## 3 Numerical Modeling and Verification
Subsequently, an error is observed, but the overall SOC charging and discharging trends are similar. Figure 7 shows a comparison of engine torque and the duration of fuel-injection as functions of engine speed between simulation and experimental results. Torques below 10 Nm near 1600 rpm did not occur due to the setting of the analytical model. By comparing the patterns of the main output required for vehicle driving, the most frequent output was seen at 1600 rpm, and the torque distribution was similar over the range of 800 to 3200 rpm. This comparison indicated that the analysis model was reliable because the engine in the vehicle and the analysis model performed similarly. Based on the difference in the torque between the 2000-cc and 1600-cc engines, engine outputs that were reduced by 10% and 20% were used as variables in the numerical model. A comparison between the torques of the 1600-cc and 2000-cc engines and the driving-test vehicle torque from the same manufacturer revealed a difference of approximately 20%. The lithium-ion battery capacity is another analysis variable that affects fuel efficiency, and was also reduced by 10% and 20%. These driving torque and battery capacity variables were applied to the numerical analysis, and the scenarios are listed in Tables 4 and 5. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Component** & **Input Information** & **Component Delivering** & **Output Information** \\
**Cockpit driver** & Gear indicator & Transmission & Current gear \\  & Speed & TMED Hybrid Vehicle & Velocity \\
**Drive motor** & Load signal & HEV controller & Electric motor load signal \\  & Switch & HEV controller & Electric motor switch \\
**Engine** & Load signal & HEV controller & Engine load signal \\  & Start switch & HEV controller & Engine start switch \\
**Transmission** & Desired gear & Cockpit driver & Desired gear from profile \\
**HEV controller** & Load signal & Cockpit driver & Load signal \\  & Battery status of charge & Lithium-ion battery & Net voltage \\  & Engine torque & Engine & Current brake torque \\  & Battery current & Lithium-ion battery & Current \\  & Battery voltage & Lithium-ion battery & Battery charge \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Connections between elements on the data bus. Figure 6: Comparison of experimental and numerical simulation results under IM240-mode driving: (**a**) engine torque; (**b**) driving motor torque; (**c**) state of charge. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Engine Torque**} \\ \cline{2-4} Battery capacity & \begin{tabular}{c} Rated torque \\ (Base value) \\ \end{tabular} & \
\begin{tabular}{c} 10\% less than \\ Base value \\ \end{tabular} &
\begin{tabular}{c} 20\% less than \\ Base value \\ \end{tabular} \\  & Case 1 & Case 2 & Case 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Scenarios for engine-torque variation with fixed battery capacity in the numerical analysis. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Battery Capacity**} \\ \cline{2-4} Engine torque (Base) & \begin{tabular}{c} Rated capacity \\ (Base value) \\ \end{tabular} & \
\begin{tabular}{c} 10\% less than \\ Base value \\ \end{tabular} &
\begin{tabular}{c} 20\% less than \\ Base value \\ \end{tabular} \\  & Case 1 & Case 4 & Case 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Scenarios for battery-capacity variation with fixed engine torque in the numerical analysis. Figure 7: Comparison of engine torque in the numerical simulation with the fuel-injection duration obtained by experiment: (**a**) engine torque (CRUISE analysis); (**b**) fuel-injection duration.