Accurate and Warm-Startable Linear Cutting-Plane Relaxations for ACOPF

TL;DR

This paper introduces a linear cutting-plane relaxation method for ACOPF that quickly produces tight lower bounds and effectively utilizes warm-starts from previous instances, improving computational efficiency.

Contribution

The paper presents a novel warm-startable linear cutting-plane relaxation approach for ACOPF that leverages outer-envelope cuts and modern cut management techniques.

Findings

Effective on large ACOPF instances

Rapidly proves tight lower bounds

Warm-starts improve computational speed

Abstract

We present a linear cutting-plane relaxation approach that rapidly proves tight lower bounds for the Alternating Current Optimal Power Flow Problem (ACOPF). Our method leverages outer-envelope linear cuts for well-known second-order cone relaxations for ACOPF along with modern cut management techniques. These techniques prove effective on a broad family of ACOPF instances, including the largest ones publicly available, quickly and robustly yielding sharp bounds. Our primary focus concerns the (frequent) case where an ACOPF instance is considered following a small or moderate change in problem data, e.g., load changes and generator or branch shut-offs. We provide significant computational evidence that the cuts computed on the prior instance provide an effective warm-start for our algorithm.