Coordinated scheduling of hydropower units: Risk-aware day-ahead planning and performance-driven intra-day regulation allocation

As key providers of frequency regulation in renewable-rich power systems, hydropower face two escalating challenges: cumulative fatigue from frequent operation near vibration-prone zones, and persistent underperformance in automatic generation control (AGC) compliance. This paper proposes a two-stage coordinated scheduling framework that integrates risk-aware day-ahead planning with performance-driven intra-day regulation. In the day-ahead stage, a vibration risk function is constructed via symbolic regression (SR) using historical data and embedded into a unit commitment model to steer operating trajectories away from high-risk regions. In the intra-day stage, a model predictive control (MPC) framework with plant-level AGC state-space models dynamically reallocates regulation tasks based on unit-specific response characteristics. To solve the resulting mixed-integer nonlinear problems, the framework employs a hybrid metaheuristic strategy: discrete particle swarm optimization (PSO) nested with dynamic programming for day-ahead planning, and PSO combined with simulated annealing for intra-day optimization. Case studies at Geheyan Hydropower Station demonstrate that the proposed strategy reduces cumulative vibration risk by 19.3 % and near-boundary power occurrences (NPOH) by 88.5 % in the day-ahead stage, while improving the AGC performance index by 11.2 % through intra-day adjustments. Overall, the framework offers a robust and scalable solution that enhances scheduling safety, flexibility, and responsiveness of hydropower under renewable uncertainty.