Local Solutions of Optimal Power Flow

The existence of locally optimal solutions to optimal power flow (OPF) problems has been a question of interest for decades. This paper presents examples of local optima on very simple power system networks. Usually local optima occur when the network is stressed, and the resulting voltage profiles are infeasible in practice; however, we present examples where the voltage is within practical limits. Standard local optimization techniques are shown to converge to these local optima if started close enough to them. We also give examples of local solutions in loop networks. Finally we use a two-bus example with local optima to illustrate the behaviour of a recent dual semi-definite programming approach that aims to find the global solution.