## 4 Results and Discussion
### Urban Dynamometer Driving Schedule Cycle  
The urban dynamometer driving schedule (UDDS) cycle describes the city bus driving conditions in the United States, and was developed by the United States renewable energy laboratory to adapt to the city bus driving cycle conditions. To simulate real battery operation scenarios, a current sequence  
Figure 11: The simulation output of the first-order RC model for 1C constant current discharging.  
Figure 12: The simulation output of the second-order RC model for 1C constant current discharging.  
Figure 13: Output errors of the first-order and second-order RC models for 1C constant current discharging.  
was extracted from a hybrid electric vehicle (HEV) battery pack under UDDS cycle, which is widely used in the battery model evaluation. In order to verify the accuracy of the models under UDDS cycle, the following tests were performed. First of all, the tested battery was fully charged according to the standard charging method and then the battery was left in the open-circuit condition to rest for 4 h to achieve electrochemical and heat equilibrium. Subsequently, the obtained current sequence was loaded on the tested battery through the battery tester. For the simulation models, the initial SOC was first set to 1, and then the obtained current sequence was set as the input current file running the simulation models. The simulation results of the first-order RC model are illustrated in Figure 14, where the dotted red line represents the simulation output voltage and the solid blue line represents the actual voltage value. Similarly, the simulation results of the second-order RC model are illustrated in Figure 15, where the dotted red line represents the simulation output voltage and the solid blue line represents the actual voltage. It can be seen from the figures that under UDDS cycle the simulating voltage of the both models can basically follow the battery terminal voltage variation trend except for some subtle peak shifts, while the second-order RC model has a better performance than the first-order RC model in tracking some subtle peak shifts. Obviously, this is because the second-order RC model has a stronger capability to describe the nonlinear polarization response with two RC networks instead of one RC network compared to the first-order RC model.  
Figure 14: The simulation output of the first-order RC model for the urban dynamometer driving schedule (UDDS) cycle.  
Figure 15: The simulation output of the second-order RC model for the UDDS cycle.  
For a better comparison, the output error of the first-order RC model and second-order RC model are analyzed as illustrated in Figure 16. It is seen that the second-order RC model has less output error than the first-order RC model in general, while the maximum absolute errors of both models are less than 0.06 V (i.e., relative error less than 2%). It can also be found that the output error of the first-order model tended to be partial to the positive semi axis while that of the second-order model tended to be partial to the negative semi axis, which is caused by modeling itself on the process of the parameters identification. The results can also prove the ability of the two models above to capture battery dynamic behaviors in some sense.