## 5 Simulation Analysis  
In order to verify the feasibility and effectiveness of the proposed charging system and control strategy, a simulation was performed in MATLAB/Simulink. Taking into account various factors, the required parameters are shown in Table 3 below. The grid voltage is a three-phase symmetrical voltage with an effective value of 220 V, the battery voltage is 220 V, and \(f_{T}\) is the converter switching frequency. Theoretical results of grid voltages and currents over a time frame of 0.08 s are illustrated in Figure 10. Figure 10a is the waveform in the forward direction, and Figure 10b is the waveform in the reverse direction. In the charging mode, the currents and the voltages waveforms basically change in phase  
discharging mode were measured. The slight deviation of the power factors from the unit power factor can attributed to the LC low-pass filter and tuning imperfections. In the forward transmission mode, the power can reach 1.53 kW, and it can reach 1.36 kW in the reverse transmission mode. This is because the voltage of the electric vehicle battery is relatively low compared to the grid voltage. In Figure 11, the matrix converter outputs a steady-state voltage and current waveform, which is also the steady-state voltage and current waveform of the resonant tank input. Figure 11a is the waveform in the forward direction, and Figure 11b is the waveform in the reverse direction. As can be seen from the figure, the converter realizes the conversion from low frequency to high frequency. At the same time, it can be seen that the voltage transition is always when the current is 0; that is, the on/off of the switch is performed when the current is 0, indicating that the matrix converter realizes the soft switching operation in the full range during steady state operation. It can also be seen from the figure that the current follows the change of voltage, the frequency and phase are consistent, and the converter has a high power factor. Figure 12 shows the steady-state voltage and current waveforms of the resonant loop output, and those are also the steady-state input voltage and current waveforms of the full-bridge converter. Figure 12a is the waveform in the forward direction, and Figure 12b is the waveform in the reverse direction. It can be seen that the wireless power transfer enables high power factor operation through compensation of the primary and secondary bilateral LCCL resonant tank. Full-bridge converter also  
Figure 10: Three-phase voltages and currents in (**a**) the forward direction and (**b**) the reverse direction. realizes full range soft switching operation. At the same time, it can be seen that the bilateral LCCL resonant circuit has the ability to achieve constant voltage and constant current output. Figure 13 shows the current waveforms output by the electric vehicle; Figure 13a is the waveform in the forward direction, and Figure 13b is the waveform in the reverse direction. In the forward direction, the current is negative, indicating that the electric car is charging at this time. In the reverse direction, the current is positive, indicating that the electric vehicle is discharging at this time. It can prove the feasibility of the system proposed in this paper and realize the wireless charging and discharging of electric vehicles. Figure 14 illustrates the THD of the grid current \(i_{u}\) up to the 50 th harmonic of the prototype for forward and reverse power operation against the \(\theta\), which again ranges from 6/\(\pi\) to \(\pi\)/2 in the forward direction and from \(-6\)/\(\pi\) to \(-\pi\)/2 in the reverse direction. The overall grid current's harmonic content for reverse power operation is marginally higher than that of the forward power operation; hence the THD for forward power operation is slightly lower than that of the reverse power operation, as depicted in Figure 14. The THD peaks at 4.8% and 5.1% for forward and reverse power operation, respectively, at \(|\theta|=\pi\)/6 and then maintains a steady lower trend with increasing \(|\theta|\) values.