# Thermal Time Constant of PV Roof Tiles Working under Different Conditions
## 2 Test Object--Description of an Elastic PV Roof Tile
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol and Unit** & **Value** \\ \hline Maximum power rating & \(P_{m}\)x (W) & 68 \\ Open circuit voltage & \(U_{\text{Lx}}\) (V) & 23.1 \\ Voltage at the maximum power point & \(U_{m}\) (V) & 16.5 \\ Short circuit current & \(I_{sc}\) (A) & 5.1 \\ Current at the maximum power point & \(I_{m}\) (A) & 4.13 \\ Temperature coefficient of short-circuit current & \(v_{\text{lsc}}\) (mA/C) & 5.1 \\ Temperature coefficient of open-circuit voltage & \(v_{\text{lsc}}\) (mV/C) & \(-\)88 \\ Temperature coefficient of short-circuit current & \(v_{\text{lsc}}\) (mA/C) & 5.1 \\  & \(v_{\text{lsc}}\) (\%/C) & 0.1 \\ Temperature coefficient of voltage at MPP & \(v_{\text{l}}\) (mV/C) & \(-\)51 \\  & \(v_{\text{l}}\) (\%/C) & \(-\)0.31 \\ Temperature coefficient of current at MPP & \(v_{\text{l}}\) (\%/C) & 4.1 \\  & \(v_{\text{l}}\) (\%/C) & 0.1 \\ Temperature coefficient of power & \(v_{p}\) (mW/C) & \(-\)143 \\  & \(v_{p}\) (\%/C) & \(-\)0.21 \\   Panel efficiency & \(v_{p}\) (\%) & 7.26 \\ Dimensions of PV cells & _width_\(\times\)_height_ (mm) & \(239\times 356\) \\ Number of PV cells in the panel & N\({}_{s}\) (PCs) & 11 \\ Type of PV cells & - & triple-junction, amorphous \\ Panel dimensions (global) & _width_\(\times\)_height_ \(\times\)_thickness_ (mm) & \(2880\times 395\times 2.5\) \\ Panel area (global) & \(S\) (m\({}^{2}\)) & 1.138 \\ Panel area (active) & \(S_{a}\) (m\({}^{2}\)) & 0.936 \\ Panel weight & \(m\) (kg) & 3.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Tegosolar PVL68 photovoltaic roof tile data (in STC) [27; 29]. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Layer** & **Thickness** & **Specific Heat** & **Density** & **Thermal Conductivity** \\  & \(d_{m}\) (m) & \(c_{p_{m}}\) (\(\mathbf{\text{kg/m}}\)) & \(p_{n}\) (\(\mathbf{\text{kg/m}}\)) & \(k\) (W/mK) \\ \hline
**ETFE** & \(0.5\times 10^{-3}\)[27; 29] & 1000 [30] & 1800 [30] & 0.24 [30] \\
**PV cell** & \(1\times 10^{-6}\)[27; 29] & 677 [18; 19; 31] & 3200 [18; 19; 31] & 170 [18; 31; 32] \\
**Grid connection** & \(10\times 10^{-6}\)[27; 29] & 460 [33] & 7900 [33] & 17 [33] \\
**PVDF** & \(2\times 10^{-3}\)[27; 29] & 1120 [34] & 1800 [34] & 0.12 [34] \\
**Pine board** & \(25\times 10^{-3}\)[30] & 1600 [33] & 450 [35] & 0.35 [35] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material data of PVL68 photovoltaic roof tile layers and roof. Figure 3: Construction of Tegosolar PVL68 photovoltaic elastic roof tile, where 1: ethylene-tetrafluoroethylene (ETFE); 2: silicon cell (a-SiGe for blue-colour radiation); 3: silicon cell (a-SiGe for green-colour radiation); 4: silicon cell (a-SiGe for red-colour radiation); 5: stainless steel foil (-); 6: polyvinylidene-fluoride (PVDF) base layers [27]. The photovoltaic module of the reference PV roof tile has an adhesive layer on its bottom side to facilitate its fixing to the roof structure. The dimensions of the PV panel were the same as the dimensions of standard roof-covering items (bitumen--shingles or asphalt roofing felt), which makes embedding the PV roof tiles into the roof structure very easy. In addition to electrical current generation, a PV roof tile ensures the appropriate roof strength and water insulation, much like traditional roof covering. According to the recommendations of the PV roof tiles manufacturer, standard roof covering is to be used ca. 0.5 m from the outer edges of the roof [27].