volume | PIER Journals

Abstract

This work presents a novel semi-analytical model for magnetic field calculation in a high-speed surface-mounted permanent-magnet machine with conducting and permeable retaining sleeve. The retaining sleeve with conducting material and non-homogeneous permeability affects the machine electromagnetic performance by altering main flux inductance and developed torque profile. This performance deviation can be attributed to eddy-current reaction field and saturation, the latter occurring due to pole-to-pole leakage flux. Saturation is modeled with a space-varying relative permeability, expressed as a Fourier series. Eddy currents are evaluated with an auxiliary winding, defined as a surface current density in the conducting region. The proposed method is based on well-established Maxwell-Fourier method. This permits other analysis, such as slotting effect through subdomain technique. The assumptions considered for the developed semi-analytical solution in two-dimensional problem are presented in depth and confronted with finite-element method results, confirming validity of proposed methodology.

1. Uzhegov, N., E. Kurvinen, J. Nerg, J. Pyrhonen, J. T. Sopanen, and S. Shirinskii, "Multidisciplinary design process of a 6-slot 2-pole high-speed permanent-magnet synchronous machine," IEEE Transactions on Industrial Electronics, Vol. 63, No. 2, 784-795, Feb. 2016.
doi:10.1109/TIE.2015.2477797

2. Shen, J., X. Qin, and Y. Wang, "High-speed permanent magnet electrical machines —Applications, key issues and challenges," CES Transactions on Electrical Machines and Systems, Vol. 2, No. 1, 23-33, Mar. 2018.
doi:10.23919/TEMS.2018.8326449

3. Lahne, H.-C. and D. Gerling, "Comparison of state-of-the-art high-speed high-power machines: Research study including a design example of a 50000 rpm induction machine," IECON 2015 — 41st Annual Conference of the IEEE Industrial Electronics Society, 003519-003524, IEEE, Nov. 2015.

4. Tenconi, A., S. Vaschetto, and A. Vigliani, "Electrical machines for high-speed applications: Design considerations and tradeoffs," IEEE Transactions on Industrial Electronics, Vol. 61, No. 6, 3022-3029, Jun. 2014.

5. Cupertino, F., R. Leuzzi, V. G. Monopoli, and G. L. Cascella, "Design procedure for high-speed PM motors aided by optimization algorithms," Machines, Vol. 6, No. 1, 5, Feb. 2018.

6. Uzhegov, N., J. Barta, J. Kurfurst, C. Ondrusek, and J. Pyrhonen, "Comparison of high-speed electrical motors for a turbo circulator application," IEEE Transactions on Industry Applications, Vol. 53, No. 5, 4308-4317, Sep. 2017.

7. Gerada, D., D. Borg-Bartolo, A. Mebarki, C. Micallef, N. L. Brown, and C. Gerada, "Electrical machines for high speed applications with a wide constant-power region requirement," 2011 International Conference on Electrical Machines and Systems, 1-6, Aug. 2011.

8. Gilson, A., F. Dubas, D. Depernet, and C. Espanet, "Comparison of high-speed PM machine topologies for electrically-assisted turbocharger applications," 2016 19th International Conference on Electrical Machines and Systems (ICEMS), 1-5, 2016.

9. Gerada, D., A. Mebarki, N. L. Brown, C. Gerada, A. Cavagnino, and A. Boglietti, "High-speed electrical machines: Technologies, trends, and developments," IEEE Transactions on Industrial Electronics, Vol. 61, No. 6, 2946-2959, Jun. 2014.

10. Pottie, D. L., G. A. Mendon¸ca, O. A. Faria, M. T. C. Faria, B. J. Cardoso Filho, and T. A. Maia, "Some aspects of the electromechanical design of high-speed microturbines for power generation," International Journal of Applied Electromagnetics and Mechanics, Vol. 63, No. 4, 621-644, Aug. 2020.

11. Hannon, B., P. Sergeant, L. Dupre, and P.-D. Pfister, "Two-dimensional fourier-based modeling of electric machines — An overview," IEEE Transactions on Magnetics, Vol. 55, No. 10, 1-17, Oct. 2019.

12. Gieras, J. F., Permanent Magnet Motor Technology, 3rd Ed., Taylor & Francis Inc., 2009.

13. Pyrhonen, V. H. and T. Jokinen, Design Rotating Electrical Machines, John Wiley & Sons, 2013.

14. Meeker, D., Finite Element Method Magnetics, v4.2, 2015.

15. Pfister, P.-D., X. Yin, and Y. Fang, "Slotted permanent-magnet machines: General analytical model of magnetic fields, torque, eddy currents, and permanent-magnet power losses including the diffusion effect," IEEE Transactions on Magnetics, Vol. 52, No. 5, 1-13, May 2016.

16. Yu, Y., D. Liang, and X. Liu, "Optimal design of the rotor structure of a HSPMSM based on analytic calculation of eddy current losses," Energies, Vol. 10, No. 4, 551, Apr. 2017.

17. Mohamed, M. R. and D. Ishak, "Optimization of surface-mounted permanent magnet brushless AC motor using analytical model and differential evolution algorithm," Journal of Electrical Engineering, Vol. 70, No. 3, 208-217, Jun. 2019.

18. Jumayev, S., K. O. Boynov, J. J. H. Paulides, E. A. Lomonova, and J. Pyrhonen, "Slotless PM machines with skewed winding shapes: 3-D electromagnetic semianalytical model," IEEE Transactions on Magnetics, Vol. 52, No. 11, 1-12, Nov. 2016.

19. Tiegna, H., Y. Amara, and G. Barakat, "Overview of analytical models of permanent magnet electrical machines for analysis and design purposes," Mathematics and Computers in Simulation, Vol. 90, 162-177, Apr. 2013.

20. Dubas, F. and K. Boughrara, "New scientific contribution on the 2-D subdomain technique in cartesian coordinates: Taking into account of iron parts," Mathematical and Computational Applications, Vol. 22, No. 1, 17, Feb. 2017.

21. Rahideh, A., H. Moayed-Jahromi, M. Mardaneh, F. Dubas, and T. Korakianitis, "Analytical calculations of electromagnetic quantities for slotted brushless machines with surface-inset magnets," Progress In Electromagnetics Research B, Vol. 72, 49-65, 2017.

22. Yu, Y., Q. W. Xiang, X. Zhang, and W. Zhang, "Analytical model of the magnetic field distribution of a generator combined with magnetic bearing in wind turbines," Progress In Electromagnetics Research B, Vol. 81, 25-44, 2018.

23. Benmessaoud, Y., D. Ouamara, F. Dubas, and M. Hilairet, "Investigation of volumic permanent-magnet eddy-current losses in multi-phase synchronous machines from hybrid multi-layer model," Mathematical and Computational Applications, Vol. 25, No. 1, 14, Mar. 2020.

24. Oner, Y., Z. Q. Zhu, L. J. Wu, X. Ge, H. Zhan, and J. T. Chen, "Analytical on-load subdomain field model of permanent-magnet vernier machines," IEEE Transactions on Industrial Electronics, Vol. 63, No. 7, 4105-4117, Jul. 2016.

25. Lubin, T., S. Mezani, and A. Rezzoug, "Improved analytical model for surface-mounted PM motors considering slotting effects and armature reaction," Progress In Electromagnetics Research B, Vol. 25, 293-314, 2010.

26. Zhu, Z., D. Howe, and C. Chan, "Improved analytical model for predicting the magnetic field distribution in brushless permanent-magnet machines," IEEE Transactions on Magnetics, Vol. 38, No. 1, 229-238, 2002.

27. Ackermann, B. and R. Sottek, "Analytical modeling of the cogging torque in permanent magnet motors," Electrical Engineering, Vol. 78, No. 2, 117-125, Mar. 1995.

28. Roubache, L., K. Boughrara, F. Dubas, and R. Ibtiouen, "Semi-analytical modeling of spoke-type permanent-magnet machines considering the iron core relative permeability: Subdomain technique and taylor polynomial," Progress In Electromagnetics Research B, Vol. 77, 85-101, 2017.

29. Faiz, J., M. Hassanzadeh, and A. Kiyoumarsi, "Analytical calculation of magnetic field in surfacemounted permanent-magnet machines with air-gap eccentricity," COMPEL — The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 38, No. 2, 893-914, Mar. 2019.

30. Djelloul-Khedda, Z., K. Boughrara, F. Dubas, A. Kechroud, and A. Tikellaline, "Analytical prediction of iron-core losses in flux-modulated permanent-magnet synchronous machines," IEEE Transactions on Magnetics, Vol. 55, No. 1, 1-12, Jan. 2019.

31. Boughrara, K., T. Lubin, and R. Ibtiouen, "General subdomain model for predicting magnetic field in internal and external rotor multiphase flux-switching machines topologies," IEEE Transactions on Magnetics, Vol. 49, No. 10, 5310-5325, Oct. 2013.

32. Devillers, E., J. L. Besnerais, T. Lubin, M. Hecquet, and J.-P. Lecointe, "A review of subdomain modeling techniques in electrical machines: Performances and applications," 2016 XXII International Conference on Electrical Machines (ICEM), 86-92, IEEE, Sep. 2016.

33. Ortega, A. J. P., "Fast design of asymmetrical permanent magnet synchronous machines that minimize pulsating torque," Progress In Electromagnetics Research B, Vol. 76, 111-123, 2017.

34. Alam, F. R. and K. Abbaszadeh, "Magnetic field analysis in eccentric surface-mounted permanentmagnet motors using an improved conformal mapping method," IEEE Transactions on Energy Conversion, Vol. 31, No. 1, 333-344, Mar. 2016.

35. Boughrara, K., T. Lubin, R. Ibtiouen, and N. Benallal, "Analytical calculation of parallel double excitation and spoke-type permanent-magnet motors; simplified versus exact model," Progress In Electromagnetics Research B, Vol. 47, 145-178, 2013.

36. Brahim, L.-C., K. Boughrara, and R. Ibtiouen, "Cogging torque minimization of surfacemounted permanent magnet synchronous machines using hybrid magnet shapes," Progress In Electromagnetics Research B, Vol. 62, 49-61, 2015.

37. Djelloul-Khedda, Z., K. Boughrara, F. Dubas, and R. Ibtiouen, "Nonlinear analytical prediction of magnetic field and electromagnetic performances in switched reluctance machines," IEEE Transactions on Magnetics, Vol. 53, No. 7, 1-11, Jul. 2017.

38. Roubache, L., K. Boughrara, F. Dubas, and R. Ibtiouen, "Elementary subdomain technique for magnetic field calculation in rotating electrical machines with local saturation effect," COMPEL — The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 38, No. 1, 24-45, Jan. 2019.

39. Holm, S. R., H. Polinder, and J. A. Ferreira, "Analytical modeling of a permanent-magnet synchronous machine in a ywheel," IEEE Transactions on Magnetics, Vol. 43, No. 5, 1955-1967, May 2007.

40. Ouamara, D. and F. Dubas, "Permanent-magnet eddy-current losses: A global revision of calculation and analysis," Mathematical and Computational Applications, Vol. 24, No. 3, 67, Jul. 2019.

41. Boubaker, N., D. Matt, P. Enrici, F. Nierlich, G. Durand, F. Orlandini, X. Longere, and J. Aıgba, "Study of eddy-current loss in the sleeves and Sm-Co magnets of a high-performance SMPM synchronous machine (10 kRPM, 60 kW)," Electric Power Systems Research, Vol. 142, 20-28, Jan. 2017.

42. Zhu, Z., K. Ng, N. Schofield, and D. Howe, "Analytical prediction of rotor eddy current loss in brushless machines equipped with surface-mounted permanent magnets. I. Magnetostatic field model," ICEMS’2001, Proceedings of the Fifth International Conference on Electrical Machines and Systems (IEEE Cat. No.01EX501), Int. Acad. Publishers, 2001.

43. Zhou, F., J. Shen, W. Fei, and R. Lin, "Study of retaining sleeve and conductive shield and their in fluence on rotor loss in high-speed PM BLDC motors," IEEE Transactions on Magnetics, Vol. 42, No. 10, 3398-3400, Oct. 2006.

44. Zhang, C., L. Chen, S. Yu, X. Ma, X. Wang, and R. Tang, "Performance characteristics of high speed permanent magnet machine with different rotor retaining sleeve," 2019 22nd International Conference on Electrical Machines and Systems (ICEMS), IEEE, Aug. 2019.

45. Qiu, H., Q. Duan, L. Yao, Y. Dong, R. Yi, G. Cui, and W. Li, "Analytical analysis of sleeve permeability for output performance of high speed permanent magnet generators driven by micro gas turbines," Applied Mathematical Modelling, Vol. 40, No. 21-22, 9017-9028, Nov. 2016.

46. Patel, A. N. and A. Kapil, "Effect of magnet retaining sleeve thickness on cogging torque of radial flux permanent magnet brushless DC motor," 2016 International Conference on Emerging Trends in Engineering, Technology and Science (ICETETS), 1-3, IEEE, Feb. 2016.

47. Hannon, B., P. Sergeant, and L. Dupre, "Evaluation of the torque in high-speed PMSMs with a shielding cylinder and BLDC control," IEEE Transactions on Magnetics, Vol. 54, No. 10, 1-8, Oct. 2018.

48. Li, W., H. Qiu, X. Zhang, J. Cao, and R. Yi, "Analyses on electromagnetic and temperature fields of superhigh-speed permanent-magnet generator with different sleeve materials," IEEE Transactions on Industrial Electronics, Vol. 61, No. 6, 3056-3063, Jun. 2014.

49. Zhu, Z., Y. Huang, J. Dong, F. Peng, and Y. Yao, "Rotor eddy current loss reduction with permeable retaining sleeve for permanent magnet synchronous machine," IEEE Transactions on Energy Conversion, 1-1, 2020.

50. Yon, J. M., P. H. Mellor, R. Wrobel, J. D. Booker, and S. G. Burrow, "Analysis of semipermeable containment sleeve technology for high-speed permanent magnet machines," IEEE Transactions on Energy Conversion, Vol. 27, No. 3, 646-653, Sep. 2012.

51. Mendonca, G., T. Maia, and B. C. Filho, "Magnetic field analytical solution for non-homogeneous permeability in retaining sleeve of a high-speed permanent-magnet machine," Mathematical and Computational Applications, Vol. 23, No. 4, 72, Nov. 2018.

52. Ramakrishnan, K., M. Curti, D. Zarko, G. Mastinu, J. J. H. Paulides, and E. A. Lomonova, "Comparative analysis of various methods for modelling surface permanent magnet machines," IET Electric Power Applications, Vol. 11, No. 4, 540-547, Apr. 2017.

53. Polinder, H. and M. J. Hoeijmakers, "Modelling a PM machine with shielding cylinder," 9th International Conference on Electrical Machines and Drives, 16-20, IEE, 1999.

54. Maia, T. A., J. E. Barros, B. J. C. Filho, and M. P. Porto, "Experimental performance of a low cost micro-CAES generation system," Applied Energy, Vol. 182, 358-364, Nov. 2016.

55. Maia, T. A., O. A. Faria, J. E. Barros, M. P. Porto, and B. J. C. Filho, "Test and simulation of an electric generator driven by a micro-turbine," Electric Power Systems Research, Vol. 147, 224-232, Jun. 2017.

56. Dutta, R., K. Ahsanullah, and F. Rahman, "Cogging torque and torque ripple in a direct-drive interior permanent magnet generator," Progress In Electromagnetics Research B, Vol. 70, 73-85, 2016.

57. Boyce, W., Elementary Differential Equations and Boundary Value Problems, Wiley, 2005.

58. Dubas, F. and C. Espanet, "Analytical solution of the magnetic field in permanent-magnet motors taking into account slotting effect: No-load vector potential and flux density calculation," IEEE Transactions on Magnetics, Vol. 45, No. 5, 2097-2109, May 2009.

59. Wu, L., Z. Zhu, D. Staton, M. Popescu, and D. Hawkins, "Analytical prediction of electromagnetic performance of surface-mounted PM machines based on subdomain model accounting for toothtips," IET Electric Power Applications, Vol. 5, No. 7, 597, 2011.

60. Tiang, T. L., D. Ishak, and M. K. M. Jamil, "Complete subdomain model for surface-mounted permanent magnet machines," 2014 IEEE Conference on Energy Conversion (CENCON), 140-145, IEEE, Oct. 2014.

61. Rahideh, A. and T. Korakianitis, "Analytical calculation of open-circuit magnetic field distribution of slotless brushless PM machines," International Journal of Electrical Power & Energy Systems, Vol. 44, No. 1, 99-114, Jan. 2013.

62. Boutora, Y., N. Takorabet, and R. Ibtiouen, "Analytical model on real geometries of magnet bars of surface permanent magnet slotless machine," Progress In Electromagnetics Research B, Vol. 66, 31-47, 2016.

63. Jassal, A., H. Polinder, and J. Ferreira, "Literature survey of eddy-current loss analysis in rotating electrical machines," IET Electric Power Applications, Vol. 6, No. 9, 743, 2012.

64. Gurdal, O., "A new approach to graphically reveal some unknown properties of theorthogonal coordinate systems in quadric form, by using the square root scaled chart," Journal of the Faculty of Engineering and Architecture of Gazi University, Vol. 23, No. 2, 317-327, 2008.

65. Gurdal, O., "Graphical exploration of the trajectories of electric fields and equipotentials outside the conducting strip carrying steady current,", 2018, doi: 10.13140/RG.2.2.15757.79843.

66. Gurdal, O., "Graphical exploration of the trajectories of electric fields and equipotentials inside & outside infinitely long bottleneck shaped sloppy conducting strips carrying steady current,", 2020, doi: 10.13140/RG.2.2.25959.19367.

67. Wu, L. J., Z. Q. Zhu, D. Staton, M. Popescu, and D. Hawkins, "Analytical model for predicting magnet loss of surface-mounted permanent magnet machines accounting for slotting effect and load," IEEE Transactions on Magnetics, Vol. 48, No. 1, 107-117, Jan. 2012.

68. Polinder, H., On the losses in a high-speed permanent-magnet generator with rectifier, Ph.D. Thes.

69. Hannon, B., P. Sergeant, and L. Dupre, "Two-dimensional fourier-based modeling of electric machines," 2017 IEEE International Electric Machines and Drives Conference (IEMDC), 1-8, IEEE, May 2017.

Mr. Gabriel Alves Mendonça

Dr. Thales Alexandre Carvalho Maia

Dr. Braz de Jesus Cardoso Filho