A Laplacian-Based Approach for Finding Near Globally Optimal Solutions to OPF Problems

TL;DR

This paper introduces a novel Laplacian-based method that adaptively determines penalization to find near-globally optimal solutions for optimal power flow problems, improving upon existing SDP relaxation techniques.

Contribution

It proposes an algorithmic approach that constrains generation costs and uses Laplacian weights to efficiently find near-optimal solutions without manual penalty parameter tuning.

Findings

Successfully finds near-global solutions for small and large OPF problems.

Demonstrates effectiveness on European power system test cases.

Guarantees solutions are close to the global optimum.

Abstract

A semidefinite programming (SDP) relaxation globally solves many optimal power flow (OPF) problems. For other OPF problems where the SDP relaxation only provides a lower bound on the objective value rather than the globally optimal decision variables, recent literature has proposed a penalization approach to find feasible points that are often nearly globally optimal. A disadvantage of this penalization approach is the need to specify penalty parameters. This paper presents an alternative approach that algorithmically determines a penalization appropriate for many OPF problems. The proposed approach constrains the generation cost to be close to the lower bound from the SDP relaxation. The objective function is specified using iteratively determined weights for a Laplacian matrix. This approach yields feasible points to the OPF problem that are guaranteed to have objective values near the global optimum due to the constraint on generation cost. The proposed approach is demonstrated on both small OPF problems and a variety of large test cases representing portions of European power systems.