## 5 Simulation Results
### Simulation Results of the Improved FA  
Tables 4 and 5 list the parameter settings used in the conventional and the improved version of the firefly algorithm. Table 6 lists five scenarios, representing five different shading conditions, in which shading effects on P-V characteristic curves of a 4 series-3 parallel (4S-3P) configuration were demonstrated. As will be seen below, multiple peaks occurred in the P-V curves in Scenarios 2-5 where the GMPP  
2 Scenario 2  
In this scenario, 50% of a module was shaded. As illustrated in Figure 13, there were two peaks on the P-V curve, and the maximum power fell from 239.1 to 201.7 W. Similar to Scenario 1, the GMPP lay near the right endpoint of the curve. As can be seen in Figure 14, the GMPP can be tracked down well using any of the three approaches, and it is noted that this work outperformed others again.  
Figure 12: A tracking performance comparison between algorithms in Scenario 1.  
Figure 13: The P-V curve in Scenario 2.  
(3) Scenario 3  
In this scenario, 50% of a PV module and 70% of another were shaded, and three peaks occurred on the P-V curve, as illustrated in Figure 15. The maximum power was further reduced to 184.7 W, and there was one more peak on the P-V curve than in Scenario 2. The GMPP lay near the right endpoint of the curve again. The tracking performance is compared in Figure 16. As it appears, this work outperformed others again. After getting trapped in a LMPP, it took the improved version of the FA a shorter period of time to get away from the trap than the original version. Here, it must be stressed that the conventional P&O method failed to track down the GMPP even after 30 iterations.  
Figure 14: A tracking performance comparison between algorithms in Scenario 2.  
Figure 15: The P-V curve in Scenario 3.  
(4) Scenario 4  
In this scenario, 70% of a module was shaded in addition to the two shaded modules in Scenario 3. As illustrated in Figure 17, the maximum output power was further reduced to 184.7 W, and there was one more peak on the P-V curve than in Scenario 3. The GMPP lay near the right endpoint of the curve again. As can be seen in Figure 18, both the improved and the original version of the FA succeeded in tracking down the GMPP as expected, while the P&O method failed again. As before, this work outperformed the original version of the FA.  
Figure 16: A tracking performance comparison between algorithms in Scenario 3.  
Figure 17: The P-V curve in Scenario 4.  
Scenario 5  
As listed in Table 6, nine modules were shaded in this scenario, that is, 70% of the first third, 80% of the second third and 90% of the last third modules were shaded. As illustrated in Figure 19, there were 4 peaks on the P-V curve, and the global maximum output power was as low as 55.8 W. Unlike in Scenarios 1-4, the GMPP instead lay near the left endpoint of the P-V curve this time. In Figure 20, it is observed that the P&O method got trapped in a LMPP more easily than others, even though all the three algorithms finally succeeded in tracking down the GMPP. Above all, this work outperformed others again.  
Figure 19: The P-V curve in Scenario 5.  
Figure 18: A tracking performance comparison between algorithms in Scenario 4.