Optimal power flow computations with constraints limiting the number of control actions

This paper focuses on optimal power flow (OPF) computations in which no more than a pre-specified number of controls are allowed to move. The benchmark formulation of this OPF problem constitutes a mixed integer nonlinear programming (MINLP) problem. To avoid the prohibitive computational time required by classical MINLP approaches to provide a (potentially sub-optimal) solution, we propose instead two alternative approaches. The first one consists in reformulating the MINLP problem as a mathematical program with equilibrium constraints (MPEC). The second approach includes in the classical OPF problem a nonlinear constraint which approximates the integral constraint limiting the number of control variables movement. Both approaches are solved by an interior point algorithm (IPA), slightly adapted to the particular characteristics of each approach. We provide numerical results with the proposed approaches on two test systems and for two practical problems: minimum cost to remove thermal congestion, and minimum cost of load curtailment to restore a feasible equilibrium point.