## 6 Simulated Results
Figure 10: P-V characteristic curve for case 3. Figure 9: Simulation results for case 2: MPPT with conventional CSO and four modified methods under solar irradiance change from 1000 to 500 W/m\({}^{2}\) and back to 1000 W/m\({}^{2}\). Test of Case 4  
Figure 12 shows the P-V characteristic curves of the PVMA in case 4 at solar irradiances of 1000 and 500 W/m\({}^{2}\) with two modules under 100% and 50% shading, where three peaks appeared with true MPP at 170.2 and 84.4 W, respectively, and the GMPP was in the middle. Figure 13 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\({}^{2}\), each method was stuck with an LMPP at 121.7 W. The four modified methods could escape from the stuck point swiftly and track the GMPP successfully. The conventional CSO under a solar irradiance of 1000 W/m\({}^{2}\) could not track the GMPP successfully within the set of 30 iterations. Although the four proposed tracking methods could track the GMPP successfully, the MCSO with the initial tracking voltage fixed at 0.8 \(V_{\rm mp}\) combined with pace adjusted with the slope of the P-V curve and inertia weight provided the fastest tracking speed response, and the oscillation amplitude near the MPP was minor. Therefore, the power generation efficiency of the PVMA could be enhanced. Figure 11: Simulation results for case 3: MPPT with conventional CSO and four modified methods under solar irradiance change from 1000 to 500 W/m\({}^{2}\) and back to 1000 W/m\({}^{2}\). Figure 12: P-V characteristic curve for case 4. (5) Test of Case 5  
Figure 14 shows the P-V characteristic curves of the PVMA in case 5 at solar irradiances of 1000 and 500 W/m\({}^{2}\) with nine modules under 30%, 60%, and 90% shading, where four peaks appeared with true MPP at 85.8 and 42.9 W, respectively, and the GMPP was at the second peak from the left. Figure 15 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\({}^{2}\), only the conventional CSO under a solar irradiance of 1000 W/m\({}^{2}\) could not track the GMPP. Although all four modified tracking methods proposed in this paper were stuck with an LMPP at 51.9 W, they could escape from the LMPP swiftly and track the GMPP successfully. Among them, the MCSO with the initial tracking voltage fixed at 0.8 \(V_{\text{mp}}\) combined with pace adjusted with the slope of the P-V curve and inertia weight could escape from the LMPP (51.9 W) the fastest. Therefore, this modified method provided optimal tracking speed response and steady performance. Figure 14: P-V characteristic curve for case 5. Figure 13: Simulation results for case 4: MPPT with conventional CSO and four modified methods under solar irradiance change from 1000 to 500 W/m\({}^{2}\) and back to 1000 W/m\({}^{2}\). Test of Case 6  
Figure 16 shows the P-V characteristic curves of the PVMA in case 6 at solar irradiances of 1000 and 500 W/m\({}^{2}\) with nine modules under 30%, 50%, and 80% shading, where four peaks appeared with true MPP at 98.2 and 48.7 W, respectively, and the GMPP was at the third peak from the left. Figure 17 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\({}^{2}\), only the conventional CSO under a solar irradiance of 1000 W/m\({}^{2}\) could not track the GMPP. Although all four modified tracking methods proposed in this paper were stuck with an LMPP at 51.9 and 85.8 W, they could escape swiftly and track the GMPP successfully under the two solar irradiance conditions.