Analyses of the coupling model combining field and circuit equations based on solenoidal coils for wireless power transfer

Abstract

A method using the coupling model combining the field and circuit equations is put forward to describe the wireless power transfer (WPT) system in this study. Hollow solenoidal resonant coils are usually excited by alternating currents in practice, doing studies related to the solutions to the solenoidal coils in alternating electromagnetic fields is important. In this study, the analytic expressions of the alternating magnetic vector potential are obtained from Maxwell's formulas for time-harmonic electromagnetic fields, and the mathematical expressions of the electric field intensity, the magnetic flux density, the induced voltage, and the mutual inductance are established for the coaxially symmetric solenoidal coils. The field-circuit coupling model is built for WPT, and the relationship between the input and output variables is obtained. The equations contain the dielectric information of the transmission space and the coils' radii and turn numbers, and can be used for analysing the dielectric effects of the space at lower or higher frequencies. The results are verified by experiments of 2-coil and 4-coil structures. The advantages of being able to analyse the distribution of the fields are illustrated by a comparison experiment with a laterally displaced coil, which is valuable to WPT design.