A Low-Rank Coordinate-Descent Algorithm for Semidefinite Programming Relaxations of Optimal Power Flow

TL;DR

This paper introduces a new low-rank coordinate-descent algorithm for solving semidefinite programming relaxations of the AC optimal power flow problem, improving computational efficiency and solution quality.

Contribution

It proposes a novel reformulation of ACOPF using rank-constrained SDP relaxations and develops a first-order coordinate descent method with a closed-form step for enhanced performance.

Findings

Efficient solution of SDP relaxations for ACOPF.

Improved convergence using the coordinate descent method.

Potential for better handling of large-scale power systems.

Abstract

The alternating-current optimal power flow (ACOPF) is one of the best known non-convex non-linear optimisation problems. We present a novel re-formulation of ACOPF, which is based on lifting the rectangular power-voltage rank-constrained formulation, and makes it possible to derive alternative SDP relaxations. For those, we develop a first-order method based on the parallel coordinate descent with a novel closed-form step based on roots of cubic polynomials.