## 2 HEV Modeling and Baseline Energy Management
### HEV Modeling Approach  
A quasi-static approach was adopted for modeling the HEV in Matlab/Simulink(r) software (Mathworks Inc., Natick, MA, US). This approach is largely used in design and analysis activities for HEV powertrains thanks to its high computational efficiency [28]. A proportional-integral-derivative (PID) controller is introduced here to model the driver following the speed profile over time for given drive cycles. Lookup tables of power components employed in this paper are illustrated in Figure 2 and they have been generated using dedicated tools in Simcenter Amesim(r) software (Siemens PLM, Camberley, UK). The mathematical procedures implemented in the software to generate the lookup tables are available in the literature [29; 30]. \begin{table}
\begin{tabular}{c c c} \hline
**Component** & **Parameter** & **Value** \\ \hline \multirow{3}{*}{High-voltage battery} & Battery nominal capacity/voltage & \multirow{3}{*}{10.94/400} \\  & (kWh/V) & \\  & Cell nominal capacity/voltage (Wh/V) & 7.6/3.33 \\  & Pack configuration & 120 S; 12 P \\  & Cell type & A123 ANR26650 \\ \multirow{3}{*}{Vehicle body} & Road load coefficient A (N) & 94.04 \\  & Road load coefficient B (Ns/m) & 3.81 \\ \multirow{3}{*}{Vehicle body} & Road load coefficient C (Ns2/m2) & 0.48 \\  & Wheel radius (m) & 0.322 \\ \hline \end{tabular}
\end{table} 
Table 1: _Cont._The total vehicle resistive force \(F_{res}\) can be easily computed from the vehicle free body diagram using Equation (1):  
\[F_{res}=F_{zero}+F_{roll}+F_{misc}+F_{grad} \tag{1}\]  
where \(F_{zero}\) is the aerodynamic drag, \(F_{roll}\) represents the rolling resistance, \(F_{misc}\) incorporates some miscellaneous terms, whereas \(F_{grad}\) is the grading resistance related to road slope angle \(\vartheta\). Specifically, the above resistive terms were evaluated as follows:  
\[F_{zero}+F_{roll}+F_{misc}=A+Bv+Cv^{2} \tag{2}\]  
\[F_{grad}=m_{veh}gsin\vartheta \tag{3}\]  
Figure 2: Efficiency maps of _ICE_, _MGP0_, and _MGP4_ generated by means of Simcenter Amesim® software. where \(A,B,\text{ and }C\) are the vehicle road load coefficients [31], \(v\) is the longitudinal speed of the vehicle, \(g\) represents the gravitational acceleration, and \(m_{veh}\) is the total mass of the vehicle in kilograms that was assumed to be related to the number of passengers \(n_{pass}\):  
\[m_{veh}=1768+100\cdot n_{pass}. \tag{4}\]  
The tractive or braking force \(F_{puct}\) that is provided at the wheels by the powertrain was introduced. Then, the equilibrium equation at the vehicle level could be written as follows:  
\[m_{veh}a=F_{puct}-F_{res,tot} \tag{5}\]  
where \(a\) indicates the longitudinal acceleration of the vehicle. The powertrain torque \(T_{puct}\) requested at the wheels could thus be computed as follows:  
\[T_{puct}=F_{puct}r_{wheel} \tag{6}\]  
where \(r_{wheel}\) is the radius of the wheels. All possible terms contributing to \(T_{puct}\) were considered, and Equation (7) could thus be obtained:  
\[T_{puct}=T_{ICE,wheel}+T_{MGP4,wheel}+T_{MGP0,wheel}-T_{ brakes} \tag{7}\]  
where the terms \(T_{ICE,wheel}\), \(T_{MGP4,wheel}\), and \(T_{MGP0,wheel}\) represent the values of torque provided at the wheels by the respective power components, while \(T_{ brakes}\) is the braking torque supplied by the brake system. The torques of power components \(T_{ICE}\), \(T_{MGP4}\), and \(T_{MGP0}\) were evaluated backwardly from the respective torques outputted at the wheels by means of relations using the transmission ratios reported in Table 1 and appropriate efficiencies [32]. The wheel angular speed \(\omega_{wheel}\) could be defined as follows:  
\[\omega_{wheel}=\frac{v}{r_{wheel}}. \tag{8}\]  
\(\omega_{MGP4},\omega_{ICE}\), and \(\omega_{MGP0}\) that respectively represent angular speeds of \(MGP4\), \(ICE\), and \(MGP0\) can be evaluated by multiplying times transmission ratios.