Magnetic Loss Versus Frequency in Non-Oriented Steel Sheets and Its Prediction: Minor Loops, PWM, and the Limits of the Analytical Approach

Abstract

The pulsewidth modulation (PWM) technique is commonly used to supply modern high-speed electrical machines. The fundamental frequency is typically in the kilohertz range, with switching frequencies of several tens of kilohertz, as determined by the new SiC- or GaAs-based power transistors modules. Switching introduces minor loops in the major hysteresis cycle, with durations of the order of $100~\mu \text{s}$ or lower, with the resulting magnetization dynamics influenced by strong skin effect. However, since these minor loops have relatively small amplitude, their constitutive equation may be described by an equivalent permeability (real or complex), depending on the mean slope of the minor loop and its static energy loss. By retrieving this permeability, the classical loss is straightforwardly calculated by analytical solution of Maxwell's equations. In this paper, we measure and calculate, according to the quasi-linear approximation for the minor loops, the magnetic energy losses of 0.194 mm thick non-oriented Fe–Si 3.2% sheets subjected to PWM induction waveform. Minor loop peak amplitudes ranging between 50 mT and 0.2 T and frequencies up to 10 kHz are investigated. The results are consistent with the proposed model, to within 5%.