Adjustment of mutant vector elements in the differential evolution method for solving the problem of power shortage minimization in electric power systems

Abstract

The article is aimed at increasing the effectiveness of numerical optimization methods in calculations of problems concerning power shortage minimization in electric power systems, specifically the differential evolution (DE) method and its variations–aDE and jDE. Experimental studies and testing of the proposed adjustments were carried out on complex electric power systems of different order. These systems are represented and realized by means of mathematical models of power shortage minimization with the possibility of their analysis using the developed software package as part of adequacy assessment. The performed analysis of the DE method elements and the existing variants of the mutation process revealed that the existing approaches can be further modified. This can subsequently increase the speed of problem-solving. It is shown that the main changes include an additional check that the mutant vectors meet the upper and lower bounds, and if they fail to do so, three adjustment options are considered. Existing approaches propose to generate new vector elements beyond the bounds by applying random numbers within the bounds. The present authors propose to use the “projections” of the found vector elements, i.e., to use the values of upper or lower bounds when they are exceeded for a particular element as mutant vector values. The implemented method involving the adjustment of mutant vector elements is shown to offer an advantage of a 47% reduction in problem-solving time over existing adjustment methods while maintaining the same accuracy. It is noted that aDE and jDE are the most effective variations for solving stated problems. The obtained results of experimental studies confirm the effectiveness and advantages of applying the proposed adjustment method in mutation process of in the form of “projections”, as well as using aDE and jDE variations of the DE method to solve the problems of power shortage minimization in electric power systems.