Skin effect in Iron-Silicon steel sheets: from low inductions to saturation

High frequencies are ubiquitous in power applications: most electrical equipment such as electrical 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, lasting a few microseconds. Such minor loops can cause deep skin effect, even if the thinnest laminations (0.20 mm thick laminations or even lower) provided by steel sheets manufacturers are used. Moreover, common mode currents in the megahertz range, flowing from electrical machines windings to the machine’s chassis through capacitive effects, can be responsible of strong electromagnetic disturbances and bearing damages. A correct prediction of these high frequency phenomena is necessary for an accurate calculation of the common mode filter, requiring a magnetic model of the laminated cores adapted to high frequencies and low inductions. For power conversion applications, such as the transformers embedded in planes, the necessity to reduce the core volume, often made of high-permeability grain-oriented (HGO) materials, has increased the conversion frequency from a few hundreds of hertz to several kilohertz. However, the peak induction remains very high, to reduce the cross-sectional area of the laminations. Consequently, HGO materials can be subjected to high induction values in the kHz range. Although the problem is quite different from the low induction case, skin effect must be considered. This case is made especially complex by the material non-linearity and calls for specific models and experimental methods. In this work, we summarize recent modeling advances we have achieved in this field. We treat first the low induction case, with focus on the behavior of thin non-oriented (NO) sheets. We consider then the case of high-permeability grainoriented (HGO) sheets magnetized at high polarization values, which requires non-linear models, and we validate our predictions by magneto-optical observations of the domain wall dynamics.