## 3 Results and Discussion
### Models Comparison  
At this stage, the recorded data in 2019 from three locations in Vietnam (Group 1 in Table 1) were taken out for evaluating the proposed models. After removing the samples which were recorded in the nighttime and all incorrect intervals, the total number of sampling points and corresponding time steps are presented in Table 5.  
Besides comparing experimental measurements and model predictions, a comparison between proposed and literature models was also implemented and presented in Table 1 (see Appendix A). As was to be expected, our proposed model with wind presented the best correlation between calculations and measurements with \(R^{2}\) greater than 95% compared to other models, while the without-wind proposed model was the best in the group of models without wind speed. Moreover, the proposed model with wind illustrates that it has the most stable performance compared to all other models from the literature, as it is the only one that provided _RMSE_ values less than 3\({}^{\circ}\)C for all regions. In contrast, the _RMSE_ values for other models changed significantly between the three locations. Moreover, this method \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Time Step** **(Minute)**} & \multicolumn{3}{c}{**Sampling Point**} \\ \cline{2-4}  & **Tri An** & **Da Nang** & **Ha Noi** \\ \hline
1 & 246,982 & 247,703 & 198,476 \\
5 & 49,401 & 49,542 & 39,703 \\
10 & 24,395 & 24,467 & 19,597 \\
15 & 16,136 & 16,187 & 12,975 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The sample size of measurements in different time steps for three regions in Vietnam. also obtained better results for both \(R^{2}\) and \(RMSE\) coefficients at all time steps compared to the original Sandia model. It was clear that the accuracy of all models was proportional to the interval time. As mentioned above, these models describe the temperature of PV modules under the assumption of their thermal equilibrium. Therefore, if this condition is not satisfied, then large differences can result. Moreover, it is known that the time response to changes in the temperature depends on the thermal mass of the module and the prevailing conditions [26], so that if the time resolution of the data is shorter than the typical thermal response times, the performance of the models will not be as good. The difference between the predicted and measured values of the PV module back-surface temperature, \(\Delta T\), is illustrated in Figure 2. As we can see in the picture, the calculation for Sandia is proportional to the magnitude of fluctuating POA between two consecutive sampling points. The larger the variation, the greater the difference is. While the corresponding values for our proposed models tend to approach zero and are evenly distributed around zero across the range of \(\Delta G_{g}\). We also took into account the implementation of temperature models at different POA levels, which strongly affected the accuracy of the predicting process. The results displayed in Figure 3 demonstrate that the accuracy of the temperature models will decrease when the radiation intensity reaches the module surface increase. This circumstance occurred because the fluctuations among high POA values happen more frequently than those of low POA levels. Moreover, the greater POA the module gets, the higher the temperature of the module will be. Subsequently, the thermal inertia of the PV modules will have a stronger effect when POA increases, which explains why our proposed models perform better than literature models at high POA levels but remain equivalent when POA levels are low. Figure 4 showed that the on-site wind speed of all regions remained stable during the observed period, while the average POA irradiance occurred in different ways. The POA irradiance in Tri An is distributed across the whole range of values, while the values of that parameter in Ha Noi are mainly concentrated below 500 W/m\({}^{2}\).