## 4 Experimental Setup and Simulation Results
In this problem we have chosen maximum value of \(\mu_{max}\) as No. of population/5, i.e., 20/5 = 4. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Parameter** & **Values** \\ \hline PSO & \(C_{1},C_{2}\),\(w\) & 1.5, 1.5, 0.9 \\ \hline EHO & \(\alpha\), \(\beta\) & 0.5, 0.5 \\ \hline PPA & \(\mu_{max}\) & Population number/5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters for different metaheuristic algorithms. Figure 8: Simulink model for real-time machine-in-loop (MIL) simulation in OPAL-RT: (**a**) RTLAB-based Simulink interface; (**b**) sc_user_interface block; (**c**) sm_computation block. Hence each of the solutions can generate a maximum of four different solutions from its original solution. As a result, in each generation, the total number for population can vary from 20-80. But to maintain uniformity, after completion of each generation only the 20 best populations are chosen from the 20-80 populations. The process repeats in each iteration. Figure 10 shows the gain parameter trajectory over time. For PSO _Kp_ (DC link voltage controller) gain value changes until the 21 st generation, But _Ki_ (DC link voltage controller) gain reaches the minimum value of the range at the fifth generation and could not improve further. _Kp_ (current control loop) for PSO finally stops changing at iteration 21, whereas _Ki_ (current control loop) reaches the maximum value at the fourth generation. For EHO, there is no such incident of reaching the maximum or minimum values without further improvement. In the case of PPA, there is only such a case (_Ki_ (DC link voltage controller)) where it reaches the minimum value and could not improve further. However, due to the increase of the degree of freedom in control action with the help of \(\lambda\) parameter, it still improves the overall response and hence reduces the error. Table 4 represents the optimal values of the controller parameters, in other words, the final values of the gain parameters from the trajectory plot of Figure 10.  
The optimal response of the DC link voltage controller, d-axis current and reactive power/q-axis current control loop is given in Figure 11. Optimization was done under the maximum irradiance of 1000 w/m\({}^{2}\) and a fixed temperature of 25 \({}^{\circ}\)C. In Figure 11b, unlike Figure 11a,c, there are different individual reference values for each of the optimization algorithms. This is because the reference value for the d-axis current controller comes from the output of the DC link voltage controller. As responses from different optimization techniques provide different outputs from the DC link voltage controller, the reference value also changes for the d-axis current controller. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Controller** & \multicolumn{2}{c}{**DC Link Voltage Controller**} & \multicolumn{3}{c}{**Current Controller**} \\ \hline
**Parameter** & _Kp_ & _Ki_ & \(\lambda\) & _Kp_ & _Ki_ & \(\lambda\) \\ \hline PSO & 1.0054 & 100 & - & 0.6820 & 40 & - \\ \hline EHO & 1.5398 & 169.8523 & 0.9707 & 0.6498 & 18.9024 & 0.9394 \\ \hline PPA & 1.3858 & 100 & 0.8431 & 0.6654 & 17.5034 & 0.9757 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Optimal value of gain parameters. Figure 9: Fitness value. The settling time was calculated by finding the response when it comes to the \(\pm 2\%\) band of the desired response.