To explore the advantages in the flexibility of ternary pumped storage units (T-PSUs) compared with fixed-speed pumped storage units (FS-PSUs) and variable-speed pumped storage units (VS-PSUs) in the day-ahead optimal scheduling of power systems, this paper firstly establishes the mathematical model of T-PSUs which is suitable for the target application, and establishes a new hybrid pumped storage model combining both FS-PSUs and T-PSUs for the purpose of improving existing FS-PSUs. Secondly, a day-ahead optimal scheduling model used for a wind-thermal-pumped storage bundled transmission system with the goal of obtaining the lowest operating cost is established. Additionally, various indicators are proposed to comprehensively evaluate the flexibility of different pumped storage unit types on day-ahead optimal scheduling. Finally, a sensitivity analysis is conducted from three aspects: covering the wind power capacity, load rate, and pumped storage capacity. The results indicate that T-PSUs are superior to FS-PSUs and VS-PSUs in maintaining the smooth, economic, and robust operation of thermal power units, as well as in promoting wind power consumption. This provides a significant reference for evaluating the technical and economic benefits of the different types of pumped storage units in applications of future power grids.