# Thermal and Performance Analysis of a Photovoltaic Module with an Integrated Energy Storage System
## 4 Temperature Extrapolation
It should be noted that the decrease is rather noticeable, in the order of 6%, but this is representing the worst case scenario (i.e., the highest daily radiation and temperature considered for each month at solar midday on a sunny day). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{3}{c}{**Temperatures (\({}^{\circ}\)C)**} & **Power** \\ \cline{2-5}  & \(T_{e,pp}\) & \(T_{e,pp+batt}\) & \(\Delta\)T & \(\Delta\)P\% \\ \hline
**January** & 24.3 & 34.1 & 9.8 & \(-\)5.1 \\
**February** & 30.9 & 42.1 & 11.2 & \(-\)5.8 \\
**March** & 40.0 & 52.3 & 12.3 & \(-\)6.4 \\
**April** & 46.7 & 59.6 & 12.9 & \(-\)6.7 \\
**May** & 51.4 & 64.3 & 12.9 & \(-\)6.7 \\
**June** & 55.7 & 68.2 & 12.4 & \(-\)6.5 \\
**July** & 58.0 & 70.2 & 12.3 & \(-\)6.4 \\
**August** & 57.1 & 69.3 & 12.2 & \(-\)6.3 \\
**September** & 51.8 & 63.6 & 11.8 & \(-\)6.1 \\
**October** & 42.0 & 53.0 & 11.0 & \(-\)5.7 \\
**November** & 31.8 & 41.5 & 9.8 & \(-\)5.1 \\
**December** & 24.8 & 33.8 & 9.1 & \(-\)4.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: PV cell temperatures obtained by thermal models in the case of PV conversion (\(P_{pp}\
eq 0\), \(\eta=12\%\)) and corresponding percentage decrease of electric power. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Commercial PV Module**} & \multicolumn{6}{c}{**Modified PV Module with Integrated Energy Storage**} \\ \cline{2-13}  & \({}^{\circ}\)C & **W/m\({}^{2}\)** & **Without Batteries (\({}^{\circ}\)C)** & \multicolumn{6}{c}{**Area Covered by Batteries (\({}^{\circ}\)C)**} & \multicolumn{6}{c}{**Area Not Covered by Batt. (\({}^{\circ}\)C)**} & **avg (\({}^{\circ}\)C)** & \multicolumn{6}{c}{**(\({}^{\circ}\)C)**} \\ \cline{2-13}  & \(T_{a}\) & \(G_{m}\) & \(T_{f}\) & \(T_{e,pp}\) & \(T_{b}\) & \(T_{f}\) & \(T_{c}\) & \(T_{b}\) & \(T_{batt-b}\) & \(T_{batt-g}\) & \(T_{f}\) & \(T_{c}\) & \(T_{b}\) & \(T_{e,pp+batt}\) & \(\Delta\)T \\ \hline
**January** & 2.9 & 741 & _26.6_ & _27.7_ & _27.2_ & 42.6 & 44.6 & 44.5 & 9.3 & 9.3 & 33.9 & 35.4 & 35.1 & 38.9 & 11.2 \\
**February** & 5.8 & _869_ & 33.4 & 34.8 & 34.1 & 52.0 & 54.3 & 54.2 & 13.3 & 13.3 & 41.7 & 43.4 & 43.0 & 47.5 & 12.8 \\
**March** & 12.1 & 994 & 42.7 & 44.3 & 43.6 & 63.6 & 66.2 & 66.1 & 20.3 & 20.3 & 51.5 & 53.5 & 53.0 & 58.3 & 14.0 \\ April & 17.0 & 1079 & 49.6 & 51.3 & 50.5 & 71.6 & 74.4 & 74.3 & 26.0 & 26.0 & 58.6 & 60.7 & 60.2 & 65.9 & 14.6 \\
**May** & 21.5 & 1106 & 54.2 & 55.9 & 55.6 & 76.4 & 79.3 & 79.2 & 30.3 & 30.2 & 63.0 & 65.2 & 64.6 & 70.5 & 14.6 \\
**June** & 26.3 & 1107 & 58.5 & 60.2 & 59.4 & 80.0 & 82.9 & 82.8 & 34.8 & 34.8 & 66.9 & 69.1 & 68.5 & 74.3 & 14.1 \\ July & 28.9 & 1107 & 60.7 & 62.4 & 61.6 & 82.0 & 84.9 & 84.8 & 37.3 & 37.3 & 68.9 & 71.1 & 70.5 & 76.3 & 13.9 \\
**August** & 28.3 & 1095 & 59.8 & 61.6 & 60.7 & 81.0 & 83.8 & 83.8 & 36.6 & 36.6 & 68.0 & 70.2 & 69.7 & 75.4 & 13.8 \\
**September** & 24.1 & 1034 & 54.4 & 56.1 & 55.3 & 74.8 & 77.5 & 77.4 & 32.2 & 32.1 & 62.5 & 64.6 & 64.1 & 69.5 & 13.4 \\
**October** & 17.0 & 914 & 44.5 & 45.9 & 45.6 & 63.2 & 65.6 & 65.5 & 24.6 & 24.6 & 25.3 & 54.1 & 53.7 & 58.5 & 12.5 \\ November & 10.0 & 777 & 33.9 & 35.2 & 34.7 & 50.4 & 52.4 & 52.3 & 16.5 & 16.4 & 41.2 & 42.8 & 42.4 & 46.4 & 11.2 \\
**December** & 4.8 & 701 & 26.9 & 28.0 & 27.5 & 41.8 & 43.6 & 43.6 & 10.5 & 10.4 & 33.8 & 35.2 & 34.9 & 38.4 & 10.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Environmental data and temperatures obtained by thermal models (open circuit, \(P_{pp}=0\)). As a further example of the application of the proposed thermal model, the daily profile of the PV cell's temperature (averaged over the PV module area) with and without integrated storage batteries is given in Figure 11. Weather conditions were assumed to be a typical sunny day in Bologna on April 15.