## 8 Results and Discussion  
This work considers PSS, which was designed for the SMIB system, and three optimisation algorithms to perform the small signal stability analysis. Numerous operating loading conditions were considered to assess the angle stability analysis. Eigenvalues were obtained by using MATLAB software to gauge the system stability. A metaheuristic optimisation algorithm, namely, SCA, was considered to fine-tune the PSS parameters. The results were validated with MFO and EP optimisation algorithms. \(K_{stb}\), \(T_{1}\) and \(T_{2}\) were the optimised enlisted parameters of a single lead lag compensator for the SMIB system. \(K_{stb}\) is gain constant, \(T_{1}\) is the phase lead constant, and \(T_{2}\) is the phase lag constant. The parameters for SMIB and PSS are presented in Table 4[1, 34]. A comparison amongst the SMIB with unoptimised PSS parameters, SMIB system with optimised PSS parameters \begin{table}
\begin{tabular}{l} \hline \hline
**Evolutionary Programming Algorithm Pseudocode** \\ \hline Initialise the population \\ for \(i=1\) to \(n\) do \\ //parents // \\ for \(j=1\) to \(K\) populations do \\ describe \(x_{j,par}(i)\) and J(\(x_{j,par}(i)\)) \\ end for \\ //offspring // \\ for j = 1 to N populations do \\ \(x_{j,off}(i)=\alpha\times(x_{j,par}(i)_{max}-x_{j,par}(i)_{max})\times\frac{x_{ j,par}(i)}{x_{j,par}(i)_{max}}\) \\ Calculate \(x_{j,off}(i)\) \\ end for \\ merge both offspring and parents \\ sort _x(i)_ in descending arrangement of _l(x(i))_ \\ pick best one-half x(i) value, the same as brand-new \(x_{j,par}(i)\) \\ if \(\mid\)\(\left\{\left(x(i)_{max}\right)-\ J(x(i)_{min})\mid<10^{-4}\ \text{then}\right.\) \\ end if \\ \(i=i+1\) \\ end for \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Pseudocode of EP. by SCA, SMIB system with optimised PSS parameters by MFO and SMIB system with optimised PSS parameters by EP were carried out with five loading conditions (Table 5). Where \(T_{ux}\), \(K_{A}\) and \(T_{R}\), denote the washout time constant of PSS, exciter gain constant and time constant, respectively; \(X_{L}\), \(X_{e}\) and \(R_{e}\) represent load reactance, transmission line reactance and resistance, respectively; \(E_{t}\) denotes the machine terminal voltage; \(K_{sq}\) and \(K_{sd}\) refer to machine filed torque coefficients in the \(q\)-axis and \(d\)-axis, respectively; \(X_{q}\) and \(X_{d}\) express the machine armature reactance in the \(q\)-axis and \(d\)-axis, respectively; and \(T_{do}\) refers to the armature machine open circuit field time constant. Optimisation algorithms SCA and MFO that used the following parameter range as stated in Table 6 were considered for fine-tuning PSS parameters: \(r_{1}\) is the random number that determines the region of position, and its value reduces from 2 to 0 with the increase in iteration to the maximum number iteration; \(r_{2}\) is a random number that defines the direction towards or outwards the destination point, and its value is in the range 0 to 2\(\pi\); \(r_{3}\) is random number weight of the destination, and its value is in the range of 0 to 2; and \(r_{4}\) is the random number that determines which equation (sine or cosine) of the algorithm is used in the current iteration. The value of parameter \(\beta\) of the EP algorithm for tuning of the PSS parameters is illustrated in Table 6.  
The work presents a performance analysis of three optimisation techniques to conduct the small signal stability analysis for the SMIB system. The PSS parameters were optimised by using different optimisation techniques, and eigenvalues related to electromechanical modes were obtained. The damping ratio was selected as an objective function. The damping ratio of loading condition 1 for SMIB was obtained, and is provided in Table 7. The region of eigenvalue locations in the s-plane and rotor angle deviation are shown in Figures 6 and 7, respectively. The proposed PSS-SCA technique provides better damping of angle deviation and location of eigenvalues compared with the other optimisation