Physics-Informed Transformer-Enhanced Graph Neural Networks with Rooted-Forest Repair for Distribution Network Reconfiguration

Distribution network reconfiguration requires switch-state decisions subject to topological and electrical constraints. This paper presents a graph-based surrogate with rooted-forest repair for a modified IEEE 69-bus, two-substation system. The model combines local graph propagation, node-index embeddings, global self-attention, multi-task prediction and physics-informed regularization. The model uses bus-level demand, distributed generation, network data and pre-decision electrical quantities, without including global scenario-scaling factors or the source-cost ratio as input features. The dataset contains 10,000 scenarios at a fixed source-cost ratio of 1.30. On 1500 held-out scenarios, the evaluated model achieved 100% repaired topological feasibility, 79.87% open-switch F1 and 24.93% exact-topology accuracy. A descriptive summary of five training runs yielded 80.09 ± 0.28% and 25.91 ± 0.90%, respectively. Mean inference-plus-repair time was 11.08 ms, compared with 0.151 s for Gurobi over 100 cases. Component-wise AC checks converged for 297 of 300 learned topologies, with no observed voltage or branch apparent-power violations among converged cases under relaxed source limits. The results support fast prediction with topological repair on this benchmark; source-capacity feasibility and optimality are not established by these checks.