###### Abstract  
Distributed renewable energy sources with significant output fluctuations can negatively impact the power grid stability when it is connected to the power grid. Therefore, it is necessary to develop a capacity configuration method that improves the output stability of highly uncertain energy sources such as wind and photovoltaic (PV) power by integrating pumped storage units. In response, this study proposes a capacity configuration method for a cascade small hydropower-pumped storage-wind-PV complementary system. The method utilizes the regulation capacity of cascade small hydropower plants and pumped storage units, in conjunction with the fluctuating characteristics of local distributed wind and PV, to perform power and energy time-series matching and determine the optimal capacity allocation for each type of renewable energy. Furthermore, an optimization and scheduling model for the cascade small hydropower-pumped storage-wind-PV complementary system is constructed to verify the effectiveness of the configuration under multiple scenarios. The results demonstrate that the proposed method reduces system energy deviation, improves the stability of power output and generation efficiency, and enhances the operational stability and economic performance of the system. capacity configuration; cascade small hydropower; pumped storage; multi-energy complementarity 25 April 202516 June 2025  
the stable operation of the power grid and maximizing the consumption of clean energy in the region. In complementary systems of hydropower with renewable energy sources such as wind and PV, pumped storage is often used as an economical and clean energy storage method. By providing fast regulation capabilities, it helps mitigate the volatility of renewable energy, ensuring the safe and stable operation of the power system while enhancing the system's ability to absorb wind, PV, and other renewable energy sources [3]. In reference [4], the flexible regulation characteristics of pumped storage plants are used to mitigate the output fluctuations of distributed generation sources. Reference [5] presents a multi-objective optimization scheduling model that integrates pumped storage plants, aiming to minimize coal consumption and pollutant emissions costs from thermal power units. The model is verified through practical grid case studies, showing significant improvements in system economy and stability. Reference [6] develops an optimization model that minimizes operating costs by leveraging the flexibility of pumped storage and thermal power units. This approach effectively alleviates the supply-demand imbalance caused by the \"duck curve\", which refers to the sharp dip in midday electricity demand and a steep ramp-up in demand during the evening as PV generation decreases and people return home, resulting in significant fluctuations in the power grid. However, in practice, the construction of pure pumped storage plants faces significant technical and economic challenges due to regional constraints such as terrain, geology, and water resources. But, in practical engineering, due to regional constraints such as terrain, geology, and water resources, the construction of pure pumped storage plants faces significant technical and economic challenges. In contrast to pure pumped storage plants, cascade hybrid pumped storage plants offer the following advantages:  
1. In terms of technical difficulty and construction conditions, a cascade hybrid pumped storage plant can be built by adding units and transforming an existing hydropower station, which involves relatively small engineering work [7]. 2.