## 4 Numerical Studies
### Effects of Different Key Factors on Single-Vehicle Simulation  
To analyse the effects of the initial vehicle speed, WCL length, and charging efficiency on the model performance and differences between the three passing strategies, nine scenarios are considered in this study to determine the SOC. According to Table 5, scenarios A, B, and C are constructed for different initial speeds with a fixed WCA and charging efficiency. Scenarios D, E, and F and G, H, and I are constructed for different charging area lengths and charging efficiencies, respectively. Figure 3 shows the trajectory, speed, and SOC values of CAEFVs obtained for different scenarios. Figure 3a indicates that for the CPS, the time required for CAEFVs to arrive at the intersection is approximately 65 s and that the total time required to cross the control section is approximately 70 s, while for the TPS, the vehicles arrive at the intersection in 35 s and pass through the CA in 42 s or less. For the BPS, the vehicles arrive at the intersection through the CA in 50, 53, and 56 s, which indicates that the CAEFVs driving in the TPS mode can cross the intersection faster than the vehicles using the other strategies and thus reduce the total travel time. Figure 3b, c show that the trajectory curves obtained for the BPS are more dispersed than those constructed for the TPS and that the time at which the vehicles arrive at the intersection is uncertain. The temporal trajectory curves obtained for the TPS are more concentrated, and the vehicles arrive at the intersection stop line when the traffic light changes from red to green. Meanwhile, the CPS ensures that a vehicle passes through the intersection and CA before the traffic light turns red. For BPS, the increase in the charging efficiency effectively extends the charging time of CAEFVs. Similarly, the vehicles following the TPS require less time to cross the CA. Figure 3d-f indicate that the speed of the vehicle driving in the TPS mode is generally higher than those of the vehicles driving in the other two modes and that its speed fluctuations are small. Overall, the average speed in the CPS mode is lower than those in the other two modes, especially the minimum speed. The minimum speed in the CPS mode is approximately equal to the minimum speed of the vehicle, while the minimum speeds achieved in the BPS and TPS modes amount to 4-9 and 10-15 m/s, respectively. For the CPS, a vehicle requires more charging power, which necessitates travelling at a lower speed in the charging zone. For the TPS, the charging weighting coefficient is not a major factor; therefore, driving at a lower speed is not required when passing through the wireless charging zone. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Comparative Indicator** & **No Control** & **CPS** & **BPS** & **TPS** \\ \hline Travel time (s) & 47.5 & 70 & 48 & 40 \\ Pure consumption (kWh) & 0.1442 & 0.1427 & 0.1391 & 0.0984 \\ Brake recovery power (kWh) & 0.0619 & 0.054 & 0.0528 & 0.0356 \\ Charging power (kWh) & 0.055 & 0.2628 & 0.1486 & 0.0812 \\ Passing consumption (kWh) & 0.0273 & \(-\)0.1741 & \(-\)0.0623 & \(-\)0.0184 \\ Power savings (kWh) & / & 0.2014 & 0.0896 & 0.0457 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Numerical results obtained with and without a model control strategy. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Scenario** & **Initial Velocity (m/s)** & **WCA (D1, D2) (m)** & **Charging Efficiency** \\ \hline A & 20 & \((50,250)\) & 90\% \\ B & 18 & \((50,250)\) & 90\% \\ C & 16 & \((50,250)\) & 90\% \\ D & 20 & \((50,150)\) & 90\% \\ E & 20 & \((50,250)\) & 90\% \\ F & 20 & \((50,350)\) & 90\% \\ G & 20 & \((50,250)\) & 30\% \\ H & 20 & \((50,250)\) & 60\% \\ I & 20 & \((50,250)\) & 90\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Parameters of nine different scenarios. The SOC curves of the vehicles driving in different modes are shown in Figure 3g-i. The maximum capacity of the battery is assumed to be 60 kWh with an initial SOC of 0.5.