Solving Reactive Power Optimization Problem Using Weight Improved PSO Algorithm

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Proc. of the International Conference on Electrical, Computer, Communications and Mechatronics Engineering (ICECCME)
7-8 October 2021, Mauritius
978-1-6654-1262-9/21/$31.00 ©2021 IEEE
Solving Reactive Power Optimization Problem
Using Weight Improved PSO Algorithm
Shaima Hamdan Shri
Electrical Techniques Department
Al Suwaira Technical Institute
Middle Technical University
Iraq
shaima123@mtu.edu.iq
Mohammed B. Essa
Electrical Techniques Department
Al Suwaira Technical Institute
Middle Technical University
Iraq
Moh.Bahlol@mtu.edu.iq
Ayad Fadhil Mijbas
Electrical Techniques Department
Al Suwaira Technical Institute
Middle Technical University
Iraq
eaadfadhil@mtu.edu.iq
Abstract— The losses in electrical power systems are a
significant problem. The proper adjusting of reactive
power resources is one of the ways for minimizing the
Power Loss ( P_L ) in any power system. Reactive Power
Optimization ( RPO ) is recorded as a complex
optimization problem. The calculations of this problem are
a part of Optimal Power Flow ( OPF ) calculations . In this
work , a new algorithm called Weight Improved Particle
Swarm Optimization ( WIPSO ) algorithm is presented on
enhancing the function of weight parameters for solving
this problem. Weight Improved Particle Swarm
Optimization is presented as a useful optimization tool to
search for optimal settings of reactive power independent
variables during dealing with a number of equality, and
inequality constraints at same time by minimizing the goal
function ( P_L ) . The Weight Improved Particle Swarm
Optimization is tested on the IEEE 14 - bus system.
Simulation results obtained WIPSO was effective, and
attain the best results and has best convergence
characteristic and performance in terms of decreasing
( P_L ) compared to simple ( PSO) algorithm .
Keywords:- Optimal Power Flow ( OPF ) , Reactive
Power Optimization ( RPO ), Weight Improved Particle
Swarm Optimization ( WIPSO ) algorithm.
I. INTRODUCTION
The Reactive Power Optimization ( RPO ) problem
is considered a complicated, multi-variables, and
non_linear optimization problem.
So, the basic aims of this study were to Reactive Power
Optimization, enhance voltage profile, and decrease
power losses for the system. And these aims can be
attained via proper change of reactive power
independent parameters such as generator voltage(VG)
the value of(VAR) source that injected from the shunt
capacitors(QC), in addition to transformer taps(Tap),
[1] . In the recent years , the Optimal Power Flow (
OPF ) problem as usual abundant interest due to its
ability to find the optimal solutions for look the systems
security [2],the calculations of (RPO) problem are
considered as a part of the(OPF) calculations.
Carpentier is a French electrical engineer who was the
first to situation the concept of(OPF)in the early 1960 s
[ 3 , 4]. Thereafter, many researchers have been various
studies to solving(OPF) problems through utilizing
multi methods, such as recursive quadratic, linear and
nonlinear programming and interior point method [5-8],
etc. Sun et al. have presented newton approach for the
solution of (OPF) [9]. Lai et al. have presented
improved Genetic Algorithm (GA) for solving (OPF)
[10].
In the past, a number of traditional optimization
techniques has been presented for solving (RPO)
problem like Interior Point Methods(IPM) [11], Linear
Programming(LP) [12], nonlinear program
ing[13], Gradient Search(GS) [14], Quadratic
Programming(QP) [15] ,and Dynamic
Programming(DP), etc. [16]. Those algorithms have
some restrictions like, unable to deal with non-
continuous complex optimization problems and slip to
local optimal. So, it becomes necessary to improve and
developing methods are able for avoiding these
restrictions.
Recently, various computational optimization
techniques have been offered to avert the limitations of
traditional optimization algorithms like; Genetic
Algorithm (GA) [17], hybrid GA IPM [18], fuzzy
technique [19], Genetic Search (GS) [20], and Particle
Swarm Optimization (PSO) [21], Lateef et al.,
Presented Fully Informed PSO (FIPSO) to a solution of
(RPO) problem. The researchers applied this approach
on IEEE 6 – Bus, 18 - Bus and 30 – Bus systems to
decrease the loss [22]. Mehdi Mehdinejad et al.
investigated the improvement hybrid PSO and
Imperialist systems. Competitive ( PSO – ICA ) so as
to solution the ( RPD ) problem in power system.
IEEE 118 – bus and 57 – bus systems are utilized for
solution of this problem with two objectives for
decreasing of Total Voltage Deviation ( TVD ) Power
Habibi et al. suggested a new [23]. )
L
P ( Loss
hybrid algorithm to manage discrete and continuous
variables for solving (RPD) problem [24].
The voltage deviation problem could be mitigated
by managing the reactive power of the systems, by
means choosing proper capacitorcompensation capacity
2021 International Conference on Electrical, Computer, Communications and Mechatronics Engineering (ICECCME) | 978-1-6654-1262-9/21/$31.00 ©2021 IEEE | DOI: 10.1109/ICECCME52200.2021.9590931
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or installing a dynamic reactive power compensation
device [25].
Between all these algorithms, PSO has appeared as
a beneficial tool for engineering global optimization in
solving this problem. The benefits of PSO technique are
simple, fast, easy to implement, but it does not mean
that the PSO does not contain some disadvantages.
However, for solving the complex and noncontinuous
problem this algorithm was declining very easily to
local minimal. The weight parameters is very essential
in PSO algorithm because it is effects on precision and
speed of the convergence. So, many researchers have
proposed a new enhancements on the function of weight
parameters. So, in this study to avoiding these
disadvantages, and to boost, develop the seeking,
WIPSO algorithm is presented based on enhancing the
function of weight parameters for solving this problem.
Undeniably, this improvement can be the active method
to slip very easily from local optima compared with the
Simple PSO.The WIPSO algorithm is utilized as an
optimization tool so as to search for best values of the
reactive power independent parameters (i.e. VG , Tap
and QC ) in order to decrease power loss (PL) and boost
voltage profile. The WIPSO is evaluated and examined
on IEEE 14-bus system for solving RPO problem.
II. PROBLEM FORMULATION
A. Objective function:
The great purpose of RPO problem in this work is to
reduce the Power Loss ( PL ) for the system via a proper
control of reactive power independent parameters ( VG,
Tap, and QC ), the PL can be expressed as shown below
[26]:
( )
(
)
Ntl 2 2
K i j i j i j
K=1
Min P = G V +V - 2VV cos -
L
φ φ
(1)
From Eq. (1), PL: Power loss, Ntl: Number of
branches , GK : Conductance of branch K , ( Vi , and Vj
) : Are the voltage magnitude at bus i and j . ϕi, ϕj: Are
the difference angles voltage at bus i and j.
B. Constraints:
1. Equality Constraints :
These constrains are Load Flow equations and
define as follows [27]:
( ) ( )
(
)
NB
Gi Di i j ij ij ij ij
j=1
P -P = VV G cos
δ +B sin δ
 (2)
( ) ( )
(
)
NB
Gi Di i j ij ij ij ij
j=1
Q -Q = VV G sin
δ - B cos δ
 (3)
From the above equations, ( PGi , QGi ) are real and
reactive power generation respectively, ( PDi , QDi ) are
the real and reactive power load demand
respectively,(Gij, Bij) are the mutual and susceptance
conductance between i and j bus.
δij is voltage angle value in the bus i and j.
2. Inequality Constraints:
These constrains contain[28]:
Constrains of generator: these constrains have
voltage in generator buses (VG) and reactive power
output (QC) of all generators are limited by their min
and max bounds:
V V V ,i 1,...., N
Gi_min Gi Gi_max G
≤ ≤ = (4)
Q Q Q ,i=1,...., N
Gi_min Gi Gi_ max G
≤ ≤ (5)
Transformer constrains: this constrains have lower
and upper bounds as shown below:
Tap Tap Tap ,i=1,...., N
i_ min i i_max T
≤ ≤ (6)
Shunt(VAR) source ( QC ) constrains: switch-able
(VAR) compensation ( QC) are bounded as shown
below:
Q Q Q , i=1,...., N
Ci _ min Ci Ci_ max C
≤ ≤ (7)
Security constrains: t
j
his constrain contain the limit
of load bus voltages as shown below:
V V V , i=1,...., N
Li_ min Li Li_ max PQ
≤ ≤ (8)
C. General Objective Function:
In this work, the variables ( VL , QG ) can be
merged with Eq. ( 1) as a quadratic term, so Eq. ( 1 )
can be represented as explain below [28]:
2 2
NL N G
lim lim
Min F= P +λ V -V +λ Q - Q
L V li li Q Gi Gi
i=1 i=1
   
 
   
   
(9)
from the above equation,PL depicts in Eq.(1), λV ,
λQ are the penalty terms and these terms are big
positive constants. NL depict the number of loads buses
that violate the limits. NG depict the number of reactive
power output of generator buses that outside the
bounds. Vli lim , Q Gi lim are described as shown
below[28]:
min min
V if V V
Li Li Li
lim
VLi
max max
V if V V
Li Li Li
 
<
 
=
 
 
>
 
(10)
min min
Q if Q Q
Gi Gi Gi
lim
QGi
max max
Q if Q Q
Gi Gi Gi
 
<
 
=
 
 
>
 
(11)
III. OPTIMIZATION PROCESS
A. Simple PSO algorithm:
In 1995, Eberhart and Kennedy have proposed the
basic concept of the PSO algorithm. PSO has better
kind to stochastic optimization technique , They
inspired it from the social behavior of birds and fish
flocking looking for food [29]. Each bird in this
optimization algorithm is presented as a particle while
the whole particles make a group or swarm. The
advantages of this algorithm are fast, simple, can be
utilized to solving complex optimization problems, and
doesn't has the mutation, and crossover operations such
as a Genetic Algorithm. Each individual in PSO
algorithm has the best position discover by the
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experience of the individual itself, and it's saved in the
memory that called local best position(Pbest), and the
best position discovered between all (Pbest)in the
swarm is also saved in memory that knows as global
best position(Gbest). The velocity and position
from(Pbest) and (Gbest) locations will be changed by
using Eq. (12)and Eq. (13) [30].
( ) ( )
k 1 k k
k k k
V W V C old R P - X C old R G - X
i PSO i 1 1 i 2 2 i
best i best i
 
   
+= + +
 
   
   
 
(12)
k 1 k k 1
X X V
i i i
+ +
= + (13)
From the above equations:
V: The velocity of agent.WPSO : The inertia
weight.C1old, C2old: The old constant learning factors
between (0─2.5). R1,R2: The uniformly distributed
positive number within limit ( 0 ─ 1 ) . Pbest (i) :- Best
position of agent. Gbest (i) :- Global best position of agent.
X i : Position of agent [31].
In this work,(WPSO) given in Eq. (12), is reducing
linearly from (0.9 to 0.4) during the computational run
so as to make the balancing between Pbest(i) and Gbest(i)
position .
W - W
max min
W W - iter
PSO max max iteration
= ∗ (14)
Where,Wmax: The max. inertia.Wmin: The min.
inertia. iter: :The present iteration. maxiteration : The max.
iterations.
B. Weight Improved Particle Swarm Optimization (
WIPSO ) algorithm
The Simple PSO algorithm mainly relies on its
parameters, and this made it difficult and sometimes
unable to reach the precise solution criteria in some
cases, especially when the number of variables of the
optimization problem was very large. WIPSO algorithm
is utilize to improve the quality, search behavior and the
performance of Simple ( PSO ) algorithm , so as to get
best global solution, the Simple PSO technique was
enhanced by altering the weight parameter, self-
confidence ( cognitive factor ) and swarm confidence (
social factor ) . Based on Eq. (12) the velocity equation
for the proposed WIPSO algorithm is obtained as
follows[32]:
( ) ( )
k 1 k k
k k k
V W V C new R P - X C new R G - X
i new i 1 1 i 2 2 i
best i best i
   
+= + +
   
   
(15)
W W W R
new min PSO 3
= + ∗ (16)
1 1
1 1
C max - C min
C new C max - iter
max iteration
= ∗ (17)
2 2
2 2
C max - C min
C new = C max - iter
maxiteration
∗ (18)
From the above equations:
R3:The uniformly distributed positive number within
limit (0 ─ 1). WPSO: Depicts in Eq. (14).
C1max ,C1min:The max. and min. cognitive factor.
C2max ,C2min:The max. and min. social factor.
iter:The present iteration. maxiteration : The max.
iterations.
C. Representation of WIPSO algorithm for solving RPO
problem
The WIPSO based approach to solving RPO
problem steps are summarized in Fig.1 [32].
Fig1. Flowchart of Weight Improved Particle Swarm Optimization
( WIPSO ) Algorithm.
IV. CASE STUDY AND RESULTS
For testing the efficiency, ability and performance of
the presented WIPSO algorithm and also to discover the
optimal solution for RPO problem, WIPSO applied on
IEEE 14 - Bus system . The Simple PSO and WIPSO
algorithms have been developed , and simulated in
MATLAB program , and the number of maximum
iterations and particles (n) in this study is 200 and 50,
respectively. IEEE 14-bus System involves 20
branches, 5 generators, 1 reactive power VAR source
compensation (capacitor bank) and 3 transformers; bus,
line, generator data, the bounds of reactive power (QG)
for generators and other operating data were tabulated
in reference [33]. TableI shows constrains of
independent variables. This system has 9 dimensions
search space that need to be optimized as listed in
TableII. Simulation results of this system were tested
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through a series of comparisons among Simple PSO and
WIPSO with other optimization methods in the
literature such as EP and SARGA [31], which are
reported below in Table II . From this table it's clear that
the reduction in PL from the base case are 9.6% at
WIPSO, 9.1% at PSO, 1.5% at Evolutionary
Programming (EP)and 2.5% at Self-Adaptive Real
coded Genetic ( SARGA) algorithms. Fig.2 and Fig.3
shown the convergence of Simple PSO and WIPSO
algorithms for this system and Fig. 4 demonstrates the
voltage profile for this system with Simple PSO and
WIPSO algorithms. Fig.4 it's explain that the average
voltage at initial was about 1.048 and at PSO is about
1.059 and at WIPSO was about 1.082.
TABLE I. Control variables bounds for ( IEEE 14-Bus ) system .
Power
system type Independent Variables Minimum
(p.u.)
Maximum
(p.u.)
IEEE
14 - Bus
Generator bus ( VG ) 0.95 1.10
Transformer tap (Tap) 0.90 1.10
VAR sources (QC) 0.0 0.20
TABLE II. Simulation Implications of ( IEEE 14 -Bus ) System.
Control
Variables
Base
Case (WIPSO) ( PSO) ( EP )
[34]
(SARGA)
[34]
V G -1 1. 060 1. 100 1. 100 - -
V G – 2 1. 045 1. 087 1. 086 1. 029 1. 096
V G - 3 1. 010 1. 058 1. 056 1. 016 1. 036
V G – 6 1. 070 1. 096 1. 067 1. 097 1. 099
V G - 8 1. 090 1. 100 1. 060 1. 053 1. 078
Tap4-7 0.978 0.975 1.019 1. 04 0. 95
Tap4-9 0.969 0.975 0.988 0. 94 0. 95
Tap5-6 0.932 1.020 1.008 1. 03 0. 96
QC-9 0.19 0.174 0.185 0.18 0. 18
Reduction
in PL (%). 0 9. 6 9. 1 1. 5 2. 5
Total PL
( Mw ). 13 .55 12. 246 12.315 13.346 13. 216
Fig 2. The Convergence for (IEEE 14-Bus) System With
Simple ( PSO ) Algorithm.
Fig 3. The Convergence for ( IEEE 14-Bus ) System With ( WIPSO )
Algorithm.
Fig 4 .The Voltage Profile for (IEEE 14-Bus) System.
V. CONCLUSIONS
In this action, the main aim is to enhance the
performance, quality and to increase computational
speed and to attain good accuracy for solution and to
avoid premature convergence of Simple PSO technique,
WIPSO algorithm is presented for solving RPO
problem. This technique is based on enhancement of
weight parameters function. WIPSO algorithm is
utilized as a useful tool to search for optimal tuning of
independent variables (i.e.VG,Tap and QC) by minimize
the objective function. The main goal of utilizing the
objective function is to decreasing of Power Loss ( PL )
and enhancing voltage profile of the system through a
proper control for the reactive power devices (i.e.
independent variables). The WIPSO algorithim is tested
and applied on IEEE 14 -Bus system. From the
simulation implications, it's confirm that WIPSO
algorithm is best in convergence speed characteristic to
obtain optimal values of reactive power devices (i.e.
independent variables) that decreasing the PL as well as
improving voltage profile of the system. In addition, the
simulation implications demonstrate the efficiency and
potential of presented WIPSO algorithm for solving
RPO problem and these results confirm that WIPSO
algorithm is able to obtain best quality solutions in
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lesser time than Simple PSO for solving RPO and other
complex problem in the power system. With its
benefits, it is believe that WIPSO algorithm has
recorded as one of the good candidate algorithms and
has a great interest from the authors due to versatility,
capability and achieve fruitful result in solving complex
and multi-variables problem such as RPO problem and
cost minimization.
ACKNOWLEDGMENT
The authors would like to offer thanksgiving Al
Suwaira Technical Institute , Middle Technical
University for their support and encouragement .
REFERENCES
A.H. Khazali,and M. Kalantar, "Optimal reactive power
dispatch based on harmony search algorithm", Electr Power
Energy Syst ,Vol.33,pp.684–692, 2011.
[1]
M. Al-Kaabi1, and L. Al-Bahrani, "Modified Artificial Bee
Colony Optimization Technique with Different Objective
Function of Constraints Optimal Power Flow", International
Journal of Intelligent Engineering and Systems, Vol.13,
No.4,pp.378-388, 2020.
[2]
J.Carpentier, “Contribution to the economic dispatch
problem,”Bulletin Society Francaise Electriciens, Vol. 3, No.
8, pp. 431- 447,1962.
[3]
Sh.H.Shri, A.F.Mijbas "
Chaotic theory incorporated with PSO
algorithm for solving optimalreactive power dispatch problem
of power system", Indonesian Journal of Electrical
Engineering and Computer Science, Vol. 22, No.3 PP. 1739-
1747, 2021.
[4]
H. Habiabollahzadeh, G.X. Luo, and A. Semlyen
,"Hydrothermal optimal power flow based on a combined linear
and nonlinear programming methodology". IEEE Trans Pwr
Syst , Vol.4,No.2,pp.530-537, 1989.
[5]
K. Aoki, A. Nishikori, and R.T. Yokoyama. "Constrained load
flow using recursive quadratic programing", IEEE Trans Pwr
Syst Vol.2,No.1,pp.8-16, 1987.
[6]
X .Yan,and V.H. Quintana. "Improving an interior point based
OPF by dynamic adjustments of step sizes and tolerances",
IEEE Trans Pwr Syst ,Vol.14,No.2,pp.709-717, 1999.
[7]
J.A. Momoh,and J.Z. Zhu ,"Improved interior point method for
OPF problems", IEEE Trans Pwr Syst ,Vol.14,No.3,pp.1114-
1120,1999.
[8]
D.I. Sun, B. Ashley, B. Brewer, A. Hughes, and W.F. Tinney,
“Optimal power flow by Newton approach”, IEEE Trans Pwr
Appar Syst , Vo1. 103, No. 10, pp. 2864-2875, 1984.
[9]
L.L. Lai, and J.T. Ma ,“Improved genetic algorithms for
optimal power flow under both normal and contingent states”,
Int J Elec Pwr Energy Syst , Vo1. 19, No. 5, pp. 287-292,1997.
[10]
S. Granville, “Optimal reactive dispatch through interior point
methods,” IEEE Trans. Power Syst., Vol. 9, No. 1, pp. 136–
146, 1994.
[11]
R. Hooshmand ,and M. Joorabian, “Application of artificial
neural networks in controlling voltage and reactive power”,
Scientia Iranica, Vol. 12, No. 1, pp. 99–108, 2005.
[12]
D. Pudjianto, S. Ahmed, and G. Strbac, “Allocation of VAR
support using LP and NLP based optimal power flows,” IEE
Proc. Gen. Trans. Dist., Vol. 149, No. 4, pp. 377–383, 2002.
[13]
D.C. Yu, J.E. Fagan, and B. Foote, "Aly AA. An optimal load
flow study by the generalized reduced gradient approach",
Elect Power Syst Res, Vol. 10,pp.47–53,1986.
[14]
K. Lo,and S. Zhu,"A decoupled quadratic programming
approach for optimal power dispatch", Electr Power Syst Res,
Vol. 22,pp.47–60. 1991.
[15]
F.C. Lu,and Y.Y. Hsu, "Reactive power/voltage control in a
distribution substation using dynamic programming", IEE
Proc. Gen. Trans. Distrib, Vol. 142 ,pp.639–645, 1995.
[16]
K. Iba, "Reactive power optimization by genetic algorithm",
IEEE Trans. Power Syst, Vol. 2 ,pp.685–692, 1994.
[17]
W. Yan, F. Liu, C.Y. Chung,and K.P.Wong, "A hybrid genetic
algorithm-interior point method for optimal reactive power
[18]
flow", IEEE Trans. Power Syst, Vol. 21 ,pp.1163–1168, 2006.
K.H. AbdulRahman, and S.M. Shahidehpour," Optimal reactive
power dispatch with fuzzy variables", IEEE ,pp.2188–2191,
1993.
[19]
Q..H. Wu,and J.T. Ma, "Genetic search for optimal reactive
power dispatch of power systems", IEEE Control Conf. No.
389, pp. 717–722. 1994.
[20]
H. Yoshida, K. Kawata, Y. Fukuyama, S. Takayama, and Y.
Nakinishi, "A particle swarm optimization for reactive power
and voltage control considering voltage security assessment",
IEEE Trans. Power Syst. Vol.15 ,pp.1232–1239, 2000.
[21]
H.T.U.I. Hassan, R. Zafar, S.A. Mohsin, O. Lateef, "Reduction
in power transmission loss using fully informed particle swarm
optimization". Int J Elect Power, Energy, Syst., Vol.43,pp. 364-
368, 2012.
[22]
M. Mehdinejad, B. Mohammadi, R.D.Bonab and K. Zare,
"Solution of optimal reactive power dispatch of power systems
using hybrid particle swarm optimization and imperialist
competitive algorithms", Int J Elect Power Energy Syst.,
Vol.83,pp. 104–116, 2016.
[23]
M. Ghasemi, S. Ghavidel, M.M. Ghanbarian, and A.Habibi ,
"A new hybrid algorithm for optimal reactive power dispatch
problem with discrete and continuous control variables", Appl
Soft Comput.,Vol. 22,pp.126-140, 2014.
[24]
I. Winarno, M. Ashari, and H. Suryoatmojo, "Voltage
Deviation Minimization of Grid Connected Wind Generation
System Using Hybrid PI-Fuzzy Logic Controller Based Static
Var Compensator",International Journal of Intelligent
Engineering and Systems, Vol.13, No.2, pp.216-227, 2020
[25]
K. Lenin, "Solving optimal reactive power problem by
enhanced fruit fly optimization algorithm and status of material
algorithm", International Journal of Applied Power Engineering
(IJAPE) , Vol. 9, No. 2, pp. 100-106, 2020
[26]
D. Ramakrishnan, and S. Pushparajan, "Unified Particle Swarm
Optimization Based Distributed Generation Placement in
Radial Power Systems",International Journal of Intelligent
Engineering and Systems, Vol.11, No.1, pp.104-112, 2018.
[27]
A. Rajan, and T. Malakar. “Optimal reactive power dispatch
using hybrid Nelder–Mead simplex based firefly algorithm”,
Int J Elec Pwr Energy Syst , Vo1. 66, pp. 9-24, 2015.
[28]
T. Kennedy, and R. Eberhart, "Particle swarm optimization", In
Proc. Of the IEEE international conf. on Neural networks, , pp.
1942-1948,1995.
[29]
M. Damdar and V.C.V. Reddy, “Capacitor Placement Using
Fuzzy And Particle Swarm Optimization Method For
Maximum Annual Savings” , ARPN Journal of Engineering
and Applied Sciences, Vol. 3, No. 3, PP. 25–30, 2008.
[30]
R.C. Eberhart and Y. Shi, “ Comparing inertia weights and
constriction factors in particle swarm optimization ”, In
Proceedings of the 2000 Congress on Evolutionary
Computation, (CEC00), pp. 84–88, 2000.
[31]
R. Arulraj, N.Kumarappa,and T. Vigneysh, “Optimal location
and sizing of DG and capacitor in distribution network using
Weight-Improved Particle Swarm Optimization Algorithm
(WIPSO)", IEEE Automation, Computing, Communication,
Control and Compressed Sensing (iMac4s), International
Multi-Conf. on 22-23 March 2013.
[32]
The IEEE 14-Bus Test System [online].
Availableat:http://www.ee.washington.edu/research/pstca
pf14/pg tca14bus.htm.
[33]
P. Subbaraj, and P.N. Rajnarayan, " Optimal reactive power
dispatch using self-adaptive real coded Genetic algorithm” ,
Electrical power system research., Vol. 79, No. 2, pp. 374-381,
2009.
[34]
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