Quasi-Stationary Approximation of Dynamic Inductive Wireless Power Transfer

Dynamic Inductive Wireless Power Transfer (DIWPT), used for charging and powering electric vehicles (EVs), has been presented lately as a solution for increasing the distance range of electric vehicles and reducing the utilization of heavy and bulky battery systems. In most DIWPT designs, the voltage induced by the movement of the receiving coil over a time-varying magnetic field is neglected and never quantified. In this work, a simplified phasor expression for the total induced voltage on a coil that is moving in a sinusoidal time-variant magnetic vector field is developed. If no rotation is observed in the coil, a 90◦ out of phase voltage component proportional to the speed of the coil is added to the induced voltage that would be calculated if the coil was stationary. The phase of this voltage component is delayed or advanced with respect to the stationary induced voltage, according to whether the coil is moving into or out of a region of higher magnetic ux. Then, under some assumptions on the geometry of inductive coil configurations, it is possible to estimate the minimum induction frequency for which the quasi-stationary approximation can be considered. The resulting frequency value for a representative geometry is calculated, indicating that, for automotive applications, the relative error in the induced voltage is actually negligible, except in the vicinity of the points of zero-crossing in the magnetic ux, where the absolute value of the induced voltage is low anyway.