View metadata, citation and similar papers at core.ac.uk
brought to you by
CORE
provided by Elsevier - Publisher Connector
Available online at www.sciencedirect.com
ScienceDirect
Procedia Technology 11 (2013) 65 – 74
The 4th International Conference on Electrical Engineering and Informatics (ICEEI 2013)
New Coordinated Design of SVC and PSS for Multi-machine Power
System Using BF-PSO Algorithm
M. R. Esmailia, R. A. Hooshmandb, M. Parastegarib, P. Ghaebi Panahc,*, S. Azizkhanid
a
Esfahan Regional Electric Company, Isfahan, Iran
Department of Electrical Engineering, University of Isfahan, Isfahan, Iran
c
Electrical Engineering Group, Ragheb Isfahani Higher Education Institute, Isfahan, Iran
d
Faculty of Engineering, Multimedia University, Cyberjaya, Malaysia
b
Abstract
Nowadays, flexible AC transmission system (FACTS) devices are increasingly used in power systems. They have remarkable
effects on increasing the damping of the system. In this paper, a bacterial-foraging oriented by particle swarm optimization (BFPSO) algorithm is employed to design the coordinated parameters of power system stabilizer (PSS) and static VAR compensator
(SVC). With regard to nonlinearities of power system, linear methods can’t be used to design coordinated parameters of
controllers. In this paper, nonlinear model of power system and SVC is used to design parameters of PSS and SVC. For this
purpose, this design problem is firstly converted to an optimization problem and then the BF-PSO algorithm is used to solve it.
Simulations are carried out on four machine 11 bus power system in MATLAB software. The results confirm the efficiency of
the proposed method for stabilizing the power system oscillations. Comparing BF-PSO algorithm with other intelligent methods,
(PSO, BFA) verifies better performance of the BF-PSO method.
2013 The
The Authors.
Authors.Published
PublishedbybyElsevier
ElsevierB.V.
Ltd. Open access under CC BY-NC-ND license.
© 2013
Selection
and peer-review
peer-review under
under responsibility
responsibility of
of the
the Faculty
Faculty of
ofInformation
InformationScience
Science&and
Technology,
Universiti
Kebangsaan
Selection and
Technology,
Universiti
Kebangsaan
Malaysia.
Malaysia.
Keywords: Power system stabilizer, static VAR compensator, bacteria foraging algorithm, PSO, BF-PSO
1. Introduction
One of the important problems in large interconnected power system is low frequency oscillations. These
* Corresponding author. Tel.:+98-912-445-1689.
E-mail address: payam.ghaebi@yahoo.com
2212-0173 © 2013 The Authors. Published by Elsevier Ltd. Open access under CC BY-NC-ND license.
Selection and peer-review under responsibility of the Faculty of Information Science & Technology, Universiti Kebangsaan Malaysia.
doi:10.1016/j.protcy.2013.12.163
66
M.R. Esmaili et al. / Procedia Technology 11 (2013) 65 – 74
oscillations occur at low frequency in the range of 0.2-2.5 Hz and can be particularly cause instabilities. PSSs are
very effective controllers in enhancing the damping of these oscillations because they can increase the damping
torque of local modes of system by introducing additional signals into the excitation controllers of the generators
[1,2]. They are used as supplementary control devices to provide extra damping.
Traditionally, power system stabilizers are designed using a linear model. However, power systems are complex,
nonlinear and it is crucial to use the methods capable of handling any nonlinearity within the system [3]. In the other
hand, only conventional PSS may not provide sufficient damping for stabilizing inter-area oscillations [2]. In these
cases, FACTs power oscillation damping (POD) controllers are effective solutions for stabilizing inter-area
oscillations [3].
FACTS devices are widely used in power systems [4,5]. They play a vital role in stabilizing power system. The
coordination between PSS and FACTs POD controllers are also necessary to improve the overall damping
performance of power system [6-8].
In conventional methods, power systems are designed and operated conservatively in a region where behaviour is
mainly linear. In the event of large disturbance, power system operating point changes considerably. However, in
these conditions, nonlinearities of power system have significant effects and linear methods can not be able to
maintain its stability. Therefore, it is crucial to consider the effect of nonlinearities of power system [9].
Resent years, intelligent optimization algorithms have been extensively used to design power system stabilizers. In
this order, genetic algorithm [10], tabu search algorithm [11], simulated annealing [12], small population-based PSO
(SP-PSO) algorithm and bacterial foraging algorithm (BFA) [13] are applied as intelligent algorithms for the
simultaneous coordination of PSSs in power systems.
Although the shunt FACTS devices, such as SVC, are originally used to control the reactive power flow to the
power network and, the system voltage fluctuations, they can also increase the power system damping. A
supplementary damping controller added to SVC can be designed to modulate its bus voltage in order to improve the
damping of system oscillations, especially for inter-area modes [1, 13]. In [14,15], in order to damp out power
system oscillations PSO technique is used to tune the controller parameters of the thyristor controlled series
capacitor (TCSC) and PSS coordinately. The particle swarm optimization [16,17] and chaotic optimization
algorithm [18] are used to tune the parameters of the unified power flow controller (UPFC) to increase the damping
of the system.
Nevertheless, as shown in [19] the interaction between PSSs and STATCOM-based controller may degrade the
damping of some oscillating modes. In order to improve the overall damping performance of power system, the
coordination between PSS and FACTS controllers seems to be necessary [20]. In [21], an application of
probabilistic theory using probabilistic sensitivity indices (PSIs) was used for a robust coordinate design of power
system stabilizer and FACTs controllers
Recently, BFA technique appeared as a promising evolutionary technique for handling the optimization
problems. The Bacterial Foraging, itself, is a stochastic optimization algorithm. The involvement of a number of
stages in BFA greatly reduces the possibility of getting trapped in the local minima during the search process [12].
Although it covers a wide search region, it has a low convergence speed [22]. The PSO algorithm is a local search
optimization method and is flexible, robust and easy to be programmed. It has got a high convergence speed [23].
Therefore, these two techniques can be combined [24] to obtain the search capability of the intelligent and the speed
of PSO simultaneously to solve optimization problems.
This paper proposes the use of an intelligent algorithm named BF-PSO, to design the PSS and Static VAR
compensators (SVC) controllers coordinately. A nonlinear four-machine power system is used to show the
advantage of this technique. This coordinated design damps out the rotor oscillations and greatly enhances the
system stability [25]. The results are compared with other intelligent algorithms such as BFA, PSO, showing the
superiority of the proposed method.
2. Power System Modelling
2.1. Synchronous Generator
Consider an n-generator power system. Each generator can be modelled by a five-order dynamic system. The
equations corresponding to the dynamic model of the i-th generator can be written as follows[1]:
67
M.R. Esmaili et al. / Procedia Technology 11 (2013) 65 – 74
dG i
Zo Zi
dt
dZi
1
>Pmi Pei DiZi @
dt
2 Hi
c
dedi
1
c xqi xdi
c I qi
edi
c
dt
Tqoi
>
c
deqi
dt
dE fd i
(1)
(2)
@
(3)
>
1
c xdi xdi
c I di
E fdi eqi
c
Tdoi
@
(4)
K
1
(5)
E fdi E fdi0 Ai Vti Vti0
dt
TAi
TAi
c , E fdi , Tdoi
c , K Ai , TAi , Vti are rotor angle, rotor speed, rotor
c , eqi
where, Gi , Zi , Zo , H i , Pmi , Pei Di , edi
synchronous speed, damping coefficient, moment of inertia, internal voltage of components for d- and q-axis, field
voltage, transient time constant, gain and time constant of field voltage, terminal voltage of i-th synchronous
generator respectively.Figure 1 also shows the conventional lead-lag PSS.
VS max
'Z
TW
1 STW
KPSS
1 ST1
1 ST2
1 ST3
1 ST4
uPSS
VS min
Fig. 1. Conventional lead-lag PSS.
2.1. Static VAR Compensator (SVC)
The SVCs is a flexible and continuous reactive power compensator that has been used in power systems to
regulate the reactive power and voltage to the actual system needs [26]. It operates in two modes as capacitive and
inductive. It consist of a thyristor-switched capacitor (TSC) and/or thyristor-controlled reactor (TCR) shown in
Figure 2.
Vt
G
i→
Line 1
Pulses
Exciter
AVR
Y=G+jB
Vt - +
V
Upss
Voltage
measurement
CPSS
Pulses
Δω
Vm
+
Vref
PI
Controller
B ref
Distribution alfa
Unit
PLL Phase
Generator
Fig. 2. A single-line diagram of a SVC and a simplified block diagram of its control system.
68
M.R. Esmaili et al. / Procedia Technology 11 (2013) 65 – 74
The current of SVC's reactor should be controlled in a way that a suitable control range between capacitive mode
and inductive mode of SVC is determined. The SVC can be modelled as a first order linear differential equation
model [11]. This could be at the middle of a transmission line or at a load bus.
K
B ( K p i ).(VSVC VSVC,ref )
s
Bmin d B d Bmax
(6)
When the SVC is operating in voltage regulation mode, its response speed to a change of system voltage depends on
the voltage regulator gains (proportional gain Kp and integral gain Ki).
3. Proposed Optimization Problem
Minimizing the speed deviation of the whole system is the objective function of the proposed optimization
problem. Overshoot, undershoot, rise time and settling time of speed deviation signal are the main specifications of
the speed deviation signal. Therefore, the goal of the design problem is minimizing all of these specifications.
Instead of minimizing all of these specifications separately, an index which contains all of these specifications can
be used. For this purpose, Integral of Time multiplied Absolute Error (ITAE) performance index is used [27-28].
Following relation represents ITAE performance index for the generator speed which can be used as an objective
function;
t2
f
t | 'Z (t ) | dt
(7)
t1
³
Where t1 and t2 are the study time limits and
'Z( t ) represents the speed deviation of the generator.
3.1. The complete formulation of the optimization problem
The coordinated design of PSS and SVC controller parameters can be converted to an optimization problem. The
goal is to minimize the ITAE performance index subject to some constraints. These constraints show the upper and
lower limits of each parameter. The proposed optimization problem is formulated as follows:
min OF
n
¦ ³
t2
to
:
i 1
subject
t1
tsim
0
t. ª
¬ 'Zi º
¼ dt
min
max
K PSS
, i d K PSS , i d K PSS , i
T1,min
d T1,i d T1,max
i
i
(8)
T2,min
d T2,i d T2,max
i
i
T3,min
d T3,i d T3,min
i
i
T4,min
d T4,i d T4,max
i
i
min
max
K pt
d K pt d K pt
K itmin d K it d K itmax
By solving the proposed optimization problem the values of the PSS gain ( K PSS ) and time constants ( T1 to T4 )
and the parameters of PI controllers of SVC ( K pt , Kit ) are determined during the simulation time ( t sim ).
4. The hybrid BF-PSO algorithm
For any optimization process in order to obtain an area having a global minimum, it is essential that the whole
domain be well explored. When that area is detected, the appropriate tools must be employed to use this area and to
obtain the optimum as fast as possible. This task is hardly achieved by using only one method [23]. Therefore, in
69
M.R. Esmaili et al. / Procedia Technology 11 (2013) 65 – 74
this paper a hybrid optimization method is used for tuning the parameters of the PSS and SVC coordinately. This
method is named BF oriented by PSO algorithm (BF-PSO). It has a wide range search capability and high
convergence speed. In this section, the BF algorithm and the PSO method are first introduced. Then, the BF-PSO
combinational algorithm is presented.
4.1. BF Algorithm
BF algorithm is based on foraging process of Escherichia coli (E.coli) bacteria living in the intestine of human.
This algorithm, that consists of four steps are named chemotactic, swarming, reproduction, and elimination and
dispersal respectively, is explained in [29].
4.2. Application of PSO in BF algorithm
In the BF-PSO algorithm, the φ is updated with PSO rules. PSO is a stochastic optimization method has been
inspired by social behavior of bird flocking or fish schooling. In PSO algorithm the potential solutions, called
particles, is defined with two values of pid(t ), vid(t) and updated with two best values of Pbest(t) , gbest(t) [30]. The
Pbest(t) is the best position of ith particle achieved and gbest(t) is the global best value of any particle in the population.
During the chemotactic step new velocity and position of each particle, are called as tumble direction, is updated
according to the following equations:
vid (t 1) w(t ) ˜ vid (t ) c1 ˜ rand ( p best i , d (t ) p id (t )) c 2 ˜ rand ( g best d (t ) xid (t ))
pid (t 1)
pid (t ) vid (t 1)
(9)
(10)
Where
Rand: random value of [0, 1]
c1, c2, w: The PSO parameters
It should be mentioned that the v parameter in equation (9) is utilized instead of φ parameter in BF algorithm to
orient every bacterium [22]. This will cause to have more convergence speed in BF-PSO algorithm against of BF
algorithm. Simulation results will imply the discussion as mentioned above.
4.3. The proposed algorithm flowchart
Figure 3 shows the flowchart of the proposed method for coordinated desige of the SVC and PSS controllers. In
this way, by application of BF-PSO, PI controller parameters (mentioned in section 2) and PSS parameters are
tuned.
70
M.R. Esmaili et al. / Procedia Technology 11 (2013) 65 – 74
start
Compute the objective function by
running time domain Simulation to
minimize ITAE(i,ch) , where i is
the bacterium number
Input initial
data
Elimination and
dispersal loop,
counter, EL=EL+1
ITAE(i,j)<
ITAE(i,j-1)
No
Yes
stop
EL>N
Yes
No
Swim, m=m+1
SW(i)=m
Reproduction loop
counter, K=K+1
No
SW(i)<Ns
K>Nre
Yes
Tumble
Chemotactic loop
counter, j=j+1
No
i>S
j>Nc
Yes
Yes
No
Update Δ using
PSO rules
Fig. 3. Proposed algorithm flowchart
5. Simulation result
In this study, BF-PSO algorithm is used to design parameters of PSS and SVC controller coordinately by solving
equation (10). In order to validate the proposed method, the simulations are carried out multi-machine power system
in MATLAB software. The ranges considered for PSS parameters of multi-machine system are given in [12]. For PI
controllers given in Figure 2, the parameter ranges are
0 K pt 200
and
0 K it 10 .The BF-PSO
algorithm parameters are presented in appendix.
These parameters are determined using trial and error method. In this study in order to evaluate the performance
of BF-PSO method, its results are compared with results of PSO and BF methods. Values of the C1 and C2 in PSO
are 2.05 [31]. The number of particles is the same as number of bacteria in the in BF and BF-PSO methods.
Furthermore, by using the settings introduced in [30] number of iterations is considered to be equal to 100.
Now the performance of the proposed coordinated method is studied for a multi-machine system shown in Figure
4 with a SVC of 300 MVA installed at bus 8 [19-20]. The parameters of this two-area system are given in [1]. The
parameters of PSS and PI controllers of SVC obtained by BF-PSO algorithm are given in Table 1. Also, the
parameters of PSS and PI controller of SVC obtained by other algorithms are given in Table 2.
M.R. Esmaili et al. / Procedia Technology 11 (2013) 65 – 74
6
Z1
G1
Z3
Z2
Load 1
SVC
2
10
Z2
Z3
XT
9
Z3
G2
11
Z1
XT
3
G3
Z3
XT
Load 2
1 XT
8
7
5
4
G4
Fig. 4. Two-area 4 machine power system [1] with SVC
Table 1. Parameters of PSS and PI controller of SVC for Multi-Machine power system given by BF-PSO algorithm
Machine
Kpss
T1
T2
T3
T4
G1
16
0.53
0.38
0.53
0.38
G2
10
0.86
0.75
0.86
0.75
G3
10
0.81
0.65
0.81
0.65
G4
17
0.74
0.84
0.74
0.84
PI-Controller SVC
Kpt
Kit
Qc
Qi
0.19
162.3
100
-100
Table 2. Parameters of PSS and PI controllers of SVC for multi-machine power system given by PSO and BF algorithms
Generator
G1
PSO optimized
parameters
T1=0
T2=0
T3=0
T4=0
Kpss=15.36
G2
G3
G4
SVC
BF optimized parameters
T1=5.45
T2=7.61
T3=5.45
T4=7.61
Kpss=48.07
T1=3.18
T2=2.66
T1=9.21
T2=10
T3=3.18
T4=2.66
T3=9.21
T4=10
Kpss=14.18
T1=3.95
T2=4.45
Kpss=12.42
T1=6.96
T2=9.85
T3=3.95
T3=6.96
T4=4.45
T4=9.85
Kpss=21.22
T1=2.98
T2=3.28
Kpss=51.19
T1=6.64
T2=8.08
T3=2.98
T3=6.64
T4=3.28
T4=8.08
Kpss=11.13
Kpt=3.57
Kit=101.9
Kpss=17.23
Kpt=9.73
Kit=36.46
Qc=100
Qc=100
Qi=-100
Qi=-100
71
72
M.R. Esmaili et al. / Procedia Technology 11 (2013) 65 – 74
Following a 200 m-sec three-phase fault at bus 8 at t
in Figures 5(a) and 5(b), respectively.
1sec , the peed deviation of generators G1 and G3 are shown
(b)
(a)
Fig. 5. System response for a 100 m-sec, 3-phase fault at Bus 8:
(a) Speed deviation of G1 and (b) Speed deviation of G3
From Figures 5(a) and 5(b), it can be seen that the transient performance of BF-PSO algorithm is better than those
of conventional and PSO algorithms. The SVC bus voltage is shown in Figure 6.
From Figures 5 and 6, it can be concluded that the coordinate design of PSS and SVC using BF-PSO method
improves the performance of power system in comparison with other algorithms.
Voltage terminal of SVC bus (p.u)
1.1
BF-PSO
PSO
BF
1.05
1
0.95
0.9
0.85
0.8
0.75
0
1
2
3
4
5
6
time(sec)
Fig.6. Voltage terminal of SVC Bus for a 100 m-sec, 3-phase fault at Bus 8
Figure 7 also represents that the objective function value corresponding to BF-PSO algorithm is converged faster
than the other methods. Furthermore, this figure represents that other algorithms converged to local optimal points.
73
M.R. Esmaili et al. / Procedia Technology 11 (2013) 65 – 74
14
x 10
-3
BF-PSO
BF
PSO
13
12
cost function
11
10
9
8
7
6
5
4
0
5
10
15
20
25
30
35
40
45
50
iteration
Fig.7. Convergence properties of different optimization algorithms for Two-area 4 machine power system
6. Conclusions
In this paper a new method for coordinated design of parameters of PSS and SVC in power system is presented.
For this purpose, the design procedure is converted to an optimization problem. In order to solve this optimization
problem in a wide search region with a high convergence speed, a hybrid method named BF-PSO was used. For
evaluation of the proposed coordinated algorithm, its performance is compared with conventional, PSO and BFA
based methods. Simulation and analytical results for multi-machine power system confirmed the effectiveness and
the robustness of the proposed design technique to enhance the dynamic characteristics of the power system.
Appendix
Parameters of BF-PSO algorithm
parameters
S
Nc
Ns
Nre
Ned
dattract
ωattract
Value
50
5
4
5
2
0.01
0.4
hrepellent
0.01
ωrepellent
k
k
C1
C2
0.42
0.5
2
2.05
2.05
References
[1]. Kundur, P., “Power System Stability and Control. Ontario,” McGraw-Hill, 1994.
[2]. Yuan, S.Q., Fang, D.Z., “Robust PSS Parameters Design Using a Trajectory Sensitivity Approach,” IEEE Trans Power Syst, 2009,Vol. 24,
No. 2, p. 1011-1018,.
[3]. Kazemi, A., Jahed Motlagh, M.R., Naghshband, A.H., “Application of a new multi-variable feedback linearization method for improvement
of power systems transient stability,” Int J Electr. Power Energy Syst, 2007,Vol. 29, No. 4, p. 322-328.
[4]. Bomfim, A.L.B., Taranto, G.N., “Simultaneous tuning of power system damping controllers using genetic algorithms,” IEEE Trans. Power
Syst, 2000,Vol. 15, No. 1, p. 163-169.
[5]. Sharma, P.R., Kumar, A., “Optimal location for shunt connected FACTS devices in a series compensated long transmission line,” Turk J
Elec. Eng & Comp Sci., 2007, Vol. 15, No. 3, p. 321-328.
[6]. Abido, M.A., “A novel approach to conventional power system stabilizer design using tabu search,” Int J Electr Power Energy Syst,
1999,Vol. 21, No. 6, p. 443-454.
[7]. Eslami, M., Shareef, H., Mohamed, A., Khajehzadeh, M., “Coordinated design of PSS and SVC damping controller using CPSO,” Power
Engineering and Optimization Conference (PEOCO), 2011.
74
M.R. Esmaili et al. / Procedia Technology 11 (2013) 65 – 74
[8]. Eslami, M., Shareef, H., Mohamed, A., Khajehzadeh, M., “Particle Swarm Optimization for Simultaneous Tuning of Static Var
Compensator and Power System Stabilizer,” Przegląd Elektrotechniczny, 2011, p. 343-347.
[9]. Abido, M.A., “Robust design of multimachine power system stabilizers using simulated annealing,” IEEE Trans Energy convers, 2000,Vol.
15, No. 3, p. 297-304.
[10]. Shayeghi, H., Shayanfar, H.A., Safari, A., Aghmasheh, R., “A robust PSSs design using PSO in a multi-machine environment,” Energy
Convers Manage, 2010,Vol. 51, No. 4, p. 696–702.
[11]. Shayeghi, H., Shayanfar, H.A., Jalilzadeh, S., Safari, A., “Multi-machine power system stabilizers design using chaotic optimization
algorithm,” Energy Convers Manage, 2010, Vol. 51, No. 7, p. 1572–80.
[12]. Das, T.K.,. Venayagamoorthy, G.K., Aliyu, U.O., “Bio-Inspired Algorithms for the Design of Multiple Optimal Power System Stabilizers:
SPPSO and BFA,” IEEE Trans Industry Appl, 2008 ,Vol. 44, No. 5, p. 1445-1457.
[13]. Mutale, J., Strbac, G., “Transmission network reinforcement versus FACTS: an economic assessment,” IEEE Trans Power Syst, 2000,Vol.
15, No. 3, p. 961-967.
[14]. Shayeghi, H., Shayanfar, H.A., Jalilzadeh, S., Safari, A., “TCSC robust damping controller design based on particle swarm optimization for
a multi-machine power system,” Energy Convers. Manage, 2010, Vol. 51, No. 10, p. 1873-1882.
[15]. Ali, E.S., Abd-Elazim, S.M., "Coordinated design of PSSs and TCSC via bacterial swarm optimization algorithm in a multimachine power
system," International Journal of Electrical Power and Energy Systems , 2012, Vol. 36, No. 1, p. 84-92.
[16]. Shayeghi, H., Shayanfar, H.A., Jalilzadeh, S., Safari, A., “A PSO based unified power flow controller for dampi ng of power system
oscillations,” Energy Convers. Manage, 2009, Vol. 50, No. 10, p. 2583-2592.
[17]. Shayeghi, H., Shayanfar, H.A., Jalilzadeh, S., Safari, A., “Design of output feedback UPFC controller for damping of electromechanical
oscillations using PSO,” Energy Convers Manage, 2009, Vol. 50, No. 10, p. 2554-2561 .
[18]. Shayeghi, H., Shayanfar, H.A., Jalilzadeh, S., Safari, A., “COA based robust output feedback UPFC controller design,” Energy Convers
Manage, 2010, Vol. 51, No. 12, pp. 2678–2684.
[19]. Panda, S., Padhy, N.P.,” Optimal location and controller design of STATCOM for power system stability improvement using PSO,” J
Franklin Institute, 2008, Vol. 345, No. 2, pp. 166-181.
[20]. Liu, Q.J., Sun, Y.Z., Shen, T.L., Song, Y.H.,” Adaptive nonlinear coordinated excitation and STATCOM controller based on Hamiltonian
structure for multimachine power system stability enhancement,” IEE Proc Generat Transm Distrib, 2003, Vol. 150, No. 3, pp. 285-294.
[21]. Bian, X.Y., Tse, C.T., Zhang, J.F., Wang, K.W., “Coordinated design of probabilistic PSS and SVC damping controllers,” Int J Electr
Power Energy Syst, 2011, Vol. 33, No. 3, pp. 445-452.
[22]. Korani, W.M., “Bacterial foraging oriented by particle swarm optimization strategy for PID tuning,” Genetic and Evolutionary Computation
Conference, GECCO Atlanta GA USA, 2008, p. 1-4.
[23]. Rajasekhar, A., Jatoth, K.R., Abraham, A., Snasel,V., “A novel hybrid ABF-PSO algorithm based tuning of optimal FOPI speed of optimal
FOPI speed controller for PMSM Drive,” 12th International Carpathian Control Conference, 2011, p. 324-329.
[24]. Hooshmand, R., Ezatabadipour, M., “Corrective action planning considering FACTS allocation and optimal load shedding using bacterial
foraging oriented by particle swarm optimization algorithm,” Turk J Elec Eng & Comp Sci, 2010, Vol. 18, No. 4, p. 597-612.
[25]. AL-Biati, M.A., El-kady, M.A., Al-ohaly, A.A., “Dynamic stability improvement via coordination of static var compensator and power
system stabilizer control actions,” Electric power systems research , 2001, Vol. 58, No. 1, pp. 37-44.
[26]. Gelen, A., Yalcinoz, T., “Experimental studies of a scaled-down TSR-based SVC and TCR-based SVC prototype for voltage regulation and
compensation,” Turk J Elec Eng & Comp Sci, 2010, Vol. 18, No. 2, pp. 147-157.
[27]. Fraile-Ardanuy, J., Zufiria, P.J., “Adaptive Power system stabilizer using ANFIS and genetic algorithms,” Computational Intell Bioinspired
Syst, IWANN'05 Proceedings of the 8th international conference on Artificial Neural, 2005, p. 1124-1131.
[28]. Fraile-Ardanuy, J., Zufiria, P.J., “Design and comparison of adaptive power system stabilizers based on neural fuzzy networks and genetic
algorithms,” Neurocomputing, 2007, Vol. 70, No. 16-18, p. 2902-2912.
[29]. Hooshmand, R., Parastegari, M., Morshed, MJ., “Emission, reserve and economic load dispatch problem with non-smooth and non-convex
cost functions using the hybrid bacterial foraging-nelder mead algorithm,” Appl Energy, 2012, Vol. 89, No. 1, pp. 443–453.
[30]. Sahoo, N.C., Panigrahi, B.K., Dash, P.K., Panda, G., “Application of a multivariable feedback linearization scheme for STATCOM
control,” Electr Power Syst Res, 2002, Vol. 62, No. 2, pp. 81-91.
[31]. Mancer, N., Mahdad, B., Srairi, K., “Multi objective optimal reactive power flow based STATCOM using three variant of PSO,”
International Journal of Energy Engineering , 2012, Vol. 2, No. 2, pp. 1-7.