Development of an analytical model for determining the magnetic leakage flux through the stator teeth of a synchronous electric machine with a fractional tooth winding
https://doi.org/10.29235/1561-8358-2022-67-1-75-85
Abstract
As a result of the study of a two-dimensional finite element model of the magnetic field of a synchronous electric machine with fractional tooth windings, typical magnetic fluxes (fundamental, edge effect, scattering) in its magnetic system have been identified. The analysis of the degree of influence of magnetic fluxes of the edge effect and scattering on the magnitude of the main magnetic flux is carried out and equivalent circuits of the magnetic circuit of the studied synchronous electric machine with fractional tooth windings are constructed for different positions of the stator teeth relative to the rotor poles. An analytical model has been developed to determine the main magnetic flux through the coil of the working winding of a synchronous electric machine with fractional toothed windings. A feature of the proposed model is taking into account the dependence of the main magnetic flux through the coil of the working winding on the coordinate of the rotor position, the magnetic fluxes of the edge effect and scattering. The developed model allows solving the problem of quantitative determination of the value of the main magnetic flux through the coil of the working winding with high accuracy. In addition, the proposed model makes it possible to determine the influence of the main geometrical parameters of the magnetic circuit on the nature of the change in the main magnetic flux through the coil of the working winding with the least amount of time. The developed analytical model can be applied in the process of optimizing a synchronous electric machine with fractional tooth windings.
About the Authors
S. V. Panteleev
Military Academy of the Republic of Belarus
Belarus
Belarus
Stanislav V. Panteleev – Teacher of the Chair of Electrical Equipment and Power Supply Systems
220, Nezavisimosti Ave., 220057, Minsk
A. B. Menzhinski
Military Academy of the Republic of Belarus
Belarus
Belarus
Andrey B. Menzhinsky – Ph. D. (Engineering), Assistant Professor of the Chair of Electrical Equipment and Power Supply Systems
220, Nezavisimosti Ave., 220057, Minsk
A. N. Malashin
Military Academy of the Republic of Belarus
Belarus
Belarus
Andrey N. Malashin – Ph. D. (Engineering), Assistant Professor, Professor of the Chair of Electrical Equipment and Power Supply Systems
220, Nezavisimosti Ave., 220057, Minsk
References
1. Vol’dek A. I., Popov V. V. Electric Cars. AC Machines. St. Petersburg, Piter Publ., 2008. 350 p. (in Russian).
2. Levi E. Multiphase Electric Machine for Variable Speed Applications. IEEE Transactions on Industrial Electronics, 2008, vol. 55, no. 5, pp. 1893–1909. https://doi.org/10.1109/tie.2008.918488
3. Shevchenko A.F. Electromechanical Energy Converters with Modulated Magnetic Flux. Novosibirsk, Novosibirsk State Technical University, 1999. 340 p. (in Russian).
4. Chestyunina T.V. Research of Multi-Pole Synchronous Magnetoelectric Generators with Fractional Slot Windings. Novosibirsk, Novosibirsk State Technical University, 2012. 176 p. (in Russian).
5. Ivanov-Smolenskii A. V., Avanesov M.A., Kaz’min E. V. Application of the method of conductivity of toothed contours for calculating synchronous machines with permanent magnets on the surface of the rotor. Elektrichestvo, 2009, no. 8, pp. 42–51 (in Russian)
6. San Ju. Submersible Valve Motors with Toothed Stator Winding Pitch. St. Petersburg, St. Petersburg State Marine Technical University, 2017. 153 p. (in Russian).
7. Shrejner R. T. Mathematical Modeling of AC Electric Drives with Semiconductor Frequency Converters. Yekaterinburg, Ural Branch of the Russian Academy of Sciences Publ., 2000. 583 p. (in Russian).
8. Panteleev S.V., Malashin A. N. Analysis of features of the magnetic field of a synchronous electric ma-chine with a multi-phase fractional slot winding in a polyharmonic mode of operation. Vestsi Natsyyanal’nai akademii navuk Belarusi. Seryya fizika-technichnych navuk = Proceedings of the National Academy of Sciences of Belarus. Physical-technical series, 2021, vol. 66, no. 3, pp. 343–355 (in Russian). https://doi.org/10.29235/1561-8358-2021-66-3-343-355
9. Li W., Chau K., Liu C., Gao S., Wu D. Analysis of Tooth-Tip Flux Leakage in Surface-Mounted Permanent Magnet Linear Vernier Machines. IEEE Transactions on Magnetics, 2013, vol. 49, no. 7, pp. 3949–3952. https://doi.org/10.1109/TMAG.2013.2244581
10. Gao P., Gu Y.X., Sha S. H., Abubakar U., Wang X.Y. Calculation and Analysis of Flux Leakage Coefficient of Interior Permanent Magnet Synchronous Motors with Fractional Slot Concentrated Windings. IEEE Transactions on Applied Superconductivity, 2019, vol. 29, no. 2, Art. no. 0602004. https://doi.org/10.1109/TASC.2019.2893740
11. Balagurov V.A., Galteyev F.F. Electric Machines with Permanent Magnets. Moscow, Energoatomizdat Publ., 1988. 280 p. (in Russian).
12. Khiterer M.Ya., Ovchinnikov I. E. Synchronous Electric Reciprocating Machines. St. Petersburg, Korona-Print Publ., 2013. 368 p. (in Russian).
13. Mеnzhinskii A. В., Malashin A.N., Koval J.G. Mathematical model of the generator of the combined design of reciprocating type. Vestnik Gomelskogo technicheskogo universiteta = Bulletin of Gomel State Technical University, 2018, no. 2, pp. 74–85 (in Russian).
14. Zaharenko A.B., Avdonin A. F. Design Optimization of a Low-Speed Brushless Motor. Elektrotehnika = Electrical Engineering, 1999, no. 12, pp. 6–13 (in Russian).
15. Ponomarev P., Lindh P., Pyrhonen J. Effect of Slot-and-Pole Combination on the Leakage Inductance and the Performance of Tooth-Coil Permanent-Magnet Synchronous Machines. IEEE Transactions on Industrial Electronics, 2013, vol. 60, no. 10, pp. 4310–4317. https://doi.org/10.1109/TIE.2012.2216246
16. Phyong Le Ngo. Calculation of inductance of the interior permanent magnet synchronous motor. Enеrgеtika. Izvestiya Vysshikh uchebnykh zavedenii i energeticheskikh ob”edinenii SNG = ENERGETIKA. Proceedings of CIS Higher Education Institutions and Power Engineering Associations, 2017, vol. 60, no. 2, pp. 133–146 (in Russian). https://doi.org/10.21122/1029-7448-2017-60-2-133-146
17. Panteleev S.V., Malashyn A. N. Increasing the energy performance of an electric machine by applying a multiphase toothed winding. Vestnik Voennoi akademii Respubliki Belarus’ = Bulletin of the Military Academy of the Republic of Belarus, 2017, no. 3, pp. 80–86 (in Russian).
18. ELCUT Modeling of Electromagnetic, Thermal, and Elastic Fields by the Finite Element Method. Version 6.3.1.: User’s Hands. St. Petersburg, Tor Publ., 2018. Available at: https://elcut.ru/downloads/manual_r_pocket.pdf (accessed 24 May 2018) (in Russian).
19. Menzhinski A.B., Malashin A. N., Menzhinski P.B. Development of Refined Electromagnetic Models of Reciprocating Electric Generators with Permanent Magnets. Enеrgеtika. Izvestiya vysshikh uchebnykh zavedenii i energeticheskikh ob”edinenii SNG = ENERGETIKA. Proceedings of CIS Higher Education Institutions and Power Engineering Associations, 2021, no. 4, pp. 291–302 (in Russian). https://doi.org/10.21122/1029-7448-2021-64-4-291-302
20. Balagurov V.A., Galteev F. F., Larionov A. N. Electric Machines with Permanent Magnets. Moscow, Energiya Publ., 1964. 480 p. (in Russian).
Review
Views: 363
Email this article 
