## 2 Bifacial PV Module Structure and Resulted Incident Irradiance Evaluation
### Bifacial PV Modeling  
The energetic characterization of a PV module is based on the module's current-voltage characteristic, typically represented by the I-V curve. This curve describes the relationship between the operating current \(I\) and the operating voltage \(V\) of the PV module. Three key points (conditions) are considered along the entire curve: the short-circuit point, the maximum power point, and the open-circuit point. The short-circuit point indicates the conditions where the operating voltage is zero. The maximum power point indicates the conditions for generating the most power. Finally, the open-circuit point indicates the conditions where the operating current is equal to zero. The voltage-current characteristic depends on the constructive characteristics of the module and various operating and environmental parameters. Among these, the two most influential operating parameters are the incident irradiance and the operating temperature of the module. The effect of these parameters is represented by Figure 4, where a generic I-V curve is plotted at different irradiance levels and operating temperatures. The evaluation of the effects of irradiance and temperature on the electrical parameters is performed using three models, one for each physical interaction mechanism. With reference to Figure 5, these models are denoted as the optical, thermal, and electrical models. Their use is sequential and aimed at quantifying the electrical power produced by the module under different operating conditions. However, this paper focuses on the optical modeling of bi-PVs, showing the most significant changes compared to the monofacial counterpart. Therefore, the subsequent sections assume familiarity with the thermal and electrical models, focusing solely on concepts related to optical aspects. Figure 4: Characteristic curve of a generic PV module and its qualitative deviation for variation in incident irradiance (**a**) and operating temperature (**b**). Figure 3: Normalized spectral responsivity of front and rear surfaces of 3 bifacial photovoltaic modules. Image retrieved from [31]. The optical model aims to evaluate the incident irradiance on the PV module surface. In particular, the model calculates the magnitude of the front incident irradiance \(G_{\text{front}}\) and the rear incident irradiance \(G_{\text{rear}}\). This model can be constructed using two possible approaches: the view-factor approach and the ray-tracing approach. The ray-tracing approach calculates the irradiances by graphically projecting virtual rays from a viewpoint (i.e., the analyzed point) in a pre-described 3D computer scene. Therefore, the approach evaluates the incident irradiance on the entire PV module by analyzing the incident irradiance on several single points homogeneously distributed along the module surface. In contrast, the view-factor approach considers the incident radiation on the PV surface \(G_{\text{x-PV}}\) as proportional to the reciprocal visibility between the light source (\(x\)), or reflecting surface, and the PV surface. Thus, the approach is based on the following equation:  
\[G_{\text{x-PV}}=G_{\text{x}}\alpha_{\text{x}}VF_{\text{x-PV}}\;, \tag{2}\]  
where \(G_{\text{x}}\) represents the radiation coming from the light source, or incident radiation on \(x\) (if \(x\) is a reflecting surface), \(\alpha_{\text{x}}\) the reflectivity coefficient of \(x\) (equal to one if \(x\) is a light source), and \(VF_{\text{x-PV}}\) the view-factor between \(x\) and the PV module surface [39]. The view-factor for each reflecting surface is determined by considering a 2D geometry and the spatial arrangement of the PV module and the reflecting surface. Therefore, each light source, or reflecting surface, is considered in the simulation through a coefficient.