## 5 Discussion  
The main objective of this research is to develop a robust damping controller that dampens the low frequency oscillations in a power system. This is done by developing a mathematical model of a PIDF controller and its modelling with a FACTS-based damping scheme (TCSC), an objective function, and an optimization algorithm. The results section of this article shows that proposed EPSCA optimized all the parameters of the PIDF controller using the proposed multi objective function, and it linearized the nonlinear PIDF-TCSC system and eigenvalue analysis method to dampen the low frequency oscillations as compared to standard algorithms. This was tested with four different loading conditions.  
The hybrid EPSCA technique combines the features of SCA and EP techniques. Figure 6 show both the SCA section and the EP section in the flow chart of the EPSCA technique. The first half and second half iterations of the SCA allow for exploration and exploitation in a search space, respectively. This technique differs from other algorithms due to this capability. When exploring search space and using the eigenvalue analysis to locate maxima or minima, SCA optimisation generally yields superior results. The search exploitation strategy for quick convergence has the only restriction with SCA. For a system that needs a lot of parameters to optimise, the SCA optimization process requires a lot of  
\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} & \(K_{P}=0.013117\) & \(K_{P}=0.018126\) & \(K_{P}=0.062337\) & \(K_{P}=0.048779\) \\  & \(K_{D}=0.001151\) & \(K_{D}=0.001107\) & \(K_{D}=0.000297\) & \(K_{D}=0.000879\) \\  & \(K_{I}=0.007107\) & \(K_{I}=0.057536\) & \(K_{I}=0.0859279\) & \(K_{I}=0.2615544\) \\  & N = 77.75017 & N = 88.88804 & N = 180.39036 & N = 192.05312 \\ \hline \multirow{4}{*}{Objective function value} & 0.1615 & 0.1625 & 0.1220 & 0.1282 \\  & DR = 0.9069 & DR = 0.9126 & DR = 0.8457 & DR = 0.7947 \\  & DF = \(-0.276312\) & DF = \(-0.276305\) & DF = \(-0.275601\) & DF = \(-0.27621\) \\ \hline No. of iterations & 14 & 42 & 49 & 8 \\ \hline Settling time (s) & 0.95 & 1.05 & 3.5 & 2.1 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison of PDF-EPSCA, PIDF-SCA, PIDF-MFO, and PIDF-EP for Scenario A-4.  
Figure 26: Eigenvalue distribution of the TCSC-PIDF controller system using PIDF-EPSCA, PIDF-SCA, PIDF-MFO, and PIDF-EP techniques for Scenario A-4.  
time to produce quality solutions, and it has limitations with consistent solutions. The solution inconsistency of the SCA is due to its low convergence rate. The cure of this pitfall of SCA is the hybrid EPSCA, which utilises the best features of EP, which has high convergence rate and delivers solution performance by raising its convergence rate and solution consistency and is a modified form of SCA.  
The results of the TCSC-PIDF controller system's angle deviation responses, speed deviation responses, and eigenvalue distributions using the EPSCA technique under various loading conditions demonstrate that the suggested optimisation strategy offers a system that enhances the damping capabilities by using the proposed multi objective function. By assigning both DF and DR equal weight during the optimization process, MO, the objective function, is able to simultaneously enhance both DF and DR metrics. In contrast to conventional methods, the results illustrate how the recommended EPSCA strategy may stabilise the signal in an SMIB power system and optimise the TCSC-PIDF controller parameter settings with maximum objective function values and a high convergence rate.