Unified Load Flow Modeling and Boundary-Aware RoPINN Framework for Particle-Like EV Aggregation Dynamics

Accurate modeling of electric vehicle (EV) charging dynamics is essential for optimizing charging infrastructure and grid integration, especially when dealing with sparse data and random charging behavior. This paper proposes a unified load flow (ULF) model that captures the spatio-temporal evolution of charging behavior, incorporating EV arrival and departure dynamics as boundary conditions. A classical point optimization physics-informed neural network (PoPINN) is used to solve the ULF model, with a novel boundary condition design that ensures physical consistency during training. To enhance model consistency and robustness under stochastic and data-sparse conditions, a boundary-aware region-optimized PINN (RoPINN) is developed. This approach incorporates boundary information into regional optimization, enforcing arrival–departure consistency within local spatiotemporal regions and enabling reliable learning from incomplete data. The proposed framework provides a coherent data–physics integration strategy for modeling uncertain and incomplete EV charging information, enabling accurate prediction of charging power and load flow evolution. Simulation results on both synthetic and real-world datasets demonstrate the robustness, accuracy, and practical applicability of the proposed method for large-scale EV charging optimization and smart grid management.