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Документ Mathematical apparatus for modeling of the propagation the magnetic field electric machines with a given accuracy(Національний технічний університет "Харківський політехнічний інститут", 2022) Levchenko, Larysa; Glyva, Valentyn; Burdeina, NataliiaThe problem of modeling the propagation local magnetic fields and spatially dispersed sources is large errors compared to field measurements. An important aspect of dequate 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 harmo nics 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 present ed approach makes it possible to nambiguously 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 me asurements 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 odeling the propagation of the magnetic field around the source.Документ Modeling of the external magnetic field of electric machines(Національний технічний університет "Харківський політехнічний інститут", 2024) Levchenko, Larysa; Ausheva, Nataliia; Karaieva, Nataliia; Glyva, Valentyn; Burdeina, NataliiaThe goal of the work. Proposals for methods of solving systems of linear homogeneous and nonhomogeneous differential equations with constant and variable coefficients that defined in interval form and intended for modeling exchange processes in multicomponent environments. Research subject: systems of linear homogeneous and nonhomogeneous differential equations with constant and variable coefficients defined in interval form. Powerful electric machines – such as electric generators, electric motors generate a magnetic field of great tension. These fields negatively effect on personnel and can to violate the stability of electronic equipment. To determine safe areas for workers, laying communication cables and placing sensitive electronic equipment, it is advisable to model the propagation of magnetic fields of electrical machines. This will make it possible to rationalize the placing of electrical equipment at design stages. The most common high-power electrical machines are four-pole electrical machines with a dipole-quadrupole structure of the external magnetic field. The purpose of the research is a development of models of the propagation of the external magnetic field generated by alternating current electric machines. Results of the research: it is substantiated that to simulate the propagation of the magnetic field of electric machines, it is advisable to use the Gauss equation for the magnetic scalar potential. This will make it possible to take into account the required number of spatial harmonics of the magnetic field to ensure an acceptable calculation error. An electric machine is considered in a spherical approximation. Calculations were carried out in spherical coordinates. The distances were determined in relative radii of the electric machine – the ratio of the radius of the machine to the definition of field strength. The calculations were made for two planes of spherical coordinates and a three-dimensional image was obtained. As a result of the simulation, it is possible to determine the magnetic field strength of a four-pole electric machine at selected distances and directions around the electric machine with the required accuracy. It has been established that there are points of zero external magnetic field strength around electrical machines. Verification of the simulation results was carried out using the method of full-scale measurements of the magnetic field strength around a real four-pole machine. The measurement results showed acceptable agreement with the calculated data. Conclusions: the chosen approach and the results of modeling the propagation of the external magnetic field of electrical machines can be used to design the placement of electrical equipment, taking into account the requirements for electromagnetic safety and electromagnetic compatibility of technical equipment.