Hybrid Quantum Genetic Particle Swarm Optimization Algorithm For Solving Optimal Reactive Power Dispatch Problem

International Journal of Recent Research in Electrical and Electronics Engineering (IJRREEE)
Vol. 1, Issue 1, pp: (7-17), Month: April - June 2014, Available at: www.paperpublications.org
Hybrid Quantum Genetic Particle Swarm
Optimization Algorithm For Solving Optimal
Abstract: This paper presents hybrid particle swarm algorithm for solving the multi-objective reactive power dispatch
problem. Modal analysis of the system is used for static voltage stability assessment. Loss minimization and
maximization of voltage stability margin are taken as the objectives. Generator terminal voltages, reactive power
generation of the capacitor banks and tap changing transformer setting are taken as the optimization variables.
Evolutionary algorithm and Swarm Intelligence algorithm (EA, SI), a part of Bio inspired optimization algorithm,
have been widely used to solve numerous optimization problem in various science and engineering domains. In this
paper, a framework of hybrid particle swarm optimization algorithm, called Hybrid quantum genetic particle swarm
optimization (HQGPSO), is proposed by reasonably combining the Q-bit evolutionary search of quantum particle
swarm optimization (QPSO) algorithm and binary bit evolutionary search of genetic particle swarm optimization
(GPSO) in order to achieve better optimization performances. The proposed HQGPSO also can be viewed as a kind of
hybridization of micro-space based search and macro-space based search, which enriches the searching behavior to
enhance and balance the exploration and exploitation abilities in the whole searching space. In order to evaluate the
proposed algorithm, it has been tested on IEEE 30 bus system and compared to other algorithms.
Keywords: quantum particle swarm optimization, genetic particle swarm optimization, hybrid algorithm
Optimization, Swarm Intelligence, optimal reactive power, Transmission loss.
Optimal reactive power dispatch problem is one of the difficult optimization problems in power systems. The sources of the
reactive power are the generators, synchronous condensers, capacitors, static compensators and tap changing transformers.
The problem that has to be solved in a reactive power optimization is to determine the required reactive generation at various
locations so as to optimize the objective function. Here the reactive power dispatch problem involves best utilization of the
existing generator bus voltage magnitudes, transformer tap setting and the output of reactive power sources so as to minimize
the loss and to enhance the voltage stability of the system. It involves a non linear optimization problem. Various
mathematical techniques have been adopted to solve this optimal reactive power dispatch problem. These include the gradient
method [1, 2], Newton method [3] and linear programming [4-7].The gradient and Newton methods suffer from the difficulty
in handling inequality constraints. To apply linear programming, the input- output function is to be expressed as a set of
linear functions which may lead to loss of accuracy.
Recently Global Optimization techniques such as genetic algorithms have been proposed to solve the reactive power flow
problem [8.9]. In recent years, the problem of voltage stability and voltage collapse has become a major concern in power
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Reactive Power Dispatch Problem
K. Lenin1, Dr.B.Ravindranath Reddy2, Dr.M.Surya Kalavathi3
1Research Scholar, 2Deputy Executive Engineer,
3Professor of Electrical and Electronics Engineering,
1,2,3Jawaharlal Nehru Technological University Kukatpally ,Hyderabad 500 085, India.
I. INTRODUCTION
Paper Publications

system planning and operation. To enhance the voltage stability, voltage magnitudes alone will not be a reliable indicator of
how far an operating point is from the collapse point [10]. The reactive power support and voltage problems are intrinsically
related. Hence, this paper formulates the reactive power dispatch as a multi-objective optimization problem with loss
minimization and maximization of static voltage stability margin (SVSM) as the objectives. Voltage stability evaluation
using modal analysis [10] is used as the indicator of voltage stability. The PSO is inspired by observing the bird flocking or
fish school [15]. A large number of birds/fishes flock synchronously, change direction suddenly, and scatter and regroup
together. Each individual, called a particle, benefits from the experience of its own and that of the other members of the
swarm during the search for food. Comparing with genetic algorithm, the advantages of PSO lie on its simple concept, easy
implementation and quick convergence. The PSO has been applied successfully to continuous nonlinear function [15], neural
network [16], nonlinear constrained optimization problems [17], etc.
Most of the applications have been concentrated on solving continuous optimization problems [18]. To solve discrete
(combinatorial) optimization problems, Kennedy and Eberhart [19] also developed a discrete version of PSO (DPSO), which
however has seldom been utilized. DPSO essentially differs from the original (or continuous) PSO in two characteristics.
First, the particle is composed of the binary variable. Second, the velocity must be transformed into the change of probability,
which is the chance of the binary variable taking the value one. Furthermore, the relationships between the DPSO parameters
differ from normal continuous PSO algorithms [20] [21]. Though it has been proved the DPSO can also be used in discrete
optimization as a common optimization method, it is not as effective as in continuous optimization. When dealing with
integer variables, DPSO sometimes are easily trapped into local minima [19]. Therefore, Yang et al. [22] proposed a quantum
particle swarm optimization (QPSO) for discrete optimization in 2004. Their simulation results showed that the performance
of the QPSO was better than DPSO and genetic algorithm. Recently, Yin [23] proposed a genetic particle swarm optimization
(GPSO) with genetic reproduction mechanisms, namely crossover and mutation to facilitate the applicability of PSO to
combinatorial optimization problem, and the results showed that the GPSO outperformed the DPSO for combinatorial
optimization problems. QPSO uses a Q-bit, defined as the smallest unit of information, for the probabilistic representation
and a Q-bit individual as a string of Q-bits. The Q-bit individual has the advantage that it can represent a linear superposition
of states (binary solutions) in search space probabilistically [22] [24]. Thus the Q-bit representation has a better characteristic
of population diversity than other representations. However, the performance of simple quantum-inspired PSO is often not
satisfactory and is easy to be trapped in local optima so as to be premature convergence. In the binary genetic particle swarm
optimization, genetic reproduction, in particular, crossover and mutation, have been combined to form a discrete version
particle swarm optimization, is suitable for solving combinatorial optimization problems. In QPSO, the representation of
population is Q-bit and evolutionary search is in micro-space (Q-bit based representation space). Differently, in GPSO the
representation is binary number and evolutionary search is in macro-space (binary space). It is quite different between QPSO
and GPSO in terms of representation and evolution operators.
However, as QPSO, the performance of GPSO is also often not satisfactory and is easy to be trapped in local optima so as to
be premature convergence. In contrast to the continuous PSO algorithm that has been widely studied and improved by a large
body of researchers, the discrete PSO and its application to combinatorial optimization problems has not been as popular or
widely studied. Therefore, it is an important topic to develop a new or improved discrete particle swarm optimization
algorithm with applications to combinatorial optimization problems. The performance of (HQGPSO) has been evaluated in
standard IEEE 30 bus test system and the results analysis shows that our proposed approach outperforms all approaches
investigated in this paper. The performance of (HQGPSO) has been evaluated in standard IEEE 30 bus test system and the
results analysis shows that our proposed approach outperforms all approaches investigated in this paper.
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II. Voltage Stability Evaluation
Paper Publications
A. Modal analysis for voltage stability evaluation
The linearized steady state system power flow equations are given by.
ΔP
=
ΔQ
Jpθ Jpv
Jqθ JQV
(1)

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I ΔQ (8)
Paper Publications
Where
ΔP = Incremental change in bus real power.
ΔQ = Incremental change in bus reactive
Power injection
Δθ = incremental change in bus voltage angle.
ΔV = Incremental change in bus voltage Magnitude
Jpθ , J PV , J Qθ , J QV jacobian matrix are the sub-matrixes of the System voltage stability is affected by both P and
Q. However at each operating point we keep P constant and evaluate voltage stability by considering incremental
relationship between Q and V.
To reduce (1), let ΔP = 0 , then.
ΔQ = JQV − JQθ JPθ−1 JPV ΔV = JRΔV (2)
ΔV = J−1 − ΔQ (3)
Where
JR = JQV − JQθ JPθ−1 JPV (4)
JR is called the reduced Jacobian matrix of the system.
B. Modes of Voltage instability:
Voltage Stability characteristics of the system can be identified by computing the eigen values and eigen vectors
Let
JR = ξ˄η (5)
Where,
ξ = right eigenvector matrix of JR
η = left eigenvector matrix of JR
∧ = diagonal eigenvalue matrix of JR and
JR−1 = ξ˄−1η (6)
From (3) and (6), we have
ΔV = ξ˄−1ηΔQ (7)
or
ΔV = ξi ηi
λi
Where ξi is the ith column right eigenvector and η the ith row left eigenvector of JR.
λi is the ith eigen value of JR.
The ith modal reactive power variation is,
ΔQmi = Ki ξi (9)

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where,
Ki = j ξij2 − 1 (10)
i (12)
i (13)
Paper Publications
Where
ξji is the jth element of ξi
The corresponding ith modal voltage variation is
ΔVmi = 1 λi ΔQmi (11)
In (8), let ΔQ = ek where ek has all its elements zero except the kth one being 1. Then,
ΔV =
ƞ1k ξ1
λ1
ƞ1k k th element of ƞ1
V –Q sensitivity at bus k
∂VK
∂QK
=
ƞ1k ξ1
i = Pki
λ1
λ1
III. Problem Formulation
The objectives of the reactive power dispatch problem considered here is to minimize the system real power loss and
maximize the static voltage stability margins (SVSM).
A. Minimization of Real Power Loss
It is aimed in this objective that minimizing of the real power loss (Ploss) in transmission lines of a power system. This is
mathematically stated as follows.
Ploss = gk(Vi
2+Vj
2−2Vi Vj cos θij
)
n
k=1
k=(i,j)
(14)
Where n is the number of transmission lines, gk is the conductance of branch k, Vi and Vj are voltage magnitude at bus i
and bus j, and θij is the voltage angle difference between bus i and bus j.
B. Minimization of Voltage Deviation
It is aimed in this objective that minimizing of the Deviations in voltage magnitudes (VD) at load buses. This is
mathematically stated as follows.
Minimize VD = nl Vk − 1.0
k=1 (15)
Where nl is the number of load busses and Vk is the voltage magnitude at bus k.
C. System Constraints
In the minimization process of objective functions, some problem constraints which one is equality and others are
inequality had to be met. Objective functions are subjected to these constraints shown below.
Load flow equality constraints:
푃퐺푖 – 푃퐷푖 − 푉푖 푉푗
푛푏
푗=1
퐺푖푗 cos 휃푖푗
+퐵푖푗 sin 휃푖푗
= 0, 푖 = 1,2 … . , 푛푏 (16)
푄퐺푖 − 푄퐷푖 − 푉푖 푉푗
푛푏
푗=1
퐺푖푗 cos 휃푖푗
+퐵푖푗 sin 휃푖푗
= 0, 푖 = 1,2 … . , 푛푏 (17)

where, nb is the number of buses, PG and QG are the real and reactive power of the generator, PD and QD are the real and
reactive load of the generator, and Gij and Bij are the mutual conductance and susceptance between bus i and bus j.
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Paper Publications
푖푚
Generator bus voltage (VGi) inequality constraint:
푉푚푖푛 퐺푖
≤ 푉퐺푖 ≤ 푉퐺푎푥 , 푖 ∈ 푛푔 (18)
Load bus voltage (VLi) inequality constraint:
푚푖푛 ≤ 푉퐿푖 ≤ 푉퐿푖푚
푉퐿푖
푎푥 , 푖 ∈ 푛푙 (19)
푖푚
Switchable reactive power compensations (QCi) inequality constraint:
푄푚푖푛 퐶푖
≤ 푄퐶푖 ≤ 푄퐶푎푥 , 푖 ∈ 푛푐 (20)
Reactive power generation (QGi) inequality constraint:
푚푖푛 ≤ 푄퐺푖 ≤ 푄퐺푖
푄퐺푖
푚푎푥 , 푖 ∈ 푛푔 (21)
Transformers tap setting (Ti) inequality constraint:
푚푖푛 ≤ 푇푖 ≤ 푇푖
푇푖
푚푎푥 , 푖 ∈ 푛푡 (22)
Transmission line flow (SLi) inequality constraint:
푚푖푛 ≤ 푆퐿푖푚
푆퐿푖
푎푥 , 푖 ∈ 푛푙 (23)
Where, nc, ng and nt are numbers of the switchable reactive power sources, generators and transformers.
IV. Hybrid QGPSO
A. Quantum Particle Swarm Optimization (QPSO)
In the quantum theory, the minimum unit that carries information is a Q-bit, which can be in any superposition of state 0 and
1. Let Qi (t) = (qi1(t),qi2 (t),.., qiD (t)) , qid (t)∈ [0,1] , be quantum particle I with D bits at iteration t, where qid (t) represents the
probability of d-th bit of i-th particle being 0 at iteration t. Let Xi (t) = (xi1(t), xi2 (t),.., xiD (t)) , xid (t)∈ {0,1} be binary particle
i with D bits at iteration t. Xi (t) is the corresponding binary particle of the quantum particle Qi (t) and also can be treated as a
potential solution. A binary particle Xi(t) can be got from quantum particle Qi(t) by performing a random observation as
following:
푥푖푑 푡 =
1 푖푓 푟푎푛푑() > 푞푖푑 (푡)
0 표푡푕푒푟푤푖푠푒
(24)
Where rand () is a random number selected from a uniform distribution in [0,1]. Let Pi(t) = ( pi1 (t), pi2 (t),..., piD (t)) be the
best solution that binary particle Xi (t) has obtained until iteration t, and Pg (t) = ( pg1(t), pg2 (t),..., pgD (t)) be the best solution
obtained from Pi (t) in the whole swarm at iteration t. The QPSO algorithm can be described as [22]:
푞푙표푐푎푙푏푒푠푡 (푡) = 훼 ∙ 푃푖푑 푡 + 훽 ∙ 1 − 푃푖푑 푡 (25)
푞푔표푙푏푎푙푏푒푠푡 (푡) = 훼 ∙ 푃푖푑 푡 + 훽 ∙ 1 − 푃푖푑 푡 (26)
푞푖푑 (푡 + 1) = 푐1 ∙ 푞푖푑 푡 + 푐2 ∙ 푞푙표푐푎푙푏푒푠푡 푡 + 푐3 ∙ 푞푔푙표푏푎푙푏푒푠푡 푡 (27)

Where α + β = 1 , 0 <α ,β < 1 are control parameters. The smaller of α , the bigger of the appear probability of the desired
item. c1 + c2 + c3 = 1 , 0 < c1,c2 ,c3 < 1 represent the degree of the belief on oneself, local best solution and global best
solution, respectively. In order to keep the diversity in particle swarm and further improve QPSO performance, we
incorporated a mutation operator into the QPSO. The mutation operator independently changes the Q-bit of an individual
with a mutation probability p as following:
B. Genetic Particle Swarm Optimization (GPSO)
Denote by N the number of particles in the swarm. The GPSO with genetic recombination for the d-th bit of particle i is
described as follows:
where 0 < w1 < w2 < 1, w( ) and rand() are a threshold function and a probabilistic bit flipping function, respectively, and they
are defined as follows:
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qid (t) = 1− qid (t) , if rand( ) < p (28)
xid (t +1) = w(0,w1 )rand(xid (t)) + w(w1,w2 )rand( pid (t)) + w(w2 ,1)rand ( pgd (t)) (29)
Paper Publications
푤 푎, 푏 =
1 푖푓 푎 ≤ 푟1 ≤ 푃푚
0 표푡푕푒푟푤푖푠푒
, (30)
푟푎푛푑 푦 =
1 − 푦 푖푓 푟2 ≤ 푝푚
푦 표푡푕푒푟푤푖푠푒
(31)
where r1 and r2 are the random numbers uniformly distributed in [0,1]. Thus, only one of the three terms on right hand side of
Eq. (29) will remain dependent on the value r1 , and rand(y) mutates the binary bit y with a small mutation probability pm .
The updating rule of the genetic PSO is analogue to the genetic algorithm in two aspects. First, the particle derives its single
bit from the particle xid , pid and pgd . This operation corresponds to a 3-way uniform crossover among X i , Pi and Pg , such
that the particle can exchange building blocks (segments of ordering or partial selections of elements) with personal and
global experiences. Second, each bit attained in this way will be flipped with a small probability pm , corresponding to the
binary mutation performed in genetic algorithms. As such, genetic reproduction, in particular, crossover and mutation, have
been added to the particle swarm optimization. This new genetic version, named GPSO, is very likely more suitable for
solving combinatorial optimization problems than the original one.
V. Procedure of HQGPSO
It is concluded from „„No Free Lunch‟‟ theorem [25] that there is no any method can solve all the problems optimally, so that
hybrid optimization algorithms have gained wide research in recent years [26] [27]. Based on the description of last section,
it can be seen that it is quite different between QPSO and GPSO in terms of representation and evolution operators. In QPSO,
the representation of population is Q-bit and evolutionary search is in micro-space (Q-bit based representation space).
Differently, in GPSO the representation is binary number and evolutionary search is in macro-space (binary space). We
consider the hybridization of QPSO and GPSO to develop hybrid QPSO characterized the principles of both quantum
computing and evolutionary computing mechanisms.
Algorithm for solving reactive power dispatch problem.
1. Initialize.
1.1 Set t = 0 , and initialize the QP(t).
1.2 Make BP(t) by observing the states of QP(t).
1.3 Evaluate the BP(t), and update the local best solutions and the global best solution.
1.4 Store BP(t) into Parent(t).

In the main loop the above procedure, firstly, quantum swarm is evolved by the evolution mechanism of the QPSO (Step
2.2). After one generation evolution of quantum swarm, a random observation is performed on quantum swarm (Step 2.3).
Thus, binary swarm is made by the random observation and prepares to be evolved by the evolution mechanism of the GPSO
in succession. Note that the individuals to perform GPSO are based on all the individuals resulted by QPSO in current
generation and all the individuals resulted by GPSO in last generation (Step 2.5). That is, if a binary individual in the
population resulted by QPSO in current generation is worse than the corresponding binary individual in the population
resulted by GPSO in last generation, then the worse one is replaced by the better one. This selection process is something like
the (μ +λ ) selection in evolutionary algorithm [28]. The selection in the hybrid algorithm is helpful to reserve better solutions
and speed up the evolution process. After the one or more generation GPSO evolution of binary swarm (Step 2.7), the best
solutions that each particle has obtained and the best solution that obtained from the whole swarm are recorded and
transferred to quantum swarm to guide a new generation evolution of quantum swarm (Step 2.8). In the hybrid algorithm, the
best solutions that each binary particle has obtained and global best solution of whole swarm can also be considered as
additional swarm individuals. They not only guide the evolution of quantum swarm, but also guide evolution of binary swarm
observed from quantum swarm.
Therefore, quantum swarm co-evolves with binary swarm and the information of evolution is exchanged between them by
the best solutions and global best solution. With the hybridization of different representation spaces and various particle
swarm optimization operators, it can not only enrich the searching behaviour but also enhance and balance the exploration
and exploitation abilities to avoid being trapped in local optima. Moreover, to balance the effort of QPSO and GPSO,
different parameters can be used, such as population size. On the other hand, the initial inspiration for the PSO was the
coordinated movement of swarms of animals in nature, for example schools of fish or flocks of birds. It reflects the
cooperative relationship among the individuals within a swarm. However, in natural ecosystems, many species have
developed cooperative interactions with other species to improve their survival. Such cooperative co-evolution is called
symbiosis [29]. According to the different symbiotic interrelationships, symbiosis can be classified into three main
categories: mutualism (both species benefit by the relationship), commensalism (one species benefits while the other species
is not affected), and parasitism (one species benefits and the other is harmed) [30]. The co-evolution between quantum swarm
and binary swarm in the proposed hybrid algorithm is similar to the mutualism model, where both swarms benefit from each
other.
The soundness of the proposed HQGPSO Algorithm method is demonstrated on IEEE-30 bus system. The IEEE-30 bus
system has 6 generator buses, 24 load buses and 41 transmission lines of which four branches are (6-9), (6-10) , (4-12) and
(28-27) - are with the tap setting transformers. The lower voltage magnitude limits at all buses are 0.95 p.u. and the upper
limits are 1.1 for all the PV buses and 1.05 p.u. for all the PQ buses and the reference bus. The simulation results have been
presented in Tables 1, 2, 3 &4. And in the Table 5 shows clearly that proposed algorithm powerfully reduce the real power
losses when compared to other given algorithms. The optimal values of the control variables along with the minimum loss
obtained are given in Table 1. Equivalent to this control variable setting, it was found that there are no limit violations in any
of the state variables.
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2. Repeat until a given maximal number of iterations (MaxIter) is achieved.
2.1 Set t = t +1.
2.2 Update QP(t) using QPSO.
2.3 Make BP(t) by observing the states of QP(t).
2.4 Evaluate the BP(t).
2.5 Select better one between BP(t) and Parent(t-1) for each individual to update BP(t).
2.6 Update the local best solutions and the global best solution.
2.7 Update BP(t) using GPSO for a given maximal number of iteration (gMaxIter).
2.8 Evaluate the BP(t), and update the local best solutions and the global best solution.
VI. Simulation Results
Paper Publications

ORPD including voltage stability constraint problem was handled in this case as a multi-objective optimization problem
where both power loss and maximum voltage stability margin of the system were optimized concurrently. Table 2 indicates
the optimal values of these control variables. Also it is found that there are no limit violations of the state variables. It
indicates the voltage stability index has increased from 0.2471 to 0.2486, an advance in the system voltage stability. To
determine the voltage security of the system, contingency analysis was conducted using the control variable setting obtained
in case 1 and case 2. The Eigen values equivalents to the four critical contingencies are given in Table 3. From this result it is
observed that the Eigen value has been improved considerably for all contingencies in the second case.
Table 2. Results of HQGPSO -Voltage Stability Control Reactive Power Dispatch Optimal Control Variables
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Table1. Results of HQGPSO – ORPD optimal control variables
Control variables Variable setting
V1 1.044
V2 1.044
V5 1.04
V8 1.032
V11 1.012
V13 1.04
T11 1.09
T12 1.02
T15 1
T36 1
Qc10 3
Qc12 2
Qc15 4
Qc17 0
Qc20 3
Qc23 4
Qc24 3
Qc29 3
Real power loss 4.4345
SVSM 0.2471
Control Variables Variable Setting
V1 1.045
V2 1.044
V5 1.041
V8 1.033
V11 1.009
V13 1.034
T11 0.09
T12 0.091
T15 0.092
T36 0.091
Qc10 4
Qc12 3
Qc15 2
Qc17 4
Paper Publications

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Qc20 0
Qc23 4
Qc24 4
Qc29 4
Real power loss 4.9799
SVSM 0.2486
Table 3. Voltage Stability under Contingency State
Sl. No Contigency ORPD Setting VSCRPD Setting
1 28-27 0.1410 0.1435
2 4-12 0.1658 0.1669
3 1-3 0.1774 0.1779
4 2-4 0.2032 0.2049
Table 4. Limit Violation Checking Of State Variables
Paper Publications
State variables
limits
ORPD VSCRPD
Lower upper
Q1 -20 152 1.3422 -1.3269
Q2 -20 61 8.9900 9.8232
Q5 -15 49.92 25.920 26.001
Q8 -10 63.52 38.8200 40.802
Q11 -15 42 2.9300 5.002
Q13 -15 48 8.1025 6.033
V3 0.95 1.05 1.0372 1.0392
V4 0.95 1.05 1.0307 1.0328
V6 0.95 1.05 1.0282 1.0298
V7 0.95 1.05 1.0101 1.0152
V9 0.95 1.05 1.0462 1.0412
V10 0.95 1.05 1.0482 1.0498
V12 0.95 1.05 1.0400 1.0466
V14 0.95 1.05 1.0474 1.0443
V15 0.95 1.05 1.0457 1.0413
V16 0.95 1.05 1.0426 1.0405
V17 0.95 1.05 1.0382 1.0396
V18 0.95 1.05 1.0392 1.0400
V19 0.95 1.05 1.0381 1.0394
V20 0.95 1.05 1.0112 1.0194
V21 0.95 1.05 1.0435 1.0243
V22 0.95 1.05 1.0448 1.0396
V23 0.95 1.05 1.0472 1.0372
V24 0.95 1.05 1.0484 1.0372
V25 0.95 1.05 1.0142 1.0192
V26 0.95 1.05 1.0494 1.0422
V27 0.95 1.05 1.0472 1.0452
V28 0.95 1.05 1.0243 1.0283
V29 0.95 1.05 1.0439 1.0419
V30 0.95 1.05 1.0418 1.0397

In this paper a novel approach HQGPSO algorithm used to solve optimal reactive power dispatch problem. The effectiveness
of the proposed method has been demonstrated by testing it on IEEE 30-bus system and simuation results reveals about the
reduction of real power loss when compared with other standard algorithms in table 5 and also volatge profiles are within the
limits .
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Page | 16
Table 5. Comparison of Real Power Loss
Method Minimum loss
Evolutionary programming[11] 5.0159
Genetic algorithm[12] 4.665
Real coded GA with Lindex as
SVSM[13]
4.568
Real coded genetic algorithm[14] 4.5015
Proposed HQGPSO method 4.4345
VII. CONCLUSION
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