Optimal power flow in distribution networks under stochastic N−1 disruptions

It is important to include contingencies in operations and have a post-contingency recovery plan for distribution systems, akin to transmission systems. We consider a multi-period optimal power flow (OPF) problem in distribution systems subject to stochastic N−1 contingency (disruption) in a distribution line or a distributed energy resource. The disruption is stochastic in nature, a type of infrequent event with random magnitude and timing, and that every disruption typically has an associated recovery time. We formulate a multi-stage stochastic convex program, considering modeling features like linearized AC power flow physics, engineering limits and battery devices with efficiencies curves, and develop an efficient decomposition algorithm. We demonstrate the computational effectiveness of our algorithm over the extensive formulation and show that the stochastic-disruption-aware operating costs can be 60% cheaper than the deterministic counterparts.