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Dual Conic Proxies for AC Optimal Power Flow

Guancheng Qiu, Mathieu Tanneau, Pascal Van Hentenryck

TL;DR

This work tackles the lack of certified dual bounds in ML-based AC-OPF proxies by introducing Dual Conic Proxies (DCP) that exploit the SOC relaxation of AC-OPF and a dual-feasibility completion to guarantee dual feasibility. A novel self-supervised training regimen enables end-to-end learning without expensive data generation, while a carefully designed representation (including polar form for certain dual variables) enhances learning performance. Empirical results on grids with up to 2869 buses show that DCP can produce valid dual bounds in milliseconds, achieving average gaps well below 1% for large systems and offering three-order-of-magnitude speedups over conventional solvers. The approach thus provides real-time certified dual bounds for AC-OPF proxies and lays out a scalable path to further high-performance, bound-certified MLOPF tools. The findings demonstrate the practical impact of combining convex relaxations, conic duality, and self-supervised learning for reliable, fast power-system optimization.

Abstract

In recent years, there has been significant interest in the development of machine learning-based optimization proxies for AC Optimal Power Flow (AC-OPF). Although significant progress has been achieved in predicting high-quality primal solutions, no existing learning-based approach can provide valid dual bounds for AC-OPF. This paper addresses this gap by training optimization proxies for a convex relaxation of AC-OPF. Namely, the paper considers a second-order cone (SOC) relaxation of AC-OPF, and proposes \revision{a novel architecture} that embeds a fast, differentiable (dual) feasibility recovery, thus providing valid dual bounds. The paper combines this new architecture with a self-supervised learning scheme, which alleviates the need for costly training data generation. Extensive numerical experiments on medium- and large-scale power grids demonstrate the efficiency and scalability of the proposed methodology.

Dual Conic Proxies for AC Optimal Power Flow

TL;DR

This work tackles the lack of certified dual bounds in ML-based AC-OPF proxies by introducing Dual Conic Proxies (DCP) that exploit the SOC relaxation of AC-OPF and a dual-feasibility completion to guarantee dual feasibility. A novel self-supervised training regimen enables end-to-end learning without expensive data generation, while a carefully designed representation (including polar form for certain dual variables) enhances learning performance. Empirical results on grids with up to 2869 buses show that DCP can produce valid dual bounds in milliseconds, achieving average gaps well below 1% for large systems and offering three-order-of-magnitude speedups over conventional solvers. The approach thus provides real-time certified dual bounds for AC-OPF proxies and lays out a scalable path to further high-performance, bound-certified MLOPF tools. The findings demonstrate the practical impact of combining convex relaxations, conic duality, and self-supervised learning for reliable, fast power-system optimization.

Abstract

In recent years, there has been significant interest in the development of machine learning-based optimization proxies for AC Optimal Power Flow (AC-OPF). Although significant progress has been achieved in predicting high-quality primal solutions, no existing learning-based approach can provide valid dual bounds for AC-OPF. This paper addresses this gap by training optimization proxies for a convex relaxation of AC-OPF. Namely, the paper considers a second-order cone (SOC) relaxation of AC-OPF, and proposes \revision{a novel architecture} that embeds a fast, differentiable (dual) feasibility recovery, thus providing valid dual bounds. The paper combines this new architecture with a self-supervised learning scheme, which alleviates the need for costly training data generation. Extensive numerical experiments on medium- and large-scale power grids demonstrate the efficiency and scalability of the proposed methodology.
Paper Structure (17 sections, 4 theorems, 14 equations, 1 figure, 6 tables, 1 algorithm)

This paper contains 17 sections, 4 theorems, 14 equations, 1 figure, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Convex Relaxations of AC-OPF
  4. Optimization Proxies for AC-OPF
  5. Optimization Proxy Verification
  6. AC-OPF and a Second-Order Cone Relaxation
  7. The AC Optimal Power Flow Formulation
  8. The Second-Order Cone Relaxation of the AC-OPF
  9. The Dual-Feasible Proxy Architecture
  10. Dual Feasibility Completion
  11. Rectangular vs Polar Representation
  12. The Dual Conic Proxy Architecture and Training
  13. Experimental Results
  14. Data Generation
  15. Performance Evaluation
  16. ...and 2 more sections

Key Result

Lemma 1

Let $\mathbf{y}$ be dual-optimal. Then,

Figures (1)

  • Figure 1: The Proposed Dual Conic Proxy Architecture.

Theorems & Definitions (8)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Theorem 1
  • proof