Statistical tuning of DEEPSO soft constraints in the Security Constrained Optimal Power Flow problem

The optimal solution provided by metaheuristics can be viewed as a random variable, whose behavior depends on the value of the algorithm's strategic parameters and on the type of penalty function used to enforce the problem's soft constraints. This paper reports the use of parametric and non-parametric statistics to compare three different penalty functions implemented to solve the Security Constrained Optimal Power Flow (SCOPF) problem using the new enhanced metaheuristic Differential Evolutionary Particle Swarm Optimization (DEEPSO). To obtain the best performance for the three types of penalty functions, the strategic parameters of DEEPSO are optimized by using an iterative algorithm based on the two-way analysis of variance (ANOVA). The results show that the modeling of soft constraints significantly influences the best achievable performance of the optimization algorithm.