# Towards Improving the Durability and Overall Performance of PV-ETICS by Application of a PCM Layer
## 2 En-ActivETICS as a Proposed Solution for Active External Walls
### Computational Model  
The thermal performance of the three considered wall cases is mainly influenced by the physical processes taking place on the outer surface of the wall. The difference in the thermal behaviour mainly comes from the varied absorptivity of solar radiation, its photoelectric conversion and the ability for thermal energy storage. It can be assumed that external convection and long-wave radiation as well as the processes of heat conduction are the same. The key parameters of the three considered walls are presented in Table 1.  
Photovoltaic conversion of solar irradiance incident on the surface of PV cells in ESP-r can be modelled using one of three models: a simple model with constant PV cell efficiency or one-diode circuit models--[PERSON]'s model and WATSUN-PV model. The last one is characterized by the most comprehensive consideration of cell temperature impact on the energy performance of PV panels. Therefore, the WATSUN-PV model is predominantly used to calculate the PV energy performance [8]. In the presented paper, the WATSUN-PV model was also chosen to model the PV panel performance. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **ETICS** & **PV-ETICS/En-ActivETICS** \\ \hline External surface absorptivity \(\alpha\) [-] & 0.22 & 0.84 \\ External surface emissivity \(\varepsilon\) [-] & & 0.90 \\ Thermal transmittance of the wall \(U\) [W/(m\({}^{2}\) K)] & & 0.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic parameters of the three considered cases. Figure 1: Cross-section of the wall covered with (**a**) ETICS (**b**) PV-ETICS and (**c**) En-ActivETICS. The WATSUN-PV model was implemented into ESP-r and validated in accordance with [PERSON] et al. [28] as a consequence of the recommendations of [PERSON] [29]. The model considers the impact of PV cell temperature (\(T_{cell}\)) on the main PV panel electrical characteristics--the short-circuit current (\(I_{sc}\)) and the open-circuit voltage (\(V_{\infty}\))--as is presented in Equations (1) and (2). \[I_{sc}=I_{sc,\ ref}\frac{E_{T,\ eff}}{E_{T,\ ref}}\Big{[}1+\alpha\Big{(}T_{ cell}-T_{cell,ref}\Big{)}\Big{]} \tag{1}\]  
\[V_{\infty}=V_{\infty,\ ref}\Big{[}1-\gamma\ \Big{(}T_{cell}-T_{cell,\ ref}\Big{)} \Big{]}\ max\Bigg{\{} \begin{array}{c}0\\ 1+\beta\ ln\Big{(}\frac{E_{T,eff}}{E_{T,eff}}\Big{)}\end{array} \Bigg{\}} \tag{2}\]  
where  
\(I_{sc,ref}\)-short-circuit current in reference conditions [A]  
\(V_{\infty,ref}\)--open-circuit voltage in reference conditions [V]  
\(E_{T,eff}\)-effective irradiance incident on the surface of PV cells [W/m\({}^{2}\)]  
\(E_{T,ref}\)-irradiance incident on the surface of PV cells in reference conditions, \(E_{T,ref}\)= 1000 W/m\({}^{2}\)  
\(T_{cell}\)--PV cell temperature [\({}^{\circ}\)C]  
\(T_{cell,ref}\)--PV cell temperature in reference conditions, \(T_{cell,ref}\) = 25 \({}^{\circ}\)C  
\(\alpha\)--temperature coefficient of \(I_{sc}\) [1/\({}^{\circ}\)C]  
\(\gamma\)--temperature coefficient of \(V_{\infty}\) [1/\({}^{\circ}\)C]  
\(\beta\)--irradiance coefficient of \(V_{\infty}\) [-]  
In the WATSUN-PV model, the maximum power of the PV panel, \(P_{mp}\), depends on the short-circuit current and open-circuit voltage, as given by Equation (3):  
\[P_{mp}=I_{mp,\ ref}\ V_{mp,ref}\ \Bigg{(}\frac{I_{sc}\ V_{\infty}}{I_{sc, ref}\ V_{\infty,ref}}\Bigg{)} \tag{3}\]  
where  
\(I_{mp,ref}\)--maximum power point current in reference conditions [A]  
\(V_{mp,ref}\)--maximum power point voltage in reference conditions [V]  
The model of heat transfer with latent heat storage adopted for this study was previously validated [30]. The investigated case was very similar when the PCM layer was semi-exposed to the external environment. Through the definition of the special material properties, latent heat storage is estimated based on the effective heat capacity method [31]. The apparent heat capacity method using the Crank-Nicolson explicit scheme was applied (i.e., the heat capacity was calculated from the node temperature at the previous time step).