Load Variation Enables Escaping Poor Solutions of Time-Varying Optimal Power Flow

摘要

This paper analyzes solution trajectories for optimal power flow (OPF) with time-varying load. Despite its nonconvexity, it is common to solve time-varying OPF sequentially over time using simple local-search algorithms. We aim to understand the local and global optimality behavior of these local solution trajectories. An empirical study on California data shows that local solution trajectories initialized at different points may converge to the time-varying global solution of the data-driven OPF, even if the problem has multiple local solutions throughout time. That is, these trajectories can avoid poor solutions. To explain this phenomenon, we introduce a backward mapping that relates a neighborhood of the time-varying OPF’s global solution at a given time to a set of desirable initial points. We show that this proposed backward mapping could act as a stochastic gradient ascent algorithm on an implicitly convexified formulation of OPF, which justifies the escaping of poor solutions over time.