Neural-optimization integration for AC optimal power flow: A differentiable warm-start approach

Accelerating the convergence of AC optimal power flow (AC-OPF) problems is crucial for real-time power system operation, especially as modern grids face increasing complexity from renewable energy integration and dynamic operational requirements. The AC-OPF problem, characterized by its nonlinear and non-convex nature, presents significant computational challenges for large-scale networks where traditional optimization methods often require excessive iteration counts. While warm-start techniques have shown promise, existing approaches rely on heuristics or two-stage frameworks that fail to fully exploit the synergy between machine learning and optimization solvers. This paper proposes a novel end-to-end learning-based warm-start framework that integrates neural networks with conventional solvers to achieve superior convergence acceleration while maintaining solution optimality and constraint satisfaction. The key innovation lies in enabling gradient backpropagation through the optimization process by transforming constrained problems into unconstrained subproblems and deriving explicit gradient computation using Newton steps and automatic differentiation. Validation on IEEE test systems demonstrates that our method reduces solver iterations over 45% and computational time by over 44% compared to standalone model-based optimization, while maintaining perfect constraint satisfaction.