Advanced Cutting-Plane Algorithms for ACOPF

TL;DR

This paper introduces a scalable linear cutting-plane method for SDP relaxations of the ACOPF problem, enabling tight bounds for large-scale instances beyond current nonlinear solvers.

Contribution

It presents a numerically stable, warm-startable linear cutting-plane approach that improves bounds for large-scale ACOPF relaxations.

Findings

Achieves tighter bounds than existing methods on benchmark instances.

Demonstrates scalability to large multi-period problems.

Shows promising preliminary results on PGLIB datasets.

Abstract

We propose a disciplined, numerically stable, and scalable approach to SDP relaxations of the ACOPF problem based on linear cutting-planes. Our method can be warm-started and, owing to its linear nature, enables the computation of tight and accurate bounds for large-scale multi-period relaxations -- well beyond what nonlinear convex solvers can achieve. Preliminary experiments show promising results when benchmarked against state-of-the-art bounds on PGLIB instances.