Skin effect and losses in soft magnetic sheets: from low inductions to magnetic saturation

High frequencies are ubiquitous in present-day power applications: most electrical equipment, like rotating machines, are supplied by Pulse Width Modulation (PWM) switching inverters, often working at tens or hundreds of kilohertz. PWM is responsible of minor cycles along the major hysteresis loop of the magnetic core, lasting a few microseconds. Such minor loops can cause deep skin effect, even if the thinnest today available laminations (0.1 - 0.2 mm thick sheets) are used. Common mode currents in the megahertz range, flowing from the electrical machine windings to the machine chassis through capacitive effects, can engender strong electromagnetic disturbances and bearing damages. A correct prediction of high frequency phenomena is necessary, for example, for the accurate calculation of common mode filters, requiring a magnetic model of the laminated cores suited to high frequencies and low induction values and the ensuing dramatic skin effect. For power conversion applications, such as embedded planar transformers, the mandatory reduction of volume and cross-sectional area of the core, often made of high-permeability grain-oriented (HGO) sheets, imposes the increase of the conversion frequency from a few hundred hertz to several kilohertz and high peak induction values. The skin effect in this case is affected by the non-linear saturable magnetic response of the material and its treatment requires non-trivial experimental methods and modeling approaches. In this work, we discuss physically based modeling of magnetization process and energy loss in magnetic sheets at high frequencies. We focus first on the low induction regimes occurring in thin non-oriented (NO) Fe-Si laminations. We consider then the case of high inductions, as encountered in power conversion devices using NO, HGO, and Fe-Co alloys, where non-linear models, possibly validated by magneto-optical observations of the domain wall dynamics, are developed and implemented.