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.DOI: http://dx.doi.org/10.5755/j01.eie.23.4.18716
Highlights
The usage of a properly selected numerical fitting method is a common characteristic of the majority of phenomenological approaches to the magnetic curves analysis and modelling
1Abstract—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
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
Summary
The usage of a properly selected numerical fitting method is a common characteristic of the majority of phenomenological approaches to the magnetic curves analysis and modelling. The interpolation method has been proposed in the symmetric hysteresis loop (SHL) modelling by M. This remarkable work does not provide an explicitly derived error estimation of a chosen set of the interpolation nodes for the measured SHLs. Secondly, the very interpolation procedure for an arbitrary SHL prediction was omitted. This work proposes the SHL measurement at nonequidistant values of magnetic flux at the loop tip matching the Chebyshev nodes of the second kind. The measurements were done for the series of 13 supply voltages matching the Chebyshev nodes of the second kind 13.81 V, 41.22 V, 67.98 V, 93.67 V, 117.88 V, 140.23 V, 160.37 V, 177.98 V, 192.78 V, 204.55 V, 213.08 V, 218.26 V, 220.00 V
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