A Physics-Informed Graph Convolution Network for AC Optimal Power Flow via Refining DC Solution

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Abstract
Solving alternating current optimal power flow (AC-OPF) problems for large-scale power systems is essential for operations integrating renewable energy. However, conventional numerical methods for AC-OPF face challenges such as high computational costs and convergence difficulties as system size increases. To address these challenges, existing research utilizes direct current OPF (DC-OPF) or data-driven methods. DC-OPF linearizes the AC-OPF problem by considering inherent physical characteristics of the power system, such as voltage variations, providing an approximate solution. Meanwhile, data-driven methods leverage its strong end-to-end learning capabilities to solve AC-OPF effectively. Although both methods are sufficiently fast, DC-OPF can suffer from accuracy limitations due to its simplifying assumptions, which neglect reactive power and voltage deviations. On the other hand, data-driven approaches may exhibit degraded performance when trained on limited data and are prone to constraint violations. To address these problems, this study proposes PrOPF, a physics-informed framework that refines DC solutions to solve AC-OPF. Instead of learning from scratch, PrOPF treats DC-OPF results as physical priors and learns the mapping from DC to AC solutions using a graph neural network. A physics-informed loss with soft constraints is introduced during training, and hard constraints are enforced during inference to improve physical consistency. Extensive simulations are conducted on various IEEE test systems with renewable energy. The results demonstrate that our PrOPF achieves higher prediction accuracy and lower constraint violations compared to other data-driven OPF methods, and attains up to 30x acceleration over the traditional interior point method.
Funding Information
  • National Natural Science Foundation of China (62422308)
  • Foundation for Outstanding Research Groups of Hubei Province of China (2025AFA012)

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