Application of interior point methods to power flow unsolvability

This paper describes an application of an optimal power flow, solved by a direct interior point (IP) method, to restore system solvability. Using the P-Q load representation, power flow unsolvability occurs when, for a given set of active and reactive bus injections, the power flow equations have no real solution. The set of control actions in the IP algorithm includes rescheduling of active power of generators, adjustments on terminal voltage of generators, tap changes on LTC transformers, and as a last resort, minimum load shedding. The IP formulation allows observation of the impact of each control optimization in system solvability. Also described is a framework to calculate probabilistic indicators of solvability problems taking into account the probability of contingencies. The role of control optimization is illustrated in a real 11-bus power system and the probabilistic approach is applied to a 1600-bus power system derived from the Brazilian South/Southeast/Central West system.