In the previous works, based on winding function theory, the calculation of reluctance machine inductances is carried out using numerical integration or inexact analytical equations based on approximated Fourier series expansions of the inverse air gap function. In this paper, development in Fourier series of the inverse air gap function has not been used, but a closed form analytical equation is developed for inductances calculation. This leads to a very precise computation of the inductances of the faulted machine and more accurate results. Moreover, all space harmonics ignored by the Fourier series expansions of the inverse air gap function will be included in the model. Derived comprehensive equation allows calculating time varying inductances of reluctance machines with different static, dynamic and mixed eccentricities in the frame of a single program. Inductances obtained by the proposed method are compared to those obtained from FE results. A satisfactory match was found between them.
2. Faiz, J. and B. M. Ebrahimi, "Static eccentricity fault diagnosis in an accelerating no-load three-phase saturated squirrel-cage induction motor," Progress In Electromagnetics Research B, Vol. 10, 35-54, 2008.
3. Meshgin-Kelk, H., J. Milimonfared, and H. Toliyat, "Interbar currents and axial fluxes in healthy and faulty induction motors," IEEE Transactions on Industry Applications, Vol. 40, No. 1, 128-134, 2004.
4. Faiz, J. , B. M. Ebrahimi, and M. B. B. Sharifian, "Different faults and their diagnosis techniques in three-phase squirrel-cage induction motors --- A review," Electromagnetics, Vol. 26, No. 7, 543-569, 2006.
5. Faiz, J., B. M. Ebrahimi, and M. B. B. Sharifian, "Time stepping finite element analysis of rotor broken bars fault in a three-phase squirrel-cage induction motor," Progress In Electromagnetics Research, Vol. 68, 53-70, 2007.
6. Torkaman, H. and E. Afjei, "FEM analysis of angular misalignment fault in SRM magnetostatic characteristics," Progress In Electromagnetics Research, Vol. 104, 31-48, 2010.
7. 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, 2009.
8. Torkaman, H. and E. Afjei, "Hybrid method of obtaining degrees of freedom for radial air gap length in SRM under normal and faulty conditions based on magnetostatic model," Progress In Electromagnetics Research, Vol. 100, 3754, 2010.
9. De Bortoli, M. J., S. J. Salon, and C. J. Slavic, "Effect of rotor eccentricity and parallel winding on induction behavior: A study using ¯nite element analysis," IEEE Transactions on Magnetics, Vol. 29, No. 2, 1676-1682, 1993.
10. Toliyat, H., T. A. Lipo, and J. C. White, "Analysis of a concentrated winding induction machine for adjustable speed drive applications, part-1 (motor analysis)," IEEE Transactions on Energy Conversion, Vol. 6, 679-692, 1991.
11. Milimonfared, J., H. M. Kelk, A. Der Minassians, S. Nandi, and H. A. Toliyat, "A novel approach for broken bar detection in cage induction motors," IEEE Transactions on Industry Applications, Vol. 35, 1000-1006, 1999.
12. Joksimovic, M. G. and J. Penman, "The detection of inter turn short circuits in the stator windings of operating motors," IEEE Transactions on Industry Application, Vol. 47, 1078-1084, 2000.
13. Al-Nuaim, N. A. and H. Toliyat, "A novel method for modeling dynamic air-gap eccentricity in synchronous machines based on modified winding function theory," IEEE Transactions on Energy Conversion, Vol. 13, 156-162, 1998.
14. Tabatabaei, I., J. Faiz, H. Lesani, and M. T. Nabavi-Razavi, "Modeling and simulation of a salient pole synchronous generator with dynamic eccentricity using modified winding function approach," IEEE Transactions on Magnetics, Vol. 40, No. 3, May 2004.
15. Joksimovic, G. M., "Dynamic simulation of cage induction machine with air gap eccentricity," IEE Proc. Electr. Power Appl., Vol. 152, No. 4, 803-811, Jul. 2005.
16. Faiz, J., B. M. Ebrahimi, and M. Valavi, "Mixed eccentricity fault diagnosis in salient pole synchronous generator using modified winding function method," Progress In Electromagnetics Research B, Vol. 11, 155-172, 2009.
17. Akbari, H., J. Milimonfared, and H. Meshgin Kelk, "Axial static eccentricity detection in induction machines by wavelet technique," International Review of Electrical Engineering, Vol. 5, No. 3, 2010.
18. Akbari, H., H. Meshgin Kelk, and J. Milimonfared, "Extension of winding function theory for radial and axial non-uniform air gap in salient pole synchronous machines," Progress In Electromagnetics Research, Vol. 114, 407-428, 2011.
19. Lubin, T. and T. Hamiti, "Comparison between finite-element analysis and winding function theory for inductances and torque calculation of a synchronous reluctance machine," IEEE Transactions on Magnetics, Vol. 43, No. 8, 2007.
20. Neti, P. and S. Nandi, "Performance analysis of a reluctance synchronous motor under abnormal operating conditions," Can. J. Elec. Comput. Eng., Vol. 33, No. 2, 2008.
21. Hamiti, T., T. Lubin, and A. Rezzoug, "A simple and efficient tool for design analysis of synchronous reluctance motor," IEEE Transactions on Magnetics, Vol. 44, No. 12, Dec. 2008.
22. Obe, E. S., "Direct computation of AC machine inductances based on winding function theory," Energy Conversion and Management, Vol. 50, 539-542, 2009.
23. Hamiti, T., T. Lubin, L. Baghli, and A. Rezzoug, "Modeling of a synchronous reluctance machine accounting for space harmonics in view of torque ripple minimization," Mathematics and Computers in Simulation, Vol. 81, 354-366, 2010.
24. Akbari, H., J. Milimonfared, and H. Meshgin Kelk, "Improved MWFA for computation of salient pole machine inductances," International Review of Electrical Engineering, Vol. 5, No. 6, 2593-2600, 2010.
25. Ostovic, V., "Computer Aided Analysis of Electrical Machines, A Mathematical Approach," Prentice Hall, 1994.