## 4 Case Analysis
### Protection System State Evaluation and Fault Prediction in a Single Case  
The characteristic monitoring information of conventional sampling and merging unit DSP module 24 h before fault in the high voltage line protection system of 220 KV intelligent station described above was taken as a case to analyze and verify the equipment state evaluation and fault prediction model based on digital twin technology. (1) The 24 h before the fault was divided into six time periods, and set as moments 1-7. According to the real-time monitoring information of the secondary monitoring system, the characteristic sequence data of moments 1-7 was obtained by digital processing, as shown in Table 9.  
Moment 3 was selected as the verification example of equipment status evaluation. The normalized result was \(u\) = {0,0,0,0.333,0,0,0,0,0.333}. The state of the equipment at this time was regarded as the matter element to be evaluated. By using formulas (11) and (12), the closeness degree between the sequence of the time and the three classical domains of \"normal\", \"attention\" and \"severe\" was calculated, and the closeness degree between the characteristic sequence and each state level was obtained as shown in Table 10.  
The closeness indicates the closeness degree of the current equipment to be evaluated to each state level. The higher the value was, the closer it was to the state level, so it was judged to be \"normal\". It can be seen that the equipment was close to the \"attention\" state, indicating that some components of the equipment have a certain deterioration trend, but the equipment was running in normal state, and the eigenvalues were in the normal range, which was also consistent with the actual situation of the equipment. It can be seen that the algorithm can accurately evaluate the current state of the device at the exact time. (2) According to the characteristic sequence of moments 1-7 in Table 9, the characteristic weight of each time was calculated, and the closeness of the equipment to the three state levels of \"normal\", \"attention\" and \"severe\" at each time was calculated, so as to judge the state level of the equipment at each time. The weight change of each characteristic quantities is shown in Figure 8. The change trend of equipment status level is shown in Figure 9. \begin{table}
\begin{tabular}{c c c c} \hline  & **Normal** & **Attention** & **Severe** \\ \hline Closeness & 0.9996 & 0.9988 & 0.9953 \\ Relative Closeness & 1 & 0.7874 & 0 \\ \hline \end{tabular}
\end{table} 
Table 10: Closeness of protection system at moment 3 to each state level. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Moment** & \(\mathbf{c_{1}}\) & \(\mathbf{c_{2}}\) & \(\mathbf{c_{3}}\) & \(\mathbf{c_{4}}\) & \(\mathbf{c_{5}}\) & \(\mathbf{\epsilon_{6}}\) & \(\mathbf{c_{7}}\) & \(\mathbf{c_{8}}\) & \(\mathbf{c_{9}}\) \\ \hline
2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\
3 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 \\
4 & 1 & 0 & 0 & 2 & 0 & 1 & 0 & 0 & 2 \\
5 & 1 & 0 & 0 & 2 & 0 & 2 & 1 & 1 & 2 \\
7 & 3 & 3 & 0 & 3 & 0 & 3 & 3 & 1 & 6 \\ \hline \end{tabular}
\end{table} 
Table 9: Characteristic quantity sequence at moments 1-7. The vertical coordinates in Figure 8 indicate the weight values of each characteristic quantity at each moment. It can be seen from the figure that the weights of each characteristic quantity could be adjusted in real time when the frequency of the characteristic quantity changed at different moments. When the frequency of a certain characteristic quantity increased in a period of time, the degree of its influence on the equipment status would increase, and the weights of these characteristics should be increased at this time, so that the equipment status rating decreased. Take \"\(c_{4}\) protection DSP sampling errors\" as an example, as shown in Table 9; the frequency of this characteristic increased at moments 3, 4, and 6, respectively, so its weight was increased at these moments, while the weight of other characteristics that did not appear was reduced.