*4.2. Energy Consumption*

To evaluate the effectiveness of the proposed energy management strategy (denoted as Strategy A), another energy management strategy (denoted as Strategy B) is employed in the following to make a comparison study. Two strategies are implemented with same driving conditions. The two strategies are based on the same control algorithm and optimization process. The only difference is that the impacts of battery aging are not considered in Strategy B while the varying control parameters enable the Strategy A to be adaptive to the battery aging process according to the current SOH value. The simulation conditions are provided as follow. The prices of fuel and electricity are 5.86 CNY-¥/L and 0.82 CNY-¥/kWh, respectively, the thresholds δ<sup>1</sup> and δ<sup>2</sup> are set as 0.5 and 0.2, respectively. Since the optimization is not implemented when SOC ≥ δ1, the initial SOC in this study is set as 0.5. The impact of temperature is neglected in this simulation.

The comparison results of the energy cost from two strategies are summarized in Tables 4 and 5. The optimal energy cost is enhanced by up to 15.19% in UDDS driving cycle and 14.28% in EUDC driving cycle when SOH changes from 96.21% to 79.34% if the battery aging is not concerned in energy management (Strategy B). Without replacing the aging battery pack, using the presented energy management strategy can reduce the effect of battery aging to some certain extent. The energy cost is decreased by up to 2.24% both in UDDS driving cycle and in EUDC driving cycle compared with the strategy without considering the battery aging. The detailed simulation results of power allocation in UDDS driving cycle are shown in Figure 7.


**Table 4.** Comparison on cost functions of two strategies: with the case of UDDS.


**Table 5.** Comparison on cost functions of two strategies: with the case of EUDC.

**Figure 7.** Simulation results in UDDS (50 km): (**A**) Battery power of healthy battery; (**B**) battery power of aging battery with Strategy B; (**C**) battery power of aging battery with Strategy A; (**D**) engine power of healthy battery; (**E**) engine power of aging battery with Strategy B; (**F**) engine power of aging battery with Strategy A; (**G**) SOC trajectory; (**H**) energy cost.

Figure 7A–C show the apparently fade of maximum battery power. When battery is deeply aging, the battery performance is influenced, resulting in an improper energy management result. Therefore, adjusting the energy management parameters at varying battery SOH is necessary. The battery power in Strategy A is properly reduced and well-distributed compared with that in Strategy B. From Figure 7D–F show the engine power distribution. The engine power in Strategy B becomes very large near the terminal of the trip leading in a low efficient performance. This is because the battery energy is insufficient near the end of the trip, see Figure 7G. The battery SOC in Strategy B drops to bottom earlier than that in Strategy A, and then the higher cost power from the engine supply the power demand. On the contrary, the SOC trajectory in Strategy A has a good agreement with that of health battery. The optimal cost of Strategy A at the terminal of trip is decreased effectively in comparison with Strategy B. Similar analysis results can also be found in Figure 8. When trip length is long, the impact of battery aging tends to be minor because the energy cost from engine system (gasoline) occupies a larger proportion than that of short trip length. Although the battery aging cannot

be eliminated through the energy management approach, a proper design of energy management strategy can partly reduce its negative impacts on energy cost of the PHEV.

**Figure 8.** Simulation results in UDDS (100 km). (**A**) Battery power of healthy battery; (**B**) battery power of deeply aged battery with Strategy B; (**C**) battery power of deeply aged battery with Strategy A; (**D**) engine power of healthy battery; (**E**) engine power of deeply aged battery with Strategy B; (**F**) engine power of deeply aged battery with Strategy A; (**G**) results of SOC; (**H**) energy cost.
