Reduced-Complexity Semidefinite Relaxations of Optimal Power Flow Problems

TL;DR

This paper introduces a new, computationally cheaper method for generating semidefinite relaxations of optimal power flow problems using chordal conversion techniques, often maintaining solution quality while reducing complexity.

Contribution

It proposes a novel relaxation approach that drops certain constraints to lower computational costs, offering a practical alternative to standard methods.

Findings

New relaxations often match standard relaxation results

Reduced computational cost compared to standard semidefinite relaxation

Potentially weaker but still effective relaxations

Abstract

We propose a new method for generating semidefinite relaxations of optimal power flow problems. The method is based on chordal conversion techniques: by dropping some equality constraints in the conversion, we obtain semidefinite relaxations that are computationally cheaper, but potentially weaker, than the standard semidefinite relaxation. Our numerical results show that the new relaxations often produce the same results as the standard semidefinite relaxation, but at a lower computational cost.