Moment Relaxations of Optimal Power Flow Problems: Beyond the Convex Hull

TL;DR

This paper investigates the effectiveness of higher-order moment relaxations from the Lasserre hierarchy in globally solving optimal power flow problems, especially those with infeasible minima within the convex hull of non-convex constraints.

Contribution

It extends previous work by analyzing the capability of moment relaxations to handle problems with infeasible minima inside the convex hull.

Findings

Higher-order moment relaxations can approach the convex hulls of OPF problems.

Moment relaxations can globally solve certain non-convex OPF problems.

The study highlights limitations when minima are infeasible within the convex hull.

Abstract

Optimal power flow (OPF) is one of the key electric power system optimization problems. "Moment" relaxations from the Lasserre hierarchy for polynomial optimization globally solve many OPF problems. Previous work illustrates the ability of higher-order moment relaxations to approach the convex hulls of OPF problems' non-convex feasible spaces. Using a small test case, this paper focuses on the ability of the moment relaxations to globally solve problems with objective functions that have unconstrained minima at infeasible points inside the convex hull of the non-convex constraints.