Performance evaluation of artificial, physics-informed and graphical neural network models for load flow analysis in smart and resilient power grids: Case study of IEEE and Nigerian power systems

Load flow analysis is essential for periodic planning, scheduling, and reliable operation of traditional and modern power grids. This study evaluates the effectiveness of Artificial, Physics-Informed and Graph Neural Network (NN) models in performing load flow analysis on standard benchmark systems (IEEE 14- and 30-bus) and practical Nigerian networks (28- and 52-bus) under steady-state, Fault, and Distributed Generation (DG) penetration scenarios. Newton-Raphson (NR) method was used to generate base case voltage magnitudes and phase angles as reference targets for model training. Models were implemented in MATLAB (R2025a) and evaluated using standard statistical metrics (MSE, RMSE, MAE, MAPE) and Line Voltage Stability Index (LVSI). Simulation results showed that ANN achieved MSE values between 0.385-1.079, RMSE 0.62-1.039, MAE 0.037-0.105, MAPE 2.005-5.562%, and LVSI 0.594-0.87. GNN recorded MSE 0.731-1.828, RMSE 0.855-1.352, MAE 0.068-0.18, MAPE 3.073-8.903%, and LVSI 0.524-0.724. PINN showed MSE 1.622-2.552, RMSE 1.274-1.597, MAE 0.158-0.238, MAPE 6.197-10.77%, and LVSI 0.563-0.752. The results demonstrate the suitability of the individual models for rapid and reliable load flow analysis across varying network sizes and operating conditions. The findings of this study will serve as practical guidance for model selection in modern power systems, supporting efficient planning, operation, and integration of DG resources.