# Calculations of eddy currents in electrical steel sheets taking into account their magnetic hysteresis

Zbigniew Szular (Institute of Electromechanical Energy Conversion, Cracow University of Technology, Krakow, Poland)
Witold Mazgaj (Institute of Electromechanical Energy Conversion, Cracow University of Technology, Krakow, Poland)

ISSN: 0332-1649

Article publication date: 15 July 2019

Issue publication date: 14 August 2019

## Abstract

### Purpose

The purpose of this paper is to present the method which relatively easily allows to approximate the hysteresis loop of the dynamo or transformer steel sheets. The paper also looks into the formulation of an equation allowing determination of distribution of the flux density and eddy currents in cross-section of these sheets.

### Design/methodology/approach

An exponential function was applied in the presented method relating to the approximation of the hysteresis loop. When the field strength changes its value, then, the flux density are the sum or difference of a function, describing the lower or upper hysteresis curve and some “ransient” component. On the basis of Maxwell’s equations and Amper’s law, one non-linear differential equation was formulated which allows to calculate the flux density and eddy currents in a cross-section of a transformer sheet.

### Findings

The method which relatively easily allows approximation of the hysteresis loop of ferromagnetic material is presented in the paper. The paper presents the derivation of one non-linear differential equation, allowing calculation of the flux density and eddy currents in the cross-section of the transformer sheets, taking into account the hysteresis phenomenon.

### Practical implications

The paper presents the method that can be used in modeling of the hysteresis loops of dynamo or transformer sheets, and the final non-linear differential equation can be applied in calculations of the magnetic field and eddy currents in cross-section of the transformer sheets.

### Originality/value

The paper refers to important issues of modeling and calculations of the magnetic and eddy current field distribution in transformer steel sheets.

## Citation

Szular, Z. and Mazgaj, W. (2019), "Calculations of eddy currents in electrical steel sheets taking into account their magnetic hysteresis", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 38 No. 4, pp. 1263-1273. https://doi.org/10.1108/COMPEL-10-2018-0424

## Publisher

:

Emerald Publishing Limited

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