## 4 Results of the Analysis  
### Reliability Analysis Results  
Figure 16 shows the fragility curves of all functionalities. The fragility curves of different \(F_{\rm s}\) values should be different, but when \(F_{\rm s}\) is less than 8/10, the results of adjacent \(F_{\rm s}\) values are highly similar or consistent (for example, when \(F_{\rm s}\) is 6/10 and 7/10, the median capacity is 0.18323 and 0.18268, respectively, and when \(F_{\rm s}\) is 0 and 1/10, the median capacity is 0.29582). Figure 16 shows that the fragility curves of \(F_{\rm s}=5/10\) and \(F_{\rm s}=4/10\) \begin{table}
\begin{tabular}{c c c c c} \hline \(F_{\rm s}\) & **Median Capacity, g** & **Log Standard Deviation** & **R Squared** & **RMSE** \\ \hline
0 & 0.29582 & 0.2063 & 0.9994 & 0.01061 \\
1/10 & 0.29582 & 0.2062 & 0.9995 & 0.01071 \\
2/10 & 0.26955 & 0.1989 & 0.9995 & 0.01009 \\
3/10 & 0.26955 & 0.1987 & 0.9995 & 0.01020 \\
4/10 & 0.23598 & 0.2168 & 0.9992 & 0.01238 \\
5/10 & 0.20867 & 0.2243 & 0.9993 & 0.01149 \\
6/10 & 0.18323 & 0.2493 & 0.9989 & 0.01453 \\
7/10 & 0.18268 & 0.2449 & 0.9988 & 0.01524 \\
8/10 & 0.14414 & 0.3271 & 0.9961 & 0.02497 \\
9/10 & 0.13574 & 0.3216 & 0.9968 & 0.02241 \\ \hline \end{tabular}
\end{table} 
Table 4: Fragility curve parameters for different functionalities of the substation system. Figure 17: Comparison of the calculation times of different algorithms. are significantly different. This shows that the reliability of the line-in unit is high, and the system functionality depends on the reliability of the transformer unit and the line-out unit. Since there is 20% redundancy in the line-in unit, the system functionality is affected only when the second line-in unit is damaged. At this time, the destruction of a line-in unit can cause the system functionality to drop by 20%. The transformer unit is similar, with 50% redundancy. The destruction of one transformer unit does not cause the system functionality to decline, but when a second transformer unit is broken, the system functionality is reduced by 50%. Table 4 shows that most functional units can still operate normally when the median capacity of the \(PGA\) is lower than 0.136 g. The functionality of the substation depends on the operating status of the line-out unit. The failure of one line-out unit leads to a 10% drop in substation functionality. At this time, the transformer unit and the line-out unit are redundant, and there is a high probability that the number of instances of damage to the transformer unit and the line-out unit will not exceed one. The functionality of the system is determined by the line-out unit, and the destruction of one line-out unit can cause a 10% functionality drop. With increasing \(PGA\), the redundancy of the line-in unit begins to decrease. When the second line-in unit is destroyed, the functionality of the substation is reduced by 20%. To illustrate this point more clearly, Figure 18 shows the frequency of the substation system with different functionalities at various \(PGA\)s. When the \(PGA\) is less than 0.16 g, the substation remains fully operational, and when the \(PGA\) is greater than 0.23 g, the substation loses most of its functions. It can be observed that \(F_{\rm S}=6\) does not show a gradual decline with \(F_{\rm S}=8\), \(F_{\rm S}=4\), and \(F_{\rm S}=2\), and the peak frequency of \(F_{\rm S}=6\) is much smaller than that of \(F_{\rm S}=4\), which indicates that the fragility of the transformer unit is too large. As a result, its redundancy cannot effectively guarantee the seismic reliability of the substation. When the \(PGA\) is small, the function of the substation depends on the line-out unit and the 110 kV connection unit. When the \(PGA\) is large, the function of the substation mainly depends on the line-in unit, 220 kV connection unit, and transformer unit.