Comparative study of methods for optimal reactive power dispatch

Electrical and Electronics Engineering: An International Journal (ELELIJ) Vol 3, No 3, August 2014
COMPARATIVE STUDY OF METHODS FOR OPTIMAL
REACTIVE POWER DISPATCH
Tejaswini Sharma1, Alka Yadav2, Sangeeta Jamhoria3 and Ritu Chaturvedi4
1, 2, 3, 4 Department of Electrical Engineering, Madhav Institute of Technology & Science
Gwalior, India
ABSTRACT
Reactive power dispatch plays a main role in order to provide good facility secure and economic operation
in the power system. In a power system optimal reactive power dispatch is supported to improve the voltage
profile, to reduce losses, to improve voltage stability, to reduce cost etc. This paper presents a brief
literature survey of reactive power dispatch and also discusses a comparative study of conventional and
evolutionary computation techniques applied for reactive power dispatch. The paper is useful for
researchers for further research and study so that it can apply in the various areas of power system.
KEYWORDS
Optimal Reactive Power Dispatch, Conventional Techniques, Evolutionary Computation Techniques.
1. INTRODUCTION
Optimal power flow (OPF) is a main concern in the power systems. This problem can be divided
into problems, real power and reactive power dispatch is a sub problem of OPF[1]. Optimal
Reactive power dispatch is a crucial task for both planning and operations of power systems [2].
Transformer and transmission lines introduce inductance as well as resistance and both
transformer and transmission lines oppose the flow of the current [3].
Throughout the decades, research on reactive power has been going on. The problem of
reactive power dispatch for improving economic operation and control of power system has
arriving much more attention [4]. To regulate the power system voltage stability, voltage profile
and to reduce the power loss appropriate reactive power and voltage are required [5, 6]. The
control variables of ORPD are namely, generator voltage magnitude, the tap ratios of transformer,
static VAR sources; etc. The constraints contain the voltage limits of buses, tap ratio limits, VAR
voltage limits of generators, VAR source limits etc. Sources of Reactive Power are two types
namely: static and dynamics. Static reactive power sources are Shunt Capacitors, Filter banks,
Underground cables, Transmission lines, Fuel cells, PV systems. Dynamic reactive power sources
are FACTS devices, Synchronous Condensers, Synchronous Generators [1, 3, 6].
There are so many approaches have been proposed for optimal reactive power dispatch in a power
system over the past decades. Conventional techniques like Mixed integer Programming,
Predictor Corrector Primal Dual Interior Point Method Nonlinear Programming, Linear
Programming, gradient method, interior point method Successive Quadratic Programming etc. are
used for solving optimal reactive power dispatch problem [7,8]. These methods have to fail to
handle due to non-convex, non-differential, non-linearity, multi-modal characteristic and non-smoothness
nature of the problem [5].
DOI : 10.14810/elelij.2014.3305 53

In Recent years, various evolutionary computation techniques like Optimization toolbox of
MATLAB, cat swarm optimization, Gravitational Search Algorithm, Modified shuffled frog
algorithm, Big Bang – Big Crunch (BB-BC) algorithm, differential Evolution, Strength Pareto
Evolutionary Algorithm and Simulated Annealing etc. are able to solve all types of ORPD
problems and these techniques do not required the objective function and type of the problem [8,
9, 10]. At present, researchers usually use aggregate method to deal with multi-objective reactive
power optimization problem, namely, convert multi objective optimization problem to single-objective
optimization problem. The solution set can provide users the choice of diversification.
54
This requires a compromise to get a satisfactory solution [1, 2].
2. PROBLEM FORMULATION
Optimal reactive power dispatch problem can be solved as a single objective optimization
problem as well as multi objective optimization.
2.1. Single Objective Optimization (SOO) Problem
A single objective optimization problem is a problem in which only one objective function is
considered at a time. Mathematical representation of SOO is defined as follows –
Min / maximization f(x)
Subjected to gi (x) 0 where i= 1, 2, 3…..i
hj (x) = 0 where k= 1,2,3…..j
Where x= (x1, x2, x3……xm) is a vector of n design decision variable.
gi (x), hj(x) = inequality and equality constraints,
I = index for inequality constraints.
j = index for equality constraints,
i and j = number of inequality and equality constraints.
2.2. Multi Objective Optimization (MOO) Problem
Multi objective optimization problem is defined as follows-
Min / maximization F(x) = [f1(x), f2(x), f3(x) …….fk(x)]
Subjected to gi (x) 0 where i= 1, 2, 3…..i
hj (x) = 0 where k= 1,2,3…..j
Where [f1(x), f2(x), f3(x) …….fk(x)] are the objective function.
3. DESCRIPTION OF METHODS
Numerous techniques have been proposed in the literature to solve the reactive power planning
problem. They are categorized in to the following two groups [8] namely, conventional
techniques and evolutionary computation techniques.
3.1 Conventional Techniques
Grudinin [11], proposed Successive Quadratic Programming (SQP) methods for solving a
reactive power optimization model. To solve IEEE 30 bus and 278 bus system 6 optimization

methods were used. Simulation results proved that the proposed SQP based approach was better
than the SLP method.
Yan et.al [12], presented Predictor Corrector Primal Dual Interior Point Method (PCPDIPM) for
solving the Optimal Reactive Power Flow (ORPF) problem. A new model of optimal reactive
power flow in a rectangular form was proposed with the help of this method. In that model the
Hessian matrices were constants and need to be evaluated only one time in the whole optimal
process. Entire time required for PCPDIPM was always shorter than that for the traditional model
for the 7 test cases.
Granville [13], proposed an Interior Point Method to solve the ORPD problem. This method was
based on the primal dual logarithmic barrier method. The algorithm was tested on large power
systems and 398.9 seconds CPU time was required. The proposed method has the following
compensation: required less number of iterations or less number of control variables, robustness,
no active set recognition problems and efficiency in dealing with optimal reactive power
allotment and real power loss reduction problems in large scale and unhealthy network.
Lin et.al [14], proposed sequential quadratic programming to solve the OPF problem. The
problem formulation was taken as integrated cost analysis and voltage stability analysis for
competitive market. ORPD was establishing under a range of voltage stability margin desires in
both normal and outage circumstances. The proposed method was demonstrated on IEEE 14-bus
test system and the simulation result was compared with other methods.
Xiaoying et.al [15], proposed an Interior Point Branch and Cut Method for solving decoupled
OPF problem. The Modern Interior Point Algorithm was used to solve Active Power suboptimal
Problem and use IPBCM for solving linearization of Reactive Power Suboptimal Problem. The
control variables and constraints of reactive power suboptimal problem were lesser than that of
original OPF problem were the advantage of this method, it also improves the speed but this
method fail to dealing with degenerate problem.
Alsac et.al [16], proposed linear programing was applied to the on-line reactive power
rescheduling and optimal reactive power dispatch problem (ORPD) was formulated in a separable
form. The main objectives of this paper were to minimize real power losses and the control
variable for ORPD were for generator voltages, transformer taps etc.
This proposed method was used for on-line scheduling; the deviations from set points were
minimized. A linear programing method was also suggested for solving non separable objective
functions such as total real power loss. In this paper was also discussed that, mostly loss reduction
occurs in the early iterations. The loss minimization has been achieved for three types of
networks with 700, 1200 and 1330 buses in power system.
Torres et.al [17, 18], proposed the methods for calculate the price of reactive power support
service in a multi-area power system. These methods were nonlinear convex network flow
programming and cost-benefit analysis. With the help of several cost-benefit indexes, the reactive
power maintains settlement regarding power rescue raises of tie lines were compute.
Pudjianto et.al [19] proposed linear programming and nonlinear programming for distributing
reactive power between conflicting generators in a deregulated environment which was based on
reactive OPF. It was concluded that by using LP method the total cost of the system which are
associated with the requirement of reactive power was convincingly accurate. Whereas, nonlinear
programming offer a more rapidly computation speed and precision for the solution but the
convergence could not be guaranteed for every condition.
55

56
3.2 Evolutionary Computation Techniques
Bhushan [20], proposed Differential Evolution (DE) algorithm for improves the voltage profile
and simultaneously line loss reduction in power system. In this algorithm with the help of
differential evolution optimal setting of Reactive power control variable were carried out. The
proposed differential evolution algorithm was tested on three standard IEEE system and obtained
satisfactory simulation result.
Suresh et.al [21], was proposed gravitational search algorithm (GSA) for solving optimal reactive
power flow problem in a power system. This algorithm is used to reduce power losses and
improves the voltage stability of the power system. This algorithm is also improving the
economic operation of the system. Generator bus voltage magnitude, SVC controllers and
transformer tap settings were the control variables for reactive power flow optimization.
Gravitational search algorithm was a recently developed nature inspired algorithms for global
optimization. GSA based algorithm was implemented on IEEE 30 bus test system and the results
were compared with other algorithm and found superior results.
Kumara et.al [22], proposed cat swarm optimization (CSO) algorithm for optimal settings of RPD
control variables. Cat swarm optimization algorithm was used for solving the multi-objective
optimal reactive power dispatch problem in a power system. Model analysis of the system was
used for static voltage stability assessment. The main objectives of this paper are to maximize of
voltage stability margin and loss minimization. The control variables of this paper were Generator
voltages, the capacitor banks and tap changing transformer settings. The proposed approach was
examined and tested on the standard IEEE 30- bus test system.
Sakthivel et.al [23], proposed evolutionary programming algorithm was used to optimally
position the FACTS devices. Real and reactive power optimization was necessary for economic
operation and voltage security of power systems. This algorithm helps to improve power system
condition by controlling the real power and reactive power dispatch. Real power generation was
optimized by minimizing the fuel cost and real power loss was reduced to optimize reactive
power dispatch. The low cost but fast respond thyristor controlled series capacitor (TCSC) and
static VAR compensator (SVC) devices were used to achieve the objectives. Aggregate of
generator bus voltages power generation, transformer tap settings and constraint locations of
TCSC and SVC were taken as the control variables. The effectiveness of the proposed work was
tested on IEEE-30 Bus test system and the results obtained were really encouraging.
Ankaliki et.al [24], proposed that paper to improve the voltage profile in distribution system by
optimal reactive power maintain. It also helps in reduction of total real and reactive power loss of
the power system thus resultant in reduction in energy loss of the system. Their effectiveness of
the optimum reactive power support were show, the method was tested on 13-Bus Distribution
System.
Lenin et.al [25], proposed a new search-acceleration parameter into the formulation of the
original shuffled frog leaping (SFL) algorithm to create a modified form of the shuffled frog
algorithm (MSFL) for solving reactive power dispatch problem. The formulation of this proposed
algorithm is draws from other two techniques i.e. particle swarm optimization and shuffled
complex evolution techniques. Shuffled frog leaping algorithm was used for solving the multi-objective
reactive power dispatch problem in a power system. Modal analysis of the system was
used for static voltage stability calculation. Reduce power losses and improve voltage stability
margin were taken as the objectives. Generator voltages magnitude, tap changing transformer
setting and reactive power generation of the capacitor banks were taken as the optimization
variables.

Anuradha et.al [26], proposed Optimization toolbox of Matlab for solving ORPD problem.
Optimal Reactive Power Dispatch was required for power system control and proper operation.
The main objective function of this paper was to minimize power system losses and improved the
voltage profile and overall system operation. The control variables like switchable VAR sources,
generator voltage magnitude, transformer tap-settings were used to solve ORPD problem.
The ORPD problem was taken as multi objective nonlinear constrained optimization problem
with equality and inequality constraints The Optimization toolbox has been demonstrated on
IEEE 30-bus system to solve multi objective optimization problem i.e. to minimize power losses
and to reduce the voltage deviation and the obtained simulation results were compared with the
differential evolution algorithm.
Duman et.al [27], proposed Gravitational Search Algorithm (GSA) for solving the optimal
reactive power dispatch problem. The ORPD problem was formulated as a single-objective
optimization problem and it also formulated as a non linear constrained problem. The aim of this
paper real power loss and voltage deviations were to be minimized individually. This algorithm
has been applied on IEEE 30 bus system consisting six generators and compared other algorithms
reported those before in literature. Results showed that GSA was more efficient than others for
solution of single-objective ORPD problem.
Sakthivel et.al [28], proposed Big Bang – Big Crunch (BB-BC) algorithm was used for solving
the multi constrained optimal reactive power problem. The important tasks of this proposed
algorithm were minimizing the real power loss and the voltage deviation at the same time. The
presented algorithm ensures for protected operation and control of power system. The main
advantages of this algorithm, it is free from large number of operators and this algorithm can be
easily coded. The various decision variables were Generator voltage magnitude, transformer tap
settings and static VAR compensators. BB-BC algorithm was tested on the standard IEEE-30 bus
test system and the results were compared with other methods to prove the effectiveness of the
new algorithm. The results were quite encouraging and the algorithm was found to be efficient.
Abido [29], proposed Strength Pareto Evolutionary Algorithm (SPEA) for solving ORPD
problem. The optimal reactive power dispatch problem was formulated as a true multi objective
optimization problem. The proposed algorithm solved the ORPD problem as a multi objective
optimization problem where the real power loss and the voltage stability were minimized
simultaneously. The simulation results verified the capability of the SPEA to make true and well-distributed
Pareto optimal front solutions of the multi objective optimal reactive power dispatch
57
problem in only one trail.
Tejaswini [30], proposed new meta-heuristic optimization algorithm, called Cuckoo Search
algorithm, to solved the optimal reactive power dispatch (ORPD) problem. The main objective
functions of this paper to minimize real power losses and to improve the voltage profile in a
power system simultaneously. The optimal reactive power dispatch problem has been handled as
a multi objective optimization problem while satisfying all security constraints. The evaluation
shows the success and the advantage of the cuckoo search approach for solving ORPD problem.
This algorithm has been demonstrated on standard IEEE 30 bus test system and the obtained
simulation results were superior to differential evolution algorithm.

4. SUMMARY OF DIFFERENT METHODS APPLIED TO OPTIMAL REACTIVE
POWER DISPATCH PROBLEM
58
Table 1 A Summary of Methods Which Are Considered In This Paper
S. No Reference No. Objective function Solution Method
1 Grudinin [11] Economical And Security Successive
Quadratic
Programming
2 Wei Yan et.al [12] Reduce Power Losses,
Improvement Of Voltage Profile
Voltage Stability
Predictor Corrector
Primal Dual Interior
Point Method
3 Sergio Granville
[13]
Reduce Power Losses
Improvement Of Voltage Stability
Interior Point
Method
4 Lin et.al [14] Reduce Power Losses
Sequential
Quadratic
Programming
5 Xiaoying et.al [15] Fuel Cost, Reduce Real Power
Losses
Interior Point
Branch And Cut
Method
6 Alsac et.al [16] Reduce Power Losses
Linear
Programming
7 Torres et.al [17
,18]
Cost Cost-Benefit
Analysis
8 Pudjianto et.al [19] Cost Interior Point
Method, Linear
Programming
9 Bhushan [20] Reduce Power Losses
Differential
Evolution
10 Suresh et.al [21] Reduce Power Losses
Gravitational Search
Algorithm
11 Kumara et.al[22] Reduce Power Losses
Cat Swarm
Optimization
12 Sakthivel et.al [23] Fuel Cost, Reduce Real Power
Losses
Evolutionary
Programming
Algorithm
13 Ankaliki et.al [24] Reduce Power Losses
Radial Distribution
System
14 Lenin et.al[25] Reduce Power Losses
Margin
Modified Shuffled
Frog Algorithm
15 Anuradha et.al
[26]
Reduce Power Losses
Optimization
Toolbox Of Matlab
16 Duman et.al [27] Reduce Power Losses Voltage
Deviation
Gravitational Search
Algorithm
17 Sakthivel et.al [28] Reduce Power Losses Voltage
Deviation
Big Bang – Big
Crunch (BB-BC)
Algorithm
18 Abido [29] Reduce Power Losses
Strength Pareto
Evolutionary
Algorithm
19 Tejaswini [30]
Reduce Power Losses
Cuckoo Search
Algorithm

59
Table 2 Comparison between conventional techniques and evolutionary computation techniques
S. No Object Conventional Techniques Evolutionary
Computation Techniques
1 Time Less consuming More consuming
2 Accuracy More accurate Less accurate as compare
to conventional techniques
3 Problem type and
problem nature
Depend on type and nature of
the problem
Does not Depend on type
and nature of the problem
4 Parameter tuning Less required Is must
5 Solution Provide local optimum Provide near global
optimum
5. CONCLUSION
The discussion shows the different methods involved in solving the optimal reactive power
dispatch problems. The conventional techniques as well as evolutionary computation techniques
based methods have been reported in literature for optimal reactive power dispatch problem. The
conventional techniques methods are fast and accurate, but complex in nature whereas
evolutionary computation techniques are easy to be applied, but time consuming and more
parameter tuning required. In addition, Comparison between conventional techniques and
evolutionary computation techniques are also discussed.
ACKNOWLEDGEMENTS
The authors sincerely thank her ME, Dissertation guide and the Director, MITS Gwalior, India to
carried-out this research work.
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Authors
Tejaswini Sharma was born in Bulandshahr in UP, on September 22, 1990.Her graduation in
Electrical and electronics Engineering from the Maa Kaila Devi Institute of Information
technology and management in Gwalior and pursuing M.E at Madhav Institute of
Technology and Science (MITS) in Gwalior. Tejaswini received honorary degree from
institutions of RGPV University.
Alka Yadav was born in Dispur in Assam, on June 20, 1988.Her graduation in Electrical
Engineering from the Maharana Pratap College of Technology (MPCT) in Gwalior and
pursuing M.E at Madhav Institute of Technology and Science (MITS) in Gwalior. Alka
received honorary degree from institutions of RGPV University.
Sangeeta Jamhoria was born on November 24, 1990. Her graduation in Electrical
Engineering from the Maharana Pratap College of Technology (MPCT) in Gwalior and
pursuing M.E at Madhav Institute of Technology and Science (MITS) in Gwalior.
Ritu Chaturvedi was born on January 08, 1991. Her graduation in Electrical Engineering
from the Maharana Pratap College of Technology (MPCT) in Gwalior and pursuing M.E at
Madhav Institute of Technology and Science (MITS) in Gwalior.

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