## 2 Models and Methods  
To address the impact of mutual inductance variation on the output voltage, a DC-DC converter is cascaded after the diode rectifier of the WPT system to achieve constant voltage output. The adjustment ranges of the input resistance and output voltage of DC-DC converters with different topologies are shown in Table 1, where \(R_{\text{L}}\) is the load resistance; \(U_{\text{in}}\) is the DC-DC converter input voltage; and \(D\) is the duty cycle. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Topology** & **Output Voltage** & **Input Resistance** \\ \hline Buck & \(DU_{\text{in}}\) & \(R_{\text{L}}/D^{2}\) \\ \hline Boost & \(U_{\text{in}}/(1-D)\) & \((1-D)^{2}R_{\text{L}}\) \\ \hline Buck–Boost & \(DU_{\text{in}}/(1-D)\) & \((1-D)^{2}R_{\text{L}}/D^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Input resistance and output voltage adjustment ranges of the typical DC–DC converters. Table 1 indicates that the Buck-Boost converter has a wider range of output voltage regulation and input resistance regulation, compared to the Buck converter and Boost converter. A larger range of output voltage regulation means that constant voltage output can be achieved within a wider range of the mutual inductance variation. Therefore, a Buck-Boost DC-DC converter is adopted in this article. Figure 1 illustrates the schematic diagram of the proposed WPT system with a cascaded Buck-Boost converter, where \(U_{\text{dc}}\) is the DC input voltage source; \(L_{1}\), \(L_{2}\), and \(M\) are the self-inductances and mutual inductance of the coupling coils; \(R_{1}\) and \(R_{2}\) are the resistances of the coils; the primary side LCC compensation network includes the inductance \(L_{\text{p1}}\), the parallel capacitance \(C_{\text{p1}}\), and the series capacitance \(C_{\text{p2}}\); \(C_{\text{s1}}\) is the secondary side compensation capacitance; \(L_{\text{f}}\) and \(C_{\text{o}}\) are the inductance and the output capacitance of the Buck-Boost converter; \(R_{\text{L}}\) is the system load resistance; \(G_{\text{1}}\)-\(G_{\text{4}}\) constitute the full-bridge inverter; \(D_{\text{1}}\)-\(D_{\text{4}}\) constitute the full-bridge rectifier; S and VD are the MOSFET and diode of the Buck-Boost converter, respectively; \(i_{\text{p1}}\), \(i_{\text{l1}}\) and \(i_{\text{l2}}\) are the inverter output current, the current in the transmit coil and receive coil, respectively; \(u_{\text{inv}}\) is the equivalent output voltage of the inverter; \(U_{\text{f}}\) is the voltage across the rectifier output capacitance \(C_{\text{f}}\); \(U_{\text{out}}\) and \(I_{\text{out}}\) are the voltage and current of the system load; and \(\varphi_{\text{opt}}\) is the calculated optimal phase shift angle. First, the RMS value of the inverter equivalent output voltage \(U_{\text{inv}}\) can be given by (1), where \(\varphi\) is the phase shift angle of the inverter. \[U_{\text{inv}}=\frac{2\sqrt{2}}{\pi}U_{\text{dc}}\cos\Bigl{(}\frac{\varphi}{2 }\Bigr{)} \tag{1}\]  
Then, the components after the secondary side compensation capacitance \(C_{\text{s1}}\) are equivalent to an equivalent resistance \(R_{\text{e}}\). Therefore, the WPT equivalent circuit model with the LCC-S compensation network can be obtained and shown in Figure 2, where \(u_{\text{rec}}\) is the rectifier input voltage, and the expression of \(R_{\text{e}}\) is given by (2). \[R_{\text{e}}=\frac{8}{\pi^{2}}\biggl{(}\frac{U_{\text{f}}}{U_{\text{out}}} \biggr{)}^{2}R_{\text{L}} \tag{2}\]  
Figure 1: Schematic diagram of the WPT system with cascaded Buck–Boost converter and the presented coordinated control method. According to the WPT equivalent circuit model in Figure 2, the KVL equation is given by (3), where \(\omega\) is the system operation angular frequency. \[\left\{