## 4 Results
situation demonstrated how the suggested EPSCA technique can stabilise the signal in an SMIB power system and optimise the TCSC-PIDF controller values with a maximum objective function as the proposed MO function. The angle deviation response for Scenario A-2 is shown in Figure 18. When compared with the other conditions, PIDF-EPSCA exhibited the smoothest response and shortest swing for angle deviation response. Within 1.1 s of the start of the simulation, the system was damped. The PIDF-SCA ranked second, followed by the PIDF-MFO and PIDF-EP. The PIDF-EP system was in the last position and took the longest to damp the oscillation. Other approaches, except PIDF-EPSCA, required damping times greater than 5 s.  
Figure 19 depicts the Scenario A-2 speed deviation effect. In comparison to other conventional approaches, PIDF-EPSCA showed an improvement in oscillatory mode responses, and speed deviation decayed earlier. After the simulation began, the suggested system took 1.1 s to decay the speed deviation oscillations, followed by the PIDF-SCA, PIDF-MFO, and PIDF-EP approaches, in that order. The final and slowest of the four methods to soften speed deviation swings was the PIDF-EP system. All other methods except PIDF-EPSCA had damping times that were longer than five seconds. The eigenvalue sectors for Scenario A-2 are displayed in Figure 20. Overall, all methods succeeded in moving the eigenvalue location to the left side of the phase plan, demonstrating the stability of all systems. When compared with the other three strategies, PIDF-EPSCA was able to allocate the majority of the eigenvalue locations further to the left. The closest point to the origin was where one of the eigenvalues of the other three approaches was mapped. In comparison to PIDF-EPSCA, which was at \(-0.6242\) p.u on the real axis, the coordinates, which were nearly at the same point between \(-0.6227\) p.u to \(-0.5176\) p.u, were assumed to be in a less stable condition. The output of PIDF-EPSCA further demonstrated that the eigenvalue sector was moved to the real-imaginary plane's nearest point towards the real axis. The fact that the PIDF-MFO and PIDF-EP systems both had a pair of eigenvalues that were closest to the imaginary axis and furthest from the real axis, respectively, supports the notion that these two approaches were the worst. Thus, PIDF-EPSCA was validated as the top option for improving SMIB system stability. Figure 18: Angle deviation response of the TCSC-PIDF controller using PIDF-EPSCA, PIDF-SCA, PIDF-MFO, and PIDF-EP techniques for Scenario A-2. method offered a greater shift towards the real axis of the s-plane to reduce the abrupt variation in the amplitude of angle deviation and boosted system stability by moving the eigenvalues farther to the left of an imaginary axis line. Unlike other optimisation techniques, the PIDF-EPSCA system needed 13 iterations to converge the solution (Table 4). In contrast to other optimisation techniques, the PIDF-SCA system needed 32 iterations to converge the maximum objective function (Table 4). The MFO and EP systems converged on the results after 52 and 6 iterations, respectively. The minimal objective function value of the PIDF-EP system resulted in a higher convergence rate. The suggested method offered better computing efficiency than the PIDF-EP system and a superior objective function than the three other techniques. As a result, the suggested optimisation strategy, which used MO as the objective function, was able to simultaneously improve DF and DR by giving them equal weight in the development process for a system with improved damping capabilities. This demonstrated how the suggested EPSCA technique can stabilise the signal in an SMIB power system and optimise the TCSC-PIDF controller parameters with a maximum objective function as the proposed MO function. The response to the angle deviation in Scenario A-3 is shown in Figure 21. In terms of responsiveness to angle variation, PIDF-EPSCA had the smoothest response and the least swing when compared with the other methods.