Soft Computing Techniques for Optimal Capacitor Placement - Complex System Modelling and Control Through Intelligent Soft Computations - page 598

The active power losses (P Loss ) and reactive power loss (Q Loss ) in the distribution
line are given as:

r ij P j þ Q j x ij P j þ Q j

P Loss ¼ ; Q Loss ¼ ð 17 Þ

V j V j

Loss sensitivity S L , for any bus j can be given as
S Lj ¼ @

P Loss
@

2 Q j r ij

Q i ¼

ð 18 Þ

V j

Based on S Li the buses are ranked in descending order of its values. The bus having
greatest value is ranked top in the priority list and is considered first for capacitor

placement. The buses having the highest S, along with voltage ratio V/0.9 > 1.1, is
selected as candidate buses for capacitor placement.

4.1.2 Bus Sensitivity

Bus sensitivity method (Silva et al. 2008 ) is the sensitivity of buses based on
reactive power and voltage at the buses. It suggest to provide reactive compensation
mainly on those buses where reactive power demand is high and bus voltages are
below nominal value. For ith bus the bus sensitivity index (S Bi )isde ned as

S Bi ¼ k Qi Ql i
V i

ð 19 Þ

where, λ Qi , Qli, i , and V i are Lagrange multiplier, load reactive power, and voltage at

bus i, respectively.
Lagrange multiplier is calculated as implicit first order derivative of the cost

function with respect to the right side with parameter of constraint providing
information about the sensitivity. For the capacitor placement problem,

ʻ

ects
the sensitivity of objective function to changes in the reactive power injection in ith
bus. S Bi gives cost required to increase the voltage at bus i, having unit $/V.

re fl

4.2 Determination of Capacitor Size

To determine the size of the capacitor, for the installation at the locations deter-
mined using the methods discussed above, several methods are available. The
methods developed can be broadly classified as:

(a) Analytical Methods,
(b) Numerical Programming Methods, and
(c) Soft Computing Based Methods.