# Thermal Time Constant of PV Roof Tiles Working under Different Conditions
## 7 Conclusions  
This paper presents known RC and PET models of photovoltaic cells that make up traditional PV panels and has been adapted to determine the thermal time constant of cells included in the photovoltaic roof tiles. They were confirmed to be correct for the PV roof tiles, but only in the case of their operation as a free-standing element, like traditional PV panels and not integrated with the roof. Differences in the values of the thermal time constant of PV roof tiles were also shown depending on the model used (RC or PET). The RC model, based on the material data of the PV roof tile layers, does not consider the weather conditions in which the tile works. Using the PET model (considering only the process of the free convection of heat exchange), convergent values of the time constant were obtained with the values obtained by means of the RC model (ca. 19-21 min). The use of the PET model allowed more accurate time constant results to be obtained (ca. 5-6 min), because it considers different forms of heat exchange as well as the current weather conditions (i.e., irradiance, ambient temperature, wind speed). Furthermore, it was shown that the available models cannot be used to determine the thermal time constant of PV roof tiles integrated in the roof, due to the additional thermal capacity and thermal resistance of the roof structure with which they are integrated. The authors modified the available RC model with a member representing a roof structure (composed of boards), taking into account its thermal resistance and thermal capacity. Also, in the PET model, the total thermal capacity of the system was taken into account, which is the sum of the thermal capacities of the PV roof tile and the roof structure. Accounting for the roof structure in both models caused about a five-fold increase in the value of the thermal time constant of PV cells. The earlier dependences of changes in the time constant value (taking into account only the free convection) were also met in the analysis of the entire roof with PV roof tiles. In simulation tests nos. 1 and 2, the irradiance change of 400 W/m\({}^{2}\) at a wind speed of 3 m/s caused a difference in the maximum temperature of the PV cells roof tile of 22 \({}^{\circ}\)C. During experimental investigations, with irradiance of 330 W/m\({}^{2}\) and wind speed of 3.1 m/s, the temperature of PV cells increased by approx. 14-16 \({}^{\circ}\)C above ambient temperature, confirming the correctness of the proposed RC model of photovoltaic roof tiles. The experimental tests carried out also confirmed the changes in the values of the thermal time constants of the PV cells of free-standing and integrated photovoltaic roof tiles. The temperature of the PV cells of a free-standing roof tile quickly responded to changes in the environment in which it worked compared to a PV roof tile built into the roof. However, further long-term studies are necessary, under different environmental conditions, so that the values of the time constants of the tested systems from experimental research can be unambiguously determined. The temperature of roof tile PV cells did not change abruptly as a result of rapid changes in ambient conditions, and this was related to heat energy accumulation in the item's mass. Hence, the determined time constant of a PV roof tile and the entire roof helped to estimate the speed of changes in PV cells during heating and cooling. In turn, the changes determine the electrical energy generation efficiency. A length of time of between three and five time constants was assumed as the time necessary to reach the maximum temperature of an item. The knowledge of thermal processes and PV cell temperature changes enables more precise estimation of the amount of electrical energy generated by a photovoltaic system built into a roof, depending on the roof structure type. The better the roof insulation, the higher the time constant value of the system and the longer the time necessary for PV cells to become heated and to cool down.