Graph Attention Reinforcement Learning with Electrical Prior Knowledge for Distribution System Restoration

Distribution system restoration (DSR) has become increasingly challenging due to frequent topology changes and complex nodal interactions, especially in systems with a high penetration of distributed energy resources (DERs). Existing deep reinforcement learning (DRL) methods remain limited in representing inter-nodal relationships and incorporating domain prior knowledge. Therefore, this paper proposes a graph attention-based coupling-aware reinforcement learning method. From a non-Euclidean spatial perspective, the proposed method uses the distribution power transfer factor (DPTF) to quantify the strength of electrical coupling between nodes. The resulting coupling strengths are embedded as entries of the graph adjacency matrix, allowing the model to capture complex nodal interactions driven by power transfer. An aware graph attention network (AGAT) is further developed, where adjacency matrix with prior knowledge is introduced as a bias term in the attention coefficient calculation. This design guides GAT to generate differentiated node representations enriched with physical information. Based on the extracted graph features, proximal policy optimization (PPO) is employed to determine restoration decisions. Case studies on the IEEE 34-bus system demonstrate that the proposed method outperforms benchmark algorithms in training convergence, restored power, and online decision efficiency, enabling fast and effective distribution system restoration.