This paper presents an analytical calculation of magnetic field and electromagnetic performances of 3-, 5-, 7-, 9-, 11-phases cage rotor induction machines in healthy, broken bars and open phase's conditions. This model is formulated to consider all types of multi-phase/multipoles windings and used for the identification of electrical equivalent circuit (EEC) parameters. It's based on the subdomain model and the resolution of Poisson's, Laplace's, and Helmholtz's equations in each subdomain issued from Maxwell equations using the method of separation of variables and Fourier series when the machines are fed with sinusoidal current and voltage. The developed analytical model permits the calculation of magnetic field distribution, eddy current, circuit model parameters, and unbalanced magnetic radial force due to broken bars, electromagnetic torque and absorbed stator current. A comparative analysis between the studied five multi-phases machines is done with considering identical power rate. The analytical results are validated by those issued from the finite-element method (FEM).
2. Pereira, L. A., C. C. Scharlau, L. F. A. Pereira, and J. F. Haffner, "General model of a five-phase induction machine allowing for harmonics in the air gap field," IEEE Trans. Energy Conversion, Vol. 21, No. 4, 891-899, December 2006.
3. Abdel-khalik, A. S., M. I. Masoud, A. Shehab, and A. M. Massoud, "Effect of current harmonic injection on constant rotor volume multiphase induction machine stators: A comparative study," IEEE. Trans. Ind. Apps., Vol. 48, No. 6, 2002-2013, November-December 2012.
4. Matyas, A. R., K. A. Biro, and D. Fodorean, "Multi-phase synchronous motor solution for steering applications," Progress In Electromagnetics Research, Vol. 131, 63-80, September 2012.
5. Apsley, J. and S. Williamson, "Analysis of multiphase induction machines with winding faults," IEEE Trans. Ind. Apps., Vol. 42, No. 2, 465-472, March-April 2006.
6. Vaseghi, B., N. Takorabet, and F. Meibody-Tabar, "Transient finite element analysis of induction machines with stator winding turn fault," Progress In Electromagnetics Research, Vol. 95, 1-18, 2009.
7. Mori, D. and T. Ishikawa, "Force and vibration analysis of induction motors," IEEE Trans. on Magnetics, Vol. 41, No. 5, 1948-1951, May 2005.
8. 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 Magnetics, Vol. 51, No. 2, 8200317-8200334, February 2015.
9. Lubin, T., S. Mezani, and A. Rezzoug, "Anlytic calculation of eddy currents in the slots of electrical machines application to cage rotor induction motors," IEEE Trans. on Magnetics, Vol. 41, No. 11, 4650-4659, November 2011.
10. 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 Magnetics, Vol. 50, No. 12, 7028214-7028228, December 2014.
11. Kim, D. Y., G. H. Nam, and G. H. Jang, "Reduction of magnetically induced vibration of a spoke- type IPM motor using magnetomechanical coupled analysis and optimization," IEEE Trans. on Magnetics, Vol. 49, No. 9, 5097-5105, September 2013.
12. 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.
13. Pyrhonen, J., T. Jokinen, and V. Hrabovcova, Design of Rotating Electrical Machines, John Wiley & Sons, Ltd., 2008.
14. Meeker, D. C., Finite Element Method Magnetics, Version 4.2, April 1, 2009 Build, http://www.femm.info.