Physics‐Informed Graph Reinforcement Learning for Hosting Capacity Maximization in Distribution Networks

ABSTRACT High penetration of distributed generation (DG), battery energy storage systems (BESS) and electric vehicles (EVs) makes hosting‐capacity (HC) maximization a high‐dimensional constrained planning problem. This paper presents a physics‐informed graph reinforcement learning (PI‐GRL) framework for HC maximization and, importantly, to isolate why physics‐informed learning improves multi‐DER siting and sizing. The network is represented as a heterogeneous graph and processed by a multi‐relational GNN actor–critic, while linearized‐DistFlow residuals are embedded as differentiable regularizers. The physics component is not used as a surrogate power‐flow solver; instead, it shapes policy gradients, whereas all rewards and reported HC values are evaluated using an exact backward–forward‐sweep AC power flow. On balanced radial IEEE 33‐, 69‐ and 136‐Bus systems (ten seeds, nine baselines), PI‐GRL improves HC by 3.7%–4.6% over the strongest ablation (GNN‐Lagrangian‐PPO), 13.0% over Lagrangian‐PPO and 29.5% over metaheuristics, while reducing constraint violations to 0.4%. These results show that topology‐aware representation and predictive physics gradients jointly improve feasibility, scalability, and transferability.