 Open Access
 Total Downloads : 37
 Authors : Habib Danaeefar , Hasaan Barati , Seyyed Arman Shirmardi
 Paper ID : IJERTV8IS050013
 Volume & Issue : Volume 08, Issue 05 (May 2019)
 Published (First Online): 09052019
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Optimal Control of PIDFUZZY based on Gravitational Search Algorithm for Load Frequency Control
Habib Danaeefar, Hasaan Barati, Seyyed Arman Shirmardi
Department of Electrical and Computer Engineering, Islamic Azad University Dezful Branch,
Dezful, Iran
Abstract: In this paper, an efficient and effectual optimization algorithm called Gravitational Search Algorithm (GSA) is suggested to optimally tune the PID FUZZY parameters toward accurate frequency control of twoarea power system. An effective and precise optimization algorithm i.e., GSA has been constructed based on the gravity law and mass interactions. In this algorithm, the explorer operators are a masses collection which interacts with each other according to the motion laws and Newtonian gravity. To appropriately and accurately confirm the dynamic performance of suggested GSAbased PIDFuzzy, four performance indexes, i.e.: ISE, ITSE, IAE and ITAE have been considered as objective functions. Furthermore, the simulations results by the suggested GSA base PIDFUZZY have been compared with the simulation results based on Particle Swarm Optimization (PSO) and Artificial Bee Colony (ABC) algorithms which are generally realized as conventional heuristic algorithms and extensively applied by the researchers and scholars. Finally, optimal GSAbased PIDFUZZY presents a high dynamic performance as compared to PSObased PIDFUZZY and ABCbased PIDFUZZY.
Keywords: Power system dynamic stability, low frequency oscillation, automatic generation control, optimization algorithms, gravitational search algorithms.

INTRODUCTION
The value of consumed power around the world exhibits the state of the art level of countries that shows the importance of power quality, voltage regulation and system frequency stability issues. That is to say, all criterions of power quality have been studied and analyzed on frequency and voltage of power system. Since the system frequency control is highly longer than the voltage control, it is regarded as salient benchmark in the power system. Thus, system frequency stability should be principally investigated and involved in many researches and projects [1]. Integration of many different power sources or areas has constructed the interconnected power system. Any power variations in power source and load which happen in these areas can disturb other connected areas. The tieline characteristic between these areas is one other important item in impressing the frequency stability. During the high variations in system frequency which go beyond the defined limits, they can create severe power system instability, which will stop the connected power plants and even shut down the entire
system in the later step. In this instance, the fed areas of the system remain without energy and cause vast economic damages [2]. Consequently, considering these vast economic damages due to system collapse, the frequency control of loads is regarded a salient problem which must be considered to hinder such damages.
Automatic Generation Control (AGC) has decreased the deviations of tieline power and frequency in order to swiftly restore its nominal frequency [35]. The conventional controller such as: classical Proportional Integral Derivative (PID) controller has been widely used for AGC in interconnected power systems. But, this controller cannot effectively suppress the fluctuations tieline power and frequency during severe perturbations. Considering the benefits of PID controller, it has been integrated with Fuzzy controller to construct PIDFuzzy controller aimed at suppression of low frequency oscillations. As reported in various literatures, Fuzzy controller provides good performance during the normal, unbalance and transient conditions [68]. The parameters of PIDFuzzy can be tuned in real time in accordance with load perturbations to enhance its accuracy and robustness toward acquiring the best control aims.
In recent years, the evolutionary optimization algorithms such as Bacteria Foraging (BF), Particle Swarm Optimization (PSO) and Artificial Bee Colony (ABC), Ant Colony Optimization (ACO) have been widely used by researchers to solve the various objective functions in different problems [913]. Although aforementioned algorithms seem to be excellent to optimally tune the parameters of controller, they introduce a slow convergence with local minimums. Gravitational Search Algorithm (GSA), a new evolutionary optimization algorithm, presents a fast convergence and accurate performance in these aspects [1416]. In this regard, it is applied to optimally tune the parameters of PIDFuzzy for stabilizing the interconnected power system.
In this study, the parameters of PIDFuzzy have been tuned by GSA, PSO and ABC so that its performances can be well compared and appraised. The relevant studies have been performed in twoarea interconnected power system. Severe load perturbation has affected the interconnected power system to deal with the dynamic stability criterions with presence of PIDFUZZY. Finally, optimal GSAbased PID FUZZY presents a high dynamic performance as compared to PSObased PIDFUZZY and ABCbased PIDFUZZY.

INTERCONNECTED POWER SYSTEM
STRUCTURE
Kinetic and potential energy has been transformed into mechanical energy using turbines, following that, the
mechanical energy has been transformed into electrical energy using power plants generators. Simple motion equation based on the mentioned concept can be presented by:
Tm Te J d
dt
(1)
Where, Tm and Te are respectively mechanical and electrical torque. J and are respectively the inertia and angular speed.
The understudy power system contains two interconnected areas via tieline. Note that, all available generators in each area have a combined construction. Occurrence of any perturbations in each area of power system leads to frequency deviation in other areas. Then, this deviation creates fluctuation in tieline power. In this regard, both the tieline power and frequency deviations must be damped to maintain the dynamic stability of interconnected power system. The tieline power can be presented by:
Pline12
V1 V2
X12
sin(1 2 )
(2)
Where, V1 and V2 are respectively voltage of first and second areas. 1 and 2 are respectively machine angle of first and second areas. X12 indicates tieline impedance. The machine angle deviation of each area can be presented by:
2 fdt
The tieline power deviation can be presented by:
(3)
P V1 V2 cos(
)(
)
(4)
12 X12
1 2 1 2
Where, the synchronous coefficient is written as follows:
T V1 V2 cos( )
(5)
12 X12 1 2
The tieline power deviation is rewritten by:
Ptie T12(1 2 )
(6)
Thereupon load deviation PL, tieline power deviation, frequency deviation and Area Control Error (ACE) of each area can be given by following equations:
PL1( 1 D2 )
Ptie
1 1
R1 R2
R2
D1 D2
(7)
f
PL1
(8)
1 1
R1 R2
D1 D2
ACE1 Ptie B1 f1
ACE2 B2 f2 a12 Ptie
(9)
(10)
B1 1/R1
AREA 1
Gg1(s)
Xg1
Gg1(s)
Xg1
pL1(s)
+ ACE1
+
–
Gc1(s)
Gc1(s)
Pref1
– PG1
+ –
Grp(s)
Prp
Grp(s)
Prp
Gt1(s)
Pt1
Gt1(s)
Pt1
Gps1(s)
–
f1
a12
a12
–
–
+ ACE2
Controller 1
Gc2(s)
Pref
Gc2(s)
Pref
2
Governor 1 Reheater 1
Ptie
Turbine 1
+
+
Pt2 –
Power System 1
+
Gtl(s)
a12
a12
–
Tie line
f2
PG2
–
+ –
Gt2(s) G
ps2
(s)
Gg2(s)
Xg2
Gg2(s)
Xg2
Grp(s)
Prp
Grp(s)
Prp
Controller 2
Governor 2 Reheater 2
Turbine 2
Power System 2
B2 1/R2
AREA 2
pL2(s)
Figure 1. Twoarea interconnected power system
Figure 1 presents the linearized model of twoarea interconnected power system. The following equations give the transfer function of each block:
Governor:
Gg1(s) Gg 2 (s)
Reheater:
Kh
Th s 1
(11)
Grp(s) Grh 2 (s) (Kr12 Tr11) s 1
Tr1 s 1
(12)
Turbine:
Gt1(s) Gt 2 (s)
Power system:
Kt
Tt s 1
(13)
Gps1
(s) G
ps 2
(s)
Kg
Tg s 1
(14)
Tieline:
Gtl (s) 2 T12
s
(15)
The understudy two areas of interconnected power system are thermal plant. Rate of each area is 2000 MW with 1000 MW (nominal load). This system has been widely studied in different literatures which propose, design and analyze the required controller for AGC to enhance the power system dynamic stability [1719].

CONSTRUCTION OF PIDFUZZY CONTROLLER
A PIDFuzzy controller enhances the dynamic performance of PID controllers, because Fuzzy logic can appropriately control the changes in parameters of power systems or operating point via autotuning gains of PID controller [20]. Precise design of Fuzzy controller has been performed by choosing an appropriate membership functions and rule formulation. So, general membership functions and rules
have been selected for input/output while the parameters of PID controller can be optimally tuned to enhance the overall dynamic performance of PIDFuzzy controller [21]. Two dimensional rule base PIDFuzzy controller has been designed by the error signal along with its derivative for input signal PID controller for output signal [22. As mentioned above, PIDFuzzy controller which is shown in Fig. 2 (a) is designed for AGC to enhance the dynamic performance of power system. K1 and K2 are input gains of PIDFuzzy controller while KP, KI and KD are its output gains. The fuzzy rules and its input membership function are respectively presented in Table 1 and Fig. 2(b).The membership functions are defined by: PB (Positive Big), PM (Positive Medium), PS (Positive Small), ZE (Zero), NS (Negative Small), NM (Negative Medium) and NB (Negative Big) as fuzzy measure.
ACE
Fuzzy Logic Controller
K1
KP
u
du/dt
KI
K2 KD
1/s
d/dt
Figure 2(a). PIDFuzzy controller model
NB NM NS ZE PS
PM PB
1 0.5 0 0.5 1
Figure 2(b). Normalized membership function for inputs
Table 1. Lookup table of fuzzy rules
ACE
NB
NM
NS
ZE
PS
PM
PB
ACE
NB
NB
NB
NB
NB
NM
NS
ZE
NM
NB
NM
NM
NM
NS
ZE
PS
NS
NB
NM
NS
NS
ZE
PS
PM
ZE
NB
NM
NS
ZE
PS
PM
PB
PS
NM
NS
ZE
PS
PS
PM
PB
PM
NS
ZE
PS
PM
PM
PM
PB
PB
ZE
PS
PM
PB
PB
PB
PB

GRAVITATIONAL SEARCH ALGORITHM
GSA is a heuristic stochastic evolutionary algorithm proposed by Rashedi et al in 2009 [17]. It is inspired by the mass interactions and gravitation newton principle. All objects are absorbed by a gravitational force, which forces all objects to move toward heavy masses as shown in Fig. 3(a). It exhibits a natural behavior between earth and the moon. The weightiest object suggests the problem solution. The Flowchart of GSA process is given in the Fig. 3(b), and also
M1
F14
its general Pseudo code is provided in Fig. 3(c). According to GSA procedure, each mass includes four statements: position, inertial mass, active gravitational mass, and passive gravitational mass [18]. The mass position related to the problem solution, and its gravitational and inertial masses have been defined via an objective function. That is to say, each mass gives a result that GSA is navigated via correct tuning the gravitational and inertia masses [19]. By time span, it is expected that masses to be pulled by the weightiest mass which gives an optimal response in the search space.
M4
F12 a1
M2
F13
F1 M3
Figure 3(a). Every mass accelerate towards to the resultant force
Generate initial population
Evaluate the fitness for each agent
Update G, best and worst of population
Calculate M and a for each agent
Update velocity and position
No Meeting end of criterion?
Yes
Return best solution
Return best solution
Figure 3(b). Flowchart of GSA procedure
Random initialization of the population
Find the best and worst solutions in the initial population
while (stop criterion)
for i=1:N (for all elements)
update G(t), best(t), worst(t) and Mi(t) for i=1,2,N calculate the mass of individual Mi(t)
calculate the gravitational constant G(t)
calculate the acceleration aih(t)
Random initialization of the population
Find the best and worst solutions in the initial population
while (stop criterion)
for i=1:N (for all elements)
update G(t), best(t), worst(t) and Mi(t) for i=1,2,N calculate the mas of individual Mi(t)
calculate the gravitational constant G(t)
calculate the acceleration aih(t)
update the velocity and position of each individual vih , xi
end for i=1:N (for all elements)
Find the best individual
end while (stop criterion)
Display the best individual as the solution
update the velocity and position of each individual vih , xi
end for i=1:N (for all elements)
Find the best individual
end while (stop criterion)
Display the best individual as the solution
h
h
Figure 3(b). GSA Pseudo code

SIMULATIONS AND RESULTS
The performance of control systems has been assessed based on an especial performance index depends on the required objective function. The performance index is alternatively used to design of controllers which are commonly known by: integral of squared error (ISE), integral of time multiplied squared error (ITSE), integral of
absolute error (IAE) and integral of time multiplied absolute error (ITAE) [2325]. To appropriately and accurately confirm the dynamic performance of suggested GSAbased PIDFuzzy, all aforementioned have been taken into account for designed optimization problem. These objective functions are given as follows:
T
ISE F12 0
F22

Ptie,12
2 .dt
(16)
T
ITSE F12 0
F22

Ptie,12
2 .t.dt
(17)
T
T
IAE F1 F2
0

Ptie,12 .dt
(18)
T
T
ITAE F1 F2
0

Ptie,12 .t.dt
(19)
The PIDFuzzy parameters have been optimally tuned by GSA in order to alleviate the tileline power and frequency deviations. Furthermore, the controller parameters have been optimized by PSO and ABC to more validate the dynamic performance of GSAbased PIDFuzzy controller. The operational constraints of controller parameters are given as follows:
K min K K max
1 1 1
K2min K2 K2max
KPmin KP KPmax
KDmin KD KDmax
KI min KI KI max
(20)
In the simulations, a step load perturbation occurs in first area of the interconnected power system to affect the dynamic stability. The optimization problem has been performed with GSA, PSO and ABC considering all chosen performance indexes. The load perturbation occurs at t=10 s with PL=0.01. The optimal parameters of PIDFuzzy controller optimized by GSA, PSO and ABC are tabulated in Table 2. Meanwhile, the values of defined performance indexes, i.e.: ISE, ITSE, IAE and ITAE are presented in Table 3. Also, three stability benchmarks i.e.: settling time, overshoot and undershoot are tabulated in Table 4.Both the timevarying frequency and tieline power deviations are respectively presented in Fig. 4(ac).
Table 2. The parameters of PIDFuzzy optimized by GSA, PSO and ABC
GSA
ABC
PSO
Area 1
Area 2
Area 1
Area 2
Area 1
Area 2
K1
1.1854
1.6210
1.5021
1.8428
1.8029
2.2367
K2
0.5649
0.7431
0.6712
0.9142
0.8291
1.0056
KP
0.6094
0.7885
0.7003
0.9462
0.9906
1.2049
KI
0.7951
1.0359
0.9615
1.3410
1.2986
1.372
KD
0.4932
0.6372
0.58960
0.7743
0.5765
0.9211
Table 3. The optimal value of dynamic performance indexes achieved by GSA, PSO and ABC
Parameter indexes
GSA
ABC
PSO
ISE
2.7025
4.0962
4.7643
ITSE
0.1496
0.1924
0.2241
IAE
2.5618
3.4577
3.9553
ITAE
71.7942
110.4983
130.3509
Table 4. The optimal value of dynamic performance indexes achieved by GSA, PSO and ABC
Stability benchmarks
GSA
ABC
PSO
Overshoot
0.0116
0.0148
0.0156
Undershoot
0.0192
0.01984
0.0208
Settling time
55.31
62.12
68.76
Figure 4(a). Change in frequency deviation of area1
Figure 4(b). Change in frequency deviation of area2
Figure 4 (c). Change in tieline power deviation between area1 and area2
As for the Table 24, all performance indexes optimized by GSA present less values as compared to corresponding indexes optimized by PSO and ABC. The presented results prove that the overall dynamic stability of interconnected power system has been highly improved by GSAbased PID Fuzzy more than two others. The timevarying curves presented in Fig. 4(ac) have better portrayed the dynamic performance of GSAbased PIDFuzzy.


CONCLUSION
In this paper, PIDFuzzy controller is suggested for AGC appropriately enhance the dynamic stability of twoarea interconnected power system. GSA algorithm has been complementary applied to optimize the parameters of PID Fuzzy so that its maneuverability to be increased. Hence, PSO and ABC have been taken part in optimization problem to clear the accuracy and capability of GSA. Dynamic stability analysis has been more carried out with consideration of four performance indexes i.e.: ISE, ITSE, IAE and ITAE. The pertinent dynamic stability studies have been performed by affecting the interconnected power system caused by load perturbation occurrence in area1. Eventually, the simulation results confirm the high dynamic performance of GSAbased PIDFuzzy via damping the low frequency oscillations of tieline power and frequency deviations.
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