Integrating water delay time into short-term hydropower scheduling with spinning reserve capacity allocation and execution

The hydraulic spatiotemporal relationships involving water delay time and the grid’s stochastic power balance demands result in the highly uncertain and coupled characteristics of hydropower operations. These factors pose significant challenges to the allocation and secure execution of spinning reserve capacity in hydroplants. This paper proposes a stochastic optimization framework for short-term hydropower scheduling that integrates water delay time with the allocation and execution of spinning reserve capacity. The framework captures the stochastic nature of power balance demands across multiple regional grids and considers the differences in upward and downward flexibility of hydroplants. It allocates spinning reserve capacity from multiple regional grids to individual hydroplants, establishes the hydropower response mechanism to power balance demands, and incorporates water delay time to represent the stochastic operational states and constraints during the response process. Lagrangian duality and convex hull theory are introduced to linearize the stochastic constraints and enable efficient solution. Multi-scenario simulations, sensitivity analyses, method comparisons, and applicability assessments were conducted to comprehensively evaluate the proposed method. The results demonstrate that the proposed method improves computational efficiency by 96% compared to conventional approaches. It effectively guides the allocation and efficient execution of spinning reserve capacity, demonstrating strong engineering applicability and economic performance.