## 4 Case Study
### Accommodation Level and Regulation Marginals  
In utilizing data from the test system and solving the optimization model both with and without the implementation of coupling integration and the retrofitting of TPUs (abbreviated as before/after coupling integration), the evaluation results are shown in Table 3.  
The table shows that the accommodation levels for WT and PV systems, as well as for the overall RES, have significantly improved following the coupling integration with retrofitted TPUs. Specifically, the accommodation levels are increased by 2.59% for the WT, 4.69% for PV, and 3.6% for overall RESs. These increases demonstrate the enhanced capability of the  
Figure 4: Historical data of WT, PV, and load demand. (**a**) Wind data; (**b**) Photovoltaic data; (**c**) Load demand data. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \begin{tabular}{c} **After Coupling Integration with** \\ **Retrofitted TPUs** \\ \end{tabular} & \
\begin{tabular}{c} **Before Coupling Integration and** \\ **without Retrofitted TPUs** \\ \end{tabular} &
\begin{tabular}{c} **Improvement** \\ \end{tabular} \\ \hline \(I_{\text{WT}}^{\text{AL}}\) (\%) & 100 & 97.41 & 2.59 \(\uparrow\)\({}^{1}\) \\ \(I_{\text{PV}}^{\text{AL}}\) (\%) & 99.97 & 95.28 & 4.69 \(\uparrow\) \\ \(I_{\text{RES}}^{\text{AL}}\) (\%) & 99.99 & 96.39 & 3.6 \(\uparrow\) \\ \(I_{\text{TPU}}^{\text{FM}+}\) & 154.0386 & 154.8457 & 0.08 \(\downarrow\) \\ \(I_{\text{TPU}}^{\text{FM}-}\) & 280.1582 & 212.1972 & 67.96 \(\uparrow\) \\ \(\sum_{t=1}^{T}P_{t}^{\text{WT}}\Delta t\) (MWh) & 6.1327 \(\times\) 10\({}^{5}\) & 5.9737 \(\times\) 10\({}^{5}\) & 1.59 \(\times\) 10\({}^{4}\)\(\uparrow\) \\ \(\sum_{t=1}^{T}P_{t}^{\text{PV}}\Delta t\) (MWh) & 5.5930 \(\times\) 10\({}^{5}\) & 5.3302 \(\times\) 10\({}^{5}\) & 5.63 \(\times\) 10\({}^{4}\)\(\uparrow\) \\ Annual revenues (CNY) & 2.1887 \(\times\) 10\({}^{9}\) & 2.1736 \(\times\) 10\({}^{9}\) & 1.51 \(\times\) 10\({}^{7}\)\(\uparrow\) \\ \hline \hline \end{tabular}  
\({}^{1}\)\(\uparrow\): Improved value.  
\end{table} 
Table 3: Evaluation results before/after coupling integration and retrofitting of TPUs. coupling integration with retrofitted TPUs to accommodate RESs effectively. Notably, the accommodation level for PV generation improved more substantially than that for the WT. This difference can be attributed to the larger installed capacity of PV within the test system and the considerable power fluctuations that can occur at sunrise and sunset. Such fluctuations require substantial regulation resources from TPUs to provide adequate support. The marked increase in PV accommodation capabilities highlights the importance of retrofitting TPUs and coupling integration to ensure sufficient flexibility in the power grid. The upward flexibility marginals \(I_{\text{TUT}}^{\text{FM}+}\) of TPUs remain almost identical before and after coupling and TPU retrofitting. This consistency suggests that TPUs are unlikely to face issues with insufficient generation and can meet the requirement for upward regulation in both scenarios. On the contrary, the capability for downward regulation, which is critical to prevent the curtailment of wind and solar power, shows a significant improvement from 212.1972 to 280.1582. The enhanced downward flexibility marginal after coupling integration with TPU retrofitting allows for more comprehensive accommodation of RESs. The total energy production of WTs and PV over the year also increased following the retrofit and integration, with WT generation rising by approximately 15.9 GWh and PV generation rising by approximately 56.3 GWh. Through these increases, the generation revenues of WT and PV can increase by about 13.52 and 41.66 million CNY, which significantly improves the efficiency and economy of RESs. The overall generation revenues of power sources can also be improved by about 15.1 million CNY after coupling coordination.