Capacity Optimization of a Generation–Pumped-Storage System with Fixed- and Variable-Speed Pumped-Storage Units Considering Distributionally Robust Coordinated Dispatch

Under high renewable energy penetration, the uncertainty of wind and photovoltaic (PV) power outputs increases system operating costs and intensifies the pressure of renewable energy accommodation. To address these challenges, this paper develops a bi-level capacity optimization model with distributionally robust coordinated dispatch for an integrated generation–pumped-storage system. At the upper level, the installed capacities of wind and PV power, together with the number and rated capacity of fixed-speed and variable-speed pumped-storage units (FS-PSUs and VS-PSUs), are jointly optimized to minimize the annualized total cost. At the lower level, a distributionally robust optimization (DRO)-based coordinated dispatch model minimizes the daily operating cost under wind and PV output uncertainty and feeds the resulting operating cost back to the planning level. The case study is based on ten years of hourly historical wind and PV output data, which are clustered into four representative typical days for hourly dispatch analysis. Compared with the base case without coordinated pumped-storage operation, the proposed coordinated dispatch mode increases the annual system net benefit by 29.8% and reduces the wind and PV curtailment rate by 73.5%. Moreover, FS-PSUs and VS-PSUs show complementary roles in capacity support and flexible regulation, and their combined configuration can balance economic efficiency and operational flexibility. The results provide useful insights for the capacity planning and coordinated operation of pumped-storage units in power systems with high renewable energy penetration.