# Coupled Model of Heat and Power Flow in Unventilated PV/PCM Wall-Validation in a Component Scale
###### Abstract  
The paper concerns the problem of the modeling of the thermal interaction between the phase change material (PCM) and photovoltaic (PV) panel, in the case of unventilated construction. The study aims to develop the numerical model of such a building element to support its proper future design under variable boundary conditions. The need for such a study comes from the realization of the research project which aims at developing a novel energy-activated thermal insulation composite system. Two different methods of PCM simulation using ESP-r software were compared. The model that was finally proposed was validated against experimental data, which proved its robustness. The MBE for the simulated and measured temperatures on the back of the PV panel did not exceed 2.0 \({}^{\circ}\)C and the maximum observed energy production difference was 4 Wh/m\({}^{2}\). phase change materials; photovoltaics; modeling; solar facade; PV thermal regulation; building integrated photovoltaic (BIPV); experimental validation +
Footnote †: journal: _Applied_  
temperature of 85 \({}^{\circ}\)C. This led to an improvement in the thermal inertia of the external layer by application of a PCM-cement composite. Finally, the developed En-ActivETICS is a multifunctional component characterized by power generation and latent heat storage. For further optimization of the system and performance prediction, it was necessary to analyze the system numerically. The main challenge was to investigate both phenomena (power generation and latent heat storage) in one coupled domain. The numerical simulations were considered to be one of the best techniques for investigating the En-ActivETICS in practice. The proposed model was initially calibrated based on short-term experiments. Finally, the results were compared with a double-repeated single-day experiment under sunny weather conditions. The numerical tools needed for addressing the solution of the heat transfer with phase change can generally be subdivided into the following three different types [15]: fixed grid method [16], deformed grid method [17] and hybrid fixed/deformed method [18]. In building performance simulation programs, e.g., ESP-r, TRNSYS, or EnergyPlus, the most adequate and the easiest applicable solution/approach are fixed grid methods: enthalpy-based (EB), apparent heat capacity (AHC), or heat source (HS). The first implementation of a PCM model in TRNSYS using the EB method was done by [19] which was further developed and refined by [20; 21; 22]. The same approach was used in EnergyPlus by [23]. The apparent heat capacity method was compared with the heat source method [22; 24], giving much better convergent results, and therefore it was originally implemented into ESP-r [25] and numerically validated [26]. The last integration of a latent heat storage model for Modelic using both EB and AHC methods was done by [27]. The comprehensive empirical validation and comparison of PCM modeling algorithms (mainly the EB method compared to the AHC method), commonly used in COMSOL, ESP-r, EnergyPlus and WUFI, were performed by [28]. In the EB method, the heat capacity is presented in terms of its integral form, H(T). The effective heat capacity (cp) is obtained as the derivative (dh/dT) of the enthalpy curves. The AHC method deals with heat capacity as a function of temperature within the temperature range of the phase transition. The RMSE values obtained for all PCM models by [PERSON] et al. were similar. Considering different photovoltaic and power flow models, from the simplest one to WATSUN-PV available in ESP-r, the authors decided to further develop a combined model in ESP-r. In ESP-r, the heat capacity as a linear function of temperature is defined within subroutine special materials [29]. This approach was implemented for the first time to model power generation from building-integrated PV systems [30], evaporative surfaces, latent heat storage in phase change materials and finally smart insulation materials [31].