AC Power Flow Feasibility Restoration via a State Estimation-Based Post-Processing Algorithm

This paper presents an algorithm for restoring AC power flow feasibility from solutions to simplified optimal power flow (OPF) problems, including convex relaxations, power flow approximations, and machine learning (ML) models. The proposed algorithm employs a state estimation-based post-processing technique in which voltage phasors, power injections, and line flows from solutions to relaxed, approximated, or ML-based OPF problems are treated similarly to noisy measurements in a state estimation algorithm. The algorithm leverages information from various quantities to obtain feasible voltage phasors and power injections that satisfy the AC power flow equations. Weight and bias parameters are computed offline using an adaptive stochastic gradient descent method. By automatically learning the trustworthiness of various outputs from simplified OPF problems, these parameters inform the online computations of the state estimation-based algorithm to both recover feasible solutions and characterize the performance of power flow approximations, relaxations, and ML models. Furthermore, the proposed algorithm can simultaneously utilize combined solutions from different relaxations, approximations, and ML models to enhance performance. Case studies demonstrate the effectiveness and scalability of the proposed algorithm, with solutions that are both AC power flow feasible and much closer to the true AC OPF solutions than alternative methods, often by several orders of magnitude in the squared two-norm loss function.