A Detailed Analytical Modeling of Eddy Current Losses in an Underwater Medium for Wireless Power Transfer

Eddy current loss (ECL) in underwater wireless power transfer (UWPT) systems can significantly affect the efficiency of underwater vehicles. This study provides comprehensive modeling of the eddy current effects in circular planar coils. The analytical model has been extended to any number of transmitter and receiver coils' turns exposed to different conductive regions, providing a general formulation applicable to various scenarios. From the circuit perspective, ECLs appear as the additional resistances in both primary and secondary coils, as well as the newly introduced mutual resistance that in turn contributes to power loss. To derive the general formulas for additional resistances, the electric field intensities are calculated by solving the Helmholtz equation within different surrounding environments, considering geometrical parameters such as the number of turns, coil radii, and spacing between turns. Three frequently occurring scenarios in underwater applications are selected to provide a comprehensive understanding of ECLs. The general formulas are solved by properly defining the boundary condition, and then the additional resistances are calculated specifically for each scenario. Finite Element Method (FEM) simulations and measurements are conducted to validate the analytical formulation. The results confirm the high accuracy and reliability of the model. It effectively captures the impact of changes in the geometrical parameters of the coils on additional resistances, well predicts the effect of increasing the input source frequency, and demonstrates how the effects of eddy currents change with the volume of the surrounding conductive medium.