## 4 Results and Discussion
speeds, the engine's optimal operating power is limited to almost below 30 kW, where it does not reach the most efficient range for SI combustion; this can explain why the average BSFC of the engine is significantly higher with NVH constraints than without them under the NYCC cycle, as shown in Table 3. On the other hand, even without considering NVH constraints, once the engine is turned on and is operating at the most efficient point, the battery will be charged at a high rate and consequently be subject to larger SOC fluctuations, while with the dual-mode combustion engine, the battery power is reduced and SOC is better sustained. Figure 12 shows the distribution of engine operating modes under different strategies for all five testing cycles. Under Strategy 1, the EV mode without the engine on is the overwhelmingly dominant mode; this is because the global optimal engine operating power is significantly higher than the average driving load. Under Strategy 2, the engine operating power is limited by the NVH constraint and, in some of the cases, it is lower than the global optimum; therefore, the engine must have more opportunities to run to sustain the battery's SOC. Under Strategy 3, besides the increase in engine operating time, there are two detailed facts to be noted. One is that, among the five testing cycles, SI combustion only occurs in the US06 cycle, specifically at a high driving load; in all of the other four cycles, the engine only operates in the HCCI combustion mode. This shows that, based on the powertrain system configuration of this particular vehicle, it is more economical to run the engine in the HCCI mode under normal driving conditions. Only when the load power is relatively high is it better to switch to the SI mode at the global optimal point to avoid  
Figure 11: Simulation results under the NYCC driving cycle. large amounts of power being used to operate the battery, as well as to save fuel. The other fact is that, in the HWFET cycle, the engine is on for around 80% of the driving time. This is mainly due to the coincidence that the average load power is close to the optimal HCCI operating power. This can also explain why the battery loss in this case is much smaller than that under the other two strategies, as shown in Table 3.  
Based on the simulation results and the analysis above, it can be seen that the control parameters and operating behaviors of the engine are driving-condition-dependent. However, normally, in real-world driving, the driving conditions for a whole trip are unknown, and it is not possible to run the cycles repeatedly through a dual-loop PSO to determine the optimal EF of the ECMS. Therefore, a further investigation into the control parameters was conducted to fix an EF for online applications. From Table 2, it can be seen that there is a relationship between \(\alpha\) and vehicle speed or load; at a lower vehicle speed, the average driving load is relatively low, and a larger \(\alpha\) is needed to increase the opportunities to turn on the engine. This can be achieved by increasing the weight of the equivalent fuel consumption of the battery to avoid a continuous decrease in the SOC. On the contrary, a smaller \(\alpha\) is needed at higher vehicle speeds to increase the opportunities to turn off the engine. Based on the average speed of each testing cycle and the corresponding optimal \(\alpha\), a vehicle-speed-based approach is applied in the final online control algorithm, as shown in Figure 13.  
The parameter \(\beta\) in the EF is used for SOC tracking. The simulation shows that, with a fixed \(\alpha\) in a certain driving cycle, a larger \(\beta\) can obtain a smaller SOC fluctuation, and worsen the fuel consumption as a trade-off. For the convenience of control, a constant value of 0.025 is chosen for \(\beta\) in the real-time application. Finally, the WLTC driving cycle is chosen to validate the proposed ECMS with a predetermined EF and a single-loop PSO algorithm.