Application of Chaotic Maps to Economic Load Dispatch Problem

Abstract

This paper aims to solve the economic load dispatch problem (ELD) by using random numbers generated by chaotic maps with particle swarm optimization (PSO). The randomly generated coefficients r1 and r2 in the velocity equation of the PSO algorithm are generated by three different chaotic map methods namely logistic map, gaussian map, and tent map. As a result, three different methods are proposed: PSO with logistic map (LMPSO), PSO with Gaussian map (GMSPO), and PSO with tent map (TMPSO). These algorithms are applied to a 40-unit test system that includes transmission line losses, and the results are compared with the standard PSO algorithm. Each algorithm was run 50 times, and the maximum, minimum, and average values were recorded. All the proposed methods found lower costs than the standard PSO algorithm. Although the lowest cost was achieved with the GMPSO algorithm, the LMPSO algorithm was observed to be more successful on average.