Restoring AC Power Flow Feasibility from Relaxed and Approximated Optimal Power Flow Models

TL;DR

This paper introduces a novel method inspired by state estimation techniques to restore AC power flow feasibility from relaxed or approximated OPF solutions, significantly improving accuracy in power system analysis.

Contribution

It proposes a new approach that treats inconsistent power system quantities as noisy measurements, enabling feasible AC power flow solutions from relaxed or approximated OPF models.

Findings

Up to several orders of magnitude improvement in accuracy.

Effective across various relaxations and approximations.

Enhances the practical utility of relaxed OPF solutions.

Abstract

To address computational challenges associated with power flow nonconvexities, significant research efforts over the last decade have developed convex relaxations and approximations of optimal power flow (OPF) problems. However, benefits associated with the convexity of these relaxations and approximations can have tradeoffs in terms of solution accuracy since they may yield voltage phasors that are inconsistent with the power injections and line flows, limiting their usefulness for some applications. Inspired by state estimation (SE) techniques, this paper proposes a new method for obtaining an AC power flow feasible point from the solution to a relaxed or approximated optimal power flow (OPF) problem. By treating the inconsistent voltage phasors, power injections, and line flows analogously to noisy measurements in a state estimation algorithm, the proposed method yields power injections and voltage phasors that are feasible with respect to the AC power flow equations while incorporating information from many quantities in the solution to a relaxed or approximated OPF problem. We improve this method by adjusting weighting terms with an approach inspired by algorithms used to train machine learning models. We demonstrate the proposed method using several relaxations and approximations. The results show up to several orders of magnitude improvement in accuracy over traditional methods.