## 4 Results and Discussion
The reason is that, under SI/HCCI combustion, the gap between the engine-generator set's output power and the required power for driving is greatly narrowed (since the optimal operating range of the engine in SI mode is at high loads) and the average battery power is lowered; thereby, the battery loss due to the internal resistance is reduced. Then, based on energy conservation, the total work of the engine-generator set for a certain driving cycle is lower than that which has higher battery loss. From Table 2, we can see a decrease in the average battery power by around 9.2%-64.1% for different driving cycles. There are two major benefits to lowering the battery power: (1) the battery will have a longer cycle life with a lower charge/discharge rate; (2) the heat generated by the battery's internal resistance will be less, and therefore the extra energy used to cool down the battery could be reduced. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Cycle** & **Strategy** & **Avg. BSFC** & **Engine–Generator Set** & **Battery Loss** & **Avg. Battery Power** \\  & **(g/kWh)** & **Total Work (kWh)** & **(kWh)** & **(kW)** \\ \hline \multirow{3}{*}{UDDS} & SI w/o NVH & 263 & 2.017 & 0.0533 & 10.14 \\  & SI w/NVH & 278.48 & 2.007 & 0.0411 & 9.32 \\  & SI/HCCI & 264.5 & 1.986 & 0.0233 & 6.48 \\ \hline \multirow{3}{*}{HWFET} & SI w/o NVH & 263 & 3.072 & 0.0698 & 18.63 \\  & SI w/NVH & 272.91 & 3.049 & 0.0425 & 15.15 \\  & SI/HCCI & 264.52 & 3.016 & 0.0107 & 5.47 \\ \hline \multirow{3}{*}{MANHATTAN} & SI w/o NVH & 263 & 0.732 & 0.0189 & 5.74 \\  & SI w/NVH & 294.08 & 0.726 & 0.0092 & 4.51 \\  & SI/HCCI & 264.97 & 0.725 & 0.0085 & 4.34 \\ \hline \multirow{3}{*}{NYCC} & SI w/o NVH & 263 & 0.416 & 0.0109 & 5.81 \\  & SI w/NVH & 291.05 & 0.411 & 0.0069 & 4.81 \\  & SI/HCCI & 265.47 & 0.411 & 0.0067 & 4.69 \\ \hline \multirow{3}{*}{US06} & SI w/o NVH & 263 & 2.812 & 0.0735 & 19.64 \\  & SI w/NVH & 268.81 & 2.815 & 0.0753 & 19.81 \\ \cline{1-1}  & SI/HCCI & 265.23 & 2.807 & 0.0726 & 17.98 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of engine and battery performances between different strategies. Figure 10 shows the simulation results chosen from a part of the UDDS driving cycle to investigate the behavior of the engine and battery under different strategies. Note that discharging is defined as a positive current. Strategy 1 optimizes the operation of the engine by minimizing the instantaneous \"equivalent fuel consumption\" and could lead to two special situations: (1) the engine is operating at the optimal high load while the power required for driving is relatively low; (2) the engine stops while the battery provides the total required power, which is positive. These will result in relatively large charge and discharge currents in the battery, and the engine could start and stop frequently; however, fuel economy is optimized. Under Strategy 2, the engine-generator set's output power is limited by the NVH constraint and may no longer be inside the efficient range. For example, during the time period from 180 s-185 s, the engine-generator set was running at 10 kW, since the driver released the acceleration pedal soon after the engine was on but the engine could not shut down due to the \"minimum engine-on time\" constraint. However, this NVH constraint can improve the drivability of the vehicle and lower the battery power. The \"minimum engine-on time\" constraint can also avoid overly frequent engine on/off switching. Under Strategy 3, HCCI combustion allows the engine to operate at a low load with high efficiency; thus, it brings benefits to fuel economy, SOC stability, and battery health. The other case is chosen from the NYCC driving cycle, reflecting urban driving conditions, as shown in Figure 11. Due to the relatively tight NVH constraint at low vehicle  
Figure 10: Simulation results under the UDDS driving cycle.