The increasing integration of renewable generation introduces highly stochastic operating conditions, substantially enlarging the operating space and posing severe computational challenges for traditional iterative power flow solvers. To address this, we propose a Physics-Informed Graph Attention Network (PI-GAT) for fast and physically consistent power flow assessment in power systems with high renewable penetration. PI-GAT represents buses and branches as graph-structured inputs and employs edge-aware multi-head attention to adaptively capture electrical interactions between connected nodes. By embedding AC power flow equations as residuals in the training loss, PI-GAT promotes physical consistency, improving nodal power balance consistency even under high renewable variability and N−1 contingency scenarios. Experimental results on IEEE 30-bus and 118-bus systems demonstrate that PI-GAT reduces active and reactive power mismatches by up to approximately 62% across the two benchmark systems relative to the edge-aware GAT baseline. This improvement in physical consistency is accompanied by a modest increase in point-wise voltage and phase-angle errors. Moreover, PI-GAT achieves substantial inference-time speedups over conventional numerical solvers, especially under batched multi-scenario inference. These findings indicate that PI-GAT provides a reliable and efficient surrogate model for real-time security assessment and contingency screening in power systems with high penetration of renewable generation.

With the number of prosumers rising quickly, energy sharing markets in distribution networks are emerging. The trading of active power influences the power flow in the distribution network, which will cause voltage fluctuation when the line resistance is not trivial. In this paper, we investigate the voltage regulation problem of distribution networks with the consideration of electricity markets. We first formulate the problem in the form of a non-cooperative game. The uniqueness of generalized Nash Equilibrium (GNE) is proved. Then, a feedback-based GNE seeking algorithm is proposed with online parameter estimation without knowing accurate values of resistance and reactance. The estimation error is proved to be accurate in expectation. The convergence of the algorithm is also guaranteed theoretically. Finally, numerical results in the IEEE 33-bus system validate the effectiveness of the algorithm.