## 2 Model and Methodology
### Estimation of the Residual Driving Range for a Battery Electric Vehicle  
Of all the different methods for the estimation of SoC [12], the ECC approach was chosen. In classic coulomb counting method (CC), battery capacity is considered as a constant value, therefore the influence of any battery operating condition on its available capacity is neglected [7]. Conversely, according to the ECC approach, multiple correction factors must be included when estimating the real battery capacity, such as the temperature and aging of the battery pack. The additional features we considered for the application of the ECC were:  
* A higher accuracy with respect to the reference approach [13];
* A low computational burden [25];
* The lack of parameters to be tuned [12]. Thereby, relying upon the ECC approach, a more precise estimation of the battery SoC variation can be made according to the following equation:  
\[SoC=SoC_{0}-\frac{Q}{\lambda_{tot}*C_{b}}=SoC_{0}-\frac{\int I_{b}dt}{\lambda_ {t_{bp}}*\lambda_{SoH}*C_{b}}\left[-\right] \tag{22}\]  
where \(Q=\int I_{b}dt\) represents the charge consumed, \(\lambda_{tot}\) is an overall correction factor constituted by the product of a correction factor related to the battery pack temperature \(\left(\lambda_{t_{bp}}\right)\), and a correction factor that considers the battery SoH \(\left(\lambda_{SoH}\right)\). Equation (22) shows a different formulation with respect to (21), as a given set of additional parameters must be estimated. To achieve this, the two correction factors were estimated based on the relative variation of the available battery capacity with respect to the battery capacity nominal value (100%). The data were processed according to the technical specifications of the L-7 BEV considered within the STEVE project [23], and two different LUTs were generated. In terms of the correction factor for the battery pack temperature, the trend of the battery capacity as a function of the battery pack temperature is reported in Figure 7. A particular phenomenon was highlighted by temperatures over 25 \({}^{\circ}\)C as the battery capacity tended to overcome the nominal value. Nevertheless, high battery pack temperatures were typically responsible for producing faster aging and a drastic reduction in battery performance. More precisely, a reduction in the battery internal resistance and a higher frequency of over-discharging phenomena occurred, as shown in [26]. However, allowing the battery to work at any temperature level did not represent a beneficial solution. The fluctuations of battery capacity due to a variation of the battery pack temperature was considered through the value \(\lambda_{t_{bp}}\) in the range (0.64, 1.03). With regard to the correction factor accounting for the reduction in battery capacity due to its SoH, the trend shown in Figure 8 was considered for the analyses. To clarify, a life-cycle was considered as a complete discharge until the DoD was reached, followed by a complete recharge of the battery. It can be noted that a significant effect on the available capacity was produced by a change in the DoD. In fact, increasing the DoD can lead to an increase in the driving range of the vehicle but also to a reduction of the maximum life-cycles admitted. Specifically for the data shown in Figure 8, a DoD equal to 80% could allow the battery to improve the life cycles by 50%, increasing from 400 (with DoD equal to 100%) to 600 life-cycles. This value was selected on the assumption that it could represent the best trade-off between battery usage (i.e., battery longevity) and electric range. Accordingly, two distinct scenarios were analysed in the present paper regarding \(\lambda_{SoH}\): within the first scenario, the maximum DoD admitted was set to 100%; in the second scenario, the maximum DoD admitted was reduced to 80%.