## 3 Parameter and Model  
All configuration candidates adopt the same parameters as shown in Table 2. It is assumed that there is only a pure rolling state of the wheel, no sliding between the wheel and the ground. And the yaw stability of the vehicle is not considered. The driving force \(F_{out}\), driving torque \(T_{out}\) and the speed of output shaft \(\omega_{out}\) for the vehicle are shown in Equations (10) and (11).  
\[\left\{\begin{array}{l}F_{out}=mgf_{r}\cos a+\frac{1}{2\Gamma 15}C_{D}Av^{2}+mg\sin a+\delta m\frac{\mathrm{d}v}{ \mathrm{d}t}\\ T_{out}=F_{out}\cdot r\\ T_{pg}=\frac{T_{out}}{\eta_{CUT}t_{CUT}t_{0}}\end{array}\right. \tag{10}\]  
\[\left\{\begin{array}{l}\omega_{out}=\frac{v}{r}\\ \omega_{pg}=\omega_{out}t_{0}t_{CUT}\end{array}\right. \tag{11}\]  
where \(m\) is the vehicle mass; \(v\) is the driving speed; \(a\) is the climbing slope; \(f_{r}\) is the rolling resistance coefficient; \(C_{D}\) is the aerodynamic drag coefficient; \(A\) is the front section; \(\delta\) is the rotating mass coefficient; \(g\) is the gravity acceleration, the value is 9.8 m/s\({}^{2}\); \(r\) is the radius of wheel; \(i_{0}\) is the gear ratio of final drive; \(i_{CUT}\) is the speed ratio of \(CUT\); \(\eta_{CUT}\) is the operating efficiency of \(CUT\), its value is related to \(CUT\) input torque and \(CUT\) speed ratio by look-up table. The structure and efficiency model of \(CUT\) are shown in Figure 7.  
In this paper, the internal resistance model is selected as the battery model [30]. As shown in Figure 8a. The battery power based on this model is calculated by Equation (12).  
\[P_{batt}=V_{oc}I_{batt}-I_{batt}^{2}R \tag{12}\]  
where \(P_{batt}\) is battery power; \(V_{oc}\) is open circuit voltage; \(I_{batt}\) is current; \(R\) is internal resistance; \(V_{oc}\) and \(R\) are related to SOC (state of charge), as shown in Figure 8b.  
Figure 6: The generation process of configuration candidate.  
The current is obtained by solving Equation (13).  
\[I_{batt}=\frac{V_{oc}-\sqrt{V_{oc}^{2}-4 RP_{batt}}}{2R} \tag{13}\]  
The SOC can be calculated by Equation (14).  
\[SOC_{t}=SOC_{0}-\frac{1}{Q_{N}}\int_{0}^{t}I_{batt}\mathrm{d}t \tag{14}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Component** & **Parameter** & **Value** \\ \hline \multirow{4}{*}{Vehicle} & Mass (kg) & 1600 \\  & Aerodynamic drag factor & 0.301 \\  & Rolling resistance factor & 0.012 \\  & Wheel radius (m) & 0.307 \\ \hline \multirow{4}{*}{Engine} & Maximum power (kW) & 93 \\  & Maximum torque (Nm) & 138 \\  & Range of speed (r/min) & 800–5600 \\ \hline \multirow{2}{*}{MG} & Maximum torque (Nm) & 271 \\  & Maximum speed (r/min) & 10000 \\ \hline \multirow{2}{*}{Battery} & Capacity (Ah) & 6.5 \\  & Nominal voltage (V) & 352 \\ \hline \multirow{2}{*}{Transmission system} & Range of CVT speed ratio & 0.442–2.432 \\  & Final drive gear ratio & 3.95 \\  & \(R_{1}\):\(S_{1}\)(\(k_{1}\)), \(R_{2}\):\(S_{2}\)(\(k_{2}\)) & 2.6, 2.63 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Basic parameters of the vehicle.  
Figure 8: Battery model. (**a**) Internal resistance model; (**b**) Open circuit voltage and internal resistance.  
Figure 7: Continuously variable transmission (CVT) structure and efficiency model. (**a**) Structure; (**b**) Efficiency model.  
where \(SOC_{t}\) is the SOC at \(t\) time; \(SOC_{0}\) is the SOC at the initial time; \(Q_{N}\) is the capacity of battery; \(t\) is the time for battery charging and discharging.