A Physics-Informed Machine Learning Method for Long-Term Hydropower Output Simulation and Scheduling

Accurate simulation of hydropower output characteristics is a prerequisite for optimizing long-term reservoir scheduling. However, traditional empirical formulas often fail to capture the complex non-linear relationships between hydraulic head, turbine discharge, and power output, while purely data-driven models lack adherence to physical laws. This paper proposes a Physics-Informed Machine Learning (PIML) method that couples physical prior knowledge with data-driven modeling. By embedding strictly defined physical constraints—specifically dynamic head-dependent capacity limits, hydraulic monotonicity, and tailwater elevation effects—into the loss function of a Deep Neural Network (DNN), the proposed model guarantees physically consistent predictions. The PIML model is further integrated as a high-fidelity surrogate into a long-term scheduling optimization model solved by Particle Swarm Optimization (PSO). Case studies on the Shuibuya Hydropower Station demonstrate that the PIML method achieves high simulation accuracy with an RMSE of 12.25 MW and zero physical violations. Furthermore, under identical hydrological conditions, the PIML-based scheduling strategy increases annual power generation by 4.72% and reduces the water consumption rate by 4.50%, effectively identifying high-efficiency operating zones compared to traditional methods.