*2.2. BEV Powertrain*

In the BEV powertrain layout illustrated in Figure 1b, the fuel tank, ICE and AMT of the CV powertrain are replaced with a high-voltage battery, an electric motor (EM) and a direct drive, respectively. Finally, power electronics enable the proper operation of the electric powertrain components. In this framework, speed *ωEM* and torque *TEM* of the EM can be evaluated at each time step following the same procedure illustrated for the CV case in Equations (1)–(3). A gear shift logic does not need implementation in this case, given the embedment of a direct drive. The EM electrical losses *lossEM*, including inverter losses as well, can be evaluated in this case by interpolating in a two-dimensional lookup table with *ωEM* and *TEM* as independent variables. Finally, the battery state-of-charge (SOC) over time can be evaluated as a function of the requested battery power *Pbatt* by adopting an equivalent circuit approach and following Equations (4)–(6) [34].

$$SOC(t) = \int\_{t\_0}^{t\_{end}} S \dot{O} \mathcal{C} \left[ P\_{batt}(t), SOC(t) \right] dt \tag{4}$$

with:

$$P\_{\rm hatt}(t) = \omega\_{EM}(t) \cdot T\_{EM}(t) + \log \text{s}\_{EM}[\omega\_{EM}(t), T\_{EM}(t)] + \log \text{s}\_{\rm aux}(t) \tag{5}$$

$$\begin{array}{l} \text{S\dot{O}C} \text{[}P\_{\text{batt}}(t)\text{,SOC}(t)\text{]}\\ = \frac{V\_{\text{OC}}[\text{SOC}(t)] - \sqrt{\{V\_{\text{OC}}[\text{SOC}(t)]\}^2 - 4 \cdot R\_{IN}[\text{SOC}(t)] \cdot P\_{\text{batt}}(t)}}{2 \cdot R\_{IN}[\text{SOC}(t)]} \cdot \frac{n\_P}{A h\_{\text{batt}} \cdot 3600} \end{array} \tag{6}$$

where . *SOC*, *t*<sup>0</sup> and *tend* are the instantaneous rate of SOC, the initial time instant and the final time instant of the drive cycle, respectively. *lossaux* is the power requested by the accessories (e.g., air conditioning, lubrication), and it is modeled as having a constant value in this work. *RIN* and *VOC* represent the internal resistance and the open-circuit voltage of the battery pack, as obtained by interpolating in 1D lookup tables with SOC ad independent variables. *nP* is the number of cells in parallel according to the battery pack layout, while *Ahbatt* represents the battery pack energy capacity in ampere-hours. The factor of 3600 is considered here to convert energy units in ampere-seconds.
