## 5 Simulation Results and Discussion
### Performance Evaluation Under SLP  
In this scenario, the two-area interconnected power system, as shown in Figure 1, is incorporated with the FOFP-iPID controller in each area as a secondary controller, individually. Then, the 1% step load perturbation is subjected to area-1 to investigate the performance of the concerned power plant. The controller's gains are attained by the ALO algorithm and are provided in Table 3. The performance of the designed controller is compared with the other controller's techniques, such as the FOPID and FOiPID controllers, for an identical power plant, and the comparative performances are tabulated in Table 4. It is clearly inspected from Table 4 that the minimum ITAE value is obtained with FOFP-iPID controller (ITAE = 0.7057) compared to the FOiPID controller (ITAE = 0.9714) and the FOPID controller (ITAE = 1.178). It is clear from the above discussion that the FOFP-iPID controller gives a better performance compared to FOPID and FOiPID controllers. The dynamic responses of the plant like area frequencies, tie-line power exchange and area control error (ACE) deviations corresponding to best gains of each controller are attained and displayed in Figure 6a-d. The settling time, peak overshoots/undershoots and ITAE are remarked on and depicted in Table 4. It is clear from the Figure 6a-d and Table 4 that the hybrid coordinated FOFP-iPID controller gives a better performance compared to the FOPID and FOiPID controllers from the point of view of settling time, the magnitude of peak overshoots/undershoots deviations and the ITAE value index.  
Figure 6: Dynamic responses of the SLP in area-1: (**a**,**b**) Frequency deviation in area-1 and area-2, respectively, (**c**) ACE deviation in area-1 (**d**) deviation power in tie-line 12.  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Controller**} & \multicolumn{6}{c}{**Selling Time (Sed for 55- Band**} & \multicolumn{6}{c}{**Peak Overshoot**} & \multicolumn{6}{c}{**Peak Undershoot (-\(\times\))**} & **TATE** \\ \cline{2-13}  & \(\mathbf{A_{f}}\) & \(\mathbf{A_{f}}\) & \(\mathbf{A_{f_{1},1}}\) & \(\mathbf{A_{f}}\) & \(\mathbf{A_{f}}\) & \(\mathbf{A_{f}}\) & \(\mathbf{A_{f}}\) & \(\mathbf{A_{f}}\) & \(\mathbf{A_{f}}\) & \(\mathbf{A_{f}}\) & \(\mathbf{A_{f}}\) & \(\mathbf{A_{f}}\) \\ \hline POPID [17] & 11.57 & 10.72 & 11.49 & 9.951 & 0.009 & 0.006 & 0.0001 & 0.0023 & 0.0027 & 0.0037 & 0.0038 & 0.0127 & 1.780 \\ POPID [17] & 8.058 & 7.664 & 8.764 & 6.009 & 0.0052 & 0.0047 & 0.0014 & 0.0028 & 0.0330 & 0.0098 & 0.0176 & 0.0784 \\ Proposed controller & 5.325 & 4.371 & 8.750 & 4.250 & 0.0034 & 0.0033 & 0.0 & 0.0 0243 & 0.0307 & 0.0053 & 0.0157 & 0.2767 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Performance analysis of the system by employing different controllers.  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Controller**} & \multicolumn{6}{c}{**Selling Time (Sed for 55- Band**} & \multicolumn{6}{c}{**Peak Overshoot**} & \multicolumn{6}{c}{**Peak Undershoot (-\(\times\))**} & **TATE** \\ \cline{2-13}  & \(\mathbf{A_{f}}\) & \(\mathbf{A_{f}}\) & \(\mathbf{A_{f_{1},1}}\) & \(\mathbf{A_{f}}\) & \(\mathbf{A_{f}}\) & \(\mathbf{A_{f}}\) & \(\mathbf{A_{f}}\) & \(\mathbf{A_{f}}\) & \(\mathbf{A_{f}}\) & \(\mathbf{A_{f}}\) & \(\mathbf{A_{f}}\) & \(\mathbf{A_{f}}\) \\ \hline POPID [17]