# Study of the surface effect in steel at the industrial frequency by means of magnetoelectric equivalent circuits

## Authors

• M. V. Ostrenko Zaporizhzhia National Technical University, Ukraine
• K. A. Mishenko Zaporizhzhia National Technical University, Ukraine
• D. G. Patalakh Zaporizhzhia National Technical University, Ukraine
• S. M. Tykhovod Zaporizhzhia National Technical University, Ukraine

## Keywords:

magnetic field, equivalent magneto-electric circuits, magnetic capacitors, splinе

## Abstract

Purpose. To work out the methodology and computer program for calculation of processes of the commercial frequency electromagnetic field penetration into steel body taking into account non-linearity of magnetizing steel characteristics.

Research methods. The method of magnetoelectric equivalent circuits is used to calculate electromagnetic fields in a ferromagnetic medium. A feature of the method is the use of so-called "magnetic current" - the derivative of the magnetic flux. This made it possible to introduce “magnetic capacitors” into the circuit, which significantly simplified the equations of state, which are compiled on the basis of Kirchhoff's laws for electric and magnetic circuits, the law of electromagnetic induction, and the law of total current. Methods of numerical integration of differential equations are taken in the form of additional equations, which are attached to the state equations. The result is a system of linear algebraic equations, which at each step of integration has a unique solution. The magnetization curve of steel is approximated by splines, which allows to refine variable coefficients of the system of equations at each integration step..

The results. The developed methodology and algorithm allowed developing the computer program for calculating the dynamics of penetration of an electromagnetic field into a steel body. Calculations for this program allowed us to calculate the depth of penetration of the electromagnetic field into the steel body. The proposed method allows a coil with a ferromagnetic core to be considered as a linear element in the intervals of the applied voltage determined in this method, to calculate the equivalent magnetic permeability of the core, as well as the inductance of the coil.

Originality. For the first time, the method of using nonlinear magnetoelectric equivalent circuits was used to analyze the transient processes of penetration of an electromagnetic field into a steel body, which made it possible to reduce the calculation time by more than two.

Practical value.  Based on the research, the limits of magnetic field strength values are determined, in which linear methods of analysis can be applied. This allows the use of linear analysis methods for modeling electromagnetic fields in the structural elements of transformers using the finite element.

## Author Biographies

### M. V. Ostrenko, Zaporizhzhia National Technical University

Senior Lecturer of Zaporizhzhia National Technical University, Zaporizhzhia

### K. A. Mishenko, Zaporizhzhia National Technical University

Postgraduate student of Zaporizhzhia National Technical University, Zaporizhzhia

### D. G. Patalakh, Zaporizhzhia National Technical University

Postgraduate student of Zaporizhzhia National Technical University, Zaporizhzhia

### S. M. Tykhovod, Zaporizhzhia National Technical University

Doctor technical sciences, Associate professor, Chief of the department of the Theoretical and general electronics, Zaporizhzhia National Technical University, Ukraine

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2019-07-01

## How to Cite

Ostrenko, M. V., Mishenko, K. A., Patalakh, D. G., & Tykhovod, S. M. (2019). Study of the surface effect in steel at the industrial frequency by means of magnetoelectric equivalent circuits. Electrical Engineering and Power Engineering, (2), 23–33. https://doi.org/10.15588/1607-6761-2019-2-2

Electrotechnics