Linearization approach for symmetric hysteresis loop modelling and core loss prediction

Abstract

First, the paper proposes the method for interpolation of any experimentally obtained symmetric hysteresis loop curve (SHLC) with accuracy and computation efficiency at discrete Fourier transformation (DFT) level. Second, the method has been further developed so that, based on the family of the properly chosen and measured SHLCs, it reliably and accurately predicts an arbitrary inner SHLC. Sinusoidal magnetic flux, along with applied zero crossing sampling system, allows for the introduction of the pure linearization approach. The novelty of this approach is a direct transformation of a cosine polynomial (CP) interpolating of one SHLC over the set of equidistant nodes in the electric angle (EA) domain to the algebraic polynomial (AP) interpolating the same SHLC over the set of nonequidistant Chebyshev nodes in the magnetic flux (MF) domain, with the accuracy remaining unchanged. Based on the results of the interpolation error analyses, the SHLC measurement has been proposed for nonequidistant values of magnetic flux at the loop tip, matching the Chebyshev nodes of the second kind. This is the second novelty which enables a successful prediction of an arbitrary inner SHLC.