volume | PIER Journals

Abstract

Beside magnetic equivalent circuit and finite element methods, sub-domain analysis (SDA) is an alternative method, which can be used to evaluate electrical machines behavior. It has a reasonable accuracy, and its parametric nature is allowed to apply to optimization or sensitivity analysis. Commonly this method is based on variables separation technique of Maxwell equations and Fourier series, eigenvalues and eigen-functions are so important for obtaining accurate results. In this paper, Maxwell equations are solved for two adjacent regions, i.e., copper (Cu) and permanent magnet (PM). It was paid less attention before, and it introduces supplementary eigenvalue and eigen function for asymmetry conditions in Cu or PM magnetic field regions.

1. Devillers, E., et al., "A review of subdomain modeling techniques in electrical machines: Performances and applications," XXII International Conference on Electrical on Electrical Machines (ICEM), Lausanne, Switzerland, Sep. 4–7, 2016.

2. 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.
doi:10.2528/PIERB17051001

3. Dubas, F. and K. Boughrara, "New scientific contribution on the 2D subdomain technique in Cartesian coordinates: Taking into account of iron parts," Math. Comput. Appl., 2017.

4. Ivrii, V., Partial Differential Equations, Textbook, 2017.

5. Li, J., K. T. Chau, and W. Li, "Harmonic analysis and comparison of permanent magnet vernier and magnetic-geared machines," IEEE Trans. on Magnetics, Vol. 47, No. 10, 3649-3652, 2011.
doi:10.1109/TMAG.2011.2159105

6. Jabbari, A., "Exact analytical modeling of magnetic vector potential in surface inset permanent magnet DC machines considering magnet segmentation," Journal of Electrical Engineering, Vol. 69, No. 1, 39-45, 2018.
doi:10.1515/jee-2018-0005

7. Lubin, T., S. Mezani, and A. Rezzoug, "Two-dimensional analytical calculation of magnetic field and electromagnetic torque for surface-inset permanent-magnet motors," IEEE Trans. on Magnetics, Vol. 48, No. 6, 2080-2091, 2012.
doi:10.1109/TMAG.2011.2180918

8. Jabbari, A., "Analytical modeling of magnetic field distribution in inner rotor brushless magnet segmented surface inset permanent magnet machines," Iranian Journal of Electrical and Electronic Engineering, Vol. 14, No. 3, 259-269, 2018.

9. Thierry, L., S. Mezani, and A. Rezzoug, "2D exact analytical model for surface-mounted permanent-magnet motors with semi-closed slots," IEEE Trans. on Magnetics, Vol. 47, No. 2, 479-492, 2011.
doi:10.1109/TMAG.2010.2095874

10. Ma, F., et al., "Analytical calculation of armature reaction field of the interior permanent magnet motor," Journal of Energies, Vol. 11, No. 9, 1-12, 2018.

11. Jabbari, A. and F. Dubas, "A new subdomain method for performances computation in interior permanent-magnet (IPM) machines," Iranian Journal of Electrical and Electronic Engineering, Vol. 16, No. 1, 26-38, 2020.

12. Hannon, B., P. Sergeant, and L. Dupre, "2-D analytical subdomain model of a slotted PMSM with shielding cylinder," IEEE Trans. on Magnetics, Vol. 50, No. 7, 2014.
doi:10.1109/TMAG.2014.2309325

13. Rahideh, A., H. Moghbelli, and T. Korakianitis, "Two-dimensional analytical magnetic field calculations for doubly-salient machines," IJST Trans. of Electrical Engineering, Vol. 38, No. E1, 33-57, 2014.

14. Ben Yahia, M., K. Boughrara, and F. Dubas, "Two-dimensional exact subdomain technique of switched reluctance machines with sinusoidal current excitation," Math. Comput. Appl., Vol. 23, No. 4, 59, 2018.

15. Djelloul-Khedda, Z. and K. Boughrara, "Nonlinear analytical prediction of magnetic field and electromagnetic performances in switched reluctance machines," IEEE Trans. on Magnetics, Vol. 53, No. 7, 2017.
doi:10.1109/TMAG.2017.2679686

16. Oner, Y., et al., "Analytical on-load sub-domain field model of permanent magnet Vernier machines," IEEE Trans. on Industrial Electronics, Vol. 63, No. 7, 4105-4117, 2016.
doi:10.1109/TIE.2016.2532285

17. Boughrara, K., T. Lubin, and R. Ibtiouen, "General subdomain model for predicting lagnetic field in internal and external rotor multiphase flux-switching machines topologies," IEEE Trans. on Magnetics, Vol. 49, No. 10, 5310-5325, 2013.
doi:10.1109/TMAG.2013.2260827

18. Male, G., et al., "Analytical calculation of the flux density distribution in a superconducting reluctance machine with HTS bulks rotor," Elsevier, Mathematics and Computers in Simulation, Vol. 90, 230-243, 2013.
doi:10.1016/j.matcom.2013.01.003

19. Wu, J., B. Wen, Y. Zhang, and Q. Zhang, "Complete subdomain model for radial-flux slotted PM machines with toroidal windings accounting for the iron-part," IOP Conference Series: Materials Science and Engineering, Vol. 569, No. 3, 032054, 2019.
doi:10.1088/1757-899X/569/3/032054

20. Cheng, D. K., Field and Wave Electromagnetics, Tsinghua University Press, 2006.

Dr. Sohrab Amini Velashani

Professor Jawad Faiz