# Design of WPT System Based on Interleaved Boost Converter
## 4 Stress Analysis and Parameter Design  
The stress of passive components includes voltage stress and current stress. Excessive voltage stress is not conducive to the selection of compensation capacitors and the safe operation of the system. Excessive current stress and large loss on the coils are not conducive to the improvement of system efficiency. When the winding area of a loosely coupled transformer is fixed, the coupling coefficient between the primary and secondary sides generally does not change. Through simulation analysis, the coupling coefficient before and after the offset of the loosely coupled transformer in this paper changes from 0.10686 to 0.0778. Next, this paper designs the self-inductance of the primary and secondary sides according to the voltage stress and current stress. Since the system is a WPT system with a miniaturized secondary side, the optimization range of primary side self-inductance is 500-1500 \(\mu\)H. The optimization range of the secondary side self-inductance value is 100-500 \(\mu\)H. The  
Figure 4: The equivalent circuit of the proposed WPT system. Figure 5: The voltage and current waveforms at each node of the system in an aligned case. relationship between the primary side current \(I_{\text{LP}}\) and other circuit parameters can be obtained as follows:  
\[I_{\text{LP}}=\frac{2\sqrt{2}}{\text{j}\omega k\pi\sqrt{L_{\text{P}}L_{\text{S}}} }U_{\text{O}} \tag{17}\]  
According to Equation (17), the contour image of the change of the primary side current with self-inductance when the primary and secondary sides are aligned and offset to the farthest distance (i.e., the coupling coefficient is reduced to the lowest value) can be drawn, as shown in Figure 6. In order to reduce the loss, the value of primary side current is generally less than 5 A. When the primary and secondary sides are offset, the current of the primary side increases significantly. In order to integrate the two situations before and after the offset, the 5 A contour line after the offset is retained, that is, the purple curve in Figure 6b. The secondary side current has nothing to do with the self-inductance of the primary and secondary sides, and the RMS is 5.55 A. In a WPT system with a miniaturized secondary side, the parasitic resistance of the secondary side coil is generally small, so the current value is within a reasonable range. In this paper, the voltage stress at both ends of the compensation capacitor on the primary and secondary sides is analyzed. The peak value of the voltage \(U_{\text{C1}}\) of the compensation capacitor \(C_{1}\) is:  
\[U_{\text{C1}}=\frac{4L_{\text{P}}U_{\text{O}}}{k\pi\sqrt{L_{\text{P}}L_{\text{ S}}}} \tag{18}\]  
According to Formula (18), the change of \(U_{\text{C1}}\) with the self-inductance of the primary and secondary sides before and after the offset can be drawn, as shown in Figure 7. When the primary and secondary sides are offset, the voltage across \(C_{1}\) increases significantly. In order to synthesize the two situations before and after the offset, the 4 kV contour line after the offset is retained in this paper, the voltage across \(C_{1}\) is less than 4 kV. The relationship between the voltage \(U_{\text{C2}}\) on the compensation capacitor \(C_{2}\) and the parameters in the circuit is:  
\[U_{\text{C2}}=\sqrt{2}\text{j}\omega L_{\text{S}}I_{\text{LS}} \tag{19}\]  
Similarly, the change of \(U_{\text{C2}}\) with the self-inductance of the primary and secondary edges can be drawn, as shown in Figure 8. According to Equation (19), \(U_{\text{C2}}\) is only related to the primary edge self-inductance \(L_{\text{S}}\). In the secondary side-miniaturized WPT system, the secondary side self-inductance is relatively small, so the impedance of the secondary side compensation capacitor is small, and the limit of \(U_{\text{C2}}\) can be appropriately reduced. In this paper, the limit of \(U_{\text{C2}}\) is 1.5 kV. Through the stress limit of passive devices, the stress limit area surrounded by three stress contours can be obtained.