Advanced magnetic hysteresis model describing polarization and frequency dependence

Abstract

In this paper a hysteresis model for electrical steel based on a numerical Fourier expansion of the magnetic field as function of magnetic polarization and frequency is proposed. The model setup relies on measured data. A single sheet tester is used for gauging hysteresis curves from minor to major loops with a frequency range starting at 50 Hz up to 250 Hz. The polarization is controlled to be cosinusoidal, as required by the standard IEC 60404-3. Whereas the magnetic polarization has a cosine waveform the corresponding magnetic field has a non-sinusoidal waveform. As a matter of the non-linear dependence between polarization and field, all harmonics are part of the magnetic field. A Fourier analysis of the magnetic field delivers harmonics as summation of cosine and sine waves. Two relationships can be found: one between the amplitudes of these waves and the amplitude of the polarization and another between the amplitudes of these waves and the frequency of the polarization. They are described via cubic spline interpolation. With an interpolation for each harmonic, the magnetic field is created as a sum of cosine and sine functions. Measured and modeled hysteresis loops are compared. The error of the model is determined. Finally, a hysteresis model for electrical steel is developed which is able to calculate a magnetic field for arbitrary polarization amplitudes and frequencies. Measured and modeled hysteresis loops are compared. The error of the model is determined. Finally, a hysteresis model for electrical steel is developed which is able to calculate a magnetic field for arbitrary polarization amplitudes and frequencies.