A hybrid technique using particle swarm optimization and differential evolution to solve economic dispatch problem with valve-point effect

Scarcity of energy resources, increasing power generation cost and ever-growing demand for electric energy necessitates optimal economic dispatch in today´s power systems. The main objective of economic dispatch is to reduce the total power generation cost, while satisfying various equality and inequality constraints. Traditionally in economic dispatch problems, the cost function for generating units has been approximated as a quadratic function which doesn´t provide accurate results. Moreover, to obtain accurate fuel cost, valve-point effect in thermal power plant has to be taken into account. The inclusion of valve-point effect makes the modeling of the fuel cost functions of generating units more practical. In this paper a new hybrid evolutionary algorithm called Hybrid PSO, has been employed to solve economic dispatch problem with the valve-point effect. The hybrid PSO algorithm integrates evolutionary operators, such as selection and mutation, with the standard PSO algorithm. The algorithm synergistically combines PSO with a very powerful member of the Evolutionary algorithm (EA) family, well-known as Differential Evolution (DE). Using Hybrid PSO technique the non-linear cost function is solved for three unit system and the results are compared with the traditional PSO, DE and Genetic Algorithm (GA) method. These results prove that Hybrid PSO method is capable of getting higher quality solution including mathematical simplicity, fast convergence, and robustness to solve hard optimization problems.