# Array Design and Transmitter Coils Selection for Underwater Wireless Power Transfer System
## 3 Coupling Mechanism Design and Array Switching Control Strategy
### Transmitting Array Switching Control Strategy Based on Receiving Coil Position Estimation
#### 3.2.2 Simulation Verification  
Because the effect of longitudinal displacement is similar to that of transverse displacement, the simulation study of longitudinal displacement is omitted. Therefore, based on the above analysis, this section combines Maxwell-Simplorer-Simulink to build a simulation system, selects seawater as the transmission medium, and verifies the initial position estimation method of the receiving coil and the effectiveness of the transmitting array switching control strategy in the case of transverse displacement and two-dimensional offset. The simulation parameters are shown in Table 1.  
For context, \(M_{\text{TX}}\) = 1.46 uH (adjacent transmitter coils) is 29% of the peak transmitter-receiver mutual inductance \(M_{(x,\,y)}\approx\) 5 uH (from Figure 7). This moderate coupling is accounted for in calculations but remains small enough to validate the single-coil strategy, as unpowered coils induce minimal voltage compared to active coupling. (1) Parallel misalignment  
When the receiving coil RX is shifted laterally from the top of the transmitting coil TX(2, 2) to the top of the TX(2, 3), the change of the RX trajectory of the receiving coil and the reflection impedance of the receiving end is shown in Figure 11.  
It can be seen from Figure 11 that the transmitting coil TX(2, 2) is powered at the beginning, and \(Z_{\max}\) = \(Z_{(2,\,2)}\) at this time, while \(Z_{(2,\,2)}\) gradually decreases with the RX offset. When the transverse displacement distance \(dx\) = 100 mm, \(Z_{\max}\) = \(Z_{(2,\,2)}\) = \(Z_{(2,\,3)}\). As the transverse displacement distance \(dx\) continues to increase, \(Z_{(2,\,3)}\) > \(Z_{(2,\,2)}\). At this time, \(Z_{\max}\) = \(Z_{(2,\,3)}\), the receiving coil is offset above the transmitting coil TX(2, 3), and the transmitting array is switched to the transmitting coil TX(2, 3) for power supply. After that, \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline \(L_{\text{a}}\) & 25.703 uH \\ \(L_{\text{b}}\) & 66.275 uH \\ \(C_{\text{b}}\) & 52.899 nF \\ \(R_{\text{a}}\) & 0.5 \(\Omega\) \\ \(R_{\text{b}}\) & 0.5 \(\Omega\) \\ \(R_{\text{L}}\) & 20 \(\Omega\) \\ \(M_{\text{TX}}\) & 1.46 uH \\ \(C_{\text{a}}\) & 136.401 nF \\ \(U_{\text{in}}\) & 24 V \\ \(f\) & 85 kHz \\ \hline \end{tabular}
\end{table} 
Table 1: Experimental Parameters. \(dx\) continues to increase, and \(Z_{\max}\) is always equal to \(Z_{(2,3)}\), without switching the power supply coil. Notably, the \(Z_{\max}\) tracking strategy leverages relative comparison of reflection impedances between the active coil and its neighbors, rather than absolute impedance values. This approach inherently reduces sensitivity to measurement noise and environmental variations (e.g., seawater conductivity drift), as such factors affect all coils uniformly and preserve the relative \(Z_{(x,y)}\) relationships critical for accurate tracking. The simulation results show that the transverse displacement of the receiving coil proposed in this paper can achieve the optimal transmitting coil switching control. (2) 2D Migration  
When the receiving coil RX is shifted from the top of the transmitting coil TX(2, 2) to the top of the TX(1, 3), the change of the receiving coil RX trajectory and the receiving end reflection impedance is shown in Figure 12.  
Figure 11: Simulation result of lateral migration. (**a**) Receiving coil motion trajectory. (**b**) Receiver reflection impedance curve. Figure 12: 2D migration simulation results. (**a**) Receiving coil motion trajectory. (**b**) Receiver reflection impedance curve. It can be seen from Figure 12 that the transmitter coil TX(2, 2) is powered at the beginning, and \(Z_{\text{max}}=Z_{\text{(2, 2)}}\). As RX moves, \(Z_{\text{(2, 2)}}\) gradually decreases. When the offset distance \(dx=dy=100\) mm, \(Z_{\text{max}}=Z_{\text{(2, 2)}}=Z_{\text{(1, 2)}}=Z_{\text{(2, 3)}}\). As the offset distance \(dx\) and \(dy\) continue to increase, \(Z_{\text{(1, 2)}}\) and \(Z_{\text{(2, 3)}}\) are gradually larger than \(Z_{\text{(2, 2)}}\).