Physics-guided Chebyshev graph convolution network for optimal power flow

As the penetration of renewable energy sources (RES), such as wind and solar, continues to increase, deep learning methods provide solutions to meet the real-time demand of rapidly changing grid operations with efficient data processing capabilities. However, existing approaches struggle to balance the sufficient extraction of data features and the learning of physical properties, resulting in undesired learning effects and limited generalization. To address this issue, this paper proposed a physics-guided Chebyshev graph convolution network (PG-CGCN) for real-time solving of the alternating current optimal power flow (AC-OPF) problem. First, by utilizing the maximal information coefficient, we developed a self-adaptive adjacency matrix based on topological embedding. This matrix not only carries the inherent topological structure of the grid but also reflects complex inter-node relationships, enhancing the model's robustness. Next, Chebyshev convolution based on spatial domain graph convolution was implemented and combined with a convolutional layer and a multilayer perceptron to further strengthen the model's learning capability. This structure enables effective extraction of both local and global topological features simultaneously accounting for both local correlations and global temporal characteristics. Additionally, a physics-guided loss function was constructed, with dynamic weighted updates applied to corresponding multipliers based on Lagrangian duality. This encourages mapping the optimal solution to the feasible space while mitigating stability challenges introduced by the physics-guided term. Finally, experimental results from three different IEEE test cases demonstrate that, in unseen N-1 contingency scenarios, PG-CGCN achieves superior predictive performance compared to state-of-the-art methods, with its predictions showing a higher degree of alignment with the underlying physical properties.