# Shading by Overhang PV Collectors
## 3 Results
### Bifacial PV Modules  
Bifacial PV modules have been developed with the purpose of enhancing the power output over conventional (mono-facial) PV modules because bifacial modules can absorb solar radiation from both the front and the rear side. Their applications are useful when the nearby ground or other surfaces are  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(R(m)\) **Distance** & \( \begin{array}{c}E_{b-top}(kWh)\\ \textbf{Beam-top}\end{array} \) & \( \begin{array}{c}E_{d-top}(kWh)\\ \textbf{Diffuse-top}\end{array} \) & \( \begin{array}{c}E_{g-top}(kWh)\\ \textbf{Global-top}\end{array} \) & \( \begin{array}{c}E_{b-bot}(kWh)\\ \textbf{Beam-bottom}\end{array} \) & \(\begin{array}{  
highly reflective [19; 20; 21; 22]. The application and mainly the physics of bifacial cells are presented in the dissertation [19]. A study by simulation and field testing of vertical installed bifacial modules appear in [20]. Reference [21] compares the performance of vertical and south facing bifacial PV collector fields. A recent article [22] on simulating the energy yield of a bifacial photovoltaic plant investigates the influence of ground size, cast ground shadow and ground reflectivity on the energy yield. The only reference, as far as we know, on bifacial PV modules suggested for window shading by overhangs is mentioned in [23]. The overhang uses white semitransparent reflector sheet placed behind the bifacial modules to enhance the reflected radiation on the rear side of the PV module. The present study suggests using bifacial PV modules in its natural manner without providing additional external reflective material, i.e., using the natural reflectance from walls and grounds of the building to assess the additional energy contribution of the rear side of the PV bifacial module. The global incident irradiance \(G_{\varepsilon}\), in (W/m\({}^{2}\)), on the front side of the PV collector modules inclined by \(\varepsilon\) with respect to a wall is given by [24] (see Figure 16):  
\[G_{\varepsilon}=G_{b}\cdot\cos\theta+F^{f}_{H\to sky}\cdot G_{dh}+ref^{f}_{wall }\cdot F^{f}_{H\to wall}\cdot G_{g} \tag{43}\]  
The global incident irradiance on the rear side of the PV collector modules consists of the irradiance from ground, from shaded wall S and from unshaded wall:  
\[G_{\varepsilon}=al\cdot F^{r}_{H\to grd.}\cdot G_{dh}+ref_{wall.s}\cdot F^{r} _{H\to walls}G_{dh}+ref_{wall.ush}\cdot F^{r}_{H\to wall.ush}\cdot G_{g} \tag{44}\]  
where \(F^{f}_{H\to sky}\) is the view factor of front surface \(H\) to sky; \(F^{f}_{H\to wall}\) is the view factor of the front surface \(H\) to wall; \(F^{r}_{H\to grid. }\) is the view factor of the rear surface \(H\) to ground; \(F^{r}_{H\to wall.s}\) is the view factor of rear side surface to shaded wall; \(F^{r}_{H\to wall.ush}\) is the view factor of rear surface \(H\) to unshaded wall; \(al\) is the ground albedo; \(ref^{f}_{wall}\) is the reflectance of the wall above the collector; \(ref_{wall.s}\) is the reflectance of the shaded wall; \(ref_{wall.ush}\) is the reflectance of the unshaded wall below the collector. The different view factor expressions were developed in [24] and adaptations were made to the configuration in Figure 16. In multiple overhangs, the bottom of the top collector receives also reflected radiation from the top of the bottom collector. The view factor of the rear-side of the collector to shaded wall is developed in [24] and is:  
\[F^{r}_{H\to wall.s}=\frac{H+S-\left[H^{2}+S^{2}-2 HS\cos\varepsilon\right]^{1 /2}}{2H} \tag{45}\]  
Note that the shaded wall \(S\) varies with time during the day with the position of the sun, see Figure 5.  
Figure 16: View factor to sky, wall and ground.