Soft Computing Techniques for Optimal Capacitor Placement - Complex System Modelling and Control Through Intelligent Soft Computations - page 596

C j u j

k e X

X X

nl nc L C

Y ¼ 1 ð

Y 1

u i u 0

min f ð ; Þ¼ T i P i þ k p P l þ þ M tc ð k ef Þ Þð 13 Þ

i ¼ 1 j ¼ 1

1 þ m

where, M tc is Maintenance cost, k ef is economic factor given as k ef ¼

1 þ f , m is

in ation rate, f is interest rate.

The reformulated objective function consists of four terms, i.e., the energy cost,
peak power loss, capacitor cost, and maintenance along with the variation in cost
due to market in

ation, interest rates etc., respectively.
Both the objective functions are non-differentiable, making it unsolvable by
conventional methods. The cost function described in this way, being a non-linear
mixed integer, optimization problem can be solved ef

fl

ciently by soft computing
techniques. The constraints applied to these objective functions are discussed
below.

3.4 Constraints

(a) Load constraints
Load constraints are implied by the load connected at the buses. These con-
straints are imposed on the power fl flow equation by the loads. A three-phase

flow method has been used in this study for the problem.
(b) Operational constraints
Voltages are required to follow a certain limit to remain within upper and
lower limits. These constraints need to be followed before and after the
capacitor placement.

load fl

In the next section, problem of optimal capacitor placement, the approaches and
algorithm for its solution are discussed.

4 Optimal Capacitor Placement Problem

The reactive power provided by the power capacitor in the distribution system
depends upon the location of the capacitor and the size of the capacitor bank
installed. Thus, the problem for the capacitor placement can be sub-divided into two
problems, namely, (1) location of the capacitor and the (2) sizing of the capacitors.
For both of these problems separate techniques exist. The methods used for
determination of location and size are discussed below. The location of the
capacitor can be determined using analytical methods based on reasoning, whereas
the size of capacitors can be determined by solving the above-mentioned planning