Dynamic flexibility management for pumped hydro storage: Enhancing frequency stability and economic efficiency in cascade hydro-wind-solar-storage integrated delivery systems

The integration of substantial variable renewable energy (VRE) into the cascade hydro-wind-solar-storage integrated delivery system (CHIDS) poses significant challenges in maintaining frequency stability and optimizing economic performance. This study proposes a balance-oriented strategy for the flexible operation of pumped hydro storage (PHS) to address these issues, enhancing both frequency stability and economic efficiency. A quantitative method is developed to evaluate flexibility supply capacity, incorporating both fixed-speed (FS-PHS) and variable-speed (VS-PHS) units. A multi-level flexibility balance constraint model is introduced to facilitate steady-state power regulation, transient frequency response, and quasi-steady-state frequency recovery. Additionally, a multi-timescale scheduling strategy is employed to optimize power delivery by balancing frequency stability and economic performance through flexibility constraints. Results indicate that the proposed strategy reduces the probability of insufficient flexibility by 15 % and 4 % for the CHIDS involving FS-PHS and VS-PHS, respectively, compared to conventional frequency security-based scheduling. Furthermore, the strategy ensures frequency stability, with recovery probabilities stabilizing at 98 %. At a VRE penetration of 62 %, the system achieves optimal performance, with delivery reliability approaching 99 % and curtailment reduced to 3 %. Compared to strategies that do not account for frequency security constraints, the internal rate of return increases by 0.08 % and 0.24 % for the FS-PHS and VS-PHS cases, respectively. These findings underscore the critical need to balance flexibility supply and demand to improve system reliability and economic efficiency in future high-VRE systems.