## 4 Simulation and Analysis
### Test Case 3: LE Identification in the Scenario Where Multiple Nodes Contain Wind Farms  
This case is aimed at the scenario where multiple bus nodes contain wind farms and the penetration of wind power gradually increases. The adaptability of the conventional calculation method of the APEV and the proposed method are compared. In the simulation process, conventional generators are replaced with wind farm models of 1.08 times the capacity. Table 5 shows the nodes where the replaced generators are located under different wind power penetration and the corresponding wind active power output change value at two moments before and after branch 5-6 is removed. The sensitivity of bus nodes containing wind farms to each branch within the CLS of branch 5-  
From Figure 8, for the scenario where multiple nodes contain wind farms, the APEV calculated by the proposed method is closer to the APMV than that calculated by the conventional method under different wind power penetrations. With the increase in wind power penetration, under the condition that the proportion of wind power output change value to the total installed capacity of wind farms is basically the same--that is, the wind power output is 92.6% of the wind power installed capacity before branch 5-6 is removed and is about 85% at a certain moment after the branch 5-6 is removed--the error between the APEV calculated by the conventional method and the APMV is increasing, while the error between the APEV calculated by the proposed method and the APMV is still small and basically unchanged, which validates that the proposed method has good adaptability for systems under different penetrations. It is worth stating that the essential reason for the proposed method is that the proposed method is not able to predict the wind power output. Figure 8: Comparison of the APEV and the APMV between two methods under different penetrations of wind power. (**a**) The penetration is 20%; (**b**) the penetration is 40%; (**c**) the penetration is 60%; (**d**) the penetration is 80%. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Line** \\ **Number** \\ \end{tabular} } & \multirow{2}{*}{\(\mathbf{P_{k}^{0}}\) **(MW)**} & \multirow{2}{*}{\(\mathbf{P_{k}^{\prime}}\) **(MW)**} & \multicolumn{2}{c}{**20\%**} & \multicolumn{2}{c}{**40\%**} & \multicolumn{2}{c}{**60\%**} & \multicolumn{2}{c}{**80\%**} \\ \cline{3-12}  & & & \(\mathbf{P_{k}^{\prime}}\) **(MW)** & \(\mathbf{P_{k}^{\prime}}\) **(MW)** & \(\mathbf{P_{k}^{\prime}}\) **(MW)** & \(\mathbf{P_{k}^{\prime}}\) **(MW)** & \(\mathbf{P_{k}^{\prime}}\) **(MW)** & \(\mathbf{P_{k}^{\prime}}\) **(MW)** & \(\mathbf{P_{k}^{\prime}}\) **(MW)** & \(\mathbf{P_{k}^{\prime}}\) **(MW)** \\ \hline L1 & 317.64 & 3.42 & 19.25 & 24.10 & 49.78 & 53.78 & 81.62 & 84.88 & 93.37 & 95.66 \\ L2 & 191.57 & 498.72 & 528.90 & 547.06 & 576.14 & 594.02 & 619.61 & 637.48 & 683.93 & 701.04 \\ L3 & 426.81 & 753.70 & 783.92 & 785.72 & 831.24 & 833.32 & 874.78 & 877.42 & 939.27 & 942.03 \\ L4 & 168.08 & 2.59 & 25.42 & 24.09 & 55.72 & 53.74 & 87.33 & 84.79 & 89.93 & 95.54 \\ L5 & 260.93 & 400.41 & 393.24 & 392.57 & 403.17 & 402.88 & 402.41 & 402.62 & 438.84 & 421.64 \\ L6 & 299.47 & 460.19 & 478.46 & 481.86 & 527.47 & 532.34 & 581.09 & 587.94 & 612.05 & 626.61 \\ L7 & 306.02 & 452.16 & 466.59 & 470.84 & 511.31 & 517.10 & 560.25 & 568.08 & 593.47 & 603.57 \\ L8 & 343.98 & 198.08 & 133.67 & 129.16 & 87.62 & 82.90 & 38.71 & 31.92 & 5.52 & 4.57 \\ L9 & 339.85 & 180.00 & 112.29 & 108.19 & 63.57 & 57.56 & 10.27 & 10.69 & 25.96 & 27.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The simulation results after branch 5-6 is removed under different penetrations of wind power. the error between the APEV and the APMV calculated by the conventional method is not related to the wind power penetration but to the integration location of the wind farm and the change value of wind power output.