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2012-11-07
Critical Review of the Modified Winding Function Theory
By
Progress In Electromagnetics Research, Vol. 133, 515-534, 2013
Abstract
The Modified Winding Function Theory (MWFTh), regarded as a very powerful and general theory, has been extensively used for the last 15 years. This paper performs an in-depth review of the mathematical and physical framework on which the MWFTh is based, showing that it is indeed very well suited to analyse machines with small air gaps of arbitrary shape. However, contrary to what is usually stated in the literature, it is also proved that its general formulae fail when applied to large air gaps. This major finding is deduced from two different approaches, both of which are later reinforced by numerical examples. In spite of that, there is an important industrial field (diagnosis techniques of salient-pole synchronous machines eccentricities) in which very good theoretical results are reported by applying the MWFTh to these large air-gap machines. This issue is addressed and clarified in the paper.
Citation
Luis Serrano-Iribarnegaray, Pedro Cruz-Romero, and Antonio Gomez-Exposito, "Critical Review of the Modified Winding Function Theory," Progress In Electromagnetics Research, Vol. 133, 515-534, 2013.
doi:10.2528/PIER12091301
References

1. Schmitz, N. L. and D. W. Nowotny, Introductory Electromechanics, The Ronald Press Company, New York, 1965.

2. Luo, X., Y. Liao, H. A. Toliyat, A. El-Antably, and T. A. Lipo, "Multiple coupled circuit modeling of induction machines," IEEE Trans. Ind. Applicat., Vol. 31, No. 2, 311-318, 1995.
doi:10.1109/28.370279

3. Toliyat, H. A. and T. A. Lipo, "Transient analysis of cage induction machines under stator, rotor bar and end ring faults," IEEE Transactions on Energy Conversion, Vol. 10, No. 2, 241-247, 1995.
doi:10.1109/60.391888

4. Milimonfared, J., H. M. Kelk, A. Der Minassians, S. Nandi, and H. A. Toliyat, "A novel approach for broken rotor bar detection in cage induction motors," IEEE Trans. Ind. Applicat., Vol. 35, 1000-1006, 1999.
doi:10.1109/28.793359

5. Joksimovic, M. G. and J. Penman, "The detection of inter-turn short circuits in the s stator windings of operating motors," IEEE Trans. Ind. Electron., Vol. 47, 1078-1084, 2000.
doi:10.1109/41.873216

6. Faiz, J. and B. M. Ebrahimi, "Mixed fault diagnosis in three-phase squirrel-cage induction motor using analysis of air-gap magnetic field," Progress In Electromagnetics Research, Vol. 64, 239-255, 2006.
doi:10.2528/PIER06080201

7. Faiz, J., B. M. Ebrahimi, and M. B. B. Sharifian, "Time stepping finite element analysis of broken bars fault in a three-phase squirrel-cage induction motor," Progress In Electromagnetics Research, Vol. 68, 53-70, 2007.
doi:10.2528/PIER06080903

8. 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.
doi:10.2528/PIER09052004

9. Toliyat, H. A., M. Areffen, and A. Parlos, "A method for dynamic simulation of air-gap eccentricity in induction machines," IEEE Trans. Ind. Applicat., Vol. 32, 910-918, 1996.
doi:10.1109/28.511649

10. Joksimovic, M. G., D. M. Durovic, J. Penman, and N. Arthur, "Dynamic simulation of dynamic eccentricity in induction machines-winding function approach," IEEE Transactions on Energy Conversion, Vol. 15, 143-148, 2000.
doi:10.1109/60.866991

11. Faiz, J. and I. Tabatbaei, "Extension of winding function theory for non-uniform air gap in electric machinery," IEEE Transactions on Magnetics, Vol. 38, No. 66, 2002.

12. Ballantine, S., "Reciprocity in electromagnetic, mechanical, acoustical, and interconnected systems," Proc. of the Institute of Radio Engineers, Vol. 17, No. 6, 927-951, 1929.

13. Al-Nuim, N. A. and H. A. 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.
doi:10.1109/60.678979

14. Faiz, J. and B. M. Ebrahimi, "Static eccentricity fault diagnosis in an acceleration no-load three-phase saturated squirrel-cage induction motor," Progress In Electromagnetics Research B, Vol. 10, 35-54, 2008.
doi:10.2528/PIERB08081702

15. Müller, G., Elektrische Maschinen. Betriebsverhalten Elektrischer Maschinen, VEB Verlag Technik, Berlín, 1990.

16. Doherty, R. E. and C. A. Nickle, "Synchronous Machines. I. An extension of Blondel's two-reaction theory. II. Steady state power-angle characteristics," AIEE Trans., Vol. 45, 912-947, 1926.

17. Seely, S., Electromechanical Energy Conversion, Mc. Graw Hill, New York, 1962.

18. Ivanov-Smolensky, A., Machines Electriques, MIR, Moscu, 1983.

19. Gray, C. B., "Electrical Machines and Drive Systems," Longman Scientific and Technical, Essex, 1991.

20. Palit, B. B., "Einheitliche Untersuchung der elektrischen Maschinen mit Hilfe des Poynting-Vektors und des elektromagnetischen Energieflusses im Luftspaltraum," Zeitschrift für Angewandte Mathematik und Physik, Vol. 31, 384-412, 1980.
doi:10.1007/BF01590664

21. Faiz, J., I. Tabatabaei, and H. A. Toliyat, "An evaluation of inductances of a squirrel-cage induction motor under mixed eccentric conditions," IEEE Transactions on Energy Conversion, Vol. 18, No. 2, 252-258, 2003.
doi:10.1109/TEC.2003.811740

22. 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, 2004.
doi:10.1109/TMAG.2004.826611

23. Akbari, H., H. Meshgin-Kelk, and J. Milimonfared, "Extension of winding function theory for radial and axial nonuniform air-gap in salient pole synchronous machines ," Progress In Electromagnetics Research, Vol. 114, 407-428, 2011.