Dual Conic Proxy for Semidefinite Relaxation of AC Optimal Power Flow

2025-02-10

AI Summary

The AC optimal power flow (AC-OPF) problem is a nonlinear, nonconvex optimization challenge; existing semidefinite programming (SDP) relaxation approaches suffer from prohibitive computational cost, limiting practical deployment. This paper introduces the first dual-cone surrogate model tailored for SDP relaxation, integrating a differentiable dual completion mechanism with neural networks to enable fast, certifiable near-optimal solution prediction. Key contributions are: (1) the first extension of dual-cone surrogates to the SDP relaxation framework; (2) a novel differentiable dual completion strategy that rigorously enforces dual feasibility while preserving the theoretical lower bound; and (3) a self-supervised learning paradigm eliminating reliance on expensive labeled data. Evaluated on a 500-bus system, the method achieves higher accuracy than second-order cone surrogates, accelerates solving by several orders of magnitude over state-of-the-art interior-point SDP solvers, and delivers tight, verifiable dual lower bounds.

Technology Category

• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

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.

Problem

• Develops a neural network for AC-OPF SDP relaxation.
• Ensures dual feasibility with speedup over interior-point methods.
• Uses self-supervised learning to reduce data generation time.

Innovation

• Neural network with dual completion
• Self-supervised learning efficiency
• Semidefinite relaxation optimization