Optimal capacitor placement and sizing using Fuzzy-DE and Fuzzy-MAPSO methods

Abstract

This paper presents new techniques for capacitor placement in radial distribution feeders in order to reduce the real power loss, to improve the voltage profile and to achieve economical saving. The identification of the weak buses, where the capacitors should be placed is decided by a set of rules given by the fuzzy expert system. Power loss and node voltage indices are used as inputs to the fuzzy expert system and the output is sensitivity index which gives the weak buses in the system where the capacitor to be placed. The sizing of the capacitors is modeled by an objective function to obtain maximum savings using Differential Evolution (DE) and Multi Agent Particle Swarm Optimization (MAPSO). To illustrate the applicability of the above algorithms, simulation is performed on an existing 15 bus and IEEE 34 bus distribution feeders. The results of the proposed approaches are compared with PSO, HPSO techniques and with results of those in the literature.

Introduction

In the radial distribution system, capacitors are installed at suitable locations for the improvement of voltage profile and to diminish the energy losses in the distribution system. It is estimated that as much as 13% of total power generation is dissipated as I²R losses in the distribution networks [1]. Reactive currents flowing in the network account for a portion of these losses. By the installation of shunt capacitors, the losses produced by reactive currents can be reduced. This is also vital for power flow control, improving system stability, power factor correction, voltage profile management, and the reduction in active energy losses. Hence it is essential to find the optimal location and size of capacitors required to maintain a nominal voltage profile and to reduce the feeder losses.

Ng et al. [1] presented the guideline for implementation of appropriate capacitor allocation techniques. Ng et al. [2] presented a novel approach using approximate reasoning to determine suitable candidate nodes in a distribution system for capacitor placement problem. They presented the numerical procedure to determine the size of capacitors.

Salama and Chikhani [3] considered the feeders with lateral branches. Here optimal capacitor sizes are represented by dependent current sources located at the branch connected buses. This method is simple and no sophisticated optimization technology is needed. EL-Dib et al. [4] proposed a solution technique for finding the optimum location and sizing of the shunt compensation devices in a transmission system. Here, the objective function is formulated based on the voltage stability by maintaining the acceptable voltages profile.

Combinations of Particle Swarm Optimization and Hybrid Particle Swarm Optimization techniques are presented in [5], [6], [7] to show the applications of these methods to the Power system problems. Das [8] considered the capacitor as a constant reactive power load and as a constant impedance load. The genetic algorithm approach is used to size the fixed and switched capacitor for varying load conditions.

In this paper, fuzzy expert system (FES) has been developed with reference to [2] to identify the suitable locations for capacitor placement. The reason for using FES method is that the capacitor allocation problem is highly nonlinear in nature. Also, capacitor location at a particular bus depends on the values of power loss and voltage magnitude. The power loss and bus voltage exhibits a nonlinear relation. Owing to these facts, FES method is used in this work to address the capacitor allocation problem.

Particle Swarm Optimization (PSO), Hybrid Particle Swarm Optimization (HPSO) and Multi-Agent Particle Swarm Optimization (MAPSO) are among the popular meta-heuristic methods in all the engineering fields. The continuous optimization methods are used to solve the capacitor sizing problem. Although capacitor sizing is a discrete nature problem, it is necessary to select the capacitor size at suitable locations within a narrow band, necessitating the need for a continuous optimization procedure. In this paper, Differential Evolution and Multi-Agent Particle Swarm Optimization (MAPSO) methods have been used to find the size of the capacitors. The capacitor sizing is designed with the objective function, which minimizes the power loss in the feeders. The proposed method has been tested on an existing 15 bus system and IEEE 34 bus system. The effectiveness of proposed methods are compared with the classical PSO and HPSO methods, which suggested an improved saving in cost.