Dual Conic Proxy for Semidefinite Relaxation of AC Optimal Power Flow

TL;DR

The paper tackles the challenge of obtaining reliable, fast lower bounds for the nonconvex AC-OPF by developing a dual conic proxy for the SDP relaxation. It introduces a dual-feasible architecture with a differentiable dual completion layer that enforces the PSD constraint, enabling end-to-end self-supervised training without ground-truth duals. Empirical results on power systems up to 500 buses show the SDP-based proxy can achieve tighter dual bounds than SOC-based proxies and deliver orders-of-magnitude speedups over interior-point SDP solvers. The work highlights the practical potential of SDP-based dual proxies and points to chordal sparsity as a key avenue for scaling to larger grids.

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.

Figures (2)

• Figure 1: The AC-OPF model
• Figure 2: The SDP-OPF model