Solution of Optimal Power Flow Problems using Moment Relaxations Augmented with Objective Function Penalization

TL;DR

This paper enhances the application of moment relaxations to solve large-scale optimal power flow problems by introducing an objective function penalization technique that improves solution quality and computational tractability.

Contribution

It proposes combining objective function penalization with moment relaxations to globally solve large OPF problems, eliminating the need for penalty parameter tuning.

Findings

Successfully solves large OPF problems minimizing active power losses.

Achieves solutions close to the global optimum.

Reduces computational intractability for complex problems.

Abstract

The optimal power flow (OPF) problem minimizes the operating cost of an electric power system. Applications of convex relaxation techniques to the non-convex OPF problem have been of recent interest, including work using the Lasserre hierarchy of "moment" relaxations to globally solve many OPF problems. By preprocessing the network model to eliminate low-impedance lines, this paper demonstrates the capability of the moment relaxations to globally solve large OPF problems that minimize active power losses for portions of several European power systems. Large problems with more general objective functions have thus far been computationally intractable for current formulations of the moment relaxations. To overcome this limitation, this paper proposes the combination of an objective function penalization with the moment relaxations. This combination yields feasible points with objective function values that are close to the global optimum of several large OPF problems. Compared to an existing penalization method, the combination of penalization and the moment relaxations eliminates the need to specify one of the penalty parameters and solves a broader class of problems.