## 4 Optimal Tilt Angle Dependencies
### Optimal Tilt Angle Dependence on the Weather Conditions  
This section focuses on the variation in \(\gamma_{\text{opt}}\) as a function of the weather conditions. The annual mean irradiance values recorded by the Italian Atlas of Solar Radiation, created by ENEA [81], were used to parametrize the deviation in clear-average annual sky conditions for the city of Bologna [80]. To parametrize the deviation from the actual weather conditions to the clear-sky conditions, two parameters were used: \(C_{\text{dir}}\) and \(C_{\text{diff}}\). \(C_{\text{dir}}\) refers to the deviation in \(G^{\text{beam}}\) and \(C_{\text{diff}}\) to the deviation in \(G^{\text{diffuse}}\). \(C_{\text{dir}}\) and \(C_{\text{diff}}\) were used to modulate the irradiance components homogeneously along the year and were obtained as  
\[\begin{cases}C_{\text{dir}}&=G_{\text{act}}^{\text{beam}}/G_{\text{cs}}^{ \text{beam}}\\ C_{\text{diff}}&=G_{\text{act}}^{\text{diffuse}}/G_{\text{cs}}^{\text{diffuse}} \end{cases} \tag{11}\]  
where the subscript \"act\" indicates the actual value, and \"cs\" is the clear-sky value. \(C_{\text{dir}}\) and \(C_{\text{diff}}\) were applied uniformly along the year. In the study, six scenarios were considered, all of which utilized the same \(\alpha\) equal to 0.75, module height of 2 m, bifaciality factor of 0.85, number of modules per string and number of strings equal to one. The deviation factors are reported in Table 4. While scenario E reflected the actual deviation for the city of Bologna, the other five were used to evaluate the influence at lower and higher weather condition deviations. For each scenario, \(C_{\text{diff}}\) and \(C_{\text{dir}}\) were obtained by linear interpolation between scenario A (clear sky) and scenario E.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Scenario** & \(C_{\text{dir}}\) & \(C_{\text{diff}}\) \\ \hline A & 1.00 & 1.00 \\ B & 0.90 & 1.14 \\ C & 0.80 & 1.28 \\ D & 0.70 & 1.42 \\ E & 0.60 & 1.55 \\ F & 0.50 & 1.69 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Weather conditions used to determine weather conditions’ influence.  
Figure 13: Rear insolation’s annual energy gain, equivalent insolation’s annual energy gain, and bifacial gain, at different hub-heights, for a bi-PV with a 41\({}^{\circ}\) tilt angle and faced southward.  
Figure 14 shows the magnitude of \(G_{\text{front}}\) and \(G_{\text{rear}}\), on the left axis, and \(\gamma_{\text{opt}}\) on the right axis, for the different scenarios. Scenario A corresponded to clear-sky conditions, while scenario E corresponded to the actual weather conditions. It is visible that the weather conditions affected \(\gamma_{\text{opt}}\) by \(1^{\circ}\). In particular, for scenarios C, D, E, and F, \(\gamma_{\text{opt}}\) was \(46^{\circ}\), while for scenarios A and B, it was \(45^{\circ}\). This happened because from scenario A to F, \(BG\) increased; thus, \(\gamma_{\text{opt}}\) moved towards \(\gamma_{\text{opt,r}}\). However, it was also found that the difference in energy yield per year, between \(45^{\circ}\) and \(46^{\circ}\), was below 0.05% for all scenarios. Thus, the considered meteorological conditions were believed not to affect the decision of \(\gamma_{\text{opt}}\).