## 3 Results
### Main Results
Figure 11a,b show the MAPE between the DAQ and model data for the I-V and output power curves, reaching values below 20%, but higher than the MAPE obtained during the optimization of the standard conditions parameters. This may occur because the values of temperature and solar irradiance may not be constant along the whole PV panel, as Table 7 shows. To be able to compare the model with the experimental data, average temperature and irradiance values were used, so this high MAPE between the DAQ and model data may occur due the fact that in the optimization process, the experimental data used as reference was obtained at constant operational temperature and solar irradiance, conditions that are not feasible in a real operation. The data in Table 7 reveals a significant thermal gradient across the panel's surface, with a temperature standard deviation reaching up to 2.84 \({}^{\circ}\)C. This indicates that different cells on the panel were operating at notably different temperatures. A single-diode model,  
Figure 9: Measurements results: (**a**) output power and (**b**) I–V curves. which relies on a single average operating temperature, cannot fully capture the complex effects of this non-uniformity on the panel's real-world behavior. Similarly, the use of a single pyranometer in the experimental setup assumes that solar irradiance is uniform across the entire panel area. In practice, factors such as localized soiling or the passing shadows of clouds can create uneven illumination, causing some cells to generate less current than others. This electrical mismatch also affects the overall I-V curve in a way that a model using a single irradiance value (G) cannot predict. These simplifications (using an average temperature and a single-point irradiance measurement) are key sources of the observed error between the model and the experimental data. Therefore, to further enhance model performance in future work, deploying multiple pyranometers to better map the irradiance distribution could provide a more accurate input for the model. This highlights the limitations of idealized models and reinforces the necessity of empirical field data to develop more robust and predictive simulations. This issue resulted in an overestimation of the output power and energy efficiency (\(\eta\)) by the model, especially for lower values of G (relative difference of approx. 27% for G = 246.33 W/m\({}^{2}\)), as Table 8 shows. Using the experimental results obtained with the DAQ to optimize the model parameters can reduce this average difference in the model results. Figure 11: Model results: (**a**) I–V curves and (**b**) output power. Figure 10: Panel characteristic curve: (**a**) constant solar irradiance, T\({}_{\text{op}}\) = 48.69 °C; (**b**) variable solar irradiance, T\({}_{\text{op}}\) = 49.66 °C. Using the experimental results for \(G=615.45\) W/m\({}^{2}\), the optimized values obtained were \(I_{\text{ph,ref}}=3.4694\) A, \(R_{\text{sb,ref}}=244.2973\,\Omega\), \(n=0.95688\), \(I_{\text{s,ref}}=2.92672\times 10^{-11}\) A, and \(R_{\text{s}}=0.5809\,\Omega\). Figure 12a,b shows the results of using these new optimized parameters. The MAPE of the I-V curves and output power curves reduced from 18.23 and 18.54% to 7.06 and 7.22%, respectively, and the relative difference between the panel efficiency reduced from around 27% to around 15%. Table 9 presents a comparative analysis of the model's performance before and after parameter re-optimization using Differential Evolution. Notably, all metrics exhibit substantial improvement following re-optimization, particularly in irradiance levels below 700 W/m\({}^{2}\), where initial accuracy was lower. For instance, at 827.59 W/m\({}^{2}\), the RMSE for current dropped from 0.2888 A to 0.0495 A, and the \(R^{2}\) for power increased from 0.8951 to 0.9959. Similarly, for the lowest irradiance level (246.33 W/m\({}^{2}\)), \(R^{2}\) improved from 0.5178 to