# Research on Three-Phase Wireless Power Transfer System
## 2 Topology of WPT System  
The leakage inductance and excitation inductance of the wireless charging coil in practical applications are very high, which makes the whole coil strongly inductive. Therefore, the coil needs to absorb a large amount of reactive power before transmitting the active power to the load. The reactive current in the circuit is large, and the loss of the converter also increases. In order to avoid this situation, the compensation network model can be introduced to eliminate the reactance parameters in the circuit of the transmitting end and the receiving end and effectively offset the reactive power generated by the inductance coil, so as to improve the output power factor of the system, the transmission efficiency, and the load power. Therefore, this section mainly analyzes the topology of the wireless charging system. The most common compensation schemes for wireless coils typically consist of four types of topological compensation structures: S-S type, S-P type, P-S type, and P-P type, as shown in Figure 1. Notably, in transmission systems with only S-S type and S-P type topologies, \(R_{L}\) will not be affected by the value of \(C_{p}\), and the fluctuation of \(R_{L}\) at the receiving end will not affect the resonant frequency of the transmitting end. Moreover, the S-S type topology can withstand greater power, and the structure is simple and easy to implement. Therefore, the S-S topology is selected in this paper. According to the proposed three-phase wireless power transfer system, the three-phase coil adopts the Y-Y connection method, and the topology shown in Figure 2 is built. The topology of the three-phase wireless power transfer system is mainly composed of a DC power supply, an inverter circuit, a three-phase coupling mechanism, and a load. The three-phase high-frequency inverter is composed of six MOSFETs (\(S_{1}\)-\(S_{6}\)), and the \(U_{dc}\) is the DC input voltage source for its power supply. \(L_{p}\) and \(L_{s}\) are the self-inductance of the transmitting coil and the receiving coil, respectively, and \(R_{p}\) and \(R_{s}\) are the corresponding coil resistances, respectively. \(C_{p}\) is the transmitting side compensation capacitor in series with \(L_{p}\), and \(C_{s}\) is the receiving side compensation capacitor in series with \(L_{s}\). The full-bridge uncontrolled rectifier on the load side consists of six diodes (\(D_{1}\)-\(D_{6}\)). The three-phase coil adopts a Y-Y connection, and the capacitance value is  
\[C=\frac{1}{\omega^{2}L} \tag{1}\]  
where \(L\) is the inductance of coils, \(L=L_{s}=L_{p}\). Figure 3 is the equivalent model of the three-coil WPT system. In the three-coil wireless power transfer system, each coil has its own self-inductance, and they also interact with each other through the magnetic field to generate mutual inductance. According to  
Figure 1: Four resonant compensation circuit topologies: (**a**) S-S type; (**b**) S-P type; (**c**) P-S type; (**d**) P-P type. Figure 2: Topology of three-phase wireless power transfer system. [PERSON]'s voltage law, the mutual inductance model of the three-phase wireless charging system shown in Formula (2) can be obtained, which shows the electromagnetic induction relationship amongst the three coils and the energy transmission mechanism between them. By utilizing this model, in-depth research can be conducted into the design, layout, and control of the coils in the wireless power transfer system, which enables the achievement of high-efficiency energy transmission. \[\left[ \begin{array}{c}U_{a}\\ U_{b}\\ U_{c}\end{array} \right]=\left[ \begin{array}{ccc}Z_{p}&jwM&jwM\\ jwM&Z_{p}&jwM\\ jwM&jwM&Z_{p}\end{array} \right]\cdot\left[ \begin{array}{c}I_{a}\\ I_{b}\\ I_{c}\end{array} \right]+\left[ \begin{array}{ccc}-jwM_{X1}&-jwM_{X}&-jwM_{X}\\ -jwM_{X}&-jwM_{X}&-jwM_{X}\\ -jwM_{X}&-jwM_{X}&-jwM_{X1}\end{array} \right]\cdot\left[ \begin{array}{c}I_{A} \\ I_{B}\\ I_{C}\end{array} \right] \tag{2}\]  
\[ \begin{bmatrix}0\\ 0\\ 0\end{bmatrix} =\left[