Residual Correction Models for AC Optimal Power Flow Using DC Optimal Power Flow Solutions

TL;DR

This work addresses the computational bottleneck of AC OPF by introducing a residual learning framework that uses fast DC OPF solutions as a baseline and learns nonlinear corrections via a topology-aware Graph Neural Network. The model integrates DC features at local and global stages and enforces AC feasibility with a physics-informed loss, achieving improved accuracy, feasibility, and scalability across 57-, 118-, and 2000-bus systems, with up to 13× runtime speedups. Key contributions include a two-level DC feature fusion strategy, typed-message GNN with local attention, and residual heads that predict corrections to the DC baseline, along with robust performance under $N{-}1$ contingencies and the ability to generate synthetic AC-feasible data for training. The approach offers a practical bridge between linear approximations and AC-feasible OPF, enabling near real-time operational decision-making in modern grids and providing a foundation for data-driven strengthening of OPF workflows.

Abstract

Solving the nonlinear AC optimal power flow (AC OPF) problem remains a major computational bottleneck for real-time grid operations. In this paper, we propose a residual learning paradigm that uses fast DC optimal power flow (DC OPF) solutions as a baseline, and learns only the nonlinear corrections required to provide the full AC-OPF solution. The method utilizes a topology-aware Graph Neural Network with local attention and two-level DC feature integration, trained using a physics-informed loss that enforces AC power-flow feasibility and operational limits. Evaluations on OPFData for 57-, 118-, and 2000-bus systems show around 25% lower MSE, up to 3X reduction in feasibility error, and up to 13X runtime speedup compared to conventional AC OPF solvers. The model maintains accuracy under N-1 contingencies and scales efficiently to large networks. These results demonstrate that residual learning is a practical and scalable bridge between linear approximations and AC-feasible OPF, enabling near real-time operational decision making.

Figures (3)

• Figure 1: Pipeline for the proposed methodology
• Figure 3: Cumulative proportion of the absolute error in the power predicted with and without additional training data
• Figure 4: Cumulative proportion of the absolute error in the voltage angle predicted with and without additional training data