Moment-Based Relaxation of the Optimal Power Flow Problem

TL;DR

This paper introduces moment-based relaxations for the optimal power flow problem, which are tighter than previous relaxations and can find global solutions for a wider range of power system cases.

Contribution

It develops a novel moment-based relaxation approach derived from polynomial optimization theory for solving OPF problems.

Findings

Moment-based relaxations are generally tighter than semidefinite relaxations.

The approach can find global solutions for a broader class of OPF problems.

Exploration of test systems shows the effectiveness of the relaxation.

Abstract

The optimal power flow (OPF) problem minimizes power system operating cost subject to both engineering and network constraints. With the potential to find global solutions, significant research interest has focused on convex relaxations of the non-convex AC OPF problem. This paper investigates ``moment-based'' relaxations of the OPF problem developed from the theory of polynomial optimization problems. At the cost of increased computational requirements, moment-based relaxations are generally tighter than the semidefinite relaxation employed in previous research, thus resulting in global solutions for a broader class of OPF problems. Exploration of the feasible space for test systems illustrates the effectiveness of the moment-based relaxation.