Approximation of Hysteresis Changes in Electrical Steel Sheets

Abstract

This paper describes a simple method of approximating hysteresis changes in electrical steel sheets. This method is based on assumptions that flux density or field strength changes are a sum or a difference of functions that describe one curve of the limiting hysteresis loop and a certain ‘transient’ component. Appropriate formulas that present the flux density as functions of the field strength and those that present inverse dependencies are proposed. An application of this approximation requires knowledge of the measured limiting hysteresis loop and a few minor loops. Algorithms for determining changes in the flux density or field strength are proposed and discussed. The correctness of the proposed approximation of hysteresis changes was verified through a comparison of measured hysteresis loops with the loops calculated for several different excitations of the magnetic field occurring in dynamo and transformer steel sheets. Additionally, an example of the application of the proposed approximation of hysteresis changes is discussed in the paper. The proposed approximation of hysteresis changes is recommended for numerical calculations of the magnetic field distribution in dynamo and transformer steel sheets.

Modelling of magnetisation processes in transformer steel sheets

“…As mentioned in the introduction, the magnetic hysteresis can be taken into account in the methods based on the integral form of Maxwell's equations. The dependences between the magnetic flux density and field strength for individual elementary segments of the division of the magnetic field area are introduced into the equations of the magnetic field distribution [29].…”

“…However, both models have disadvantages, as discussed in [28]. In the proposed approach to modelling the magnetisation processes, the method of approximation of hysteresis changes presented in [29] was applied. This study extensively describes how to determine minor hysteresis loops for any field strength value, and the model of the magnetisation process in transformer steel sheets can be universal when it allows the determination of changes in flux density for any value and direction of the field strength.…”

Internal Characterization of Magnetic Cores, Comparison to Finite Element Simulations: A Route for Dimensioning and Condition Monitoring

“…From its first description by Werner in 1949 [36] and up to its most recent published version (2020-21 [22]- [24]), numerous studies have focused on an accurate description of the ideal experimental conditions to ensure accuracy and MNPM reproducibility: _ As described in [35], the voltage drop between positions 1 and 2 in Fig. 1 below can be approximated by using the following expression:…”

Review on magnetic spinel ferrite (MFe2O4) nanoparticles: From synthesis to application

“…Although the hysteresis mechanism is well understood, creating an appropriate mathematical model based on an understanding of the phenomena that explain the magnetization process is still a difficult issue. As a result, extensive research has been conducted over many decades to create a hysteresis model that is accurate and helpful in the field computations of ferromagnetic materials [ 52 ]. Measurements of hysteresis loops in technologically essential magnetic structures have revealed significant discrepancies from several fundamental and widely accepted ferromagnetism physics concepts [ 53 ].…”