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

Abstract

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 coil turns exposed to different conductive regions, providing a general formulation applicable to various scenarios. From the circuit perspective, ECLs appear as additional resistances in both primary and secondary coils, as well as a newly introduced mutual resistance that contributes to power loss. To derive the general formulas for these additional resistances, the electric field intensities are calculated by solving the Helmholtz equation in different surrounding environments, considering geometric parameters such as number of turns, coil radii, and spacing between turns. Three common scenarios in underwater applications are selected to provide a thorough understanding of ECLs. For each scenario, boundary conditions are properly defined, and the additional resistances are explicitly computed. Finite Element Method (FEM) simulations and physical measurements are conducted to validate the analytical formulation. The results confirm high accuracy and reliability of the model—it effectively captures how geometric coil parameters influence added resistances, accurately predicts the effect of increasing source frequency, and demonstrates how eddy current impacts vary with the volume of the conductive medium.