Homotopy-Guided Self-Supervised Learning of Parametric Solutions for AC Optimal Power Flow

TL;DR

This paper presents a homotopy-guided self-supervised learning approach for AC optimal power flow that enhances convergence and feasibility without relying on labeled data, enabling faster decision-making in power systems.

Contribution

It introduces a novel homotopy-based training method for learning parametric AC-OPF solutions, improving stability and feasibility in nonconvex optimization landscapes.

Findings

Increased feasibility rates on IEEE benchmarks

Achieved objective values comparable to traditional solvers

Enhanced convergence stability without labeled solutions

Abstract

Learning to optimize (L2O) parametric approximations of AC optimal power flow (AC-OPF) solutions offers the potential for fast, reusable decision-making in real-time power system operations. However, the inherent nonconvexity of AC-OPF results in challenging optimization landscapes, and standard learning approaches often fail to converge to feasible, high-quality solutions. This work introduces a \textit{homotopy-guided self-supervised L2O method} for parametric AC-OPF problems. The key idea is to construct a continuous deformation of the objective and constraints during training, beginning from a relaxed problem with a broad basin of attraction and gradually transforming it toward the original problem. The resulting learning process improves convergence stability and promotes feasibility without requiring labeled optimal solutions or external solvers. We evaluate the proposed method on standard IEEE AC-OPF benchmarks and show that homotopy-guided L2O significantly increases feasibility rates compared to non-homotopy baselines, while achieving objective values comparable to full OPF solvers. These findings demonstrate the promise of homotopy-based heuristics for scalable, constraint-aware L2O in power system optimization.