## 4 Simulation and Analysis
### Test Case 2: LE Identification in the Scenario Where a Single Node Contains Wind Farms  
This case is aimed at the scenario where a single node of the power system contains a wind farm, and the penetration level of wind power generation is low. The accuracy of the conventional calculation method of the APEV and the calculation method that considers the fluctuation of the wind power output proposed in this paper are compared. The wind farm model is integrated into the IEEE 39-bus New England system through bus node 26 for analysis. The wind farm is composed of 40 wind turbines, with a single unit capacity of 1.5 MW, divided into four columns, ten wind turbines in each column, and the total installed capacity of the wind farm is 60 MW. After boosting, the 40 wind turbines are integrated into the 35 kV collector line and then into the IEEE 39-bus New England system through the 35/110 transformer. The cut-in, rated, and cut-out wind speeds of each turbine are 3 m/s, 11 m/s, and 25 m/s, respectively, and the active power, reactive power, and voltage data of each turbine required for the modeling process are obtained from the SCADA system. The sensitivity and generalized sensitivity of each branch of the CLS of branches 5-6 to node 26 are shown in Table 3. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Paths** & **Length of the Path** & \(N\) \\ \hline \(P_{1}\):5-8-7-6 & 0.0250 p.u. & 2 \\ \hline \(P_{2}\):5-4-14-13-10-11-6 & 0.0526 p.u. & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Two shortest paths that constitute the CLS of branch 5-6. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Branch \(k\)** & \(d_{k-l}\) & **Branch \(k\)** & \(d_{k-l}\) \\ \hline
5-8 & \(-\)0.6606 & 14-13 & 0.3307 \\
8-7 & 0.6729 & 13-10 & 0.3007 \\
7-6 & 0.6726 & 10-11 & \(-\)0.3002 \\
5-4 & \(-\)0.3405 & 11-6 & \(-\)0.3289 \\
4-14 & 0.2870 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: LERPF. Figure 6: Graph model and its dimension reduction of the IEEE 39-bus New England system. Using the simulation data of PSASP as the data uploaded by WAMS, before branch 5-6 was removed, the wind power output was 93.33% of the installed wind power capacity, and the active power of branch 5-6 was 456.45 MW. The wind power output was 76.7% of the installed wind power capacity at a certain moment after branch 5-6 was removed. The branch active power and the wind active power output at two moments are recorded, respectively. The APEV of each branch within the CLS of branch 5-6 is calculated using the conventional and proposed methods after branch 5-6 is removed, respectively. On this basis, LEEs are obtained. The APEV and the LEE obtained based on the proposed method are denoted as \(\mathrm{P}_{k}^{\prime}\) and \(\alpha\), respectively, and those obtained based on the conventional calculation method are denoted as \(\mathrm{P}_{k}^{\prime\prime}\) and \(\beta\), respectively. All data are obtained as shown in Table 4 and processed to obtain Figure 7.  
Assuming the permitted value of active power of branch 7-6 is [\(-\)700 MW, 700 MW], according to the simulation results: the active power on branch 7-6 after branch 5-6 is removed is 733.87 MW, and overloading occurs on branch 7-6. Based on the LE identification criterion, the LEE calculated by the method proposed in this paper is 0.0003, which satisfies \(\left|\left(\mathrm{P}_{k}^{\prime}-\mathrm{P}_{k}^{\prime}\right)\right|/ \mathrm{P}_{k}^{\prime}\right|<\varepsilon\). Therefore, it is concluded that branch 7-6 is overloaded due to LE. The