## 7 Conclusions  
In the context of vehicle fuel consumption calculation over a drive cycle, it is common to model the engine with steady-state maps. This assumption might lead to a 2-8% underestimation of the fuel consumption for the vehicle with a conventional powertrain compared with experimental results. The fuel consumption during transient is obtained by multiplying a correction factor, whose parameters can be identified from experimental data to the fuel consumption obtained from a steady-state map. The comparison of total fuel consumption on UDDS, US06, and HW driving cycles shows a good match with the experimentally measured data. The simulations for HEV were performed for a P2 off-axis HEV with a battery capacity of 1.8 kWh (14s12p) using an ECMS control strategy. The temperature limitation of the battery pack was not considered. By integrating the obtained TCF model to the objective function of the ECMS, the torque split was modified. This resulted in less transient operations of the engine, as the introduction of TCF penalized the use of the engine in regimes with high torque change rates. Therefore, the transient phases were supported mainly by EM. This  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Drive Cycle** & **ECMS with Steady-State Map** & **ECMS with TCF** & **Fuel-Saving** \\ \hline UDDS & 620.7 g & 616.3 g & 4.4 g \\ \hline HW & 754.2 g & 751 g & 3.2 g \\ \hline US06 & 922.7 g & 917.6 g & 5.1 g \\ \hline \hline \end{tabular}
\end{table}
Table 5: Total fuel consumption under ECMS with and without TCF.  
Figure 9: Comparison of engine and EM operations under control of ECMS with/without TCF: (a) the engine torque profile, (b) the EM torque profile, (c) fuel consumption rate of the engine, (d) a plot is zoomed in 50–100 s (e) b plot is zoomed in 50–100 s (f) c plot is zoomed in 50–100.  
led to a fuel consumption reduction of 0.4-0.7%, depending on the drive cycle, with respect to the case when no transient corrections were accounted for in the controller. However, further improvement of the fuel efficiency could be achieved by considering larger battery capacity. Doubling the battery capacity will reduce the impact of battery limitations. In this case, ECMS with the TCF strategy shows an improvement of 1.4% in fuel economy. In this paper, the thermal constraint of the battery was not considered as in the previous work [18]. For the same 14s12p battery configuration and vehicle, the battery temperature for different drive cycles was within desired operation range. However, in the current work, the developed management strategy, which included transient behavior, allowed the ICE to operate in a stable mode; thus, the EM was exposed to more transient performance. This can increase temperature rise in the battery with respect to ECMS without TCF. This effect could be included in future research.  
Conceptualization, G.Y., S.R., E.E., A.T., and N.A.; Data curation, G.Y. and E.E.; Formal analysis, G.Y. and S.R.; Funding acquisition, E.E., A.T., and N.A.; Investigation, G.Y., S.R., and E.E.; Methodology, S.R.; Project administration, G.Y., A.T., and N.A.; Resources, S.R.; Software, G.Y. and S.R.; Supervision, A.T. and N.A.; Validation, G.Y., S.R., and E.E.; Writing--original draft, G.Y.; Writing--review & editing, S.R., E.E., A.T., and N.A. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. Not applicable. Not applicable. Not applicable. Data Availability Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest.