AC LOAD FLOW STUDIES USING NUMERICAL METHOD (RELATE

THEORETICAL CALCULATION AND MATLAB PROGRAM)

A Project report submitted in partial fulfillment

Of the requirements for the degree of B. Tech in Electrical Engineering

by

DEBARATI SIKDAR (11701617064)

PRANABESH HAZRA (11701617053)
MD NASIR (11701617057)

Under the supervision of

Mr. Dipankar Santra

Associate Professor
Department of Electrical Engineering

Department of Electrical Engineering

RCC INSTITUTE OF INFORMATION TECHNOLOGY
CANAL SOUTH ROAD, BELIAGHATA, KOLKATA–700015, WEST BENGAL
Maulana Abul Kalam Azad University of Technology (MAKAUT)

1
 CERTIFICATE
To whom it may concern

This is to certify that the project work entitled AC LOAD FLOW STUDIES USING NUMERICAL
METHOD (RELATE THEORETICAL CALCULATION AND MATLAB PROGRAM) is the work
carried out by DEBARATI SIKDAR (11701617064), PRANABESH HAZRA (11701617053),
MD NASIR (11701617057), the students of B.Tech in the Department of Electrical Engineering,
RCC Institute of Information Technology (RCCIIT), Canal South Road, Beliaghata, Kolkata-700015,
affiliated to Maulana Abul Kalam Azad University of Technology (MAKAUT), West Bengal, India,
during the academic year 2020-21, in partial fulfillment of the requirements for the degree of Bachelor of
Technology in Electrical Engineering and this project has not been submitted previously for the award of any
other degree, diploma or fellowship.

Signature of the Guide Signature of the HOD

Name: Mr. Dipankar Santra Name:

Designation: Associate Professor, Dept Designation:

of EE

Signature of the External Examiner

Name:

Designation:

2
 PREFACE

This report comprises the summary of work we DEBARATI SIKDAR, PRANABESH HAZRA,
MD NASIR achieved during our final year project the task we have chosen to carry out during this year is
AC LOAD FLOW STUDIES USING NUMERICAL METHOD
(RELATE THEORETICAL CALCULATIONS AND MATLAB PROGRAM). The effort is conducted
under the supervision of Mr. DIPANKAR SANTRA, Department of Electrical Engineering,
RCC Institute of Information Technology.

The goal of this thesis is to do a performance analysis on numerical methods including Gauss-Seidel method
for a load flow run to achieve less run time and verify the results obtained in theoretical calculations using the
MATLAB program.

3
 ACKNOWLEDGEMENT

It is our great fortune that we have got the opportunity to carry out the project work under the
supervision of Mr. Dipankar Santra in the Department of Electrical Engineering, RCC Institute of
Information Technology (RCCIIT), Canal South Road, Beliaghata, Kolkata-700015, affiliated to
Maulana Abul Kalam Azad University of Technology (MAKAUT), West Bengal, India. We express
our sincere thanks and deepest sense of gratitude to my guide for his constant support, unparalleled
guidance and limitless encouragement.

We would also like to convey our gratitude to all the faculty members and the staffs of Department of
Electrical Engineering, RCCIIT for their whole-hearted cooperation to make this work turn into reality.
Last but not the least thanks to the fellow members of our group for working as a team.

DEBARATI SIKDAR (11701617064)

PRANABESH HAZRA (11701617053)

MD NASIR (11701617057)

NAME AND SIGNATURE OF STUDENTS

Place: Kolkata
Date: 09/07/2021

4
 TABLE OF CONTENTS
Topics Page No.

Abstract 7

Chapter 1 Introduction to Load Flow Analysis 8

1.1 Introduction 9

1.2 Objectives of load flow 11

1.3 Bus Classification 12

1.4 Overview 15

1.5 Organization of Thesis 17

Chapter 2 Literature Review 18

Chapter 3 Load Flow Studies 20

3.1 Real and Reactive power injected in bus 21

3.2 Preparation of data for load flow 23

Chapter 4 Load Flow Conventional Method 24

4.1 Gauss-Seidel Method 25

4.2 Numerical problem and solution of Gauss-Seidel method 28

4.3 Flowchart for implementing Gauss-Seidel method 33

4.4 Algorithm of Gauss-Seidel method 34

Chapter 5 MATLAB Program of Gauss-Seidel method 35

Chapter 6 Result and Limitations 37

6.1 Result 38

6.2 Limitation of Gauss-Seidel method 39

6.3 Limitation of us 39

Chapter 7 Conclusion and Future Scope 40

5
 7.1 Conclusion 41

7.2 Future Scope 41

Chapter 8 Reference 42

Appendix 43

6
 ABSTRACT

The goal of this thesis is to do a performance analysis on numerical methods including Gauss-Seidel method
for a load flow run to achieve less run time. Unlike the proposed method, the traditional load flow analysis
uses only one numerical method at a time. These algorithms perform all the computation for finding the bus
voltage angles and magnitudes, real and reactive powers for the given generation and load values, while
keeping track of the proximity to convergence of a solution. This work focuses on finding the most effective
algorithm. The proposed method is implemented on a 5-bus system and the solutions obtained are verified
with MATLAB a commercial software for load flow analysis.

Key Words: Load flow, Gauss-Seidel method, convergence time.

7
 CHAPTER 1

INTRODUCTION TO LOAD FLOW ANALYSIS

8
1.1 Introduction

Concept of Power Flow:

The power flow analysis is a very important tool in power system analysis. Power flow studies are routinely
used in planning, control, and operations of existing electric power systems as well as planning for future
expansion. The successful operation of power systems depends upon knowing the effects of adding
interconnections, adding new loads, connecting new generators or connecting new transmission line
before it is installed. The goal of a power flow study is to obtain complete voltage angle and magnitude
information for each bus in a power system for specified load and generator real power and voltage
conditions. Once this information is known, real and reactive power flow on each branch as well as
generator reactive power can be analytically determined. Due to the nonlinear nature of the problem,
numerical methods are employed to obtain solution that is within an acceptable tolerance.

Figure 1 PQ bus system

Load flow studies are one of the most important aspects of power system planning and operation.
The load flow gives us the sinusoidal steady state of the entire system − voltages, real and reactive power
generated and absorbed and line losses. Since the load is a static quantity and it is the power that flows
through transmission lines, the purists prefer to call this Power Flow studies rather than load flow studies.
9
We shall however stick to the original nomenclature of load flow. Through the load flow studies,
we can obtain the voltage magnitudes and angles at each bus in the steady state. This is rather
important as the magnitudes of the bus voltages are required to be held within a specified limit.
Once the bus voltage magnitudes and their angles are computed using the load flow, the real and reactive
power flow through each line can be computed.

Also based on the difference between power flow in the sending and receiving ends, the losses in a
particular line can also be computed. Furthermore, from the line flow we can also determine the over and
under load conditions.

The steady state power and reactive powers supplied by a bus in a power network is expressed in terms of
nonlinear algebraic equations. We therefore would require iterative methods for solving these equations. In this
chapter, we shall discuss two of the load flow methods. We shall also delineate how to interpret the load flow
results.

10
1.2 OBJECTIVES OF LOAD FLOW

• Power flow analysis is very important in planning stages of new networks or addition
to existing ones like adding new generator sites, meeting increase load demand and
locating new transmission sites.

• The load flow solution gives the nodal voltages and phase angles and hence the power
injection at all the buses and power flows through interconnecting power channels.

• It is helpful in determining the best location as well as optimal capacity of proposed

generating station, substation and new lines.

• It determines the voltage of the buses. The voltage level at the certain buses must be
kept within the closed tolerances.

• System transmission loss minimizes.

• Economic system operation with respect to fuel cost to generate all the power needed.

• The line flows can be known. The line should not be overloaded, it means, we should
not operate the close to their stability or thermal limits.

11
1.3 BUS CLASSIFICATION

For load flow studies it is assumed that the loads are constant and they are defined by their real
and reactive power consumption. It is further assumed that the generator terminal voltages are
tightly regulated and therefore are constant. The main objective of the load flow is to find the
voltage magnitude of each bus and its angle when the powers generated and loads are pre-
specified. To facilitate this, we classify the different buses of the power system as listed below.

There are 3types of buses-

i. Load Buses
ii. Voltage Controlled Buses
iii. Slack or swing Buses

Load bus or PQ Bus

 A bus at which Active power and Reactive power are specified.

 Magnitude and phase angle of the voltage need to be calculated.
 This type of buses is most common, comprising 80% of all buses in power
system.
 In these buses no generators are connected and hence the generated realpower
PGi and reactive power QGi are taken as zero. The load drawn by these buses
are defined by real power -PLi and reactive power -QLi in which the negative
sign accommodates for the power flowing out of the bus. This is why these
buses are sometimes referred to as P-Q bus. The objective of the load flow is to
find the bus voltage magnitude Viand its angle i

12
Voltage controlled Bus

 A bus at which the magnitude of voltage and active power is defined.

 Reactive power and phase angles need to be determined through load flow
equation.
 This bus is always connected to generator and is also known as PV bus.
 This type of bus comprises of 10% of all buses in power system.
 These are the buses where generators are connected. Therefore,
the power generation in such buses is controlled through a prime
mover while the terminal voltage is controlled through the
generator excitation. Keeping the input power constant through
turbine-governor control and keeping the bus voltageconstant
using automatic voltage regulator, we can specify constant PGi
and Vi for these buses. This is why such buses are also
referred to as P-V buses. It is to be noted that their active power
supplied by the generator QGi depends on the system
configuration and cannot be specified in advance. Furthermore,
we have to find the unknown angle i of the bus voltages.

Slack bus

 Voltage magnitude and voltage phase angle are specified and real and reactive
power are to be obtained.
 Normally there is only one bus of this type present in a given power system.
 One generator bus is selected as the reference bus.
 In slack bus voltage angle and magnitude is normally considered 1+j0 pu.
 This bus sets the angular reference for all the buses. Since it is the angle
difference between two voltage sources that dictates the real and reactive power
flow between them, the particular angle of the slack bus is not important.

13
 Figure 2 Bus classification

Figure 3

Now consider a typical load flow problem in which all the load demands are known. Even if the generation
matches the sum total of these demands exactly, the mismatch between generation and load will persist
because of the line I2R losses. Since the I2R loss of a line depends on the line current which, in turn,
depends on the magnitudes and angles of voltages of the two buses connected to the line, it is rather
difficult to estimate the loss without calculating the voltages and angles. For this reason, a generator bus is
usually chosen as the slack bus without specifying its real power. It is assumed that the generator connected to
this bus will supply the balance of the real power required and the line losses.

14
1.4 OVERVIEW

The power flow algorithm written in this thesis is based on the Gauss-Seidel method. A
software program has been developed. The program gives the power flow solution for a
given problem as well as computes the complete voltage angle and magnitude information
for each bus in a power system for specified load and generator real power and voltage
conditions.

Power flow analysis is the backbone of power system analysis and design. They are necessary
for planning, operation, economic scheduling and exchange of power between utilities. Power
flow analysis is required for many other analyses such as transient stability, optimal power flow
and contingency studies. The principal information of power flow analysis is to find the
magnitude and phase angle of voltage at each bus and the real and reactive power flowing in
each transmission lines.

Power flow analysis is an importance tool involving numerical analysis applied to a power
system. In this analysis, iterative techniques are used due to there no known analytical method
to solve the problem. This resulted nonlinear set of equations or called power flow equations
are generated. To finish this analysis there are methods of mathematical calculations which
consist plenty of step depend on the size of system. This process is difficult and takes much
time to perform by hand. By develop a toolbox for power flow analysis surely will help the
analysis become easier.

Power flow analysis software can help users to calculate the power flow problem. Over the past
decade, a few versions of educational software packages using advanced programming
languages, such as C, C++, Pascal, or FORTRAN have been developed for power engineering
curriculums. These choose an integrated study platform with support of database and GUI
functions.

15
Power flow analysis software develops by the author use MATLAB software. MATLAB as a
high-performance language for technical computation integrates calculation, visualization and
programming in an easy-to-use environment, thus becomes a standard instructional tool for
introductory and advanced courses in mathematics, engineering and science in the university
environment. Most of the students are familiar with it.

MATLAB is viewed by many users not only as a high-performance language for technical
computing but also as a convenient environment for building graphical user interfaces (GUI).
Data visualization and GUI design in MATLAB are based on the Handle Graphics System in
which the objects organized in a Graphics Object Hierarchy can be manipulated by various
high and low-level commands. If using MATLAB7 the GUI design more flexible and versatile,
they also increase the complexity of the Handle Graphics System and require some effort to
adapt to.

16
1.5 ORGANISATION OF THESIS

1. Contains the introduction. Each part is different from the other and is described along
with the necessary theory required to comprehend it.

2. Deals with the literature review. From this we can see before our project who else
worked on this topic and how our project is different.

3. Deals with load flow studies or power flow concept, explained with necessary
equations for power flow.

4. Deals with conventional methods of numerical methods to solve load flow problems,
flowchart and algorithm for MATLAB program.

5. Focuses on the MATLAB program using Gauss-Seidel method.

6. Concludes about the load flow performance by the conventional method from the
results obtained from MATLAB.

7. References

8. Appendix-software is listed here.

17
 CHAPTER 2
LITERATURE REVIEW

18
 LITERATURE REVIEW

Power flow analysis came into existence in the early 20th century. There were many research
works done on the power flow analysis. In the beginning, the main aim of the power flow
analysis was to find the solution irrespective of time. Over the last 20 years, efforts have been
expended in the research and development on the numerical techniques. Before the invention
of digital computers, the load flow solutions were obtained using the network analysis.

In the year 1956 the first practical automatic digital solution was found. The early generation
computers were built with less memory storage, the Y-Bus matrix iterative method was well
suitable for these computers. Although performance was satisfactory on many power flow
problems, the time taken to convergence was very slow and sometimes they never converged.
In order to overcome the difficulties of this method a new method was developed based on the
Z-Bus matrix.

This new method converges more reliably compared to the Y-Bus matrix method, but it
requires more memory storage when solving large problems. During this time, the iterative
methods were showing very powerful convergence properties but were difficult in terms of
computation. In the mid 1960’s major changes in the power system came with the development
of very efficient sparsity programmed ordered elimination by Tinny.

19
 CHAPTER 3

LOAD FLOW STUDIES

20
3.1 REAL AND REACTIVE POWER INJECTED IN A BUS

For the formulation of the real and reactive power entering a bus, we need to define the
following quantities. Let the voltage at the ith bus be denoted by,

Vi = Vii = Vi(cosi+jsini) ()

Also, let us define the self-admittance at bus-i as,

Yii = Yii ii=|Yii(cosii+jsinii)=Gii+jBii (3.2)

Similarly, the mutual admittance between the buses i and j can be

written as,

Yij = Yij ij= |Yij(cosij+jsinij)=Gij+jBij (3.3)

Let the power system contains a total number of n buses. The current injected at bus-i is given as,
Ii=Yi1V1+Yi2V2+….+YinVn

n
= ∑Yik Vk (3.4)

k=1

It is to be noted we shall assume the current entering a bus to be positive and that leaving the
bus to be negative. As a consequence, the power and reactive power entering a bus will also be
assumed to be positive. The complex power at bus-i is then given by,

n
Pi - jQi = Vi*Ii = Vi* ∑YikVk
k=1
n

= |Vi|(cosi – jsini)∑YikVk|(cosik + jsinik)(cosk + jsink)

k=1

21
 n

= ∑ |YikViVk| (cosi – jsini) (cosik + jsinik) (cosk + jsink) (3.5)

k=1

=(cosi-jsini) [cos(ik+k) +jsin(ik+k)]

=cos(ik+k-i) +jsin(ik+k-i)

Therefore, substituting in (3.5) we get the real and reactive power as,

Pi= ∑ |YikViVk|cos(ik+k-i) (3.6)

k=1

Qi = - ∑ |YikViVk|sin(ik+k-i) (3.7)

k=1

22
3.2 PREPARATION OF DATA FOR LOAD FLOW

Let real and reactive power generated at bus-i be denoted by PGi and QGi respectively. Also let
us denote the real and reactive power consumed at the ith bus by PLi and QLi respectively. Then
the net real power injected in bus-i is,

Pi,inj= PGi−PLi (3.8)

Let the injected power calculated by the load flow program be Pi,calc .

Then the mismatch between the actual injected and calculated values

is given by,

Pi= Pi,inj−Pi,calc= PGi− PLi− Pi,calc (3.9)

In a similar way the mismatch between the reactive power injected and calculated values is given by,

Qi= Qi,inj−Qi,calc=QGi−QLi−Qi,calc (3.10)

The purpose of the load flow is to minimize the above two mismatches. It is to be noted that

(3.6) and (3.7) are used for the calculation of real and reactive power in (3.9) and (3.10).

However, since the magnitudes of all the voltages and their angles are not known prior, an iterative

procedure must be used to estimate the bus voltages and their angles in order to calculate the

mismatches. It is expected that mismatches Pi and Qi reduce with each iteration and the load flow

is said to have converged when the mismatches of all the buses become less than a very small number.

23
 CHAPTER 4
Load Flow Conventional Method

24
 4.1 Gauss-Seidel Method
Gauss-Seidel method is also known as the method of successive displacements.
To illustrate the technique, consider the solution of the non-linear equation given by,

F(x)=0 (1)

Above function is rearrange and written as,

x=g(x) (2)

If x=(k) is an initial estimate of the variable x, the following iterative sequence is formed,

X(k+1)=g(x(k)) (3)

A solution is obtained when the difference between the absolute value of the successive iteration is less
than a specified accuracy, i.e.,
|x(k+1)-x(k)|≤ε (4)
Where ε is the desired accuracy.

The process is repeated until the change in variable is within the desired accuracy. So, the Gauss-Seidel
method needs much iteration to achieve the desired accuracy, and there is no guarantee for the
convergence.

LOAD FLOW BY GAUSS-SEIDEL METHOD

The basic power flow equations (3.6) and (3.7) are nonlinear. In an n-bus power system, let the number
of PQ buses be np and the number of PV (generator) buses be ng such that n = np + ng + 1. Both
voltage magnitudes and angles of the P-Q buses and voltage angles of the P-V buses are unknown
making a total number of 2np+ ng quantities to be determined. Amongst the known quantities are 2np
numbers of real and reactive powers of the P-Q buses, 2ng numbers of real powers and voltage
magnitudes of the P-V buses andvoltage magnitude and angle of the slack bus. Therefore, there are
sufficient numbers of known quantities to obtain a solution of the load flow problem. However, it is
rather difficult to obtain a set of closed form equations from (3.6) and (3.7). We therefore have to
resort to obtain iterative solutions of the load flow problem.

25
At the beginning of an iterative method, a set of values for the unknown quantities are chosen. These
are then updated at each iteration. The process continues till errors between all the known and actual
quantities reduce below a pre-specified value. In the Gauss-Seidel load flow we denote the initial
voltage of the ith bus by Vi , i = 2, , n. This should read as the voltage of the ith bus at the 0th
(0)

iteration, or initial guess. Similarly, this voltage after the first iteration will be denoted by Vi (1). In this
Gauss-Seidel load flow the load buses and voltage controlled, buses are treated differently. However,
in both these types of buses we use the complex power equation given in (3.5) for updating the voltages.
Knowing the real and reactive power injected at any bus we can expand (3.5) as,

Pi,inj– jQi,inj = Vi* ∑YikVk =Vi*[Yi1V1+Yi2V2+….+YiiVi+….+YinVn] (4.1)

k=1

We can rewrite (4.1) as,

Vi = 1/Yii [ (Pi,inj– jQi,inj )/Vi* - Yi1V1 -Yi2V2 - ….. YinVn] (4.2)

Let us start the procedure with bus-2. Since this is load bus, both the real and reactive power into this
bus is known. We can therefore write from (4.2),

V2 (1) =1/Y22 [(P2, inj– jQ2, inj)/V2*(0) - Y21V1 -Y23V3(0)-Y24V4(0)-Y25V5(0)] (4.3)

The first iteration voltage of bus-3 is given by,

V3 (1) =1/Y33 [(P3, inj – jQ3, inj )/V3*(0) – Y31V1 -Y32V2(1)-Y34V4(0)-Y35V5(0)] (4.4)

26
Now in case of PV bus although its real power is specified, its reactive power is unknown. Therefore, to update
the voltage of this bus, we must first estimate the value of reactive power of that bus by using formula,
n
Qi,inj= -Im[Vi*∑YikVk] = -Im[Vi*{Yi1V1+Yi2V2+….YiiVi+….YinVn}] (4.5)
k=1

And hence we can write the kth iteration values as,

Qi,inj(k)= -Im[Vi*(k-1){Yi1V1+Yi2V2(k)+….YiiVi(k-1)+….YinVn(k-1)}] (4.6)

However sometimes the magnitude of the voltage obtained is not equal to the magnitude given. We must
therefore force this voltage magnitude to be equal to that specified. This is accomplished by,

Vcorrected = |V| x V(1)/|V(1)|

This will correct the voltage magnitude while retaining the phase. The corrected iteration is used in the next
iteration.

27
4.2 Numerical problem and solution of Gauss-Seidel method:

28
29
30
31
32
4.3 Flow-chart for implementing Gauss-Seidel method:

33
4.4 ALGORITHM OF GAUSS-SEIDEL

Step 1: Form the nodal admittance matrix (Yij).

Step 2: Choose a tolerance value.
Step 3: Assume the initial voltage values to be 1pu and 0 degree except for the slack bus.
Step 4: Start iteration for bus i =1 with count 0.
Step 5: Check for the slack bus if for i=slack bus or PV bus update the value of Qi.
Step 6: Calculate the new bus voltage Vi from the load flow equation.
Step 7: Find the difference in the voltages,
dVi(k+1) =Vi(k+1) - Vi(k)
Step 8: The new calculated value of the bus voltage is updated in the old bus voltage value and is used
for the calculations at the next bus.
Step 9: Go for the next bus and repeat the steps 5 to 7 until a new set of values
of bus voltages are obtained for all the buses.
Step 10: Continue the iteration from 5 to 9 until the value of dVik at all the buses is within the chosen
tolerance value,
dVi(k+1) < e, where k gives the number of iterations.

34
 CHAPTER 5
MATLAB PROGRAM OF GAUSS-SEIDEL

35
MATLAB PROGRAM

clear % Gauss Seidal method for load flow solution

y12= 2-8j;
y23= 0.666-2.664j;
y34= 1-4j;
y45= 2-8j;
y15= 0.2j;

p2= 0.5;
q2= 0.2;
p3= 0.4;
q3= 0.3;
p5= 0.5;
q5= 0.2;

v1= 1.06;
v2= 1+0j;
v3= 1+0j;
v4= 1+0j;
v5= 1+0j;

iter=0;

for k=1:20
iter=iter+1
v2=((p2-q2)/conj(v2) +y12*v1+y23*v3)/(y12+y23)
v3=((p3-q3)/conj(v3) +y23*v2+y34*v4)/(y23+y34)
v5=((p5-q5)/conj(v5) +y15*v1+y45*v4)/(y15+y45)
end

36
 CHAPTER 6
RESULT AND LIMITATIONS

37
6.1 RESULT:

Gauss-Seidel Iteration output:

Ybus =
Column 1 through 5

3-11.8j -2+8j 0 -1+4j -0.2j

-2+8j 2.66+10.66j -0.66+2.66j 0 0
0 -0.66+2.66j 1.66-6.66j -1+4j 0
-1+4j 0 -1+4j 4-16j -2+8j
-0.2j 0 0 -2+8j 2-7.8j

Enter the acceleration constant: 1.6

GS LOAD FLOW CONVERGES IN ITERATIONS index= 24
FINAL VOLTAGE ARE:

v2=1.0688+0.0493i

v3=1.0752+0.0974i

v4=1.0760+0.1073i

v5 =1.0811 + 0.1437i

38
6.2 Limitations of Gauss-Seidel method:

GS method is very useful for very small systems. It is easily adoptable; it can be generalized and it is very
efficient for systems having less number of buses. However, GS load flow analysis fails to converge in systems
with one or more of the features as under:

• Systems having large number of radial lines

• Systems with short and long lines terminating on the same bus
• Systems having negative values of transfer admittances
• Systems with heavily loaded lines, etc.

GS method successfully converges in the absence of the above problems. However, convergence also depends
on various other set of factors such as: selection of slack bus, initial solution, acceleration factor, tolerance
limit, level of accuracy of results needed, type and quality of computer/ software used, etc.

6.3 Limitations of Us:

The output value of MATLAB program and the value of calculation are not matched sometimes after 2decimal
place. It may be decimal point error of us.

39
 CHAPTER 7
CONCLUSION AND FUTURE SCOPE

40
7.1 CONCLUSION:

The load flow case problem has been successfully solved for interconnected systems with Gauss-Seidel
load flow method and obtained results have been compared to the theoretical calculations which came
to be same. The Gauss-Seidel method was successfully designed and implemented to solve the Load
flow problem.

7.2 FUTURE SCOPE:

This project concentrates on MATLAB programming to enable the users to calculate power flow
problem easily. MATLAB is used to program the power flow solution and GUI interface helps a user
to use easily.
To achieve all the project’s objectives, the developer must have fulfilled all the scope below:
i. Studies MATLAB programming.
ii. Identify appropriate command for MATLAB M-files
iii. Build MATLAB program for the power flow analysis using M-files

41
CHAPTER 8
REFERENCES:

[1] John Grainger; William Stevenson's classic, Elements of Power System Analysis;
Science/Engineering/Math; 1 ed., pp.783., January 1, 1994.
[2] Elgerd, O.L. (2012) Electric Energy Systems Theory: An Introduction. 2nd Edition, Mc-Graw-Hill.
[3] Kothari, I.J. and Nagrath, D.P. (2007) Modern Power System Analysis. 3rd Edition, New York.
[4] Keyhani, A., Abur, A. and Hao, S. (1989) Evaluation of Power Flow Techniques for Personal Computers.
IEEE Transactions on Power Systems, 4, 817-826.
[5] Hale, H.W. and Goodrich, R.W. (1959) Digital Computation or Power Flow—Some New Aspects. Power
Apparatus and Systems, Part III. Transactions of the American Institute of Electrical Engineers, 78, 919-923.
[6] Sato, N. and Tinney, W.F. (1963) Techniques for Exploiting the Sparsity or the Network Admittance
Matrix. IEEE Transactions on Power Apparatus and Systems, 82, 944-950.
[7] Aroop, B., Satyajit, B. and Sanjib, H. (2014) Power Flow Analysis on IEEE 57 bus System Using Mathlab.
International Journal of Engineering Research & Technology (IJERT), 3.
[8] Milano, F. (2009) Continuous Newton’s Method for Power Flow Analysis. IEEE Transactions on Power
Systems, 24, 50-57.
[9] Grainger, J.J. and Stevenson, W.D. (1994) Power System Analysis. McGraw-Hill, New York.
[10] Tinney, W.F. and Hart, C.E. (1967) Power Flow Solution by Newton’s Method. IEEE Transactions on
Power Apparatus and Systems, PAS-86, 1449-1460.
[11] Bhakti, N. and Rajani, N. (2014) Steady State Analysis of IEEE-6 Bus System Using PSAT Power Tool
Box. International Journal of Engineering Science and Innovation Technology (IJESIT), 3.
[12] Hadi, S. (2010) Power System Analysis. 3rd Edition, PSA Publishing, North York.
[13] Kabisama, H.W. Electrical Power Engineering. McGraw-Hill, New York.
[14] Gilbert, G.M., Bouchard, D.E. and Chikhani, A.Y. (1998) A Comparison of Load Flow Analysis Using
Dist Flow, Gauss-Seidel, and Optimal Load Flow Algorithms. Proceedings of the IEEE Canadian Conference
on Electrical and Computer Engineering, Waterloo, Ontario, 24-28 May 1998, 850-853.
[15] Glover, J.D. and Sarma, M.S. (2002) Power System Analysis and Design. 3rd Edition, Brooks/Cole,
Pacific Grove.
[16] Stott, B. and Alsac, O. (1974) Fast Decoupled Load Flow. IEEE Transactions on Power Apparatus and
Systems, PAS-93,859-869.
[17] Stott, B. (1974) Review of Load-Flow Calculation Methods. Proceedings of the IEEE, 62, 916-929.
[18] Adejumobi, I.A., et al. (2014) Numerical Methods in Load Flow Analysis: An Application to Nigeria
Grid System.International Journal of Electrical and Electronics Engineering (IJEEE), 3.58
42
APPENDIX(SOFTWARE)

MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment. A proprietary

programming language developed by MathWorks, MATLAB allows matrix manipulations, plotting
of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs
written in other languages, including C, C++, C#, Java, Fortran and Python.

Although MATLAB is intended primarily for numerical computing, an optional toolbox uses the MuPAD
symbolic engine, allowing access to symbolic computing abilities. An additional package, Simulink, adds
graphical multi-domain simulation and model-based design for dynamic and embedded systems.

VERSION: 2016a

Structures
MATLAB has structure data types. Since all variables in MATLAB are arrays, a more adequate name is
"structure array", where each element of the array has the same field names. In addition, MATLAB supports
dynamic field names (field look-ups by name, field manipulations, etc.). Unfortunately, MATLAB JIT does
not support MATLAB structures, therefore just a simple bundling of various variables into a structure will
come at a cost.

Functions
When creating a MATLAB function, the name of the file should match the name of the first function in the
file. Valid function names begin with an alphabetic character, and can contain letters, numbers, or underscores.
Functions are often case sensitive.

Function handles
MATLAB supports elements of lambda calculus by introducing function handles, or function references,
which are implemented either in .m files or anonymous/nested functions.

Classes and object-oriented programming

MATLAB supports object-oriented programming including classes, inheritance, virtual dispatch, packages,
pass-by-value semantics, and pass-by-reference semantics. However, the syntax and calling conventions are
significantly different from other languages. MATLAB has value classes and reference classes, depending on
whether the class has handle as a super-class (for reference classes) or not (for value classes).
43