# Dependence of PV Module Temperature on Incident Time-Dependent Solar Spectrum
## 5 Photovoltaic (PV) Module Temperature-Simulation Results  
This section deals with the calculation of the operating temperature \(T_{c}^{spec}(^{\circ}C)\) for four different PV module technologies that are based on the solar spectrum model, as in Equations (5) and (7). The integration limits of the spectrum correspond to the spectral response of each technology. Table 3 lists the details. The transmittance factors \((1-R_{cell}(\lambda))\) of the absorbed solar irradiance in the PV cells (see Equation (8)) are shown in Figure 3 for the four types of the modules that were derived from articles in [28; 29] while using interpolations to match specx points for SPECTRAL(2). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Module**} & \multirow{2}{*}{**Technology**} & \multirow{2}{*}{\(\beta_{e}(\%/^{\circ}C)\)} & \(T_{c}^{spec}\) & \(NOCT\) & \(NOCT-T_{c}^{spec}\) \\  & & & \((^{\circ}C)\) & \((^{\circ}C)\) & \((^{\circ}C)\) \\ \hline SCHOTT MONO\({}^{\text{m}}\) 190 & c-Si & \(-\)0.44 & 43.2 & 46 & 2.8 \\ SCHOTT AST\({}^{\text{m}}\) 100 & a-Si/\(\mu\)C-Si & \(-\)0.20 & 44.6 & 49 & 4.4 \\ FirstSolarFS-280 Series 2\({}^{\text{m}}\) & CdTe & \(-\)0.25 & 43.6 & 45 & 1.4 \\ Wurth Solar GeneCIS 80 & CIGS & \(-\)0.36 & 45.2 & 47 & 1.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Module type and manufacturer. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Inputs**} & **Sde Boker** & **Eilat** \\  & **Feb 1, 16:00** & **Aug 4, 12:00** \\ \hline
1. longitude (deg.) & 34.8 & 34.9 \\
2. latitude (deg.) & 30.9 & 29.5 \\
3. altitude (m) & 480 & 15 \\
4. alpha (-) & 2.17 & 1.4 \\
5. tau500 (-) & 0.084 & 0.209 \\
6. watap (cm) & 0.85 & 2.4 \\
7. ozone & 0.257 & 0.279 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Data for obtaining the solar spectrum. Figure 2: Spectrum at Sde Boker and Eilat-global, direct, diffuse. The calculated module temperatures \(T_{c}^{spec}(^{\circ}C)\) in Table 3 are average maximum values based on the solar spectrum model at Sde-Boker site. The results pertain to module inclination angle 25\({}^{\circ}\) facing due south, calculated for noontime (at 12:00) for each day for the period of six months and for an average ambient temperature 29.7 \({}^{\circ}\)C at the location. Table 3 also includes the NOCT temperature (specified by the manufacturers) for the four PV module technologies. The \(T_{c}^{spec}(^{\circ}C)\)in Table 3 was calculated at 12:00, as the module temperature is expected to be the highest since in the morning and in the afternoon hours the solar irradiance is lower as well the ambient temperature. The solar spectrum in the morning and afternoon is usually different than at noon, however the lower ambient temperature might affect the module temperature more than the difference in the spectrum. Table 3 also shows that the difference in the module temperature based on \(T_{c}^{spec}(^{\circ}C)\) model and NOCT is \(2.8^{\circ},4.4^{\circ},1.4^{\circ},1.8^{\circ}(^{\circ}C)\) for c-Si, a-Si/\(\mu\)c-Si, CdTe, and CIGS technologies, respectively. Simulation results of the operating temperature for c-Si module are shown in Figure 4 based on the spectrum model and NOCT for 21 st of each month for the period from December to June. Differences in the operating temperature are apparent for module temperature above 30 degrees. parameters, which are material and system dependent. Therefore, one must be careful in applying a particular expression for the operating temperature of the PV module, because the expressions have been developed for particular deployments of the PV system. For that reason, one cannot compare the methods and results of the operating temperature for different types of PV systems and at different locations. The simulation results for the operating temperature that are obtained by the proposed spectrum model at the specific location where the study pertains are close to the manufacturers' NOCT temperatures, thus verifying, by simulation, the validity of the new spectrum approach.