## 5 Case Study
### Performance Analysis of the Pareto Optimal Planning Results  
To illustrate the effectiveness of the obtained planning results, a total of 30,000 testing scenarios, which are generated by MCS with consideration to wind speed correlation [26], are applied to test the performance of each planning result.  
The robustness of planning schemes R1 is verified by estimating the robustness degree with testing scenarios [3; 8]. Two robust planning schemes R1-A and R1-B, which are obtained by the  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \begin{tabular}{c} **Planning** \\ **Schemes** \\ \end{tabular} & \begin{tabular}{c} **Cost (\(\times 10^{5}\) S)** \\ \end{tabular} & \begin{tabular}{c} **Wind Curtailment** \\ **Percentage** \\ \end{tabular} & \multicolumn{3}{c}{**Planning Schemes**} \\ \hline R1 & 165.0 & 0.00\% & \begin{tabular}{c} \(n_{1-2}=2\), \(n_{1-5}=1\), \(n_{6-10}=1\), \(n_{7-8}=4\), \(n_{8-9}=1\), \(n_{10-12}=1\), \\ \(n_{14-16}=1\), \(n_{2-8}=1\), \(n_{16-25}=3\), \(n_{7-26}=3\), \(n_{1-27}=3\) \\ \hline R2 & 145.1 & 0.15\% & \begin{tabular}{c} \(n_{1-2}=2\), \(n_{1-5}=1\), \(n_{10-1}=1\), \(n_{7-8}=3\), \(n_{7-26}=3\), \(n_{7-27}=3\) \\ \(n_{14-16}=1\), \(n_{1}=n_{16-25}=3\), \(n_{7-26}=2\), \(n_{1-27}=2\) \\ \hline R3 & 123.8 & 0.40\% & \
\begin{tabular}{c} \(n_{1-2}=2\), \(n_{6-10}=1\), \(n_{7-8}=3\), \(n_{10-12}=1\), \(n_{14-16}=1\), \\ \(n_{16-25}=3\), \(n_{7-26}=2\), \(n_{1-27}=2\) \\ \end{tabular} \\ \hline R4 & 108.2 & 0.82\% &
\begin{tabular}{c} \(n_{1-2}=2\), \(n_{6-10}=1\), \(n_{7-8}=3\), \(n_{10-12}=1\), \(n_{14-16}=1\), \\ \(n_{16-25}=2\), \(n_{7-26}=2\), \(n_{1-27}=2\) \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 1: Four planning schemes for IEEE RTS-24 system.  
Figure 7: Feasible planning results for IEEE RTS-24 system.  
genetic algorithm combined with [PERSON]'s orthogonal array testing (TOAT) [8] and robust TNEP (RTNEP) [3], respectively, are also evaluated for comparison. Table 2 gives the comparison results of three robust planning schemes.  
As shown in Table 2, the planning scheme under RTNEP, which can satisfy the load demand and wind power consumption in all testing scenarios, has the best robustness. However, owing to the conservativeness of RTNEP, the investment cost of RTNEP is 13.58% and 15.54% higher than that of R1 and TOAT, respectively. It can be observed that planning scheme R1 is not only economical but also has a high robustness degree of 99.90%. The above analysis proves that the proposed method can be effectively applied to the robust TNEP design.  
The effectiveness of the hybrid clustering method in dealing with uncertainty is further analyzed. For planning schemes R2, R3, and R4, their actual wind curtailment percentages are evaluated by MCS and are compared with the given wind curtailment percentages simulated by the typical scenario set. The comparison results are shown in Table 3.  
It can be noted that the absolute errors between the typical scenario set and MCS are extremely small, which indicates that the typical scenario set can accurately simulate uncertain wind generation. This further proves that the hybrid clustering method can effectively recognize the typical power distribution characteristics of the basic scenario set and provide accurate clusters for scenario generation.