## 3 Optical Model Comparison and Evaluation of Influences on the Incident Irradiance on the PV Module
### Optical Model Comparison  
The two approaches have been widely implemented in multiple tools. Some of the most well-known tools that implement the view-factor approach include PVsyst, developed by PVsyst SA [41], bifacialVF [16; 42; 43] and SAM [44], both developed by NREL, and MoBiDiG [45], developed by Fraunhofer. The ray-tracing approach is adopted by commercial software like PVNOV [46], developed by Electricite de France (EDF), COMSOL Multiphysics [47], the Python library Bifacial_radiance [48], by NREL, and Raytrace3D [49] by Fraunhofer ISE. [PERSON] et al. [50] compared the results obtained from MoBiDiG and PVNOV with data measured from a single bi-PV with a variable tilt angle. The comparison was conducted on the total (front plus rear) incident irradiance, and it used the root-mean-square error (RMSE) and the mean bias error (MBE) to quantify the accuracy of the tool. The results showed the overall correctness of the models. Values of 4.8% (44.9 W/m\({}^{2}\)) and 2.6% (24.4 W/m\({}^{2}\)) for the RMSE and MBE, respectively, were obtained by MoBiDiG, while 3.1% (29.2 W/m\({}^{2}\)) and -0.8% (-7.9 W/m\({}^{2}\)) were obtained by PVNOV, for the same parameters. However, it is helpful to evaluate the accuracy of the models when considering each irradiance component singularly. For this reason, [PERSON] et al. in [51] compared results from the PVsyst and Fraunhofer ISE tools with real data from two test benches, labeled as A and B, and evaluated the front and rear irradiances separately using both the RMSE and MBE. PV plant A consisted of a single string, with peak power of 2.28 kW\({}_{\text{p}}\), at a height of 1.5 m from the floor, and measured floor-reflectivity of 0.5. PV plant B, instead, was an agrivoltaic system with peak power of 194 kW\({}_{\text{p}}\), at a height of 6.58 m, and estimated ground-reflectivity of 0.20. The comparison, reported in Table 1, showed that the estimation of rear irradiance was much less accurate than that of front irradiance. As pointed out by several other works, this inaccuracy is due to the difficulty in estimating the reflected irradiance, especially when the reflecting surface is not uniform (as in the case of soil). [PERSON] et al. in [52], and many others in [19; 53; 54; 55; 56], investigated in more detail the irradiance modeling accuracy when considering different points of the rear surface. In particular, in [56], the accuracy of the rear incident irradiance modeling was evaluated when considering points along a tilted PV module rear surface. It was concluded that the accuracy depended on where the measurement was taken due to the view-factor (cell-ground) variation along the module and the visibility of ground shades (created by the hosting structure of the module). A reference solar cell placed closer to the ground  
Figure 6: (**a**) Example of a raytracing representation. (**b**) example of a 2D view-factor representation. Image elaborated from [40]. was characterized by a lower view-factor compared to a solar cell placed farther from the ground. However, the ground viewed by the first cell was less susceptible to shading from mounting structures. Thus, during a clear-sky day and low Sun-zenith values, the cell closest to the ground was the one that produced the most energy. Conversely, on cloudy days, the cell closest to the ground produced the least energy because it had the lowest view-factor, and the ground shading was insignificant. Because of this duality, the lowest overall discrepancies between the model and the measurements were obtained for the cells in the center section of the module. Average discrepancies were +6% and +4.5% for the bottom and top sections, respectively, while for the middle section, the value was less than \(\pm\)4%. To confirm the view-factor deviation along the module, it is possible to compare the magnitude of the rear incident irradiance at the two edges of the module.