# Research on Three-Phase Wireless Power Transfer System
## 3 Experiment and Analysis
### Comsol Simulation
R is the coil diameter of the circular transmitting and receiving coils, or the side length of the square coil, and r is the wire radius. The specific process of COMSOL simulation is as follows:In the new model wizard, select the three-dimensional space, and then, according to the required physical quantities, select the appropriate circuit field and magnetic field environment. 2. According to the elements of the wireless power transfer system, the geometric model is designed and built. 3. The material properties are set for the model. The coil is selected as copper, the shielding material is set as ferrite, and the gap is set as air. 4. The boundary conditions and initial values are set to add the excitation source to the system: the input boundary and loss calculation are added to the coil and the magnetic field properties of the shielding material are set. 5. The circuit is added to the physical field option, and then the power supply resistor and capacitor are added, and the peripheral circuit of the system is built by connecting the nodes according to the circuit topology shown in Figure 2.
6. The system model grid is divided, and the grid is automatically generated according to the physical field setting in the model. The unit size is selected as the conventional size, and the circuit and magnetic field are selected as the contribution items. 7. The appropriate solver for the calculation and the physical quantities to be measured are selected, and the results of the calculations are displayed. The COMSOL simulation parameters are shown in Table 1.  
In the above COMSOL simulation, the power is constant, and the loss of the coil has been considered when calculating the efficiency. The loss mainly comes from the resistance heat shown in Formula (9). And the results show that the multi-coil structure is more efficient than a single coil when transmitting the same power. In particular, the transmission effect of the three-phase coil ring placement is better than that of the Double-D Quadrature (DDQ) coil, and the transmission effect of the three-phase ring overlapping winding coil is obviously better than that of the single-layer winding coil structure. At the same time, we also carried out a horizontal displacement COMSOL simulation on a single coil, a DDQ coil, and a three-phase overlapping coil. The relationship between coil efficiency is shown in Figure 4 when the coil transmission distance is 100 mm. When lateral offset occurs, the efficiency of a single coil decreases rapidly, while the efficiency of a DDQ coil and a three-phase coil decreases slowly. And the overall efficiency of the three-phase coil is greater than the overall efficiency of the DDQ line, and when deviating from a radius, the overall efficiency increases slightly. Therefore, an overlapping and symmetrical three-phase coil coupling mechanism is proposed in this paper, and its steady-state analysis is carried out. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Coil structure** & & & & \\
**Wire diameter r** & 2 mm & 2 mm & 2 mm & 2 mm \\
**Outer diameter R** & 150 mm & 150 mm & 150 mm & 150 mm \\
**Number of turns n** & 10 & 10 & 10 & 10 \\
**Inductance L** & 80 \(\mu\)H & 80 \(\mu\)H & 80 \(\mu\)H & 80 \(\mu\)H \\
**Shielding structure** & 400 \(\times\) 400 mm\({}^{2}\) & 400 \(\times\) 400 mm\({}^{2}\) & 400 \(\times\) 400 mm\({}^{2}\) & 400 \(\times\) 400 mm\({}^{2}\) \\
**Coil distance D** & 100 mm & 100 mm & 100 mm & 100 mm \\
**Frequency f** & 47.5 kHz & 47.5 kHz & 47.5 kHz & 47.5 kHz \\
**Efficiency n** & 93.67\% & 94.89\% & 95.12\% & 96.49\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of WPT coil structure and characteristics. The coils in this paper are arranged in a circular shape and are completely symmetrical. Compared to the existing three-coil system, the three-coil structure in this paper is closer. In addition, the mutual inductance of the coils is also completely symmetrical, which reduces the analyzing and calculating difficulty of the mutual inductance model.