## 5 Simulation Results
### Discussion of the Simulation Results  
For readers' convenience, a tracking performance comparison in Scenarios 1-5 is listed in Table 7. The tracking performance was measured as the average number of iterations and the average tracking time required to track down the GMPP in 10 trials. Obviously, this work outperformed its counterparts, which highlights the robustness of this work against various shading conditions. At present, four test cases have been selected to conduct tracking performance tests for the number of peaks and the different locations of the peaks in different P-V characteristic curves generated under different shading conditions; they are compared with the conventional perturbation and observation (P&O) [3], the conventional grey wolf optimization (GWO) [18] and the conventional artificial bee colony (ABC) [24] algorithms, respectively, for tracking performance, the test results of which are summarized in Table 8. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & \multirow{2}{*}{
\begin{tabular}{c} **No. of Peaks on** \\ **Respective P-V** \\ **Curve** \\ \end{tabular} } & \multicolumn{2}{c}{**Average Number of Iterations/Average Tracking Time**} \\ \cline{3-5}  & & **Conventional** & **Conventional** & **Improved FA** \\ \hline
1 & Single & 10.4/5.2 s & 5.6/2.8 s & 3.4/0.7 s \\ \hline \multirow{3}{*}{2} & Double & & & \\  & (MPP was on the right peak) & 19.5/7.6 s & 8.4/3.4 s & 5.7/0.9 s \\ \hline \multirow{3}{*}{3} & Triple & & & \\  & (MPP was on the rightmost peak) & & 14.1/4.0 s & 12.7/1.3 s \\ \hline \multirow{3}{*}{4} & Quadrup & & & \\  & (MPP was on the rightmost peak) & & 14.3/4.2 s & 12.8/1.6 s \\ \hline \multirow{3}{*}{5} & Quadrup & & & \\  & (MPP was on the leftmost peak) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: A comparison of the average number of iterations and tracking time required to track down the GMPP in 10 trials. Figure 20: A tracking performance comparison between algorithms in Scenario 5. Take Scenario 2 from the simulation results of the maximum power tracking conducted by the conventional P&O algorithm, the conventional FA and the improved FA in Figure 21 as an example; if the area of the region (such as the interval with black dotted lines) from the start point of tracking to the global maximum power point tracked by all methods acts as the optimal output energy of the PVMA in the tracking process, and the area of the region between the tracking curve for various methods to the tracked global maximum power point acts as its actual output energy, followed by calculating its tracking efficiency from the ratio of both areas, then the tracking efficiencies of five scenarios using different methods can be listed in Table 9 for comparison. It can be seen from Table 9 that, in different scenarios, the tracking efficiencies of the improved firefly optimization algorithm are the most optimal compared to the other methods, and all of them are above 89.76%. Whereas, in Scenarios 3 and 4, the conventional P&O achieves tracking efficiencies of as low as 67.88-42.48% within 30 iterations because the global maximum power point cannot be tracked. Table 6 shows five test cases of the PVMA in 4 series-3 parallel form used under different shading conditions herein, in which all P-V characteristic curves of the PVMA are obtained from the simulation under standard test conditions (STC). Although the changes in both temperature and sunshine would affect its maximum power output, the impact on  
Figure 21: MPPT efficiency diagram of Scenario 2 obtained using the conventional P&O algorithm, conventional FA and improved FA.