## 5 Results and Discussion
### Simulation Results
#### 5.2.2 Comparison of Different Controller Cases Under Different Scenarios  
To further demonstrate the effectiveness of the controllers tuned using the proposed method, we analyzed it under three critical scenarios, as shown in Table 5.  
Tables 6-8 describe the results obtained by tuning controllers using the proposed method under different scenarios. The probabilistic indices describing SSS instability are very low without controllers, and improve a bit, particularly for Modes 1-3 in the case with connecting only BESS controllers. Furthermore, except for a few modes (1-3), the likelihood of the system being dynamically stable is high in the case of the system with only PSSs, and highest in the case of the proposed strategy of coordinating PSS and BESS controllers for all scenarios. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{2}{c}{**No Controllers**} & \multicolumn{2}{c}{**PSSs**} & \multicolumn{2}{c}{**BESS Controllers**} & \multicolumn{2}{c}{**PSSs and BESS Controllers**} \\ \cline{2-9}  & \(P(\boldsymbol{\varepsilon}>-\boldsymbol{0.1})\) & \(P(\boldsymbol{\varepsilon}<\boldsymbol{0.1})\) & \(P(\boldsymbol{\varepsilon}>-\boldsymbol{0.1})\) & \(P(\boldsymbol{\varepsilon}<\boldsymbol{0.1})\) & \(P(\boldsymbol{\varepsilon}>-\boldsymbol{0.1})\) & \(P(\boldsymbol{\varepsilon}<\boldsymbol{0.1})\) & \(P(\boldsymbol{\varepsilon}>-\boldsymbol{0.1})\) & \(P(\boldsymbol{\varepsilon}<\boldsymbol{0.1})\) \\  & \{**\%**\} & \{**\%**\} & \{**\%**\} & \{**\%**\} & \{**\%**\} & \{**\%**\} & \{**\%**\} & \{**\%**\} \\ \hline
1 & 100 & 100 & 0 & 98.9374 & 0 & 0 & 0 & 0 \\
2 & 100 & 100 & 6.0612 & 100 & 0 & 0 & 0 & 0 \\
3 & 96.4595 & 100 & 93.4344 & 100 & 0 & 0 & 0 & 0 \\
4 & 98.9926 & 100 & 0 & 0 & 0 & 100 & 0 & 0 \\
5 & 0 & 100 & 0 & 0 & 0 & 100 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Stability indices under different controller conditions for Scenario 1 using the proposed method. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{2}{c}{**No Controllers**} & \multicolumn{2}{c}{**PSSs**} & \multicolumn{2}{c}{**BESS Controllers**} & \multicolumn{2}{c}{**PSSs and BESS Controllers**} \\ \cline{2-9}  & \(P(\boldsymbol{\varepsilon}>-\boldsymbol{0.1})\) & \(P(\boldsymbol{\varepsilon}<\boldsymbol{0.1})\) & \(P(\boldsymbol{\varepsilon}>-\boldsymbol{0.1})\) & \(P(\boldsymbol{\varepsilon}<\boldsymbol{0.1})\) & \(P(\boldsymbol{\varepsilon}>-\boldsymbol{0.1})\) & \(P(\boldsymbol{\varepsilon}<\boldsymbol{0.1})\) & \(P(\boldsymbol{\varepsilon}>-\boldsymbol{0.1})\) & \(P(\boldsymbol{\varepsilon}<\boldsymbol{0.1})\) \\  & \{**\%**\} & \{**\%**\} & \{**\%**\} & \{**\%**\} & \{**\%**\} & \{**\%**\} & \{**\%**\} & \{**\%**\} \\ \hline
1 & 100 & 100 & 93.7333 & 100 & 0 & 0 & 0 & 0 \\
2 & 100 & 100 & 98.1607 & 100 & 0 & 0 & 0 & 0 \\
3 & 97.1333 & 100 & 0 & 0 & 0 & 0 & 0 & 0 \\
4 & 98.5768 & 100 & 0 & 0 & 0 & 100 & 0 & 0 \\
5 & 0 & 100 & 0 & 0 & 0 & 100 & 0 & 0 \\  & - & - & - & - & - & - & - \\
15 & 0 & 100 & 0 & 0 & 0 & 100 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Stability indices under different controller conditions for Scenario 2 using the proposed method. \begin{table}
\begin{tabular}{c c c} \hline \hline
**No.** & **Details** & **Applied disturbance for time-domain simulation** \\ \hline
1 & Disconnection of critical Line 53–54 & Outage of Line 53–54 at 10 s \\
2 & Increase load of the whole system by 4\% & Outage of Line 53–54 at 10 s \\
3 & Increase generation of the whole system by 4\% & Outage of Line 53–54 at 10 s \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Details of different scenarios. The statistical results obtained by tuning controllers using the compared method for different scenarios is given in Tables 9-11, and the system SSS margin is always less when compared with the proposed method under all scenarios. To validate the statistical results, time-domain simulations were also run for both the proposed method and OBTM under different scenarios.