Towards an AC Optimal Power Flow Algorithm with Robust Feasibility Guarantees

With growing penetrations of stochastic renewable generation and the need to accurately model the network physics, optimization problems that explicitly consider uncertainty and the AC power flow equations are becoming increasingly important to the operation of electric power systems. This paper describes initial steps towards an AC Optimal Power Flow (AC OPF) algorithm which yields an operating point that is guaranteed to be robust to all realizations of stochastic generation within a specified uncertainty set. Ensuring robust feasibility requires overcoming two challenges: 1) ensuring solvability of the power flow equations for all uncertainty realizations and 2) guaranteeing feasibility of the engineering constraints for all uncertainty realizations. This paper primarily focuses on the latter challenge. Specifically, the robust AC OPF problem is posed as a bi-level program that maximizes (or minimizes) the constraint values over the uncertainty set, where a convex relaxation of the AC power flow constraints is used to ensure conservativeness. The resulting optimization program is solved using an alternating solution algorithm. The algorithm is illustrated via detailed analyses of two small test cases.