## 3 Numerical Modeling and Verification  
The numerical model for the vehicle in CRUISE software (AVL) used the specifications of a TMED-type HEV, and the reliability of the model was verified by detailed calibration based on the experimental data. Figure 5 shows the numerical model of the TMED-type hybrid vehicle developed for this study. The main components include the lithium-ion battery, gasoline engine, electric motor, and auto transmission module. The voltage of the Li-ion battery was 270V, and its capacity was 1.431 kW-h. The initial SOC value was set to 50% upon considering the control target value of the battery of the TMED-type HEV. The gasoline engine was considered to operate based on the Miller cycle, and the maximum torque was approximately 180 N-m. The drive motor and hybrid starter and generator (HSG) were each operated at 270 V, and the maximum torque values of the motor and HSG were 205 N-m and 43.2 N-m, respectively. The rotational speed of the HSG was 2.4 times the gasoline engine speed. Figure 4: Schematic of experimental setup. Figure 5: Full numerical model of TMED-type HEV developed using CRUISE. Table 2 shows the main elements of the HEV model used for the numerical analysis. The curb weight and gross weight of the actual vehicle were entered into the hybrid vehicle model. The elements of the hybrid system controller were from the basic model provided by the CRUISE program. In the data bus, the signals of the driving motor and the generator were modified to be suitable for a TMED-type hybrid vehicle, as shown in Table 3. The specifications of the engine were applied as the actual vehicle values. The engine torque and drive motor elements were applied with correction diagrams, considering the experimental values measured by the dynamometer. The torque values for the engine and the motor were corrected by considering the experimental values. The torque of the engine and the motor was corrected in consideration of the torque and the rotation speed of the actual experiment obtained in the engine-only mode, EV mode, and hybrid-mixed mode. The gear ratio was adjusted based on the engine torque and RPM data collected in the experiment after entering the specifications of the vehicle. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Element** & **Name** & **Major Variable** \\ \hline \multirow{2}{*}{Vehicle} & 1. Curb weight \\  & 2. Gross weight \\ \cline{2-3}  & HEV controller & 1. Controller of hybrid system \\ \cline{2-3}  & 1. Maximum charge \\  & 2. Initial charge \\ \cline{2-3}  & 3. Nominal, maximum and minimum voltage \\  & 4. Number of battery cells \\  & 5. Idle voltage \\ \cline{2-3}  & 1. Torque diagram \\  & 2. Intake method setting (Charger) \\ \cline{2-3}  & 3. Idling speed \\  & 4. Maximum speed \\  & 5. Engine displacement volume \\ \cline{2-3}  & 1. Nominal voltage \\ \cline{2-3}  & 2. Maximum speed \\ \cline{2-3}  & 3. Maximum charge/discharge current \\ \cline{2-3}  & 4. Torque diagram \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Main elements of a hybrid vehicle model under CRUISE. Figure 5(a) shows a comparison of the results of the vehicle test in IM240 mode and the numerical simulation in terms of the engine torque. A higher torque was observed in the medium- and high-speed regimes. In addition, the analysis indicates that the torque increases when the engine operation enters the idling stage. We note here that even when the engine clutch disconnected the transmission of power between the engine and motor, the experimental data was collected by disconnection of the signal in the OBD system. Figure 5(b) compares the experimental and simulation results in terms of the drive-motor torque. A torque error is observed in specific modes, such as the engine mode. However, a similar pattern is seen in the experiment and simulation throughout the driving process in the IM240 mode. Figure 5(c) shows the battery SOC throughout the vehicle test in the IM240-mode, and the simulation results are consistent with the experimental results for up to 100 seconds.