## 6 Case Analysis  
The effectiveness and accuracy of the proposed method were verified by taking an actual power system in a certain area as an example, and it was implemented based on MATLAB simulation software. The generator and load parameters are shown in Tables 3 and 4, respectively; the total load of the system was 1188 MW; and the transformer parameters are shown in [18], as well as in Table 5. To simplify the system load, the load power factor of each node was assumed to be 0.75 and the correlation coefficient between loads was 0.8. Assuming that two wind turbines with an installed capacity of 100 MW and 80 MW were connected to nodes 11 and 13 of the system, respectively; their correlation coefficient was 0.7; and operation with a constant power factor was 1; the cut-in wind speed was 4 m/s, rated wind speed was 15 m/s, cut-out wind speed was 25 m/s, scale parameter was 1.8, and shape parameter was 7. The system structure diagram as in Figure 3, the numbers marked in Figure 3 represent the number of nodes in the system. \begin{table}
\begin{tabular}{c c c} \hline
**Node** & \(p_{g}^{min}\)**(MW)** & \(p_{g}^{max}\)**(MW)** \\ \hline
1 & 0 & 332.4 \\
2 & 0 & 140 \\
3 & 0 & 100 \\
6 & 0 & 100 \\
8 & 0 & 100 \\ \hline \end{tabular}
\end{table} 
Table 4: Load node parameters. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Node** & **2** & **3** & **4** & **5** & **6** & **9** \\ \hline \(p_{L}^{max}\)**(MW)** & 100 & 430 & 220 & 35 & 50 & 135 \\ \hline
**Node** & 10 & 11 & 12 & 13 & 14 & - \\ \(p_{L}^{max}\)**(MW)** & 45 & 15 & 30 & 60 & 68 & - \\ \hline \end{tabular}
\end{table} 
Table 5: Transformer parameters. To verify the accuracy of the algorithm, by contrast, the expectation and standard deviation of 20,000 Monte Carlo simulations (MCS) were used as the benchmark. The results are shown in Table 7.  
It can be seen from Figure 4 that the PDF of loss obtained by three-point estimation was basically consistent with Monte Carlo. It can be seen from Table 7 that the error between the three-point estimation and Monte Carlo was very small, but Monte Carlo calculation required 255.29 s, whereas the three-point estimation only needed 0.94 s, indicating that the algorithm met the accuracy and the calculation speed was far superior to Monte Carlo. Comparisons with Monte Carlo will not be discussed later. The risk probability distribution of Transformer 1 can be obtained from Equation (23), as shown in Figure 5, so \(A_{1}(\otimes)=R_{1}=[52.2  
Analysis of the first group of test results: When using method 1 to evaluate, the risk condition of the transformer was overestimated, resulting in a waste of equipment maintenance resources. Since the impact of uncertainty on the loss of power grid operation caused by transformer fault was not taken into account, the calculated loss was often larger than the loss caused by the actual fault of the equipment, the final quantified risk value was too high, and the risk judgment result was biased; when method 2 was used to evaluate, the evaluation result was consistent with method 3. Analysis of the second group of test results: When using method 2 to evaluate, the tendency of the transformer risk to transfer to large risk was underestimated, which is not conducive to the arrangement of the maintenance sequence. Only the expectation of risk probability to certain quantitative was represented by the equipment risk condition--in essence, it is a certain risk quantification method that leads to deviations in its risk judgment. When using method 3 to evaluate, the risk value was based on the expectation, and each point in the left and right fields as the gray number \(A(\otimes)\) of the three-parameter interval judged the risk--that is, it was represented by the interval corresponding to the