Solving optimal power flow problems using a probabilistic α-constrained evolutionary approach

One of the most difficult tasks in any population-based approach is to deal with large-scale constrained systems without losing computational efficiency. To achieve such goal, a methodology based on two different techniques is presented. First, an evolutionary algorithm based on a cluster-and-gradient-based artificial immune system (CGbAIS) is used to improve computational time. For that, the CGbAIS uses the numerical information provided by the electrical power system and a clustering strategy that eliminates redundant individuals to speed up the convergence process. Second, to increase the capacity of dealing with constraints, a probabilistic α-level of relaxation is used. This approach treats separately the constraints and objective functions. It generates a lexicographic comparison process meaning that, if two individuals have their constraints below the current α-level, the one with the better objective function has a probability of winning the comparison. Otherwise, the individual with the lower penalty is selected regardless the value of the objective function. Combining these concepts together generates a computational framework capable of finding optimal solutions within a very interesting computational time. Applications using a mixed integer and continuous variables will illustrate the performance of the proposed method.