## 4 Case Study  
### Test System and Basic Data  
In this case study, the proposed approach is applied to evaluate the flexibility potential of retrofitted TPUs for accommodating RESs from a real-world project situated in the Liaoning Province, Northeast China. This project encompasses two 600 MW TPUs, a wind farm with an installed capacity of 300 MW, and two PV plants with a combined capacity of 400 MW. These power sources can achieve coupling integration through the 500 kV HH substation, as depicted in Figure 3.  
Figure 2: Flowchart of the evaluation process for RESs accommodation capability and TPUs’ flexibility.  
In this project, a coordinated control and optimization management center has been established at the dispatch center of the substation to implement optimal economic scheduling. The TPUs have undergone a comprehensive technical retrofit, which includes the auxiliary adjustment of condensate water systems, feedwater bypass systems, and high-pressure valve regulation. Consequently, post-retrofit, the TPUs' maximum ramp rate is improved from 1.5% per minute to 3% per minute, and their minimum operation output is decreased from 30% to 25% of their maximum output. The main performance parameters of the 600 MW TPU before and after retrofitting are shown in Table 2. In addition, the TPU plant has been equipped with a rapid response control system, a steam-water control system, and a flexible operation monitoring system, enabling flexible TPU operation in response to real-time outputs from wind and solar power sources. Similarly, rapid response control and status monitoring systems have been installed at both the wind farm and PV plants to facilitate real-time control and gather operation data, enhancing the overall integration and efficiency of RESs.  
The data for WT, PV, and load demand data are collected on a 30 min interval scale, totaling 17,520 time-steps throughout the year from the study area, as illustrated in Figure 4. The PDFs of fluctuations are derived from Reference [32], and the parameters of the fluctuations are calculated from historical data. \(C_{0}=375\), \(C_{1}=400\), \(C_{2}=1000\), \(C_{u}^{\text{ON}}=2.6\times 10^{5}\), \(C^{\text{PV}}=740\), \(C^{\text{WT}}=850\), \(C^{\text{CU}}=10^{4}\), \(P_{t}^{\text{c,max}}=20\), \(P_{t}^{\text{c,min}}=-20\), \(D_{u}^{\text{TPU,on,min}}=D_{u}^{\text{TPU,off,min}}=8\) h. For the winter season (November to next April), \(k_{\text{t}}=1\). For the summer season (May to October), \(k_{\text{t}}^{\text{TPU}}=0.5\). Additional parameters about TPUs such as operation costs and pollution treatment functions, can be found in [35]. The MILP is solved by the Gurobi solver Version 10.0.1 [36] coded in the Matlab 2022a software. The case study is run on a PC with an Intel core i7-13700K (Intel, Santa Clara, CA, USA), 3.40 GHz, and 32 GB of RAM. The establishe  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(R_{u}^{\text{I}}\) (MW/min) & \(R_{u}^{\text{II}}\) (MW/min) & \(P_{u}^{\text{TPUR,min}}\) (MW) & \(P_{u}^{\text{TPUD,min}}\) (MW) \\ \hline Before & 9 & 6 & 300 & 180 \\ After & 18 & 12 & 300 & 150 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Main performance parameters of the 600 MW TPU before and after retrofit.  
Figure 3: Schematic diagram of the real-world project.  
192,720 continuous variables and 122,640 binary variables. The solution time is about 2 h for both before and after coupling integration.