## 8 Results and Discussion
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Optimisation Techniques** & **Parameters Range** & **Optimised PSS Parameter Range Limit** \\ \hline \multirow{2}{*}{SCA} & \(r_{1}=2\) to 0, \(r_{2}=0\) to \(2\pi\), \(r_{3}=0\) & \\  & to 2, \(r_{4}=0\) to 1 & \(T_{1,min}=0.001\), \(T_{1,max}=0.2\) \\ \hline MFO \(d=0.00025\), \(t=-1\) to 1 & \(T_{2,min}=0.001\), \(T_{2,max}=0.1\) \\ \hline EP & \(\beta=0.1\) & \(K_{s4,min}=9\), \(K_{s4,max}=200\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Parameters for optimisation techniques. \begin{table}
\begin{tabular}{c c} \hline \hline
**Modules** & **Parameters** \\ \hline \multirow{2}{*}{Generator} & \(H=3.50\), \(E_{t}=1.0<36^{\circ}\), \(X_{d}^{\prime}=0.30\), \(R_{a}=0.0030\), \\  & \(X_{d}=1.810\), \(X_{q}=1.760\), \(T_{do}=8\), \(K_{sd}=0.84910\), \\  & \(K_{sq}=0.84910\). \\ \hline Power line & \(X_{e}=0.650\), \(X_{L}=0.160\), \(R_{e}=0.0\) \\ \hline AVR with PSS-LL controller & \(T_{R}=0.020\), \(T_{w}=1.40\), \(K_{A}=200.0\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters for the SMIB and PSS. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Loading Conditions** & **Active Power, P (p. u)** & **Reactive Power, Q (p. u)** \\ \hline
1 & P = 0.9 & Q = 0.2 \\
2 & P = 0.9 & Q = 0.3 \\
3 & P = 0.9 & Q = 0.4 \\
4 & P = 0.5 & Q = 0.5 \\
5 & P = 0.2 & Q = 0.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Different loading conditions. methods. The location of eigenvalues in 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 the system stability by moving eigenvalues more to the left of an imaginary axis line. The PSS-SCA system required 46 iterations to converge to the maximum objective function having its exact optimisation parameter values \(r_{1}=1.54\), \(r_{2}=5.7675\), \(r_{3}=1\) and \(r_{4}=0.6481\) for loading condition 1 compared with the other methods of optimisation (Table 7). The PSS-MFO and PSS-EP systems take 103 and 19 iterations to converge on the results and have exact optimisation parameter values \(d=0.00025\), \(t=-0.5556\) and \(\beta=0.1\). The PSS-EP system has a better convergence with minimum objective function value. The proposed technique offers better objective function with respect to the other two procedures and has satisfactory computational efficiency compared with the PSS-EP system. The PSS parameters were optimised by using different optimisation techniques, and the eigenvalues related to the electromechanical modes were obtained. The damping \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & & & \\ \hline \hline \multicolumn{5}{c}{**Loading Condition 1**} \\ \hline
**Methods** & **PSS–SCA** & **PSS-MFO** & **PSS-EP** & **PSS-U** \\ \hline \multirow{2}{*}{PSS optimised parameters} & \(T_{1}=0.03224\) & \(T_{1}=0.03739\) & \(T_{1}=0.06511\) & \(T_{1}=0.1\) \\  & \(T_{2}=0.00179\) & \(T_{2}=0.0050\) & \(T_{2}=0.00142\) & \(T_{2}=0.04\) \\  & \(K_{\text{sdB}}=31.75167\) & \(K_{\text{sdB}}=31.52837\) & \(K_{\text{sdB}}=35.44624\) & \(K_{\text{sdB}}=9\) \\ \hline \multicolumn{5}{c}{Objective function} & 0.7420 & 0.7240 & 0.6770 & 0.1267 \\ \hline \multicolumn{5}{c}{Number of iterations} & 46 & 103 & 19 & NA \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of the PSS optimised parameters, eigenvalues and damping ratio for loading condition 1 of the SMIB. Figure 6: Eigenvalue’s location on the complex s-plane for loading condition 1 of the SMIB with PSS. Figure 7: Rotor angle deviation for loading condition 1 of the SMIB with PSS. ratio as objective function and the damping ratio of loading condition 2 for the SMIB are provided in Table 8. The region of eigenvalue locations in the s-plane and rotor angle deviation are shown in Figures 8 and 9, respectively. The proposed PSS-SCA technique provides better damping of angle deviation and location of eigenvalues compared with other optimisation methods.