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INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING & 
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), 
ISSN 0976 – 6553(Online) Volume 5, Issue 9, September (2014), pp. 17-28 © IAEME 
TECHNOLOGY (IJEET) 
ISSN 0976 – 6545(Print) 
ISSN 0976 – 6553(Online) 
Volume 5, Issue 9, September (2014), pp. 17-28 
© IAEME: www.iaeme.com/IJEET.asp 
Journal Impact Factor (2014): 6.8310 (Calculated by GISI) 
www.jifactor.com 
17 
 
IJEET 
© I A E M E 
PSO BASED FRACTIONAL ORDER AUTOMATIC GENERATION 
CONTROLLER FOR TWO AREA POWER SYSTEM 
CH. Ravi Kumar Dr. P.V.Ramana Rao 
Assistant Professor/E.E.E, Professor  H.O.D/E.E.E, 
University College of Engg  Tech. University College of Engg  Tech. 
Acharya Nagarjuna University Acharya Nagarjuna University 
ABSTRACT 
This paper presents the development and application of Fractional order PID controllers 
based on particle swarm optimization (PSO) for load frequency control of two-area inter connected 
system. The dynamic response of the system has been studied for 1% and 10% step load 
perturbations in area2. The performance of the proposed FOPID controller is compared against the 
traditional PID controllers based on PSO and ANFIS based intelligent controller. Comparative 
analysis demonstrates that proposed FOPID controllers based on PSO reduces the settling time and 
overshoot effectively, against small step load disturbances. Simulations have been performed using 
MATLAB / Simulink. 
Keywords: Adaptive Neuro Fuzzy Inference System (ANFIS), Fractional PID Controller, Particle 
Swarm Optimization (PSO), Automatic Generation Control (AGC). 
I. INTRODUCTION 
In an interconnected power system Automatic Generation control or Load frequency control 
is important in Electrical Power System design and operation. Large scale power system comprises 
of interconnected subsystems (control areas) forming coherent groups of generators, where as 
connection between the areas is made using tie-lines [1-2]. Each control area has its own generation 
and is responsible for its own load and scheduled interchanges with neighbouring areas. The load in 
a given power system is continuously changing and consequently system frequency deviates from 
the desired normal values. Therefore to ensure the quality of power supply, a load frequency
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), 
ISSN 0976 – 6553(Online) Volume 5, Issue 9, September (2014), pp. 17-28 © IAEME 
controller is needed to maintain the system frequency and inter-area flows at the desired nominal 
values. 
18 
 
The PI and PID controllers are well-known and widely used in power system control 
applications as they are simple to realize, easily tuned and several rules were developed for tuning 
their parameters [15]. These controllers are commonly used to dampen system oscillations, increase 
stability and reduce steady-state error. These controllers are integer order controllers as power of 
derivative or integral in these controllers is one. 
In recent years, researchers reported that controller making use of fractional order derivatives 
and integrals could achieve performance and robustness, superior to those obtained with 
conventional controllers. Fractional calculus deals with the concept of differentiation and integration 
to non-integer order. It is an extension of the concept dny(t)/dtn with n is an integer number to the 
concept dy(t)/dt where  is non-integer number with possibility to be complex [15]. The classical 
IO controllers are particular cases of FOPID controllers. As the FOPID has two more extra tuning 
knobs than the classical IOPID controller, it gives more flexibility for the design of a control system 
and gives better opportunity to adjust system dynamics especially if the original system to be 
controlled is a fractional system. In many cases, fractional calculus can be applied to improve the 
stability and response of such a system through the use of non-integer order integrals and derivatives 
in place of the typical first order ones. 
The fractional control theory extends traditional integer order to the fractional-order and 
plural order. Fractional PID controller not only has three parameters Kp, Ki, Kd but also has integral 
order  and differential order μ which are two adjustable parameters [8]. The application of fractional 
control theory, yields performance better than IOPID and (ANFIS controllers) hybrid artificial 
intelligence controllers. 
In this paper a fractional PIDμ controller is designed for AGC of a two area power system. 
The parameters Kp, Ki, Kd, , μ were optimized using Particle Swarm Optimization [8]. Simulation 
results showed that fractional order controller based on PSO had better performance than integer 
order PID controller based on PSO and ANFIS controllers. 
II. CONFIGURATION OF TWO-AREA POWER SYSTEM 
Plant model description 
The two-area inter connected power system is taken as a test system in this study. The 
model of the system under consideration is as shown in fig1. where symbols have their usual 
meanings. The conventional AGC has two control loops the primary control loop, which control the 
frequency by self-regulating feature of the governor, however, frequency error is not fully eliminated 
and the supplementary control loop which has a controller that can eliminate the frequency error. The 
main objective of the supplementary control is to restore balance between each control area load and 
generation after a load perturbation so that the system frequency and tie-line power flows are 
maintained at their scheduled values. So the control task is to minimize the system frequency 
deviations in the two areas under the load disturbances Pd1 or Pd2 in two areas. This is achieved 
conventionally with the help of suitable integral control action. The supplementary control of the ith 
area with integral gain Ki is therefore made to act on ACEi given by equation (1) which is an input 
signal to the controller [15-17].
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), 
ISSN 0976 – 6553(Online) Volume 5, Issue 9, September (2014), pp. 17-28 © IAEME 
 
1 
t
s G2 1+ 
 
19 
 
P12 
 
1 
R 
 
1 
R 
1 
t 
1 
t 
1 
2p T 
12 
 
1 
Fig.1: Block diagram of AGC for Two area system with secondary loop 
 
+ 
i ACE = DP + B Df 
i i 
j 
n 
=1 
tie,ij (1) 
Where ACEi is area control error of the ith area 
i Df = Frequency error of ith area 
tie,ij DP = Tie-line power flow error between ith and jth area 
Bi = frequency bias coefficient of ith area 
III. INTEGER ORDER PID CONTROLLER 
The PID control is a widely used approach for designing a simple feedback control system 
where in three constants are used to weigh the effect of the error (the P term), the integral of the error 
(I term) and the derivative of the error(the D term). A typical structure of classical IOPID controlled 
system [15] is shown in Fig.2. 
Fig.2: Structure of PID control 
+ 
 
 
1 
t 
 
2 
 
s T2 1+ 
 
2 H 
2s+D2 
 
B2 
w 
	
 
ACE2 
 + 
 
+
ACE1 +
s + G1 1+ 
2 H 
1s+D1 
 
s T1 1+ 
 
1 
B1 
S
w
+ 
 
+  
+  
+ 
 
System 
KP 
Kd 
Ki 
d/dt 
 
+ 
 
 
r(t) 
e(t) u(t) y(t)
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), 
ISSN 0976 – 6553(Online) Volume 5, Issue 9, September (2014), pp. 17-28 © IAEME 
a (2) 
a t f t Kh 
( ) = (3) 
20 
 
 
To implement a PID controller that meets the design specifications of the system under 
control, the parameters [Kp, Ki, Kd, B1, B2] must be determined for the given system. An IOPID 
controller is designed for frequency control in power system in this paper, whose parameters were 
optimized using Particle swarm optimization. 
IV. FRACTIONAL CALCULUS 
Fractional calculus can have different definitions in different perspectives [15]. There are two 
commonly used definitions for fractional calculus so far, that is Grunwald-Letnikov definition, 
Reiman-Liouville definition. 
− 
 
® 
− 
G 
( + ) 
G 
G 
[( ) / ] 
1 
h 0 =0 
( ) 
( +1) 
( )h 
( ) = lim 
t a h 
K 
K 
K 
D f t 
a 
a a 
t 
n 
d 
( ) 
1 
 − − G − 
a t 
a t d 
n n 
t 
f 
dt 
D f t 
a 
a 
t 
t 
a 1 ( ) ( ) 
(n - ) 
Grunwald-Letnikov definition is perhaps the best known one due to its most suitability for the 
realization of discrete control algorithms. The m order fractional derivative of continuous function 
f(t) is given by [10] 
( ) 
 
[ x ] 
m 
j 
( ) 
( ) 
d f t 
dt 
m 
m 
f t jh 
j 
j 
h 
m 
Lt 
h 
m 
D f t 
= 
 
−   
  
= 
− 
− 
® 
= 
0 
( 1) 
0 
(4) 
Where [x] is a truncation and 
t m 
h 
x 
( ) 
= 
− 
 
 
j 
;   
  
m 
is binomial coefficients 
, 
  
K 
m − − 
( 1) ( +1) 
m m m j 
! 
= 
j 
j 
  
  
= 1, ( j = 0), 
m 
j 
 
  
 
  
it can be Replaced by Gamma function, 
( m 
+1) 
G 
j! ( +1) 
= 
m j 
m 
j 
G − 
 
  
  
. The general calculus operator including fractional order and integer order 
is defined as [10]
a 
/ ( )  0 
a 
1 ( ) = 0 
	 	 	 

 
d dt R 
t 
 − 
a 
a t 
R 
a 
d R 
D 
( ) ( )  0 
=  
t a 
a 
a (5) 
Where a and t are the limits related to operation of fractional differentiation,  is the calculus order.
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), 
ISSN 0976 – 6553(Online) Volume 5, Issue 9, September (2014), pp. 17-28 © IAEME 
The Laplace transform of the fractional derivative of f(t) is given by 
1 { ( )} = ( ) [ ( )]t L D f t s F s D f t − − a a a (6) 
 
Dμ) controller involves an integrator of fractional order  and a 
c p ( ) = + + (8) 
−l μ (9) 
21 
 
=0 
Where F(S) is the Laplace transform of f(t). The Laplace transform of the fractional integral of f(t) is 
given as follows. 
L{D f (t)} = s F(s) −a −a (7) 
V. FRACTIONAL PID (PIDμ) CONTROLLER 
The FOPID (or PI 
differentiator of order μ, which has the following fractional order transfer function. 
μ 
K 
i 
G s K d 
l K S 
S 
Where  is the fractional order of the integrator and μ is the fractional order of the 
differentiator, which both can take any value of complex numbers. The classical 
controllers are particular cases of the FOPID controller. If =μ=1, the classical IOPID 
controller is obtained. For =μ=0, the P controller is obtained, for =0, μ=1 the PD controller is 
obtained. Illustration of different types of integer and fractional order controllers as  and μ vary as 
shown [15] in Fig3. 
Fig.3: Illustration of IO and FO controllers 
As the FOPID has two more extra tuning knobs than the classical integer-order PID 
controller, the use of fractional controller ( and μ are non-integers) gives more flexibility for the 
design of a control system and gives better opportunity to adjust system dynamics if the original 
system to be controlled is fractional system. In time domain input to the system to be controlled takes 
the following form. 
u(t) = K e(t) + K D e(t) + K D e(t) p i d 
Where  is the integral order, μ is the differential order Kp, Ki, Kd are the parameters of PID 
controller.
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), 
ISSN 0976 – 6553(Online) Volume 5, Issue 9, September (2014), pp. 17-28 © IAEME 
A. Optimization of PIDμ Controller’s parameters 
2 = ( ) (10) 
−1 − − − − × × × − × × − t 
t 
id v w v r p x r p x (11) 
t 
id x x t 
id v (12) 
22 
 
Fractional controller has five parameters and currently there are no practical engineering 
applications in frequency control of power system. Determine its parameters based on experience 
like traditional controllers are not possible and so a fast and efficient way to optimize its parameters 
must be found. 
Particle swam optimization (PSO) is a kind of swarm intelligence algorithm, simulating 
biological predation phenomenon in nature. PSO employs swarm intelligence, which comes from 
cooperation and competition between particles of a group, to guide the optimization search, with 
strong convergence, global optimization and computation-efficiency [10, 15]. 
B. Calculation of fitness function 
The design of PIDμ controller is actually a multi dimensional function optimization problem. 
The objective of controller parameters optimization is to make the control error tend to zero and 
there is smaller over shoot and faster response. In order to obtain satisfactory transition of the 
dynamic characteristic, the paper has used Integral squared error (ISE) performance index for the 
parameter’s minimum objective function. ISE can be expressed as follows [15]. 
 t 
ISE e t dt 
0 
C. Particle swarm optimization 
Particle swarm optimization is a new population based evolutionary computation. The PSO 
algorithm attempts to mimic the natural process of group communication of individual knowledge, 
which occurs when such swarms flock, migrate; forage etc in order to achieve some optimum 
property such as configuration or location. 
In PSO the ‘swarm’ is initialized with a population of random solutions. Each particle in the 
swarm is a different possible set of the unknown parameters to be optimized. Representing a point in 
the solution space, each particle adjusts its flying experience and shares social information among 
particles. The goal is to efficiently search the solution space by swarming the particle towards the 
best fitting solution encountered in previous iterations with the intent of encountering better solutions 
through the course of process and eventually converging on a single minimum error solution [10]. 
In PSO, a swarm consists of N particles moving around in a D-dimensional search space. The 
random velocity is assigned to each particle. Each particle modifies its flying based on its own and 
companion’s experience at every iteration. 
The formulas (11) and (12) are the particles velocity and position update formulas [11]. 
= + c ( ) + c ( ) 1 1 
2 2 
1 1 
1 1 
id 
t 
gd 
t 
id 
t 
id 
t 
id 
= + t−1 
id 
The ith particle is denoted as = ( , ) i i1, i2 id X x x Kx whose best previous solution Pbest is 
represented as is = ( , ) i i1, i2 id P p p Kp current velocity (position change rate) is described 
by = ( , ) i i1, i2 id V v v Kv . Finally, the best solution achieved so far by the whole swarm is represented 
as = ( , ) g i1, i2 gd P p p Kp .

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Pso based fractional order automatic generation controller for two area power system

  • 1. INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING & International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 9, September (2014), pp. 17-28 © IAEME TECHNOLOGY (IJEET) ISSN 0976 – 6545(Print) ISSN 0976 – 6553(Online) Volume 5, Issue 9, September (2014), pp. 17-28 © IAEME: www.iaeme.com/IJEET.asp Journal Impact Factor (2014): 6.8310 (Calculated by GISI) www.jifactor.com 17 IJEET © I A E M E PSO BASED FRACTIONAL ORDER AUTOMATIC GENERATION CONTROLLER FOR TWO AREA POWER SYSTEM CH. Ravi Kumar Dr. P.V.Ramana Rao Assistant Professor/E.E.E, Professor H.O.D/E.E.E, University College of Engg Tech. University College of Engg Tech. Acharya Nagarjuna University Acharya Nagarjuna University ABSTRACT This paper presents the development and application of Fractional order PID controllers based on particle swarm optimization (PSO) for load frequency control of two-area inter connected system. The dynamic response of the system has been studied for 1% and 10% step load perturbations in area2. The performance of the proposed FOPID controller is compared against the traditional PID controllers based on PSO and ANFIS based intelligent controller. Comparative analysis demonstrates that proposed FOPID controllers based on PSO reduces the settling time and overshoot effectively, against small step load disturbances. Simulations have been performed using MATLAB / Simulink. Keywords: Adaptive Neuro Fuzzy Inference System (ANFIS), Fractional PID Controller, Particle Swarm Optimization (PSO), Automatic Generation Control (AGC). I. INTRODUCTION In an interconnected power system Automatic Generation control or Load frequency control is important in Electrical Power System design and operation. Large scale power system comprises of interconnected subsystems (control areas) forming coherent groups of generators, where as connection between the areas is made using tie-lines [1-2]. Each control area has its own generation and is responsible for its own load and scheduled interchanges with neighbouring areas. The load in a given power system is continuously changing and consequently system frequency deviates from the desired normal values. Therefore to ensure the quality of power supply, a load frequency
  • 2. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 9, September (2014), pp. 17-28 © IAEME controller is needed to maintain the system frequency and inter-area flows at the desired nominal values. 18 The PI and PID controllers are well-known and widely used in power system control applications as they are simple to realize, easily tuned and several rules were developed for tuning their parameters [15]. These controllers are commonly used to dampen system oscillations, increase stability and reduce steady-state error. These controllers are integer order controllers as power of derivative or integral in these controllers is one. In recent years, researchers reported that controller making use of fractional order derivatives and integrals could achieve performance and robustness, superior to those obtained with conventional controllers. Fractional calculus deals with the concept of differentiation and integration to non-integer order. It is an extension of the concept dny(t)/dtn with n is an integer number to the concept dy(t)/dt where is non-integer number with possibility to be complex [15]. The classical IO controllers are particular cases of FOPID controllers. As the FOPID has two more extra tuning knobs than the classical IOPID controller, it gives more flexibility for the design of a control system and gives better opportunity to adjust system dynamics especially if the original system to be controlled is a fractional system. In many cases, fractional calculus can be applied to improve the stability and response of such a system through the use of non-integer order integrals and derivatives in place of the typical first order ones. The fractional control theory extends traditional integer order to the fractional-order and plural order. Fractional PID controller not only has three parameters Kp, Ki, Kd but also has integral order and differential order μ which are two adjustable parameters [8]. The application of fractional control theory, yields performance better than IOPID and (ANFIS controllers) hybrid artificial intelligence controllers. In this paper a fractional PIDμ controller is designed for AGC of a two area power system. The parameters Kp, Ki, Kd, , μ were optimized using Particle Swarm Optimization [8]. Simulation results showed that fractional order controller based on PSO had better performance than integer order PID controller based on PSO and ANFIS controllers. II. CONFIGURATION OF TWO-AREA POWER SYSTEM Plant model description The two-area inter connected power system is taken as a test system in this study. The model of the system under consideration is as shown in fig1. where symbols have their usual meanings. The conventional AGC has two control loops the primary control loop, which control the frequency by self-regulating feature of the governor, however, frequency error is not fully eliminated and the supplementary control loop which has a controller that can eliminate the frequency error. The main objective of the supplementary control is to restore balance between each control area load and generation after a load perturbation so that the system frequency and tie-line power flows are maintained at their scheduled values. So the control task is to minimize the system frequency deviations in the two areas under the load disturbances Pd1 or Pd2 in two areas. This is achieved conventionally with the help of suitable integral control action. The supplementary control of the ith area with integral gain Ki is therefore made to act on ACEi given by equation (1) which is an input signal to the controller [15-17].
  • 3. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 9, September (2014), pp. 17-28 © IAEME 1 t
  • 4. s G2 1+ 19 P12 1 R 1 R 1 t 1 t 1 2p T 12 1 Fig.1: Block diagram of AGC for Two area system with secondary loop + i ACE = DP + B Df i i j n =1 tie,ij (1) Where ACEi is area control error of the ith area i Df = Frequency error of ith area tie,ij DP = Tie-line power flow error between ith and jth area Bi = frequency bias coefficient of ith area III. INTEGER ORDER PID CONTROLLER The PID control is a widely used approach for designing a simple feedback control system where in three constants are used to weigh the effect of the error (the P term), the integral of the error (I term) and the derivative of the error(the D term). A typical structure of classical IOPID controlled system [15] is shown in Fig.2. Fig.2: Structure of PID control + 1 t 2 s T2 1+ 2 H 2s+D2 B2 w ACE2 + +
  • 6. s + G1 1+ 2 H 1s+D1 s T1 1+ 1 B1 S
  • 7. w
  • 8. + + + + System KP Kd Ki d/dt + r(t) e(t) u(t) y(t)
  • 9. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 9, September (2014), pp. 17-28 © IAEME a (2) a t f t Kh ( ) = (3) 20 To implement a PID controller that meets the design specifications of the system under control, the parameters [Kp, Ki, Kd, B1, B2] must be determined for the given system. An IOPID controller is designed for frequency control in power system in this paper, whose parameters were optimized using Particle swarm optimization. IV. FRACTIONAL CALCULUS Fractional calculus can have different definitions in different perspectives [15]. There are two commonly used definitions for fractional calculus so far, that is Grunwald-Letnikov definition, Reiman-Liouville definition. − ® − G ( + ) G G [( ) / ] 1 h 0 =0 ( ) ( +1) ( )h ( ) = lim t a h K K K D f t a a a t n d ( ) 1 − − G − a t a t d n n t f dt D f t a a t t a 1 ( ) ( ) (n - ) Grunwald-Letnikov definition is perhaps the best known one due to its most suitability for the realization of discrete control algorithms. The m order fractional derivative of continuous function f(t) is given by [10] ( ) [ x ] m j ( ) ( ) d f t dt m m f t jh j j h m Lt h m D f t = − = − − ® = 0 ( 1) 0 (4) Where [x] is a truncation and t m h x ( ) = − j ; m is binomial coefficients , K m − − ( 1) ( +1) m m m j ! = j j = 1, ( j = 0), m j it can be Replaced by Gamma function, ( m +1) G j! ( +1) = m j m j G − . The general calculus operator including fractional order and integer order is defined as [10]
  • 10. a / ( ) 0 a 1 ( ) = 0 d dt R t − a a t R a d R D ( ) ( ) 0 = t a a a (5) Where a and t are the limits related to operation of fractional differentiation, is the calculus order.
  • 11. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 9, September (2014), pp. 17-28 © IAEME The Laplace transform of the fractional derivative of f(t) is given by 1 { ( )} = ( ) [ ( )]t L D f t s F s D f t − − a a a (6) Dμ) controller involves an integrator of fractional order and a c p ( ) = + + (8) −l μ (9) 21 =0 Where F(S) is the Laplace transform of f(t). The Laplace transform of the fractional integral of f(t) is given as follows. L{D f (t)} = s F(s) −a −a (7) V. FRACTIONAL PID (PIDμ) CONTROLLER The FOPID (or PI differentiator of order μ, which has the following fractional order transfer function. μ K i G s K d l K S S Where is the fractional order of the integrator and μ is the fractional order of the differentiator, which both can take any value of complex numbers. The classical controllers are particular cases of the FOPID controller. If =μ=1, the classical IOPID controller is obtained. For =μ=0, the P controller is obtained, for =0, μ=1 the PD controller is obtained. Illustration of different types of integer and fractional order controllers as and μ vary as shown [15] in Fig3. Fig.3: Illustration of IO and FO controllers As the FOPID has two more extra tuning knobs than the classical integer-order PID controller, the use of fractional controller ( and μ are non-integers) gives more flexibility for the design of a control system and gives better opportunity to adjust system dynamics if the original system to be controlled is fractional system. In time domain input to the system to be controlled takes the following form. u(t) = K e(t) + K D e(t) + K D e(t) p i d Where is the integral order, μ is the differential order Kp, Ki, Kd are the parameters of PID controller.
  • 12. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 9, September (2014), pp. 17-28 © IAEME A. Optimization of PIDμ Controller’s parameters 2 = ( ) (10) −1 − − − − × × × − × × − t t id v w v r p x r p x (11) t id x x t id v (12) 22 Fractional controller has five parameters and currently there are no practical engineering applications in frequency control of power system. Determine its parameters based on experience like traditional controllers are not possible and so a fast and efficient way to optimize its parameters must be found. Particle swam optimization (PSO) is a kind of swarm intelligence algorithm, simulating biological predation phenomenon in nature. PSO employs swarm intelligence, which comes from cooperation and competition between particles of a group, to guide the optimization search, with strong convergence, global optimization and computation-efficiency [10, 15]. B. Calculation of fitness function The design of PIDμ controller is actually a multi dimensional function optimization problem. The objective of controller parameters optimization is to make the control error tend to zero and there is smaller over shoot and faster response. In order to obtain satisfactory transition of the dynamic characteristic, the paper has used Integral squared error (ISE) performance index for the parameter’s minimum objective function. ISE can be expressed as follows [15]. t ISE e t dt 0 C. Particle swarm optimization Particle swarm optimization is a new population based evolutionary computation. The PSO algorithm attempts to mimic the natural process of group communication of individual knowledge, which occurs when such swarms flock, migrate; forage etc in order to achieve some optimum property such as configuration or location. In PSO the ‘swarm’ is initialized with a population of random solutions. Each particle in the swarm is a different possible set of the unknown parameters to be optimized. Representing a point in the solution space, each particle adjusts its flying experience and shares social information among particles. The goal is to efficiently search the solution space by swarming the particle towards the best fitting solution encountered in previous iterations with the intent of encountering better solutions through the course of process and eventually converging on a single minimum error solution [10]. In PSO, a swarm consists of N particles moving around in a D-dimensional search space. The random velocity is assigned to each particle. Each particle modifies its flying based on its own and companion’s experience at every iteration. The formulas (11) and (12) are the particles velocity and position update formulas [11]. = + c ( ) + c ( ) 1 1 2 2 1 1 1 1 id t gd t id t id t id = + t−1 id The ith particle is denoted as = ( , ) i i1, i2 id X x x Kx whose best previous solution Pbest is represented as is = ( , ) i i1, i2 id P p p Kp current velocity (position change rate) is described by = ( , ) i i1, i2 id V v v Kv . Finally, the best solution achieved so far by the whole swarm is represented as = ( , ) g i1, i2 gd P p p Kp .
  • 13. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 9, September (2014), pp. 17-28 © IAEME 23 At each time step, each particle moves towards Pbest and gbest locations. The fitness function evaluates the performance of particle to determine whether the best fitting solution is achieved. w is the inertia weight factor, c1 and c2 are acceleration constant. 1 r and 2 r are random numbers between zero and one. w can be adjusted by the following formula (13), max min = . t T max max w w w w − − (13) max w and min w are maximum and minimum values of inertial weight coefficient, Tmax is the maximum of iterations, t is the current number of iterations. D. Design of fractional order PID controller using pso When PIDμ controller’s parameters are optimized using particle swarm optimization, the five parameters of the fractional controller and B1,B2 frequency bias coefficients of area1 and area2 can be viewed as a particle, that is K= [Kp, Ki, Kd, , μ, B1,B2].The seven members are assigned as real values. If there are n individual in a population, then the dimension of that population is n*7. In this paper n is set as 10. In order to limit the evaluation value of each individual of the population, feasible range must be set for each parameter as follows Kp1max = Kp2max =1.5; Kp1min = Kp2min= 0; Ki1max = Ki2max = 1.5; Ki1min = Ki2min= 1; Kd1max= Kd2max=1.5; Kd1min= Kd2min=0; Kp1vmax=Kp1max/10; Ki1vmax=Ki1max/10; Kd1vmax=Kd1max/10; Kp1vmin=Kp1min; Ki1vmin=Ki1min; Kd1vmin=Kd1min; 1max= 2max=2; 1min= 2min=0; μ1max= μ2max=2; μ1min= μ2min=0; 1vmax= 1max/10; 1vmin= 1min; μ1vmax= μ 1max/10; μ 1vmin= μ1min; Kp2vmax=Kp2max/10; Ki2vmax=Ki2max/10; Kd2vmax=Kd2max/10; Kp2vmin=Kp2min; Ki2vmin=Ki2min; Kd2vmin=Kd2min; B1max= B2max =35; B1min= B2min=15; B1vmax=B1max/35; B1vmin=B1min; B2vmax=B2max/25; B2vmin=B2min; C1=2, C2=2. Now the design steps are as follows [11-14]: 1. Randomly initialize the individuals of the population including position and velocities in the feasible range. 2. For each individual of the population, calculate the values of the performance criterion in (10). 3. Compare each individual’s evaluation value with its personal best Pid. The best evaluation value among all Pid is denoted as Pg. 4. Modify the member velocity of each individual according to (11) where the value of w is set by equation (13). 5. Modify the member position of each individual according to (12). 6. If the number of iterations reaches the maximum, then go to step 7 otherwise go to step2. 7. The latest Pg is the optimal controller’s parameters. In this study optimal parameters of fractional controller for 1% and 10% step load perturbations are: B1=17.4191, B2=25, Kp1=0.2819, Ki1=1.5, Kd1=1.2618, 1=1.1869, μ1=0.5524. Kp2=1.3213, Ki2=1.5, Kd2=1.1813, 2=0.8336, μ2=1.0770.
  • 14. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 9, September (2014), pp. 17-28 © IAEME -3 Change in frequency with ANFIS Control for 1% step load perturbation -4 Change in f requency w ith PSO based FOPID Controller for 1% step load perturbation 24 VI. RESULTS AND DISCUSSIONS In the present work Automatic Generation Control of two area interconnected power system has been developed using PSO based IOPID Control, ANFIS controller and PSO based FOPID controller using Matlab/Simulink package. Figs 4 to 9 respectively represent the plots of change in system frequency for 1% and 10% step load variations in area1. The results obtained are also given in Tables 3 and 4. Case I: For 1% Step load Perturbation -4 0 2 4 6 8 10 12 14 16 18 20 0.5 0 -0.5 -1 -1.5 -2 -2.5 -3 x 10 Time in Seconds Deviation in frequency (p.u.) Change in f requency w ith PSO based IOPID control for 1% step load perturbation Del f1 Del f2 Fig 4: Frequency deviations f1, f2 with PSO based IOPID control 0 2 4 6 8 10 12 14 16 18 20 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 x 10 Time in Seconds Deviation in frequency (p.u.) Del f1 Del f2 Fig 5: Frequency deviations f1, f2 with ANFIS control 0 2 4 6 8 10 12 14 16 18 20 2 1 0 -1 -2 -3 -4 -5 x 10 Time in seconds Deviation in frequency (p.u.) Del f1 Del f2 Fig 6: Frequency deviations f1, f2 with PSO based FOPID controller
  • 15. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 9, September (2014), pp. 17-28 © IAEME -3 Change in frequency with ANFIS Controller for 10% step load perturbation Change in f requency w ith PSO based FOPID controller for 10% step load perturbation 25 Case II: For 10% Step load Perturbation -3 0 2 4 6 8 10 12 14 16 18 20 0.5 0 -0.5 -1 -1.5 -2 -2.5 -3 x 10 Time in Seconds Deviaion in frequency (p.u.) Change in f requency w ith PSO based IOPID Controller for 10% step load perturbation Del f1 Del f2 Fig 7: Frequency deviations f1, f2 with PSO based IOPID Control 0 2 4 6 8 10 12 14 16 18 20 1 0 -1 -2 -3 -4 -5 -6 -7 x 10 Time in Seconds Deviation in frequency (p.u.) Del f1 Del f2 Fig 8: Frequency deviations f1, f2 with ANFIS control -3 0 2 4 6 8 10 12 14 16 18 20 1 0 -1 -2 -3 -4 -5 x 10 Time in Seconds Deviation in frequency (p.u.) Del f1 Del f2 Fig 9: Frequency deviations f1, f2 with PSO based FOPID controller
  • 16. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 9, September (2014), pp. 17-28 © IAEME 26 VII. CONCLUSIONS Table 1: Comparative study of Settling time and Peak overshoots for 1% step load variation Controllers Settling time in (Sec) Peak overshoot (p.u.) X 10-4 f Area 1 f Area 2 f Area 1 f Area 2 IOPID Control (PSO based) 20 20 -3 -0.5 ANFIS 12 12 -2.5 -0.4 FOPID Control (PSO based) 9 9 -4 -0.4 Table 2: Comparative study of Settling time and Peak overshoots for 10% step load variation. Controllers Settling time in (Sec) Peak overshoot (p.u.) X 10-3 f Area 1 f Area 2 f Area 1 f Area 2 IOPID Control (PSO based) 16 16 -3 -0.5 ANFIS 12 16 -6 -1 FOPID Control (PSO based) 9 9 -4 -0.4 This paper presents a fractional PIDμ frequency controller for a Two area interconnected system, whose parameters are optimized using PSO algorithm. The paper presents the comparative analysis of PSO based IO controller, ANFIS controller and PSO based FO controllers of interconnected systems. The paper has shown that a FOPID, which has two more extra tuning knobs
  • 17. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 9, September (2014), pp. 17-28 © IAEME than the classical IOPID controller, gives more flexibility for the design of a control system and gives better opportunity to adjust system dynamics. Simulation results shows that the proposed Fractional controller has better dynamic performance than the Integer order controller and ANFIS controller with faster response and smaller overshoot. 27 REFERENCES [1] O.I.Elgerd, Electric Energy Systems Theory: An Introduction. Newyork: McGraw-Hill, 1982. [2] Kundur. P, Power system stability and control, McGraw-Hill, Inc., 1994. [3] Ibraheem, Prabhat Kumar, and Dwaraka P.Kothari, “Recent philosophies of automatic generation control strategies in power systems,” IEEE Transactions on Power Systems, 20, no.1, pp. 346-57, February 2005. [4] J. Talaq and F. Al-Basri,”Adaptive fuzzy gain scheduling for load – frequency control,” IEEE Trans.Power Syst., vol.14, no.1, pp.145-150, Feb.1999. [5] Y.L. Karnavas and D.P.Papadopoulos,” AGC for autonomous Power System using combined intelligent techniques,” Elect. Power Syst.Res. vol.62, no.3,pp. 225-239, Jul.2002. [6] Sathans and A.Swarup “Intelligent Automatic Generation Control of Two area Interconnected Power System using Hybrid Neuro Fuzzy Controller”, World academy of Science, Engineering and Technology 60 2011. [7] Gayadhara Panda, Siddhartha Panda and C.Ardil, “Hybrid Neuro Fuzzy Approach for Automatic Generation Control of Two –Area Interconnected Power System”, International Journal of Computational Intelligence 5:1 2009. [8] Jifeng Wang. Control Performance analysis for Fractional order systems. Bei Jing: Publishing House of Electronics Industry, 2010. [9] Jiliu Zhou, Yifei Pu, Ke Liao. The Theory of Fractional calculus and its application in modern signal analysis and processing. Bei Jing: Science Press, 2010. [10] Jun-Yi Cao and Bing-Gang Cao. Design of Fractional Order Controller Based on Particle Swarm Optimization. IJCAS, vol.4, no.6, pp.775-781, Dec 2006. [11] Xiuye Wei, Hongxia Pan. Particle Swarm Optimization and Intelligent Fault Diagnosis. Bei Jing: National Defence Industry Press, 2010. [12] Ling Wang, Bo Liu. Particle Swarm Optimization and Scheduling Algorithm. Bei Jing: Tsinghua University Press, 2008. [13] Yishu Zhao, Zhijian Hu, Yang Gao, etc. Study of Fractional Order PID Conrollers for STATCOM. Southern Power System Technology, 2009, 3(4): 26-30. [14] Shuncai Yao, Hongxia Pan. Fractional order PID Controller for Synchronous Machine Excitation using Particle Swarm Optimizaion. Proceedings of the CSEE, 2010, 30(21): 91-97. [15] Muwaffaq Irsheid Alomoush. Load frequency control and automatic generation control using Fractional order controllers. Electr Eng (2010) 91:357-368. [16] Guishu Liang, Zhilan Wang. Design of fractional load frequency controller. International Conference on Control Engineering and Communication Technology, 2012. [17] Ch.Ravi Kumar, Dr.P.V.Ramana Rao, “Application of Hybrid Neuro Fuzzy Controller for Automatic Generation Control of Three Area Power System Considering Parametric Uncertainties”, International Journal of Electrical Engineering Technology (IJEET), Volume 4, Issue 5, pp. 104-114, 2013. ISSN Print: 0976-6545, ISSN Online: 0976-6553. [18] P. Sobha Rani and Dr. A. Lakshmi Devi, “Performance Improvement of Distribution System with Multi Distributed Generation using Particle Swarm Optimization”, International Journal of Electrical Engineering Technology (IJEET) volume 5, issue 2, pp. 44 - 50, 2014. ISSN Print: 0976-6545, ISSN Online: 0976-6553.
  • 18. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 9, September (2014), pp. 17-28 © IAEME 28 BIOGRAPHY Ch.Ravi Kumar was born in India in 1981; He received the B.Tech degree in Electrical and Electronics Engineering from A.S.R.College of Engineering and Technology, Tanuku in 2003 and M.Tech degree from JNTU Anantapur, A.P.-India in 2005. Currently he is pursuing Ph.D in Electrical Engineering and working as Asst.Professor in University college of Engineering and Technology, Acharya Nagarjuna University, Andhra Pradesh India. His areas of Interest are Power system operation and control, Application of Intelligent control techniques to Power systems. P.V.Ramana Rao was born in India in 1946; He received the B.Tech degree in Electrical and Electronics Engineering from IIT Madras, India in 1967 and M.Tech degree from IIT Kharagpur, India in 1969. He received Ph.D from R.E.C Warangal in 1980. Total teaching experience 41 years at NIT Warangal out of which 12 years as Professor of Electrical Department. Currently Professor of Electrical Department in University college of Engineering and Technology, Acharya Nagarjuna University, Andhra Pradesh, India. His fields of interests are Power system operation and control, Power System Stability, HVDC and FACTS, Power System Protection, Application of DSP techniques and Application of Intelligent control techniques to Power systems.