# Power Prediction of Bifacial Si PV Module with Different Reflection Conditions on Rooftop
## 2 Modeling and Method  
### Rear Side Reflection  
The solar radiation directly affects the output of the solar module. The sun's altitude and direction of incidence, which vary with the seasons, account for a large amount of sun entering the solar module. Therefore, in this paper, we try to predict the output power using the solar radiation, which varies with altitude and date, rather than acquiring the incident irradiance into a simple pyranometer attached on the rear side [19]. It is assumed that the total irradiance (\(I_{Total}\)) entering the back of the bifacial solar module is the sum of the direct irradiance (\(I_{Rear,dir}\)) and diffuse irradiance (\(I_{Rear,diff}\)) [20; 21]. At the rear, it is divided into the amount of irradiance reflected directly from the ground and the amount reflected from the surroundings. The total irradiance is expressed in terms of the GHI (Global Horizontal Irradiance), which is the amount of irradiance incident on the horizontal surface. The total irradiance includes both Direct Normal Irradiance (_DNI_) and Diffuse Horizontal Irradiance (_DHI_) [16].  
Direct irradiance and reflected irradiation incident on the inclined module were measured by [PERSON] et al. [22], and the scattered radiation dose is based on the Perez model [23]. In this paper, the view factor is used to determine the element of back reflection to be predicted. The concept of view factor based on heat transfer was introduced to explain the directional effect of radiant heat transfer between two surfaces [24]. View factor is a pure geometric quantity that is independent of heat and surface properties. The view factor from \(i\) to \(j\) is defined as \"\(F_{i\to j}\)\" or \"\(F_{ij}\)\". \(F_{ij}\) is the part of the irradiation that directly strikes from surface \(i\) to \(j\).  
For example, the view factor \"\(F_{12}\)\" represents the amount of direct radiation from Surface 1 to Surface 2, and \"\(F_{12}\)\" represents the amount of radiation from Surface 2 to Surface 1. The basic principle for obtaining the view factor is shown in Figure 2.  
Equation (1) is used to obtain \(F_{12}\).  
\[F_{12}=\frac{1}{A_{1}}\int_{A_{2}}\int_{A_{1}}\frac{cos\theta_{1}cos\theta_{2} }{\pi r^{2}}dA_{1}dA_{2} \tag{1}\]  
In this paper, the total area of irradiance affecting the rear side of the module is obtained by using the view factor, assuming that the area of the module is \(A_{m}\) and \(A_{s}\) is the area of the ground where the irradiance that affects the back of the module is reflected. \(A_{NS}\) is the area that could not directly affect the back of the module.  
Therefore, it can be said that the irradiance reflected on the rear side of the module is determined by the shadow of the module and the outer part of the shadow. Figure 3 shows the two components of the irradiance reflected on the rear side of the module.  
Figure 2: The view factor between two surfaces.  
The total area of the irradiance affecting the rear of the module can be expressed by the view factor. \(F_{ms}\) is the View Factor of region \(A_{S}\) of irradiance affecting the area of \(A_{m}\). \(\beta\) is the angle between the module and the ground, as shown in Equation (2).  
\[F_{ms}=\frac{1-cos(180^{\circ}-\beta)}{2} \tag{2}\]  
Therefore, the irradiance incident on the rear surface can be expressed as the sum of the amounts of direct irradiance and scattered irradiance on the area of the module (\(A_{m}\)). The albedo coefficient \(\alpha\) is used for determining the direct irradiance (\(I_{Rear,dir}\)) and scattered irradiance (\(I_{Rear,diff}\)) incident on the rear side as shown in Equation (3).  
\[I_{Rear}=\alpha DNIF_{A_{S}\to A_{m}}+\alpha(GHI-DNI)F_{A_{S}\to A_{m}} \tag{3}\]