The Armature Reaction Inductive Reactances of Synchronous Machines with Permanent Magnets Nonmagnetic Holder
Keywords:
simulation, contact surface temperature, overheating prediction, control, dynamic monitoring mode, bolted connection, rectangular bus
Abstract
The most widely used design scheme of synchronous machines with radially magnetized permanent magnets and a nonmagnetic magnet holder is considered. To calculate the armature reaction inductive reactances in these machines, it is proposed to use the conventional approach and the expressions obtained on its basis for the armature reaction inductive reactances of synchronous machines with electromagnetic excitation. The features of permanent magnet machines can be taken into account by special calculated coefficients included in these expressions. On the basis of the magnetic field analytical solution of the armature reaction, the special calculated coefficient for the design scheme with a cylindrical yoke of the inductor was determined taking into account the increased nonmagnetic gap between the armature magnetic core and inductor yoke core. By applying the Schwartz method with the use of a scalar magnetic potential, a new magnetic field analytical solution of the armature reaction with a polyhedral yoke of the inductor is obtained. On the basis of this solution, the field form factors of the longitudinal and transverse armature reaction were determined, which take into account the real geometry of this design scheme. Graphical dependences of the special calculated coefficients on the active zone geometric parameters are given.
References
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11. Wu Sh., Guo L., Wang H., et al. Inductance Calculation of Interior Permanent Magnet Machines Considering Asymmetrical Saturation of the Bridge. – IEEE Transactions on Magnetics, 2019, DOI:10.1109/TMAG.2019.2926358.
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15. ГОСТ Р 54521-2011. Статистические методы. Математические символы и знаки для применения в стандартах. М.: Стандартинформ, 2012, 31 с.
#
1. Zhuravlev S.V., Zechikhin B.S., Kuz’michev R.V. Vestnik Moskovskogo aviatsionnogo instituta – in Russ. (Bulletin of MAI), 2016, Vol. 23, No. 1, pp. 197–209.
2. Xia Z.P., Zhu Z.Q., Howe D. Analytical Magnetic Field Analysis of Halbach Magnetized Permanent-Magnet Machines. – IEEE Transactions on Magnetics, 2004, vol. 40, No. 4, pp 1864–1872.
3. Amuliu Bogdan Proca, Ali Keyhani, Ahmed EL-Antably, et al. Analytical Model for Permanent Magnet Motors with Surface Mounted Magnets. – IEEE Transactions on Energy Conversion, 2003, vol. 18, No. 3, pp 386–391.
4. Wang A., Jia Yi., Soong W.L. Comparison of Five Topologies for an Interior Permanent-Magnet Machine for a Hybrid Electric Vehicle. – IEEE Transactions on Magnetics, 2011, vol. 47, No. 10,
pp 3606–3609.
5. Jin P., Yuan Yu., Lin H., et al. General Analytical Method for Magnetic Field Analysis of Halbach Magnet Arrays Based on Magnetic Scalar Potential. – Journal of Magnetics, 2013, vol. 18, No. 2, pp 95–104.
6. Ni Yo., Chen K., Xiao B., et al. Analytical Modeling of PM Electrical Machines with Eccentric Surface-Inset Halbach Magnets. – IEEE Transactions on Magnetics, 2021, vol. 57, No. 4, DOI: 10.1109/tmag.2021.3058095.
7. Minhyeok Lee, Bonkil Koo, Kwanghee Nam. Analytic Optimization of the Halbach Array Slotless Motor Considering Stator Yoke Saturation. – IEEE Transactions on Magnetics, 2021, vol. 57, No. 2, DOI:10.1109/TMAG.2020.3019353
8. Yang Yu., Wang X., Zhang R., et al. The Optimization of Pole Arc Coefficient to Reduce Cogging Torque in Surface-Mounted Permanent Magnet Motors. – IEEE Transactions on Magnetics, 2006, vol. 42, No. 4, pp 1135–1138, DOI:10.1109/TMAG.2006.871452.
9. Zechikhin B.S., Zhuravlev S.V., Sitin D.А. Elektrichestvo – in Russ. (Electricity), 2009, No. 3, pp. 35–40.
10. Bellara A., Amara Ya., Barakat G., et al. Two-Dimensional Exact Analytical Solution of Armature Reaction Field in Slotted Surface Mounted PM Radial Flux Synchronous Machines. – IEEE Transactions on Magnetics, 2009, vol. 45, No. 10, pp 4534–4538, DOI:10.1109/TMAG.2009.2021527.
11. Wu Sh., Guo L., Wang H., et al. Inductance Calculation of Interior Permanent Magnet Machines Considering Asymmetrical Saturation of the Bridge. – IEEE Transactions on Magnetics, 2019, DOI:10.1109/TMAG.2019.2926358.
12. Vol’dek A.I, Popov V.V. Elektricheskie mashiny. Mashiny peremennogo toka (AC electrical machines). SPb.: Piter, 2010, 350 p.
13. Zechikhin B.S. Elektricheskie mashiny letatel'nyh apparatov. Garmonicheskiy analiz aktivnyh zon (Aircraft electrical machines. Harmonic analysis of active zones). М.: Mashinostroenie, 1983, 149 p.
14. Kantorovich L.V., Krylov V.I. Priblizhennye metody vysshego analiza (Approximate methods of high-level analysis). L.: Fizmatgiz, 1962, 708 p.
15. GOST R 54521-2011. Statisticheskie metody. Matematicheskie simvoly i znaki dlya primeneniya v standartah (Statistical methods. Mathematical symbols and signs to be used in the standards). М.: Standartinform, 2012, 31 p.
2. Xia Z.P., Zhu Z.Q., Howe D. Analytical Magnetic Field Analysis of Halbach Magnetized Permanent-Magnet Machines. – IEEE Transactions on Magnetics, 2004, vol. 40, No. 4, pp 1864–1872.
3. Amuliu Bogdan Proca, Ali Keyhani, Ahmed EL-Antably, et al. Analytical Model for Permanent Magnet Motors with Surface Mounted Magnets. – IEEE Transactions on Energy Conversion, 2003, vol. 18, No. 3, pp 386–391.
4. Wang A., Jia Yi., Soong W.L. Comparison of Five Topologies for an Interior Permanent-Magnet Machine for a Hybrid Electric Vehicle. – IEEE Transactions on Magnetics, 2011, vol. 47, No. 10, pp 3606–3609.
5. Jin P., Yuan Yu., Lin H., et al. General Analytical Method for Magnetic Field Analysis of Halbach Magnet Arrays Based on Magnetic Scalar Potential. – Journal of Magnetics, 2013, vol. 18, No. 2, pp 95–104.
6. Ni Yo., Chen K., Xiao B., et al. Analytical Modeling of PM Electrical Machines with Eccentric Surface-Inset Halbach Magnets. – IEEE Transactions on Magnetics, 2021, vol. 57, No. 4, DOI: 10.1109/tmag.2021.3058095.
7. Minhyeok Lee, Bonkil Koo, Kwanghee Nam. Analytic Optimization of the Halbach Array Slotless Motor Considering Stator Yoke Saturation. – IEEE Transactions on Magnetics, 2021, vol. 57, No. 2, DOI:10.1109/TMAG.2020.3019353
8. Yang Yu., Wang X., Zhang R., et al. The Optimization of Pole Arc Coefficient to Reduce Cogging Torque in Surface-Mounted Permanent Magnet Motors. – IEEE Transactions on Magnetics, 2006, vol. 42, No. 4, pp 1135–1138, DOI:10.1109/TMAG.2006.871452.
9. Зечихин Б.С., Журавлев С.В., Ситин Д.А. Расчетные коэффициенты синхронных машин с редкоземельными магнитами. – Электричество, 2009, № 3, с. 35–40.
10. Bellara A., Amara Ya., Barakat G., et al. Two-Dimensional Exact Analytical Solution of Armature Reaction Field in Slotted Surface Mounted PM Radial Flux Synchronous Machines. – IEEE Transactions on Magnetics, 2009, vol. 45, No. 10, pp 4534–4538, DOI:10.1109/TMAG.2009.2021527.
11. Wu Sh., Guo L., Wang H., et al. Inductance Calculation of Interior Permanent Magnet Machines Considering Asymmetrical Saturation of the Bridge. – IEEE Transactions on Magnetics, 2019, DOI:10.1109/TMAG.2019.2926358.
12. Вольдек А.И., Попов В.В. Электрические машины. Машины переменного тока. СПб.: Питер, 2010, 350 с.
13. Зечихин Б.С. Электрические машины летательных аппаратов. Гармонический анализ активных зон. М.: Машиностроение, 1983, 149 с.
14. Канторович Л.В., Крылов В.И. Приближенные методы высшего анализа. Л.: Физматгиз, 1962, 708 с.
15. ГОСТ Р 54521-2011. Статистические методы. Математические символы и знаки для применения в стандартах. М.: Стандартинформ, 2012, 31 с.
#
1. Zhuravlev S.V., Zechikhin B.S., Kuz’michev R.V. Vestnik Moskovskogo aviatsionnogo instituta – in Russ. (Bulletin of MAI), 2016, Vol. 23, No. 1, pp. 197–209.
2. Xia Z.P., Zhu Z.Q., Howe D. Analytical Magnetic Field Analysis of Halbach Magnetized Permanent-Magnet Machines. – IEEE Transactions on Magnetics, 2004, vol. 40, No. 4, pp 1864–1872.
3. Amuliu Bogdan Proca, Ali Keyhani, Ahmed EL-Antably, et al. Analytical Model for Permanent Magnet Motors with Surface Mounted Magnets. – IEEE Transactions on Energy Conversion, 2003, vol. 18, No. 3, pp 386–391.
4. Wang A., Jia Yi., Soong W.L. Comparison of Five Topologies for an Interior Permanent-Magnet Machine for a Hybrid Electric Vehicle. – IEEE Transactions on Magnetics, 2011, vol. 47, No. 10,
pp 3606–3609.
5. Jin P., Yuan Yu., Lin H., et al. General Analytical Method for Magnetic Field Analysis of Halbach Magnet Arrays Based on Magnetic Scalar Potential. – Journal of Magnetics, 2013, vol. 18, No. 2, pp 95–104.
6. Ni Yo., Chen K., Xiao B., et al. Analytical Modeling of PM Electrical Machines with Eccentric Surface-Inset Halbach Magnets. – IEEE Transactions on Magnetics, 2021, vol. 57, No. 4, DOI: 10.1109/tmag.2021.3058095.
7. Minhyeok Lee, Bonkil Koo, Kwanghee Nam. Analytic Optimization of the Halbach Array Slotless Motor Considering Stator Yoke Saturation. – IEEE Transactions on Magnetics, 2021, vol. 57, No. 2, DOI:10.1109/TMAG.2020.3019353
8. Yang Yu., Wang X., Zhang R., et al. The Optimization of Pole Arc Coefficient to Reduce Cogging Torque in Surface-Mounted Permanent Magnet Motors. – IEEE Transactions on Magnetics, 2006, vol. 42, No. 4, pp 1135–1138, DOI:10.1109/TMAG.2006.871452.
9. Zechikhin B.S., Zhuravlev S.V., Sitin D.А. Elektrichestvo – in Russ. (Electricity), 2009, No. 3, pp. 35–40.
10. Bellara A., Amara Ya., Barakat G., et al. Two-Dimensional Exact Analytical Solution of Armature Reaction Field in Slotted Surface Mounted PM Radial Flux Synchronous Machines. – IEEE Transactions on Magnetics, 2009, vol. 45, No. 10, pp 4534–4538, DOI:10.1109/TMAG.2009.2021527.
11. Wu Sh., Guo L., Wang H., et al. Inductance Calculation of Interior Permanent Magnet Machines Considering Asymmetrical Saturation of the Bridge. – IEEE Transactions on Magnetics, 2019, DOI:10.1109/TMAG.2019.2926358.
12. Vol’dek A.I, Popov V.V. Elektricheskie mashiny. Mashiny peremennogo toka (AC electrical machines). SPb.: Piter, 2010, 350 p.
13. Zechikhin B.S. Elektricheskie mashiny letatel'nyh apparatov. Garmonicheskiy analiz aktivnyh zon (Aircraft electrical machines. Harmonic analysis of active zones). М.: Mashinostroenie, 1983, 149 p.
14. Kantorovich L.V., Krylov V.I. Priblizhennye metody vysshego analiza (Approximate methods of high-level analysis). L.: Fizmatgiz, 1962, 708 p.
15. GOST R 54521-2011. Statisticheskie metody. Matematicheskie simvoly i znaki dlya primeneniya v standartah (Statistical methods. Mathematical symbols and signs to be used in the standards). М.: Standartinform, 2012, 31 p.
Published
2021-04-27
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