# Reliability of Supply and the Impact of Weather Exposure and Protection System Failures +
## 4 Case Study
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Set Information**} & \multicolumn{4}{c}{**Method 1**} \\ \hline  & & \multicolumn{2}{c}{**Approximate**} & \multicolumn{2}{c}{**Time Series**} \\ \cline{3-6}
**Connection** & **Components** & **No PS** & **PS** & **No PS** & **PS** \\ \hline - & Cable & 0.570 & 0.773 & 0.570 & 0.773 \\ - & Line & 12.250 & 15.534 & 12.250 & 15.534 \\ - & Transformer & 0.100 & 0.673 & 0.100 & 0.673 \\ \hline None & Cable-Cable & 0.000 & 0.001 & 0.000 & 0.001 \\ None & Cable-Line & 0.027 & 0.035 & 0.027 & 0.038 \\ None & Cable-Trans & 0.004 & 0.006 & 0.004 & 0.006 \\ None & Line-Line & 0.155 & 0.202 & 0.627 & 0.755 \\ None & Line-Trans & 0.094 & 0.127 & 0.093 & 0.138 \\ None & Trans-Trans & 0.000 & 0.003 & 0.000 & 0.003 \\ \hline
1 bus & Cable-Line & 0.003 & 0.172 & 0.003 & 0.173 \\
1 bus & Cable-Trans & 0.001 & 0.026 & 0.001 & 0.026 \\
1 bus & Line-Line & 0.020 & 1.477 & 0.111 & 1.581 \\
1 bus & Line-Trans & 0.015 & 0.330 & 0.015 & 0.332 \\
1 bus & Trans-Trans & 0.000 & 0.007 & 0.000 & 0.007 \\ \hline
2 buses & Line-Line & 0.001 & 0.204 & 0.010 & 0.214 \\ \hline \hline \end{tabular}  
* Approximate and time-series method, excluding and including protection system failures (PS).  
\end{table} 
Table 1: Annual failure rate for outages within different set categories [\(\lambda/y\)]. Figure 6: Individual failure probability of components in cut-set [26; 27] and dependency mode failure probability for a 40 hour time-window. Failure probability and unavailability of cut-set, including and excluding protection system failures. In terms of unavailability of sets of components, Table 2 shows a somewhat different story. The single contingency of a transformer has a 5.7 times increase in failure probability when protection systems are included in the analysis but has nearly no change in expected unavailability. This is due to the short outage durations associated with protection systems failures in the model. Again, sets of components which are both exposed to correlated weather, such as overhead transmission lines, experience the largest increase in annual unavailability. The most extreme being the case of two overhead lines sharing both buses, where the time-series method including protection systems reliability has an expected unavailability 20 times higher than what is found using the approximate method without including protection systems failures. ENS for the system calculated using the different methods is shown in Table 3. The transmission system is usually operated by the N-1 criterion, and only second order contingencies are considered here. Considering cut-sets consisting of two components with no shared buses, the majority of increase in ENS stems from the inclusion of weather effects in the model, affecting overhead transmission line cut-sets. For cut-sets with adjacent components, the inclusion of protection systems has the largest impact compared to the base case, although weather effects have almost the same impact as the inclusion of protection systems for overhead transmission line cut-sets within this category. The impact seen in second order cut-sets suggests that protection systems and weather effects are important aspects to consider when evaluating the reliability of supply.