## 4 Results
After the simulation began, the system was damped in 1.47 s. Following PIDF-MFO and PIDF-EP, PIDF-SCA came in second. The PIDF-EP system was in the final position and took the longest time to dampen the oscillation out of the four strategies. Other approaches, apart from PIDF-EPSCA, had damping times longer than 3.9 s.  
The Scenario A-3 speed deviation effect is shown in Figure 22. PIDF-EPSCA displayed an improvement in oscillatory mode responses, and speed deviation decayed earlier as compared to other conventional techniques. The simulation showed that the proposed system, followed in that order by the PIDF-SCA, PIDF-MFO, and PIDF-EP techniques, took 1.47 s to decay speed deviation oscillations. The PIDF-EP system was the fourth and slowest way to smooth speed deviation fluctuations. Except for PIDF-EPSCA, all other techniques had damping times that were greater than 3.9 s.  
The Scenario A-3 eigenvalue sectors are displayed in Figure 23. Overall, all methods were successful in moving the eigenvalue location to the left side of the phase plan, indicating that all systems were stable. In this case, PIDF-EPSCA outperformed the other three strategies by allocating the majority of the eigenvalue locations to the far left. One of the eigenvalues from the other three mapping methods was placed closest to the origin. The coordinates, which were nearly at the same point from \(-\)0.4760 p.u to \(-\)0.4543 p.u on the real axis, were thought to be in a less stable condition than PIDF-EPSCA, which was at \(-\)0.4765 p.u on the real axis. The PIDF-EPSCA result also demonstrated that the eigenvalue sector had been moved to the closest position to the real axis of the real-imaginary plane. One set of eigenvalues for the PIDF-MFO and PIDF-EP systems was situated in positions \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Type** & **PIDF-EPSCA** & **PIDF-SCA** & **PIDF-MFO** & **PIDF-EP** \\ \hline \multirow{4}{*}{Parameters optimised} & \(K_{p}=0.020772\) & \(K_{P}=0.033540\) & \(K_{p}=0.039233\) & \(K_{p}=0.040951\) \\  & \(K_{D}=0.000686\) & \(K_{D}=0.000612\) & \(K_{D}=0.000148\) & \(K_{D}=0.000198\) \\  & \(K_{I}=0.0892724\) & \(K_{I}=0.216218\) & \(K_{I}=0.0694360\) & \(K_{I}=0.0894365\) \\  & N = 142.90544 & N = 180.87885 & N = 158.67512 & N = 189.86943 \\ \hline \multirow{4}{*}{Objective function value} & 0.1895 & 0.1915 & 0.1289 & 0.1244 \\  & DR = 0.9221 & DR = 0.8635 & DR = 0.8613 & DR = 0.8258 \\  & DF = \(-\)0.6242 & DF = \(-\)0.6227 & DF = \(-\)0.5176 & DF = \(-\)0.5339 \\ \hline No. of iterations & 13 & 32 & 52 & 6 \\ \hline Settling time (s) & 1.1 & 1.16 & 5 & 4.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of PIDF-EPSCA, PIDF-SCA, PIDF-MFO, and PIDF-EP for Scenario A-2. that were farthest from the real axis and closest to the imaginary axis, respectively. This finding indicates that these two approaches were the poorest ones. Thus, the optimum option for improving SMIB system stability is PIDF-EPSCA. Figure 21: Angle deviation response of the TCSC-PIDF controller using PIDF-EPSCA, PIDF-SCA, PIDF-MFO, and PIDF-EP techniques for Scenario A-3. Figure 22: Speed deviation response of the TCSC-PIDF controller using PIDF-EPSCA, PIDF-SCA, PIDF-MFO, and PIDF-EP techniques for Scenario A-3. The parameters' (N, \(K_{\text{P}}\), \(K_{\text{D}}\), and \(K_{\text{I}}\)) objective functions, iterations, and settling times for the four optimisation approaches are shown in Table 5 for Scenario A-3. When compared with existing optimisation techniques, the proposed hybrid EPSCA strategy offered greater damping of angle deviation and eigenvalue location. The suggested EPSCA algorithm shifted eigenvalues closer to the left of an arbitrary axis line, which improved system stability while reducing the abrupt variation in angle deviation amplitude. Compared with other optimisation methods, the PIDF-EPSCA system needed 12 iterations to converge the solution (Table 5). The PIDF-SCA system, in contrast to previous optimisation techniques, needed 32 iterations to converge the maximum objective function (Table 5).