## 2 Model and Methodology
### Battery Model and Estimation of the Battery State of Charge  
In terms of the battery model, [24] stated that a low-throughput battery model can represent the best trade-off between the accuracy of the model and the computational effort required for the simulations. Given the aim of the present paper, consisting of the assessment of the driving range of an L-7 BEV, such a low-throughput model was used in the analyses. In Figures 5 and 6, the curves of the open-circuit voltage (OCV) \(OCV_{cell}\) and the equivalent resistance \(R_{eq,cell}\) considered for the battery cells are presented, respectively. The curves are considered as a function of the battery SoC. Figure 5: Battery cells open-circuit voltage as a function of the state of charge. Figure 6: Battery cells resistance as a function of the state of charge. In particular, the OCV increased with the battery SoC, whereas the equivalent resistance showed a significant drop for low SoC values and plateaued for SoC higher than 20-30%. The battery features are reported in Table 1 and refer to a valve-regulated lead-acid (VRLA) battery. To clarify, a VRLA battery was considered in the study only because of data availability. Nevertheless, the entire methodology would not be affected by a change in the battery model (e.g., Li-Ion or others) and could easily be adapted. In terms of the battery pack architecture, a single module constituted by six parallel units (\(n_{unit}\)) was considered in the analyses. Each battery unit was assumed to be constituted by six cells in series. The battery current \(I_{b}\) can be assessed along with the information of the electric power demand \(P_{b}\):  
\[I_{b}=\frac{OCV_{b}-\sqrt{OCV_{b}^{2}-4\cdot R_{eq,b}\cdot P_{b}}}{2\cdot R_{ eq,b}}\left[A\right] \tag{17}\]  
in which \(OCV_{b}\) and \(R_{eq,b}\) represent the OCV and internal resistance of the battery, respectively, based on the battery architecture considered in the present study. The maximum value of the battery current \(I_{b,max}\) was set to 200 \(A\) and included in the model. This value was considered constant for any traction phase, while a saturation was analysed during braking conditions. Since relevant power might flow into the system due to impressive regenerative braking phases, the possibility of cutting the maximum current at the AC/DC converter might be necessary to avoid harmful events in the battery. Accordingly, several levels of the maximum recharging current (saturation current, \(I_{sat}\)) were considered in the following analyses and an assessment of the effects on the overall battery SoC trajectory was carried out over experimental driving missions. To clarify, the efficiency of the AC/DC converter \(\eta_{AC/DC}\) was considered as a constant value despite different values of the saturation current. Hence, the maximum power that can be provided by the battery during traction phases can be computed by identifying the minimum value between the two following power contributions:  
\[P_{b,max,chem,tract}=OCV_{b}*I_{b,max}-R_{eq,~{}b}*I_{b,max}^{2}\left[W\right] \tag{18}\]  
\[P_{b,max,~{}d,tract}=\frac{OCV_{b}^{2}}{4*R_{eq,b}}\left[W\right] \tag{19}\]  
For details about the distinction between the battery power expressed through (16) and (17), please refer to [24]. Alternatively, the maximum power admitted by the battery during braking phases can be estimated as:  
\[P_{b,max,brak}=-\left(OCV_{b}\cdot I_{b,max}+R_{eq,~{}b}\cdot I_{b,max}^{2} \right)=-\left(OCV_{b}\cdot I_{sat}+R_{eq,~{}b}\cdot I_{sat}^{2}\right)\left[W\right] \tag{20}\]  
in which \(I_{b,max}\) is equal to \(I_{sat}\) during braking events. Once the current requested by the battery is estimated, the variation of the battery SoC can be calculated as:  
\[SoC=SoC_{0}-\int\frac{I_{b}}{C_{b}}dt\left[-\right] \tag{21}\] \begin{table}
\begin{tabular}{c c} Number of units in series & 6 \\ OCV & 72 V \\ Resistance of a unit & 27 m\(\Omega\) \\ Capacity & 140 Ah \\ Mass & 168 kg \\ \end{tabular}
\end{table} 
Table 1: Characteristics of the considered battery pack.