4.2.1. Uniform Irradiance and Temperature

Eight cases under uniform conditions were set up to explore the effects of irradiance and temperature separately. The cases can be divided into five irradiances at 25 ◦C: 1000, 800, 600, 400, and 200 W/m2 and four temperatures at 1000 W/m2: 25, 40, 55, and 70 ◦C. Their I-V and P-V output characteristics are shown in Figures 6 and 7. In the figures, the output current increases with increasing irradiance, and the maximum power point voltage decreases with increasing temperature.

**Figure 6.** Characteristic curves in various irradiance: (**a**) I-V (**b**) P-V.

**Figure 7.** Characteristic curves in various temperatures: (**a**) I-V (**b**) P-V.

From the above characteristic plots, it is evident that when environmental factors change, corresponding parameters change accordingly to achieve a high degree of fit to the output curve. The unknown parameters extracted using GSK are illustrated in Table 21. When the irradiance is the variable, *Iph* increases linearly with increasing irradiance, and *Rs* decreases in a non-linear fashion with increasing irradiance. When the temperature is the variable, *Iph* increases weakly with increasing temperature, and *Issd* increases in a non-linear manner. Meanwhile, the RMSE increases with decreasing temperature, indicating that the lower the temperature, the lower the identification result's accuracy.


**Table 21.** Parameters of the KC200GT at different irradiances and temperatures.

Some methods counted in Section 3 simulated PV modules at different irradiances and temperatures. The methods are gathered together, as illustrated in Table 22. The methods' quantity is 22, indicating that the proportion of methods discussing these cases is low and that more consideration needs to be placed on these cases in future research work. Most of the 22 methods discussed irradiance and temperature together, and the cases they used most frequently are SM55, ST40, and KC200GT. Thus, other cases could be added to these three implementations in the future so that further generalizability can be demonstrated.

**Table 22.** Various methods with different irradiance and temperature experiments.



**Table 22.** *Cont.*


**Table 22.** *Cont.*

The "√" means that there are temperature or irradiance experiments in the literature.

#### 4.2.2. Partial Shade Conditions

Four groups of KC200GTs were connected in series to obtain the multi-peak curve exhibited by the output of the PV power system when partially shaded (PSC). Four sets of comparison tests were designed: standard case (STC: 4 × 1000 W/m2), type I partial shading (PSC-1: 1000, 800, 400, 400 W/m2), type II partial shading (PSC-2: 800, 600, 400, 200 W/m2), and type III partial shading (PSC-3: 800, 600, 400, 400 W/m2). The output characteristics are shown in Figure 8. In the figure, STC has a single peak, PSC-1 and PSC-3 have three peaks, and PSC-2 has four. Additionally, STC has only one irradiance, PSC-1 and PSC-3 have three irradiances, and PSC-2 has four irradiances. Therefore, the PV's peaks are related to the irradiance types on the series-connected PV modules.

The mathematical models developed in Section 2 cannot generate multiple inflection points. Thus, the characteristic curve of the PSC fitted using these mathematical models will still have only one inflection point, and the accuracy of the fit will be very low. It is reflected in a large minimum RMSE. The extracted parameters are shown in Table 23, and it is clear that the RMSE at STC is much lower than that at PSC. Although the corresponding mathematical model was developed by Chellaswamy et al. [147], it requires human judgment and input of the number of modules to be shaded, which is difficult to achieve in reality. Therefore, more mathematical models need to be developed in future work to improve the accuracy of the parameters of the extracted PSCs. It is important to note that, due to the presence of parallel diodes in the system, the PV modules are in an idle state when the output current of the system is more significant than its photogenerated current.

The mathematical models developed to simulate the output characteristics of the PSC must take this critical point into account.

**Figure 8.** Characteristic curves in partial shade conditions: (**a**) I-V (**b**) P-V.


**Table 23.** Parameters of the KC200GT at partial shade conditions.
