*2.1. Selection of the Hybrid Powertrain Topology*

Internal combustion engines (ICEs) intended for HD vehicles are remarkably efficient in a wide range of operating modes. Brake-specific fuel consumption (BSFC) becomes significantly higher only at small loads, which, in a hybrid electric vehicle (HEV), may be avoided by electric driving or, in the case of insufficient battery energy, by additional loading of the ICE. The concept of the optimal operating line (OOL), i.e., the locus of operating points having a minimum BSFC for a given power, is undoubtedly efficient in light duty applications where ICEs have a significant BSFC gradient; however, in the case of HD engines, the OOL is not as clear. In the first place, it requires employing a continuously variable transmission (CVT), which in the case of HD vehicles, can be either electric (corresponding to a series HEV topology) or electromechanical (the power-split topology). Both options (frequently called e-CVTs [17]) imply using two electric machines, which complicates the transmission and makes it more expensive. Generally, e-CVTs have a lower efficiency than stepped mechanical transmissions, and using them only makes sense if OOL tracking provides an increase of the ICE efficiency, which is significantly higher than the effect of impairing the efficiency using an e-CVT. In the case of an HD engine, OOL tracking may increase its efficiency only slightly, and considering a relatively low e-CVT efficiency, the overall fuel-saving effect will most likely be small or, in some cases, even negative [13]. This, together with the first aspect (complex and expensive transmission), makes e-CVT-based topologies hardly affordable, especially when it comes to issues of producing and owning such vehicles.

The parallel topology (Figure 2) can be derived from a conventional transmission (with an automated stepped gearbox) through moderate design changes. It implies placing an electric machine (EM) between the ICE shaft and the gearbox input shaft. It is advisable to place the automated clutch between the ICE and the EM to disconnect the former from the transmission and therefore allow the vehicle to be driven solely by the electric machine. The energy storage system (ESS) is connected to the traction electric drive using a DC link shown by the dotted line in Figure 2. The direct mechanical connection established between the ICE and the EM when the clutch is locked allows for the efficient transmission of power from the ICE to the ESS when it is necessary to replenish the latter or to load the former to avoid non-efficient operating regimes.

**Figure 2.** Parallel hybrid powertrain topology with a stepped automated gearbox. EM: Electric machine, ESS: Energy storage system, ICE: Internal combustion engine.

Placing the EM before the gearbox allows for providing a considerable range of electric driving (in terms of both speed and tractive force) without oversizing of the electric machine, which usually takes place in the topologies where the EM is connected to the driving wheels through a reduction gear that has a constant speed ratio. On the other hand, losses in the gearbox reduce the efficiency of the transmitting power from the EM to the driving wheels and backwards (regenerative braking).

Taking into account the above considerations and the previous studies performed by the authors (see, for example [18]) and other researchers [13,14], it was decided that for this study, the parallel topology would be selected for the analysis of powertrain hybridization.
