Pumped-Storage Hydropower Scheduling: An Event-based Convex-hull Approach

Abstract

Pumped-storage hydropower scheduling couples discrete operating-mode transitions with continuous dispatch decisions through intertemporal reservoir and ramping constraints. Existing convexification methods do not simultaneously accommodate multiple operating modes, persistent continuous reservoir and ramping states, and interval costs that depend on both incoming and outgoing states of the operating modes. We develop an event-based dynamic programming formulation in which mode transitions define variable-length events and mode-specific linear programs optimize continuous within-event operation. We prove that this formulation is equivalent to the conventional time-indexed mixed-integer linear program. Enumerating the finite set of discrete event paths and scaling their boundary-coupled polyhedra then yields an exact finite-dimensional convex-hull LP without state discretization. For tractability, we develop a finite-grid formulation that discretizes reservoir and ramping states only at event boundaries while retaining continuous within-event trajectories. Its feasible set contains that of the corresponding stagewise discretization. Moreover, the resulting LP provides an exact convex-hull representation of the grid-restricted model and admits an error bound linear in the grid resolutions. An event-based branch-and-bound method provides an independent computational verification of the continuous-state reformulation. Standalone experiments verify the theoretical results, while tests on a modified IEEE 24-bus Reliability Test System show that the finite-grid LP substantially reduces computation time with a negligible increase in system cost.