## 2 Material and Methods
### PV Technology Description and Modeling
#### 2.3.2 Thermal Modeling of the Simple PV  
The simple PV is the conventional PV design and below, a thermal model is given to estimate its performance for different operating conditions by taking into consideration the variation in solar irradiation (\(\mathrm{G_{T}}\)), environmental temperature (\(\mathrm{T_{am}}\)) and wind speed (\(\mathrm{V_{w}}\)).  
The absorbed energy by the PV cell (\(\mathrm{Q_{abs}}\)) is calculated by considering the optical losses of the cover and the cell surface. The glass transmittance (\(\mathrm{\tau}\)) and the cell absorbance (\(\mathrm{\alpha}\)) are multiplied by the solar energy as follows:  
\[\mathrm{Q_{abs}=\tau\cdot a\cdot Q_{sol}} \tag{20}\]  
The energy balance in the PV cell can be expressed by considering that the absorbed solar irradiation is separated into electricity production and into total thermal losses (\(\mathrm{Q_{loss,tot}}\)) [29]:  
\[\mathrm{Q_{abs}=P_{el}+Q_{loss,tot}} \tag{21}\]The electricity production can be found as follows:  
\[\rm{P_{el}}=\eta_{ref}\cdot[1-\beta\cdot(T_{cell}-T_{am})]\cdot Q_{sol} \tag{22}\]  
The total thermal losses (\(Q_{loss,tot}\)) are separated into upper thermal losses (\(Q_{loss,u}\)) and back thermal losses (\(Q_{loss,b}\)):  
\[Q_{loss,tot}=Q_{loss,u}+Q_{loss,b} \tag{23}\]  
The upper thermal losses are calculated by neglecting the conductive effect in the glass due to its very small thickness and its high thermal conductivity. Practically, it is considered that \(T_{cell}\approx T_{glass}\). The upper thermal losses are separated into convective and radiative thermal losses:  
\[Q_{loss,u}=Q_{loss,u,conv}+Q_{loss,u,rad} \tag{24}\]  
The upper convection thermal losses are calculated as follows:  
\[Q_{loss,u,conv}=A_{pv}\cdot h_{u}\cdot(T_{cell}-T_{am}) \tag{25}\]  
The heat convection coefficient is calculated according to the wind speed velocity as follows [31]:  
\[h_{u}=5.7+3.8\cdot V_{w} \tag{26}\]  
The upper radiation thermal losses are calculated as follows:  
\[Q_{loss,u,rad}=A_{pv}\cdot\epsilon_{u}\cdot\sigma\cdot\left(T_{cell}^{4}-T_{ sky}^{4}\right) \tag{27}\]  
where (\(\epsilon_{u}\)) is the upper emittance, (\(\sigma\)) is the Stefan-Boltzmann constant at \(5.67\cdot 10^{-8}\) W/m\({}^{2}\) K\({}^{4}\) and (\(T_{sky}\)) is the sky equivalent temperature which is calculated as follows [32]:  
\[T_{sky}=0.0558\cdot T_{am}^{1.5} \tag{28}\]  
The temperature levels that are used in the radiation thermal losses calculation are used in Kelvin units.  
The PV cell thermal energy losses from its back surface are equal to the conduction thermal losses through the back material. These thermal losses can be written as follows:  
\[T_{sky}=0.0558\cdot T_{am}^{1.5} \tag{29}\]  
where (\(k_{b}\)) is the thermal conductance of the back material, (\(L_{b}\)) is the thickness of the back and (\(T_{b}\)) is the back temperature which comes in touch with the ambient below the PV.  
The thermal losses from the back side to the environment are separated into convective and radiative thermal losses as follows:  
\[Q_{loss,b}=Q_{loss,b,conv}+Q_{loss,b,rad} \tag{30}\]  
The back convection thermal losses are calculated as follows:  
\[Q_{loss,b,conv}=A_{pv}\cdot h_{b}\cdot(T_{b}-T_{am}) \tag{31}\]  
The heat convection coefficient is calculated according to the wind speed velocity as follows [31]:  
\[h_{b}=5.7+3.8\cdot V_{w} \tag{32}\]  
The back radiation thermal losses are calculated as follows:  
\[Q_{loss,b,rad}=A_{pv}\cdot\epsilon_{b}\cdot\sigma\cdot\left(T_{cell}^{4}-T_{ am}^{4}\right) \tag{33}\]Solving all the previous equations together makes it possible to calculate (T\({}_{\text{cell}}\)) and consequently determine the value of (P\({}_{\text{el}}\)), avoiding the use of a specific value of the (f) parameter.