23-05-2012, 11:46 AM
Loss Minimization Using Optimal Power Flow Based on Swarm Intelligences
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INTRODUCTION
Optimal power °ow is one of nonlinear constrained
and occasionally combinatorial optimization prob-
lems of power systems. The various algorithms for
solving such problems can be found in the literature.
The optimal power °ow problem has been developed
continually since its introduction by Carpentier in
1962 [1]. It is useful to determine the goals of op-
timal power °ow problems.
OPTIMAL POWER FLOW PROBLEMS
Problem Formulation
The optimal power °ow problem is a nonlinear op-
timization problem. It consists of a nonlinear ob-
jective function de¯ned with nonlinear constraints.
The optimal power °ow problem requires the solution
of nonlinear equations, describing optimal and/or se-
cure operation of power systems. The general optimal
power °ow problem can be expressed as a constrained
optimization problem as follows.
System Constraints
The controllable system quantities are generator
MW, controlled voltage magnitude, reactive power
injection from reactive power sources and transformer
tapping. The objective use herein is to minimize the
power transmission loss function by optimizing the
control variables within their limits. Therefore, no
violation on other quantities (e.g. MVA °ow of trans-
mission lines, load bus voltage magnitude, genera-
tor MVAR) occurs in normal system operating con-
ditions. These are system constraints to be formed
Particle Swarm Optimization (PSO)
Kennedy and Eberhart developed a particle swarm
optimization algorithm based on the behavior of in-
dividuals (i.e., particles or agents) of a swarm [17].
Its roots are in zoologists modeling of the movement
of individuals (i.e., ¯sh, birds, and insects) within a
group. It has been noticed that members of the group
seem to share information among them to lead to in-
creased e±ciency of the group.
Di®erential Evolution (DE)
Di®erential Evolution (DE) [21-22] is a recently de-
veloped evolutionary computation technique. DE is
an extremely powerful yet simple evolutionary algo-
rithm that improves a population of individuals over
several generations through the operators of muta-
tion, crossover and selection for global optimization
introduced by Price and Storn. Di®erential evolu-
tion presents great convergence characteristics and
requires few control parameters which remain ¯xed
throughout the optimization process and need mini-
mum tuning. DE di®ers from other EA in the mu-
tation and recombination phase.