## 3 The Proposed CC&OV-PT Control  
In order to suppress the low-frequency oscillations of the output voltage, a capacitor current and output voltage based pulse train, CC&OV-PT, control strategy is designed in this study. Note, that between the front-stage buck converter and the output load, there is one inverter, two contactless resonant LC circuits and one rectifier. At the beginning of each switching cycle, the output voltage of the secondary side of the WPT system is sampled and then added to the capacitor current sampled from the output side of the front-stage power converter to obtain the feedback signal \(v_{\text{o}}+\alpha i_{\text{C}}\). If \(v_{\text{o}}+\alpha i_{\text{C}}\) is less than \(V_{\text{ref}}\), the high power pulse \(P_{\text{H}}\) will be selected to drive the power switch; if \(v_{\text{o}}+\alpha i_{\text{C}}\) is greater than \(V_{\text{ref}}\), the low power pulse \(P_{\text{L}}\) will be chosen to regulate the power switch. The output voltage, inductor current \(i_{\text{L}}\) and feedback signals are illustrated in Figure 6. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Pulse \(P\)** & **Inductor Current Variation** & \(i_{\text{L}}(nT)\) **Region** & **Capacitor Voltage Variation** \\ \hline \multirow{2}{*}{\(P_{\text{H}}\)} & \multirow{2}{*}{\(\Delta i_{\text{L}}>0\)} & I, II & \(\Delta v_{\text{C}}>0\) \\  & & III & \(\Delta v_{\text{C}}<0\) \\ \hline \multirow{2}{*}{\(P_{\text{L}}\)} & \multirow{2}{*}{\(\Delta i_{\text{L}}<0\)} & I & \(\Delta v_{\text{C}}>0\) \\  & & II, III & \(\Delta v_{\text{C}}<0\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Influence of \(i_{\text{L}}(nT)\) on input voltage of inverter. Figure 5: Regions of inductor current \(i_{\text{L}}\). In Figure 6, without the capacitor current feedback, there is a phase difference of about \(\pi/2\) between the load voltage and the inductor current in the front-stage Buck converter. By introducing the capacitor current, the phase difference between the inductor current and the feedback signal \(v_{0}+\alpha i_{\text{C}}\) is much less than \(\pi/2\), which is instrumental to the timely regulation of output voltage. As listed in Table 1, when \(i_{\text{L}}(nT)\) sits in Region II, the inverter input voltage \(v_{1}\) can be increased by \(P_{\text{H}}\) and reduced by \(P_{\text{L}}\). The ripples of the inverter input voltage can be suppressed and hence the stability of the output voltage of the WPT system can be improved. In order to ensure that the inductor current is restricted in Region II, the control pulse must be correctly selected to adjust the inductor current. Namely, as the inductor current reaches the lower current boundary \(i_{\text{b1}}\), the feedback signal \(v_{0}+\alpha i_{\text{C}}\) should be less than \(V_{\text{ref}}\), and hence \(P_{\text{H}}\) is selected to increase the inductor current. As the inductor current reaches the upper current boundary \(i_{\text{b2}}\), \(v_{0}+\alpha i_{\text{C}}\) is greater than \(V_{\text{ref}}\), and hence \(P_{\text{L}}\) is selected to decrease the inductor current. Therefore, we have:  
\[\left\{ \begin{array}{l}v_{0}+\alpha i_{\text{C}}<V_{\text{ref}}\;i_{\text{L} }=i_{\text{b1}}\\ v_{0}+\alpha i_{\text{C}}>V_{\text{ref}}\;i_{\text{L}}=i_{\text{b2}}\end{array} \right. \tag{21}\]  
For the given output load voltage and current, the feedback coefficient \(\alpha\) should be configured to satisfy the following condition:  
\[\frac{v_{0}-V_{\text{ref}}}{i_{0}-i_{\text{b2}}}<\alpha<\frac{v_{0}-V_{\text{ ref}}}{i_{0}-i_{\text{b1}}} \tag{22}\]  
An example of t = \(nT\) when \(i_{\text{L}}(nT)>i_{\text{b2}}\) and \(v_{0}(nT)<V_{\text{ref}}\) is shown in Figure 6. For the traditional PT controlled Buck converter, the high power pulse \(P_{\text{H}}\) will be selected since \(v_{0}(nT)<V_{\text{ref}}\), and the inductor current will be increased to escape from Region II.