## 3 Simulation Results
### Result of Pattern 2, Pattern 3 and Pattern 4  
In this section, the design of the PV system to accommodate dynamic changes in irradiation (from pattern 2 to pattern 3 to pattern 4) is discussed. The comparison results of the four algorithms are described below. For pattern 2, it can be seen in Figure 11 that CS, TSO, and ITSO-INC were able to reach the maximum power of the PV system and maintain a zero state occupation, with maximum power values of 6468.86 w, 6470.66 w, and 6265.27 w, respectively. INC failed to maintain GMPP due to the large amplitude of oscillation, resulting in an average power value of 6044.33 w. These results indicate that the efficiency of INC was the lowest. In terms of algorithm optimization time, the minimum time of INC was 0.022 s, but under PSCs, INC could not maintain zero steady-state optimization. \begin{table}
\begin{tabular}{l l l l l} \hline
**Parameter/Method** & **TSO** & **ITSO-INC** & **CS** & **INC** \\ \hline Extracted power (w) & 6165.51 & 6166.72 & 6153.07 & 6145.29 \\ Tracking efficiency (\%) & 99.97 & 99.99 & 99.77 & 99.62 \\ Tracking time (s) & 0.340 & 0.048 & 0.275 & 0.41 \\ \hline \end{tabular}
\end{table} 
Table 8: Numerical results of TSO, ITSO-INC, CS, and INC methods in pattern 1. Figure 9: The obtained power by the algorithms in constant irradiance condition from pattern 1. (**a**) TSO; (**b**) ITSO-INC; (**c**) CS; (**d**) INC.  
Figure 11: _Cont_. Figure 10: The obtained duty cycle by the algorithms in constant irradiance condition from pattern 1. (a) TSO; (b) ITSO; (c) CS; (d) INC. The time of TSO, ITSO-INC, and CS algorithms was 0.272 s, 0.095 s, and 0.188 s, respectively. On the premise of ensuring the efficiency of the algorithm, the ITSO-INC method took the shortest time and had a small frequency of oscillation, which could ensure stable operation in GMPP. In the case of dynamic change in irradiation in pattern 3, when irradiance suddenly changed at 0.4 s, INC fell into LMPP with a value of 4489.89 w. TSO, ITSO-INC, and CS reached GMPP again after the disturbance. The recovery time of ITSO-INC after the disturbance was 0.054 s, which shows that the improved algorithm has better robustness. In terms of algorithm efficiency, the maximum power of the four methods in pattern 3 were 4352.33 w, 4701.45 w, 4702.89 w, and 4489.89 w.  
When the irradiance suddenly changed at 0.8s, TSO, CS, and INC all exhibited significant oscillations. The ITSO-INC method proposed in this study had a lower oscillation amplitude and frequency, resulting in better performance. In terms of tracking efficiency, the proposed algorithm outperformed the other two metaheuristic algorithms. The INC method could not be maintained near MPP. Compared with TSO and CS, the ITSO-INC method improved tracking time by 26.89% and 60.29%. It can be concluded from Table 9 that ITSO-INC has better robustness, algorithm efficiency, and algorithm tracking speed. As can be seen from Figure 12, TSO, ITSO-INC, and CS could maintain zero steady-state dispersion before and after disturbance in the four comparison algorithms. Although the INC algorithm had fast tracking speed, it could not maintain stable operation, and the curve continued to oscillate in constant amplitude. The ITSO-INC algorithm had the  
Figure 11: The obtained power by the algorithms over the step changes from pattern 3 and pattern 4. (a) TSO; (b) ITSO-INC; (c) CS; (d) INC.