# Power Grid Reliability Evaluation Considering Wind Farm Cyber Security and Ramping Events
## 6 Case Studies and Results
### Reliability Assessment with the Imperfect Attack  
An IPA directly affects the bearing of a WT. As such, in this subsection, the impacts of an IPA on the reliability of WTs and power systems are both discussed. The remaining lives of four typical bearings with and without an IPA were estimated. The rated life of bearing defined by the American Bearing Manufacturers Association (ABMA) standards was applied from the empirical data [34]. Firstly, the remaining lives of four typical bearings attacked by an IPA were tested. The remaining lives of bearings in a wind farm with a normal cyber-defense capability have been included in Table 5. \(S_{N}\), \(S_{L}\), \(S_{M}\) and \(S_{S}\) are the initial states of bearings as introduced in Table 2. The subscript \"N\" means that the bearing works under the normal condition, while the subscript \"A\" means it is attacked by an IPA. As the table shows, an IPA shortens bearing lives to varying degrees. In general, the remaining lives of bearings with the initial state \"\(S_{N}\)\" were shortened by an average of 20%. The bearing with a better initial status was the most affected. The probability distribution of a bearing with a rated life of 100,000 h is presented in Figure 10. Each color represents a bearing state, and the length of the block is the state probability. The left subgraph is the result that bearing works in a normal operating condition. In a normal condition, the  
Figure 8: Distribution of load shedding caused by wind power ramping events (WPRs). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Rated Life [h]**} & \multicolumn{2}{c}{\(S_{N}\)} & \multicolumn{2}{c}{\(S_{L}\)} & \multicolumn{2}{c}{\(S_{M}\)} & \multicolumn{2}{c}{\(S_{S}\)} \\ \cline{2-9}  & **N** & **A** & **N** & **A** & **N** & **A** & **N** & **A** \\ \hline
30,000 & 5 & 4 & 3 & 3 & 2 & 2 & 0.2 & 0.2 \\
60,000 & 11 & 9 & 7 & 6 & 4 & 4 & 0.4 & 0.4 \\
80,000 & 14 & 11 & 9 & 8 & 5 & 5 & 0.6 & 0.4 \\
100,000 & 18 & 14 & 12 & 10 & 6 & 6 & 0.6 & 0.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Remaining lives of bearings in different states [year]. Figure 9: EENS caused by cyber-attacks and WPRs. remaining life of bearing is approximately 18 years (see the red block). After being attacked by an IPA, the failure state appeared four years earlier, as shown in the right subgraph. The duration of the normal state was decreased by 22%, and the probability of failure state also increased in the same year. Furthermore, the remaining lives of bearings were tested in systems with different defense capabilities. As listed in Table 6, the bearings with longer rated lives were more affected. Additionally, system defense capability was important to protect the bearings. The bearing life in the system with weak defense capability could be shortened by nearly 40%. Compared to the good or perfect system, the life reduction could be controlled below 20%. Finally, the power grid reliability considering an IPA was tested. The time-varying failure rates of WTs were modeled according to Equations (9) and (10). The rated lives of the WTs on Bus 2 and Bus 15 were set at 14 years, and the rated lives of WTs on Bus 22 were set at 18 years. Suppose all the generators are new and put into operation at the first year. If wind turbines are involved with an IPA at the first year, the system reliability results within 22 years are presented in Figure 11.  
The reliability indices show that the power system suffered a huge power loss in the later stage. Since the IPA reduced the rated WT life, as seen in Table 6, the reliability indices of systems attacked had a rapid growth over time from the 10 th year. As shown in Figure 11, there was an obvious gap between the systems with and without being attacked. Especially the weak system, its LOLP reached 0.1 in the 12 th year. In comparison, although the WTs had exceeded their rated lives at 18 th year, the LOLP of the system without being attacked was far below 0.1.