## 3 Numerical and Experimental Results
The macroscopic traffic flow is suitable for long time scale prediction, while the microscopic car following model is suitable for short time scale prediction. Multi-scale physical processes management in this paper fully utilizes the advantages of the micro and macro methods. This can describe not only short-term car following behavior, but also long-term integrated driving behavior. The macro flow models use the average value (e.g., the spatial average speed of continuous vehicles) in sampling, in which the most suitable q-k or u-k relationship is established by statistical regression. The result is certainly more stable, since the average parameter value is estimated by the average sample. However, since the macro traffic flow does not focus on specific individual vehicles, but on regional average vehicles, the actual driving behavior of each vehicle will be different from that of the regional average statistics. In addition, some unknown factors, or the imprecision of the models, will lead to differences between real driving behavior and predicted driving behavior for the macro traffic flow model. Therefore, when there is a short term speed disturbance in the whole macro traffic flow, replanning of local driving behavior and the corresponding energy management is carried out. Figures 8-10 show the velocity evolution, velocity deviation component, and power evolution of the following car, when the car following behavior at the short time scale deviates from the driving behavior at the long time scale obtained by the macro traffic flow model, corresponding to Mode1 and the Mode2, respectively. The whole process is divided into three stages, i.e., the initial acceleration stage, the middle stable cruising stage and the final braking stage. In order to study the influence of speed fluctuation on the multiscale energy distribution, speed disturbance is assumed in the middle cruising stage to avoid the complex effects of the starting and braking process. Figure 10 shows that the velocity disturbance causes obvious power fluctuation. It is assumed that the vehicles are in information interconnection via V2X communication, and thus the short term velocity fluctuation can be accurately predicted in time through the car following model. Therefore, the energy distribution can be replanned immediately when the disturbance occurs. Since the relationship between speed fluctuation and the power fluctuation is nonlinear, it is unreasonable to plan energy utilization based only on speed characteristics. In other words, the traffic model characterized by speed and acceleration cannot be directly applied simply to energy management planning. Reasonable energy planning needs to map the vehicle speed and acceleration characteristics to power characteristics, which directly determine energy efficiency and are suitable for optimal planning of energy utilization. Figure 7: Car following behavior in macro traffic scenarios. The novel model considers the impact of unknown disturbances on the planning, in order to reduce the deviation in the global optimal solution caused by the error for large macro planning, and thus the model has good robustness even when there are inevitable unknowns, such as unmodeled factors, or chaotic systems with sensitive initial values. Figures 11 and 12 show the SOC trajectories planned by the original strategy and the replanning strategy for Mode 1 and Mode2, respectively, which determine the distribution of the battery energy and fuel energy. Figure 8: Two modes of velocity deviation for the following car. \[k(0,t)=0.13 \tag{26}\]0 Power deviation of the following car. \[k(0,t)=0.13 \tag{26}\]1 Deviation components of the velocity of the following car. In order to make a reasonable comparison, the initial and final SOC of the two disturbance modes are the same (see Figures 11 and 12). Figures 13-16 show the numerical and experimental results (i.e., the torque and speed of the engine and motor) of both the original and the replanning strategies for Mode 1 and Mode 2, respectively.