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

2025-11-11

AI Summary

Learning-to-optimize (L2O) methods for AC optimal power flow (AC-OPF) suffer from unstable convergence and infeasible solutions due to the inherent nonconvexity of the problem. Method: This paper proposes a homotopy-guided self-supervised learning framework—first integrating homotopy continuation into the L2O paradigm—where the objective and constraints are progressively deformed from a convex relaxation to the original nonconvex AC-OPF, leveraging the relaxation’s large basin of attraction to guide neural network parameter optimization. The entire training is end-to-end and fully self-supervised, requiring neither ground-truth labels nor external solvers. Results: Experiments on IEEE benchmark systems demonstrate a substantial increase in feasibility rate and near-optimal objective values closely matching those of exact OPF solvers. The model exhibits significantly improved robustness and practicality, establishing a scalable, learning-based solving paradigm for nonconvex power system optimization.

Technology Category

• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Computer Vision: Learning & Optimization for CV

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

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 extit{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.

Problem

• Addressing nonconvex optimization landscapes in AC optimal power flow
• Improving convergence stability for parametric solution approximations
• Enhancing feasibility rates without requiring labeled optimal solutions

Innovation

• Homotopy-guided self-supervised learning for parametric AC-OPF
• Continuous deformation from relaxed to original problem
• Improves convergence stability and feasibility without solvers