## 3 Methodology  
### Energy Consumption and Wireless Charging Model for CAEFVs  
Because the vehicle speed and acceleration data can be easily obtained from the intelligent transportation system, this study uses a physical model proposed by [PERSON] et al. [33], which is a backward-structured EFV-ECM, to calculate the energy consumption of EVs. It utilises the instantaneous speed, acceleration, and road gradient as the input parameters and the instantaneous power or energy consumption as the output and calculates the instantaneous energy consumption and power state of the vehicle by inputting the speed and acceleration data obtained every second.  
\[P_{W}(t)=\Big{[}m_{total}\cdot a(t)+mgcos(\theta)\cdot\frac{c_{r}}{1000}(c_{1} v(t)+c_{2})+\frac{1}{2}\rho_{air}\cdot A_{f}\cdot c_{d}\cdot v^{2}(t)+mgsin( \theta)\Big{]}v(t), \tag{1}\]  
where \(m_{total}=m_{v}+m_{p}\) is the actual mass of the vehicle, with \(m_{v}\) being the vehicle tare and \(m_{p}\) the payload; \(v(t)\) is the vehicle speed at moment \(t\); \(a(t)\) is the vehicle acceleration at moment \(t\); \(g\) is the acceleration of gravity; \(\theta\) is the road grade; \(c_{r}\), \(c_{1}\), and \(c_{2}\) are the rolling resistance parameters; \(\rho_{air}\) is the air mass density; \(c_{d}\) is the aerodynamic drag coefficient; and \(A_{f}\) is the front area of the vehicle.  
After determining the instantaneous power \(P_{W}(t)\) at the wheels, the traction power \(P_{T}(t)\) and regenerative braking power \(P_{R}(t)\) of CAEFVs are obtained based on the positive and negative \(P_{W}(t)\) values.  
\[\begin{cases}P_{T}(t)=(P_{W}(t)+\rho_{Aux})/(\eta_{m}\cdot\eta_{d}\cdot\eta_{ b})\;\;if\;P_{W}(t)\geq 0\\ P_{R}(t)=-(P_{W}(t)+\rho_{Aux})\cdot(\eta_{m}\cdot\eta_{d}\cdot\eta_{b}\cdot \eta_{RB}(t))\;if\;P_{W}(t)<0,\end{cases} \tag{2}\]  
where \(\rho_{Aux}\) is the power of the auxiliary system, \(\eta_{EM}\) is the motor efficiency factor, \(\eta_{DL}\) is the transmission efficiency factor, \(\eta_{BAT}\) is the battery efficiency factor, and \(\eta_{RB}(t)\) is the regenerative braking energy efficiency factor determined for the studied vehicles at time step \(t\). The \(\eta_{RB}(t)\) function is related to the instantaneous acceleration of the vehicles, in accordance with [32].  
\[\eta_{RB}(t)=\begin{cases}e^{-\frac{\alpha}{|a(t)|}}\;\;if\;a(t)<0\\ \;\;0\;\;if\;a(t)\geq 0,\end{cases} \tag{3}\]  
where \(\alpha\) is the specific parameter of \([0,1]\).  
Integrating \(P_{T}(t)\) and \(P_{R}(t)\) over time enables the calculation of the traction energy-consumption \(E_{Con}\) and regenerative braking response energy \(E_{Re}\) for the entire period as follows:  
\[\begin{cases}E_{Con}=\int_{t_{0}}^{t_{f}}P_{T}(t)d_{t}\\ E_{Re}=\int_{t_{0}}^{t_{f}}P_{R}(t)d_{t},\end{cases} \tag{4}\]where \(t_{0}\) is the initial moment when the vehicle enters the CA, and \(t_{f}\) is the terminal moment when the vehicle leaves the CA.  
In addition to the energy-consumption model of CAEFVs, it is necessary to define the SOC during wireless charging in the WSCCI and calculate the WCL supplementary energy. Without considering the effect of the vehicle speed on the charging power and charging power variations due to grid voltage fluctuations, this study assumes that the wireless charging power \(P_{C}\) is a constant [46; 47]. In this case, the wireless charging model of CAEFVs can be expressed as follows:  
\[E_{C}=\mu\cdot P_{C}\cdot T_{C}, \tag{5}\]  
where \(E_{C}\) is the wireless charging power, \(\mu\) is the charging efficiency, and \(T_{C}\) is the wireless charging time.  
The charge state of CAEFVs in the CA can be calculated via the following formula:  
\[SOC_{CA}=SOC_{t_{0}}-\frac{E_{Cm}-E_{Re}-E_{C}}{C_{b}}, \tag{6}\]  
where \(SOC_{t_{0}}\) is the SOC of the vehicles at the start of the CA, and \(C_{b}\) is the cell capacity.