## 4 Results
The MFO and EP systems required 62 and 7 iterations, respectively, to converge on the results. With the lowest objective function value, the PIDF-EP system had a higher rate of convergence. In comparison to the three other techniques, the proposed technique provided a superior objective function and was as computationally efficient as the PIDF-EP system. Therefore, the suggested optimisation strategy can be used to improve the system's performance when MO is used as the objective function. This improvement may be achieved by providing similar weights to DF and DR to increase the system's damping capacity. This finding demonstrates that the suggested EPSCA technique can stabilise the signal in an SMIB power system and optimise the TCSC-PIDF controller variables with a maximum objective function as the provided MO function. The angle deviation response for Scenario A-4 is shown in Figure 24. PIDF-EPSCA exhibited the smoothest response and the smallest swing for angle deviation response when compared with the other methods. Following the start of the simulation, the system was damped in 0.95 s. PIDF-SCA ranked second followed by PIDF-MFO and PIDF-EP, respectively. The PIDF-EP system ranked last among the four strategies and took the longest time to damp the oscillation. All other approaches except PIDF-EPSCA needed longer than 3.5 s to damp the oscillation. Figure 23: Eigenvalue distribution of TCSC-PIDF controller system using PIDF-EPSCA, PIDF-SCA, PIDF-MFO, and PIDF-EP techniques for Scenario A-3. Figure 25 depicts the Scenario A-4 speed deviation effect. In comparison to other standard approaches, PIDF-EPSCA showed an improvement in oscillatory mode response and speed deviation decayed response. The simulation demonstrated that the suggested system took 0.95 s to decay speed deviation oscillations, followed by the PIDF-SCA, PIDF-MFO, and PIDF-EP approaches, respectively. The fourth and slowest method for reducing speed deviation fluctuations was the PIDF-EP system. All other approaches had damping times that were longer than 3.5 s, apart from PIDF-EPSCA. The eigenvalue sector for Scenario A-4 is shown in Figure 26. Overall, all strategies were successful in moving the eigenvalue location to the phase plan's left side, indicating that all systems were stable. PIDF-EPSCA, in contrast to the other three strategies, was able to allocate the majority of the eigenvalue location on the far-left side of the imaginary axis. The eigenvalue that was mapped closest to the origin by the other three methods was each of theirs. When compared with PIDF-EPSCA, which was at \(-0.276312\) p.u on the real axis, the coordinates, which were practically at the same location from \(-0.27630\) p.u to \(-0.27560\) p.u, were thought to be in a less stable situation. The output of PIDF-EPSCA demonstrated that the eigenvalue sector was moved to the real-imaginary plane's closest point to the real axis. The fact that the PIDF-MFO and PIDF-EP systems both pairs of  
Figure 24: Angle deviation response of the TCSC-PIDF controller using PIDF-EPSCA, PIDF-SCA, PIDF-MFO, and PIDF-EP techniques for Scenario A-4. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & **PIDF-EPSCA** & **PIDF-SCA** & **PIDF-MFO** & **PIDF-EP** \\ \hline \multirow{4}{*}{Parameters optimised} & \(K_{P}=0.011841\) & \(K_{P}=0.020819\) & \(K_{P}=0.050461\) & \(K_{P}=0.048138\) \\  & \(K_{D}=0.000825\) & \(K_{D}=0.000705\) & \(K_{D}=0.000182\) & \(K_{D}=0.000213\) \\  & \(K_{I}=0.004116\) & \(K_{I}=0.070581\) & \(K_{I}=0.0815191\) & \(K_{I}=0.025814\) \\  & N = 77.39919 & N = 100.06704 & N = 182.95746 & N = 197.6818 \\ \hline \multirow{4}{*}{Objective function value} & 0.1240 & 0.1221 & 0.1247 & 0.1244 \\  & DR = 0.8596 & DR = 0.8600 & DR = 0.8282 & DR = 0.8258 \\  & DF = \(-0.4765\) & DF = \(-0.4760\) & DF = \(-0.4543\) & DF = \(-0.5339\) \\ \hline No. of iterations & 12 & 32 & 62 & 7 \\ \hline Settling time (s) & 1.47 & 1.7 & 5 & 3.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of PIDF-EPSCA, PIDF-SCA, PIDF-MFO, and PIDF-EP for Scenario A-3.