# MATHEMATICAL APPARATUS FOR MODELING OF THE PROPAGATION THE MAGNETIC FIELD ELECTRIC MACHINES WITH A GIVEN ACCURACY

## Abstract

. The problem of modeling the propagation local magnetic fields and spatially dispersed sources is large errors compared to field measurements. An important aspect of adequate modeling is the use of the correct mathematical apparatus. It is shown that in order to obtain reliable models of the propagation magnetic fields around electrical machines (generators, electric motors of different power, geometric dimensions and poles), it is advisable to apply the Gauss equation for a scalar potential. The solution of the equation in polar coordinates makes it possible to take into account not only the fundamental, but also other harmonics of the magnetic field (dipole, quadrupole, octupole). This allows, depending on the number of spatial harmonics taken into account, to obtain a model with the required accuracy (error) for predicting the magnetic field strength at any point around the machine.   It is considered in the paper that an electronic machine is an object of base radius R0. The presented approach makes it possible to unambiguously determine the location of zero field points at a distance from the source (for a quadrupole source and zero field lines, for an octupole source). The results of modeling and their verification by full-scale measurements for the most common four-pole machines (quadrupole source) are presented. The main task of modeling the propagation the magnetic field of such sources is to ensure the required accuracy based on the goals of modeling. It is shown that the modeling accuracy and the presence of zero field points are due to different field levels near the electrical machine housing for different harmonics. The dipole harmonic at the cabinet is 20% of its own harmonic. But it falls more slowly with distance. This necessitates taking into account a different number of harmonics depending on the value of the ratio R0/R, R is the distance to the point of determining the field strength from the source. Therefore, with the ratio R0/R=2/3, the eighth harmonic is essential. At R0/R=1/5, already the fourth spatial harmonic can be neglected. Such data allow you to choose a rational number of harmonics. This reduces the amount of calculations and simplifies the process of modeling the propagation of the magnetic field around the source.

## Article Details

How to Cite
Levchenko, L., Glyva, V., & Burdeina, N. (2022). MATHEMATICAL APPARATUS FOR MODELING OF THE PROPAGATION THE MAGNETIC FIELD ELECTRIC MACHINES WITH A GIVEN ACCURACY. Advanced Information Systems, 6(2), 5–9. https://doi.org/10.20998/2522-9052.2022.2.01
Section
Information systems modeling
Author Biographies

### Larysa Levchenko, National Technical University of Ukraine «Igor Sikorsky KPI», Kyiv

Doctor of Technical Sciences, Associate Professor, Professor of Department automation of projection of power processes and systems

### Valentyn Glyva, Kyiv National University of Construction and Architecture, Kyiv

Doctor of Technical Sciences, Professor, Professor of Department of Physics

### Nataliia Burdeina, Kyiv National University of Construction and Architecture, Kyiv

Candidate of Pedagogical Sciences, Associate Professor, Vice-Rector for Educational and Organizational- Educational Work

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