A Fourier descriptor model of hysteresis loops for sinusoidal and distorted waveforms

Abstract

This work is concerned with the use of the Fourier descriptor technique for reproducing the hysteresis loop for both sinusoidal and distorted flux-density waveforms that produce minor hysteresis loops. The hysteresis curve is characterized only at discrete points. Approximating the curve by a polygon with a limited number of sides, the Fourier series coefficients of the normalized cumulative angular function are computed. The shape of the hysteresis loop for a pure sinusoidal waveform can be reconstructed easily when these coefficients are determined. The procedure can be extended for the distorted waveform by taking account of the dips in the exiting waveform that cause minor loops in the hysteresis curve. The deviation between the original curve and the generated one depends upon the number of Fourier coefficients. As the number of the Fourier coefficients used in the synthesis is increased, the generated curve becomes closer to the original one. However, the use of a large number of the Fourier coefficients requires a greater execution time.