## 5 Results and Discussion
### Simulation Results
#### 5.2.2 Comparison of Different Controller Cases Under Different Scenarios
Figure 14 shows the power-flow plots through critical Line 53-54, \(P_{53-54}\) when a circuit is disconnected under different controller configurations (tuned using both the proposed method and OBTM) for different scenarios. \(P_{53-54}\) oscillates largely without any controller, and time response improves with the separate application of PSS and BESS controllers. Furthermore, both oscillation settling time and amplitude are lowest with the proposed strategy of utilizing PSS and BESS controllers in a coordinated manner when compared with other controller configurations, thus highlighting the efficiency of the proposed control strategy. Furthermore, it can also be seen that the time response of \(P_{53-54}\) following a disturbance is much better when the power-system controllers are tuned using the proposed method than with the compared method. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**No Controllers**} & \multicolumn{3}{c}{**PSSs**} & \multicolumn{3}{c}{**BESS Controllers**} & \multicolumn{3}{c}{**PSSs and BESS Controllers**} \\ \cline{2-9}
**No.** & \(P(\mathbf{\alpha}>-\mathbf{0.1})\) & \(P(\mathbf{\zeta}<\mathbf{0.1})\) & \(P(\mathbf{\alpha}>-\mathbf{0.1})\) & \(P(\mathbf{\zeta}<\mathbf{0.1})\) & \(P(\mathbf{\alpha}>-\mathbf{0.1})\) & \(P(\mathbf{\zeta}<\mathbf{0.1})\) & \(P(\mathbf{\alpha}>-\mathbf{0.1})\) & \(P(\mathbf{\zeta}<\mathbf{0.1})\) \\  & **\{\%\}** & **\{\%\}** & **\{\%\}** & **\{\%\}** & **\{\%\}** & **\{\%\}** & **\{\%\}** & **\{\%\}** & **\{\%\}** \\ \hline
1 & 100 & 100 & 99.0866 & 100 & 0 & 0 & 0 \\
2 & 100 & 100 & 99.3710 & 100 & 0 & 0 & 0 \\
3 & 97.1333 & 100 & 0 & 0 & 0 & 0 & 2.8950 \\
4 & 98.5768 & 100 & 0 & 0 & 0 & 100 & 0 \\
5 & 0 & 100 & 0 & 0 & 0 & 100 & 0 \. & \" & \" & \" & \" & \" & \" & \" \\
15 & 0 & 100 & 0 & 0 & 0 & 100 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Stability indices under different controller conditions for Scenario 2 using OBTM. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**No Controllers**} & \multicolumn{3}{c}{**PSSs**} & \multicolumn{3}{c}{**BESS Controllers**} & \multicolumn{3}{c}{**PSSs and BESS Controllers**} \\ \cline{2-9}
**No.** & \(P(\mathbf{\alpha}>-\mathbf{0.1})\) & \(P(\mathbf{\zeta}<\mathbf{0.1})\) & \(P(\mathbf{\alpha}>-\mathbf{0.1})\) & \(P(\mathbf{\zeta}<\mathbf{0.1})\) & \(P(\mathbf{\alpha}>-\mathbf{0.1})\) & \(P(\mathbf{\zeta}<\mathbf{0.1})\) & \(P(\mathbf{\alpha}>-\mathbf{0.1})\) & \(P(\mathbf{\zeta}<\mathbf{0.1})\) \\  & **\{\%\}** & **\{\%\}** & **\{\%\}** & **\{\%\}** & **\{\%\}** & **\{\%\}** & **\{\%\}** & **\{\%\}** \\ \hline
1 & 100 & 100 & 100 & 100 & 0 & 0 & 0 \\
2 & 96.8426 & 100 & 1.8218 & 100 & 0 & 0 & 0 \\
3 & 95.1850 & 100 & 100 & 100 & 0 & 0 & 0 \\
4 & 98.2310 & 100 & 0 & 0 & 0 & 100 & 0 \\
5 & 0 & 100 & 0 & 0 & 0 & 100 & 0 \. & \" & \" & \" & \" & \" & \" \\
15 & 0 & 100 & 0 & 0 & 0 & 100 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Stability indices under different controller conditions for Scenario 3 using OBTM. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**No Controllers**} & \multicolumn{3}{c}{**PSSs**} & \multicolumn{3}{c}{**BESS Controllers**} & \multicolumn{3}{c}{**PSSs and BESS Controllers**} \\ \cline{2-9}
**No. ** & \(P(\mathbf{\alpha}>-\mathbf{0.1})\) & \(P(\mathbf{\zeta}<\mathbf{0.1})\) & \(P(\mathbf{\alpha}>-\mathbf{0.1})\) & \(P(\mathbf{\zeta}<\mathbf{0.1})\) & \(P(\mathbf{\alpha}>-\mathbf{0.1})\) & \(P(\mathbf{\zeta}<\mathbf{0.1})\) & \(P(\mathbf{\alpha}<\mathbf{0.1})\) \\  & **\{\%\}** & **\{\%\}** & **\{\%Overshoot [43] and settling-time [43] values for both the proposed and compared method for the time characteristics of \(P_{53\text{-}54}\) are given in Tables 12 and 13. The overshoot and settling-time values were less for all cases when controllers were tuned using the proposed method when compared to OBTM, highlighting the effectiveness of the developed method.