Event-Based Dynamic Programming for Pumped-Storage Hydropower Scheduling

Abstract

This paper studies the single-unit pumped-storage hydropower (PSH) plant scheduling problem with reservoir dynamics, generation and pumping limits, ramping constraints, start-up and shut-down costs, and minimum up/down-time requirements. A new event-based formulation is proposed in which an operating schedule is represented as a sequence of mode-specific events, with dispatch decisions within each event determined by linear programs. Based on this construction, the original time-indexed mixed-integer formulation is reformulated exactly as a deterministic dynamic program on an event network. The framework is modular and can be extended to incorporate additional operating modes, such as hydraulic short-circuit operation, by introducing corresponding event modules without significantly changing the overall event-network structure. To obtain tractable solution methods, a finite-grid approximation of the event network is developed, leading to a linear programming formulation for the discretized model. In addition, an event-based branch-and-bound algorithm with linear program-based bounds is proposed for the continuous-state problem. Numerical results demonstrate that the proposed event-based framework provides a computationally effective alternative to the conventional time-indexed formulation, while offering substantial modeling flexibility for PSH scheduling problems.