## 2 Materials and Methods
### Dynamic Temperature Model of the Photovoltaic Module  
The dynamic thermal model of the PV module is presented differently within several papers [10; 21; 22; 41; 42; 43; 44]. The authors focus primarily on 1-D models of temperature distribution in PV module layers. Based on the thermal model of the PV module presented by [10], the dynamic heat balance presented in this paper consists of additional layers of Ethylene-vinyl acetate (EVA) foils. Therefore, the dynamic equations for all five layers, namely glass, EVA, PV cell, EVA and tedlar or PVF film-based backsheet, can be expressed by (7)-(11).  
\[\begin{array}{c}A_{\rm PV}\cdot\rho_{\rm g}\cdot d_{\rm g}\cdot C_{\rm g} \cdot\frac{d_{\rm T}g}{dt}=\\ A_{\rm PV}\cdot\left(\alpha_{\rm g}\cdot G-\left(1-\phi_{1}\right)\cdot h_{\rm conv,a-g}\cdot\left(T_{\rm g}-T_{\rm a}\right)-h_{\rm cond,g-PV}\cdot\left(T_{ \rm g}-T_{\rm PV}\right)\right.\end{array} \tag{7}\]  
\begin{table}
\begin{tabular}{c c} \hline \hline  & **PV Future—PVF 60M** \\ \hline Dimensions (l \(\times\) w \(\times\) s) [mm] & 993 \(\times\) 1648 \(\times\) 40 \\ Cell size [mm\({}^{2}\)] & 156 \(\times\) 156 \\ \(P_{\rm MPP}\) [W] & 260 \\ \(V_{\rm MPP}\) [V] & 31 \\ \(I_{\rm MPP}\) [A] & 8.45 \\ \(V_{\rm OC}\) [V] & 37.8 \\ \(I_{\rm SC}\) [A] & 8.9 \\ \(\mu_{\rm ISC}\) [\(\%\)/\({}^{\circ}\)C] & 0.040 \\ \(\mu_{V_{\rm OC}}\) [\(\%\)/\({}^{\circ}\)C] & \(-\)0.330 \\ \(\mu_{\rm BAP}\) [\(\%\)/\({}^{\circ}\)C] & \(-\)0.445 \\ NOCT [\({}^{\circ}\)C] & 45 \\ Number of series connected cells & 60 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Electrical parameters of the considered mono-crystalline PV module for STC.  
\[A_{\text{PV}}\cdot\rho_{\text{EVA}}\cdot d_{\text{EVA}}\cdot C_{\text{EVA}} \cdot\frac{dT_{\text{EVA}}}{dt}= \tag{8}\] \[A_{\text{PV}}\cdot(\tau_{\text{g}}\cdot\alpha_{\text{EVA}}\cdot G -(h_{\text{cond.EVA-g}}\cdot(T_{\text{EVA}}-T_{\text{g}})-h_{\text{cond.EVA-PV}} \cdot(T_{\text{EVA}}-T_{\text{PV}}))\] \[A_{\text{PV}}\cdot\rho_{\text{PV}}\cdot d_{\text{PV}}\cdot C_{ \text{PV}}\cdot\frac{dT_{\text{PV}}}{dt}=\] (9) \[A_{\text{PV}}\cdot(\tau_{\text{g}}\cdot\alpha_{\text{PV}}\cdot G \cdot FF-(h_{\text{cond.PV-g}}\cdot(T_{\text{PV}}-T_{\text{g}})-h_{\text{cond. PV-t}}\cdot(T_{\text{PV}}-T_{\text{t}}))-P_{\text{DC}}\] \[A_{\text{PV}}\cdot\rho_{\text{EVA}}\cdot d_{\text{EVA}}\cdot C_{ \text{EVA}}\cdot\frac{dT_{\text{EVA}}}{dt}=\] (10) \[A_{\text{PV}}\cdot(\tau_{\text{g}}\cdot\alpha_{\text{EVA}}\cdot G -(h_{\text{cond.EVA-PV}}\cdot(T_{\text{EVA}}-T_{\text{PV}})-h_{\text{cond.EVA- t}}\cdot(T_{\text{EVA}}-T_{\text{t}}))\] \[A_{\text{PV}}\cdot\rho_{\text{t}}\cdot d_{\text{t}}\cdot C_{ \text{t}}\cdot\frac{dT_{\text{t}}}{dt}=\] (11) \[A_{\text{PV}}\cdot(\tau_{\text{g}}\cdot\alpha_{\text{t}}\cdot G \cdot(1-FF)-(1-\phi_{2})\cdot h_{\text{conv.t-a}}\cdot(T_{\text{t}}-T_{\text{ a}})-h_{\text{cond.PV-t}}\cdot(T_{\text{t}}-T_{\text{PV}}))\]  
where \(G\) is the solar radiation, \(A_{\text{PV}}\) is the surface area of PV module, \(\varphi_{1}\) is the heat flux ratio (equal to 0.46 [44]), \(\varphi_{2}\) is the thermal radiation flux (equal to 0.52 [10]) between a tedlar layer and an ambient for the open-racked PV module, \(T_{\text{a}}\) is the ambient temperature, \(h_{\text{conv}}\) and \(h_{\text{cond}}\) are the convective and conductive heat transfer coefficient (described in Appendix A), \(P_{\text{DC}}\) is the output power, \(FF\) is the fill factor and \(\rho\), \(d\), \(C\), \(T\), \(\tau\) and \(\alpha\) are the density, thickness, heat capacity, temperature, transmissivity and absorptivity of different layer, respectively. The indexes in the above-mentioned parameters describe the glass, EVA, PV cell and tedlar layers.  
Thermal and mechanical parameters of the considered mono-crystalline PV module are presented in Table 3 (based on the literature [10; 13; 14; 41]).