Loss minimization by the predictor–corrector modified barrier approach

This paper presents a new approach, predictor–corrector modified barrier approach (PCMBA), to minimize the active losses in power system planning studies. In the PCMBA, the inequality constraints are transformed into equalities by introducing positive auxiliary variables, which are perturbed by the barrier parameter, and treated by the modified barrier method. The first-order necessary conditions of the Lagrangian function are solved by predictor–corrector Newton's method. The perturbation of the auxiliary variables results in an expansion of the feasible set of the original problem, reaching the limits of the inequality constraints. The feasibility of the proposed approach is demonstrated using various IEEE test systems and a realistic power system of 2256-bus corresponding to the Brazilian South-Southeastern interconnected system. The results show that the utilization of the predictor–corrector method with the pure modified barrier approach accelerates the convergence of the problem in terms of the number of iterations and computational time.