Feasible Path Identification in Optimal Power Flow with Sequential Convex Restriction

Nonconvexity induced by the nonlinear AC power flow equations challenges solution algorithms for AC optimal power flow (OPF) problems. While significant research efforts have focused on reliably computing high-quality OPF solutions, identifying a feasible path from an initial operating to a desired operating point is a topic that has received much less attention. However, since the feasible space of the OPF problem is nonconvex and potentially disconnected, it can be challenging to transition between operating points while avoiding constraint violations. To address this problem, we propose an algorithm which computes a provably feasible path from an initial operating point to a desired operating point. The algorithm solves a sequence of quadratic optimization problems over conservative convex inner approximations of the OPF feasible space, each representing a so-called convex restriction. In each iteration, we obtain a new, improved operating point and a feasible transition from the operating point in the previous iteration. In addition to computing a feasible path to a known desired operating point, this algorithm can also be used to locally improve the operating point. Extensive numerical studies on a variety of test cases demonstrate the algorithm and the ability to arrive at a high-quality solution in few iterations.