**1. Introduction**

60 An Update on Power Quality

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Static Var Compensator (SVC) has been commonly used to provide reactive power compensation in distribution systems [1]. The SVC placement problem is a well-researched topic. Earlier approaches differ in problem formulation and the solution methods. In some approaches, the objective function is considered as an unconstrained maximization of savings due to energy loss reduction and peak power loss reduction against the SVC cost. Others formulated the problem with some variations of the above objective function. Some have also formulated the problem as constrained optimization and included voltage constraints into consideration.

In today's power system, there is trend to use nonlinear loads such as energy-efficient fluorescent lamps and solid-state devices. The SVCs sizing and allocation [2-4] should be properly considered, if else they can amplify harmonic currents and voltages due to possible resonance at one or several harmonic frequencies and switching actions of the power electronics converters connected. This condition could lead to potentially dangerous magnitudes of harmonic signals, additional stress on equipment insulation, increased SVC failure and interference with communication system.

SVC values are often assumed as continuous variables whose costs are considered as proportional to SVC size in past researches. Moreover, the cost of SVC is not linearly proportional to the size (MVAr). Hence, if the continuous variable approach is used to choose integral SVC size, the method may not result in an optimum solution and may even lead to undesirable harmonic resonance conditions.

Current harmonics are inevitable during the operation of thyristor controlled rectifiers, thus it is essential to have filters in a SVC system to eliminate the harmonics. The filter banks can not only absorb the risk harmonics, but also produce the capacitive reactive power. The SVC

uses close loop control system to regulate busbar voltage, reactive power exchange, power factor and three phase voltage balance.

A PSO Approach in Optimal FACTS Selection with Harmonic Distortion Considerations 63

*m m y* <sup>1</sup> 1

. . . . . . . . . . . .

cos 1,2,3 *<sup>m</sup>*

sin 1,2,3 *<sup>m</sup>*

1

*ij*

111 1, 1,

*i i i i ci <sup>y</sup> if i j Y Y if i j yyy*

At fundamental frequency, the real power losses in the transmission line between buses *i*

<sup>2</sup> 1 1 1 1

1 , <sup>1</sup> 1 0 *N m <sup>n</sup> loss loss i i n i P P*

 

The objective function of SVC placement is to reduce the power loss and keep bus voltages and total harmonic distortion (HDF) within prescribed limits with minimum cost. The constraints are voltage limits and maximum harmonic distortion factor, with the harmonics

1 2 ,

<sup>1</sup> *P Q* <sup>1</sup> , <sup>2</sup> *P Q* <sup>2</sup> , *l i P Q l i* , *P <sup>m</sup>* <sup>1</sup> *Q <sup>m</sup>* <sup>1</sup> , *P <sup>m</sup> Q <sup>m</sup>* , *P n i Q n i* , *c i y*

(1)

(2)

*i m*

*i m*

*PPP i li ni* (3)

*QQQ i li ni* (4)

*ii ii ii Y B G j* (6)

(8)

, 1 <sup>1</sup> , 1 , 1 *i i i i i i PR Y loss i i V V* (7)

(5)

012 *i* m-1 m

1

1

1

*j i*

1 1 1

*ij ij ij*

 

*j i P V G V V Y*

*Q V VV B Y*

 

<sup>2</sup> <sup>1</sup> 11 1 1 1 <sup>1</sup>

<sup>2</sup> <sup>1</sup> 11 1 1 1 <sup>1</sup>

*<sup>i</sup> i ii i j ij ij j i <sup>j</sup>*

*<sup>i</sup> <sup>i</sup> ii i j ij ij j i <sup>j</sup>*

*y* 0 1

**Figure 1.** One-line diagram of the radial distribution feeder.

1 *y*

where

**2.4. Real power losses** 

So, the total real losses is:

**2.5. Objective function and constraints** 

and *i*+1 is:

This chapter describes a method based on Particle Swarm Optimisation (PSO) [5] to solve the optimal SVC allocation successfully. Particle Swarm Optimisation (PSO) method is a powerful optimization technique analogous to the natural genetic process in biology. Theoretically, this technique is a stochastic approach and it converges to the global optimum solution, provided that certain conditions are satisfied. This chapter considers a distribution system with 9 possible locations for SVCs and 27 different sizes of SVCs. A critical discussion using the example with result is discussed in this chapter.
