## 4 Experimental Setup and Simulation Results  
The experiment was set up with the data given in Table 1. For the machine-In-loop experiment, the help of OPAL-RT (OP5600) real-time digital simulator was taken. The model was built in RTLAB using Simulink-based toolbox, and optimization source-codes were written in MATLAB script. The experimental setup is shown in Figure 7. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Values** & **Parameters** & **Values** \\ \hline Plant Capacity & 3026 kVA & Filter Resistance & 0.0015 pu \\ Grid Voltage & 4.16 kV (\(V_{LL},rms\)) & Filter Inductance & 0.15 pu \\ Frequency & 60 Hz & Filter Capacitance & 0.1 pu \\ DC Link Capacitance & 0.0720 F & Transformer Resistance & 0.0012 pu \\ DC Link Voltage & 1450 Vdc & Transformer Inductance & 0.03 pu \\ Each Unit Capacity & 213.15 W & Switching Frequency & 1980 Hz \\ No. of Series Units & 50 & Sampling Time & 50 μs \\ No. of Parallel Units & 213 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System parameters. For a global solution, a closed search space is required, or in other words, the solutions must be bounded within where the optimal value can be tracked. Mathematically,  
\[x_{min}\leq x\leq x_{max}.\]  
However, in some systems if the search space boundary is unknown then it is difficult to find an initial value for starting the optimization. Hence, before conducting the actual optimization process, we randomly ran the simulation 30 times with a random data range to find a valid search space within where we can find the optimal solution. After such trials, the following range was found for each of the parameters given in Table 2.  
In every metaheuristic algorithm, it is required to deal with some parameters to control the convergence speed of the algorithm. These parameters are generally user-defined parameters, which means the user can set those parameters and examine for which set of values optimal results are achieved. For example, for PPA algorithm the only such parameter is \(\mu_{max}\), which controls the number of runners created by a solution. If this number increases, a solution will create more runners, but simulation time will increase. Hence it should be chosen in such a way that optimal result is found under minimum possible simulation time. For the considered algorithms, the parameters and their values are given in Table 3. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter** & \(K_{pp}\) & \(K_{ip}\) & \(\lambda_{p}\) & \(K_{pl}\) & \(K_{il}\) & \(\lambda_{I}\) \\ \hline Max value & 0.8 & 40 & 1.5 & 4 & 400 & 1.5 \\ \hline Min value & 0.2 & 10 & 0.75 & 1 & 100 & 0.75 \\ \hline \hline \end{tabular} \(K_{pp}\), \(K_{ii}\), and \(\lambda_{o}\) are parameters related to the outer voltage control loop, and \(K_{pl}\), \(K_{il}\), and \(\lambda_{I}\) are related to inner current control loop.  
\end{table} 
Table 2: Search space boundary values for gain parameters. Figure 7: Experimental setup. Also, the population number and number of generation were taken as 20 and 30, respectively. In Figure 8, the simulation figure in the RT-LAB environment has been shown. Unlike Simulink environment, RTLAB-based simulator requires two different blocks for real-time operation. The first block is sm_computation block, where the main system and corresponding controllers were developed. In the second block, sc_user_interface, the input for the system and data visualization blocks are drawn. Fractional order PI controller has been implemented using FOMCON toolbox. The inputs of the system were the solar irradiance and temperature. After the completion of the simulation, the best fitness value can be obtained from Figure 9 and it can be understood that PPA outperforms EHO- and PSO-based controllers. For PSO, conventional PI controller was used; for EHO and PPA, FOPI was used. The reason behind the better solution from PPA is due to the creation of multiple runners from each solution (Equation (17)) and storing only the best population in each generation.