# A Method to Reduce Eddy Current Loss of Underwater Wireless Power Transmission by Current Control
## 4 Electromagnetic Field Simulation Analysis and Discussion
### Change Current Phase Difference  
Since there is no phase loss in the air medium, the phase of the field intensity excited by the coil and its current phase difference is fixed at 90\({}^{\circ}\), so the phase difference of the coil excitation field strength depends on the phase difference of their current. According to Equation (37), it can be seen that increasing the field strength phase difference between the primary and secondary sides can reduce the eddy current loss; in other words, it can increase the current phase difference between the primary and secondary sides. In order to achieve this goal, there are three methods that can be adopted: the primary side resonates and the secondary side does not resonate, the primary and secondary sides do not resonate, and the secondary side resonates and the primary side does not resonate. The latter two methods will cause the current in the primary side circuit to flow back into the power supply, causing additional loss and harm to the inverter, while the primary side circuit of the first method is purely resistive and will not cause harm to the inverter. Although the secondary side circuit is not resonant, it can enter the load after current regulation and voltage stabilization, which is relatively safe as a whole. Therefore, we selected the first method in this paper. When the frequency is 200 kHz and the output current on the equivalent load resistance is equal to 1A, we change the parameters of the compensation circuit to adjust the phase difference \(\Delta\varphi\) of the primary side and secondary side. We can obtain the electric field intensity distribution, energy loss density distribution, and AC-AC efficiency \(\eta\), as shown in Figure 10. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Meaning** & **Value** \\ \hline \multirow{2}{*}{d} & Distance between two planar power transmission & \\  & coils/mm & 103 \\ \hline \multirow{2}{*}{r} & Inner radius of coil/mm & 50 \\ \hline \multirow{2}{*}{r\({}_{\text{line}}\)} & Radius of line/mm & 1.5 \\ \hline \multirow{2}{*}{n} & Turns of coils & 19 \\ \hline \multirow{2}{*}{f} & Frequency/kHz & 200, 300 \\ \hline \multirow{2}{*}{\(\mu_{\text{air}}\), \(\eta_{\text{seawater}}\), \(\eta_{\text{copper}}\)} & Relative permeability for air, seawater, and copper & 1, 1, 0.99990 \\ \hline \(\sigma_{\text{air}}\), \(\sigma_{\text{seawater}}\), \(\sigma_{\text{copper}}\) & Conductivity for air, seawater, and copper/(S/m) & 0, 4.5, 5.998 \(\times\) 10\({}^{7}\) \\ \hline \(\varepsilon_{\text{air}}\), \(\varepsilon_{\text{seawater}}\), \(\varepsilon_{\text{copper}}\) & Relative permittivity for air, seawater, and copper & 1, 81, 1 \\ \hline \multirow{2}{*}{R\({}_{\text{L}}\)} & Equivalent load resistance/\(\Omega\) & 30 \\ \hline \multirow{2}{*}{R\({}_{\text{ot}}\)} & Equivalent resistance of rectifier circuit and filter & \\  & circuit/\(\Omega\) & 0.1 \\ \hline \multirow{2}{*}{R\({}_{\text{in}}\)} & Equivalent internal resistance/\(\Omega\) & 0.2 \\ \hline \multirow{2}{*}{R\({}_{\text{P}}\)} & Primary side coil resistance/\(\Omega\) & 1.7 \\ \hline \multirow{2}{*}{L\({}_{\text{P}}\)} & Primary side coil inductance/uH & 63.45 \\ \hline \multirow{2}{*}{R\({}_{\text{S}}\)} & Secondary side coil resistance/\(\Omega\) & 1.7 \\ \hline \multirow{2}{*}{L\({}_{\text{S}}\)} & Secondary side coil inductance/uH & 64.49 \\ \hline \multirow{2}{*}{M\({}_{\text{sea}}\)} & Mutual inductance in seawater/uH & 13.31 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The meanings and value of parameters in simulation. Figure 10: _Cont_. Figure 10: Electric field intensity, energy loss density, and AC-AC efficiency under different phase differences.