## 5 Simulation Analysis  
The effectiveness of the proposed algorithm is verified with simulation in the MATLAB/Simulink environment. The circuit model is shown in Figure 6. This system consists of a PV panel, boost converter, MPPT controller, and load [67]. The boost converter is chosen in this application due to its popularity among researchers as it has a low voltage ripple [11]. The parameters of the boost converter are listed in Table 1. The converter is connected to a resistive load of 50 \(\Omega\). A PV module, PMS50W, with specifications as listed in Table 2 is used. Figure 5: Modified Levy flight optimization. Initial particles D are set to 0.1, 0.2, 0.5, and 0.7. This is highly important as the initial execution process is to scan the full range before converging on the best solution. The duty cycle limit is also set from \(\mathrm{d_{min}}\) to \(\mathrm{d_{max}}\). The setting of limitations on the duty cycle is included in the algorithm. Here, \(\mathrm{d_{min}}\) is set to 0.1 and \(\mathrm{d_{max}}\) is set to 0.75. The stopping criterion in this algorithm is set by assigning maximum iteration in the proposed algorithm. Here, the maximum iteration is set to 10. The other parameters are also set as follows: the P coefficient is set to 0.8, \(\mathrm{\beta_{1}}\) is set to 1.5, \(\mathrm{\beta_{2}}\) is set to 2.0, and \(\upsilon\) is set to 1. In this simulation, the sampling time is 0.1 s with a sampling frequency of 10 Hz. Table 3 summarizes the parameter setting of the proposed algorithm. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Symbols** & **Values** \\ \hline Input capacitor & \(\mathrm{C_{in}}\) & 220 uF \\ Inductor & \(\mathrm{L}\) & 270 uH \\ Switching frequency & \(\mathrm{f_{s}}\) & 20 kHz \\ Output capacitor & \(\mathrm{C_{out}}\) & 220 uF \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Boost converter specifications. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters at STC** & **Specifications** \\ \hline Maximum power, \(\mathrm{P_{max}}\) & 50 W \\ Open circuit voltage, \(\mathrm{V_{oc}}\) & 22.5 V \\ Maximum power voltage, \(\mathrm{V_{mp}}\) & 18.0 V \\ Short circuit current, \(\mathrm{I_{sc}}\) & 3.00 A \\ Maximum power current, \(\mathrm{I_{mp}}\) & 2.78 A \\ Number of series cells, \(\mathrm{N_{s}}\) & 36 \\ Temperature coefficient of \(\mathrm{I_{sc}}\) & 0.05\(\%\)/\({}^{\circ}\mathrm{C}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: PV module, PMS50W. Figure 6: Simulation circuit of a standalone PV system with a boost converter. Firstly, the proposed algorithm is evaluated under uniform irradiance (STC). The tested conditions are investigated under three different irradiances which are high (1000 W/m\({}^{2}\)), medium (600 W/m\({}^{2}\)), and low (200 W/m\({}^{2}\)) as shown in Figure 7. Based on Figure 7, it is noted that the MPP of the PV module varies with irradiance. Higher irradiance contributes to a higher value of maximum power at a constant temperature. It is also observed that there is only one peak power point for each irradiance. This peak is known as the local maximum power point (LMPP). Next, the proposed algorithm is tested under the partial shading condition (PSC) as shown in Figure 8. The characteristics of the I-V and P-V curves under PSCs are shown for three different conditions. Based on Figure 8, it can be noted that multiple peaks occur along the curve. This phenomenon happens due to non-uniform irradiances that penetrated into the PV module as shown in Figure 9. Multiple peaks here include LMPP and GMP. The irradiance patterns of the PSCs are summarized in Table 4. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline d\({}_{\text{min}}\) & 0.1 \\ d\({}_{\text{max}}\) & 0.75 \\ iter\({}_{\text{max}}\) & 10 \\ Number of particles & 4 \\ Initial position of particles & 0.1, 0.2, 0.5, 0.7 \\ P coefficient & 0.8 \\ \(\beta_{1}\) & 1.5 \\ \(\beta_{2}\) & 2.0 \\ Sigma \(\upsilon\) & 1 \\ Sampling time & 0.1 s \\ \hline \hline \end{tabular}
\end{table}