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

Abstract

The Pulse Width 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 µs 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 the Maxwell's equations. In this work, 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%.

Iron Loss Modelling of Electrical Traction Motors for Improved Prediction of Higher Harmonic Losses

“…In the absence of skin effect, the instantaneous classical loss p class (t), which is due to a homogeneous distribution of eddy currents flowing in the lamination, is given by [10,12]:…”

“…When the material exhibits a linear permeability and when a sinusoidal excitation is applied, it is possible to find an analytical solution for Equation (9) [10]:…”

“…where ω is the electrical pulsation, and B p is the peak value of the average flux density through the material. The resulting eddy current loss density can then be calculated as follows [10]:…”

“…Such an analysis can easily be implemented as a postprocessing operation to the main 2D FE model using standardly available dynamic solvers. Alternatively, when it is acceptable to assume linear material properties and adopt a constant permeability, closed-form analytical equations can be used to predict the flux re-distribution and eddy current losses [10,11]. However, this potentially leads to an overestimate of the skin effect due to the absence of saturation.…”

“…In [17], hysteresis, excess and eddy-current losses associated with each minor loop are calculated based on the loss coefficients that were obtained for the major loop, without additional tuning factor. The bias field at which minor loops occur and the skin effect that appears at high frequencies is accounted for in [10], where a linear analytical model is used to predict flux redistribution within the lamination. Hysteresis and eddy current losses are then calculated based on the calculated flux distribution within the lamination.…”