## 4 Simulation and Analysis
### Test Case 3: LE Identification in the Scenario Where Multiple Nodes Contain Wind Farms
The LEEs calculated by two methods under different penetrations are shown in Table 9 and processed to obtain Figure 9. From Figure 9a, the LEEs calculated by the proposed method are all within the threshold value with the penetration increase. From Figure 9b, when the APMV and the APEV are small, the situation wherein the LEE is greater than the threshold value occurs, such as for L1 and L4, which indicates that the calculation result of the conventional calculation method under high penetration of wind power is not accurate enough, easily causing the misjudgment of the cause of the branch overload. It is assumed that the permitted value of the active power of branch 7-6 is [\(-700\) MW, \(700\) MW], that of branch 8-7 is [\(-500\) MW, \(500\) MW], and that of branch 14-13 is [\(-450\) MW, \(450\) MW]. From Table 8, overloading occurs on branch 7-6, branch 8-7, and branch 14-13 after branch 5-6 is removed under different penetrations of wind power. Figure 10 compares the LEEs of overloaded branches calculated by the proposed and conventional methods under different penetrations of wind power. From Figure 10a, the LEEs of three branches calculated by the proposed method all satisfy LE identification criteria; it is concluded that three branches were overloaded due to LE, and the proposed method can accurately identify the LE under different penetrations of wind power. From Figure 10b, when the penetration does not exceed 60%, the LEEs of the three branches calculated by the conventional method satisfy the identification criteria. It can be judged that the three branches are all overload due to LE. However, when penetration reaches 80%, it will misjudge that branches 7-6 and 14-13 are all overloaded due to faults within the protection range. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**20\%**} & \multicolumn{2}{c}{**40\%**} & \multicolumn{2}{c}{**60\%**} & \multicolumn{2}{c}{**80\%**} \\ \cline{2-9}  & \(\alpha\) & \(\beta\) & \(\alpha\) & \(\beta\) & \(\alpha\) & \(\beta\) & \(\alpha\) & \(\beta\) \\ \hline L1 & 0.2519 & 6.0468 & 0.0804 & 14.7251 & 0.0399 & 23.8187 & 0.0245 & 26.9708 \\ L2 & 0.0343 & 0.0970 & 0.0310 & 0.1911 & 0.0288 & 0.2782 & 0.0250 & 0.4057 \\ L3 & 0.0023 & 0.0425 & 0.0025 & 0.1056 & 0.0030 & 0.1642 & 0.0029 & 0.2499 \\ L4 & 0.0523 & 8.3012 & 0.0355 & 19.7490 & 0.0291 & 31.7375 & 0.0343 & 35.8880 \\ L5 & 0.0017 & 0.0196 & 0.0007 & 0.0062 & 0.0005 & 0.0055 & 0.0392 & 0.0530 \\ L6 & 0.0071 & 0.0471 & 0.0092 & 0.1568 & 0.0118 & 0.2776 & 0.0238 & 0.3616 \\ L7 & 0.0091 & 0.0413 & 0.01132 & 0.1436 & 0.0140 & 0.2564 & 0.0170 & 0.3349 \\ L8 & 0.0337 & 0.3479 & 0.0539 & 0.5815 & 0.1754 & 0.8389 & 0.1721 & 0.9820 \\ L9 & 0.0365 & 0.3989 & 0.0945 & 0.6802 & 0.0409 & 0.9906 & 0.0508 & 0.7929 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The LEEs calculated by two methods under different penetration. Figure 9: Comparison of LEEs calculated by two methods under different penetration. (**a**) The proposed method; (**b**) the conventional method. Thus, unlike the traditional calculation method that may misjudge in the scenario of high penetration of wind power, the method proposed in this paper is applicable under any high wind power penetration.