*4.1. Optimization Results under Uniform Irradiance*

Under a standard light intensity of 1000 W/m<sup>2</sup> and a standard ambient temperature of 25 ◦C, it is observed that the output power demonstrated a single peak characteristic. The P-V characteristic of the output is depicted in Figure 10. Specifically, the GMPP of the PV arrays is observed to be 8517 W.

**Figure 10.** P-V characteristic of PV array under uniform irradiance.

The GMPP is searched using the aforementioned four algorithms in this article. Figure 11 presents the simulation results for these four algorithms, with a simulation time of 2 s.

**Figure 11.** Power outputs of three algorithms under no shading condition at the MPP. (**a**) PSO-BOA algorithm; (**b**) PSO algorithm; (**c**) BOA; and (**d**) P&O algorithm.

Figure 11 demonstrates that all four algorithms (PSO-BOA, PSO, P&O, and BOA) are capable of tracking GMPP under uniform irradiance. In this situation, the P&O algorithm can track the MPP relatively quickly, but it suffers from significant oscillations and fails to converge to the MPP. Therefore, this paper does not provide further comparisons for the other complex conditions. When reaching the stable state, the power tracked by the other three algorithms is 8517 W, which is the theoretical maximum power. However, the convergence rate of the three algorithms varies. The PSO algorithm converges rapidly but tends to exhibit fluctuations around the maximum power point for an extended period of time, whereas the BOA has the slowest convergence rate. The PSO-BOA algorithm requires the least amount of time and significantly improves the convergence speed.

### *4.2. Optimization Results during Static Shading*

In the setting of standard ambient temperature conditions at 25 ◦C, each of the five PV panels is subjected to varying light intensities: 800 W/m2, 800 W/m2, 600 W/m2, 600 W/m2, and 400 W/m2. In this situation, the output power of the PV array exhibits multi-peak characteristics, with the GMPP measuring at 4374 W, as depicted in Figure 12.

**Figure 12.** P-V characteristics of array output under static shading.

The GMPP at this time is determined using the three algorithms mentioned earlier. The simulation curves of these algorithms with a simulation time of 2 s are depicted in Figure 13.

**Figure 13.** Power outputs of three algorithms under static shading. (**a**) PSO-BOA algorithm; (**b**) PSO algorithm; and (**c**) BOA algorithm.

Figure 13 shows that both the PSO-BOA and BOA algorithms have the capability to track the theoretical GMPP accurately. However, the PSO algorithm tracks a slightly lower GMPP of 4373 W, with a deviation value of 1 W, and exhibits small oscillations even reaching the steady state (after 0.4 s). In contrast, the BOA has slower convergence and larger power oscillations. Under static shading conditions, the PSO-BOA algorithm displays significant improvement in convergence speed and reduction in power oscillation.

#### *4.3. Optimization Results under Abrupt Alterations for Irradiance Conditions*

To test the response of a PV array to rapid changes in light intensity, this paper conducts a series of tests involving exposing the array to different light intensities at specific time intervals. Specifically, the array is devised to varying light intensities of 1000 W/m2, 1000 W/m2, 800 W/m2, 800 W/m2, and 400 W/m2 from 0 to 0.8 s, and is then designed by 800 W/m2, 800 W/m2, 600 W/m2, 400 W/m2, and 400 W/m2 from 0.8 to 2 s. These simulations are carried out under the environmental temperature of 25 ◦C, and the resulting P-V characteristics are depicted in Figure 14. During the two stages, the corresponding GMPP values of the array are 4606 W and 3337 W. Further evaluation of the system's performance is conducted by comparing the dynamic shading simulations for three algorithms with a simulation time of 2 s. The comparison is depicted in Figure 15.

**Figure 14.** P-V characteristics of PV array output under abrupt alterations for irradiance conditions.

Figure 15 shows that the PSO-BOA algorithm accurately tracks the theoretical GMPP under varying irradiance conditions. The BOA also displays good performance in this regard, albeit with a slight tracking error. However, the PSO algorithm exhibits a significant deviation from the theoretical GMPP and is susceptible to local optima, thus resulting in low convergence accuracy. Furthermore, in terms of convergence time, the BOA requires around 0.7 s to converge, with more oscillations during varying irradiance conditions. In contrast, the PSO algorithm has relatively faster convergence, requiring about 0.4 s. Meanwhile, the PSO-BOA algorithm exhibits the fastest convergence time of about 0.3 s, accompanied by less oscillation, thereby demonstrating its superior tracking performance under dynamic local shading conditions. Overall, compared to both the PSO and BOA algorithms, the PSO-BOA algorithm offers improved tracking accuracy and less oscillation.

**Figure 15.** Power outputs of three algorithms under abrupt alterations for irradiance conditions. (**a**) PSO-BOA algorithm; (**b**) PSO algorithm; and (**c**) BOA.
