International Journal of Recent Technology and Engineering (IJRTE)

ISSN: 2277-3878, Volume-7 Issue-6S2, April 2019

Implementation of SSA based two-degree-of

freedom fractional order PID controller for
AGC with diverse source of generations
Tapas Kumar Mohapatra, Asim Kumar Dey, *Binod Kumar Sahu

controller. Since the dimension, structure and load demand of

Abstract: This article presents a novel salp swarm algorithm power system is gradually increasing; the task of AGC is
(SSA) to design optimal controllers for automatic generation becoming more challenging. Literature survey reveals that a
control of a multi-area, multi-source power system. Every area of number of control strategies have been presented in various
the power system has a thermal, a hydro and a gas unit. Initially
conventional PID controllers are designed using SSA. Results research articles for AGC study in power system. Control
obtained are compared with that of conventional controller based techniques like classical, optimal, fuzzy logic based, ANFIS
on Differential Evolution (DE), Teaching Learning Based based etc. and many metaheuristic algorithms like genetic
Optimization (TLBO) and Imperialist Competitive Algorithm algorithm, particle swarm optimization (PSO), DE, TLBO,
(ICA). After ensuring superior performance with SSA based etc. have been projected for controller design to study the
conventional PID controller, the study is extended to design
two-degree of freedom conventional PID (2DOF-PID) and
dynamic behaviour of AGC systems. So, now a day’s
two-degree of freedom fractional order PID (2DOF-FOPID) researcher are paying more attention in proposing innovative
controller for the same power system implementing SSA optimization and control techniques to tackle problems
techniques. It is proved that SSA based 2DOF-FOPID controller associated with AGC of power system.
demonstrates better dynamic response as compared to other Nanda et al. (1983) implemented integral (I) controller
controllers. The study is carried out by applying a step load
based AGC scheme for a hydrothermal system in both
disturbance of 1 pu in area-1 and integral time absolute error
(ITAE) is chosen as objective function in designing the continuous and discrete mode considering generation rate
controllers. Robustness analysis is carried out by varying the constraint (GRC). They also recommended an optimum
systems’ parameters and applying a randomly changing loading sampling period for discrete mode. Nanda et al. (2006)
pattern in area-1. In both the cases the proposed SSA based investigated AGC issues in hydrothermal system using I- and
2DOF-FOIPD controller is found firmly robust. proportional-integral (PI) controllers. Dynamic responses are
analyzed by taking mechanical & electric governor for hydro
Index Terms: Automatic generation control (AGC); Fractional
order PID (FOPID) controller; Salp Swarm Algorithm (SSA), unit and single & double stage reheat turbine for thermal unit.
Two degree of freedom FOPID (2DOF-FOPID).. Abraham et al. (2007) studied AGC issues in hydrothermal
interconnected power system considering superconducting
I. INTRODUCTION magnetic energy storage (SMES) and thyristor controlled
phase shifter (TCPS) units respectively. Nanda et al. (2009)
A multi-area interconnected power system is basically
optimized various important parameters of a three unequal
developed to generate, transmit and distribute power with
area thermal power system for AGC studies using Bacteria
nominal system frequency and voltage. Frequency of power
Foraging (BF) algorithm. (Tan.W, 2010) proposed a
system depends on the equilibrium between power generation
combined tuning method based on 2-DOF internal model
and actual load demand (Kundur P, 1994). If power
control (IMC) and PID approximation approach for LFC of
demanded by loads is more than the generated power,
interconnected power system. Bacteria Foraging based
generator speed reduces resulting in reduced system
I-controller (BFIC) and multilayer perception neural network
frequency and vice versa. So automatic generation control
(MLPNN) controllers are implemented by Saikia et al. (2011)
(AGC) plays a significant role to regain the system nominal
for AGC of a three unequal area hydrothermal power system.
frequency and tie-line power flow at their predefined
They proved that MLPNN controller yields better transient
scheduled values, under both normal and perturb condition.
performance as compared to BFIC controller. GA based
Maintaining a constant frequency profile is very much
integral controller for AGC of a three area interconnected
essential for a healthy energy system and good power quality.
realistic thermal power system considering GRC, governor
Performance and Stability of a power system is
dead band (GDB) and time delay imposed by thermodynamic
considerably affected by the type and suitable design of
process, governor, turbine, filters and communication
channels is implemented by Golpira et al. (2011). DE based
Revised Manuscript Received on December 22, 2018. 2DOF-PID controller for AGC of a two area thermal power
Tapas Kumar Mohapatra, Department Electrical Engineering, ITER, system incorporating GDB,
SOA University, Bhubaneswar 751030, Odisha, India.
Asim Kumar Dey, Department Electrical Engineering, ITER, SOA
University, Bhubaneswar 751030, Odisha, India.
Binod Kumar Sahu, Department Electrical Engineering, ITER, SOA
University, Bhubaneswar 751030, Odisha, India.

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346 & Sciences Publication
Implementation of SSA based two-degree-of freedom fractional order PID controller for AGC with diverse
source of generations

GRC, time delay and reheat type turbine is presented by and good quality electric power supply.
(Sahu et al., 2013). ii. 2-DOF controllers are superior to conventional
controllers (Sahu et al., 2013). .
Panda and Yegireddy presented design of PI and PID iii. Fractional order controllers exhibit superior dynamic
controller using multi-objective NSGA-II technique for AGC performance as compared to integer order controllers.
of a two area linear and non-linear power system in (Panada iv. Innovative control techniques and implementation of
et.al 2013), (Mohanty et al. 2014) presented an optimally new optimization techniques to solve the problems related to
tuned DE algorithm to design I, PI and PID controllers for AGC issues are always encouraged.
AGC of a single and two area multi-source power system Critical analysis of literature survey also reveals that only
consisting of a thermal, a hydro and a gas unit in each area. few articles have dealt with study of AGC systems
(Sahu et al., 2015) hybridized Firefly Algorithm and Pattern implementing 2-DOF-FOPID controllers. Therefore this
Search technique (hFA-PS) to design PID controllers to deal research article deals with development of SSA technique to
with AGC issues in a multi-area multi-source hydrothermal optimally design conventional, fractional order, 2-DOF
system considering GRC, GDB and time delay. (Kumar et al. conventional and 2-DOF fractional PID controllers. Main
2016) designed a dual mode fuzzy controller to tackle the contributions of the article are as follows:
LFC issue in power system with parallel AC/DC tie-lines and i. Application of SSA technique in the field of AGC.
SMES unit. ICA tuned PID controller is implemented by ii. Development of a two area interconnected power system
(Kumar et al. , 2016) to study the AGC related issues in a with various sources of generation in each area in MATLAB
restructured power system. (Padhy and Panda, 2017) Simulink environment.
implemented hybrid Stochastic Fractal Search and Pattern iii. Optimal design of PID, FOPID, 2DOF-PID and
Search (hSFS-PS) algorithm to optimally design cascade 2DOF-FOPID controller using SSA optimization techniques.
PI-PD controller for AGC of multi-source power system in iv. Study of convergence characteristic of PID, FOPID,
presence of Plug in Electric Vehicles (PEVs). In (Arya and 2DOF-PID and 2DOF-FOPID controllers tuned by both SSA
Kumar, 2017) BFOA based fuzzy PI and PID controllers to techniques to show the effectiveness of SSA based
deal with AGC related issues in both traditional and 2DOF-FOPID controller.
deregulated electrical power system. v. Comparison of the proposed results with DE based PID
(Cao & Cao, 2006) designed and tested the effectiveness controller (Cao & Cao, 2006), hybrid Stochastic Fractal
of fractional order PID (FOPID) controller over conventional Search-Pattern Search (hSFS-PS) based PID controller
PID controller. They implemented PSO algorithm to design (Padhy and Panda, 2017), Teaching Learning Based
various parameters of the controllers. (Hamamci, 2008) Optimization tuned PID (TLBO-PID) (Barisal, 2015),
implemented FOPID controller to study the stability of Imperialist Competitive Algorithm optimized fractional order
fractional dynamic system. Auto-tuning method for FOPID fuzzy PID controller (ICA-FOFPID) (Arya, 2017).
controller is presented by (Monje et al., 2008). (Alomoush, vi. Robustness analysis of the proposed SSA based two
2010) implemented FOPI and FOPID controllers for load degree FOPID controller (SSA-2DOFOPID) against systems’
frequency control of both isolated and interconnected power parametric variation.
system. (Li et al., 2010) presented a novel tuning method for
FOPID controller for a second order plant to obtain better II. SYSTEM UNDER INVESTIGATION
dynamic performance and robustness. Optimal design of The system under investigation involves a two-area
fractional order fuzzy-PID (FOFPID) controller, fuzzy-PID interconnected power system. Each area of the power system
(FPID) controller and PID controller for a closed loop consists of a non-reheat type thermal unit, a hydro unit with
feedback system is presented by (Liu et al., 2014). They mechanical governor and a gas power unit. Transfer function
compared the simulation result and proved that FOFPID model of the power system is shown in Figure 1.
controller exhibits superior dynamic performance as Rating of each generating unit is taken as 2000 MW and the
compared to other controllers. (Martin et al., 2015) optimally considered power system model is simulated in MATLAB
designed FOPID controller employing DE algorithm to Simulink environment with zero initial conditions. Initial
carryout both simulation & experimental study on a DC motor loading on the power system is taken as 1740 MW. Nominal
and proved that FOPID controller exhibits superior dynamic values of all the systems’ parameters are depicted in
performance as compared to conventional PID controller. appendix. Inputs to proposed controllers are their respective
(Saha and Agashe, 2016) presented a review paper on area control error (ACE) and outputs are ΔPTg, ΔPHg and
fractional order controllers investigating their progress in the ΔPGg which acts as actuating signals for the governors of
field of control system engineering. thermal, hydro and gas generating unit respectively. ACE is a
linear combination of frequency & tie-line power error of
Literature review reveals that performance and stability of
corresponding area and for a two area system expressed as:
any plant to be controlled is considerably affected by the type
and appropriate design of controller. Critical analysis of
ACE1 = B1f1 + Ptie,12 (1)
various literatures related to AGC studies in interconnected
ACE2 = B2 f2 + Ptie,21 (2)
power system reveals that,
i. Basically electrical power generation is from various Where, ΔPtie12 is the tie-line
sources in a definite control area. So the study of dynamic power deviation from area-1
behavior of more realistic power system consisting of to area-2, β1 and β2 are the
different energy sources in each area is essential for reliable

Published By:
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Retrieval Number: F9072047619\19©BEIESP 347 & Sciences Publication
 International Journal of Recent Technology and Engineering (IJRTE)
ISSN: 2277-3878, Volume-7 Issue-6S2, April 2019

frequency bias factor of area-1 and area-2 and Δf1 and Δf2 are Where, a Dt is the fractional operator, ‘  ’ is the
the frequency deviations in area-1 and area-2, respectively.
When the system is subjected to a small disturbance, ACE is calculus order, ‘ n ’ is the first integer greater then ‘  ’, i.e.
used as an actuating signal to the controller for damping out 
systems’ oscillation and reducing the steady state error to
n −1    n and  (  ) = t e dt is the gamma function.
0
−1 − t
zero. In this article SSA based conventional, fractional order,
2DOF-PID and 2DOF-FOPID PID controllers are
implemented to enhance the transient behaviour of AGC In general the integro-differential operator a Dt is
system. From the profound analysis, results clearly show the
dominance of SSA based 2DOF-FOPID controller over other expressed as:
controllers.
 d
  for   0
III. OVERVIEW OF PID, FOPID AND 2DOF-FOPID  dt
 
a Dt = 1 for  = 0
CONTROLLER
(7)
t
 ( d  )− for   0
A. PID controller  a
As the name suggests, a PID controller basically consists of
three modes of operations, i.e. proportional mode, integral Laplace transformation of fractional differential
mode and derivative mode. It is by far the most commonly equation expressed in (5) is given by:
used controller in almost all controller design studies because
n −1
of its simple structure which needs few empirical rules.
Structure of the PID controller implemented for thermal unit
L  

a Dt f (t ) = s F ( s ) −  s a Dt
 k − k −1

k =0
f (t ) |t = 0 (8)
of the power system under consideration is shown in Figure 2.
Output of PID controller in time and in Laplace domain can With zero initial condition equation (8) becomes:

 
be expressed as:
t L 0 Dt f (t ) = s  F ( s) (9)
dACE1 (t )
u1 (t ) = K p ACE1 (t ) + Ki 
0
ACE1 (t )dt + K d
dt
(3)
From equation (9) it is clear that, with zero initial
Ki condition, the fractional derivatives and fractional
U1 ( s) = K p ACE1 ( s) + ACE1 ( s) + K d sACE1 ( s ) (4) integrations make the transfer functions of a dynamic systems
s
fractional order of ' s ' . Structure of FOPID controller is
shown in Figure 3 and its output in time and Laplace domain
B. Fractional Order PID (FOPID) controller are expressed in equations (10) and (11) respectively.
Fractional Order PID (FOPID) controller is accepted as an d − d
u1 = K p1 ACE1 (t ) + Ki1 ACE1 (t ) + K d1 ACE1 (t ) (10)
efficient controller in industrial applications and research in dt − dt 
comparison to conventional PID controller. Alomoush (2010) Ki1
attempted implementation of FOPID controller in AGC study ACE1 ( s) + K d1s  ACE1 ( s) (11)
U1 ( s) = K p1 ACE1 ( s) +
for the first time. Several other literatures also deals with s
fractional order controllers in various fields of science and Where, K p1 , Ki1 & Kd1 are the controller gains,  is the order
engineering. The concept of fractional order controller deals of integrator and  is the order of differentiator of thermal
with differential equations having fractional calculus. So,
units. ACE1 is the area control error of area1.
FOPID controller is the extension of conventional PID
controller incorporating fractional calculus i.e. the derivative Equations (10) and (11) clearly depicts that all
and integral order are not integers but are taken as fractions. conventional controllers (PID) are specific cases of
Incorporation of non-integer order controllers for integer fractional controller, where λ and μ are equal to one. Various
order plants provides higher degree of flexibilities to adjust points of classical PID controller and the plane of FOPID
the gain and phase characteristics as compared to that of controller are shown in Figure 4.
integer order controllers. These flexibilities make fractional
order control strategy more powerful in designing robust In Figure 4 it is seen that,
control system. The most frequently used definition for If λ = 1 and μ = 1, then it is classical PID controller.
fractional differentiation and integration proposed by If λ = 0 and μ = 1, then it is classical PD controller.
Riemann-Liouville (R-L) are given in equations (5) and (6) If λ = 1 and μ = 0, then it is classical PI controller.
respectively. If λ = 0 and μ = 0, then it is classical P controller.
If λ = fraction and μ = fraction, then it is FOPID
t
1 dn controller.
 (t − ) f (  )d 
 n −−1
a Dt f (t ) = (5)
(n − ) dt n a

t
1
( t −  ) f (  )d 
−1

−
a Dt f (t ) = (6)
 ( ) a

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Implementation of SSA based two-degree-of freedom fractional order PID controller for AGC with diverse
source of generations

Step load change

1
1 in area-1
RTH
RG
1
B1 RHY - 1 1 + sKRTR 1
+ KT
1+ sTSG 1 + sTR 1 + sTT
Governor Reheat Turbine
ACE1 PID/2DOF-
-
PID/FOPID/
Thermal Unit
2DOF-FOPID
+
- PID/2DOF- +
- 1 1 + sTRS 1− 0.5sTW KPS f1
PID/FOPID/ KH +
- 2DOF-FOPID 1+ sTGH 1 + sTRH 1+ 0.5sTW 1+ sTPS
- Mechanical Hydraulic Governor Hydro Turbine +
PID/2DOF- +
PID/FOPID/
2DOF-FOPID Hydro Unit
-
1+ sXG 1 1 − sT CR 1
KG
1+ sYG cg + sbg 1 + sT F 1+ sTCD
Gas Governor Valve Positioner Fuel System & Gas Turbine
Combustor
Gas Unit
2T12 +

 Ptie s -
a12
a12
ACE2 PID/2DOF-
PID/FOPID/
+
KT -
-
2DOF-FOPID
+
- PID/2DOF- + Generating units of area-2 KPS f2
PID/FOPID/ KH +
- are same as those in area-1
1+ sTPS
-
2DOF-FOPID
+
PID/2DOF- +
PID/FOPID/ KG
2DOF-FOPID
- -
B2
Step load change
1 in area-2
1 1
RTH RHY RG

Figure 1. Transfer function model of two area

multi-source power system.

K p1 K p1
+
+
t ACE1 d − u1
ACE1
K i1  dt u1 K i1 +
+
dt −
0
+
+

Kd1 d
d dt 
Kd1
dt

Figure 3. Structure of FOPID controller

Figure 2. Structure of PID controller

Published By:
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 International Journal of Recent Technology and Engineering (IJRTE)
ISSN: 2277-3878, Volume-7 Issue-6S2, April 2019

 Output of 2DOF-PID controller shown in Figure 5 in

PD Controller (0, 1)
(1, 1) PID Controller time and Laplace domain are expressed in equations (12) and
(13).
Fractional
Order PID t
Controller u1 (t ) = K p1  ACE1 (t )  PW 1 − f1 (t ) + K i1   ACE (t ) − f (t ) dt
0
1 1


d
 ACE1 (t )  DW 1 − f1 (t )
(0, 0) (1, 0)
P Controller PI Controller + K d1
dt
Figure 4. Points of classical PID controller and plane of (12)
FOPID controller.

ACE1 ( s) − F1 ( s)
FOPID controller has better performance due to the
U1 ( s) = K p1  ACE1 ( s)  PW 1 − F1 (s ) + Ki1
following reasons: s
i. It is more robust and stable than conventional PID + K d1s  ACE1 ( s)  DW 1 − F1 (s )
controller. (13)
ii. For systems having large time delays, it provides better
results than conventional PID controller.
iii. It can easily accomplish the property of iso-damping, in D. Two degree of freedom fractional order PID
comparison to PID controller. (2DOF-FOPID) controller
iv. It provides five different operating conditions as stated It is evident from recently published research articles that
above, which is not possible in the case of conventional 2DOF-PID controller can effectively control and enhance the
PID controller. dynamic performances while dealing with complicated
v. It can attain improved response for non-minimum phase control related problems. However, it is also proved in
system. literatures that, incorporation of fractional order calculus
vi. It provides better results for higher order systems as instead of integer order calculus in control system design
compared to conventional PID controller. lengthens the prospect of additional performance
enhancement. Therefore in this article a two-degree of
C. Two degree of freedom PID (2DOF-PID) controller. freedom fractional order PID (2DOF-FOPID) controller is
implemented in the field of AGC. Structure of 2DOF-FOPID
The degree of freedom of a control system is characterized as controller is shown in Figure 6 and input and output
the quantity of closed-loop transfer functions that can be relationships in time and Laplace domain are given in
adjusted independently. A two degree of freedom PID equations (14) and (15).
(2DOF-PID) controller has the ability of smooth set point Proportional set
tracking and good disturbance rejection as compared to PID Point Weight
controller. Its output signal is based on the difference between PW +
the reference signal and the system output. In general, a Kp
_
2DOF-PID controller improves the overall closed loop
ACE1 +
dynamic performance of the system to be controlled. Figure 5 +
d −
shows structure of a 2DOF-PID controller for the thermal Ki +
dt −
_ u
units of the power system shown in Figure 1. So, in a +
2DOF-PID controller, in addition to the PID controller gains ∆f1
( K p , Ki , Kd ), two more parameters like proportional set point _
d
Kd
weight ( PW ) and derivative set point weight ( DW ) are to be DW +
dt 
Derivative set
optimally designed. Point Weight
Proportional set
Point Weight Figure 6. Structure of 2DOF-FOPID controller for
PW 1 +
thermal units
K p1

d −
_
u1 (t ) = K p1  ACE1 (t )  PW 1 − f1 (t ) + K i1  ACE1 (t ) − f1 (t )
dt −
ACE1 +
+ t
K i1  dt
d
+ u1
_ 0
+ K d1  ACE1 (t )  DW 1 − f1 (t )
+
dt 
∆f1
_ (14)
d
Kd1
DW 1 + dt
Derivative set
Point Weight

Figure 5. Structure of 2DOF-PID controller for thermal units.

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Implementation of SSA based two-degree-of freedom fractional order PID controller for AGC with diverse
source of generations

X i = X min + ( X max − X min )  rand (17)

ACE1 ( s) − F1 ( s)
U1 ( s) = K p1  ACE1 ( s)  PW 1 − F1 (s ) + Ki1
s Where, Xmin & Xmax are the minimum and maximum
+ K d 1s 
 ACE1 (s)  DW 1 − F1 (s) values of the variables to be optimally designed and rand
is a random number in the range [0-1]. After evaluation
(15) of the fitness, the solution vector of size [NP x D] are
From the above discussion it is clear that a PID controller has sorted keeping the best solution in 1st position called the
three gains ( K p , Ki , Kd ), an FOPID controller has five leader, 2nd best solution in 2nd position and so on.
parameters ( K p , Ki , Kd , ,  ), a 2DOF-PID controller has
five parameters ( K p , Ki , Kd , PW , DW ) and a 2DOF-FOPID
controller has seven parameters ( K p , Ki , Kd , , , PW , DW ).
All these gains are optimally designed using Salp Swarm
Algorithm (SSA) by considering integral time absolute error
(ITAE) expressed in equation (16) as objective function.
Overviews of proposed SSA algorithms are discussed in (a) (b)
Figure 7 depicts strategy adopted in this article to optimally Figure 8 (a) An individual salp, (b) Salp chain.
design various gains of the controllers.
tsim ii. Updation of leader:- Position of the leader is updated
ITAE =  ( f 1 + f 2 + Ptie ) t dt (16) using the relation:
0
 i + (c1 ( xi,max − xi,min )c2 + xi ,min )
 F if c3  0
x1i =  (18)
 Fi − (c1 ( xi,max − xi,min )c2 + xi,min )
 if c3  0
Controller for
Thermal unit
Where, xi1 is the updated position of the leader, xi,max & xi,min
− are the maximum and minimum values of various variables
+
Reference error Controller for
Hydro unit Power System respectively and c1, c2 and c3 are random numbers. ‘c1’ is one
of the very important parameter in SSA since it balances both
Controller for
exploration and exploitation. It is updated in every iteration
GAS unit using the relation:
2
 4iter 
− 
Slap Swarm Algorithm (SSA) for c1 = 2e  itermax  (19)
determining optimal controller gains by
minimizing ITAE objective function Where, ‘iter’ is the current number and ‘itermax’ is the
maximum number of iteration. c2 and c3 are random numbers
in the range [0-1].
Frequency and tie-line power
deviations iii. Updation of followers:- Position of the followers are
Figure 7. Strategy adopted to optimally design updated using the relation:
controllers’ gains.

IV. OVERVIEW OF PROPOSED OPTIMIZATION

xim =
2
(
1 m
xi − xim −1 ) (20)

ALGORITHMS Where, m  2 is the position of mth follower.

Swarm Algorithm (SSA) iv. Imposition of limits and evaluation of newly generated
Salps have their place in the family of Salpidae. Their tissues population after updation:-
are very similar to those of jelly fish also they move in a very
similar manner to jelly fish. Figure 8 (a) shows an individual In this stage limits on the newly generated population are
salp and 8 (b) depicts a group of salp forming a chain. imposed based on the upper and lower bounds. Then fitness of
Swarming behaviour of salps is one interesting activity and is newly generated population is evaluated and the best
mathematically modelled by (Mirjalili et al., 2017) to develop performing solution is stored.
Salp Swarm Algorithm (SSA). To mathematically model the v. Steps ‘ii-iv’ are repeated until stopping criteria are met.
salp chains the entire population is divided into two groups
namely leader and followers. The leader salp is considered to
be at the front of the chain and rest of the salps are considered
to be the followers. The leader guides entire swarm and the
other salps follow the salp ahead of it.
Various steps involved in SSA algorithm are:
i. Initialization: - In this stage initial population is
randomly generated in the predefined range using the
relation:

Published By:
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Retrieval Number: F9072047619\19©BEIESP 351 & Sciences Publication
 International Journal of Recent Technology and Engineering (IJRTE)
ISSN: 2277-3878, Volume-7 Issue-6S2, April 2019

V. RESULT AND DISCUSSION above discussion manifests that the proposed SSA designed
This paper presents a comparative performance analysis of 2DOF-FOPID controller is yielding better dynamic response
Salp Swarm Algorithm (SSA) tuned PID, FOPID, 2DOF-PID in all aspects as compared to other proposed controllers and
and 2DOF-FOPID controllers to analyse the frequency controllers reported in some recently published articles.
stabilization capability of an AGC system. Each area of the
two-area power system considered for the study has a thermal
unit, a hydro unit and a gas unit. The power system model is
simulated in MATLAB Simulink environment and SSA
techniques are written in .m file which calls the Simulink
model and run it to design the optimal controller gains.
Number of populations and maximum number of iterations
both are considered as 100. ITAE expressed in equation (16)
is selected as objective function and minimized to obtain the
optimal gain parameters for the controllers. Step load
perturbation of 0.01 pu is applied in area-1 to analyse the
dynamic performance of the system. Optimal gains of various Figure 9 Frequency deviation in area-1 with PID and FOPID controllers.
controllers obtained with SSA techniques are given in Table
1.
Objective function (ITAE) values for different controllers are
shown in the last row of Table 1. It is seen that a minimum
value of ITAE (=0.0305) is obtained with SSA based
2DOF-FOPID controller in comparison with other
controllers. An improvement of 7.54 %, 10.76 %, 14.29 %,
59.54 %, 64.26 %, 72.83 %, 78.36 %, 92.61 % and 95.64 % in
ITAE is obtained with SSA optimized 2DOF-FOPID
controller in comparison with SSA-2DOF-PID,
SSA-2DOF-PID, SSA-FOPID, SSA-PID, hSFS-PS-PID and
DE-PID respectively. Undershoots, overshoots and settling
times (with a band of 0.0005 %) of frequency deviations in
both the areas and tie-line power deviations with proposed Figure 10 Frequency deviation in area-2 with PID and FOPID controllers.
controllers and with some of the controllers recently proposed
by researchers are depicted in Table 2. Frequency deviations
in area-1 and area-2 and tie-line power deviations are
depicted in Figure 9-14. Figure 9-11 shows the deviations
with PID and FOPID controllers whereas Figures 12-14
depicts the deviations with two-degree of freedom PID and
FOPID controllers.
From Table 2 and Figures 9-14 it is obvious that a significant
improvement is achieved with SSA based controllers in
comparison with other controllers. Again it is seen that
2-DOF fractional order controllers are better than fractional
order controllers and fractional controllers are performing
Figure 11 Tie-line power deviation with PID and FOPID controllers.
better as compared to conventional controllers. The results
obtained are compared with recently published articles and
found to be superior. It is observed that SSA based PID
controller outperforms DE based PID, TLBO-PID, hSFS-PS
based PID. It is also seen that SSA optimized 2-DOF-FOPID
and 2-DOF-PID controllers are superior to ICA-FOFPID
controller. It is also evident that SSA designed 2-DOF-FOPID
is yielding better transient performance amongst all the
controllers.
Robustness analysis of the proposed SSA based
2-DOF-FOPID controller is carried out by varying all the
systems’ parameters from -20 % to + 20 % in steps of 10 %
and by applying randomly varying loads in both area-1 and Figure 12 Frequency deviation in area-1 with FOPID and 2DOF-FOPID
controllers.
area-2 as shown in Figure 15. Deviations in frequency of
area-1, area-2 and tie-line power due to random load
variations are shown in Figure 16.
From Figures 15-16 it is seen that there is no significant
change in dynamic behavior of the system i.e. the proposed
controller is robust enough to tackle any change in systems’
parameter and random change in load variation. So finally the

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Implementation of SSA based two-degree-of freedom fractional order PID controller for AGC with diverse
source of generations

VI. CONCLUSION

In this research article, fractional order PID (FOPID) and

2DOF-FOPID controllers are optimally designed employing
Salp Swarm Optimization Algorithm (SSA) to tackle the
AGC related issues in two area interconnected power system.
Each area of the power system consists of a thermal unit,
hydro unit and a gas unit. Comparative performance analysis
is done to validate the efficacy of SSA based 2DOF-FOIPD
Figure 13 Frequency deviation in area-2 with FOPID and 2DOF-FOPID controller over SSA based PID, SSA based FOPID
controllers. controllers and DE, TLBO, hSFS-PS PID controllers and ICA
tuned fractional order fuzzy-PID controller. Sudden step load
change of 1% is applied in area-1 and ITAE is taken as
objective function to optimally design the controllers. It is
observed that SSA based 2DOF-FOPID controller
outperforms other controllers by exhibiting less undershoot,
overshoot and settling time Finally robustness analysis of
SSA based 2DOF-FOPID controller is performed by varying
all the systems’ parameters and by applying randomly varying
loads to both the areas. It is observed that the projected SSA
designed 2DOF-FOPID controller is robust against
parametric variations and random load variations.
Figure 14 Tie-line power deviation with FOPID and 2DOF-FOPID
controllers.

Figure 15 Randomly varying loading pattern in area-1 and area-2.

Figure 16 Frequency and tie-line power deviations due to randomly varying

load shown in figure 17.

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 International Journal of Recent Technology and Engineering (IJRTE)
ISSN: 2277-3878, Volume-7 Issue-6S2, April 2019

Table 1 Optimal gain of different controllers.

For Thermal Units
PW DW Kp Ki Kd  
SSA-2DOF-FOPID 5.0000 4.6732 5.0000 3.7649 5.0000 0.9678 1.0000
PW DW Kp Ki Kd

SSA-2DOF-PID 4.2655 0.0100 4.9181 4.9976 4.6698

Kp Ki Kd  
SSA-FOPID 4.8847 5.0000 4.8884 0.8418 0.9913
Kp Ki Kd
SSA-PID 5.0000 4.8652 5.0000
For Hydro Units
PW DW Kp Ki Kd  

SSA-2DOF-FOPID 0.6200 3.6043 0.0100 4.0737 3.7327 0.7197 0.3404

PW DW Kp Ki Kd

SSA-2DOF-PID 5.0000 1.2229 4.8719 4.8401 0.0262

Kp Ki Kd  

SSA-FOPID 1.3362 0.0100 2.4515 0.8771 0.5549

Kp Ki Kd

SSA-PID 4.2323 2.0128 2.5646

For Gas Units
PW DW Kp Ki Kd  

SSA-2DOF-FOPID 1.7449 3.2356 4.8321 4.7251 4.8181 0.8062 0.0328

PW DW Kp Ki Kd
SSA-2DOF-PID 2.6385 2.1094 5.0000 5.0000 0.8384
Kp Ki Kd  

SSA-FOPID 4.5825 4.6676 5.0000 0.6788 1.0000

Kp Ki Kd

SSA-PID 0.0100 2.4760 2.5756

ITAE with different control approach
SSA-2DOF-FOPID SSA-2DOF-PID SSA-FOPID SSA-PID hSFS-PS-PID DE-PID [12]
[16]
0.0305 0.0329 0.0789 0.1303 0.3818 0.6464

Table 2 Undershoot, Overshoot and settling time in frequencies and tie-line power deviations.

f1 f 2 Ptie
Parameters
(Ush×10-3) (Osh×10-3) Ts (Ush×10-3) (Osh×10-3) Ts (Ush×10-3) (Osh×10-3) Ts
in Hz in Hz in sec in Hz in Hz in sec in p.u. in p.u. in sec
SSA-2DOF-FOPID -3.2273 0.0579 10.9401 -0.4650 0.0123 6.6276 -0.3169 0 11.0435
SSA-2DOF-PID -6.1642 0.1870 10.0586 -0.7865 0.0244 3.8599 -0.4268 0.0147 6.4586
10.1536
5.4542 6.6908
(with
(with (with
0.00005
0.00005 0.00005
band)
ICA-FOFPID [26] -8.6 -- band) -2.6 -- -0.8 -- band)
3.343
1.7907 2.2248
(with
(0.0005 (0.0005
0.0005
band) band)
band)
SSA-FOPID -9.5679 0.3115 11.2262 -3.4750 0.0652 11.8101 -1.1391 0.0303 6.2940
SSA-PID -11.8862 2.1601 13.4073 -4.3189 1.2512 14.8073 -1.3381 0.2498 12.3073
hSFS-PS: PID [16] −20.2 4.0577 15.2937 −13.4 2.1471 19.7937 −3.25 0.2481 18.3937
TLBO-PID [27] −13.9 3.7600 19.0180 −5.5 2.2955 19.5790 −1.46 0.2541 14.2154
DE-PID [12] -26.5801 2.0342 36.8446 -22.1397 0.7714 42.8446 -4.7585 0.1935 38.6446

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Implementation of SSA based two-degree-of freedom fractional order PID controller for AGC with diverse
source of generations

interconnected power systems with parallel AC–DC

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Appendix: Nominal values of power systems’ parameters.

Tapas Kumar Mohapatra received his
Parameters Symbols Values Parameters Symbols Values B.Tech degree in 2002 and M.Tech
Hydro degree in 2008. He has 15 Years of
turbine Teaching experience. He is currently
Area rated 28.749
Prt 2000 MW governor TRH working as a Faculty in SOA University,
Capacity sec
time Bhubneswar, India. He is also persuing
constant
his Ph.D degree in electrical engineering
Nominal area Resetting
P0L 1740 MW TR 4.9sec in SOA university. His research interest
load time
includes power system control, application of Power elctronic
Governor
Nominal system
fs 60 Hz time TGH 0.2sec
devices in power system, Optimization techniques, and
frequency different types of controller.
constant
Power system 68.9655 Water
KPS TW 1.1sec Asim Kumar Dey received his B.Tech
gain Hz/puMW starting time
Lead time degree in 2012 and M.Tech degree in
Power system constant of 2014 from SOA university,
TPS 11.49 sec X 0.6sec
time constant gas turbine Bhubaneswar , India. He is persuing his
governor Ph.D degree in electrical engineering in
Lag time SOA university. power system control,
Steam Turbine constant of application of Power elctronic devices in
TT 0.3 sec Y 1.1sec
time constant gas turbine
power system, Optimization techniques,
governor
and different types of controller.
Steam Turbine Valve
.
Reheat time Tr 10.2 sec positioner a=c 1
constant gains
Valve Binod Kumar Sahu received the
Steam Turbine positioner Ph.D. degree from SOA University,
Kr 0.3 b 0.049sec Bhubaneswar in 2012. He is working
Reheat constant time
constant as an Associate Professor at the
Governor speed electrical engineering department of
Gas turbine
regulation
2.4 combustion
SOA University , Bhubaneswar, India
parameters of R TCR 0.01sec from 2008. His research interests are
Hz/puMW reaction
thermal, hydro in the area of power system control,
time delay
and gas units application of Power elctronic devices
Gas turbine
Frequency bias 0.4312 in power system, Optimization techniques, and different types
β fuel time TF 0.239sec
coefficient puMW/Hz of controller.
constant
Compressor
Synchronisation discharge
T12 0.0433 TCD 0.2sec
coefficient volume time
constant
Participation
factors of 0.5747,
KT, KG,
Gain α12 -1 thermal, gas, 0.1380,
KH,
and hydro 0.2873
units
Governor time
constant in TG 0.06 sec Gain of RFB KRFB 1.8
steam plant

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