## 5 Case Study
### Sensitivity Analysis  
In the analysis above, only three wind farms are considered in TNEP. Since the smart grid tends to have more renewable power plants, it is necessary to investigate the impact of the increasing number of renewable power plants on TNEP. Here, two additional cases are tested on the modified IEEE RTS-24 system; the corresponding information of integrated wind farms is given in Table 4.  
Likewise, the typical scenario set is generated first for each case. For C1, the basic scenario set is divided into eight clusters, and a total of 148 scenarios are selected with the \(t_{\text{min}}\) set as 8. For C2, the basic scenario set is divided into seven clusters, and a total of 140 scenarios are selected with \(t_{\text{min}}\) set as 10. It can be observed that the number of scenarios is not affected by the increased uncertainties, which means that the proposed method can maintain the stable computational efficiency of TNEP solving. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Planning Schemes** & \multicolumn{2}{c}{**Solution**} & \multicolumn{2}{c}{**Cost (\(\times\)10\({}^{5}\) S)**} & \multicolumn{2}{c}{**Robustness Degree**} \\ \hline R1 & \(n_{1-2}=2\), \(n_{1-5}=1\), \(n_{6-10}=1\), \(n_{7-8}=4\), \(n_{8-9}=1\), \(n_{10-12}=1\), & 165.0 & 99.90\% \\  & \(n_{11+6}=1\), \(n_{7-8}=1\), \(n_{11+6}=25\), \(n_{7-26}=3\), \(n_{7-26}=3\), \(n_{12-7}=3\) & & \\ \hline R1-A by TOAT & \(n_{1-2}=2\), \(n_{1-5}=1\), \(n_{12-4}=1\), \(n_{16-10}=1\), \(n_{7-8}=4\), \(n_{8-9}=1\), & 162.2 & 99.48\% \\  & \(n_{8-10}=1\), \(n_{8-1}=1\), \(n_{16-25}=3\), \(n_{7-26}=3\), \(n_{12-2}=3\) & & \\ \hline R1-B by RTNEP & \(n_{1-2}=2\), \(n_{1-5}=1\), \(n_{2-4}=1\), \(n_{3-24}=1\), \(n_{15-10}=1\), \(n_{6-10}=1\), & & \\  & \(n_{7-8}=4\), \(n_{8-9}=1\), \(n_{8-10}=1\), \(n_{10-12}=1\), \(n_{14-16}=1\), & 187.4 & 100\% \\  & \(n_{15-24}=1\), \(n_{16-17}=1\), \(n_{16-25}=3\), \(n_{7-26}=3\), \(n_{1-27}=3\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Robustness analysis. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Planning Scheme**} & \multicolumn{2}{c}{**Wind Curtailment Percentage**} & \multirow{2}{*}{**Absolute Error**} \\ \cline{2-3} \cline{4-4}  & **Typical Scenario Set** & **MCS** & \\ \hline R2 & 0.1473\% & 0.1487\% & 0.0014\% \\ R3 & 0.4007\% & 0.4267\% & 0.0260\% \\ R4 & 0.8177\% & 0.8165\% & 0.0012\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison results for wind curtailment percentage. Figure 8 gives the feasible planning schemes from the Pareto fronts of C1 and C2, respectively. The robustness analysis for the robust planning schemes of two cases is given in Table 5. It can be noted that both of the planning schemes have good robustness. MCS evaluation is also conducted on two economic planning schemes, C1-R2 and C2-R2. The comparison results in Table 6 show that the hybrid clustering method still has good performance for uncertain simulation under increased uncertainties. In addition, for the proposed TNET method, its capability to save transmission investment by curtailing appropriate wind generation is further discussed. This paper defines the cost-saving ratio as the ratio of the cost savings of an economic planning scheme to the investment cost of the corresponding robust planning scheme. To investigate the impact of increased wind farms on the cost-saving ratio, the planning schemes R3, C1-R2, and C2-R2, which all have a similar wind curtailment percentage close to 0.4%, are selected for comparison. Figure 9 illustrates the comparison results of transmission investment cost and cost-saving ratio under different cases.