Constraint‐Guided BO‐GCN Surrogate for Three‐Phase Unbalanced Power Flow in DER‐Integrated Distribution Systems

ABSTRACT Fast and reliable three‐phase power flow evaluation is increasingly required in feeders with a high number of distributed energy resources, stochastic photovoltaic generation and electric vehicle charging, where time‐series assessment and uncertainty screening may involve thousands of operating points. Classical nonlinear solvers remain reliable but can become computationally intensive when embedded in large scenario loops. Learning surrogates offer speed, yet two gaps persist because vectorised predictors often underuse electrical connectivity. In this paper, an admittance‐informed Bayesian‐Optimised Graph Convolutional Network model (BO‐GCN) is developed to map nodal injections to per‐phase voltages and phase angles. Neighbourhood aggregation is weighted by coupling strengths derived from the feeder admittance matrix; a stabilised multi‐layer encoder improves training robustness, and a physically structured decoder bounds voltages and enforces a unit‐circle sine–cosine angle representation to prevent wrap‐around errors. Moreover, OpenDSS‐based datasets with 10,000 scenarios are constructed for the IEEE 13‐bus and IEEE 123‐bus feeders. On the IEEE 13‐bus benchmark, relative to a standard GCN, Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) decrease by 31.6% and 26.0%, respectively, and the P95 tail metric drops by 44.3%. Angle MAE and RMSE are reduced by 90.2% and 91.9%, with larger margins over compared models.