Refining Graphical Neural Network Predictions Using Flow Matching for Optimal Power Flow with Constraint-Satisfaction Guarantee

TL;DR

This paper introduces a physics-informed two-stage neural network framework combining Graph Neural Networks and Continuous Flow Matching to efficiently solve the DC Optimal Power Flow problem with guaranteed feasibility and near-optimal solutions.

Contribution

It presents a novel method integrating physical laws into GNN training and refines solutions with flow matching, ensuring feasibility and optimality in power flow problems.

Findings

Achieves near-zero cost gap under nominal load conditions.

Maintains 100% feasibility across tested scenarios.

Effective for real-time power system dispatch with high renewable penetration.

Abstract

The DC Optimal Power Flow (DC-OPF) problem is fundamental to power system operations, requiring rapid solutions for real-time grid management. While traditional optimization solvers provide optimal solutions, their computational cost becomes prohibitive for large-scale systems requiring frequent recalculations. Machine learning approaches offer promise for acceleration but often struggle with constraint satisfaction and cost optimality. We present a novel two-stage learning framework that combines physics-informed Graph Neural Networks (GNNs) with Continuous Flow Matching (CFM) for solving DC-OPF problems. Our approach embeds fundamental physical principles--including economic dispatch optimality conditions, Kirchhoff's laws, and Karush-Kuhn-Tucker (KKT) complementarity conditions--directly into the training objectives. The first stage trains a GNN to produce feasible initial solutions by learning from physics-informed losses that encode power system constraints. The second stage employs CFM, a simulation-free continuous normalizing flow technique, to refine these solutions toward optimality through learned vector field regression. Evaluated on the IEEE 30-bus system across five load scenarios ranging from 70\% to 130\% nominal load, our method achieves near-optimal solutions with cost gaps below 0.1\% for nominal loads and below 3\% for extreme conditions, while maintaining 100\% feasibility. Our framework bridges the gap between fast but approximate neural network predictions and optimal but slow numerical solvers, offering a practical solution for modern power systems with high renewable penetration requiring frequent dispatch updates.