## 6 Simulated Results  
Figure 5 shows the architecture of maximum power point tracking (MPPT) for cat swarm optimization (CSO) and modified cat swarm optimization (MCSO). In this paper, CSO and four types of MCSO are used to control the duty cycle of the boost converter, with the goal of tracking the maximum power point of the photovoltaic module array. The basic principle is to use the seeking and tracking modes in cat swarm optimization to find and track the maximum fitness (i.e., maximum PVMA output power) that was determined. The duty cycle of the boost converter's switch (S) is then adjusted via the pulse width modulation control circuit to ensure that the PVMA operates at the maximum power point voltage, allowing the PVMA to output the maximum power. MATLAB software was used to build the model of a four-series, three-parallel (total capacity: 239.1 W) PVMA assembled from single SWM20W photovoltaic modules. The solar irradiance of all 12 photovoltaic modules was suddenly reduced to half under different shading percentages at 0.1 s. Various proposed MCSO methods were utilized for the MPPT test, in which the tracking speed response and steady performance under various different tracking methods were compared. The status of different peak numbers based on the shading percentage of each test case and the corresponding P-V characteristic curves are shown in Table 5. The parameters for the conventional CSO and MCSO utilized in this paper are shown in Table 6. \begin{table}
\begin{tabular}{c c} \hline
**Component** & **Specifications** \\ \hline Input capacitor, \(C_{in}\) & 220 \(\mu\)F, withstand voltage: 400 V \\ Filter capacitance, \(C_{out}\) & 470 \(\mu\)F, withstand voltage: 450 V \\ Energy storage inductance, \(L_{m}\) & 1.67 mH, withstand voltage: 450 V \\ Fast diode, D (IQVD60E60A1) & Withstand voltage: 600 V, withstand current: 60 A \\ Switch, S (IREP460B) & Withstand voltage: 500 V, withstand current: 20 A \\ \hline \end{tabular}
\end{table} 
Table 4: Component specifications for boost converter [23]. \begin{table}
\begin{tabular}{c c c} \hline
**Scenario** & **Peak Numbers on P-V** & **4-Series, 3-Parallel Shading \%** \\  & **Characteristic Curve** & **(0\% shading + 0\% shading + 0\% shading)//** \\ \hline \multirow{4}{*}{1} & Single-peak & (0\% shading + 0\% shading + 0\% shading + 0\% shading)// \\  & & (0\% shading + 0\% shading + 0\% shading + 0\% shading)// \\  & & (0\% shading + 0\% shading + 0\% shading + 0\% shading) \\  & & (50\% shading + 0\% shading + 0\% shading + 0\% shading)// \\ \multirow{2}{*}{2} & Double-peak & (0\% shading + 0\% shading + 0\% shading + 0\% shading)// \\  & (MPP at right) & (0\% shading + 0\% shading + 0\% shading)// \\ \hline \end{tabular}
\end{table} 
Table 5: Peak numbers on P-V characteristic curve of 4-series, 3-parallel PVMA under 6 shading conditions. Test of Case 3  
Figure 10 shows the P-V characteristic curves of PVMA in case 3 at solar irradiances of 1000 and 500 W/m\({}^{2}\) with two modules under 80% and 100% shading, where three peaks appeared with true MPP at 159.4 and 80.7 W, respectively, and the GMPP was at the far right. Figure 11 shows the simulation results for MPPT with the conventional CSO and four proposed MCSO methods. From the figure, it can be seen that under a solar irradiance change from 1000 to 500 W/m\({}^{2}\) and back to 1000 W/m\({}^{2}\), although all five tracking methods could track the GMPP successfully, each was stuck with an LMPP at 121.7 and 154.8 W. Even though all five tracking methods could track to the GMPP eventually, it could be clearly observed that the conventional CSO required a longer duration, and the oscillation amplitude during the tracking process was greater. In view of this, the proposed MSCO with an initial tracking voltage fixed at 0.8 \(V_{\mathrm{mp}}\) combined with pace adjusted with the slope of the P-V curve and inertia weight not only provided the fastest tracking speed response, but the oscillation amplitude near the GMPP was lower compared to the other methods.