## 3 Simulation Verification and Analysis  
In order to verify the effectiveness of the proposed method, a WPT simulation is conducted through MATLAB/Simulink. Consistent with the schematic shown in Figure 1, the simulation system consists of a DC power supply, LCC-S compensation network, transmit coil, receive coil, Buck-Boost converter, CV controller, and phase shift controller. In order to simulate the actual situation, the simulation parameter values are selected according to those of the experimental WPT prototype and shown in Table 2.  
First, simulation results of the output voltage, transmission efficiency, and phase shift angle variations are shown in Figure 3 when the load resistance changes from 20 \(\Omega\) to 40 \(\Omega\). It suggests that before the load resistance changes, the output voltage is stable at 48 V, the transmission efficiency is 90.20%, and the phase shift angle is 78\({}^{\circ}\). At 0.02 s, the load resistance changes suddenly, and after a 15 ms adjustment period, the output voltage returns to 48 V, with a transmission efficiency of 90.00% and a phase shift angle of 120\({}^{\circ}\). In addition, Figure 3 suggests that the system overshooting is 10.4% when the load resistance changes from 20 \(\Omega\) to 40 \(\Omega\). Meanwhile, the system output voltage is finally stabilized at 48 V after an adjustment time of 15 ms, which indicates that the system has good stability under variable load conditions. Simulation results of the output voltage, transmission efficiency, and phase shift angle variations are shown in Figure 4 when the mutual inductance changes from 45 uH to 35 uH. In Figure 4, when the mutual inductance is 45 uH, the system transmission efficiency is 91.50%, and the phase shift angle is 122\({}^{\circ}\). After the mutual inductance suddenly changes \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Symbol** & **Values** \\ \hline System operating frequency & \(f\) & 85 kHz \\ DC source voltage & \(U_{dc}\) & 80 V \\ Primary side compensation inductance & \(L_{p1}\) & 55.95 uH \\ Primary side parallel compensation capacitance & \(C_{p1}\) & 62.94 nF \\ Primary side series compensation capacitance & \(C_{p2}\) & 28.18 nF \\ Self-inductance of the transmit coil & \(L_{1}\) & 181 uH \\ Self-inductance of the receive coil & \(L_{2}\) & 179.24 uH \\ Resistance of the transmit coil & \(R_{L1}\) & 149 mG \\ Resistance of the receive coil & \(R_{L2}\) & 128 mG \\ Secondary side series compensation capacitance & \(C_{s1}\) & 19.5 nF \\ Switching frequency of the Buck–Boost converter & \(f_{s}\) & 50 kHz \\ Inductance of the Buck–Boost converter & \(L_{f}\) & 120 mH \\ Output filter capacitance & \(C_{0}\) & 220 μF \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter values of the developed WPT prototype. Figure 3: Simulation results of the output voltage, transmission efficiency, and phase shift angle, when the load resistance changes from 20 \(\Omega\) to 40 \(\Omega\). to 35 \(\upmu\)H, the system transmission efficiency is 90.10%, and the phase shift angle is 122\({}^{\circ}\). In addition, before and after the mutual inductance variation, the voltage across the load can be maintained at 48 V and the system works stably. Figure 4 suggests that the overshooting is 6.25% during the mutual inductance variation. Meanwhile, the system output voltage is stabilized at 48 V after a 10 ms adjustment time, which shows that the system has good stability under the variable coupling conditions. In addition. Figure 5 shows the open-loop transfer baud plot of the system after adding a constant voltage PID controller, from which can be seen that the phase angle margin is 70.1 deg, indicating that the system has good stability after adding a constant current output PID controller. Figure 4: Simulation results of the output voltage, transmission efficiency, and phase-shift angle, when the mutual inductance changes from 45 \(\upmu\)H to 35 \(\upmu\)H.  
Figure 5: Bode diagram of open-loop transfer function for constant voltage control.