volume | PIER Journals

Abstract

This article presents a novel contribution to the improvement of the analytic modeling of electrical machines using two-dimensional (2-D) subdomain technique with Taylor polynomial. To validate this novel method, the semi-analytical model has been implemented for spoke-type permanent-magnet (PM) machines (STPMM). Magnetostatic Maxwell's equations are solved in polar coordinates, and in all parts of the machine. The global solution is obtained using the traditional boundary conditions (BCs), in addition to new radial BCs (e.g., between the PMs and the rotor teeth) which are traduced into a system of linear equations according to Taylor series expansion. The magnetic field calculations are performed for two different values of iron core relative permeability (viz., 10 and 1,000) and compared to finite-element method (FEM) predictions. The results show that a very good agreement is obtained.

1. Dubas, F. and K. Boughrara, "New scientific contribution on the 2-D subdomain technique in cartesian coordinates: Taking into account of iron parts," Math. Comput. Appl., Vol. 22, No. 1, 17, 2017, DOI: 10.3390/mca22010017.

2. 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 Trans. on Magn., Vol. 45, No. 5, 2097-2109, 2009.
doi:10.1109/TMAG.2009.2013245

3. Devillers, E., J. Le Besnerais, T. Lubin, M. Hecquet, and J. P. Lecointe, "A review of subdomain modeling techniques in electrical machines: Performances and applications," Proc. ICEM, Lausanne, Switzerland, Sep. 4–7, 2016.

4. Tiegna, H., Y. Amara, and G. Barakat, "Overview of analytical models of permanent magnet electrical machines for analysis and design purposes," Mathematics and Computer in Simulation, Vol. 90, 162-177, 2013.
doi:10.1016/j.matcom.2012.12.002

5. Curti, M., J. J. H. Paulides, and E. A. Lomonova, "An overview of analytical methods for magnetic field computation," Proc. EVER, Grimaldi Forum, Monaco, Mar. 31–Apr. 02, 2015.

6. Sprangers, R. L. J., J. J. H. Paulides, B. L. J. Gysen, and E. A. Lomonova, "Magnetic saturation in semi-analytical harmonic modeling for electric machine analysis," IEEE Trans. on Magn., Vol. 52, No. 2, Art. ID 8100410, 2016.

7. 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 Trans. on Magn., Vol. 52, No. 5, Art. ID 8103013, 2016.

8. Dubas, F. and A. Rahideh, "Two-dimensional analytical permanent-magnet eddy-current loss calculations in slotless PMSM equipped with surface-inset magnets," IEEE Trans. on Magn., Vol. 50, No. 3, Art. ID 6300320, 2014.

9. Yilmaz, M. and P. T. Krein, "Capabilities of finite element analysis and magnetic equivalent circuits for electrical machine analysis and design," Proc. PESC, Rhodes, Greece, Jun. 15–19, 2008.

10. Sulaiman, E. B., F. Khan, and T. Kosaka, "Field-excited flux switching motor design, optimization and analysis for future hybrid electric vehicle using finite element analysis," Progress In Electromagnetics Research B, Vol. 71, 153-166, 2016.
doi:10.2528/PIERB16092502

11. Konwar, R. S., K. Kalita, A. Banerjee, and W. K. S. Khoo, "Electromagnetic analysis of a bridge configured winding cage induction machine using finite element method," Progress In Electromagnetics Research B, Vol. 48, 347-373, 2013.
doi:10.2528/PIERB12112205

12. Schutte, J. and J. M. Strauss, "Optimization of a transverse flux linear PM generator using 3D finite element analysis," Proc. ICEM, Rome, Italy, Sep. 6–8, 2010.

13. Espanet, C., C. Kieffer, A. Mira, S. Giurgea, and F. Gustin, "Optimal design of a special permanent magnet synchronous machine for magnetocaloric refrigeration," Proc. ECCE, Denver, CO, USA, Sep. 15–19, 2013.

14. Benlamine, R., F. Dubas, S.-A. Randi, D. Lhotellier, and C. Espanet, "3-D numerical hybrid method for PM eddy-current losses calculation: Application to axial-flux PMSMs," IEEE Trans. on Magn., Vol. 51, No. 7, Art. ID 8106110, 2015.

15. 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.
doi:10.2528/PIERB16091502

16. Teymoori, S., A. Rahideh, H. Moayed-Jahromi, and M. Mardaneh, "2-D analytical magnetic field prediction for consequent-pole permanent magnet synchronous machines," IEEE Trans. on Magn., Vol. 52, No. 6, Art. ID 8202114, 2016.

17. 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.
doi:10.2528/PIERB12111306

18. 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 Magn., Vol. 48, No. 6, 2080-2091, 2012.
doi:10.1109/TMAG.2011.2180918

19. Boughrara, K., R. Ibtiouen, and F. Dubas, "Analytical prediction of electromagnetic performances and unbalanced magnetic forces in fractional-slot spoke-type permanent-magnet machines," Proc. ICEM, Lausanne, Switzerland, Sep. 4–7, 2016.

20. Boughrara, K., N. Takorabet, R. Ibtiouen, O. Touhami, and F. Dubas, "Analytical analysis of cage rotor induction motors in healthy, defective, and broken bars conditions," ” IEEE Trans. on Magn., Vol. 51, No. 2, Art. ID 8200317, 2015.

21. Roubache, L., K. Boughrara, and R. Ibtiouen, "Analytical electromagnetic analysis of multi-phases cage rotor induction motors in healthy, broken bars and open phases conditions," Progress In Electromagnetics Research B, Vol. 70, 113-130, 2016.
doi:10.2528/PIERB16072510

22. Boughrara, K., F. Dubas, and R. Ibtiouen, "2-D analytical prediction of eddy currents, circuit model parameters, and steady-state performances in solid rotor induction motors," IEEE Trans. on Magn., Vol. 50, No. 12, Art. ID 7028214, 2014.

23. Sprangers, R. L. J., J. J. H. Paulides, B. L. J. Gysen, J. Waarma, and E. A. Lomonova, "Semi analytical framework for synchronous reluctance motor analysis including finite soft-magnetic material Permeability," IEEE Trans. on Magn., Vol. 51, No. 11, Art. ID 8110504, 2015.

24. Djelloul, K. Z., K. Boughrara, R. Ibtiouen, and F. Dubas, "Nonlinear analytical calculation of magnetic field and torque of switched reluctance machines," Proc. CISTEM, Marrakech-Benguerir, Maroc, Oct. 26–28, 2016.

25. Djelloul, K. Z., K. Boughrara, F. Dubas, and R. Ibtiouen, "Nonlinear analytical prediction of magnetic field and electromagnetic performances in switched reluctance machines," IEEE Trans. on Magn., 2017, DOI: 10.1100/TMAG.2017.2679686.

26. Meeker, D. C., Finite Element Method Magnetics ver. 4.2, [Online], Available: http://www.femm.info, Apr. 1, 2009.

Dr. Lazhar Roubache

Dr. Kamel Boughrara

Dr. Frederic Dubas

Dr. Rachid Ibtiouen