## 3 Optical Model Comparison and Evaluation of Influences on the Incident Irradiance on the PV Module
### Sky Conditions' Influence  
The sun radiation, \(G\), can be divided into a direct component \(G^{\text{beam}}\) and a diffuse component \(G^{\text{diffuse}}\). \(G^{\text{beam}}\) is the radiation not affected by aerosol and particulate matter in the atmosphere. Conversely, \(G^{\text{diffuse}}\) represents the portion of the radiation that reaches the ground after being affected by scattering phenomena with aerosol and particulate matter. The division of \(G\) into its two components depends on the Sun's position and on the atmospheric conditions [61; 62]. The former is responsible for the length of atmosphere light has to pass through to reach ground changes, and so is the probability of light being scattered by air. The latter is attributable to the fact that different air mass densities and different probabilities of light scattering characterize different atmospheric conditions. Due to its nature, the scattering phenomenon changes the direction, making it impossible to discern a precise direction of light. Hence, while \(G^{\text{beam}}\) is characterized by the Sun's direction, \(G^{\text{diffuse}}\) is not. Merging the fact that the incident irradiance on a bifacial module is composed of a front, \(G_{\text{front}}\), and a rear component, \(G_{\text{rear}}\), the considerations regarding \(G^{\text{beam}}\) and \(G^{\text{diffuse}}\), and the possibility of light being reflected by nearby surfaces before being incident on the module, it is possible to express \(G_{\text{front}}\) and \(G_{\text{rear}}\) as the sum of a beam, diffuse, and reflected component (described through the schematization proposed in Figure 9), as  
\[G_{\text{front}}=G_{\text{front}}^{\text{beam}}+G_{\text{front}}^{\text{ diffuse}}+G_{\text{front}}^{\text{ref}} \tag{6}\]  
\[G_{\text{rear}}=G_{\text{rear}}^{\text{beam}}+G_{\text{rear}}^{\text{diffuse}}+ G_{\text{rear}}^{\text{ref}} \tag{7}\]  
where the apex \"ref\" stands for reflected. Reflected radiation components, similar to \(G^{\text{diffuse}}\), are not characterized by a unique direction because of the nature of reflection. This division is particularly important to understand the influence that the tilt angle of the module \(\gamma\) has on \(G_{\text{front}}\) and \(G_{\text{rear}}\)[63; 64; 65]. Evaluating each component and its relationship with \(\gamma\), the maximization of \(G_{\text{front}}^{\text{beam}}\) relies on minimizing the angle of incidence (AOI), which is the angle between the Sun's direction and \(\gamma\). The variation in \(G_{\text{front}}^{\text{ref}}\) with the module orientation, instead, is typically negligible concerning the \(G_{\text{front}}^{\text{beam}}\) variation, thus, it is not considered further. Regarding the rear side, \(G_{\text{rear}}^{\text{beam}}\) is considered significant only when the Sun's azimuth deviates more than 90\({}^{\circ}\) from the bi-PV's azimuth, which means to have the rear surface of the module facing the Sun. \(G_{\text{rear}}^{\text{ref}}\), instead, is, for the most part, due to ground reflection. Thus, it is maximized when the rear module surface is horizontal, and the visibility between the module and the ground is maximized. Lastly, since \(G_{\text{rear}}^{\text{diffuse}}\) and \(G_{\text{front}}^{\text{diffuse}}\) are not characterized by a direction,  
Figure 8: (**a**) Points to measure the irradiance. (**b**) Rear irradiance value and related non-uniformity for multiple sets of points along the bifacial PV module. Images retrieved from [35]. they find their maximum value when the visibility between the sky and the reference surface is as it maximum [66]. Therefore, to ascertain the optimal orientation, it is essential to evaluate the magnitude of each light component and its relative maximization strategy. In clear-sky conditions, \(G^{\text{beam}}\) has the greatest maximum value. Hence, to maximize the incident irradiance on the PV module, the AOI has to be minimized (i.e., front surface towards the Sun) [54; 55; 64; 67]. However, during overcast weather conditions, such an assumption is no longer true.