## 3 Wireless Power Transfer System in Seawater
### Power Loss of Coreless Coupler  
Figure 5a is a three-dimensional model of a coreless coupler; the transmitter and receiver are only composed of coils. For the wireless power transfer system in the air, the loss of the coreless coupler is mainly caused by the AC resistance of the coils, which is defined as a copper loss. However, when it comes to the application in the seawater environment, due to the conductivity of seawater, the alternating electric field generated by the coils will cause additional power consumption in the seawater, which is eddy current loss. The eddy current loss in the seawater will reduce the ability of the WPT system to transmit power, resulting in a decrease in transmission efficiency. According to [PERSON]'s law, the eddy current loss can be expressed by  
\[P_{eddy}=\int_{V}\mathbf{E}_{T}\mathrm{J}dV=\int_{V}\sigma\mathbf{E}_{T}^{2}dV \tag{10}\]  
where \(V\) is the area where eddy current loss occurs. From (10), we can see that the eddy current loss is directly related to electrical conductivity. The conductivity of seawater is 3-5 S/m while the air is non-conductive. Therefore, the seawater environment has a non-negligible eddy current loss compared with the air environment. Figure 6 shows the eddy current loss distribution of the external environment of the coupler in air and seawater; there is a noticeable loss in the seawater environment but no loss in an air environment. In Figure 6a, there is no eddy current loss around the coupler since the air does not conduct electricity. In Figure 6b, the alternating magnetic field around the coupler causes eddy current loss in the seawater due to the conductivity of seawater. The red area indicates where the loss is greatest, and the blue area indicates no loss. Therefore, we must consider the eddy current loss when designing the underwater wireless power transfer system. Figure 5: Three-dimensional model of coupler. (**a**) Coreless coupler. (**b**) Coupler with ferrite core. From (10), we can also see that the eddy current loss is proportional to the square of the modulus of the electric field intensity, while the electric field intensity is greatly affected by the operating frequency, the permeability of the medium the electrical conductivity and the coil structure. We obtained the relationship between the eddy current loss in the seawater environment and the frequency through simulation, as shown in Figure 7. The parameters of the coupler model used in the simulation are: the outer diameter of the transmitter and receiver is 250 mm and 200 mm, respectively. The number of turns of the transmitter and receiver is 10 and 8, the distance between the turns is 2 mm, the gap between the transmitter and receiver is 20 mm, the coils are wound with litz wire with a diameter of 4 mm and the excitation current of the transmitter and receiver is 10 A and 8 A. Figure 7 indicates that the eddy current loss rises as the resonant frequency increases. Therefore, the operating frequency of the magnetically coupled wireless power transfer system used in the seawater environment should not be too large to avoid large eddy current loss. Figure 6: Eddy current loss distribution. (**a**) Air environment. (**b**) Seawater environment. The change in the coil structure will cause the change in the magnetic field distribution, which will affect the integration result of the eddy current loss. Therefore, the influence of the coil structure should be considered when designing the coupler for wireless charging in the underwater environment, and a structure that can achieve high-efficiency transmission should be selected. We can calculate the electric field intensity in the space by changing the distance between each turn of the coils, then obtain the eddy current loss of the WPT system. However, adjusting the distance between each turn of the coils not only affects the distribution of the magnetic field in the space but also affects the self-inductance and mutual inductance of the coils.