Emission, reserve and economic load dispatch problem with non-smooth and non-convex cost functions using epsilon-multi-objective genetic algorithm variable

•Introduce the εv-MOGA to solve emission, reserve and ELD problem.•Form the εv-MOGA based on the idea of ε-dominance.•Consider the valve-point, prohibited zones, frequency, and practical constraints.•Increase the social welfare for consumers and GENCOs by frequency constraints.•Illustrate the more speed and effectiveness of the εv-MOGA than other algorithm.

This paper addresses a novel method for the multi-objective economic load dispatch (ELD) problem. Power generation, spinning reserve costs and emission are considered in the objective function of the frequency ELD problem. The frequency deviation, minimum frequency limits and other practical constraints are also taken into account in this problem. It is a highly constrained multi-objective optimization problem that involves conflicting objectives with both equality and inequality constraints. In this paper, an elitist evolutionary multi-objective optimization algorithm based on the concept of ε-dominance, called ε-multi-objective genetic algorithm variable (εv-MOGA), is proposed to solve the frequency ELD problem. In this study, the performance of the proposed εv-MOGA algorithm is compared with the performance of other classic and intelligent algorithms. The proposed method is tested on 6, 10, 13 and 40 generating units, and the simulation results of four power systems demonstrate the advantages of the proposed method for reducing the cost function.

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