Calculating mutual inductance of misaligned circular coils using secondary coil projection

Abstract This paper presents an analytical projection method for calculating mutual inductance between arbitrarily aligned circular coils in wireless power transfer (WPT) systems. Numerical flux calculations are performed using a novel methodology, taking the wire diameter into account to avoid any mathematical singularity and accurately represent physical reality. One of the coils is fixed whilst the projection of the secondary coil is used to determine the limits of the integration area. The vertical distances of points on the secondary coil are represented by an angle-dependent function . We use its projection d A in the primary coil plane instead of the conventional area element in the secondary plane, where the flux is to be evaluated. Moving the integration domain to the projection significantly reduces numerical and analytical complexity, thereby decreasing computational time.