## 2 Macro-Micro Physical Processes of Traffic Management
### Multi-Scale Mixed Traffic Modeling
\begin{array}{l}\eta_{e}=f_{e,\eta}(T_{e},\omega_{e})\\ \eta_{\mathrm{m}}=\eta_{m,\eta}(T_{m},\omega_{m})\\ b_{e}=f_{\mathrm{b}}(T_{e},\omega_{e})\end{array}  \tag{12}\]  
where \(T_{e},\omega_{e}\) are the engine's torque and velocity; and \(T_{m},\omega_{m}\) are the motor's torque and velocity. The fuel consumption can be calculated by the following formula based on the bench test data:  
\[\dot{m}=T_{e}\cdot\omega_{e}\cdot b_{e} \tag{13}\] \begin{table}
\begin{tabular}{c c} \hline Engine & Maximum torque 100 Nm \\ Motor/generator & Maximum torque \(\pm\) 100 Nm \\ Battery & Ternary Li, capacity: 60 A h 138 V \\ Transmission & CVT, 0.5–2.5, Torque converter \\ Final drive & Ratio 8 \\ \hline \end{tabular}
\end{table} 
Table 1: Main parameters of PHEVs. Figure 3: The configuration of the selected PHEV powertrain. The motor/generator power and the SOC changes are obtained as follows:  
\[P_{EM}=\left\{ \begin{array}{l}\frac{T_{m}\omega_{m}}{\eta_{out}},T_{m}>0\\ T_{m}\omega_{m}\eta_{gen},T_{m}\leq 0\end{array} \right. \tag{14}\]  
\[V_{oc}(t)=d_{0}SOC(t)+d_{1} \tag{15}\]  
\[SOC=\frac{dSOC}{dt}=-\frac{V_{oc}-\sqrt{V_{oc}^{2}-4R_{bat}\frac{P_{EM}}{\eta_{ out}}}}{2R_{bat}Q_{bat}}\in[I_{\min},I_{\max}] \tag{16}\]  
where \(V_{oc},R_{bat},Q_{bat},I\) are the battery pack's open circuit voltage, internal resistance, capacity and electric current respectively; \(\eta_{mat},\eta_{gen}\) are the motor's driving efficiency and generation efficiency; and \(d_{0},d_{1}\) are constants. Step 3: Rolling optimization of the feasible working point set of engine, motor and transmission system obtained in Step 2 for every time step, which dominate the micro process, including the chemical reaction of the engine and the electrochemical reaction of the battery. The state quantity x and control quantity u are defined as:  
\[x=\left[ \begin{array}{c}SOC\\ v_{n}\end{array} \right] \tag{17}\]  
\[u=\left[ \begin{array}{c}T_{e}\\ T_{m}\\ T_{b}\\ i_{CVT}\end{array} \right] \tag{18}\]  
Considering the practicability of the energy management strategy, the constraints of state quantity and control quantity are as follows:  
\[ \begin{array}{l}T_{e,\min}(\omega_{e})\leq T_{e}(\omega_{e})\leq T_{e,\max} (\omega_{e})\\ T_{m,\min}(\omega_{m})\leq T_{m}(\omega_{m})\leq T_{m,\max}(\omega_{m})\\ g_{CVT}(k-1)-2\leq g_{CVT}(k)\leq g_{CVT}(k-1)+1\\ \Delta T_{e,\min}(\omega_{e})\leq\Delta T_{e}(\omega_{e})\leq\Delta T_{e,\max }(\omega_{e})\\ \tilde{T}_{e,\min}\leq\tilde{T}_{e}\leq\tilde{T}_{e,\max}\end{array}  \tag{19}\]  
where \(g_{CVT}\) is gear position and \(\Delta T_{e}\) is the engine torque fluctuation. The control variables are optimized within the above constraints, and the cost function of the multi-scale physical processes management is defined as:  
\[J=\int_{t_{0}}^{t_{f}}\bigg{\{}L_{e}\bigg{(}\frac{1}{\eta_{e}}\bigg{)}+L_{m}[ SOC(\tau)-SOC_{r}(\tau)]+L_{u}\bigg{(}\dot{T}_{e}\bigg{)}\bigg{\}}d\tau \tag{20}\]  
where \([t_{0},t_{f}]\) is the time domain for prediction, and \(L_{e},L_{m},L_{u}\) are the weight coefficients for engine efficiency, the target SOC\({}_{r}\) tracking and engine torque fluctuation. The reference SOC\({}_{r}\) is calculated according to the vehicle power:  
\[SOC_{r}=SOC_{ini}-(K\cdot P_{v})\cdot[SOC_{ini}-SOC_{L}] \tag{21}\]  
where SOC\({}_{ini}\), SOC\({}_{L}\) are the initial SOC and the minimum SOC, \(K\) is the proportionality factor, and \(P_{v}\) is the vehicle's demand power. In order to extend the high-efficiency operating range of the engine, the engine efficiency weight \(L_{e}\) was improved through reinforcement learning (RL), which has the ability to learn anthropomorphic behavior:  
\[