A modified differential evolution based solution technique for economic dispatch problems

Md. Abul Kalam Azad; Edite M.G.P. Fernandes

doi:10.3934/jimo.2012.8.1017

Article Contents

2012, Volume 8, Issue 4: 1017-1038. Doi: 10.3934/jimo.2012.8.1017

This issue Previous Article A model for buyer and supplier coordination and information sharing in order-up-to systems Next Article State transition algorithm

A modified differential evolution based solution technique for economic dispatch problems

Md. Abul Kalam Azad^1, and
Edite M.G.P. Fernandes^1,

1.
Algoritmi R&D Centre, School of Engineering, University of Minho, 4710-057 Braga

Received: June 30, 2011

Revised: April 30, 2012

Published: September 2012

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Abstract

Economic dispatch (ED) plays one of the major roles in power generation systems. The objective of economic dispatch problem is to find the optimal combination of power dispatches from different power generating units in a given time period to minimize the total generation cost while satisfying the specified constraints. Due to valve-point loading effects the objective function becomes nondifferentiable and has many local minima in the solution space. Traditional methods may fail to reach the global solution of ED problems. Most of the existing stochastic methods try to make the solution feasible or penalize an infeasible solution with penalty function method. However, to find the appropriate penalty parameter is not an easy task. Differential evolution is a population-based heuristic approach that has been shown to be very efficient to solve global optimization problems with simple bounds. In this paper, we propose a modified differential evolution based solution technique along with a tournament selection that makes pair-wise comparison among feasible and infeasible solutions based on the degree of constraint violation for economic dispatch problems. We reformulate the nonsmooth objective function to a smooth one and add nonlinear inequality constraints to original ED problems. We consider five ED problems and compare the obtained results with existing standard deterministic NLP solvers as well as with other stochastic techniques available in literature.

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Mathematics Subject Classification: 90C30, 90C56, 90C59, 90C90.

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