Dual Conic Proxy for Semidefinite Relaxation of AC Optimal Power Flow

TL;DR

This paper introduces a novel dual conic proxy architecture for the SDP relaxation of AC-OPF problems, combining neural networks and convex optimization to achieve faster solutions with valid dual bounds.

Contribution

It is the first to develop a dual conic proxy for SDP relaxation of AC-OPF, enhancing computational efficiency and dual feasibility through a neural network and dual completion strategy.

Findings

Achieves several orders of magnitude speedup over interior-point SDP solvers.

Outperforms weaker conic relaxations in solution quality.

Successfully applies self-supervised learning for efficient training.

Abstract

The nonlinear, non-convex AC Optimal Power Flow (AC-OPF) problem is fundamental for power systems operations. The intrinsic complexity of AC-OPF has fueled a growing interest in the development of optimization proxies for the problem, i.e., machine learning models that predict high-quality, close-to-optimal solutions. More recently, dual conic proxy architectures have been proposed, which combine machine learning and convex relaxations of AC-OPF, to provide valid certificates of optimality using learning-based methods. Building on this methodology, this paper proposes, for the first time, a dual conic proxy architecture for the semidefinite (SDP) relaxation of AC-OPF problems. Although the SDP relaxation is stronger than the second-order cone relaxation considered in previous work, its practical use has been hindered by its computational cost. The proposed method combines a neural network with a differentiable dual completion strategy that leverages the structure of the dual SDP problem. This approach guarantees dual feasibility, and therefore valid dual bounds, while providing orders of magnitude of speedups compared to interior-point algorithms. The paper also leverages self-supervised learning, which alleviates the need for time-consuming data generation and allows to train the proposed models efficiently. Numerical experiments are presented on several power grid benchmarks with up to 500 buses. The results demonstrate that the proposed SDP-based proxies can outperform weaker conic relaxations, while providing several orders of magnitude speedups compared to a state-of-the-art interior-point SDP solver.