

outgoing current of ‘diesel
generator 1’ bus (G8) B10 (non linear load) 3.38
B6 (furnace) 7.53
B1 (battery storage) 3.8
B2 (linear load) 3.8
B3 (linear load 1) 3.8

6 Rule Set

A rule set has been developed based upon the above results and observations.
• Outgoing currents of the bulk generator bus is the least affected by the LG faults
occurring in different load buses of the microgrid system shown in Fig. 1. For LG
fault in Non-linear load bus THD value is less than 0.4%, furnace bus THD value
is more than 0.4%. For LG faults in buses where battery storage unit and linear
loads are connected (B1, B2 and B3 respectively), maximum amount of distortion
is occurring in the current waveform which results into THD value in excess of
0.5%.
• Outgoing currents of the PV cell bus is the most affected among all the generator
buses. For LG fault in furnace bus (B6), current waveform is most distorted with a
THD value close to 50%. THD value is exactly 20% for LG faults in buses where
battery storage unit and linear loads are connected (B1, B2 and B3 respectively),
while THD value stays below 20% mark for LG fault in non-linear load bus.
84 S. Datta et al.

8
7
6
THD Values

5
4
3
2
1
0
B10 (Non linear B6 (Furnace) B1 (BaƩery B2 (Linear load) B3 (Linear load 1)
load) storage)
Place of occurrence of LG fault

Fig. 5 THD values of outgoing current of ‘diesel generator 2’ (G3) for LG fault in the load buses

• Outgoing current of ‘Diesel generator 1’ bus is the most affected in case of an LG

fault at furnace bus (B6) with THD value above 6%. For LG fault in non-linear
load bus (B10) THD value is 4.4%. In case of LG faults in other three load buses
THD value stays fixed at 4.3%.
• Outgoing current of ‘Diesel generator 2’ bus is also the most affected in case of an
LG fault at furnace bus (B6) with THD value of 7.5%. Comparing Figs. 4 and 5 it
is observed that among the two diesel generators, diesel generator 2 is the worst
affected when LG fault takes place at furnace bus (B6). For LG fault in non-linear
load bus (B10) THD value is 3.38%. In case of LG faults in other three load buses
THD value stays fixed at 3.8%.

7 Specific Outcome

Due to LG faults at different load buses the outgoing current of PV cell bus is the
most affected and an LG fault in furnace bus creates the most distortion. It has also
been observed that amount of distortion in a specific generator bus currents does not
depend on the distance of the load bus at which LG fault is taking place, rather it is
dependent upon the nature of the load which is connected to the load bus where LG
fault is occurring.

8 Conclusion

In this paper LG faults in a microgrid system has been assessed by FFT based THD
analysis. Different THD values in the outgoing currents of the generator buses have
FFT Based Harmonic Assessment of Line to Ground … 85

been observed for LG fault in different load buses. From the THD values, a rule set
has been developed which would be helpful for identification of location of the LG
fault.

References

1. A. Hooshyar, E.F. El-Saadany, M. Sanaye-Pasand, Fault type classification in microgrids

including photovoltaic DGs. IEEE Trans. Smart Grid 7(5), 2218–2229 (2016). INSPEC Acces-
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Harmonics Assessment Based
Symmetrical Fault Diagnosis in PV
Array Based Microgrid System

Tapash Kr. Das, Surajit Chattopadhyay and Arabinda Das

1 Introduction

With the increase of power demand different types of non-conventional energy

resources are being used. Among different types of non-conventional energy
resources, solar PV array based power supply has become popular in domestic as well
as in small Industrial applications. To cope with the ever increasing power demand,
microgrid systems are becoming more popular in day by day.
A lot of research works are going on in this regard. Anwar et al. (2013) per-
formed detail harmonics assessment for micro grid system [1]. Power quality at
voltage source converter based micro grid operation [2] has been analyzed by Dhar
et al. (2015). Kumar and Zare (2015) has done performance analysis for low voltage
microgrid distribution networks connected with power electronics system [3]. Wang
and Yaz (2016) performed detail analysis of smart power grid synchronization with
fault tolerant nonlinear estimation [4], where computer simulation techniques have
demonstrated that the proposed fault tolerant extended Kalman filter (FTEKF) pro-
vides more accurate voltage synchronization results than the extended Kalman filter
(EKF). Rashid et al. (2015) introduced transient stability enhancement of doubly fed
induction machine-based wind generator by bridge-type fault current limiter [5] for
microgrid power quality improvement, where various simulations were carried out in
Matlab/Simulink environment to demonstrate the effectiveness of the BFCL and its

T. Kr. Das (B) · S. Chattopadhyay

Department of Electrical Engineering, GKCIET (Under MHRD, Govt. of India),
Malda, West Bengal, India
e-mail: p_tapash_das@yahoo.co.in
S. Chattopadhyay
e-mail: surajitchattopadhyay@gmail.com
A. Das
Department Electrical Engineering Department, Jadavpur University, Kolkata, India
e-mail: adas_ee_ju@gmail.com
© Springer Nature Switzerland AG 2019 87
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_9
88 T. Kr. Das et al.

performance is compared with that of the series dynamic braking resistor (SDBR).
Chen et al. (2015) modeled doubly fed induction generator wind turbine systems
subject to recurring symmetrical grid faults [6]. In this attempt, the performance
of the doubly fed induction generator (DFIG) wind turbine system under recurring
symmetrical grid faults is analyzed. Chen et al. (2014) observed the nontechnical
loss and outage detection using fractional-order self-synchronization error-based
fuzzy Petri nets in micro-distribution systems [7], where different computer sim-
ulations were carried out using an IEEE 30-bus power system and medium-scale
micro-distribution systems to show the effectiveness of this proposed method. Math-
ematical morphology-based islanding detection for distributed generation has been
introduced [8] by Farhan and Swarup (2016) where basic MM operators like dilate
erode difference filter (DEDF) has been used to operate on three-phase voltage and
current signals on target DG location. Attempt has been taken to track the island-
ing condition from non-islanding condition, a new operator called the MM ratio
index (MM RI) computed is used for distributed generation. A GPS- based control
framework for accurate current sharing and power quality improvement in Micro-
grids [9] has been introduced by Golsorkhi et al. (2016) to improve the current
sharing accuracy at high loading conditions. A special technique for symmetrical
and asymmetrical low-voltage ride through of doubly-fed induction generator wind
turbines using gate controlled series capacitor [10] has been observed in detail by
Mohammadpour et al. (2015), where extensive time-domain simulations using MAT-
LAB/SIMULINK were performed to validate the effectiveness of this methods during
grid faults. Rashad et al. (2016) described control methodology of inverter used in
standalone micro-grid system [11]. Harmonic mitigation [12] of power distribution
network in minigrid has been studied by Sabu and George (2016). Sreekumar et al.
(2015) introduced a new virtual harmonic impedance scheme for harmonic power
sharing in an islanded microgrid [13], where a control strategy employs negative
virtual harmonic impedance to compensate the effect of line impedance on harmonic
power. Zhu et al. (2015) introduced novel technique for virtual damping flux-based
LVRT Control for DFIG-Based Wind Turbine [14] where the simulation has been
carried out and verified with a 2-MW DFIG in MATLAB/Simulink environment to
smooth the electromagnetic torque and minimized different grid faults. Taj et al.
(2015) introduced an adaptive neuro-fuzzy controlled-flywheel energy storage sys-
tem [15] for transient stability enhancement. In recent years many mathematical tools
have been introduced for harmonics assessment [16] and they have been found very
effective in fault assessment [17].
However very few works are found on harmonics assessment based microgrid
based power system. This has motivated to work on harmonic assessment based
fault detection in microgrid system. Attempt has been taken to model a micro grid
then to perform FFT based harmonics assessment for fault diagnosis in microgrid
system.
Harmonics Assessment Based Symmetrical Fault Diagnosis … 89

2 Modeling of 400 KW PV Array Based Micro Grid

In this work, PV Array based micro Grid of 400KW system (MATLAB, version-
15) has been modeled as shown in Fig. 1. Four numbers of PV array are con-
nected in parallel. Each PV array contains 64 strings. Each string contains 5 num-
bers of series connected modules having following specifications: Maximum pow-
er—315.072 W, Cells per module—86, Open circuit voltage—64.6 volts, Shot circuit
current—6.14 A, voltage at maximum power point—54.7 volts, current at maximum
power point—5.76 A, temperature coefficient at open circuit voltage—“−0.27269”
%/°C, temperature coefficient at short circuit current—“0.061694” %/°C, Light-
generated current 6.1461 A, Diode saturation current 6.5043 × 10−12 A, Diode ide-
ality factor 0.9507, Shunt resistance 430.0559 ohms, Series resistance 0.43042 ohms.
Parallel combinations of PV arrays are connected with DC to DC charge controller.
Average model based VSC having 3 bridge arms has been considered in Inverter unit.
Inverter output is fed to three phase 400KVA, 260 V/25 kV, 60 Hz star/delta trans-
former. Transformer output is fed to load Bus (BUS-2). The load bus is also connected
with conventional 120 kV, 2500MVA grid supply through three phase 400KVA,
260 V/25 kV, 60 Hz star/delta transformer. Load of 47 MVA, 120 kV/25 kV.2.1 MW
has been applied to load Bus.

Fig. 1 Single line diagram of 400KW PV array based microgrid

90 T. Kr. Das et al.

3 FFT Based Harmonics Assessments of Line Current

The model described in model of Fig. 1 has been used for computer simulation.
Three different current measurement units have connected at each phase output of
inverter. Through these current measurement units individual phase currents have
been captured. The waveform of phase currents are observed and analyzed by Fast
Fourier Transform (FFT) at normal condition, LLL and LLLG faults. FFT spectrums
are monitored and total harmonics distortions are measured. Continuous symmetrical
fault at load bus (Bus 2) has been considered in this work.

3.1 Normal Condition

At first, line currents are captured at normal condition and FFT spectrums are gen-
erated as shown in Fig. 2a–c for phase-A, phase-B and phase-C respectively. THD
at normal conditions are determined accordingly.

3.2 Fault Condition (LLL)

Then line currents are captured at LLL fault condition and FFT spectrums are gen-
erated as shown in Fig. 3a–c for phase-A, phase-B and phase-C respectively. THD
at LLL fault conditions are determined accordingly.

3.3 Fault Condition (LLLG)

Then line currents are captured at LLLG fault condition and FFT spectrums are
generated as shown in Fig. 4a–c for phase-A, phase-B and phase-C respectively.THD
at LLLG fault conditions are determined accordingly.
Harmonics Assessment Based Symmetrical Fault Diagnosis … 91

Fig. 2 Line currents and their FFT spectrum at inverter output at normal condition: a phase—A,
b Phase—B and c Phase—C
92 T. Kr. Das et al.

Fig. 2 (continued)

4 Comparative Study

FFT spectrums at different conditions are compared. Comparison shows significant

changes in FFT spectrums of symmetrical fault conditions from that of normal con-
dition. Also FFT spectrums at LLLG fault differ from FFT spectrums at LLL fault.
The comparative results are presented in Table 1. After, FFT based spectrum com-
parison, THD values obtained at different conditions are compared. Maximum THD
values at normal condition which reduces drastically at symmetrical fault condition.
THD at LLLG and THD at LLL are found very closed to each other; however THD
is found minimum at LLL fault condition as shown in Figs. 5 and 6 respectively.

5 Outcome

Specific outcome of this work is achievement of harmonics assessment based sym-

metrical fault diagnosis in solar PV array based micro grid system. FFT Based spec-
trum and THD comparison shows significant changes in those features and param-
eters at fault condition from that of normal condition. Also by this way significant
changes in features and parameters are observed among ungrounded symmetrical
fault and grounded fault conditions. THD values decrease at fault conditions and
become lowest in LLL fault.
Harmonics Assessment Based Symmetrical Fault Diagnosis … 93

Fig. 3 Line currents and their FFT spectrum at inverter output during LLL Fault at load end: a
phase—A, b Phase—B and c Phase—C
94 T. Kr. Das et al.

Fig. 3 (continued)

6 Conclusion

Harmonics assessment based symmetrical fault diagnosis in PV array based micro-

grid system.
The paper deals with harmonics assessment based symmetrical fault diagnosis
in PV array based microgrid system. This has been achieved by modeling a micro
grid system consisting of 400KW PV array based power unit coupled with conven-
tional power grid. Computer simulation performed at normal condition as well as
symmetrical faults at load bus. Both grounded (LLLG) and ungrounded fault (LLL)
are considered. Line currents are captured from the output currents of output system
of inverter system and currents are obtained at different conditions. THD values are
also determined and compared at different conditions. Based on the observation of
grounded (LLLG) and ungrounded fault (LLL) of micro grid systems with respect
those useful electrical parameters may be useful for synchronization, protection and
performance analysis of various micro grid systems. The comparative results may
be useful for symmetrical fault diagnosis and can be extended for diagnosis of other
faults also.
Harmonics Assessment Based Symmetrical Fault Diagnosis … 95

Fig. 4 Line currents and their FFT spectrum at inverter output during LLLG fault at load end: a
phase—A, b Phase—B and c Phase—C
96 T. Kr. Das et al.

Fig. 4 (continued)

Fig. 5 THD of line currents at Phase-A, B and C during normal, LLL and LLLG fault conditions
Harmonics Assessment Based Symmetrical Fault Diagnosis … 97

Table 1 Result of FFT analysis at normal, LLL and LLLG fault conditions of average model
400 KW microgrid
Parameters Phase Normal Fig. 2a–c LLL Fig. 3a–c LLLG Fig. 4a–c
SAMPLE PER A 333 333 333
CYCLE B
C
DC A 0.2347 12.5 13.75
COMPONNENT B 24.12 24.23 26.11
C 24.35 36.74 39.86
Fundamentals A 1009 1720 1726
peak
B 1011 1754 1756
C 989.1 1711 1712
Fundamentals A 713.3 1216 1220
rms B 7.5 1241 1242
C 699.4 1210 1210
THD (%) A 26.46 11.76 11.82
B 22.03 9.89 9.81
C 24.67 9.81 9.40
Frequency Phase Amplitude Angle Amplitude Angle Amplitude Angle
(HZ) (%) (%) (%)
0 A 0.02 90.0° 0.73 90.0° 0.80 90.0°
B 2.39 90.4° 1.38 90.0° 1.49 90.0°
C 2.46 270.0° 2.15 270.0° 2.33 270.0°
60 A 100.00 69.4° 100.00 71.2° 100.00 −71.2°
B 100.00 169.2° 100.00 167.8° 100.00 167.7°
C 100.00 49.8° 100.00 47.3° 100.00 47.4°
180 A 1.98 5.7° 1.00 4.8° 1.16 3.5°
B 0.95 222.1° 0.89 235.7° 0.89 224.7°
C 1.36 160.7° 0.83 126.1° 0.77 132.4°
300 A 1.10 4.8° 0.70 9.2° 0.77 8.2°
B 0.46 208.7° 0.63 189.2° 0.64 193.8°
C 0.72 169.4° 0.12 131.6° 0.14 162.8°
420 A 0.77 5.2° 0.48 16.9° 0.58 10.2°
B 0.31 202.7° 0.36 201.8° 0.41 193.2°
C 0.49 174.1° 0.12 181.8° 0.17 182.9°
660 A 0.48 6.6° 0.45 2.7° 0.60 30.0°
B 0.19 197.8° 0.14 174.6° 0.23 228.6°
C 0.31 179.7° 0.32 186.3° 0.39 199.1°
780 A 0.41 7.3° 0.79 5.3° 0.54 32.3°
(continued)
98 T. Kr. Das et al.

Table 1 (continued)
Frequency Phase Amplitude Angle Amplitude Angle Amplitude Angle
(HZ) (%) (%) (%)
B 0.16 196.4° 0.55 207.0° 0.34 238.0°
C 0.26 181.7° 0.35 148.2° 0.28 179.0°
900 A 0.35 7.5° 2.10 −15.0° 0.17 −32.6°
B 0.13 195.0° 0.86 104.3° 0.89 56.5°
C 0.22 183.1° 1.84 189.8° 1.50 184.8°
960 A 0.32 9.6° 0.42 203.1° 0.59 −34.9°
B 0.12 198.1° 0.73 −70.5° 0.59 230.9°
C 0.21 184.5° 0.88 80.8° 0.81 97.4°

Fig. 6 THD of line currents

at Phase-A, B and C during
LLL and LLLG fault
conditions

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Optimal Design of KVAr Based SVC
for Improvement of Stability in Electrical
Power System

Sayantan Adhikary and Sandip Chanda

1 Introduction

In modern power system, sudden change of load, faults has a substantial frequency
of occurrences. A considerable amount of research of all over the globe is going on
for presenting and economical reliable fast response controller to cope up with this
changed environment, FACTS controller is one of them.
A method has been on developed [1] “Optimal location and sizing of static VAR
compensator (SVC) based on Particle Swarm Optimization for minimization of trans-
mission losses considering cost function. The method however is, Artificial Intelli-
gence based and requires extensive computational time.”
This method explained [2] “A novel global harmony search algorithm (NGHS) is
used to determine the optimal location and size of shunt reactive power compensators
such as shunt capacitors, static VAR compensators (SVCs), and static synchronous
compensators (STATCOMs) in a transmission network. The algorithm though a quite
efficient, requires large memory for its binary search operation.”
This method approach [3] “A method to seek the optimal location of several static
VAR compensators (SVCs) in a power system based on their primary function. Taking
advantages of the flexible ac transmission system (FACTS) devices depends largely
on how these devices are placed in the power system, namely, on their location and
size.”
In the work explained [4] “Advanced load flow models for the static VAR compen-
sator (SVC) are presented in this paper. The models are incorporated into existing load
flow (LF) and optimal power flow (OPF) Newton algorithms. Unlike SVC models

S. Adhikary (B) · S. Chanda

Department of Electrical Engineering, Narula Institute of Technology, Kolkata, India
e-mail: sayantanaad@gmail.com
S. Chanda
e-mail: sandipee1978@gmail.com

© Springer Nature Switzerland AG 2019 101

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_10
102 S. Adhikary and S. Chanda

available in open literature, the new models depart from the generator representation
of the SVC and are based instead on the variable shunt susceptance concept. The
work though manages to determine the optimal location of SVC but does not an
enlighten, the physical design of SVC.”
This method approaches [5] “Optimal location of SVC in power system based on
the primary function taking advantage of faults device depends largely on how these
devices are placed in power system.”
This method states that [6] “Dynamic reactive power compensation is used to an
increasing extended improve voltage and reactive power system. Additional takes
can also be performed SVC to increase in power transmission capability.”
In the work explained [7] “Power system stability enhancement via robust coor-
dinated design of a power system stabilizer and a static VAR compensator-based
stabilizer is thoroughly investigated in this paper. The coordinated design problem
of robust excitation and SVC-based controllers over a wide range of loading condi-
tions and system configurations are formulated as an optimization problem with an
eigenvalue-based objective function. This work again fails to substantial the voltage
level at a desired value.”
In this method develop by [8] “The enhancement of power system stability proper-
ties by use of thyristor controlled series capacitors (TCSCs) and static VAR systems
(SVCs). Models suitable for incorporation in dynamic simulation programs used to
study angle stability are analyzed.”
This method approaches [9] “Power demand has increased substantially while
the expansion of power generation and transmission has been severely limited due
to limited resources and environmental restrictions.”
This method states that [10] “Different control techniques for damping undesir-
able inter area oscillation in power systems by means of power system stabilizers
(PSS), static VAR compensators (SVCs), and shunt static synchronous compensators
(STATCOMs).”
This method approaches [11] “The location of SVC (static VAR compensators)
and other types of shunt compensation devices for voltage support is an important
practical question. This paper considers a tool based on the determination of critical
modes. Critical modes are computed by studying the system modes in the vicinity
of the point of collapse. System participation factors for the critical mode are used
to determine the most suitable sites for system reinforcement.”
This method states that [12] “A novel method for optimal location of FACTS
devices in a multi machine power system using Genetic Algorithm (GA). Using the
proposed method, the location of FACTS controllers, their type and rated values are
optimized simultaneously. Among the various FACTS controllers, Static VAR con-
troller (SVC), Thyristor Controlled Series Compensator (TCSC) and Unified power
Flow Controller (UPFC) are considered. This method again requires computational
facility and also memory.”
A method has been developed on [13] “A new SVC (static VAR compensation)
control for damping of power system oscillations has been developed. To increase
system damping an SVC uses a phase angle signal estimated from the measurement
of voltage and power at the SVC location.”
Optimal Design of KVAr Based SVC for Improvement of Stability … 103

In this method develop by [14] “A new power system stabilizer (PSS) design for
damping power system oscillations focusing on inters area modes. The input to the
PSS consists of two signals. The first signal is mainly to damp the local mode in the
area where PSS is located using the generator rotor speed as an input signal. The
second is an additional global signal for damping inters area modes.”
A method has been developed on [15] “Analysis and simulation of SVC controller
have been investigated to improve the dynamic stability of power systems. Eigen-
values calculated by linear system models, the impact and changes the controller
parameters on the dynamic behavior of the system will be study.”
From the above litterateur review it has been understood that all the controller’s
design for optimal locative is voltage based SVC and PSS. In this work a KVAr
based SVC has been developed to limit a variation of voltage even in worst possible
loading of reactive power. Simulation has been carried out in MATLAB software the
result was wide encouraging and promising.

2 Theory

2.1 Use of SVC in Transmission Line

A static VAR compensator (or SVC) is an electrical device for providing fast-acting
reactive power on high-voltage electricity transmission networks. SVCs are part of
the Flexible AC transmission system device family, regulating voltage and stabiliz-
ing the system. The term “static” refers to the fact that the SVC has no moving parts
(other than circuit breakers and disconnects, which do not move under normal SVC
operation). Prior to the invention of the SVC, power factor compensation was the
preserve of large rotating machines such as synchronous condensers. The SVC is an
automated impedance matching device, designed to bring the system closer to unity
power factor. If the power system’s reactive load is capacitive (leading), the SVC
will use reactors (usually in the form of Thyristor-Controlled Reactors) to consume
var from the system, lowering the system voltage. Under inductive (lagging) con-
ditions, the capacitor banks are automatically switched in, thus providing a higher
system voltage. They also may be placed near high and rapidly varying loads, such
as arc furnaces, where they can smooth flicker voltage. It is known that the SVCs
with an auxiliary injection of a suitable signal can considerably improve the dynamic
stability performance of a power system. It is observed that SVC controls can signif-
icantly influence nonlinear system behavior especially under high-stress operating
conditions and increased SVC gains.
104 S. Adhikary and S. Chanda

2.1.1 Principle

Typically, an SVC comprises one or more banks of fixed or switched shunt capacitors
or reactors, of which at least one bank is switched by thyristors. Elements which may
be used to make an SVC typically include:
• Thyristor controlled reactor (TCR), where the reactor may be air- or iron-cored
• Thyristor switched capacitor (TSC)
• Harmonic filter(s)
• Mechanically switched capacitors or reactors (switched by a circuit breaker)
(Fig. 1).
By means of phase angle modulation switched by the thyristors, the reactor may
be variably switched into the circuit and so provide a continuously variable MVAR
injection (or absorption) to the electrical network. In this configuration, coarse voltage
control is provided by the capacitors; the thyristor-controlled reactor is to provide
smooth control. Smoother control and more flexibility can be provided with thyristor-
controlled capacitor switching.
The thyristors are electronically controlled. Thyristors, like all semiconductors,
generate heat and deionized water is commonly used to cool them. Chopping reactive
load into the circuit in this manner injects undesirable odd-order harmonics and so

Fig. 1 One-line diagram of a typical SVC configuration; here employing a thyristor controlled
reactor, a thyristor switched capacitor, a harmonic filter, a mechanically switched capacitor and a
mechanically switched reactor
Optimal Design of KVAr Based SVC for Improvement of Stability … 105

banks of high-power filters are usually provided to smooth the waveform. Since the
filters themselves are capacitive, they also export MVARs to the power system.
More complex arrangements are practical where precise voltage regulation is
required.
Voltage regulation is provided by means of a closed-loop controller. Remote super-
visory control and manual adjustment of the voltage set-point are also common.
Generally, static var compensation is not done at line voltage; a bank of trans-
formers steps the transmission voltage (for example, 230 kV) down to a much lower
level (for example, 9.0 kV). This reduces the size and number of components needed
in the SVC, although the conductors must be very large to handle the high currents
associated with the lower voltage. In some static var compensators for industrial
applications such as electric arc furnaces, where there may be an existing medium-
voltage bus bar present (for example at 33 or 34.5 kV), and the static var compensator
may be directly connected in order to save the cost of the transformer.
Another common connection point for SVC is on the delta tertiary winding of
Y-connected auto-transformers used to connect one transmission voltage to another
voltage.
The dynamic nature of the SVC lies in the use of thyristors connected in series
and inverse-parallel, (forming “thyristor valves”). The disc-shaped semiconductors,
usually several inches in diameter, are usually located indoors in a “valve house”.
The main advantage of SVCs over simple mechanically switched compensation
schemes is their near-instantaneous response to changes in the system voltage. For
this reason they are often operated at close to their zero-point in order to maximize
the reactive power correction they can rapidly provide when required.
They are, in general, cheaper, higher-capacity, faster and more reliable than
dynamic compensation schemes such as synchronous condensers. However, static
var compensators are more expensive than mechanically switched capacitors, so
many system operators use a combination of the two technologies (sometimes in
the same installation), using the static var compensator to provide support for fast
changes and the mechanically switched capacitors to provide steady-state var.

2.2 Traditional Operation of SVC

2.2.1 Generation, Transmission, Distribution

In any power system, the creation, transmission, and utilization of electrical power
can be separated into three areas, which traditionally determined the way in which
electric utility companies had been organized.
• Generation
• Transmission
• Distribution.
106 S. Adhikary and S. Chanda

Although power electronic based equipment is prevalent in each of these three

areas, such as with static excitation systems for generators and Custom Power equip-
ment in distribution systems, the focus of this paper and accompanying presentation
is on transmission, i.e., moving the power from where it is generated to where it is
utilized.

2.2.2 Power System Constraints

As noted in the introduction, transmission systems are being pushed closer to their
stability and thermal limits while the focus on the quality of power delivered is
greater than ever. The limitations of the transmission system can take many forms
and may involve power transfer between areas or within a single area or region and
may include one or more of the following characteristics:
• Steady-State Power Transfer Limit
• Voltage Stability Limit
• Dynamic Voltage Limit
• Transient Stability Limit
• Power System Oscillation Damping Limit
• Inadvertent Loop Flow Limit
• Thermal Limit
• Short-Circuit Current Limit
• Others.
Each transmission bottleneck or regional constraint may have one or more of these
system-level problems. The key to solving these problems in the most cost-effective
and coordinated manner is by thorough systems engineering analysis.

3 Proposed Methodology of SVC

See Fig. 2.

4 Development of Relation Between KVAr and SHUNT

Compensation by Simulation

A 2 machine system with a load and variable susceptance support has been demon-
strated in figure [3] MATLAB (Fig. 3).
The system has loaded KVAr as depicted, in table for each value of KVAr loading
the variable susceptance in adjusted, to provide a voltage band of 0.9–1 pu for worst
possible reactive power loading, this susceptance has been calculated and the relation
Optimal Design of KVAr Based SVC for Improvement of Stability … 107

Fig. 2 Proposed
methodology of SVC flow
chart
108 S. Adhikary and S. Chanda

Fig. 3 Transient stability of a two-machine transmission system with power system stabilizers
(PSS) and static var compensator (SVC)

between required susceptance subsequent KVAr is plotted. In figure [3] from the
curve sample points were extracted and for each of the points a hyperbolic equation
has been formed.

2.5 × [(10)]∧ 6x_(1∧ 2) + 1.2 × [(10)]∧ 6x_1 + 1 × [(10)]∧ 6  15 (1)

∧ ∧ ∧ ∧
3.5 × [(10)] 6x_(2 2) + 3 × [(10)] 6x_2 + 2 × [(10)] 6  20 (2)
∧ ∧ ∧ ∧
4 × [(10)] 6x_(3 2) + 5 × [(10)] 6x_3 + 3 × [(10)] 6  25 (3)

By solving the above 3 equation, the following relation has been obtained

63.5x_(1∧ 2) − 1.979x_1 + 0.0822  B

where, x  KVAR and, B  Susceptance

This equation becomes (Fig. 4).

63.5kV A R 2 − 1.97kV A R + 0.0822  B (4)

Optimal Design of KVAr Based SVC for Improvement of Stability … 109

Fig. 4 Curve fitting the

susceptence with respect to
KVAr loading

5 Development of MATLAB Model

A Matlab based model of SVC based on equation no [4] has been developed. This
model being operation, in care voltage based SVC, the range is very limited. As the
span of variation is also limited (Figs. 5 and 6).

6 Description of the Blocks (with Svc and with Out Svc)

6.1 Parameters

The SVC parameters are grouped in two categories: Power Data and Control Param-
eters. Use the Display list box to select which group of parameters you want to
visualize.

Fig. 5 Improvement of transient stability with svc diagram using MATLAB

110 S. Adhikary and S. Chanda

Fig. 6 Improvement of transient stability without svc diagram using MATLAB

6.2 Power Tab

Ignore negative-sequence current

The SVC is modeled by a three-wire system using two current sources. The SVC
does not generate any zero-sequence current, but it can generate negative-sequence
currents during unbalanced system operation. The negative-sequence susceptance of
the SVC is assumed to be identical to its positive-sequence value, as determined by
the B value computed by the voltage regulator.
Select this box to ignore negative-sequence current. Default is selected (Fig. 7).

6.3 Nominal Voltage and Frequency

The nominal line-to-line voltage in Vrms and the nominal system frequency in hertz.
Default is [500e3, 50].

6.4 Three-Phase Base Power

Three-phase base power, in VA, used to specify the following parameters in pu: droop
reactance Xs, gains Kp and Ki of the voltage PI regulator, and reference susceptance
Brief. This base power is also used to normalize the output B susceptance signal.
Default is 200e6 (Fig. 8).
Optimal Design of KVAr Based SVC for Improvement of Stability … 111

Fig. 7 Delta connected

thyristor bridge

Fig. 8 Computation of
PWM pulse
112 S. Adhikary and S. Chanda

6.5 Reactive Power Limits

The maximum SVC reactive powers at 1 pu voltage, in vars. Enter a positive value
for the capacitive reactive power Qc (var generated by the SVC) and a negative value
for the inductive reactive power Ql (var absorbed by the SVC). Default is [200e6,
−200e6].
Average time delay due to thyristor valves firing Average time delay simulating the
non-instantaneous variation of thyristor fundamental current when the distribution
unit sends a switching order to the pulse generator. Because pulses have to be syn-
chronized with thyristor commutation voltages, this delay normally varies between
0 and 1/2 cycle. The suggested average value is 4 ms. Default is 4e-3 (Fig. 9).

6.6 Susceptance Brief

This parameter is not available when the Mode parameter is set to Voltage regulation
(Fig. 10).

6.7 Reference

Susceptance, in Pu/Phase, when the SVC is operating in var control mode. Default
is 0.0.

Fig. 9 KVAr sampling

Optimal Design of KVAr Based SVC for Improvement of Stability … 113

Fig. 10 Computation of
requires susceptance

6.8 Simulation and Case Study

After development of improvement stability with SVC Diagram using Matlab, we

get 5 simulation figures
(a) Voltage without SVC
(b) RMS Value
(c) KVAr Calculated
(d) Susceptance Calculated
(e) Carrier Signal
(f) Susceptance (RMS)
(g) PWM (Pulse Width Modulation).

1. Firstly voltage measurement block applied then we get voltage without SVC
Curve.
2. Current Measurement block applied then we get RMS value.
3. We applied repeating sequence triangular value, then we get Carrier Signal,
Susceptance (RMS) and PWM (Pulse Width Modulation) (Figs. A, B, C, D, E.1,
E.2, and E.3).

6.9 Case Study

Comparison between with SVC and without SVC

After the development of the model a comparison between presence of develop
model of SVC and without SVC has been demonstrated in the table, from this table
it can be asserted that the develop model of with SVC is capable of regulating the
voltage with desired level, in adverse of reactive power loading.
114 S. Adhikary and S. Chanda

Fig. A Voltage without SVC

Fig. B RMS value

7 Conclusion

The work presented in this paper mainly focuses on the aspects related to Flexible
AC Transmission Systems (FACTS) based controller design and assessment of their
contribution to system stability improvement ensuring secure and stable operation
of the power system. Most of the SVC controllers, with substantial survey has been
found to be voltage based, and sub sequentially they offer less scope of making
the control action in the work presented in this paper. Focuses on developing a
Optimal Design of KVAr Based SVC for Improvement of Stability … 115

Fig. C KVAR calculated

Fig. D Susceptance calculated

Fig. E.1 Carrier signal

KVAr based model of SVC, which without the help of in any optimization technique
effectively stabilizes, the voltage profile of given power system network for adverse
variation of reactive power loading. This idea may be pursuit to develop to static var
compensator (SVC) for future power network.
116 S. Adhikary and S. Chanda

Fig. E.2 Susceptance (RMS)

Fig. E.3 PWM

Load (KVAR) With SVC line voltage With out SVC line voltage
4000e6 0.6 * 106 6 * 105
5000e6 6 * 105 7 * 105
7000e6 6.5 * 105 8 * 105
8000e6 7 * 105 8 * 105
9000e6 8* 105 8 * 105
10000e6 9 * 105 8.25 * 105
20000e6 10 * 105 8.9 * 105
30000e6 10 * 105 9 * 105
40000e6 12 * 105 9 * 105
50000e6 12 * 105 10 * 105

References

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mization Technique. Dec 2011
2. R. Sirjani, A. Mohamed, in Optimal allocation of shunt Var compensatorsin power systems
using a novel global harmony search algorithm. Dec 2012
3. M.M. Farsangi, H. Nezamabadi, in Placement of SVCs and selection of stabilizing signals in
power systems. Aug 2007
4. J.A.P. Filho, H. Pinto, in Advanced SVC models for Newton-Raphson load flow and Newton
optimal power flow studies, vol. 15. no. 1, Feb 2000
5. E.Z. Zhou, in Application of static Var compensator to increase power system damping. June
1982
6. M.A. Abido, Y.L. Abdel-Magid, in Coordinated design of a PSS and an SVC based controller
to enhance power system stability. June 2003
7. S. Gerbex, R. Cherkaoui, J. Germone, in Optimal location of FACTS device to enhance power
system security. June 2003
Optimal Design of KVAr Based SVC for Improvement of Stability … 117

8. M. Noroozian, I. Hiskens, in A robust control strategy of shunt and series reactive compensator
to damp electromechanical oscillations. Oct 2001
9. R. Sirjani, A. Mohamed, in optimal allocation of shunt Var compensator in power system using
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10. C.A. Canizares, J. Reeve, in Comparison of PSS, SVC and statcom controllers for damping
power system oscillations. Aug 2003
11. Y. Mansoar, W. Xu, in SVC Placement using critical modes of voltage stability. May 1994
12. S. Gerbex, A.J. Gevaond, in Optimal location of multi-machine system SVC using genetic
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global signals. June 1996
An Improved Reactive Power
Compensation Scheme for Unbalanced
Four Wire System with Low Harmonic
Injection Using SVC

Sankar Das, Debashis Chatterjee and Swapan K. Goswami

1 Introduction

The loads in power distribution system are generally single-phase loads supplied from
a /Y three-phase transformer with grounded neutral [1]. The other commonly used
loads are nonlinear loads, single-phase and three-phase rectifiers, power-electronics-
based equipment etc. The increased use of these types of loads generates various
power quality problems in the distribution network. These are poor voltage regulation,
high reactive power demand, harmonic currents, unbalanced load, excessive neutral
current, etc. [2, 3]. The unequal load current due to asymmetrical load contains
positive, negative, and zero sequence component. It will increase system losses and
can also be harmful on industrial machines and generators. Many techniques are
suggested for load balancing as well as neutral current compensation along with
load harmonic elimination for three-phase four-wire distribution system.
Pulse width modulation (PWM) based switching compensator, known as ‘active
power filters’ [4, 5], or ‘power conditioner’, as reactive power compensator, or both of
them as hybrid devices can be applied to diminish the power quality problems effec-
tively. It includes distribution static compensator (DSTATCOM) [6, 7] for solving
power quality problem in current, dynamic voltage restorer (DVR) for compensating
power quality problem in voltage, and unified power-quality conditioner (UPQC) for
both current and voltage power quality problem. However, all of these techniques
increase system losses; implementation cost and requires complex control strategy
[8].

S. Das (B)
Department of Electrical Engineering, Government College of Engineering and Textile
Technology, Berhampore, Murshidabad, WB, India
e-mail: sankar05ju@gmail.com
D. Chatterjee · S. K. Goswami
Department of Electrical Engineering, Jadavpur University, Kolkata, WB, India
e-mail: debashisju@yahoo.com
© Springer Nature Switzerland AG 2019 119
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_11
120 S. Das et al.

The SVC based compensation scheme can also be used to solve power quality
problems in four-wire distribution system. The combination of Y-SVC and -SVC
can be used to mitigate both ZPS and NPS currents simultaneously [9, 10] as single
SVC configuration can not serve both the purposes. However, the operation of TCR
releases significant odd harmonic currents [11] into the supply system, whereas FC
or TSC amplifies the harmonic currents generated from TCR and the other nonlinear
load. Thus, a combination of reactive power compensator using SVC along with
passive filter [12] or combination of shunt passive filter in series with an active power
filter topology [13–16] have been proposed to solve power quality problem. However,
these schemes require additional investment [17] and space to accommodate filtering
stages. Thus, improvement of switching schemes of SVC is also investigated to
minimize harmonic generation internally [18–20] without using additional filter.
The load compensation as well as source power factor improvement with minimum
line harmonic injection is studied for three-phase three-wire system [21]. However,
there are no suitable schemes for load balancing, neutral current compensation and
source power factor correction with minimum line harmonic injection for three-phase
four-wire distribution system.
In this paper, reactive power compensation is achieved by using a combined
-SVC and Y-SVC. At the same, the minimum harmonic injection of SVC is real-
ized by optimizing switching function of SVC. Thus, the proposed scheme removes
additional filter requirement. Both the SVCs use TSC-TCR in the proposed system
modeling. The switching function of TCR is optimized using gravitational search
algorithm [22, 23] and the optimized switching angles are computed offline at close
interval of modulation indices which can be expressed as the ratio between funda-
mental component of reactor voltage to the rated load voltage. The corresponding
reactive power drawn by TCR is calculated based on computed switching angles.
These switching angles corresponding to minimum injected harmonics along with
reactive power compensation are stored in the processor memory as a function of
modulation index for online application. Different simulation results on a practical
system are presented to validate the proposed concept.

2 Proposed Compensation Model Using Symmetrical

Component Approach

The Fig. 1 shows schematic diagram of a Y-SVC and -SVC connected to three-
phase four-wire distribution system for reactive power compensation with minimum
line harmonic injection. The subscript “x” denotes phase a, b and c. The IxL is the
line current; VxS is the source voltage; VxL is the grid voltage; IxT Y , IxCY , IxT  and
IxC are the Y-TCR, the Y-TSC, the -TCR and the -TSC current respectively;
Z x is the line impedance and Z n is the neutral impedance. The distribution system
is assumed to be a constant balanced voltage source and equal line impedances. For
an unbalanced three-phase loads, the unbalanced distribution line currents causes
An Improved Reactive Power Compensation Scheme for Unbalanced … 121

∆-SVC
∆-TCR ∆-TSC
Gate Pulses
CaΔ CbΔ CcΔ
LaΔ LbΔ LcΔ

IaTΔ I TΔ IacΔ IbcΔ IccΔ

b

Vas Za(La,Ra)
IcTΔ
L a
Ias Z (L R ) Va IaL
Vbs b b, b
bThree-phase
VbL IbL Four-Wire
V cs Ibs Zc(Lc,Rc) Balanced/
Unbalanced
c Loads
VcL IcL
Ics Zn
s n
IbL In
IcL InL
L
VaL VbL Vc TY
IaL IaTY IbTY Ic IacY IbcY IccY
Sensor Circuits Y
LcY Ca Cb
Y
LaY LbY C cY
ADC
dSPACE
DAC
Driver Circuits Y-TCR Y-TSC
Y-SVC
Gate Pulses

Fig. 1 Representation of distribution substation with Y and -type SVC

unequal line voltage drops which make load bus voltages to be unbalanced. In order
to compensate line currents and improve source power factor, SVCs are placed at the
load bus to generate or absorb unbalanced reactive power. The unbalanced reactive
power combined with load demand makes balanced load to the supply system. The
phase-wise unbalanced loads are PLa + j Q La , PLb + j Q Lb and PLc + j Q Lc while the
phase-wise load seen by the source after compensation is Ps + j Q s . The phase-wise
reactive power absorbed by Y-TCR is Q aT Y , j Q bT Y and j Q cT Y while for -TCR is
TΔ TΔ TΔ
j Q ab , j Q bc and j Q ca . The phase-wise reactive power generation by Y-TSC is
Q a , j Q b and j Q c while by -TSC is j Q CΔ
CY CY CY
ab , j Q bc and j Q ca . The prefix T
CΔ CΔ

in all the variables denotes TCR quantities, where as prefix S, C and L denotes the
source, TSC and load quantities respectively.
The compensation requirements for neutral current compensation, load balancing
and source power factor improvement combining are,
122 S. Das et al.
⎧      
⎪
⎪ Re I0L + Re I0T Y  Re I0CY
⎪
⎪
⎪
⎪      
⎪
⎪ Im I0L + Im I0T Y  Im I0CY
⎪
⎨          
Re I2L + Re I2T Y + Re I2T Δ  Re I0CY + Re I0CΔ (1)
⎪
⎪          
⎪
⎪
⎪
⎪ Im I2L + Im I2T Y + Im I2T Δ  Im I0CY + Im I0CΔ
⎪
⎪        
⎪
⎩ Im I L + Im I T Y  Im I CY + Im I S
1 1 1 1

where I0 , I1 and I2 denotes the zero, positive and negative sequence current com-
ponent respectively. The (1) has infinite solutions due to six unknowns with five
constraints. Thus an additional constraint is considered to compute a unique solu-
tion. The additional constraint with a consideration that -SVC doesn’t generate
imaginary part of positive sequence currents can be expressed as,
   
Im I1T Δ  Im I1CΔ (2)

The compensating reactive power required by each phase of -TCR and Y-TCR
for load balancing, neutral current compensation and power factor correction can
be expressed in terms of load power by solving (1) and (2) after substitution of
each sequence component. The per phase compensating reactive power required by
-TCR can be calculated as,
⎧
⎪
⎪ TΔ
Q ab  2(PLa√−P Lb )
− Q CΔ
⎪
⎪ 3 ab
⎨
TΔ 2(PLb√−PLc )
Q bc  − Q bc
CΔ
(3)
⎪
⎪
3
⎪
⎪
⎩ Q ca
TΔ
 2(PLc√−P
3
La )
− Q CΔ
ca

Similarly, the per phase compensating reactive power required by Y-TCR can be
calculated as,
⎧  PLb −PLc
⎪
⎪ Q a  Q La − Q a − Q s + √3
⎪ TY CY
⎪
⎨  PLc −PLa
Q bT Y  Q Lb − Q CY
b − Qs +
√ (4)
⎪
⎪
3
⎪
⎪  −PLb
⎩ Q cT Y  Q Lc − Q CY
c − Qs +
PLa√
3

Now, it is required to find out the appropriate switching angles corresponding to

compensating reactive power. The per phase reactive power absorbed by TCR can
be controlled independently by changing the firing delay angle of individual phases
of TCR. For any delay angle α of a particular phase, the reactive power absorbed by
-TCR (Q  ) and Y-TCR (Q Y ) can be calculated [33] as,
An Improved Reactive Power Compensation Scheme for Unbalanced … 123
⎧   2
⎨ Q   2π−2α−sin 2α
3V1
π x0
 2π−2α−sin 2α  2 (5)
⎩ QY  V1
π x0


where x 0 is the reactance for full conduction of thyristor α  00 and V1 is the
per phase fundamental component of TCR voltage. Similarly, the per phase reactive
power absorbed by Y-TCR can be calculated for any delay angle α and V1 . The per
phase fundamental component of TCR voltage V1 also depends on delay angle α.
The amplitude of reactor voltage fundamental component (for n  1) in terms of
switching angle α can be expressed as,


2 1
V1  (π − α) + sin(2α) . (6)
π 2

TΔ
Thus for required reactive power Q ab of -TCR calculated from (3), correspond-
ing switching angle (α) can be obtained from (5) using (6). The direct solution of (5)
to obtain α requires a suitable numerical technique to be applied which can result in
multiple values of α with different THDs. Thus a heuristic search based method is
necessary to obtain the optimum value of α for minimum reactor voltage THD. Sim-
ilar equations can be written to find α for the other two phases. The same procedure
can be used to compute appropriate angle α for Y-TCR.

2.1 Control Scheme

The Fig. 2 shows control schematic for load balancing, neutral current compensation
and power factor correction with minimum line harmonic injection in a three-phase
four-wire system using SVC. In the control scheme, the reactive power requirement
for the individual phases are calculated using (3) and (4) with a consideration of
set power factor and set reactive power of TSC (Q TSC ). The zero crossing detector
(ZCD) is used for detecting the zero crossing of input signal.
In the proposed scheme, the harmonic minimization (HM) from reactor voltage
is realized by computing those values of α for solution of (5) which results in lower
reactor voltage THD. Thus in this paper, a GSA based technique is used for off-line

computation of the switching angles (αoff ) as a function of modulation index m ∗d
for individual phases. Then these computed switching angles are used to calculate
reactive power (Q off ) absorbed by TCR in each phase using (5). The modulation
indices, corresponding switching angles for optimum THD and phase wise VAr
absorption are stored in the processor memory for load balancing, neutral current
compensation and power factor correction with minimum reactor voltage THD.
124 S. Das et al.

is iL vL
Load
Source

ILr.m.s VLr.m.s
ZCD Δ-SVC Y-SVC
∫
SL
PL QL
Computation of reactive power (Q comp) by Set QS
Δ- & Y-TCR using (3) &(4) Set QTSC

Microcontroller
Piecewise mixed model
Gate m d*
driver α
m d*
Qcomp

Computation of Q off Computation of αoff

using (16) Characterizing HM with GSA
varying modulation
Off-line computation using MATLAB

Fig. 2 Control schematic for the proposed compensation scheme

3 Proposed GSA Based Harmonic Minimization

In the proposed technique, solution of (5) for optimum switching angle is obtained
through GSA based optimization technique considering minimum reactor voltage
THD. The configuration of per phase thyristor controlled reactor (TCR) consisting
of a reactor (L) connected in series with two anti parallel thyristors (T1 , T2 ) is shown
in Fig. 3a. The reactor voltage (VTCR ) is shown in Fig. 3b. The general expression for
amplitude of nth odd harmonic for n > 1 for the reactor voltage, shown in Fig. 3b,
is given by,


2 sin(n + 1)α sin(n − 1)α
Vn  − . (7)
π (n + 1) (n − 1)

For a three-phase balanced system the triple n harmonics will be absent in the line
and thus these are not considered in the present problem. Thus possible values of n
are n  6i ± 1 (i  1, 2, 3, . . .).
Mathematically the optimization problem can be formulated as,
An Improved Reactive Power Compensation Scheme for Unbalanced … 125

Fig. 3 Single-phase thyristor controlled reactor a configuration, b voltage across reactor

⎧
⎪ V1  M
⎪
⎪
⎪
⎨ Vn ≤∈n
Subjected to (8)
⎪
⎪
⎪
⎪
⎩ π ≤ α ≤ π.
2
where V1 , . . . , Vn are in per unit and M is the desired amplitude of the fundamental
component of reactor voltage to rated load voltage which is also known as modulation
index and ∈n is the allowable limits of all individual harmonics and n up to 31st order.
The proposed objective function f (α) for the GSA satisfying (8) can be defined
as,
31
f (α)  K 1 |V1 − M|2 + K n |Vn − ∈n |2 . (9)
n5,7,11,..

where n  6i ± 1(i  1, 2, 3, . . .)
In (9), the coefficient K 1 needs to have larger value than K 5 to K n for giving more
priority to maintain fundamental component, at the same time K 5 to K n are adjusted
to descending order such that more priority is given to reduce lower order harmonics.
Moreover, all the coefficients need to be properly adjusted so that GSA can perform
nonbiased optimization. Trial and error method [23] is used until a good balance is
found. For this problem, K 1  257, K 5  51, K 7  12, K 11 . . . K 31  5. For each
harmonic component, the ∈n is selected as 0.03 according to IEEE std 519-1992.
The GSA, developed by Rashedi et al. in 2009 is the recent meta-heuristic search-
ing algorithm [22]. It is based on Newton’s law of gravity and motion. In this algo-
rithm, agents are considered as objects and the performance of agents are measured
by their masses. Hence, all these agents attract each other by a gravity force, and this
force causes a global movement of all agents towards the agents with heavier masses.
The heavier masses have better fitness value. Thus they describe good optimal solu-
tion to the problem and move more slowly than lighter ones. In GSA, each mass has
four identifications: its position, its inertial mass, its active and passive gravitational
mass [22, 23]. The position of the mass is equivalent to a solution of the problem
126 S. Das et al.

Table 1 Parameters of the System parameters Value

simulation system
Line impedance (per phase) (0.02 + j 0.07) 
Load: a-phase (20 + j12) kVA
b-phase (25 + j13) kVA
c-phase (30 + j15) kVA

and its gravitational and inertial masses are calculated by using a fitness function.
Thus each mass represent a solution of the problem and the algorithm is navigated
by properly adjusting the gravitational and inertia masses.
In the present problem, each solution (position) is composed of the switching
angle α in half cycle. To start the algorithm, initial populations (number of agents)
of
 π switching angles are randomly generated with satisfying the constraint equation
2
≤ α < π for the chosen number of population. Then velocities of the agents
are calculated and their next positions are updated. The other parameters of the
algorithm such as gravitational constant, masses and acceleration are updated at
each iteration cycle and the algorithm is terminated if it satisfies the maximum
number of iterations. To get an optimal solution using GSA, the optimum settings
of different input parameters are to be needed. Different trials have been performed
for optimum values of input parameters. Based on these trials, the following input
parameters are found to be best for optimal performance of the current problem:
G 0  100, γ  20, T  1000, N  no. of agents  30. Where the initial value of
gravitational constant is G 0 , γ is the user-specified constant for gravitational constant
and T is the maximum number of iterations. The basic flowchart of GSA is shown
in Fig. 4.

4 Simulation Results

The proposed scheme has been modeled and simulated using MATLAB and its
Simulink and SimPower System toolboxes for a three-phase four-wire system. A
6.6 kV/415 V, 200 kVA distribution substation feeding a variable load is consid-
ered for simulation purpose. Thyristor switched capacitor-thyristor controlled reac-
tor (TSC-TCR) type of SVC with 10 kVAr capacity of TCR and TSC that can vary
reactive power between 0 and 30 kVAr through five steps (0, 5, 10, 20 and 30 kVAr)
per phase is chosen. The line and load parameters are listed in Table 1.
The switching angles are computed at closed interval of modulation indices using
GSA with minimum reactor voltage harmonics. The computed switching angles are
used to calculate phase wise reactive power absorbed by TCR for each modulation
index using (5). The computed switching angle α for minimum reactor voltage THD
and the corresponding per phase reactive power consumption by -TCR with mod-
An Improved Reactive Power Compensation Scheme for Unbalanced … 127

Fig. 4 Flowchart of the

Start
GSA algorithm

Step1(Initialization):
Generate initial position of agents

Step2(Evaluation):
Evaluate fitness of each agents

Step3(Updation):
Update gravitational constant, best
and worst fitness of the population

Step4(Computation):
Calculate mass and acceleration of
each agent

Step5 (Modification):
Modify velocity and position of
each agent

No Maximum
iteration

Yes
End

ulation index (m d ) are shown Fig. 5a, b respectively. In the proposed scheme, these
two curves are stored in the processor memory for on-line applications.

4.1 Dynamic Response of the System Without

and with Proposed Compensator

The performance of the proposed scheme for load balancing, along with neutral
current compensation and source power factor improvement of a three-phase four-
wire unbalanced load with low line harmonic injection is shown in Fig.
6.
L
At 0.03 s, the SVCs are switched into the line. The voltages
 L V at the point of
common
 S coupling (PCC),
 unbalanced load currents I , balanced source currents

I , -SVC currents I  , Y-SVC currents I Y , source neutral current InS , load
neutral current InL , balanced active power taken from source (PS ) and balanced
128 S. Das et al.

Fig. 5 Variation of a optimum switching angle for minimum reactor voltage THD, and b per phase
reactive power consumption with modulation index (m d )

Fig. 6 Dynamic response of proposed scheme for load balancing, neutral current compensation
and power factor correction when the SVCs are switched into the line at t  0.03 s

reactive power drawn from source (Q S ) are demonstrated

 L in Fig. 6. It is noticed that
for
 S an unbalanced three-phase load currents I the
 compensated source currents
I become balanced and the source neutral current InS is maintained at nearly zero
after the SVC is switched into the line at t  0.03 s. The active (PS ) and reactive power
(Q S ) seen by the source after compensation become balanced through proposed
scheme. Also it can improve the source power factor by reducing the reactive power
drawn from source. The harmonic spectrum of the a-phase source current (IaS ) in
steady state condition is shown in Fig. 7 which justifies the low harmonic injection
by the proposed scheme
An Improved Reactive Power Compensation Scheme for Unbalanced … 129

Fig. 7 Harmonic spectrum

of the a-phase source current
in steady condition

4.2 Dynamic Response of the System Under Sudden Load

Change

The performance of the proposed scheme has also been studied under a sudden change
of load condition. Initially a balanced load of (10 + j5) kVA per phase was connected
to the system, then at t  0.1 s, three-phase linear load is changed to two-phase and
again to single-phase
 load at 0.2 s. These loads are reconnected again at 0.3 s. The

PCC voltage V L , unbalanced
load currents I L
, balanced source
 currents I S ,

-SVC currents I  , Y-SVC currents I Y , source neutral current InS , load neutral
current InL , balanced active power taken from source (PS ) and balanced reactive
power drawn from source (Q S ) under varying loads are demonstrated in Fig. 8a.
From Fig. 8a it can be observed that the source current is balanced before and after
the changeover which justify the effectiveness of the proposed method. Moreover,
THD of the source current is within permissible limit as shown in Fig. 8b–d during
different load conditions.
(a) Dynamic response of proposed scheme when load is changed from three-phase
to two-phase at t  0.1 s, to single-phase at t  0.2 s and again reconnected to
three-phase at t  0.3 s.
(b) Harmonic spectrum of the a-phase source current during three-phase load
(c) Harmonic spectrum of the a-phase source current during two-phase load
(d) Harmonic spectrum of the a-phase source current during single-phase load.

5 Conclusion

An improved switching scheme for load balancing, neutral current compensation and
source power factor improvement with minimum possible line harmonic injection
without using external filter has been proposed in this paper. The proposed scheme
has been implemented using TSC-TCR based combined -SVC and Y-SVC. The
Y-SVC is used for neutral current compensation and source power factor improve-
ment whereas -SVC is used for load balancing. The switching angles for TCR
compensation are calculated by optimizing the switching function of TCR using
GSA with varying modulation indices. These computed switching angles for min-
imum line harmonic injection along with phase-wise compensating reactive power
requirement are stored in the processor memory for on-line application. From the
130 S. Das et al.

Fig. 8 Dynamic simulation results and harmonic spectrum of source current

simulation results, it is verified that the proposed SVC switching results in load bal-
ancing, neutral current compensation and source power factor improvement with
reduced harmonic injection to source.

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A Comprehensive Review on Distribution
System

Anirban Chowdhury, Ranjit Roy, Kamal Krishna Mandal

and S. Mandal

1 Introduction

The significant features of DS are its radial nature and high R/X ratio. These features
make the analysis of DS different from a transmission system. The performance
parameters of a DS are active power loss and voltage profile. The conventional
LF techniques for transmission systems cannot be adopted for DS because of their
inability to converge. Researchers have developed special/modified LF methods for
analysis of DS. The above mentioned performance parameters of DS can be improved
network reconfiguration which is switching combination of the distribution feeders.
Overloading of DS is another issue which mal-triggers the protective devices and it
can be handled by network reconfiguration as well. The reliability and cleanliness of
a DS can be enhanced by RES based DG. The intermittent nature of power from DG
can be improved by high capacity network storage elements. DR is a measure taken by
power distributors to prevent situations like abnormally high load demand or power
outages by sending explicit requests to the customers or by providing incentives

A. Chowdhury · R. Roy (B)

Department of Electrical Engineering, Dr. Sudhir Chandra Sur
Degree Engineering College, Kolkata 700074, India
e-mail: rroy.svnit@gmail.com
A. Chowdhury
e-mail: anirbanee2015@gmail.com
K. K. Mandal
Department of Power Engineering, Jadavpur University,
SaltLake Campus, Sector III, Kolkata 700098, India
e-mail: kkm567@yahoo.co.in
S. Mandal
Department of Electrical Engineering,
Jadavpur University, Kolkata 700032, India
e-mail: shm.here@gmail.com

© Springer Nature Switzerland AG 2019 133

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_12
134 A. Chowdhury et al.

which will make the customers change their load usage patterns. In the last few
years, research on DS have been presented under four sections namely, distribution
system reconfiguration, load flow studies on distribution system, impact of renewable
energy on distribution systems and effect of demand response on distribution system.

2 Distribution Network Reconfiguration

2.1 Introduction to Distribution System Reconfiguration

The configuration of most DS is radial to carry out their protection. In DS, each feeder
is connected to various types of loads viz. commercial, industrial and residential. The
patterns of daily load demands for the said types of load are different having different
instants of occurrences of peak values. It is a problem if the DS gets overloaded as it
will lead to disconnection of branches caused by actuation of the protective devices
and voltage collapse. Overloading of the DS can cause problems starting from the
disconnection of branches due to triggering of protective devices and can lead to a
general voltage collapse resulting in financial losses for customers and the utilities.
The line losses are significant in DS due to high resistance to reactance ratio. The main
aim of the researchers is to investigate every possible means to reduce distribution
power loss and maintain voltages within the specified limits.
In order to improve the performance of a radial distribution networks, reconfigu-
ration is an effective solution. Reconfiguration is done by switching operation, either
manually or automatically, so that the power losses are reduced resulting in enhance-
ment of system security, power quality and reduction in network overloading. Two
types of switching operations are possible, either opening sectionalizing (normally
closed) switches or closing tie (normally open) switches of the network. The switch-
ing operation should ensure transfer of power to all the connected loads maintaining
the radial nature of the network. The distribution network reconfiguration problem
has been solved by researchers by adopting several techniques.

2.2 A Review on Distribution System Reconfiguration

Active power loss minimization by reconfiguration using several variants of Ant

Colony Optimization (ACO) has been implemented widely by several researchers.
ACO in Hyper-Cube framework (ACO-HC) has been implemented by Abdelaziz
et al. [1] by applying a modified local heuristic approach and a standard state tran-
sition rule. Alemohammad et al. [2] have presented a model for seasonal reconfig-
uration of actual distribution network and it has been solved by Genetic Algorithm
(GA). A multi-objective algorithm have been implemented by Alonso et al. [3] to
reduce the network power losses which improves the reliability index using artifi-
A Comprehensive Review on Distribution System 135

cial immune systems technique (AIS) and applying graph theory considerations to
improve computational performance and pareto-dominance rules. Amanulla et al.
[4] proposed a binary particle swarm optimization-based search algorithm (BPSO)
to find the optimal status of the switches and its effectiveness is demonstrated on a
IEEE 33-bus and a IEEE 123-bus radial DS. A new method based on shuffled frog
leaping algorithm (SFLA) by Arandian et al. [5], aimed reduction of network power
losses and control of power generation from DGs, has been successfully tested on
33-bus and 69-bus test systems. A bi-level optimization procedure is developed by
Arasteh et al. [6] using PSO, considering DR for sensitivity analysis in order to cover
the effects of uncertain parameters on a distribution network and its performance has
been tested on IEEE 33-bus standard test system. A novel adaptive fuzzy-based
parallel GA is proposed by Asrari et al. [7] that employs the concept of parallel com-
puting in identifying the optimal configuration of a dc distribution network. Bahrami
et al. [8] worked on hybrid Big Bang-Big Crunch optimization (HBB-BC) algorithm,
having faster rate of convergence and high efficiency, to solve the single -objective
reconfiguration of the functions of the problem such as system average interruption
frequency index, system average interruption duration index, average energy not sup-
plied, in DS. A fuzzy multi-objective approach based reconfiguration of distribution
networks have been presented by Banerjee et al. [9] considering different types of
load. Bayat et al. [10] proposed a heuristic approach based on uniform voltage distri-
bution based constructive reconfiguration algorithm (UVDA) for simultaneous DG
placement, sizing and network reconfiguration. The above algorithm is applied by
Bayat [11] for optimal reconfiguration of large- scale distribution networks and it was
tested with various practical distribution networks varies from 16-bus system with
3 tie-switches up to 835-bus system with 146 tie-switches. Capitanescu et al. [12]
explored how the DG penetration capacity of DS can be increased by both static and
dynamic reconfiguration of network under thermal and voltage constraints by solving
a non-linear, mixed-integer and multi-period optimal power flow problem (MP-OPF).
Improvement of network reliability and reduction of network power losses based on
an enhanced GA has been presented by Duan et al. [13]. Silva et al. [14] proposed
a heuristic algorithm for electrical DS reconfiguration based on movement of firefly
towards preys or partners where the insects positions in the space correspond to the
positions of the switches in the electrical system. Oliveira et al. [15] as well as Souza
et al. [16] have implemented bio-inspired metaheuristic AIS on network reconfig-
uration satisfying operational and network constraints, considering different load
levels. Pons and Repetto [17] presented a topological reconfiguration procedure for
maximizing local consumption of renewable energy in (Italian) active distribution
networks. Niknam et al. [18] presented Honey Bee Mating Optimization (HBMO)
approach to investigate the Distribution Feeder Reconfiguration (DFR) problem sat-
isfying the operating limits and constraints. An efficient Modified bacterial foraging
optimization algorithm (MBFOA) has been applied by Naveen et al. [19] on network
reconfiguration to reduce active power losses at IEEE 16, 33 and 69 bus systems.
Nguyen et al. [20] have implemented the cuckoo search algorithm (CSA) on network
reconfiguration problems and it proved to be efficient and promising. Back tracking
search algorithm (BSA) on network reconfiguration problems have been proposed by
136 A. Chowdhury et al.

Nguyen et al. [21] and its effectiveness was tested on 69- node distribution network
system. Network reconfiguration based on minimum spanning tree algorithm(MST)
have been tested on 33- bus, 69-bus and a real 210-bus MV utility DS by Li et al. [22]
and the results were found to be very effective. Network reconfiguration based on a
mixed- integer second-order conic programming (MISOCP) model has been devel-
oped by López et al. [23] and applied on 136 node DS considering the minimization of
active power losses and reliability constraints. To solve the reconfiguration problem
of radial DS, a scatter search, which is a metaheuristic-based algorithm, is proposed
by Rupolo and Mantovani [24].

3 Load Flow Studies on Distribution System

3.1 Load Flow Approach in DS Due to a Different Topology

LF studies are performed to determine the parameters of steady-state line power

flow and connected load. They provide guidance for proper planning, operation,
control and optimization of power system. LF analysis helps to verify whether all
the operational constraints including line voltage limits are satisfied. It is one of the
most frequently carried out study by power utilities and are essential for power sys-
tem planning, operation, optimization and control. It is required to explore different
arrangements necessary to maintain the required voltage profile and to minimize
the system losses. LF is also used as a sub problem like contingency analysis of a
system. The bus voltage magnitudes of a distribution network, their phase angles,
active and reactive power flows of different lines and the transmission power losses
are determined from load flow studies. Some of the basic LF algorithms were devel-
oped such as Newton Raphson (NR), Gauss Seidel (GS) and were applied to the
transmission network. In DS, these methods may become inefficient due to its radial
nature, high resistance to reactance ratio, load unbalance etc. Thus, the LF analysis
becomes complex in case of DS and fail to converge using the techniques in case of
transmission systems. In the past, many approaches for DS load-flow analyses have
been developed by the researchers. With respect to the nature of generation and load,
there are two types of LF, probabilistic (PLF) and deterministic (DLF). In PLF, the
analysis takes care of stochastic or statistical uncertainties with generation or load
while in DLF the natures are taken to be consistent. Some of the works on LF in the
recent years are stated below.

3.2 A Review on Load Flow Methods on Distribution Systems

Melhorn and Dimitrovski [25] proposed a three phase PLF in radial and weakly
meshed distribution network for both balanced and unbalanced conditions without
A Comprehensive Review on Distribution System 137

explicitly using Y-bus matrix and it was applied on IEEE 123 node and 13 node
test feeder. A novel direct method to LF has been developed by Singh et al. [26]
which saves computation time and power. Wang et al. [27] presented the explicit
conditions for existence of a unique LF solution for distribution networks having
generic topology. Murari et al. [28] developed a LF solution for IEEE 33 DS using
matrix method. The steady-state analysis and working of an electrical DS using multi-
linear probabilistic Monte Carlo (MC) simulation technique has been proposed by
Carpinelli et al. [29] with integration of photo-voltaic (PV) and wind (WD) power
generation. Harmonic LF in electrical distribution network has been analyzed using a
fuzzy-based Monte Carlo simulation technique has been developed by Šošić et al. [30]
in order to identify the weak zones of the network leading to power quality problems.
PLF of unbalanced power in a DS using a point estimate method has been developed
and analyzed by Delgado and Domínguez-Navarro [31], considering penetration of
PV and WD sources. A new, simple and efficient LF algorithm for weakly meshed
DS has been presented by Li et al. [32], using power flow variables as active and
reactive powers. Ruiz-Rodriguez et al. [33] developed a hybrid modified algorithm
combining jumping frog and PSO (JFPSO) and PLF in three phase network based
on the MC simulation for reducing voltage unbalance in DS with PV generators.
A PLF for DS with uncertain PV generation has been presented by Kabir et al.
[34] using Latin Hypercube Sampling with Cholesky Decomposition (LHS-CD) in
order to quantify the overvoltage issues. Voltage stability analysis of unbalanced DS
has been performed by Abdel-Akher [35] using backward/forward (BF) sweep LF
analysis method with secant predictor. PLF for three phase networks using binary
SFLA with technical constraints has been proposed by Gomez-Gonzalez et al. [36]
which handled the voltage regulation problem of a PV-connected grid within a small
number of iterations. Khan et al. [37] proposed a novel LF algorithm for different
radial DS which employs only three recursive equations devoid of any complex
parameters and it proved to be computationally efficient and faster than other existing
methods. Kocar et al. [38] tested and compared three LF solution algorithms using
the modified-augmented- nodal-analysis (MANA) formulation on IEEE 8500-node
distribution test feeder by means of a regulator tap-control strategy. A PLF-based
approach regarding the effects of RES on the voltage quality in a DS has been
proposed by Sexauer and Mohagheghi [39].

4 Impact of Renewable Energy on Distribution System

4.1 Renewable Energy—An Alternative for a Clean

and Reliable Distribution System

Fossil fuel based power generation became a practice for hundreds of years. The
environmental hazards related to emissions, especially CO2 , from a conventional
power plant are increasing day by day. Customers and utilities have widely accepted
138 A. Chowdhury et al.

clean and green renewable energy based generators viz., WT, PV system and fuel-
cells, among others as alternate sources of energy. Distributed Generation (DG) based
on renewable energy is one of the most promising solutions to the problem of high
greenhouse gas emissions and research efforts across the globe are being put into this
topic. But for its successful implementation, a number of challenges need to be faced.
As a DS is passive, allocating a DG to it means addition of a new dynamic element
to the system which needs to undergo a stability analysis. Integration of renewable
distributed energy resources (DER) has the ability to affect the operation of DS by
affecting the equipment reliability and customer power quality. To increase reliability,
Battery Energy Storage Systems (BESS) are incorporated to the distribution network
to mitigate the intermittent nature of renewable energy generation. The impact of
renewable energy on DS has been a preferred area of research these years.

4.2 A Review on Renewable Energy Based Distribution

Systems

Abdullah et al. [40] worked on the integration of distribution network with renew-
able DG which revealed the influence power output from renewable energy based
generators on time varying load demand. Self-consumption and storage of power
by consumers generated from PV micro grid are best means to keep the voltage
levels within specified limits as suggested by Camilo et al. [41]. Optimal allocation
of renewable energy based DGs in unbalanced IEEE 37-node feeder DS using Big
Bang- Big crunch method has been tested by Abdelaziz et al. [42]. Kayal and Chanda
[43] proposed integration of photovoltaic (PV) array, wind turbine (WT) and capac-
itor bank in distribution network, a sustainable way to meet the ever increasing load
demand. A novel dynamic energy management strategy in integrating large-scale
renewable energy sources (RES) with the distribution network has been developed
by Lv and Ai [44]. The benefits of customers correlated with harvesting of renewable
energy has been shown through a multi-level optimization approach for DS planning
by Zeng et al. [45]. Jiang et al. [46] proposed a synchrophasor based auxiliary con-
troller to increase voltage stability of a DS with distributed WT generators. Optimal
scheduling of renewable energy integrated distribution network for BESS operation
with plug in electric vehicles (PEV) have been shown by Yang et al. [47], in order
to minimize active power loss, voltage fluctuation and cost of electricity. A novel
stochastic programming model for active and reactive power scheduling in DS with
renewable energy resources and their influence on the daily Volt/Var control (VVC)
is presented by Samimi and Kazemi [48]. A novel hybrid approach to allocate RES
in DS is proposed by Singh and Parida [49] and it has been demonstrated on 15-node
radial DS and 69-node mesh DS. Reconfiguration problem of distribution network
has been investigated by Taghi et al. [50] to improve power quality, reliability and
reduce power loss by placement of solar-cell and wind turbine. Fluctuations in the
magnitude of voltages at different nodes in the DS with RES have been predicted
A Comprehensive Review on Distribution System 139

by a mathematical model developed by Iyer et al. [51]. An interval optimization

based day-ahead scheduling scheme for RE management considering renewable RE
uncertainties in smart DS has been presented by Chen et al. [52] and it has been
tested on 33-node and 119-node systems resulting in lower active power losses and
improved voltage profile. The effects of EV with vehicle to grid connectivity capa-
bility on renewable energy integrated distribution have been analyzed by Fathabadi
[53]. Nijhuis et al. [54] have shown the impacts of the renewable energy and ICT
driven energy transition on distribution networks and it made the energy system to
be more sustainable. Tsiftsis et al. [55] suggested that the efficiency of power distri-
bution network (PDN) can be enhanced by deployment of wireless sensor network
in dispersed RES.

5 Effect of Demand Response on Distribution System

5.1 Demand Response and Its Objective

DR, an outcome of demand side management (DSM), is the change in power con-
sumption of an electric utility customer to match power demand with supply. It is
not possible to throttle the power output from the supply-side like taking generating
units on/off-line or importing power from other utilities at all times due to time con-
sumption and high expense. The main objective of DR is to manage the load side
demand meticulously instead of changing the supply side power level. Utilities may
send signal to the customers to cut out some of the unnecessary load during peak
load hours in a number of ways like making the per unit cost of electricity cheaper
in the off peak load hours than the peak load hours or by smart metering through
which explicit requests or price change are intimated to the customers. In a broader
sense, DR encourages the electricity customers to shift their electricity usage pattern
during the peak load hours or power crisis.

5.2 A Review on Performance of Distribution System

with Demand Response

Nunna and Doolla [56] presented an agent based intelligent management system to
facilitate power trading among micro grids and encourage customers to participate
in DR. An analytical study is reported by Homaee et al. [57] to show the impact of
DR on voltages profile of DS. Zeng et al. [58] presented an integrated methodology
that accounts renewable DG and DR as options for clean and sustainable planning
of distribution network. A novel voltage sensitivity matrix based voltage control
in a real time environment using DR in an automated DS has been presented by
Zakariazadeh et al. [59]. Venkatesan et al. [60] proposed a model for DR by utilizing
140 A. Chowdhury et al.

consumer levels of rationality and behavior for different scenarios and applied it
to IEEE 8500-node test feeder resulting in improvement of voltage profile. Degefa
et al. [61] showed how DR can be an integral part for smart grid planning in terms
of reliability, contingency and improvement of voltage profile. Williams et al. [62]
have designed a self-regulating, smart, wind power integrated DS where the LF
fluctuations are controlled by self-regulating air-source heat pump (HP) cycling.
Mistry and Roy [63] presented the combined effects of DR program, wind generator,
as a renewable energy source and network reconfiguration on distribution network.

6 Conclusion

In this paper, research in the last few years on four topics on DS has been presented
namely distribution network reconfiguration, LF techniques, integration of renewable
energy based generators with or without BESS and effect of DR on DS. It is very
important for a researcher to know the fore mentioned areas of DS, willing to carry out
research in this field. The research works presented above aimed at analysis and/or
improvement of voltage profile, efficiency, reliability and contingency of a DS. These
parameters are performance indicators of a DS which needs to be improved so that
transmitted power can reach to the consumer end both safely and efficiently in a
cleaner way.

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Solution of Multi-objective Combined
Economic Emission Load Dispatch Using
Krill Herd Algorithm with Constraints

D. Maity, M. Chatterjee, S. Banerjee and C. K. Chanda

Nomenclature

Fi (Pi ) Fuel cost function

E i (Pi ) Emission cost function
Pi Output power of generator i
N Number of generators
ai , bi , ci , di , ei Cost coefficients of unit i
αi , βi , γi Emission cost co-efficient
Pimin Minimum operating limits of generator i
Pimax Maximum operating limits of generator i
PD Load demand
PL Transmission losses
Bi j Transmission loss co-efficient
PN Output of Nth generator
Mi Change in movement due to induction

D. Maity (B)
Electrical Engineering Department, Netaji Subhash Engineering
College Garia, Kolkata, West Bengal, India
e-mail: deblina14@gmail.com
M. Chatterjee · S. Banerjee
Electrical Engineering Department, Dr. B. C. Roy Engineering
College, Durgapur, West Bengal, India
e-mail: madhuragungun@gmail.com
S. Banerjee
e-mail: sumit_9999@rediffmail.com
C. K. Chanda
Electrical Engineering Department, IIEST, Shibpur,
Howrah, West Bengal, India
e-mail: ckc_math@yahoo.co.in
© Springer Nature Switzerland AG 2019 145
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_13
146 D. Maity et al.

Xi Foraging action
Di Random diffusion of each individual
Mimax The maximum is induced speed
αi Swarm density effect
ωn Inertia weight
MiPrevious Previous induced speed
Vf Foraging speed
ωx Inertia weight of the foraging motion
βi Current food location
X iPrevious Previous speed
R Dmax Maximum diffusion speed
σ Random directional vector
TV Total number of the variables
UL and LL Upper limit and the lower limit of the individual

1 Introduction

In electrical engineering mainly in power system many real life optimal problem
are flattering very complex and difficult. It is very time consuming to solve these
problems using conventional iterative techniques. But time cost is very important.
That’s why a new optimization technique i.e. krill herd algorithm is required to solve
complex optimal problem like economic load dispatch (ELD) and economic emission
load dispatch (EELD).
The cost function of economic load dispatch is represented by quadratic func-
tion. To find minimum fuel cost lambda iteration method is used in [1]. Problems
of economic load dispatch including transmission losses are solved using dynamic
programming method [2]. Basu proposed optimization technique based on artificial
bee colony for solving ED problem including transmission losses, multiple fuels etc.
[3].
Teaching learning based optimization technique is newly developed population
based algorithm based on relationship between teacher and learners in a class [4, 5]. It
has the ability to obtain convergence characteristics in relatively faster computation
time to genetic algorithms [6], particle swarm optimization techniques (PSO) [7]
and artificial bee colony (ABC) [8]. A new modified particle swarm optimization
technique has been proposed to solve EELD problem in [9]. Gaurav Prasad et al. [10]
proposed artificial bee colony optimization to solve ELD problem with considering
generator constraints. It does not include emission dispatch problem. Y. Sonmez et al.
[11] presented the same optimization techniques to solve the multi-EELD problem
by the penalty factor approach.
In [12] also, same algorithm regarding clonal selection is proposed to find the
solution of DED problem for generating units with VPL effect. A new optimization
technique ABC-PSO has been proposed to solve combined EELD problem in [13].
Solution of Multi-objective Combined Economic Emission Load … 147

A modified teaching learning based optimization techniques based on bare bones has
been proposed to solve minimization algebraic problem in [14].
KH algorithm is proposed in this paper with various constraints. Here transmission
losses are not included. Section 2 describes overview of EELD problem, Sect. 3
discusses KH and TLBO technique, Sect. 4 discuss the steps of implementation of
KH on EELD problems, Sect. 5 presents the result done by simulation and Sect. 6
presents the conclusion of this paper.

2 Overview of Economic Emission Load Dispatch Problems

A. Fuel and Emission Cost Function

The objective of EELD is to minimize fuel and emission cost satisfying load demand.
The cost function of EELD is quadratic nature. It is indicated by equation no. 1.

Fi (Pi )  ai Pi2 + bi Pi + ci (1)

E i (Pi )  αi Pi2 + βi Pi + γi + ηi ∗ exp(δi ∗ Pi ) (2)

Min · [Fi (Pi ) + E i (Pi )]

B. Constraints
ELD has many constraints. It has two types (I) Constraints described by equality
nature (II) Constraints described by inequality nature.
(I) Constraints with equality
The generated power of each generator should be equals to summation of load demand
and transmission losses.


N
Pi (t)  Load Demand + T ransmission Losses (3)
i1

(II) Constraints with inequality

The generator’s output should operate in operating bounds.

Pimin ≤ Pi ≤ Pimax (4)

Here Pimin and Pimax are the min and max operating limits of generator i.
C. VPL (valve point loading) effect on ELD
148 D. Maity et al.

The effect of VPL on ELD is non-linear. When load is changed, the cost equation of
ELD is represented in (5).
 N 

F  min Fi (Pi )
i1
 N 
     
 
 min ai Pi2 + bi Pi + ci + ei ∗ sin f i ∗ Pimin − Pi 
i1 (5)

where ai , bi , ci , di , ei are the cost coefficients of unit i.

Pimin Minimum generated power of unit i.

3 Overview of Krill Herd Algorithm and Teaching

Learning Based Optimization Algorithm

• Krill Herd Algorithm

In Krill herd (KH) algorithm the objective is the higher population size of the krill
individual and searching process of food i.e. higher krill density which means that
to achieve higher food density that leads to the optimal solution.
The fitness function of each krill individual is defined as its distances from food
and highest density of the swarm.
Three essential actions considered to determine the time-dependent position of an
individual krill are (i) movement induced by other krill individuals, (ii) foraging
activity, and (iii) random diffusion.

i. Initialization
Reduction in the population size from the food location because of predator
attack affects the objective value, this step is termed as initialization process.
Position of each individual depends upon three function viz. (i) change in move-
ment due to induction. (ii) Foraging action (iii) diffusion.
So, in the n- dimensional space the Lagrangian model is defined as
dyi
 Mi + X i + Di (6)
dx
ii. Change In Movement Due To The Induction
Due to other individual effect each individual try to keep optimal density. The
direction is effected by local population size, target population size and repulsive
population size. Thus, for each individual it is given as:

MiCurr ent  Mimax αi + ωn Mi

pr evious
(7)

iii. Foraging Motion

Solution of Multi-objective Combined Economic Emission Load … 149

It is obtained by the mean of two parameters. Optimal solution position and the
previous result i.e.

X f  V f βisolution + ωx X iPrevious (8)

iv. Random Diffusion

It is given as

R Di  R Dmax σ (9)

v. Movement Process
Using the result obtained from the different parameters, the position vector is
given as:
dz i
Z t (t + t)  Z i (t) + t (10)
dt
vi. Crossover Operators
In this operation the gene of an individual at next process is produced from the
previous one i.e. in this operation the gene of an individual at next process is
produced from the previous one i.e.
⎧
⎨ Z G i f random number < C R
ji
Z iG+1  (11)
⎩ Z G+1 else
i

vii. Mutation Operation

Mutation operators is given as

Z t  {Z best + μ(Z 1 − Z m ); i f random number < Mμ

else
Zt  Zt (12)

• Teaching Learning Based Optimization Algorithm

In TLBO, population is randomly initialized within their limits. TLBO is separated
also two parts.

i. Teacher Phase
ii. Learner Phase

i. Teacher Phase

The mean parameter of each subject of the learners in the class at generation g is
given as

g g g g
M g  m1 , m2 , . . . , m j , . . . , m D (13)
150 D. Maity et al.

To get a new population set of learners a vector is formed using (14)

g g  g 
X newi  X i + rand X T eacher − TF ∗ M g (14)

TF is the teaching factor. Value can be either 1 or 2.

g g g
If X newi is found to be better than X i in generation g, than it replaces on X i
g
otherwise it remains X i .
ii. Learner Phase
In learner phase the students can increase their knowledge by interaction of stu-
g
dents or sharing their knowledge. For a learner X i , randomly select another learner
g
X r as i  r . To set a new vector in learner phase Eqs. (15) and (16) is to be under-
stood.
g g  g   g  
X newi  X i + rand ∗ X i − X rg i f f X i < f X rg (15)
g g  g  g  
X newi  X i + rand ∗ X rg − X i i f f X i > f X rg (16)

When the stopping criteria is satisfied and means after completion of all iteration,
optimum result is got.

4 Implementation of KH Algorithm to Economic-Emission

Load Dispatch Problem

The steps are following

1. Initialize the Fitness Function i.e. Total cost function from the individual cost
function of the various generating stations.
2. Input the Fuel cost Functions, MW limits of the generating units and the total
power demand.
3. Perform change in movement due to induction when indicates minimum fuel
cost.
4. Calculate mean of two parameters.
5. Movement process also is performed. For each vector of active power the value
of the fitness function is calculated.
6. Crossover and mutation operation is performed.
7. By comparing two vectors new initialized vectors are formed.
8. When the stopping criteria that means when MAXIT iteration is completed, then
the algorithm is stop.
Solution of Multi-objective Combined Economic Emission Load … 151

5 Simulation Results with Discussions

The KH and TLBO algorithm has been applied on two cases. Case one is 6 unit
systems [9] and case two is 10 unit systems [13]. MATLAB 7.01 is used for develop
the program for obtaining the results.
Case 1: System including six generators (6 unit system)
The proposed two algorithm i.e. KH and TLBO has been applied on six unit sys-
tems. The coefficients of costs and limits of power generation are taken from [9]. Here
emission is considered. Power generation limits are also included. Table 1 shows the
solution of conventional ELD i.e. optimal power allocation for finding minimum
fuel cost using KH and TLBO compared with PSO [9] shows the better convergence
characteristics in proposed algorithms. The optimal allocation of generators for get-
ting minimum emission cost is shown in Table 2. The graph between no. of iterations
and fuel cost in $/hr for load of 700 MW using KH and TLBO algorithm is shown
in Figs. 1 and 2 respectively. The graph between no. of iterations and emission cost
in $/hr for load of 700 MW using KH and TLBO algorithm is shown in Figs. 3 and
4 respectively.

Table 1 Optimal allocation of power corresponding minimum fuel cost for 6 generator system for
(700 MW) load demand
Power output KH TLBO PSO [9]
P1(MW) 20.9519 10.3888 30.712
P2(MW) 12.9622 15.8524 18.681
P3(MW) 102.6855 146.2914 130.568
P4(MW) 108.4169 154.3727 134.288
P5(MW) 249.4204 275.0659 206.088
P6(MW) 205.5631 298.0289 198.252
Fuel cost($/hr) 36,022 45,553 1663066.3

Table 2 Optimal allocation of power corresponding minimum combined cost for 6 generator sys-
tem for (700 MW) load demand
Power output KH TLBO PSO [9]
P1(MW) 78.7743 44.5437 80.3178
P2(MW) 65.1203 92.2446 83.4732
P3(MW) 112.0194 104.3898 111.0704
P4(MW) 109.7429 115.9925 116.6904
P5(MW) 164.1777 172.3243 157.919
P6(MW) 170.1654 170.5051 167.0772
Emission cost ($/hr.) 422.2757 425.0248 432.048
152 D. Maity et al.

Fig. 1 Convergence 4
x 10
3.64
characteristics of fuel cost
versus iteration for six unit 3.635
systems using KH algorithm
3.63

3.625

Total Cost
3.62

3.615

3.61

3.605

3.6
0 50 100 150 200 250 300 350 400 450 500
Iteration

4
Fig. 2 Convergence x 10
4.566
characteristics of fuel cost
versus iteration for six unit
systems using TLBO 4.564

4.562
Fuel Cost

4.56

4.558

4.556

4.554
0 100 200 300 400 500 600 700
Iteration

Case 2: System including ten generators (10 unit system)

The proposed two algorithm i.e. KH algorithm and TLBO has been applied on ten
unit systems. The coefficients of costs and limits of power generation are taken from
[13]. Here valve point loading effects and emission is considered. Power generation
limits are also included. Table 3 shows the solution of combined EELD i.e. optimal
power allocation for finding minimum fuel and emission cost. The graph between
no. of iterations and cost in $/hr for load of 2000 MW using KH and TLBO algorithm
is shown in Figs. 5 and 6 respectively.
Solution of Multi-objective Combined Economic Emission Load … 153

Fig. 3 Convergence 438

characteristics of emission
cost versus iteration for six 436

unit systems using KH

434
algorithm

Emission Cost
432

430

428

426

424

422
0 50 100 150 200 250 300 350 400 450 500
Iteration

Fig. 4 Convergence 438

characteristics of emission
cost versus iteration for six 436
unit systems using TLBO
434
Emission Cost

432

430

428

426

424
0 50 100 150 200 250 300 350 400 450 500
Iteration

6 Conclusion

The proposed optimization techniques based on interaction of teacher and students

i.e. KH and TLBO algorithm has been successfully applied on linear and non-
linear economic emission load dispatch problems. Here transmission losses are not
included. The obtained results from proposed algorithms have better convergence
characteristics compared to other optimization techniques. So in a word it is very
efficient population based method to find optimum results in EELD problems.
154 D. Maity et al.

Table 3 Optimal allocation of power corresponding minimum fuel cost for 10 generator system
for (2000 MW) load demand
Unit power KH TLBO ABC_PSO DE [15] NSGA-II SPEA-2
output [13] [15] [15]
P1 (M W ) 41.5470 30.8835 55 54.9487 51.9515 52.9761
P2 (M W ) 73.7694 79.2830 80 74.5821 67.2584 72.813
P3 (M W ) 111.4648 96.6791 81.14 79.4294 73.6879 78.1128
P4 (M W ) 71.1654 130.0000 84.216 80.6875 91.3554 83.6088
P5 (M W ) 76.0255 103.0483 138.3377 136.8551 134.0522 137.2432
P6 (M W ) 88.1139 70.000 167.5086 172.6393 174.9504 172.9188
P7 (M W ) 293.9184 297.4562 296.8338 283.8233 289.435 287.2023
P8 (M W ) 335.9943 294.0677 311.5824 316.3407 314.0556 326.4023
P9 (M W ) 466.2090 436.3312 420.3363 448.5923 455.6978 448.8814
P10 (M W ) 441.7923 462.2510 449.1598 436.4287 431.8054 423.9025
Fuel 108,470 109,880 113,420 113,480 113,540 113,520
cost($/h)
Emission 5785.3 945.6188 4120.1 4124.9 4130.2 4109.1
cost (1b/h)

Fig. 5 Convergence 5
x 10
1.103
behavior of fuel cost and
iteration of ten unit systems 1.1025
of load demand 2000 MW
with VPL effect using KH 1.102
algorithm
1.1015
Total Cost

1.101

1.1005

1.1

1.0995

1.099

1.0985
0 50 100 150 200 250 300 350 400 450 500
Iteration
Solution of Multi-objective Combined Economic Emission Load … 155

5
Fig. 6 Convergence x 10
1.156
behavior of combined cost
and iteration of ten unit
1.154
systems of load demand
2000 MW with VPL effect
1.152
using TLBO

Total Cost
1.15

1.148

1.146

1.144

1.142
0 50 100 150 200 250 300 350 400 450 500
Iteration

References

1. H. Saadat, Power System Analysis (Tata McGraw Hill Publishing Company, New Delhi, 2002)
2. Z.X. Liang, J.D. Glover, A zoom feature for a dynamic programming solution to economic
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Energy Syst. 49, 181–187 (2013)
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for constrained mechanical design optimization problems. CAD Comput. Aided Des. 43(3),
303–315 (2011)
5. R.V. Rao, V.J. Savsani, D.P. Vakharia, Teaching-learning-based optimization: an optimization
method for continuous non-linear large scale problems. Inf. Sci. 183(1), 1–15 (2012)
6. D.E. Goldberg, Genetic Algorithms in Search Optimization and Machine Learning (Addison-
Wesley, Reading, MA, USA, 1989)
7. J. Kennedy, R. Eberhart, Particle swarm optimization, in Proceedings of the IEEE International
Conference on Neural Networks, December 1995, pp. 1942–1948
8. D. Karaboga, B. Basturk, On the performance of artificial bee colony (ABC) algorithm. Appl.
Soft Comput. J. 8(1), 687–697 (2008)
9. G. Anurag, K.K. Swarnka, K. Wadhwani, Combined economic emission dispatch problem
using particle swarm optimization. Int. J. Comput. Appl. (0975–8887) 49(6), 1–6 (2012)
10. G.P. Dixit, H.M. Dubey, M. Pandit, B.K. Panigrahi, Economic load dispatch using artificial
bee colony optimization. Int. J. Adv. Electron. Eng. 1(1), 119–124 (2011)
11. Y. Sonmez, Multi-objective environmental/economic dispatch solution with penalty factor
using artificial bee colony algorithm. Sci. Res. Essays 6(13), 2824–2831 (2011)
12. S. Chakraborty, T. Senjyu, A. Yona, A.Y. Saber, T. Funabashi, Solving economic load dispatch
problem with valve-point effects using a hybrid quantum mechanics inspired particle swarm
optimization. IET Gener. Transm. Distrib. 5(10), 1042–1052 (2011)
13. E.D. Manteaw, N.A. Odero, Combined economic and emission dispatch solution using
ABC_PSO hybrid algorithm with valve point loading effect. Int. J. Sci. Res. Publ. 2(12),
1–9 (2012)
14. F. Zou, L. Wang, X. Hei, D. Chen, Q. Jiang, H. LI, Bare-bones teaching-learning-based opti-
mization. Sci. World J. 2014, 1–17 (2014). Article ID 136920
15. K. Basu, Economic environmental dispatch using multi-objective differential evolution. Appl.
Soft Comput. 11, 2845–2853 (2011)
Classification of Crossover Faults
and Determining Their Location
in a Double Circuit Power Transmission
System with Multiple Sources

Nabamita Roy

1 Introduction

Faults in overhead transmission lines are more likely to happen due to lightning,
falling trees and insulators breakdown. The electrical power is transmitted either by
single circuit system or double circuit system. Short circuit faults are quite common
and in a double circuit system there remains a scope of crossover short-circuit in
which two phases of different circuits are involved. Identification of such faults and
determining their location is a challenging task.
A scheme of determination of fault location for a double circuit compensated
transmission lines has been proposed in [1] where the location has been estimated by
using Discrete Wavelet Transform (DWT) and KNN with less than 1% error. A new
approach of fault classification has been presented in [2] for EHV transmission lines
using Rough Membership Neural network (RMNN). DWT has been used for feature
extraction and a comparative analysis has been shown between RMNN and BPNN
to establish that RMNN is faster and more accurate than BPNN as a classifier. The
fault location has not been determined here. A hybrid method of ANN and DWT has
been suggested in [3] for identification of faulty section and obtaining its location in
a distribution network. The proposed method in this paper has been tested on a IEEE
system but the effect of noise on the features extracted has not been discussed here.
The paper [4] proposes an approach by combining independent component analysis
(ICA) with travelling wave (TW) theory and Support Vector Machine (SVM) for fault
analysis of HV Transmission lines. This method gives better performance in presence
of noise. A new technique for fault location on transmission lines using only voltage
measurements obtained from Wide Area Measurement Systems (WAMS) and the

N. Roy (B)
Electrical Engineering Department, MCKV
Institute of Engineering, Liluah, Howrah,
West Bengal, India
e-mail: roynab@gmail.com

© Springer Nature Switzerland AG 2019 157

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_14
158 N. Roy

network bus admittance matrix has been reported in [5]. Fault classification has also
been included in this paper using the same technique. In [6] inter-circuit shunt faults
and cross-country faults in a double circuit system have been identified and classified
using DWT and SVM. In this paper, the method of determining fault location and
the effect of noise has not been discussed. A hybrid framework has been designed in
[7] for classifying and locating short circuit faults in power transmission lines and
this framework consists of a proposed two-stage finite impulse response (FIR) filter,
four support vector machines (SVMs), and eleven support vector regressions (SVRs).
SVM has been also applied in [8] for fault classification in a long transmission line
in which the features have been selected using wavelet packet transform.
In this paper, a method is proposed for identification of the type of fault and obtain-
ing its corresponding location in a double circuit system. ANN has been involved
here in which PNN is used for fault classification and BPNN for obtaining the fault
location. The input features of both the PNN and BPNN have been obtained from
DST of the current signals measured at any one terminal of the network. All the faults
have been simulated in MATLAB environment. The scope of this paper is limited to
the simulation of only double line short—circuit faults.
The rest of the paper is organized as follows. The simulation of faults in a double
circuit network is described in Sect. 2. DST is briefly discussed in Sect. 3. The features
needed for fault analysis and the method of regression applied on the features have
been described in Sect. 4. Section 5 explains the method of fault classification and
obtaining its location. The effect of noise has also been studied in this section.

2 Simulation of Faults and the System Under Study

A 400 kV, 50 Hz, 3-phase double circuit power system network is simulated using
the Simpower Toolbox of MATLAB-7 and is shown in Fig. 1. The length of each
transmission line is 300 km. The double circuit network has similar sources at both
its ends.
System parameters:
Generator 1, 2: Voltage  400 kV, Impedance of generator  (0.2 + j4.49) , X/R
ratio  22.45.

Fig. 1 Single line diagram of three phase double circuit network

Classification of Crossover Faults and Determining Their … 159

Each Transmission Line: Length  300 km, R1  0.02336 /km, R2 

0.02336 /km, R0  0.38848 /km, L1  0.95106 mH/km, L2  0.95106 mH/km,
L0  3.25083 mH/km, C1  12.37 nF/km, C2  12.37 nF/km, C0  8.45 nF/km.
All the signals have been simulated with a sampling time of 78.28 µs. The time
period of simulation in MATLAB has been taken up to 0.04 s. The sampling frequency
is 12.8 kHz.
Crossover two phase short-circuit faults have been simulated in the following way
as given below:
Double Line (L-L) Faults:
A1 A2 : Phase A of Line 1, A1 shorted to phase A of line 2, A2
A1 B2 : Phase A1 of Line 1, A1 shorted to phase B of line 2, B2
A1 C2 : Phase A1 of Line 1, A1 shorted to phase C of line 2, C2
B1 A2 : Phase B1 of Line 1, B1 shorted to phase A of line 2, B2
B1 B2 : Phase B1 of Line 1, B1 shorted to phase B of line 2, B2
B1 C2 : Phase B1 of Line 1, B1 shorted to phase C of line 2, C2
C1 A2 : Phase C of Line 1, C1 shorted to phase A of line 2, A2
C1 B2 : Phase C of Line 1, C1 shorted to phase B of line 2, B2
C1 C2 : Phase C of Line 1, C1 shorted to phase C of line 2, C2
All the faults have been initiated at 19 different locations starting from B1, each
being 10 km apart. The fault resistances considered for the simulation are from the
range of 0–100 in steps of 20. Fault inception angle is considered to be 0°. The
total number of fault simulations made in this system is 9 × 19 × 6  1026.

3 Discrete S-Transform (DST)

An electrical signal h(t) can be expressed in discrete form as h(kT), k  0, 1, …, N −

1 and T is the sampling time interval, [9, 10].
The discrete Fourier transform of h(kT) is obtained as,

 n  N −1
1  −i2πk
H  h(kT )e N (1)
NT N k1

where n  0, 1, …, N − 1.
Using (4), the ST of a discrete time series is obtained by letting f → n/N T and
τ → j T as

 n   m + n 
N −1
S j T,  H G(m, n)ei2πm j/N (2)
NT m0
N T

and G(m, n)  e−2π m 2 /n 2

2
, n  0 where j, m  0, 1, 2, …, N − 1 and n  1, 2, …,
N − 1.
160 N. Roy

A complex matrix (S-matrix) is produced from Eq. (2). The rows of the matrix
represent frequencies and the columns signify times. The absolute value of the S-
matrix gives the amplitude of the ST spectrum. Hence, each column of the matrix
can be considered as the local spectrum at any point and time. The amplitude of the
signal at different frequency resolutions remains unaffected in the matrix.
DST of a given signal provides the privilege of obtaining both the amplitude and
phase informations at any point of time and at any frequency. These informations
remain almost unaffected in presence of noise. Hence, in the present paper DST has
been used for feature extraction. However, only the amplitude matrix has been used
here for obtaining the features.

4 Feature Extraction from the S-Matrix and Regression

The waveforms of the current signals measured at the busbar B1 after simulation in
Fig. 1 have been shown in Figs. 2 and 3 respectively.
The Fig. 4 shows the plot of magnitude of a parameter XB1totalphA with respect
to time which has been obtained from S-matrix of a current signal corresponding to
a A1 B2 fault occurring at a distance 100 km from B1 and B2. XB1totalphA has been
calculated by summing up each column of S-matrix.
The feature XareaB1 has been obtained by calculating the area under the curve
plotted in Fig. 4. The other feature XreaB2 has been obtained in a similar way.
The variation of feature XareaB1 at different fault locations has been shown in
Fig. 5. The curves of Fig. 5 demonstrate an irregular pattern of the feature XareaB1

Fig. 2 Current waveforms of the three phases A1 , B1 , C1 for a A1 B2 type of fault at 100 km from
B1 with RF  0  and fault inception angle  0°
Classification of Crossover Faults and Determining Their … 161

Fig. 3 Current waveforms of the three phases A2 , B2 , C2 for a A1 B2 type of fault at 100 km from
B1 with RF  0  and fault inception angle  0°

Fig. 4 Profile of magnitude of the parameter XB1 totalphA

with respect to distance of fault location. It is difficult to get a satisfactory result if such
features are used for training a neural network. Henceforth, polynomial regression
has been adopted to obtain a suitable pattern of the features that can be trained by a
neural network to produce satisfactory results.
162 N. Roy

Fig. 5 Profile of the change in magnitude of the feature XareaB1 for different fault locations

4.1 Polynomial Regression

In case of Linear Regression Models, polynomial models represent a special case of

the linear models. Polynomial models are simple. They have the ability and familiarity
in their properties in following the data trends with reasonable flexibility. These
models are unaffected by any changes in the location and scale of the data. The
model should be selected in such a way that it should provide simple description of
overall data trends and make reasonably accurate predictions.
In the present work, polynomial regression is applied on the features XareaB1 and
XareaB2 by programming in MATLAB. The profiles of the features after regression
have been shown in Figs. 6 and 7 respectively.
From Figs. 6 and 7 it is evident that after regression the features XareaB1 and
XareaB2 follow a regular pattern with change in fault location and the regressed
features can be conveniently used for training a neural network to obtain an acceptable
output from an unknown input parameter.

5 Fault Classification and Determination of Fault Location

Different ANN architectures are suitable for a varied range of tasks. Selection of a
particular network depends on the type of problem. PNN is widely used for the task
of classification. In the present work, PNN has been used for fault classification.
The architecture of the PNN used for fault classification involves two hidden layers.
The working function of the first hidden layer is radial basis transfer function, and
Classification of Crossover Faults and Determining Their … 163

Fig. 6 Profile of the change in magnitude of the feature XareaB1 after regression

Fig. 7 Profile of the change in magnitude of the feature XareaB2 after regression

that of the second hidden layer is competitive transfer function, [11]. PNN has many
advantages. Its training process is fast and it has an inbuilt parallel structure that
has the highest scope of converging to an optimal classifier as the dimension of the
representative training set enhances. There is a huge scope of adding or removing
the training samples without involving vigorous retraining of PNN.
164 N. Roy

BPNN is relatively suitable for function approximation problems. The network

is trained by input vectors and the corresponding target vectors until a function
is approximated. Standard backpropagation is based on Widrow-Hoff learning rule
[12] which is a gradient descent algorithm. The term backpropagation means the way
in which the gradient is calculated for nonlinear multilayer networks. Reasonably
satisfactory answers are obtained from a properly trained backpropagation network
when unknown inputs are given to it. The unknown input features should be similar
to the input vectors used for training so that the output feature obtained from a BPNN
corresponding to the new input feature is quite close to the correct output. In this
way, BPNN is generalised to be trained on a representative set of input/target pairs to
produce satisfactory results without the need for training on all possible input/output
pairs.

5.1 Fault Classification

The features XareaB1 and XareaB2 of the six phases have been used as input param-
eters. The regressed features of 10 current signals of each phase are used for training
and the rest are used for testing purpose. The output of the PNN is summarised in
Table 1. The average of correct predictions is 98.7%.

5.2 Determination of Fault Location

The fault location has been obtained from a BPNN. The BPNN in this paper is a
2-layer feed-forward network which consists of only one hidden layer and an output
layer. The input layer consists of the input vector. In this paper, the elements of the

Table 1 Results of fault classification from the PNN

Type of fault PNN output % of correct predictions
A1 A2 1 97.8
A1 B2 2 98.9
A1 C2 3 98.5
B1 A2 4 97.6
B1 B2 5 99.5
B1 C2 6 98.7
C1 C2 7 98.5
C1 B2 8 98.6
C1 A2 9 99.6
No fault 10 99.6
Classification of Crossover Faults and Determining Their … 165

Table 2 Fault location in case of A1 B2 type of fault with fault resistance, RF  0 

Actual fault location (km) BPNN output (km) % error
20 21.23 1.59
40 39.36 −1.60
60 60.34 0.57
80 81.87 2.34
100 102.69 2.69
120 120.46 0.38
140 140.58 0.42
160 159.49 −0.32
180 180.85 0.47
200 200.10 0.05
220 220.57 0.26
240 241.36 0.57
260 259.06 −0.36
280 281.53 0.55

input vector are the features of 10 current signals obtained from DST. The number
of neurons for the hidden layer is taken to be 100 and the transfer function used is
Tan-Sigmoid. Only one neuron has been used for the output layer and the transfer
function used is Purelin. The BPNN architecture has been initially tested with 60,
80, 100 and 120 neurons. It was observed that the selection of 100 neurons gives
the output with satisfactory accuracy and speed. If the number of neurons is lesser
than 100 then the accuracy is affected and if the number is greater than 100 then the
speed of convergence of training becomes higher with a small improvement in the
accuracy.
Once the short-circuited phases have been identified from the PNN either the
parameter XareaB1 or XareaB2 of any one of the faulty phases has been used as
the input feature. In case of A1 B2 type of fault, the features XareaB1 obtained cor-
responding to phase A1 for different fault locations has been used for training the
BPNN. The features of 10 current signals have been used for training and the rest
are used for testing purpose. Levenberg–Marquardt (LM) algorithm has been used
for training the BPNN. The percentage error is calculated during estimation of fault
location as shown in Table 2 and according to Eq. (3). Table 2 show the results of
fault location obtained from the BPNN in case of a A1 B2 type of fault.
B P N N out put − Actual Fault Location
× 100 (3)
Actual Fault Location
From Fig. 8 it is evident that within 4 epochs convergence is reached and the
result is obtained fast corresponding to a new input parameter. The maximum error
achieved in determination of fault location is 2.69%.
166 N. Roy

Fig. 8 Training of BPNN for obtaining fault location by LM method

5.3 Implementation of Noisy Signals

The current signals obtained at the Bus B1 from simulation have been impregnated
with 20 dB white Gaussian noise by programming in MATLAB. As an illustration,
the magnitude of the feature XareaB1 has been calculated for noisy current signals
and the same has been plotted with respect to the signals without noise as shown in
Fig. 9. The type of fault considered in Fig. 9 is A1 B2 with fault resistance being 0
. The results of classification and estimation of fault location have been given in
Tables 3 and 4. The average of correct classifications from PNN is 98.6% and the
maximum error achieved in obtaining fault location is 4.62%.

6 Conclusion

The selection of features is an important part that determines how effectively and
accurately the faults can be classified. In this paper, only the current signals of one
terminal of the network have been used for extracting features. Six features are needed
for the six lines to identify the affected phases from PNN. Only one feature of the
affected phase is needed for obtaining fault location from the BPNN. The technique
of regression applied on the features obtained from S-matrix has produced quite
accurate and fast results. The faults have been simulated at different locations with
variation in fault resistance. The effect of noise has also been studied. The average
Classification of Crossover Faults and Determining Their … 167

Fig. 9 Magnitude of the regressed feature XareaB1 for noisy signals and signals without noise

Table 3 Results of fault classification from the PNN with noisy current signals
Type of fault PNN output % of correct predictions
A1 A2 1 97.7
A1 B2 2 98.7
A1 C2 3 98.9
B1 A2 4 97.7
B1 B2 5 99.4
B1 C2 6 98.6
C1 C2 7 98.3
C1 B2 8 98.4
C1 A2 9 99.5
No fault 10 99.5

percentage of correct classifications from the PNN is 98.7% without noise and 98.6%
in presence of noise. The faults have been located by the BPNN with a maximum
error of 2.69% without noise and 4.62% in presence of noise. The results indicate
that the proposed method of fault classification and estimation of fault location can
be effectively implemented for other systems as well.
The present work can be further extended for the analysis of Line-Ground faults,
Double-line Ground Faults and Three phase short-circuit faults in which phases of
different circuits are also involved.
168 N. Roy

Table 4 Fault location in case of A1 B2 type of fault with fault resistance, RF  0 

Actual fault location (km) BPNN output (km) % error
20 19.82 −0.90
40 39.87 −0.33
60 62.77 4.62
80 81.56 1.95
100 98.96 −1.04
120 119.56 −0.37
140 141.22 0.87
160 160.56 0.35
180 179.45 −0.31
200 203.56 1.78
220 223.55 1.61
240 240.88 0.37
260 262.87 1.10
280 279.76 −0.09

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Optimal Value of Excitation
of Self-excited Induction Generators
by Simulated Annealing

Writwik Balow, Arabinda Das, Amarnath Sanyal

and Raju Basak

1 Introduction

Generally generating stations are located far away from rural areas. Sometimes it
may not be possible to deliver power to the rural areas, because of the distance and
cost involved in generation and transmission. Researchers are currently giving stress
on dispersed generation using alternative energy sources to generate energy at a
cheap rate. Wind is found to be the best alternative among all the energy sources
available in rural areas. The fuel cost is nil, however, the source is of variable energy.
Under the circumstances, Induction Generator has been found to be the most effective
machine used to generate energy while driven by wind turbine. Self-excited induction
Generator shows better performance for generating energy from the renewable energy
sources.

W. Balow
Electrical Engineering Department,
Ideal Institute of Engineering, Kalyani, India
e-mail: writwik.balow@gmail.com
A. Das
Electrical Engineering Department,
Jadavpur University, Kolkata, India
e-mail: adas_ee_ju@yahoo.com
A. Sanyal
Electrical Engineering Department,
Calcutta Institute of Engineering and Management, Kolkata, India
e-mail: ansanyal@yahoo.com
R. Basak (B)
GEP Department, University Claude Bernard Lyon1,
Villeurbanne, France
e-mail: basak.raju@yahoo.com

© Springer Nature Switzerland AG 2019 171

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_15
172 W. Balow et al.

When induction motor runs at super-synchronous speed i.e. at a negative slip, it is

called an induction generator [1, 2]. In this mode, it converts mechanical energy of
the wind turbine into electrical energy. In this case, reactive power is consumed by the
motor instead of being generated as in a synchronous machine. While the machine
is driven at super-synchronous speed, it starts delivering active power. The output
variables like voltage, frequency, and load are highly influenced by the amount of
excitation of the capacitor bank.
There are two kinds of operations for a Squirrel cage induction generator. The
generator running at super-synchronous speed may be connected to grid, or a capac-
itor bank may be connected in parallel with the system [3–5]. The configuration of
Self-excited Induction Generator (SEIG) is shown in Fig. 1 and it is used to develop
an objective function for excitation of the capacitor. A case study is made for four
machines having rating 4, 7.5, 15, 37 kW whose excitation is optimized by the pro-
cess of Simulated Annealing (SA). The final result has been presented graphically
to show the variation in results.

2 Excitation of Self-excited Induction Generator (SEIG)

Induction Generator is excited initially by residual magnetism of the core which

feeds the capacitor bank—the voltage builds up as in a self-excited D.C generator.
The Capacitor bank is connected in parallel with the system to supply the reactive
power [6].

Fig. 1 Self-excited induction generator (SEIG) connected with load

Optimal Value of Excitation of Self-excited Induction … 173

3 Simulated Annealing

There are many types of optimization technique—the nature of the problem is also
diverse. Sometimes it becomes quite difficult to choose the proper optimization
scheme for a particular problem. The choice depends on the nature of the objective
function. It is found that the excitation function of self excited induction generator is
non-linear by nature [7, 8]. An attempt has been made for global search by Simulated
Annealing within an area widened by lower and upper limits of variables. Choice
of number of variables, number of generators, bounds of the variables, constraint-
functions etc. have been chosen step by step for SA and then with proper coding
in Mat lab the function have been optimized. Flow Chart for algorithm is shown in
Fig. 2.
Annealing is a process used to crystallize metals. When a metal is strongly heated,
the atoms reach high energy level and are set to motion. The cooling process helps the
atoms to reach the equilibrium condition at minimum energy. The expression of prob-
ability is given by P (E)  e(−E/KT) , where T is temperature and K is Boltzmann’s
constant. The function, which is to be optimized, is started with a high temperature
and then it is slowly cooled down to its global optima. e(−E/KT) is calculated and
a random number ‘r’ is generated between 0 and 1. If r ≤ e(−E/KT) then it is saved,
otherwise discarded. Thereafter we move to the next step.

4 Variables

Self-excited Induction Generator is largely influenced by its excitation—if it is not

excited properly its output voltage cannot build up. Here three variables have been
chosen and then the objective function (i.e. excitation of the capacitor) has been
framed with these variables. Variables have been chosen in a way such that, they
can governs the objective function i.e. load, frequency and speed. The variables are
allowed to vary within a certain range—the range in p.u. is given below:

x1  Load [0.5 ≤ x1 ≤ 1.3]

x2  Frequency [1.3 ≤ x2 ≤ 1.6]
x3  Speed [0.5 ≤ x3 ≤ 1.3]

The output voltage is selected as inequality constraint: [gi (x) − x2 · k ≥ 0]

5 Objective Function

The equivalent circuit of the Induction generator is shown in Fig. 3.

174 W. Balow et al.

A function is derived from the equivalent circuit and is taken as an objective

function of excitation. Capacitive reactance is taken, which is to be optimized and
expressed in terms of load resistance, output frequency and speed. The function can
be expressed as:

Minimize  [Ax1 x22 + Bx1 x2 ]/[C x1 + Dx2 (x2 − x3 ) + E] (1)

Fig. 2 Flowchart
Optimal Value of Excitation of Self-excited Induction … 175

Fig. 3 Equivalent circuit of induction generator

Generated Voltage is as follows:

Vg  (1.6 − 0.36xm )x2 (2)

Three Variables are bound with their limits. Simulated Annealing is applied to
reach the optimum, under the constraints, e.g. the output voltage should not be below
a certain limit [9, 10]. Optimality is reached in about thousands of iterations. First
hundred convergence data for 4 kW machine is shown in Fig. 4 and last thirty-six
convergence data is shown in Table 1.

Convergence graph of SA for table given below

2.5

2
Value of Excitation

1.5

0.5

0
0 5 10 15 20 25 30 35 40

No. of iterations

Fig. 4 Graph of convergence

176 W. Balow et al.

Table 1 First 36 convergence data of the above graph

No. F(x) No. F(x) No. F(x)
1 0.4869 13 0.7596 25 0.9002
2 0.4437 14 0.7961 26 0.6821
3 0.4194 15 0.9895 27 0.8132
4 0.419 16 0.8294 28 0.4901
5 0.4268 17 0.6782 29 0.7673
6 0.417 18 0.668 30 0.8608
7 0.424 19 0.7871 31 0.7977
8 0.417 20 0.8031 32 0.36812
9 0.4134 21 0.8215 33 0.3683
10 0.4135 22 0.5242 34 0.36883
11 0.4134 23 0.6525 35 0.36883
12 0.4134 24 0.903 36 0.36883

Table 2 Equivalent circuit parameters

Machines RE Rr LLS LLr Lm
rating (kW) in
p.u.
4.0 0.0351 0.0348 0.0458 0.045 1.352
7.5 0.0346 0.0347 0.0448 0.044 1.827
15 0.0201 0.0206 0.0291 0.029 1.89
37 0.0190 0.0116 0.0526 0.052 1.97

6 Case Study

Four machines are taken for case study having ratings of 4, 7.5, 15 and 37 kW
respectively. The parameters of the machines are shown in Table 2 and the constant
of objective function is shown in Appendix.
Optimal value of the excitation is determined by the method of simulated annealing
for each machine with their corresponding value of the variables in p.u. Simulated
annealing works well, as an optimizing tool, for global search within the search space
created by the bounds of the variables [11, 12]. The optimality is reached through
two thousand iterations without violating the constraints [13].

7 Conclusion

The output parameters are shown in Table 3, which are capacitive reactance, and
generated voltage per phase in p.u for different machines. Optimized results are
obtained by varying three function variables namely, load (0.5–1.3 p.u), frequency
Optimal Value of Excitation of Self-excited Induction … 177

Table 3 Optimized output

Machine rating (kW) (p.u) Xc Vg
4.0 0.3688 1.782
7.5 0.3500 1.720
15 0.4270 1.680
37 0.5779 1.620

(1.3–1.6 p.u) and speed (0.5–1.3 p.u) [14, 15]. The generated voltage is determined
in each case by using Eq. (2).
To show the variation of excitation and output voltage per phase, two graphs have
been plotted and shown in Fig. 5 with different rating of the machine. The results for
4 kW machine give the minimum excitation of 0.3688 p.u.
Figure 5 shows two lines, blue and red in colour. The red colour represents the
variation of output voltage in p.u. against rating of the machines in kW*10 scale.
The graph shows that output voltage firstly decreases and then almost remains
constant with the machine rating. The blue line shows the variation of excitation in
p.u. against rating, which is almost flat initially and then increases when the rating
increases.

Fig. 5 Excitation and 1.8

frequency with m/c rating for Excitati on
optimal excitation output v oltage
1.6

1.4

1.2
Plot of Excitation & output Voltage
1

0.8

0.6

0.4

0.2
0 0.5 1 1.5 2 2.5 3 3.5 4
KW*10(Machine rating)
178 W. Balow et al.

Appendix: Constants of Objective Function for 4 kW

Machine

A  0.1010604, B  −0.050717, C  0.03513, D  0.2564, E  0.001714, K 

1.0642 p.u, Xm  1.35 p.u

References

1. S. Vadhera, K. Sandhu, Genetic algorithm toolbox based investigation of terminal voltage and
frequency of self excited induction generator. Int. J. Adv. Eng. Appl. 1(1), 243–250 (2010)
2. R.C. Bansal, Three phase self-excited induction generators-An overview. IEEE Trans. Energy
Convers. 20(2), 292–299 (2005)
3. L. Sridhar, B. Singh, C.S. Jha, B.P. Singh, S.S. Murthy, Selection of capacitors for the self-
regulated short shunt self-excited generator. IEEE Trans. Energy Convers. 10(1), 10–17 (1995)
4. B.I.J. Nagrath, D.P. Kothari, Electrical Machines, 2nd edn. (Tata McGraw-Hill, New York,
1997)
5. S.K. Jain, J.D. Sharma, S.P. Singh, Transient performance of three-phase self-excited induction
generator during balanced and unbalanced faults. IEE Proc. Gener. Trans. Distrib. 149(1), 50–57
(2002)
6. T.F. Chan, Analysis of self-excited induction generators using an iterative method. IEEE Trans.
Energy Convers. 10(3), 502–507 (1995)
7. E.D. Besant, F.M. Potter, Capacitor excitation for induction motors. AIEE Trans. 54, 540–545
(1935)
8. M.H. Haque, A novel method of evaluating performance characteristics of a self-excited induc-
tion generator. IEEE Trans. EC 24(2), 358–365 (2009)
9. L.A. Alolah, M.A. Alkanhal, Optimization-based steady state analysis of three phase self-
excited induction generator. IEEE Trans. on Energy Conversion 15(1), 61–65 (2000)
10. R. Basak, H. Yahoui, N. Siauve, Study of optimal excitation of self-excited Induction generators
by genetic algorithm. IJSRD-Int. J. Sci. Res. Dev. 4(12), 590–593 (2017)
11. L. Wang, J.Y. Su, Dynamic performance of an isolated self-excited induction generator under
various loading conditions. IEEE Trans. EC-14(1), 93–100 (1999)
12. A.H. Al-Bahrani, N.H. Malik, Voltage control of parallel operated self-excited induction gen-
erators. IEEE Trans. EC-8(2), 236–242 (1993)
13. A. Nejmi, Y. Zidani, M. Naciri, Investigation on the self excited induction generator provided
with a hydraulic regulator, in FIER (2002), pp. 494–499
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applications: A review, in Proceedings of 24th National Renewable Energy Conversion, Bom-
bay, India, Nov. 30/Dec. 2, 2000, pp. 462–467
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a remote area power supply. Int. J. Renewable Energy Eng. 2(1), 234–239 (2000)
Different Setting of Unified Power Flow
Controller (UPFC) and Its Effect
on Performance of Distance Relay

Rajib Sadhu and P. S. Bhowmik

1 Introduction

For efficient power supply from generating station to load-centers with high reliabil-
ity, inter-connection of grids is not solely sufficient to provide satisfactory transmis-
sion line capacity. Again the available capacity of the line is confined within a limit
due to the cost of transmission, line losses and various other economic and environ-
mental factors. These factors also restrict up-gradation of network by construction
of new transmission lines. Thus to keep an optimum balance between quality and
reliability of service, new technologies should be welcomed. Advancement in the
field of Power Electronics and Semiconductor devices has made power engineers
to propose FACTS (Flexible AC Transmission System) as an alternative solution.
It will help in controlling power as well as enhance the usability of available and
planned lines. Installation of FACTS devices adds more complexity to the network
and also affects the performances of distance relay and other protective devices in the
network. Under a fault condition, transients superimposed on the power frequency
voltage and the current waveforms can significantly differ from a system without
FACTS devices.
The Unified Power Flow Controller is the most versatile FACTS device and it
consists of two voltage source converters, using gate turn-off (GTO) thyristor valves.
Out these converters, one is shunt type (STATCOM) and other is series type (SSSC),
and they are connected through a common dc storage capacitor. SSSC provides the

R. Sadhu (B)
Department of Electrical Engineering,
University Institute of Technology, Bardhaman, West Bengal, India
e-mail: rajib_sadhu@rediffmail.com
P. S. Bhowmik
Department of Electrical Engineering,
National Institute of Technology, Durgapur, West Bengal, India
e-mail: psbhowmik@ee.nitdgp.ac.in

© Springer Nature Switzerland AG 2019 179

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_16
180 R. Sadhu and P. S. Bhowmik

main function of the UPFC by injecting an ac voltage with controllable magnitude

and phase angle. This injected voltage can be considered essentially as a synchronous
ac voltage source. The real and reactive power flow can be controlled by this type of
arrangement. The basic function of STATCOM is to supply or absorb the real power
demanded by SSSC at the common dc link. STATCOM can also generate or absorb
controllable reactive power, if it is desired, and thereby it can provide independent
shunt reactive compensation for the line [1].
Amongst some of the research work carried over impact of various FACTS device
on distance relays, the study carried out in [2–6] shows the effect of STATCOM on
distance relay under different fault conditions, fault locations and system configura-
tions.
The impacts of SSSC on measured impedance at relay point for different fault
location are discussed in [7–9].
Zhou et al. in [10] have presented analytical and simulation results of the applica-
tion of distance relays for the protection of transmission systems employing FACTS
device such as the unified power flow controller (UPFC) and how the performance
of distance relay influenced by the UPFC for single-phase-earth and phase-phase
faults.
Apparent impedance calculation procedure for digital distance relay of transmis-
sion line involving UPFC and its effects on the trip boundaries for the locations
are observed in [11–15]. A new cross-differential protection algorithm for parallel
transmission lines including UPFC in one of the lines is presented in [16]. Moravej
et al. in [17] analyzes the distance relay performance during power swing conditions
for an uncompensated and compensated transmission line with a UPFC.
All the studies discussed so far clearly show that the performance of distance
relays is greatly affected by STATCOM and SSSC operating simultaneously (UPFC)
or individually. At the time of fault voltage and current injection of these devices
will affect both the steady and transient components of voltage and current. For this
apparent impedance of system without FACTS devices and with FACTS devices seen
by a conventional distance relay will be different.

2 Proposed Model

2.1 Model of Transmission Line with UPFC

An uncompensated 132 kV transmission line of a typical power system network is

taken for simulation study, corresponding single line diagram of the model with VSC
based FACTS device like UPFC is shown in the Fig. 1. Two 200 km parallel 132-kV
transmission lines with two 6000-MVA short-circuit levels (SCLs) sources and the
angle difference between them is 20°.
The two lines have same line parameters. The line positive and negative sequence
impedance is 0.0255 + j0.352 /km. The line zero sequence impedance is 0.3864 +
Different Setting of Unified Power Flow Controller (UPFC) … 181

Fig. 1 Single line diagram

j1.5556 /km. Shunt connected converter of UPFC named as STATCOM, it uses

one 48-pulse voltage source converter which connects with two 2000 µF series DC
capacitors. The shunt connected convert injects or consumes reactive power from
the transmission line to regulate the voltage at the connecting point. The series part
of UPFC or SSSC injects an almost sinusoidal voltage of variable magnitude and
angle, in series with the transmission line to regulate the power flow through the
transmission line.

2.2 STATCOM and SSSC Model Using 48-Pulse VSC

Static synchronous compensators (STATCOM) using Multi-pulse converters gener-

ally based on elementary six-pulse GTO—VSC (gate turn off based voltage source
converter). Practically, a quasi-harmonic 48-pulse (4 × 12pulse) configuration is used
with the phase angle control algorithm employing proportional and integral (PI)
control methodology with a phase displacement of 7.5º. It can be shown that the
fundamental component of the output voltage of a quasi-48 pulse converter is given
by.
√ π  π 
2 2
E 1,48  4 · Vdc cos cos (1)
π 24 48
The harmonic component of order h is given by,
√    
2 2 hπ hπ
E h,48  4 · V d c cos cos ; h  12k ± 1, k  1, 2, 3, . . . (2)
π 24 48

It is observed that the DC bus (V dc ) is connected to the four 3-phase inverters.

The four voltages generated by the inverters are applied to secondary windings of
182 R. Sadhu and P. S. Bhowmik

four zig-zag phase-shifting transformers connected in Wye (Y) or Delta (D). The
four transformer primary windings are connected in series and the converter pulse
patterns are phase shifted so that the four voltage fundamental components sum in
phase on the primary side.
Each 3-level inverter generates three square-wave voltages which can be +V dc , 0,
−V dc . The duration of the +V dc or −V dc level can be adjusted between 0° and 180° by
varying the conduction angle (σ ) of the Firing Pulse Generator. Each inverter uses a
Three-Level Bridge block where specified power electronic devices are GTOs. Each
leg of the inverter uses 3 ideal switches to obtain the 3 voltage levels (+V dc , 0, −V dc ).
Except for the 23rd and 25th harmonics, this transformer arrangement neutralizes
all odd harmonics up to the 45th harmonic. Y and D transformer secondary cancel
harmonics 5 + 12n (5, 17, 29, 41, …) and 7 + 12n (7, 19, 31, 43, …). In addition,
the 15° phase shift between the two groups of transformers allows cancellation of
harmonics 11 + 24n (11, 35, …) and 13 + 24n (13, 37, …).Considering that all 3n
harmonics are not transmitted by the transformers (delta and ungrounded Y), the
first harmonics that are not cancelled by the transformers are therefore the 23rd,
25th, 47th and 49th harmonics. By choosing the appropriate conduction angle for
the three-level inverter (σ  172.5°), the 23rd and 25th harmonics can be minimized.
The first significant harmonics generated by the inverter will then be 47th and 49th.
SSSC model employing 48-pluse GTO based VSC is same as STATCOM only
change is there for variable amplitude of injected voltage conduction angle is not
fixed.

2.3 Apparent Impedance Calculation for Distance Relay

This calculation is generally based on symmetrical component transformation by the

use of power frequency components of current and voltage signals, which is measured
at relay point. In this calculation, certain assumptions are performed beforehand such
as signal acquisition, pre-processing, and sequence component calculations.
When a single phase to ground fault occurs on the transmission line and the
distance between the fault point and the relay point is p × L, then at the time of fault
the positive, negative and zero sequence networks of the system are as shown in
Fig. 2.

V1  I1 0.5Z 1 + Vi j1 + Il1 ( p − 0.5)Z 1 + R f I f 1 (3)

V2  I2 0.5Z 1 + Vi j2 + Il2 ( p − 0.5)Z 1 + R f I f 2 (4)
V0  I0 0.5Z 0 + Vi j0 + Il0 ( p − 0.5)Z 0 + R f I f 0 (5)
Il1  I1 + Ii j1 (6)
Il2  I2 + Ii j2 (7)
Il0  I0 + Ii j0 (8)
Different Setting of Unified Power Flow Controller (UPFC) … 183

Fig. 2 a Positive sequence network. b Negative sequence network. c Zero sequence network of
the system from the relay location to fault

where, V 1 , V 2 , V 0 are the sequence phase voltages at the relay location. V ij1 , V ij2 , V ij0
are series sequence phase voltages injected by SSSC. I 1 , I 2 , I 0 are sequence phase
currents at the relay location. I l1 , I l2 , I l0 are sequence phase currents in transmission
line. I f1 , I f2 , I f0 are sequence fault currents. I ij1 , I ij2 , I ij0 are shunt sequence phase
currents injected by SATCOM. Z 1 , Z 0 are sequence impedance of the transmission
line. p is per-unit distance of a fault from the relay location. From above, the voltage
at the relay point can be derived as

V  p I Z 1 + p I0 (Z 0 − Z 1 ) + Iij ( p − 0.5)Z 1 + ( p − 0.5)Iij0 (Z 0 − Z 1 ) + Vi j + R f If

(9)

where,

V  V1 + V2 + V0 (10)
I  I1 + I2 + I0 (11)
Iij  Ii j1 + Ii j2 + Iij0 (12)
184 R. Sadhu and P. S. Bhowmik

Vi j  Vi j1 + Vi j2 + Vi j0 (13)

In the transmission system without UPFC, for a single phase-to-ground fault, the
apparent impedance of distance relay can be calculated using the equation
V V
Z Z 0 −Z 1
 (14)
I+ Z1
× I0 Ir

where, V , I phase voltage and current at relay point. I 0 is zero sequence phase current.
I r is the relaying current.
If this conventional distance relay is applied to the transmission system with
UPFC, the apparent impedance seen by this relay can be expressed as,

Iij Ii j0 Vi j If
Z  p Z1 + Ir (
p − 0.5)Z 1 + Ir (
p − 0.5)(Z 0 − Z 1 ) + Ir
+ Ir
Rf (15)

In practice, one side of the shunt transformer is in delta connection, and thus there
is no zero sequence current injected by STATCOM, so, I ij0  0, then the equation
can be rewritten as
Iij Vi j I f
Z  p Z1 + ( p − 0.5)Z 1 + + Rf. (16)
Ir Ir Ir

From the above, it is observed that the impact of UPFC on the apparent impedance,
can be divided two parts; one results from the shunt current STATCOM and another
is the impact of the series voltage injected by the SSSC; the last part of the apparent
impedance is due to the fault resistance.
Now, if the UPFC working as STATCOM only, the apparent impedance seen by
relay is given by,
In general, one side of shunt transformer has a delta connection, as a result there
is no zero sequence current injected by STATCOM, so Iij0  0. So, the modified
equation is
Iij If
Z  p Z1 + ( p − 0.5 Z 1 ) + Rf (17)
Ir Ir

When solid single phase to ground fault occurs, then the equation become,
Iij
Z  p Z1 + ( p − 0.5 Z 1 ) (18)
Ir

For SSSC, the apparent impedance seen by relay is given by,

Vi j If
Z  p Z1 + Ir
+ Ir
Rf (19)
Different Setting of Unified Power Flow Controller (UPFC) … 185

2.4 Relay Model

The flowchart shown in Fig. 3 gives the procedure to calculate the apparent impedance
for drawing apparent impedance trajectory. The relay point three phase current and
voltage phasors are sent to current and potential transformers (CT and PT) respec-
tively where they are scaled down to acceptable voltage levels for the subsequent
process. ‘Signal Conditioner’ converts these signals into a form that can be converted
to digital values. ‘Sample and Hold circuit’ samples time varying analog signals and
holds the instantaneous sample values constant during conversion period of ‘Analog
to Digital Converter’ (ADC). ADC converts these samples to equivalent numerical
values and outputs in binary. In ‘Fourier Transform’, fast Fourier transform (FFT) is
used to extract fundamental frequency components from the post-fault relaying sig-
nals and remove dc offset from signals. The output is used for ‘Apparent Impedance
calculation’ Z. Real (R) and imaginary (X) components of Z are obtained and used
for drawing apparent impedance trajectory.

3 Result Analysis

Simulation is carried out with step length of 0.02 ms. A single phase to ground (SLG)
fault is introduced at 150 km distance from source 1 in the second transmission line.

Fig. 3 Flowchart of distance

relay
186 R. Sadhu and P. S. Bhowmik

The UPFC is connected between buses B1 and B2 and it can act in STATCOM, SSSC
or UPFC mode. The distance relay is connected after bus BS .

3.1 Statcom Results

UPFC is operated in STATCOM mode for voltage control with V ref = 1 pu. STATCOM
adjusts the three phase voltages and currents in such a way that line voltage remains
constant at 1 pu. Also during fault, the line voltages have remained close to Vref
due to lagging current injection on healthy phases and leading current injection on
faulty phase by the device, reducing voltages for higher current of healthy phases
and increasing voltage for reduced current of faulty phase. In this manner it controls
system voltage.
Figure 4 shows when the system is working under no-load with STATCOM, the
reactive power oscillates near zero axis with slight negative average value, employing
STATCOM is exchanging reactive power to maintain constant voltage. During fault,
the reactive power nearly doubles (80 MVAr) system reactive power (40 MVAr)
indicating STATCOM lagging power injection to maintain line constant voltages.
For introduction STATCOM two things happened. They are,
1. Voltage control—The voltage of the power system remains almost constant at
1.0 pu and phase displacement between all the buses is reduced. These things are
observed even during fault.

Fig. 4 Reactive power injunction by STATCOM

Different Setting of Unified Power Flow Controller (UPFC) … 187

2. Reactive power control—Due to inclusion of STATCOM, at no fault system

reactive power oscillates around uncompensated system no fault reactive power
implying STATCOM power exchange to maintain constant line voltage. Also it
injects extra power during fault to keep up bus voltage at reference value.
From Figs. 5 and 6 it is observed that during fault, apparent resistance decreases
and apparent reactance increases for STATCOM. The apparent resistance starts from
higher value (~40 ohms) for STATCOM than uncompensated line (~30 ohms). Also
apparent reactance steady value is greater (~60 ohms) from uncompensated system
(~40 ohms).
Figure 7 shows the apparent impedance trajectory of the uncompensated system
and STATCOM compensated system and relay characteristics. Clearly, the really
detects fault in case of uncompensated system but with STATCOM the R-X trajectory
goes outside the circle, thereby under-reaching the relay and it does not trip. So with
STATCOM, relay settings should be adjusted.

3.2 SSSC Results

By selecting SSSC mode from UPFC settings (controlling series connected GTO
converter) and choosing SSSC injected voltage V ij in p.u results show comparatively
least effect than STATCOM in Figs. 5, 6 and 7 respectively.

Fig. 5 Apparent resistance trajectory

188 R. Sadhu and P. S. Bhowmik

Fig. 6 Apparent reactance trajectory

Fig. 7 Mho-relay characteristics and apparent impedance trajectory

Different Setting of Unified Power Flow Controller (UPFC) … 189

3.3 UPFC Results

In UPFC mode by controlling both shunt and series connected GTO converters
simultaneously and setting UPFC active power reference Pref and reactive power
reference Qref in p.u within a given boundary, UPFC can control both active and
reactive power flow also the voltage of the system. Figures 5 and 6 shows UPFC
has more adverse effect on distance protection relay operation than STATCOM or
SSSC. Also in Fig. 7 for UPFC, the impedance trajectory goes very much outside of
the circle and relay under-reach occurs more.

4 Conclusion

STATCOM, SSSC and UPFC always help to improve power system efficiency by
controlling system current, voltage and power. Though they help the power system
but they always have harmful effect on reliability of the distance protection schemes.
STATCOM in voltage control mode, keep the bus voltage nearly constant by reduc-
ing the faulted phase current during fault. SSSC can transfer desired active power
through the line under fault condition in voltage injection mode. Incorporation of
UPFC with power (active and reactive) flow control, desired (within a limited range)
active and reactive power can be transferred through line with medium varying sys-
tem conditions (for faults reactive power becomes uncontrollable). As a result the
apparent resistances for STATCOM and UPFC connected systems start from higher
value than uncompensated system, for SSSC apparent resistance starts from nearly
same value as in uncompensated system but attain slightly higher value than uncom-
pensated system in steady state for STATCOM and SSSC, and very high value for
UPFC. Apparent reactances for these compensated networks start from nearly same
value as in uncompensated system but attain higher and very higher steady state val-
ues for STATCOM and UPFC respectively and more or less same value for SSSC.
Within UPFC, STATCOM and it-self have greater effect on apparent resistance and
reactance hence it is observed in impedance trajectory more than SSSC. Employ-
ment of these FACTS devices causes distance relay to under-reach in this study and
the relay settings have to be reconsidered. The results thus obtained significantly
show that the performance and characteristics of a distance relay under fault or nor-
mal conditions significantly depend upon the presence of FACTS devices, their type
and control parameters setting. Hence, study of the effects of FACTS devices laid
upon the performance of distance relays is of paramount importance for ensuring
satisfactory and reliable operation of the system.
190 R. Sadhu and P. S. Bhowmik

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controller. Electric Power Syst. Res. 54(3), 189–198 (2000)
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tion, in IEEE Power and Energy Society General Meeting-Conversion and Delivery of Electrical
Energy in 21st Century, 2008
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in double-circuit lines, IEEE Power and Energy Society General Meeting, 2009
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via UPFC from distance relay point of view, in Transmission and Distribution Conference and
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Assessment of Discrimination Between
Fault and Inrush Condition of Power
Transformer by Radar Analysis
and Wavelet Transform Based Kurtosis
and Skewness Analysis

Sushil Paul, Shantanu Kr Das, Aveek Chattopadhyaya

and Surajit Chattopadhyay

1 Introduction

In ever increasing power system scenario power transformer plays a vital role for
proper and reliable operation of power system. Being one of the most important
components of power system, power transformer needs adequate protection for its
proper operation. When a transformer in unloaded or lightly loaded condition is
connected to a power supply, then a large transient current may appear due to flux
asymmetries and saturation in the core of the transformer which is known as inrush
current [1]. Inrush current decays very fastly for few cycles then it varies slowly.
Inrush current may take 4–6 s to subside. There are some factors which affect mag-
nitude and duration of inrush current, like (i) residual flux in the transformer (ii) type
of magnetic material which is used in the core (iii) size of power system (iv) size
of transformer (v) switching instant of energization of the transformer [1]. Inrush
current of transformer may be divided into three categories: energization inrush,
recovery inrush, sympathetic inrush [1]. Simple model has been proposed to sim-

S. Paul (B) · S. K. Das · A. Chattopadhyaya

Department of Electrical Engineering, SKFGI, MAKAUT, Kolkata, West Bengal, India
e-mail: sushilpaul28@gmail.com
S. K. Das
e-mail: shantanu.das95@gmail.com
A. Chattopadhyaya
e-mail: aveek_chatterjee40@yahoo.com
S. Chattopadhyay
Electrical Engineering Department,
Ghani Khan Chaoudhury Institute of Engineering and
Technology (Under Ministry of HRD, Government of India),
Malda, West Bengal, India
e-mail: surajitchattopadhyay@gmail.com

© Springer Nature Switzerland AG 2019 191

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_17
192 S. Paul et al.

ulate the magnetizing inrush current of transformers using real-time measurements

and then simulation data used for harmonic analysis [2]. Different techniques have
been proposed by different researchers to assess the inrush current. Hidden Markov
Model (HMM) based method proposed in [3], to detect inrush current of power trans-
former. Three factors like the conventional second harmonic content, the decaying
DC time constant, and the ratio between the fundamental component and the first
peak magnitude based dynamic filter has been proposed to identify inrush current and
fault current of power transformer [4]. Correlation coefficient between the sampling
waveform based method proposed in [5] to discriminate between inrush current and
fault current of power transformer. Inrush current plays a vital role in differential
protection of power transformer. Phase angle difference between primary and sec-
ondary current based method proposed by the authors to avoid unwanted tripping of
differential protection on magnetizing inrush current [6]. In [7], authors proposed a
method distinguish between inrush currents and internal faults based on the differ-
ential current gradient. Different signal processing techniques and soft computing
techniques used by the researchers to assess the inrush current of power transformer.
Wavelet Transform (WT) based feature has been extracted in [8], to identify the
inrush and fault current of power transformer. Median Absolute Deviation (MAD)
of wavelet coefficients based method proposed by the researchers to distinguish of
different nature of currents of power transformer where five level of decomposition
have been considered in DWT decomposition [9]. WT and correlation coefficient
based method proposed in [10] to discriminate between inrush and fault current.
S-transform based technique used as another signal processing based technique to
assess inrush and fault current [11, 12], where in [12] probabilistic neural network
used as a classifier for classification of inrush and fault current. Slantlet transform
(S-transform) and Artificial Neural Network (ANN) based method used for classi-
fication of over current and inrush current of power system where ANN used as a
classifier [13]. Back propagation algorithm based ANN has been used as a tool to
discriminate between inrush and fault current of power transformer [14]. Multi reso-
lution analysis and space vector analysis based method proposed in [15] for solution
of dilemma of fault and inrush current of power transformer. WT and PNN based
method proposed as another technique to assess inrush current [16], where EMTP
simulation has been used to simulate inrush current along with other transients cur-
rent for this purpose. Fuzzy and neuro fuzzy based approach have been proposed by
the researchers to distinguish inrush current from fault current in power system [17,
18]. To analyze the abnormal condition of electrical systems some techniques based
on Clarke and Park plane have been proposed by the researchers [19–23]. Radar
analysis, FFT and THD based approach proposed in [24] to discriminate between
inrush and fault current of power transformer.
None of the research works, inrush and fault condition of power transformer has
been assessed by the CWT, Radar analysis and DWT based skewness, kurtosis, rms
and mean value analysis. For this reason an attempt has been made to discriminate
between inrush and fault condition of power transformer based on CWT, Radar
analysis and DWT based skewness, kurtosis, rms and mean value analysis. Different
feature patterns have been observed in CWT and Radar analysis and DWT based
Assessment of Discrimination Between Fault and Inrush Condition … 193

different parameters values have been noted of primary current of power transformer
in different conditions form there inrush and fault conditions of power transformer
have been assessed.

2 Model for Simulation of Inrush and Fault Current

of Power Transformer

Two MATLAB models [25] have been prepared to simulate inrush and inrush with
fault condition in a three phase power transformer which are depicted in Figs. 1
and 2 respectively. A three phase two winding 6.3 MVA, 33/11 kV, 50 Hz power
transformer has been connected to three phase source of 33 kV through a three phase
circuit breaker. Primary current values of three phase transformer have been stored in
workspace after the sampling. All the three phases, which were initially open, were
closed at a transition time of 0.1 s by the three phase breaker. Sampling time was
taken as 50e-6 s (available in MATLAB) for the analysis. Using two models three
different conditions have been created which are, normal condition, inrush condition
and short circuit fault with inrush condition. In all the cases primary side current of the
transformer have been used for assessment of inrush condition of power transformer.

3 Wavelet Transform (WT) Analysis

To analyse non-stationery signal in better ways WT was introduced [26, 27]. WT is

used to get better time frequency representation from a non-stationery signal which
was the limitation of Fourier Transform (FT) and Short Time Fourier Transform
(STFT). Different signals aspects like trends, breakdown points, discontinuities etc.

Fig. 1 MATLAB model for simulation—of inrush current of transformer

194 S. Paul et al.

Fig. 2 MATLAB model for—simulation of fault current of transformer

can be analysed by WT from a particular signal. It can be classified as (i) Continuous

Wavelet Transform (CWT) (ii) Discrete Wavelet Transform (DWT).
Continuous Wavelet Transform (CWT)
The formula of CWT, which is used to achieve time frequency representation
from a signal x(t) is defined as [26, 27],
  
1 t −τ
XWT(τ, s)  √ x(t) · ψ ∗ dt (1)
|s| s

The transformed signal XWT (τ, s) is a function of the translation parameter τ and
the scale parameter s. The mother wavelet is denoted as ψ (t) and the *(asterisk)
indicates the complex conjugate which is used in case of a complex wavelet. For
the CWT analysis, signal can be discretized arbitrarily without violating the Nyquist
criterion.
Discrete Wavelet Transform (DWT)
Calculation of wavelet coefficients at every possible scale is a fair amount of work
and it generates lots of data not only that, the computation of CWT may consume
significant amount of time and resources depending on the resolution required. In
DWT [26, 27], the signal which is to be analysed is passed through filters with
different cut off frequencies at different scales. In this work ‘db4’ is used as the
mother wavelet because it is compactly supported in time frame and this mother
wavelet is used to detect sudden jump or notch in the signal. Some parameters like
skewness, kurtosis, rms and mean values of approximation (approximate) coefficients
have been found out in all the cases after decomposed the signal by ‘db4’ based DWT.
Assessment of Discrimination Between Fault and Inrush Condition … 195

4 Assessment of Inrush, Normal and Fault with Inrush

Condition of Power Transformer

Different conditions of power transformer have been assessed by CWT, Radar anal-
ysis and DWT based parameter analysis which is given below.

4.1 Results and Observation of Continuous Wavelet

Transform (CWT)

Figures 3, 4, 5 and 6 are used to depict the result of CWT of R-phase primary current
of power transformer in different conditions. In short circuit conditions CWT result of
R phase current is almost same where as in inrush and normal condition it is different
in nature. Different critical areas have been observed in different CWT results and
observing the feature pattern of the CWT results, normal, inrush and short circuit
conditions of power transformer can be discriminated properly.

Critical Area

Fig. 3 CWT of R-phase primary current under inrush condition

196 S. Paul et al.

Critical Area

Fig. 4 CWT of R-phase primary current under normal condition

Critical Area

Fig. 5 CWT of R-phase primary current under inrush with short circuit fault (L-L-L) condition

4.2 Discrete Wavelet Transform (DWT)

The main disadvantage of CWT is that, it generates lots of data which sometimes
very cumbersome to properly handle it. For this reason in this work DWT based
parameter analysis has been done to discriminate normal, inrush and fault conditions
of power transformer which is very easy to implement to detect and discriminate
Assessment of Discrimination Between Fault and Inrush Condition … 197

Critical Area

Fig. 6 CWT of R-phase primary current under inrush with short circuit fault (L-G) condition

those conditions. Kurtosis, skewness, rms and mean values have been found out
of R phase primary current in different conditions to detect different conditions of
power transformer. Skewness [28] can be mathematically defined as the averaged
cubed deviation from the mean divided by the standard deviation cubed where as
kurtosis [28] is used as an indicator in distribution analysis as a sign of flattening or
“peakedness” of a distribution.

4.2.1 Assessments of DWT Based Parameter Analysis of R Phase

Current

Figure 7 is used to depict the results of DWT based kurtosis values of approximate
coefficients in normal, inrush and short circuit fault conditions of power transformer.
In this figure constant and clear differences of kurtosis values have been observed
in three different conditions where maximum difference have been observed from
DWT decomposition level 8–9.
Maximum and constant differences have been observed of DWT based mean
values of approximate coefficients in all those mentioned conditions which are shown
in Fig. 8.
Figure 9 is used to show the results of DWT based rms values of approximate
coefficients in normal, inrush and short circuit fault conditions, where differences
are maximum up to DWT decomposition level 7 then it is decreasing in nature.
Figure 10 depicts the result of DWT based skewness values of approximate coef-
ficients of R phase primary current in different conditions. One distinct feature has
198 S. Paul et al.

Fig. 7 Kurtosis values of approximate coefficients for normal, inrush, LLL fault and LG fault
condition of R phase current

Fig. 8 Mean values of approximate coefficients for normal, inrush, LLL fault and LG fault condition
of R phase current

been observed that, up to DWT decomposition level 6 skewness values of R phase

current in inrush and fault conditions is same then it is increasing in nature where as
maximum difference of skewness values in three conditions have been observed in
DWT decomposition level 9.
Assessment of Discrimination Between Fault and Inrush Condition … 199

Fig. 9 Root mean square values of approximate coefficients for normal, inrush, LLL fault and LG
fault condition of R phase current

Fig. 10 Skewness values of approximate coefficients normal, inrush, LLL fault and LG fault con-
dition of R phase current
200 S. Paul et al.

Fig. 11 Radar chart of R

phase primary current in
inrush condition

Fig. 12 Radar chart for R

phase primary current in
normal condition

4.3 Radar Analysis

Radar analysis has been done of R phase current at inrush, normal and fault conditions
after taking the primary currents of power transformer which are shown in Figs. 11,
12 and 13, where clear difference of pictorial representation has been observed in
those figures; from there inrush normal and fault conditions can be discriminated
properly.
Assessment of Discrimination Between Fault and Inrush Condition … 201

Fig. 13 Radar chart for R

phase primary current in
different fault (L-L-L and
L-G) conditions

5 Algorithm of Assessment of Different Conditions

of Power Transformer

An algorithm for assessment of different conditions of power transformer has been

made as follows which can be implemented in numerical protection of power trans-
former:
(a) Step down the three phase primary currents of power transformer through current
transformer
(b) Sample them at proper sampling frequency
(c) Capture the sampled values through data acquisition system
(d) Apply CWT and Radar analysis on the captured signal
(e) Determine skewness, kurtosis, rms and mean values of approximation (approx-
imate) coefficients from DWT decomposition levels (up to 9th level).
(f) Diagnose the results to assess different conditions of power transformer.

6 Specific Outcome

Normal condition, Inrush condition and short circuit fault condition of power trans-
former have been assessed by Radar analysis, CWT and DWT based skewness,
kurtosis, rms and mean value analysis of approximation coefficients based tech-
nique. Different patterns have been observed in CWT and Radar analysis of primary
current of power transformer in different conditions and different parameters values
have been noted in DWT based parameter analysis of ‘R’ phase primary current of
202 S. Paul et al.

power transformer from where all these three conditions of power transformer have
been assessed properly.

7 Conclusion

In this paper, inrush, fault and normal condition of power transformer have been
discriminated by Radar analysis, CWT and DWT based skewness, kurtosis, rms and
mean value analysis based techniques. Different patterns have been observed for
all those conditions of power transformer in Radar analysis and CWT based tech-
niques from there different conditions of power transformer have been discriminated
properly. DWT based skewness, kurtosis, mean and rms values also calculated to
assess fault, inrush and normal condition of power transformer where approxima-
tion coefficients of DWT has been used for this purpose. Using all these parameters,
different conditions of power transformer have been assessed properly which can be
implemented for numerical protection of power transformer in real time applications.

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SCADA Based Real Time Reactive Power
Compensation Scheme for Assessment
and Improvement of Voltage Stability
in Power System

Kabir Chakraborty and Arghyadeep Majumder

1 Introduction

In present day, the topic voltage stability is taking a great collapses places around
the world. The recent power networks are undergrounding frequent modifications
and introducing extra complexity in the power networks from operation, stability,
control and protection point of view to meet up the ever-growing electrical consumer
requirement. The main difficulty which is linked with such a stressed network is
voltage instability [1]. In recent years a great deal of effort has been devoted to
analyse voltage stability of power network [2–6].
An electrical power network is supposed to go into a situation of voltage instability
when a disturbance results an unmanageable drop in voltage profile of load buses.
The cause behind this is the inability of the system to meet the increased reactive
power demand. Due to the lack of adequate reactive power in power networks when
the system experiences huge load demand and/or serious contingencies the voltage
instability occurs. During voltage instability, magnitude of some load bus voltages
decreases slowly and afterward quickly reaches the voltage collapse point. The major
voltage collapse occurrences are believe to be connected to heavily loaded systems
when necessary quantity of real and reactive power are not obtainable to preserve
standard voltage magnitudes of the network buses.
In this paper, a method for real time SCADA system has been suggested for reac-
tive compensation scheme in power system to assess and improve the voltage stability.
The system consists of measuring instruments for data acquisition, simulation soft-
ware for supervisory control and FACTS devices for reactive power compensation.

K. Chakraborty · A. Majumder (B)

Department of Electrical Engineering, Tripura Institute of Technology,
Narsingarh, Tripura, India
e-mail: arghyadeep.majumder@gmail.com
K. Chakraborty
e-mail: kabir_jishu@rediffmail.com
© Springer Nature Switzerland AG 2019 205
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_18
206 K. Chakraborty and A. Majumder

This system has been applied to a standard power network and load flow solution of
the network is obtained. Weakest segment of the power system has been find out by
dV/dQ indicator [2] values. Integrated Voltage Stability Indicator values has been
find out and compared with reactive power for different system conditions to evaluate
the voltage instability of power network. In addition, the operation of the system has
been shown with closed loop feedback algorithm for real time application.

2 Concept of Proposed Methodology

In Fig. 1 the measuring instruments of RTUs [3] are connected to the transmission
network. The data acquisition are done through this section. For real time implemen-
tation, real time data are needed from the measuring instruments but generally, these
data are not in Per Unit values. Generally, all the parameters are like line data, bus
data, impedances, resistance, reactance, half line charging etc. are calculated in Per
Unit values because Per Unit values do not change when they are referred to one side
of a transformer to other side of transformer.

Per Unit Value  Actual value/Base Value (1)

This can be a major advantage as because in a large power system huge numbers
of transformers are interconnected. That is why, to make complex power system cal-
culation more convenient all parameters are expressed in the same units irrespective
of their ratings.
Real time data can be converted to Per Unit Value through simulation using above
formula in Eq. (1). This information then can be fed to the ECC (Energy Control
Centre) for load flow solution purpose. For analysis purpose, the data is considered
for a particular instant of standard IEEE 6-bus power system. To solve any power
system problem load flow solution [4] must be solved and this is solved by simulation.

Fig. 1 Real time SCADA system

SCADA Based Real Time Reactive Power Compensation Scheme … 207

Fig. 2 Basic load flow diagram

The load flow in a power system has been shown in Fig. 2. Basic load flow
expression based on N-R method is given as
    
P J1 J2 ∂
 (2)
Q J3 J4 |V |

The value of ∂V/∂Q i.e. the variation of voltage with respect to reactive component
is highest for weakest bus of the system. So, it is required to find the highest value
of [∂V/∂Q] from J4 elements in the jacobian matrix.
Now, multi-bus electrical power network can be symbolized by an correspondent
two-bus system comprising of one slack bus having bus voltage magnitude Vs and
generated power (Pg + jQg ) is supplied along with one load bus having bus voltage
magnitude Vr and load (Pload + jQload ) is connected to this bus [1]. The line connected
these two buses having equivalent impedance Z eq . The active and reactive power
losses of the equivalent system are given by Eqs. (3) and (4)
 
Req Pg2 + Q 2g
Ploss  (3)
Vs2
 
X eq Pg2 + Q 2g
Q loss  (4)
Vs2

Integrated voltage stability indicator (IVSI) has been used for the detection of
weaker segment of the network using the equivalent system methodology. Based on
these quantities maximum transferred power, i.e., maximum values of reactive power
and the maximum values real power and reactive power loss of the transmission line,
the expressions for integrated voltage stability indicators can expressed in the Eqs. (5)
and (6) as
Pr Qr
I V S I (P)   (5)
Pr (max) Q r (max)
Pl Ql
I V S I (L)   (6)
Pl(max) Q l(max)
208 K. Chakraborty and A. Majumder

Since, voltage collapse is considered imminent when the value of IVSI is near or
equal to 1, the which means that smaller the value of IVSI more healthy is the system
state [1].

3 Simulation

A standard IEEE 6-bus power system has been taken for simulation purpose. The main
objective lies with Integrated Voltage Stability Indicator (IVSI) & dV/dQ indicator
values for formulation of the real time application. Load flow simulation results for
a particular instant are given as follows in Table 1.
To locate the weakest bus [6] in the network, the Jacobian Matrix (J) is computed
and [∂V/∂Q] value for all the load buses are calculated and shown in Table 2.
From this simulation, it is obtained that the ∂V/∂Q value is the highest for bus
no. 5 whose value is equal to 0.0653022. Therefore, bus no. 5 is the weakest bus
of the network [7] for that particular instant. The value of IVSI obtained from this
simulation is shown in the Table 3.
From this simulation, it is obtained that the IVSI value is closer to the 1. Bus
number 5 is the weakest bus of the system as the value of IVSI calculated for bus
number 5 in the IEEE 6-bus power system is greatest. Therefore, the system is
imminent to voltage collapse [8].
CASE STUDY-1: Change of ∂V/∂Q values and IVSI values with respect to reac-
tive compensation given to the weakest bus shown in Fig. 3.

Table 1 Load flow solution

Bus Voltage Angle Active power Reactive power
No. Per unit Radian Per unit Per unit
1 1.050 0.000 0.015 −0.485
2 1.080 −0.609 0.010 0.046
3 1.080 0.576 0.018 −0.137
4 1.076 0.469 −0.014 −0.006
5 1.083 −0.644 −0.012 −0.004
6 1.084 −0.658 −0.009 −0.004

Table 2 ∂V/∂Q values for weakest bus identification

Bus no. 4 5 6
∂V/∂Q Value 0.0635343 0.0653022 0.054249

Table 3 IVSI values IVSI (power) IVSI (loss)

0.744932 0.488930
SCADA Based Real Time Reactive Power Compensation Scheme … 209

For Condition-1 where no reactive compensation is provided [9], the IVSI value
(power) is quite high. In Condition-2 a little amount of reactive power (0.3 pu) is
injected in the weakest bus. so the IVSI value (power) has been reduced. Further
reactive power injection is increased to 0.6 pu and the IVSI value (power) has been
decreased significantly as shown in condition 3. The system condition after further
increase of reactive compensation (equal or more than 0.6 pu) to the weakest is as
shown in condition 4.
CASE STUDY-2: Change of ∂V/∂Q values and IVSI values with respect to reac-
tive load connected to the weakest bus shown in Fig. 4.
In condition-1 small reactive load connected to the weakest bus. ∂V/∂Q values
& IVSI values (power) are very less. In condition-2 a larger reactive load (0.4 pu)
is linked to the weakest bus, now ∂V/∂Q value is increased little bit but IVSI value
(power) has been increased significantly. By connecting a large load (0.8 pu), as
shown in condition 3, to the weakest bus the voltage collapse is considered to be
more imminent because IVSI value (power) is very closer to the unity (i.e. 0.67).

1
∂V / ∂Q IVSI Reactive Comp.(P.U.)
0.8

0.6

0.4

0.2

0
Condition 1 Condition 2 Condition 3 Condition 4

Fig. 3 Change of ∂V/∂Q value and IVSI value with respect to reactive compensation given to the
weakest bus

0.9
∂V / ∂Q IVSI Reactive Load (P.U.)
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Condition 1 Condition 2 Condition 3

Fig. 4 Change of ∂V/∂Q value and IVSI value with respect to reactive load connected to the
weakest bus
210 K. Chakraborty and A. Majumder

Table 4 IVSI values before compensation

∂V/∂Q IVSI Reactive compensation
0.0653022 0.744932 0.00

Table 5 IVSI values after compensation

∂V/∂Q IVSI Reactive compensation
0.0652831 0.33631 0.25

4 Closed Loop Feedback Algorithm

From the above simulation results and case studies, it can be seen that reactive
compensation is correlated with ∂V/∂Q values and IVSI values. To apply in the real
time system it is required to use closed loop feedback algorithm, which is shown in
Fig. 1.
The reference point for IVSI value is considered as 0.35 that means if in real time
IVSI is equal or less then the reference value then the system will be considered as in
the safe state in terms of voltage stability [10]. The simulated result for a particular
instant show that the real time IVSI value as given in Table 4 is much higher than
the reference IVSI value 0.35.
Therefore, a new simulated program is required which will now calculate the
reactive compensation needed (supplied by FACTS devices) [11] for the system to
lower down the real time IVSI value equal or less than the reference IVSI value 0.35.
From Table 5, it can be observed that the reactive compensation given here is
0.25 in per unit [12] and indicator values are calculated by the simulated program.
Therefore, the new real time IVSI value is 0.33631, which is below or lower than
the reference IVSI value. This way, the system will continuously track the real time
data and simulated calculation; will try to keep real time IVSI value closer to the
reference IVSI value.

5 Conclusion

A SCADA based real-time reactive power compensation scheme has been presented
in the paper to assess and improve the stability in terms of bus voltage in multi-bus
power system using closed loop feedback algorithm.
Load flow solution and weakest segment of the electrical power network is
obtained. Integrated Voltage Stability Indicator (IVSI) value, which indicate the
system voltage stability is obtained and it has been reduced by reactive power com-
pensation given to the weakest bus of standard IEEE 6- bus system. The operation of
close loop feedback algorithm has been shown in this paper with IVSI values. Some
case studies are presented with IVSI and reactive compensation values. The per-
SCADA Based Real Time Reactive Power Compensation Scheme … 211

formance of the system depends upon data acquisition speed, software processing,
calculation and operation of FACTS devices.
This SCADA system will be very much helpful in ECC (Energy Control Centre)
for real time voltage stability control because ECC operator has to monitor only
parameter i.e. to keep real time IVSI value closer to the reference IVSI value. These
will ease the ECC operator stress and make voltage control operation more reliable.

References

1. K. Chakraborty, A. Chakrabarti, Soft Computing Techniques in Voltage Security Analysis

(Springer, Berlin, 2015)
2. K. Chakraborty, S.D. Biswas, An offline simulation method to identify the weakest bus and its
voltage stability margin in a multibus power network, in International Conference on Modelling
and Simulation, MS 2007, India, December 3–5, 2007
3. A. De, K. Chakraborty, A. Chakrabarti, Classification of power system voltage stability con-
ditions using Kohonen’s self-organising feature map and learning vector quantization. Euro.
Trans. Electr. Power 22(3), 412–420 (2012)
4. P. Srikanth, O. Rajendra, A. Yesuraj, M. Tilak, K. Raja, Load flow analysis of IEEE 14 bus
system using Matlab. Int. J. Eng. Res. Technol. 2(5), 149–155 (2013)
5. K. Chakraborty, A. Chakraborty, A. De, Integrated voltage stability indicator based assessment
of voltage stability in a power system and application of ann. Iranian J. Electr. Comput. Eng.
10(2), 85–92 (2011)
6. K. Chakraborty, B. Saha, S. Das, A method for improving voltage stability of a multi-bus power
system using network reconfiguration method. Int. J. Electr. Eng. 8(1), 91–102 (2015). ISSN
0974-2158
7. P. Gao, L. Shi, L. Yao, Multi-criteria integrated voltage stability index for weak buses identifica-
tion, in Transmission & Distribution Conference and Exposition: Asia and Pacific, ISBN: 978-
1-4244-5230-9, 2009
8. M.S.S. Danish, A. Yona, T. Senjyu, A review of voltage stability assessment techniques with
an improved voltage stability indicator. Int. J. Emerging Electr. Power Syst. 16(2), 107–115
(2015)
9. P. Roy, P. Bera, S. Halder, P.K. Das, Reactive power sensitivity index based voltage stability
analysis to a real system. Int. J. Electron. Commun. Technol. (IJECT) 4(1), 167–169 (2013)
10. K. Chakraborty, A. De, A. Chakraborty, Assessment of voltage security in a multi-bus power
system using artificial neural network and voltage stability indicators. J. Electr. Syst. 6(4),
517–529 (2010)
11. A.K. Mohanty, Power system stability improvement using facts devices. Int. J. Mod. Eng. Res.
(IJMER) 1(2), 666–672 (2011)
12. S. Dudhe, Reactive power compensation techniques in transmission lines. Int. J. Recent Inno-
vation Trends Comput. Commun. 3(5), 3224–3226 (2015). ISSN: 2321-8169
Part III
Energy
Solar Photovoltaic Power Supply
to Utility Grid and Its Synchronization

Sonalika Dutta, Soumya Kanti Bandyopadhyay

and Tapas Kumar Sengupta

1 Introduction

SPV roof top system is widely used in the world, employ as clean technology to
reduce CO2 emission. Whenever SPV roof top system is connected to grid for supply
power in grid, it needs a grid connected inverter to couple with grid. In this paper
discusses about multistage grid connected inverter due to the SPV generated voltage
level is low as compare to the grid voltage. Grid connected inverter is also named
as grid tie inverter (GTI). The applications are in net metering, dual metering, SPV
without use battery storage system. The multistage inverter consists with two stage
converter (a boost converter, a dc-dc converter with high frequency transformer)
and a grid connected inverter. A LCCL filter is connected between GTI and utility
grid to reduce harmonic distortion. By using PLL control technique of GTI, reduce
complexity and it more reliable for synchronization. The Grid connected inverter is
nothing but an H- Bridge single phase VSI inverter but its control mechanism is differ
from traditional inverter. The GTI and utility grid are synchronized by a special type
Phase locked Loop (PLL) and is designed and verified by PSIM software.
PSIM is a platform for engineering simulation and design; for research, develop-
ment and application in various sectors i.e. power supply and generation, Noncon-
ventional generation, motor drives, power conversion and control systems. T. Lesster
has first developed the PSIM software in 1994, PSIM is capable to develop power

S. Dutta (B) · S. K. Bandyopadhyay · T. K. Sengupta

Department of Electrical Engineering,
Supreme Knowledge Foundation Group of Institutions,
MAKAUT, Kolkata, India
e-mail: sonalika.dutta.35@gmail.com
S. K. Bandyopadhyay
e-mail: soumya.bandyopadhyay@skf.edu.in
T. K. Sengupta
e-mail: tksg1948@yahoo.co.in
© Springer Nature Switzerland AG 2019 215
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_19
216 S. Dutta et al.

electronics simulation and design for various power electronic applications. Here the
circuit is developed PSIM 9.0 version which is shown in Fig. 1 and the graphical
results of this simulation shown in Figs. 3, 4, 5, 6, 7, 8, 9, 10 and 11. Moreover
by reducing components harmonic distortion is reduced, the size of LCCL filter is
reduced (Fig. 2).

2 DC-DC Converter

Multistage GTI topology is used for low voltage (12 V) SPV generation. First stage
is voltage increased by a boost converter. In second stage a dc-dc converter with high
frequency transformer is use to increase voltage further step. Now the circuit detail
is discussed in below.

Fig. 1 Simulation model of synchronized solar photo voltaic power supply to utility grid

Fig. 2 Simulation model

Subtractor circuit
Solar Photovoltaic Power Supply to Utility Grid … 217

Fig. 3 Output waveform of subtractor circuit

Fig. 4 Output waveform of comparator circuit

2.1 Boost Converter

The boost converter is a dc–dc step up converter. This converter is desired in here to
reduce turns ratio of transformer in next stage, otherwise leakage reactance increase
in transformer and switching of MOSFETs are affected [1]. The converter consist of
two solid state devices one is a MOSFET(M) switch and other is diode and energy
218 S. Dutta et al.

Fig. 5 Output wave form of demultiplexer for gate pulse of IGBT 1

Fig. 6 Output waveform of demultiplexer for gate pulse of IGBT 2

storage passive elements i.e. an Inductor and a filter capacitor. The filter capacitor
reduces the ripple output voltage. To get a steady state voltage applies a Zener diode
across voltage output.
Boost converter operates in two modes,
At mode 1, t  t1, inductor L charging at switch M is on. At that condition inductor
current raises initial value I1 to final value I2.
Solar Photovoltaic Power Supply to Utility Grid … 219

Fig. 7 Output wave form of demultiplexer for gate pulse of IGBT 4

Fig. 8 Output wave form of demultiplexer for gate pulse of IGBT 3

Vs  LI /t1 (1)

I L
t1  (2)
Vs
At mode 2, t  t2 , L discharge still MOSFET switch is open next at cycle.
In this cycle,
220 S. Dutta et al.

Fig. 9 Output waveform of grid tie inverter

Fig. 10 Output wave forms of grid tie inverter and utility grid

I L
t2  (3)
Va − Vs

The switching period T is found by from adding Eqs. (2) and (3)
I L Va 1
T  t1 + t2  and , T 
Vs (Va − Vs ) f
Solar Photovoltaic Power Supply to Utility Grid … 221

Fig. 11 Output waveforms of grid tie inverter and utility grid at when grid couple switches are
connected

From this we get switching frequency (f) of MOSFET switch in boost converter.

2.2 Full Bridge High Frequency Converter

The second stage of conversion is implied through a full bridge converter, a high
frequency (HF) step up transformer and a diode bridge rectifier. The full bridge
converter is H-bridge PWM inverter with faster MOSFET switches. The Switching
frequency high for matching the frequency of the HF transformer. The HF transformer
use for reduce the size, higher order harmonics and cost [2]. The output voltage of
transformer followed by the equation which is given below
N2
Vout  2 DVdc (4)
N1

Here D is the duty cycle of Switching element (here use MOSFET), NN21 the turn
ratio of transformer [3].
The ac output voltage fed in a full bridge diode rectifier to get dc regulated voltage.
A LC filter use to reduce ripple from dc output voltage.
222 S. Dutta et al.

3 Grid Connected Inverter with Filter

The interfacing between a SPV system and utility grid is by a Grid tie inverter. The
GTI play an important role when dc power resource is connected to an ac grid.
After analyzing all criteria for synchronization, the GTI connect with grid. The DC
voltage fed to inverter input from Diode Bridge rectifier. The basic difference from
conventional VSI inverter from GTI is in its control mechanism. The inverter consists
of four IGBT switches alien in two limb of inverter. Two switches of each limb is
operated at a time. The line commuted inverter is operated with grid reference [4]
which is consist of a close loop control system. The PWM gate pulses of IGBT
switches are generated by using an analog—digital combination circuit of PLL.
These pulses are controlled the inverter for grid synchronization. After match the
frequency, voltage amplitude and phase angle the inverter is switched to grid [5]
as per IEEE standard 1547.2 [6]. In between inverter and grid a LCCL filter is
placed to reduce harmonic contain and improve power quality of inverter output.
The Simulation model is shown in Fig. 1.

4 Control Technique of GTI Switching Devices

The most important part of this paper is the control technique of GTI. It is different
form PLL control of grid tie inverter. The analog and digital circuits generate the
pulses with reference of grid values. These pulses are the PWM pulse feed to gates
of IGBT switches as per need and directs by demultiplexer selector switches. The
control circuit consists of a subtrator, a comparator and a demultiplexer with two OR
gates.

4.1 Subtractor

The inputs of subtractor fed from grid and inverter. Grid and inverter phases are
synchronized (locked) here. The subtractor’s one input (+) voltage fed from grid and
other input (-) take voltage from Grid connected inverter output.
If all external resistors(R) have equal value, the output voltage is derived by using
‘superposition theorem’ [7].
First we take V2  0, V1 is only input source of op-amp, the circuit is now like
non inverting amplifier.
The output voltage

V01  V1 /2(1 + R/R)  V1 (5)

Solar Photovoltaic Power Supply to Utility Grid … 223

Similarly, the output V02 due to input V2 only, V1  0, can be express as inverting
amplifier i.e.

V02  −V2 (6)

Then the output voltage

V0  V01 + V02  V1 − V2 (7)

V1 is the grid voltage and V2 is the inverter output voltage.

4.2 Comparator

The comparator has a reference dc input and other is from phase detector (subtractor).
In here the comparator use with open loop mode to get high open loop gain [8]. In
here Vr e f takes (12 V DC) in one input (+) and in another input (-) take a signal from
the subtractor output. Any minimum change in voltage the comparator gets signal
[9] and error is signified by this.
 
Vout  Av0 V + − V −

In open loop mode the amplifier voltage gain is nearly equal to Av0 . This Vout is
the input of digital pulse generator, PWM Pulse control the firing angle of IGBTs of
GTI.

4.3 Demultiplexer

The gates of IGBT switches of GTI are got pulse from 1 line to 4 lines demultiplexer
[10]. Demultiplexer consists of two select inputs, one data input and four outputs.
The select inputs are select which output (AND Gate) of Demultiplexer is active at a
time among the four output switches. The four outputs are generating pulses for each
gate of IGBT switches. The data input is here the pulse from comparator. Any change
in grid value sense by the subtractor and in demultiplex through the comparator. The
IGBTs of GTI are also getting this effect through gates switching. The firing angle
is controlled by phase angle control by using of PLL. So it is the model based close
loop control system of GTI.
Output waveforms of PLL control circuit, Grid Tie Inverter and Utility Grid are
shown in Fig. 3.
224 S. Dutta et al.

5 Latest Trends and Scope of Future Developments

In present trend the SPV power is supplied to utility grid as three phase or single phase
system. For grid synchronization the GTI is controlled by using various technologies.
PLL is a popular control technology among these. The single phase GTI already has
four types of PLL control [11].
This paper is proposed a new type of PLL for synchronizes GTI and utility grid.
After taking grid value i.e. voltage amplitude, frequency and phase angle the PLL is
senses and send signal to inverter, then the inverter produce sine wave and achieve
synchronization criteria.
To improve power quality further may be used of H5 structure [12] inverter in
future development. In case of grid contingency, isolation will be required and for
resynchronization different control circuit will be designed and adopted.

6 Conclusion

In this paper is monitoring and synchronizing of Grid tie inverter by use a new
variation of PLL. This synchronization experiment has been developed by simulation
model of PSIM-software. Here the isolation of low pass filter [11] the PLL system is
more robust in configuration and cost is also reduced. The LCCL filter components
size is reduced by using digital signal of control circuit which reduced harmonic
distortion. The compactness of overall circuit which maintains power quality and by
using line commutated inverter the complexity and cost are also reduced.

Acknowledgements The authors would like to thank Electrical Department, Supreme Knowledge
Foundation Group of Institutions, MAKAUT, Kolkata, India, for coordination and support.

References

1. A Grid Tie Inverter For Solar Systems, solar.smps.us, 17.08.2015

2. Design of High Frequency Pulse Transformer www.electrical4u.com, 26.03.2017
3. A. Singh, V.S. Jabir, Voltage Fed Full Bridge DC-DC and DC-AC Converter for High-Frequency
Inverter Using C2000. (Texas Instruments, Texas, Application Report) June 2015
4. Line-commutated Inverter, definedterm.com, 10.03.2017
5. U. Solanke Tirupati, A. Kulkarni Anant, Effective microgrid synchronization in islanded mode:
controlled input/output PI-Fuzzy-PI algorithm. Int. J. Comput. Appl. (0975–8887) 75(16),
39–45 (2013)
6. Standard for interconnecting Distributed Resources with Electric Power System, IEEE standard
1547.2, 2008
7. D. De, K. Prasad Ghotok, Basic Electronics (Pearson Education, London, 2012)
8. Op amp Comparator, www.electronics-tutorials.ws, 22.03.2017
9. D. Roy Choudhury, S.B. Jain, Linear Integrated Circuits, 3rd edn. (New age international
publishers, London, 2007)
Solar Photovoltaic Power Supply to Utility Grid … 225

10. A. Anand Kumar, Fundamentals of Digital Circuits (Prentice-Hall of India Pvt. Ltd, Delhi,
2007)
11. Y. Yang, F. Blaabjerg, Synchronization in single-phase grid-connected photovoltaic systems
under grid faults, in 3rd IEEE International Symposium on PEDG Conference, Aalborg, Den-
mark, June 2012, pp. 476–482, 2012
12. R. Teodorescu, M. Liserre, P. Rodriguez, Grid Converters for Photovoltaic and Wind Power
Systems (Wiley, Hoboken, 2011)
Optimum Sizing and Economic Analysis
of Renewable Energy System Integration
into a Micro-Grid for an Academic
Institution—A Case Study

Nithya Saiprasad, Akhtar Kalam and Aladin Zayegh

1 Introduction

World energy demand has been estimated to be greater than 800EJ by 2050. For
this estimation, with the present scenario of escalating oil prices when considered,
renewable energy could promise to be an alternate option as an energy resource [1].
Alternately, the global concern towards pollution and global warming has supported
this cause. In recent years, there has been much technical advancement in renewable
energy systems (RES) including the storage units. Many countries have been striv-
ing to reach their renewable energy target towards the global energy contribution;
Australia being one among them.
Australia is the world’s 9th largest energy producer using coal and the largest
exporter of uranium [2]. In its share of renewable energy generation, Australia’s
renewable energy contribution is far too minimal for the abundance of natural
resources it possesses. Despite the fact of the volatility of the conventional energy
market, this cheaper environmentally unfriendly energy has been dominant in the
energy market. Although several studies conducted on Australia being 100% renew-
able have given negative results [3, 4]. However, pondering renewable energy being
a part of the modern grid has equally been dealt with [5–10].

N. Saiprasad (B) · A. Zayegh

College of Engineering and Science, Victoria University,
Melbourne, VIC 3011, Australia
e-mail: nithya.saiprasad@live.vu.edu.au
A. Zayegh
e-mail: Aladin.Zayegh@vu.edu.au
A. Kalam
Smart Energy Research Unit, College of Engineering and Science,
Victoria University, Melbourne, VIC 3011, Australia
e-mail: Akhtar.Kalam@vu.edu.au

© Springer Nature Switzerland AG 2019 227

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_20
228 N. Saiprasad et al.

Designing and optimizing a micro-grid and analyzing their economic and envi-
ronmental impacts have been the template of this study. Similar studies have been
conducted using Solar cells or Photo-voltaic (PV), wind turbines, fuel cells (used
either as an energy source or as a storage unit) for isolated villages, islands, wind
farms, resorts [5, 8, 11–20]. The current study is aiming at integrating renewable
energy like PV and wind turbine connected to the grid for Victoria University located
at the St Albans campus in Melbourne, Australia. The location map is shown in Fig. 1.
To design and optimize any micro-grid, it is significant to understand and study
the load requirement of the desired location. This crucial step during the design
of a micro-grid should not terminate in underestimating or overestimating the con-
sumption, either of which could result in unmet load or oversized setup respectively.
Various methods have been used to optimize a micro-grid including genetic algo-
rithm and swarm optimization techniques. However, many software have been used
in such studies like MATLAB/SIMULINK, HOMER etc. [21].
HOMER (Hybrid Optimization of Multiple Energy Resources) is a software that
was initially created by the National Renewable Energy Laboratory and now mar-
keted by a company called HOMER Energy. HOMER consists of 3 main modules
Simulation, Optimization, and Sensitivity Analysis. The crucial task lies in the archi-
tecture of the micro-grid setup for the load demand of the university with least cost
demand and greater efficiency. The aforementioned problem has been studied using
HOMER software which designs and optimizes the setup with least Net Present
Cost (NPC) of the system [22]. The study conducted also includes the environmental
impact of the designed system by analyzing the amount of harmful gases they emit
to the environment.

2 System Description

The RES designed here, considers the total cost of the system which includes the
total capital cost and the maintenance cost. The architecture of this system consists
of PV arrays, wind turbine, controller, batteries and grid support. To minimize the
cost of the system and meet the load demand, HOMER defines a few terminologies
which are deciding factors for the suggested model [22].
They are expressed as follows:
a. Net Present Cost (NPC): Net Present Cost determines the profitability of the
project, which is the total net present value of the component subtracted by the
(income) profit it incurs for the complete lifetime of the project.

 
N PC  T otal Cash f low/ (1 + I nter est rate)(Pr oject Li f e time)

− I nitial I nvestment (1)

b. Annualized cost of the system (ACS): Annualized cost is that cost of the set up
when factored equally over the entire lifetime of the project considered.
 Optimum Sizing and Economic Analysis of Renewable Energy …

Fig. 1 Victoria university St. Albans location map from Google and campus access map
229
230 N. Saiprasad et al.

 
AC S  (Cost o f the Pr oject × Discount rate) / 1 − (1 + Discount rate)−Pr oject li f e time
(2)

c. Levelised Cost of Energy (COE): It is the average cost of useful electrical energy
produced by the system. To calculate the levelised cost of energy, HOMER divides
the annualized cost of producing electricity (the total annualized cost minus the
cost of serving the thermal load) by the total electric load served, using the
following equation:

C O E  (T otal annual electricit y pr oduction) / (Load Ser ved by the system) (3)

d. Renewable Energy penetration (REP): It is the amount of renewable energy that

serves the load annually

R E P  (Power pr oduced f r om r enewable energy) / (T otal electrical load ser ved)

(4)

To design and optimize the RES into the grid for this study it is necessary to
identify the sensitive variables along with evaluating their electricity load profile,
solar irradiation and wind energy which are introduced in this section.

2.1 Solar Radiation Data

The solar radiation data has been analyzed from the National Renewable Energy
Laboratory (NREL) data for St. Albans, Melbourne. This data is used to design the
RES to integrate into a micro-grid to meet the load demand. Figure 2 shows the
average solar radiation at the given place is 4.13 kWh/m2/day. Clearness index for
the same location was used to design the micro-grid setup using HOMER.

2.2 Wind Resource

The wind resource data has been analyzed from NASA Surface meteorology for the
desired location which provides monthly averaged values of wind speed at 50 m
above the Earth’s surface over a period of 10 years (July 1983–June 1993). Figure 3
shows the wind distribution at the desired location with an average wind speed of
4.53 m/s.
However, since the data seem to have been collected till June 1993, to understand
the wind speed over recent years was also considered from Bureau of Meteorology,
Australian Government. The site details closest to the university were found out to
Optimum Sizing and Economic Analysis of Renewable Energy … 231

Fig. 2 Daily solar radiation and clearness index for the desired location

Fig. 3 Average wind speed for a year at desired location

be Melbourne airport (lat 37.67 °S, long 144.83 °E) and the mean 9 am wind speed
statistics from 1970 to 2010 was 5.28 m/s. It is noted that the data measured was at
an elevation of 113 m.
To use the above information in the simulation the wind speed was evaluated for
50 m (similar to NASA surface meteorology data) using Power law of wind profile
given by Eq. (5).

(u/u r  (z/zr )α ) (5)

where u is the wind speed at a height z and ur is the known wind speed at a reference
height. From Eq. (5), the wind speed at a height of 50 m using the data measured
from Bureau of Meteorology, is measured as 4.708 m/s with the power law exponent
factor (α) to be 0.14.
232 N. Saiprasad et al.

Table 1 Sensitive variables Inflation period (%) 2.5

used as boundary conditions
in simulation 3.5
5
Discount rate (%) 6.7
3.5
8
Lifetime of the project (years) 15
25
Feed in tariffs $0.05/kWh
$0.03/kWh
$0.1/kWh
Electricity price $0.226512/kWh
$0.5/kWh

2.3 Electrical Load Analysis

The Electric power consumption of the university was studied using their electricity
bill procured for one year. The average electricity consumption is 11091.27 kWh/d.
A few variables reflect on the economics of the system, they are: inflation period,
discount rate, lifetime of the project, feed in tariffs, electricity price. These were
considered as the sensitive variables or the boundary conditions in the analysis and
their values are shown in Table 1.

3 HOMER Simulation Model

The simulated model shown in Fig. 4 considers integration of Solar cells or PV and
wind turbine into the grid. Wind energy and solar energy complement each other as
distributed energy resources in the micro-grid. The fact of their energy production
benefits and drawbacks has resulted in studying such renewable energy systems
penetration into the grids. The intent to use a grid supported system instead of battery
is its resilience and the fact that the presence of battery would escalate the cost of the
setup which is already high due to the presence of wind turbine. Supplementing the
above criteria, excess of power generation from this RES can be fed into the grid to
acquire an additional profit in the form of energy sell back through Feed-in Tariffs
(FiTs). The presence of converter in the system is to converts DC source output from
PV to AC.
For the HOMER simulation, the size of the PV and converters was scaled for a
definite range of numbers whilst the number of wind turbines to be integrated was
varied between 1 and 10 and the details are provided in Table 2.
Optimum Sizing and Economic Analysis of Renewable Energy … 233

Fig. 4 Schematic diagram

of the micro-grid considered

Table 2 Component details considered in the analysis

Component Size Details Capital cost ($) Operational and
maintenance cost
($/year)
PV (1 kW) 0 ≤ 107 Generic flat plate 680 10
Converter 0 ≤ 107 Generic system 240 –
converter
Generic 1.5 MW 1.5 MW of Rated capacity 3,900,000 39,000
wind turbine Quantity 1–5 1500 kW, hub
(G1500) height 80 m

4 Results and Discussion

The setup for simulation considers PV and Wind turbines as RES. HOMER simulates
a set of values having least NPC, considering the sensitive variables, and optimizing
the size of the system. However, when the current Discount rate of 6.7% and current
inflation rate of 3.5% and a sell back of $0.03/kWh was considered [23, 24]. HOMER
optimized the size of the RES having least NPC, the results are shown in Table 3.
The architecture of the above model considered are about 2400–3200 kW of PV.
A single 1.5 MW wind turbine scaled for different wind speeds integrated into a
grid through converters ranging from 1400 to 1600 kW. The lifetime for the project
and turbine lifetime considered are 15 and 25 years. The smallest architecture for
the RES is about 2.4 MW PV and one 1.5 MW wind turbine connected to the grid
through converter of about 1.4 MW with a wind speeds 5.3 m/s and project lifetime
of 15 years and turbine lifetime of 15 and 25 years.
The above architecture of the RES from Table 3 has NPC ranging between $7 M
and $12 M. The renewable energy penetration for these systems with an average of
83% is tabulated in Table 4. The unmet load from renewable energy of less than 20%
is bought from the grid, while the excess of renewable energy being sold using the
RES for a year converts to a profit or revenue.
234 N. Saiprasad et al.

Table 3 Architecture details of optimized model by homer

Architecture
Project 1.5 MW Wind speed PV (kW) 1.5 MW Grid (kW) Converter
lifetime wind scaled wind (kW)
(years) turbine average turbine
lifetime (m/s)
(years)
15 25 5.277778 2441.406 1 999999 1424.154
15 25 4.708428 2644.857 1 999999 1424.154
15 15 5.277778 2441.406 1 999999 1424.154
15 15 4.708428 2644.857 1 999999 1424.154
25 25 5.277778 2644.857 1 999999 1424.154
25 25 4.708428 3255.208 1 999999 1627.604
25 15 5.277778 2644.857 1 999999 1424.154
25 15 4.708428 3255.208 1 999999 1627.604

Table 4 Energy and economics details of the optimized model

Energy and economics
COE ($) NPC ($) Operating Initial Renewable Energy Excess
cost ($) capital ($) energy purchased energy sold
fraction (%) in kWh in kWh
(percent- (percent-
age) age)
0.087219 7016055 93945.19 5901953 84.94 1021381 2734872
(14.1%) (40.3%)
0.101916 7651731 135881.8 6040300 81.82 1150687 2282596
(16.6%) (36.1%)
0.099501 8004071 177258.3 5901953 84.942 1021381 2734872
(14.1%) (40.3%)
0.115076 8639745 219194.9 6040300 81.82 1150687 2282596
(16.6%) (36.1%)
0.081688 9729412 214030.5 6040300 85.62 993156 2861718
(13.2%) (41.4%)
0.090606 1.07E + 07 241373 6504167 84.32 1070182 2780436
(14%) (40.7%)
0.097329 1.16E + 07 322105.6 6040300 85.62 993156 2861718
(13.2%) (41.4%)
0.106432 1.25E + 07 349448 6504167 84.32 1070182 2780436
(14%) (40.7%)
Optimum Sizing and Economic Analysis of Renewable Energy … 235

Table 5 Annual energy production details of the micro-grid sources considered

Energy production kWh/yr Percentage
Generic flat plate PV 3,537,357 51.08
Generic 1.5 MW wind turbine 2,236,621 32.3
Grid purchases 1,150,687 16.62
Total 6,924,664 100

Comparing the results of Tables 3 and 4, it is observed that there are two archi-
tectures of RES with a project lifetime of 15 years and wind speed 4.7 m/s, size
of PV and converter is 2645 and 1424 kW respectively. However, the lifetime of
1.5 MW generic wind turbine are 15 and 25 years. These two architectures of RES
have about 82% of renewable energy fraction, energy purchased from the grid and
energy sold to the grid are 1150687 and 2282596 kWh respectively. The architecture
of the system with the 1.5 MW wind turbine of 15 years have larger NPC, COE
and smaller renewable energy penetration of about 81.8% compared to the system
discussed earlier. This larger value of NPC and COE is due to the performance of
1.5 MW wind turbine for the lower wind velocity of about 4.7 m/s. It is also observed
that for RES consisting of 1.5 MW wind turbine performing at velocity of 4.7 m/s
result in smaller energy purchased or sold compared to the system operating with
wind velocity of 5.3 m/s.
When monthly average electric production is considered for the above discussed
RES, PV and Wind turbine contributed the major share of energy to reach the load
demand as shown in Fig. 5. The maximum energy produced by the RES are during
the months when solar energy radiation and wind energy are at their maximum.
Table 5 summarizes the annual energy production details of the micro-grid sources
considered. 51% of energy contribution is by PV and 32% of energy production is
from Generic 1.5 MW wind turbine. Total Grid purchase of about 17% is noted. The
contribution of grid energy is mainly when the PV and wind turbine is not able to
meet the load requirement when there is not enough sunlight or wind.
Figure 6 discusses the toxic gas emissions of the winning system. The data shows
it illustrates the net toxic gas of carbon dioxide being maximum compared to Sulphur
dioxide and Nitrogen dioxide.

5 Conclusion

In this project, we considered integrating RES like generic flat plate solar PV, wind
turbine optimized according to the sensitive values and HOMER presented a list of
values according to the least NPC. However, with the present condition of discount
rate, sell back price for 15 years considered, and NPC of $8.64 M resulted with 82%
of renewable energy penetration. The negative emission of Carbon dioxide explains
the fact that the energy sold is greater than the energy purchased through the grid.
 236

Fig. 5 Monthly average electric production of the desired model

N. Saiprasad et al.
Optimum Sizing and Economic Analysis of Renewable Energy … 237

Fig. 6 Toxic gas emissions of the model considered

This system proves to be environmental friendly when the toxic gas emissions are
considered. Further considerations on Small-scale Technology Certificates (STC)
and other Government aided subsidies along with the solar energy installation costs
are not considered in our current studies [25]. However, it could lead to future research
work.

Acknowledgements The authors wish to acknowledge Anil Chaudhary from Greenova Solutions
Pty Ltd, St Albans, VIC 3021 for helping us in providing the current market prices of the RES used
in our study.

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Modelling and Simulation of Solar Cell
Under Variable Irradiance and Load
Demand

Payel Ghosh and Palash Kumar Kundu

1 Introduction

The breakneck depletion of fossil fuels taken together with the overloading of the
atmosphere (with global warming emissions) due to human activity has shifted the
focus towards the exploration of more abundant and benign energy resources over the
past few decades. The tried-and-true technique of energy production from renewable
energy resources (viz. the wind, solar, geothermal, hydroelectric, and biomass) is
not only more sustainable but requires very less maintenance, causes considerably
less noise pollution, effectively less or no production of the greenhouse or net carbon
emissions as compared to traditional generators and hence render minimal impact
on the environment.
The life-giving Sun is a cornucopia of energy which is harvested by photovoltaic
and solar thermal technologies to produce electricity. A number of solar cells (the
fundamental block of PV systems) are assembled, wired and sealed together in an
environmentally protective laminate to form PV Modules. In order to meet the power
requirements in terms of voltage and current one or more photovoltaic modules are
connected in series and parallel (or a combination of both) to form a PV array—in
parallel to increase current and in series to produce a higher voltage [1]. The power
output of PV system varies from kilowatt range in residential applications increasing
to the megawatt range, in utilities. Domestic installation of PV array is typically
done on the rooftop where partial shading of the cells from neighboring structures or
trees is often ineludible [2]. Hence the sum of the individually rated power of each
module is, however, more than the total power in such an array [3]. Earlier studies

P. Ghosh (B)
Department of Electrical Engineering, Meghnad Saha Institute of Technology, Kolkata, India
e-mail: payel4ever@gmail.com
P. K. Kundu
Department of Electrical Engineering, Jadavpur University, Kolkata, India
e-mail: palashm.kushi@gmail.com
© Springer Nature Switzerland AG 2019 239
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_21
240 P. Ghosh and P. K. Kundu

assume that this decrease in the array output is proportional to the shaded area i.e.
reduction in solar irradiance causing the solar cells being unevenly illuminated, thus
introducing the concept of shading factor. This concept may be true for a single cell,
but the decrease in power at the module or array level is often far from linearity with
the shaded portion [2]. The reverse bias of the shaded cells makes it act as a load thus
draining power from other fully illuminated cells [1]. Apart from reduced output, if all
the cells are not equally illuminated, hot spot problem may arise causing the system
to be irreversibly damaged. In order to maintain continuity of supply and to meet the
power demand even in shading condition switching of cells is necessary. Switching
of cells uses the idea of two or more cells operating in parallel or series mode (as
desired) whenever due to decreased ambient irradiance the output from a respective
cell is not enough for the load. This article aims to show the switching of cells
at various irradiance levels and also under various load demand using SIMULINK
models and embedded MATLAB function.

2 Photovoltaic System

2.1 Single Diode Model

A p-n junction when illuminated acts as a solar cell. A solar cell is basically a current
source connected in parallel with a diode. However, the model changes taking into
account the non-ideality factors—especially the parasitic series and shunt resistances.
It generates current when illuminated. However, it acts as a diode i.e. the solar cell is
an inactive device resulting in zero voltage and current during darkness. This section
briefly describes the single diode model of a solar cell taking into account the effects
of ambient irradiance and temperature and the associated equations are:
The Shockley diode equation can be stated as:
 q VD 
I D  I0 e n K T − 1 (1)

where ID is the diode current (in Ampere), I0 is the reverse saturation bias current (or
scale current in Ampere) of the diode corresponding to working temperature T (in
Kelvin). I0 is not constant for any given device but varies widely with T. For every
10 °C temperature rise, I0 doubles itself. q is the charge of an electron equal to 1.602 ×
10−19 C, VD is the voltage across the diode (in Volts), n is the ideality factor (also
termed as the quality factor or sometimes emission coefficient) of the diode typically
varying between 1 and 2, however, it can be more based on the fabrication process
and semiconductor material. It is set to 1 for an ideal diode. K is the Boltzmann
Constant equal to 1.38 × 10−23 J/K.
The diode equation can also be expressed as:
 VD 
I D  I0 e nVT − 1 (2)
Modelling and Simulation of Solar Cell … 241

where VT is the thermal voltage equal to Boltzmann constant times temperature of

p-n junction whole divided by the elementary charge of an electron and is denoted
as
KT
VT 
q

It is approximately 25.85 mV at 300 K.

Under ideal conditions, the output current (in Ampere), I  IL − ID neglecting
the parasitic series and shunt resistances. IL is the photon current (in Ampere) cor-
responding to a particular irradiance level and given temperature, varying directly
with irradiance level. Thus,
 q VD 
I  I L − I0 e n K T − 1 (3)

The series resistance RS (in Ohms) is the equivalent resistance in contacts, metal
grids as well as the resistance encountered (internal losses) by the current flow in the
p-n layers of the semiconductor material. Shunt resistance RSH (in Ohms) corresponds
to the leakage current of the p-n junction. Hence the expression for output current,
I, corresponds to:
With series resistance RS ,
 q(V +I RS ) 
I  I L − I0 e n K T − 1 (4)

With series resistance RS and shunt resistance RSH (Fig. 1)

I  I L − I D − I RS H (5)
 q(V +I RS )  V + I R 
S
I  I L − I0 e n K T − 1 − (6)
RS H

Fig. 1 Model of a solar cell with equivalent series resistance and shunt resistance
242 P. Ghosh and P. K. Kundu

However RS  0 in an ideal solar cell [4]. In this paper, RSH is neglected hence
considering a moderately complex model with series resistance only [5]. The other
equations involved can be listed as:
G
I L (T1 )  I SC (T1,N O M ) (7)
GNOM

where GNOM and T1,NOM are the values of suns and temperature at standard test
condition (i.e. GNOM  1000 W/m2 , T1,NOM  25 °C).

I L  I L (T1 ) + K 0 (T − T1 ) (8)
I SC (T2 ) − I SC (T1 )
K0  (9)
(T2 − T1 )
I SC (T1 )
I0 (T1 )   q VOC (T1 )  (10)
e n K T1 − 1
  n3 q Vg (T1 )
 
T 1
T − T1
1
I0  I0 (T1 ) ×
nK
e (11)
T1
q q V OC (T1 ) 1
X V  I0 (T1 ) e n K T1 − (12)
n K T1 XV
dV 1
RS  − − (13)
d I VOC XV

[6] where T1 is the normalized temperature (= 25 °C STC) in Kelvin, VOC is the open
circuit voltage in Volts, G is the number of Suns in Watt/metre2 (1 Sun  1000 W/m2 ),
K0 is current/temperature coefficient in Ampere/Kelvin [A/K], Vg is the voltage of
the Crystalline Silicon (Vg  1.12 and 1.75 eV for Amorphous Silicon) in Electron
volt [eV], dV/dIVoc is the dV/dI coefficient at VOC .
The basic parameters characterizing the solar cell are:
(I) Short circuit current (ISC ): ISC is the maximum value of current (roughly
equal to the photon current for very small values of series parasitic resistance)
of the solar cell under short circuit conditions i.e. zero voltage appearing across
the terminals.
(II) Open circuit voltage (VOC ): VOC is the maximum voltage under open circuit
(zero current) condition. Neglecting the parasitic resistances,
 q VD 
I  I L − I0 e n K T − 1 .

Under open circuit conditions when I  0, VD  VOC and

 
nK T IL
VOC  ln +1 .
q I0
Modelling and Simulation of Solar Cell … 243

The equation clearly indicates that VOC is widely controlled by the dark satu-
ration current.
(III) Maximum power point (MPP): ISC and VOC do not occur simultaneously and
hence maximum output power, PMAX that can be delivered to the connected
load by the PV cell is not equal to ISC X VOC rather PMAX is the product
of IMAX and VMAX (Current and Voltage corresponding to Maximum Power
Point), which are much less than ISC and VOC respectively.
(IV) Efficiency of PV cell (η): Efficiency is the ratio of output of PV cell i.e. the
maximum current times the maximum voltage (at MPP) to the input light
power and is denoted as
POU T PM AX I M AX VM AX I M AX VM AX
Efficiency    
PI N G GA 1000 A

where G is the ambient irradiation taken as 1000 W/m2 at Standard test con-
ditions and A corresponds to exposed PV cell area. Efficiency ranges are:
6%-amorphous silicon-based solar cell to 42.8% with multiple cells: 14–19%
for commercially available multi-crystalline solar cells and widely depends on
several critical factors like temperature, irradiance, shading, snow, etc.
(V) Fill Factor (FF): The product of current and voltage corresponding to the
maximum power point (IMAX VMAX ) divided by the product of short circuit
current, ISC times the open circuit voltage, VOC is termed as Fill Factor. The
idea about the cell quality is conveyed by the fill factor which typically ranges
between 0.7 and 0.8 for good cells.
I M AX VM AX
FF  .
I SC VOC

2.2 Solar Cell Module and Array Model

(I) Series
In order to increase the module voltage, N solar cells are connected in series and
the module output voltage is given by VOUT  V1 + V2 + V3 + V4 + ··· + VN .N, the
number of cells to be connected in series, is decided according to the voltage demand
by the load. Some examples are shown of possible series combinations:

(A) Similar Solar cells in Series: Using the same three 2 V/1 A solar cells in series,
the output voltage is 6 V (2 + 2 + 2) at the same rated current of 1A (Fig. 2a).
(B) Solar cells in Series with different Voltage: Three solar cells of different voltage
rating are connected in series (2 V/1 A, 3 V/1 A, and 4 V/1 A) yielding the
same amperage of 1 A but an augmented voltage of 9 V (2 + 3 + 4) (Fig. 2b).
(C) Solar cells in Series with different Voltage and Current: Three solar cells
(2 V/1 A, 3 V/2 A, and 4 V/3 A) are connected in series resulting in a voltage
244 P. Ghosh and P. K. Kundu

jump of 9 V (2 + 3 + 4) but the current is restricted to the lowest rating of the

module i.e. 1 A here (Fig. 2c).
(II) Parallel

Connecting N solar cells in parallel increases the output current of the module
which is given by IOUT  I1 + I2 + I3 + I4 + ··· + IN N, the number of cells to be
connected in parallel is decided according to the current demand by the load. Some
examples are shown of possible parallel combinations:

(A) Similar Solar cells in Parallel: Using the same three 2 V/1 A solar cells in
parallel, the output current is increased to 3 A (1 + 1 + 1) at the same rated
voltage of 2 V (Fig. 3a).
(B) Solar cells in Parallel with different voltage and current: Three solar cells
(3 V/1 A, 5 V/3 A, and 7 V/4 A) are connected in parallel resulting in an
increase in current equal to 8 A (1 + 3 + 4) but the module voltage is restricted
to the lowest rated i.e. 3 V here (Fig. 3b).

In order to increase both module voltage and the current series-parallel combina-
tion is preferred. In the photovoltaic module with NP cells branches in parallel and
NS cells in series, total shunt resistance in Ohm is equal to,
 
NP
R S H,M O DU L E  R S H,C E L L
NS

where RSH,CELL corresponds to shunt resistance in one photovoltaic cell, Ohm.

Total series resistance is Ohm is given by,

Fig. 2 a Similar solar cells

in series b Solar cells in
series with different voltage
c Solar cells in series with
different voltage and current
Modelling and Simulation of Solar Cell … 245

Fig. 3 a Similar solar cells

in parallel b Solar cells in
parallel with different
voltage and current

 
NS
R S,M O DU L E  R S,C E L L
NP

where RS,CELL corresponds to series resistance in one photovoltaic cell, Ohm.

Therefore for a module with NP and NS , we will add RSH,MODULE and RS,MODULE
instead of RS and RSH in Eq. (6) of Single Diode Model section. In order to find the
specifications of the module the equations already stated in the previous section will
be applied and finally, the characteristic curves (I-V and P-V) are obtained according
to values of ambient temperature and irradiance [7, 8].
Total short circuit current in the module (in Ampere) is

I SC,M O DU L E  (N P )I SC,C E L L

where ISC,CELL is the short circuit current of one photovoltaic cell, in Ampere. The
open circuit voltage of the photovoltaic module (in Volts) is

VOC,M O DU L E  (N S )VOC,C E L L

where VOC,CELL is the open circuit voltage of one photovoltaic cell, in Volts [9].
Modules in a PV system are typically connected to form arrays. With MP parallel
branches each with MS modules in series, VA is the applied voltage at the terminals
of the array and the array current, IA is denoted by


MP
IA  Ii
i0

where A correspond to the branches number. But I A  M P I M if it is assumed that

the ambient irradiation is same on all the identical modules (Fig. 4).
246 P. Ghosh and P. K. Kundu

Fig. 4 Solar cell array with

MP parallel branches, with
MS modules in series in each
branch

2.3 Characteristic Curves of Solar Cell

Solar cell I-V and P-V characteristic curves are the input-output analysis of the cell
which helps in determining the cell output and solar efficiency. The I-V Curve is
a plot of all possible values of output current corresponding to each voltage levels
exhibiting an inverse relationship (i.e. the current decreases from a maximum value
to zero as we sweep the voltage from zero to its maximum value). In any DC electrical
circuit, Power (P) in Watts (W)  the Current (I) in Amperes (A) X the Voltage (V) in
Volts (V). Thus the P-V curve is the measure of the output power (product of current
and voltage from I-V curve) corresponding to respective voltage levels (Fig. 5).

2.4 Effect of Ambient Irradiance and Temperature

The variation of solar irradiation and temperature throughout the day results in differ-
ent characteristic curves. At fixed temperature, with increasing solar irradiance the
maximum power point varies as both the short-circuit current and the open-circuit
voltage increase. ISC exhibits a linear variation as more electron-hole pairs are formed
but VOC increases marginally with the increase in irradiance.
The rate of photon generation increases with the increase in temperature which in
turn rapidly increases the reverse saturation current and thus the band gap is reduced.
Although this leads to marginal changes in current, the voltage undergoes major
changes (roughly around −0.35%/°C or −2.2 mV/°C). Thus temperature acts like a
negative factor adversely affecting solar output. Thus with regards to both irradiance
and temperature, it can be inferred that temperatures between 26 and 30 °C coupled
Modelling and Simulation of Solar Cell … 247

Fig. 5 Ideal IV and PV

curve

with high irradiance are necessary for high panel output on sunny days with low
temperature [10].

3 Results

The characteristic parameters of SUNPOWER A-300 solar cell are used as a ref-
erence (Table 1). The four ranges of irradiance used are obtained by dividing the
maximum irradiance (approximate) of Kolkata equal to 0.27 Suns into equal ranges
and respective maximum power output are evaluated in each case for a single cell
and also when switching takes place.
This paper widely explains the switching of cells due to varying irradiance and load
demand. The same is implemented by MATLAB script and is used as an embedded
MATLAB function in SIMULINK. The logic as per which the switching of cells
takes is as follows:
(I) For an irradiance of a ≤ 0.0675 Suns, 4 solar cells will be operating in parallel.
(II) For an irradiance of value in the range, 0.0675 Suns < a ≤ 0.135 Suns, if user
defined load demand is less than or equal to 0.5533 W, 3 solar cells will be
operating in parallel. Whereas if user defined load demand is greater than
0.5533 W, 4 solar cells will be operating in parallel.
(III) For an irradiance of 0.135 Suns < a ≤ 0.2025 Suns, if user defined load demand
is less than or equal to 0.7554 W, 2 solar cells will be operating in parallel. If
0.7554 W < user defined load demand ≤1.331 W, 3 solar cells will be operating
248 P. Ghosh and P. K. Kundu

Table 1 Typical electrical performance of SUNPOWER A-300 solar cell a (mono crystalline sili-
con)
Parameter Symbol Value
Open circuit voltage VOC 0.665 V
Short circuit current I SC 5.75 A
Maximum power voltage VM AX 0.560 V
Maximum power current I M AX 5.35 A
Rated power PR AT E D 3.0 W
Efficiency η 20.0% minimum
Temperature coefficient of −1.9 mV/°C
voltage
Temperature coefficient of −0.38%/°C
power
a Dataare given at STC: Illumination 1000 W/m2 , Temperature: 25 °C and spectrum of light AM
1.5 [11]

in parallel. When user defined load demand is greater than 1.331 W, 4 solar
cells will be operating in parallel.
(IV) For an irradiance of a > 0.2025 Suns, if user defined load demand is less
than or equal to 0.5602 W, only 1 cell will operate. If 0.5602 W < user
defined load demand ≤1.1410 W, 2 solar cells will be operating in paral-
lel. If 1.1410 W < user defined load demand ≤ 1.7115 W, 3 solar cells will be
operating in parallel. When user defined load demand is greater than 1.7115 W,
4 solar cells will be operating in parallel.
The SIMULINK model (Fig. 6a) operates on the above-stated logic which takes
irradiance and load demand as input (shown in the subsystem Fig. 6b, c). The indi-
vidual scopes in the
SIMULINK model give the respective I-V and P-V curves under varying irradi-
ance and load demand. In the plots, the blue color is used for single cell operation
and red for multiple cell operation.

3.1 Analysis with Various Irradiance and Load Demand

Values

Some of the possible cases are:

(a) Input Irradiance: 0.0675 Suns, User Defined Load Demand: 0.50 W, Results:
Number of cells operating in parallel: 4, 1 cell: PMAX  0.1842 W and ISC 
0.4056 A. 4 cells: PMAX  0.7366 W and ISC  1.6225 A (Fig. 7).
(b) Input Irradiance: 0.05 Suns, User Defined Load Demand: 0.7 W, Results: Num-
ber of cells operating in parallel: 4, 1 cell: PMAX  0.1360 W and ISC  0.3050 A.
Modelling and Simulation of Solar Cell … 249

(a) COMPARATOR
4
NUMBER OF CELLS1- 2-3-4 I-V PLOT
(>0.2025)
0.27 Out1 1-2-3-4
In1
IRRADIANCE Out2
In2 Out3 P-V PLOT
PV(1-4) 1-2-3-4
0 I-V PLOT
In1 Out1 NUMBER OF CELLS
1.8 2-3-4
COMPARATOR COMPARATOR I-V PLOT
Out2
USER DEFINED (>0.135) (<=0.2025) 2-3-4
LOAD DEMAND In2 Out3
P-V PLOT P-V PLOT
PV(2-4) 2-3-4

I-V PLOT 3-4

In1 Out2
0
Out1
COMPARATOR NUMBER OF CELLS
COMPARATOR In2 Out3
(>0.0675) 3-4
(<=0.135) 3 -4 PV P-V PLOT 3-4

I-V PLOT 4 0
NUMBER OF CELLS
4
In1 Out2

COMPARATOR COMPARATOR Out1

(>=0) (<0.0675) In2 Out3
P-V PLOT 4
4 PV

(b) Enable

2 Out1 1
In1 Out2 Out1
In2 Out3
COMPARATOR Enabled
(<0.=5602) Subsystem
1
In1 Out1
COMPARATOR COMPARATOR In1 Out2
Out3 2
(>0.5602) (<0=1.1410) Out2
Enabled
Subsystem2

Out1
In1 Out2
COMPARATOR COMPARATOR Out3
(>1.1410) (<=1.7115) Enabled
Subsystem3

Out1
COMPARATOR In1 Out2
(>1.7115) Out3
Enabled
Subsystem4 3
Out3

(c) Enable 4
Constant
1
Out 1

u y
IV
voltage2 a1 P 2
1 Out 2
Embedded
In1 MATLAB Function 1
u y
IV
a1 P

Embedded
MATLAB Function 2

u y
IV
a1 P
Embedded
MATLAB Function 3 3
Out 3
u y
IV
a1 P
Embedded
MATLAB Function 4

Fig. 6 a SIMULINK model. b Subsystem model. c Subsystem model

4 cells: PMAX  0.544 W and ISC  1.22 A. Here even the parallel operation of
4 cells fails to supply the load demand and calls for more cells to be connected
in parallel.
250 P. Ghosh and P. K. Kundu

(a) I-V PlOT P-V PLOT

1.8
(b)
4 CELLS
4 CELLS
1.6 SINGLE CELL
SINGLE CELL 0.8
1.4
CURRENT(A)

1.2

POWER(W)
0.6
1

0.8 0.4
0.6

0.4 0.2
0.2

0 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
VOLTAGE(V) VOLTAGE(V)

Fig. 7 I-V and P-V curves under irradiance 0.0675 Suns and load demand 0.50 W

(c) Input Irradiance: 0.135 Suns, User Defined Load Demand: 0.55 W, Results:
Number of cells operating in parallel: 3, 1 cell: PMAX  0.3748 W and ISC 
0.7937 A. 3 cells: PMAX  1.124 W and ISC  2.381 A ((Fig. 8).
(d) Input Irradiance: 0.135 Suns, User Defined Load Demand: 0.7 W, Results: Num-
ber of cells operating in parallel: 4, 1 cell: PMAX  0.3748 W and ISC  0.7937 A.
4 cells: PMAX  1.499 W and ISC  3.175 A (Fig. 9).
(e) Input Irradiance: 0.140 Suns, User Defined Load Demand: 0.75 W, Results:
Number of cells operating in parallel: 2, 1 cell: PMAX  0.3892 W and ISC 
0.8225 A. 2 cells: PMAX  0.7784 W and ISC  1.645 A (Fig. 10).
(f) Input Irradiance: 0.2025 Suns, User Defined Load Demand: 1.3 W, Results:
Number of cells operating in parallel: 3, 1 cell: PMAX  0.5702 W and ISC 
1.1819 A. 3 cells: PMAX  1.7106 W and ISC  3.545 A (Fig. 11).

I-V PlOT
(a) P-V PLOT
2.5
3 CELLS
(b) 3 CELLS
SINGLE CELL SINGLE CELL
1.2
2
1
CURRENT(A)

POWER(W)

1.5 0.8

1 0.6

0.4
0.5
0.2

0 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
VOLTAGE(V) VOLTAGE(V)

Fig. 8 I-V and P-V curves under irradiance 0.135 Suns and load demand 0.55 W
Modelling and Simulation of Solar Cell … 251

(a) I-V PlOT P-V PLOT

(b)
4 CELLS 4 CELLS
SINGLE CELL
1.6 SINGLE CELL
3
1.4
2.5
1.2
CURRENT(A)

POWER(W)
2 1

1.5 0.8

0.6
1
0.4
0.5
0.2

0 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
VOLTAGE(V) VOLTAGE(V)

Fig. 9 I-V and P-V curves under irradiance 0.135 Suns and load demand 0.7 W

I-V PlOT
(a) P-V PLOT
1.8 2 CELLS (b) 1
2 CELLS
SINGLE CELL
1.6 SINGLE CELL
0.9

1.4 0.8
CURRENT(A)

1.2 0.7
POWER(W)

0.6
1
0.5
0.8
0.4
0.6
0.3
0.4
0.2
0.2 0.1

0 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
VOLTAGE(V) VOLTAGE(V)

Fig. 10 I-V and P-V curves under irradiance 0.140 Suns and load demand 0.75 W

(g) Input Irradiance: 0.2025 Suns, User Defined Load Demand: 2 W, Results: Num-
ber of cells operating in parallel: 4, 1 cell: PMAX  0.5702 W and ISC  1.1819 A.
4 cells: PMAX  2.2808 W and ISC  4.7276 A (Fig. 12).
(h) Input Irradiance: 0.27 Suns, User Defined Load Demand: 0.5 W, Results: Num-
ber of cells operating in parallel: 1, 1 cell operates to meet the load demand of
PMAX  0.7682 W and ISC  1.57 A.
(i) Input Irradiance: 0.27 Suns, User Defined Load Demand: 0.6 W, Results: Num-
ber of cells operating in parallel: 2, 1 cell: PMAX  0.7682 W and ISC  1.57 A.
2 cells: PMAX  1.5364 W and ISC  3.14 A.
(j) Input Irradiance: 0.27 Suns, User Defined Load Demand: 1.5 W, Results: Num-
ber of cells operating in parallel: 3, 1 cell: PMAX  0.7682 W and ISC  1.57 A.
3 cells: PMAX  2.3046 W and ISC  4.71 A.
252 P. Ghosh and P. K. Kundu

I-V PlOT
(a) P-V PLOT
3.5
3 CELLS
SINGLE CELL
(b)
3 CELLS
1.8
SINGLE CELL
3
1.6

2.5 1.4
CURRENT(A)

POWER(W)
1.2
2
1
1.5 0.8

1 0.6

0.4
0.5
0.2

0 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
VOLTAGE(V) VOLTAGE(V)

Fig. 11 I-V and P-V curves under irradiance 0.2025 Suns and load demand 1.3 W

I-V PlOT (b) P-V PLOT

(a) 4 CELLS
2.5
4 CELLS
4.5 SINGLE CELL SINGLE CELL

4 2
3.5
CURRENT(A)

POWER(W)

3 1.5
2.5
2 1
1.5
1 0.5
0.5
0 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
VOLTAGE(V) VOLTAGE(V)

Fig. 12 I-V and P-V curves under irradiance 0.2025 Suns and load demand 2 W

(k) Input Irradiance: 0.27 Suns, User Defined Load Demand: 1.8 W, Results: Num-
ber of cells operating in parallel: 4, 1 cell: PMAX  0.7682 W and ISC  1.57 A.
4 cells: PMAX  3.0782 W and ISC  6.28 A.

4 Conclusion

Switching of cells according to irradiance and load demand is shown with the help
of SIMULINK model which uses embedded MATLAB function. The I-V and P-V
plots for some possible cases are shown and the logic of execution is clearly stated
in the Results section. There is a restriction of maximum power output that can be
delivered by connecting all cells in parallel and whenever it is less than the user
Modelling and Simulation of Solar Cell … 253

defined load input, it calls for more number of parallel cells to be operated to meet
the load demand.

Acknowledgements Authors would like to thank Jadavpur University for support to do this work.

References

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of RES’08 WSEAS Press (2008)
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11. SunPower Corporation. Document Number 70-0006 Rev 02, 2003
Power Management of Non-conventional
Energy Sources Connected to Local Grid

Siddhartha Singh and Biswarup Basak

1 Introduction

Solar and wind have huge amount of potential for the energy requirement of the world.
If 14% of earth’s surface is installed with conventional onshore wind turbines of 80-m
tower height, renewable power generated will be around 70 TW (five times of global
power consumption). Another renewable resource is SP having incredible potential
to meet the world energy demand only by installing solar panels with efficiency
of 8% around 0.22% of earth’s surface. Roughly 85,000 TW of SP is available on
earth’s surface. In order to utilise the SP and WP directly across the TPL, it should
be connected to the GS which can fill the gap in TPL and generated Power. But
without power management it is uneconomical, so the Power management of NCES
connected to GS is necessary for proper operation.

2 Simple Block Diagram

The aim is to build up a power network for any island system or some small area
network whose power can be managed. As the name suggests the power management
of non-conventional energy sources, is an attempt to control the power of two means
i.e. the wind generation and the solar generation. From Fig. 1 we can see that the
three phase GS, WP generation and SP generation are connected in parallel to feed
a common load.

S. Singh (B) · B. Basak

Electrical Engineering, IIEST, Shibpur, Howrah 711103, India
e-mail: singhsiddhartha1811@gmail.com
B. Basak
e-mail: biswarup_basak@yahoo.com

© Springer Nature Switzerland AG 2019 255

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_22
256 S. Singh and B. Basak

Fig. 1 Simple block diagram

Grid power can not be controlled directly so the WP and SP are tracked and
controlled to produce its rated power. WP controlled by blade pitch angle and wind
speed to generate rated electrical power with the help of induction machine and
supplied to the grid. SP generation is depending on irradiance of sunlight. The output
voltage of solar panel is boosted to higher suitable value using boost converter and
then converted in ac with the help of three phase inverter so that it can be fed to
the grid directly without any transformer. Whether if the WP and SP are not enough
to supply the load than in the case, remaining load is being fed by the GS. So,
indirectly the GS power supply dependency is also controlled and hence we are
capable of reducing the consumption of power generation by means of conventional
methods. By this approach the Renewable resources and non-renewable resources
can be implied together to feed the same load.

3 Interconnected Overall Simulink Model

See Fig. 2.

3.1 Induction Machine Model

IM Simulink model is comprised of three blocks voltage transformation block, IM

d-q equation block and current transformation block. Voltage transformation block
is used to convert three phase a-b-c to d-q voltages, following by the IM block in d-q
equations is developed and the output current is again transformed from d-q to a-b-c
by Current transformation block. All the equations used are shown below.
Power Management of Non-conventional Energy Sources Connected … 257

Fig. 2 Interconnected overall network

The equations used for voltage a-b-c to d-q transformations:

Va  Vm ∗ sin(ωt) (1)
 
Vb  Vm ∗ sin ωt − 1200 (2)
 
Vc  Vm ∗ sin ωt + 1200 (3)

The parks transformation (a-b-c to d-q) is defined as follows:

2
Vd  (Va ∗ sin(θ ) + Vb ∗ sin(θ − 120◦ ) + Vc ∗ sin(θ + 120◦ )) (4)
3
2 
Vq  Va ∗ cos (θ ) + Vb ∗ cos (θ − 1200 ) + Vc ∗ cos(θ + 1200 ) (5)
3
The equations used for induction machine d-q model [1]:
Stator circuit equations:

Vds  rs ∗ i ds + pλds − ωe λqs (6)

Vqs  rs ∗ i qs + pλqs + ωe λds (7)

where p = d/dt operator.

258 S. Singh and B. Basak

Rotor circuit equations:

Vdr  rr ∗ i dr

+ pλdr − (ωe − ωr )λqr

(8)
Vqr  rr ∗ 
i qr + 
pλqr + (ωe − ωr )λdr (9)

Flux linkage expressions:


λds  L ls ∗ i ds + L m ∗ (i ds + i dr ) (10)
λdr  L lr
∗  
+ L m ∗ (i ds + i dr
i dr ) (11)

λqs  L ls ∗ i qs + L m ∗ (i qs + i qr ) (12)

λqr  L lr ∗ i qr
 
+ L m ∗ (i qs + i qr ) (13)

λdm  L m ∗ (i ds + i dr ) (14)

λqm  L m ∗ (i qs + i qr ) (15)
λds ∗ (L lr + L m ) − L m ∗ λdr

i ds  (16)
L ls ∗ L lr + (L ls + L lr ) ∗ L m
λqs ∗ (L lr + L m ) − L m ∗ λqr 
i qs    (17)
L ls ∗ L lr + (L ls + L lr ) ∗ L m
λ ∗ (L lr + L m ) − L m ∗ λds
i dr  dr (18)
L ls ∗ L lr + (L ls + L lr ) ∗ L m


λqr ∗ (L lr + L m ) − L m ∗ λqs
i qr  (19)
L ls ∗ L lr + (L ls + L lr ) ∗ L m

where L m  23 ∗ M
M = Stator to rotor mutual inductance in phase variable mode.
 
Te  P ∗ L m (i qs ∗ i dr − i ds ∗ i qr ) (20)

P
ωr  (Te − Tl )dt (21)
2J

Based on Eqs. (6)–(21) the IM model is developed.

The inverse parks transformation equations used for current (d-q to a-b-c) trans-
formations:

i a  i ds ∗ sin(θ ) + i qs ∗ cos(θ ) (22)

i b  i ds ∗ sin(θ − 120 ) + i qs ∗ cos(θ − 120 )
0 0
(23)
i c  i ds ∗ sin(θ + 120 ) + i qs ∗ cos(θ + 120 )
0 0
(24)
Power Management of Non-conventional Energy Sources Connected … 259

3.2 Turbine Model

A wind turbine generates electricity from moving air with the help of an alternator
or generator. Energy of moving wind is transferred to the spinning shaft, which is
mechanically coupled with the alternator. This shaft power depends on wind speed
and swept area of turbine blades, is given as: [2]

Ps  0.5C P (λ, β)ρ Av 3 (25)

where
Rnπ
λ (26)
30v
The Eq. (27) is the performance coefficient of wind turbine [2], is;
 
c2 c
− 5
C P  c1 − c3 β − c4 e λi + c6 λ (27)
λi

where
1 1 0.035
 − 3 (28)
λi λ + 0.08β β +1

c1  0.5176 c2  116 c3  0.4 c4  5 c5  21 c6  0.0068.

Based on above equations a Turbine Simulink model is generated to provide shaft
power as an output.
The parameters provided as input are:
• v =wind speed (m/s)
• n =rotor speed (rpm)
• ß = blade pitch angle (degree).

3.3 Solar Panel Model

The schematic of a single-diode solar cell is shown in Fig. 3. A light generated current
source, is connected in parallel with an ideal diode, together with a parallel and series
resistance respectively [3].
The Current I is given by:

I  I L − I D − Ish (29)

The Voltage across diode is given by:

260 S. Singh and B. Basak

Fig. 3 Single diode solar

cell

VD  V + I R S (30)

The diode current by employing Shockley diode equation

 VD 
I D  Io e ηVT − 1 (31)

where
kT
VT 
q

The shunt current is given by

VD
Ish  (32)
Rsh

The load current is defined as

 
φ  

IL  ∗
I SC + α I sc TC∗ − TC (33)
φ

The Short Circuit current is provided by

 
∗ φ  

I SC  I SC ∗
1 + α I sc TC − TC∗ (34)
φ

The Open Circuit Voltage is provided by

∗
 

VOC  VOC 1 + βV oc TC − TC∗ (35)

By employing all of the above equations from Eq. (29) to Eq. (35) a single solar
cell model is generated in Simulink platform which gives output voltage and out-
put current. The series and parallel combination of solar cell is used to generate
Power Management of Non-conventional Energy Sources Connected … 261

solar panel model. Actual irradiance is a variable which can vary in the range of
1000–2000 W per square meter.

3.4 Boost Converter Model

A step-up dc-dc boost converter is having four components: inductor, electronic

switch, diode and output capacitor. The converter is capable of operating in two
different modes depending on the length of switching period and energy storing
capacity [4].
The Boost converter is designed by using component modelling as seen in Fig. 4
PI-controller and closed loop feedback system are used to limit the output voltage at
600 volts. The values of component parameters are defined by following equations:
D ∗ T imeperiod ∗ Idcload
Capacitance Cout  (36)
V ppload
Vi ∗ T imeperiod ∗ D
Inductance L  (37)
i pp

Specification of Boost Converters:

Prated  10 kW
Input Voltage  200 V
Output Voltage  600 V.
Depending on above parameters the calculated values of capacitance, inductance
and load resistance is coming out to be as follows
Load  25 
Cout  192 µF
L  1.68 mH.
For PI controller the values used are
Kp  0.01
Ki  5.

Fig. 4 Step-up dc-dc

converter
262 S. Singh and B. Basak

3.5 Three Phase Inverter Model

The job of inverter is to convert DC input into AC output. Sinusoidal Pulse Width
Modulation (SPWM) technique is used as PWM technique in the three-phase inverter
model to control the inverter output voltage and output frequency [5].
The SPWM signals are generated by comparing reference sine wave with the
carrier triangular wave. The two signals are compared by using relational operators,
whenever the value of reference sine wave is more than the carrier triangular wave,
the output is set to +1 else 0. In this way, a switching pulse signal is generated.
Reference signals are

VSa  sin(ωt) (38)

◦
VSb  sin(ωt − 120 ) (39)
VSc  sin(ωt + 120) (40)

Q1 and Q4 are generated by using V sa

Q3 and Q6 are generated by using V sb
Q5 and Q2 are generated by using V sc .

The line to neutral voltages of the three-phase inverter are defined as:

Van  V sin(ωt) (41)

◦
Vbn  V sin(ωt − 120 ) (42)
◦
Vcn  V sin(ωt + 120 ) (43)

And the line voltages are found from

Vab  Van − Vbn (44)

Vbc  Vbn − Vcn (45)
Vca  Vcn − V an (46)

3.6 Voltage Grid and Load Model

In this a small voltage grid is designed along with three phase load which is having
logic to get connected in star and delta format of its own. The voltage of grid is
415-line voltage and 50 Hz frequency. The Load value is R  11.022  and L 
26.27 mH with power factor of 0.8 lagging.
Power Management of Non-conventional Energy Sources Connected … 263

4 Operation Results of Model

The Model needs a startup which is described as the without Active Power control
mode and once it reaches complete startup than after switching it is brought in Active
Power Control Mode.

4.1 Operation of Model Without Active Power Control

In above Fig. 1 the Actual Irradiance Parameter is shifting from 1000 to 1200 (W/m2 )
at 0.05 s of simulation time. Initially all the three manual switches are at constant
side. The simulation is started and output of boost converter and induction machine
speed is kept in consideration. The boost converter output during starting is shown
in Fig. 5.
Similarly, we have to wait for the induction machine speed is to reach above
synchronous speed i.e. 1500 rpm. Under this consideration, the steady state output
results for 30 kW 0.8 pf lagging Delta connected load are as follows:
• Boost converter output line voltage  600 V
• Boost converter output current  varying in between 0 and 20 A
• Active Power at terminals of three phase VSI  9330–9450 W
• Reactive Power at terminals of three phase VSI  −4980 to −5150 VAR
• Induction machine speed  1580 rpm
• Induction machine Active Power  10.4 kW
• Induction machine Reactive Power  −6112 VAR
• Grid Active Power  10.22 kW
• Grid Reactive Power  33.64 kVAR

Fig. 5 Boost converter output during starting (y-axis) versus time (x-axis) (s)
264 S. Singh and B. Basak

• Load Active Power  30.03 kW

• Load Reactive Power  22.48 kVAR.

4.2 Operation of Model with Active Power Control

The steady state is reached and corresponding output values are noted down. At this
all the manual switches are thrown back to feedback mode and wait for steady state
results. The switching point leads to a transition which is visible in all the graph
plots. Boost converter output is used to show the behavior of transition.
Figure 6 shows how switching transition is affecting the boost converter results
from earlier steady state reached value. From Fig. 7 it is clearly visible that the boost
converter trying to reach its steady state again in this condition.
In Fig. 2 the manual switches are used for connecting the feedback loop. There are
three manual switches in the model, one switch is used to transfer the frequency from
open loop to closed loop and the other two switches are for Active Power control
method of induction machine and inverter.
Kp  1 and Ki  30 is used for induction machine active power control, whereas
Kp  0.7 and Ki  10 is used for inverter active power control.
The overall steady state results for 30 kW 0.8 pf lagging Delta connected load are
as follows:
• Boost converter output line voltage  600 V
• Boost converter output current  varying in between 0 and 20 A.
• Active Power at terminals of three phase VSI  8900–9020 W
• Reactive Power at terminals of three phase VSI  −5020 to −5140 VAR
• Induction machine speed  1570 rpm

Fig. 6 Switching transition in Boost converter results (y-axis) versus time (x-axis) (s)
Power Management of Non-conventional Energy Sources Connected … 265

Fig. 7 Boost converter trying to attain steady state (y-axis) versus time (x-axis) (s)

Fig. 8 Steady state input and output of boost converter (y-axis) after switching versus time (x-axis)
(s)

• Induction machine Active Power  10 kW

• Induction machine Reactive Power  −5967 VAR
• Grid Active Power  11.10 kW
• Grid Reactive Power  33.58 kVAR
• Load Active Power  30.03 kW
• Load Reactive Power  22.48 kVAR (Figs. 8, 9, and 10).
266 S. Singh and B. Basak

Fig. 9 Induction machine speed Nm (rpm) along y-axis versus time (s) on x-axis

Fig. 10 Line current (red), (blue), (green) (Amps) respectively on y-axis versus time (s) on x-axis

5 Conclusion

For Power management of NCES in smart grid the various individual models are
developed working efficiently in standalone cases.
The models completed are:
1. Induction Machine
2. Wind Turbine
3. Solar cell and Solar panel
4. Boost Converter
5. Three phase VSI
6. Voltage Grid and Load.
In complete interconnected model, the same common load under steady state
condition is being fed by three sources:
Power Management of Non-conventional Energy Sources Connected … 267

1. Induction Machine
2. Solar Panel via Boost converter followed by Three phase VSI
3. Grid.
The output Active power of Induction Machine and Solar Panel side (i.e. at Three
phase VSI terminals) is controlled by the PI controller method. Induction Machine
Active Power control is Providing nearly perfect result, whereas the Solar Panel Side
Active Power control is providing good result although a very small variation in
power is observable but still the results are widely acceptable.
Hereby it can be said that the Power Management of Non-Conventional Energy
sources when connected to a local grid is performed with good result.

References

1. G. Renukadevi, K. Rajambal, “Generalized d-q model of n-phase induction motor drive”, World
Academy of Science, Engineering and Technology. Int. J. Electr. Comput. Energ. Electron.
Commun. Eng. 6(9), 1066–1075 (2012)
2. A.B. Cultura II, Z.M. Salameh, in Modeling and Simulation of a Wind Turbine-Generator System,
http://www.ieee.org, IEEE 2011
3. D. Stefan, in Matlab/Simulink Solar Cell Model Based on Electrical Parameters at Only One
Operating Condition, 18th International Conference on System Theory, Control and Computing,
Sinaia, Romania, pp. 709–714, 17–19 Oct. 2014
4. M.R. Dave, K.C. Dave, Analysis of boost converter using PI control algorithms. Int. J. Eng.
Trends Technol. 3(2), 71–73 (2012). http://www.internationaljournalssrg.org
5. N.I. Raju, Md Shahinur Islam, A.A. Uddin, Sinusoidal PWM signal generation technique for
three phase voltage source inverter with analog circuit & simulation of PWM inverter for stan-
dalone load & micro-grid system. Int. J. Renew. Energy Res. 3(3), 647–658 (2013)
Smart Coordination Approach for Power
Management with PEV Based on Real
Time Pricing

Purbasha Singha, Debanjan Ghosh, Sayan Koley,

Rishiraj Sarkar and Sawan Sen

1 Introduction

A restructured electrical grid that integrates the behaviours of suppliers and con-
sumers using modern information and communications technology, to improve the
efficiency, reliability and sustainability of the production of power and distribute the
same to the consumer, is called smart grid. With the application of these new technolo-
gies peak power prices were effectively averaged out and passed on to all power mar-
ket participants equally. In Smart Grid scenario, inclusion of demand response (DR)
may be found out to be a significant input to power network operations for achieving
operational excellence. The unprecedented and growing concerns over environmen-
tal issues from traditional fossil-fired power stations turned the engineering minds
towards efficient use of large amounts of renewable energy. The impediments of
high generation cost and intermittent nature of wind power and solar power needed
more advanced control systems to facilitate the connection to the grid. Moreover,
to improve reliability and to respond to natural disaster or malicious sabotage, the
Smart Grid is designed such that it can mend the fault by itself which means it has got

P. Singha (B) · D. Ghosh · S. Koley · R. Sarkar · S. Sen

Electrical Engineering, Kalyani Government Engineering College,
Nadia, West Bengal, India
e-mail: purbasha.singha95@gmail.com
D. Ghosh
e-mail: dbnjnghosh1996@gmail.com
S. Koley
e-mail: sayanko1000@gmail.com
R. Sarkar
e-mail: rishiraj1000sarkar@gmail.com
S. Sen
e-mail: sawansen@gmail.com

© Springer Nature Switzerland AG 2019 269

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_23
270 P. Singha et al.

self healing property [1]. Proper installation of information network integrated with
Smart Grid can appear to be an invaluable resource for regulation of the operational
condition of the system [2, 3]. Over the last decade, Plug-in Electric Vehicles (PEV)
has taken the transportation sector to reach a new level. The concept of PEV has
been very popular as dependence on petroleum is to be reduced for nature’s sake.
Preliminary studies indicate that PEVs will become the key solution of the electricity
industry in the near future as pollution-free alternatives to the conventional petroleum
based transportation. The high acceptability of PEVs in electrical market have sig-
nificant impacts on power market especially at the distribution level [4, 5]. In the
quest of optimizing the utilization of these new resources, researchers in the recent
past have been proposing indigenous methodologies and solution algorithm. The
popularity of PEV is favourable utilization of Off-peak periods of power networks
that is to charge the batteries to supply for the vehicles during peak loading periods
when the price of electricity is high. But PEV is also capable of supplying electricity
to grid when demand curve is high. While the power system planners heavily rely
upon the methodologies in [6, 7] that introduced a distinctive work where operat-
ing conditions were optimized with a coordination methodology of PEV charging.
Plug-In Vehicles in a Smart Grid has been depicted in [8, 9]. A prediction based
charging method of PEVs was depicted in [10] where dynamic price information
was utilized to produce optimum charging schedule of PEVs. Ref. [11] designed an
OPF to produce an optimum schedule of charging of PEVs considering the operating
condition but the methodology could not minimize generation cost by maximizing
load catering. The advantages of battery storage were utilized in [12] for optimal
operation of micro-grids that is optimizing both generation and loading schedule but
it could not assure a standard of operating conditions. All these methods pointed
towards effective utilization of DR to optimize the PEV and Smart Grid operation.
Ref. [13] A framework of future transmission grid is portrayed while [14–16] identi-
fying the challenges faced with implementation of DR in distribution of the existing
grid. During the inclusion of renewable energy sources, immense difficulty to sys-
tem optimization is posed by the unparalleled sporadic nature and cost curve. Refs.
[17–20] proposed optimization methodologies to intensify the operational status of
power grid endorsing a particular renewable energy source. Effective deployment of
chargeable batteries has been depicted for optimization of intermittent or renewable
energy resources. The literature survey has shown that PEVs can be made to work in
conjunction with demand response, intermittent renewable energy sources and it is
also capable of standardizing the conditions prevailing during operation in terms of
voltage and loss profile of the system. Moreover it is efficient in peak load flattening
to reduce the dynamics of electricity price [21–24]. Social welfare has been taken on
ground as an objective but applied less importance on enduring operating conditions
of the system or the load shedding technique whereas [25, 26] some new approaches
have been considered. PEVs schedule of charging and discharging has been planned
in such a way that energy can be uprooted from grid to vehicle or from vehicle to
grid respectively. A no of other authors have adopted different methodologies for
charging profiles of PEV using recorded vehicle usage data.
Smart Coordination Approach for Power Management with PEV … 271

Thus, the above literature review necessitates of an algorithm that ensures a stan-
dard parametric operational state with a goal to minimize the electricity price with
favourable load catering without contravening the price equilibrium of the market
by harmonizing multiple charging and discharging of PEVs, that can greatly affect
grid repeatability, security and performance. The proposed algorithm in this paper
not only integrates the DR and generation characteristics but also involves price sen-
sitivity of voltage profile, line loss, transmission congestion and load curtailment
to accomplish all the features of Smart Grid. To compare the solution obtained, a
standard OPF [27] has been embraced. To ratify the power management infrastruc-
ture and distribution network loss minimization, the smart coordination strategy is
incorporated on modified IEEE 30 bus system that consists of a mix of residential,
commercial and industrial customers penetrated with PEVs.

2 Theory

An electrical grid that comprises a variety of functioning and energy measures with
higher order of reliability. Researchers designed charging and discharging schedule of
PEVs under smart grid, in which one category of research was focused on charging
and discharging schedule based on the information about the present state of the
power grid and the second category is the one in which charging or discharging
schedule is based on forecasted estimates of the state of the grid. Unlike classic
grids, here local sub networks generate more power than it is consuming. System
Operator will be able to reach everywhere of network to maintain optimized operating
conditions under the worst possible states of the system with the help of deployment
of new resources. In this context ISO will be able to identify the state variable creating
imbalance. The price change response of the state variables of modern power markets
incorporating PEVs have been elaborated in the following sections.

2.1 Electric Vehicles and Distribution Networks

PEVs are turning out for being the most innovative and environment friendly alter-
native of only traditional fuel based automobiles. The term Plug-in relates to the
electric power storage system in built in these kind of vehicles to accumulate elec-
trical power from power outlet. Scarcity of fossil fuel and their corresponding price
hike are forcing the development of more of these kinds of vehicles [28–30]. But
exploitation of PEV in improper way has a great impact on power distribution net-
work. If simultaneous charging of the vehicles would be accomplished in a small
geographic area, the increased demand caused due to charging could cause major
troubles for the utility. While PEVs are charged all along at system peak, it could
result in supply shortages or create an urge for large new investments in expansion
of capacity of generation and setting up new generation plants, congestion problem
272 P. Singha et al.

at distribution level for most utilities will be the most noted concern due to PEVs
charged all along. Thus, PEVs must be able to communicate bi-directionally with
the grid where the grid can inform PEV about its constraints, generation capabilities,
load catering priorities, and the price at which it can afford to sell power to PEVs
and the PEVs need to express its requirements time of charging and price it can to
buy power from the grid.

2.2 State Space Modeling of Power Network Including PEVs

If numbers of generators  N and Numbers of PEV loads  M and Number of other

loads  m, the price sensitive state variables of a power network can be written as,

x  [PG1 PG2 ..PG N L p1 L p2 . . . L M L 1 L 2 . . . L m Pc TL Vmin Pl max ]T (1)

where Pc  load retrenched, TL  Total line loss, Vmin  minimum bus voltage,
Pl max  maximum line flow.
As the market players are connected with ISO through smart metering, on receipt
of the price information at the nth hour, the participants either change or persevere
with their propositions best suitable to them. Under the fencing of social welfare the
ISO determines the price dependent state variables x(n + 1) at the (n + 1)th hour
based on the price of nth hour. Mathematically

x(n + 1)  f ( p)  Ax(n) + Bu(n) (2)

where A is the sensitivity matrix and B is the contingency or state modification

matrix, which will arise only when participant, characteristics are reoriented by
either deliberately or inadvertently.

3 Problem Statement

The aim of power management is to make the total power losses least and energy
transferred to the PEVs highest over time duration [1, T] maintaining other operating
condition. Thus, the multi-objective function considering overall social welfare may
be defined as follows:


T 
max   C(dk ) + max E D − C(glv) (3)
k1

where function C(·) is strictly increasing and convex. Convexity of the above cost
function causes heavier penalty on larger instantaneous power losses, which is impor-
Smart Coordination Approach for Power Management with PEV … 273

tant
in alleviating power loss values. PEVs over time duration [1, T] is represented
by E D and finally, C(glv) represents the operational limit violation constrained
generation cost function. Mathematically, these terms can be expressed as follows:


M+m
C(dk )  2
ak Pd(M+m)k + bk Pd(M+m)k + ck (4)
k1
 ng 

C(glv)  ai Pgi2 + bi Pgi + ci + Pc .P F1 + TL .P F2 + Vmin .P F3 + Pl max .P F4
i1
(5)

Subject to the power balance equations at all buses and other constraints are as
follows:

Pgimin ≤ Pgi0 ≤ Pgimax ∀i ∈ N (6)

Q min
gi ≤ Q 0gi ≤ Q max
gi ∀i ∈ N (7)
Pgimin ≤ Pgi ≤ Pgimax ∀i ∈ N
j
(8)
Q min ≤ Q gi ≤ Q max
j
gi gi ∀i ∈ N (9)
     
 min     max 
Vk  ≤ Vk ≤ Vk ∀k ∈ M + m (10)

and PEV charging constraint for every t ∈ {1, . . . . . . T },


T
PEk [t]  Ck ∀k ∈ N , t ∈ {1, . . . T }
t1

ai , bi , ci are cost coefficients of the ith generating station, Pgi is generation of

the ith generator, ak , bk are bid coefficients of jth consumer, Pd(M+m)k denotes the
power demand of the M numbers of PEV loads and m number of other loads,
P F1 , P F2 , P F3 are the penalties for operational limit violation set by ISO, Ck is
the capacity of PEV battery connected to bus k.

4 Simulation and Result

As the proposed methodology claims that apposite charging and discharging sched-
ule of PEVs may lead to an operating condition which overall is beneficial for all
the power market participants, the case study has been performed in modified IEEE
30 bus system having both generator characteristics and price responsive demand
characteristics as input to cost optimization algorithm. This modified system has
six GENCOs connected to buses 1, 2, 5, 8, 11, 13 and 24 Load Despatch Cen-
274 P. Singha et al.

tres (LDCs) with which PEV may be connected for charging or discharging as per
consumers’ requirement. Aside from the elastic/inelastic PEV loads, each LDCs
excluding GENCOs, k ∈ {1, 2, . . . , 24} is connected to an inelastic load as well. The
system description has been tabulated in Table 1.
To check the efficacy of the proposed methodology for maintaining the standard
operational constraints with an aim of sustaining both individual and social welfare
maximum by smart coordination approach of PEV with inelastic power demand of
consumer, without violating the price equilibrium of the power market, the simula-
tions have been performed in different steps. In the first step, different LDCs have been
grouped (HIG and LIG) through price depending zone-clustering algorithm. In next
step, generation-demand schedule has been prepared with PEV charging-discharging
plan. With this charging and discharging schedule of PEV, market demand can be
flattened during peak time and can be enhanced during off peak time to maintain the
base demand. This has been shown in step 3 of the simulation. Charging and discharg-
ing of PEV is not only significant to fulfil the purpose of a vehicle, but maintaining
appropriate charging-discharging schedule of PEV has assisted to maintain the price
equilibrium of the power market. In step 4 of simulation, it can be shown that suit-
able charging-discharging schedule of PEV leads toward the equilibrium of market
demand as well as price of electricity. Once more, to prepare a charging-discharging
schedule of PEV, it is not efficient to prove the adequacy of proposed methodology
without judging its efficiency for maintaining standard operational constraints of the
power network. Hence, inspections of various operational standards (making trans-
mission line loss less, maintaining voltage profile, etc.) are the important parts of
step 5 of simulation.

4.1 Clustering of LDCs Through Price Depending

Zone-Clustering Algorithm

The proposed algorithm depends on non-linear relation between system demand and
price of electricity, which may vary throughout the whole day. Higher Income Group
(HIG) consists of LDCs where with minimal change of demand, the change of cost

Table 1 System description

Serial no. Specifications Provision
1. LDCs 24
2. PEV 1000
3. GENCOs 6
4. Maximum elastic/inelastic 283.4
demand (MW)
5. Maximum reactive demand 126
(MVAr)
Smart Coordination Approach for Power Management with PEV … 275

is more than Lower Income Group (LIG). This non-linear relation between system
demand and electricity price depends on the fact that, the consumers from HIG are
willing to pay more for maintaining the reliability and quality of power. It has been
shown from the following graph that 17 LDCs may be assembled in HIG group and
remaining LDCs are under LIG group in projected system (Fig. 1).

4.2 Preparation of Generation-Demand Schedule with PEV

Charging-Discharging Plan

Now here, the generation-demand map has been shown for demand-price equilibrium
condition, depending on that different LDCs can plan their offering price to have their
inelastic demand with PEV charging and discharging. But in Smart Grid arena, price
of electricity is not fixed; it fluctuates all over the day-night depending on demand
pattern. Following graph shows the power market inelastic demand plan throughout
a whole day, where total 24 h have been subdivided into four sectors depending on
variable price schedule.
From (Fig. 2), ISO can fix up the PEV charging-discharging schedule to maintain
the market equilibrium, which can be broadcasted to the consumer through smart
meter. Consequently the willing participants of power market can reschedule their
demand to enjoy quality power at lowest possible price. Thus the proposed algorithm
for smart coordination has got a short-term forecasting module and an optimization
section. This short term module remits information about the number of PEVs in the
parking garage which are ready for charging during off peak time or supply power
to consumer during peak time in the course of stored power and the objective of the
optimization module is to make the energy delivered to PEV maximum and satisfy
optimization conditions for the PEV incorporating operational constraints which is
connected to the power grid and customer demands.

Fig. 1 Zone clustering of

LDCs
276 P. Singha et al.

4.3 Demand Response of the Power Market with PEV

Charging and Discharging Schedule

From the above demand schedule (Fig. 2) it is apparently clear that, during 4 PM
to 10 PM, the market demand is high (peak load condition). Thus it becomes very
essential to make PEV ready for discharging when peak loading condition prevails,
which in turn reduces the demand peak to base demand. Again, the cost of electricity
does not remain same throughout the whole day (it will be high during peak demand
and low during off peak time under Smart Grid arena), so it is desirable to charge the
PEV during low cost time duration (off peak state: 10 am to 4 pm) after reaching the
office when the purpose of vehicle is over for few hours. Similarly, during evening
time period (4 pm to 10 pm), the cost of electricity will be high; hence it is desirable
to use stored energy in PEV, which in turn flatten the peak demand in one side and
other side it will reduce the expenses of power consumers. The competence of the
proposed algorithm is to heal the power market by its own under the rearrangement of
operating conditions particularly during peak periods, when the available generation
is most costly (Fig. 3a, b).

4.4 Cost Evaluation to Estimate the Economical Benefits

of Power Consumer

With the base generation schedule of GENCOs, the performance of the proposed
algorithm has been observed to be remarkably superior in sustaining the operat-
ing conditions within safe limit, owing to the fact that the proposed algorithm not

Fig. 2 Power market

demand for a whole day
Smart Coordination Approach for Power Management with PEV … 277

Fig. 3 a Enhancement of load line with proper charging of PEVs. b Flattening of load line with
proper use of stored energy of PEVs

only manages generation with optimal cost but also manages loads of PEVs with
efficiency to distribute maximum demand at minimum cost in the most favourable
way, maintaining all operating constraints. Table 2 shows the economical benefits
of power consumer with proposed methodology for proper charging and discharg-
ing plan of PEVs. Projected algorithm efficiently administers both circumstances of
power market, where cost of electricity is independent of demand and dependent of
demand.
With economical benefits of power consumers, this algorithm as well can be used
to manage PEV as supplier of power (other than GENCOs) to consumers during peak
load time and enhance the load line during off-peak time. Following graph (Fig. 4)
shows that change of electricity cost during off peak time as well as peak time under
variable demand-price condition.

Table 2 Economical benefits of power consumers

Savings 4–5 PM 5–6 PM 6–7 PM 7–8 PM 8–9 PM 9–10 PM
during
discharging
Fixed price 7.31 10.79 71.72 72.12 72.43 25.5
(Rs.)
Variable 27.1 39.9 257.2 258.1 259.4 93.7
price (Rs.)
278 P. Singha et al.

Fig. 4 Change of electricity

cost due to inclusion of
PEVs in market demand

4.5 Applicability of Proposed Algorithm to Maintain

Standard Operational Constraints

Planning of charging-discharging schedule of PEV, maintaining load line close to

base load, sustaining power market price equilibrium are not sufficient to prove the
competence of proposed methodology without evaluating its efficiency for maintain-
ing standard operational constraints of the power network. Therefore, the optimiza-
tion section also monitors the distribution network losses and voltages of all affected
LDCs considering all other operational constraints. Thus, following studies have
been carried out to formalize the power management infrastructure and distribution
network loss minimization (Fig. 5).

5 Conclusion

The approachability to smart metering communications has obtained profound

changes in power grid operation. Here this paper presents a methodology to illustrate
optimal and efficient operations of Smart Grid with the presence of PEVs. The model
effectively regulates the charging-discharging schedule of PEVs to reach prolific
solutions negotiating with generator characteristics, demand response of shiftable
loads, PEVs, voltage stability and transmission loss limits. Simulation results con-
vincingly shows that the application of proposed methodology palliate network
constraints while regaling peak demand and reducing the cost of electricity even
under worst possible states of the system operation. Comparing with the conven-
Smart Coordination Approach for Power Management with PEV … 279

Fig. 5 a Voltage pattern of affected LDCs during charging of PEVs. b Voltage pattern of affected
LDCs during discharging of PEVs. c Comparison of transmission loss pattern during charging-
discharging schedule of PEVs

tional system functioning based on only GENCOs scheduling between highest and
lowest possible generation, the proposed algorithm implements consumer or PEVs
charging-discharging schedule with a smart communication facility where not only
GENCOs but also power consumer with PEV characteristics can take part to change
their position for their own and social benefit.

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rating Voltage Stability Margin Criterion, www.pserc.wisc.edu. Accessed Nov. 2001
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Fault Analysis in Grid Connected Solar
Photovoltaic System

Nirjhar Saha, Atanu Maji, Subhra Mukherjee

and Niladri Mukherjee

1 Introduction

In hugely increasing power demand scenario solar energy plays a vital role. In solar
energy system, photovoltaic (PV) array is used to convert the solar energy to electri-
cal energy. The output from the photovoltaic (PV) array is dependent on the weather
conditions. To get the maximum power output various maximum power point track-
ing (MPPT) algorithm has been developed throughout the years. Connecting the PV
array to the grid is a challenging part as in order to connect it needs synchronization
to the grid. After connecting to the grid it is very essential to analyze the effect of
different types of faults on the system to enhance the reliability of the system. It is
very essential to detect the different types of faults as early as possible and from the
protection point of view it is very much obvious that, the protection system should
be able to detect different faults in the system properly.
Detail simulation diagram of grid connected photovoltaic system has been devel-
oped using PSCAD, a transient software package [1]. The detail modeling of inverter
to connect the PV system to the grid and the control of active and reactive power has
been discussed in [2]. F. Liu, Y. Kang and Y. Zhang proposed an effective maximum
power point tracking (MPPT) algorithm named as perturb and observe (P and O)

N. Saha (B) · S. Mukherjee

Electrical Engineering Department, NIT, MAKAUT, Kolkata, West Bengal, India
e-mail: nirjharsaha94@gmail.com
S. Mukherjee
e-mail: subhra.reek@gmail.com
A. Maji · N. Mukherjee
Electrical Engineering Department, SKFGI, MAKAUT, Kolkata, West Bengal, India
e-mail: atanu.maji@skf.edu.in
N. Mukherjee
e-mail: niladrimukherjee88@gmail.com

© Springer Nature Switzerland AG 2019 283

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_24
284 N. Saha et al.

and using this method performance of the system has been evaluated and compared
with the other methods [3]. Similarly another MPPT method, incremental conduc-
tance (IC) has also been employed with variable step size for more accuracy and
good adaptability with the rapid changing weather conditions [4]. Different types
of unbalanced faults have been simulated and their effects in the grid system have
been analyzed [5]. Another method to detect the fault condition has been devel-
oped taking the power loss on DC side which is used as an indicator [6], where an
automatic supervision system has been used for reliable discrimination. A control
scheme has been proposed for grid faults with unbalanced grid voltage by controlling
various control parameters and sensing the current harmonics distortion [7]. Fault
analysis of three phase grid connected solar system has been discussed in [8], where
synchronously-rotating d-q reference theory is used to model the converter. Three-
phase grid-connected Photovoltaic (PV) system based on Current Source Inverter
(CSI) has been developed in [9] and fault analysis has been done. Dynamic mod-
eling based grid connected hybrid system proposed in [10], where hybrid system
consists of photovoltaic (PV) and wind energy system. Voltage and current signature
analysis based different techniques already proposed by the researchers to analyze
the faults in electrical systems where different planes (Clarke and Park plane), differ-
ent signal processing and soft computing techniques have been used for this purpose
[11–17].
None of the research works, fault condition of grid connected solar PV system
has been assessed by the THD inter harmonics groups and DWT based skewness,
kurtosis, rms and mean value analysis. For this reason an attempt has been made to
assess the fault condition of grid connected solar PV system by THD, inter harmonics
and DWT based skewness, kurtosis, rms and mean value analysis. In this work
different short circuit faults are considered in grid side and inverter output side
current (system current) is used for fault analysis which is shown in Fig. 1.

Fig. 1 Block diagram of grid connected solar PV system

Fault Analysis in Grid Connected Solar Photovoltaic System 285

2 System Description

The simulink model which is shown in Fig. 1 is used for fault analysis. A 250 kW solar
array is considered for simulation. The power output from solar array is fed to the
boost converter, whose duty cycle is controlled by the maximum power point tracking
(MPPT) block. The controlled dc output is fed to the inverter which converts the dc
voltage to ac voltage (250 V) which is stepped up by a transformer and ultimately
it was connected to 25 kV grid. Different short circuit faults are considered on the
grid side and all the analysis has been done based on ‘R’ phase system current or
inverter output side current. Fast Fourier transform (FFT) based THD, inter harmonics
calculations and Discrete Wavelet transform (DWT) based parameter analysis has
been done on the captured ‘R’ phase system current for fault analysis.

3 Mathematical Techniques Used for Fault Analysis

3.1 Total Harmonic Distortion (THD)

The Total Harmonic Distortion (THD) of a signal is the measurement of the harmonic
distortion which is present in the signal and it can be defined as the ratio of the square
root of the sum of the currents of all harmonic components to the current of the
fundamental frequency. It is used for linearization the power quality of electric power
systems. The current waveform of ‘R’ phase has been taken in normal condition and
as well as in different fault conditions then using Fast Fourier Transform (FFT), the
total harmonic distortion (THD) has been calculated. Table 1 shows the THD values
of ‘R’ phase current signal in different conditions from where normal and different
fault conditions can be assessed properly. Following formula is used to calculate the
THD of ‘R’phase current [18].

(I22 + I32 + I42 + . . . . . . .In2 )
THD  × 100 (1)
I1

Table 1 THD results of ‘R’ phase current in different conditions

Conditions dc com- 2nd har- 3rd har- 4th har- 5th har- 6th har- 7th har- THD
ponent in monics in monics in monics in monics in monics in monics in
% % % % % % %
Normal 0.01 0.34 0.04 0.03 0.28 0.01 0.01 0.443509
L-G 13.29 0.55 0.26 0.07 0.06 0.06 0.03 0.618951
L-L-L-G 11.66 0.44 0.1 0.11 0.08 0.01 0.04 0.473075
L-L 13.87 0.48 0.22 0.09 0.04 0.04 0.03 0.539444
L-L-G 13.85 0.47 0.21 0.09 0.04 0.03 0.03 0.525833
286 N. Saha et al.

where

I1 Current in fundamental frequency

In Current harmonics. n  2, 3… n.

3.2 Inter-harmonics Group Analysis

For further analysis of the signals the magnitude of inter harmonics has been observed
and the inter harmonics group has been calculated using the following formula.

11
I Gk  Ik∗n+5i × 100 (2)
i1

where
IG Inter-harmonic Group
k Group number, k  0, 1, 2, 3…
n fundamental frequency of the signal
In this work up to second inter-harmonics group (i.e. k  2) of ‘R’ phase system
current signal has been considered for fault analysis and the results has been given
in Table 2.

3.3 Discrete Wavelet Transform (DWT) Analysis

Using Wavelet Transform (WT) better time frequency representation can be achieved
from non-stationery signals which were the short-comings of other signal processing
techniques like, FFT, STFT etc. Continuous Wavelet Transform (CWT) and Discrete
Wavelet Transform (DWT) are the two classifications of WT [15]. Due to some
computational difficulties of CWT; in this work DWT is considered as a technique
to assess the transient conditions occurring due to different types of fault. In DWT,
signal is passing through high pass and low pass filter bank in each decomposition

Table 2 Inter-harmonics group analysis of ‘R’ phase current in different conditions

Inter- Normal L-G condition L-L-L-G L-L condition L-L-G
harmonics condition condition condition
group
IG0 0.722011 20.09749 20.1727 25.33755 25.76861
IG1 0.822496 6.186186 5.271243 13.05052 12.27778
IG2 0.091104 0.78905 0.744983 0.94016 0.855161
Fault Analysis in Grid Connected Solar Photovoltaic System 287

level, to get different frequency band present in the signal. Here, nine (9) levels of
DWT decomposition and ‘db4’ mother wavelet is considered for DWT analysis.
For assessment of different conditions DWT has been done on ‘R’ phase cur-
rent in all the conditions. In DWT up to level nine is considered in all the cases.
Mean, r.m.s, Skewness and kurtosis parameters have also been calculated in all these
decomposition levels to detect and discriminate the fault and normal conditions in
grid connected solar PV system.

3.4 Skewness

Skewness can be mathematically defined as the averaged cubed deviation from the
mean divided by the standard deviation cubed. If the result of the computation is
greater than zero, the distribution is positively skewed. If it’s less than zero, it’s
negatively skewed and equal to zero means it’s symmetric [19].

3.5 Kurtosis

Kurtosis refers to the degree of peak in a distribution. More peak than normal means
that a distribution also has fatter tails and that there are lesser chances of extreme
outcomes compared to a normal distribution. The kurtosis formula measures the
degree of peak [19].

4 Results of Fault Analysis Using Different Techniques

See Fig. 2.
DWT Analysis
In this analysis, at first ‘R’ phase current signal has been decomposed up to
DWT level nine by ‘db4’ based mother wavelet and then rms, mean, skewness and
kurtosis has been calculated for detail level and approximation (approximate) level
coefficients in different conditions which is shown from Figs. 3, 4, 5, and 6.
Results of Mean Values
Results of rms Values
Results of Skewness Values
Results of Kurtosis Values
288 N. Saha et al.

30
25
Magnitude

20
15
10
5
0
IG0 IG1 IG2
Normal 0.72201108 0.822496201 0.091104336
LG 20.09749487 6.186186224 0.789050062
LLLG 20.17270185 5.271242738 0.744983221
LL 25.33754526 13.05051723 0.940159561
LLG 25.76861075 12.27778074 0.855160804

Fig. 2 Pictorial representation of inter-harmonics group analysis of ‘R’ phase current in different
conditions

(a) (b) -5
10
mean values of approximation coefficient

50 1.5
mean values of detail coefficient

0
1

-50 Normal
L-G 0.5
L-L-L-G
-100
0
-150

-0.5
-200 L-L-L-G
Normal
L-L L-L-G
-1 L-L-G
-250 L-G
L-L
-300 -1.5
1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9

DWT Decomposition Level DWT Decomposition Level

Fig. 3 Mean values of a approximation coefficients and b detail coefficients versus DWT decom-
position levels

5 Observations

From the FFT based THD results (Table 1), different fault conditions and normal
condition can be classified properly because THD is found minimum at normal
condition and is higher (different values) at different fault conditions.
In this work, three inter harmonics group has been calculated of ‘R’ phase current
signals in different conditions which is given in Table 2. In this results, maximum
Fault Analysis in Grid Connected Solar Photovoltaic System 289

inter-harmonics group values has been observed in L-L and L-L-G fault conditions
and minimum inter-harmonics group values has been observed in normal condition.
Figure 3a, b is used to depict the results of mean values of approximation and
detail coefficients respectively in different DWT decomposition levels at different
conditions. In Fig. 3a differences between mean values in different conditions is
constant up to level nine and in Fig. 3b difference is maximum at DWT decomposition
level eight (8).
In Fig. 4a, a constant difference has been observed between rms values of approx-
imation coefficients in all those mentioned conditions and in Fig. 4b, maximum
difference has been observed between rms values of detail coefficients at DWT
decomposition level nine but for both the cases minimum values of both the coeffi-
cients has been observed in normal condition.
Figure 5a is used to depict the skewness values of approximate coefficients with
respect to different DWT decomposition levels, where the differences of skewness

(a) (b)
2
3500
rms values of approximaton coefficient

1.8
rms values of detail coefficient

3000
1.6
L-L L-L-G L-L-L-G
2500 L-L-L-G 1.4

1.2
2000 L-L-G
1 L-L

1500 0.8 L-G

Normal
0.6
1000 L-G
Normal 0.4
500
0.2

0 0
1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9
DWT Decomposition Level DWT Decomposition Level

Fig. 4 RMS values of a approximation coefficients and b detail coefficients versus DWT decom-
position levels

(a) (b)
0 150
Skewness values of detail coefficient
Skewness values of approximation

L-L L-L-G L-L-L-G

-0.1 100
Normal Normal L-G
-0.2
50
-0.3
0
coefficient

-0.4
-50
-0.5
-100
-0.6
L-L-L-G
L-G L-L L-L-G
-0.7 -150

-0.8 -200

-0.9 -250
1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9
DWT Decomposition Level DWT Decomposition Level

Fig. 5 Skewness values of a approximation coefficients and b detail coefficients versus DWT
decomposition levels
290 N. Saha et al.

values between normal condition and different fault conditions are almost constant
and maximum negative skewness values has been observed in L-L, L-L-G condi-
tions. In Fig. 5b zig-zag differences of skewness values of detail coefficients has
been observed in different conditions, where the difference is maximum at DWT
decomposition level one (1).
Figure 6a, b is used to show the kurtosis values of approximation and detail coeffi-
cients respectively in different conditions with respect to DWT decomposition levels.
In Fig. 6a, constant differences has been observed where as in Fig. 6b decreasing
differences has been observed up to DWT level six (6) though maximum difference
among all those conditions has been observed at DWT decomposition level one (1).

6 Algorithm of Assessment of Different Conditions of Grid

Connected Solar PV System

An algorithm for assessment of different conditions of grid connected solar PV

system has been made as follows which can be implemented in numerical protection
of grid connected solar PV system:
(a) Step down the any phase system current of solar PV side.
(b) Sample it at proper sampling frequency.
(c) Capture the sampled values through data acquisition system.
(d) Calculate THD, inter-harmonics group of the captured signal.
(e) Determine skewness, kurtosis, rms and mean values of approximation (approx-
imate) and detail coefficients at DWT decomposition levels (up to 9th level).
(f) Diagnose the results to assess different conditions of grid connected solar PV
system.

(a) (b) 5
kurtosis values of approximation coefficient

7 7 10

6.5
Kurtosis values of detail coefficient

6
6
L-L-L-G L-G L-L
L-L-G 5
5.5

5 L-L
4
L-G
4.5
3 Normal
4

3.5 2 L-L-G

Normal L-L-L-G
3
1
2.5

2 0
1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9
DWT Decomposition Level DWT Decomposition Level

Fig. 6 Kurtosis values of a approximation coefficients and b detail coefficients versus DWT decom-
position levels
Fault Analysis in Grid Connected Solar Photovoltaic System 291

7 Specific Outcome

In this paper, Normal condition and different short circuit fault conditions of grid
connected solar PV system has been analyzed by THD, inter-harmonics group and
DWT based parameter analysis. Minimum THD value has been recorded at normal
conditions and maximum THD values has been recorded at L-G fault condition. In
case of inter-harmonics group analysis, minimum inter-harmonics has been observed
at normal condition where as maximum inter-harmonics has been observed at L-
G and L-L-G fault conditions. In DWT based parameter analysis maximum and
constant differences among parameter values have been observed for approximation
coefficients in different conditions where as in detail coefficients it is different for
different cases.

8 Conclusion

In this work, Normal condition and different short circuit fault conditions of grid
connected solar PV system has been analyzed by THD, inter-harmonics group and
DWT based parameter analysis. Incremental conductance (IC) is used here to extract
maximum power from solar PV system which has been fed to the grid and then dif-
ferent fault conditions at grid side have been analyzed. Different THD and different
inter-harmonics group values has been observed at different conditions which can be
used to assess the fault conditions of grid connected solar PV system. DWT based
skewness, kurtosis, mean and rms values also calculated in different conditions for
approximation and detail coefficients where maximum differences of these param-
eters values have been observed for approximation coefficients which can be used
further to analyze the fault conditions in grid connected solar PV system. It can be
also used for numerical protection of microgrid system.

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Sub-harmonics Based String Fault
Assessment in Solar PV Arrays

Tapash Kr. Das, Ayan Banik, Surajit Chattopadhyay

and Arabinda Das

1 Introduction

Application of photo voltaic (PV) system as energy resource in microgrid is becoming

more popular. Modeling and simulation of such system have become important area
in such system. One of the major issues in such system is monitoring of photo voltaic
system and its fault diagnosis. An extensive research work is progressing to study the
various aspects of PV array connected inverter system. Kuitche et al. (2014) analyzed
in detail about a new dominant failure mechanism for field-aged crystalline silicon
photo voltaic modules during extreme weather conditions [1] where, encapsulate dis-
coloration of PV modules were noticed during desert condition. In this attempt, the
several risk priority number based quantitative measures and sizable datasheet have
been developed for dominant failure modes. New leakage current detection tech-
nique for solar photo voltaic modules [2] has been introduced by Dhere et al. (2014)
where, different tests under high voltage condition have been performed and charac-
teristics of leakage current for poly crystalline modules dependent on construction,
material and different climatic condition have been observed. Hariharan et al. (2016)

T. Kr. Das (B) · S. Chattopadhyay

Department of Electrical Engineering, GKCIET (Under MHRD, Government of India),
Malda, West Bengal, India
e-mail: p_tapash_das@yahoo.co.in
S. Chattopadhyay
e-mail: surajitchattopadhyay@gmail.com
A. Banik
Department of Electrical Engineering,
Cooch Behar Government Engineering College, Cooch Behar, West Bengal, India
e-mail: ayanbanik97@gmail.com
A. Das
Department of Electrical Engineering, Jadavpur University, Kolkata, India
e-mail: adas_ee_ju@gmail.com
© Springer Nature Switzerland AG 2019 293
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_25
294 T. Kr. Das et al.

developed a whole new partial shading based fault investigation system for photo
voltaic array [3]. In this attempt, to improve the reliability and efficiency under dif-
ferent irradiation conditions various experiments have been carried out where, photo
voltaic array has been classified into three categories. A new optimization method
for solar PV system to increase the output under irregular irradiation [4] has been
introduced by Obane et al. (2012) where, to minimize losses the reconnection of PV
field has been observed. Yi et al. (2017) presented a DC short circuit fault identi-
fication technique under low irradiance conditions for photovoltaic systems where,
multi-resolution signal decomposition and fuzzy inference based schemes have been
used [5]. A new logic based intelligent fault detection system in solar power elec-
tronic converter [6] has been developed by Chen and Bazzi (2017). In this attempt the
proposed model has been experimentally validated and tested under the environment
of different computer simulations and hardware. Hejri and Mokhtari (2017) intro-
duced a new parameterization scheme of solar Photo voltaic cells and module [7].
Cárdenas et al. (2017) proposed another new single diode based parameter extraction
technique of solar photo voltaic module [8]. Irradiance and temperature dependence
of photovoltaic modules in solar photo voltaic system [9] has been analyzed in detail
by Sauer et al. (2015) where an optimized model relative to standard model has been
demonstrated for improving the energy yield prediction. A new luminescent materi-
als based technique for photovoltaic modules [10] has been developed by Klampaftis
et al. (2015) where, both color and graphical design were used in photo voltaic pro-
duction technologies to improve the efficiency. Manganiello et al. (2015) reviewed in
detail about aging and mismatching mechanisms occurred in photovoltaic modules
[11]. In this attempt, cause and effect of aging and mismatching mechanisms of PV
cells have been discussed.
A whole new cost effective MOSFET based RC circuit driven educational tool
to identify different characteristics of photo voltaic modules [12] has been designed
by Dos Santos et al. (2017) where, different data and curves were captured and dis-
played with the help of digital oscilloscope. In this attempt, estimation of eradiation,
maximum power point and temperature of PV module have been analyzed. In some
recent work, harmonic assessment based fault diagnosis approaches [13–16] have
also been introduced. However, very few works have been found to utilize subhar-
monics component in monitoring and fault assessment of solar PV arrays.
In this work, an attempt has been taken to study the effect of disconnection of
few strings in solar arrays. Based on subharmonic assessment, an algorithm has been
proposed for such string fault monitoring and has been validated by simulation.

2 Data Acquisition

PV array based microgrid system has been considered and has been modeled as shown
in Fig. 1. Four PV arrays connected in parallel each consisting of 64 strings are used
as energy resource. Combination of PV arrays is connected to three phase average
model based voltage source converter (VSC) through DC to DC charge controller.
Sub-harmonics Based String Fault Assessment in Solar PV Arrays 295

Fig. 1 PV arrays connected

with inverter unit

Inverter output is connected to load through three phase 400 KVA, 260 V/25 kV,
60 Hz star/delta transformer.
Current signals from the three phase inverter output terminal have been captured.
Data capturing has been carried out both at normal condition and string fault. In
simulation current measurement blocks have been connected in series with each phase
of inverter output. From the captured current signals various frequencies present in
the waveform have been measured for further assessment.

3 Fault Simulation

At normal condition four arrays have been used; each having 64 numbers of strings.
All-together 256 numbers of strings has been used in normal condition. Then faults
have been created in certain portion of the string. Gradually the numbers of faulty
strings have been increased from 0 to 25%. For each condition current signal is
captured and harmonic assessment has been done out on starting transient. Inverter
output current at normal condition (0% String fault) has been shown Fig. 2 and
inverter output current at 9.38% string fault has been shown in Fig. 3.

Fig. 2 Inverter output current at normal condition (0% string fault)

296 T. Kr. Das et al.

Fig. 3 Inverter output current at 9.38% string fault condition

4 Sub-harmonics Feature Extraction

Sub-harmonics component with 12 Hz interval have been measured from the inverter
output current signal both at normal condition as well as string fault conditions.
String fault has been considered up to 25% considering 256 numbers of total strings.
String fault refers disconnection of faulty strings or inactiveness of faulty strings in
contributing energy to the microgrid system through inverter input terminals. The
magnitudes of sub-harmonic components present in the inverter output current at
different conditions have been presented in Table 1.
Magnitudes of sub-harmonic components versus frequency of sub-harmonic com-
ponents of have been shown in Fig. 4 and their comparative bar chart representation
has been shown Fig. 5. The Fig. 4 shows that sub-harmonic components having fre-
quencies of 12 and 36 Hz are decreasing gradually with the increase in percentage
of fault. The other two components remain almost constant.

Fig. 4 Magnitude of sub-harmonics versus percentage of string fault

Table 1 Magnitudes of sub-harmonic components present in inverter output current at different conditions
Percentage 0 3.125 6.25 9.375 12.5 15.625 18.75 21.875 25
string fault
(%)
Frequency Magnitude of sub-harmonics components
(Hz)
12 11.5 10.47 10.38 11.12 12.98 15.04 12.74 3.94 5.03
24 25.9 22.5 20.16 19.61 20.12 18.92 13.86 4.44 6.91
36 52.46 47.52 43.4 38.9 33.46 26.31 17.05 6.27 10.34
48 83.25 79.3 75.87 71.28 63.9 52.34 36.24 20.99 26.36
Sub-harmonics Based String Fault Assessment in Solar PV Arrays
297
298 T. Kr. Das et al.

5 Curve Selection and Linier Approximation

Among the four relations shown in Figs. 4 and 5, Amplitude (A) versus string
fault(SF ) corresponding to sub-harmonic component having frequency 48 and 36 Hz
are very close to linear nature and therefore these two natures have selected for further
assessment.
Linear approximation of these two natures has been done as shown in Fig. 6. Math-
ematical equation of these two approximate linearized natures has been determined
as follows:

for 48Hz, A48  −2.751 S F +86 (1)

for 36 Hz, A36  −1.981 S F +55 (2)

from Eq. (1) string fault( S F ) can be written as

Fig. 5 Sub-harmonics amplitude comparison

Fig. 6 Linear approximate nature of selected sub-harmonic components

Sub-harmonics Based String Fault Assessment in Solar PV Arrays 299

86 − A48
SF  (3)
2.751
from Eq. (2) string fault( S F ) can be written as
55 − A36
SF  (4)
1.981
Equations (3) and (4) have been used for assessment of string faults.

6 Algorithm and Validation

6.1 Algorithm

Based on curve selection and linear approximation mathematical expressions have

been established by Eqs. (3) and (4) among amplitudes of selected sub-harmonics
components and percentage of string fault. Using these equations an algorithm pro-
posed as follows:
i. Capture inverter output current
ii. Select starting transient
iii. Determine sub-harmonic component
iv. Assess string fault using Eqs. (3) and (4).

6.2 Validation

The above algorithm has been validated in the same type of system. As in practical
cases percentage of string faults remains low at initial stage, validation has been done
for very small percentage of string fault conditions (considering 5 and 10 numbers
faulty strings). First amplitude of 48 and 36 Hz components of inverter output currents
corresponding to 5 and 10 numbers faulty strings have been determined and then
percentage of string faults have been calculated using Eqs. (3) and (4). The results
obtained in validation have been presented in Table 2.
Comparative study of the results obtained in Table 2 shows very similarities with
the actual. Among 48 and 36 Hz the result obtained from the equation using 36 Hz
of sub-harmonic component is closer to the actual than other.
300 T. Kr. Das et al.

Table 2 Percentage of string fault obtained in validation

Known number of faulty string Amplitude of sub-harmonic Percentage of string fault
components
5 (1.95%) A36  51.56 1.736
A48  82.54 1.276
10 (3.91%) A36  50.71 2.165
A48  81.36 1.712

6.3 Discussion

Accuracy of Eq. (3) is better than that of Eq. (4) this is because original nature of
amplitude versus percentage of string fault for 36 Hz sub-harmonic component is
more nearer to linear nature. The accuracy of the proposed algorithm can be improved
by using polynomial expression of the natures of sub-harmonic components. It may
be noted that the best frequency component is system dependent and may vary in other
system. However, the present approach may be an effective means of monitoring
string fault. Use of starting transient reduces the effect of loading in the relative
amount of different sub-harmonic components.

7 Conclusion

The work has presented monitoring of string fault in PV arrays. An attempt has been
taken to monitor the string fault which refers to disconnection of few strings con-
nected with PV arrays feeding energy to the inverter. Waveforms of inverter output
currents have been captured and monitored. Staring transient of inverter output cur-
rent has been selected and sub-harmonic components have been extracted. Specific
relations have been observed among for amplitudes of selected frequencies versus
string faults. Frequency selection has been carried out and linear approximations
have been done in the relation between amplitude versus percentage of string faults.
At the end, algorithm has been proposed for monitoring the number of faulty strings
and has been validated; limitation as well as utility has been highlighted.

References

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 Part IV
Control Techniques
Design of Bacterial Foraging
Optimization Algorithm Based Adaptive
Sliding Mode Controller for Inverted
Pendulum

Rajeev Ranjan Pathak and Anindita Sengupta

1 Introduction

Traditional Sliding Mode Control, also called variable structure systems (VSS), was
designed for the systems with uncertainties due to its excellent robustness. But it also
presents some drawbacks such as undesired large control authority and chattering
problem. These drawbacks were overcome by Slotine and Sastry [1] by replacing
control switching at a fixed sliding surface by a smooth control interpolation in a
boundary layer neighboring a time varying sliding surface. This eliminated the exci-
tations of high-frequency un-modeled dynamics and leads to an explicit trade-off
between the model uncertainty and controller tracking performance. In recent years
a large amount of research into the area of sliding control has been developed. Fer-
nanderz and Hedrick [2] generalized the sliding mode approach to a larger class of
multivariable systems. Shyu and Tsai [3] introduced a multiple sliding surfaces in
the sliding controller design to eliminate control chattering. In Oh and Khalil [4]
a VSS controller with a high-gain observer was designed as a function of the state
estimates to ensure attractiveness of sliding manifold. Won and Hedrick [5] devel-
oped a ‘multiple-surface’ sliding control for a class of single-input single-output
(SISO) non-linear systems whose uncertainties do not satisfy the matching condi-
tion. Edwards and Spurgeon [6] presented a controller/observer pair based on sliding
mode ideas, provided robust output tracking of a reference signal. Chen and Toshio
[7, 8] used the transfer function method based on the VSS theory to estimate the
disturbance. The estimated disturbance was employed to construct a VSS-type state
observer. Further, the estimated disturbance and the state observer were applied to a

R. R. Pathak (B) · A. Sengupta

Electrical Engineering Department, IIEST, Shibpur, Howarh, India
e-mail: rajeevpathak27@yahoo.in
A. Sengupta
e-mail: aninsen2002@yahoo.com

© Springer Nature Switzerland AG 2019 305

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_26
306 R. R. Pathak and A. Sengupta

controller to place the desired stable poles and to cancel the disturbance [8]. A com-
mon assumption of these studies was that the bounds of model uncertainties must
be known. If the bounds of model uncertainties were unknown, traditional sliding
control schemes would not work.
In this work, a new Adaptive Sliding Control scheme is proposed for non-linear
systems with unknown bound time varying uncertainties, Sliding-Mode Control the-
ory and adaptive control scheme has been used to solve the tracking reference input
for non-linear systems with bounded unknown parameters and external disturbances.
First, a non linear system has been linearized using feedback linearization technique
with the assumption of system parameters which are known a priori. Second, the
structure of adaptive sliding-mode controller has been developed using the so-called
certainty equivalent principle of adaptive control theory. At this point we consider
appropriate techniques to eliminate the effect of approximation errors and distur-
bances to achieve a desired control objective. The gain of Adaptive SMC has been
optimized using BFOA. The proposed method is not only robust against approxi-
mate errors, disturbances and un-modeled dynamics, but also guarantees the overall
system stability.

2 The Principle of Bacterial Foraging Optimization

Algorithm

Bacteria Foraging Optimization Algorithm (BFOA), proposed by Passino [9], is a

new comer to the family of nature-inspired optimization algorithms. BFOA [10]
is developed by simulating the bacterial foraging process of human E. coli, which
contains three steps: chemotaxis, reproduction and finally Elimination and Dispersal
operation.

2.1 Chemotaxis Operation

This process simulates the movement of an E. coli cell through swimming and tum-
bling via flagella. Biologically an E. coli bacterium can move in two different ways
[11]. It can swim for a period of time in the same direction or it may tumble and alter-
nate between these two modes of operation for the entire lifetime. Suppose θ i ( j, k, l)
represents ith bacterium at jth chemotaxis, kth reproductive and lth elimination-
dispersal step and C(i) is the size of the step taken in the random direction specified
by the tumble (run length unit). Then in computational chemotaxis the movement of
the bacterium may be represented by
(i)
θ i ( j + 1, k, l)  θ i ( j, k, l) + C(i)  (1)
 (i)(i)
T
Design of Bacterial Foraging Optimization Algorithm … 307

where  indicates a vector in the random direction whose elements lie in [−1, 1].

2.2 Reproduction

The least healthy bacteria eventually die when each of the healthier bacteria (which
yielding lower value of the objective function) asexually split into two bacteria, which
are then placed in the same location. This keeps the swarm size constant.

2.3 Elimination and Dispersal Operation

Gradual or sudden changes in the local environment where a bacterium population

lives may occur due to various reasons. Events can occur such that all the bacteria
in a region are killed or a group is dispersed into a new part of the environment. For
example, a significant local rise of temperature may kill a group of bacteria that are
currently in a region with a high concentration of nutrient gradients. Events can take
place in such a fashion that all the bacteria in a region are killed or a group is dispersed
into a new location. Over long periods of time, such events had spread various types
of bacteria into every part of our environment from our intestines to hot springs and
underground environments. To simulate this phenomenon in BFOA some bacteria
are liquidated at random with a very small probability while the new replacements
are randomly initialized over the search space. Elimination and dispersal events
have the effect of possibly destroying chemotaxis progress, but they also have the
effect of assisting in chemotaxis, since dispersal may place the bacteria near good
food sources. From a broad perspective, elimination and dispersal are parts of the
population-level long-distance motile behavior.

3 The Fundamental Principle of Adaptive Sliding Mode

Controller

Sliding mode control, or SMC, is a non-linear control method that alters the dynamics
of a system by application of a discontinuous control signal that forces the system
to “slide” along a sliding surface (as designed by the designer). The control law of
SMC is based on state feedback control law, but it is not a continuous function of
time. Instead, it can switch from one continuous structure to another based on the
current position in the state space. Hence, sliding mode control is a variable structure
control method. The main advantages of this approach are:
(A) While the system is on the sliding manifold it behaves as a reduced order system
with respect to the original plant.
308 R. R. Pathak and A. Sengupta

(B) The dynamic of the system, while in sliding mode is insensitive to model
uncertainties and disturbances.
Adaptive control [12] is an appealing approach for controlling uncertain dynamic
systems. In principle, the systems can be uncertain in terms of its dynamic structure
or its parameters. So far, however, Adaptive control can only deal with parameter-
uncertain systems. Furthermore, existing adaptation methods generally require linear
parameterization of the control law or the system dynamics. Systematic theories
exist on how to design adaptive controllers for general linear systems. If the full
state is available, adaptive control design and implementation is quite simple. If
only output feedback is available, however, adaptive control design is much more
involved because of the need to introduce dynamics into the controller. Some classes
of nonlinear systems can also be adaptively controlled (Fig. 1).

4 Design of Adaptive Sliding Mode Controller Based

on BFOA

4.1 Design of BFOA Encoding

Adaptive Sliding Mode controller is an algorithm based on the estimation of the

information of the past, present and future. The control system is mainly combined
with Adaptive Sliding Mode Controller and the optimal gain of controller has been
obtained using BFOA encoding. Schematic diagram of Inverted Pendulum is shown
in Fig. 2.
State space model of lab based inverted pendulum is given by

Fig. 1 Adaptive sliding mode controller based on BFOA

Design of Bacterial Foraging Optimization Algorithm … 309

Fig. 2 Schematic diagram

of inverted pendulum

⎡ ⎤ ⎡ ⎤⎡ ⎤ ⎡ ⎤
ẋ1 0
1 0 0 x1 0
⎢ ẋ ⎥ ⎢ ⎥ x ⎥ ⎢ ⎥
⎢ 2 ⎥ ⎢0 0 −0.97 0 ⎥⎢ ⎢ 2⎥ ⎢⎢ 0.9124 ⎥
⎥u(t)
⎢ ⎥⎢ ⎥ +
0 0 1 ⎦⎣ x3 ⎦ ⎢
⎣ ẋ3 ⎦ ⎣ 0 ⎣ 0 ⎦
⎥
ẋ4 0
0 21.57 0 x4 −1.824
⎡ ⎤
x1

⎢ x 2 ⎥
Y  0010 ⎢⎣ x3 ⎦
⎥ (2)
x4

where
Linear displacement of cart (x)  x1
Linear velocity of cart ẋ  x2
Angular position of pendulum θ  x3
Angular velocity of pendulum θ̇  x4 .
Adaptive Sliding Mode Controller [13, 14] designed for inverted pendulum is
given below
1    

u eq    465.27 + 64.71λ2 x3 + 64.71λ + λ3 x4 (3)

1.824 21.57 + 3λ 2

where u eq is the equivalent control law of ASMC, and λ is gain of ASMC, our main
objective is to find optimal gain λ using BFOA technique
310 R. R. Pathak and A. Sengupta

That is the objective function, means the index of the fitness value which is
calculated by using of input variables, output variables and intermediate variables.
Although different control systems have different objective fitness function and even
the control systems have changed dramatically, the algorithm has little change rela-
tively. Even the transfer function has been changed, gain of controller can be obtained
easily, this is the fundamental principle of Adaptive Sliding Mode controller which
can be realized.

4.2 Design of Fitness Function

Fitness function is obtained from objective function of control system. It is the

key performance index which determines the stability of control system [15]. The
objective function of Adaptive Sliding Mode controller can be determined based on
the principle of ASMC as:
∞ ∞
J  0.3I AE + 0.7 I T AE  0.3 |e(t)| + 0.7 t|e(t)| (4)
0 0

Fitness function is F  1/J.

Chemotaxis operation is the main part of algorithm, which determines the algo-
rithm’s local search ability and direction. The individual of the population is good
or not is determined by the index of fitness functions’ value. If a bacterium obtains
a better fitness function value at a new location, the information of the position will
be stored, and then the bacterium continues to swim. Otherwise the storage value is
not changed until up to the maximum number of steps Ns.
Reproduction and elimination–dispersal operations are to speed up the conver-
gence of the control system, and also to avoid local optimum. The sorting method is
used in this research work with elimination dispersion probability 0.5.

4.3 Flow Chart of BFOA Encoding

See Fig. 3 and Table 1.

5 Experimental Simulation and Results Analysis

A Simulation design of Adaptive Sliding Mode Controller has been framed for lab
based Inverted Pendulum for tracking angular position of Inverted Pendulum hav-
ing unknown parameters and unbound disturbances. The gain of ASMC has been
optimized using BFOA and its value is 102.1 for given objective function. The no
Design of Bacterial Foraging Optimization Algorithm … 311

Fig. 3 Simulink model of inverted pendulum with sliding mode controller

Table 1 Control parameters of bacterial foraging optimization algorithm

Sl No. Parameter Values
1 Number of bacterium, S 30
2 Number of chemotaxis steps, 10
Nc
3 Number of reproduction steps, 4
Nre
4 Number of 4
elimination-dispersal steps,
Ned
5 Elimination dispersal 0.5
probability, Ped
6 Size of step C(i) 0.1

bacteria taken for simulation is 30 and it has been found that, the simulation process
slows down when the no of bacteria is increased (Fig. 4).
The Inverted Pendulum is found to be highly unstable non linear system. In that
case initially PID Controller was used to track the reference angular position of
pendulum. But it was found that in terms of external unbound disturbance, the PID
could not track the desired reference signal. The same tracking response is shown in
Fig. 5.
Finally AMSC was applied to the Inverted Pendulum which could track the angular
reference signal even in presence of unbound external disturbance and unknown
Parameter uncertainties which is shown in Fig. 6.
312 R. R. Pathak and A. Sengupta

Fig. 4 Tracking response of angular position of inverted pendulum with PID controller without
external unbounded disturbances

Fig. 5 Tracking response of angular position of inverted pendulum with PID controller with exter-
nal disturbances

6 Comparison of Different Controller Performances

See Table 2.

7 Conclusion

According to the above principle and simulation results, the parameter of different
control system can be easily proposed by just changing initialization parameter by
using BFOA. Adaptive Sliding Mode Controller shows good robustness properties in
presence of known external disturbances as compared to that shown by conventional
PID controller.
Design of Bacterial Foraging Optimization Algorithm … 313

Fig. 6 Tracking response of inverted pendulum with adaptive sliding mode controller different
value of lamda

Table 2 Comparison of different controllers for time  2 s

Different Gain of controller J  0.3IAE + 0.7ITAE Remark
controller
Without With disturbance
disturbance
Adaptive sliding Lamda  20 0.3434 0.4434
mode
Controller with
different gain
Lamda  50 0.09342 0.09942
Lamda  80 0.057 0.097
Lamda  100 0.04827 0.05827
Lamda  130 0.0474 0.0574
Lamda  140 0.05278 0.05278
BFOA based Lamda  102.1 0.04385 0.04352 Minimum value
ASMC of J among all
controller

References

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application to robot manipulators. Int. J. Control 38, 465–492 (1983)
2. B. Fernanderz, J.K. Hedrick, Control of multivariable non-linear systems by the sliding mode
method. Int. J. Control 46, 1019–1040 (1987)
3. K.K. Shyu, Y.W. Tsai, C.F. Yung, A modified variable structure controller. Automatica 28,
1209–1213 (1992)
314 R. R. Pathak and A. Sengupta

4. S. Oh, H.K. Khalil, Output feedback stabilization using variable structure control. Int. J. Control
62, 831–848 (1995)
5. M. Won, J.K. Hedrick, Multiple-surface sliding control of a class of uncertain non-linear
systems. Int. J. Control 64, 693–706 (1996)
6. C. Edwards, S. Spurgeon, Robust output tracking using a sliding-mode controller/observer
scheme. Int. J. Control 64, 967–983 (1996)
7. X. Chen, T. Fukuda, Variable structure system theory based disturbance identifications. Int. J.
Control 68, 373–384 (1997)
8. C. Xinkai, F. Toshio, Variable structure system theory based disturbance identification and its
applications. Trans. Int. J. Control 68(2), 373–384 (1997)
9. K.M. Passino, Biomimicry of bacterial foraging for distributed optimization and control. IEEE
Control Syst. Mag., 52–67 (2002)
10. S. Das, A. Biswas, S. Dasgupta, in Bacterial Foraging Optimization Algorithm: Theoretical
Fundamental Analysis and Application, Foundations of Computer Intel (2009), pp. 23–55
11. S. Dasgupta, S. Das, A. Abraham, Adaptive computational chemotaxis in bacterial foraging
optimization. IEEE Trans. Evol. Comput., 919–941 (2009)
12. S.S. Sastry, A. Isidori, Adaptive control of linearizable systems. IEEE Trans. Autom. Control,
1123–1131 (1989)
13. A. Dhar, A. Sengupta, in Sliding Mode Control Algorithm with Adaptive Gain and Implemen-
tation on Inverted Pendulum System, IET International Summit MFIIS-2015 (2015), pp. 8–13
14. A. Sen, A. Sengupta, in Parameter Selection Strategy for Robust Sliding Mode Controller and
Its Implementation in Real Time System, IEEE International Conference on Power Electronics,
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Design of Sliding Mode Excitation
Controller to Improve Transient Stability
of a Power System

Asim Halder, Debasish Mondal and Manas kr. Bera

1 Introduction

The stability problem due to poor damping of the electromechanical oscillations is

the intrinsic dynamic characteristics of an electrical power system. Power transfer in a
single machine power system (SMIB) or in a large interconnected power systems may
be limited causing this poor damping of the electrical machines. To improve the power
transfer capability of SMIB or interconnected power systems, damping controllers are
generally used. The most economical and common damping controllers are the power
system stabilizers (PSSs) [1]. PSSs are the type of feedback controllers installed at
generators and they use locally available signals as their inputs. Though PSSs served
the purpose partially and lot of research work has been done for the same, but still
there is a scope to improve transient stability of the power systems.
To improve the small signal stability of the power systems a nonlinear control
scheme [2] has been proposed for Thyristor Controlled Series Capacitor (TCSC) to
damped out the electromechnical oscillation of the power system. In this method the
affine nonlinear model of a SMIB system with TCSC controller has been linearized
with the help of feedback linearization and transformed to a linear system. Then, the
control law for TCSC has been derived from that linear model. A different approach

A. Halder (B)
Applied Electronics and Instrumentation Engineering, Haldia Institute of Technology,
M.A.K.A.U.T., Haldia, Kolkata, India
e-mail: asim_calcutta@yahoo.com
D. Mondal
Electrical Engineering, RCC Institute of Information Technology, M.A.K.A.U.T., Kolkata, India
e-mail: mondald12@yahoo.in
M. kr. Bera
Electronics and Instrumentation Engineering, National Institute of Technology (NIT), Silchar,
India
e-mail: manas.bera@gmail.com

© Springer Nature Switzerland AG 2019 315

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_27
316 A. Halder et al.

of exact linearization process of nonlinear model of power system has been reported
in [3]. Here, at first optimal parameters are introduced to the system and then power
system is exactly linearized without any approximation. In [4] a nonlinear control
strategy has been proposed for the Static Synchronous Series Compensator (SSSC) in
which the control strategy has been derived from the Lyapunov’s theory. A different
approach, know as Zero Dynamic Design, has been proposed in [5] where the system
is partially linearizable. Here, it has been proposed that if the system is not fully or
exactly linearizable, then the zero dynamic design approach is the effective and
simpler one to derive control law.
To improve the transient stability of power systems, coordinated control schemes
has also been proposed by some researchers. A coordinated excitation and governor
control system approach has been presented in [6]. This method shows that the coor-
dination control system between nonlinear robust excitation control (NREC) and
governor power system stabilizer (GPSS) in multimachine power system in order
to mitigate transient oscillations. Another approach of coordinated control design
has been depicted in [7], in which a coordinated H∞ controller is designed for
excitation and governor of hydroturbo-generator sets on the basis of port-controlled
Hamiltonian (PCH) method. In [8] a TCSC controller along with a robust nonlinear
generator excitation controller has been designed as a nonlinear coordinated con-
troller to enhance the transient stability of power systems. A probabilistic approach
has been proposed in [9] to design coordinate controller. Here, the parameters of
power system stabilizers (PSSs) and static VAR compensator (SVC) has been coor-
dinated and optimized to improve the probabilistic small-signal stability of power
systems with large-scale wind generation. In [10] another FACTS device, Static
Synchronous Compensator (STATCOM), has been considered to design nonlinear
coordinated STATCOM and excitation controller to mitigate transient oscillations of
SMIB system.
It has been observed that most of the research work of the design of conventional
or nonlinear damping controllers are based on the information of the operating con-
ditions of the system and proper tuning of the parameters of the controllers. These
methods have serious limitations like slugiesh convergence property, complex com-
putation process etc. Some research works based on global optimization methods like
Artificial Neural Network (ANN), Genetic Algorithm (GA), Particle Swarm Opti-
mization (PSO) and Evolutionary Programming (EP) has been reported in [11–14].
These methods showed reliable optimization of several power system problems.
This paper presents the design of a nonlinear excitation controller based on Super
twisting Sliding Mode Control along with robust exact differentiator to damp the
transient stability as well as to reject external disturbances of an SMIB system. Fur-
ther, its performance has been compared with Zero Dynamic Design of nonlinear
excitation controller. The simulation results predict that the proposed nonlinear con-
troller is more advantageous and effective. To the best of author’s knowledge the
proposed work has not been explored in the existing literature.
The whole paper is organized as follows; Sect. 2 describes the design process of
excitation controller which consists of three sub-sections. The Sect. 2.1 describes the
affine form of nonlinear model of SMIB system and the estimation of relative degree
Design of Sliding Mode Excitation Controller to Improve … 317

has been described in Sect. 2.2. The derivation of control law based on STSMC has
been presented in Sect. 2.3. Section 3 describes the design of excitation controller
based on Zero Dynamic Design Approach. Finally, the performances of nonlinear
controller has been compared with the Zero Dynamic Design based controller in
Sect. 4.

2 Design of Nonlinear Excitation Controller Based

on STSMC

2.1 Affine Model of an SMIB System

To develop the nonlinear control scheme, a simple third-order power system model of
Single Machine Infinite Bus (SMIB) system is adopted in Fig. 1. The basic equations
of motion of a SMIB power system can be written as [15];

1  1 xd − xd 1
Ė q  − E
 q +   Vs cos δ + Vf (1)
Td Tdo xd Tdo
 
ωs D(ω(t) − ωs )
ω̇(t)  PM − − Pe (2)
H ωs
δ̇(t)  ω(t) − ωs (3)

where, V f is the excitation control voltage, δ: rotor angle of the machine, ω: machine
E  Vs sin δ
speed. PM and Pe  qX   are the mechanical and electrical power of the generator
d
in p.u. respectively. H is the inertia constant and D is the damping coefficient. ωs :
x 
synchronous speed. Td  Tdo xdd   time constant of the field winding for closed
stator circuit. xd   xd + x L + x T and xd   xd + x L + x T . xd and xd are direct-
axis synchronous and transient reactance respectively. x T , x L , E q have their usual
meanings.
The Eqs. (1)–(3) can be rewritten in an affine nonlinear from as follows;

Ẋ  f (X ) + g(X )u (4)

Fig. 1 Simplified model of

SMIB system
318 A. Halder et al.

y  h(X ) (5)
 T
where, X  E q ω δ ; with the initial condition X (0)  X 0 ; X 0 
 T

E q0 ω0 δ0 ;
⎡ 
⎤
1 xd −xd
− T1 + Tdo xd 
Vs cos δ
 T ⎢ d ⎥
⎢ ⎥
g(X )  1
00 and f (X )  ⎢
⎢ ωH0 PM − − ω0 ) −

ω0 E q vs ⎥
sin δ ⎥
H (ω
Tdo D

⎣ H xd ⎦
(ω − ω0 )

Now, choosing the rotor angle ‘δ’ as the output function i.e., h(X )  δ, the relative
degree of the test system, which is an important factor to calculate nonlinear control
law, is derived in the following sub-section.

2.2 Estimation of Relative Degree of the Test System

To design a nonlinear feedback controller, one of the important factors is the calcula-
tion of the relative degree of the system. The standard procedure of the relative degree
estimation is given in [15]. According to this procedure, if the lie derivatives of the
output function h(X ) i.e. L rf−1 h(X ) along a vector field g(X ) is not equal to zero in

a neighbourhood R̂ i.e. L g L rf−1 h(X )  0 , then the system has the relative degree
‘r’ in the neighbourhood R̂. Therefore, by choosing output function y  h(X )  δ,
the relative degree of the system expressed by the Eqs. (1)–(3) can be derived as
follows;

f h(X )  L f h(X )  ω
L 1−1 0
(6)

Therefore,
∂h(X )
L g L 0f h(X )  g(X )  0 (7)
∂X
∂h(X )
For r = 2, f h(X )
L 2−1  L f h(X )  f (X ) 
   ∂X
ω0 ω0 E q Vs
H
PM − H (ω
D
− ω0 ) − H xd 
sin δ
Hence,
1 ω0 Vs
f h(X )  L g L f h(X )  −
L g L 2−1 sin δ  0 (8)
Tdo H xd 
Design of Sliding Mode Excitation Controller to Improve … 319

Therefore, the relative degree of the test system is ‘r’  2. The design of sliding
surface followed by the derivation of the control law is given in the next sub-section.
It is to be noted that the conventional sliding (1-sliding) mode can only be achieved
with relative degree ‘1’, while the second-order sliding (2-sliding) mode requires
relative degree ‘2’ with respect to discontinuous control.

2.3 Estimation of Control Law by Super Twisting Sliding

Mode Control (STSMC)

The detail theory of design of conventional sliding mode and Super Twisting Sliding
Mode Control (STSMC) is given in [16]. According to this theory, under uncertain
condition, the classical sliding modes provide robust and highly accurate solution for
a wide range of control problem. However, there are two main restrictions present.
First, the constraint to be made zero in conventional sliding mode control must have
the relative degree one, which means that the control needs to explicitly appear in
the first derivative of the constraint. Thus, one has to find an appropriate constraint.
Second, the chattering effect may cause unacceptable practical complications if the
control has any physical sense. These restrictions may be solved by STSMC. There-
fore, to derive the control law using STSMC, the output of the system in (5) can be
represented as constraint and represented as follows;

y(t)  e(t)  δ − δ0 (9)

where ‘δ’ and ‘δ0 ’ are the instantaneous and initial value of the rotor angle respec-
tively.
The nonlinear constraint function for an affine nonlinear system given in (4) and
(5), usually chosen as;

σ  C1 ė + C0 e (10)

where, C 1 and C 0 are real valued constant. The Eq. (10) also known as the sliding
surface of the above control strategy.
Now for t → ∞, if the error e(t) → 0 is considered. Then (10) can be modified
to;

C1 ė + C0 e  0

or,
 
C0
e(t)  exp − t e(0) (11)
C1
320 A. Halder et al.

Here, ‘e’ is the error signal which is the deviation of the rotor angle of the machine
from equilibrium position. The aim is to minimize the error, i.e. Lt e(t)  0.
t→∞
Now, the time derivative of (10) is as follows;

σ̇  C1 ë + C0 ė (12)

Combining (2), (3) and (12) the time derivative of constraint function can be
written as;
  
ωs D(ω − ωs ) E q Vs sin δ
σ̇  C1 PM − −  + C0 (ω − ωs ) (13)
H ωs X d

In the next step the method of design of robust exact differentiator has been
described which is required for the design of constraint function or the sliding surface
represented in Eq. (10).
In order to design the robust exact differentiator as shown in (Fig. 2) an auxiliary
system is considered as;

Ż 0  v (14)

In the robust exact differentiator,

σ0  −e(t) + Z 0 or σ̇0  −ė(t) + Ż 0 or σ̇0  −ė(t) + v
and the task is to keep σ0  0.

Fig. 2 Block diagram representation of the nonlinear system with STSMC controller
Design of Sliding Mode Excitation Controller to Improve … 321

According to 2-sliding mode control [16], σ0  σ̇0  0. Therefore,

and

e(t)  z 0
(15)
Ż 0  ė(t)  v

Thus, the resulting form of the robust exact differentiator is;

1
Ż 0  v  −λ1 |Z 0 − e(t)| 2 sign(Z 0 − e(t)) + Z 1 (16)

and Ż 1  −λ2 sign(Z 0 − e(t))

where, λ1  L 1/2 and λ2  2L, L is any positive integer here.
Finally, constraint function (10) can be designed by combining (9)–(15) and the
super twisting sliding mode control law is obtained as;

u  −α1 |σ |1/2 sign(σ ) + v
(17)
v̇  β1 sign(σ )

where, α1 and β1 are real valued constant. The phenomenon of chattering can be
minimized by proper selection of the values of α1 and β1 .
The Eq. (17) will be used in section-4 for simulation and performance evaluation
of the STSMC controller.

3 Zero Dynamic Design of Excitation Controller

The theory of zero dynamics design of nonlinear controller [15] is applicable for a
system which has the relative degree (r) less than the order of the system (n). From
Eq. (8) it can be seen that the relative degree of the system (r  2) is less than the
order of the system (n  3). Therefore, the theory of zero dynamics design is applied
to derive the control law.
Now, the system described by (4) and (5) has to be linearized by the nonlinear
coordinate transformation. The process of mapping from X space to Z space is given
as follows;

Z 1  y  h(X )  L 1−1
f h(X ) (18)

then the time derivative of Eq. (18) it can be written as

∂h(X )
Ż 1  Ẋ (19)
∂X

Now substituting Eq. (4) in (19) for Ẋ , we have

322 A. Halder et al.

∂h(X ) ∂h(X )
Ż 1  f (X ) + g(X )u  L 2−1
f h(X ) + L g L f h(X )u
1−1
∂X ∂X

f h(X )  0, then the above equation can be transformed as

As L g L 1−1

Ż 1  L f f (X )  Z 2 (20)
 −1   −1 
Ż 2  L 2f h ϕ (Z ) + L g L 2−1f h ϕ (Z ) u (21)
 
Ż 3  L f ϕ3 ϕ −1 (Z ) (22)

considering the fact that Ż r  L rf h(X ) + L g L rf−1 h(X )u for the first r equations and
 
Ż n  L f ϕn ϕ −1 (Z ) for the rest (n-r) equations.
Hence, the coordinate transformation Z  ϕ(X ) can be written as;

Z 1  ϕ1 (X )  δ

ω0 D ω0 E q Vs
Z 2  ϕ2 (X )  PM − (ω − ω0 ) − sin δ
H H H xd 

D ω0 Ė q Vs
Z3  − ω̇ − sin δ
H H xd 

 coordinate transformation is valid if the Jacobian Matrix at X  X 0 , Jϕ 

This
∂ϕ(X ) 
is non singular and the function ϕ3 (X ) satisfies L g ϕ3 (X )  0.
∂ X  X X
0
The key idea of the zero dynamics design approach is that at any time ‘t’, the
deviation of the output response of the system from its equilibrium point should be
zero. Therefore, the output response can be expressed as;

y(t)  h(X (t))  0 0 ≤ t ≤ ∞

As y(t)  h(X )  Z 1 (t) has been set to zero at any time. Therefore, Eq. (18) can
 T
be written as Z 1 (t)  0. So, the first r components of coordinates Z are Z 1 Z 2 
0 for all t ≥ 0 and there exists

Ż 2 (t)  0 (23)

Under such condition, from (21) the control input ‘u’ can be computed as follows;
   −1 
0  L 2f h ϕ −1 (Z ) + L g L 2−1
f h ϕ (Z ) u (24)
 
L 2f h ϕ −1 (Z ) L 2f h(X )
u−   − (25)
L g L f h ϕ −1 (Z ) L g L f h(X )
Design of Sliding Mode Excitation Controller to Improve … 323

The term L 2f h(X ) can be computed as;

ωs E q Vs ω0 Vs2 1   Dωs
L 2f h(X )     sin δ − 2
xd − xd sin δ cos δ − PM
H Td xd H xd  Tdo H2
D2 Dωs E q Vs
+ (ω − ωs ) + sin δ
H2 H 2 xd 
ω0 E q Vs
− (ω − ωs ) cos δ (26)
H xd 

Thus, on substituting L 2f h(X ) from (26) and L g L f h(X ) from (8) in the Eq. (25),
the nonlinear excitation control law via zero dynamic design becomes;
 
Tdo E q Vs2 Tdo E q D
u  V f  Eq − Qe + 
ω − ω̇ (27)
Pe xd  Pe H

x    Vs E  V2
where, E q  xd  E q − x − xd xV s cos δ; Q e  x  q cos δ − x  s and
ω  ω − ωs
d d d d
are the basic electrical equations of an SMIB power system. The Eq. (27) will be used
for simulation and performance analysis in the following section. The block-diagram
of the SMIB system with non-linear excitation controller is presented in the Fig. 3.

4 Performance Analysis

The dynamic behaviour of electromechanical oscillations of the SMIB test system

(Fig. 3) with proposed nonlinear STSMC controller is investigated here under three-
phase-to-earth fault scenario for a simulation time 7 s. The three-phase-to-earth
fault is applied in the generator bus at t  1.0 s. and the fault is cleared at t 
1.2 s successfully. It has been observed that the rotor angle (Fig. 4) of the machine

Fig. 3 SMIB system with

nonlinear excitation
controller based on zero
dynamic design
324 A. Halder et al.

increases exponentially after the occurrence of fault. It is further observed that with
the application of proposed nonlinear STSMC controller the rotor angle reaches
to its equilibrium position very quickly in comparison to the zero dynamic design
of nonlinear controller. Moreover, from the simulation, it has been observed that
there is a considerable steady state error in the response of rotor angle applying zero
dynamic design of nonlinear controller. The dynamic behaviour of the machine speed
is shown in Fig. 5. Here, the occurrence of fault, fault clearance time and the total
simulation time is considered as that of the case of rotor angle. The machine speed
increases monotonically after the occurrence of fault at t  1.0 s. It has been found
that at post fault clearance condition the machine speed reaches to its equilibrium
position immediately and becomes asymptotically stable. The simulation results for
rotor angle and machine speed presented in the Figs. 4 and 5 are signifying that the
transient stability of the test SMIB system is substantially improved applying STSMC
controller compared to the controller designed through zero dynamic approach. In
Fig. 4 after fault clearance the system becomes stable at around 1.3 s whereas using
zero dynamic design of nonlinear controller not only the oscillation continues but
also there is a considerable steady state error remains.
In study of machine speed response in Fig. 5, the machine speed of the sys-
tem becomes stable and settled quickly after clearance of the fault when nonlinear
STSMC controller is applied. But for use of the zero dynamic design of nonlinear
controller, the oscillation of the system continues and it appears from the figure
that it requires larger time more than specified simulation time (7 s) to attain stable
operating condition.

Fig. 4 Dynamic response of rotor angle of SMIB system

Design of Sliding Mode Excitation Controller to Improve … 325

Fig. 5 Dynamic response of machine speed of SMIB system

5 Conclusion

This paper presents a novel approach to design a nonlinear Variable Structure (VS)
based sliding mode excitation control for a Single Machine Infinite Bus (SMIB)
power system. The Super Twisting Sliding Mode Control (STSMC) has been uti-
lized to formulate the nonlinear control law. The performance of the propose non-
linear controller has been compared with the performance of zero dynamic design
based nonlinear excitation controller. The obtained simulation results confirm that
the proposed nonlinear STSMC is more effective than the zero dynamic design of
nonlinear controller. Moreover, in the proposed controller design method there is no
need of linearization of nonlinear model of the system. The control law can be derived
directly from the nonlinear model of the system where as in zero dynamic design
method the nonlinear system must be linearize to derive control law. Furthermore, in
zero dynamic design approach the stability analysis of internal states of the system
is essential which introduces further mathematical complexity. Thus it is possible to
conclude that the proposed nonlinear control strategy have good performance and is
superior than the zero dynamic design approach in mitigating transient stability in a
SMIB power system. The present approach of nonlinear controller design can also
be implemented in multimachine power systems.
326 A. Halder et al.

Appendix

Parameters of the SMIB Test System

H = 2.37 s; D = 0.0; Rs = 0.0 pu; Re = 0.02 pu; T d = 5.90 s; ωs = 314 rad/sec; X d
= 1.70 pu; X’d = 0.245 pu; X e = 0.7 pu; X q = 1.64 pu; V inf = 1.00  0o pu; V t = 1.72
 19.31o pu. δ = 130 deg.

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Modelling of an Optimum Fuzzy Logic
Controller Using Genetic Algorithm

Piyali Ganguly, Akhtar Kalam and Aladin Zayegh

1 Introduction

Fuzzy logic has emerged as one of the active areas of research, particularly in control
applications. It is a very powerful method of reasoning when mathematical models
are not available and input data are imprecise [1]. Nowadays, the T-S fuzzy mod-
elling technique is becoming powerful engineering tool for modelling and control of
complex nonlinear dynamic systems [2]. T-S fuzzy models represent fuzzy dynamic
models or fuzzy systems which are described by fuzzy if-then rules that can give a
local linear representation of the non-linear system [3]. For the reason that it employs
the linear model in the consequent part, conventional linear system theory can be
applied for the system analysis and synthesis easily, The methods for learning T-S
fuzzy models from data are based on the idea of consecutive structure and parameter
identification [2].
A major drawback of FLC is that the tuning process becomes more difficult
and very time consuming when the number of the system inputs and outputs are
increased. Different evolutionary algorithms regarding tuning the membership func-
tion parameters of FLC have been studied in the literature [4]. Genetic Algorithm
(GA) is very efficient and systematic technique to optimise the FLC [5]. Genetic
algorithms (GA), which are adopted from the principle of biological evolution, are
efficient search techniques that manipulate the coding representing a parameter set
to reach a near optimal solution [6].

P. Ganguly (B) · A. Kalam · A. Zayegh

Department of Engineering and Science, Victoria University, Melbourne, Australia
e-mail: Piyali.ganguly@live.vu.edu.au
A. Kalam
e-mail: Akhtar.Kalam@vu.edu.au
A. Zayegh
e-mail: aladin.zayegh@vu.edu.au

© Springer Nature Switzerland AG 2019 327

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_28
328 P. Ganguly et al.

In this present work, a T-S type FLC is optimised using GA to control the liquid
level of a tank. The performance of the GA optimised FLC is compared with that of
the conventional PID controller. The MATLAB/SIMULINK software forms part of
the modelling and design tools employed in this research.

2 Fuzzy Logic Controller (FLC)

Recently fuzzy control techniques have been applied to many industrial processes.
FLCs are rule-based systems which are useful in the context of complex ill-defined
processes, especially those which can be controlled by a skilled human operator
without knowledge of their underlying dynamics [7, 8]. Fuzzy control system a
control mechanism based on fuzzy set theory. As per the fuzzy theory and logic,
a decision is made by mainly three operations: fuzzification process, an inference
engine for rule base and defuzzification process [9]. It is a mathematical system that
analyses analogue input values in terms of logical variables that takes a continuous
value between 0 and 1, unlike classical logic and operates on discrete values of either
1 or 0. It utilises the expert knowledge of an experienced user to design the knowledge
base of the controller. Figure 1 represents the configuration of fuzzy logic.

3 Takagi-Sugeno Type Fuzzy Logic Controller

The T-S fuzzy model is a system described by fuzzy IF-THEN rules which can give
local linear representation of the nonlinear system by decomposing the whole input
space into several partial fuzzy spaces and representing each output space with a
linear equation [2]. This FLC model is capable of approximating a wide class of
nonlinear systems.

Fig. 1 Configuration of fuzzy logic

Modelling of an Optimum Fuzzy Logic Controller … 329

Takagi-Sugeno model (for short TS model) consists of a set of if-then rules, where
the rule premises are expressed by fuzzy sets and the rule consequents are considered
to be mostly linear functions of input variables. Therefore, we can formulate the
model as follows [10]
Ri : If xi is Ai1 and … xn is Ain then

gi  pi1 x1 + · · · pin xn + pi(n+1) , i  1, . . . M, (1)

where x  [x1 ,…xn ]T is the vector of input variables, gi the output variable, Ri i-th
fuzzy rule,
Ai1 ,…Ain fuzzy sets defined in the premise space by membership functions μAij
(xj ) and pi1 …, pi(n+1) consequent parameters. The output y of the model is given as
a weighted mean of the individual fuzzy rule contributions:
M
βi gi
y  i1
M
, (2)
i1 βi

where βi denotes the degree of fulfilment of the i-th rule:


n
βi  Ai j (x j ), i  1, . . . , M, (3)
j1

where Aij (x j ) is the membership of input variable x j in the fuzzy set Aij .
Generally, the selections of fuzzy rules and premise inputs and consequent param-
eters are made by trial and error method or using some clustering methods. In this
work, the pi1 …, pi(n+1) (consequent parameters) of a T-S type FLC are optimized
using GA to control the liquid level of a tank.

4 Genetic Algorithm

Genetic algorithms are search algorithms based on the mechanics of natural selection,
natural genetics [11]. They combine survival of the fittest among string structures with
a structured yet randomised information exchange to form search algorithms. Genetic
algorithm searches the solution space of a function through the use of simulated
evolution, i.e., the survival of the fittest strategy. In general, the fittest individuals of
any population tend to reproduce and survive to the next generation, thus improving
successive generations [12].
The genetic algorithms developed by Holland [12] is to simulate the natural evo-
lution process that operates on chromosomes [5]. The simple genetic algorithm that
yields satisfactory results in many practical problems. The central theme of research
on genetic algorithm has been robustness, if the artificial systems can be more robust,
330 P. Ganguly et al.

a costly redesign can be reduced or eliminated. If a higher level of adoption can be

achieved, existing systems can perform longer and better.
Any simple GA is composed of three operators [5]
1. Reproduction
2. Crossing over
3. Mutation.
GA can be summarized in Fig. 2.

5 Modelling of Liquid Level System

For the present work, the liquid level system shown in Fig. 3, has been considered
[13]. The system includes one inflow and one outflow. The objective of this work is
to design a heuristic fuzzy logic controller capable of driving the liquid level in the
tank to a given set point. In the present work the level of the liquid will be controlled
by adjusting only the input or inlet valve.
The system variables are defined as follows:
• Qin : the rate of flow of liquid into the tank at time t, m3 /s.
• Qout : the rate of flow of liquid out of the tank at time t, m3 /s.
• qi : small deviation of inflow rate from its steady-state value, m3 /s.
• qo : small deviation of outflow rate from its steady-state value, m3 /s.
• H: the steady state height, m.
• h: small deviation of head from its steady-state value, m.
• R: the resistance for the liquid flow out, s/m2 .
• A: the cross-sectional area, m2 .
The present design assumes that angular position of the value equal to the rate of
flow in liquid or in other words, ratio between the steady-state flow rate (before any
change has occurred) and the rate of flow in liquid is equal to one.

Fig. 2 GA optimization algorithm

Modelling of an Optimum Fuzzy Logic Controller … 331

Fig. 3 Liquid level system [13]

The flow rate is considered as turbulent flow rate in this work, not laminar flow
rate, hence the resistance R for the liquid flow consider as Rt .
√
Qk× H (4)

Where K is coefficient. The resistance Rt for turbulent flow, which can be obtained
as:
dH
Rt  (5)
dQ

From Eq. (4) it can be written as:

k
dQ  √ dH (6)
2 H
√ √ √
dH 2 H 2 H H 2H
   (7)
dQ k Q Q

Since Rt  2HQ
The value of turbulent-flow Rt depend on the flow rate and the head. By using the
turbulent flow resistance, the relationship between Q & H can be expressed as:
2H
Q (8)
Rt

The difference between the inflow and the outflow during the small time interval
dt is equal to the additional amount stored in the tank which can be represented as:

Adt  (qi −qo )dt (9)

332 P. Ganguly et al.

From the definition of resistance, the relationship between qo and h is:

h
qo  (10)
R
for a constant value of R, the differential equation for this system becomes
dh
RC + h  Rqi (11)
dt
RC is the time constant of the system. Taking the Laplace transforms of both sides
of Eq. (11) assuming zero initial condition:

(RCs + 1)H (s)  R Q i (s) (12)

where H(s)  L[h(t)] and Qi (s)  L[qi (t)]

Considering Qi as input and H as output, the transfer function can be represented
as:
H (s) R
 (13)
Q i (s) RCs + 1

Considering H  1 m, k  1 and C = 0:5 m2

2H
R (14)
Q

√ 2H
Q  K H  1 and R  √  2
k H

Hence the transfer function is:

H (s) 2
 (15)
Q(s) s+1

6 Fuzzy Logic Controller Design

The T-S type FLC is implemented using MATLAB/SIMULINK environment. The

block diagram of the control system is shown in Fig. 4. The simulated controller
has two input variable: e(t) (error) which is the difference between the set value and
the process value, de(t)
dt
, (rate)is the differential of e(t) and an output variable which
is the control signal of the actuator [14]. Triangular shaped built-in membership
functions have been used in the Sugeno-type fuzzy algorithm for the input variables.
The membership functions of the input variables are shown in Figs. 5 and 6.
Modelling of an Optimum Fuzzy Logic Controller … 333

Fig. 4 The SIMULINK block diagram of the liquid level control system

Fig. 5 Membership functions of the input variable ‘error’

Fig. 6 Membership function of the input variable ‘rate’

Output membership functions have three constant parameters. The surface of the
FLC before optimisation is represented in Fig. 7.
The fuzzy controller output is applied to the actuator in order to control of liquid
level. Then, the flow of liquid has been adjusted to obtain the desired level. The FLC
has five rules. The output of the T-S type FLC can be calculated using Eqs. (1)–(3).
The parameters of the T-S type FLC is optimized using GA within a specified limit.
334 P. Ganguly et al.

Fig. 7 The control surface of the un-optimized FLC

The optimization is done using MATLAB programing. The programme optimises the
15 variables (population) (for 5 rules using 3 variables at a time used for the present
problem) with the help of GA. This programme continues until 200 generations, and
gets the optimized result. The evaluation function (fitness function) used here can be
represented by Balochian and Ebrahimi [14]:

Fitness  sse(y − ŷ) + 100 × Overshoot

where ‘sse’ is sum squared error performance function, y is reference input and ŷ
is output of the Simulink model. The optimized values of the parameters of the T-S
type FLC are fed into the controller to get the optimized controller for the system.

7 Simulation and Results

Figure 8 shows the output (liquid level) of the system using un-optimized FLC against
the reference input. Figure 9 represents the system output using PID controller against
a set input and Fig. 10 represents the output of the system with optimized FLC against
the reference input. In first two cases, the water level of the tank follows the input
signal with a significant error in case of both maximum and minimum specified limit.
It can be observed that with the optimised FLC, the error is reduced to a great extent.
The optimised FLC can maintain the water level to the specified maximum value. It
can also track the specified minimum level with a minimum error.
Hence, it can be stated that comparison between the control results obtained
from the un-optimized FLC, PID controller and optimized FLC clearly shows that
Modelling of an Optimum Fuzzy Logic Controller … 335

Fig. 8 Liquid level of the tank with un-optimized FLC. Purple line represents the set input and the
blue line shows the actual liquid level

Fig. 9 Liquid level of the tank with PID controller. Orange line represents the set input and the
purple line shows the actual liquid level

optimized FLC has more accurate and acceptable results. Figure 11 represents the
control surface of the optimum FLC.
336 P. Ganguly et al.

Fig. 10 Liquid level of the tank with optimized FLC. Pink line represents the set input and the red
line shows the actual liquid level

Fig. 11 Control surface of the optimized FLC

8 Conclusion

In this paper, an efficient and effective tuning approach-based on Genetic Algorithm

(GA) is presented to obtain the optimal Takagi-Sugeno type fuzzy controller param-
eters to control the liquid level of a tank. The results obtained clearly shows that
one can improve the performance of fuzzy controller by optimizing the parameters.
Modelling of an Optimum Fuzzy Logic Controller … 337

Simulation results show clearly that the optimized controller have better performance
compared with un-optimised FLC or conventional PID controller. GA could tune up
fuzzy controller parameters promptly with uppermost level of accuracy.

References

1. D. Su, K. Ren, J. Luo, C. He, L. Wang, X. Zhang, Programmed and simulation of the fuzzy
control list in fuzzy control, in IEEE/WCICA, 2010, pp. 1935–1940
2. H. Du, N. Zhang, Application of evolving Takagi-Sugeno fuzzy model to nonlinear system
identification. Appl. Soft Comput. 8(1), 676–686 (2008)
3. M. Männle, FTSM-fast Takagi-Sugeno fuzzy modeling, in Fault Detection, Supervision and
Safety for Technical Processes (SAFEPROCESS’00) (Budapest, Romaina, 2000), pp. 663–668
4. Y.-C. Chiou, L.W. Lan, Genetic fuzzy logic controller: an iterative evolution algorithm with
new encoding method. Fuzzy Sets Syst. 152(3), 617–635 (2005)
5. K.C. Ng, Y. Li, Design of sophisticated fuzzy logic controllers using genetic algorithms, in
Fuzzy Systems. Proceedings of the IEEE World Congress on Computational Intelligence, 1994
6. S. Khan et al., Design and implementation of an optimal fuzzy logic controller using genetic
algorithm. J. Comput. Sci. 4(10), 799–806 (2008)
7. S. Balochian, E. Ebrahimi, Parameter optimization via cuckoo optimization algorithm of fuzzy
controller for liquid level control. J. Eng. (2013)
8. Francisco Herrera, Manuel Lozano, Jose L. Verdegay, Tuning fuzzy logic controllers by genetic
algorithms. Int. J. Approximate Reasoning 12(3-4), 299–315 (1995)
9. L.A. Zadeh, Outline of a new approach to the analysis of complex systems and decision
processes. IEEE Trans. Syst. Man Cybern. 1, 28–44 (1973)
10. H. Roubos, S. Magne, Compact fuzzy models and classifiers through model reduction and
evolutionary optimization, in The Practical Handbook of Genetic Algorithms: Applications
(Chapman & Hall/CRC 2001)
11. D.E. Goldberg, Genetic algorithms in search, optimization and machine learning (Addison-
Wesley, Reading, 1989)
12. J.H. Holland, Adaptation in natural and artificial systems (University of Michigan Press, Ann
Arbor, 1975)
13. E.A. Elayan, Design of heuristic fuzzy logic controller for liquid level control, in International
Conference on Intelligent System Modelling and Simulation, 2014
14. S. Balochian, E. Ebrahimi, Parameter optimization via cuckoo optimization algorithm of fuzzy
controller for liquid level control. J. Eng. 2013
Evolutionary Smith Predictor
for Control of Time-Delay Systems

Neelbrata Roy, Anindita Sengupta and Ashoke Sutradhar

1 Introduction

In most cases, plants having time delay can’t be controlled efficaciously using Propor-
tional plus Integral plus Derivative controller as the lag in phase added by the delay
term tries to make the closed-loop system unstable. By decreasing the controller gain
the stability problem can be addressed even though the output becomes very nebbish
in nature [1, 2]. An exclusive approach for the control of systems accompanying a
certified time-delay was developed by Otto. J. Smith in the 1950s by balancing the
delayed response using input entities stored over a time frame [t − t1 ] and evaluates
the response of the system employing a calculated plant prototype [3].
This philosophy of compensating the time delay was extended for unstable plants
using finite-time integrals of the delayed input values thereby avoiding unstable
pole-zero cancellations that may occur in Smith’s controller [4].
Different versions of designs on Smith predictor has been developed after the
invention led by Smith, followed by Astrom et al., Matusek et al., Majhi et al., Liu
et al. and Kaya [1–6].
Liu et al. proposed an efficient design of smith predictor [1]. It consists of a
set point tracking controller and disturbance estimator. The estimator constants are
the gain’s of the traditional PID controller and the parameter of setpoint tracking
controller is λc and kc respectively that are being dealt in the Liu’s model of smith

N. Roy (B) · A. Sengupta · A. Sutradhar

Department of Electrical Engineering, IIEST, Shibpur,
Howrah 711103, India
e-mail: neelbrataroy.rs2016@ee.iiests.ac.in
A. Sengupta
e-mail: aninsen@ee.iiests.ac.in
A. Sutradhar
e-mail: as@ee.iiests.ac.in

© Springer Nature Switzerland AG 2019 339

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_29
340 N. Roy et al.

predictor. Two examples had been discussed here, an unstable plant [1, 2] and another
stable plant [7–11]. The accomplishment of the closed-loop system realized in this
study on the plants discussed in section two as well as in paper [1] is better than the
outcomes reported in [1, 2] and hence the design procedure was applied for other
plants also [7–11]. The Optimization technique used are PSO [12, 13], ACO [14],
HSO [15], and GWO [16]. The results have overshoot within 5%, which is quite
acceptable for practical systems [17, 18].

2 System Identification and Mathematical Model

The system considered for testing is a single tank system. The mathematical modeling
is discussed briefly below. The single tank system has a uniform cross-sectional area
A, a flow resistance R is attached to the bottom this can be a valve or a pipe. The
layout of Liquid Level system (LLS) is shown in Fig. 1.
The rate of flow of fluid through the resistance is related to the head of tank ‘h’
by linear relationship given by [7–11].
h(t)
q0 (t) 
R
Thus we can say the difference in flow rate is directly proportional to height and
inversely proportional to the flow resistance that can be mathematically stated using
the following differential equation.
dh(t)
qi (t) − q0 (t)  A
dt
Using the above equations,

Fig. 1 Single tank system

Evolutionary Smith Predictor for Control of Time-Delay Systems 341

h(t) dh(t)
qi (t) − A
R dt
Thus the system transfer function is given by
H (s) R

Q i (s) 1 + Ts

From experimental datasheet of the instrument, it was found that R = 5380 and
T = 204. Therefore overall transfer function of the system is
H (s) 5380

Q i (s) 1 + 204s

The delay of the LLS is approximately 2s multiplying the additional delay to the
transfer function stated above the overall TF of the LLS is written as
H (s) 5380 −2s
 e
Q i (s) 1 + 204s

And the close loop Transfer Function of the system was found to be

5380e−2s
G(s) 
1 + 204s + 5380e−2s
It can easily be inferred from the step response of the system that the system is
unstable as illustrated in Fig. 2.

Fig. 2 Closed loop response of STS

342 N. Roy et al.

2.1 An Introduction of Smith Predictor Scheme for Processes

with Dead Time

The paper [1] details the smith predictor scheme that controls a class of unstable
system with dead time generally called FODT system; the schema results in a lucid
control structure and refine tuning capability for reference inputs along with load
perturbations. The control system scheme is shown below [1] (Fig. 3).
Looking to the above scheme and literature cited the disturbance estimator and
setpoint tracking controller parameters namely K p , K i K d and λ are revised using
all the optimization procedure stated above keeping the objective function ITAE
[12–16].

3 Ant Colony Optimization Technique

It’s seen in nature that ants move in a random fashion and upon finding food return to
their respective colony while putting down pheromone trails. If another ant discovers
the same path, they do not keep traveling at random, but instead, they follow the laid
trail, retracing and enriching it if they eventually find food in the same location.
Over time, however, the pheromone trail fades away, thus making feeble the time
taken by pheromone to evaporate is equivalent to a summation of go and return time
of the ant. Therefore the ants move over the same path more frequently, and thus
the pheromone density becomes higher on shorter paths than the longer ones. The
procedure is explained below.
STEP 1: Initially a random number of ants visits a random number of nodes and
ramblingly moves by the edges moving from one node to other node.
STEP 2: Based on constraints all ants build his own solution.

Fig. 3 Smith predictor scheme. Courtesy Liu et al. [1]

Evolutionary Smith Predictor for Control of Time-Delay Systems 343

STEP 3: The next node is selected based on the pheromones accumulated at edge of
each node.
STEP 4: The probability of choosing next node ‘j’ from current node ‘i’ is given by:
β
[τiαj ][ηi j ]
Pikj (t)   β
[τilα ][ηil ]

where

τi j symbolizes the pheromone concentration with the edges

ηi j Symbolizes the heuristic information which is given by
ηi j  d1i j ; di j is the distance between two nodes.
α0 If nodes closer to each other are chosen.
β0 If probability depends on pheromone intensification.

STEP 5: if all nodes are traversed then, pheromone yoked with each node is amended
by:


m
τi j (t + 1)  (1 − ρ).τi j (t) + τikj ∀(i, j)
k1

τikj (t) is the quantity of pheromone would be supplemented in the route k traversed
by a ant, and ρ is assumed to be vanishing rate of pheromone
⎧
⎨ 1
τi j (t)  L k
k
⎩
0

L k L k , is the net distance of path k. Now, as is inversely equivalent to τikj there-

fore with the increase τikj increase in τi j (t + 1) is obvious. Thus the quantity of
pheromones yoked with that particular path is more and hence quintessential solu-
tion of the cost function is obtained [14].

4 Particle Swarm Optimization Technique

It is a nature-based optimization technique. It continuously tries to improve a can-

didate solution with regard to a given measure of quality i.e. the cost function. It
elucidates a problem by having a populace of candidate solutions, these particles
percolate around in the search-space according to simple mathematical formulae
over the particle’s position and velocity. The movement of particles can be altered
by its local best-known position and all of them try to move towards the best-known
positions in the search-territory. The better positions are updated by other particles.
344 N. Roy et al.

Thus the swarm is expected to move toward the best solutions [12, 13]. The algorithm
is detailed as follows.
STEP 1: The numbers of particles, total no of iterations, size of swarm, the locus of
intervals of the maximum and minimum bound of the parameters are being initialized.
STEP 2: Assessment of the function ITAE (standard cost function).

(a) The particles initialized are hied to the standard cost function.
(b) The functional value obtained is assigned as the pioneer Pbest of the swarm.
The pick of the liter among Pbest’s is known as gbest.

STEP 3: Until the cessation requirement is reached the looping is to be continued

(amendment of velocity and position of particles).

(a) The velocity of the particle is updated using the following formula as shown
below

V1 (t + 1)  V1 (t) + c1 (P1 − x1 (t))R1 + c2 (g − x1 (t))R2

here the amended velocity vi (t + 1) is, Pi the Pbest, g is the gbest, c1 is

the self-learning rate, c2 is the global erudition coefficient, these values are
any two random numbers between zero and four respectively, R1 and R2 are
diagonal matrices generated using unifrand command the range is in between
[0,1] respectively.
(b) The up gradation of the position of the particle in the swarm done using the
following formula

xi (t + 1)  xi (t) + vi (t + 1)

(c) The amended particles are again passed to the cost function.
(d) The Pbest and gbest are amended as follows

If G(xi (t + 1)) > G( pi ) then pi  xi (t + 1)

If G(xi (t + 1)) > G(gi ) then gi  xi (t + 1)

Step 4: As the process ends gbest gives the prime estimate of the disturbance estimator
parameters and setpoint tracking controller parameter [12, 13, 18].

5 Harmony Search Algorithm

Harmony search is a music-based metaheuristic optimization algorithm. It is seen

that the aim of music is to achieve for a sublime position of harmony. The venture
Evolutionary Smith Predictor for Control of Time-Delay Systems 345

to get the harmony in music is as equivalent to achieve optimality in an optimization

problem. A music virtuoso always intends to produce a piece of music with perfect
harmony. The process goes similarly for an optimization process to find the best
solution available for the problem under the given cost functions and restricted to
constraints and other inequality. The procedure of harmony search is shown below
[15].
STEP 1: The HM (Harmony Memory) is generated. This generated matrix has the
solutions for the problem discussed in Sect. 2.1. The content of the matrix is generated
randomly.
STEP 2: A set of solution is created from the HM [x1 , x2 , . . . xn ] and each component
of the solution is based on harmony memory (HM) considering rate (HMCR). The
HMCR is the probability of selecting a component from the HM. The solution is
further muted according to pitch adjustment rate (PAR). The PAR decides the prob-
ability of a candidate from the HM to be metamorphosed. Thus the phenomenon is
similar to the production of the progeny.
STEP 3: Update the HM. The new solution from Step 2 is evaluated. If it yields
a better fitness than that of the worst member in the HM, it will replace that one.
Otherwise, it checks out.
STEP 4: Repeat Step 2 to Step 3 until the maximal number of iterations, is met [15].

6 Grey Wolf Optimization

The GWO algorithm adopts the leadership level and hunting strategy of grey wolves
and is proposed by Mirjalili et al. in 2014. Four types of grey wolves such as alpha,
beta, delta, and omega are employed for simulating the leadership levels. In addition,
three main steps of hunting, searching for prey, encircling prey, and attacking prey,
are implemented to perform optimization. The algorithm is as follows [16].
STEP 1: The Pack of grey wolves (prospective solutions), ‘N’ and a guess for no of
required iteration, ‘N iter ’ is being entered by the end user for the cost optimization
problem.
STEP 2: With, xα , the initial pack position, the value of f (xα ) is calculated.
STEP 3: Based on the fitness value the grey wolves are categorized as α, β, δ.
STEP 5: The looping process is started until cessation condition is met.
STEP 6: Another looping process is started for all successive wolf j attached to the
pack.
STEP 7: The place of the wolf is amended by the following relationship:

−
→
x1 + −
→
x2 + −
→
−
→
x (t + 1) 
x3
3
This marks the end of step 7.
346 N. Roy et al.

STEP 8: Amend the trade-off parameter ‘a’ using the formula a  2 − t Max2I ter , A 
2ar1 − a, C  2r2 a, the parameter ‘a’ is the deciding factor between investigation
and profiteering between the pack. The parameter A and C are vectors that represent
the position or solutions of the prey or the problem cast.
STEP 9: The cost function is again examined with this value of position, β, and δ
are updated. This Marks the End of Step 5. α, β are subjected as the best solution for
control problem cast [16, 18].

7 Results and Discussions

On simulating the above four optimization algorithms, the comparative performances

of the unstable system [1] have been illustrated in Fig. 4.
Example 1. Consider the unstable time delay process as in [1].

4e−2s
G p (s) 
4s − 1

For the above plant the set point tracking controller and disturbance estimator
designed is as follows.
s + 0.75
G c (s) 
2s + 1
Keeping the tuning Parameter λc  2 and
1
F(s)  0.5186 + + 0.4s
32.7873s
A unit step input is added at t  0 and an inverse step load disturbance with
magnitude 0.1 is added to the process input at t  30 s [1].

Fig. 4 Comparison of responses of four tuning algorithm for Smith predictors

Evolutionary Smith Predictor for Control of Time-Delay Systems 347

Table 1 Computed estimator/controller parameter values for the unstable system

Name of algorithm Ant colony Particle Harmony Grey wolf
algorithm swarm search algorithm
optimization algorithm
Estimator/controller
parameters
G p (s)  Kp 0.61274 0.6529 0.61274 0.6529
4e−2s
4s−1
Ki 0.045864 0.0941 0.0941 0.0941
Kd 0.69508 0.6392 0.69508 0.6392
λc 0.36121 0.0305 0.0305 0.0305

The computed values of the estimator/controller parameters in different optimiza-

tion methods have been given in Table 1.
The above algorithms had also been tested for the single tank system [7–11] with
delay. The comparative performances for controllers optimized using four above
algorithms have been shown in Fig. 5 and the corresponding values of the computed
estimator/controller parameters have been shown in Table 2.

8 Conclusion

This paper adduces a tuning procedure of smith predictor based on Liu et al. [1] model
for time-delay systems using four different evolutionary algorithms. The optimization
process tuned the disturbance estimator and setpoint tracking controller minimizing

Fig. 5 Response Smith predictors for a single tank system with time delay
348 N. Roy et al.

Table 2 Computed estimator/controller parameter values for stable liquid level system
Name of algorithm Ant colony Particle Harmony Grey wolf
algorithm swarm Search algorithm
optimization algorithm
Estimator/controller
parameters
G p (s)  Kp 0.0253 0.0242 0.0244 0.024259
5380 −2s
1+204s e
Ki 0.0063 0.0059 0.0061 0.0059498
Kd 0.0243 0.0221 0.0226 0.0221
λc 0.0714 0.0890 0.0786 0.078584

the performance index ITAE. The responses for all the cases show improved rise
time and disturbance rejection than that reported by Liu et al.
The obtained outcome had improvised the reported results even though a little
peak is observed but it is within 5% of the desired result so it is quite acceptable.
Further development in the stabilizing controller and setpoint tracking controller may
improve the results in terms of settling time and disturbance rejection.

References

1. T. Liu, Y.Z. Cai, D.Y. Gu, W.D. Zhang, New modified Smith predictor scheme for integrating
and unstable processes with time delay, IEE Proc.-Control Theory Appl. 152(2) (2005)
2. Ibrahim Kaya, A new Smith predictor and controller for control of processes with long dead
time. ISA Trans. 42, 101–110 (2003)
3. O.J.M. Smith, A controller to overcome dead time. ISA J. 6(2), 28–33 (1959)
4. S. Majhi, D.P. Atherton, Obtaining controller parameters for a new Smith predictor using
auto-tuning. Automatica 36, 1651–1658 (2000)
5. M.R. Matausek, A.D. Micic, On the modified Smith predictor for controlling a process with
an integrator and long dead-time. IEEE Trans. Autom. Control 44(8), 1603–1606 (1999)
6. K.J. Astrom, C.C. Hang, B.C. Lim, A new Smith predictor for controlling a process with an
integrator and long dead time. IEEE Trans. Autom. Control 39, 343–345 (1994)
7. R. Paul, A. Sengupta, Discrete wavelet packet transform based controller for liquid level system
and its performance analysis. Measurement 97, 226–233 (2017)
8. S. Sen, S. Chakraborty, A. Sutradhar, Estimation of vehicle yaw rate and lateral motion
for dynamic stability control using unscented Kalman filtering (UKF) approach. IET Digi-
tal Library, MFIIS-2015
9. U. Mondal, A. Sengupta, Rajeev R. Pathak, Servomechanism for periodic reference input:
discrete wavelet transform-based repetitive controller. Trans. Inst. Meas. Control 38(1), 14–22
(2016)
10. R. Paul, A. Sengupta, R.R. Pathak, Wavelet-based denoising technique for the liquid level
system. Measurement 46(6), 1979–1994 (2013)
11. U. Mondal, A. Sengupta, A. Roy, Repetitive controller: an advanced s servomechanism for
periodic reference input. Int. J. Dyn. Control 4(4), 428–437 (2016)
12. M. Clerc, Standard particle swarm optimization. HAL open access archive, 2012
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13. R. Baskarane, T. Sendhil Kumar, Hybrid optimization for multiobjective multicast routing.
IJRAT 2(3) (2014)
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Berlin, 2009)
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On-line Adaptation of Parameter
Uncertainties of a Practical Plant
Employing L1 Adaptive Controller

Roshni Maiti, Kaushik Das Sharma and Gautam Sarkar

1 Introduction

Adaptive controllers are introduced to handle system with uncertainties, time varying
disturbances and nonlinearities. Different types of adaptive controllers such as model
reference adaptive sliding mode control [1], fuzzy adaptive controller [2, 3] are used to
control different types of systems. Adaptive controller [4] estimates the uncertainties
present in the system and adapt them to produce control signal. Error between the
output of the reference model and system is used to produce adaptation law and the
controller reduces the error asymptotically is commonly known as direct adaptive
control whereas when the system parameters are dynamically estimated to produce
adaptive law and control signal is called indirect adaptive control [5].
Conventional model reference adaptive controller (MRAC) [6] has some disad-
vantages like slow transient performance, dependency upon systems input etc. To
cope up with such problem in the year of 2006 Cao and Hovakimyan introduces a
novel adaptive controller named as L 1 adaptive controller [7] inserting a filter to elim-
inate the high frequency introduces into the control signal due to high adaptation rate.
They guarantee high robustness and stability with quick transient performance [7].
Different systems such as aircraft [8, 9], single-link armed robot [7] are controlled
using L 1 adaptive controller in simulation environment efficiently. It is very much
important to validate a controller in real life experimentation. Now in this paper
the effectiveness of this method is tested in real time environment. A dc motor is

R. Maiti (B) · K. Das Sharma · G. Sarkar

Department of Applied Physics, University of Calcutta, Kolkata, India
e-mail: roshni.maiti@gmail.com
K. Das Sharma
e-mail: kdassharma@gmail.com
G. Sarkar
e-mail: gautamgs2010@yahoo.in

© Springer Nature Switzerland AG 2019 351

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_30
352 R. Maiti et al.

tested with different trajectories to justify the quick transient performance with high
robustness in real time. L 1 adaptive controller at first estimates the uncertainties,
unknown constant present in the system and then adapt those and produce control
signal [10, 11]. Rate of adaptation is made high to give swift transient performance.
Robustness is also guaranteed by use of low pass filter and projection operator. To
obtain non-adaptive parameters of L 1 adaptive controller a well known stochastic
optimization technique named as particle swarm optimization (PSO) [12, 13] is
used. Adaptive parameters are adapted online continuously in each time step to give
desired results.
There are a very few literature where L 1 adaptive controller is tested online.
Maalouf et al. [11] test L 1 adaptive controller in real time experiment to control an
AC-ROV submarine which is an under-actuated underwater vehicle. They augment
L 1 adaptive controller with proportional integral (PI) controller to drastically reduce
the tracking time lags. Here in this proposed method no other controller is required
in conjunction with L 1 adaptive controller to get proper controlling parameters. In
simulation environment PSO is giving the optimal parameter setting which is capable
of controlling systems without using any further with L 1 adaptive controller. This
naturally reduces the online computational burden as well as computational time
which are of great importance.
The paper is arranged as follows. Second section lights up on L 1 adaptive controller
architecture. Third section describes the L 1 adaptive controller implementation in
online mode with two sub section as inclusion of model uncertainties, online L 1
adaptive controller. Experimental results are tabulated and depicted in section four.
Discussion and conclusion ends up the paper in fifth section.

2 Problem Formulation

2.1 L1 Adaptive Controller Architecture

L 1 adaptive controller shows in Fig. 1 comprises of system with time varying uncer-
tainties, disturbances, unknown constant in it, predictor, adaptive law block and
controller with low pass filter. Cao and Hovamikiyan clearly describe the different
parts of it [7]. State predictor predicts those uncertainties and estimates them in
adaptive manner with some adaptive law derived from Lyapunov stability criteria.
Control signal will produce and filtered to remove high frequency introduced due to
high adaptation gain and given to the system.
The state predictor [7], described by this equation

x̂˙  Am x̂(t) + b(ω̂(t)u(t) + θ̂ (t)x(t) + σ̂ (t))

T
(1)
On-line Adaptation of Parameter Uncertainties … 353

Fig. 1 Architecture of L 1 adaptive controller

gives the adaptive estimates of unknown constants, ω̂(t) ∈ ; uncertainties, θ̂(t) ∈

n ; time varying disturbances σ̂ (t) ∈  present in the system model described by
these equations,

ẋ(t)  Am x(t) + b(ωu(t) + θ T (t)x(t) + σ (t))

x(0)  x0 , (2)
y(t)  c x(t)
T
(3)

where, Am is the Hurwitz matrix ∈ n×n . b ∈ n , c ∈  are known constant vector.

x is the state vector ∈ n . u is the control input to the system ∈  and y ∈  is
the output of the system. ω is the unknown constant ∈ , θ ∈ n is the unknown
uncertainties and σ (t) ∈  is the time varying disturbances present in the system.
The adaptation law can be derived from the stability analysis of the system. The
Lyapunov equation for this system is:
  1 1
v x̃(t), ω̂(t), θ̂ (t)  x̃T (t)P x̃(t) + ω̃T (t)1−1 ω̃(t)
2 2
1 T 1
+ θ̃ (t)2−1 θ̃(t) + σ̃ T (t)3−1 σ̃ (t) (4)
2 2

where, x̃  x̂ − x is the state error vector, ω̃  ω̂ − ω is the error for unknown

constant term, θ̃  θ̂ − θ is the error for unknown uncertainties and σ̃  σ̂ − σ is
the error of disturbances.
354 R. Maiti et al.

The derivative of it is:

  1 T 1 ˙
˙ + ω̃T (t) −1 ω̂(t)
v̇ x̃(t), ω̂(t), θ̂ (t)  x̃˙ (t)P x̃(t) + x̃T (t)P x̃(t) 1
2 2
T ˙ + σ̃ T (t) −1 σ̂˙ (t),
+ θ̃ (t) −1 θ̂(t) (5)
2 3

From Lyapunov stability theorem it must hold that v̇ < 0 to make the system
stable.
Satisfying the above stability condition the adaptive law will be as follows:

˙  1 Proj(ω̂(t), −x̃T (t)Pb u(t))

ω̂(t) (6)
θ̂˙ (t)   Proj(θ̂ (t), −x(t)x̃T (t)Pb)
2 (7)
σ̂˙ (t)  3 Proj(σ̂ (t), −(x̃ (t)Pb) )
T T
(8)

Now, the projection (Proj(,)) operator [14] will limit the values of adapted param-
eters. Therefore, all the terms with adaptive parameters of Eq. (5) are bounded and
they belongs to some compact set [ω θ σ ] ∈ [  ]. The state error vector
Lim x̃  0 as t → ∞. Therefore, v̇ will become <0 and the system will be stable.
Now the aim is to produce a control signal that the system can track the desired
trajectory properly. The control law of L 1 adaptive controller is:
 
u(s)  −kC(s) η̂(s) − kg r(s) . (9)

where, k is the gain, kg is the pre filter feed forward gain, η̂(s) is the Laplace transform
of η̂(t) given by,
T
η̂(t)  ω̂(t)u(t) + θ̂ (t)x(t) + σ̂ (t). (10)

Due to high value of   [1 2 3 ], high frequency signals introduce into the
control channel which will affect the stability of the system. Therefore, one low pass
filter
fc D(s)
C(s)  (11)
1 + fc D(s)

with C(0)  1 is attached in the control channel to remove the high frequencies and
to give high robustness with quick transient response. fc is the cut off frequency of
the filter.
On-line Adaptation of Parameter Uncertainties … 355

3 L1 Adaptive Controller Implementation in Online Mode

From L 1 norm condition the values of the L 1 adaptive controller parameters can be
found out but that may not give optimal results. A stochastic optimization technique
named as particle swarm optimization is used along with L 1 adaptive controller at the
time of simulation to get optimal result which is used at the time of online adaptation.
PSO is very efficient method in finding optimal parameter setting for controllers [15,
16]. At first parameter estimation has done which includes the uncertainties into
the model and to cope up with those uncertainties online L 1 adaptive controller is
implemented and tested successfully.

3.1 Inclusion of Parameter Uncertainties

In this paper, a DC motor is used as experimental setup as shown in Fig. 2. Voltage

signal is given as the input to the motor through driver circuitry and speed of the
motor is the output. A fly wheel is attached with the shaft and one permanent magnet
is so arranged that it can produce load disturbances to the motor. For parameter
estimation the DC motor runs in open loop environment where a pre-defined voltage
input is given to the motor and output speed is recorded.
The model of the DC motor is gives as:
   
Ra B BRa Kb KT KKT
ω̈ + + ω̇ + + ω u(t) (12)
La J JLa JLa JLa

where, ω is the angular speed of the motor in rad/sec. u is the dc voltage input and
angular speed is taken as the output. Unknown motor parameters such as inertia
(J), damping ratio (B), armature resistance (Ra ), armature inductance (L a ), motor
back emf coefficient (K b ), motor torque coefficient (K T ) and motor driver circuit
coefficient (K) are obtained from parameter estimation of the motor. At the time of
parameter estimation, uncertainties includes into the model. Let, the uncertainties are

Fig. 2 DC motor experimental setup

356 R. Maiti et al.

J ,
B,
Ra ,
La ,
Kb ,
KT and
K respectively for the above mentioned param-
eters. Now the DC motor model with uncertainties and time varying disturbances
d (t) can be represented as,
   
Ra +
Ra B +
B (B +
B) (Ra +
Ra ) (Kb +
Kb ) (KT +
KT )
ω̈ + + ω̇ + + ω + d (t)
La +
La J +
J (J +
J ) (La +
La ) (J +
J ) (La +
La )
 
(K +
K) (KT +
KT )
 u(t) (13)
(J +
J ) (La +
La )

or, ω̈ + C1 ω̇ + C2 ω + d (t)  C3 u(t)

 
Ra +
Ra B +
B
C1  + ,
La +
La J +
J
   
(B +
B) (Ra +
Ra ) (Kb +
Kb ) (KT +
KT ) (K +
K) (KT +
KT )
C2  + , C3 
(J +
J ) (La +
La ) (J +
J ) (La +
La ) (J +
J ) (La +
La )
 
Ra La
Ra − Ra
La B J
B − B
J
C1  + + +
La La (La +
La ) J J (J +
J )
 
Ra B La
Ra − Ra
La J
B − B
J
 + + +
La J La (La +
La ) J (J +
J )

⎛ ⎞
BRa Ra
B+B
Ra +
B
Ra −BRa (La
J +J
La +
J
La )
JLa
+ JLa (J +
J ) (La +
La )
C2  ⎝ ⎠
KT
Kb +Kb
KT +
Kb
KT −Kb KT (La
J +J
La +
J
La )
+ KJL
b KT
a
+ JLa (J +
J ) (La +
La )
⎛ ⎞
BRa Kb KT Ra
B+B
Ra +
B
Ra −BRa (La
J +J
La +
J
La )
JLa
+ JLa
+ JLa (J +
J ) (La +
La )
⎝ ⎠
+ KT
Kb +Kb
KT +
K b
KT −Kb KT (La
J +J
La +
J
La )
JLa (J +
J ) (La +
La )

 
KKT KT
K + K
KT +
K
KT − KKT (La
J + J
La +
J
La )
C3  +
JLa JLa (J +
J )(La +
La )

Therefore, Eq. (13) can be written as:

     
Ra B BRa Kb KT KKT
ω̈ + + +
P1 ω̇ + + +
P2 ω + d (t)  +
P3 u(t)
La J JLa JLa JLa
(14)

where,
P1  LaL
R a −Ra
La
a (La +
La )
+ J J
B−B
J
(J +
J )
,
Ra
B + B
Ra +
B
Ra − BRa (La
J + J
La +
J
La )

P2 
JLa (J +
J )(La +
La )
and
KT
Kb + Kb
KT +
Kb
KT − Kb KT (La
J + J
La +
J
La )
+
JLa (J +
J )(La +
La )
On-line Adaptation of Parameter Uncertainties … 357

P3  KT
K+K
KT +
K
K T −KKT (La
J +J
La +
J
La )
JLa (J +
J ) (La +
La )
are the uncertainty terms with
angular speed, angular acceleration and voltage input of the machine respectively.
Therefore, the state space representation of the model with time varying uncertainties
and disturbances become,
 ⎡ ⎤
 
ẋ1 0 1 x1
 ⎣     ⎦
ẋ2 − RLa + BJ +
P1 − BR
a JL
a
+ Kb KT
JL
a
+
P 2 a
x2
⎡ ⎤ 
0
+ ⎣  KK  ⎦u + 0
(15)
JLa
T
+
P3 d (t)

or,
 ⎡ ⎤
0 1  
ẋ1  ⎦ x1
 ⎣  Ra B   BRa
ẋ2 − La + J − JLa + Kb KT
JL
a
x2
     x  
0 KKT 1
+ +
P3 u + −
P1 −
P2 + d (t) (16)
1 JLa x2

Comparing (2) and (16) the unknown constant, uncertainties and disturbance
become,     
ω  KK JLa
T
+
P3 , θ  θ 1 θ2  −
P 1 −
P 2 and σ  d (t) respectively.
Equation (16) represents the dc motor model with parameter uncertainties, dis-
turbances and unknown constant.
To estimate those parameters the DC motor is run for 10 min with time step 0.1 s
in open loop condition. Variable step input with two different voltage steps is given
as input to the motor, such as:

28.8 ∗ 0.5 u(t) 0 < t ≤ 300 s.
uoc (t) 
28.8 ∗ 0.9 u(t) 300 < t ≤ 600 s.

Figure 3 shows the open loop input given to the motor. In this condition the output
voltage is measured and converted back into speed in rpm which is given in Fig. 4.
Parameter estimation is done with that speed set as reference and the DC motor
model is run in open loop with same input uoc (t) in simulation and the parameter
values are estimated by help of a stochastic search algorithm, named PSO. This
process is repeated 10 times with 30 particles and 200 iterations of PSO run to get
minimum integral absolute error value. From those results the obtained nominal
parameter values are tabulated in Table 1 and the result is given in Fig. 5.
358 R. Maiti et al.

30

25

Control effort u(t)

20

15

10

0
0 100 200 300 400 500 600
Time(second)

Fig. 3 Variable step input given to open loop system in real time environment

2000

1500
Amplitude

1000

500

Open loop system response

0
0 100 200 300 400 500 600
Time(second)

Fig. 4 Open loop system response in real time environment

Table 1 Estimated nominal parameter values of DC motor

Ra La J B K Kb KT
0.43401 0.00073 0.00620 0.00043 0.43025 0.00329 0.00329
On-line Adaptation of Parameter Uncertainties … 359

2000

1500

Amplitude
1000

500

Reference signal
System output
0
0 100 200 300 400 500 600
Time(second)

Fig. 5 Open loop system response in simulation environment

From Fig. 5 it can be clearly shown that due to parameter uncertainties and
unknown constant, the real time output varies from simulation output though same
input is given to the real time DC motor model (16) as well as to the simulation
model (12). To produce effective control law for such system the uncertainties must
be properly estimated and adapted. In this present paper, L 1 adaptive controller is run
in an online manner to get proper estimation of those uncertainties and then from L 1
adaptive law those uncertainties are adapted to produce efficient control signal.

3.2 Online L1 Adaptive Controller

Theoretically L 1 adaptive controller is robust and gives fast transient performances.

It is of great importance to validate it in real time environment.
Parameters of L 1 adaptive controllers can be classified into two groups such as
adaptive parameters and non-adaptive parameters. The parameter vector can be seen
as: P L1  [ω|θ|σ ||k|kg |fc ], where the adaptive parameters are: [ ω|θ |σ ] and non-
adaptive parameters are [|k|kg |fc ]. In this paper, first the PSO is used in an offline
manner to get the non-adaptive parameters and the adaptive parameters are adapted
in each time step from L 1 adaptation rule.
360 R. Maiti et al.

Table 2 Offline and online adaptation results in terms of IAE

Integral absolute error (IAE)
Offline adaptation Online adaptation
Input 1 19216.2484 18793.5851
Input 2 21852.4425 21506.4504
Input 3 32627.1874 30465.4716

2000 30
(a) (b)
25
1500

Control effort u(t)

Amplitude

20

1000 15

10
500
5
Reference signal
System output
0 0
0 100 200 300 400 500 600 0 100 200 300 400 500 600
Time(second) Time(second)

2000
1500
(c)
1000
500
Error

0
-500
-1000
-1500
-2000
0 100 200 300 400 500 600
Time(second)

Fig. 6 Online adaptation responses of L 1 adaptive controller with input 1 for a system response
with reference, b control effort, c error signal

With high adaptation gain the transient response is satisfactory enough, although
it introduces high frequency into the control signal. Projection operator limits the
values of adaptive parameters into the compact set given by [  ] and the filter
eliminates the high frequency contents into the bandwidth of the control channel and
the system in real time gives very good results.
On-line Adaptation of Parameter Uncertainties … 361

4 Experimental Results

The motor is run for 10 min with sampling time

t  0.1 second to get the results.
Two different variable
 step trajectories are given as reference such as:
1000 u(t) 0 < t ≤ 300 s.
Input 1: r(t) 
1500 u(t) 300 < t ≤ 600 s.

1200 u(t) 0 < t ≤ 300 s.
Input 2: r(t) 
1800 u(t) 300 < t ≤ 600 s.
Input 3: r(t)  1000 u(t) 0 < t ≤ 600 s with certain full load disturbances.
Offline Adaptation: Here in simulation, the criteria of selecting the parameters
P L1 of the L 1 adaptive controller is calculated from L 1 norm condition and from that
mathematical calculation, some arbitrary values are chosen and adaptive parameters
are adapted. For different trajectories the DC motor is then tested with those obtained
non-adaptive and final values of adaptive parameters in real time.
Online Adaptation: Here in simulation, particle swarm optimization is used to
select optimized parameter P L1 values satisfying the L 1 norm condition and adaptive
parameters are adapted following L 1 adaptive law. When this is tested in real time then
optimized values are taken for non-adapted parameters and adaptive parameters are
adapted spontaneously. Online adaptation of estimated uncertainties and unknown
constant gives better result than offline adaptation process.

4.1 Real Time Case Study

At first the DC motor is run in offline adaptation mode using the L 1 adaptive controller
parameters getting from the mathematical calculation of L 1 norm condition. Those
results are given in Table 2 in terms of IAE.
Then the results are given for online L 1 adaptive controller where non-adaptive
parameters are set from PSO and adaptive parameters are adapted in each step online.
IAEs are tabulated in Table 2 and results are given in Figs. 6, 7 and 8 for input 1, input
2 and input 3 respectively. Figures 6a, 7a and 8a show the system output compared
with reference signal whereas, Figs. 6b, 7b and 8b show the control effort required
and Figs. 6c, 7c and 8c portray the error signal.
Comparing those results it can be clearly shown that the online adaptation of L 1
adaptive controller gives better results than L 1 adaptive controller implementation in
offline adaptation mode.
362 R. Maiti et al.

2000 30
(a) (b)
25

Control effort u(t)

1500
Amplitude

20

1000 15

10
500
Reference signal
5
System output
0 0
0 100 200 300 400 500 600 0 100 200 300 400 500 600
Time(second) Time(second)

2000
1500
(c)
1000
500
Error

0
-500
-1000
-1500
-2000
0 100 200 300 400 500 600
Time(second)

Fig. 7 Online adaptation responses of L 1 adaptive controller with input 2 for a system response
with reference, b control effort, c error signal

5 Conclusion

In this paper on-line adaptation of L 1 adaptive controller is implemented success-

fully for speed control of a DC motor with unknown parameters and time varying
disturbances. PSO provides the optimal parameter setting for non-adaptive parame-
ters which give perfect selection of adaptive gain, filter parameters which are most
important parameters in designing of L 1 adaptive controller. Adaptive parameters of
the controller are adapted on-line to produce fast transient performance with high
robustness. The proposed method is successfully applied on DC motor experimental
setup and the results are compared in terms of integral absolute error to prove its
effectiveness.
On-line Adaptation of Parameter Uncertainties … 363

2000 30
(a) Reference signal
System output (b)
25

Control effort u(t)

1500
Amplitude

20

1000 15

10
500
5

0
00 100 200 300 400 500 600 0 100 200 300 400 500 600
Time(second) Time(second)

2000
(c)
1500
1000
500
Error

0
-500
-1000
-1500
-2000
0 100 200 300 400 500 600
Time(second)

Fig. 8 Online adaptation responses of L 1 adaptive controller with input 3 for a system response
with reference, b control effort, c error signal

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Two-Degree-of-Freedom Control
of Non-minimum Phase Mechanical
System

Mita Pal, Gautam Sarkar, Ranjit Kumar Barai and Tamal Roy

1 Introduction

Designing of Controller for a Non-minimum phase is a challenging tasks due to

its Right-hand plane (RHP) zero dynamics. RHP zero of NMP system is respon-
sible for large phase lag in the frequency domain and initial undershoot cannot be
avoided in time domain analysis of NMP system. This special characteristic is not
desirable for any appropriate system. Many Industrial processes like flexible link
manipulator, aircraft, steam generator, electronic circuits etc. [1] has non-minimum
phase characteristics, and it is an attractive job to handle this type of system, as unde-
sirable phenomena is obvious in the system’s dynamic response. Various methods
have been developed during past decade for the control processes with non-minimum
phase characteristics. QFT design method for NMP unstable system is revisited in
2001 [2]. Predictive control with PID structure [3], Filter basis function [4] has been
studied for discrete type NMP system. Flight Control has been proposed by approx-
imating non-linear NMP system by minimum phase system [5]. Recent research
works on designing of a control system for NMP system have been performed using
filter basis function and sliding mode learning control method [6, 7]. Input-output

M. Pal (B) · G. Sarkar · R. K. Barai

Electrical Engineering Department, Jadavpur University,
Kolkata 700032, India
e-mail: mitapal91@gmail.com
G. Sarkar
e-mail: sgautam63@gmail.com
R. K. Barai
e-mail: ranjit.k.barai@gmail.com
T. Roy
Electrical Engineering Department, MCKV Institute of Engineering,
Liluah, Howrah 711204, India
e-mail: tamalroy77@gmail.com
© Springer Nature Switzerland AG 2019 365
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_31
366 M. Pal et al.

linearization of the non-linear system has been tried to achieve local asymptotic
stability [8] and recently, a Proportional plus Integral current-output observer based
linear quadratic discrete tracker(LQDT) methodology has been theoretically applied
on a discrete time NMP system [9]. One peculiar characteristic of NMP system is
being experimented, where, the series combination of inverse and non-inverse trans-
fer function model of NMP system always produce oscillatory and unbounded output
response [10, 11]. It is well understood, that this phenomenon is not true for minimum
phase system. This unusual nature of RHP zero dynamics inspired the researcher to
design an appropriate control system for NMP system. The degree of freedom in
control system engineering is the number of variables that can be manipulated or
regulated in a process. In another way, it may be stated that a number of closed loop
transfer functions which have to be controlled, indicates the DOF of the system [12].
The Two-degree-of-freedom (2DOF) strategy in design technique of control system
has obviously been a better way to get precise control performance. The Recent devel-
opment of 2DOF controller has been found in Ball and Beam system [13], where
the ball can track the square wave with certain given specifications. Single input sin-
gle output industrial processes with model uncertainty are automatically tuned with
Model Predictive Control in 2DOF structure [14]. By surfing others literature regard-
ing 2DOF, it is observed that 2DOF concept becomes a reliable tool for researchers.
The combination of Feed-forward and feedback compensators in 2DOF structure
may be an effective tool for NMP system also. Adaptive feed-forward zero phase
error tracking control in 2DOF structure shows the good result for the minimum as
well as NMP System [15].
Among all Adaptive Controller, Model Reference Adaptive Control (MRAC) is
very much popular as it is a direct approach to force the uncertain system to obtain
the desired performance [16]. Here is an added advantage for control designer that,
they can choose the shape of the transient part of the output response, and it is only
possible by reference model, which is an essential part of the MRAC design [17].
A Model Reference Adaptive Controlled Permanent Magnet Synchronous Motor
has been simulated successfully, where time response shows optimum performance
[18]. Both MIT rule and Lyapunov stability rule can apply for designing of Model
Reference Adaptive Control and its efficiency has been observed by implementing
on a Chemical Reactor [19], that the stability of the Controller is completely granted
for Lyapunov stability theory. To improve the lateral stability of articulated heavy
vehicles (AHVs), MRAC has been theoretically applied to active trailer steering
(ATS) [20]. The transient performance of closed loop Model reference adaptive con-
trolled fractional order nonlinear system improves in the sense of generating smooth
system output [21]. Proportional plus Integral (PI), Proportional plus Integral plus
Derivative (PID), Phase lead or Phase lag Controller may not be able to control all
the poles of the higher order system independently. To circumvent these difficul-
ties, state feedback control with arbitrary pole placement approach can solve this
problem independently under certain condition, that the system must be completely
state controllable [22]. Transient dynamics of piezo-actuated bimorph atomic force
microscopy (AFM) probe is controlled by state feedback controller, where quality
factor and the resonance frequency of the probe have been adjusted simultaneously
Two-Degree-of-Freedom Control of Non-minimum … 367

Fig. 1 Block diagram of two-degree-of-freedom control scheme

[23]. An optimal state feedback design has been considered for the classical unsta-
ble plant like Inverted Pendulum by calculating the appropriate state feedback gains
using flower pollination algorithm (FPA) [24]. The efficiency of MRAC and Pole
placement method encourages us to design a suitable controller for inversion based
Non-minimum phase system.
The objective of this paper is to present a Two-degree-of-freedom controller for
NMP system, in which inverse transfer function model becomes compensated by
Model Reference Adaptive Control as feed-forward technique and non-inverse trans-
fer function model is controlled by arbitrary pole placement method as feedback
counter part of the 2DOF structure. This proposed method is verified with a practical
mass spring damper system [25] theoretically and compared it with two different
compensators, like PID and State Feedback Controller.
This paper is organized as follows, Sects. 2, 3, 4 and 5 represent brief descriptions
of the 2DOF, MRAC, State feedback and PID controller respectively. The mathe-
matical background of MRAC is provided by Sect. 3.1. Section 6 describes problem
formulation. Description of NMP mechanical system is provided by Sect. 7. Simu-
lation results observation and analysis of simulation results discussed in Sects. 8 and
9 respectively. The demonstration ended with concluding remarks in Sect. 10.

2 Two-Degree-of-Freedom

The number of closed loop transfer function that can be actuated independently is
known as Degree-of-Freedom. 2DOF structure not only guarantees stability, it also
tries to achieve the desired performances.
The 2DOF control structure consists of feed-forward and feedback controller and
they are connected in various fashion. In this block diagram (Fig. 1), it is shown
that output signal of feed-forward controller becomes the control input of feedback
controlled plant. The two controllers are decoupled with each other. Basically, feed-
back control is used to stabilize the system, whereas feed-forward controller help to
satisfy the desired dynamic characteristics of the given system.
368 M. Pal et al.

Fig. 2 Model reference adaptive system

3 Model Reference Adaptive Control

In the domain of Adaptive Control System, Model Reference Adaptive system is an

effective Adaptive control scheme. Originally it was applicable for Flight Control
System, where the reference model describes the desired trajectories of the Aircraft
[26]. The block diagram shown in Fig. 2 has two control loops, inner loop, and outer
loop. The inner loop is an ordinary feedback loop composed of Plant and Controller
and the outer control loop consists of the adjustment mechanism and reference model.
Outer loop calculates the control parameters on the basis of error which is produced
by the difference of reference and plant model outputs. In a model reference adaptive
control, the mechanism for adjusting the parameters can be obtained in two ways,
by using gradient method or by using stability theory.

3.1 Design of 2DOF Controller Using Model Reference

Adaptive Control

The desired plant response to a command signal is specified by means of a paramet-

rically defined reference model. An adaptation mechanism keeps track of the process
output, and reference model output, and calculates the suitable control parameters so
that the difference of these outputs tends to zero. In addition to the process output, y,
plant or control input, u and reference input, r may be used in adaptation mechanism.
Tracking error, e is simply the difference between the plant output, y and the
reference model output, ym refer to Fig. 3. Considering,
Reference Model:

d 2 ym dym
 −am + bm r (1)
dt 2 dt
Two-Degree-of-Freedom Control of Non-minimum … 369

Fig. 3 Model reference adaptive control system

Plant Model:

d2 y dy
 −a + bu (2)
dt 2 dt
Let, Control input:
dy
u  θ1r − θ2 (3)
dt
Tracking error:

e  y − ym (4)

By subtracting Eq. (1) from Eq. (2), we get,

d 2e d2 y d 2 ym dy dym
2
 2 −  −a + bu − (−am + bm r ) (5)
dt dt dt 2 dt dt
Replacing u in Eq. (5) from Eq. (3), we get,

d 2e dy dy dym
2
 −a + b(θ1 r − θ2 ) + am − bm r (6)
dt dt dt dt

By adding and deducting am dy

dt
with Eq. (6), we get,
370 M. Pal et al.

Fig. 4 Block diagram of state feedback controlled system

d 2e dy dy dy dy dym
 −a + am + bθ1 r − bθ2 − am + am − bm r (7)
dt 2 dt dt dt dt dt
d 2e dy dym dy
2
 −am ( − ) − (bθ2 + a − am ) + (bθ1 − bm )r (8)
dt dt dt dt
d 2e de dy
2
 −am − (bθ2 + a − am ) + (bθ1 − bm )r (9)
dt dt dt
Assuming the initial values of the control parameter θ1 and θ2 , and integrating
Eq. (9) with respect to t, we get,
de
 −am e − (bθ2 + a − am )y + (bθ1 − bm )r (10)
dt
From the error dynamics it is observed that the tracking error will go to zero if
bθ2  am − a and bθ1  bm . The parameter adjustment rule thus achieve the goal.

4 Description of State Feedback Controller

Any System can be represented by state model, which consists of the following state
equation and output equation Ẋ  AX + Bu and Y  C X + DU where, X is state
vector (n-vector), U is control signal (scalar), Y is output vector (scalar), A is n × n
system matrix, B is n × 1 input matrix, C is 1 × n output matrix D is input-output
coupling matrix (1 × 1) [27] (Fig. 4).
In Pole Placement technique, all the closed loop poles are placed at desired loca-
tions. It may be assumed that the entire state variable is measurable and are available
for feedback. A necessary condition for this arbitrary pole placement technique is
that, the system must be stated controllable. If the condition is satisfied, the control
Two-Degree-of-Freedom Control of Non-minimum … 371

Fig. 5 Block diagram of PID controlled NMP System

signal will be u  −K X . It means that the control signal is determined by the instan-
taneous state. Such a scheme is called State feedback Control scheme and the matrix
is called the state feedback gain matrix. The Eigen values of the closed loop system
may be placed at any desired location through this state feedback gain matrix. The
state equation will be modified to Ẋ (t)  ( A − B K )X (t). If the Eigen values of the
new system matrix placed at Left hand plane (LHP) of jω axis, the state model will
be stable in sense of Hurwitz.

5 Description of Proportional Plus Integral Plus Derivative

(PID) Control

PID Controller is a classical controller, which include three different control modes,
proportional action P, an Integral action I and derivative action D in Fig. 5. All
the three control modes require three independently operational amplifiers to be
adjusted separately and it needs electronics circuits. The mathematical  t model of
PID controller
 is given by the following
 equation, u(t)  k p e(t) + k i 0 e(τ )dτ +
t
kd dt  k p e(t) + Ti 0 e(τ )dτ + Td dt , where, u(t) is control input, e(t) is an error
de 1 de

signal, and k p ki , kd are the proportional, integral and derivative adjustable constant
respectively. The transfer function of PID Controller is k p + kSi + kd S. To meet given
performance specification of the control system, adjustable gains are selected by
using a particular tuning method or by trial and error method. Ziegler-Nichols tuning
method has been used here as it is very effective technique.
372 M. Pal et al.

Fig. 6 Block diagram of cascaded inverse with non-inverse transfer function model of NMP system

Fig. 7 Block diagram of decoupled 2DOF controlled NMP plant

6 Problem Formulation

When an inverse transfer function model connected in cascade with the original trans-
fer function model, exact reference input trajectory must be achieved as numerator
denominator canceled to each other (Fig. 6).
From the above diagram, it is needless to say, that exact reference input trajec-
tory can be possible by canceling the numerator denominator polynomial, but it is
applicable for minimum phase only where R(S) is reference input signal. But for
Non-minimum phase system, actual output trajectory not only unable to meet the
desired trajectory, it also produces unbounded output response (Fig. 7).
Two-degree-of-freedom consists of feed-forward and the feedback controller,
where MRAC controller as feed-forward part includes the inverse transfer func-
tion model and State feedback controller as feedback controller has been taken the
original transfer function model of the NMP system. A practical Non-minimum
phase system has been taken for experimental simulation.

7 Mechanical System Model

Mechanical Experimental set up developed by Freeman et al. [25], where non-

minimum phase component has been placed in the upper left corner of the test bed and
Two-Degree-of-Freedom Control of Non-minimum … 373

Fig. 8 Schematic representation of mechanical realization of non-minimum phase system

two more mass-spring-damper systems have been connected with the non-minimum
phase system (Fig. 8).
Electrical analogous to the above mechanical system shows non-minimum phase
characteristics. This NMP system consists of inertias, a damper, a torsional spring,
timing belt, pulleys, and gears. In the schematic diagram [25], inertias are represented
by J, Jg , G represents gear and B, K represents damping friction co-efficient and
spring constant respectively. Two spring mass damper systems have been inserted
before the non-minimum phase component to increase the relative degree of the entire
system. The mechanical experimental set up has been formulated by the following
transfer function model.

123.853 ∗ 104 (3.5 − S)

G(S)  (11)
(S 2 + 6.5S + 42.25)(S + 45)(S + 190)

8 Simulation Result

Unit step signal is applied to the uncontrolled NMP system, inverse transfer function
model of NMP system and series connected NMP system with its inverse transfer
function model. Square wave signal has been used as a set point for all the three,
state feedback, PID and 2DOF controlled NMP systems. All the simulation exper-
iments have been performed in a MatLab environment. An illustrative example for
simulation is briefly described in Sect. 7.

9 Result Analysis

Here, Fig. 9 shows output response of uncontrolled NMP system, where a deep
undershoot has been found. Inverse NMP system is obviously an unstable system
and Fig. 10 shows it’s unbounded output response. Unlike minimum phase system,
374 M. Pal et al.

Fig. 9 Unit step response of uncontrolled NMP system

Fig. 10 Unit step response of uncontrolled inverse NMP system

Fig. 11 Unit Step response of series connected NMP system with it’s inverse transfer function
model

NMP system connected in cascaded with its inverse transfer function model produce
unbounded output response (Fig. 11). It is observed that Two-degree-of-freedom con-
trolled NMP system produce far better result (Fig. 14) than PID controlled (Fig. 13)
Two-Degree-of-Freedom Control of Non-minimum … 375

Fig. 12 State feedback controlled NMP system with square wave signal as reference input

Fig. 13 PID controlled NMP system with square wave signal as reference input

Fig. 14 2DOF controlled NMP system with square wave signal as reference input

and state feedback controlled (Fig. 12) NMP system when Square Wave signal has
been applied as Reference input signal. Unit step response of state feedback, PID
and 2DOF controlled NMP system have been superimposed (Fig. 15). It is found
that output trajectory of 2DOF controlled NMP Plant is very near to reference input
trajectory and also initial undershoot becomes completely nullified. Percentage RMS
errors from the square wave responses of the 2DOF controlled NMP system with the
existing compensation technique have been listed below.
376 M. Pal et al.

Fig. 15 Unit step responses of state feedback, PID and 2DOF controlled NMP system

Type of controller State feedback PID 2DOF

% error in RMS 46% 7.8% 0.79%

Comparison chart of State feedback, PID and 2DOF controlled system dynamics
has been listed below.

Name of the controller Initial undershoot Steady state error Rise time (sec)
State feedback 1.27 0.04 0
PID 0.47 20 6.1
2DOF 0.03 0.04 3.8

10 Conclusion

This paper presents a theoretical technique for designing a Model Reference Adap-
tive control (MRAC) in Two-degree-of-Freedom (2DOF) framework for a prac-
tical Mechanical System, which has Non-minimum phase (NMP) characteristics.
Decoupled Feed-forward and feedback compensators are the main components of
the 2DOF controller. As the inverse model connected NMP systems are not able to
produce bounded output, here, inverse model NMP system is compensated by MRAC
scheme as feed-forward part and non-inverse NMP system has been taken care by
state feedback controller in the 2DOF control structure. The simulation study of this
proposed 2DOF methodology has been shown the effectiveness of the proposed con-
trol methodology, especially, initial undershoot, which is unavoidable phenomena in
NMP system becomes almost nullified. After comparing with PID control and State
feedback control technique, it has been observed that proposed control method can
contribute satisfactory result than other two control schemes.
Two-Degree-of-Freedom Control of Non-minimum … 377

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LFT Modeling of Differentially Driven
Wheeled Mobile Robot

Tamal Roy, Ranjit Kumar Barai and Rajeeb Dey

1 Introduction

Popular mobile robotic systems result from the synergistic integration of mechanical
systems, microelectronics and intelligent computer control [1]. As the various subsys-
tems of control systems are interconnected in a delicate manner to serve the primary
objective of precise and stable control, the overall closed-loop system is very com-
plex. As demand increases, it becomes necessary to improve the performance of the
WMR for conventional applications. It is possible to improve the performance of the
WMR through the better modelling of the system. Model-based control approaches
are widely accepted technique to control WMR and the ability to develop a real-
istic model will greatly benefit the development of advanced controllers. From the
perspective of the design of an appropriate control law for WMR; such complicated
model may be inconvenient due to the high degree of computational complexity.
Moreover, from a wide range of control law, a particular control law may be most
suitable for a particular class of systems from the perspective of tackling the nonlin-
earities, parameter variation, model uncertainties, noise, and disturbance. Therefore,
it becomes necessary to select an appropriate mathematical model of the system for
the design of a particular control law in order to obtain optimum control performance.

T. Roy (B)
Electrical Engineering Department, MCKV Institute of Engineering,
Liluah, Howrah 711204, India
e-mail: tamalroy77@gmail.com
R. K. Barai
Electrical Engineering Department, Jadavpur University, Kolkata 700032, India
e-mail: ranjit.k.barai@gmail.com
R. Dey
Electrical Engineering Department, NIT, Silchar, Assam 788 010, India
e-mail: rajeeb.iitkgp@gmail.com

© Springer Nature Switzerland AG 2019 379

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_32
380 T. Roy et al.

In order to achieve the intended control performance, research efforts have been
directed towards the development of control-oriented modeling of a benchmark
mechatronics system namely, differentially driven wheeled mobile robot (WMR).
Owing to its widespread industrial applications, cost-effectiveness and availability
of its small-scale laboratory-based model and highly nonlinear cross-coupled dynam-
ics, WMR has become a test-bed for the development of robust controller among
control community. Kinematic modeling of the WMR has been discussed in the
numerous literature related to engineering mechanics [2] and analytical mechanics
[3]. There has been growing interest among the control community researchers on
dynamic modeling of WMR due to the challenge posed by this system as in this case
the interaction between the outer wheel and the ground surface is the contact point
with the environment and has a considerable influence in the dynamic motion of the
system [4–6]. Although effort has been made to derive a systematic framework of the
system include the dynamics into the overall mathematical modeling [7, 8]. However,
due to the various uncertainties associated with the dynamic model of the WMR,
some kinds of robustness measure in the control law are incorporated to develop a
controller that is effective in the real-world situation [9]. H∞ control strategy has
been proved useful to overcome or compensate the effects of these model uncertain-
ties [10, 11]. Thus, a modeling structure has been proposed to develop LFT based
model uncertainty representation of WMR would make it convenient for the appli-
cation of modern robust control technique like µ-analysis and synthesis in addition
to H∞ -control.
Over the last two decades, there has been a widespread interest to design a robust
controller where system model is considered to be consisting of a nominal model and
a model uncertainty part [12]. There are different forms of model uncertainty repre-
sentation for robust control design like: additive or multiplicative model uncertainty
bounds, or parametric uncertainty regions, co-prime factor uncertainty, uncertainty
representation in a feedback-like connection as in case of linear fractional trans-
form (LFT) modeling, and the performance of the robust controller depends on the
appropriate representation of the model uncertainty.
The model of nonlinear systems varies due to changes in system configuration
and operating conditions. This system variation can be characterized as model uncer-
tainties [13] and can be represented in the linearized model by expressing the system
state-matrices as matrix polynomials in the uncertain parameters in the form of a
linear fractional transform (LFT) [12, 14]. This LFT based model uncertainty rep-
resentation of the nonlinear system is essential for the application of modern robust
control technique like µ-analysis and synthesis [15] in addition to H∞ -control and
H∞ -Loop Shaping [14, 16–18]. Linearization of uncertain nonlinear systems as LFT
model relates each of the uncertainty with a physically meaningful parameter of
the actual system [19]. Linear Fractional Transform (LFT) technique offers a uni-
fied framework for parameter identification problems [20]. In the LFT framework,
a wide variety of identification problems concerning structured nonlinear systems,
linear parameter varying (LPV) systems, and also the various parametric linear sys-
tem model structures can be accommodated due to its general nature. Moreover, LFT
framework is convenient to address the issues such as identifiability and persistence
LFT Modeling of Differentially Driven Wheeled … 381

of excitation for a large class of model structures. The main aspect of the LFT-based
uncertainty modeling is the generation of the lower order LFT modeling [21] but it is
only applicable to those nonlinear systems where the linearization of the mathemat-
ical modeling is possible [22]. The LFT representation consists known or invariant
part separated from the uncertain or variable parts which are summarized and stacked
together in the “perturbation” matrix.
In view of the above discussion on the modelling aspects of WMR, the authors
propose a novel methodology of uncertainty modelling in the linear fractional trans-
formation (LFT) modelling framework, considering the nonlinear model of WMR
with non-holonomic constraints that arise from constraining the wheels of the robots
to roll without slipping [23]. A versatile and well-organized uncertainty modelling
representation of WMR in LFT framework has never been addressed in the literature.
The rest of the paper has been organized as follows. The system dynamics of
WMR is described in Sect. 2. The LFT modeling formulation of differentially driven
WMR has been described in Sect. 3. Section 4 explains the frequency domain model
validation of the proposed modeling structure of WMR.

2 Differentially Driven Wheeled Mobile Robot

The most popular construction of the wheel mobile robot is the two-wheeled mobile
robot differentially driven by two independent DC motor shown in Fig. 1. Two DC
motors are used for left and right drive wheels of the robot in a horizontal axis and one
free caster wheel is used to keep the platform stable. The control of the robot depends
on the angular velocities of the two drive wheels [24]. If the angular velocities of the
two drive wheels are identical in values and in same relative rotational senses, the
robot makes a spin motion. If the angular velocities of the two wheels are identical
in values but opposite in relative rotational senses, the robot makes a linear motion
and if the angular velocities of the two drive wheels are different in values, the robot
makes a curve motion.
The robot configuration is represented by the position of the centre of the axis
between the two wheels in the Cartesian space (x c and yc ) and by its orientation θ
(angle between the vector of the robot orientation and the abscissas) is shown in
Fig. 1.
The kinematic modelling describes the relations between the derivatives of robot
position and orientation and the robot linear and angular speeds, v and ω. While, the
dynamic model of WMR is derived from the physics laws. All the physical parameters
are taken into the consideration in the dynamic modelling of the WMR [24]. In the
dynamic modelling of WMR non-holonomic constraints have been considered which
results from assuming no slip between the ground and the wheels. In our present
work, dynamic modelling of the wheel mobile robot is considered to formulate the
control-oriented modelling in LFT modelling framework.
382 T. Roy et al.

Fig. 1 Schematic diagram

of wheeled mobile robot

2.1 Kinematic Modeling

In kinematic modelling, the main purpose is to point out the structural properties
of the WMR by introducing the concepts of the degree of mobility and degree of
steribility in the variety of possible robot constructions and wheel configurations.
WMR is operating on a horizontal plane and considered as the rigid body on wheels
and out of these three dimensionalities of the robot chassis, two for position in the
plane and one for orientation along the vertical axis, which is orthogonal to the plane.
The kinematic model of the differential-drive
 robot
 relates the forward and angular
velocities (v, ω) to cartesian velocities ẋ, ẏ, θ̇ [8, 14]. The x component of the
forward velocity can be expressed as

ẋ  v cos θ (1)

and the y component can be expressed as

ẏ  v sin θ (2)

The kinematic model can then be represented as

q̇  q TV .V (3)
⎡ ⎤ ⎡ ⎤
  ẋ cos θ 0
v ⎢ ẏ ⎥
where V  , q̇  ⎣ ⎦ and q
TV  ⎣ sin θ 0 ⎦
ω
θ̇ 0 1
LFT Modeling of Differentially Driven Wheeled … 383

2.2 Dynamic Modelling

The parameterized dynamic model of a differential drive wheeled mobile robot is

derived from the physical laws that govern the robot subsystems, including the actu-
ator dynamics like electrical and the mechanical characteristics of the actuators,
friction and robot dynamics (movement equations) [24].
The modelling of the WMR can be presented by the differential equation as given
below

M V̇ + BV  K u (4)

where,
⎡ ⎤
Jd 
m+ 0
⎢ rd2 ⎥ J1 0
M ⎣ ⎦ 
Je b2 0 J2
0 J+ 4re2

where

Jd Je b2
J1  m + and J2  J +
rd2 4re2

⎡ ⎤
1 Kd
2 
β1 + ( + βd ) 0 β1 + α1
⎢ rd2 Rd ⎥ 0
B⎣ ⎦
0 β2 + b2 K e
(
2
+ βe ) 0 β2 + α2
4re2 Re

where,

1 K d2 b2 K 2
α1  (
2 R
+ βd ) and α2  2 ( e + βe )
rd d 4re Re

and
⎡ ⎤ 
Kd
0 K1 0
K ⎣ ⎦
Rd r d

0 − 2R
Ke b
e re
0 K2

where,
Kd Keb
K1  and K 2  −
Rd r d 2Re re
384 T. Roy et al.

 V  [v, ω] represent the linear and the angular velocity of the robot
T
The vector
er
and u  contains the input signals mainly armature voltages applied to the
el
right and left actuators (motors). K ∈ n×n is the matrix which transforms the
applied electrical signals u into forces to the robot wheels for movement. M ∈ n×n
is inertia matrix of the WMR and B ∈ n×n is the damping matrix which includes
terms of viscous friction and electric resistance. Parameterized dynamic modelling
of a differential-driven wheeled mobile robot is taken into the consideration for the
formulation of robust control oriented modelling in LFT framework.

3 LFT Modelling of Differentially Driven Wheeled Mobile

Robot

The equations of motion of WMR are obtained using the Newtonian as well as
Euler formula [30,24]. The moment of inertia and the co-efficient of viscous friction
of WMR are supposed to be uncertain with bounded uncertainties. These associ-
ated model uncertainties can be lumped into one single perturbation block . LFT
modeling of WMR consisting of the nominal model represented by known transfer
function and the uncertain block  is represented by an unknown transfer function
matrix. The dynamic modeling of WMR is shown in Fig. 4.

M V̇ + BV  K u (5)
−1 −1
V̇  −M BV + M Ku (6)

Based on the practical consideration, moments of inertia and the viscous fric-
tion coefficient are uncertain parameters within the system but we assumed that
the moments of inertia are constants with possible relative error of 10% around the
nominal values; similarly, the viscous friction coefficients may have with 15% rel-
ative errors around the nominal values [25]. In the uncertainty representation of the
moments of inertia of WMR inverse additive perturbation representation technique
is used.
Therefore, the actual moments of inertia are presented as

Ji  J¯i (1 + pi δ Ji ) where i  1, 2 (7)

J¯i is the nominal value of the corresponding moment of inertia, pi  0.1 is the
maximum relative uncertainty in each of these moments and −1 ≤ δ Ji ≤ 1.
Matrix M contained the moment of inertia Ji , then matrix M decomposed as

M  M + M pJ (8)
LFT Modeling of Differentially Driven Wheeled … 385

where the elements of M is determine by the nominal values of the moment of inertia
and  J represents the uncertain part of the matrix M
 ⎡ ⎤ 
J¯1 0 J¯1 p1 0 δ J1 0
M , Mp  ⎣ ⎦ and  J 
0 J¯2 0 J¯2 p2 0 δ J2

The upper LFT representation of M −1 matrix is defined with

M −1  FU (Q J ,  J )  Q J22 + Q J21  J (I2 − Q J11  J )−1 Q J12 (9)

The block partition matrix Q J represented as

⎡ QJ QJ12 ⎤ ⎡ − M −1M p M −1 ⎤
QJ = ⎢ 11 ⎥=⎢ ⎥ (10)
⎢⎣QJ 21 QJ 22 ⎥⎦ ⎣⎢ − M −1M p M −1 ⎦⎥

The uncertainty representation of the viscous friction coefficient matrix B is

express in terms of the uncertain parametric representation can be described by

βi + αi  (βi + ᾱi )(1 + si δβi ), i  1, 2 (11)

where βi + ᾱi is the nominal value of the corresponding viscous friction coefficients,
si  0.15 is the maximum relative uncertainty in each of these coefficient and
−1 ≤ δβi ≤ 1, i  1, 2.
Matrix B can be decomposed as

B  B + B (12)

where the elements B are determined by the nominal values of the viscous friction
coefficient
⎡ ⎤
β̄1 + ᾱ1 0
B⎣ ⎦
0 β̄2 + ᾱ2

The uncertainty matrix B in Eq. (12) can be further decomposed as

B  B f β Bg (13)
⎡ ⎤   
β1 s1 0 δβ1 0 10
where B f  ⎣ ⎦, β  and Bg 
0 β2 s2 0 δβ2 01
The upper LFT representation of the viscous friction coefficients matrix B is given
by
386 T. Roy et al.

Fig. 2 Block diagram of

wheeled mobile robot

Fig. 3 Block diagram of WMR in LFT structure

B  FU (Q β , β )  Q β22 + Q β21 β (I2 − Q β11 β )−1 Q β12 (14)

The block partition matrix Q β is represented as

⎡ Qβ11 Qβ12 ⎤ ⎡02×2 Bg ⎤

Qβ = ⎢ ⎥=⎢
⎢⎣Qβ21 Qβ22 ⎥⎦ ⎣ B f B ⎥⎦ (15)

Using LFT structure of matrices M −1 and B in (9) and (14) the block diagram of
WMR in Fig. 2, now redrawn with nominal block partition matrices Q J and Q β and
uncertainty matrices  J and β as shown in Fig. 3.
Now considering u J , u β being the output of the uncertainty blocks  J and β are
fed as an input to Q J and Q β blocks respectively. Similarly, y J , yβ are the outputs
of Q J and Q β blocks that are fed as an input to the  J and β blocks respectively.
Assuming x1  v and x2  ω.
The state vector of WMR can be defined as
 T
X  x1 x2 (16)
LFT Modeling of Differentially Driven Wheeled … 387

Next, V̇ is represent in terms of state variables as defined above

 T  T
V̇  v̇ ω̇  ẋ1 ẋ2 (17)

The controlled output vector is defined in terms of state variable as

 T  T  T
yc  x1 x2  yc1 yc2  vω (18)

Now, output of WMR can be expressed as

yc  V (19)
 T
where V  v ω
The measured output vector of the system is represented as
 T
ym  ym v ym ω (20)

It is to be noted that the output are measured using position encoder for the system
under study. Considering the resolution of the encoder to measure output ym is further
written as

ym  m V (21)

The LFT representation of WMR can be represent

⎡ ⎤
ẋ1 ⎡ ⎤
⎢ ⎥ x1
⎢ ẋ2 ⎥ ⎢ x2 ⎥
⎢ ⎥
⎢ yJ ⎥  ⎢ ⎢u ⎥
⎥
⎢ ⎥ ⎢ J⎥ (22)
⎢ yβ ⎥ ⎢ ⎥
⎢ ⎥ ⎣ uβ ⎦
⎢ ⎥
⎣ yc ⎦ u
ym

where
⎡ ⎤
−1 −1 −1 −1
⎢ −M B̄ −M M p −M B f −M K ⎥
⎢ ⎥
⎢ −M −1 B̄ −M −1 M p −M −1 B f −M −1 K ⎥
 ⎢ ⎥
⎢
⎢ Bg 02×2 02×2 02×2 ⎥
⎥
⎢ ⎥
⎢ I 02×2 ⎥
⎣ 2×2 02×2 02×2 ⎦
Γm 02×2 02×2 02×2
10×8

Input output expression of the uncertainty blocks can be represent as

388 T. Roy et al.

Fig. 4 Input output block

diagram of the WMR

 
uJ yJ
 (23)
uβ yβ


J 0
where  
0 β
4×4
Input-output representation of WMR is expressed as The open loop block diagram
representation of LFT structure of WMR with three inputs (uJ , uβ , u) and four outputs
(yJ , yβ , yc , ym ), is shown in Fig. 4.
Input-output representation of WMR in LFT framework is expressed as
⎡ ⎤
ẋ ⎡ ⎤
⎢ yJ ⎥ x
⎢ ⎥ ⎢ uJ⎥
⎢y ⎥
⎢ β⎥  G wmr ⎢
⎣
⎥ (24)
⎢ ⎥ uβ ⎦
⎣ yc ⎦
u 8×1
ym
10×1

where

⎡A B1 B2 ⎤
Gwmr = ⎢⎢ C1 D11 D12 ⎥⎥
⎣⎢C2 D21 D22 ⎦⎥

and
 −1
    −1

A  −M B̄ , B1  −M −1 M p −M −1 B f , B2  −M K
2×2 2×4 2×2
⎡ ⎤ ⎡ ⎤ 
−1 −1 −1 −1
−M B̄ −M M −M B −M K
C1  ⎣ ⎦ , D11  ⎣ p f ⎦ , D12 
Bg 02×2 02×2 02×2
4×2 4×4 4×2
LFT Modeling of Differentially Driven Wheeled … 389

Fig. 5 LFT representation

of perturbed WMR

  
I2×2 02×2 02×2 02×2
C2  , D21  , D22 
Γm 02×2 02×2 02×2
4×2 4×4 4×2

The Upper LFT representation of the WMR with uncertainty block  can be
represented by

y  FU (G wmr , )u (25)


J 0
where  
0 β
The uncertain modeling structure of WMR can be described by an upper LFT
representation with the diagonal uncertain matrix is shown in Fig. 5.
Frequency response of the perturbed open-loop WMR is shown in Fig. 6.

4 Frequency Domain Validation

The frequency domain validation of uncertainty modeling in LFT framework has

been investigated in the context of robust control theory [8, 14]. The objective is to
design an H∞ controller that achieves certain performance specification and remain
stable in the presence of all possible uncertainties.

4.1 Simulation Result

The (sub) optimal H∞ control law has been implemented for the interconnected
system as shown in Fig. 7. The H∞ optimum control minimizes the  .∞ norm
of the nominal transfer function matrix FL (P, K ) over the stabilizing controller
390 T. Roy et al.

Fig. 6 Frequency response of perturbed open-loop systems

Fig. 7 Closed-loop LFTs in

H∞ design

transfer matrix K , where P is the transfer function matrix of the augmented system.
The nominal closed loop transfer function matrix FL (P, K ) of WMR is expressed in
terms of references, disturbances and noises (the signal r, d and ρ) to the weighted
output e yc and eu is shown in Fig. 7.
The interval for γ iteration is chosen between 1 and 100 with a tolerance of 0.0001.
The controller of the closed loop system achieves the  .∞ norms equal to 1.0001.
The most suitable property of the controller is that it has all stable poles, which makes
the proposed modeling structure of the WMR more acceptable in practice. The closed
loop system with H∞ controller achieves the robust stability and the maximum value
of μ is 0.17461 is shown in Fig. 8 and also achieve the robust performance with a
maximum value of the μ is 0.94528 shown in Fig. 9.
LFT Modeling of Differentially Driven Wheeled … 391

Fig. 8 Robust stability test

of H∞ controller

Fig. 9 Nominal and robust

performance of H∞
controller

Numerical values of the WMR are given in Table 1.

5 Conclusions

In this paper, LFT modeling of a nonlinear cross couple multivariable WMR system
has been derived for implementing robust control law. A novel modeling technique,
which can truly integrates control objectives of the robust control law, may be most
suitable for the particular class of systems from the perspective of tackling the non-
linearities, parameter uncertainties, reduction of model order, disturbances and noise.
392 T. Roy et al.

Table 1 Numerical values of WMR

Symbol Value Unit Symbol Value Unit
m 0.352 Kg Kd 2.05 × 10−2 –
b 0.075 m Ke 2.01 × 10−2 –
rd 0.0251 m J1 0.003 × 10−6 kg − m2
re 0.0254 m J2 0.005 × 10−6 kg − m2
Rd 17.33 ohm βd , βe 7.004 × 10−5 –
Re 17.00 ohm β1 0.1002 –
J 13.02 × 10−6 kg − m2 β2 7.004 × 10−5 –

A popular cross coupled nonlinear WMR system has been considered for develop a
compact and manageable mathematical representation in LFT framework for imple-
menting a particular control law in order to obtain optimum control performance.
Frequency domain validation technique has been introduced for ensuring satisfactory
results for validating uncertainty model of the WMR in LFT framework.

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 Part V
Neuro Fuzzy, Control System and
Optimization
Automatic Electronic Excitation Control
in a Modern Alternator

Avik Ghosh, Sourish Sanyal, Arabinda Das

and Amaranth Sanyal

1 Introduction

The alternators commonly used for generation of a.c. power are of the synchronous
type. The magnetic field of such alternator rotates at synchronous speed—hence
the name. These generators have their armatures in the stator and the field winding
in the rotor. The armatures are the power-producing parts and are of the 3-phase
type. EMFs are induced in the armature conductors due to change in flux-linkage
produced by rotation of the field winding. The field winding is excited by d.c. power,
mostly through slip-rings and brushes. Brushless excitation is another possibility.
There are various schemes for supplying d.c. power to the field winding. It may be
obtained from a separate d.c. generator or an alternator-rectifier or from the stator
itself through controlled rectification [1–3].

A. Ghosh (B)
Department of Electrical Engineering, Ideal Institute of Engineering,
Kalyani, Nadia, West Bengal 741235, India
e-mail: avik_be@yahoo.com
S. Sanyal
Department of Electronics and Communication Engineering,
Techno India College, Salt Lake, Kolkata, India
e-mail: maysourish2013@gmail.com
A. Das
Department of Electrical Engineering, Jadavpur University, Kolkata
700032, India
e-mail: adas_ee_ju@yahoo.com
A. Sanyal
Department of Electrical Engineering, Calcutta Institute of Engineering
and Management, Kolkata 700040, India
e-mail: ansanyal@yahoo.co.in

© Springer Nature Switzerland AG 2019 397

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_33
398 A. Ghosh et al.

The modern alternators are invariably high voltage high power units. Their voltage
and the frequency must be closely controlled to maintain the quality of supply.
The excitation system (AVR) is to provide controlled excitation to a synchronous
machine to keep the generator terminal voltage (or at the terminal of generator-
transformer) constant [4]. The reactive power generation is also controlled by the
excitation system, thus controlling the power factors of the generators operating in
parallel. The excitation system also has protective functions viz. it imposes limits
on under-excitation and over-excitation. The frequency is controlled by the turbine-
governor. It is kept within close limits (between 49 and 50.5 Hz. as per ABT) but is not
held constant in our country. We do not use an automatic frequency controller (AFC)
due to technical and economic reasons. However the use of electronic automatic
voltage regulator (AVR) is a must.

2 Mathematical Description

From the basic voltage equation of the alternator, we get:

EV+I·Z (1)

where E  induced voltage, V  terminal voltage, I  armature current, and Z 

synchronous impedance
To maintain the terminal voltage constant, the induced emf and hence the field
current has to be continuously adjusted with change in loading. This is the main task
of the AVR. It has also additional functions e.g., proper sharing of reactive power
between alternators in parallel, boosting up the excitation to ceiling under sudden
disturbance etc.
There is a limit to the power that a generator can develop. For a cylindrical pole
turbo-generator, the power developed and the maximum power are given as:

P  Pmax sin δ, Pmax  (E V / X s ) (2)

where Xs  synchronous reactance.

If the power demand exceeds Pmax , then the machine will not be able to deliver
any power and will fall out of synchronism. This is the power limit at steady state.
Actually the machine will become unstable at a much lower power, if the load change
be sudden or there be a sudden disturbance like short-circuit. This lower power
limit is the transient stability limit which must not be exceeded in order to maintain
synchronism between generators operating in parallel. This transient stability limit
is enhanced by modern fast-acting exciter control which forces the excitation to
its ceiling on occurrence of a fault. Thereby it increases the value of field current,
If , hence induced emf, E and consequently maximum power, Pmax . This is called
field-forcing [5–7].
Automatic Electronic Excitation Control in a Modern Alternator 399

3 Evolution of the Exciter System

Therefore, we note that the exciter has multiple functions—both control and pro-
tective. The AVR is embedded in it which is the heart of the excitation control.
Earlier versions of AVR were slow and sluggish and could not respond to changes
immediately. Such systems employed d.c. generators as exciters and vacuum tubes,
Magamps etc. for control. In a later stage came the a.c. exciters with rectifiers—either
static or rotating. They were much faster. In a still later stage, solid state excitation
(using high power SCRs) was brought in. In this method a part of the a.c. power
generated by the alternator is rectified in a controlled manner and is applied to the
field winding [8]. This happens to be the fastest. For various reasons the rotating
rectifier system is also being used for many modern alternators.

4 Modern Alternators and Their Excitation

Modern turbo-generators are designed with low value of air-gap which gives rise
to low short-circuit ratio (SCR). This practice reduces the requirement of excitation
current and gives rise to a lighter rotor of smaller inertia. The lighter rotor obviously
reduces the bearing losses, but increases the amplitude of oscillation under transients.
It also increases the synchronous reactance and the operating power angle. It reduces
the maximum power, the angle margin and the coupling coefficient. For example in
BTPS, the length of air-gap for the 210 MW set of BHEL is 70 mm. The unsatu-
rated value of synchronous reactance is 2.22 p.u. and inertia constant is 4.18 s. The
corresponding values for the Westinghouse 89.25 MW sets are 1.6 p.u. and 7.0 s.
All modern generators are equipped with fast-acting excitation controllers and
automatic voltage regulators. Such devices have radically improved the transient
stability. The high value of synchronous reactance and the reduced angle margin are
of no significance, now-a-days. The excitation controllers with excitation forcing
facility under fault condition can bring back the generator into stable zone from a
power angle of even 140°, without pole-slip. The modern excitation controllers using
solid state devices are extremely fast. But their use may cause dynamic instability
if the parameters of the controller are not properly tuned with the generator and the
system [9].
The synchronous reactance of a generator is many times larger than its resistance.
So the synchronous reactance is largely responsible for the voltage drop. We want to
closely regulate the terminal voltage of the generator (sometimes or the generator-
transformer), we make use of automatic control systems—the excitation controller
and the AVR. The AVR also fixes up the reactive power allocation.
The frequency also falls with loading. It can also be regulated by using Automatic
Frequency Controllers (AFC). As yet, we do not use AFC in our systems for various
reasons.
400 A. Ghosh et al.

Fig. 1 Alternator with

under-excitation (leading
p.f.)

Fig. 2 Alternator with

over-excitation (lagging p.f.)

5 Change of Excitation with Change in Load

The power factor of the aggregate load is an important factor. At leading power factor
the field current decreases. This is called under-excitation. It reduces the stability
margin. Leading p.f. may occur due to charging current of cable transmission and long
distance high voltage transmission while the load is small. If the load power factor is
too much lagging, the field current becomes too high. This is called over-excitation.
Too much of over-excitation is not good as it increases the rotor temperature and
may cause thermal injury. The phasor diagrams of alternator under over-excited and
under-excited conditions are given in Figs. 1 and 2 respectively. It is observed that
the induced e.m.f. must vary over wide range with change in load and its power factor
if we like to keep the terminal voltage constant. That is why an excitation controller
is used. Manual control is inaccurate and human response to changes in voltage and
corrective action are extremely sluggish. Therefore the excitation controller must be
automatic [10].
Automatic Electronic Excitation Control in a Modern Alternator 401

6 Requirements of the Excitation System

Functionally, the excitation system is to provide regulated direct current to the field
winding of a synchronous machine. It has both control and protective functions. It
has to control the terminal voltage by regulating the field current and, as and when
necessary, to boost up the excitation to ceiling for system protection.
The excitation control aims at improved quality, greater reliability and higher
stability margins in a generating system. It is, in essence, the heart of the generator
control.
The most important requirements of excitation systems are as follows:
(a) The excitation system should ensure good damping of free and forced oscillation
of small and large amplitude. Good damping increases the resultant stability,
enhances the transient stability margin and reduces the voltage fluctuations at
the load nodes.
(b) The excitation system should have high operational reliability. It has to choose
the operating variables to be controlled and the circuit components. The exci-
tation system should enable the generators to operate under overexcited and
under-excited conditions. It must ensure single-unit and multi-unit control and
proportional distribution of reactive power between synchronous machines.
(c) The excitation control should ensure high quality of voltage under steady state
i.e. it must accurately maintain the voltage at system nodes to which the con-
trolled synchronous machines are connected. This is obtained by choosing high
gains for automatic excitation regulators.
(d) The automatic excitation control system should ensure steady state stability of
the electrical system under all possible operating conditions including the fol-
lowing cases: a loaded or unloaded synchronous machine is disconnected from
the system, a synchronous generator is connected to an unloaded transmission
line, a synchronous machine is operating under overload and under-excited con-
dition, normal load conditions, post fault condition.
(e) The automatic excitation control of generators connected to a long transmission
line should provide maximum transmitted power equal to the maximum capacity
of the line with a constant voltage at the system nodes to which large controlled
synchronous machines are connected.
(f) A desired limit of transient stability must be ensured by the excitation system.
It has to respond to a sudden disturbance with field forcing. The forcing during
transience must conform to the instantaneous and short term capabilities of the
generator. The generator capabilities in this regard are limited by factors such
as:

i. rotor insulation failure due to high field voltage

ii. rotor heating due to high field current
iii. stator heating due to high armature current
iv. core-end heating during under-excited operation and
v. heating due to excess flux (volts/Hz).
402 A. Ghosh et al.

The thermal limits are time-dependent. The short-term overload capability of the
generators extends from 15 to 60 s.

7 Types of Exciter

The exciters may either be of the proportional type or of the over-action type. The
P-type control responds to the polarity and the magnitude of variations in the signal.
But the over-action type also responds to the rate of change of the signals. The P-type
control is slow and is associated with a static error. The over-excitation controllers
operate more quickly and keep the voltage at generator terminals or at the terminals
of the generator-transformer practically constant.

8 Change of Excitation with Load and Its P.F

The phasor diagrams of a cylindrical pole turbo-generator under both leading and
lagging power factor conditions with terminal voltage constant are shown in Figs. 1
and 2. It is observed that the excitation requirement is high under lagging p.f. condi-
tion. So this condition is called over-excitation. The power angle at this condition is
relatively low and hence there is enough of steady state stability margin. On the other
hand the excitation requirement is low under leading p.f. condition. This condition
is called under-excitation. The corresponding power angle is high and the stability
margin low. The excitation requirement and the angle margin remains at intermediate
values under unity p.f.
When no automatic control is incorporated the induced emf is determined by the
invariable value of the field current and remains constant under changing load and
fault condition (E  const). The power limit is given by:

P  E V sin δ/ X S  Pmax sin δ (3)

With increasing load at lagging p.f., characteristic of power system, the terminal
voltage will gradually fall and hence the value of Pmax . This will not only make
the quality of power supply unacceptable for the consumers but also will increase
the power angle thus reducing the stability margin. But if the terminal voltage is to
be kept constant by automatic devices, the value of E is to be regularly adjusted in
conformity with the following equation:

E  V + I · Z or E < δ  V < 0 + I < −θ · (r + j · X) (4)

The values of induced emf required to keep the terminal voltage constant at rated
value at different loads and at different power factors can be computed for an alterna-
Automatic Electronic Excitation Control in a Modern Alternator 403

tor by using an appropriate program. The synchronous reactance method is generally

adopted, neglecting the effect of saturation. Infinite bus idealization has been made.

9 Induced Voltage at Different Loads and P.F

Bus is assumed to be infinite. All quantities are in p.u. The machine is connected to
the bus through a transformer as shown in Fig. 3.

The MW-rating of the generator  210 Transformer resistance  0.005 (machine base)
Voltage at infinite bus  1.0 Transformer reactance  0.1367 (do)
Synchronous reactance  2.225 Total line resistance  0.0069
Armature resistance  0.0019 Total line reactance  2.3617

It is revealed from Table 1 that the variation of emf. is through a very wide range
as the load and its p.f. changes. Leading p.f. occurs during lean period, generally it
is not less than 0.95. At 70% load, the emf becomes 1.5692. At peak hours, the p.f.
does not fall below 0.9 lag. At 90% load, the induced emf becomes 2.6013. So the
range of variation in excitation, hence the field current, is quite large.

10 Automatic Excitation Control

From this table it is evident that the excitation must be controlled continuously to
keep the terminal voltage (at generator terminal or generator-transformer terminal)
constant. This is electronically done using power electronic components, at present
making use of microprocessor/microcontroller or digital computer for close control.
Much research work has been made in this area and bulk of papers published. Some
publications in this area [11–14] have been referred to.

Fig. 3 Synchronous generator on infinite bus

404 A. Ghosh et al.

Table 1 Induced e.m.f. versus varying load and p.f

PU load Power factor Induced PU load Power factor Induced
emf emf
0.5 0.8 Lag 1.8916 0.6 0.8 Lag 2.0954
 28.00  30.57

0.85 1.8481 0.85 2.0484

 30.71  33.57

0.9 1.7927 0.9 1.9883

 33.90  37.11

0.95 1.7143 0.95 1.9036

 38.02  41.73

1.0 Upf 1.4982 1.0 Upf 1.6705

 47.95  53.05

0.95 Lead 1.2448 0.95 Lead 1.3987

 58.21  65.19

0.9 1.1287 0.9 1.2751

 62.68  70.69

0.7 0.8 Lag 2.2528 0.8 0.8 Lag 2.5126

 35.91  34.43

0.85 2.1891 0.85 2.4603

 39.75  37.87

0.9 2.1250 0.9 2.3938

 42.25  41.93

0.95 2.0994 0.95 2.3001

 44.76  47.26

1.0 Upf 1.8535 1.0 Upf 2.0444

 57.18  60.54

0.95 Lead 1.5692 0.95 Lead 1.7514

 70.72  75.14

0.9 1.4411 0.9 1.6207

 76.95  81.88

0.9 0.8 Lag 2.7245 1.0 0.8 Lag 2.9380

 35.92  37.19

0.85 2.6703 0.85 2.8821

 39.51  40.92

0.9 2.6013 0.9 2.8112

 43.77  45.34

0.95 2.5045 0.95 2.4422

 49.36  65.66

1.0 Upf 2.2411 1.0 Upf 2.

 63.33 4422 65.65
0.95 Lead 1.9420 0.95 Lead 2.1388
 78.70  81.62

0.9 1.8098 0.9 2.0058

 85.80  88.97
Automatic Electronic Excitation Control in a Modern Alternator 405

11 Conclusion

The excitation system of an alternator must effectively control the terminal volt-
age under varying load and at the same time enhance the system stability. It must
respond quickly to a disturbance for enhancing transient stability and for modulat-
ing the generator field for enhancing dynamic stability. Modern excitation systems
have almost instantaneous response along with high ceiling voltages. The high field
forcing capability, along with auxiliary stabilizing signals substantially enhance the
overall dynamic performance of the system. The excitation system parameters must
be properly matched with the network under all quiscent conditions. Otherwise, the
transient stability may be enhanced but there may be dynamic instability due to grow-
ing oscillations. The excitation parameters are tuned with the system by simulation
studies.
The power angle depends very much on the load and its power factor. The task of
AEC is to bring forth necessary changes in excitation to keep the voltage constant
at generator terminal (or generator-transformer). As the magnitude of induced emf
changes with loading conditions, Pmax also changes. The effect of AEC on static
stability is an increase of power limit. Modern AEC can bring back a rotor swinging
beyond 120°–130° even by its over-action. For this reason AEC is so important.

References

1. P.M. Anderson, A.A. Fouad, Power System Control and Stability, 2nd edn. (IEEE Press, Wiley-
Interscience, 2011)
2. M. Watanabe, Y. Mitani, H. Iki, Y. Uriu, Y. Urano, Dynamic stability assessment of customer’s
power systems with detailed models implementation, in 17th Power Systems Computation
Conference, Stockholm, Sweden, 22–26 Aug 2011
3. M.J. Basler, R.C. Schaefer, Understanding power-system stability. IEEE Trans. Ind. Appl. 44(2)
(2008)
4. M.J. Basler, R.C. Schaefer, Understanding power-system stability. IEEE Trans. Ind. Appl. 44(2)
(2008)
5. P. Kundur, et al., Definition and classification of power system stability. IEEE Trans. Power
Syst. 19(2) (2004)
6. M. Klein, G.J. Rogers, P. Kundur, A fundamental study of inter-area oscillations. IEEE Trans.
PWRS-6(3), 914–921 (1991)
7. J. Arilagga, N.R. Watson, Computer Modeling of Electrical Power System, 2nd edn. (Wiley)
8. P. Kundur, Power System Stability and Control. The EPRI Power System Engineering Series
(McGraw-Hill Inc.)
9. S. Hasan Saeed, Automatic Control Systems (with MATLAB Programs), 5th edn. (S.K. Kataria
and Sons)
10. Bharat Heavy electrical Ltd. (Operating manual on 210 Mw turbogenerator set)
11. R. Jamil, I. Jamil, Z. Jinquan, L. Ming, W. Y. Dong, Control and configuration of generator
excitation system as current mainstream technology of power system. ISSR J. (2013)
406 A. Ghosh et al.

12. A.K. Datta, M. Dubey, S. Jain, Modelling and Simulation of Static Excitation System in Syn-
chronous Machine Operation and Investigation of Shaft Voltage (Hindawi Publishing Corpo-
ration) Advances in Electrical Engineering, vol. 2014, Article ID 727295
13. M. Prajapati, J. Patel, H. Chandwanic, V. Patel, Digital excitation system for synchronous
generator. J. Electr. Eng
14. B. Shanngguan, Analysis of strong excitation control of A.C. synchronous generator based on
excitation voltage regulation. Electrotehnica Electronica Automatica (EEA, English version),
64(3) (2016)
Analysis of Linear Time Invariant
and Time Varying Dynamic Systems
via Taylor Series Using a New Recursive
Algorithm

Suchismita Ghosh

1 Introduction

The Taylor series represents a function as an infinite sum of terms calculated from
the values of its different order derivatives at a single point. This kind of expansion
technique was formally introduced by Brook Taylor in 1715. Even after three cen-
turies, the concept, though quite old, has much potential to be of importance in many
areas of mathematics.
This paper solves dynamic differential equations or the state equations of differ-
ent systems [1] using Taylor series. The method is essentially recursive algebraic
formulation using both the first order and second order Taylor series [2] to solve
time invariant and time varying systems. Earlier some works have been done where
operational matrices were employed using Taylor series [3]. In this method, the oper-
ational matrix and subsequently matrix inversions for obtaining desired solution are
avoided.
State space problem has been investigated with the framework of several orthogo-
nal basis functions, e.g., Haar function, Walsh function [4], block pulse function [5].
Recently, triangular functions [6], hybrid functions [7] have been used extensively in
this area. However, the Taylor series recursive technique seems to be much simpler
and a powerful tool as well. In fact, some works on time varying system analysis,
optimal control, system identification problem etc. have been done earlier using the
Taylor series [8–12], But these never focused on recursion so that the computation
can be much faster.
Further, integral equations have been solved by Taylor series [13], and delay
systems are solved using the hybrid of block pulse functions and Taylor series

S. Ghosh (B)
Department of Electrical Engineering, Faculty, MCKV Institute
of Engineering, 243, G. T. Road, Liluah, Howrah 711204, India
e-mail: suchismita.ghosh@ymail.com

© Springer Nature Switzerland AG 2019 407

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_34
408 S. Ghosh

[14, 15]. In recent studies, a variety of works are found on the recursive solution
using Taylor series [16–19] for the state analysis.

2 Function Approximation via Taylor Series

2.1 First Order Taylor Approximation [2]

A time function f (t) defined over an interval h, t ∈(ih, (i+1)h), can be approximated
about a point if the function exists at that point.
A first order Taylor approximation f¯1(t) of the function f (t) [19] around a specific
point µi is given by

f¯1(t)  f (µi ) + f˙(µi )(t − µi ) (1)

where, µi is a point in the (i + 1)-th interval with µi ∈ (i h, (i + 1) h) and i  0,

1, 2,…, (m − 1). Thus, f (t) may be approximated up to the m-th interval. The time
intervals in [0, T ) are of equal width h so that h = mT . It should be mentioned that for
the approximation to be pertinent, (t − µi ) should be small compared to T .
Assuming µi  i h, Eq. (1) becomes

f¯1(t) = f (i h) + f˙(i h) (t − i h) (2)

Putting t  (i + 1) h in (2),
⎫
f¯1{(i + 1)h}  f (i h) + h f˙(i h) ⎬
(3)
f¯1{(i + 2)h}  f¯1{(i + 1)h} + h f˙¯1{(i + 1)h} ⎭

Equation (3) provide a recursive solution of f (t) using first order Taylor series.
By changing the index i, approximate values of the function f (t) can be obtained
at m equidistant points, knowing the initial value f (0) and f˙(0). For the very next
interval t ∈ ((i + 1)h, (i + 2)h), the Taylor approximated value f¯1{(i + 1)h} and
f˙¯1{(i + 1)h} are considered as the initial values for computation.

2.2 Second Order Taylor Approximation

The function f (t) can also be represented using the second order Taylor series [19]
around the point µi , knowing the function value at the point. Thus
1 ¨
f¯2(t)  f (µi ) + f˙(µi )(t − µi ) + f (µi )(t − µi )2 (4)
2!
Analysis of Linear Time Invariant and Time Varying … 409

where, as before, µi is a point in the (i + 1)th interval with µi ∈ (i h, (i + 1)h) and i 

0, 1, 2,…, (m − 1). Thus, f (t) may be approximated up to the mth intervals of equal
width h within span t ∈ [0, T ) so that h = mT . For a good approximation, (t − µi )
should be small compared to T .
As in the previous case, if µi coincides with the point ih, i.e., µi  i h, then Eq. (4)
becomes
1 ¨
f¯2(t) = f (i h) + f˙(i h)(t − i h) + f (i h)(t − i h)2 (5)
2!
Assuming t  (i + 1)h,
⎫
f¯2{(i + 1)h}  f (i h) + h f˙(i h) + h2! f¨(i h)
2 ⎪
⎬
(6)
⎪
f¯2{(i + 2)h}  f¯2{(i + 1)h} + h f¯˙2{(i + 1)h} + h2
2! f¨¯2{(i + 1)h} ⎭

Equation (6) provide a recursive solution of f (t) using second order Taylor series
approximation. By changing the index i, approximate values of the function f (t) can
be obtained at m equidistant points, knowing three initial values f (0), f˙(0) and f¨(0).
For the very next interval t ∈ ((i + 1)h, (i + 2)h), the Taylor approximated value
f¯2{(i + 1)h}, f˙¯2{(i + 1)h} and f¨¯2{(i + 1)h} are considered as the initial values for
computation.
Now, state equations of different linear systems are solved using both first order
and second order Taylor series based upon the recursive technique elaborated in
Eqs. (3) and (6) respectively.

3 Analysis of the State via Taylor Approximation

3.1 Linear Time Invariant (LTI) System

The state equation of a linear non-homogenous time invariant (LTI) system is

ẋ(t)  Ax(t) + Bu(t) and x(0)  x0 (7)

where, the notations are having usual significances.

Here, the state x(t) has to be solved knowing A, B, u(t) and the initial values of
the states.
Differentiating (7), we have

ẍ(t)  Aẋ(t) + Bẋ(t) (8)

Putting t  ih in Eqs. (7) and (8)

410 S. Ghosh

ẋ(i h)  Ax(i h) + Bu(i h) (9)

ẍ(i h)  Aẋ(i h) + Bu̇(i h) (10)

Calling the first order Taylor approximation of x(t) as x̄1(t), one can write an
equation similar to (9). That is

˙ h)  Ax̄1(i h) + B u(i h)
x̄1(i (11)

Now, to apply second order Taylor approximation, similar equations may be writ-
ten following (9) and (10). Hence,

˙ h)  Ax̄2(i h) + B u(i h)
x̄2(i (12)
x̄2(i ˙ h) + B u̇(i h)
¨ h)  Ax̄2(i (13)

where, the second order Taylor approximation of x(t) is considered as x̄2(t).

Following Eq. (3), we can write the recursive equations to determine the states
via first order Taylor series, as under

˙
x̄1(h)  x̄1(0)+h x̄1(0) (14)

and

˙ h)
x̄1{(i + 1)h}  x̄1(i h)+h x̄1(i (15)

where, x̄1(0)  x(0) and i  1, 2, 3, …, m.

Substituting (11) in Eqs. (14) and (15), we can write

x̄1(h)  [I + Ah]x̄1(0) + hBu(0); for i  0, (16)

x̄1{(i + 1)h}  [I + Ah]x̄1(i h) + hBu(i h); for any i. (17)

Equation (17) along with (16) provides a recursive solution of state vector x(t)
using the first order Taylor series. The solution known at any point of the time scale
is the data required for obtaining the solution at the next point, where the step size h
is very small. As the initial values of the state vector x(0) are known, we can start the
recursive process from x(0). Hence, knowing the input vector u(t) and by changing
the index i up to m, the process gives a point wise solution of the state vector x(t).
When higher derivative terms of the states are considered, the recursive Eq. (15)
becomes more and more accurate. Hence, to obtain a better approximation, second
order Taylor approximation may be employed and Eqs. (14) and (15) can be modified
based on Eq. (6) to determine the states. Thus

˙ h2 ¨
x̄2(h)  x̄2(0)+h x̄2(0) + x̄2(0) (18)
2!
Analysis of Linear Time Invariant and Time Varying … 411

2
˙ h) + h x̄2(i
x̄2{(i + 1)h}  x̄2(i h) + h x̄2(i ¨ h) (19)
2!

where, x̄2(0)  x(0) and i  1, 2, 3, …, m.

Substituting (12) and (13) in Eq. (19), we get
   
h2 2 h2 h2
x̄2{(i + 1) h}  x̄2(i h) 1 + hA + A + u(i h) hB + AB + Bu̇(i h)
2! 2! 2!

So,
   
h2 h2 h2
x̄2(h)  x̄2(0) 1 + hA + A2 + u(0) hB + AB + Bu̇(0); for i  0,
2! 2! 2!
(20)
 2   2 
h h
x̄2{(i + 1)h}  1 + hA + A2 x̄2(i h) + hB + AB u(i h)
2! 2!
2
h
+ Bu̇(i h); for any i. (21)
2!
Thus, from Eqs. (20) and (21) knowing the initial values of the states x(0) and the
input vector u(t), the solution of the states can be determined recursively by changing
the index i up to any chosen m.
One particular advantage of this approach is, the step size h may be constant or it
may be varied during computation dynamically.

3.2 Linear Time Varying System

The state equation of a linear non-homogenous time varying (LTI) system is

ẋ(t)  A(t)x(t) + B(t)u(t) and x(0)  x0 (22)

where, the notations are having usual significances.

Knowing the initial values of the states x(0), we are to determine the solution of
the states x(t). Differentiating (22), we get

ẍ(t)  Ȧ(t)x(t) + A(t)ẋ(t) + Ḃ(t)u(t) + B(t)u̇(t) (23)

Putting t  ih, Eqs. (22) and (23) reduce to

ẋ(i h)  A(i h)x(i h) + B(i h)u(i h) (24)

ẍ(i h)  Ȧ(i h)x(i h) + A(i h)ẋ(i h) + Ḃ(i h)u(i h) + B(i h)u̇(i h) (25)
412 S. Ghosh

For first order Taylor approximation, we can modify another equation similar to
(24) as

˙ h)  A(i h)x̄1(i h) + B(i h)u(i h)

x̄1(i (26)

Again, Eqs. (24) and (25) can be modeled using second order Taylor series as,

˙ h)  A(i h)x̄2(i h) + B(i h)u(i h)

x̄2(i (27)
¨ h)  Ȧ(i h) x̄2(i h)+A(i h)x̄2(i
x̄2(i ¨ h) + Ḃ(i h)u(i h) + B(i h)u̇(i h) (28)

Based on Eq. (3), the following recursive equations are formed to determine the
states using first order Taylor approximation. Substituting (26) in Eqs. (14) and (15),

x̄1(h)  [I + hA(0)]x̄1(0) + hB(0)u(0); for i  0, (29)

x̄1{(i + 1)h}  [I + hA(i h)]x̄1(i h) + hB(i h)u(i h); for any i. (30)

Equations (29) and (30) provide a recursive solution of the state vector x(t) for
the linear time varying system described by (22). Since initial values of the states
x(0) are known, the recursive process can be started easily by choosing i  0 in (30)
or using Eq. (29). Here, the input of the system u(t) should be known as in the earlier
case. But additionally, the time varying matrices A(t) and B(t) should also be known
at various points of time as sample values.
Use of second order derivative term of the state in Eq. (15) gives a better approx-
imation. So, substitution of (27) and (28) in Eq. (19) yields,
 
h2 h2
x̄2{(i + 1)h}  x(i h) 1 + hA(i h) + Ȧ(i h) + A2 (i h)
2! 2!
 2 
h h2
+ u(i h) h B(i h)+ A(i h)B(i h)+ Ḃ(i h)
2! 2!
2
h
+ B(i h)u̇(i h)
2!
So, for i  0;
 
h2 h2
x̄2(h)  x(0) 1 + hA(0) + Ȧ(0) + A2 (0)
2! 2!
 2 
h h2
+ u(0) h B(0)+ A(0)B(0)+ Ḃ(0)
2! 2!
2
h
+ B(0)u̇(0) (31)
2!
and in general,
Analysis of Linear Time Invariant and Time Varying … 413

Fig. 1 Schematic block diagram of the algorithm for approximating x(t) via first and second order
Taylor series

 
h2 h2
x̄2{(i + 1) h}  1 + hA(i h) + Ȧ(i h) + A2 (i h) x(i h)
2! 2!
 2 
h h2
+ h B(i h)+ A(i h)B(i h)+ Ḃ(i h) u(i h)
2! 2!
2
h
+ B(i h)u̇(i h) (32)
2!
Equation (32) is the recursive equation of the state using second order Taylor
series. Changing the value of i up to any integer m will give point wise solution
of x(t). Similar to the first order Taylor approximation, in this case also, we should
know the initial value of the state x(0), the input u(t) as well as the time varying
matrices A(t) and B(t).
One important feature of this approach is, the step size h may be fixed or variable,
which means the interval length h can be changed dynamically during recursion.
The method above mentioned can be implemented for online process for the
determination of state simply by programming Eqs. (17), (21) or (30), (32) using
microprocessor or microcontroller. To assist this algorithm other requirements are
sampler and the differentiator. A block diagram for state analysis of time varying
system is shown in Fig. 1. It is quite obvious that the time invariant system would
follow the same process, but as the matrices A and B are constant in nature, so, the
differentiation of those is not needed.

4 Numerical Example

(i) Consider the linear non-homogeneous time invariant system.

414 S. Ghosh

Fig. 2 Pointwise solution of the states x1 and x2 using a first order Taylor series (Taylor1) from
Eq. (17) and b second order Taylor series (Taylor2) from Eq. (21) in recursive way for T  1 s and
m  16. The exact solutions of the states x1 and x2 of Eqs. (34) and (35) are given in solid line



−0.8 −2.2 2.2
ẋ(t)  x(t) + u(t) (33)
1 −1 0


0
and x(0)  x0  with unit ramp input. Applying traditional Laplace and inverse
0
Laplace on (33), the exact solution is obtained as 
−1
 −1
−0.8 −2.2
x(t)  L (sI − A) {x(0) + BU(s)} ; where, A  ,B 
1 −1


2.2
and thereby the exact solution becomes,
0
 √ √ √ 
34 219 sin 219t
22 cos 219t
10
+ 219
10
11t 22
x1(t)  −  9t  + ; (34)
15 75 exp 10 75
 √ √ √ 
23 219 sin 219t
11 cos 219t
10
− 657
10
11t 11
x2(t)  +  9t  − (35)
15 25 exp 10 25

Using Eqs. (16), (17) and (20), (21) states of the system can be solved via first and
second order Taylor series approximations respectively. Table 1 shows the results
obtained via two methods. For computation, time T is considered to cover the range
0–1 s, with the number of steps m  16. Thus, h  T /m  0.0625 s.
For clarity, the solutions are also presented graphically in Fig. 2(a) and (b). For
both the cases, the time interval T and the number of steps m are taken to be the
same. Along with the Taylor solutions, both the figures present the exact curves of
the states x1 and x2 from Eqs. (34) and (35) to judge the quality of Taylor series
based results.
It is noted that, the second order Taylor approximation is much better than the
first order approximation.
Analysis of Linear Time Invariant and Time Varying … 415

Table 1 Recursive solution of the state x1 and state x2 obtained via first order and second order
Taylor approximation compared with the exact solution (for T  1 s, m  16 and h  0.0625 s)
Time (s) Pointwise solution of state x1(t) Pointwise solution of state x2(t)
Exact data Approximated data Exact data Approximated data
using using
First order Second First order Second
Taylor order Taylor order
series Taylor series Taylor
series series
0 0 0 0 0 0 0
1/16 0.0042 0 0.0043 0.0001 0 0
2/16 0.0166 0.0086 0.0167 0.0007 0 0.0005
3/16 0.0366 0.0254 0.0368 0.0022 0.0005 0.0020
4/16 0.0637 0.0498 0.0641 0.0051 0.0021 0.0049
5/16 0.0974 0.0814 0.0978 0.0096 0.0051 0.0094
6/16 0.1371 0.1196 0.1376 0.0161 0.0098 0.0159
7/16 0.1822 0.1638 0.1828 0.0248 0.0167 0.0246
8/16 0.2321 0.2135 0.2329 0.0359 0.0259 0.0357
9/16 0.2864 0.2680 0.2872 0.0494 0.0376 0.0492
10/16 0.3444 0.3268 0.3453 0.0655 0.0520 0.0654
11/16 0.4056 0.3892 0.4066 0.0843 0.0692 0.0842
12/16 0.4696 0.4548 0.4706 0.1057 0.0892 0.1057
13/16 0.5357 0.5229 0.5367 0.1297 0.1120 0.1298
14/16 0.6036 0.5931 0.6046 0.1564 0.1377 0.1566
15/16 0.6728 0.6648 0.6738 0.1856 0.1662 0.1858
16/16 0.7430 0.7376 0.7440 0.2173 0.1973 0.2176

(ii) Consider the linear homogeneous time varying system [8].



00 1
ẋ(t)  x(t); x(0)  x0  with step input (36)
t 0 1

The exact solution is

1
x1(t)  1 and x2(t)  1 + t 2 (37)
2
This system is solved by using the recursive Eqs. (29)–(32). The solutions are
exhibited in Table 2. For computation, a time interval of T  1 s is considered and
the number of steps m  4, so that h  T /m  0.25 s.
The first order Taylor approximation, compared with the exact solution, is shown
in Fig. 3(a), while the second order Taylor approximation is shown in Fig. 3(b). The
exact curves are drawn from the exact solutions provided in Eq. (37).
416 S. Ghosh

Table 2 Recursive solution of the state x1 and state x2 obtained via first order and second order
Taylor approximation compared with the exact solution (for T  1 s, m  4 and h  0.25 s)
Time (s) Pointwise solution of state x1(t) Pointwise solution of state x2(t)
Exact data Approximated data Exact data Approximated data
using using
First order Second First order Second
Taylor order Taylor order
series Taylor series Taylor
series series
0 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
1/4 1.0000 1.0000 1.0000 1.0313 1.0000 1.0313
2/4 1.0000 1.0000 1.0000 1.1250 1.0625 1.1250
3/4 1.0000 1.0000 1.0000 1.2813 1.1875 1.2813
4/4 1.0000 1.0000 1.0000 1.5000 1.3750 1.5000

Fig. 3 Pointwise solution of the states x1 and x2 using a first order Taylor series (Taylor1) from
Eq. (30) and b second order Taylor series (Taylor2) from Eq. (32) in recursive way for T  1 s and
m  4. The exact solution in Eq. (37) of the states x1 and x2 of are shown in solid line

In Fig. 4, first order Taylor approximation results are shown with more number
of steps (m  60) within T  1 s and reasonably match the exact results. However,
the improved accuracy is achieved in lieu of increased computational burden.
(iii) Consider the linear non-homogeneous time varying system [11].



0 te−t 0 1
ẋ(t)  x(t) + u(t); x(0)  x0  with step input (38)
0 0 1 1
Analysis of Linear Time Invariant and Time Varying … 417

Fig. 4 The exact solutions

of Eq. (37) along with
solution via first order
approximation (Taylor1) of
Eq. (30) for T  1 s and
more number of steps i.e., m
 60. It shows better
approximation than Fig. 2(a),
which has less number of
steps, m  4

The exact solution is

 
x1(t)  4 − 3 + 3t + t 2 e−t and x2(t)  1 + t (39)

The time varying system given in this example is solved by using the recursive
Eqs. (29)–(32). The point wise solutions are shown in Table 3 along with the exact
samples obtained from (39). For computation, time interval T  1 s. is considered
and the number of steps m  10, so that h  T /m  0.1 s.
The comparison of the exact solution with the first order Taylor approximation is
shown in Fig. 5(a) and the comparison with the second order Taylor approximation
is presented in Fig. 5(b). In both the cases, the time interval considered is T  1 s
and the number of steps m  10, i.e., h  0.1 s.
Decreasing the step size obviously improves the accuracy of approximation with
increased computational burden. This is established in Fig. 6, where first order Taylor
approximation is shown with m  40 and T  1 s.

5 Error Estimates

In case of time invariant and time varying systems, for first order approximation
using fixed intervals, the solution appreciably deviates from the exact results. But for
the second order Taylor approximation using the same number of steps, the solution
almost overlaps with the exact solution. The accuracy level for different step size can
be measured with respect to mean integral square error (MISE). This is presented in
Table 4 for three numerical examples.
418 S. Ghosh

Table 3 Recursive solution of the state x1 and state x2 obtained via first order and second order
Taylor approximation compared with the exact solution (for T  1 s, m  10 and h  0.1 s)
Time (s) Pointwise solution of state x1(t) Pointwise solution of state x2(t)
Exact data Approximated data Exact data Approximated data
using using
First order Second First order Second
Taylor order Taylor order
series Taylor series Taylor
series series
0 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
1/10 1.0050 1.0000 1.0050 1.1000 1.1000 1.1000
2/10 1.0198 1.0100 1.0199 1.2000 1.2000 1.2000
3/10 1.0441 1.0296 1.0443 1.3000 1.3000 1.3000
4/10 1.0774 1.0585 1.0777 1.4000 1.4000 1.4000
5/10 1.1190 1.0960 1.1194 1.5000 1.5000 1.5000
6/10 1.1681 1.1415 1.1686 1.6000 1.6000 1.6000
7/10 1.2241 1.1942 1.2247 1.7000 1.7000 1.7000
8/10 1.2861 1.2533 1.2868 1.8000 1.8000 1.8000
9/10 1.3532 1.3180 1.3541 1.9000 1.9000 1.9000
10/10 1.4248 1.3875 1.4259 2.0000 2.0000 2.0000

Table 4 Error estimates based on mean integral square error (MISE) for three numerical examples
with a specified number of recursions (m) and length of interval (h), using first and second order
Taylor series
Examples along with For states x(t) Approximation error (MISE) using
number of recursion
points (m) and length
of intervals (h)
First order Taylor Second order Taylor
series series
Example (i) State x1(t) 10−3 × 0.1864 10−5 × 0.1108
m  16; h  0.0625 s
State x2(t) 10−3 × 0.1393 10−5 × 0.0045
Example (ii) State x1(t) 0 0
m  4; h  0.25 s
State x2(t) 0.0046 10−4 × 0.3255
Example (iii) State x1(t) 10−3 × 0.5581 10−5 × 0.1163
m  10; h  0.1 s
State x2(t) 0 0
Analysis of Linear Time Invariant and Time Varying … 419

Fig. 5 Pointwise recursive solution of the states x1 and x2 using a first order Taylor series (Taylor1)
from Eq. (30) and b second order Taylor series (Taylor2) from Eq. (32) for T  1 s and m  10.
The exact solution in Eq. (39) of the states x1 and x2 of are shown in solid line

Fig. 6 The exact solutions of Eq. (39) along with solution via first order approximation (Taylor1)
of Eq. (30) for T  1 s and more number of steps i.e., m  40. It shows an approximation better
than Fig. 4a, which has less number of steps, m  10

As expected, it shows, the second order Taylor approximation is a stronger tool

than the first order approximation.
420 S. Ghosh

6 Conclusion

A simple recursive method for solving the states of linear time invariant as well as time
varying control systems using Taylor series expansion have been presented. Here,
the solution which results in every iteration, changes into the new initial value for the
next iteration. The solutions are compared with the exact samples using different step
sizes. It is shown that, to reach the efficiency of first order Taylor series based method
like second order Taylor approximation, requirement of iteration increases, which in
turn increases computational burden. Four tables and eight figures are presented to
compare the results in quantitative threadbare manner. Comparison with the exact
solutions shows this recursive approach to be attractive and quite reliable as well.
In some papers [9–11, 13–15], where the state is analyzed using the Taylor series,
is a way which needs operational matrix of integration. This matrix has a fixed
dimension that depends on the length of interval h or number of interval m, which
has to be set prior the computation of state, whereas, this approach avoids this kind
of matrix. Hence during computation, one can easily change h or m and thereby
perform a dynamic computation.
Being the algorithm recursive in nature, avoids the complexity of handling large
matrices and its inversion too unlike traditional approaches. The memory requirement
and time consumption during computation is reduced considerably in this context.

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Severity and Location Detection of Three
Phase Induction Motor Stator Fault
Using Sample Shifting Technique
and Adaptive Neuro Fuzzy Inference
System

S. Samanta, J. N. Bera and G. Sarkar

1 Introduction

In industry, Induction motors are most commonly used due to various mechanical
and economical reasons like low cost, reasonably small size, ruggedness, low main-
tenance, smooth operation etc. When in operation, various stresses are imparted on
the induction motor which may lead to incipient failures/faults in the motor. If these
incipient faults are not detected in an early stage, a permanent or damage of the motor
could be the result. Different kinds of machine faults are studied in literature [1, 2]
like stator inter turn fault, broken rotor bar fault, bearing fault, unbalanced stator
and rotor parameters, eccentricity fault etc. So, early detection of faults is a serious
issue to reduce consequential damage, increase life span of machine, reduces spare
parts inventories and avoid breakdown. Implementation of an efficient condition
monitoring scheme can provide warning and predict the fault at early stages.
According to an IEEE and Electric Power Research Institute motor reliability
study [3], 37% of the induction motor failure is due to stator fault. In most cases, a
stator fault starts as a turn to turn (inter turn) and finally grows as coil-to-coil, phase-
to-phase or phase-to-ground failures, and ultimately causes motor breakdown. In
modern system, due to the advancement in the condition monitoring technologies,

S. Samanta (B)
Electrical Engineering Department, MCKV Institute of Engineering,
243 G. T. Road (N), Liluah, Howrah 711204, India
e-mail: sudeep0809@gmail.com
J. N. Bera · G. Sarkar
Applied Physics Department, University College of Science and Technology,
92, A.P.C Road, Kolkata 700009, India
e-mail: jitendrabera@rediffmail.com
G. Sarkar
e-mail: gautamgs@yahoo.co.in

© Springer Nature Switzerland AG 2019 423

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_35
424 S. Samanta et al.

automation in diagnosis process are being implemented with the adoption of different
soft computing techniques [4–6].
Recently different kinds of soft computing techniques like expert system, neural
network, fuzzy logic, adaptive neural fuzzy inference system, genetic algorithm etc.
are being employed to assist the diagnostic task with correct interpretation of the fault
condition. These techniques become popular over other conventional techniques as
they are easy to extend and modify, improved performance, with increased precision
and accuracy of the monitoring system.
In [7, 8] Fuzzy logic based motor condition monitoring and fault diagnosis is
presented. Filippetti et al. [9] has introduced an expert system based comprehensive
study about the application of artificial intelligence along with Fuzzy logic in machine
monitoring and fault diagnosis. In [10], stator three phase rms values of currents and
the variance are used as the input to the fuzzy logic system for fault diagnosis of
induction motor. Bouzid [11] has suggested a feed forward multi layer perceptron
neural network approach for automatically detection of an inter-turn short circuit
fault in the stator windings of an induction motor. Tan and Huo [12] have introduced
a generic neuro-fuzzy model based approach for rotor broken bar fault detection of an
induction motor. This approach overcomes the practical limitations of model based
strategies because it reduces the amount of experimental data needed to design the
fault detector. Ballal et al. [13] have approached an adaptive neural fuzzy inference
system for the detection of inter-turn insulation and bearing faults in induction motor.
The sequence components [14, 15] are used as very important tool for fault detec-
tion in electrical system. In normal operating condition, the negative sequence com-
ponent of current is nearly equal to zero. But, during stator inter turn fault in any
phase, this component of current increases to a considerable amount due to the flow
of huge current through the corresponding phase causing an unbalance in the stator
current.
In this proposed paper, Sample Shifting Technique (SST) is utilized for the eval-
uation of sequence components based on three phase current samples only. The
intricacy of SST is discussed briefly in next section. An ANFIS based fault detection
strategy is then developed based on the various sequence based index for detection of
fault location and fault severity. The proposed work is simulated by modeling a three
phase induction motor with inter turn fault condition in MATLAB. The proposed
diagnosis method is also tested on a real three phase motor hardware to justify its
effectiveness.

2 Materials and Methods

2.1 Sequence Component Evaluation Using SST

Based on Fortescue’s theorem, any unbalance quantity can be resolved to three inde-
pendent sequence components namely, Positive, Negative and Zero Sequence com-
Severity and Location Detection of Three Phase Induction … 425

ponent. In a three phase system, the positive and negative sequence component of
currents can be calculated as [16, 17]:
⎡ ⎤
  Ia
Ia1  ⎢ ⎥
 A−1 ⎣ Ib ⎦ (1)
Ia2
Ic
   
1 a2 a  −1  1 1 a a 2
where, [A]  and A 3
1 a a2 1 a2 a
The operator a = 1 120° and a  1 40°, I a1 and I a2 are positive and negative
2

sequence components of current respectively.

In this paper, Sample Shifting Technique (SST) [18] is used to calculate the
sequence components. Sample Shifting Technique stands on the fact that shifting
of any sinusoidal wave at any angle actually means shifting the time of occurrence
of instantaneous amplitudes of the sinusoidal wave by that angle. So, very easily a
shifted sine wave can be generated from its original waveform, only by rearranging
its sample values. Let us consider, a sine wave has 360 samples per cycle (Sampled
at 1° interval), then only by shifting 121st to 360th samples of original wave to 1st to
240th position and 1st to 120th samples of original wave to 241th to 360th position,
we can generate its 120° shifted sine wave.
For calculation of Positive and Negative sequence components using Sample
Shifting Technique, it is considered that the multiplication with operator ‘a’ to a
sine wave is equivalent to 120° sample shifting from its original samples and mul-
tiplication with operator ‘a2 ’ is equivalent to 240° sample shifting from its original
samples. So, to evaluate current sequence component in a three phase system using
SST, Eqs. (2)–(3) are utilized.
1 N 2N
I1 (n)  [Ia (n) + Ib (n + ) + Ic (n + )] for, 1 ≤ n ≤ N/3;
3 3 3
1 N N
 [Ia (n) + Ib (n + ) + Ic (n − )] for, N/3 < n ≤ 2N/3;
3 3 3
1 2N N
 [Ia (n) + Ib (n − ) + Ic (n − )] for, 2N/3 < n ≤ N; (2)
3 3 3
1 2N N
I2 (n)  [Ia (n) + Ib (n + ) + Ic (n + )] for, 1 ≤ n ≤ N/3;
3 3 3
1 N N
 [Ia (n) + Ib (n − ) + Ic (n + )] for, N/3 < n ≤ 2N/3;
3 3 3
1 N 2N
 [Ia (n) + Ib (n − ) + Ic (n − )] for, 2N/3 < n ≤ N; (3)
3 3 3
where, N is total no. of samples in a cycle of the sinusoidal wave.
426 S. Samanta et al.

2.2 Formulation of Fault Detection Methodologies

For detection of stator inter turn fault, the magnitude and phase angle of nega-
tive sequence component are used. In healthy condition, the magnitude of negative
sequence component is approximately zero. But, when inter turn fault occurs, due to
current unbalance negative sequence component are generated. As the fault sever-
ity goes on increasing, magnitude of negative sequence component also increases.
Again, depending on the different fault location, different phase relationship between
positive and negative sequence component are introduced. On the basis of these two
characteristics, the fault location and severity are detected by introducing two unique
parameters, defined as Sequence Component Amplitude Index (SCAI) and Sequence
Component Phase Index (SCPI). SCAI is used to detect the severity of fault whereas
the faulty phase is detected using SCPI parameter. The formulations SCAI and SCPI
are described as follows.

2.2.1 Formulation of SCAI

Sequence Component Amplitude Index (SCAI) is defined as per unit change in

magnitude of negative sequence components with respect to positive sequence com-
ponent.

SC AI  (I1 − I2 )/I1 (4)

Here, I 1 is the magnitude of positive sequence component and I 2 is the magnitude

of negative sequence component.

2.2.2 Formulation of SCPI

Sequence Component Phase Index (SCPI) is defined as per unit change in phase angle
of negative sequence components with respect to positive sequence component.

SC P I  (φ1 − φ2 )/120 (5)

Here, Φ 1 is the phase angle of positive sequence component and Φ 2 is the phase
angle of negative sequence component.
Severity and Location Detection of Three Phase Induction … 427

2.3 Adaptive Neuro Fuzzy Inference System (ANFIS)

for Fault Diagnosis

Though, Artificial Neural Network (ANN) is capable for machine condition moni-
toring and fault diagnosis using an inexpensive and reliable procedure, it does not
provide heuristic reasoning about fault detection process. On the other hand, Fuzzy
logic can easily provide heuristic reasoning but fails to provide exact solution. So, by
merging the good features of ANN and Fuzzy logic, a simple noninvasive fault detec-
tion technique ANFIS [19] has been developed. ANFIS become popular over other
fault detection technique because of its knowledge extraction feasibility, domain
partitioning, rule structuring and modifications [20]. ANFIS based fault detection
system has a fuzzy inference system along with five layers feed-forward network.
Knowledge is extracted in terms of membership functions and Takagi Sugeno type
Fuzzy if then rule. By using hybrid learning procedure, ANFIS can construct an
input—output in the form of Takagi-Sugeno type if-then rules.
In this paper, a suitable ANFIS program as written in MATLAB for interturn fault
detection purposes. Fault detection system is prepared with two input parameters
namely SCAI and SCPI. The main objective of ANFIS based fault diagnostic system
is to learn the relationships between the fault signature under different load conditions
(ANFIS inputs) and the corresponding operating condition (ANFIS outputs) which
will be able to provide fault information correctly. In Fig. 1, The ANFIS based fault
diagnostic system is given.

2.4 Preparation of Suitable Training Data Set for ANFIS

In this work, a suitable training data set for ANFIS is prepared for collecting three
phase current samples with stator interturn fault at different phases under different
loading conditions such as no load, 5 Nm load, 10 Nm load. Here, eight different

Input Input μf Rules Output μf Output

SCPI

Motor Condition

SCAI

Fig. 1 ANFIS based fault diagnostic system

428 S. Samanta et al.

Healthy A phase fault B phase fault C phase fault

Fig. 2 Simulated training input data set

parentages of inter turn fault are considered like 2, 5, 8, 10, 12, 15, 18 and 20%.
For all conditions, SCAI and SCPI are calculated, which are used for training. Thus
for three load conditions, total (3 × 8  24) numbers of inputs are considered. Thus
for three phase fault, 72 (24 × 3) number and 3 number for healthy condition, all
together 75 number of training and testing data patterns are generated for two inputs,
shown in Fig. 2.

3 MATLAB Simulation

3.1 Simulink Model of Three Phase Induction Motor

In this paper, 3- Squirrel cage Induction motor model is developed in MAT-
LAB/SIMULINK by assuming that identical three phase stator windings with equiv-
alent no. of turns N s and resistance r s , stator windings are symmetrically distributed
and displaced from each other at angle 120°.
The rotor windings are also considered as three identical sinusoidal distributed
windings with equivalent no. of turns N r and resistance r r and displaced at 120° with
each other. The uniform air gap is also considered in between stator and rotor.
Considering all of these, stator and rotor voltage equations of the 3- induction
motor can be derived as:
Severity and Location Detection of Three Phase Induction … 429

d
Vabcs  rs i abcs + ψabcs (6)
dt
d
Vabcr  rr i abcr + ψabcr (7)
dt
For, squirrel cage induction motor
⎡ V abcr ⎤  0. ⎡ ⎤
rs 0 0 rr 0 0
⎢ ⎥ ⎢ ⎥
Where, Stator resistance, rs  ⎣ 0 rs 0 ⎦ and rotor resistance rr  ⎣ 0 rr 0 ⎦
0 0 rs 0 0 rr
In above equations, stator and rotor voltages are
⎡ ⎤ ⎡ ⎤
Vas Var
⎢ ⎥ ⎢ ⎥
Vabcs  ⎣ Vbs ⎦, Vabcr  ⎣ Vbr ⎦
Vcs Vcr

stator and rotor currents are

⎡ ⎤ ⎡ ⎤
Ias Iar
⎢ ⎥ ⎢ ⎥
Iabcs  ⎣ Ibs ⎦, Iabcr  ⎣ Ibr ⎦
Ics Icr

Flux linkage equations can be expressed as,

    
ψabcs L s L sr i abcs
 (8)
ψabcr T
L sr Lr i abcr

Here, stator winding inductance matrix L s , rotor winding inductance matrix L r

and stator to rotor mutual inductance matrix L sr can be expressed as,
⎡ ⎤ ⎡ ⎤
L ls + L ms − 21 L ms − 21 L ms L lr + L mr − 21 L ms − 21 L ms
⎢ ⎥ ⎢ ⎥
⎢ ⎥ ⎢ ⎥
L s  ⎢ − 21 L ms L ls + L ms − 21 L ms ⎥ and Lr  ⎢ − 21 L ms L lr + L mr − 21 L ms ⎥
⎣ ⎦ ⎣ ⎦
− 21 L ms − 21 L ms L ls + L ms − 21 L ms − 21 L ms L lr + L mr

where, L ls , L lr , L ms , L mr  stator and rotor leakage and magnetizing inductance.

Considering, electrical angular velocity ωr and displacement θ r ,
⎡ ⎤
cos θr cos(θr + 2π ) cos(θr − 2π )
⎢ 3 3 ⎥
⎢ 2π ⎥
Lsr (θr )  ⎢ cos(θr − 2π ) cos θr cos(θr + 3 ⎥
) (9)
⎣ 3 ⎦
cos(θr + 3 ) cos(θr − 3 )
2π 2π
cos θr

The electromagnetic torque produced by a three phase Induction motor can be

derived from energy conversion principles [21],
430 S. Samanta et al.

Theta Theta

ias iar’
diar’/dt dias/dt

ibs ibr’
dibr’/dt dibs/dt

ics icr’
dicr’/dt dics/dt

dias/dt diar’/dt
ωr ωr

dibs/dt
Subsystem 1 dibr’/dt 2
Subsystem

Subsystem 1 Subsystem 2

ias

ibs

Te
ics
ωr
iar’
Theta
ibr’

Subsystem 3

Fig. 3 Simulink model of three phase induction motor


d L sr
Tem  [i abcs ]T [i abcr ] (10)
dθr

The rotor mechanical equation [21] has been given in Eq. 11.
dωr
Tem  J + Bωr + TL (11)
dt
where, J is the rotor inertia, ωr is rotor angular speed in rad/sec, B is the friction
coefficient and T L is the load torque.
Severity and Location Detection of Three Phase Induction … 431

Using Eqs. (6)–(11), the dynamic model of a healthy 3- squirrel cage induction
motor are developed in MATLAB/SIMULINK, which is shown in Fig. 3. Here, three
different subsystems are created viz. subsystem 1 is for stator current calculation,
subsystem 2 is for rotor current calculation and subsystem 3 is for torque and rotor
speed calculation.
In this model, stator inter-turn fault is externally created by dividing the phase
winding associated with inter turn fault in two series part. Considering N s is total
no. of stator turns per phase, then N s = N us + N sh , where N sh is no of shorted turns
and N us is no of unshorted turns. So, the percentage of fault can be determined by
(N sh /N s ) × 100%.

3.2 Simulation Result

Training data of all input parameters (SCAI and SCPI) are applied to fault detector for
obtaining the optimized architecture to detect stator inter-turn fault of an induction
motor. Here, up to 5% of inter turn fault has been considered as less damaged, 5–15%
has been considered as medium damaged and above 15% has been considered as
severely damaged condition. Figure 4 shows the ANFIS output when motor condition
is less damaged inter turn fault on phase A. Here, circle line represents the target
value, the star one is the actual output. Similarly, Figs. 5 and 6 will represent ANFIS
output for medium damaged and severe damaged inter turn fault at phase A.
Figure 7 represents B phase medium damaged condition output, Figs. 8 and 9
represent C phase medium and severe damaged condition output.
When fault occurs on any phase A then depending upon its severity the output
should equal be to one and others are zero. The result clearly shows that there is very

Fig. 4 ANFIS output for Stator A phase winding inter turn fault with less damaged condition
432 S. Samanta et al.

Fig. 5 ANFIS output for Stator A phase winding inter turn fault with medium damaged condition

Fig. 6 ANFIS output for Stator A phase winding inter turn fault with severe damaged condition

little deviation between the target and the actual output. So the error which is the
difference between the target value and the actual output is considerable.
Severity and Location Detection of Three Phase Induction … 433

Fig. 7 ANFIS output for Stator B phase winding inter turn fault with medium damaged condition

Fig. 8 ANFIS output for Stator C phase winding inter turn fault with medium damaged condition

4 Experimental Verification

To validate the proposed fault classification approach, a case-study on a 3-phase,

415 V, 0.5 HP, 50-Hz Squirrel cage induction motor was performed with no load
condition. This motor was tested under healthy and Stator inter turn fault condi-
tion. 5–20% of inter turn fault data has been considered here for testing purpose. The
434 S. Samanta et al.

Fig. 9 ANFIS output for Stator C phase winding inter turn fault with severe damaged condition

Fig. 10 ANFIS output for Stator A phase winding less damaged inter turn fault

three phase stator current samples were collected simultaneously using hall sensor
and stored in PC. Then SST is applied to calculate positive and negative sequence
components for every current cycle. From sequence components, SCAI and SCPI
has been calculated which has been used as ANFIS input. In Figs. 10, 11 and 12, test
result has been given to validate the accuracy of proposed fault detection system.
Severity and Location Detection of Three Phase Induction … 435

Fig. 11 ANFIS output for Stator B phase winding medium damaged inter turn fault

Fig. 12 ANFIS output for Stator C phase winding severe damaged inter turn fault

5 Conclusion

In this paper, ANFIS based fault diagnosis of three phase induction motor is pre-
sented. The main advantage of this work is only three phase current samples are
required. Using current samples, sequence components are calculated by Sample
Shifting Technique which is used for fault diagnosis. It is very simple method as
sequence components are calculated by only repositioning current sample values,
which can be implemented by using an ordinary microcontroller and protection cost
436 S. Samanta et al.

can be reduced. Sequence current components are not so much affected by power
supply quality as calculated using Sample Shifting Technique (SST). The main pur-
pose of using the Neuro-Fuzzy approach is to automatically realize the fuzzy system
by using the neural network methods. Once the system is trained for specific data
over a wide range, it can be applicable to similar types of motor used in plants,
and thus there is no need to train the model for each motor. So, proposed diagnosis
method can be applied to any type of small and high power induction motors.

References

1. P.F. Albrecht, J.C. Appiarius, R.M. McCoy, E.L. Owen, D.K. Sharma, Assessment of the
reliability of motors in utility applications—updated. IEEE Trans. Energy Convers. EC-1(1),
39–46 (1986)
2. A.H. Bonnett, G.C. Soukup, Cause and analysis of stator and rotor failures in three-phase
squirrel-cage induction motors. IEEE Trans. Ind. Appl. 28(4), 921–937 (1992)
3. A. Siddique, G.S. Yadava, A review of stator fault monitoring techniques of induction motors.
IEEE Trans. Energy Convers. 20(1), 106–114 (2005)
4. S. Rajakarunakaran, P. Venkumar, K. Devaraj, K.S.P. Rao, Artificial neural network approach
for fault detection in rotary system. Appl. Soft Comput. 8(1), 740–748 (2008)
5. P.V.J. Rodriguez, A. Arkkio, Detection of stator winding fault in induction motor using fuzzy
logic. Appl. Soft Comput. 8(2), 1112–1120 (2008)
6. V. Uraikul, C.W. Chan, P. Tontiwachwuthikul, Artificial intelligence for monitoring and super-
visory control of process systems. Eng. Appl. Artif. Intell. 20(2), 115–131 (2007)
7. M.H. Benbouzid, A simple fuzzy logic approach for induction motor stator condition monitor-
ing, in Electric Machines and Drives Conference, IEMDC 2001, (IEEE International, 2001),
pp. 634–639
8. X.Z. Gao, S.J. Ovaska, Soft computing methods in motor fault diagnosis. Elsevier, Appl. Soft
Compu. 1, 73–81 (2001)
9. F. Filippetti, G. Franceschini, C. Tassoni, Recent developments of induction motor drives fault
diagnosis using AI techniques. IEEE Trans. Ind. Electron. 47(5), 994–1003 (2000)
10. P.V.J. Rodriguez, A. Arkkio, Detection of stator winding fault in induction motor using fuzzy
logic. Appl. Soft Comput. 8(2), 1112–1120 (2008)
11. M.B.K. Bouzid, G. Champenois, N.M. Bellaaj, L. Signac, K. Jelassi, An effective neural
approach for the automatic location of stator inter-turn faults in induction motor. IEEE Trans.
Ind. Electron. 55(12), 4277–4289 (2008)
12. W.W. Tan, H. Huo, A generic neuro-fuzzy model-based approach for detecting faults in induc-
tion motors. IEEE Trans. Ind. Electron. 52(5), 1420–1427 (2005)
13. M.S. Ballal, Z.J. Khan, H.M. Suryawanshi, R.L. Sonolikar, Adaptive neural fuzzy inference
system for the detection of inter-turn insulation and bearing wear faults in induction motor.
IEEE Trans. Ind. Electron. 54(1), 250–258 (2007)
14. J. Faiz, R. Iravani, Improved over current protection using symmetrical components. IEEE
Trans. Power Deliv. 22(2), 843–850 (2007)
15. R.E. Fehr, “A Novel Approach for Understanding Symmetrical Components and Sequence
Networks of Three-Phase Power Systems”, IEEE Trans. on Power Delivery, pp. 213– 217,
2007
16. C.F. Wagner, R.D. Evans, Symmetrical Components (Mc-Graw-Hill Book Company, New York,
1933)
17. C.L. Wadhwa, Electrical Power System (New Age International Publishers) ISBN no. 81-224-
1722-1
Severity and Location Detection of Three Phase Induction … 437

18. R. Saha, G. Sarkar, J.N. Bera, S. Chowdhuri, A. Deb, Sample shifting technique (SST) for
estimation of harmonic power in polluted environment, in IEEE Conference Publications on
Circuits, Power and Computing Technologies (ICCPCT), pp. 535–539 (2013)
19. M.S. Ballal, Z.J. Khan, H.M. Suryawanshi, R.L. Sonolikar, Adaptive neural fuzzy inference
system for the detection of inter-turn insulation and bearing wear faults in induction motor.
IEEE Trans. Ind. Electron. 54(1), 250–258 (2007)
20. S. Altug, M.Y. Chow, H.J. Trussell, Fuzzy inference system implemented on neural architec-
tures for motor fault detection and diagnosis. IEEE Trans. Ind. Electron. 46(6), 1069–1079
(1999)
21. M.E. El-Hawary, Principles of Electric Machines with Power Electronic Applications (Prentice-
Hall, Englewood Cliffs, NJ) 07632
Level Adjustment of Hydrofoil Sea-Craft
Under Wave Disturbance

Sohorab Hossain, Sourish Sanyal and Amarnath Sanyal

1 Introduction

Hydrofoil sea-crafts must be capable of moving through waves of large amplitude, as

such of large energy content. A hydrofoil is simply a lifting surface, or foil, that oper-
ates in water. These are similar to aerofoils used in aeroplanes. As a hydrofoil craft
gains speed, the hydrofoils lift the boat’s hull out of the water. It decreases drag and
allows greater speeds. Hydrofoil boats incorporating the use of hydrofoil to help
them propel much faster on the water was an attraction for the shipping industry
for quite some time. They were created by A.G. Bell and Casey Baldwin in 1908
and were used extensively during the First World War by American troops to avoid
the waters trapped by mines. The interest in hydrofoil ships flagged away after a
few years as the design of other types of ships were found to be better. However, in
modern times, the hydrofoil ships are again gaining momentum on account of their
faster and speedier movement through the waters [1–4].

S. Hossain (B)
EE Department, MCKV Institute of Engineering, Howrah, India
e-mail: sohorab.hossain@gmail.com
S. Sanyal
ECE Department, Cooch Behar Government Engineering College, Cooch Behar, India
e-mail: maysourish2013@gmail.com
A. Sanyal
EE Department, Calcutta Institute of Engineering and Management, Kolkata, India
e-mail: ansanyal@yahoo.co.in

© Springer Nature Switzerland AG 2019 439

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_36
440 S. Hossain et al.

Fig. 1 Hydrofoil sea-craft control: block diagram

2 Operation of Hydrofoil Ships

A hydrofoil ship operates in a simple way: the hydrofoil based on the base allows the
ship to move easily through the waters and ensures that the body of the ship (known
as hull) does not come in contact with the water. As the hydrofoil works only if the
ship is on the surface of the water, it prevents the ship from rising out of water. In
case, the ship arises out of water, its design forces it to come back into the water and
get submerged till adequate thrust is generated to lift the ship. These ships are mostly
used for multiple purposes e.g. fishing in the sea etc. and for warfare. However, as
the density of water is much greater than that of air, the hydrofoils are much smaller
in size compared to the aerofoils and are compact [3, 4].
As of now, the use of hydrofoil ships is limited. But in foreseeable future, the
hydrofoil ships may revolutionize the market for their speed advantage. The only
requirement is greater efficiency and stability. The design methodology given in this
paper suggests the path to make them stable with adequate margin.
H.S. Denison was the first large hydrofoil sea-craft built by United States [5]. The
craft was capable of moving at a speed of 60 knots in wavy seas. The block diagram
of the control system is given in Fig. 1.

3 The Control System

The control system consists of transducers to sense the craft motion and a com-
puter to transmit commands to electro-hydraulic actuators [6]. The heave rate is fed
symmetrically to the forward flaps—also the roll and the roll rate. The pitch rate is
fed to the stern foil. The stabilizing circuit maintains a level flight by means of two
main surface-piecing foils located ahead of the center of gravity and an all-movable
submerged foil aft.
The craft is to maintain a constant level of travel in spite of wave disturbance U(s),
whose energy is concentrated around 1 r/s. The pitch loop has to maintain a gain of
40 db at 1 r/s, in order to minimize the wave disturbance and a gain crossover of
160 r/s for adequate response time. The phase margin must be at least 60° and the gain
margin 12 db. We are to find out the amplifier gain K and design the compensation
network Gc (s) and weigh the rate feedback required to fulfill the specs [7–9].
Level Adjustment of Hydrofoil Sea-Craft Under … 441

4 The Control System Design

The understanding of a control system is rather simpler than its design itself. Certain
specifications, equality or inequality constraints are imposed before the designer. He
has to conform to them. Very often some of the design constraints are contradictory
e.g. the requirement of steady state accuracy and the stability margins—a reasonable
tradeoff has to be made between the contradictory elements. Both time domain
and frequency domain specifications have to be met by the design. For this reason,
compensators have to be interposed in the system. The commonly used compensators
are [10]:
(i) Proportional-Derivative (PD) control
(ii) Proportional-Integral (PI) control
(iii) Proportional-Derivative-Integral (PID) control
(iv) Phase-lag compensator
(v) Phase-lead compensator
(vi) Phase-lag-lead compensator etc.
or a combination of some of these elements [8]. The choice has to be judiciously
made, either by mathematical or graphical procedure or by trial and error using the
control system tool-box of MATLAB [9, 10].
The present problem has its own constraints and it has been solved by a combi-
nation of PD-control and phase lag using the later procedure [11].

5 Specification

The following specifications are to be fulfilled:

a. System gain is to be about 30 db at 1 r/s to combat the sea-waves. It fixes up the
forward path gain: K  31.4
b. Phase crossover is to occur at about 160 r/s and the gain margin to be more than
12 db
c. The gain crossover is to be at about 3 r/s and the phase margin is to be adequate
(more than 60°)
d. The % overshoot is to be less than 5%, and the settling time less than 1 s.

6 The Mathematical Description

The open loop T.F. for the uncompensated system is given as (obtained from the
manufacturer’s data):
442 S. Hossain et al.

K 8100
G u (s)   2  (1)
s s + 50s + 8100

For the uncompensated system, the system gain to be 30 db at 1 r/s, open loop
gain must be 31.4.
The analysis is being made by using MATLAB tool [12, 13]. The t-domain
response (Fig. 2) shows a peak overshoot of 12.2% which is not admissible (it has
to be less than 5%).
The f-domain characteristic (Bode plot, Fig. 3) shows a negative gain margin and
declares the system as closed loop unstable. The stability has to be ensured. So some
sort of compensation has to be made.
To stabilize the system and to fulfill the specifications a compensator is to be
cascaded, along with addition of an appropriate rate feedback. Many authors in
recent times have made recourse to different compensation techniques to fulfill the
requirements [13] and have become successful in implementing appropriate control.
We insert a lag compensator in the forward path and add a rate feedback. The
compensator is made of static elements as shown in Fig. 4.
The transfer function of the lag compensator has been taken as:
1 + 4s
G c (s)  (2)
1+s
by trial and error method and that of the feedback path as:

Fig. 2 t-domain response to step input

Level Adjustment of Hydrofoil Sea-Craft Under … 443

Fig. 3 Bode plot of the uncompensated system

Fig. 4 A lag compensator

made of static elements

(1 + 0.06s) (3)

The t-domain performance of the compensated system with PD feedback is

depicted in Fig. 5.
The f-domain characteristic (Bode plot) for the compensated system is shown in
Fig. 6.
Now with the lag compensator and the PD system, for the hydrofoil ship Denisson,
we get the following:
System gain is 30 db at 1 r/s to combat sea-waves, which fixes up the value of open
loop gain K  31.4.
Gain margin  12.2 db at 164 r/s; Phase margin  166° at 2.75 r/s.;
The system is slightly underdamped—the peak overshoot is 2.11%.
The settling time is 0.553 s and rise time is 0.192 s.
So the system specifications have been fulfilled by this design.
444 S. Hossain et al.

Fig. 5 t-domain response of the compensated system

Fig. 6 Bode plot of the compensated system

7 Conclusion

The design of a control system has to be made fulfilling the requirements or the given
specifications. The fulfillment has to be made optimally [14]. Often, the requirements
are contradictory and a trade-off has to be made between contradictory elements. To
Level Adjustment of Hydrofoil Sea-Craft Under … 445

conform to the specifications we may have to insert a compensator of a particular

type or a combination of two or more of them [7, 9, 10]. Sometimes, computational
intelligence is made use of to reach the optimal conditions [15]. In this paper the
control system design of a large hydrofoil sea-faring aircraft “Denisson” [5] has
been made. The parameters of the uncompensated system have been given—also
the specifications. It is required to have a gain of 30 db at 1 r/s to combat the sea-
waves. This requirement fixes up the forward path gain. With this gain, the system is
found to be highly oscillatory and closed loop unstable. By using MATLAB-tools,
a combination of PD-control and phase lag compensation have been found out by
a trial and error procedure, which has enabled the design to match with the given
specifications. Previously, the design procedure was suggested by Goswami et al. in
one paper [16].

References

1. T.J. Cutler, The Bluejacket’s Manual, 22nd edn. (Naval Institute Press, Annapolis, MD, 1999)
ISBN: 1-55750-065-7
2. T.J. Cutler, Dutton’s Nautical Navigation, 15th edn. (Naval Institute Press, Annapolis, MD,
2003) ISBN: 978-1-55750-248-3
3. G. William, Stability and Trim for the Ship’s Officer (Cornell Maritime Press, Centreville, MD,
2005) ISBN: 978-0-87033-564-8
4. E.S. Maloney, Chapman, “Piloting and Seamanship”, 64th edn. (Hearst Communications Inc.,
New York, NY, 2003) ISBN [Spl: Book Sources/1-58816-098-0|1-58816-098-0]
5. S.M. Shinners, Modern Control System Theory and Design (Wiley, 1992) ISBN: 978-0-471-
24906-1
6. D. Patranabis, Sensors and Transducers, 2nd edn. (PHI, New Delhi, 2008)
7. K. Ogata, Modern Control Engineering (Pearson Education) ISBN 10: 0136156738; ISBN
13: 9780136156734
8. N.S. Nise, Control System Engineering, 5th edn. (Wiley Student) ISBN: 978-81-265-2153-1
9. A.M. Law, W.D. Kelton, Simulation, Modeling and Analysis, 2nd edn. (Mcgraw-Hill, New
York, 1991)
10. C.J. Herget, A.J. Laub, Special issue on computer-aided control system design. IEEE Control
Syst. Mag. 2(4), Dec’82
11. Lecture Notes in Control and Information Science, vol. 162. (Springer, 1991), pp. 106–124
12. J.J. D’Azzo, C.H. Houpis, S.N. Sheldon, Linear Control System Analysis and Design with
MATLAB, 5th edn. (Marcel Dekker Inc. New York, BASEL)
13. A.J. Grace, N. Laub, J.N. Little, C. Thomson, Control System Tool Box for use with MATLAB,
User Guide (Mathworks, 1990)
14. K. Deb, Optimization for Engineering Design (PHI, 2010)
15. D. Poole, A. Mackworth, R. Goebel, Computational Intelligence (Oxford University Press,
1998)
16. R. Goswami, S. Sanyal, A.N. Sanyal, Design of compensator for a hydrofoil ship. Int. J. Emerg.
Technol. Adv. Eng. 2(9), 266–271 (2012). available online
 Part VI
Computation Technique
Law of Time and Mathematical Axioms

Hiran Das Mahar

1 Introduction

Mathematicians have views that in Philosophy of Time, observer has significance

role to measure and use the time [1–3]. Social Sciences apply the time commercially,
in regard with time management for Industrial production [4]. In Bioelectronics Dept.
Manchester University, UK. make prospectus for ultra measurement of life energy in
micro level i.e. bioelectric current in nano-ampere unit [5]. Deo Sanskrit University
of Gayatree Peeth Haridwar applying time to increase bioelectric positive power,
like physicians for exercises for meataphysics [6]. Here also bioelectric power is
generated in Enthalpy (heat), therefore sweat appears. ATP, DNA and NADH are
three basic molecules in life Science. All these are consist of five basic elements C,
H, O, N and P of Environment, respectively representing to Earth, water, sky, air and
fire on the basis of percent presence and nature (e.g. evaporation point). Time  is a
measure, in which events can be ordered from the past through the present into the
future, and also the measure of durations of events and the intervals between them.
Time is often referred to as the fourth dimension. These properties of time are also
applicable for Life time.
Peter Duren et. al. [7] studied mathematical analogy between space and time
to be both have nature of ever dynamic functional state. i.e., space, S = L2 {R+,
(1/t)dt}. Functional space is Bergman space, applied for study. In nature there is no
non-functional space, since in even vacuum, weightless particles like Cosmon, Higgs
boson etc may present in functional state and cent percent vacuum is impossible [8].
Qiuhe Huang [9] introduced the logarithmic Bloch space Bqlog (Dn), a new space
of analytic functions on the unit poly disc. He investigated the composition opera-
tor · C from weighted Bergman space to logarithmic Bloch space on the unit poly
disc, and provides the sufficient and necessary conditions to ensure the bounding

H. D. Mahar (B)
R.G. Govt. P.G. Autonomous College, Ambikapur, Surguja, Chhattisgarh 497001, India
e-mail: drhdmahar@gmail.com
© Springer Nature Switzerland AG 2019 449
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_37
450 H. D. Mahar

and compactness of the composition operator · C from weighted Bergman space to

logarithmic Bloch space. A.I. Rouban [10, 11] studied “Delayed time” in a sensi-
tivity functional (SF) and formulated sensitivity coefficients (SC) of a mathematical
model. He viewed that unused time is dead time in the calculation of SC and SF.
Ming-Hua Wu [12] studied a pair of independent time series, in the phenomenon of
spurious regression and with shifts in variance. He numerically discussed the effects
of variance changes on the size of t-ratio test in model. There is a spurious regression
between sequences driven by variance shifts in his regressions model and the asymp-
totic distribution of t-ratio test is not invariant to shifts in variance. Chen et. al. [13]
studied nonparametric estimation of structural change points in volatility models for
time series in econometrics. Ramans [14] formulated an additive energy of dense set
of primes and monochromatic sums and he stated “When K ≥ 1 is an integer and S is
a set of prime numbers in the interval (N2N2, N] with |S| ≥ π*(N)/K, where π*(N)
is the number of primes in this interval, we obtain an upper bound for the additive
energy of S.” Bas C. van Fraassen [15] viewed that the words “time” and “space” are
both singular terms and John D. Barrow (2009) studied mathematics of dark energy
in space [16].

2 Law of Movement

• Time is movement of Universe. The speed of time is in a proportion of the speed

of universe. Time of any planet or any part of planet is depended upon the moving
position of the planet or place. e.g. Earth’s time is proportion to earth’s movement
and time of any country is depended on in position on earth. (a) Circular (b) Linear
(C) Serpentine spin.

Mathematical Axiom 10. A set-theoretic point (member of a set).

In Vector algebra, an ‘element’ of a set is a representation of a coalition in intensive
magnitude. A set-theoretic point (member of a set) is something else entirely. It is a
complete and singular composition employed as a unit in the process of aggregation.
It should not be called an element.
A member ‘belongs to’ a set; an element does not denote a rule of transformation
from a ‘domain set’ (A) to another set. For example, the notation f : A → B or f : A
→ A.
In other words, this notation is shorthand for saying that f defines some subset of
a Cartesian product and does not directly denote, for instance, taking.
A immediately back into itself (as the notation f : A → A merely seems to imply).
We must not confuse the abbreviated notation for the logical train of concepts this
notation is meant to convey.
Law of Time and Mathematical Axioms 451

3 Explanation:

3.1 Law of Opposition

Dimension of Time  and Life Time ε In all dimensions of time is opposite to

universe e.g.
• Linear (arrow of time): Universe (e.g. earth) came from past (through origin) ‘is’
in present and moving to future. While Time come from future is in present and
went to past to be history.
• Cycle: Earth moves anti clock wise in rotational movement.
• Spin movement, Since earth and energy moves in spin, Therefore it is assumed
spinning Time.

Axiom 9 (Axiom of Regularity)

Non-empty set s implies x exists such that x belongs to s and every y belonging to x
implies y does not belong to s.
This axiom is meant to prohibit any set s from containing itself as a member. It
was introduced by von Neumann in order to deal with certain highly technical issues
involving unwanted circumstances that were shown to be consistent with the other
axioms. One such issue was the possibility, under the system without axiom 9, of
the existence of sets that did not contain some of the ‘primary constituents’ (such as
the null set) of Zermelo’s set theory. development of Euclid’s axioms and Aristotle’s
ten ‘categories,’ the development of the axioms of set theory was historically an
empirical and somewhat trial-and-error process. Commenting on ‘system Z’ (the
modified Zermelo system, which is more or less like the one just described here),
Fraenkel wrote.
The rather arbitrary character of the processes which are chosen in the axioms of Z
as the basis of the theory is justified by the historical development of set-theory than
by logical arguments. The far-reaching aim of proving the consistency of Z, which
would exclude contradictions of types as yet unknown, is not likely to be attained in
the present stage, and in a well-defined sense cannot be attained at all, in accordance
with Gödel’s incompletability theorem.

3.2 Law of Energy

Time is energy to remain irreversible movement in Continuum is mathematical Tri-

angle (pyramid) of Energy, Time, Universe (ibe, Tinia and Uni or Vishnu, Mahesh,
Brahma).
Axiom 8 (Axiom of Choice)
If ‘a’ implies non-empty set ‘x’ is a function defined for every a belonging to ‘s’
then there is another function ‘f (a)’ for a belonging to ‘s’ and ‘ f (a)’ belongs to ‘x’.
452 H. D. Mahar

What this axiom tries to say is we can select one member from every non-empty
subset of ‘s’ and use our selections to define ‘a set x’. The axiom of choice differs
from axiom 6 in that the ‘choice function’ f , is not given any specified property that
defines the ‘choices’. The axiom lets us do an arbitrary ‘choosing’ even though we
have no property that would define the choice function between ‘a’, ‘x’ and ‘s’.

3.3 Law of Universal

Time is continuous in continuum behaves equal for all in continuum. E.g. 7 a.m. for
one individual at any place, just same for all men bethought any discriminations in
any space Universe.
There is a “Pot theory” that universe is a oval pot. In which time energy and many
continuum (spaces and galaxies) are present.
Kalashasya mukhe Wisnu, Kanthe Rudra samasita Kukhao tu sarwe sapta Deepa
Wasundhara Moole tatra sthito Brahma!!! (Rom rom prati lage, koti koti brahmand.)
Above four line are for four tense depicted from Veda and Not agree with this,
or rejection, or absence of pot (=Kalash) is A-tense. The wall pot is Vast Universe.
And elliptical as pitcher  kalash. In bracted hindi Epic says many galaxies in each
part of Universes body.
Axiom 7 (Axiom of the Power Set):
Things which are halves of the same things, are equal to one another. For any set x
the set y consisting of all the subsets of x exists. The set of all subsets of x is called
the ‘power set’ of x. Although y is defined by a property, namely that its members are
subsets of x, this case is not covered by axiom 6 because the property is not defined
as the rang of a function. For example, axiom 6b specified that the function had to
be unary (a function of one member of x), whereas in axiom 7 the property ‘is a
subset’ is not a unary function. Axiom 7 is another construction axiom since y will
have more members in it than did x if the number of members in x is finite.

3.4 Law of 05 Tense

A great tense is a space time. It controls over first three tenses,\ simply as video
recording and fore casting. Astrology and palmistry fore cast future in present. Sci-
ence says, time changes in space, even, in countries and galaxies.
A-tense is defined that before birth of the space or universe, since time is space
related. According to Newton’s theorem of “space time relativity”. If there was, no
space, no time.
I.e. before origin of Higgs Boson, there was no time. Same, after degeneration of
Universe, no space, no tense i.e. A-tense.
Law of Time and Mathematical Axioms 453

Metaphysically and socially may be, simplified, if officer is happy, signs in back
dates. If unhappy, says, sorry! I have no time. i.e. ‘A tense’ But this run off from
duty for a greater duty is whether for metaphysical exercises for priest or in surgical
science or music. There fore a-tense is supreme time. One can criticize that this
theorem of five tense is pure hypothetical. Great tense solves it. Past and future days
are in this week. Present minute become past in a minute. So that, theory of three
tense is depended on unit of time to be any tense Since death is definite with fixed
time called “Programmed Cell Death (PCD)” Therefore, present society is future
century’s imp society. Since time is infinite. So that great tense is mathematically
sum of past, present and future and absence of time is ‘a-tense’.
Axiom 6 (Axiom of Replacement):
Things which are double of the same things, are equal to one number. This is not
actually an axiom but rather a schema for an unlimited bundle of axioms. Even pro-
fessional mathematicians find it difficult to re-state the formal expression in English.
Roughly, the axiom says “any ‘reasonable’ property that can be stated in formal
language can be used to define the set y of things having the stated property.”

3.5 Law of Infinite

Time runs from infinite future to near future to present… to past to infinite past…
(start of Universe, birth of Brahma).

 f i →  f →  pr →  pa →  p I ⇒   ∞

If we assume fifth law of time, we have to add great time (e.g. dreamed time) and
Atence (hypothesis of absence of time, i.e. before and after the origin of Universe
and Time

∞   f +  pr +  pa + g + a
∴ Universe U   ∞ ⇔ Time   ∞ ⇔ Energy E  ∞
∵ ∞  ∀U  , ψ, E E ∞
volume, linfetime ε , lifeenergy

Universe  space + vacuum + volume + super dense black holes + inter galactic
spaces + all galaxies + Milky way’s + earth including Bermuda, + Jatinga, where ships
dip and birds suicide).
Axiom 5 (Axiom of Infinity):
The whole is greater than the part. There is a set x that contains the empty set and
that is such that if any y belongs to x then the union of y and {y} also belongs to x.
This one is a very strange axiom when expressed in its formal language. A
454 H. D. Mahar

3.6 Law of Particle

Mathematical definition of line L  ∞p → in a series. Line  Sigma infinite points

in a series (Points = Particle).
Corpuscular Mathematical assumption
 in linear dimension of Time.
∞…… → …… → ∞   (God Particle) (e.g. Photon, thermion Higgs
Boson, Positron, Magnetron, Cosmo).
Smallest times are Femito second  ! × 10−15 S, and Zeta second  1 × 10−25 S.
(While, greatest time  Era  4 Apouches) geologists stated, Pleistocene, Eocene,
Mesozoic Jurassic and Modern.
Axiom 4 (Axiom of the Sum Set or Union):
Things which are coincide with one another, are equal to one another. If x is a set
of sets, the union of all its members is a set. This one might make us blink a bit.
Suppose the set x is given by {A, B}. Suppose further that A is a set given as {a, b,
c} and B is a set given as {d, e, f }. The axiom says that {a, b, c, d, e, f } is also a
set. Axiom 4 is another construction axiom. Fraenkel used to describe the operation
y ∪ {y} is the following. The empty set ∅ is a member of x.
Therefore ∅∪{∅}  {∅, {∅}} is a member of x.
Therefore {∅, {∅}, {∅, {∅}}} is a member of x.

3.7 Law of Uncertainty

The velocity of time is constant on any planet and similar for all living and nonliving
at any place. but except for velocity, Time follows the law of uncertainty. E.g. present
sun rise time may differ at other continent.
Past Time: listened, read, video, images, evidences, history, memory, tradition,
rituals, etc. are records of past time. These all are based on faith and believes. Might
be fluctuating with reality.
Present time: Since time is an action (move of planet around it’s star) therefore
present time differs place to place on one planet. Therefore there is another scales of
time e.g. Greenwich, Indian Standard Time, etc. Time (action) at a place is also no
certain e.g. power cut, earth quake, volcano, accidents, death, rain, gifts, prizes, etc.
are uncertain.
Future time: Future time is a result of past plus present. Even though future time is
uncertain sciences like Mesmerism, Astrology, Horoscopy, Metaphysics, Palmistry,
etc. are developed to know the future. But yet future is uncertain.
Great time: Dream is supposed to be of Great time. It’s uncertain and being truth,
it is bethought evidence near to false.
A tense: Hypothesis of ‘atence’ (No time) is supposed to be at absence of universe,
so time absents before Universe is made by big bang and after the end of Universe.
So that atense (no-time) is totally hypothetical and uncertain.
Law of Time and Mathematical Axioms 455

Axiom 3 (Axiom of Unordered Pairs):

If equals are subtracted from equal, the remainders are equal. If x and y are sets then
the set of pairs (x, y) or the set of pairs (y, x) exists. i.e. the set of all ordered pairs of
members of A and members of B, A × B.

3.8 Law of Life Time

ε  Life time   → N→M → 

ε   ï →  μ   π (Here  ï  Birth time,  ï  Mortality time and  π 
Life particle).
Axiom 2 (Axiom of the Null Set):
If equals are added to equal, the wholes are equal. For example, if C is the set of all
cattle in Wyoming and D is the set of living dodos, we could not say C ∪ D = C 8 if
we were not permitted to use the idea of the empty set.
One theorem that comes out of the ZFS system is that the empty set (symbolize it
as ∅) is ex officio a member of every other set. This is read as, “The union of C and
D is C” or C ∩ D = ∅.

3.9 Law of Quality

Morning evening midnight/\good/bad time Proportion

ε…α Good time  +E praise/smiles  α1/Bad time  −e bad news/Hesitation
First axiom of Mathematics Differential equation, (i.e. not equal to)
Fall of the Axiom  ABA + B < 180.

Axiom 1 (Axiom of Extensionality):

Things which are equal to the same thing, are equal to one another. Two sets are equal
if and only if they have the same members. Fraenkel remarked, The axiomatization
of set-theory renounces a definition of the concept of set and of the relation between
a set s and its elements. The latter, a dyadic relation (or predicate) is denoted by
∈; x ∈ s reads “x is contained in, is an element of, belongs to, the set s” … and
its negation is x ∈
/ s. ∈ enters as an (undefined) primitive relation, the membership
relation [BERN: 4-5].
Axiom 1 is written formally as
∀x, y (∀z(z ∈ x → z ∈ y) → x  y)
Fall of the Axiom  ABA + B < 180
456 H. D. Mahar

4 Discussion

Einstein in 1905

Above is the Formula of time by Einstein (1905) and followings are some models
of time given below

Model 1 Model 2 Model-3 Model=4 Model5

These models are described by Einstein Light cone diagram showing the world line
of a moving observer in electrical experimentation [17, 18]. Y. Tian et al. [16] studied
time-delay systems for a problem of static output feedback variable structure control
to design of a static output feedback sliding mode surface and the variable structure
controller. Although time, energy, and space are homologous and everywhere, they
may be studied separately but are intermingles and unseparable called TES hypothesis
[19, 20].
Law of Time and Mathematical Axioms 457

Acknowledgements I am gratefull to Pr. C. B. Vachon to organize MS 17 in India. I am thankfull

to Pr. Surajit Chattopadhyay (Eds) for acceptance of this paper. I am also thankfull to Springer
Nature for publication in this prestigious book.

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c/8/b7268bad-67d9-4e4f-a984-24e798b3d773. Retrived on 05.08.2018
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Analysis of Resources for the Safety
and Comfort of Railway Passenger Using
Analytical Hierarchy Process

Gopal Marik

1 Introduction

In India, the first railway line was laid over a stretch of 34 km from Bombay to
Thane. The idea of railway transport first occurred to the then CHIEF Engineer of
Bombay Government. His plans were investigated by a special Committee headed by
the Chief Secretary and then approved at a meeting of the citizens of Bombay held at
the Town Hall on 19th April 1845. An association was formed to execute the scheme.
At the same time a company was incorporated in England by an act in 1849 under
the style “The great Indian Peninsula Railways Company.” The survey of this line
was completed in 12 months and on 13th October 1850 the ceremony of the turning
the first sod for a line connecting Bombay and Kalyan was performed at a place near
Sion. A contract was awarded to an English firm for the construction of the line up to
Thane. It is stated the firm employed about 100,000 workers on construction work.
On 18.11.1852 the Directors of the company traveled in the train from Bombay to
Thane, covering the distance in about 45 min. The formal inauguration of the railway
line was later performed on 16.4.1853. when 14 railway carriages carrying about 400
guests left Bori Bonder at 3.30 pm and reached Thane at about 4.45 pm. The line was
later on extended to Kallyan on 1.5.1854. The extension according to the engineering
standards then existing was a difficult and a major achievement.
After the opening of the Railway up to Kalyan in 1854, further extension of the
line over the Thalghats to Igatpuri was made on 30.12.1864, there by completing one
of the most difficult projects in railway history and laying ground for further rapid
expansion of the railway network.
In India, the origin of railways is associated with the needs of the rulers then to
exploit rich agricultural raw materials like cotton and jute to the ports for transporta-
tion by sea to the factories in England. Lord Dalhouise became Governor General

G. Marik (B)
Liluah, Howrah Department, Carriage and Wagon Workshop, Eastern Railway, Liluah, India
e-mail: gopal.marik@gmail.com
© Springer Nature Switzerland AG 2019 459
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_38
460 G. Marik

of India in 1847. Before taking up this assignment he was President of Board of

Trade in England and was well conversant with the role of railways in development
of industry and trade.
Indian Railways (IR) is an Indian state owned railway company headquartered in
New Delhi, India. It is owned and operated by Government of India through Ministry
of Railways.
In the year of India’s independence, there were forty-two rail systems. In 1951
the systems were nationalized as one unit, the Indian Railways, becoming one of
the largest networks in the world. IR operates both long distance and suburban rail
systems on a multiple-gauge network of broad, meter and narrow gauges. It also
owns locomotive and coach production facilities.
Indian Railways is a department owned and controlled by the Government of
India, via the Ministry of Railways is headed by, the Union Minister for Railways,
and assisted by two ministers of States for Railways. Indian Railways is adminis-
tered by the Railway Board, which has a chairman, five members and a financial
commissioner.
Indian Railways is divided into zones, which are further sub-divided into divisions.
The number of zones increased from six to eight in 1951, nine in 1952 to sixteen in
2003 then to seventeen in 2010. Each zonal railway is made up of a certain number
of divisions, each having a divisional headquarters. There are a total of sixty-eight
divisions.
Each of the seventeen zones is headed by a General Manager who reports directly
to the Railway Board. The zones are further divided into divisions under the control
pf Divisional Railway Manager. The divisional officers of engineering, mechanical,
electrical, signal & telecommunication, accounts, personnel, operating, commercial
and safety branches report to the respective Divisional Manager and are in charge of
operation and maintenance of assets. Further down the hierarchy tree are the Stations
Masters who control individual stations and the train movement through the track
territory under their stations’ administration
Indian Railways is the largest railway network in Asia, and second largest in
the world. The rail network consists of more than 64,000 route kilometers serviced
by over 7000 block stations, 9000 locomotives, 43,500 passenger coaches, 7500
Electrical and Diesel Multiple Units and 22,000 railway wagons. With staff strength
of 13.62 lakhs employees, the Indian Railways handle 8221 million passengers per
year [1, 2].
Rail transport indirectly best means of transportation system for the following;
(a) The safest
(b) Least liable to cause of pollution
(c) Best suitable for mass transport and
(d) Most energy efficient mode on land.
Indian Railways has increased by about 1700% passenger kilometers but route
kilometers have grown by just 23%. Railway is introducing latest technology and
moving from preventive to predictive maintenance. The augmentation of physical
infrastructure in terms of more railways lines, road over bridges, better signaling,
Analysis of Resources for the Safety and Comfort … 461

safety related works etc. is impacting the punctuality of trains a little. The augmen-
tation of passenger amenities, new train products special trains, increase in carrying
capacity etc. are some of the measures to be taken to provide comfort to passengers
[3].

2 Function of Operating Department

Railway operation encompasses all the activities connected with the running of a
railway. However, Operating Department in particular has its role in producing a
service called “Transportation”. In this category, Operating department harnesses
the efforts of all the departments of the Railways and optimizes usage of operational
assets, viz. track, signals, fixed installations and rolling stock. Broadly the function
can be categorized as under:
(a) Planning of Trans port Service
(b) Running of Trains
(c) Safety and Comfort
(d) Railway Accident and Human Elements involved
(e) Economy and Efficiency.

2.1 Planning of Transport Services

This involves both long and short term planning. A lot of spade work has to be done to
run trains on day-to-day basis. Passenger trains are planned to run on a detailed time
table issued once in six months. Arrangement of rolling stock and locomotives are
made to meet the expected demand. Railways have to plan to meet these fluctuations
in demand. Planning would involve not only the individual trains but a lot of other
activities necessitating creation of capacity to form and start trains at originating
stations. Though entire organization of the railways gets involved in this planning
process, the basic frame work is provided by the operating department to which the
plans of their departments responsible for provision and maintenance of operational
assets fit in. Coaching traffic includes passengers, parcel and luggage. Passengers
and their luggage are moved by the passenger trains. In the Railway parlance all
Mail, Express and Passengers Trains are included in this category. Passenger trains
are classified by their average speed. A faster train has fewer stops than a slower
one and usually caters to long-distance travel. The passengers trains are namely as
Duronto Express, Rajdhani Express, Satabdi Express, Garib Rath, Jana Shatabdi,
Superfast/Mail, Express, Passenger and Fast Passenger, Suburban Trains.
Duranto Express: These are the non-stop point to point rail services introduced
for the first time in 2009. These trains connect the metros and major states capitals
462 G. Marik

of India and are faster than Rajdhani Express. These trains are now of the Highest
Priority to the Indian Railways.
Rajdhani Express: These are all air-conditioned trains linking major cities to New
Delhi. The Rajdhanis have high priority are one of the fastest trains in India, traveling
at about 130 kmph. There are few stops on a Rajdhani route.
Shatabdi Express:
The Shatabdi trains are AC intercity seater-type trains for travel during day.
Garib Rath:
Fully air conditioned trains, designed for those who cannot afford to travel in the
expensive Shatabdi and Rajdhani Express. Garib Rath means “Chariot of the Poor”.
The minimum speed is 130 kmph.
Jan Shatabdi:
These are a more affordable variety of the Shatabdi Express, which has both AC
and Non-AC classes.
Superfast Mail and Express:
These are most common kind of trains in India. They have more stops in their
route.
Passenger and Fast Passenger:
These are slow trains that stop at most stations along their route and they are the
cheapest trains. The trains generally have unreserved seating accommodation but
some night trains have cheaper sleeper class compartment.
Suburban Trains:
These trains operate in urban areas, usually stop at all stations and have unreserved
seating accommodation.
Launched new train products: Humsafar, a completely air conditioned luxury
service at affordable price with improved aesthetics, amenities and Antyodaya, a
completely unreserved long distance service with improved coaches.

2.2 Running of Trains

Running of trains would involve ordering of trains booking of crew, watching that
the conditions are safe for it to run and arranging various requirements on the run.
Efficiency of operation of trains depends on the quality of planning whether short
term or long term one. Transportation staffs both at originating and terminating as
well as at the road side stations are busy round the clock to ensure timely and safe
running of trains. Passengers’ trains run to predetermined schedule and fluctuations
in the traffic also influence their running.
Analysis of Resources for the Safety and Comfort … 463

2.3 Safety and Comfort

Safe transportation of passengers is the key objective of any transportation system.

Railways are recognized as the safest mode of mass transportation and safety has
been recognized as key issue for the railways and one of its special attributes. All
business strategies emanate from this theme and service to achieve Accident Free
System. Safety is therefore, the key performance index which the top managements
need to monitor and take preventive steps based on the trend of accidents which are the
manifestations of some of the unsafe practices on the system. Therefore, safety is the
paramount importance to the Indian Railways. Highest priority is accorded to safety
and the rail mode in India continues to be the safest means of transportation for public.
No compromise is tolerated in Safety of Rail users and all levels of management keep
reviewing the Safety performance from to time. Safety and Reliability of assets are
closely linked with each other. Deterioration in the safety performance is preceded
by the increase in the number of failures. Overlooking these warning signals can be
disastrous as each of these is an accident waiting to happen. Although no technology
is fail-proof, an error rate, however small, being inherent in any man-machine system,
reliability of the equipment is the most important factor in the efficiency and safety
of a transport system. If accident has to be zero level or minimized, it is imperative
that the equipment in use is always kept in fine fettle.

2.4 Railway Accident and Human Elements Involved

A Rail accident is termed as any occurrence which does or may affect the safety
the Railways, its engine rolling stock, permanent way, works, passengers or servants
which either does or may cause delays to trains or loss to the railways. Railway
accidents can be divided in the following categories: (i) Death or injury to persons,
(ii) Damage to the property, (iii) Detention of traffic. In the last 10 years on Indian
Railways, 62% of the accidents have been caused due to failure of Railway staff, 22%
have been caused due to failure of other than Railways staff, failure of equipment has
contributed 8%, sabotage has contributed 3% and balance 5% have been contributed
by miscellaneous reasons. From the break-up, it is more than evident that human error
from Railway staffs the major factor in causing the accidents on Indian Railways.
Higher incidence of Human failures surface as technical safeguards and backups do
not always replace the human effort. Though an accident occurs only when both
fail but it usually gets logged as “human error” with a tendency of glossing over
technical failure. Under optimum field conditions and with the best of intensions,
a human being is likely to commit a mistake from time to time. This is the reason
why operating rules included many redundancies in safety procedures and operating
practices involve number of checks and balances. More and more automation is
resorted to prevent human errors.
464 G. Marik

2.5 Transport Economy and Efficiency

While maintenance departments are responsible for making the assets available to
the operating department in proper fettle, it is the responsibility of the latter to make
the most optimum utilization thereof. Operating department is, therefore, responsible
for the productivity of the system. This is measured in terms of operating indices
passenger kilometers. The Indian Railways are not only a transport agency but also
have a social obligation to serve the national objectives by providing necessary
infrastructure for healthy economic development and rapid industrialization. In other
words, railways are not only a commercial enterprise but also a public utility service
catering to the needs of the society. As a result, the Railways are obliged to operate on
some social services, both passenger and freight, in the interests of community. The
losses accruing from such uneconomic services can be called “social burden”—as
distinct from commercial deficits. As many other countries, railways in India have
also certain obligations, and a definite role to play in the economic development.

3 Modernization

In the area of modernization a quantum jump in technology was achieved when RCF,
association with RDSO, came out with AC Double Decker Coaches having latest
features enhancing safety, comfort, passenger amenities and aesthetics all in one go
besides increasing the seating capacities by more than 50%. The new Double Decker
trains have become eye-candy and all geographical regions are aspiring to have one
such service in their area. In the year 2011, another quantum jump towards safety
features available in LHB design coaches was recognized and the High Level Safety
Review Committee under the Chairmanship of Dr. Anil Kakodkar strongly recom-
mended introduction of LHB design in all mail express trains by introducing non-AC
stainless steel coaches. On the technology front, introduction of jerk free couplers
on stainless steel coaches, reversible cycle air-conditioning for energy efficiency,
fire and smoke detection system, passenger information systems etc. for enhanced
travel experience in trains. Indian Railways face a daunting challenge ahead over its
envisioned resolve to take a giant leap forward in infrastructure development and
modernization of its rolling stock.
(a) Anti Collision Device
(b) Failure Indication and Brake Application Device
(c) Wheel Slide Protection.
Analysis of Resources for the Safety and Comfort … 465

3.1 Anti Collision Device

Anti Collision Device is a fully integrated Electronic Control system designed to min-
imize collisions and increase safety on Railway system. It is a non signaling system
and provides additional cover of safety in train operations to prevent dangerous train
collisions caused due to human errors or limitations and equipment failure. Being the
non-signaling and inter locking system it does not replace any existing signaling and
interlocking system and does not alter any procedures of train operations in vogue.
More than 2000 Anti Collision Devices have already been installed over 2700 Route
Kms of track on Indian Railways system out of which about 1900 Route Kms on
North East Frontier Railway and balance are on Konkan Railway. Moreover, Hyder-
abad Based Company, Hyderabad Batteries Limited (HBL) developed a new anti
collision safety device which is path breaking technology in ensuring safe traveling
and minimize accidents. The device is based on a combination of railway signal-
ing data with radio communications, global position, radio frequency identification
devices, software and logic. During the trials, the effectiveness was demonstrated
for prevention of head- on collisions, over-speeding of trains and disregard of red
signal. The new anti collision device had essential features of both automatic train
protection and collision prevention in one solution.

3.2 Failure Indication and Brake Application Device

There are different types of coaches which are used in Indian Railways. Some of
these coaches are used for carrying passengers over long distances. In order to have
smooth journey these coaches are fitted with Air Spring Bellows which absorbs the
Shocks and jerks which are created due to undulation of track and many other reasons.
Since Air spring bellows are filled with compressed air some mechanism is required
to detect and apply the brakes in the train in case of any such failure. Most of these
designs involve a large number of parts and are comparatively bulkier in size. These
reasons have made it a very expensive device. In order to make it more affordable
there is need of doing further research on it so that it can be made economical without
compromising on its functionality and can be used on all kind of passenger trains

3.3 Wheel Slide Protection

Wheel Slide Protection equipment is generally fitted to passenger trains to manage the
behavior of the wheel sets in “Low adhesion” (reduced wheel/rail friction) conditions.
It is used when braking, and may be considered analogous to anti-lock braking (ABS)
for cars. The system can also be used to control (or provide an input to) the traction
system to control wheel spin when applying power in low adhesion conditions. Low
466 G. Marik

adhesion at the rail potentially causes damage to wheels and rails. Typically, low
adhesion conditions are associated with environmental causes arising from seasonal
leaf fail, or industrial pollution. Occasionally the cause can be another less obvious
factor such as light oxidation of the railhead or even swarms of insects. When a train
is braking, the low adhesion manifests as wheel slip where the wheel set is rotating
at a lower velocity (speed) that the forward speed of the train. The most extreme
example of this is where the wheel stops rotating altogether (wheel slide) whilst the
train is still moving and can result in a “wheel flat” caused by the softer wheel being
abraded away by the harder rail steel. In traction, low adhesion may cause a wheel
set to accelerate more quickly than the train (wheel spin) to the point where it can
damage the train propulsion system or result in damage to the wheel and rail (rail
burn).

4 Tools of Analysis

After collection of the primary and secondary data from the different sources they
are to be analyzed by Analytical Hierarchy Process.

4.1 Analytical Hierarchy Process

AHP is a multi-objective decision making technique which takes care both qualita-
tive and quantitative analysis. It was developed by American Scientist Satty [Satty,
1980]. Formation of Judgment Matrix is the most important factor in AHP. The ana-
lytic hierarchy process is a structured technique for organizing complex decisions,
based on mathematics and psychology. It was developed by Thomas L. Satty in the
1980 and has been extensively used, studied and refined since then. It provides a
comprehensive and rational framework for structuring a decision problem, for rep-
resenting and quantifying its elements, for relating those elements to over goals and
for evaluating alternative solution [4, 5]. The applications of AHP to complex deci-
sion situations have numbered in the thousands, and have produced extensive results
in problem involving planning, resource allocation, priority setting, and selection
among alternatives.

4.2 Steps of Analytical Hierarchy Process

Step 1 The problem and scopes are identified before analyzing relations between
factors. This step signifies the key aspect of the entire process because the
final result is directly related to the correctness of the logical relations of the
factors.
Analysis of Resources for the Safety and Comfort … 467

Step 2 The layer structure and A matrix are to be established. The factors involved
in each layer are made definite because the matrix will be the sticking point
of this step. The difference between the factors is compared based on the
criterion mentioned below:

The significance of 1–9 scales

Scale Meanings
1 Comparing the two factors which are of same importance
3 The later is more important than the former
5 The later is important than the former
7 The later is less important than the former
9 The later is extremely less important than the former
2, 4, 6, 8 The middle value between the above results
Reciprocal If the degree of importance between the factors “i” and “j” is “aij, then
comparing “j” and “i” is “aji” which is equal to 1/aij.

The Eigen Vector or the Weight Vector is computed. The weight of each factor
based on the matrix A and the vector sum of each column are computed. A new
weight matrix B, is then constructed. Then normalized principal Eigen Vector will
be obtained by averaging across the rows. The normalized principal Eigen Vector is
also called Priority Vector. Aside from the relative weight checking of the Consistency
Ratio is to be obtained. For this Principal Eigen Value (λmax) is obtained from the
summation of products between each elements of Eigen Vector and the sum of the
columns of the reciprocal matrix [6]. Based on the structured and Semi structured
interview, views of the experts and their opinion in terms of guidelines provided in
the table.
λmax − n CI
CI  , CR 
n−1 RI

where, CI is the deviation degree in matrix above, which is called consistency index,
CR is the consistency ratio, RI is the random ratio of consistency that is change-
able with the number of factors (as per table below). When CR < 0.1, the result is
considered to be reasonably good.

5 Objective of the Study

1. To analysis the resource available for safe and comfort of passengers during
journey.
2. Improvement of quality of the service.
3. Resource planning.
468 G. Marik

First level
Goal: safety and comfort of passenger
Second level
Criteria:
Skilled man Availability Machine Infrastructure Adaptation Socio- Working
power of material of modern economic environ-
technology factor ment
Third level
Alternatives:
1. Qualifi- 1. Store 1. Upgraga- 1. Commu- 1. Enhance 1. Social 1. Basic
cation from tion of nica- safety equity amenities
outside existing tion/Inform.
machine Tech
2. 2. In-house 2. 2. Better 2. 2. 2.
Knowledge production Purchasing signaling Reduction Reduction Workplace
and of new in-service of fare safety
experience machine failure
3. Training 3. Logistic 3. 3. More 3. Radically 3. 3. Pollution
Preventive railway reduced Reduction control
mainte- lines cost of travel
nance time
4. Salary 4. Supply 4. Safety 4. Enhance 4. Reaching 4. Compen-
chain related customer to common sation
work service people
5. Perfor- 5. Create 5. Provision 5.
mance barrier to of extra Grievance
analysis entry benefit

Weight analysis R-E judgment matrix

E R1 R2 R3 R4 R5 R6 R7 W NW λmax CI RI CR
R1 1 2 4 4 3 6 5 2.36 0.32
R2 1/2 1 3 3 3 4 3 1.55 0.21
R3 1/4 1/3 1 1 1/2 3 1 1.2 0.16
R4 1/4 1/3 1 1 3 3 3 0.92 0.12 7.47 0.078 1.35 0.057
R5 1/3 1/3 2 1/3 1 5 1 0.73 0.09
R6 1/6 1/4 1/3 1/3 1/5 1 1 0.28 0.03
R7 1/5 1/3 1 1/3 1 1 1 0.42 0.05

The RI changeable with the number of factors

n 1 2 3 4 5 6 7
RI 0 0 0.58 0.89 1.12 1.26 1.36

4. Modern procedure for the recruitment and selection of the personnel.

5. Financial performance of the different.
6. To study the recommendation made towards the safety and comfort passenger
services.
Analysis of Resources for the Safety and Comfort … 469

Weight analysis R1—C1 to C5 judgment matrix

R1 C1 C2 C3 C4 C5 W NW λmax CI RI CR
C1 1 3 1 4 3 1.72 0.34
C2 1/3 1 2 1 3 0.925 0.18
C3 1 1/2 1 3 7 1.08 0.22 5.107 0.027 1.12 0.024
C4 1/4 1 1/3 1 5 1.09 0.22
C5 1/3 1/3 1/7 1/5 1 0.27 0.05

Weight analysis R2—C6 to C9 judgment matrix

R2 C6 C7 C8 C9 W NW λmax CI RI CR
C6 1 2 1 5 1.778 0.368
C7 1/2 1 1 5 1.257 0.26 4.06 0.021 0.9 0.022
C8 1 1 1 5 1.495 0.309
C9 1/5 1/5 1/5 1 0.299 0.062

Weight analysis R3—C10 to C12 judgment matrix

R3 C10 C11 C12 W NW λmaxCI RI CR
C10 1 1/3 5 0.84 0.28
C11 3 1 7 1.92 0.64 3.09 0.045 0.58 0.077
C12 1/5 1/7 1 0.21 0.07

Weight analysis R4—C13 to C16 judgment matrix

R4 C13 C14 C15 C16 W NW λmax CI RI CR
C13 1 2 1 3 1.33 0.33
C14 1/2 1 3 2 1.09 0.27 4.15 0.05 0.9 0.05
C15 1 1/3 1 5 1.02 0.25
C16 1/3 1/2 1/5 1 0.38 0.09

Weight analysis R5—C17 to C21 judgment matrix

R5 C17 C18 C19 C20 C21 W NW λmax CI RI CR
C17 1 2 3 4 5 2.39 0.55
C18 1/2 1 2 1 2 0.92 0.17
C19 1/3 1/2 1 2 3 0.82 0.15 5.428 0.105 1.12 0.09
C20 1/4 1 1/2 1 3 0.69 0.13
C21 1/5 1/2 1 1/3 1 0.42 0.08

7. To make suggestions for resources and economic planning.

6 Plan of Work

1. Identification of resources and their activity in the department attached.

470 G. Marik

Weight analysis R6—C22 to C26 judgment matrix

R6 C22 C23 C24 C25 C26 W NW λmax CI RI CR
C22 1 2 4 3 3 1.98 0.39
C23 1/2 1 1 2 4 1.12 0.22
C24 1/4 1 1 3 1 0.85 0.17 5.24 0.06 1.12 0.05
C25 1/3 1/2 1/3 1 2 0.59 0.11
C26 1/3 1/4 1 1/2 1 0.46 0.09

Weight analysis R7—C27 to C31 judgment matrix

R7 C27 C28 C29 C30 C31 W NW λmax CI RI CR
C27 1 3 2 4 2 1.85 0.37
C28 1/3 1 3 2 3 1.22 0.24
C29 1/2 1/3 1 2 3 0.92 0.18 5.42 0.105 1.12 0.09
C30 1/4 1/2 1/2 1 2 0.63 0.12
C31 1/2 1/3 1/3 1/2 1 0.44 0.08

2. Identification of the particular units requires modernization with the scope of

work.
3. The specification of the kind of the information sought concerning with the
comfort of passengers.
4. Collection of relevant data from different department and shops.
5. Delineation of the environment in which the data will be collected.
6. Analysis of the data available in order to summaries the result.
7. Interpretation of the results.
8. Drawing suggestions for implementation.

7 Conclusion

The result shows that Skilled Manpower (32%), Availability of Material (21%) and
Machine (16%) are the three vital factors for the Safety and Comfort of passengers.
The weight Analysis shows that infrastructure development (12%) is also a vital
factor as the Railways is keenly need of proper infrastructure. Again, from expert
point of view, adaptation of New and Modern technology is a crucial in the present
age without which total development of Railway system is impossible. It is also
experienced that implementation of new technology is very difficult. Till date the
Railway people is keen to stick to previous technology and for transferring them to
adopt the new technology, proper infrastructure and training is required. Moreover
it is practical, due to vastness of Railway system it is not so easy job to implement
the same technology to all the Workshops, Divisions and production Unit because
before completion of one technology or modification another new one is came into
being.
Analysis of Resources for the Safety and Comfort … 471

References

1. Magazine—“ Indian Railways”—published by Shri Prasant Kr. Pattanaik, on behalf of Ministry

of Railway (Rail Board), Rail Bhawan, New Delhi, Monthly issue—Oct. 2013, on “Integral
Coach Factory”, pp. 53–65 (2013)
2. Special Message of Railway Minister on the present statistics of Indian Railways on 9 Jan 2017
3. Magazine—“Indian Management”—published by All India Management Association, New Del-
hi—special issue on Indian Railway, pp. 18–28, 2015
4. C.L. Hwang, K.P. Yoon, Multiple Attribute Decision Making: An Introduction (Sage University
Paper Series on Quantitative Application in Social Science, 1995), pp. 7–104
5. Dr. B. Nag, Operation Research Applications in Railways
6. K.D. Goepel, Implementing the analytical hierarchy process as a standard method for multi-
criteria decision making in corporate enterprises, in International Symposium on Analytic Hier-
archy Process, Conference 2013, Kuala Lumpur, Malaysia, pp. 4–8 (2013)
Electrocardiogram Signal Analysis
for Diagnosis of Congestive Heart Failure

Santanu Chattopadhyay, Gautam Sarkar and Arabinda Das

1 Introduction

Congestive heart failure (CHF) has become very common type of disease observed
among infant to old persons. It is a chronic progressive condition and affects the
pumping power of muscles of heart. It refers to the situation when fluid builds up
around the heart causing the pump inefficiently. Most common types of CHF is
Left-sided CHF when left ventricle doesn’t properly pump blood out to body and
as a result fluid can build up in lungs, causing breathing difficult. Left-sided CHF
is divided into two categories: Systolic heart failure and Diastolic failure. Causes of
CHF are mainly hypertension, Coronary artery disease, Bad Valve conditions, other
conditions like diabetes, thyroid disease, and obesity, etc. First stage symptoms of
CHF are fatigue, swelling, weight gain, increased need for urinate. Second stage
symptoms of CHF are irregular heartbeat, cough developing from lungs, wheezing,
shortness of breath, etc. last stage or severe symptoms of CHF are chest pain in upper
body, rapid breathing, blue skin, fainting, etc. it may be noted that Chest pain radiating
through upper body may be an indication of a heart attack. For heart failure in children
and infants, symptoms are poor feeding, excessive sweating, difficulty breathing, etc.
CHF diagnosis is normally done by electrocardiogram, echocardiogram, MRI, Stress
tests, Blood tests, Cardiac catheterization.
CHF patients require utmost care and demands early diagnosis. Research is going
on to study the main cause of CHF, its effect and different methods for its diagnosis

S. Chattopadhyay (B) · G. Sarkar · A. Das

Jadavpur University, Kolkata, India
e-mail: sansur12ct@yahoo.com
G. Sarkar
e-mail: sgautam63@gmail.com
A. Das
e-mail: adas_ee_ju@yahoo.com

© Springer Nature Switzerland AG 2019 473

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_39
474 S. Chattopadhyay et al.

[1–3]. Classification of different heart diseases has been done in [1]. Effectiveness
of electrocardiogram in diagnosis of heart diseases have been found effective in
[4–7]. Different monitoring scheme have been introduced for monitoring of electro-
cardiogram [8–12]. Time domain analysis and wavelet transform have been used for
assessment of electrocardiogram in [13, 14].
In some recent work DWT based statistical parameters have been found in charac-
terization for non-stationary signals and diagnosis of various diseases [15, 16]. How-
ever, very few works have been found which apply DWT based statistical parameter
for CHF diagnosis. This has motivated authors to classify ECG signals based on
DWT based statistical parameter to extract specific features for diagnosis of CHF.

2 DATA Collection

ECG signals of normal healthy person and patients suffering from congestive
heart failure have been collected from well-established data bank of phisionet.com.
Collected data are passed through Savizky–Goalay numerical filter for denoising.
Denoised data of normal healthy person and CHF patients have been used for further
assessment. De-noised ECG signal of normal healthy person and CHF patient have
been shown in Fig. 1.

ECG signal of CHF patient after 15th level of denoising

1

0.8

0.6

0.4
Voltage in mv

0.2

-0.2

-0.4

-0.6

-0.8
0 500 1000 1500 2000 2500
Time in m sec

Fig. 1 De-noised ECG signal of CHF patient

Electrocardiogram Signal Analysis for Diagnosis … 475

3 Radar Comparison of ECG Signals

At first radars of de-noised ECG signals collected from normal person and patients
suffering from congestive heart failure have been shown in following Figs. 2 and 3
respectively.
The radars of de-noised ECG signals of normal person and CHF patients as shown
in Figs. 2 and 3 are different in shape and as well as in area. Thus to make visual
inspection radar observation may be better than observation of ECG signals itself

1
486
481
476 496
4911 6 11162126
471
466
461 3136
41
456
451 46
51
446
441 56
61
436 0.5 66
431
426 71
76
421
416 81
86
411 0 91
406 96
401 101
396 -0.5 106
391 111
386 116
381 121
376 -1 126 Series1
371 131
366 136
361 141
356 146
351 151
346 156
341 161
336
331 166
171
326
321 176
181
316
311 186
191
306
301 196
201
296
291 206
211
286
281
276 216
221
226
271
266
261
256 246 231
236
241
251

Fig. 2 Radar of ECG signal of normal healthy person

RADAR OF ECG OF CHF PATIENT

1
2501 26
2476
2451
2426
2401
2376 1.5 51
76
101
126
2351
2326
2301 151
176
201
2276
2251 226
251
2226
2201 1 276
301
2176
2151 326
351
2126
2101 0.5 376
401
2076
2051 426
451
2026 0 476
2001 501
526
1976
1951 -0.5 551
1926 576
601
1901
1876 626
1851 -1 651
1826 676
701
1801
1776 726
1751
1726 751
776
1701
1676 801
826
1651
1626 851
876
1601
1576 901
926
1551
1526 951
976
1501
1476 1001
1026
1451
1426
1401 1051
1076
1101
1376
1351
1326
1301 1126
1151
1176
1201
1226
1276 1251

Fig. 3 Radar of ECG signal of CHF patient

476 S. Chattopadhyay et al.

which is normal practice in diagnosis as because radars (i.e. polar plot) of ECG
signals are taking less area in the two dimensional frame of reference. However
more information is available in the area and critical shape of the radars which are
difficult to be noted in visual inspection.

4 Discrete Wavelet Transformation of ECG Signals

As ECG signals are non-stationary periodic and are collected through digital instru-
ment, Discrete Wavelet Transform(DWT) based assessment have been performed
to overcome the limitation of comparison of radars made from ECG signals as pre-
sented in previous section. Wavelet Decomposition has been performed on ECG
signals for both normal person and CHF patients. In wavelet decomposition, ‘db4’
has been used as mother wavelet and decomposition is performed up to level 9. At
each decomposition level, approximate coefficients have been calculated. To observe
the variation of large number of approximate coefficient, there skewness feature have
been extracted for large number of approximate coefficient single skewness value
(SA) have been obtained. Thus for 9 decomposition level 9 number of SA have been
obtained. Sets of 9 SA values have been obtained both for normal person and CHF
patients presented in Table 1. SA versus DWT levels for normal person and CHF
patients have been shown Fig. 4. The figure shows significant change of SA versus
DWT level nature for congestive heart failure. SA in both cases remains constant up
to level 3 and then start decreasing in irregular way. Up to DWT level 3 and at | DWT
level 9, SA for CHF patient is higher than that of normal person.

Table 1 Skewness of approximate coefficients of the ECG signal at different DWT level of CHF
patient
DWT level SA of normal healthy person SA of CHF patient
1 0.854003 2.09009
2 0.854079 2.081993
3 0.859776 2.072368
4 1.412921 1.811709
5 1.001586 1.117819
6 0.276683 0.2094
7 0.368491 −0.17752
8 −0.07648 0.158719
9 −0.7627 0.087164
Electrocardiogram Signal Analysis for Diagnosis … 477

SA versus DWT Level

2.5

1.5

1 SA of normal healthy
person
SA

0.5
SA of CHF patient
0
1 2 3 4 5 6 7 8 9
-0.5

-1
DWT Level

Fig. 4 SA versus DWT levels for normal person and CHF patient

1
2.5
9 2 2
1.5
1
0.5
0 SA of normal healthy
8 -0.5 3
person
-1
SA of CHF patient

7 4

6 5

Fig. 5 Radars of SA for normal person and CHF patient

5 Comparison of Radar of SA

Radars of SA both for normal person and CHF patient have been made as shown in
Fig. 5. These radars are different in shape and area. The difference was also observed
in Sect. 3, but here it is easy to distinguish radar of SA of CHF patients from that of
normal patients. Area of radar of SA decreases for CHF.

6 Histogram Assessment of SA

Histogram of skewness of DWT based approximate coefficients (SA) are analyzed

both for normal person and CHF patient as shown in Figs. 6 and 7 respectively.
478 S. Chattopadhyay et al.

4.5

3.5

2.5

1.5

0.5

0
-1 -0.5 0 0.5 1 1.5 2

Fig. 6 Histogram of SA of normal healthy person

Fig. 7 Histogram of SA of normal CHF patients

Minimum value of the histogram changes due to CHF. Minimum value of histogram
increases due to such disease and peak values remains almost same as that of normal
person.

7 Conclusion

In this work diagnosis of congestive heart failure with the help of wavelet decompo-
sition based approximate coefficients. These coefficients have been determined from
Electrocardiogram Signal Analysis for Diagnosis … 479

ECG signals both for normal person and patients suffering from congestive heart
failure (CHF). Skewness property of approximate coefficients has been determined
at different decomposition levels and comparative study has been carried out on SA
for healthy person and CHF patient. Radars and histograms have also been made and
compared. Significant difference has been observed which helps to easily distinguish
ECG signals having CHF. The proposed method may be effective for diagnosis such
disease.

References

1. S Mitra, M. Mitra, S Chattopadhyay, S Sengupta, An approach to a rough set decision system for
classification of different heart diseases, MS-04, Lyon, France, 5–9 July, 2005, pp. 1.17–1.20
2. M. Al-Abed, M. Manry, J.R. Burk, E.A. Lucas, K. Behbehani, A method to detect obstruc-
tive sleep apnea using neural network classification of time-frequency plots of the heart rate
variability, in 29th Annual International Conference of the IEEE Engineering in Medicine and
Biology Society, 2007, pp. 6101–6104. https://doi.org/10.1109/IEMBS.2007.4353741
3. O. Karadeniz, A. Yilmaz, T. Dundar, Design of portable holter recorder with MMC memory
for prephase sleepapnea diagnosis, in 14th National Biomedical Engineering Meeting, 2009.
BIYOMUT, 2009, pp. 1–4. https://doi.org/10.1109/BIYOMUT.2009.5130337
4. M.O. Mendez, A.M. Bianchi, M. Matteucci, S. Cerutti, T. Penzel, Sleep apnea screen-
ing by autoregressive models from a single ECG lead. IEEE Trans. Biomed. Eng. 56(12),
pp. 2838–2850 (2009). https://doi.org/10.1109/TBME.2009.2029563
5. D. Alvarez, R. Hornero, J.V. Marcos, F. del Campo, Multivariate analysis of blood oxygen
saturation recordings in obstructive sleep apnea diagnosis. IEEE Trans. Biomed. Eng. 57(12),
2816–2824 (2010). https://doi.org/10.1109/TBME.2010.2056924
6. A. Burgos, A. Goni, A. Illarramendi, J. Bermudez, Real-time detection of apneas on a PDA.
IEEE Trans. Inf. Technol. Biomed. 14(4), 995–1002 (2010). https://doi.org/10.1109/TITB.
2009.2034975
7. N.J.B.N. Mazlan, K.I. Wong, A wireless ECG sensor and a low-complexity screening algorithm
for obstructive sleep apnea detection, in 2012 IEEE EMBS Conference on Biomedical Engi-
neering and Sciences (IECBES), 2012, pp. 279–283. https://doi.org/10.1109/IECBES.2012.
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8. H. Guruler, M. Sahin, G. Ordek, A. Ferikoglu Sakarya, Sleep apnea diagnosis via single channel
ECG feature selection, in 38th Annual Northeast Bioengineering Conference (NEBEC), 2012,
pp. 159–160. https://doi.org/10.1109/NEBC.2012.6207012
9. C.-W. Wang, A. Hunter, N. Gravill, S. Matusiewicz, Unconstrained video monitoring of breath-
ing behavior and application to diagnosis of sleep apnea. IEEE Trans. Biomed. Eng. 61(2),
396–404 (2014). https://doi.org/10.1109/TBME.2013.2280132
10. S.H. Hwang, H.J. Lee, H.N. Yoon, D.W. Jung, Y.J.G. Lee, Y.J. Lee, D.-U. Jeong, K.S. Park,
Unconstrained sleep apnea monitoring using polyvinylidene fluoride film-based sensor. IEEE
Trans. Biomed. Eng. 61(7), 2125–2134 (2014). https://doi.org/10.1109/TBME.2014.2314452
11. L. Chen, X. Zhang, C. Song, An automatic screening approach for obstructive sleep apnea diag-
nosis based on single-lead electrocardiogram. IEEE Trans. Autom. Sci. Eng. 12(1), 106–115
(2015). https://doi.org/10.1109/TASE.2014.2345667
12. A. Jezzini, M. Ayache, L. Elkhansa, Z. al abidin Ibrahim, ECG classification for sleep
apnea detection, in 2015 International Conference on Advances in Biomedical Engineering
(ICABME), 2015, pp. 301–304. https://doi.org/10.1109/ICABME.2015.7323312
13. A.R. Hassan, M.A. Haque, Computer-aided sleep apnea diagnosis from single-lead electro-
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cessing and autonomous scoring capability. IEEE Trans. Biomed. Circ. Syst. 9(1), pp. 96–104
(2015). https://doi.org/10.1109/TBCAS.2014.2314301
15. S. Chattopadhyay, R.R. Majhi, S. Chattopadhyay, A. Ghosh, Analysis of electro-cardiogram
by radar and DWT based Kurtosis comparison, in Michael Faraday IET International Summit
2015, p. 108 (5). https://doi.org/10.1049/cp.2015.1704, ISBN: 978-1-78561-186-5, Kolkata,
India, Conference date: 12–13 Sept 2015
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decomposition based skewness of ECG signals, in Michael Faraday IET International Summit
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India, Conference date: 12–13 Sept 2015
Condition Assessment of Structure
Through Non Destructive
Testing—A Case Study on Two Identical
Buildings of Different Age

Bhaskar Chandrakar, M. K. Gupta and N. P. Dewangan

1 Introduction

1.1 Conditional Assessment

Conditional assessment of any structure is must to check its suitability for the purpose
which it serves. This is done of both old and new structures for new structure it is
performed to check the quality of the work carried out by the contactor. The old
buildings are assessed to know the remaining life [1] or to repair the structure. Mainly
the old, weird, partially damaged, abandoned structure need conditional assessment
to check weather that is it still serviceable and if so then for how long or if not
then can it be retrofitted and made safe for the desired purpose. Also the conditional
assessment is performed when the structure has to be expanded i.e. more number
of floors are to be constructed on the existing old structure. Thus it becomes very
important to assess the condition [2] of the structure. Concrete is mainly tested to
assess the condition of a structure since it all depends on the properties of the concrete.

B. Chandrakar (B)
Department of Civil Engineering, Chhattisgarh Swami Vivekanand Technical University,
Bhilai, Chhattisgarh, India
e-mail: chandrakar_bhaskar@yahoo.com
M. K. Gupta
Department of Civil Engineering, BIT Durg, Durg, Chhattisgarh, India
N. P. Dewangan
Department of Civil Engineering, Sarguja University, Ambikapur, Chhattisgarh, India
e-mail: npdewangan@gmail.com

© Springer Nature Switzerland AG 2019 481

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_40
482 B. Chandrakar et al.

1.2 Non Destructive Testing on Concrete

NDT is gaining popularity for testing concrete with a swift pace since these are mostly
convenient to perform; these tests are insitu so actual concrete can be tested in its
existing condition. Non-destructive testing methods [3] are being used for about four
decades ago. They are now considered a powerful tool for evaluating existing concrete
structures with regard to their strength and durability [4] apart from assessment and
control of quality of hardened concrete. In certain cases the investigation of crack
depth, micro cracks [5] and progressive deterioration are also studied by this method.
NDT methods are relatively simple to perform but the analysis and interpretation of
the test results is not easy.

2 Experimental Work

An extensive survey was carried out to find the suitable structure for the testing
and evaluation, the task was to find out a RCC structure on which both [6] Rebound
Hammer and Ultrasonic Pulse Velocity Test [7] can be carried out. Finally Residential
building at Tatibandh Raipur was selected to perform the testing.
After all the necessary arrangements for carrying out the NDT such as method of
testing was finalized, instruments for the tests were selected and arranged, site was
also selected, the experiment had to be commenced, before that a visual inspection
was needed.

2.1 Visual Inspection

Visual inspection was the first step in the conditional assessment, both the buildings
were carefully observed and found that the old building whose column, beam and
slab was constructed seven years ago and then left abandoned developed cracks in
both micro and macro forms, reinforcement bars were also seen at some parts.
The new building is under construction on its sixth floor and no signs of physical
damage appeared on any of the surfaces, it gave the same appearance of the fresh
constructed building with smooth surfaces, sharp edges etc. After the thorough visual
inspection outline for performing the test was planned.
Condition Assessment of Structure through Non Destructive … 483

2.2 Specifications of the Instruments Used

2.2.1 Silver Schmidt Digital Rebound Hammer

The Rebound Hammer Test was performed by the Silver Schmidt Digital Rebound
Hammer manufactured by Proceq from Switzerland. The Hammerlink software com-
patible with the operating system of the computer gives the result in the form of bar
chart when the digital Silver Schmidt Rebound Hammer is connected with the com-
puter which has Hammerlink software installed in it (Figs. 1, 2 and 3).

2.2.2 Concrete Ultrasonic Testing Equipment

Ultrasonic Velocity Test was performed by the Concrete Ultrasonic testing equipment
manufactured by Canopus Instruments.
Concrete Ultrasonic testing equipment displays the time taken by the pulse to
travel from the pulse sending probe to the pulse receiving probe. The time is displayed
on the screen of the equipment in micro seconds which is used to calculate the velocity
of the pulse by dividing it with the distance travelled by the pulse between sending
and the receiving probe.

Fig. 1 This curve was used to interpret the strength from corresponding rebound coefficient
484 B. Chandrakar et al.

Fig. 2 Digital silver schmidt rebound hammer being calibrated on the standard Anvil

Fig. 3 Ultrasonic pulse velocity meter being calibrated before testing

2.3 Setting Out for the Tests

The bottom three floors of the building were decided to be tested; the old building
had only three floors it was not possible to go higher.
Condition Assessment of Structure through Non Destructive … 485

48 Columns, 24 Beams and 6 Slabs to be tested were marked on both the old and
new building, thus each building was to be tested for 24 column, 12 beams and 3
slabs.
After the selection of points of application for the testing instruments, it was time
to test the marked parts for their strength and quality.

2.3.1 Steps Followed in Performing the Tests

(a) The gridlines were marked on the surface of columns, beams and slabs. Grids
of 300 mm X 300 mm were marked on surface of column and slabs, 250 mm X
250 mm grids were marked on the surface of beams.
(b) Surface preparation was done by rubbing and smoothing the surface at the
junction points of the grids.
(c) Grease was applied on the junction points of the grids.
(d) The Ultrasonic pulse velocity apparatus was connected to its probes, battery and
the complete set up was made ready for the test.
(e) Before starting the test, instrument has to be calibrated this is done on a standard
mild steel bar by cross probing on its ends and then calibrating the reading to
23.7 micro seconds.
(f) On successful calibration of the instrument the tests were performed on the
required points that were already marked and prepared for the test.
(g) Readings were recorded by cross probing and surface probing methods depend-
ing on the accessibility of the faces of the structural members.
(h) Readings of the Ultrasonic pulse velocity test was recorded in micro seconds
the value of which was displayed on the screen of the instrument.
(i) Silver Schmidt Digital Rebound hammer test was followed by the ultrasonic
pulse velocity test at the same points and the readings were recorded.
(j) Readings of the Rebound Hammer test was displayed on the screen of the digital
Rebound hammer which are known as rebound coefficients Q.

Performing both the tests on number of points on both the buildings was a
hectic process and it took a long period for the completion of the test since
around 2200 hundred points were tested in total, also weather not at all times
favoured the suitability for the test conditions, other constraints also some-
times opposite, but ultimately the Non Destructive Testing of both the buildings
completed (Figs. 4, 5, 6, 7, 8 and 9).
486 B. Chandrakar et al.

Fig. 4 Internal view of the old building to be tested

Fig. 5 Gridlines marked on the surface of column

Condition Assessment of Structure through Non Destructive … 487

Fig. 6 Slab surface prepared for the ultrasonic test

Fig. 7 Direct or cross probing method i.e. on the opposite faces of column
488 B. Chandrakar et al.

Fig. 8 Reading displayed while performing the test

Fig. 9 Silver schmidt digital rebound hammer used on the column

Condition Assessment of Structure through Non Destructive … 489

3 Results

The results tabulated here is the average of 2200 readings for each type of the test
performed.

Comparison of cumulative result of rebound hammer test

Old building New building
S. no. Member Actual initial Present Decreased Present
design strength Mpa strength Mpa strength Mpa
strength Mpa
1 Column 30 28.87 1.13 33.88
2 Beam 30 26.82 3.18 33.9
3 Slab 25 23.48 1.52 26.68

Comparison of cumulative result of ultrasonic pulse velocity test

Old building New building
Sl. no. Member Actual initial Present quality of Present quality of
designed quality concrete concrete
of concrete
1 Column Good Medium Good
2 Beam Good Medium Good
3 Slab Good Medium Good
490 B. Chandrakar et al.

Quality of Concrete Medium 3

Good 6
Good Good Good
6
5

Medium

Medium

Medium
4
3
2
1
0
Member Column Beam Slab
Old Building 3 3 3
New Building 6 6 6

Overall comparison
Old building New building
S.no. Member Strength Mpa Quality of Strength Mpa Quality of
concrete concrete
1 Column 28.87 Medium 33.88 Good
2 Beam 26.82 Medium 33.9 Good
3 Slab 23.48 Medium 26.68 Good

40
Qualityof concrete Medium 10 & Good 20

33.88 33.9
35
28.87
30 26.82 26.68
23.48
Good

Good

Good

25
Strength MPa

20
Medium

Medium

Medium

15
10
5
0
Column Column Beam Beam Slab Slab
Member Strength Quality Strength Quality Strength Quality
Old Building 28.87 10 26.82 10 23.48 10
New Building 33.88 20 33.9 20 26.68 20

4 Discussion

The test results presented in the form of tables and charts give a clear idea of the
strength [8] and quality of the concrete in the different structural parts (column, beam
and slab) of both the buildings.
Condition Assessment of Structure through Non Destructive … 491

The result shows that there is a difference in terms of strength and quality in
the old and new building and also among different structural members of the same
building.
The old building shows a decrement [9] in its strength and quality while the new
one has better strength and quality than its initial design grades. Since the initial
design and drawing of the building was available for reference it became easier to
analyze and compare the changes in the strength and quality of the buildings.
The result of the methods adopted for the test of the buildings are influenced by
many factors which were taken good care off so those may not affect the test results.
For example moisture content influences the readings of the Ultrasonic pulse velocity
test to a large extent hence the tests were not performed during the rains and moist
weather conditions.
For the most efficient results of the Ultrasonic pulse velocity test direct or cross
probing method of test must be adopted but due to inaccessibility of the opposite
faces in some of the cases surface probing was used and the necessary corrections
has been applied.
As far as possible point of application was kept same for both the tests so that
comparison of the results could be justified. The same structural members were tested
on both the buildings and in the same conditions to make a fair comparison between
the old and the new building.

5 Conclusion

• The result concludes a reduction of 6.81% in the strength and decrement of good
to medium in the quality of concrete in the old building that was built seven years
ago shows that the concrete loses its quality and strength with time.
• Carbonation due environmental effects on the bare surfaces for very long since
neither plaster nor paints were applied to protect the concrete in extreme environ-
mental conditions and internal chemical reactions in the concrete the reduction
in the grade and quality of concrete although initially the strength might have
increased when hydration would have been taking place.
• Since the strength is not considerably reduced but the quality of the concrete is
decreased from good to medium which is a matter of concern. This also leads to
conclude that the decrease in the strength is actually due to the loss of quality.
• As a result of cracking and various chemical reactions occurring internally in
concrete due to its chemical composition and external environmental conditions
the concrete became porous and the density reduced lead to decrease in the quality
ultimately showing loss of strength.
• The building is located in vicinity of the most polluted areas and the building
is affected this concludes that environmental effects are considerable during and
after the construction.
• The overall strength of the new building was found 10.3% more than the initial
design strength which concludes that the concrete might be still hydrating and
492 B. Chandrakar et al.

hence its strength is increasing since the building started construction last year
and is yet under construction.
• The quality of concrete is also found to be good which concludes that the density
of concrete is intact and the concrete has a good bond with all the reinforcement
bars and its components.
• Finally this can be concluded that the new building is better than the old one in
all respects, since the strength and quality of the old building has decreased from
its initial value whereas the strength of new building is greater than its design
strength.
• The comparison among different structural members of the old building shows that
the flexural member. Beam lost its strength by 10.6% as compared to 3.76% loss
in strength by the columns, axial stress bearers where as the slabs loss in strength
is 6.08% which is intermediate to axial and flexural losses in their respective
members. Hence it can be concluded that flexural members are subjected to more
stresses and lose their strength faster than the other structural members which is
often observed in most of the practical cases when the failure of the beams in the
structure first of all shows the sign of failure.
• The owner wanted to extend more number of floors in the old building, so it
is advisable that before commencing the expansion repairing through grouting or
other methods must done strictly followed by other tests again to check the strength
and condition after repairing.
• This concludes that the old building can be expanded of more floors but only after
retrofitting the building.
• The importance and need for condition assessment of structures for evaluating
their serviceability and safety have been highlighted in this piece of work.
• It can be seen that detailed visual inspection and Non Destructive Testing (NDT)
plays an important role in condition assessment of existing buildings.
• An overview of the procedures and different investigations including tests involved
in condition assessment and evaluation of safety is presented in a simple.

Concluding Remark
It may be emphasized here that a great deal of expertise is required for interpretation
of field observations and non destructive testing results to make a proper assessment
of the condition as well as for analyzing and evaluating condition of the structure.
Although utmost care and every possible aspect has been considered and sincerely
followed to come out with the conclusion but still the results of this work may not
be considered standard or its not necessary that all structures follow the same trend.

6 Further Scope of Work

Based on the results of this work retrofitting methods for the old building could be
suggested so that the building can be made suitable for extending the construction
of more number of floors above the existing top floor.
Condition Assessment of Structure through Non Destructive … 493

After suggesting suitable methods of retrofitting when the building is repaired it

can be tested again with suitable methods for its condition assessment.
Also in the present situation further investigation and testing of the building can
be performed by some partial destructive methods and compare with the result of
this work.

References

1. P. Shaw, A. Xu, Assessment of the deterioration of concrete in NPP- causes, effects and inves-
tigation methods. NDT.Net 3(2) (1998)
2. N.V. Mahure, G.K. Vijh, P. Sharma, N. Sivakumar, Correlation between pulse velocity and
compressive strength of concrete. Int. J. Earth Sci. Eng. 4(6), 871–874 (2011)
3. S. Baby, T. Balasubramanian, R.J. Pardikar, M. Palaniappan, R. Subbaratnam, Time-of-
flight diffraction (TOFD) technique for accurate sizingof surface-breaking cracks. Insight 45,
426–430 (2003)
4. S.K. Verma, S.S. Bhadauria, S. Akhtar, Review of nondestructive testing methods for condition
monitoring of concrete structures. J. Constr. Eng. 2013, 1–11 (2013)
5. F. Nucera, R. Pucinotti, Destructive and non-destructive testing on reinforced concrete structure:
the case study of the museum of Magna Graecia in Reggio Calabria (2009). https://www.ndt.
net/article/defektoskopie2009/papers/Nucera-and-Pucinotti-8.pdf. Accessed 20 March 2014
6. S.S. Bhadauria, M. Chandra Gupta, In situ performance testing of deteriorating water tanks for
durability assessment. J Perform. Constr. Fac. 21(3), 234–239 (2007)
7. G. Pascale, A. Di Leo, V. Bonora, Nondestructive assessment of the actual compressive strength
of high-strength concrete. J. Mater. Civil Eng. 15(5), 452–459 (2003)
8. Y. Yoshida, H. Irie, in NDT for concrete using the ultrasonic method. Proceedings of the 12th
Asia Pacific Conference of Non Destructive Testing (A-PCNDT ‘06), Auckland, New Zealand
(2006)
9. D. Breysse, G. Klysz, X. Dérobert, C. Sirieix, J.F. Lataste, How to combine several non-
destructive techniques for a better assessment of concrete structures. Cem. Concr. Res. 38(6),
783–793 (2008)
10. M.V. Felice, A. Velichko, P.D. Wilcox, Accurate depth measurement of small surface-breaking
cracks using an ultrasonic array post-processing technique. Ndt & E Int. 68, 105–112 (2014)
A Real Time Health Monitoring
and Human Tracking System Using
Arduino

P. L. Lekshmy Lal, Arjun Uday, V. J. Abhijith

and Parvathy R. L. Nair

1 Introduction

This project aims at health monitoring and human tracking in real time basis. Health
monitoring system consists of a pulse rate and body temperature sensor. The sys-
tem consists of a microcontroller based heart rate and body temperature measuring
devices along with LCD output. A threshold value range will be set for heart rate
and temperature. When the set threshold condition is violated, the device sends an
alarm message. The threshold value is decided by the programmer. It can be amended
whenever necessary. The information is transferred to the appropriate person wire-
lessly. A heart patient should be monitored continuously. But being at a hospital for
rest of the life after a heart disease is detected is not practical option. Thus, the system
can be used by the patients outside the hospital and their location can be traced in
real time.
Soldiers fight in the most difficult of terrains for his country and people. By this
project the system will be useful for providing health status and medical help for the
needy soldiers in the battle field. The system tracks the health by focusing on soldier’s
heart beat and temperature [1]. If an alarming situation occurs, there will be change
in the heart beat patterns and thus a message will be sent along with the location of

P. L. Lekshmy Lal (B) · A. Uday · V. J. Abhijith · P. R. L. Nair

ECE Department, Rajadhani Institiute of Engineering and Technology, Nagaroor,
Trivandrum, Kerala, India
e-mail: lekshmylalpl@gmail.com
A. Uday
e-mail: arjunuday123@gmail.com
V. J. Abhijith
e-mail: abhijithvj@gmail.com
P. R. L. Nair
e-mail: parvathyrlnair@gmail.com

© Springer Nature Switzerland AG 2019 495

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_41
496 P. L. Lekshmy Lal

Fig. 1 Block diagram of the system

the soldier to the base camp for necessary help. The system is also equipped with
a distress switch [2]. When the soldiers press this switch, a distress message will
be sent to the base station or to the concerned ones [3]. ECG waveform can also be
viewed from this device.

2 System Description

Block diagram of the system is shown in Fig. 1. The Arduino mega 2560 is the
heart of the system through which the input output communications to the system is
carried out. The 16 × 2 LCD acts as the output display device. GSM module is used
for the sending and reception of messages and the GPS module is used for the 24 ×
7 tracking of the user position with reference to latitudes and longitudes. The health
sensors are used for the heart beat and temperature monitoring. The hex keypad is
used as the input device. Micro SD module is used as the data storage system.

3 Flow Chart Description

This project has two sections, Transmitter and Receiver section.

A Real Time Health Monitoring and Human Tracking System … 497

Fig. 2 Flow chart of transmitter section

3.1 Transmitter Section

Flow chart of the transmitter section is shown in Fig. 2. When the transmitter section
is initialized, the system starts monitoring the health parameters. The health details
will be sent to the reception unit. If an emergency press or a health problem is
detected, reception unit will be informed to send reply message.

3.2 Receiver Section

The flow chart of the receiver section is shown in Fig. 3. The module gets initialized
and the input details like mobile number and threshold temperature is given. Then
the data will be received from the transmitter. If an emergency press at transmitter
section or an SMS “BTRACK” is received or a health problem is detected, an SMS
consisting of health details and location will be sent to the registered mobile number
and it will be saved to an SD card module. If an SMS “STRACK” is received, the
data will stop to get saved in the SD card module.
498 P. L. Lekshmy Lal

Fig. 3 Flow chart receiver section

4 Result

Figure 4 shows the hardware model of the project. Arduino Uno is the heart of the
transmitter. LCD is the component that displays the output information like heart beat
and temperature. The module consists of the heart beat sensor and the temperature
sensor. The readings like heart beat and temperature can be transmitted at the same
time. Arduino Mega 2560 is the core of receiver section. Hex keypad is provided
to input the threshold values of heart beat and temperature and to register a mobile
number. SD card stores the data pertaining to the health and the location. While a
message “BTRACK” is sent to the receiver, the data regarding the health status and
location will be sent to the registered mobile number and the server will get uploaded
with the values. When a message “STRACK” is received, the data will stop getting
saved to the SD card and the updation to the server will end. If an emergency press or
the threshold values gets cut, then the receiver will sent a message to the registered
mobile number with the health details and location automatically.
A Real Time Health Monitoring and Human Tracking System … 499

Fig. 4 Hardware model of transmitter section and receiver section

Fig. 5 Screen shot of the message exchanged by the system

Figure 5 shows the screen shot of the message exchanged by the system. When
a message B TRACK is sent from the registered mobile number, first the system
checks whether it is from a valid user. Once the message received is identified as
that from a valid user, the system finds out the health parameters and the location
and sends SMS to the valid number. When a message “STRACK” is sent from the
registered user the message will not be sent. By using Google Map the location of
the patient could be determined, and appeared in the SMS.
Figure 6 shows the screenshot of the health details being uploaded to the server.
Server shows the last updated time and the heart beat chart and temperature chart by
which the person is constantly monitored.

5 Conclusion

The health monitoring and human tracking system aims at bringing out a multi
application system which is useful for the public as well as soldiers. The project is
expected to provide with the functionality of locating a person and tracking him at the
500 P. L. Lekshmy Lal

Fig. 6 Screen shot of the data exchanged by the system

same time, it gives a detailed insight on his current health condition. It is aimed that
a second person related to the user will be able to monitor the user‘s location as well
as health condition. The project aims at designing a low cost as well as low power
system so that it can be used by the public. The project aims at running using a very
simplified program so that only very little EPROM memory of the microcontroller
is used; this in turn will increase the life and reliability of the system. The project
is also expected to produce a system that can be used by aged people so that their
health and location can be monitored by their near ones.

References

1. S. Atalla, K. Aziz, S. Tarapiah, S. H. Ismail, Smart real-time healthcare monitoring and tracking
system using GSM/GPS technologies, in 2016 3rd MEC International Conference on Big Data
and Smart City (ICBDSC), vol 142, No 14 (2016), pp. 19–26
2. K. Aziz, S. Tarapiah, M. Alsaedi, S.H. Is-mail, Shadi Atalla, Wireless sensor networks for road
traffic monitoring. Int. J. Adv. Comput. Sci. Appl. 1(6), 265–270 (2015)
3. C. Karthick, S. Idrissyedismail, E. Arunkailasam, S. Dhanapal, T. Devika, A Novel Based on Sol-
dier Tracking and Health Monitoring system using Embedded Technology, in The International
Journal of Science and Technology, vol. 3, Issue 3 (2015), pp. 212–217
Study of Arrhythmia Using Wavelet
Transformation Based Statistical
Parameter Computation
of Electrocardiogram Signal

Santanu Chattopadhyay, Gautam Sarkar and Arabinda Das

1 Introduction

Electrocardiogram (ECG) signal has become an important medium for study and
diagnosis of different types of heart diseases. By nature electrocardiogram signal is
periodic but non stationary. Shapes of the ECG signals is divided into different parts
whose magnitude and duration are measured in conventional method of study [1].
However with the advancement of research, different mathematical tools have been
introduced for such signals. Rough set decision system based on ECG signal have
been introduced for classification of different heart diseases [2]. FFT and wavelet
transform based techniques have been used for analysis of electrocardiogram sig-
nals [3–5]. Dual tree complex wavelet transform have also been applied for analysis
of electrocardiogram signal [3]. Application of radar is also found in classification
of different types of heart diseases using electrocardiogram analysis [5]. Artificial
neural network is being used for classification of heart diseases [6]. Auto regres-
sive model has been introduced for analysis of ECG signals [7]. Compact method
using unidirectional loop antenna having wideband performance having introduced
for detection of heart failure [8]. Hemodynamic model using fuzzy logic has been
introduced for the detection of heart failure [9]. In wavelet decomposition method
large number of coefficient appear which some time makes the computation a little bit
difficult to overcome this limitation use of different statistical parameters instead of
using coefficients directly has become popular [10]. In this work study of arrhythmia

S. Chattopadhyay (B) · G. Sarkar · A. Das

Jadavpur University, Kolkata, India
e-mail: sansur12ct@yahoo.com
G. Sarkar
e-mail: sgautam63@gmail.com
A. Das
e-mail: adas_ee_ju@yahoo.com

© Springer Nature Switzerland AG 2019 501

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_42
502 S. Chattopadhyay et al.

Fig. 1 ECG signal of arrhythmia patient

has been carried out into wavelet transform based statistical parameter computation
of electrocardiogram signal.

2 Data Collection

From well-established data bank of phisionet.com ECG signals of normal healthy

person and patients suffering from arrhythmia have been collected. Collected signals
are denoised by numerical filter and the denoised signal of normal healthy person
and arrhythmia patients have been used for further assessment. Sample ECG signal
of arrhythmia patient has been shown in the Fig. 1.

3 Wavelet Decomposition

Denoised ECG signal are then decomposed by discrete wavelet transformation

(DWT). Both for normal and arrhythmia patient, wavelet decomposition is performed
up to DWT level 9. As the mother wavelet ‘db 4’ has been used. At each decomposi-
tion level approximate coefficient are determined and then corresponding kurtosis of
approximate coefficients (KA) are calculated. KA obtained at DWT level 1–9 both
for normal and arrhythmia have been presented in Table 1.

4 Observation

Kurtosis of approximate coefficient for normal and arrhythmia patient versus DWT
level has been plotted has shown in Fig. 2.
It shows two different line: one for normal healthy person another for arrhythmia
patient. From DWT level 1–3 KA are constant; However magnitude of KA is higher
than that of normal person. Then KA decreases up to DWT level 6 and then becomes
almost horizontal up to DWT level 8. After this again change of slope of KA is
Study of Arrhythmia using Wavelet Transformation based … 503

Table 1 Kurtosis of approximate coefficients (KA) of ECG signal at different DWT level of normal
healthy person and arrhythmia patient
DWT level Kurtosis of approximate Kurtosis of approximate
coefficients (KA) of normal coefficients (KA) of
healthy person arrhythmia patients
1 9.184569 10.14906
2 9.184136 10.15704
3 9.111071 10.14601
4 9.353461 7.792513
5 4.803909 3.812185
6 1.68599 2.577378
7 1.696927 2.876802
8 1.456951 2.954453
9 2.351525 1.687806

KA versus DWT level

12

10

0
1 2 3 4 5 6 7 8 9

Kurtosis of approximate coefficients (KA) of Normal healthy person

Kurtosis of approximate coefficients (KA) of arrhythmia patients

Fig. 2 KA versus DWT level of normal healthy person and arrhythmia patient

observed from DWT level 8–9. For better comparison radars of KA are formed both
for normal person and arrhythmia patient in same polar plane as shown Fig. 3.
It shows two different loops of different shapes. Area of radar of KA for normal
person is slightly less than that of arrhythmia patient. Thus KA analysis shows distinct
difference for normal and arrhythmia patient which may be useful for the study and
detection of arrhythmia.
504 S. Chattopadhyay et al.

Radars of KA

Kurtosis of approximate coefficients (KA) of Normal healthy person

Kurtosis of approximate coefficients (KA) of arrhythmia patients

1
15
9 2
10

5
8 3
0

7 4

6 5

Fig. 3 Radars of KA of normal healthy person and arrhythmia patient

5 Conclusion

This work presents analysis of electrocardiogram signal based on wavelet decomposi-

tion for detection of arrhythmia. Electrocardiogram signal of normal and arrhythmia
patient have been collected from normal database and denoised. After denoising
wavelet decomposition has been performed up to DWT level 9. At each level kur-
tosis has been calculated for all approximate coefficient of that particular level. KA
obtained in this way is compared. Magnitudes of KA have been found different from
DWT level 1–3. Also radars of KA corresponding to normal person and arrhythmia
patient are different in shape and area. These feature may be useful for detection of
arrhythmia and study of electrocardiogram signal of arrhythmia patient. The work
may be extended for the study of other heart diseases also.

References

1. S. Chattopadhyay, S. Chattopadhyay, A. Das, Elecctrocardiogram signal analysis for diagnosis

of Apnea. AMSE J. Series: Modell. C; Chem., Geol., Environ. Bioeng., 77(1) 28–40 (2016).
ISSN: 1259-5977
2. S. Mitra, M. Mitra, S. Chattopadhyay, S. Sengupta, An approach to a rough set decision system
for classification of different heart diseases, MS-04, Lyon, France, 5–9 July, 2005, pp. 1.17–1.20
3. A.R. Hassan, M.A. Haque, Computer-aided sleep apnea diagnosis from single-lead electro-
cardiogram using dual tree complex Wavelet Transform and spectral features. in International
Conference on Electrical & Electronic Engineering (ICEEE), (2015), pp. 49–52. https://doi.
org/10.1109/ceee.2015.7428289
Study of Arrhythmia using Wavelet Transformation based … 505

4. S. Chattopadhyay, R.R. Majhi, S. Chattopadhyay, A. Ghosh, Analysis of electro-cardiogram

by radar and DWT based Kurtosis comparison. in Michael Faraday IET International Summit
2015, (2015), p. 108 (5 .). https://doi.org/10.1049/cp.2015.1704, ISBN: 978-1-78561-186-5,
Kolkata, India, 12–13 Sept 2015
5. S. Chattopadhyay, R.R. Majhi, S. Chattopadhyay, A. Ghosh, Radar assessment of wavelet
decomposition based Skewness of ECG signals. in Michael Faraday IET International Summit
2015, (2015), p. 109 (5 .), https://doi.org/10.1049/cp.2015.1705, ISBN: 978-1-78561-186-5,
Kolkata, India, 12–13 Sept 2015
6. M. Al-Abed, M. Manry, J.R. Burk, E.A. Lucas, K. Behbehani, A Method to detect obstruc-
tive sleep apnea using neural network classification of time-frequency plots of the heart rate
variability, in 29th Annual International Conference of the IEEE Engineering in Medicine and
Biology Society, (2007), pp. 6101–6104. https://doi.org/10.1109/iembs.2007.4353741
7. M.O. Mendez, A.M. Bianchi; M. Matteucci, S. Cerutti, T. Penzel, Sleep apnea screening by
autoregressive models from a single ECG lead, in IEEE Transactions on Biomedical Engineer-
ing (2009), vol 56, Issue 12, pp. 2838–2850. https://doi.org/10.1109/tbme.2009.2029563
8. S.A. Rezaeieh, A. Zamani, K.S. Bialkowski, A.M. Abbosh, Unidirectional slot-loaded loop
antenna with wideband performance and compact size for congestive heart failure detection,
in IEEE Transactions on Antennas and Propagation (2015), vol 63, Issue 10, pp. 4557–4562.
https://doi.org/10.1109/tap.2015.2457935
9. C.M. Held, R.J. Roy, Hemodynamic management of congestive heart failure by means of a
multiple mode rule-based control system using fuzzy logic. IEEE Trans. Biomed. Eng. 47(1)
115–123 (2000). https://doi.org/10.817626
10. S. Chattopadhyay, G. Sarkar, A. Das, Spider and histogram assessment of electrocardio-
gram for Apnea diagnosis, in International Conference of IMBIC MSAST-2016, vol 5 (2016),
pp. 149–153. ISBN 978-81-925832-4-2
 Part VII
Modelling and Simulation in General
Application
Analysis of Retinal OCT Images
for the Early Diagnosis of Alzheimer’s
Disease

C. S. Sandeep, A. Sukesh Kumar, K. Mahadevan and P. Manoj

1 Introduction

Alzheimer’s disease (AD) is one of the prominent types of brain disorder related to
memory that is increasing worldwide. The relevant incidence shows that the preva-
lence of AD increases as the age of population increases [1]. AD leads to continuous
memory loss and cognitive dysfunction leading to a drop in executing routine func-
tions and learning. The other symptoms of AD are visual abnormalities, apraxia,
aphasia, and agnosia [2, 3]. The problems on vision are usually seen in AD patients
that affects the routine life. The usual vision complaints seen in AD are loss of
contrast responsiveness related to space, unable to identify locomotion discernment,
cannot discriminate color tone and ocular loss, influencing the principal ocular cor-
tex and other stipulated regions of the brain [4–6]. For the early diagnosis of AD,
a noninvasive neuroimaging technique like Magnetic Resonance Imaging (MRI) is
essential and widely used technique that provides detailed information about brain
structure and cerebral imaging in AD patients. The most usual findings that are seen
in MRI are degeneration of cells in the entorhinal cortex, medial temporal lobes and
hippocampus.. In addition to this there is an enlargement in ventricles and depletion

C. S. Sandeep (B) · A. Sukesh Kumar

Department of ECE, College of Engineering, Trivandrum, Kerala, India
e-mail: sandeepcs07nta@gmail.com
A. Sukesh Kumar
e-mail: drsukeshkumar@yahoo.in
K. Mahadevan
Department of Ophthalmology, SGMC&RF, Trivandrum, India
e-mail: eyemahadevan@rediffmail.com
P. Manoj
Department of Neurology, SGMC&RF, Trivandrum, India
e-mail: mnjparameswaran@gmail.com

© Springer Nature Switzerland AG 2019 509

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_43
510 C.S. Sandeep et al.

of entire brain mass [7]. The investigations and reports made on AD were not able
to explain the morphological and functional modification of brain in Alzheimer’s
patients. The evidence as well as researches regarding clinical and histological AD
on retina suggests in such a manner that the identical neuronal disintegration affects
brain through the retina. The physical changes that were observed in animals and post
mortem of human retina are loss of axons and retinal ganglion cell (RGC) [8–11].
The aggregates of tau and Amyloidβeta protein build up inside the retina region and
its microvasculature. By another study, the early indications of inflammation in the
neurons were present in the retina [12–16]. Consequently, the studies made on num-
ber of clinical observations and microscopic structure of retina of AD shows that
there is strong confirmation of retinal dysfunction in AD patients [17–19].
OCT is one of the promising non-invasive retinal imaging technique for deter-
mining the different section of eye images of neuronal disintegration. OCT scanning
technique has emerged as one of the mostly used technology to detect and find
out the damage in axonal region of different neuronal diseases. The damage in the
axonal region can be evaluated by computing the thickness of retinal nerve fiber layer
(RNFL), gives an unintended approximation of RGC layer dysfunction. The loss of
neurons in the retina can be instantaneously determined by measuring thickness of
macular of the eye because around 30–35% of this section mainly consists of RGCs
and their fibers [20–22]. The brain and retina shares a common embryological origin
eye is the outermost extension of brain. Due to this the OCT scans are becoming pop-
ular. After obtaining the OCT images of AD patient, next step is to make a database of
OCT AD images. For computer based assessment of OCT images we need different
processes like segmentation of the input image, after that feature extraction, feature
selection and classification of OCT images should be done.
Segmentation of OCT images and dimensionality reduction is the most important
process in the area of image analysis. The different Artificial Intelligence (AI) tech-
niques used for analyzing Biomedical images are Support Vector Machine, Genetic
Algorithms, Fuzzy Logic And Artificial Neural Networks (ANNs) [23, 24]. The other
powerful tool used for analyzing medical images is Wavelet Networks (WNs), based
on wavelets which are mathematical functions used to divide the information into
its constituent frequency components. With the help of WNs, better signal to noise
ratio can be obtained, the information that is outside the image can be minimized, the
features of information can be extracted easily and finally it allows universal capac-
ity calculation using Artificial Neural Network (ANN) [25–28]. Because of these
out comings, WNs are used in different applications [29, 30]. In ANNs, radial basis
functions (RBFs) and multilayer perceptrons (MLP) are used for building algorithm
for medical image analysis. But WNs can create optimized algorithm structure than
ANNs thereby reducing complexities in calculation [31]. In this research work, a new
scheme for analyzing medical OCT images are developed based on WNs. Adaptive
wavelet networks (AWNs) and static or Fixed-Grid Wavelet Networks (FGWNs) are
the two types of WNs [32]. AWNs uses continuous wavelet transforms (CWTs), are
continuous in nature whereas FGWN is a discrete wavelet transform (DWT), dis-
crete in nature. In this research work we have used FGWNs due to the various short
comings on initial value computation in AWNs [32].
Analysis of Retinal OCT Images for the Early Diagnosis of … 511

The features of the proposed method based on FGWN are as follows. By using
the proposed method we can find out the shift and scale parameters, as well as the
number of wavelets can be calculated very easily. The parameters such as number
of wavelets, scale, and shift parameters value can be determined easily. The least
square algorithms are used for calculating the neuronal weights. Another feature of
the proposed work is that there is no need of specifying random initial values as in
AWNs. For analyzing OCT images, segmentation is the most important section. In
this research work, for the segmentation of OCT images, a wavelet network with
three layers is used; one input layer, one hidden layer and an output layer. In the
segmentation section, first we have to select the OCT image from the database. The
image is filtered by using median filter. The next step is the channel separation.
After this process is over, next step is to normalization of the input image. After
normalization we have introduced the Marr wavelet due to its excellent features
such as simple calculation, better SNR and easier adaptation of Gaussian structures
[33]. Using Marr wavelet, a static or fixed wavelet structure is formed by primary
and secondary screening. Therefore we can calculate the function accurately. After
this the Wavelet network is formed. Next step is the training process in which neural
network training is employed. After training is completed we get the wavelet network
output which is further improved using post processing. Then the segmentation of
the OCT image is performed and at last the region of interest (ROI) processing can
be done in this section. Next is the feature extraction of the segmented images. We
have used different features like elliptical calculation, thickness ratio calculation,
variance of curvature and salience, average of regional minima of OCT image, area,
perimeter as well as second, third, and fourth moments. The necessary features are
selected and finally the classification of OCT images has been done. The objective
of this research work is to summarize the different findings on OCT images of AD
patients, to consider the role of OCT in AD patients and how OCT scans involved
in the retinal changes for diagnosing AD at its earlier stage. The previous related
works of the author’s in diagnosing AD will definitely provide a new solution with
this scheme for diagnosing AD [1–5].

2 Segmentation Using Wavelet Network

Image acquisition is the first step in the analysis of OCT images. This is done with the
help of OCT device as shown in Fig. 1. OCT is an eye or retina imaging technique used
to find out the different eye related disorders. After image acquisition, the unwanted
salt pepper noise on the obtained OCT image of the eye from the OCT device is
removed by using median filter. Next step is to build a Wavelet Network (WN) using
FGWN as explained in the previous section. During processing, initially a wavelet
scan is performed using primary or “mother wavelet”. This mother wavelet produces
a multidimensional wavelet frame for providing better regularities.
In this research work for creating wavelet framework, the Marr wavelet with d-
dimension is used. After creating mother wavelet, the secondary or “child wavelets”
512 C.S. Sandeep et al.

Fig. 1 A typical OCT device

are obtained through shifting and scaling of primary or mother wavelet. Wavelets
are mostly helpful for reducing the size of OCT image value from a bigger one. The
structure of WN is similar to ANN. The output equation of a WN with ‘d’ inputs,
‘q’ wavelets in the middle layer and one output as in Eq. (1).


n 
n
wl ψ pl,ql (X )  wi 2− pl d/2 ψ(2 pl X − ql) (1)
l1 l1

where weight coefficients ‘wl ’, ranges from l  1, 2,…, n, ‘ψ’ denotes primary wavelet
function, ‘pl’ denotes shift parameter ‘ql’ denotes scale parameter, ‘ψpl,ql’ stands
for dilated and translated versions of a mother wavelon function [31]. The WNs
can construct networks with systematic algorithms easier than ANNs. [34]. After
constructing the networks, the weights wl in (1) can be find out using linear evaluation
schemes that helps in constructing the proposed discrete wavelet network or FGWN.
In WNs the input data changes for a broad range of values, minimize the efficiency
in different investigations. Therefore in the proposed work, to limit the scattering
of input data, normalization is applied as the preprocessing stage. In this stage each
OCT image’s red, green and blue values of RGB matrix are mapped into [0, 1] [35].
This can be done using the Eq. (2).
Analysis of Retinal OCT Images for the Early Diagnosis of … 513

(k)
xn,old − tk
(k)
xn,new  (2)
Tk − tk
(k)
where xn,new is the value of each red, green and blue color matrix after normalization,
t k is the initial value and T k is the final values of these matrices, respectively. Next
step in the proposed work is to select the primary wavelet. In this work we have used
multi or d-dimensional Marr wavelet is used as the primary or mother wavelet. We
have chosen Marr wavelet because it gives better regularities and can produce wavelet
frame with single scale multi-dimensional structure [36]. From the mother wavelet,
we can produce necessary child wavelets. The Eq. (3) shows the Marr wavelet scheme
employed in this research work is given as:
   
ψ(x)  ηx  d − x∧ 2 e∧ −x∧ 2|2 (3)

Next step in the proposed FGWN construction is to determine two parameters

namely, scale and shift parameters. Therefore, the employment of two scale levels
in this stage is required, minimum and maximum levels [ pmin , pmax ] and also the
shift parameter. The wavelet function with grit on the wavelon parameters space is
used to find out the input vectors as in expressed in Eq. (4).

ψ pl.q j (x)  2− pld/2 ψ(2 pl x − q j ) (4)

The creation of wavelon lattice structure is required in the next step. In this process
we have to provide two screening stages. In the first screening stage, for every input
vector, we have to create I k set for every scale level selected. In the second screening
process, the parameters, shift and scale are selected from at least two sets are calcu-
lated and set I or wavelet matrix is formed with input data. After the formation of
set I, some matrix values are no longer needed. They can be eliminated in the next
stage from the redundant values formed during the set I using an efficient algorithm
as described below. In this step we have used orthogonal least squares (OLS) algo-
rithm, a fast and reliable algorithm for creating determination models [31]. By using
OLS algorithm the best subset of wavelet W can be selected as follows. First is to
select the most important wavelets formed on the previous stage. Then the redun-
dant wavelons are made perpendicular to the selected. As the next step in OLS, the
remaining redundant wavelons are made perpendicular to the selected and so on.
Thus the selected wavelets can easily isolate for the proposed WN construction [37]
and the wavelelon network is defined as in Eq. (5)


s
f  wl ψl (x) (5)
l1

In the above equation, ‘s’ denotes number hidden layer wavelons and ‘wl’ is
denotes weight of wavelons. By using wavelons, the proposed WNs hidden layer
514 C.S. Sandeep et al.

Fig. 2 a input image. b Marr Wavelet output. c segmented image

nodes can be constructed. Next is to find the index of the proposed wavelet network
and desired error value is measured. This is calculated in Eq. (6) [8].

1  ˆ(k)
P
2
MSE  ( f − f (k) ) (6)
P k1

Image segmentation is prominent of the different steps involved in the analysis of

medical images like OCT. For the segmentation of OCT image, the proposed algo-
rithm from the preceding stage is required. The dataset used in this work is obtained
from Sree Gokulam Medical College and Research Foundation, Trivandrum, India
and is not publicly available. From the OCT dataset, ten images are selected randomly
for constructing the proposed wavelet network or FGWN. The network is created
from the OCT images in such a way that the output is zero, if the pixel is inside the
OCT image and vice versa and consequently the proposed network is constructed.
The input image, Marr Wavelet output and segmented image of OCT image WN
segmentation of the proposed network shown on Fig. 2.
From the above, we have segmented the OCT image with the proposed DWN
called Fixed Grid Wavelet Network. In AD patients, Retinal Nerve Fiber Layer
(RNFL) thinning occurs in the retina. This retinal change can be identified in an
OCT image. For the automatic analysis of OCT images, this proposed method reduces
complexity and very useful as it extracts the RNFL layer for further processing and
Analysis of Retinal OCT Images for the Early Diagnosis of … 515

Table 1 Comparison of Method Accuracy Precision Sensitivity Specificity

FGWN, NN and GVF (all
values are in percentage) FGWN 99.65 94.77 94.32 99.82
NN 99.53 92.15 93.34 99.73
GVF 98.83 82.28 83.94 98.83

for detecting AD at its earlier stage. We have compared the segmentation process of
the proposed FGWN with Neural networks (NN) and Gradient Vector Flow (GVF)
for different parameters like accuracy, precision, sensitivity and specificity as shown
in Table 1. The proposed approach shows better results than the other two.

3 Feature Extraction

After segmentation part is done for OCT images, the succeeding stage is to extract
the features from the image. The extraction of RNFL is the most significant process
after segmentation from the OCT image for diagnosing AD. In this paper, for RNFL
feature extraction, at first we have removed the unwanted noise and additional parts on
the background are eliminated. Thus the required RNFL is extracted using necessary
morphological processes like area, perimeter, third and fourth moments, ellipticity,
thickness ratio calculation, curvature variance, salience variance, and average number
of regional minima [38].

4 Classification of OCT Images

After the selection of the most necessary features, the remaining process involved
is the classification of images. In this research work, we have focused on Back
Propagation (BP) and Radial Basis Function (RBF) of Neural Networks (NNs) for
the classification.
A. Classification using BP
The weight parameters of input-to-hidden neurons are calculated as in Eq. (7).

∂ E (m)
wnp
m+1
 wnp
m
−η (7)
∂wnp

From the above, ‘m’ denotes the repeated sequence number; ‘n, p’ stands for the
ratio of input neuron and hidden neuron, and ‘η’ denote step size. The hidden layer
in the BP networks consist of more than one sigmoid neurons succeeded by linear
neurons in the output layer. The BP allows more number of nonlinear neuronal layers
with transfer functions for learning input and output linear-nonlinear relationships.
516 C.S. Sandeep et al.

The output neuronal layer produces a range of values starting from negative one to
positive one in the NNs [30].
B. RBF Classification
In RBF type classification of neural networks, supervised training method is used to
accomplish function mapping as identical to multi-layer neural network. The RBF
Neural network classifier consists of ‘l’ values in the input layer to accept ‘l’ multi-
dimensional input non magnitude elements. The output layer of the network is find
out by multiplying hidden layer neuron with the weighting factor w(n, p). Therefore
in each RBF unit ‘m’, the center value is chosen as the mean that belong to class ‘m’
as calculated in Eq. (8).

1 
Nm
μm  xn (8)
Nm n1 m

In the above equation, ‘xmn ’ stands for the eigenvector of the ‘nth’ image in class
‘m’, and ‘N m ’ stands for trained images in class ‘m’. The input vector and vector
distance is used for calculating hidden or middle layer activation function [31].
From the BP and RBF classification of neural network performed for OCT image
analysis, RBF shows better results than BP in accuracy, specificity and time taken
during execution.

5 Experimental Results

The dataset required for this research work of OCT images is taken from Sree Goku-
lam Medical College and Research Foundation (SGM & RF), Trivandrum, India and
it is not publicly available. The authors are directly included in the study as per the
permission received from the ethics committee. The consent from the participants
has been obtained through interviewing. For making an automated computerized
analysis for early diagnosis, OCT dataset is required. We cannot directly get OCT
images with the support of physicians in Neurology and Ophthalmology. In this
regard we have selected 50 patients for the study. The patients are initially diag-
nosed by the Neurologist through MRI and found that 25 are AD victims. For further
investigations, all the 50 patients from the Neurologist were sent to Ophthalmologist
for OCT scanning. From those 50 patients, 100 OCT images were obtained from
both eyes because AD may affect in a single eye or both. The OCT images procured
from the OCT machine are saved as bitmap file extension for further processing. The
each OCT image obtained from OCT machine is 535,974 bytes. Consequently all
the OCT images have been saved successfully for analysis. The dimension of the
saved image is high and so we have reduced the images to 256 × 256 sizes for further
processing. From the OCT images, unwanted noise are removed in the preprocessing
stage and made free from distortion [36]. Next step is to segment the image using
Analysis of Retinal OCT Images for the Early Diagnosis of … 517

Table 2 Comparison Method FAR in % FRR in %

proposed method with GVF
and FBSM Proposed 1 1
GVF 2 2.5
FBSM 3 3.7

the proposed wavelet network or FGWN. For the various steps included in the seg-
mentation process that is already described in Sect. 2, out of 100 OCT images, 10
images is sufficient for the construction of wavelet lattice, calculating shift and scale
parameters, and weight coefficients. The proposed method has achieved good results
as compared to NN and GVF, already explained in Sect. 2. The different features
like area, perimeter, third and fourth moments, ellipticity, thickness ratio calculation,
curvature variance, salience variance, and average number of regional minima are
extracted after the segmentation process. The classification of OCT images were
done using BP and RBF, the later showed good results. In this experiment RBF clas-
sifier which we selected is compared with GVF and fuzzy based split-and-merge
algorithm (FBSM) using false acceptance rate (FAR) and false rejection rate (FRR).
The proposed system achieved good results compared to GVF and FBSM which is
shown in Table 2.

6 Conclusion

In this research work, a new scheme is introduced using wavelet networks or FGWN
for the analysis of medical OCT images for diagnosing AD at its earlier stage. Here
the segmentation has been on wavelet networks and classification on Neural Net-
works. By comparing the RNFL between AD and control subjects we can measure
the changes in retinal layer for early diagnosis. In this paper we have used Marr
Wavelet function for constructing multidimensional wavelet lattice. Also the weight
of wavelons, shift and scale parameters has calculated using this scheme. The opti-
mization of the network structure for segmenting OCT images has been done using
the proposed algorithm. After that different feature of OCT images are extracted. We
have compared the proposed method of WN with NN and GVF, the former shows
better results. In our method, the training and testing a wavelet network several times
with the same data would lead to the same results improving the accuracy, speci-
ficity, precision and sensitivity. After that feature selection has done and classified
the features using NN. For classification, we used Neural Network RBF classifier
as it achieves good results than BP, the former needs less time for training. In this
work we have compared the proposed work with GVF and FBSM using FAR and
FRR, give better results than the other two. From the findings, it is clear that the
proposed method on WN can be used for automatic analysis of OCT medical images
for detecting AD. As for a future study an efficient algorithm could be used for WN
construction.
518 C.S. Sandeep et al.

Acknowledgements The authors in this research work are very much thankful to SGM & RF,
Trivandrum, India for the support for conducting the study and providing the required dataset.
The authors are also thankful to the Institutional Ethics Committee Sree Gokulam Medical Col-
lege & Research Foundation standard operating Procedures (SGMC-IEC: SOPS) members, Dr.V
Mohanan Nair (Chairman), Dr. Regi Jose (Member Secretary IEC), Dr. K K Manojan (Member,
Institution Review Board (IRB), IEC), Dr. P.Sivasankarapillai (Chairman IRB) and Dr. Jeesha C
Haran (Secretary IRB) for giving the permission for the study.

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Real Time Diagnosis of Rural Cardiac
Patients Through Telemedicine

R. Ramu and A. Sukesh Kumar

1 Introduction

Telemedicine in India will allow patients in rural areas to have access to specialist
doctors in urban hospitals. Leading cause of death in rural areas is due to cardiac
diseases. Prevalence of cardiovascular diseases in India is higher than other countries
of the same region [1]. Early detection of heart disease has important significance
for heart disease prevention and timely treatment. Developments in telemedicine due
to the new technologies in electronics industry helps in the monitoring of patients
with cardiac disorders within the home or rural hospitals. Change in the rate of
heart rhythm is called arrhythmia and are difficult to obtain on an ECG tracing
which are captured within few seconds. Some of the arrhythmia are dangerous like
ventricular fibrillation which is the main cause of cardiac arrest or stroke. So early
detection of these arrhythmias for people living in rural areas can be made possible
by Telemedicine.
Telemedicine uses electronic communications to exchange medical information
for improving the patient’s health. There are three main categories of Telemedicine
namely remote monitoring, store and forward and interactive telemedicine. In this
work remote monitoring category is used for diagnosis of cardiac patients. Develop-
ments in wireless technologies leads to wireless telemedicine in which doctors can
view physiological data of patients from anywhere at any time. There are different
wireless technologies that are used to transmit ECG signals such as Bluetooth, Zigbee
Wi-Fi and GSM. This work is an extension of the earlier works of the authors [2–4].
Wireless ECG monitoring using Bluetooth low energy (BLE) technology consist of

R. Ramu (B)
Rajadhani Institute of Engineering and Technology, Trivandrum, Kerala, India
e-mail: mail2ramureghu@gmail.com
A. Sukesh Kumar
Rajiv Gandhi Institute of Development Studies, Trivandrum, Kerala, India
e-mail: drsukeshkumar@yahoo.in
© Springer Nature Switzerland AG 2019 521
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_44
522 R. Ramu and A. S. Kumar

Fig. 1 Block diagram of the system

acquisition module Bluetooth module and smart phone. It capture ECG signal and
transmit the ECG data via the Bluetooth wireless link and display it in a smart phone
[5]. ECG transmission using Wi-Fi technology is developed which consist of a single
chip ECG signal acquisition module, Wi-Fi module and a smart phone [6]. Zigbee
technology is used to transmit the ECG signals in real time. Using Zigbee transmitter
and receiver are used for transmission and LabVIEW is used to plot the signal in the
laptop. The ECG signals transmitted to a remote laptop using zigbee are stored in
the same lap top configured as server and are finally plotted in another laptop using
internet [7]. In this work ECG signal from the acquisition module is transmitted to
the laptop using zigbee module. ECG signal from the laptop is transmitted to the web
server from the local server. The ECG signals are stored in the database of virtual
private server and plotted in the browser of any laptop using internet.

2 System Description

The aim of the work is to design an inexpensive highly accurate ECG acquisition and
wireless transmission system using zigbee and web server. The Fig. 1 shows the main
block diagram of the system. The ECG acquisition system consists of electrodes,
instrumentation amplifier, filters and microcontroller. It captures the ECG signal
from the surface of the body, amplifies the signal to volt range. Filters will remove
undesired signal and pass only the ECG signal.
The analog output from the filter is given to microcontroller for analog to digital
conversion (ADC) and the serial data from the output of microcontroller is converted
to USB standard and fed to laptop using USB cable. Wamp server is used as local
server and it takes the incoming serial data and transmit it to the web server. The
transmitted ECG signals are stored in the data base of the server. Virtual private server
is used as server and finally, the ECG signals are then plotted in the website www.
ecgtrack.com. Doctor in the specialty hospital can view the ecg signal of patient from
rural area in real time and can diagnose the patient.
Real Time Diagnosis of Rural Cardiac Patients Through … 523

Fig. 2 Block diagram of ECG acquisition system

3 ECG Acquisition System

The signals acquired from the electrodes are amplified, filtered, digitized, and trans-
mitted. Block diagram of ECG acquisition system is shown in Fig. 2. For three lead
systems, electrodes Right arm (RA), Left arm (LA) and Left leg (LL) are used, two
of the electrodes are used to form lead and the third is used as the ground.
Lead I configuration is used, it is the voltage between Left arm electrode and
Right arm electrode (I  LA − RA). ECG signals vary from microvolt to the millivolt
range due to this small range, the signals measured need to be amplified in order to
be better interpreted [8]. Texas Instrument’s instrumentation amplifier INA321 EA
is used here. With an internally set gain of 5, the INA321 can be programmed for
gains greater than 5 [9].
Instrumentation amplifier is a differential amplifier with additional input buffer
stages. It has low offset voltage, high Common mode rejection ratio(CMRR), high
input impedance and high gain. Driven Right leg drive is used to reduce the common
mode interference. Filters using op-amps are used to remove the unwanted signals
and line frequency noise. The last stage of the acquisition system is ATmega 328
microcontroller which is a low power CMOS 8 bit microcontroller based on AVR
enhanced RISC architecture with 32 K bytes of FLASH 1 Kbytes of EEPROM and
2Kbytes of SRAM. Real time ECG signals are first digitized and converted to serial
data using ATmega 328 which have an in built 10 bit ADC. The output serial data
from the microcontroller is then converted to USB standard using FT232RL USB to
Serial UART adapter.
The ECG acquisition system used in this work is light weight and easily portable
device. This device can be placed at the patient side for capturing the real time
ecg signals. For transmitting the signals to nearby PHC this acquisition system can
be interfaced with wireless modules. Among the different wireless technologies
available Zigbee technology is used here to transmit ecg signals to PHC.
524 R. Ramu and A. S. Kumar

4 Wireless Transmission

Zigbee technology is used in this work to transmit ECG signal from acquisition
system to a laptop in PHC. It is a low-cost, low power, wireless mesh network standard
which operates in the industrial, scientific and medical (ISM) radio bands [10]. It
is less expensive and can transmit signals up to 100 m. The ZigBee network layer
natively supports star, tree and mesh networks, Zigbee series 2 module is used as
transmitter and receiver.
This module allow very reliable and simple communication between microcon-
trollers and systems. Analog ECG signals are digitized and converted to serial data
by Atmega microcontroller. This serial data is fed to zigbee module and are then
transmitted wirelessly using zigbee technology.

5 Reception and Display of the ECG Signal

Zigbee module and MAX232 IC are used in the receiver side. The received signal
from the Zigbee module is TTL level, so it should be converted into RS232 level.
For this level conversion MAX232 IC is used. The Signals from Zigbee module is
connected to MAX232 IC where this TTL signals are converted to RS232. The output
serial data from MAX232 are fed to PC using serial connector DB9. For connecting
to laptop FT232 can be used for serial to USB conversion.

6 Ecg Display on Laptop Using Labview

Before plotting the ECG in the browser the signals are viewed in the laptop using
LabVIEW. LabVIEW programs consist of two windows a front panel and block
diagram. XY graph is used in this work to display the ECG in real time. The back
panel, which is a block diagram, contains the graphical source code. Figure 3 shows
the block diagram for receiving the serial ECG data and plotting it in real time.

7 Ecg Display on Local Server

Before loading ECG signals in the database of Virtual private server(VPS) and ploting
in web page, these signals are plotted in local server for testing. ECG signals are
wirelessly transmitted using Zigbee technology to a remote laptop. The Serial ECG
data received by the laptop are stored in the data base of the server configured
as local server. These Signals are then retrieved and plotted in the browser of the
system configured as server. Web servers are computers that deliver web pages and
Real Time Diagnosis of Rural Cardiac Patients Through … 525

Fig. 3 Block diagram for ECG display in LabVIEW

any computer can be turned into a Web server by installing server software. In this
work WAMP Server is used to make the laptop as local server. It is a Windows OS
based program that installs and configures Apache web server, MySQL database and
PHP scripting language [11].

8 ECG Display on Internet

ECG signals stored in the database of local server are send to the data base of web
server and stored there. It is retrieved and plotted in the web browser. Domain name
www.ecgtrack.com is taken and hosted on a web server. Virtual private server is used
in this work for web hosting. It has many advantages over shared hosting such as
complete control, can customize the appearance and settings etc. JQuery is used to
plot the ECG signal in real time in the browser of the server. For viewing patients
ECG in real time doctor can log on to the web site www.ecgtrack.com. First page is
the login page for the doctor for authentication. Figure 4 shows the login page for
doctor. After entering the required username and password it direct to display page
for ECG. When the leads are properly placed and transmitting and receiving sections
are ON the ECG signals will be first stored in the local server database and finally in
database of virtual private server. From there it is finally plotted in this display page.
JQuery is a fast JavaScript Library and Flot is a pure JavaScript plotting library for
JQuery are used in this work to plot the ECG signal. It is simple to use, have attractive
looks and also have interactive features [12]. ECG signal of remote cardiac patient
can be transmitted from patient side to nearby PHC by Zigbee wireless technology.
Signals are received with the help of zigbee receiver and are stored in the data base
of laptop. configured as local sever in the PHC. On logging on to the website doctor
in the specialty hospital can see the ecg of the remote cardiac patient and diagnose
him.
526 R. Ramu and A. S. Kumar

Fig. 4 Login page for doctor

9 Results

ECG signals wirelessly transmitted from patient side using Zigbee technology is
plotted and displayed in the laptop using LabVIEW software. Figure 5 shows trans-
mitted ECG signal received and plotted in PC using LabVIEW. Figure 6 shows the
ECG signal plotted in the browser of the laptop configured as server. ECG signals
from the data base of the local server are send to the web server and are stored in
the database of web server. It is plotted in the web browser of any other laptop and
can be viewed by logging on to the web site www.ecgtrack.com. Figure 7 shows the
ECG signal plotted in the web browser. Five patients ecg was taken and wirelessly
transmitted and displayed in the web page. It was successfully diagnosed by the
doctor.
Bradycardia
Bradycardia means heart rate less than 60 beats per minute. It has regular rhythm,
normal QRS duration and P wave—Visible before each QRS Complex. If heart rate
computed is less than 60 beats per minute, then it is detected as bradycardia.
Trachycardia
Trachycardia is for heart beat greater than 60 beats per minute. It also has regular
rhythm, normal QRS duration and P wave—Visible before each QRS Complex. Fifty
patients ECG has been transmitted and diagnosed by this method.
Real Time Diagnosis of Rural Cardiac Patients Through … 527

Fig. 5 Transmitted ECG signal received and plotted in PC using LabVIEW

Fig. 6 ECG signal plotted in the browser of the laptop configured as server

10 Conclusion

ECG signals of patients in a rural area can be transmitted to a laptop in the nearby
PHC by using Zigbee technology. Laptop in the PHC can be configured as local
server and the ECG data are stored in the database of the local server. Website www.
ecgtrack.com is created and hosted in a virtual private server with MySQL database.
From the local server data are send to the data base of web server. Stored signals in
528 R. Ramu and A. S. Kumar

Fig. 7 Screen shot of the potted ECG waveform in the web browser

the MySQL data base of web server are retrieved and plotted in the web browser.
So that doctor in a specialist hospital can view the ECG signal by logging on to the
web site and can give medical instructions to the doctors in the PHC. Fifty patients
diagnosis have been done with this system.

References

1. S. Chauhan, Dr. B.T. Aeri, Prevalence of cardiovascular disease in India and its economic
impact-A review, in International Journal of Scientific and Research Publications, vol 3, Issue
10, October 2013
2. R. Ramu, A. Sukesh Kumar, Real-time monitoring of ECG using Zigbee Technology, in Inter-
national Journal of Engineering and Advanced Technology (IJEAT), vol 3, Issue 6, pp. 169–172
(2014). ISSN: 2249-8958
3. R. Ramu, A. Sukesh Kumar, Monitoring of ECG using Zigbee and wamp server, in International
Journal of Innovative Research in Technology and Science (IJIRTS), vol 3, Issue 4, pp. 50–54,
July (2015). ISSN: 2321-1156
4. R. Ramu, A. Sukesh Kumar, Online Assessment of rural cardiac patients through Telemedicine,
in Proceedings of the 2nd National Conference on Advances in Computational Intelligence and
Communication Technologies, LBSIT forWomen, 25–26, February 2016
5. B. Yu, L. Xu, Y. Li, Bluetooth low energy based mobile electrocardiogram monitoring system,
in Proceedings of the IEEE International Conference on Information and Automation, China
2012
6. S. Shebi Ahammed, Binu C. Pillai, Design of Wi-Fi based mobile Electrocardiogram monitoring
system on concerto platform (Procedia Engineering, Elsevier IConDM, 2013)
7. R. Ramu, S. Kumar, Monitoring of ECG using Zigbee and Wamp Server, in International
Journal of Innovative Research in Technology and Science (IJIRTS), vol 3, Issue 4, pp. 50–54.
ISSN 2321-1156
Real Time Diagnosis of Rural Cardiac Patients Through … 529

8. Wu Baochun, Li Min, Yang Yaning and Zhang Weiwei, ECG acquisition circuit design based
on C8051F330, in Proceedings of the IEEE-EMBS International Conference on Biomedical
and Health Informatics, China, 2012
9. INA321 Datasheet by Texas instruments
10. Zigbee/Xbee Data Sheet by Digi International
11. D. Ipswich, Setting UP a WAMP Server On Your Windows Desktop, Technology Now at
Smashwords, 2011
12. S.V.O. Khanna, M. Mistry, Impact of JQuery in Web Domain, in International Journal of
Advanced Research in computer science and software engineering, vol 1, Issue 1 (2011)
A Comparative Analysis of a Healthy
Retina and Retina of a Stroke Patient

R. S. Jeena and A. Sukesh Kumar

1 Introduction

Stroke is a form of cardiovascular disease affecting the blood supply to the brain.
It remains as a leading cause of disability and death for people of all races and
ethnicities. Stroke [1] is a physical condition that occurs due to insufficient supply of
blood to the brain cells. This damages the brain cells ultimately leading to their death.
A clot in the blood vessel or a blood vessel rupture can interrupt the blood supply
to brain. Stroke can be categorized into two: ischemic and hemorrhagic. Ischemic
stroke accounts for nearly 85% of the cases. When a blood vessel providing blood
to the cerebral framework is blocked, Ischemic stroke comes about. Hemorrhagic
stroke happens when a debilitated blood vessel breaks. At the point when a hindrance
happens inside a blood vessel providing blood to brain, the vessels conveying blood
to eye will likewise be influenced amid the underlying stages. This is named as
Retinal ischemia. People experiencing Retinal ischemia are more inclined to stroke.
The retina can be viewed and analyzed using non-invasive in vivo functional
techniques. Retinal imaging permits diagnosis of different eye illnesses and also
the prognosis of diabetes mellitus, blood pressure and cerebrovascular ailments like
stroke. Research works show that microvasculature of retina and brain is closely
linked in terms of anatomy and physiology [2]. Since retina’s capacity makes it
an extremely metabolically energetic tissue with two times blood supply, the retina
permits direct noninvasive examination.
Cardiovascular ailment reveals itself in the retina in different ways. Blood pressure
and coronary heart disease cause variations in the ratio between the diameter of reti-

R. S. Jeena (B)
Department of ECE, College of Engineering, Trivandrum, Kerala, India
e-mail: jeena_rs@yahoo.com
A. Sukesh Kumar
Rajiv Gandhi Institute of Development Studies, Vellayambalam, Trivandrum, Kerala, India
e-mail: drsukeshkumar@yahoo.in
© Springer Nature Switzerland AG 2019 531
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_45
532 R. S. Jeena and A. Sukesh Kumar

nal arteries and veins. Tapering of the arteries and broadening of veins is associated
with an upgraded danger of stroke [2]. Arterioles of retina share practically identical
anatomical, physiological and embryological features with arterioles of brain. Mor-
phological changes in the outline of blood vessel, branching design, width, tortuosity,
retinal sores, fractal measurement, branching angle and coefficient are some of the
irregularities in vascular pattern of retina related with cardiovascular diseases like
stroke. This work is an extension of author’s earlier works for stroke prediction [3].

2 Literature Survey

The Retinex is a human-observation based computer vision design which offers

steadiness of color and dynamic range compression. The possibility of Retinex was
visualized by Land [4] as a model of lightness and shading view of the human vision.
Daniel J. Jobson et al. has executed multiscale retinex [5], which seals the gap
between color images and the human representation of scenes. Terai et al. [6] pro-
posed a retinex model for color image contrast improvement which lessens the com-
putation time by handling the luminance flag. The algorithm works well for gray
images.
Feng et al. [7] presented the quick Fourier calculation strategy to make the com-
putational time speedier than that of the conventional method. The strategy functions
performs well for colour pictures but not for gray scale images.

3 Methodology

Multiscale retinex has been implemented in this work for the pre processing of
retinal images. Morphological operations are done for the removal of optic disc
and background. For proper vessel segmentation, thresholding can be used to create
binary images. To reduce all objects in the vascular map to lines, skeletonization is
done. Branching points are identified and parameters like eccentricity, major axis
length and orientation are computed. This has been implemented for both healthy
retinas and retinas of stroke patients and the results are compared.

3.1 Preprocessing

The Retinex is an established preprocessing technique that can be applied to retinal

images. It can provide sharpening, shading constancy, dynamic range compression
and color rendition at the same time redressing the blurring in profound anatomical
structures and heterogenity in biomedical images. It can be applied successfully for
both color and gray scale images.
A Comparative Analysis of a Healthy Retina and Retina of a … 533

Fig. 1 Block diagram of Multiscale retinex

In Single Scale Retinex (SSR), the image is passed through the retinex filter, which
is basically a Gaussian filter. Based on the filter output, the original image is scaled
and then processed with a logarithmic function.
SSR is mathematically expressed as

Si (x, y)  log(Fi (x, y)) − log(Fi (x, y) ∗ G(x, y)) (1)

Gaussian filter G is defined by

   
G(x, y)  k exp − x2 + y2 /σ2 (2)

Fi Input image on the ith colour channel

Si Retinex output image on the ith channel

Since image filtering using retinex function require various Gaussian shaped
impulse response with different variance, MSR (Multiscale Retinex) technique [8]
is utilized. The weighted sum of the outputs of various SSRs gives the MSR output
value [6].
The MSR can be written as
   
SMSRi (x, y)  Wk . log(Fi (x, y)) − log Fi (x, y) ∗ Gk (x, y) (3)
k

N is the number of scales (k  1, 2…N), Wk is the weight of each scale.

Block diagram representation of Multiscale Retinex is given in Fig. 1.
534 R. S. Jeena and A. Sukesh Kumar

3.2 Morphological Operations

The output image obtained after retinex preprocessing is converted to grayscale and
subjected to morphological operations. Structuring elements of different shapes and
sizes are created using MATLAB functions. The morphological opening function
with disc shaped structuring element is applied on this preprocessed image to remove
the optic disk and background [9].

3.3 Skeletonization

After removing the background and optic disk, image is then converted to binary form
by thresholding. The structural outline of a plane area can be reduced to a line graph
called skeleton. The skeleton of the region can be obtained by a thinning algorithm.
Thinning shrinks the binary image objects to a set of skeletal strokes that preserve
major information about the shape of the original entity. After obtaining skeletonized
output, the branching points of skeleton are detected and the lengths of branches
are computed. MATLAB function computes the geodesic distance transform of the
binary image. A set of features for each connected component in the binary image
are computed. They include parameters [10] like eccentricity, major axis length and
orientation. Parameters have been computed for both healthy retinas and retinas of
stroke affected patients.

4 Result and Discussion

Figure 2 shows the input images of a healthy retinal fundus and retina of a stroke
patient.
Figure 3 shows the output after applying multiscale retinex for preprocessing.
Retinex output is the converted to binary form by thresholding. Figure 4 shows
the binarized output.
Figure 5 shows the skeletonized image.
After skeletonization, the branch points and end points are detected. Detection of
end points and branching points are shown in Fig. 6.
Endpoints are shown in blue and branching points are shown in red.
Length of the branches are calculated and are shown in Fig. 7a, b.
Table 1 shows the values computed for both the images by analyzing its branches.
Results show that number of branching points is much higher in the case of stroke
patients and branching vessels seems to be more tortuous, which can be observed
visually from the processed images. This methodology has been applied to images
of retinal ischemia (American retinal bank) and healthy images (DRIVE database),
which substantiated the above results. Retinal ischemia proves to be an important
A Comparative Analysis of a Healthy Retina and Retina of a … 535

Fig. 2 a Healthy Retina b Retina of a Stroke patient. (Image Courtesy: Centre for Vision Research
at Sydney University’s Westmead Millennium Institute)

Fig. 3 a Retinex preprocessed healthy Retina b Retinex preprocessed retina of a Stroke patient

Table 1 Evaluation of parameters

Retinal Major axis Eccentricity Orientation Number of Number of
fundus image length end points branch points
Healthy 25.78 0.722 1.16 102 115
person
Stroke patient 16.61 0.812 3.76 283 303

biomarker of stroke as healthy retinal fundus images seems to give a mean major
axis length in the range [20–26] and fundus images of retinal ischemia gives a mean
major axis length in the range [15–19].
536 R. S. Jeena and A. Sukesh Kumar

Fig. 4 a Binarized healthy retina b Binarized Retina of stroke patient

Fig. 5 a Skeletonized healthy retina b Skeletonized retina of stroke patient

5 Conclusion

Early detection of cardiovascular diseases like stroke through biomarkers derived

from retinal imaging would allow patients to be treated more effectively. Retinal
imaging aids in predicting the probability of stroke based on parameters evaluated
from the vascular map. Performance of the system can be improved by incorporating
more features like tortuosity and fractal dimension of the branching vessels and
requires training from a much larger database. Interdisciplinary groups will be able
to investigate the interface at the fringe between ophthalmology and neurology. Since
the microvasculature of cerebral sensory system and optic framework are interlinked,
it is unequivocal that retinal neurovascular variations are prognostic of microvascular
variations in cerebrum.
A Comparative Analysis of a Healthy Retina and Retina of a … 537

Fig. 6 a Detection of branching points and endpoints in Healthy Retina b Detection of branching
points and endpoints in Retina of Stroke patient

Fig. 7 a Length of branches computed for Healthy Retina b Length of branches computed for
Retina of Stroke patient

Acknowledgements I would like to thank Dr. Mahadevan, Sree Gokulam Medical College and
Research Foundation, Trivandrum for his valuable guidance in the smooth conduct of this work.

References

1. Barry L. Zaret, M.D., Marvin Moser, M.D., Lawrence S. Cohen, Chapter 18 Stroke - Lawrence
M. Brass, M.D., pp 215–234
2. M.L. Baker, J.J. Wang, G. Liew, et al., Differential associations of cortical and subcortical
cerebral atropy with retinal vascular signs in patients with acute stroke. Stroke 41, 2143–50
3. R.S. Jeena, Dr. A.S. Kumar, Stroke prediction using SVM, ICCCITT 2016, Tamil Nadu
538 R. S. Jeena and A. Sukesh Kumar

4. E. Land, An alternative technique for the computation of the designator in the retinex theory
of color vision. Proc. Nat. Acad. Sci. 83, 3078–3080 (1986)
5. D.J. Jobson, Z. Rahman, G.A. Woodell, A Multiscale retinex for bridging the gap between
color images and the human observation of scenes. IEEE Trans. Image Process. 6(7), 965–976
(1997)
6. Y. Terai, T. Goto, S. Hirano, M. Sakurai, Color image contrast enhancement by retinex model,
in Proceedings of IEEE 13th International Symposium on Consumer Electronics, pp. 392–393,
May 2009
7. Y. Feng, J. Huang, Z. Feng, M. Liu, The research and implementation of light compensation
algorithm in color facial image, in Electrical and Control Engineering Conference (2011),
pp. 2758–276
8. J.K. Priyanka, Dr. B.G. Sudarshanan, Dr. S.C. Prasanna Kumar, Dr. N. Pradhan, Development
of algorithm for high resolution retinex for image enhancement. Int. J. Innovative Res. Dev.
2012 (December)
9. P. Manjiri, M. Ramesh, R. Yogesh, S. Manoj, D. Neha, Automated localization of optic
disk, detection of microaneurysms and extraction of blood vessels to bypass angiography, in
Advances in Intelligent Systems and Computing, (Springer, 2014). ISBN: 978–3-319-11933-5.
https://doi.org/10.1007/978-3-319-11933-5_65
10. M.B. Patwari, R.R. Manza, Y.M. Rajput, D.D. Rathod, M. Saswade, N. Deshpande, Classifica-
tion and calculation of retinal blood vessels parameters, in IEEE’s International Conferences
for Convergence of Technology, Pune, India
Square Root Quadrature Information
Filters for Multiple Sensor Fusion

Aritro Dey, Smita Sadhu and Tapan Kumar Ghoshal

1 Introduction

The Information filters for nonlinear signal models is an emerging area of research
and continuing interest in this form is reported in recent works [1–3]. The works of
[1, 2] report square root versions of information filters based on sigma points and
cubature points which have improved numerical performance over the standard error
covariance form. The performance of such estimators, although performance wise
less accurate compared to particle filter based approach [3], require considerably less
computational effort and make real time implementation of this filters feasible. The
square root approach has advantages of enhanced numerical accuracy, preservation
of symmetry, availability of square root so that steps for Cholesky factorization
can be avoided. Because of the above referred attributes square root approach has
been recommended in previous works [1, 2, 4] over the standard error covariance
form. A variety of nonlinear information filters viz., Unscented information filters
[5], Central Difference information filters [6], Cubature and higher order cubature
information filters [7, 8, 9] have been reported in literature which focus on multiple
sensor estimation with nonlinear signal models. In these works where multi sensor
estimation is carried out satisfactorily employing these estimators with information
filters configuration. Information filtering algorithms are also extended for some

A. Dey (B)
Department of Integrated Flight Control System, Aeronautical Development Agency,
Bangalore 560017, Vimanapura, India
e-mail: aritro_dey@mail.ada.gov.in
S. Sadhu · T. K. Ghoshal
Department of Electrical Engineering, Jadavpur University, Raja S.C. Mallik Road, Kolkata
700032, India
e-mail: ssadhuju@gmail.com
T. K. Ghoshal
e-mail: tkghoshal@gmail.com
© Springer Nature Switzerland AG 2019 539
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_46
540 A. Dey et al.

critical estimation problems (specifically in target tracking) where out of sequence

measurements are obtained [10]. However, none of these cited algorithms include
the square root framework and may terminate for some applications where accuracy
of measurements are high or a linear combination of state vector components is
known with better accuracy while other combinations may not be well observable
[1]. However, these publications indicate continued interest in this special form of
the estimation algorithm. In this paper, the authors present novel algorithms for
information filters in square root framework which are based on recently reported
quadrature rule for numerical approximation of Bayesian integrals. The proposed
estimators are formulated using two different quadrature rules, viz., Gauss Hermite
rule [11] and Cubature quadrature rule [12] so that in addition to the aspects of
square root approach the accuracy of the estimators can be further improved over the
existing estimators. The proposed information filters which are not yet reported in
literature are evaluated using a non trivial aircraft tracking problem in sensor fusion
configuration where their superiority has been demonstrated over the competing
filtering available in litersture.

2 Problem Statement

We consider a nonlinear dynamic system as given below

x k  f (x k−1 ) + w k (1)
ζ ζ ζ
yk  g (x k ) + vk (2)

Here x k ∈ R n is the state vector, the noise term w k ∈ R n ∼ (0, Q k ) indicates

ζ
zero mean process noise (Gaussian). y k ∈ R m is the measurement available from
the ζ sensor among M different sensors where ζ  1, . . . , M. The measurement
th

noise of each sensor is also considered to be white noise (Gaussian) and denoted as,
 R ζ
ζ ζ Q ζ
v k ∈ R m ∼ (0,Rk ). The square root of Q k is S̄ k and that of Rk is S̄ k .

3 Square Root Quadrature Information Filters

The proposed square root quadrature information filtering algorithm is presented in

three parts. The first part presents a general approach of information filters wherein
the quadrature points are to be incorporated from the second part. Sensor fusion
method is presented in the third part.
Square Root Quadrature Information Filters for Multiple Sensor … 541

3.1 General Algorithm

Q
 R ζ
(i) Initialisation: Initialize x̂ 0 , Ŝ0 , S̄ k , S̄ k
(ii) Time update step:

Select the quadrature points as explained in Sect. 3.2

χ̂ i  Ŝ k−1 q i + x̂ k−1 (3)

Compute predicted estimate as


N
x̄ k  f (χ̂ i )wi (4)
i1

Compute the weighted, centred (updated estimate of previous instant is subtracted

off) matrix S kx such that ith element of S kx is:
   √
S kx i
 f (χ̂ i ) − x̄ k wi for i  1, 2, . . . , N (5)

The estimate of the square root of predicted error covariance is obtained as

 
S̄ k  Triangularize S kx S̄ kQ (6)

The information vector can be obtained as

−T −1
z̄ k  S̄k S̄k x̄ k (7)

The square root of the predicted information matrix is obtained as

Z
 −1 
S̄k  Triangularize S̄k (8)

(iii) Measurement update step:

Select sigma points as

χ̄ i  S̄ k q i + x̄ k (9)

The predicted estimate of measurement becomes

ζ

N
ȳ k  g ζ (χ̄ i )wi (10)
i1
542 A. Dey et al.

Compute the weighted, centred (predicted estimate of measurement is subtracted

off) matrix SYk such that ith element is:
 Y  
ζ √
S k i  g ζ (χ̄ i ) − ȳ k wi for i  1, 2, . . . , N (11)

Compute the weighted, centred (predicted estimate of state is subtracted off)

matrix Skx̄ such that ith element of Skx̄ is:
   √
S kx̄ i
 χ̄ i − x̄ k wi for i  1, 2, . . . , N (12)

The cross following covariance can be computed as

 ζ  T
P kx z  S kx̄ SYk (13)

Define the matrix

 
−T
ζ −T −1  ζ R ζ
Λk  S̄ k S̄ k P kx z S̄ k (14)

The updated estimate of information vector is obtained as

 
−1   
ζ R ζ ζ ζ ζ T
ẑ k  z̄ k + Λk S̄ k yk − ȳ k + P kx z z̄ k (15)

The square root of the updated estimate of information matrix becomes

Z
 
ζ
Ŝ k  cholupdate S̄ k , Λk , + (16)

The square root of the corresponding error covariance matrix

  
Z −1
Ŝk  Triangularize Ŝ k (17)

Hence the updated estimate of state becomes

x̂ k  Ŝk ẑ k (18)

3.2 Choice of Quadrature Points

In this part two quadrature rules have been presented which generate the quadrature
points and the corresponding weights.
Square Root Quadrature Information Filters for Multiple Sensor … 543

3.2.1 Gauss Hermite Quadrature Rule [11]

Compute J, a symmetric tri-diagonal, defined as J i,i  0 and J i,i+1  2i for
1 ≤ i ≤ N − 1 for N -quadrature points. √
The quadrature points are chosen as qi  2xi where xi are the eigen values of
J matrix.
The corresponding weights (wi ) of qi is computed as |(vi )1 |2 where (vi )1 is the
first element of the ith normalized eigenvector of J.

3.2.2 Cubature Quadrature Rule [12]

This rule has been recently proposed in [12]. The radial integral of spherical radial
cubature rule is approximated with Gauss Laguerre Quadrature rule.
2nn  numberof cubature quadrature points are to be selected as
where ξ i  2λ j e i
λ j is the solution of n  th order Chebyshev-Laguerre polynomial with α  n/2−1:
    n  n  −1    
n + α λn −1 + ( 2! ) n  + α n  + α − 1 λn −2 − · · ·  0 (19)

n
L αn   λn − 1!

Here, i  1, 2, . . . , 2nn  , j  1, 2, . . . , n  and k  1, 2, . . . , 2n

Corresponding weights are computed as
 
1 n!  α + n + 1
wi     (20)
2n(n/2) λ j L̇ α λ j 2
n

Details are provided in [12].

3.3 Multiple Sensor Fusion

The information contribution of ζ th sensor is denoted as

 
−1   
ζ ζ R ζ ζ ζ ζ T
ϕ k  Λk S̄ k yk − ȳ k + P kx z z̄ k (21)

The contributions of all the sensors starting from ζ  1, . . . , M are fused to

obtain a more reliable estimate as


M
ζ
ẑ k  z̄ k + ϕk (22)
ζ 1
544 A. Dey et al.

ζ
The information matrix contribution for the ζ th sensor is Λk . After multiple sensor
fusion the square root of the a posteriori information matrix is obtained as
Z
   
Ŝ k  cholupdate S̄ k , Λ1k · · · ΛkM , + (23)

3.4 Notes on the Algorithm

On availability of triangular matrices matrix inversion steps in the algorithm can be

replaced by backward substitution symbolized by ‘/’ as the latter is computation-
ally economic. The proposed algorithm is for the quadrature rule with non negative
weights. This has an additional advantage of unconditionally ensured positive defi-
niteness unlike Square Root Unscented information filter [1, 8].

4 Case Study Using Aircraft Tracking Problem

For demonstration a tracking problem has been considered where an aircraft execut-
ing a maneuvering turn has to be tracked. The aircraft is tracked with bearing only
measurements from two radars positioned at different locations. The system equation
and the measurement equations are provided in [9].
Further investigation revealed that this tracking problem suffers from the track
loss cases in the situation when the difference of bearing angles from the radars is
considerably low or close to π i.e., where measurements suffer from observability
problem. At this situation the lines of sight of two radars do not intersect and the
filters fail to estimate satisfactorily due to non unique solution of the observation
equation.
The performance of the proposed algorithms is evaluated with the help of RMSE
performance and track loss count from Monte Carlo (MC) simulation with 10000
runs.
 Performance
 index is defined in [9]. The condition for track loss is defined as
 2 
 ex + e y  ≥ 800 m where ex and ey are the position error sequences along x axis
2
∞
and y axis. Note that the RMSE are calculated excluding the track loss cases. For per-
formance comparison same seeds are used to generate the noise sequences for each
candidate during MC simulation. Performance of Square root version of 2nd order
Cubature Quadrature information filter (SRCQIF) & Gauss Hermite information fil-
ter (SRGHIF) is compared with recently reported Square Root Cubature information
filter (SRCIF) in [2]. Figures 1, 2 and 3 show that the performances of SRCQIF and
SRGHIF are superior to SRCIF as the susceptibility of track loss is less and RMSE
(excluding the track loss cases) is low as well compared to SRCIF. Track loss count
for SRCIF is 251 while that for SRCQIF and SRGIF are 218 (13.15% less) and 221
(11.95% less) respectively. SRGHIF and SRCQIF work equally well while the latter
uses considerably less number of quadrature points (20) compared to SRGHIF (243)
Square Root Quadrature Information Filters for Multiple Sensor … 545

135
SRCQIF
SRCIF
RMSE - position (m) 125 SRGHIF

115

105

95
20 40 60 80 100
time (sec)

Fig. 1 RMSE of position estimation for 10,000 MC run

36
SRCQIF
RMSE-velocity (m/sec)

35 SRCIF
SRGHIF

34

33

32
20 40 60 80 100
time (sec)

Fig. 2 RMSE of velocity estimation for 10,000 MC run

and therefore computationally economic. Average run time of SRGHIF is 0.2415 s

and 8.6 times more than that for SRCQIF (0.0281 s).

5 Conclusion

Square root quadrature information filters (SRGHIF and SRCQIF) have been intro-
duced and superiority of these newly proposed filters has been demonstrated over
Square root cubature information filter with the help of a tracking problem in sen-
sor fusion configuration. Between SRGHIF and SRCQIF the latter is advocated for
546 A. Dey et al.

4000

y position (m)
0
-500 1000 2500 4000 5500

true trajectory
-4000 SRGHIF
SRCQIF
SRCIF

-8000
x position (m)

Fig. 3 True and estimated trajectory for a representative run

real time applications because of its numerical stability and substantially improved
estimation accuracy at a reasonable computation effort.

Acknowledgements The first author thanks the Council of Scientific and Industrial Research
(CSIR), New Delhi, India for financial support and Aeronautical Development Agency, Ministry
of Defence, Bangalore, India for infrastructural support.

References

1. G. Liu, F. Worgotter, I. Markelic, Square-root sigma-point information filtering. IEEE Trans.

Autom. Control 57(11), 2945–2950 (2012)
2. K.B. Chandra, D.W. Gu, I. Postlethwaite, Square root cubature information filter. IEEE Sens.
J. 13(2), 750–758 (2013)
3. W. Zhang, J. Zuo, Q. Guo, Z. Ling, Multisensor information fusion scheme for particle filter.
IET Electron. Lett. 51(6), 486–488 (2015)
4. I. Arasaratnam, I.S. Haykin, Square-root quadrature Kalman filtering. IEEE Trans. Signal
Process. 56(6), 2589–2593 (2008)
5. G. Liu, F. Worgotter, I. Markelic, Nonlinear estimation using central difference information
filter, in Workshop on Statistical Signal Processing, Proc. (SSP) IEEE, pp. 593–596, Nice,
France, 2011
6. G. Liu, Bayes Filters with Improved Measurements for Visual Object Tracking, Doctoral dis-
sertation, Göttingen State and University, 2012
7. K.P.B. Chandra, D.W. Gu, I. Postlethwaite, Cubature information filter and its applications,
in Proceedings of the American Control Conference (ACC), IEEE, San Francisco, 2011,
pp. 3609–3614
8. Q. Ge, C. Wen, S. Chen, R. Sun, Y. Li, Adaptive cubature strong tracking information filter using
variational Bayesian method, in Proceedings of the 19th World Congress of the International
Federation of Automatic Control, Cape Town, South Africa, 2014, pp. 24–29
9. B. Jia, M. Xin, K. Pham, E. Blasch, G. Chen, Multiple sensor estimation using a high-degree
cubature information filter, in Sensors and systems for space applications VI, Baltimore, Mary-
land, USA, April 2013, Proc. SPIE 8739, pp. 87390T–87390T
Square Root Quadrature Information Filters for Multiple Sensor … 547

10. T.H. Kim, T.L. Song, H.J. Kim, Information filters with reduced data storage for out-of-
sequence measurements update. IET Radar Sonar Navig. 10(6), 1038–1045 (2016)
11. K. Ito, K. Xiong, Gaussian filters for nonlinear filtering problems. IEEE Trans. Automatic
Control 45(5), 910–927 (2000)
12. S. Bhaumik Swati, Cubature quadrature Kalman filter. IET Signal Proc. 7(7), 533–541 (2013)
Cost Effective, Water Controlled
Automated Gardening System

Piyali Mukherjee

1 Introduction

This paper introduces a cost-effective, water-controlled, automated gardening sys-

tem. The objective of this paper is to design and implement a simple, efficient yet cost
effective system that takes care of garden plants by constantly monitoring the mois-
ture content of the soil and ensuring that the soil remains sufficiently hydrated with-
out any kind of manual intervention. This intelligent system thus helps in conserving
water as well as watering the plants sufficiently. The need for water conservation is
well-elaborated in [1].
Decades back, watering can was used for watering the gardens at home and was
later extended to fitting pipes from the tap to the garden which resulted in enormous
loss of water. This led to the introduction of various automated watering systems
such as sprinkler system, tube, nozzles and many others, but they are often costly to
afford. Very recently, researchers have developed automated watering systems using
moisture sensors, pumps and other devices but this also turned out to be costly [2–6].
Besides this, alteration of any device, if required, after they have degraded, is also
difficult. The aim of this paper is thus to design a watering system that will reduce
cost and can be within the reach for all Indian middle-class families, to whom the
garden will no more be a luxury. Moreover the devices are easily available. It is
also easy to maintain because the devices are readily available. Though design and
development of automated gardening systems is in process for the last few years, not
much literature is available. For instance, in [7] the authors used a water sprinkler
system to build an automated plant watering system. We however, follow a different
approach.

P. Mukherjee (B)
Institute of Radiophysics and Electronics, University of Calcutta, 92, A.P.C Road, Kolkata
700009, India
e-mail: mukherjee.piyali92@gmail.com

© Springer Nature Switzerland AG 2019 549

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_47
550 P. Mukherjee

Fig. 1 System block diagram

This automated gardening system can be realized with the help of moisture sensors
or moisture probes that detects the resistivity of the soil and in turn its moisture
content, a microcontroller [8, 9] that will make decisions on when to water the
plants, and also when to terminate the watering process after sufficient hydration,
a solid state relay that acts as a switch and controls the watering mechanism and a
submerged pump that is placed in a reservoir which helps in pumping water. The
microcontroller used here is the Arduino Uno which is an open-source physical
computing platform based on a simple microcontroller board, ATmega 328 and a
development environment for writing software on the board.

2 Design Algorithm

• Moisture sensors are built using long, non-galvanised nails.

• Amplifier circuit designed using OPAMPs.
• Arduino board is then connected.
• Solid state relay is provided at the output of the Arduino.
• Submerged pump is then placed in the reservoir and proper piping is done.

3 System Block Diagram and Working

Figure 1 shows the basic block diagram of the system with its components. There
are three main functional components: the moisture sensors, the solid state relay and
the submerged pump.
Cost Effective, Water Controlled Automated Gardening System 551

Fig. 2 Moisture sensors

3.1 Moisture Sensors

The moisture sensors are developed using non-galvanized nails as shown in Fig. 2.
This results in reduction of cost in comparison to the available moisture sensors in
the market. The moisture content of the soil controls its resistivity. This property has
been used to develop moisture sensors that sense the moisture content of the soil and
convert this into an equivalent voltage which is provided to a microcontroller.

3.2 Arduino Uno

The Arduino Uno is a microcontroller board based on the ATmega328 memory chip.
It has 14 digital input/output pins (of which 6 can be used as PWM outputs), 6
analog inputs, a 16 MHz ceramic resonator, a USB connection, a power jack and
a reset button. The ATmega328 is a low-power CMOS 8-bit microcontroller. The
microcontroller has 32 KB memory. It also has 2 KB of SRAM (Static Random
Access Memory) and 1 KB of EEPROM (which can be read and written with the
EPROM library), 23 general purpose input-output lines, 32 general purpose working
registers, a serial programmable USART and a 10 bit ADC [10]. The Arduino Uno
can be programmed with the Arduino software. The ATmega328 on the Arduino Uno
comes pre-burned with a boot loader that allows uploading new code to it without
the use of an external hardware programmer.
552 P. Mukherjee

3.3 Amplifier

The moisture sensor records voltage in the order of millivolts which is very low for
the microcontroller to respond to its changes, as the board operates only on a supply
of 7–20 V. So, an amplifier is required which will amplify the received voltage to
a minimum voltage required for the Arduino to respond. OP-AMPs are very easily
available, very cheap and due to its smaller size, they consume very little space in
the circuitry. Due to these advantages it has, operational amplifiers (OP-AMPs) are
used in this system.

3.4 Solid State Relay

It is an electronic switching device that switches on or off when a small external

voltage is applied across its control terminals. It is used for its fast switching speed
and has no physical contacts to wear out.

3.5 Submersible Pump

It has a hermetically sealed motor close-coupled to the pump body and helps in
pushing water to the surface.

4 Results

The voltage equivalent of the moisture content of dry soil and moist soil (to the extent
tolerable by the plants) was measured practically in our laboratory. These voltages
were taken as reference voltages for program coding. It was found that the voltage
level of dry soil was much lower than the voltage level of moist soil. The reason
being that the resistance of dry soil is more negative compared to the resistance of
moist soil.
When the garden soil is dry, the soil needs to be watered sufficiently. Accordingly,
the relay is turned on by the Arduino which in turn, turns on the pump and watering
is done. As watering begins, the soil turns moist increasing its resistance. When the
soil becomes sufficiently hydrated, the relay is turned off by the Arduino which again
turns off the pump. So watering is done only for the required period, thus saving the
excess loss of water.
When the garden soil is moist, the soil does not need to be watered. Hence accord-
ingly, the relay is not turned on by the Arduino and no watering is done.
Cost Effective, Water Controlled Automated Gardening System 553

5 Benefits that This System Provides

• Cost effective garden management: Water is applied to the garden plants on time
and shut off on time. There is no need for human intervention and hence reduce
manpower.
• Water saving: Watering is done at optimal times. Watering is also kept in check
and excess watering is not allowed which leads to conserving water.
• The ability to be absent: One will be able to go on vacations without losing the
garden. Proper care of these garden plants will be taken by this system even in the
absence of manpower.
• Convenience: The watering is done at the time of necessity and not on our avail-
ability.

6 Conclusion

The system is designed in such a way that the plants are watered automatically without
any need for human intervention. Moreover, the water level is also kept in check, so
that the plants are watered sufficiently but not in excess and with minimum or no loss
of excess water. The novelty of this system also lies is the cost-effectiveness, so that
this system can be used by all middle-class Indian families. Moreover, the system is
assembled in a way that any devices can be replaced easily, if required at any point
of time during use. The devices are also easily available in the market at affordable
rates. This developed system will not only be limited to house gardens but can also
be extended to farmlands and might be of immense benefit to the farmers due to its
low cost.

7 Future Scope of Work

The designed system was implemented using a reservoir that has to be filled manually.
For large reservoirs, water may be filled in month’s interval. But for smooth working
of the system, a surface level detector may be designed that will sense the water level
of the reservoir. In case the level reaches below the height of the pump, water will be
pumped by a motor into the reservoir. So, no manual filling of water will be required
and the process will be fully automated.

Acknowledgements The author wish to thank the Electronics and Communication Engineering
Department, of Hooghly Engineering and Technology College, Hooghly, West Bengal, India, where
the prototype has been developed under the guidance of Ms. Writi Mitra and to all others who have
been directly or indirectly associated with this project.
554 P. Mukherjee

References

1. W.A. Jury, H.J. Vaux, The emerging global water crisis: managing scarcity and conflict between
water users. Adv. Agron. 95, 1–76 (2007)
2. P. Archana, R. Priya, Design and implementation of automatic plant watering system. Int. J.
Adv. Eng. Glob. Technol. 4(1) (2016)
3. J. Cao, S.D. Fleming, M. Burnett, An exploration of design opportunities for ‘gardening’
end-user programmers’ ideas, in IEEE Symposium on Visual Languages and Human-Centric
Computing (VL/HCC), 18–22 Sept 2011
4. Birasalapati Doraswamy, Automatic irrigation system using Arduino controller. Int. J. Adv.
Technol. Innovative Res. 8(4), 635–642 (2016)
5. K. Kansara, V. Zaveri, S. Shah, S. Delwadkar, K. Jani, Sensor based automated irrigation system
with IOT: a technical review. Int. J. Comput. Sci. Inf. Technol. 6(6), 5331–5333 (2015)
6. S. Darshna, T. Sangavi, S. Mohan, A. Soundharya, S. Desikan, Smart irrigation system. IOSR
J. Electron. Commun. Eng. 10(3), 32–36 (2015) (May–Jun)
7. S.V. Devika, Sk. Khamuruddeen, Sk. Khamurunnisa, J. Thota, K. Shaik, Arduino based auto-
matic plant watering system, Int. J. Adv. Res. Comput. Sci. Softw. Eng. 4(10), 449–456, (2014)
(Oct 10)
8. Ramesh S. Gaonkar, Microprocessor Architecture, Programming & Applications
9. B. Ram, Fundamentals of Microprocessors and Microcomputers
10. Introduction to Arduino Microcontroller, Shanghai Jiao Tong University, June 17–29, 2012
Ear Based Biometric Analysis for Human
Identification
Samik Chakraborty, Anumita Mitra, Sanhita Biswas
and Saurabh Pal

1 Introduction

Human biometric recognition system has been a demanding subject of research for
the few decades as secure surveillance received significant attention in the present
days. Biometric system based on several physiological and behavioral characteristics
of human being like fingerprint, face, iris etc. are more reliable system than the
conventional identification systems such as passwords and PINs [1, 2]. In spite of
remarkable advancement in biometric recognition system, identify of individuals in
uncontrolled and unconstrained environments remains a challenging problem like
face recognition system can be affected due to illumination variance at different
parts of the face or under different expressions. A change in voice due to cold and
cough or other pathological conditions will make the system difficult to recognize.
Recognition using finger may not be effective if the subject has dirty, deformed or cut
hand. In compare to other physiological biometric feature ear has certain advantage.
Contour of an ear is unique over the years [3] and also remain unchanged with change
in expression [4] even person’s cooperation is not necessarily required to acquire an
ear image. Anatomy of human ear is shown in Fig. 1.
Burge and Burger [5] first developed ear authentication based algorithm where a
graph model is constructed from for each ear from its edges and curves and introduces
a graph based matching algorithm. Chang et al. [6] used PCA based ear biometric
system and received 72% accuracy and also showed that due to hair or jewellary
occlusion with pose variation recognition rate drops into 30%. A multimatcher system
for ear recognition is proposed by Nanni and Lumini [7] where sub window is created

S. Chakraborty (B)
AEIE Department, Heritage Institute of Technology, Kolkata, India
e-mail: samikasan0516@gmail.com
A. Mitra · S. Biswas · S. Pal
Applied Physics Department, University of Calcutta, Kolkata, India

© Springer Nature Switzerland AG 2019 555

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_48
556 S. Chakraborty et al.

Fig. 1 Anatomy of the

human ear

from each subject and features are extracted by the convolution operation with Gabor
filters. This achieved 80% recognition rate. Yuan and Mu [8] approached an ear
recognition system based on 2 dimensional images and achieved 94% accuracy for
0% occlusion and 85% accuracy for 35% occlusion. Gabor wavelets feature based
recognition system is presented by Zhang et al. [9] to deal with partial occlusion
and achieved a success rate of 96, 91 and 86% for occlusion of 15, 25 and 35%
respectively. Anwar et al. [10] presented a new algorithm based on geometrical
features extraction for ear recognition system and achieved 98% accuracy. Chen and
Mu [11] proposed a SRC based method for improving the performance of recognition
system under pose variations and occlusions and achieved an identification rate of
95.83, 91.67 and 87.5% for occlusion percentage of 15, 25 and 35 respectively. Lei
et al. [12] presented an automatic localization of 3-D ear landmarks and classifying
poses in profile face images where ear is represented by a novel ear tree based graph.
A literature survey on ear recognition can be found in [13].
In this present work, a preliminary study of ear recognition system with 10 subjects
is made where jewellary occlusion problem is counteracting by geometrical approach.
The geometrical relationship between the points of the image is being established
and found out when without any jewellary. There is a typical closeness among the
data thus obtained. Using this data a point is predicted from that portion of the image
which is occluded by jewellary. On obtaining this point the features are then found
out, which are approximately similar to that of the original image. The general block
diagram of ear recognition system presented in Fig. 2.
Ear Based Biometric Analysis for Human Identification 557

Fig. 2 Block diagram of ear based biometric system

Fig. 3 Captured image

2 Methodology

The data input for the proposed ear recognition algorithm is right side ear image of a
subject. In this study ear images of 10 subjects are collected through a digital camera
of 5 megapixels resolution with a distance of 15–20 cm in different daylight condition
without flash as shown in Fig. 3. All the data are captured with prior permission from
the subjects.
558 S. Chakraborty et al.

Fig. 4 Detected image boundary

2.1 Image Processing

In order to obtain only the ear image, background suppression is done by using an
edge detection algorithm. In literature several well-known edge detection algorithm
have been proposed [14]. Instead of using a traditional edge detector, a simple edge
detection algorithm is designed where thresholding is used from 65 to 70% of the
maximum intensity of an image i.e. 65% is the lower level and 70% is the upper level
of thresholding as shown in Fig. 4.

2.2 Feature Extraction

After finding out the exterior contour of an ear, top most (P), bottom most (Q), left
most (R) and right most (S) point of each contour are first detected and a rectangular
is drawn by using these four points and cross point of two diagonals (O) of that
rectangular is also detected. After detecting these five points Euclidian distance
between OP, OQ, OR, OS, PR, PS, RS, RQ and SQ are determined as shown in
Fig. 5. Also few other features are determined by calculating the ratios between the
various distances as shown in Table 1.
Ear Based Biometric Analysis for Human Identification 559

Fig. 5 Dimensionality of features extracted from ear

Table 1 Feature description

Feature symbol Feature description
F1 Distance between the point O and P
F2 Distance between the point O and Q
F3 Distance between the point O and R
F4 Distance between the point O and S
F5 Distance between the point R and P
F6 Distance between the point S and P
F7 Distance between the point R and S
F8 Distance between the point R and Q
F9 Distance between the point Q and S
F10 Sum of the distance of the point PO and OQ
F11 Ratio of distance OP to OQ
F12 Ratio of distance PR to RQ
F13 Ratio of distance PS to SQ
F14 Ratio of distance RS to RQ
F15 Ratio of distance RS to SQ
F16 Ratio of distance (PO + OQ) to PS
F17 Angle between RO and SO
560 S. Chakraborty et al.

Fig. 6 Occluded ear image

Fig. 7 Extracting features for the detection of ‘Q’ point

2.3 Estimation of Occlusion Point

One of the major problem arise in ear recognition system is due to occlusion of ear
ring in the earlobe. As a result Q point could not be detected. An ear image occluded
due to ear ring is shown in Fig. 6.
In this study a basic geometric comparison method is used to point out the approx-
imate lower most point of the ear. The basic idea of this method is if two circles are
drawn in an ear image without any occlusion, by taking OQ and SQ as radius then
two intersection points of the circles will be obtained. One of them is the coordinates
of Q point as shown in Fig. 7.
Ear Based Biometric Analysis for Human Identification 561

Table 2 Ratio of OQ/OP and Subject OQ/OP SQ/RS

SQ/RS of 7 unoccluded
subjects Subject 1 0.99 1.14
Subject 2 1.01 1.23
Subject 3 1.03 1.07
Subject 4 1.03 1.18
Subject 5 1.02 1.09
Subject 6 1.07 0.96
Subject 7 1.03 0.95
Average 1.03 1.09

Table 3 Comparison between actual and estimated point

Subject Coordinate of Coordinate of Actual OQ Estimated OQ
actual Q point estimated Q point (distance) (distance)
Subject 1 (258,599) (322,599) 286.7 287
Subject 2 (320,584) (311,600) 302.7 306
Subject 3 (313,582) (308,593) 296 303
Subject 4 (282,583) (302,586) 300.4 292

Now to estimate Q point for an occluded image due to ear ring, averages of
OQ/OP and SQ/RS of seven ear images without any occlusion is first calculated as
given (Table 2).

OQ  1.03 × OP (1)
SQ  1.09 × RS (2)

After calculating the average values, OQ and SQ for an occluded image are cal-
culated using these average values and the intersection point of two circles of radius
OQ and SQ at center point O and S respectively is considered as coordinates of
measured Q point of an occluded ear image. It is also found that this coordinate of
measured Q point is in at considerable distance from the actual Q point. To minimize
this error, from the measured Q point lowest distance coordinate of the earlobe is
found out and considered as approximated coordinate of actual Q point as shown
in Fig. 8. Coordinates of estimated Q point in case of occlusion as compared to the
actual Q point for four subjects is shown in Fig. 9 and compared in Table 3.

2.4 Signature Matrix Generation

In this study, 17 different features are extracted from each ear image of 10 subjects
and produce a matrix of dimension [10 × 17] and dimension reduction is done by
562 S. Chakraborty et al.

Fig. 8 Detection of a Q point

Fig. 9 Location of actual Q point and estimated Q point

using Principal Component Analysis method where using linear combination of the
original feature vectors (F 1 , F 2 …. F n ) a new set of feature vectors with low dimension
generates on the linear subspace.
The first principal component X 1 is given by


n
X1  W1 j F j (3)
j1
Ear Based Biometric Analysis for Human Identification 563

Table 4 Signature matrix Subject SME1 SME2 SME3

element for 10 subjects
Subject 1 81.48 8.52 6.15
Subject 2 94 42 29
Subject 3 215 119 28
Subject 4 109.91 97.13 29.79
Subject 5 7199 135 24
Subject 6 1048 129 57
Subject 7 277 70 18
Subject 8 171 23 6
Subject 9 339 87 25
Subject 10 4112 209 72

where W 1 is the first weight vector and for a given constraint W1T W1  1, variance
of X 1 is maximum. The second principal component X 2 is found by using second
weight vector W 2 so that it has maximum variance for a given constraint W2T W2  1,
which is uncorrelated with X 1 .
The process is continued for deriving X 3 … X n so that each component is uncorre-
lated with the previous components and the sum of variance of both original feature
vectors and principal components variables are the same.
By using Principal Component Analysis method 17 feature matrix of each sub-
ject is converted into one dimensional array of 3 elements of its Eigen value and a
signature matrix of 3 elements for 10 subjects are stored in the database as shown in
Table 4.

3 Result and Discussion

During testing 3 elements signature matrix of a new subject is compared with each
subject and the final decision is made on basis of Root Mean Square Error (RMSE)
method.

n  2
i1 F Pstor ed,i − F Pnew,i
RMSE  (4)
n

where, FPstored,i is the stored feature matrix,

FPnew,i is the feature matrix of a new entry currently under test and the number of
variables of the feature matrix is considered as n.
This method is used against all 10 subjects and achieved an accuracy of 100%. The
RMSE value of each testing over entire database is shown in Table 5. A comparative
study of present with previously reported results is shown in Table 6.
 564

Table 5 RMSE value between stored database and new access

Access 1 Access 2 Access 3 Access 4 Access 5 Access 6 Access 7 Access 8 Access 9 Access 10
Subject 1 21.2 1912.3 48.9 73.5 4008.2 28.5 423.6 41.1 28.7 83.9
Subject 2 1944.3 23.7 1933.8 1981.4 2100.9 1952.4 1500.6 1964.3 1900.6 2006.9
Subject 3 45.5 1938 19.1 32.3 4037.4 37.2 450 47 54.5 64.2
Subject 4 69.4 1982.9 62 14.7 4082.5 58.5 494.9 57.1 98 33.1
Subject 5 4038.5 2125.7 4032.2 4079.6 14.4 4047.1 3598.7 4058.2 3996.6 4102.4
Subject 6 14.3 1937.9 45.1 51.5 4034.2 5.2 449.2 19 50.1 58.4
Subject 7 490.9 1441.8 481.3 528.6 3541 498.8 47.4 510.9 447 553.3
Subject 8 34.2 1963.9 62.1 44.9 4059.6 24.1 475.3 14.7 76.3 35.8
Subject 9 67.2 1874.4 52.3 97.4 3972.8 70.8 386.1 84.3 18.1 122.6
Subject 10 46.7 1975.1 65 36.2 4071.7 36.1 486.4 28.6 86.5 23.6
S. Chakraborty et al.
Ear Based Biometric Analysis for Human Identification 565

Table 6 Comparison table

Study No. of ear images Occluded image Accuracy (%)
Chen and Mu [11] 24 Yes 95.83
Bustard and Nixon 63 Yes 92
[15]
Arbab- Zavar et al. 63 Yes 88
[16]
This paper 10 Yes 100

4 Conclusion

Ear biometric system is more reliable source for a unimodal biometric recognition
system as the texture of external ear does not vary, in general, with age, obesity,
disease etc. unlike other common biometric parameters. In this study an effort has
been made to identify the subject by their ear. A major aim of this approach is
to estimate the significant point for feature extraction which is within the occluded
region. This work is done under a small database of 10 subjects and received a success
rate of 100%. However, further study is needed using larger database having other
artifacts like presence of earphone or hair and with different illumination exposure.

References

1. S. Chakraborty, M. Mitra, S. Pal, Biometric analysis using fused feature set from side face
texture and electrocardiogram. IET Sci. Meas. Technol. 11(2), 226–233 (2017)
2. S. Chakraborty, S. Pal, Photoplethysmogram signal based Biometric Recognition using Linear
Discriminant, in 2nd International conference on Control, Instrumentation, Energy & Com-
munication, CIEC’16, Kolkata, India, pp 183–188, January 2016
3. A.V. Iannarelli, Ear Identification (Forensic Identification Series) (Paramont, Fremont, CA,
USA, 1989)
4. J.A. Unar, W.C. Seng, A. Abbasi, A review of biometric technology along with trends and
prospects. Pattern Recogn. 47(8), 2673–2688 (2014)
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(Springer, Boston, MA, 1996), pp. 273–285
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566 S. Chakraborty et al.

11. L. Chen, Z. Mu, Partial data ear recognition from one sample per person. IEEE Trans. Hum.
Mach. Syst. 46(6), 799–809 (2016)
12. J. Lei, X. You, M. Abdel-Mottaleb, Automatic ear landmark localization, segmentation, and
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13. Ž. Emeršič, V. Štruc, P. Peer, Ear recognition: more than a survey. Neurocomputing 255, 26–39
(2017)
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PAMI-8(6), 679–698 (1986)
15. J.D. Bustard, M.S. Nixon, Toward unconstrained ear recognition from two-dimensional images.
IEEE Trans. Syst. Man Cybern. 40(3), 486–494 (2010)
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IEEE International Conference on Biometrics: Theory, Applications, and Systems, pp. 1–5,
September, 2007
An Integrated Model for Early Detection
and Monitoring of Diabetic Foot

K. S. Suresh and A. Sukesh Kumar

1 Introduction

Diabetes is a chronic disease that occurs either when the pancreas does not produce
enough insulin or when the body cannot effectively use the insulin it produces. It is a
growing global epidemic of the current century. The recent estimate of International
Diabetes Federation indicates that 387 million people, have diabetes and this may rise
to 592 million within the next twenty years [1]. A further 316 million with impaired
glucose tolerance are at high risk from the disease, with projections indicating that
over 1 billion people will be living with or at high risk of diabetes in 2035. The
World Health Organisation (WHO) estimated that 9% among adults aged 18+ years
are suffering from diabetes. In 2012, an estimated 1.5 million deaths were directly
caused by diabetes and more than 80% of diabetes deaths occur in low and middle-
income countries. WHO also projects that diabetes will be the 7th leading cause of
death in 2030 [2]. According to the statistics of the International Diabetes Federation,
there are nearly 65 million diabetics in India [3]. As the incidence of diabetes is on
the rise, there is a proportionate rise in the complications associated with diabetes.
Diabetic Foot is one of the most threatening complications of Diabetes. This is a
state that a foot exhibits any pathology that results directly from diabetes mellitus or
any long-term complication of diabetes mellitus.

K. S. Suresh (B)
Centre for Development of Imaging Technology, Trivandrum, Kerala, India
e-mail: sureshkstvm05@yahoo.com
A. Sukesh Kumar
Rajiv Gandhi Institute of Development Studies, Trivandrum, Kerala, India
e-mail: drsukeshkumar@yahoo.in

© Springer Nature Switzerland AG 2019 567

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_49
568 K. S. Suresh and A. Sukesh Kumar

2 Diabetic Foot Infection

Different types of foot problems may develop in the diabetic cases as a result of
damage to nerves and blood vessels. These problems can easily lead to infection and
ulceration, which increase a person’s risk of amputation. The maximum number of
hospital admissions in diabetics is due to foot problems. It occurs in 15–25% of all
patients with diabetes and precedes 85% of all lower leg amputations. People with
diabetes are 25 times more likely to lose a leg than people without the condition.
Throughout the world, up to 70% of all leg amputations happen to people with
diabetes [4]. More than one million people with diabetes lose a leg every year as a
consequence of their condition. Diabetic foot problems are a common occurrence
throughout the world, resulting in major economic consequences for patients, their
families and society. An estimate of International Working Group on the Diabetic
Foot reveals that every twenty seconds a lower limb is lost to diabetes somewhere in
the world [5].

3 Key Indicators of Diabetic Foot

Peripheral neuropathies and peripheral arterial disease commonly coexist in patients

with diabetes and foot ulcers [6]. Peripheral vascular diseases are circulation disor-
ders that affect blood vessels outside of the heart and brain. These typically strikes the
arteries and veins that supply the arms, legs, and organs located below the stomach.
Ultrasound techniques are most widely used to identify Peripheral vascular diseases.
Intermittent claudication is the most common symptom of Peripheral vascular dis-
ease.
Ankle-arm index, diastolic blood pressure, fasting plasma glucose, hemoglobin
A1C, high blood pressure, medial arterial calcification, nerve conduction velocity,
peripheral vascular disease, systolic blood pressure, transcutaneous oxygen tension
etc. are some of the factors provide indications of diabetic foot [7].

4 Hemodynamic Model of Blood Flow

The blood is considered as a fluid and the properties depends on the suspension of
particles. Blood plasma is a Newtonian fluid which consists mostly water. But the
cellular elements causes significant changes in the rheological properties of blood. So
the mechanical properties of whole blood is very complex and cannot be modelled
as a homogeneous fluid. The size of blood vessels and the flow behaviour is also
different and it is considered as a non-Newtonian fluid or Navier-Stokes fluid. Many
of the characteristics can be proved with the help of Navier-Stokes equation [8].
Navier-Stokes equation for an incompressible viscous fluid.
An Integrated Model for Early Detection and Monitoring of … 569

Fig. 1 Blood’s
non-newtonian property of
shear thinning

∂u
ρ + ρ(u.∇)u  −∇ p + ∇.t (1)
∂t
u and ρ denotes the blood velocity and pressure.
Viscosity and shear rate (rate of deformation) of blood can also be estimated with
Reiner-Rivlin equation. The factors which control the viscosity to inertia in linear
flow are the velocity of the fluid, u, the diameter of the tube, d; and the kinematic
viscosity of the fluid, v.
The arteries in leg are very much effected with diabetes. Atherosclerotic occlusion
is most common and effecting the popliteal and femoral arteries. Diabetes effects the
regular microcirculation. Foot skin blood falls while standing 80% in non diabetes
and 50–70% in diabetes [9]. Resting supine foot skin blood flow 20–30% above
normal in diabetes. Leukocytes also have role in changing the viscosity (Fig. 1).
A model is developed by considering the changes in blood flow and other charac-
teristics leading to diabetic foot. This result is verified with other diagnostic methods
of diabetic foot.

5 Detection Techniques

The outcome of diabetic foot is experimentally analysed with the following tech-
niques for building the model. Preliminary results are very positive, more trials have
to be accomplished for the perfect model.
570 K. S. Suresh and A. Sukesh Kumar

5.1 Ultrasonic Measurement Techniques

Examination of the legs can give valuable information on the state of the peripheral
circulation. There are a lot of indications for peripheral arterial ultrasound examina-
tion related to diabetic foot [10]. The detection of stenoses or occlusions in specified
segments of the peripheral arteries in patients with suspected arterial occlusive dis-
ease. These clinical indicators, including claudication, rest pain, ischemic tissue loss,
and suspected arterial embolizations may present in these patients.
One of the most popular technique used for initial diagnosis is the ankle brachial
pressure index (ABPI) [11]. This is the ratio of highest pressure recorded at the ankle
for that leg to the highest brachial pressure obtained for both arms. ABPI normally
>1.0. ABPI <0.92 indicates arterial disease. ABPI >0.5 and <0.9 can be associated
with claudication and if symptoms warrant a patient should be referred for further
assessment. ABPI <0.5 indicates severe arterial disease and may be associated with
gangrene, ischemic ulceration or rest pain and warrants urgent referral for a vascular
opinion [12].
Figure 2 shows This patient with pain in the Left lower limb was evaluated with
color and spectral Doppler ultrasound of the venous system of the left lower limb [13].
The images reveal a normal colour Doppler study of the veins, including the left
femoral, popliteal, anterior and posterior tibial and peroneal veins. Often, the veins
of the leg cannot be visualized in their entirety. It is often more practical to image
the upper third and distal third of the anterior, posterior tibial and peroneal veins.
[Presented with permission from Dr. Joe’s Ultrasound Scan, Cochin; www.
ultrasound-images.com].
Figure 3 shows ultrasound and colour Doppler imaging of the right lower limb
indicates early changes of diabetic arteriopathy or what is called as diabetic vascu-
lopathy. This is characterised by the features shown in these colour Doppler ultra-
sound images;
1. Spectral broadening of the arterial waveform from the popliteal artery downwards
2. Mild decrease in peak systolic velocity below the popliteal artery
3. Early changes of loss of the tri-phasic spectral waveform is seen in peroneal
artery
All these above-mentioned changes are typically seen in early diabetic arteriopa-
thy suggesting mild stenosis in a diffuse fashion below the popliteal artery.
A normal pulsed wave Doppler waveform is a sharply defined tracing with a
narrow Doppler Spectrum. Flow becomes turbulent at bifurcations and luminal nar-
rowings causing spectral broadening of Doppler waveform, with filling in of the low
velocity region in the spectral waveform as the blood cells move at a wide range of
velocities. The normal peripheral artery waveform is triphasic [14].
An Integrated Model for Early Detection and Monitoring of … 571

Fig. 2 Normal venous Doppler of lower limb

5.2 Transcutaneous Oxygen Measurements

Concentration in the blood is the so-called oxygen saturation, SO2. It indicates the
rate of oxygen delivery to and consumption by the tissues [15]. The optical extinction
coefficient of oxyhemoglobin differs significantly from that of deoxyhemoglobin.
Thus, the spectral absorption coefficient of tissue depends on the concentration and
oxygen saturation of hemoglobin within the tissue. It also established that hyperspec-
tral tissue oximetry has the ability to identify ischemic and inflammatory compli-
cations before they are visible during a clinical examination. Retrospective analysis
of hyperspectral tissue oximetry from pre-ulcerative locations showed that diabetic
foot ulcer formation can be predicted with high sensitivity and specificity [16].

5.3 Photo Plethysmography

Photoplethysmographic method is also used to identify the characteristic of blood,

which lead to diabetic foot. Hemodynamic assessment can be accomplished by this
method. Photoplethysmography employs a transducer that transmits infrared light
572 K. S. Suresh and A. Sukesh Kumar

Fig. 3 Mild diabetic arteriopathy of lower limb presented with permission from Dr. Joe’s Ultra-
sound Scan, Cochin; www.ultrasound-images.com

from an emitting diode into the tissue. Part of the transmitted light is reflected back
from the blood within the cutaneous microcirculation and is received by an adjacent
phototransistor. The amount of reflected light varies with the blood content of the
microcirculation. This photo-transducer is taped to the end of the toe with a double-
faced cellophane tape while a small digital blood pressure cuff is placed at the base of
the digit. The pressure at which the waveform obliterates corresponds to the digital
systolic pressure.

6 Conclusion

An integrated model is developed for early detection and monitoring of diabetic

foot. The hemodynamic model is developed and verified with secondary mecha-
nisms. Experiments have done and results are very satisfactory. More trials have
to be accomplished to produce a fruitful design. Ultrasound, plethysmography and
transcutaneous oxygen measurement technologies are found to be most promising.
An Integrated Model for Early Detection and Monitoring of … 573

Acknowledgements We are very much thankful to Dr. Joe’s Ultrasound Scan, Cochin and Indian
Institute of Diabetes, Trivandrum for providing clinical support for this research work.

References

1. International Diabetes Federation, Annual Report 2014

2. World Health Organization, Diabetes Programme, http://www.who.int/diabetes/en/, 2015
3. International Diabetes Federation, IDF Diabetes Atlas Sixth edition 2013
4. International Diabetes Federation, Diabetes and Foot Care Time to Act, 2005
5. International Working Group on the Diabetic Foot, Guidance documents, http://iwgdf.org/
guidelines/ 2015
6. G.E Reiber, J.W. Lemaster, Kaufman, Epidmiology and economic impact of foot ulcers and
amputations in people with diabetes, in Levin and O’Neal’s The Diabetic Foot, 7th edn. (Mosby
Elsevier, 2008), pp. 3–22
7. K.S. Suresh, Dr. A.S. Kumar, An investigation for early stage diagnosis of diabetic foot. Int. J.
Enhanced Res. Sci., Technol. Eng., 5(12), 40–43 (2016)
8. N. Bessonov, A. Sequeira, S. Simakov, Y. Vassilevskii, V. Volpert, Methods of blood flow
modelling, Math. Model. Nat. Phenom. 11(1), 1–25 (2016)
9. D.E. McMillan, Hemorheology: principles and concepts, in Levin and O’Neal’s The Diabetic
Foot, 7th edn. (Mosby Elsevier, 2008), pp. 75–88
10. AIUM practice guide line for the performance of peripheral arterial ultrasound examinations
using color and spectral doppler imaging, American Institute of Ultrasound in Medicine (2010)
11. K. Vowden, P. Vowden, Hand-held doppler ultrasound: the assessment of lower limb arterial
and venous disease. www.huntleigh-diagnostics.com (2002)
12. K.S. Suresh, Dr. A.S. Kumar, Clinical need of a diabetic foot infection detector, in National
Conference on Advances in Computational Intelligence & Communication Technologies,
pp. 125–128 (2016)
13. AIUM practice guide line for the performance of Peripheral venous Ultrasound examinations,
American Institute of Ultrasound in Medicine, 2010
14. D. Lingegowda, S. Moorthy, K.P Sreekumar, R.R. Kannan, Imaging in diabetic ischemic foot.
Int. J. Diab. Dev. Countries, 30(4), 179:184 (2010)
15. S. Zimny, F. Dessel, M. Ehren, M. Pfohl, H. Schatz, Early detection of microcirculatory impair-
ment in diabetic patients with foot at risk. Diab. Care 24, 1810–1814 (2001)
16. D. Yudovsky, A. Nouvong, K. Schomacker, L. Pilon, Assessing diabetic foot ulcer development
risk with hyperspectral tissue oximetry. J. Biomed. Opt. 16(2), 026009 (2011)
Real Time Periodic Assessment of Retina
of Diabetic Patients for Early Detection
of Diabetic Retinopathy

P. G. Prageeth, A. Sukesh Kumar and K. Mahadevan

1 Introduction

Increase of diabetic patients in INDIA is in an alarming proportion. Uncontrolled

diabetes can lead to blindness. Normally this is due to diabetic retinopathy. If it
is detected earlier and required treatments are taken, blindness can be avoided. It
may affect both the eyes simultaneously. Diabetic retinopathy is affected to 50% of
diabetic patients. Diabetic Maculopathy and Diabetic Neuropathy are the common
affected diseases in diabetic patients. The possibility of blindness for these types of
patients is 25% more. Diabetic retinopathy is of two types: Non-proliferated diabetic
retinopathy and Proliferated diabetic retinopathy [1, 2]. Vitreous heamorrhage and
retinal detachments are the immediate complications leading to blindness, if proper
treatment is not provided at the correct time. If it reaches to the complicated level and
loses vision, then it is not possible to revert. Hence diabetic patients who are affected
with vision may be monitored periodically to assess the real status of retina. Hence
apart from a multi powered disease control approach, it is highly essential to utilize
the advance technology enabling the doctors to have regular real time assessment of
retinopathy in diabetic patients through telemedicine [3].
Diabetic retinopathy is a condition occurring in persons with diabetes, which
causes progressive damage to the retina, the light sensitive lining at the back of the

P. G. Prageeth (B)
Department of ECE, College of Engineering Trivandrum, University of Kerala,
Thiruvananthapuram, Kerala, India
e-mail: prageethpg@cet.ac.in
A. Sukesh Kumar
Department of ECE, University of Kerala, Thiruvananthapuram, Kerala, India
e-mail: drsukeshkumara@cet.ac.in
K. Mahadevan
Department of Ophthalmology, Medical College, Thiruvananthapuram, Kerala, India
e-mail: eyemahadevan@rediffmail.com
© Springer Nature Switzerland AG 2019 575
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_50
576 P. G. Prageeth et al.

eye. It is a serious sight-threatening complication of diabetes. Diabetes is a disease

that interferes with the body’s ability to use and store sugar, which can cause many
health problems. Too much sugar in the blood can cause damage throughout the
body, including the eyes. Over time, diabetes affects the circulatory system of the
retina. Diabetic retinopathy is the result of damage to the tiny blood vessels that
nourish the retina. They leak blood and other fluids that cause swelling of retinal
tissue and clouding of vision. The condition usually affects both eyes. The longer
a person has diabetes, the more likely they will develop diabetic retinopathy. If left
untreated, diabetic retinopathy can cause blindness [4].
Symptoms of diabetic retinopathy include:
• Seeing spots or floaters in your field of vision
• Blurred vision
• Having a dark or empty spot in the center of your vision
• Difficulty seeing well at night
The ocular fundus is the only part of human body through which the vascu-
lar network can be observed directly and non-invasively. This can provide a lot
of pathological information about eye diseases such as glaucoma, central serous
retinopathy (CSR) and early signs of systemic diseases like diabetes, hypertension
and cardiovascular diseases. All over the world, the patients having these diseases
are increasing day by day. The medical imaging technology is developing in such
a way that mass screening of patients is possible in ophthalmology. Nevertheless,
the scarcity of medical experts in all landmarks of a country is limiting the mass
screening of patients in developing countries. Hence, development of an automated
system for analyzing digital fundus images and diagnosing the diseases is the greatest
challenge, when mass screening of patients is needed [5]. The present work involves
detection, quantification and analysis of retinal image parameters for various dis-
eases and combined so that an intelligent system is developed for the diagnosis of
glaucoma, diabetes, hypertension, stroke, heart attack and central serous retinopathy.
Large numbers of retinal images of patients with necessary pathological data were
taken from Regional Institute of Ophthalmology (Dept. of Ophthalmology), Medical
College, Thiruvananthapuram for this work. The labelled diagram of a human eye
and an image of the retina is shown in Fig. 1. Diabetes is detected from the presence
of exudates and haemorrhages and changes in blood vessel parameters like arteriolar-
to-venular diameter ratio (AVR). Images obtained from fundus camera are enhanced
using filtering. Image segmentation is done to detect optic disc, fovea, exudates area
and blood vessels. Connected component method along with concentric circle meth-
ods are used to determine the artery-vein width ratio. An algorithm is developed for
the detection and quantification of the disease level from the parameters specified.
The result is validated with the clinical data of the patient and achieved good results.
A predictor system is developed to give the status of the patient from the analysis of
the retinal image parameters using neural network techniques [6, 7].
A Fundus Camera which is used to obtain fundus images of the human retina is
shown in Fig. 2. In the camera the beams propagating from two light sources, and
Real Time Periodic Assessment of Retina of Diabetic Patients … 577

Fig. 1 Human eye

cross-sectional view and a
retinal image

Fig. 2 A fundus camera and

its accessories

incandescent lamp used for viewing the fundus and ash lamp for photography, are
optically combined by a beam splitter [8].
The fundus camera images of normal and diabetic patients are shown in Figs. 3
and 4. These images are used to detect and diagnosis the disease and the method of
automatic detection systems are explained.

2 Proposed Method

The Graphical User Interface (GUI) window for the detection of diabetic retinopathy
is designed as shown below in Fig. 5. This disease has dark red and yellow spots
in it retinal fundus images. First input the image. Then resize to required size. Find
578 P. G. Prageeth et al.

Fig. 3 Fundus image of a

normal eye

Fig. 4 Fundus image of a

diabetic patient’s eye

the hue, saturation and intensity of the image [9]. Find contrast, homogeneity and
correlation. Find threshold value for each. Use these values for disease detection.
In machine vision, colors of the pixels are composed from Red, Green and Blue,
each measured in 8 bits (2 hexadecimal bits) [10]. The complete representation of a
color would be of 6 hexadecimal bits. The problem is that a family of colors (like
the orange and the combinations close to it) cannot be easily known from that 6 bits
representation. Moreover, the changes in brightness will cause enormous changes in
the RGB representation of a certain color. Therefore, in machine vision, the most
used color representation is the HSI color space, which consists of Hue angle, Color
saturation and Intensity [11]. To be independent of the intensity variance, we use the
HS space. This will also help in making the processing and the computing faster.
The above describes histogram equalization on a gray scale image. However it
can also be used on color images by applying the same method separately to the
Red, Green and Blue components of the RGB color values of the image. However,
applying the same method on the Red, Green, and Blue components of an RGB
image may yield dramatic changes in the image’s color balance since the relative
distributions of the color channels change as a result of applying the algorithm [12].
However, if the image is first converted to another color space, then the algorithm
can be applied to the luminance or value channel without resulting in changes to the
Real Time Periodic Assessment of Retina of Diabetic Patients … 579

Fig. 5 Proposed GUI window for the detection of diabetic retinopathy

hue and saturation of the image. There are several histogram equalization methods in
2D and 3D space. However, it results in “whitening” where the probability of bright
pixels is higher than that of dark ones [13].
With a large number of variables, K-Means may be computationally faster than
hierarchical clustering (if K is small). K-Means may produce tighter clusters than
hierarchical clustering, especially if the clusters are globular. Contrast is defined
as the separation between the darkest and brightest areas of the image. Increase
contrast and you increase the separation between dark and bright, making shadows
darker and highlights brighter. Contrast enhancement plays a crucial role in image
processing applications, such as digital photography, medical image analysis and
scientific visualization. Image enhancement is a technique which reduces image
noise, remove artifacts, and preserve details [14, 15]. Its purpose is to amplify certain
image features for analysis, diagnosis and display. Contrast enhancement increases
the total contrast of an image by making light colors lighter and dark colors darker
at the same time. It does this by setting all color components below a specified
lower bound to zero, and all color components above a specified upper bound to the
maximum intensity (that is, 255). Color components between the upper and lower
bounds are set to a linear ramp of values between 0 and 255. Because the upper
bound must be greater than the lower bound, the lower bound must be between 0 and
254, and the upper bound must be between 1 and 255 [16, 17].
580 P. G. Prageeth et al.

Fig. 6 Fundus image of a

diabetic patient in RGB to
input to the GUI window

There are several reasons for an image/video to have poor contrast:

|| the poor quality of the used imaging device, |
|| lack of expertise of the operator and |
|| the adverse external conditions at the time of acquisition.|
These effects result in under-utilization of the offered dynamic range. As a result,
such images and videos may not reveal all the details in the captured scene, and may
have a washed-out and unnatural look. In graphics and imaging, color saturation is
used to describe the intensity of color in the image [18]. A saturated image has overly
bright colors. Using a graphics editing program we can increase saturation on under-
exposed images, or vice versa. Digital Image Correlation (DIC) is a full-field image
analysis method, based on grey value digital images that can determine the contour
and the displacements of an object under load in three dimensions. Due to rapid
new developments in high resolution digital cameras for static as well as dynamic
applications, and computer technology, the applications for this measurement method
has broadened and DIC techniques have proven to be a flexible and useful tool for
deformation analysis.
The image shown in Fig. 6 is that of an acute diabetic patient. Likewise we can
give normal, mild, moderate, severe levels of images as the inputs to the GUI window
and can get the corresponding output parameters and predictions [19, 20]. For the
sample input image given above, the output images of the parameters helpful for all
men to detect the disorders and the clinicians for the diagnosis, are shown in Fig. 7.
Real Time Periodic Assessment of Retina of Diabetic Patients … 581

Fig. 7 Output images for evaluating the parameters of eye of a diabetic patient

3 Conclusion

According to the above images and values, we can send all the parameters to the highly
qualified ophthalmologists. Final decisions and all other curing methods, preventive
medicines and the consultation if needed should be done by the clinicians. The above
developed system can be used by the biomedical engineers to help the doctors and
the remotely resident patients. If this system is developed to work in online way,
then the doctors can identify the eye conditions of the patients who are very far away
from hospitals. The system can be developed to work as a kiosk in remote areas like
ATM machines, X-ray labs, Clinical labs to test the blood and all etc. Then it will be
very useful and will get a maximum coverage of the patients around the globe. The
doctors need not run to all patients here and there. The patients can go to the very
nearby labs and if needed only they can go the service of the doctors.
We now designed only a prototype of the system in software model only. If this
system is to be developed in a hardware model, sufficient fund is needed just to make
a sample. Then only we can make arrangements for the commercialization of the
product.
This is going to be a great boon and boom for the common man (actual beneficia-
ries of this project) to get into the prevention of diabetes rather than cure as a result of
periodic review using this project. Unfortunately if any person gets into the diabetic
582 P. G. Prageeth et al.

disorder, then this project will help in the periodic assessment of the various levels
of the disease, thereby avoiding the progression of the disorder cent percentage.

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Product Recommendation
for E-Commerce Data Using Association
Rule and Apriori Algorithm

Soma Bandyopadhyay, S. S. Thakur and J. K. Mandal

1 Introduction

Data mining is a multidisciplinary research field as it involves database technology,

artificial intelligence (AI), machine learning (ML), statistical modeling and object
oriented approach [1] etc. Data mining is used to extract useful information and
discover knowledge from hidden patterns in available data [2]. With the application
of mining algorithm—Apriori, purchasing habits of customers can be analyzed by
finding associations among different items that customers add to their shopping cart.
From the user’s transaction dataset rules can be generated for customers’ buying ten-
dency. Based on product purchased by customers and their profile, recommendation
about products can be suggested using association rule mining technique. The dis-
covery of such association rules can assist the customers to fulfill their needs, as well
as retailers to develop marketing strategies and increase sales. In the modern world
where the numbers of choices are vast, the recommender systems assist consumers
to find items of their interest. They link users with items to purchase, view, listen
to, etc. by correlating the content of suggested items. Buying behavior of customers
for future can be predicted by the analysis using past buying behavior. The various
form of recommendation available are providing personalized product information,

S. Bandyopadhyay (B) · S. S. Thakur

Computer Science and Engineering, MCKV Institute of Engineering,
243, G.T. Road, Liluah, Howrah 711204, India
e-mail: somabanmuk@yahoo.co.in
S. S. Thakur
e-mail: subroto_thakur@yahoo.com
J. K. Mandal
Computer Science and Engineering, University of Kalyani, Kalyani,
Nadia 741235, India
e-mail: jkm.cse@gmail.com

© Springer Nature Switzerland AG 2019 585

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_51
586 S. Bandyopadhyay et al.

summarizing community opinion etc. These recommendation systems are integral

part of personalization on a website as they help the site to familiarize with each
customer [3].
Data mining techniques are incorporated in recommender system to make rec-
ommendations using knowledge gathered from different attributes about products
and actions taken by user. The architecture of data mining consists of main com-
ponents [4, 5] like data warehouse, database or other repositories of information. A
server fetches the appropriate data from repositories based on user’s request where
knowledge base is used as guide to search according to defined constraint. Charac-
terization, classification, clustering, association, regression and analysis evolution
are the essential modules of data mining engines. To accurately achieve interested
patterns, the pattern evaluation module interacts with data mining module. The user
can communicate with the data mining system through graphical user interfaces.
This paper outlines the implementation of Apriori algorithm [6] by applying asso-
ciation rules to increase product sales. This work proposes a recommender system
based on Apriori algorithm.

2 Recommender System

By correctly suggesting products to customers a relationship is created between

the customers and the website, which increases consumer loyalty. These customers
are expected to return to the same site where correct choices about products were
recommended earlier. Recommender system, discovered from association rule is a
very popular technique used, which helps to identify item-to-item correlation. More
powerful systems match an entire set of items, such as those in a customer’s shopping
cart, should be able to identify appropriate items to recommend. These rules can also
help a retailer to arrange products e.g. a consumer purchasing a child’s handheld
video game seeks batteries nearby.
Recommender system enhance E-commerce sales in three ways: Converting
Browsers into Buyers, Increasing Cross-sell and Building Loyalty as are discussed
below.
Converting Browsers into Buyers: In general, a customer or visitor browse a
website first and look over a site without purchasing anything. Recommender systems
can help them to find products, which they want to purchase as per their requirements.
Thus, the browsers may be converted into buyers.
Increasing Cross-sell: Recommender systems [7, 8] can improve cross-sell by
providing additional products for the customer, which they want to purchase in near
future. If the recommendations are satisfactory, the average order may increase.
Building Loyalty: In modern world where there is a large number of competitors,
Product Recommendation for E-Commerce Data … 587

gaining consumer loyalty is an important strategy as business is concern. By creating

a value-added relationship between the site and the customer, recommender system
can improve loyalty. Web sites invest lot of funds in learning about the customers’
behavior and finally the recommender systems provide an interface that match con-
sumer needs with products placement.

3 Proposed Approach

Product prediction and recommendation of E-commerce website emphasizes some

key areas. Work flow diagram of our proposed recommender system has been shown
in Fig. 1 in Sect. 3.1 for prediction and recommendation of E-commerce website.
Association Rule and Apriori algorithm that is used in this work is described in
Sect. 4 and 5 respectively. Experimental evaluation is discussed in Sect. 6, followed
by Results and Conclusion.

3.1 Work Flow Diagram of Proposed Recommender System

Fig. 1 Work flow diagram of proposed recommender system

588 S. Bandyopadhyay et al.

4 Association Rule

Learning item-to-item correlations or ‘association rule’ in data mining helps rec-

ommender system to identify items frequently found in “association” with items
in which a user has shown interest. Association can be based on co-purchase data,
preference given by users, or any other measures. Powerful recommender systems
match an entire set of items, which may be in a customer’s shopping basket. For e.g.,
data mining may suggest that a customer who buys a video game today is likely to
buy a pair of earplugs, in near future.

4.1 Meaning and Uses

Association rules have been used in retailing helps to analyze items [9] of prefer-
ence of product and further suggest products to consumers based on other products
they have purchased earlier. The relationship with which one product is often chosen
along with other products is expressed by association rules. There is an exponential
relationship between the numbers of possible association rules with the number of
products in a rule. However effective search space is reduced due to constraints on
confidence and support, combined with algorithms that build association rules with
itemsets of n items from the rules with (n-1) items of itemsets. If shelf layout of a
retail store is organized by maintaining association rule, it will definitely improve the
efficiency and performance of the store. To recommend items to a customer, associa-
tion rule is used as a powerful tool as domain knowledge management is concerned.
So the recommendation system using association rule can attempt to predict which
product can be most useful to a user.
4.2 Mining Association Rule

Association rules are required to satisfy a user-specified minimum support and

minimum confidence at the same time [10, 11].
Association rule generation is usually split up into two separate steps:
1. Frequent itemset is generated by applying minimum support in a data base.
2. Using these frequent item sets’ and minimum confidence constraint rules are
formed.
To find all frequent itemsets in a database, it is required to search all possible
itemsets (item combinations) from a database. The set of possible itemsets is the
power set over I and has size 2n-1 (excluding the empty set which is not a valid
itemset). Here I—mean average size of the maximum potentially large items and n
means number of items. The size of the powerset grows exponentially in the number
of items n in I. Efficient search is possible using the downward-closure property of
support which guarantees that for a frequent itemset, all its subsets are also frequent.
For an infrequent itemset, all its supersets must also be infrequent. Hence, by applying
efficient algorithms, Apriori can find all frequent itemsets, and other association rules
like Eclat and FP-Growth may be used.
Product Recommendation for E-Commerce Data … 589

5 Apriori Algorithm for Product Recommendation

The first pass of the algorithm counts item occurrences to determine the large 1-
itemsets [12, 13]. A subsequent pass, say pass i, consists of two phases. First, the
large itemsets Li-1 found in the (i-1)th pass are used to generate the candidate itemsets
Ci , using the apriori candidate generation function. After that, the database is scanned
and the support of candidates in Ci is counted. For fast counting, the candidates in Ci
that are contained in a given transaction T is to be determined. A skeleton of Apriori
Algorithm [14, 15] which has been used in this work is described below.
1. Collect the data from a retail shop.
2. In first pass, generate the candidate itemsets in C1 and save the frequent itemsets
in L1 .
3. From the frequent itemsets in Li-1 generate the candidate itemsets in Ci in ith
pass.
(a) Join Li-1 p with Li-1 q as follows:
insert into Ci
select p. item1, p. item2, …, p. itemi-1, q. itemi-1 from Li-1 p, Li-1 q
[here p. item1  q. item1, …, p. itemi-2  q. itemi-2, p. itemk-1 < q. itemk-1 ]
(b) From the candidate itemsets in Ci generate all (i-1) subsets.
(c) From Ci prune all candidate itemsets where (i-1) subset of the candidate itemsets
is not in the frequent itemsets Li-1 .

6 Experimental Evaluation

The dataset which was used in this work contains 4500 data samples and each record
contains 9 attributes. Each transaction consists of items purchased by a customer
in one interaction with developed site. Out of 4500 transactions the dataset of 15
transactions is shown in Table 1. The itemsets which was bought by the customer at
least in 3 transactions i.e. 20% of the transactions have been taken for this work.
Using transaction dataset, the candidate1-itemset is shown in Table 2. Table 3
shows the details of each transaction.
From Table 2 it can be observed that most popular transaction was A5.
Table 3 shows the details of transaction and minimum support is considered as
20%. Table 4 shows the Frequent 2-itemset. Here all the itemsets having less than
20% support have been pruned.
Finally, in Table 5 the Frequent 3-itemset is shown. It is evident that this occurrence
will happen most frequently that if a person purchases item A3 (Jeans) he/she will
also purchase A5 (T-Shirt) and A7 (Kurti) item as shown in Table 5.
From the sample dataset, the itemset {Jeans, T-Shirt, Kurti} has a support of
3/15  0.20 since it occurs in 20% of all transactions. Here 3 is the number of trans-
actions, from the dataset which contains the itemset {Jeans, T-Shirt, Kurti} while 15
 590

Table 1 Transaction dataset

Transaction Itemset
A1 Shirt A2 Pant A3 Jeans A4 Salwar A5 T-Shirt A6 Saree A7 Kurti A8 Shoe A9 Socks
Kamij
1 1 0 0 0 1 1 0 1 0
2 0 1 0 1 0 0 0 1 0
3 0 0 1 1 1 0 0 0 0
4 0 1 0 0 0 0 1 0 0
5 0 0 1 0 1 1 0 0 0
6 0 1 0 1 0 0 1 0 0
7 0 1 1 0 0 1 0 0 0
8 0 0 0 0 1 0 0 0 1
9 0 0 0 0 0 0 0 1 0
10 0 0 1 0 1 0 1 0 0
11 0 0 1 0 1 0 1 0 0
12 0 0 0 0 1 1 0 1 0
13 0 1 1 1 0 1 0 0 0
14 1 0 1 0 1 0 1 0 0
15 0 1 0 0 0 0 1 0 1
S. Bandyopadhyay et al.
Product Recommendation for E-Commerce Data … 591

Table 2 Candidate-1 itemset Itemsets X Transaction count

A1 2 Deleted
A2 6
A3 7
A4 4
A5 8
A6 5
A7 6
A8 4
A9 2 Deleted

Table 3 Details of Transaction ID Items bought

transaction
T1 {A1, A5, A6, A8}
T2 {A2, A4, A8}
T3 {A3, A4, A5}
T4 {A2, A7}
T5 {A3, A5, A6}
T6 {A2, A4, A7}
T7 {A2, A3, A6}
T8 {A5, A9}
T9 {A8}
T10 {A3, A5, A7}
T11 {A3, A5, A7}
T12 {A5, A6, A8}
T13 {A2, A3, A4, A6}
T14 {A1, A3, A5, A7}
T15 {A2, A7, A9}

Table 4 Frequent 2-itemset Itemsets X Transaction count Support X

A2, A4 3 0.20
A2, A7 3 0.20
A3, A5 5 0.33
A3, A6 3 0.20
A3, A7 3 0.20
A5, A6 3 0.20
A5, A7 3 0.20

Table 5 Frequent 3-itemset Itemsets X Transaction Support X Confidence

count (XUY)/X
A3, A5, A7 3 0.20 0.60
592 S. Bandyopadhyay et al.

represents the total number of transactions. For the rule {Jeans, T-shirt} > {Kurti}
the confidence is mentioned below:
support ({Jeans, T-Shirt, Kurti})/support ({Jeans, T-Shirt})  0.20/0.33  0.60
This means the rule is correct for 60% of the transactions containing Jeans and
T-Shirt.

7 Result and Conclusion

As computational complexity of the Apriori algorithm is concerned, the result shows

that for 60% cases the rule is correct. In our future work by using the same dataset
modified Apriori algorithm will be applied and thereafter the comparison between
the performances of the two can be measured.
This system has been implemented using JSP. The presentation layer implemen-
tation is done by using CSS and HTML, the validation layer is implemented by
JavaScript. The insertion and retrieval of information have been done using SQL
Queries and interaction with database, implemented by MySQL, is done by Java.
Thus, taking the above facts in consideration, a recommender system has been
designed which can help the customer to fulfill their needs as well as retailer to
develop marketing strategies and increase sales promotion. In future, more itemsets
will be added to our database and we will optimize the program code which may
reduce time complexity of the developed algorithm.

Acknowledgements The authors are thankful to Director, MCKVIE and Principal, MCKVIE, for
providing the Computer laboratories and other infrastructure to do the proposed work. The authors
are also thankful to Santosh Sagar, student of CSE department of MCKVIE for collecting the
required data for the proposed work.

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A Comparative Analysis Between EDR
and Respiration Signal: A Pilot Study
with Normal Subjects

Surita Sarkar, Saurabh Pal and Parthasarathi Bhattacharyya

1 Introduction

Respiration is one of the most important physiological parameters that should be

monitored and diagnosed regularly for different conditions specially in chronic dis-
eases [1, 2]. Abnormal and changing respiration is one of the earliest indicators
of major physiological instabilities [3]. Even regular follow-up of respiration can
predict the risk of serious adverse events [4]. On the other hand, obstructive lung
disease becomes a major problem globally with increasing rate of morbidity and
mortality due to this [5–7]. Continuous exposure to smoking, pollution, dust par-
ticles and various allergens are the main factors behind this [8, 9]. However, it is
unfortunate that respiration signal is often neglected in regular follow-up due to
lack of awareness and unavailability of unobtrusive and accurate respiratory moni-
tor [10, 11]. As a result most of the time the patient is unaware of the disease and
does not visit the doctor until it becomes severe [6]. Equipments like spirometry,
inductive plethysmography, impedance pneumography, respiratory belts, lung imag-
ing techniques (X-ray, CT scan etc.) are commonly used [3, 12, 13, 14] and some
new techniques like microelectromechanical system based acceleration sensor and
low power ambulatory wearable are developed [15, 16] for measurement of respira-
tion and lung obstruction. But most of these methods often exhibit several problems

S. Sarkar (B) · S. Pal

Department of Applied Physics, University of Calcutta,
92 A.P.C. Road, Kolkata 700009, India
e-mail: sarkar.surita@gmail.com
S. Pal
e-mail: spal76@gmail.com
P. Bhattacharyya
Institute of Pulmocare & Research, DG-8, Action Area-1, New Town,
Kolkata 700156, India
e-mail: ipcr_india@yahoo.com
© Springer Nature Switzerland AG 2019 595
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_52
596 S. Sarkar et al.

because commonly used equipments highly interfere with the patient and are often
prone to noise. In this situation, various researchers found that respiration signal
derived from ECG could be a useful alternative [17–19]. ECG is a common and pop-
ular test, often prescribe by the medical practitioners in regular follow-up. Moreover,
the influence of respiration on the cardiac activity has already established in previ-
ous literatures [20, 21]. During respiration, cardiac axis changes due to expansion
and contraction of chest [22]. Heart rate variability (HRV), on the other hand, is also
effected by Respiratory Sinus Arrhythmia (RSA) due to which R-R interval decreases
during inspiration and increases during expiration [21]. Using these effects, different
algorithms are developed to extract ECG derived respiration signal [22, 23].
In this study, two normal subject groups- one without any present symptoms
and one group with symptoms like cold, cough, etc. were taken for data collection.
Features extracted from the respiration signal acquired from the respiration belt are
compared with the same features extracted from the derived respiration signal from
ECG (EDR). Also the statistical significance of the features was analysed.

2 Method

The whole study was done based on real time data collection of subjects followed by
pre-processing of ECG and respiration signal, EDR extraction and feature extraction.
Each section is described elaborately.

2.1 Data Collection

In order to evaluate EDR signals, real-time datasets were used. Simultaneous record-
ing of ECG and respiration signal were collected using a data acquisition system
called MP-45, designed by Biopac Systems Inc. [24]. ECG signal was collected
using lead-II single-lead ECG, whereas, respiration signal was acquired using the
respiratory effort transducer (SS5LB) by measuring the volume change in thoracic
cavity. The respiration signal collected using the chest belt was used as the original
respiration signal in analysis. The study was done based on a protocol approved by the
Institutional Ethics Committee of Institute of Pulmocare and Research, Kolkata. Data
were collected from the subjects only after they agreed to give written informed con-
sent. Medical history of each subject was taken prior to a physical examination done
by a medical expert before enrolment. All the subjects were evaluated by spirom-
etry as per rule of the ATS guideline [25]. In this study, a total of twelve subjects
with normal ECG and spirometry were included. Among them, six normal subjects
are completely healthy and without symptoms. Other six subjects, though exhibited
normal spirometry; they had mild symptoms like sneeze, cold, cough, etc. present at
the time of data collection. Recording of each subject was done at a sampling rate of
1000 Hz and for 300 s time-duration while the patient was resting at supine condition.
A Comparative Analysis Between EDR and Respiration … 597

The real-time data were collected from the Institute of Pulmocare and Research and
further analysis was carried out in the Biomedical Instrumentation Laboratory of
Department of Applied Physics, University of Calcutta. Subjects having any kind of
lung and cardiac diseases were excluded from this study. The demographic parame-
ters of the two subject groups are shown in Table 1.

2.2 Pre-processing of ECG and Respiration Signal

ECG and respiration signals were collected simultaneously for each subject. The
design of this study is shown in Fig. 1.

Table 1 Demographic parameters of normal subjects without and with symptoms

Subject Total population Age (Mean ± Male:Female BMI (Mean ±
SD) ratio SD)
Normal without 6 27.33 ± 7.06 1:1 22.97 ± 3.7
symptom (N)
Normal with 6 37.83 ± 11.47 2:1 22.91 ± 2.24
symptoms (NS)

Fig. 1 Block diagram shows a comparative study between features extracted from both EDR and
respiration signal
598 S. Sarkar et al.

From both ECG and respiration signal, 80,000 samples were taken for data anal-
ysis purpose. Each signal was de-noised using filter. For ECG signal, a 2nd order
Bandpass Butterworth filter was used for removal of noises. R-peaks were detected
from the filtered ECG signal using sliding window technique for a window length of
2 s. The ECG waveform was then normalized to zero mean and unit variance. After
applying a threshold to identify the potential R-peaks, a 500 ms sliding window
was applied again. The peak with maximum value within the span was found out
to be recognized as the actual R-peak. The whole process was done for the entire
length of ECG samples taken. After the R-peaks were detected, their amplitudes were
calculated against the baseline and plotted against their corresponding locations. Res-
piration signals were also filtered and normalized before feature extraction.

2.3 ECG Derived Respiration

To extract a surrogate respiratory signal from ECG signal, the respiration mechanism
that affects the ECG signal, should be observed. The respiration activity influences
the cardiac activity in different ways- one of those affects beat morphology [26, 27].
The expansion and contraction of lungs during respiration cause change in apex of
heart, therefore, affecting the electrical axis direction. As a result thoracic impedance
which is closely related with the change in lung volume, also changes [26]. At the
time of inhalation the electrical impedance across lungs increases.
This respiratory induced change in thoracic impedance affects the QRS ampli-
tude of ECG signal, where the QRS amplitude decreases during inspiration and the
amplitude increases at the time of expiration.
There are several algorithms developed for EDR extraction. In this study, the
modulation change in QRS amplitude is used for EDR extraction.
After detection, R-peaks were arranged against the time axis and cubic spline
interpolation was used to create an EDR signal resembles to the original respiration
signal [28]. If the original signal be, ki  f (gi ), where i  0, 1, 2, . . . , m − 1, then
the output of the interpolation within a specific range of [ti , ti+1 ], t0 ≤ t ≤ tm−1 , can
be written as,

k  uki + vki + 1 + wki + xki + 1 (1)

With coefficients be like,

ti+1 − t 1 1
u , v  1 − u, w  (u 3 − u)(ti+1 − ti )2 , x  (v 3 − v)(ti+1 − ti )2
ti+1 − ti 6 6
A Comparative Analysis Between EDR and Respiration … 599

2.4 Feature Extraction

Respiration is one crucial physiological parameter. Breathing pattern changes upon

different physiological changes in lungs [29]. Even common disease like cough and
cold can change this pattern. Based on this, three features were extracted from both
original respiration signal and extracted EDR signal.

2.4.1 Area Ratio

The locations of the starting (S), peak (P) and ending (E) points (as shown in Fig. 2)
were detected using peak detection algorithm for one respiratory cycle. The location
of the peak against the baseline was taken as point R. Using the points S, P and R,
inspiration area was calculated and expiration area was calculated using the locations
of P, R and E. Area ratio (A) was calculated for five randomly chosen cycles and the
average was taken as the area ratio of that subject. The same procedure was done for
EDR signal. Area ratio was calculated using the following formula (Eq. 2),
E x piration ar ea
A (2)
I nspiration ar ea

2.4.2 Time Ratio

Time ratio was calculated by taking the ratio of expiration time to inspiration time.
To compute inspiration and expiration time, starting (S), peak (P) and ending (E)
point locations were detected for one respiratory cycle. The time ratio (T) can be
written as,
Time interval between points P and E
T  (3)
Time interval between points S and P

Fig. 2 ‘S’ denotes the starting point, ‘P’ denotes the peak and ‘E’ denotes the ending point of a
respiratory cycle
600 S. Sarkar et al.

The whole procedure was done for five consecutive times from randomly chosen
cycles. The same method was followed in case of EDR signal.

2.4.3 Respiration Rate

Respiration rate was calculated by counting the total number of one complete res-
piration cycle (one inspiration and one expiration) present within time interval of
60 s. The time duration between two consecutive maxima was calculated and the
respiratory rate (RR) was estimated using the following formula (Eq. 4).
60
RR 
T ime duration for occurence of [(kth − (k − 1)th] r espirator y peaks
(4)

Average respiration rate was calculated by taking the average of five consecutive
respiratory rates and the same method was applied for EDR signal also.
The statistical analysis was done using student t-test to see if the extracted features
are significant or not.

3 Result

A total of 12 subjects were included in this study for analysis. None of them were
smoker or under any kind of medication. The EDR signal derived for each subject
was compared with the original respiration signal acquired of that person. Traces of
EDR signal followed by the original respiration signal for both the subject groups
(N and NS) are shown in Fig. 3.
From the above figures it can be seen that the respiratory pattern of subject with-
out any symptom (Fig. 2a) differs from the respiratory pattern of the subject with
symptom (Fig. 2b), whereas, no significant change can be noticed in between the
EDR patterns of those subjects. The three features discussed in method section were
extracted for each of the twelve subjects. The features and their corresponding p-
values are shown in Table 2.
Table 2 shows that the p-values of respiratory rate calculated from both the sig-
nals are not statistically significant in case of both subject groups. But for other two
features (i.e. area ratio and time ratio) derived from the EDR and the original res-
piration signal, the p-value significantly changes in case of subjects with symptoms
according to Table 2. The p-values estimated for area ratio and time ratio from both
EDR and original respiration signal turn out to be statistically insignificant for those
without any symptoms.
Table 2 Features extracted from EDR and original respiration and their corresponding p-values
Name State EDR area Respiratory P value EDR time Respiratory P value EDR RR* Original RR P value
(N/NS) ratio (mean) area ratio ratio (mean) time ratio (mean) (mean)
(mean) (mean)
Subject 1 N 0.60 0.84 0.6334 0.57 0.89 0.6604 16 16 1
Subject 2 N 1.05 1.06 0.886 1.00 1.01 0.1782 20 20 1
Subject 3 N 1.01 0.92 0.4594 0.93 0.73 0.1527 15 15 0.3972
Subject 4 N 0.93 0.91 0.8231 0.74 0.65 0.5034 15 15 0.6811
Subject 5 N 1.03 0.95 0.4438 0.86 0.93 0.4416 18 18 1
Subject 6 N 1.05 0.94 0.3874 0.93 0.99 0.4654 22 22 0.6666
Subject 7 NS 1.01 1.22 0.0009 0.87 1.33 0.0001 21 21 1
A Comparative Analysis Between EDR and Respiration …

Subject 8 NS 0.93 1.25 0.0002 0.95 1.25 0.0059 18 18 0.6666

Subject 9 NS 0.78 1.68 0.0329 0.79 1.89 0.0257 10 9 0.195
Subject 10 NS 0.76 1.12 0.0035 0.72 1.47 0.0021 17 17 1
Subject 11 NS 0.83 1.38 0.0428 0.84 1.68 0.0021 21 21 1
Subject 12 NS 0.83 1.34 0.0195 0.79 1.76 0.0043 15 15 0.8548
*RR denotes Respiratory Rate
601
602 S. Sarkar et al.

1.3
(a) Original respiration signal
1.25 EDR signal
1.2

1.15
Amplitude

1.1

1.05

0.95
2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4
Samples x 10

0.6 (b) Original Respiration Signal

EDR signal
0.55

0.5
Amplitude

0.45

0.4

0.35

0.3

2 2.5 3 3.5 4 4
x 10
Samples

Fig. 3 Figure shows a The EDR and original respiration signal of a subject without symptom and
b the EDR and respiration signal of a subject with symptom

4 Discussion

In medical diagnosis, both ECG and respiration should be monitored regularly

for detecting any abnormality in cardio-pulmonary system. In countries like India,
though ECG is done in routine check-up, respiration monitoring remains neglected
most of the time. On the other hand, respiration has well-known influence on heart.
Therefore, derivation of respiratory information from ECG will be an alternative
tool to monitor both ECG and respiration. In this study, EDR signal is extracted from
the ECG signal based on the R peak amplitude variation. It is interesting to note that,
though all the twelve patients have shown normal spirometry, the respiration pattern
for those with symptoms showed difference from that of those without symptoms.
The result also reflects the same. Features extracted from the original respiration
A Comparative Analysis Between EDR and Respiration … 603

signal vary significantly with features extracted from the EDR signal in case of
subjects with symptoms only.

5 Conclusion

The study shows an interesting result of applicability of EDR which can be estab-
lished clinically by further analysis on bigger dataset. Despite of small dataset it can
be concluded that the EDR is a better alternative for respiration monitoring compare
to conventional method where respiration belt is used.

Acknowledgements The first author acknowledges the financial support obtained in the form of
CSIR-SRF fellowship provided by CSIR-HRDG, Government of India.

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Uncertainty in Fission Product Transient
Release Under Accident Condition

Subrata Bera, U. K. Paul, D. Datta and A. J. Gaikwad

1 Introduction

During power irradiation of nuclear fuel pin in Indian pressurized heavy water reac-
tor, fission product radionuclides get accumulated in the fuel matrix. Followed by a
postulated initiating event for a design extension condition without core melt [1] (e.g.,
loss of coolant accident with failure of emergency core cooling system), tempera-
tures of both fuel and clad increase even after reactor shutdown caused by protection
system. This fuel heat up is due to the decay heat generated in the fuel matrix by the
radionuclides produced in the nuclear fission reaction and subsequent radioactive
decay chain. Due to the heating up the fuel pin, the radionuclides get released to
the fuel clad region by thermal diffusion process. Once fuel pin fails on exceeding
the limiting clad temperature, radionuclides get released to the primary heat trans-
port system [2]. Based on the accident sequence and its progression, radionuclides
get transported to containment building through coolant vapour transport route. The

S. Bera (B) · U. K. Paul · A. J. Gaikwad

Nuclear Safety Analysis Division, Atomic Energy Regulatory Board,
Anushaktinagar, Mumbai 400094, India
e-mail: sbera@aerb.gov.in
U. K. Paul
e-mail: ukp@aerb.gov.in
A. J. Gaikwad
e-mail: avinashg@aerb.gov.in
S. Bera
Homi Bhabha National Institute, Mumbai 400094, India
D. Datta
Radiological Physics and Advisory Division,
Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India
e-mail: ddatta@barc.gov.in

© Springer Nature Switzerland AG 2019 605

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_53
606 S. Bera et al.

pressure build up occurs in the containment due to the accumulation of steam and
the associated radionuclides releases from primary coolant system. The incremental
raise of pressure may lead to the release of radionuclides from containment to the
environment if no mitigating accident management action is assumed to be success-
ful. The consequent amount of radionuclides released to the environment is used
for estimation of the radiological impact of a postulated accident scenario [3]. In
the whole process of source term [4–6] evaluation, the time dependent release of
radionuclides from fuel to the fuel-clad gap under elevated temperature condition
[7, 8] is governed by thermal diffusion process. In modelling this phenomenon, first
order release kinetics is considered. The rate of release is proportional to the present
inventory of the radionuclides in the fuel. The proportional constant depends on the
fuel temperature and its dependence is represented by Arrhenius equation with exper-
imentally evaluated activation energy and pre-exponential factor. Thus the fractional
release rate becomes an exponential of an exponential function of temperature. As
this is a non-linear equation, the variability of the fractional release depends on model
sensitivity parameter and variability of fuel temperature. There are many methods
to assess the aleatory uncertainty such as error propagation through direct analytical
expression, probabilistic method based on sampling from uncertain domain [9], emu-
lation approach if the mathematical model is not precisely known, stochastic response
surface formulation [10]. In this paper, it is attempted to quantify the variability of
fractional release due to known variation of temperature.

2 Theoretical Model for Uncertainty Quantification

2.1 Analytical Uncertainty Estimation Methodology

The quantification of error propagation through a general function which can be

linear or non-linear can be done using Taylor series expansion method. For a single
input variable and single output variable, the system response function determines
the sensitivity of input parameter. Based on the Taylor series expansion of a con-
tinuous function with availability of infinite number of derivatives at x  x 0 , the
expansion of f(x) at location x 0 + σ x can be written as given in Eq. (1). Where, x 0 is
the mean value of input variable x; σ x , σ y are standard deviations of input variable
x and output variable y respectively.

σx (1) σ2 σn
f (x0 + σx )  f (x0 ) + f (x0 ) + x f (2) (x0 ) + · · · + x f (n) (x0 ) + · · · (1)
1! 2! n!
In the concise notation, it can be represented as given in Eq. (2).
∞
 σi
f (x + σx )  x
f (i) (x0 ) (2)
i0
i!
Uncertainty in Fission Product Transient … 607

where, f (i) (x 0 ) represents the ith derivatives of the function f (x) at x  x 0 .

The uncertainty (i.e., σ f ) associated with the system response due to the variation
of x can be derived from Eq. (1) as given in Eq. (3).

σx (1) σ2 σn
σ f  f (x0 + σx ) − f (x0 )  f (x0 ) + x f (2) (x0 ) + · · · + x f (n) (x0 ) + · · ·
1! 2! n!
(3)

In the simplified notation the standard deviation of function, the Eq. (3) can be
written as Eq. (4).
∞
 σi
σf  x
f (i) (x0 ) (4)
i1
i!

This expansion of infinite series will be truncated depending upon the degree of
nonlinearity of the system response. It can be inferred that total uncertainty depends
on two things and these are how uncertain x is (i.e., σx ) and how sensitive f is to x
(e.g., f (1) (x0 ), f (2) (x0 ), . . .).

2.2 Transient Fission Product Release Model

Fission products get generated inside the UO2 fuel pellets, and their release to the
atmosphere outside the containment during an unmitigated accident may present a
health hazard. Significant release of most of the hazardous fission products from fuel
occur only at very high temperatures in an unmitigated accident condition.
Fission product release, like radioactive decay, is said to be of first order when it
depends on the first order of the amount present. Although not mechanistic, a model
based on this principle, agrees adequately with measured releases and hence the first
order model has been widely used.
In fractional release models, the transient release of radio-nuclides is proportional
to the radio-nuclides inventory (M) present at any instant t, which is given in Eq. (5).
dM
 −k M (5)
dt
where, k is the release rate coefficient.
The solution of this first order release rate equation on rearrangement can be
written as Eq. (6).

M  M0 e−kt (6)

where, M0 denotes the initial inventory of the radionuclide. Fractional release (f )

during the time interval t can be represented by Eq. (7).
608 S. Bera et al.

M0 − M  
f   1 − e−kt (7)
M0

Release rate coefficients follow Arrhenius equation as given in Eq. (8):

k  k0 e− RT
Q
(8)

where, T is the fuel temperature given in K; R is the universal gas constant; k0 is

pre-multiplier; and Q is the activation energy. Release rate coefficients k 0 , and Q
depend on the radionuclide under consideration. As Iodine is one of the important
radionuclides that may release from fuel during an accident, it has been considered
for this study. Release rate coefficients k 0 , and Q for Iodine is 2.0 × 105 per minute
and 63.8 kcl/mol respectively. Substituting Eq. (8) in Eq. (7), the fractional release
rate for radionuclide can be written as given in Eq. (9).
 
M0 − M −k0 te( RT )
− Q
f   1−e (9)
M0

The Eq. (9) is a non-linear equation containing an exponential of an exponen-

tial function of temperature. Therefore, fractional release is very sensitive to the
temperature.

2.3 Error Propagation in Transient Fission Product Release

Model

In this work, two steps process has been adapted for uncertainty estimation. In the first
step, the variability of rate coefficient with respect to the variability of temperature
is to be estimated. In the second step, the variability in fractional release is to be
estimated using the variability of rate coefficient, which is already estimated in the
first step. For the first step, it is required to determine the differential coefficient
of various degrees so that Eq. (4) can be used to estimate the standard deviation
of rate coefficient. It is found sensitivity analysis that up to five order of differential
coefficient is sufficient to capture the variability due to the uncertain input parameter.
The equations for the derivatives of rate coefficient up to order of five are derived
and given in Eqs. (10)–(14).
dk(T ) kQ
− (10)
dT RT 2
 
d k(T )
2
2Q Q2
k + (11)
dT 2 RT 3 R 2 T 4
 
d 3 k(T ) Q3 6Q 2 6Q
 −k + + (12)
dT 3 R 3 T 6 R 2 T 5 RT 4
Uncertainty in Fission Product Transient … 609
 4 
d 4 k(T ) Q 12Q 3 36Q 2 24Q
k + + + (13)
dT 4 R 4 T 8 R 3 T 7 R 2 T 6 RT 5
 
d 5 k(T ) Q5 20Q 4 120Q 3 240Q 2 120Q
 −k + + 3 8 + 2 7 + (14)
dT 5 R 5 T 10 R 4 T 9 R T R T RT 6

Now standard deviation of rate coefficient can be evaluated using Eq. (4) and its
derivatives. The resultant equation is given in Eq. (15).

dk(T ) 1 d 2 k(T ) 2 1 d 3 k(T ) 3 1 d 4 k(T ) 4 1 d 5 k(T ) 5

σk  σT + σ + σ + σ + σ
dT 2 dT 2 T 6 dT 3 T 24 dT 4 T 120 dT 5 T
(15)

Similarly the equations for the derivatives up to order of five for fractional release
are derived and given in Eqs. (16)–(20).
d f (k)
 −( f − 1)t (16)
dk
d 2 f (k)
 ( f − 1)(t)2 (17)
dk 2
d 3 f (k)
 −( f − 1)(t)3 (18)
dk 3
d 4 f (k)
 ( f − 1)(t)4 (19)
dk 4
d 5 f (k)
 −( f − 1)(t)5 (20)
dk 5
Now standard deviation of fractional release can be evaluated using Eq. (4) and
its derivatives. The resultant equation is given in Eq. (21).

d f (k) 1 d 2 f (k) 2 1 d 3 f (k) 3 1 d 4 f (k) 4 1 d 5 f (k) 5

σf  σk + σ + σ + σ + σ
dk 2 dk 2 k 6 dk 3 k 24 dk 4 k 120 dk 5 k
(21)

3 Results and Discussion

Design extension condition without core melt scenario in Indian pressurised heavy
water reactor may result from a postulated initiating event of loss of coolant accident
with failure of emergency core cooling system with moderator cooling available.
In this scenario, the fuel temperature can reach as high as 1900 K. The system
dynamics modelling involves uncertainty, to captured the phenomena associated with
the accident progression involves variation of fuel temperature. For the simulation
purpose, it is assumed that the standard deviation associated with fuel temperature
is about 50 K. The distribution function of fuel temperature is assumed to be a
610 S. Bera et al.

(a) (b)

Fig. 1 Error propagation in release model

normal distribution with mean 1900 K and standard deviation of 50 K. The plot
of fuel temperature distribution (i.e. pdf T ) is shown in the Fig. 1(b). In the figure,
the variation of release rate coefficient (i.e. k(T)) with respect to the temperature
has been shown with solid line. It is noted that the change of k(T) is very small in
magnitude up to fuel temperature of 1250 K. Beyond this temperature k(T) increases
very rapidly. The error due to the fuel temperature is propagated through the release
rate coefficient equation (i.e. Eq. (8)) and the variability of ‘k’ has been estimated and
found to be a normal distribution with mean 0.00907 (1/min) and standard deviation
is 0.00303 (1/min). The variation of ‘k’ has been shown as pd f K in the Fig. 1(a) and
(b). The impact of the variation of ‘k’ on the fractional release has also been studied.
The variation of release rate coefficient ‘k’ with ‘f’ (i.e. inverse of f(k)) has been
shown as a solid line in the in Fig. 1(a). Both Fig. 1(a) and (b) have same variable
(‘k’) and scale on the ordinate axis. In the graphical representation the variability of
‘k’ (i.e. dashed curve for pdf k ) is same in both left and right side graphs in Fig. 1. The
error in the variable ‘k’ is propagated through fractional release rate equation (i.e.
Eq. (7)). The estimated asymmetric distribution of ‘f’ due to ‘k’ has been shown as
dashed line (i.e. pdf F ) in Fig. 1(a). The asymmetricity of the distribution is originated
from non-linear transformation of Gaussian noise. The non-zero higher moments of
the distribution such as skewness and kurtosis come from the existing higher order
derivatives of non-linear function. The dotted lines in those graphs indicate the mean
value of the corresponding distribution.
Uncertainty in Fission Product Transient … 611

Fig. 2 Variation of fractional release with temperature for different durations

The variation of fractional release with fuel temperature is shown in Fig. 2. It is

found that the fractional release of radionuclide is very small if the fuel temperature
is below 1500 K. Hence, thermal diffusion of radionuclide below this temperature
does not play a significant role. However, for fuel temperature beyond 1500 K,
the fractional release increases very rapidly. The fractional release also depends on
the time duration for which fuel temperature persisted. The variations of fractional
releases with fuel temperatures for different durations are also shown in Fig. 2. Form
this figure, it is clear that longer the duration, more is the amount of radionuclide
release into the fuel pellet-clad gap. Similarly, the variations of fractional releases
with duration for different fuel temperatures have been shown in Fig. 3. Based on
Figs. 2 and 3, the safety importance of the fuel temperature and its persistence duration
can be drawn with respect to the radionuclide release aspect. For this purpose, a
contour plot of fuel temperature and duration has been made for various release
fraction (given in %) and shown in Fig. 4. In this evaluation, low fractional release
is considered to be safe and high fractional release will be considered as unsafe. The
contour with lower fractional release represents lower radiological impact. However,
contour with higher fractional release implies higher radiological impact.
612 S. Bera et al.

Fig. 3 Variation of fractional release with duration for different temperatures

Fig. 4 Safety importance of

temperature and duration
with respect to fractional
release

4 Conclusion

The fractional release of radionuclides from fuel matrix to the pellet-clad gap base
on thermal diffusion phenomena is an exponential of an exponential function of fuel
temperature. The fractional release is found to be very small if fuel temperature is
Uncertainty in Fission Product Transient … 613

below the 1500 K. Fuel temperature persistent duration increases fractional release.
Analytical uncertainty estimation methodology for an exponential of an exponential
function has been developed and demonstrated for radionuclide release phenomena.
The safety importance of the fuel temperature and duration from the radionuclide
release point of view is also highlighted.

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Safety Engineering, Anna University, BIT Campus, Tiruchirappalli, Tamilnadu, 13–15 Feb
2014
10. D.B. Nagrale, S. Bera, M. Prasad, R.S. Rao, D. Datta, A.J. Gaikwad, Safety margin estimation
and its comparison using various uncertainty techniques for small break loss of coolant accident
sequences, in International Conference on Facets of Uncertainty and Application (ICFUA-
2013), Ramkrishna Mission Institute of Culture, Kolkata, India, 05–07 Dec 2013
Statistical Aggregation of Extreme Value
Analysis Models

Subrata Bera, Dhanesh B. Nagrale, U. K. Paul, D. Datta

and A. J. Gaikwad

1 Introduction

Probability and statistics are the greatest inventions made in the eighteenth century
[1, 2]. The probability and statistics are in extensive use in the design of engineering
structures and safety assessment. If an experiment is repeated for large number of
times then based on central limit theory the mean of these experimental values will
follow the normal distribution [3]. However, for some specific cases, those means are
not important for design consideration. Designer may want to know the extreme value
such as minimum or maximum value of the hazard parameters to justify the design
basis of the engineering structure of nuclear facility. The design basis flood level,
tsunami height, and wind load to the tall structure such as chimney and industrial
stack are few examples where extreme value is important in design [4]. These extreme

S. Bera (B) · D. B. Nagrale · U. K. Paul · A. J. Gaikwad

Nuclear Safety Analysis Division (NSAD), Atomic Energy Regulatory Board (AERB),
Anushaktinagar, Mumbai 400094, India
e-mail: sbera@aerb.gov.in
D. B. Nagrale
e-mail: dbnagrale@aerb.gov.in
U. K. Paul
e-mail: ukp@aerb.gov.in
A. J. Gaikwad
e-mail: avinashg@aerb.gov.in
D. Datta
Radiological Physics and Advisory Division, Bhabha Atomic Research Centre,
Trombay, Mumbai 400085, India
e-mail: ddatta@barc.gov.in
S. Bera
Homi Bhabha National Institute, Mumbai 400094, India

© Springer Nature Switzerland AG 2019 615

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_54
616 S. Bera et al.

values do not follow the central limit theory. The distribution of extreme value does
not follow the normal distribution [5]. When the minimum value is of interest, the
distribution is skewed toward lower values. Similarly, the distribution skewed towards
higher value in case when the maximum value is the desired quantity. There are two
approaches to estimate the extreme value: (1) block maxima approach [6] and (2)
peak over threshold approach. There are many extreme value distribution functions
such as Gumbel distribution, Weibull distribution and Generalised Extreme Value
(GEV) distribution function, etc. [7, 8] used in block maxima approach. However,
generalised Pareto distribution is used in peak over threshold approach [9, 10]. These
distributions are utilised for estimation of extreme values. Most of the extreme value
analyses are carried out using the generalised extreme value distribution function
[11]. In the present analytical study, wind speed is considered to be an extreme value
variable. For the extreme value analysis, wind speed data for several years are required
for the analysis. For such analysis, the data based on measurement in the nearest
meteorological stations are used. In the study reported here the year wise maximum
wind speed data are fitted with generalised extreme value distribution function. With
known fitted parameters, the extreme value analysis model is generated to extrapolate
the extreme value for the desired return period. If data from multiple stations are used
and those stations are significantly away from each other, then the wind profile will be
significantly different. Extreme value analysis model can vary from station to station
and result in variation of fitted parameters based on station data. Thus individual
model may either under estimate or overestimate the extreme value parameters. For
conservative design, the overestimating model for the extreme value can be used.
However, for a realistic prediction it requires statistical aggregation of extreme values
obtained from models based on various station data. A demonstration case study of
statistical aggregation of extreme value analysis models has been carried out while
preserving the statistical properties.
In this case study, data generated by four stations are considered as for wind
speed data collected over several years and the data related to maximum value of
wind speed in a year is fitted with the generalised extreme value distribution. The
model uncertainty of each model has also been analysed and a statistical aggrega-
tion methodology has been developed to obtain an average model from the models
generated for data obtained from the four stations.

2 Theoretical Methodology

2.1 Generalized Extreme Value Analysis Model

Genaralised extreme value (GEV) distribution is a family of continuous distribution to

combine Gumbel, Frechet and Weibull distributions. The three parameter distribution
function of the standard GEV is given in Eq. (1).
Statistical Aggregation of Extreme Value Analysis Models 617
⎧  
⎪  1
⎨ ex p − 1 + k x−m − k i f k  0
s
Fk,m,s (x)    (1)
⎪
⎩ ex p − x−m
s
if k  0

where, ‘k’, ‘m’, ‘s’ are known as shape parameter, location parameter, scale parameter
respectively. Shape parameter determines the nature of the tail distribution. The
estimation of these three parameters are carried out using various methods such as
probability plots, moment methods, least square fitting method, maximum likelihood
methods, etc. [9]. The extreme value distribution in Eq. (1) is generalised in the sense
that parametric form subsumes three types of distributions which are known by other
names according to the value of ‘k’. If the data related to the year wise maximum value
of wind speed is obtained for ‘n’ number of years, then distribution function F(x)
will be calculated based on the empirical density estimation methodology. This is an
approximation of a population density function that is derived from a sample and has
no unknown parameters is the empirical density. This is basically an order statistics
[12, 13]. In order statistics, year wise wind speed data (i.e. X  {x1 , x2 , . . . , xn })
are random in nature. These data arranged in the ascending order. After shorting, the
sequence of wind speed can be represented as given in Eq. (2).

x(1) ≤ x(2) ≤ · · · ≤ x(n) (2)

In particular, the equation of minimum and maximum value of the order is given
in Eqs. (3) and (4) respectively.

x(1)  Min{x1 , x2 , . . . , xn } (3)

x(n)  Max{x1 , x2 , . . . , xn } (4)

In the order statistics, all the data is considered equally probable. The correspond-
ing density function is called empirical density f(x) and given in Eq. (5).

1
f or X  {x1 , x2 , . . . , xn }
f (x)  n (5)
0 eleswher e

The empirical distribution function F(x) is given in Eq. (6).

⎧
⎪
⎪ 0 f or x < x(1)
⎨
F(x)  ni f or x  x(i) (6)
⎪
⎪
⎩ 1 f or x > x
(n)

From the station specific measured data, empirical distribution is calculated using
Eq. (6). This distribution is used to develop the GEV model by fitting the Eq. (1).
Each GEV model will have specific set of {k, m, s} values.
618 S. Bera et al.

2.2 Probabilistic Methodology for Estimate the Model

Uncertainty

The GEV model is three parameter (i.e., k, m, s) continuous distribution function.

While fitting the Eq. (1) with measured data, it is obtained the mean value of three
parameters along with their standard deviation. Model uncertainty is the estima-
tion error due to the variation of the model parameters (i.e., k, m, s) not for the
input parameter such as wind speed. Probabilistic method has been used to estimate
the model uncertainty. In this method, random sample has been taken uncertainty
domain of three parameters with normal distribution. The model uncertainty analysis
methodology has been shown in the Fig. 1.

2.3 Statistical Aggregation Methodology

Four stations generate the four GEV models with different set of three parameters
(i.e. k, m, s). Average model from these three models has been generated weighted
average of quantile data of each model. Quantile data is mathematically represented
as inverse of the Eq. (1). Mathematically the quantile information is represented in
Eq. (7).
 s s
x  m− + (− ln F)−k (7)
k k
For a given ‘F’, four values of ‘x’ can be generated for four models using Eq. (7).
If the weight given for each model is ‘w’, then the average value of ‘x’ will be as
given in Eq. (8).
w1 x 1 + w 2 x 2 + w 3 x 3 + w 4 x 4
x̄  (8)
w1 + w2 + w3 + w4

Fig. 1 Model uncertainty analysis methodology

Statistical Aggregation of Extreme Value Analysis Models 619

Fig. 2 GEV models for four

stations

Weights can be decided based on various attributes such as the distance of the
measuring station from the site, no of data points available and reliability of the data,
etc. Weights can also be generated based on expert elicitation method/process. The
average value of ‘x’ will be generated for different value of ‘F’. These data can be
used to regenerate the average model of four models. The average GEV model will
have different set of three parameter data compared to the four station wise GEV
models. The generated average model preserved the statistical property of the GEV.

3 Results and Discussions

Year wise maximum wind speed data given in km/h unit for four stations have been
plotted in the Fig. 2. The distribution functions for four stations are different due
to different value of shape parameter, location parameter and scale parameter in the
probability density function for wind speed. It is noted that the lowest 50th percentile
value is found in the measured data in station#1. Highest 50th percentile value is found
in station#3 data. Station#1 and station#3 have enveloping distribution function for
the range of wind speed from 10 km/h to 80 km/h. Station#2 and station#4 follow the
distribution in between the enveloping distribution of station#1 and station#3. Each
data have been fitted with GEV distribution function as given in Eq. (1) in Sect. 2.1
to obtain the shape parameter, location parameter and scale parameter.
The estimated mean value and standard deviation of these three parameters are
given in Table 1. The goodness of fit has (i.e. R 2 ) also been included in the Table 1.
The best fit is obtained for the station#1 with R 2  0.99441. Highest shape parameter
is found in station#1 GEV model equal to 0.37957. Lowest shape parameter is found
to in station#4 GEV model. However, highest scale parameter is found in station#3
GEV model. Lowest scale parameter is found in station#1 GEV model.
620 S. Bera et al.

The variation of three parameters in GEV model may change the model prediction.
The model uncertainty due to the standard deviation of three model parameter as
given in Table 1 has been assessed using probabilistic methodology. Samples of
three parameter data set (k, m, s) have been generated from their uncertain domain
considering normal distribution represented as N (μ, σ ). Model uncertainties for four
GEV models due to the three parameters have been shown in the Fig. 3. Solid line for
each model corresponds to the mean value of three parameters of each model. Scatter
data represent the variation of distribution function due to the model uncertainty. It is
noted that the model uncertainty is found to be higher in the fourth quantiles. These
uncertainties are strongly dependent on the variation of scale parameter. Highest
model uncertainty is found for station#3 due to its highest standard deviation of
scale parameter (i.e. 4.85% of its mean value). Lowest model uncertainty is found to
be for station#1 due to the lowest standard deviation of scale parameter (i.e. 2.45%
of its mean value).
For the statistical aggregation needs weights of individual GEV models. In this
statistical aggregation study, equal weights are given for the each GEV model. The
estimated average GEV model is shown with circular symbol in Fig. 4. It is noted that
the average GEV distribution follows in between the four individual GEV models.
Again this average GEV model data has been fitted with GEV distribution function to
obtain the three parameters. The estimated three parameters i.e. k, m, s are −0.04216,
34.9559, 6.34007 respectively.

Table 1 GEV fitting coefficients for all stations data

Station k ± σk m ± σm s ± σs R2
Station#1 0.37957 ± 0.04058 21.70738 ± 0.05952 4.29915 ± 0.10526 (2.45%) 0.99441
Station#2 −0.25144 ± 0.06549 41.53716 ± 0.12877 4.99275 ± 0.1987 (3.98%) 0.98143
Station#3 0.04002 ± 0.07333 46.87266 ± 0.20452 8.88294 ± 0.43103 (4.85%) 0.98973
Station#4 −0.42759 ± 0.05479 29.8647 ± 0.13544 7.02751 ± 0.23419 (3.33%) 0.98832

Fig. 3 Model uncertainty

due to variation of model
parameters
Statistical Aggregation of Extreme Value Analysis Models 621

Fig. 4 Average GEV model

with statistical averaging

4 Conclusion

Wind data collected from four measuring stations are used to carry out extreme value
analysis. Year wised extreme data are fitted with generalised extreme value distri-
bution function that results model. The lowest 50th percentile value is found in the
measured data in station#1. Highest 50th percentile value is found in station#3 data.
Model uncertainty due to the variation of model parameters is also estimated. The
model uncertainty is found to be higher in the fourth quantiles. These uncertainties
are strongly dependent on the variation of scale parameter. Highest model uncertainty
is found for station#3 due to its highest standard deviation of scale parameter (i.e.,
4.85% of its mean value). Lowest model uncertainty is found to be for station#1 due
to the lowest standard deviation of scale parameter (i.e. 2.45% of its mean value).
Multiple models are developed for each measuring stations. A methodology for sta-
tistical aggregation of multiple models is developed with preserving the statistical
properties and demonstrated with considering four measuring stations. The average
GEV model is developed with model parameters i.e., ‘k’, ‘m’, ‘s’ equal to -0.04216,
34.9559, 6.34007 respectively.

References

1. J. Galambos, S. Kotz, Characterizations of Probability Distributions (Springer, Berlin, 1978)

2. D.R. Cox, D.V. Hinkley, Theoretical Statistics (Chapman and Hall, London, 1974)
3. L. de Hann, A. Ferreira, Extreme Value Theory an Introduction (Springer, 2006)
4. AERB Safety Guide, “Extreme value of mateorological parameters”, AERB/NF/SG/S-3 (2008)
5. R.D. Reiss, M. Thomas, Statistical Analysis of Extreme Values with Applications to Insurance,
Finance, Hydrology and Other Fields (Birkhauser Verlag, 2007)
6. R.A. Fisher, L.H.C. Tippett, Limiting forms of the frequency distribution of the largest or
smallest member of a sample. Proc. Camb. Philos. Soc. 24, 180–290 (1928)
622 S. Bera et al.

7. S. Kotz, S. Nadarajah, Extreme Value Distributions Theory and Applications (Imperial College
Press, 2000)
8. S. Coles, An Introduction to Statistical Modeling of Extreme Values (Springer, 2001)
9. E. Castillo, A.S. Hadi, Fitting the generalized Pareto distribution to data. J. Am. Stat. Assoc.
92, 1609–1620 (1997)
10. A.C. Davison, R.L. Smith, Models for exceedances over high thresholds (with discussion). J.
Roy. Stat. Soc. B 52, 393–442 (1990)
11. J.R.M. Hosking, J.R. Wallis, E.F. Wood, Estimation of the generalized extreme value distribu-
tion by the method of probability-weighted moments. Technometrics 27, 251–261 (1985)
12. H. Finner, M. Roters, On the limit behavior of the joint distribution function of order-statistics.
Ann. Inst. Stat. Math. 46, 343–349 (1994)
13. J. Galambos, A statistical test for extreme value distributions, in Nonparametric Statistical
Inference, ed. by B.V. Gnedenko, M.L. Puri, I. Vincze (Amsterdam: North-Holland, 2000),
pp. 221–230
Electroosmotic Effects on Rough Wall
Micro-channel Flow

Nisat Nowroz Anika and L. Djenidi

1 Introduction

The improvement of mixing in laminar flow is the major challenge to deal with
microfluidic. However, the astonishing characteristic of microfluidic is smallness-
having dimension ranging millimeter to microns μ. Such miniature technology
allows the small volume of order of micro to nano-liter. The growing availabil-
ity of the devices allows miniature technology that has reliable capability to deal
with Micro-electro-mechanical system (MEMS), Lab-on-chip devises to analyze the
biological and chemical applications outcome. In chemical engineering, some reac-
tant/solvent is inadequate in the nature. To carry out such investigations, of small
volume of those samples require large interfacial area to bring two species together
as well as to generate instability in a micro-device. The generated instability could
help to perform mixing process inside the micro-channel in which flow can be insen-
sitive to accept turbulence. In laboratory, the surface of the micro-devices may not be
smooth, rather rough. Therefore, requires strong driving force to transport the sample
species through the rough micro-channel. Because roughness along can induce pres-
sure perturbation in bulk flow to conserve the rate of mass transfer. Electrokinetic
transport phenomenon- one of the fast growing ubiquitous community- has been
receiving immense attraction dealing with electronics micro-fabrication.
The micro-electro mechanical process is critical when mixing plays a major part.
Inside the microchannels, the flow remains in a laminar regime where mixing only
occurs at molecular level (molecular diffusion) at somewhat reduced rate. In this
present study, our aim is to generate and enhance turbulence incorporating the both

N. N. Anika (B) · L. Djenidi

Discipline of Mechanical Engineering, School of Engineering,
University of Newcastle, Callaghan NSW-2308, Australia
e-mail: NisatNowroz.Anika@uon.edu.au
L. Djenidi
e-mail: Lyazid.Djenidi@newcastle.edu.au
© Springer Nature Switzerland AG 2019 623
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_55
624 N. N. Anika and L. Djenidi

active and passive methods which can help to increase the exchange area as the best
strategy to prolong mixing at Reynolds number much lower than its critical value
(Re < 10.). Relatively recent numerical work of [1] observed that the conservation
of energy in the process of effective mixing occurred in the combination of active
and passive mixer. The strategy was to develop turbulence in the rough wall with an
active triggering of jets at low Reynolds number Re  700. The flow was driven by
the pressure difference and the parabolic profile of velocity eventually affected by
the interaction of local turbulence.
Our present simulation study is motivated by the aforesaid work of [1] to accel-
erate mixing process at low Reynolds number Re ≤ 7 where the active method is
replaced by an external electric force. Also, the computational domain has been fixed
with parallel plates separated by a distance h, h being the height of the channel. The
surface of both the channel’s walls is roughened by 2D square bars. The height of
the roughness is denoted by k. The ratio between heights is numerically fixed at
2k/ h  0.1. The separation p between roughness elements is homogeneous for both
walls. Leonardi et al. [2] investigated fully developed turbulent flow with transverse
square roughness only at the bottom wall. They performed three dimensional numer-
ical parametric studies on p/k ranging from 0.33 ≤ p/k ≤ 19 to aid optimizing
the value ( p/k  7) at which viscous drag can be minimum. Form drags helped to
inject turbulence having nearly zero viscous drag. The ratio of roughness to channel
height was fixed at 2k/ h  0.1 to reduce the blockage effects in the main channel
flow. In our study, the separation is 4 times of the height of the roughness elements
at Re  7 (based on h/2; half height of the channel). As the increasing of p/k, the
viscous drag reduces. And p/k  4 is the transitional value to get viscous and form
drag due to the presence of induced pressure around each roughness elements. Hu
et al. [3] carried out finite-volume method to investigate electro-kinetic transport
phenomena on rough channel at micro-scale. Symmetric and asymmetric arrange-
ments of roughness elements have been considered where the 2k/ h ratio varies
between 0.2 ≤ 2k/ h  0.4. From their study, it can be concluded that the induced
pressure around the 3D roughness elements reduces the electoosmotic flow rate and
the effects were immense with further increase of roughness height. For symmetric
arrangement, the author had less consideration reducing the blockage effect of the
roughness elements. At our best knowledge, there was no study performed regarding
electroosmotic microchannel flow to enhance mixing considering 2k/ h ≤ 0.2.
Motivated by the aforesaid knowledge gap, a direct numerical simulation is per-
formed to investigate the electrically forced two-dimensional channel flow driven
by pressure including both active and passive methods unitedly. The passive method
involves the roughness elements where the channel height is 10 times bigger than
the height of roughness element to neglect the blockage effect on the electric flow
field. Numerical studies have been carried out on both smooth and rough channels
to see the effect of external force on roughness elements. Also, the calculations have
been analyzed for p/k ranging from 3 to 7 with electric field strength.
Electroosmotic Effects on Rough Wall Micro-channel Flow 625

2 Numerical Procedure

A direct numerical Simulation is performed based on novel numerical scheme Lat-

tice Boltzmann method (LBM). The evolution equation of Lattice Boltzmann model
results a macroscopic velocity filed which solves Naiver-Stokes equation of second
order accuracy with sufficient amount of lattice symmetry. Boltzmann equation dis-
cretized on a lattice to construct a kinetic model that describes the underlying physics
of mesoscopic averaged properties. In this study, the two-dimensional square lattice
model has been discretized on continuous Boltzmann equation. The lattice model is
composed of D2Q9 four particles (i  1, 2, 3, 4) directed along vertical and hori-
zontal directions, another four (i  5, 6, 7, 8) are directed diagonally and one particle
at rest (i  0) residing at the center of that square lattice. Therefore for D2Q9 lat-
tice model, there are three different velocities and abscissas acting to describe the
corresponding weighing factors ωi .

e0 e1 e2 e3 e4 e5 e6 e7 e8
ex 0 1 0 −1 0 1 −1 −1 1
ey 0 0 1 0 −1 1 1 −1 −1

and
⎫
4
for i  0 ⎪
⎪
9 ⎪
⎬
ωi  1
for i  1, 2, 3, 4
9 ⎪
⎪
⎪
1
36
for i  5, 6, 7, 8 ⎭

For the evolution equation of lattice Boltzmann model with external force term
of local collision operator, we always present the general form. The equation reads-
1 
x , t) + Fi
eql
x + ei ∇t, t + ∇t)  f i (
f i ( x , t) − x , t) − f i (
f i ( (1)
τ
In the above equation Eq. [1], f i denotes the microscopic distribution function
of ith discrete velocity nodes of the set of microscopic velocities (ei ), position (
x)
and time (t). The gradient, ∇ is the representation of position and velocity spacing
and  denotes the frequency of collision,   τ1 where, τ  3ν + 21 represents
relaxation time due to the collision. v is the kinematic viscosity.
The right-hand side represents the Bhatnagar-Gross-krook collision approxima-
eql
tion. The equilibrium distribution function f i for 2D nine velocities can be written
as-

eql 3ei .
u (ei .
u )2 3u 2
f i  ωi ρ 1 + 2 + 9 − 2 (2)
c 2c4 2c
626 N. N. Anika and L. Djenidi

where c the lattice speed denoted by c  x t

. Fi : an electrical force term can be
expressed as-


ei − u  eql
Fi  ωi ρe E fi (3)
ρcs2

 cs is the sound speed, for D2Q9, cs  1, ρ is characteristic

 fluid density
ρ f i , u is the macroscopic velocity ρu  f i . ρe defines the net charge
density. For single ionic bond, the ρe reads-
 
zeψ
ρe  (−1)ze2n 0 sinh (4)
kb T

The all physical parameters have their usual meaning. Noticed that all qualities
have been expressed in the lattice units [4]. Here, n 0  c0 N0 is the bulk ion concen-
tration with c0  1.0 × 10−7 mole/volume, Avogadro number, N0  6.023 × 1023 .
This study solves thin electric double layer to develop a plugged-like (zero at the
centerline and maximum at the wall) electrical potential ψ. As soon as we received ψ,
the external electrical field ( E volt/length) applied along the stream wise direction. At
the inlet and outlet, we put ∇ψ to force the EOS flow. For hydrodynamics boundary
condition, periodic condition implemented along stream wise direction and no-slip
at the wall. The Reynolds number
  is calculated based on half-height of channel h/2,
mean centerline velocity Ūc and viscosity and the value at about Re  7. The
velocity boundary condition based on non-equilibrium distribution of bounce-back
[5] has been invoked. For calculating the net charge density, the zeta potential at the
wall region of electric double layer (EDL) is about ψw  −0.027 Volt. The external
electric field strength is about 2.7 V per length. The computational domain is two
dimensional having mesh size hπ × h. 2D mesh increments are x  t  1. The
macroscopic velocities have been calculated with the presence of electric potential
everywhere in between both smooth and rough walls. The smooth wall simulation
runs for longer time for single species fluid density with external electric force and
results have been taken as a reference which helps understanding the effects of
electro-osmotic flow on rough micro-channel.

3 Results and Discussions

In present LBM model, all the statistical analysis has been performed with ensemble
averaged calculations. The time averaged kinetic energy has been calculated against
time variation first.
It is clearly evident from the Fig. 1 that the thin electric double layer and the
distribution is maximum at the wall and zero at the middle of the channel’s height
for a given small electro-static zeta potential, ψw . The ψw is homogeneous and equal
for both the walls and so for the roughness elements.
Electroosmotic Effects on Rough Wall Micro-channel Flow 627

Fig. 1 Distribution of 0
electric potential across the
channel
-0.005

-0.01

ψ(y)
-0.015

-0.02

-0.025

-0.03
-0.5 0 0.5
y/h

Fig. 2 Mean electroosmotic 1.8

flow (EOF) profile, black:
1.6
smooth wall Poiseuille flow;
blue: smooth wall with 1.4
potential; red: rough wall
EOF flow and green: rough 1.2
wall without EOF
Um /U b

0.8

0.6

0.4

0.2

0
-0.5 -0.25 0 0.25 0.5
y/h

In Fig. 2, the linear axis represents the mean velocity normalized by Ub -the bulk
velocity. The profile of mean velocities reveals the better understanding at the near
wall region where the entire mechanism relies on. It is clearly depicted that the
mean velocity for smooth channel flow without any external force is the Poiseuille
distribution with a peak value at the center of the channel. The peak is transformed
by a flatness at the middle of the channel for the EOF on both smooth and rough
wall. The situation is more pronounce on the smooth wall (symbol with blue symbol
line in Fig. 2) as compared to the rough wall (red line symbol). This transformation
is due to the presence of electric field on the near wall EDL region [6].
2k
The effect of ratio has been examined first on rough wall for p/k  3.7
h
with EOF across the channel. Figure 3 presents the visualization of velocity flow
2k
direction and their corresponding vectors for varies form 0.2 to 0.1, where the
h
628 N. N. Anika and L. Djenidi

(a) (b)
0.5 0.5

0.25 0.25

y/h
0
y/h

-0.25
-0.25

-0.5
-0.5 2.25 2.37 2.50 2.62 2.75 2.87 3.00 3.13
2.25 2.38 2.50 2.65 2.75 2.87 3.0
y/h
x/h
(c) (d)
0.5 0.5

0.25 0.25

y/h 0
y/h

-0.25
-0.25

-0.5
-0.5 2.25 2.38 2.50 2.65 2.75 2.87 3.0
2.25 2.38 2.50 2.65 2.75 2.87 3.0
x/h
x/h

Fig. 3 Instantaneous velocity-contour and vector repetition of u and v on rough wall EOF channel
2k 2k
flow. a, b  0.2 and c, d  0.1. And p/k  3.7
h h

other parameters are kept exactly same. To stress out better the results have been
magnified in between 2.25 ≤ 2x/ h ≤ 3.05 along the stream-wise direction. The
strong ejection on the crest of elements and suction at the cavity occurred in the flow
filed at the vicinity of top and bottom walls. In between two consecutive elements, the
flow is strongly disturbed by the electric field. Far from the wall, the flow behavior
is most likely laminar but contains small oscillation due to the external electric field
2k
strength. The effects are also present for  0.1 as we see in Fig. 3c, d. The EOF
h
is disturbed only at the wall region in a small amount compared to the rough wall
2k
(Fig. 3a;  0.2) EO flow but large compared to the rough wall laminar flow
h
(not shown here). For better understanding, it would worth to calculate r ms for these
cases.
Figure 4 showed the root-mean-square of the velocity fluctuations. It is clearly
evident that the mean centerline fluctuation is less in magnitude to that of wall
fluctuations. As we see that at y/ h  0 (bottom wall) and y/ h  2 (top  wall), the
 2k
u 1 (u r ms ) is maximum. The fluctuation is less evident on the rough wall  0.1 .
h
2k
It can be well understood that for the rough wall at  0.2, there is a possibility to
h
Electroosmotic Effects on Rough Wall Micro-channel Flow 629

Fig. 4 Root mean square of 0.45

the (with electro-osmotic on
smooth and rough wall) 0.4
velocity
  fluctuation
 0.35
u 1  u r ms . Black symbol:
2k 0.3
 0.2 and p/k  3.7;
h

c
0.25
2k

u 1 /u
green symbol:  0.1 and
h 0.2
p/k  3.7; blue symbol:
smooth wall EOF flow 0.15

0.1

0.05

0
-0.5 -0.25 0 0.25 0.5
y/h

achieve turbulence-like motion where there is nearly zero instability for rough wall
Poiseuille flow (not shown here).
With the increase of separation distance between two roughness elements
( p/k  6.7) there was more interfacial are to exchange energy but comparatively low
in magnitude. It is obvious that the EOF feels the surrounding pressure from the dipole
roughness elements better for the case when the ratio lies between 3 ≤ p/k ≤ 4 for
2k
 0.2.
h

4 Conclusion

A direct numerical study based on novel technique Lattice-Boltzmann model have

been carried out to simulate the electric potential distribution on rough wall channel
flow at Reynolds number Re  7, based on half height, h/2 and mean centerline
velocity. The simulation not only suggested that the effect of EOF changes with
separation length to height ratio of roughness elements but also the mean velocity
2k
affected by shear layer for ratio. There lies a great possibility that the mixing can
h
be achieved at laminar micro-channel by generating turbulent-like motion actuated
by the combination of passive and active method of mixing. The EOF based on
thin electric double layer that has been observed by analyzing the root-mean-square
fluctuation velocities and flow visualizations. The parameters 3 ≤ p/k ≤ 4 and
2k
 0.2 showed us better effect of EOF on rough microchannel that could help
h
minimize the blockage effects on microfluidic based application outcomes. In future,
it would be interesting to investigate the electroosmostic effects on laminar flow in
the presence of wall jet following the recent paper of Anika et al. [7].
630 N. N. Anika and L. Djenidi

References

1. N. Anika, L. Djenidi, S. Tardu, Pulsed jets in laminar smooth and rough wall channel flow,
ETMM11, 2016
2. S. Leonardi, P. Orlandi, R. Smalley, L. Djenidi, R. Antonia, Direct numerical simulations of
turbulent channel flow with transverse square bars on one wall. J. Fluid Mech. 491, 229–238
(2003)
3. Y. Hu, C. Werner, D. Li, Electrokinetic transport through rough microchannels. Anal. Chem.
75(21), 5747 (2003)
4. L. Djenidi, Lattice-Boltzmann simulation for grid generated turbulence. J. Fluid Mech. 552,
13–35 (2006)
5. Q. Zou, X. He, On pressure and velocity boundary conditions for the lattice boltzmann BGK
model. Phys. Fluids 9(6), 1591–1598 (1997)
6. G.H. Tang, X.F. Li, W.Q.Tao He, Electroosmotic flow of non-Newtonian fluid in microchannels.
J. Nonnewton. Fluid Mech. 157, 133–137 (2009)
7. N.N. Anika, L. Djenidi, S. Tardu, Bypass transition mechanism in a rough wall channel flow.
Phys. Rev. Fluids 3(8) (2018)
Comparative Study on Fuzzy Based
Linearization Technique Between
MATLAB and LABVIEW Platform

Joyanta Kumar Roy and Bansari Deb Majumder

1 Introduction

In the process industry like the power plant, Boiler drum level is one of the
critical parameters to be measured and controlled. The boiler is a process where
water is converted into steam, and the steam is used to turn a steam turbine and
eventually electricity is generated. Water level control is an essential parameter for
operation of boiler efficiency. Different techniques like conductivity probe type, sight
gauges, magnetic type level transmitters etc. are the sensors preferred in boiler drum
level measurement [1–3]. Unfortunately boiler drum level control is complicated by
changes in electrical load requirements or variation in the fuel and air supply. All the
available methods of measuring the boiler drum level is discrete in nature.
Admittance type level transmitter is a continuous method which can be imple-
mented in boiler drum level measurement. It can be both single electrode type and
double electrode type method of level measurement [4, 5]. But because of the pres-
ence of its significant cross sensitivity of liquid temperature and liquid property, the
analysis is not accurate [6, 7]. Hence a suitable tool needs to be developed to elimi-
nate this cross-sensitivity effect. Linearization is the method of error removal from
the measured value of the process parameter. Fuzzy based linearization using MAT-
LAB and fuzzy based linearization using LABVIEW [8, 9] in the earlier work which
found to be satisfactory. In this work, a comparative study has been made between
the two advanced linearization methods. From the competitive data, the optimum
way of linearization has been developed.

J. K. Roy (B)
MCKV Institute of Engineering, Kolkata, India
e-mail: jkroy.cal51@gmail.com
B. D. Majumder
Department of Electronics and Instrumentation Engineering,
Narula Institute of Technology, Agarpara, India
e-mail: bansari.debmajumder@nit.ac.in
© Springer Nature Switzerland AG 2019 631
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_56
632 J. K. Roy and B. D. Majumder

Table 1 Input and output variables for fuzzy based linearizer in MATLAB platform
Input variable Output variable
Admittance without error Corrected admittance value
Admittance with the effect of temperature
Admittance with the effect of ionic
concentration

Fig. 1 Fuzzy-based linearizer in Matlab window [8]

2 Fuzzy Based Linearization in MATLAB

Fuzzy logic deals with knowledge-based computation technique [10, 11] can be suit-
able for linearization, error analysis and elimination [8]. Fuzzy linearizer includes
input variables, rule base or inference engine and output variables. There exist
knowledge-based systems which related the nature of input and output variables
in different condition. In this linearizer, three inputs are given from the experimen-
tal setup. And the fuzzy-based linearizer is generating one output. So, in this fuzzy
model, there are three input variables and one output variable shown in Table 1.
The fuzzy based linearizer is designed in MATLAB window as shown in Fig. 1.
In the window, the input variables are fed to the fuzzy inference engine. The FIS
consists of the rule base, and the rules are set according to Mamdani rules of the
fuzzy system. The fuzzy data generated by the FIS is defuzzified to create crisp
value. The method of de-fuzzification used is centroid method of defuzzification.
After defuzzification, the crisp data is generated and recorded finally.
The membership functions define each of the input variables and these member-
ship functions are framed according to the relation of the variables. Now the rule base
is set following the Mamdali rule. Finally, the corrected admittance value is recorded
Comparative Study on Fuzzy Based Linearization Technique … 633

Fig. 2 Comparison between fuzzy corrected versus ideal admittance versus measured admittance
value keeping temperature constant [3]

Fig. 3 Comparison between fuzzy corrected versus ideal admittance versus measured admittance
value keeping ionic concentration constant [8]

from the output window. The recorded data of corrected admittance value is plot-
ted against the error admittance keeping either temperature or ionic concentration
constant.
Figure 2 shows the graph of ideal, actual and corrected fuzzy admittance data at
the constant temperature of 21.9 ° C. Similarly, Fig. 3 shows a graph of ideal, actual
and corrected fuzzy admittance data at constant ionic concentration of 0.184TDS.
The statistical analysis was made on data available from Matlab base simulation
and is shown in Table 2.
634 J. K. Roy and B. D. Majumder

Table 2 Comparative Statistical analysis of Level measurement error

MATLAB based analysis
Corrected, ideal and measured Corrected, ideal and measured
admittance (Temperature admittance (Ionic
constant) concentration constant)
Min. Error 0.075 −0.2337
Max. Error 0.0459 0.0673
Standard deviation 0.0769 0.0904

Fig. 4 Rule viewer page of fuzzy system designer [9]

3 Fuzzy Based Linearization in LABVIEW

The real-time data from the admittance lever transmitter is acquired using NI-DAQ
and send to the personal computer. In the personal computer, the LABVIEW software
is installed. Labview is a software platform of National instruments (NI) for analysis
of data and plays a very vital role in virtual instrumentation. In the NI Labview 2013
version, the fuzzy system designer is selected from control design and simulation
toolbox. In the fuzzy system designer, the input variables and output variables are
chosen as per Table 1. In the next step, the rule base between the fuzzified data is set
as shown in Fig. 4.
Comparative Study on Fuzzy Based Linearization Technique … 635

Fig. 5 Test system window [9]

After simulating the test system, the output values can be recorded and stored for
further analysis. Figure 5 shows the test system of the fuzzy designer.
NI Labview has two programming window. One is block diagram window where
the program is to be written, and other is front panel window where the result is to
be analyzed. The block diagram window of the fuzzy-based linearizer is shown in
Fig. 6.
In the block diagram window, all the input variables are given to the Fuzzy based
linearizer. The input values are acquired through NI DAQ 6211 card. The output of
the fuzzy-based linearizer is corrected admittance value. The data generated can be
recorded in an excel file using the write to measurement block. Figure 7 shows the
front panel window of indicators of input and output values.
From the front panel window, the corrected value of admittance can be noted. Now
the comparison chart has been prepared for the fuzzy corrected value and the ideal
value of admittance data generated from fuzzy based linearizer in Labview. The data
are recorded by considering the parameters of temperature and ionic concentration
which is shown in Figs. 8 and 9.
In Fig. 8, the temperature is kept constant at 24.3 degree Celsius. The ionic con-
centration is varied, and corresponding corrected admittance value is recorded. The
same method is repeated maintaining the ionic concentration constant at 0.203TDS,
and the temperature is varied. Eventually, the corrected admittance data is recorded.
636 J. K. Roy and B. D. Majumder

Fig. 6 Block diagram window [9]

Fig. 7 Front panel window [9]

The statistical comparison is listed in Table 3.

Comparative Study on Fuzzy Based Linearization Technique … 637

Fig. 8 Comparison chart at fixed temperature [9]

Fig. 9 Comparison chart at fixed ionic concentration [9]

Table 3 Statistical analysis chart

LABVIEW based analysis
Comparison of corrected, ideal Comparison of corrected, ideal
and measured admittance and measured admittance
(Temperature constant) (Ionic concentration constant)
Min. Error 0.063 −0.0327
Max. Error 0.0329 0.0345
Standard deviation 0.0543 0.0652
638 J. K. Roy and B. D. Majumder

4 Conclusion

The statistical analysis has compared the two methods of fuzzy based linearizer.
From the data of Tables 2 and 3 it can be concluded that MATLAB is much better
for computation than LabVIEW. The classical program code is much more suitable
for calculations than block diagrams. On the contrary, the most significant advantage
of LabVIEW is fast and simple construction of the graphical user interface that
facilitates the updating of parameters (no need to interfere with the code) and elegant
presentation of the results. Comparing the LabVIEW, the Creation of a comparable
user interface in MATLAB may be more painful and limited. The another advantage
of LabVIEW is that most MATLAB functions, that are accessible from LabVIEW via
the MathScript Node, which can pass data to m code, execute it and get results back.
Hence LabVIEW based linearizer has more advantage. From the comparative study, it
has been found that in both cases (offline in/Matlab and online in Labview) accuracies
of the measurement is very close to each other. Therefore the NI Labview in real-time
analysis, the accuracy will be good enough in developing physical level measuring
instrument using admittance method. It can be incorporated into the measurement
system by real-time basis. With the help of NIDAQ 6009, the real-time data can be
acquired. It has the advantage of signal analysis and processing simultaneously. In the
later stage cross sensitivity effect of the sensor can be used to measure three different
parameters simultaneously. This phenomenon is called multi-function sensing. In the
future work, the primary focus will be on the development of multifunction sensor.
Some of the researchers [12] already started developing a multifunction sensor for
level measurement in industrial applications. Hence this is the significant area of
research in the recent days.

References

1. W. Skierucha, Time Domain Reflectometry: Temperature-dependent Measurements of Soil

Dielectric Permittivity, in Electromagnetic waves (Institute of Agrophysics, Polish Academy
of Sciences, Poland, 2011), Chapter 17, pp. 374–379
2. L. Guirong, Z. Xianshan, A new proposal for monitoring oil-temperature and oil level,
ISBN:978-1-4244-8158-3, pp. 350–353, ICEMI-2011
3. S.C. Bera, J.K. Ray, S. Chattopadhyay, A low-cost noncontact capacitance-type level transducer
for a conducting liquid. IEEE Transac. Instrum. Measur., 55(3), 778–786 (2006)
4. J. Kumar Roy, Low-Cost Sensing Techniques of Industrial Process Variables, ISBN: 978-3-
659-11192-1LAMBERT Academic Publishing, TP-395, 2012
5. S.C. Bera, J.K. Roy, Study of an admittance type single electrode transducer for continuous
monitoring of liquid level in a metallic storage tank. J Instn. of Eng. (I), 83, 56–60, Jan (2003)
6. J. Kumar Roy, B. Deb, Investigation of Cross-sensitivity of a Single and Double Electrode of
Admittance Type Level Measurement. Sixth International Conference on Sensing Technology,
Kolkata, India, Dec 2012. Proceedings published in IEEE Digital Xplore, ISBN: 978-1-4673-
22454, pp. 234–237 (2012)
7. J. Kumar Roy, B. Deb Majumder, Cross-sensitivity of Ionic Concentration on Admittance
Type Level Measurement. Eighth International Conference on Sensing Technology, Liverpool,
Comparative Study on Fuzzy Based Linearization Technique … 639

UK September 2014. Proceedings published in International Journal on Smart and Intelligent

Systems, ISSN: 1178–5608, pp. 41–45 (2013)
8. J.K. Roy, B. Deb Majumder, Elimination of Cross-sensitivity in Admittance Type Level Mea-
surement Using Fuzzy Based Linearizer, on Smart Sensing and Intelligent Systems. Scopus
Indexed Journal 7(4), ISSN: 11785608 H Index:8, December (2014)
9. J. Kumar Roy, B. Deb Majumder, Real-Time Measurement of Water Level Using Admittance
Method and Fuzzy Based Linearizer. Tenth International Conference on Sensing Technology,
Nanjing, China. Proceedings published in IEEE Digital Xplore, ISBN: 978-1-5090-0796-7,
Nov (2016)
10. L.A. Zedeh, Knowledge representation in fuzzy logic. IEEE Trans. Knowl. Data Eng. 1(1),
89–100 (1989)
11. C. Carlsson, Fuzzy logic and hyper knowledge: a new, effective paradigm for active DSS. IEEE
environmental management, vol. 5, pp. 324–333, Print ISBN: 0-81867743, 1997
12. G. Lu, in A new proposal of multi-functional level meter, ISBN:0-7803-7987-X. IEEE Interna-
tional Conference on Multisensory Fusion and Integration for Intelligent Systems, pp. 209–212,
2003
Automated Identification of Myocardial
Infarction Using a Single
Vectorcardiographic Feature

Deboleena Sadhukhan, Jayita Datta, Saurabh Pal

and Madhuchhanda Mitra

1 Introduction

According to recent health reports [1], Myocardial Infarction (MI), more commonly
known as heart attack, continues to be the predominant cause of death all over the
world. Early stage detection and medication can largely reduce the risk of mortality.
MI is caused by occlusion of the coronary arteries which causes insufficient blood
flow to the heart muscle cells or myocardium in different regions leading to their
damage (ischemia) or complete death (necrosis) [2]. The dysfunctional tissues cause
a disruption of the heart’s electrical activity which in turn affects the synchronous
contraction and relaxation of the different heart chambers (atria and ventricles).
Electro-cardiogram (ECG), the recording of the heart’s electrical activity, is the most
predominant tool used for cardiac diagnosis. The presence of MI is manifested as
changes in the morphological features of the ECG such as the shape of T-wave,
Q-wave and ST-segment [3]. Changes in these morphological and temporal wave
features from a standard 12 lead ECG system are normally used to diagnose MI
development.

D. Sadhukhan (B) · S. Pal · M. Mitra

Department of Applied Physics, University of Calcutta,
92 A.P.C. Road, Kolkata 700009, India
e-mail: dsaphy_rs@caluniv.ac.in
S. Pal
e-mail: spaphy@caluniv.ac.in
M. Mitra
e-mail: mmaphy@caluniv.ac.in
J. Datta
Department of Electronics & Instrumentation Engineering,
Guru Nanak Institute of Technology, 157/F, Nilgunj Road,
Panihati, Kolkata 700114, India
e-mail: jayita.datta@gnit.ac.in
© Springer Nature Switzerland AG 2019 641
S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_57
642 D. Sadhukhan et al.

The need for early and reliable MI identification has led to immense research
to automate the process of cardiac analysis. Automated cardiac analysis is based
on extraction of clinically significant features from the cardiac data and employs
machine intelligence techniques for classifying these features. Most of the reported
automated MI identification tools use ECG features. Techniques [4, 5] based on
the explicit time plane features (the wave amplitudes and time durations) and ST
segment analysis relies on accurate detection of the ECG wave segments which is
difficult to achieve due to the large morphological variation of the ECG waveform and
presence of noise. Use of advanced signal processing tools have also been applied to
extract time-frequency ECG features based on Discrete wavelet transform [6, 7] and
Cross wavelet transform [8] to achieve high classification performance. But these
techniques are not only computationally complex but also suffer from the “curse
of dimensionality” due to the use large number of features. Although the standard
12-lead ECG is sufficient to represent the spatiotemporal activity of the heart in
different perspectives, but there is a loss of spatial information in each temporal ECG
tracing. Moreover, analysis of all 12 ECG leads adds to the computation burden of
the automated software and much of the information within it is still redundant.
In recent years the vector-cardiogram or VCG has drawn significant attention in
cardiac analysis. VCG enables spatio-temporal visualization by monitoring heart’s
electrical activity in three spatial planes (horizontal, frontal and sagittal) generat-
ing different loops (shown in Fig. 1) for the P, QRS and T waves representing the
activation and relaxation of the different heart chambers. It not only gives a clearer
spatial orientation of the cardiac activity but also uses a reduced lead set (VX , VY and
VZ ). Computerized VCG analysis hence proves to be more advantageous and also
provides higher specificity, sensitivity and accuracy as compared with conventional
ECG for the diagnosis of different cardiac pathologies [9].
Significant amount of literatures [10–20] are available on the topic of MI detection
using the VCG features. Most of the approaches [10–15] are based on the use of dif-
ferent morphological features of the VCG loop which includes areas, perimeters and
angles of the QRS and T loops [11–13], vector magnitudes of the Q-wave, R-wave,
T-wave [12, 14], ST change vector magnitude [10], vector magnitude differences
between the loops [14], angle between R and T vector [11], azimuth angle of the
vectors [11] and also octant based features [15]. Extraction of such features needs
segmentation of the different waves including the isoelectric point for the angle
measurements. Moreover, almost all of them consider separate features for each
wave, which significantly increases the feature dimension. Also the computation of
the angles and the 2-d area needs complex measurements achieved by projecting
3-d VCG loops in different planes. Use of the more advanced signal processing
tools like principal component analysis (PCA) and independent component analy-
sis (ICA) [16], recurrence quantification analysis [17], random walk network [18],
wavelet coherence analysis [19], self-organizing visualization and pattern matching
[20] to extract different VCG features involves intensive mathematical operations
which makes them difficult and time consuming to implement.
In this paper we propose a new a VCG feature which combines both the QRS
and ST-T loops morphological changes into one single feature, thus reducing the
Automated Identification of Myocardial Infarction … 643

Fig. 1 Representation of Vector cardiogram (VCG). VCG vector loops contain 3D recurring, near-
periodic P, QRS, and T wave activities representing each heart cycle

feature dimensionality problem. Instead of representing the morphological changes

in the loops by their angles (which requires identification of iso-electric point) or
areas (which needs projections in different planes), we simply consider the QRS
and the ST-T loop volumes evaluated by representing the loops using 3-d convex-
hull technique. Statistical analysis shows that the ratio of the QRS and ST-T loop
volumes is significantly different for healthy and the MI subjects as tested with
the PTB diagnostic ECG database [21]. Hence this single parameter has sufficient
discriminative power to identify MI.
The detailed processing steps of the algorithm are described in Sect. 2. In Sect. 3
the performance of the algorithm is validated with the PTB diagnostic database.
Finally Sect. 4 concludes the paper by analyzing the relative advantages and disad-
vantages of the proposed technique.

2 Methodology

Figure 2 shows the detailed block diagram of the proposed MI identification technique
using the VCG signal. The key concept is to extract cardiac beats from the 3 VCG
leads (VX , VY and VZ ) and segment it into the QRS and the ST-T to represent the
corresponding loops. The volumes of the loops are computed by representing them
with 3-d convex-hull. The volume ratio of the two loops is used to classify the healthy
and the MI records.
644 D. Sadhukhan et al.

Fig. 2 Block diagram representing the processing steps of the proposed technique

2.1 Data Pre-processing

The pre-processing step involves the elimination of noise from the 3 orthogonal VCG
lead data. The very low frequency baseline drifts (below 0.2 Hz), the high frequency
noises (above 80 Hz) and the power-line interference (of 50 Hz) are eliminated by
means of the Fourier co-efficient suppression technique proposed by us in [22].

2.2 Beat Extraction

One single cardiac cycle comprising of the P, QRS and the T waves is sufficient to
provide information of the presence of MI abnormalities. The R peak is the most
distinctly identifiable feature of the cardiac cycle and hence location is used for beat
extraction. The R peaks of lead VX are detected using the method proposed in [23]
based on double differencing. To account for the heart rate variation, a single beat
is extracted based on the previous and the consequent RR intervals instead of using
fixed window length. The beat start point is selected to be 1/3rd of the previous RR
interval before the current peak so as to include the P peak. The selected end point is
2/3rd of the consequent RR interval after the current peak position so as to include
the T peak. The same start and end points are used to extract time aligned beats from
the three leads.
Automated Identification of Myocardial Infarction … 645

VX VX VX
1 1
2 R R
RR1 RR2

0.5
R-75 R+75
1/3 RR1 2/3 RR2
0
0

Normalised Amplitude
VY 0 VY 1000 VY 1000
1 1
Amplitude (mV)

Amplitude
0

0
VZ 0 VZ 1000 VZ 1000
2 1 1
P
QRS
0.5
ST-T
0

0 0
0 Time (s) 3 0 Sample no. 1000 0 Sample no. 1000
BEAT EXTRACTION NORMALISATION BEAT- SEGMENTATION

Fig. 3 Beat extraction and segmentation process. Red dots denote the detected R peaks. One beat
is extracted from 1/3rd of the previous RR interval (RR1) to 2/3rd of the consequent interval (RR2).
The beats are then normalized both in time and amplitude domain. The QRS segment is identified
within the interval of ±75 data points around the R position. The remaining beat succeeding the
QRS region is considered to be ST-T segment

2.3 Beat Segmentation

Presence of infarction significantly alters the morphological pattern of the QRS

region, ST segment and T wave [3]. So, instead of the whole ECG beats the QRS
regions and the ST-T regions are considered separately to detect the identifiable
changes. To ensure parity of the loop amplitudes, the beat amplitudes are normalized
in the range of 0–1. For extraction of the QRS and ST-T regions from each beat, it is
required to identify the start and the end points of each wave by accurate delineation
algorithms which can significantly increase the computational burden. To avoid this,
all the beats are first time normalized to contain 1000 data points each using the FFT
interpolation technique. This helps in alignment of all the beats in time axis. Next the
QRS regions are identified to be within ±75 data points around the R peak location.
The remaining beat from the QRS end point is considered to be the ST-T region.
Figure 3 explains the beat extraction and segmentation process.

2.4 Drawing of VCG Loops

The QRS and the ST-T loops are obtained by drawing simultaneously on 3-D plot the
instantaneous amplitudes of the orthogonal leads for every sample of the temporal
interval corresponding to each detected QRS-complex and ST-T segments respec-
tively. Figure 4 illustrates QRS and the ST-T loops obtained from a healthy record
646 D. Sadhukhan et al.

VX
1 QRS LOOP T LOOP

1 0.8
0
VY
1

VZ
Amplitude

VZ
0
VZ 0
1 0
1 0.8
1 0.8
VY VY
VX VX
0 0 0 0 0
0 Sample 1000
(a) Healthy record no. 117-s292

VX QRS LOOP T LOOP

1

1 0.8
0
VY
1
Amplitude

VZ
VZ

0
VZ 0 0
1
1 0.8
1 0.8
VY VX VY VX
0
0 Sample 1000 0 0 0 0
(b) Infarction record no. 008-s028

Fig. 4 QRS and ST-T loops. The corresponding beats are displayed in the left hand side. a QRS
and ST-T loops for a healthy record. b QRS and ST-T loops for an infarction record. The QRS loop
volume of the healthy record is higher than that for the infarction case whereas the ST-T volume is
significantly lower

and an infarction record. It can be seen that both loop morphologies are significantly
dissimilar for the 2 cases.

2.5 Computation of Volume Ratio

As seen from Fig. 4, there is a wide variation of the 3-d QRS and ST-T loops for
healthy and MI data. Instead of using multiple features including the angles and
loop areas in different projected planes, we quantify these variations using the loop
volumes.
To accurately estimate the volume of the 3-D loops, they are first represented by
the set of points that produce the minimum convex volume containing all the points
of the loop using the “Convex Hull” algorithm [24]. This representation is illustrated
in Fig. 5. Then, the volume of the polyhedron is evaluated for each loop. To combine
the QRS and ST-T changes into a single parameter the volume ratio of the two loops
Automated Identification of Myocardial Infarction … 647

Fig. 5 3-D convex hull ACTUAL QRS LOOP 3-D CONVEX HULL
representation of a QRS
loop. The loop is represented 1 1
using a polyhedron having

VZ
the minimum convex volume
and containing all the points
of the loop 0 0
1
VY 11 1
VX
0 0 0 0

(QRS volume/ST-T volume) is considered as the final feature to discriminate between

the normal and MI data.

3 Experimental Results

3.1 Used Data

The development and validation of the proposed technique has been done with VCG
data extracted from the PTB Diagnostic ECG database available under Physionet [21]
as it contains well classified records both from healthy (H) and infarction patients
(MI). Each recording contains 15 simultaneous recorded signals from the conven-
tional 12-lead ECG and the 3-lead VCG. Data is sampled at 1 kHz with 16 bit
resolution. For our work we have used VCG recordings from 70 healthy data and
150 MI data (including inferior and anterior infarction). From these, beats extracted
from 50 records from each group is used for the identification of the feature thresh-
old value. Then randomly extracted beats from all the H and MI records are used
validation of the proposed technique.

3.2 Performance Evaluation Parameters

The overall discrimination ability of the proposed VCG parameter is evaluated using
the most commonly used performance metric- Accuracy (Acc), Sensitivity (Se) and
Specificity (Sp) defined as follows:
TP +TN
Acc  (1)
T P + T N + FP + FN
TP
Se  (2)
T P + FN
TN
Sp  (3)
FP + T N
648 D. Sadhukhan et al.

where TP denotes the number of MI beats correctly detected, TN denotes the number
of H beats correctly classified, FP denotes the number of H beats misclassified as
MI, and FN denotes the number of MI beats misclassified as H.

3.3 Performance Evaluation

As seen from Fig. 4, the QRS loop volume for the healthy records is higher than
that of the infarction cases, whereas ST-T loop volume is significantly lower. This
corresponds to higher loop volume ratios for the healthy records. The statistical
parameters (the mean and the standard deviation values) of the volume ratio for the
500 H and 500 MI beats extracted from the training data set are shown in Table 1.
To visualize the within class variation of the proposed VCG feature the box plots of
the feature value for both the classes are shown in Fig. 6. The red line in the middle
of boxplot represents the median, the blue box shows the lower quartile and upper
quartile of data distributions, and the black dash lines represent the most extreme
values within 1.5 times the interquartile range. Outliers are shown as red crosses
in the box plot. Both Table 1 and Fig. 6 strongly indicates the distinct difference
between the mean values of the feature for the H and MI cases.
From the obtained feature values for the training data set, a volume ratio value of
220 is selected as the threshold value for the classification of the H and the MI data,
giving 99% coverage to the MI data in the training set. QRS and ST-T volume ratio
below this threshold value indicates the presence of MI.
This threshold value is then used to classify 2000 beats randomly extracted from
each class in the entire dataset used for the work (eliminating the beats used in the
training phase). The classification results are displayed in Table 2.
For medical diagnosis applications misdetections of positive cases (FN) can be
more fatal. To reduce misdetections of MI data, the feature threshold value is selected

Table 1 Volume ratio values for healthy and MI data

Feature Healthy Infarction
Mean SD Mean SD
QRS 489.41 351.11 150.13 111.80
volume/ST-T
volume
SD denotes standard deviation

Table 2 Overall classification performance

True class Predicted Class Acc (%) Se (%) Sp (%)
MI Healthy
MI TP  1976 FN = 24 97.5 98.8 96.2
Healthy FP = 76 TN  1924
Automated Identification of Myocardial Infarction … 649

Fig. 6 Box plot showing the BOX PLOT OF FEATURE VALUE

variation of volume ratio
value for healthy and MI 1200
data. The red dotted line
shows the threshold feature 1000
value selected for MI
classification

Volume Ratio
800

600

400
THRESHOLD
200

HEALTHY MI

giving maximum coverage to the MI data. Hence, the proposed technique achieves
a fairly high detection sensitivity of 98.8%, whereas the specificity falls to 96.2%.

4 Conclusion and Discussion

The vector-cardiogram (VCG) proves to be a more informative and low dimensional

alternative of the 12 lead Electrocardiogram (ECG) for MI diagnosis. The automated
VCG analysis tools, reported till date, utilize a large number of features based on the
sizes, area and orientation of the QRS and the T loops. This paper proposes a novel
VCG feature—the volume ratio of the 3-d QRS and the ST-T loop. This feature can
appropriately incorporate all the morphological changes of the VCG into a single
parameter. The obtained classification performance reveals that this feature alone
can provide significantly high detection sensitivity. Moreover, the use of this single
feature for cardiac analysis can significantly reduce the computational burden and
the detection time, thus enabling more reliable and faster identification of MI. These
results are thus strongly indicative of the potential of QRS ST-T volume ratio to be
used as a MI detection parameter in the automated cardiac analysis tools.
However, in this paper we have restricted our analysis to two types of MI only (infe-
rior and anterior). But for actual clinical application the study needs to be extended
to incorporate all other types of MI as well as other cardiac diseases. Moreover, MI
localization (identification of the zone of infarction) has not been considered for the
present study.

Acknowledgements The first author acknowledges the financial support obtained in the form of
DST INSPIRE Fellowship provided by the Department of Science & Technology, Government of
India.
650 D. Sadhukhan et al.

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2020–2035 (2012)
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classification. IEEE Trans. Instrum. Meas. 63(2), 326–333 (2014)
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Content Extraction Studies
for Multilingual Unstructured Web
Documents

Kolla Bhanu Prakash and M. A. Dorai Rangaswamy

1 Introduction

Recent developments in communication and internet have brought in significant

changes in scientific, engineering and societal context and wide range of user-oriented
mobile applications like whatsapp, twitter etc. have added new dimension to modern
living and thought process. Simultaneously, the reach of these developments is still
a long way to go as long as the gap between human communication and computer-
based communication is not bridged fully. There are many barriers to overcome like
language, dialect, tradition, way of living etc.
This is where; conventional data mining approaches need to be elevated to media-
mining or content extraction approaches. Content extraction is the process of iden-
tifying main content of a web page which may consist of different forms of data in
an unstructured and non-homogeneous manner [1–3]. Added to this is the ability of
including region and language based information, thanks to the exponential growth
in use of cellular communication.
Text based information has reached different levels with different languages form-
ing the text either as a computer-generated data or acquired data through images
forming most of the pages. All these aspects bring in a necessity of using a more
general approach to extraction of information and it has become very important to
consider different kinds of web pages. A typical web page in present day context
is shown in Fig. 1. This web page has text-based information in two different lan-

K. B. Prakash (B)
Department of Computer Science and Engineering, Koneru Lakshmaiah Education Foundation,
Vaddeswaram, Guntur, India
e-mail: drkbp@kluniversity.in
M. A. Dorai Rangaswamy
St.Peters University, Avadi, Chennai, India
e-mail: drdorairs@yahoo.co.in

© Springer Nature Switzerland AG 2019 653

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_58
654 K. B. Prakash and M. A. Dorai Rangaswamy

Fig. 1 Variations in form, text and language levels in web page

guages—content may or may not be just translated one- and also different kinds of
images which may be a photo or computer-generated drawings.
This web page conveys information in the form of content even to a person who
does not know any of the languages as the images convey more than the text. So,
content extraction for such web pages can be considered as a pre-processing step
for text mining and Web information retrieval. Furthermore, such main contents are
very valuable as an input for many devices that have limited presentation capacity,
such as mobile phones, speech readers, etc. [4, 5]. The focus of the present study is
to develop a generic content extraction approach which is based on the unstructured,
non-homogeneous and text and/or non-text based data, as that of the web page shown
in Fig. 1. A typical block diagram for content extraction is shown in Fig. 2.
This is a major difference to be looked into when one considers Asian web pages,
which contain language and information, which are older than those used in European
web pages and this aspect gets much more complex in Indian context, where dialect
and text differ widely even in small regions. The present study is an attempt to develop
Content Extraction Studies for Multilingual Unstructured … 655

Fig. 2 Typical block diagram for content extraction

pixel-based approach-which gives flexibility in dealing with any language or media-

and start from generic text level to a hybrid unstructured level.

2 Content Extraction Techniques

As content extraction is different from text or data mining, where a set of keywords
form the basis, most of the previous approaches use HTML tags to separate the
main content from the extraneous items. This implies the need to employ a parser
for the entire Web page. Consequently, the computation costs of these main content
extraction approaches include the overhead for the parser.
In the early stage of the Internet, the contents of Web pages were written only in
English language. Now, especially in the last decade, a large part of information is
being published in regional or native languages, like for example Spanish, German,
French, Tamizh, Arabic, Urdu, Hindi with native tongue and usage reflected in the
text. Except for the non-English languages mentioned here, there are also many
languages using non-ASCII codes for their characters.
Typically, a modern web page for commercial intent looks like the one shown
in Fig. 3 and this is taken from a web magazine. A collage of data in the form of
text in different languages and sizes, numerals, images and blocks, forms the web
page with the intent that content is reached to the web-surfer, who may be from
different country with different languages and dialect and culture. But, the content
in terms of shoes or dresses reaches him so that he/she can follow and get more
details. This is typically an unstructured, heterogeneous and hyper media web page.
Extracting content requires language, text and image processing. Extracting main
content from web page is pre-processing of web information system. The content
extraction approach based on wrapper is limited to one specific information source,
and greatly depends on web page structure. It is seldom employed in practice. So, a
generic model employing basic features of data is needed and the proposed model
is from basic pixel level making it applicable to any kind of data or text or image or
even media to assess the content in a short period of time.
656 K. B. Prakash and M. A. Dorai Rangaswamy

Fig. 3 Multilingual and multi-tasking modern web magazine

3 Nature and Features in Web Documents

As seen earlier web pages are unstructured-not conforming to any document form-,
non-homogeneous with information and data presented in different forms from text
to images to video, and multi-lingual depending on the audience and their location.
This gets more complex and involved when Asian or Indian regional web pages dis-
play information. Indian languages are very much different from European -or other
Asian languages—like Japanese or Persian—in that regional customs and practices
bring in certain commonalities like the scripts of Tamizh or Telugu or Kannada have
similarities of different kinds as compared to the northern Hindi or Punjabi scripts.
But English being the link language both in oral and written communication and
forms the basis in higher education, some complexities in migrating from English to
regional language or vice versa exist like the ones shown in Fig. 4. Figure 4 shows a
typical web page displaying news on the same day and here web pages in Malayalam,
English and Hindi are shown and one can see that even the news content varies as
the region and language change.
Content Extraction Studies for Multilingual Unstructured … 657

Fig. 4 Web documents in regional India—different languages, different contents

For example, if one compares Malayalam with Hindi, there is variation in news
content and one finds regional news dominating over national in both the cases. So,
if one wants to continue surfing and later interact with, the content of the web is the
only way to go about and if figures or images are not there, content needs to be given
in a short period of time. It may be seen clearly that regional web documents pose
different problems in terms of comprehension, understanding and interaction in other
language regions. Even if one looks at script or character level, or even word level,
complexities are many-fold, as the web pages try to present information in easily
understandable form using words freely from different languages. As an example, a
word ‘Computer’ in English translated in other languages like Hindi, Arabic, Tamizh
and Telugu is shown in Fig. 5a. But many times, popular words in one language are
used as they are like word ‘computer’ in English is written in local scripts as in
Fig. 5b. Also one can see clearly the variations in structure of text in different forms
and these do not form part of the local language dialect.
Hence, it is preferable to assess the content even before looking at the document
fully. Images and figures do help, but, many times texts and sketches with words
pose problems as they reflect local dialect and flavour. So, it is necessary to assess
the content irrespective of the language and the way text is produced.
Hence, the objective is to develop a generic model and later apply for complexities
to check whether it is possible to assess the content in a short period of time.
658 K. B. Prakash and M. A. Dorai Rangaswamy

(a) Word ‘computer’ translated in other languages

(b) Word ‘computer’ written in other languages

Fig. 5 Complexities in Indian and Foreign languages with English

4 Text and Character Issues

One of the basic steps in any content extraction or mining approach is in processing
the data as it is, and as the data may be in different types like pictures, texts or in
different forms like media or audio or in different formats like .bmp or .jpg in either
full form or compressed form. So, the pixel map of any data can form the basis for
any form or format of data as computer processes at this level. But in unstructured
and non-homogeneous documents, complexities begin at character level and later
extend to word or document or web page form. Even in texts or documents, which
are well structured with words and sentences, language brings in variations and this
is true in education where text books written by authors in regional languages are
digitized and used in web learning. These are becoming a major source of on-line
education in different levels. To cite an example, Fig. 6 shows a Physics web page
in two different languages English and Arabic used in schools.
Here one can see free mixing of words in Arab and English in both forms of
documents. Keeping in view of all the above mentioned issues, it is preferable to
consider extracting the content of the document rather than translation or data-mining.
The present study aims at developing a generic tool based on pixel map data, to
extract content in a web page and later, using reduced attributes and features of pixel
maps, a pattern matching approach is used to assess the content.

5 Development of Pixel Map Attributes

A web document may contain texts, images, audio/video files; and in some regional
documents, scanned copies of hand-written texts or images are found. So, it is neces-
sary to look at the generic level of data which is used by computer for processing. Any
pixel map can be seen as a matrix of columns and rows with each element giving the
color scheme for the pixel. So, the characteristic and attribute of any pixel map can
Content Extraction Studies for Multilingual Unstructured … 659

Fig. 6 Text book page in two languages—Arabic and English

Fig. 7 Variation of pixel map attributes for letter ‘a’

be deduced from these three values and most of image processing and data mining
techniques depend on this basic matrix. The matrix size being large, it is preferable
to reduce it by converting into grey-scale or binary form giving 0–7 or 0–1 values
in the matrix. Typically a letter ‘a’ in English has [10 × 11 × 3] matrix and this is
reduced to [10 × 11] with 0 and 1 value and even then there are 110 values to reflect
the matrix fully. Table 1 gives pixel map attributes for letter ‘a’ in three languages,
English, Arabic and Urdu. Here, only three sets are given like Mean and Standard
deviation (std), 3-row vector attributes and 2 × 2 matrix attributes. Similarly, 3 × 3
matrix attributes can also be generated.
Figure 7 gives a comparison of features of pixel map attributes for letter ‘a’ in
English, Arabic and Urdu, all normalized with area of pixel map to get consistency.
The bar chart shows variation of values for the three pixel maps. Similarly, words
or images can also be used to generate pixel map attributes as shown in Fig. 7 and
typically, for a word like ‘computer’ translated in three languages—English, Hindi
and Arabic are shown in Fig. 8.
 660

Table 1 Pixel map attributes for letter ‘a’ in three languages

Input Mean Std. Vector Attributes 2 × 2 matrix attributes
Eng. letter ‘a’ 0.3818 0.2960 0.1000 0.2818 0 0.1091 0.1318 0.0591 0.0818
Arab letter ‘a’ 0.0889 0.1496 0.0159 0.0571 0.0159 0.0381 0.0063 0.0206 0.0238
Urdu letter 0.1414 0.0994 0.0074 0.0565 0.0774 0.0179 0.0179 0.0097 0.0960
‘a’
K. B. Prakash and M. A. Dorai Rangaswamy
Content Extraction Studies for Multilingual Unstructured … 661

(a) Mean and std. (b) 3-value vector (c) 2x2 matrix (d) 3x3matrix

Fig. 8 Pixel map variations for word ‘computer’ translated in three languages

But, contents of the matrices are different and if processed in terms of either non-
zero values—which gives the pattern, or vector matrix values with content being
same. This gives a clear idea of feature extraction.
Since, Asian language letters have characters surrounding the main body; the
pixel map may be divided into three segments like 25% top, 50% middle and 25%
bottom. Letters ‘g’ and ‘y’ in English have bottom 25% for example. And in the case
of Arabic fonts, most of them have occupancy in top and bottom halves also.
Even though a letter ‘a’ has these values in different scripts, its usage also differs
as in English ‘a’ can be a letter or a word. So, processing of text and documents
ultimately has to be considered as a problem related to the content and context and
natural language understanding.

6 Content Extraction—Results and Discussion

The method described earlier is used with pattern recognition to compare whether
any new input in the form of letter or word or image can relate to the content of base
patterns. The proposed technique is purely data driven and does not make use of
domain dependent background information, nor does it rely on predefined document
categories or a given list of topics. Character ‘a’ which is unique in content, similar in
many languages—Arabic, Hindi, Telugu, Tamizh and English. Uniqueness of letter
‘a’ is that, it has same meaning or content in all the above mentioned languages. But,
this trend completely changes when one has a character like ‘e’ which is a vowel
by itself like ‘a’ but it is not unique in any language. As an individual character
‘e’ doesn’t give any meaning, unlike ‘a’ which gives some meaning in English and
regional languages. The attribute variations of ‘e’ in comparison with ‘a’ are given
in Fig. 9.
The purpose of choosing ‘x’ in English is that it is not unique in any language by
any context, ‘x’ is not a vowel and as an individual character ‘x’ doesn’t give any
meaning, unlike ‘a’ which gives some meaning in English and regional languages.
‘x’ to be written in other languages it requires more than one character, which is
662 K. B. Prakash and M. A. Dorai Rangaswamy

(a) Indian languages (b) Arabic and Urdu languages

Fig. 9 Content extraction for ‘a’ and ‘e’

Fig. 10 Content extraction for ‘a’ and ‘x’

another interesting feature in comparison with ‘a’ and ‘e’. The attribute variations of
‘x’ in comparison with ‘a’ are given in Fig. 10.
Extending this basis to words, a typical data set of words in English relating to the
same content ‘magnetism’ are chosen, which is considered as data set-2 and using
pixel map attributes as basis, comparisons with a new data ‘magnet’ in Arabic, related
to the content and ‘flower’ in Arabic not related to content are shown in Table 2 and
Fig. 11.
One can see clearly that even though pixel map variations are significant, matching
patterns can help in identifying the content.
Content Extraction Studies for Multilingual Unstructured … 663

Table 2 Pixel map attribute S. No Pixel-map Attribute value

variations for data set-2
1 Diamagnet 0.2344
2 Dipole 0.2326
3 Ferri 0.2249
4 Filings 0.2333
5 Moment 0.2316
6 Monopole 0.232
7 Magnet-arabic 0.2181
8 Flower-arabic 0.2154

Fig. 11 Pixel map attribute

variations for data set-2

7 Conclusion

A generic model for Content Extraction for regional web documents is developed
based on the basic data system in computers, namely pixel maps. Beginning with
complexities in letters, different methods of generating attributes are presented which
form the basis for pattern matching and later for neural modeling. Some preliminary
test results are given for pattern matching of features, for letter and word level relating
to the same content. This preliminary study is focused to bring out the complexities
in regional web documents and how a generic tool based on pixel maps—which do
not have language or form of data as inputs—can be used for either text mining or
content extraction. Further enhancements and techniques are to be suitably generated
to account for the vagaries, so that, web content is extractable in any region.

References

1. T. Gottron, Content code blurring: A new approach to content extraction, DEXA ’08: 19th
International Workshop on Database and Expert Systems Applications. IEEE Computer Society,
pp. 29–33 (2008)
664 K. B. Prakash and M. A. Dorai Rangaswamy

2. S. Gupta, G. Kaiser, D. Neistadt, G. Grimm, in DOM Based Content Extraction of HTML

Documents. WWW ’03: Proceedings of the 12th International Conference on World Wide Web
(ACM Press, New York, NY, USA, 2003), pp. 207–214
3. J. Moreno, K. Deschacht, M. Moens, in Language Independent Content Extraction from Web
Pages. Proceeding of the 9th Dutch-Belgian Information Retrieval Workshop, pp. 50–55, 2009
4. D. Pinto, M. Branstein, R. Coleman, W.B. Croft, M. King, W. Li, X. Wei, in QuASM: A Sys-
tem for Question Answering Using Semi-structured Data. JCDL ’02: Proceedings of the 2nd
ACM/IEEE-CS Joint Conference on Digital libraries (ACM Press, New York, NY, USA, 2002),
pp. 46–55
5. C. Mantratzis, M. Orgun, S. Cassidy, in Separating XHTML Content from Navigation Clut-
ter Using DOM-structure Block Analysis. HYPERTEXT ’05: Proceedings of the Sixteenth
ACM Conference on Hypertext and Hypermedia (ACM Press, New York, NY, USA, 2005),
pp. 145–147
Potentiality of Retina for Disease
Diagnosis Through Retinal Image
Processing Techniques

P. G. Prageeth, A. Sukesh Kumar, C. S. Sandeep and R. S. Jeena

1 Introduction

Human eye is one of the most important organs in the body. It is estimated that
in every 5 seconds, one person goes blind somewhere in the world. There are several
diseases of the eye which when properly diagnosed could save the sight of the patient
[1]. According to the estimates of the World Health Organisation, about 80% of
human blindness is avoidable. In spite of highly effective treatment, cure rates are
unsatisfactorily low in most developing and developed countries. Hence there is great
need for the effective implementation of modern technology and investigation into
the field of eye care for a social cause.
Age-related Macular Degeneration (AMD) and Diabetic Retinopathy (DR) are
the leading causes for preventable vision loss in the country [2]. In our earlier works,
we have developed a neural network based tool from retinal images for the early
detection of AMD and diabetic retinopathy. Also we developed expert system to
detect these eye abnormalities earlier. We have done an extensive work for the early
detection of the above eye diseases through retinal image analysis and processing
[3]. It was convinced that retina is the vital part of the eye, is a potential one to
provide vital information on the eye diseases and the extraction of this information
through retinal images will definitely help to prevent the abnormalities of the eye
[4, 5]. Based on the above works, currently research works are being pursued in the

P. G. Prageeth
Department of Electronics & Communication Engineering, College of Engineering Trivandrum,
University of Kerala, Thiruvananthapuram, Kerala, India
e-mail: prageethpg@cet.ac.in
A. Sukesh Kumar (B) · C. S. Sandeep · R. S. Jeena
Electronics & Communication Engineering, Faculty of Engineering & Technology, University of
Kerala, Thiruvananthapuram, Kerala, India
e-mail: drsukeshkumara@cet.ac.in

© Springer Nature Switzerland AG 2019 665

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_59
666 P. G. Prageeth et al.

area of retinal image analysis for the detection of most of the eye diseases which
can be detected from retinal image processing.

2 Retina Based Eye Diseases and Its Detection

Currently we are concentrating on the early detection of the following eye diseases
through retina image processing.
(1) Cataract
This section focuses on fundus image analysis and fully automatic cataract classifica-
tion. Its goal is to reduce the burden of scarce resources and improve the effectiveness
and efficiency of fundus image review, through which to enable active and enhanced
healthcare services. Studies on fundus image analysis have been made for years.
Segmentation and location of retinal structures, such as retinal lesions, vessels, optic
disc and fovea have been widely studied. Based on these techniques, researchers are
also trying to develop diagnose systems for specific retina-related diseases including
micro aneurysms, diabetic retinopathy, age-related macular degeneration, glaucoma,
cardiovascular diseases [6]. It has made an effort to classify and diagnose specific
cataract automatically by split image and retro-illumination image, including nuclear
cataract, cortical cataract and posterior sub-capsular cataract. However, there is little
work reported on cataract classification and grading by using fundus images. Figure 1
shows the fundus images of non-cataract and cataract persons in different grading.
In the image (a) without cataract, the blood vessels can be shown very clearly, even
the capillary ones. The more severe cataract the patients have, the more cloud will
be in the lens, resulting in that less vessels can be observed from the fundus image.
There are less vessels details in mild cataract patients’ eye fundus image, while only
the trunk vessel and little details in the moderate cataract ones’.
Furthermore, there is hardly anything in the severe cataract ones.
(2) Glaucoma
Glaucoma is a chronic disease often called “silent thief of sight” as it has no symptoms
and if not detected at an early stage it may cause permanent blindness. Glaucoma

Fig. 1 Fundus images of non-cataract and cataract in different grading. a Non-cataract b mild c
moderate and d severe
Potentiality of Retina for Disease Diagnosis … 667

Fig. 2 a Contrast enhanced RGB colour space image b extracted green plane c negative transform
d vessel removal using opening e negative transform f region growing g edge extraction of convex
hull from f and h detected cup after ellipse fitting

progression precedes some structural changes in the retina which aid ophthalmolo-
gists to detect glaucoma at an early stage and stop its progression. Fundoscopy is
among one of the biomedical imaging techniques to analyze the internal structure
of retina. Our proposed technique provides a novel algorithm to detect glaucoma
from digital fundus image using a hybrid feature set. This section proposes a novel
combination of structural (cup to disc ratio) and non-structural (texture and intensity)
features to improve the accuracy of automated diagnosis of glaucoma. The proposed
method introduces a suspect class in automated diagnosis in case of any conflict in
decision from structural and non-structural features [7]. Figure 2 shows the images
of qualitative and quantitative evaluations of different parameters which help in the
early detection of glaucoma. The evaluation of proposed algorithm is performed
using a local database containing fundus images from 100 patients. This system is
designed to refer glaucoma cases from rural areas to specialists and the motivation
behind introducing suspect class is to ensure high sensitivity of proposed system. The
average sensitivity and specificity of proposed system are 100 and 87% respectively.
(3) Diabetic Retinopathy
Diabetes is detected from the presence of exudates and haemorrhages and changes
in blood vessel parameters like arteriolar-to-venular diameter ratio (AVR). Images
obtained from fundus camera are enhanced using filtering. Image segmentation is
done to detect optic disc, fovea, exudates area and blood vessels. Connected compo-
nent method along with concentric circle methods are used to determine the artery-
vein width ratio [8]. An algorithm is developed for the detection and quantification of
the disease level from the parameters specified. The result is validated with the clin-
ical data of the patient and achieved good results. A predictor system is developed to
668 P. G. Prageeth et al.

(a) (b)

Fig. 3 a Fundus image of a normal eye. b Fundus image of a diabetic patient

give the status of the patient from the analysis of the retinal image parameters using
neural network techniques [9]. Figure 3 shows the clear cut differences between the
images of a normal person and a diabetic patient.
(4) Retinitis Pigmentosa
The paper has referenced retinitis pigmentosa for the analysis purpose. Automated
approach for detection of micro aneurysms in digital colour retinal fundus pho-
tographs helps ophthalmologist to detect the emergence of its initial symptoms and
determine the next immediate action step for the patient. A similar mechanism for
automated early disease detection method is proposed featuring identification of dark
pigments like minute features, exudate and micro aneurysm detection and these fea-
tures extracted can prove to a greater extent as primary instances for defectiveness
of eye [10]. A good number of images along with the response from the ophthal-
mologist has proved to be a great help towards the observation as derived from this
mechanism and discussed in the paper. The proposed mechanism can be extended
up to the limit of supervised learning so as to automate the practical responses as
obtained from the ophthalmologist in real time scenario. Figure 4 shows the fundus
image of a retinitis pigmentosa patient.
(5) Retinopathy of Prematurity
Retinal imaging with remote interpretation could decrease the number of diagnos-
tic eye examinations that premature infants need for the detection of retinopathy of
prematurity and thus decrease the time demand on the relatively small pool of oph-
thalmologists who perform retinopathy of prematurity examinations. Our goal was
to review systematically the evidence regarding the reliability, validity, safety, costs
and benefits of retinal imaging to screen infants who are at risk for retinopathy of
prematurity. We searched Medline, the Cochrane library, CINAHL, and the bibliogra-
phies of all relevant articles [11]. All English-language studies regardless of design
with primary data about our study questions were included. We excluded (1) studies
that only included subjects with retinopathy of prematurity, (2) hypothetical models
Potentiality of Retina for Disease Diagnosis … 669

Fig. 4 Retinitis pigmentosa

fundus image

Fig. 5 Fundus images of evaluation of retinopathy of prematurity

other than cost-effectiveness studies and (3) validity studies without sufficient data
to determine prevalence, sensitivity and specificity or that only evaluated subjects for
1 component of retinopathy of prematurity (eg: plus disease only). Figure 5 depicts
the different evaluation windows of retinopathy of prematurity.
670 P. G. Prageeth et al.

Fig. 6 Fundus images of

retinal detachment patient

(6) Retinal Detachment

Arterial macro aneurysms are dilated places in the arteries of the retina, the lining
of the back of the eye. Macro aneurysms are weak spots, which can leak clear fluid
into the retina, causing gradually developing blurred vision. They also can pop, with
bleeding inside the eye and sudden visual loss. There is no pain associated with
macro aneurysms. Pictures of a normal retina and of a retina with a macro aneurysm
are shown below. What Causes Arterial Macro aneurysms? The causes of macro
aneurysms are unknown, but we know of certain associated risk factors [12]. Macro
aneurysms tend to occur more commonly in women than men (3:1 ratio), occur
late in life, and often occur in patients with high blood pressure and other forms of
vascular disease, such as heart attacks and strokes. From these clues, we think that
hormones, wear and tear over time, and extra stress from high blood pressure may
contribute to macro aneurysms. How Are Macro aneurysms Discovered? Sometimes
they can be found by your ophthalmologist simply looking inside the eye. Other times
they may be covered by blood, and dye pictures may be taken to help in finding
them. Occasionally, after cases of rupture, they become evident only after blood has
reabsorbed. Figure 6 depicts the qualitative and quantitative detachments of retina
in a patient.
(7) Stargardt’s disease
Eye diseases are the burning diseases nowadays. Eye diseases detection is one of
the imperative problems in computer vision. It has much relevance such as face live
detection and driver fatigue analysis. In this paper first, the captured images are
collected from different patients and are processed for enhancement. Figure 7 shows
Potentiality of Retina for Disease Diagnosis … 671

Fig. 7 Fundus camera and fundus image of a retina detached patient

a fundus camera and fundus image of a retina detached patient [13]. Then image
segmentation is carried out to get target regions (disease spots). Finally, analysis of
the target regions (disease spots) based on covariance approach to finding the phase
of the disease and then the treatment consultative module can easily be prepared on
the lookout for human being. The captured infected eye images are collected from
different patients and are processed for enhancement. Using the covariance approach
and scoring scale technique to exact intensity pattern to anterior disease accordingly
it is then possible to analyze the different Eye diseases. Then image segmentation is
carried out to get target regions (disease spots). Finally, analysis of the target regions
(disease spots) based on covariance approach to finding the phase of the disease and
then the treatment consultative module can easily be prepared on the lookout for
human being [14]. The result from the preliminary study indicated that the proposed
strategy is effective to assess disease.
(8) Cone Dystrophy
The results for each performance of the sampling bright lesion detection method
is good even for lesion based evaluation, as the proposed hybrid microaneurysm
detection method resulted in a very high sensitivity with reasonable specificity, an
ophthalmologist can take its assistance in detecting Microaneurysms, exudates and
cotton wool spot in the mass screening of diabetic retinopathy [15]. Figure 8 shows
the images of feature extractions of cone dystrophy. It achieves a sensitivity of 94%
and a specificity of 94.87% and accuracy of 95.38%. The performance of the microa-
neurysm detection method can be enhanced further by augmenting the amount of
training data for the microaneurysm candidate object classification.
(9) Cancer in relation to the Retina
Choroidal Melanoma (CM) is the most common primary malignancy of the eye. The
overall incidence is approximately 5–7 cases per million per year. In this paper the
new technique for tumours tissue structure evaluation using ultrasound spectral anal-
ysis is presented. Based on the obtained results, it can be said that radio frequency
(RF) ultrasound signals parameters at the healthy tissue area and the area with the
672 P. G. Prageeth et al.

Fig. 8 Fundus images of feature extractions of cone dystrophy

Fig. 9 ROI selection in one direction of B scan images a in healthy (control) eye b in melanoma
eye before treatment c in melanoma after brachytherapy treatment

intraocular tumour—melanoma before and after treatment statistically are signifi-

cantly different [16]. Application of spectral analysis using non-invasive ultrasound
expert system, provides the new opportunities in early diagnosis, differentiation of
tumours, evaluation of the treatment effectiveness.
This study has shown that the lower amplitude, lower spectral intercept, high
spectral slope and high momentary bandwidth are typical for choroidal melanoma if
compared with healthy tissues and the lower momentary bandwidth are typical for
choroidal melanoma after treatment if compared with melanoma before treatment
[17]. Figure 9 shows the ROI selection in one direction of B scan images (a) in
healthy (control) eye (b) in melanoma eye before treatment (c) in melanoma after
brachytherapy treatment.

3 Early Detection of Stroke Through Retinal Image

Analysis

Stroke is a form of cardiovascular disease affecting the blood supply to the brain. It
remains as a leading cause of disability and death for people of all races and ethnicities
[18]. Stroke can be subdivided into two types: ischemic and haemorrhagic. Ischemic
Potentiality of Retina for Disease Diagnosis … 673

stroke accounts for almost 85% of the cases. The retina can be viewed and analysed
using non-invasive, in-vivo functional techniques. The retina is a layered tissue lining
the inner part of the eye that enables the conversion of incoming light into a neural
signal that is appropriate for further processing in the brain. It is therefore an extension
of human brain. Research works show that microvasculature of retina and brain is
closely linked in terms of anatomy and physiology [19]. Morphological changes
in blood vessel shape, branching pattern, width, tortuosity, appearance of retinal
lesions, branching angle, branching coefficient and fractal dimension are some of the
abnormalities in vascular pattern of retina associated with cardiovascular diseases
like stroke.
The current research work focuses on the prediction of retinal ischemia from
retinal fundus images and thereby predicting the occurrence of stroke. Pre-processing
of retinal images is done by retinex processing [20] and morphological operations are
done to remove noisy background. Branching points are detected and various features
like major axis length, mean diameter, orientation, eccentricity, fractal dimension and
tortuosity are computed. This has been compared with a set of healthy retinal images
for the prediction of the possibility of retinal ischemia.
Figure 10 shows the various output stages of a healthy retinal fundus image. Reti-
nal imaging aids in predicting the probability of stroke based parameters evaluated
from the vascular map of retinal ischemia. Early detection of cardiovascular diseases
like stoke through biomarkers derived from retinal imaging would allow patients to
be treated more effectively. This work is an extension of author’s other works for the
prediction of stroke [21].

Fig. 10 Various output stages of a healthy retinal fundus image

674 P. G. Prageeth et al.

4 Early Detection of Alzheimer’s Disease Through Retinal

Image Processing

Alzheimer’s disease is an irreversible progressive neurodegenerative disorder, which

means once it is affected cannot be cured. It is a memory and behavioural distur-
bance which leads to intense and eternal loss of cognitive impairment. The two most
important causes of AD are plaques and tangles that on the neurons which blocks the
signals from brain to neuron and vice versa. AD is the most common cause of demen-
tia and its incidence is increasing worldwide associated with population ageing [22].
AD is characterised by progressive cognitive impairment such as memory deficit,
decline in learning and executive functioning, aphasia, apraxia, agnosia and visual
abnormalities [23–25]. There are lot of tests and imaging modalities to be performed
for an effective diagnosis of the disease. Conventional clinical decision making sys-
tems are more manual in nature and ultimate conclusion in terms of exact diagnosis
is remote. The American Academy of Neurology recommend that the clinical tests
which are in connection with AD includes total blood count, electrolytes, calcium,
glucose, liver function tests, thyroid function tests, sedimentation rate, urine analysis
and imaging modalities. But today profiling of human body parameters (clinical test
results) using computers can be utilized for the earlier prognosis of AD. But it is
clinically established that all the changes taking place in brain neurons will be avail-
able from retina of the eye of the patients also [26]. Currently in our works we are
including the retina image results also as a biomarker. Retina image analysis for the
early detection of AD is currently going on. More details on this will be presented
in the conference.

5 Conclusions

With the help of retinal image processing, eye diseases can be diagnosed well in
advance. An expert system for the early detection of the above eye diseases has
already been developed and it is in clinical use in local ophthalmic hospitals. Retinal
image can be utilised for the prediction of stroke also. Currently, developed a system
for the prediction of retinal ischemia from retinal fundus images for the prediction
of ischemic stroke from the global databases. Clinical trials are now going on. The
profiling of human body parameters (clinical test results) using computers for the
early detection of AD is currently done. Now the retinal image parameters are also
included in the profile for further studies.

Acknowledgements We are very thankful to Prof. (Dr). Mahadevan, a leading ophthalmology

surgeon, ophthalmology teacher and a serious and sincere researcher, who provide all the helps
to carry out the above research works successfully. Also extend our heartfelt thanks to (1) Ahalia
Hospital (2) Precise Eye Hospital and (3) Gokulam Medical College, Thiruvananthapuram for
being given all the facilities to carry out the above research work under the supervision of Prof.
(Dr). Mahadevan. K.
Potentiality of Retina for Disease Diagnosis … 675

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Generalized LFT Modeling
of an Uncertain MIMO System

Tamal Roy, Ranjit Kumar Barai and Rajeeb Dey

1 Introduction

In the past few years, a growing interest has been devoted to formulate control oriented
modeling of real physical system from the inherent need for the modeling quality
improvement and truly integrates control objectives into the system identification
process from the experimental input-output test data set [1] from the standpoint of
control system design [2], where the role of the system identification is to condense
the plant uncertainty such that the design and implementation of a robust controller
achieves the performance specifications even in the face of the plant uncertainty
and disturbances. Over the last two decades, there has been a widespread interest to
design robust controller where system model is considered to be consisting of a nom-
inal model and a model uncertainty part [3]. The classical H∞ -control based robust
control design technique has become a challenging task and very effective design
tools guaranteeing to meet the specifications provided the model of the system under
consideration leads to a system model in the form of a linear fractional transformation
(LFT) modeling. The performance of the robust controller depends on the appropriate
representation of the model uncertainty. This motivates the robust-control-oriented
system identification to explicitly consider the robust control performance require-

T. Roy (B)
Electrical Engineering Department, MCKV Institute of Engineering,
Liluah, Howrah 711204, India
e-mail: tamalroy77@gmail.com
R. K. Barai
Electrical Engineering Department, Jadavpur University,
Kolkata 700032, India
e-mail: ranjit.k.barai@gmail.com
R. Dey
Electrical Engineering Department, NIT, Silchar 788 010, Assam, India
e-mail: rajeeb.iitkgp@gmail.com

© Springer Nature Switzerland AG 2019 677

S. Chattopadhyay et al. (eds.), Modelling and Simulation in Science, Technology
and Engineering Mathematics, Advances in Intelligent Systems and Computing 749,
https://doi.org/10.1007/978-3-319-74808-5_60
678 T. Roy et al.

ments during the system identification step. The model of nonlinear systems may
vary due to changes in system configuration and operating conditions. This system
variation can be characterized as model uncertainties and can be represented in the
linearized model by expressing the system state-matrices as matrix polynomials in
the uncertain parameters in the form of a linear fractional transform (LFT) [3, 4].
This LFT based model uncertainty representation of the nonlinear system is essential
for the application of modern robust control technique like µ-analysis and synthe-
sis [5] in addition to H∞ -control and H∞ -Loop Shaping [4, 6–8]. Linearization of
uncertain nonlinear systems as LFT model relates each of the uncertainty with a phys-
ically meaningful parameter of the actual system [9]. Linear Fractional Transform
(LFT) technique offers a unified framework for parameter identification problems in
[10]. In the LFT framework, a wide variety of identification problems concerning
structured nonlinear systems, linear parameter varying (LPV) systems, and also the
various parametric linear system model structures can be accommodated due to its
general nature. This paper presents an uncertainty modeling algorithm of a generic
linear multi-input multi-output system with coupled dynamics in LFT framework
for implementing the classical H∞ -control law. During the formulation of the mod-
eling algorithm, the effect of model uncertainty has been explicitly described by a
possible mismatch between the mathematical model and the real physical system,
the presence of disturbance signal and the possible model order reduction.
The essential contribution for the derivation of LFT model of a coupled dynamic
system has been developing a comprehensive model consisting of the nominal sys-
tem model and an unknown transfer function matrix consisting various uncertainties
introduced due to unmolded dynamics, system parameters changes due to envi-
ronmental variation, the presence of disturbance signal, model order reduction etc.
Different uncertainty modeling technique in LFT framework has been reported in the
literature. A generalized descripted type LFT-based modeling approach consisting
rationally dependent parametric matrices in terms of multi-variable functions has
been discussed in [11]. An uncertainty modeling formulation of nonlinear systems
whose models parameters vary due to change in the system configuration and oper-
ating conditions have been represented in LFT framework in [4]. A symbolic LFT
modeling techniques for nonlinear systems has been presented by combining sym-
bolic modeling and LFT technique in [8]. The best LFT uncertainty model has been
proposed by minimizing the H∞ norm of the uncertainty set with respect to a nominal
model known as input- output data [12]. However, LFT modeling technique is only
applicable for those nonlinear systems where linearization of the mathematical mod-
eling is possible. In this paper, a novel methodology has been developed to formulate
generalized LFT modeling of a multi-variable dynamic system with equal number
of input output consisting a comprehensive nominal model and model uncertainties
expressed by an unknown transfer function matrix, accumulating usual dynamics of
the system represents in a form that required in μ-synthesis-based H∞ controller
design technique. To the best of the knowledge of the authors, such compact and
effective uncertainty modeling approach in generic LFT modeling framework, com-
patible with H∞ controller design for the linear multi-dimensional system has never
been addressed in the literature.
Generalized LFT Modeling of an Uncertain MIMO System 679

The effectiveness of proposed generalized control oriented LFT modeling algo-

rithm for the linear multivariable system has been verified on a Two-DOF mass-
spring-dashpot dynamic system and the recommended LFT structure has been val-
idated in the frequency domain in the context of H∞ based robust control design.
The LFT modeling structure of the Two-DOF mass-spring-dashpot dynamic system
achieves satisfactory performance criterion in μ-synthesis based frequency domain
validation.

2 Generalized LFT Modeling of Linear MIMO System

Most of the modern real physical systems result from the synergetic integration
of different subsystems. The overall system is very complicated due to the cross
coupling of the various subsystems and any attempt to derive a generalized mathe-
matical model for such a highly coupled system results into a very big and complex
and the system models vary due to change in the system configuration and operat-
ing conditions. The generalized LFT modeling of such linear coupled multi-variable
system results in a compact and manageable modeling algorithm is suitable for its
implementation in robust control theory.

2.1 Problem Formulation

A linear coupled dynamic multi-variable system consisting of an equal number of

input and output is considered for formulating the control oriented modeling in LFT
framework.
The generalized model of the coupled dynamic MIMO system is considered as

D ÿ + C ẏ + Ey + z  K u (1)
⎡ ⎤
u1
⎢ u2 ⎥
⎢ ⎥
where, input, disturbance and output vectors u  ⎢ ⎥ ,z 
⎢ .. ⎥
⎣ . ⎦
u m m×1
⎡ ⎤ ⎡ ⎤
z1 y1
⎢ z2 ⎥ ⎢ y2 ⎥
⎢ ⎥ ⎢ ⎥
⎢ . ⎥ and y  ⎢ ⎥ respectively with m  p and the associated system
⎢ . ⎥ ⎢ .. ⎥
⎣ . ⎦ ⎣ . ⎦
zp yp
p×1 p×1
parameters are
680 T. Roy et al.
⎡ ⎤ ⎡ ⎤
d11 d12 · · · d1 p c11 c12 · · · c1 p
⎢ ⎥ ⎢ c21 c22 · · · c2 p ⎥
⎢ d21 d22 · · · d2 p ⎥ ⎢ ⎥
⎢ ⎥
D⎢ . .. . . .. ⎥ , C ⎢
⎢ .. .. . . .. ⎥
⎥ ,
⎢ . ⎥ ⎣ . . ⎦
⎣ . . . . ⎦ . .
d p1 d p2 · · · d pp c p1 c p2 · · · c pp
p× p p× p
⎡ ⎤ ⎡ ⎤
e11 e12 · · · e1 p k11 k12 · · · k1m
⎢ e21 e22 · · · e2 p ⎥ ⎢ k k ··· k ⎥
⎢ ⎥ ⎢ 21 22 2m ⎥
E ⎢
⎢ .. .. . . .. ⎥
⎥ , K ⎢⎢ .. .. . . .. ⎥
⎥
⎣ . . . . ⎦ ⎣ . . . . ⎦
e p1 e p2 · · · e pp km1 km2 · · · kmm m×m
p× p

In real situations, system parameter values of the above matrices are not known
exactly and it is assumed to be varying within certain known intervals.

2.2 LFT Modeling Algorithm for Multiplicative Uncertainty

Structure

This section represents the derivation of the proposed LFT modeling algorithm for
a linear coupled dynamic MIMO system in a systematic and generalized manner.
The linear dynamic MIMO system expressed in (1) is considered for representing
uncertainty modeling in LFT framework. The parametric uncertainties of the system
are expressed in multiplicative uncertainty structure representation, which is further
decomposed appropriately to get an LFT structure. The generalized framework for
obtaining LFT structure of system represented in (1) for the case where m  p. The
details modeling algorithm is described as following:
Step 1: The linear dynamic system express by Eq. (1) can be written as

ÿ  −D −1 C ẏ − D −1 Ey − D −1 z + D −1 K u (2)

The Eq. (2) survives provided D −1 exists, the block diagram representation of the
system described by Eq. (2) is shown in Fig. 1.
Step 2: The uncertain matrices D, C and E characterizes the model uncertainties
leads to the variation in the system parameters. Let us assumed for generic system
the uncertain elements of the D matrix placed diagonally can be expressed as

dii  d̄ii (1 + sdii δdii ) where i  1, 2, . . . , p (3)

where d̄ii is the nominal values of the system parameter, sdii is the corresponding
maximum relative parameter uncertainty and lies within a bound −1 ≤ δdii ≤ 1.
Matrix D can be decomposed and the terms containing nominal and uncertain parts
given as
Generalized LFT Modeling of an Uncertain MIMO System 681

Fig. 1 Block diagram

representation of the linear
multidimensional system

D  D + Dr d (4)

where
⎡ ⎤ ⎡ ⎤
d̄11 d̄12 · · · d̄1 p d̄11 sd11 0 ··· 0
⎢ ⎥ ⎢ ⎥
⎢ d̄ d̄ · · · d̄ ⎥ ⎢ d̄22 sd22 · · · ⎥
⎢ 21 22 2p ⎥ ⎢ 0 0 ⎥
D⎢ ⎢ ⎥ , Dr  ⎢ ⎥
⎥ ⎢ .. .. .. ⎥
⎢ ... ... . . . ... ⎥ ⎢ . .
..
. . ⎥
⎣ ⎦ ⎣ ⎦
d̄ p1 d̄ p2 · · · d̄ pp 0 0 · · · d̄ pp sd pp
p× p p× p
⎡ ⎤
δd11 0 · · · 0
⎢ ⎥
⎢ 0 δd22 · · · 0 ⎥
⎢ ⎥
and d  ⎢ . . . ⎥
⎢ . . . . .. ⎥
⎣ . . . ⎦
0 0 · · · δd pp
p× p

Now the term D −1 can be written by using matrix inversion lemma

D −1  (Dr−1 D + d )−1 Dr−1 (5)

An upper LFT representation of D −1 can be written as

D −1  FU (Q d , d )  Q d22 + Q d21 d (I p − Q d11 d )−1 Q d12 (6)

−1 −1 −1 −1
where, Q d11  −D Dr , Q d12  D , Q d21  −D Dr and Q d22  D
The block partition matrix Q d is express as

Qd12 ⎤ ⎡ − D Dr
−1
D ⎤
−1
⎡ Qd11
Qd = ⎢ ⎥ = ⎢ −1 ⎥
⎣⎢Qd21 Qd22 ⎦⎥ ⎢ − D D −1
⎣ r D ⎥⎦ 2 p×2 p
682 T. Roy et al.

Now treating respective uncertain elements of matrix ‘C’ in (2) is express in terms
of the uncertain parametric representation can be described by

cii  c̄ii (1 + scii δcii ) where i  1, 2, . . . , p (7)

where c̄ii is the nominal values of the system parameter, scii is the corresponding
maximum relative parameter uncertainty and lies within a bound −1 ≤ δcii ≤ 1.
Similarly, the matrix C can be decomposed as

C  C + C (8)

The uncertainty matrix  C is decomposed as

 C  C f c C g (9)

where c is a diagonal uncertainty matrix. The elements of the matrix C g (may be

identity matrix or unit matrix) depends on the position of uncertain parameters in the
matrix  C. In generalized approach, it is assumed that the uncertain parameters in
 C is located diagonally than the matrices C f and C g can be expressed as
⎡ ⎤ ⎡ ⎤
c̄11 sc11 0 · · · 0 δc11 0 · · · 0
⎢ ⎥ ⎢ ⎥
⎢ 0 c̄22 sc22 · · · 0 ⎥ ⎢ 0 δc22 · · · 0 ⎥
⎢ ⎥ ⎢ ⎥
Cf  ⎢ . .. .. ⎥ , c  ⎢ . . . .. ⎥
⎢ . .. ⎥ ⎢ . . . . . ⎥
⎣ . . . . ⎦ ⎣ . . ⎦
0 0 · · · c̄ pp sc pp 0 0 · · · δc pp
p× p p× p
⎡ ⎤
1 0 ··· 0
⎢0 1 ··· 0⎥
⎢ ⎥
and C g  ⎢ ⎥
⎢ .. .. . . .. ⎥
⎣. . . .⎦
0 0 · · · 1 p× p

and the nominal part C is given as

⎡ ⎤
c̄11 c̄12 · · · c̄1 p
⎢ ⎥
⎢ c̄21 c̄22 · · · c̄2 p ⎥
⎢ ⎥
C ⎢ . .. . . .. ⎥
⎢ . . . ⎥
⎣ . . ⎦
c̄ p1 c̄ p2 · · · c̄ pp
p× p

Upper LFT representation of matrix C can be express as

C  FU (Q c , c )  Q c22 + Q c21 c (I p − Q c11 c )−1 Q c12 (10)

Generalized LFT Modeling of an Uncertain MIMO System 683

Fig. 2 Block diagram

representation of the system
with LFT structure

⎡ Qc11 Qc12 ⎤ ⎡0 p× p Cg ⎤
where,Qc = ⎢ ⎥=⎢
C ⎥⎦
⎢⎣Qc21 Qc22 ⎥⎦ ⎣ C f 2 p× 2 p

The similar problem of uncertainty representation as elements of the E can express

as

eii  ēii (1 + seii δeii ) where i  1, 2, . . . , p (11)

The upper LFT representation of matrix can be express as

E  FU (Q e , e )  Q e22 + Q e21 e (I p − Q e11 e )−1 Q e12 (12)

⎡ Qe11 Qe12 ⎤ ⎡0 p× p Eg ⎤
where Qe = ⎢ ⎥=⎢
E ⎥⎦
⎢⎣Qe21 Qe22 ⎥⎦ ⎣ E f 2 p× 2 p

Step 3: The block diagram representation of the linear multi-dimensional system

is redrawn in Fig. 2 treating u d , u c and u e to be the outputs of uncertainty blocks
d , c and e are fed to the nominal blocks Q d , Q c and Qe respectively. Similarly
yd , yc and ye , outputs of the nominal block Q d , Q c and Qe are fed back to the uncer-
tainty blocks d , c and e respectively.
Now consider the state vector of the system as
⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤
x1 y1 x p+1 ẏ1
⎢ x2 ⎥ ⎢ y2 ⎥ ⎢ x p+2 ⎥ ⎢ ⎥
⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢⎢
ẏ2 ⎥
⎥
⎢ . ⎥  ⎢ ⎥ and ⎢ ⎥
⎢ . ⎥ ⎢ .. ⎥ ⎢ .. ⎥  ⎢ .. ⎥ (13)
⎣ . ⎦ ⎣ . ⎦ ⎣ . ⎦ ⎣ . ⎥ ⎢
⎦
xp yp x p+ p ẏp

The generalized upper LFT representation of the linear dynamic MIMO system
considering input output of all block partition matrices Q d , Q c and Qe can be is
684 T. Roy et al.

represented as

(14)

⎡ 0 p× p I p× p 0 p× p 0 p× p 0 p× p 0 p× p 0 p× p ⎤
⎢ −1 −1 −1 −1 −1 −1 −1 ⎥
⎢− D E D C D Dr D Cf −D E f −D D K⎥
⎢ −1 −1 −1 −1 −1 −1 −1 ⎥
⎢− D E D C D Dr D Cf −D E f −D D K⎥
where, ∏=⎢ 0 Cg 0 p× p 0 p× p 0 p× p 0 p× p 0 p× p ⎥
⎢ p× p ⎥
⎢ Eg 0 p× p 0 p× p 0 p× p 0 p× p 0 p× p 0 p× p ⎥
⎢ ⎥
⎢ I p× p 0 p× p 0 p× p 0 p× p 0 p× p 0 p× p 0 p× p ⎥
⎢⎣ Γ n 0 p× p 0 p× p 0 p× p 0 p× p 0 p× p 0 p× p ⎥⎦
7 p×7 p

The input output representation of the uncertainty matrix can be expressed as

⎡ ⎤ ⎡ ⎤
ud yd
⎣ uc ⎦  sys ⎢ ⎥
⎣ yc ⎦ (15)
ue ye
⎡ ⎤
d 0 0
⎢ ⎥
where, sys  ⎣ 0 c 0 ⎦
0 0 e 3 p×3 p
The state space representation of the linear multivariable system is expressed as
⎡ ⎤ ⎡ ⎤
ẋ x
⎢ yd ⎥ ⎢ ud ⎥
⎢ ⎥ ⎢ ⎥
⎢y ⎥ ⎢ uc ⎥
⎢ c⎥
⎢ ⎥  G sys ⎢ ⎥
⎢ ue ⎥ (16)
⎢ ye ⎥ ⎢ ⎥
⎢ ⎥ ⎣ z ⎦
⎣y⎦
yn u
Generalized LFT Modeling of an Uncertain MIMO System 685

⎡A B1 B2 ⎤
where, Gsys = ⎢⎢ C1 D11 D12 ⎥⎥
⎢⎣C2 D21 D22 ⎥⎦ 7 p×7 p
Now,
⎡ ⎤ ⎡ ⎤
0 p× p I p× p 0 p× p 0 p× p 0 p× p
A⎣ −1 −1
⎦ , B1  ⎣ −1 −1 −1
⎦ ,
−D E −D C −D
Dr −D C f −D Ef
2 p×2 p 2 p×3 p
⎡ ⎤
 −D
−1
E −D
−1
C
0 p× p 0 p× p ⎢ ⎥
B2  −1 −1
, C1  ⎢
⎣ 0 p× p Cg ⎥ ⎦ ,
D T −D K 2 p×2 p Eg 0 p× p
3 p×2 p
⎡ ⎤ ⎡ ⎤
−1 −1 −1 −1 −1
−D Dr −D C f −D Ef D T −D K
⎢ ⎥ ⎢ ⎥
D11  ⎢
⎣ 0 p× p 0 p× p 0 p× p ⎥
⎦ , D12 ⎢
⎣ 0 p× p 0 p× p ⎦
⎥ ,
0 p× p 0 p× p 0 p× p 0 p× p 0 p× p
3 p×3 p 3 p×2 p
 
n 0 p× p 0 p× p 0 p× p
C2  D21  ,
I p× p 0 p× p 0 p× p 0 p× p
2 p×2 p 2 p×2 p

0 p× p 0 p× p
D22 
0 p× p 0 p× p
2 p×2 p

The generalized perturbed linear dynamic MIMO system in Upper LFT (Fig. 3)
framework can be described by


y z
 FU (G sys , sys ) (17)
yn u

Fig. 3 Upper LFT

representation of the linear
dynamic system
686 T. Roy et al.

Fig. 4 Two-DOF MSD

dynamic system

⎡ ⎤
d 0 0
⎢ ⎥
with uncertain block sys  ⎣ 0 c 0 ⎦ .
0 0 e 3 p×3 p

3 LFT Modeling of Two-DOF Mass-Spring-Dashpot

Dynamic System

An interesting linear two-DOF mass-spring-dashpot (MSD) dynamic system, pose

challenges for many linear classical control techniques, has been considered as a can-
didate system to validate the generalized algorithm of LFT modeling for uncertain
MIMO system [13]. A point masses m 2 are connected by a spring-dashpot pair con-
tains spring stiffness constants k2 and damping coefficient c2 respectively. Another
point mass m 1 is linked to the ground by another spring-dashpot pair contains spring
stiffness constants k1 and damping coefficient c1 respectively. Two known dynamic
forces f 1 and f 2 are applied on the two point masses to create displacement u 1 and u 2
from their equilibrium positions respectively (Fig. 4).
The equation of motion (EOM) of the two-DOF MSD dynamics system is repre-
sented by
 
 
 
m1 0 ü 1 c1 + c2 −c2 u̇ 1 k1 + k2 −k2 u1 f1
+ +  (18)
0 m2 ü 2 −c2 c2 u̇ 2 −k2 k2 u 2 f2

The compact matrix notation of EOM of two DOF mass-springs-dashpot systems

is represented by
Generalized LFT Modeling of an Uncertain MIMO System 687

Fig. 5 Block diagram of

Two-DOF MSD dynamic
system

M ü + C u̇ + K u  f (19)

where, M, C, and K denote the mass, damping and stiffness matrices respectively and
f, u, u̇ and ü are the force, displacement, velocity and acceleration vectors respec-
tively. Now, the block diagram representation of the system described in (19) is
shown in Fig. 5, provided M −1 exists.
In a realistic system, variation of the physical parameters mass (m 1 and m 2 ), damp-
ing coefficients (c1 and c2 ) and spring stiffness constants (k1 and k2 ) are considered
as uncertain parameters in the candidate system. It is assumed that the mass leads to
40% variation, spring stiffness constants represents up to 30% variation and damping
coefficients varying 20% around the nominal value.
The actual mass of the system with all possible uncertainties are represented as

m i  m̄ i (1 + pm i δm i ), i  1, 2 (20)

where m̄ i are the nominal value of the corresponding mass, pm i  0.4 is the maximum
relative uncertainties in each of the mass and −1 ≤ δm i ≤ 1.
As mass m i contained in the matrix M, then matrix M decomposed as

M  M + M p m (21)

where,
  
m̄ 1 0 m̄ 1 pm 1 0 δm 1 0
M , Mp  and m 
0 m̄ 2 0 m̄ 2 pm 2 0 δm 2
2×2

The block partition matrix Q m is represented as

Qm12 ⎤ ⎡ − M M p
−1
M ⎤
−1
⎡ Qm11
Qm = ⎢ ⎥=⎢ ⎥ (22)
⎣⎢Qm21 Qm22 ⎦⎥ ⎢ − M −1M
⎣ P M −1 ⎥⎦ 4×4

The damping coefficients of the system with all possible uncertainties are repre-
sented as
688 T. Roy et al.

Fig. 6 Block diagram

representation of Two-DOF
MSD dynamic system

ci  c̄i (1 + pci δci ), i  1, 2 (23)

where c̄i are the nominal value of the corresponding mass, pci  0.3 is the maximum
relative uncertainties in each of the mass and −1 ≤ δci ≤ 1.
The block partition matrix Q c is represented as

⎡ Qc11 Qc12 ⎤ ⎡02×2 Cg ⎤

Qc = ⎢ ⎥=⎢
⎣⎢Qc21 Qc22 ⎦⎥ ⎣ C f C ⎥⎦ (24)
4×4

Similarly, the actual damping coefficients of the system with all possible uncer-
tainties are represented as

ki  ki (1 + pki δki ), i  1, 2 (25)

where ki is the nominal value of the corresponding spring stiffness constant, pki  0.2
is the maximum relative uncertainty in each of this coefficient and −1 ≤ δki ≤ 1.
The block partition matrix Q k is represented as

⎡ Qk11 Qk12 ⎤ ⎡02×2 Kg ⎤

Qk = ⎢ ⎥=⎢
⎢⎣Qk21 Qk22 ⎥⎦ ⎣ K f K ⎥⎦ (26)
4×4

The block diagram representation of a two-DOF mass-spring-dashpot dynamic

system in Fig. 6 with uncertain parameters treating um , uc and uk to be the out-
put of uncertain m , c and k block respectively that are fed as input to the
nominal blocks Q m , Q c and Q k respectively. Similarly, ym , yc and yk are outputs
of Q m , Q c and Q k are fed as inputs to the m , c and k respectively.
Generalized LFT Modeling of an Uncertain MIMO System 689

Now, the state vector for the two-DOF mass-spring-dashpot dynamic system can
be defined as
 T
X  x1 x2 x3 x4 (27)

where, x1  u1 , x2  u2 , x3  u̇1 , x4  u̇2

The output vector defined in terms of state variable as
 T  T  T
y  x1 x2  y1 y2  u1 u2 (28)

The LFT representation of two-DOF mass-spring-dashpot dynamic system con-

sidering input output of all block partition matrixes Q m , Q c and Q k can be repre-
sented as

(29)

⎡ 02×2 I 2×2 02×2 02×2 02×2 02×2 ⎤

⎢ −1
− M −1C − M −1M − M −1C f − M −1 K f M −1 ⎥⎥
⎢−M K p

⎢− M −1 K − M −1C − M −1M p − M −1C f − M −1 K f M −1 ⎥

where, Π=⎢ ⎥
⎢ 02×2 Cg 02×2 02×2 02×2 02×2 ⎥
⎢ Kg 02×2 02×2 02×2 02×2 02×2 ⎥
⎢ ⎥
⎣⎢ I 2×2 02×2 02×2 02×2 02×2 02×2 ⎦⎥12×12
The input output representation of the uncertainty matrix can be expressed as
⎡ ⎤ ⎡ ⎤
um ym
⎣ uc ⎦  smd ⎢ ⎣ yc ⎦
⎥
(30)
uk yk
⎡ ⎤
m 0 0
⎢ ⎥
where, smd  ⎣ 0 c 0 ⎦
0 0 k 6×6
The state space representation of two-DOF mass-spring-dashpot system is
expressed as
690 T. Roy et al.
⎡ ⎤ ⎡ ⎤
ẋ x
⎢ ym ⎥ ⎢ u ⎥
⎢ ⎥ ⎢ m⎥
⎢y ⎥
⎢ c ⎥  G smd ⎢ c ⎥
⎢ u ⎥ (31)
⎢ ⎥ ⎣ uk ⎦
⎣ yk ⎦
y f

⎡A B1 B2 ⎤
where, Gsmd = ⎢⎢ C1 D11 D12 ⎥⎥
⎢⎣C2 D21 D22 ⎥⎦12×12
Now,
 ⎡ ⎤
02×2 I2×2 02×2 02×2 02×2
A −1 −1
, B1  ⎣ −1 −1 −1
⎦,
−M K −M C −M M p −M C f −M Kf
4×4
⎡ ⎤
 −1 −1
02×2 ⎢ −M K −M C ⎥
B2  ,  ⎢ 02×2 Cg ⎥
−1
C 1 ⎣ ⎦,
M 4×2 Kg 02×2
⎡ ⎤ ⎡ ⎤
−1 −1 −1 −1
⎢ −M M p −M C f −M K f ⎥ ⎢ −M ⎥
D11  ⎢
⎣ 02×2 02×2 02×2 ⎥ ⎢
⎦ , D12  ⎣ 02×2 ⎦
⎥
02×2 02×2 02×2 02×2
6×6 6×2
    
C2  I2×2 02×2 , D21  02×2 02×2 02×2 , D22  02×2 2×2
2×4 2×3

The generalized perturbed two-DOF mass-spring-dashpot dynamic can be

described by Upper
LFT framework (Fig. 7).

y  FU (G smd , smd )f (32)

Fig. 7 Upper LFT

representation of the
Two-DOF MSD dynamic
system
Generalized LFT Modeling of an Uncertain MIMO System 691

Fig. 8 Closed loop LFT in

H∞ design

Fig. 9 Robust stability test of MSD with H∞ controller

4 H∞ Control Based Frequency Domain Validation

The frequency domain validation of uncertainty modeling in LFT framework has

been investigated in the context of robust control theory [14]. The objective is to
design an H∞ controller that achieves certain performance specification and remain
stable in the presence of all possible uncertainties.

4.1 Simulation Results

An H∞ sub- optimal control law has been implemented for closed loop interconnected
system shown in the Fig. 8. The H∞ controller K minimizes the  .∞ norm of
the nominal transfer function matrix FL (P, K ) from the disturbance (dist) to the
weighted output e.
The interval of γ iteration for H∞ control law has been chosen in between 0 to
10 with a tolerance of 0.001. The H∞ controller of the closed loop system achieves
the  .∞ norm equal to 1.0005. All stable poles of the designed H∞ controller make
the closed loop system more acceptable in practice. The closed loop system with
H∞ controller achieves the robust stability and the maximum value of μ is 0.73995
shown in Fig. 9 and also achieve the robust performance with a maximum value of
the μ is 0.97076 shown in Fig. 10.
692 T. Roy et al.

Fig. 10 Robust performance of MSD with H∞ controller

Table 1 Numerical values of Symbol Value Unit Symbol Value Unit

Two-DOF MSD dynamics
system m1 2 Kg k1 6 N/m
m2 1 Kg k2 3 N/m
c1 0.1 N/m/s f1 sin t N
c2 0.3 N/m/s f2 sin t N

Numerical values of the two-DOF- MSD dynamics system are given in Table 1.

5 Conclusions

This paper presents the mathematical generalization of control oriented LFT model-
ing of an uncertain coupled multi-input multi-output system with an equal number
of input outputs. The uncertain physical parameters are not exactly known and it
can be assumed that the parameters values are known within certain intervals and
the uncertain parameters express in terms of possible relative error. LFT modeling
of a given linear multi input multi output system is not necessarily minimal. For the
minimal realization of any multidimensional system refers to as a smallest possi-
ble representation of the uncertainty matrix . It is entirely dependent on the field
of realization. The proposed generalized LFT modeling structure for linear multi
input multi output dynamic system is applicable only to a system having an equal
number of inputs and outputs. Proposed generalized control oriented LFT modeling
algorithm has been implemented in a two-DOF linear mass-spring-dashpot dynamic
system and the formulated model in LFT framework has been validated in the con-
text of H∞ Control law. H∞ control based frequency domain validation process
shows satisfactory results for validating uncertainty model of the two-DOF linear
mass-spring-dashpot dynamic system in LFT framework.
Generalized LFT Modeling of an Uncertain MIMO System 693

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