Soft Computing Techniques for Optimal Capacitor Placement - Complex System Modelling and Control Through Intelligent Soft Computations - page 597

methods using soft computing techniques. Sizing of the capacitor, in itself, is a
mixed-integer programming method, which includes the continuous (power loss
and energy loss) and discrete (capacitor sizes) variables.

4.1 Determination of Capacitor Location

The location for the placement of the capacitor can be determined in a number of
ways. The simplest method can be to determine the nodes with highest reactive
power demand and weak voltage pro le. Also, the placement can be done ran-

domly, through simulation, by placing the capacitor and observing its effect on the
nearby buses. Moreover, sensitivity based methods can be used to determine the
location of the power capacitors.
Sensitivity analysis refers to the determination of how

a parameter is
to the changes in the value of the other parameters of a model, or to the changes in
the structure of the model. Thus, it is de

“ sensitive ”

ned as “ ratio Δ x/ Δ y relating small changes

Δ x of some dependent variable to small changes Δ y of some independent or con-

”

trollable variable y (Peachon et al. 1968 ). Both Loss Sensitivity (Prakash and

Sydulu 2007 ) and Bus Sensitivity (Silva et al. 2008 ), can be calculated for any
particular bus in power system. Here, these two methods are employed to select the
candidate buses for optimal capacitor placement. Both sensitivity methods are
discussed in the following paragraphs (Kumar et al. 2011 ).

4.1.1 Loss Sensitivity

The loss sensitivity analysis is a systematic procedure computing the maximum
impact on the real power losses of the system with respect to the nodal reactive
power. The relationship for computing the loss sensitivity for any bus can be
derived as follows.
Consider a distribution line connected between buses i and j as shown in Fig. 6 .
Where, r ij ,x ij are resistance and reactance of lines between buses i and j, and
S j = P j + Q j is the load connected at bus j, P j is the active power and Q j is the
reactive power.

Fig. 6 Section of distribution line