## 4 Case Studies
### Test System Specification
#### 4.1.1 IEEE-8 Bus System
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Relay**} & \multicolumn{2}{c}{**Conventional**} & \multicolumn{2}{c}{**PSO–LP [55]**} & \multicolumn{2}{c}{**HHO–LP**} \\ \cline{2-7}  & **TMS** & \(\mathbf{I_{p}}\) **(kA)** & **TMS** & \(\mathbf{I_{p}}\) **(kA)** & **TMS** & \(\mathbf{I_{p}}\) **(kA)** \\ \hline
1 & 0.7 & 0.114 & 0.6 & 0.124 & 0.471 & 0.156 \\
2 & 0.8 & 0.249 & 0.806 & 0.249 & 0.685 & 0.249 \\
3 & 0.724 & 0.187 & 0.729 & 0.187 & 0.597 & 0.187 \\
4 & 0.7 & 0.213 & 0.648 & 0.21 & 0.464 & 0.27 \\
5 & 0.7 & 0.142 & 0.6 & 0.142 & 0.399 & 0.193 \\
6 & 0.743 & 0.171 & 0.677 & 0.171 & 0.592 & 0.171 \\
7 & 0.7 & 0.155 & 0.6 & 0.155 & 0.448 & 0.211 \\
8 & 0.8 & 0.164 & 0.827 & 0.164 & 0.815 & 0.163 \\
9 & 0.7 & 0.13 & 0.6 & 0.131 & 0.522 & 0.177 \\
10 & 0.8 & 0.12 & 0.767 & 0.12 & 0.742 & 0.121 \\
11 & 0.8 & 0.203 & 0.731 & 0.203 & 0.712 & 0.202 \\
12 & 0.8 & 0.183 & 0.913 & 0.183 & 0.894 & 0.183 \\
13 & 0.7 & 0.138 & 0.647 & 0.187 & 0.635 & 0.187 \\
14 & 0.7 & 0.183 & 0.605 & 0.249 & 0.594 & 0.249 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Relay settings obtained with particle swarm optimization (PSO)–LP and HHO–LP for IEEE-8 bus system at a wind speed of 10 m/s. TMS, time multiplier setting. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Pair**} & \multirow{2}{*}{**PR**} & \multirow{2}{*}{**BR**} & \multicolumn{2}{c}{**Conventional**} & \multicolumn{2}{c}{**PSO–LP [55]**} & \multicolumn{2}{c}{**HHO–LP**} \\ \cline{3-10}  & & & \(\mathbf{TOP_{PR}}\) & \(\mathbf{TOP_{BR}}\) & \(\mathbf{TOP_{PR}}\) & \(\mathbf{TOP_{BR}}\) & \(\mathbf{TOP_{PR}}\) & \(\mathbf{TOP_{BR}}\) \\ \hline
1 & 1 & 6 & 1.362 & 1.643 & 1.197 & 1.497 & 1.010 & 1.309 \\
2 & 8 & 7 & 1.322 & 2.199 & 1.3 In the first case, with the conventional relay settings, the total operation time of primary and backup relays was 28.716 s and 43.541 s, respectively. With the relay settings obtained using PSO-LP [55], the overall operation time for the same primary and backup relays was 26.470 s and 35.568 s, respectively. Lastly, the time achieved upon optimizing the relay settings with the proposed HHO-LP was 23.93 s and 32.434 s, respectively, which is much lower than that obtained using the conventional and PSO-LP methods. In the second case, with a 20 m/s wind speed, HHO-LP reduced the total operation time of primary-backup relays by 19.86% compared to conventional settings and by 11.522% compared to PSO-LP. No miscoordination was reported with HHO-LP in all 20 relay pairs. The optimal relay settings and relay operating time for the second case are shown in Figures 13 and 14, respectively. The CTI between primary and backup relay pairs with conventional settings and those obtained using PSO-LP [55] and HHO-LP for both cases is reflected in Figure 15. It can be seen that, with the proposed approach, the CTI of 0.3 was maintained in all relay pairs, and the results were satisfactory. The proposed algorithm was also verified by changing the location and size of WTGs, and it is shown in Table 6 that the proposed HHO-LP worked well in all conditions. The overall performance in terms of an improvement in the reduction of time in all cases is given in Table 7.