# Array Design and Transmitter Coils Selection for Underwater Wireless Power Transfer System
## 3 Coupling Mechanism Design and Array Switching Control Strategy
### Coupling Mechanism Design
#### 3.1.3 Receiving Coil Design  
The receiving end uses the coupling between the receiving coil and the transmitting coil to obtain electrical energy. The selection of the receiving coil size has a great influence on the transmission performance of the system, and the size ratio of the transmitting coil to the receiving coil will affect the anti-offset performance of the system. In the horizontal direction, the coupling mechanism offset mainly has three kinds of transverse displacement, longitudinal displacement, and rotational displacement. The horizontal offset of the coupling mechanism is shown in Figure 6. Among them, \(\alpha\) is the rotation offset angle, \(dx\) and \(dy\) are the transverse displacement distance and the longitudinal displacement distance respectively, and \(h\) is the height between the transmitting coil and the receiving coil. Figure 5: The transmitting array coil group. The Maxwell software used to simulate the underwater environment, and the influence of the size change between the transmitting coil and the receiving coil on the system was studied. Under the condition of different coil size ratios, when the coupling mechanism is transverse and has rotational displacement, the mutual inductance change curve between the transmitting coil and the receiving coil is shown in Figure 7.  
It should be noted that seawater, as a conductive and dielectric medium, significantly affects the UWPT system's electromagnetic characteristics. Seawater's high conductivity (\(\sigma\approx 4\) S/m) induces eddy currents in the surrounding medium during coil operation, increasing the effective series resistance of the transmitting and receiving coils and causing additional power loss. Meanwhile, its high relative permittivity (\(\epsilon_{\tau}\approx 80\)) redistributes the electromagnetic field, slightly modifying the self-inductance of individual coils and the mutual inductance between coils. To ensure accuracy, these parameters (\(\sigma=4\) S/m, \(\epsilon_{\tau}=80\)) were explicitly set in the Maxwell simulation environment during the mutual inductance analysis (Figure 7). It can be seen from Figure 7a that as the size ratio of the side length \(L_{1}\) of the transmitting coil to the side length \(L_{2}\) of the receiving coil increases, the maximum mutual  
Figure 6: Coupling mechanism offset in the horizontal direction. (**a**) Transverse displacement. (**b**) Longitudinal displacement. (**c**) Rotational displacement. Figure 7: The variation curve of mutual inductance with coil offset. (**a**) Transverse displacement. (**b**) Rotational displacement. inductance between the transmitting coil and the receiving coil increases first and then decreases, and reaches the maximum when \(L_{2}\) = 1.25\(L_{1}\). However, while \(L_{2}\) = 1.25\(L_{1}\) yields the highest mutual inductance, its anti-offset performance is not optimal. Specifically, the anti-offset range of the coil (i.e., the range over which mutual inductance remains relatively stable under misalignment) continues to expand as the size ratio \(L_{2}/L_{1}\) increases beyond 1.25. This is because larger \(L_{2}/L_{1}\) ratios result in more gradual mutual inductance variations during offset, enhancing the system's tolerance to misalignment. The same trend applies to longitudinal displacement, consistent with the transverse displacement analysis. As shown in Figure 7b, although the maximum mutual inductance still occurs at \(L_{2}\) = 1.25\(L_{1}\), further increasing \(L_{2}\) leads to a broader anti-offset range where mutual inductance fluctuations are mitigated. To quantify \"anti-offset range,\" we define it as the maximum displacement where mutual inductance \(M\) remains \(\geq\)80% of its aligned peak. For \(L_{2}\) = 1.25\(L_{1}\), \(M\) peaks at 5 \(\mu\)H, but drops to 80% (4 \(\mu\)H) at \(dx\) = 30 mm. For \(L_{2}\) = 1.75\(L_{1}\), \(M\) peaks at 4.4 \(\mu\)H, but retains 80% (3.5 \(\mu\)H) up to \(dx\) = 50 mm, almost doubling the anti-offset range.