## 6 Conclusions  
To explore the flexibility advantages of T-PSUs compared to FS-PSUs and VS-PSUs in day-ahead optimization scheduling, this paper firstly establishes a mathematical model for the participation of T-PSUs in day-ahead optimization scheduling. On this basis, the hybrid pumped storage model, which combines FS-PSUs and T-PSUs, is further developed. Furthermore, it develops a day-ahead optimization scheduling model for the wind-thermal-pumped storage system considering FS-PSUs, VS-PSUs, and T-PSUs. Finally, the day-ahead dispatch arrangements for each type of unit are determined, and based on this, various performance indicators that can reflect the flexibility of the power system, such as the wind power curtailment rate, net load curve standard deviation, thermal power average peak regulation depth, thermal power output volatility, and power generation, are all calculated.  
The experimental results show that the T-PSUs, due to their ability to pump and generate electricity simultaneously, possess a larger adjustment range and stronger flexibility compared to FS-PSUs and VS-PSUs under pumping modes. This is specifically manifested in the advantages of reducing wind power curtailment rates, decreasing thermal power peak regulation pressure, reducing thermal power generation, and saving system operation costs. Therefore, for power system operators, the T-PSUs are flexible, economical, and environmentally friendly regulatory power supplies, which have the opportunity to occupy a larger market share in the new power system. In addition, the sensitivity analysis results indicate that T-PS have higher robustness in responding to changes in wind power capacity, pumped storage capacity, and load rates, and it also shows that the models of T-PSUs established in this paper have consistent performance under different wind power capacities, pumped storage capacities, and load rates. This paper not only verifies the advantages of T-PSUs in improving the flexibility of the power system but, more importantly, also provides significant technical and economic references for the configuration of pumped storage in the power system. In the future, we will continue to explore the impact of uncertainty in wind power and load forecasting on the regulatory effect of pumped storage, and we will also conduct a more detailed exploration of the practical implementation of T-PSUs in different energy markets.  
Conceptualization, Z.W. and J.T.; methodology, Z.W., J.W. and S.P.; software, Z.W.; validation, J.W., Y.Z. and W.P.; formal analysis, Y.Z. and W.P.; investigation, Z.W., J.T. and J.W.; resources, S.P. and Y.Z.; writing--original draft preparation, Z.W.; writing--review and editing, Z.W., J.W. and J.T.; visualization, Z.W. and W.P.; funding acquisition, J.T. and S.P. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Key Planning and Special Projects of China Southern Power Grid (031000 QQ00230019).  
Not applicable.  
Data Availability Statement: Data are available on reasonable request.  
Figure 13: The pump (P_electricity) and generation (G_electricity) electricity under nine scenarios of pumped storage side.  
Conflicts of Interest: Authors [PERSON] and [PERSON] were employed by the company Guangdong Power Grid Corporation. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.