Computational Analysis of Sparsity-Exploiting Moment Relaxations of the OPF Problem

TL;DR

This paper investigates the use of sparsity-exploiting moment relaxations from the Lasserre hierarchy to solve the optimal power flow (OPF) problem efficiently, analyzing key parameters to improve computational speed and scalability.

Contribution

It provides a detailed study of the key parameter in an iterative algorithm for applying moment relaxations to large-scale OPF problems, including both real and complex hierarchies.

Findings

Analysis of the key parameter improves computational efficiency.

Sparsity exploitation enables solving larger OPF problems.

Comparison of real and complex hierarchies enhances understanding of relaxation methods.

Abstract

With the potential to find global solutions, significant research interest has focused on convex relaxations of the non-convex OPF problem. Recently, "moment-based" relaxations from the Lasserre hierarchy for polynomial optimization have been shown capable of globally solving a broad class of OPF problems. Global solution of many large-scale test cases is accomplished by exploiting sparsity and selectively applying the computationally intensive higher-order relaxation constraints. Previous work describes an iterative algorithm that indicates the buses for which the higher-order constraints should be enforced. In order to speed computation of the moment relaxations, this paper provides a study of the key parameter in this algorithm as applied to relaxations from both the original Lasserre hierarchy and a recent complex extension of the Lasserre hierarchy.