# Design of Optimized Energy Management Strategy for All-Wheel-Drive Electric Vehicles
## 2 Design of All-Wheel Driving Model
### Power System Modeling  
The source of power comes from permanent magnet synchronous motors (PMSM). In PHEV, the driving mode or braking energy recovery mode corresponds to PMSM working as a tractor motor or generator, respectively. The PMSM model is established through experiments, in which PMSM motor data that indicate the torque corresponds to different speeds calculated as motor efficiency are measured by the test platform. When \begin{table}
\begin{tabular}{l l l} \hline \hline
**Symbol** & **Parameter** & **Value/Unit** \\ \hline \(Te\) & Motor torque & Nm \\ \(T\)dem & The final drive output torque & Nm \\ \(W\) & Wheel angular speed & Rad/s \\ \(v\) & Vehicle speed & m/s \\ \(m\) & Vehicle mass & 1890 kg \\ \(A\) & Vehicle lateral surface & 3.5 m\({}^{2}\) \\ \(C_{\text{d}}\) & Aerodynamic coefficient & 0.73 \\ \(\rho\) & Aerodynamic resistance coefficient & 1.2 kg/m\({}^{3}\) \\ Faer & Aerodynamic resistance & N \\ \(P\)m & Rated power of the motor & W \\ \(P\)dem & The output power of the final drive & W \\ \(r\) & Tire radius & 0.354 m \\ \(\mu\) & Rolling coefficient & 0.8\% \\ \(\eta\) & Efficiency of transmission & 0.90 \\ \(Q_{0}\) & Maximum battery charge & C \\ SOC & Battery state of charge & \\ \(I_{\text{BT}}\) & Electric current & A \\ \(P_{\text{BT}}\) & Electric power of the battery & W \\ \(V_{\text{OC}}\) & Open circuit voltage & V \\ \(R_{\text{i}}\) & The internal resistance of the battery & \(\Omega\) \\ \(V_{\text{BT}}\) & The voltage of the load & V \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Vehicle parameters involved. PMSM works as a tractor motor, the PMSM power \(P\)m can be calculated by Equation (7). Meanwhile, when the PMSM works as a generator, \(P\)g could be obtained by Equation (8). \[P_{\text{m}}=\frac{T_{\text{m}}\cdot w_{\text{m}}}{\eta_{\text{m}}} \tag{7}\]  
\[P_{\text{g}}=T_{\text{m}}\cdot w_{\text{m}}\cdot\eta_{\text{g}} \tag{8}\]  
where \(\eta_{\text{m}}\) and \(\eta_{\text{g}}\) are PMSM efficiency while PMSM works as tractor motor or generator, respectively. \(\eta_{\text{m}}\) and \(\eta_{\text{g}}\) could be obtained through previous experiments. The PMSM efficiency diagram is shown in Figure 1.  
Power battery is established through the Rint model [19], and the battery is composed of a generous battery cell. According to [PERSON]'s law, the diagram of the equivalent circuit diagram is shown in Figure 2. The open-circuit voltage and current are expressed in:  
\[V_{\text{BT}}(SOC,\,I_{\text{BT}})= V_{\text{OC}}(SOC)-R_{\text{i}}(SOC,\text{sign}(I_{\text{BT}}))\cdot I_{ \text{BT}} \tag{9}\]  
The open voltage is related to state-of-charge (SOC). Furthermore, the voltage of the open circuit \(V_{\text{OC}}\) is measured with the battery discharge along with different \(SOC\). The battery's open-circuit voltage corresponding to SOC is shown in Figure 3. The experiment  
Figure 1: Efficiency diagram of the motor or generator. Figure 2: Model of the battery pack. carries on at an ambient temperature, so the influence of temperature on \(SOC\) is ignored. According to Equation (9), the battery power of output can be obtained:  
\[P_{\text{BT}}=V_{\text{BT}}I_{\text{BT}}=V_{\text{OC}}\cdot I_{\text{BT}}-R_{ \text{i}}\cdot I_{\text{BT}}^{2} \tag{10}\]  
where the \(R_{\text{i}}\) is initial resistance of the battery. \(V_{\text{BT}}\) (\(SOC\), \(I_{\text{BT}}\)) is battery voltage that applies to load, and \(I_{\text{BT}}\) is output current of the battery which could be calculated by:  
\[P_{\text{m}}=\frac{T_{\text{m}}\cdot w_{\text{m}}}{\eta_{\text{m}}} \tag{7}\]0  
Thus, the state equation of SOC is presented as follows:  
\[P_{\text{m}}=\frac{T_{\text{m}}\cdot w_{\text{m}}}{\eta_{\text{m}}} \tag{7}\]1  
where the Q0 is the Maximum capacity of the battery, \(SOC\)(k) is the \(SOC\) of \(k\) at this moment. The configuration of the four in-wheel motor EV is shown in \[P_{\text{m}}=\frac{T_{\text{m}}\cdot w_{\text{m}}}{\eta_{\text{m}}} \tag{7}\]2 The front-left and right motor are controlled by the front motor control unit (F-MCU).