###### Abstract  
Models based on steady-state maps estimate fuel consumption to be 2-8% lower than real experimental measured values. This is due to the fact that during transient phases, the engine consumes more fuel than in steady phases. Some literature has addressed the conventional vehicle engine model that improves fuel consumption estimation's accuracy during the transient state. However, the characteristics of the engine in the scope of hybrid electric vehicles (HEVs) with an integrated control strategy is yet to be covered. The controller is designed to minimize engine operation in the transient phase to enhance energy savings. In this paper, the correlation between fuel enrichment in transient and steady-state fuel estimation is established as transient correction factor (TCF). Its explanatory variable was the engine torque change rate. This paper describes the influence of engine transient characteristics on the fuel consumption of a mild HEV. The work attempts to improve the fuel economy of the HEV by introducing a penalty factor in the controller to optimize the use of the engine in transient regimes. A backward vehicle model was developed for a production vehicle with a conventional powertrain and validated experimentally using data available online. The corresponding hybrid vehicle model was developed by integrating the electric motor and battery components with the conventional vehicle model. A P2 off-axis configuration was chosen to this end as the HEV architecture. A conventional equivalent consumption minimization strategy (ECMS) was used to split the torque request between the engine and the electric motor. This control strategy was modified with TCF to penalize the engine torque change rate. The results of the simulation show that due to less transient operation of the engine, the fuel consumption was reduced from 923 g to 918 g under the US06 driving cycle. The fuel economy of the model has been simulated for UDDS and HW drive cycles too, and fuel consumption improved by 4.4 g and 3.2 g, respectively. It has been verified that by increasing the battery capacity twice (14s24p), the limitations imposed by the battery capacity can be minimized and the fuel usage can be reduced by 9 g in the UDDS cycle. t +
Footnote †: journal: Applied sciences  
height, using an electromechanical system which results in reduced aerodynamic resistance of the vehicle. An interest in electrification of the powertrain, i.e., using hybrid electric vehicles (HEV), as a means of improving fuel efficiency and minimizing greenhouse emissions is growing rapidly [3]. By adding an electric motor (EM) in parallel to the internal combustion engine (ICE), it is possible to recover the braking energy, store it in the battery, and use it later during the traction phase. Furthermore, ref. [4] introduced an ELPH (electrically peaking hybrid) control strategy that offers EM power usage for acceleration and deceleration phases, whereas ICE provides mean load power of the driving cycle. The main aim of this logic is to use ICE at high speeds with smooth torque demand. A great deal of research and practical work has attempted to model the performance of the HEVs for optimizing their efficiency. In most of these works, the vehicle simulation models utilized the steady-state maps of the ICE to estimate fuel consumption [3; 5]. It has been observed that measured fuel consumption data shows a higher value with respect to one calculated using the steady-state maps. This is due to the higher fuel consumption of the engine during transient phases. In [6], the measured fuel consumption was compared to that calculated with steady-state fuel consumption maps as a function of measured torque and speed of the ICE. Testing two vehicles, such as a Chevrolet Silverado with a 4.3 L Ecotec engine and a Ford F-150 with a 2.7 L EcoBoost engine, they concluded that the difference, due to transient fuel consumptions, was in the range of 2-4%.