21-06-2013, 02:51 PM
Optimal placement of capacitors in radial distribution system using a Fuzzy-GA method
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Abstract
The paper presents a genetic algorithm (GA) based fuzzy multi-objective approach for determining the optimum values of fixed and
switched shunt capacitors to improve the voltage profile and maximize the net savings in a radial distribution system. The two objectives,
i.e. maximization of net savings and minimization of the nodes voltage deviation are first fuzzified and, then, dealt with by integrating
them into a fuzzy satisfaction objective function through appropriate weighting factors. The optimization technique of the GA is then
adopted to solve the fuzzy multi-objective problem for obtaining the optimum values of shunt capacitors.
Introduction
Capacitors are widely used in distribution systems for
reactive power compensation, to achieve power and energy
loss reduction, to improve service quality via voltage regulation
and to achieve deferral of construction, if possible,
via system capacity release. The problem is to choose the
optimum capacitor allocation and the capacitor control
in order to maximize the benefits against the cost of
capacitors.
In the past, considerable efforts were put into the capacitor
placement problem. The early approaches to this problem
include (i) are based on the dynamic programming
technique to handle the discrete nature of capacitor size
[1] and (ii) one that uses analytical methods in conjunction
with heuristics [2–4]. Recently, the growing need for distribution
automation and control has regenerated interest in
the capacitor placement problem.
Problem formulation
In fuzzy domain, each objective is associated with a
membership function. The membership function indicates
the degree of satisfaction of the objective. In the crisp
domain, either the objective is satisfied or it is violated,
implying membership values of unity and zero, respectively.
On the contrary, fuzzy sets entertain varying degrees
of membership function values from zero to unity. Thus
fuzzy set theory is an extension of standard set theory [29]
Genetic algorithm
To solve the optimization problem formulated in Eq.
(9), genetic algorithm (GA) is used. Over the last few years,
it is becoming popular to solve a wide range of search, optimization
and machine learning problems. A GA (multi
path search scheme) is an iterative procedure which maintains
a constant size population p(t) of candidate solutions.
The initial population p(0) can be chosen heuristically or at
random [30,31]. The structure of the population p(t + 1)
(i.e. for next iteration called generation) are chosen from
p(t) by randomized selection procedure that ensures that
the expected number of times a structure is chosen is
approximately proportional to that structures performance
relative to the rest of the population. In order to search
other points in a search space, some variation is introduced
into the new population by means of genetic operators
(crossover and mutation).