# Thermal Time Constant of PV Roof Tiles Working under Different Conditions
## 6 Discussion  
The values of time constants \(\tau_{RC}\) of PV cells in a standalone roof tile and a tile built into the roof, working under different conditions, are listed in Table 5.  
One can observe a high convergence when comparing the time constants of a PV roof tile obtained from material data and identified from the energy balance equation, but only in the case of free convection. The PET model, also taking into account forced convection, gives real values of the time response of temperature changes of PV cells to the currently prevailing environmental conditions of the PV roof tile (wind speed, irradiance) in which the PV tiles work. Under unchanged ambient conditions, after ca. 5-6 min, the temperature of PV cells in a standalone roof tile would change by 63% compared to their potential maximum value. The proposed roof structure composed of wood boards and PV roof tiles was characterised by a time constant in the range of 23-28 min, that is, four to five  
Figure 5: Temperature change of PV cells of PVL68 photovoltaic roof tiles under different environmental conditions: (**a**) standalone roof tile; (**b**) roof tile fixed (glued) to the roof boards. times longer than the time constant of the standalone roof tile. Note that due to its structure, a PV roof tile will never work as a standalone item, but will always be integrated with a substrate such as the roof of a building. A change in the irradiance value will cause directly proportional changes in the temperature values that a PV cell can reach. The irradiance value did not greatly affect the value of the system time constant, while a reduced wind speed (at unchanged irradiance value) contributed to the PV roof tile becoming considerably heated, and to an increase in the value of the system time constant. A greater time constant is desired while the elements become heated during photovoltaic processes, so that the temperature of PV cells does not increase too quickly and does not reach too high a value, but rather has a negative impact during system cooling, when the temperature of PV cells is reduced as quickly as possible. The PV cell temperatures reached for the three presented cases (\(T_{pv\_test1}\) = 81.26 \({}^{\circ}\)C, \(T_{pv\_test2}\) = 59.08 \({}^{\circ}\)C, \(T_{pv\_test3}\) = 67.45 \({}^{\circ}\)C) for the analysed PV roof tile with a temperature coefficient of power change \(v_{p}\) = -0.21 %/\({}^{\circ}\)C may contribute to a reduction in the generated power value by a maximum of 11.81%, 7.16% and 8.91% respectively. Initial experimental research was also carried out involving the measurement of the PV cells' temperature of the free-standing PV tile and the PV tile built into the roof (glued to the boards) under real environmental conditions. The temperature chart of PV cells and the ambient conditions is shown in Figure 6. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{\(\tau_{\text{RC}}\) (min)} \\ \cline{2-7}
**PV Cell in:** & & \multicolumn{2}{c}{**Forced Convection**} & \multicolumn{2}{c}{**Free Convection**} \\ \cline{2-7}  & & **Test1** & **Test2** & **Test3** & **Test1** & **Test2** & **Test3** \\ \hline
**Standalone PV roof tile** & 18.80 & 5.32 & 5.32 & 6.27 & 20.81 & 20.81 & 20.81 \\ \hline
**Built-in PV roof tile** & 99.43 & 23.80 & 23.76 & 28.25 & 95.58 & 95.76 & 95.49 \\ \hline \hline test1: \(E\) = 1000 W/m\({}^{2}\), \(v_{wind}\) = 3 m/s, \(T_{amb}\) = 30 \({}^{\circ}\)C; test2: \(E\) = 600 W/m\({}^{2}\), \(v_{wind}\) = 3 m/s, \(T_{amb}\) = 30 \({}^{\circ}\)C; test3: \(E\) = 600 W/m\({}^{2}\), \(v_{wind}\) = 2 m/s, \(T_{amb}\) = 30 \({}^{\circ}\)C. & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Specifications of time constant values \(\tau_{RC}\) of PV cells in a PVL68 roof tile working under different conditions as standalone and built-in versions, and values determined based on material data. Figure 6: Chart of temperature changes of PV cells in free-standing configuration and as roof-mounted solar roof tiles, as well as the ambient conditions prevailing during the tests.