Abstract
A Finite Element (FE) modelling approach is presented to account for the core losses in electrical machines that are generated by higher harmonic frequencies, for example those caused by Pulse Width Modulation (PWM) switching or by space harmonics due to the machine geometry. The model builds further on a post-processing calculation tool that was recently developed to take into account the magnetic skin effect in electrical steel laminations at high frequencies, and extends this by a more detailed loss analysis of the minor hysteresis loops that are caused by the higher harmonics. Further, these tools for high-frequency loss analysis are integrated into a complete electrical machine model with separate consideration of the major and minor loops. The modelling approach relies strongly on extensive magnetic measurement data of the electrical steel, in order to accurately predict the different loss components for minor hysteresis loops as a function of the DC bias field, frequency and amplitude of the minor loop. Results from the model are shown for an automotive traction motor, illustrating the losses caused by PWM harmonics and demonstrating the relevance of including the skin effect in these calculations.
Highlights
ArcelorMittal has developed iCARe®, a specific product line of electrical steels which are optimised for automotive traction electrical machines
The presence of time- and space-harmonics, for example due to inverter-fed operation, will result in additional losses, possibly in combination with minor loops and the occurrence of skin effect in the laminations. It is the aim of this paper to present a loss modelling approach that takes into account skin effect and minor loops, whilst relying on methodologies that can be combined with commercial Finite Element (FE) software packages without the need to access FE formulations [1]
A second post-processing model was based in the time-domain, as described by Equation (7). For these first two models, skin effect was not taken into account and minor hysteresis loops were not separately analysed, they do appear as higher harmonics of the flux density and are included in the calculation of eddy current and excess losses
Summary
ArcelorMittal has developed iCARe® , a specific product line of electrical steels which are optimised for automotive traction electrical machines. The general methodology can be extended to include the effect on losses from mechanical stresses, material degradation, etc., if appropriate experimental data is available [3] When it comes to the prediction of losses caused by higher harmonics of the magnetic polarisation, the aforementioned model has its limitations as it does not take into account any skin effects within the laminations. 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] This potentially leads to an overestimate of the skin effect due to the absence of saturation. Simulations on a permanent magnet automotive traction motor are discussed
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