Stochastic Multi-Segment Scheduling of Variable-Speed Pumped Storage Hydropower for Energy and Ancillary Services Provision

Abstract

Variable-speed pumped storage hydropower (VS-PSH) offers long-duration energy storage alongside ancillary services in competitive electricity markets. However, its operation and scheduling are challenged by head-dependent nonlinearities, discrete mode transitions, and energy-continuity constraints. This study proposes a stochastic framework for VS-PSH that employs a multi-segment bidding structure to generate market-consistent energy and synchronized reserve offers in compliance with market rules. The framework explicitly incorporates physical constraints, including head-dependent capability limits, discrete pumping and generating modes, as well as state-of-charge (SoC) and head dynamics, within a stochastic mixed-integer linear programming (MILP) formulation. Price uncertainty is represented through a scenario-based modeling approach that scales base-case prices and allows variations in (dis)charging incentives. The stochastic MILP produces optimal energy and mode schedules that maintain feasible SoC trajectories across scenarios and ensure physically feasible operating strategies. Case studies under different levels of price variability demonstrate the operational feasibility and market applicability of the proposed framework, showing effective coordination between energy arbitrage and reserve provision under uncertainty. These results highlight the operational and economic value of VS-PSH as a grid-scale energy storage resource.