## 4 Results  
The results and discussion of the MO function strategy for improving oscillation stability in the SMIB system by utilising a variety of optimisation strategies are presented in this part. The four scenarios with various loading conditions are given in Table 1. The TCSC PIDF (SMIB-TCSC-PIDF) was used in MATLAB to conduct all cases. \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Loading Scenarios (P, Q)**} \\ \cline{2-3}
**Scenarios** & \multicolumn{2}{c}{**Dynamic Load (P)**} & **Reactive Load (O)** \\ \hline Scenario A-1 & P = 0.500 (p.u) & O = 0.3155 (p.u) \\ Scenario A-2 & P = 0.475 (p.u) & O = 0.3172 (p.u) \\ Scenario A-3 & P = 0.400 (p.u) & O = 0.3219 (p.u) \\ Scenario A-4 & P = 0.300 (p.u) & O = 0.3269 (p.u) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Scenarios involving the loading conditions. Figure 14: EP flowchart. The following four strategies are discussed:  
1. TCSC-PIDF controller in an SMIB system that was optimised using EPSCA (PIDF-EPSCA). 2. TCSC-PIDF controller in an SMIB system that was optimised using SCA (PIDF-SCA). 3. TCSC-PIDF controller in an SMIB system that was optimised using MFO (PIDF-MFO). 4. TCSC-PIDF controller in a SMIB system that was optimised using EP (PIDF-EP). Table 2 shows the parameters of SMIB and TCSC. Figure 15 shows the angle deviation response for Scenario A-1. When compared with other scenarios, PIDF-EPSCA exhibited the smoothest response and minimum swing for angle deviation response. The system was damped 1.35 s after the simulation began. PIDF-SCA was in second place, followed by PIDF-MFO and PIDF-EP. The PIDF-EP system was at the last position, taking a longer time to dampen the oscillation out of all four techniques. Except for PIDF-EPSCA, the damping time of the other techniques was longer than 2 s.  
The speed deviation response for Scenario A-1 is shown in Figure 16. PIDF-EPSCA displayed an improvement in oscillatory mode responses, and speed deviation decayed earlier as compared to other standard methods. The proposed system took 1.35 s to decay speed deviation oscillations after the simulation started, followed by the PIDF-SCA, PIDF-MFO, and PIDF-EP methods, respectively. The PIDF-EP system was in the last position and took the longest of the four ways to dampen speed deviation swings. The damping time of all other techniques aside from PIDF-EPSCA was greater than two seconds. \begin{table}
\begin{tabular}{l l} \hline \hline
**Modules** & **Parameters List** \\ \hline Generator & H = 4, \(x_{d}=1.0\), \(R_{a}=0.005\), \(x_{q}=0.78\), \(x_{Q}=0.73\), \(x_{D}=1.11\), T\({}_{\text{d}\text{d}^{\prime}}=6\), \(x_{ad}=1\), \\  & \(x_{aq}=0.6\tau_{D}=0.002\), M = 7, \(\tau_{Q}=0.04\). \\ Transmission Line & Re = 0, \(x_{t}=0.15\). \\ Exciter and TCSC & \(K_{A}=10\), \(T_{A}=0.02\), \(V_{ba}=1.0\), \(V_{to}=1.05\), \(x_{L}=0.054\), \(x_{tesc}=0.90837\), \(V_{b}=1\). \\ \hline \hline \end{tabular}
\end{table} 
Table 2: SMIB and TCSC parameter values. Figure 15: Angle deviation response of the TCSC-PIDF controller using PIDF-EPSCA, PIDF-SCA, PIDF-MFO, and PIDF-EP techniques for Scenario A-1. An eigenvalue consists of a real part and an imaginary part. A stable system has a negative real part of its total eigenvalues. The imaginary axis line is a vertical line in the complex s-plane, where each point represents a complex number with zero real components (only the imaginary part) and, conversely, is a real axis line. A conjugate pair of eigenvalues with the imaginary part only (zero real part) represents the oscillation mode. A conjugate pair of eigenvalues with a negative real part and an imaginary part represent the decaying oscillation mode. An eigenvalue has only the negative real part with the zero imaginary part, which represents the exponential decay of the non-oscillation mode. The amplitude of the oscillation modes depends on the imaginary part of the eigenvalues and settling time depends on the real part of the eigenvalues.