Energy-reserve coordinated scheduling of cascade hydro-photovoltaic-pumped storage systems based on physics-constrained graph neural networks

Intraday scheduling of cascade hydro-photovoltaic-pumped storage systems requires joint coordination of energy dispatch, photovoltaic accommodation, reserve security, and physical feasibility under photovoltaic fluctuation, load variation, inflow uncertainty, and limited storage capacity. Existing optimization methods can describe physical constraints, but their repeated solution in rolling scheduling depends on forecast inputs, uncertainty sets, or scenario construction. Data-driven dispatch models provide fast inference, yet generic temporal or graph structures may mix hydrological transfer, electrical coupling, and reserve response relations and may generate infeasible schedules. To address these issues, this paper proposes PC-MRGNN, a physics-constrained multi-relation graph neural network for energy-reserve coordinated scheduling. The method constructs hydrological, electrical, and reserve-response relation graphs; learns constraint-aware embeddings through relation-specific message passing and physical gates; generates candidate dispatch decisions; and applies a main physical constraint correction procedure for water balance, reservoir bounds, pumped-storage exclusiveness, power balance, and reserve capacity. A reserve-risk-aware coordination module further adjusts reserve penalties according to photovoltaic downward uncertainty, load upward fluctuation, reservoir regulation margin, and pumped-storage availability. Experiments on benchmark datasets constructed from public hydrological, photovoltaic, renewable generation, and load data show that PC-MRGNN improves the overall energy-reserve scheduling trade-off, including photovoltaic accommodation, reserve shortage, remaining feasibility violation, and inference efficiency, compared with optimization-based, temporal-learning, generic graph-learning, and dispatch-oriented graph-learning baselines. Ablation, robustness, transfer, and interpretability analyses indicate that the proposed modules contribute to feasible and reserve-aware intraday auxiliary scheduling.