DiffOPF: Diffusion Solver for Optimal Power Flow

2025-10-15

AI Summary

Optimal power flow (OPF) is inherently a multivalued, non-convex mapping from load inputs to generation setpoints, further complicated by solution multiplicity induced by variations in system parameters (e.g., admittances, topology). Existing deep learning–based solvers model OPF as a deterministic, single-valued function and thus fail to capture this intrinsic uncertainty. This paper reformulates OPF as a conditional sampling problem and proposes the first diffusion-based probabilistic generative framework that directly learns the joint distribution of loads and optimal setpoints. The method enables multimodal, statistically principled conditional sampling while ensuring constraint satisfaction and offering controllable trade-offs between solution cost and feasibility. Evaluated on standard benchmark systems, the approach yields samples with bounded optimality gaps, achieves orders-of-magnitude speedup over conventional solvers, and natively supports uncertainty modeling of system parameters.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The optimal power flow (OPF) is a multi-valued, non-convex mapping from loads to dispatch setpoints. The variability of system parameters (e.g., admittances, topology) further contributes to the multiplicity of dispatch setpoints for a given load. Existing deep learning OPF solvers are single-valued and thus fail to capture the variability of system parameters unless fully represented in the feature space, which is prohibitive. To solve this problem, we introduce a diffusion-based OPF solver, termed extit{DiffOPF}, that treats OPF as a conditional sampling problem. The solver learns the joint distribution of loads and dispatch setpoints from operational history, and returns the marginal dispatch distributions conditioned on loads. Unlike single-valued solvers, DiffOPF enables sampling statistically credible warm starts with favorable cost and constraint satisfaction trade-offs. We explore the sample complexity of DiffOPF to ensure the OPF solution within a prescribed distance from the optimization-based solution, and verify this experimentally on power system benchmarks.

Problem

• Solving non-convex multi-valued optimal power flow mapping
• Capturing system parameter variability in dispatch setpoints
• Generating credible warm starts with cost-constraint tradeoffs

Innovation

• Diffusion-based solver treats OPF as conditional sampling
• Learns joint distribution of loads and dispatch setpoints
• Enables sampling credible warm starts with cost trade-offs