Soft Computing Techniques for Optimal Capacitor Placement - Complex System Modelling and Control Through Intelligent Soft Computations - page 591

3 Modeling of Capacitor Placement Problem

For capacitor placement in the distribution system, information about the load
fl flows, capacitor sizes, and the method to solve, is very important. Here, the problem

formulation for the capacitor placement is discussed.
The problem of capacitor placement can be solved as a constrained optimization
problem

min f ð x ; u Þ ð 1 Þ

subjected to

F ð x ; u Þ¼ 0 ð 2 Þ

G ð x ; u Þ 0 ð 3 Þ

where f(x,u) is objective function. The state variable x represents the state of system
and capacitor placement scheme is represented by the variable u. F(x,u), represents
the set of equality constraints, and G(x,u) represents the set of the inequality con-
straint of the problem. Following sub-sections provides the necessary methods to
formulate the problem.
Capacitors are installed in distribution system to reduce the losses and improve
the voltage pro

ow
control. The capacitors are placed and sized by modelling the problem as an opti-
mization problem. The capacitor placement problem is modelled as an objective
function, as shown in sections below. The cost of capacitor composed of the
capacitor cost and the installation cost, as shown in Fig. 3 , is taken into discrete steps
of the size of capacitor. Here, the capacitor placement problem is reformulated

le. As the size of capacitor plays a vital role in reactive power fl

Fig. 3 Capacitor investment
cost function