Robustness Analysis in Evolutionary Multi-Objective Optimization Applied to VAR Planning in Electrical Distribution Networks

In this paper an approach to robustness analysis in evolutionary multi-objective optimization is applied to the problem of locating and sizing capacitors for reactive power compensation (VAR planning) in electric radial distribution networks. The main goal of this evolutionary algorithm is to find a non-dominated front containing the most robust non-dominated solutions also ensuring diversity along the front. A concept of degree of robustness is incorporated into the evolutionary algorithm, which intervenes in the computation of the fitness value assigned to solutions. Two objective functions of technical and economical nature are explicitly considered in the mathematical model: minimization of system losses and minimization of capacitor installation costs. Constraints refer to quality of service, power flow, and technical requirements. It is assumed that some input data are subject to perturbations, both concerning the objective functions and the constraints coefficients.