## 2 Materials and Methods
### Modeling and Modes Analysis
#### 2.2.4 Efficiency Model  
Since this paper mainly focused on the influence of the selection of a dual-motor coupling powertrain on the economic performance of a PET, it was necessary to establish efficiency models of a DICPS, including a motor efficiency model and a transmission efficiency model.  
To obtain the efficiency model of the motor, we measured the output torque, speed, bus voltage, and current of the motor through a bench test and calculated the efficiency value. The motor efficiency was defined as the function of output speed and torque, as shown in Equation (6), and the efficiency in a certain state was obtained by the interpolation method. The efficiency map of motors in this study is shown in Section 2.3.1.  
\[\eta_{m}=f(\omega_{m},T_{m})\]  
When the DICPS works in mode M1S, brake B1 is disengaged, B2 is engaged, EM_S is on, and EM_R is off. The DICPS can amplify the output torque of EM_S through the planetary mechanism to provide a high torque output, which is suitable for low-speed and high-torque operation conditions such as plowing. The power flow is shown in Figure 2a, and the dynamic model of DICPS in M1S mode was obtained based on the dynamic model of the planetary gear set.  
\[\left\{\begin{array}{l}(T_{m1}-I_{m1}\dot{\omega}_{m1})\cdot i_{s}(1+k)-\frac {T_{L}}{i_{f}l_{m}}=I_{c}\dot{\omega}_{c}\\ I_{c}\dot{\omega}_{c}=\frac{mr_{q}{}^{2}}{i_{f}^{2}i_{m}}\cdot\frac{\dot{v}_{a}i _{f}i_{m}}{r_{q}}=\frac{mr_{q}\dot{v}_{a}}{i_{f}i_{m}}\\ \omega_{m1}=\frac{\dot{v}_{a}i_{f}i_{m}}{r_{q}}\cdot i_{s}(1+k)\\ \end{array}\right. \tag{9}\]  
where \(T_{m1}\) and \(\omega_{m1}\) are the output torque and the speed of EM_S, respectively, and \(I_{m1}\) is the equivalent inertia of EM_S.  
When the DICPS operates in mode M2S, EM_S closes and EM_R operates, B1 engages to brake the ring gear, and B2 is disengaged. Figure 2b shows the power flow. The dynamic model of DICPS in M2S mode is as follows.  
\[\left\{\begin{array}{l}(T_{m2}-I_{m2}\dot{\omega}_{m2})\cdot i_{r}\frac{1+k} {k}-\frac{T_{L}}{i_{f}l_{m}}=\frac{mr_{q}\dot{v}_{a}}{i_{f}l_{m}}\\ \omega_{m2}=\frac{v_{a}i_{f}i_{m}i_{r}}{r_{q}}\cdot\frac{1+k}{k}\\ \end{array}\right. \tag{10}\]  
where \(I_{m2}\) is the equivalent inertia of EM_R, \(T_{m1}\) and \(\omega_{m1}\) are the output torque and the speed of EM_R.  
When the DICPS works in DMC mode, two motors operate simultaneously and the brakes B1 and B2 are disengaged. At this time, the output power of EM_S and EM_R is combined by the planetary gears. This mode can achieve a higher speed under medium and low loads, which is suitable for transshipment and transportation operations. Figure 2c shows the power flow. The dynamic model of the DICPS in DMC mode can be expressed as  
\[\left\{\begin{array}{l}(\min(T_{m1}i_{s},T_{m2}i_{r}/k)-I_{m1}\dot{\omega}_{ m1}i_{s}-I_{m2}\dot{\omega}_{m2}i_{r}/k)(1+k)=\frac{mr_{q}\dot{v}_{a}+T_{L}}{ i_{f}i_{m}}\\ \omega_{m1}/i_{s}+k\omega_{m2}/i_{r}=(1+k)\frac{v_{a}i_{f}i_{m}}{r_{q}}\\ \end{array}\right. \tag{11}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Working Mode** & **EM\_S** & **EM\_R** & **B1** & **B2** \\ \hline M1S & \(\bullet\) & o & o & \(\bullet\) \\ M2S & o & \(\bullet\) & \(\bullet\) & o \\ DMC & \(\bullet\) & \(\bullet\) & o & o \\ \hline \hline \end{tabular} \(\bullet\) indicates that the motor is on or the brake is engaged; o indicates that the motor is off or the brake is disengaged.  
\end{table}
Table 1: System operation status.