## 5 Conclusions  
This study establishes an MCS operation model that incorporates TPUMSTSR under RLVs. The proposed method has been validated using operational data from the northeast China power grid. Based on the numerical results and corresponding analysis, the following conclusions are drawn:  
1. The proposed TPUMSTSR model under RLVs combines the advantages of both RLVs and thermal storage retrofits. This model improves the real-time capability of thermal power units to compensate for the fluctuation of renewable generations, reduces the net load peak-valley difference, and enhances unit flexibility. As a result, the CS achieves higher overall operational revenue, improving economic efficiency. In the future, the operating costs of TPUMSTSR will be more accurately characterized to improve the accuracy of CS optimization methods.
2. The proposed three-stage economic dispatch optimization method independently optimizes the main grid and MCSs while preserving the privacy of each independent entity. By aligning with dispatch instructions from the main grid via optimal power flow, the method ensures coordinated operation. Furthermore, by introducing relaxation techniques, the approach simplifies the solution process for nonlinear  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Scheme** & **CS1** & **CS2** & **CS3** & **CS4** \\ \hline \hline \multicolumn{5}{c}{Typical summer day} \\ \hline
1 & 2.7173 & 2.0694 & 2.8643 & 5.3229 \\
2 & 2.6938 & 2.0606 & 2.7716 & 5.1967 \\ \hline \multicolumn{5}{c}{Typical winter day} \\ \hline
1 & 3.1085 & 1.7485 & 3.5280 & 5.1187 \\
2 & 3.0953 & 1.7451 & 3.4671 & 5.0689 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison of CS benefits obtained from three-stage and independent optimizations (10\({}^{6}\) CNY).  
objectives and constraints, thereby efficiently solving the mixed-integer nonlinear coordinated dispatch optimization problems. However, dividing the solution of nonlinear problems into multiple stages has a certain degree of simplification. We will study how to solve the optimization model more accurately through reinforcement learning algorithms.
3. The proposed dynamic CA method for PR revenue, which considers different time periods, enhances overall system profitability in scenarios where renewable energy penetration is high, coal-fired net load demand is low, and DPR compensation opportunities are frequent. By incorporating CA into the CS's dispatch process, this method provides a fair benefit distribution mechanism for MCSs while also encouraging thermal power unit flexibility retrofits to maximize overall system profitability. In the future, we will consider a wider range of application scenarios beyond MCSs and develop a more reasonable CA method.  
Conceptualization, N.Z. and Z.X.; methodology, Z.X., Y.C. and Y.Z.; software, Z.X. and X.D.; validation, Z.X.; formal analysis, Z.X.; investigation, Y.Z.; resources, Y.Z.; data curation, F.X.; writing--original draft preparation, Z.X.; writing--review and editing, N.Z. and Y.C.; visualization, Z.X.; supervision, Y.C.; project administration Y.C.; funding acquisition, Y.C. All authors have read and agreed to the published version of the manuscript.  
This research is supported by the National Key Research and Development Program of China (No. 2023 YFB2405900).  
Not applicable.  
Due to the nature of this research, participants of this study did not agree for their data to be shared publicly, so supporting data is not available. The data presented in this study are available on request from the corresponding author.  
The authors thank [PERSON] for assistance with the flexibility transformation of thermal power units.  
The 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.