# Battery Sizing for Mild P2 HEVs Considering the Battery Pack Thermal Limitations
## 5 Discussion and Conclusions  
Table 3 summarizes the simulation results for P2 mild HEV with a 48 V 0.9 kWh (14s6p) battery pack. It includes the overall fuel consumption, the percentage of reduction with reference to conventional vehicles and the maximum temperature over the corresponding cycle. Furthermore, the results for the 14s12p battery pack with increased capacity (1.8 kWh) and without thermal limitations implemented in the supervisory controller are reported.  
The considered battery packs have a passive cooling system. Hence the heat transfer is only by natural convection. Therefore, thermal limitations must be applied on the controller level for the 14s6p battery pack to limit battery usage and to avoid thermal runaway. However, the implementation of limitations on the controller leads to a fuel consumption increase of between 2-3%. To achieve a reduction in fuel consumption without compromising thermal behaviour, a larger battery capacity could be considered. The minimum battery capacity would be 1.8 kWh, which corresponds to a 14s12p battery pack configuration. Fuel consumption in this case is reduced by between 8-13% with reference to the fuel consumption of the conventional vehicle.  
Obviously, the increase of ambient temperature should change the minimum battery capacity towards the higher values. However, the analysis was conducted considering a constant ambient temperature of 20 \({}^{\circ}\)C. The influence of different ambient temperatures has not been validated in this work and can be addressed in future works.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Drive** \\ **Cycle** \\ \end{tabular} } & \multicolumn{8}{c}{**Fuel Consumption [g] Fuel Economy [\%] Max Temperature [\({}^{\circ}\)C]**} \\ \cline{2-13}  & \begin{tabular}{c} **Conventional** \\ **Vehicle** \\ \end{tabular} & \begin{tabular}{c} **14s6p: ECMS** \\ **no Limitation** \\ \end{tabular} & \begin{tabular}{c} **14s6p: ECMS** \\ **with On/off** \\ \end{tabular} & \
\begin{tabular}{c} **14s6p: ECMS** \\ **with Penalty** \\ \end{tabular} &
\begin{tabular}{c} **14s12p: ECMS** \\ **no Limitation** \\ \end{tabular} \\ \hline UDDS & 699.9 & 100\% & 639.9 & \(-\)8.6\% & 160 \({}^{\circ}\)C & 673 & \(-\)3.8\% & 55 \({}^{\circ}\)C & 666.2 & \(-\)4.8\% & 55 \({}^{\circ}\)C & 611.4 & \(-\)12.6\% & 50 \({}^{\circ}\)C \\ \hline NEDC & 592.3 & 100\% & 556 & \(-\)6.1\% & 85 \({}^{\circ}\)C & 563 & \(-\)4.9\% & 55 \({}^{\circ}\)C & 561.6 & \(-\)5.2\% & 55 \({}^{\circ}\)C & 544 & \(-\)8.2\% & 37 \({}^{\circ}\)C \\ \hline WLTC & 1308 & 100\% & 1218 & \(-\)6.9\% & 180 \({}^{\circ}\)C & 1269 & \(-\)2.9\% & 55 \({}^{\circ}\)C & 1261 & \(-\)3.6\% & 55 \({}^{\circ}\)C & 1185 & \(-\)9.4\% & 61 \({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table}
Table 3: Main results of the simulation.  
Figure 22: The temperature of the 14s12p battery pack on different driving cycles.  
**Author Contributions:** Conceptualization, A.T., S.R., E.E. and G.Y.; methodology, A.T. and S.R.; software, E.E. and G.Y.; validation, S.R., E.E. and G.Y.; formal analysis, A.T., S.R., E.E. and G.Y.; investigation, A.T., S.R., E.E. and G.Y.; resources, E.E. and S.R.; data curation, E.E. and G.Y.; writing--original draft preparation, E.E., G.Y. and S.R.; writing--review and editing, A.T., S.R., E.E. and G.Y.; visualization, E.E. and G.Y.; supervision, A.T.; project administration, A.T.; funding acquisition, A.T. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding and the APC was funded by Doctoral Funds of Politecnico di Torino.  
Not applicable.  
We thank the LIM--Mechatronics Lab for providing the battery testing equipment.  
The authors declare no conflict of interest.