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

TL;DR

This paper addresses the challenge of rapidly computing feasible, near-optimal solutions to the nonconvex $AC$-OPF problem by learning a parametric solution map with self-supervised L2O. It introduces homotopy-guided training that progressively morphs a relaxed problem into the original formulation via the homotopy parameter $\lambda_H \in [0,1]$, with two complementary schemes: Type I relaxation-based and Type II OPF-aware continuations. The approach uses a penalty-based loss and warm-started optimization to achieve higher feasibility rates while maintaining objective values close to those of full $AC$-OPF solvers on IEEE benchmarks. The results indicate that homotopy continuation yields more reliable convergence and constraint satisfaction, supporting scalable, constraint-aware L2O for power-system optimization.

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.

Figures (2)

• Figure 1: Supervised vs self-supervised learning to optimize (L2O).
• Figure 2: A desirable homotopy path where the previous problem solution falls within the basin of attraction for the next.