## 8 Results and Discussion
In terms of the location of eigenvalues, the proposed PSS-SCA algorithm provides more shift towards the real axis of the s-plane to limit the abrupt variation in the amplitude of angle deviation and increases system stability by moving eigenvalues more to the left of an imaginary axis line. The PSS-SCA system required 44 iterations to converge the maximum objective function having the exact optimisation parameter values \(r_{1}\) = 1.12, \(r_{2}\) = 0.3150, \(r_{3}\) = 1 and \(r_{4}\) = 0.5961 for loading condition 2 compared with the other methods of optimisation (Table 8). The PSS-MFO and PSS-EP systems take 96 and 23 iterations to converge on the results and have exact optimisation parameter values \(d\) = 0.00025, \(t\) = \(-\)0.9041 and \(\beta\) = 0.1, respectively. The PSS-EP system has better convergence with minimum objective function value. The proposed technique offered better objective function with respect to both other procedures and has satisfactory computational efficiency compared with the PSS-EP system. The PSS parameters are optimised by using different optimisation techniques, and the eigenvalues related to the electromechanical modes obtained, damping ratio as objective function and damping ratio of loading condition 4 for the SMIB are provided in Table 10. The region of eigenvalue locations in the s-plane and rotor angle deviation are shown in Figures 12 and 13, respectively. The proposed PSS-SCA technique provides better damping of angle deviation and location of eigenvalues compared with the other optimisation methods. In terms of the location of eigenvalues, the proposed PSS-SCA algorithm provides more shift towards the real axis of the s-plane to limit the abrupt variation in amplitude of angle deviation and increase the system stability by moving eigenvalues more to the left of an imaginary axis line. The PSS-SCA system required 42 iterations to converge to the maximum objective function having the exact optimisation parameter values \(r_{1}\)= 1.16, \(r_{2}\) = 5.9751, \(r_{3}\) = 1 and \(r_{4}\) = 0.8489 for loading condition 4 compared with the other methods  
Figure 8: Eigenvalue’s location on the complex s-plane for loading condition 2 of the SMIB with PSS. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Loading Condition 2**} \\ \hline
**Methods** & **PSS-SCA** & **PSS-MFO** & **PSS-EP** & **PSS-U** \\ \hline \multirow{2}{*}{PSS optimised parameters} & \(T_{1}\) = 0.02499 & \(T_{1}\) = 0.02888 & \(T_{1}\) = 0.06651 & \(T_{1}\) = 0.1 \\  & \(T_{2}\) = 0.00150 & \(T_{2}\) = 0.00413 & \(T_{2}\) = 0.00152 & \(T_{2}\) = 0.04 \\  & \(K_{\text{sth}}\) = 32.96348 & \(K_{\text{sth}}\) = 32.83729 & \(K_{\text{sth}}\) = 37.41522 & \(K_{\text{sth}}\) = 9 \\ \hline Objective function & 0.7340 & 0.7227 & 0.6609 & 0.1209 \\ \hline \multirow{2}{*}{
\begin{tabular}{c} Number of iterations \\ \end{tabular} } & \multirow{2}{*}{44} & \multirow{2}{*}{96} & \multirow{2}{*}{23} & \multirow{2}{*}{NA} \\  & & & & \\ \end{tabular}
\end{table} 
Table 8: Comparison of the PSS optimised parameters, eigenvalues and damping ratio for loading condition 2 of the SMIB. of optimisation (Table 10). The PSS-MFO and PSS-EP systems take 94 and 20 iterations to converge on the results and have the exact optimisation parameter values \(d=0.00025\), \(t=-0.0713\) and \(\beta=0.1\), respectively. PSS-EP system has better convergence with the minimum objective function value. The proposed technique offered better objective function with respect to both other procedures and has satisfactory computational efficiency compared with the PSS-EP system. The PSS parameters are optimised by using different optimisation techniques, and the eigenvalues related to the electromechanical modes were obtained. The damping ratio as objective function and damping ratio of loading condition 3 for the SMIB are provided in Table 9. The region of eigenvalue locations in the s-plane and rotor angle deviation are shown in Figures 10 and 11, respectively.