Determining resultant current harmonic composition of an electric motor symmetric four-phase winding

Electrical Engineering

Electrical engineering complexes and systems


Tereshkin V. M.

Ufa State Aviation Technical University, USATU, 12, K. Marx str., Ufa, 450008, Republic of Bashkortostan, Russia



Modern power electronics and microprocessor technology state-of-the-art allows develop DC-AC converter with any number of phases in a wide power range.

Realization of a multiphase motor (m > 3) based on the magnetic system of a 3-phase motor is also practically a feasible task with certain modernization of the winding scheme.

As an illustration the article presents a schematic diagram of the four-phase winding, its vector representation, as well as four-phase converter control algorithm while vector pulse-width modulation realization.

The electric drive based on a multiphase motor may display certain advantages in compared to the traditional electric drive based on a three-phase motor and find application wherein the higher requirements are placed on vibrations. The cause of vibrations of electromagnetic origin may be the high-order harmonics of the resulting current, which creates an m.m.f. in the air gap.

Preliminary studies revealed that symmetrical 4-phase winding had the worst figures of the spectral composition of m.m.f., compared to the 5- and 7-phase windings. However, the traction electric drive of the “Granit” electric locomotive was just realized based on the 4-phase asynchronous motor. That is the electric drive based on multiphase motor is already an alternative to the electric drive based on the three-phase motor. It imposes the necessity for comprehensive comparative analysis of multiphase windings and control algorithms for converters to which multi-phase windings are being connected.

The article considers an approach based on classical vector method. With its application harmonic analysis of a resultant current of the symmetrical 4-phase winding. The analysis revealed the phase currents' 1, 5, and 9 harmonics formed the resulting currents of positive-sequence, and the phase currents' 3, 7 and 11 harmonics formed the resulting currents of the negative sequence. Accounting for the fact, that the 1, 3 and 5 harmonics are commensurable in magnitude, significant electromagnetic ripples are theoretically possible within the first harmonic period.

The approach based on the classical vector method considered in the paper can be used to analyze the harmonic composition of the resulting current of multiphase windings with any number of phases. This makes the approach universal for the comparative analysis of multiphase windings on the harmonic composition of the resulting current.


four-phase motor winding, resultant current of a four-phase symmetrical winding, harmonic composition of the resultant current, vibrations of electromagnetic origin


  1. Chan C.C. The State of the Art of Electric, Hybrid and Fuel Cell Vehicles. Proceedings of the IEEE, 2007, vol. 95, no 4, pp. 704-718. DOI: 10.1109/JPROC.2007.892489

  2. Chan C.C., Bouscayrol A. and Chen K. Electric, Hybrid, and Fuel-Cell Vehicles: Architectures and Modeling. IEEE Transact Vehicular Technol, 2010, vol. 59, no. 2, pp.589-598. DOI: 10.1109/TVT.2009.2033605

  3. Global EV Outlook: Understanding the Electric Vehicle Landscape to 2020. Electric Vehicle Initiative, International Energy Agency, 2013, 41 p.

  4. Levi E., Bojoi R., Profumo F., Toliyat H.A. and Williamson S. Multiphase induction motor drives a technology status review. Institution of Engineering and Technology Electric Power Applic, 2007, vol. 1, no. 4, pp. 489–516. DOI: 10.1049/iet-epa:20060342

  5. Dwari S. and Parsa L. Fault–Tolerant Control of Five Phase – Permanent–Magnet Motors With Trapezoidal Back EMF. IEEE Transactions on Industrial Electronics, 2011, vol. 58, no. 2, pp. 476–485. DOI: 10.1109/TIE.2010.2045322

  6. Williamson S. and Smith S. Pulsating torque and losses in multiphase induction machines. IEEE Transactions on Industry Applications, 2003, vol. 39, no. 4, pp. 986-993. DOI: 10.1109/TIA.2003.813722

  7. Duran M.J., Barrero F.J., Toral S.L. Multi-Phase Space Vector Pulse Width Modulation: Applications and Strategies. Renewable Energies and Power Quality Journal (RE&PQJ), 2007, vol. 1, no. 5, pp. 580-586. DOI:10.24084/repqj05.341

  8. Duran M.J., Barrero F.J., Toral S.L., Levi E. Multi-dimensional space vector pulse width modulation scheme for five-phase series-connected two-motor drives. IEEE International Electric Machines & Drives Conference ( IEMDC' 07). Antalya, Turkey, 3-5 May 2007. DOI: 10.1109/IEMDC.2007.383602

  9. Levi E. Multiphase electric machines for variable-speed applications. IEEE Transactions on Industrial Electronics, 2008, vol. 55, no. 5, pp. 1893-1909. DOI: 10.1109/TIE.2008.918488

  10. Renukadevi G., Rajambal K. Generalized d-q Model of n-Phase Induction Motor Drive. World Academy of Science, Engineering and Technology International Journal of Electrical and Computer Engineering, 2012, vol. 6, no. 9, pp. 1066-1075.

  11. Le D.T., Averin S.V. Vestnik Moskovskogo aviatsionnogo instituta, 2016, vol. 23, no. 4, pp. 155-163.

  12. Le D.T., Averin S.V. Vestnik Moskovskogo aviatsionnogo instituta, 2016, vol. 23, no. 3, pp. 155–164.

  13. Texas Instruments “TMS320C2000 Motor Control Primer: User's Guide”, Literature Number: SPRUGI6, 2010,

  14. Lim C.S., Levi E., Jones M., Rahim N.A. and Hew W.P. FCS-MPC-based control of a five-phase induction motor and its comparison with PI-PWM control. IEEE Transactions on Industrial Electronics, 2014, vol. 61, no. 1, pp. 149-163. DOI: 10.1109/TIE.2013.2248334

  15. Golubev A.N., Ignatenko C.B. Elektrotekhnika, 2000, no. 6, pp. 28-31.

  16. Golubev A.N., Ignatenko C.B. Elektrotekhnika, 2001, no. 10, pp. 17-22.

  17. Anan'ev S.S., Golubev A.N. Izvestiya vuzov. Tekhnologiya tekstilnoi promyshlennosti, 2006, no. 4(292), pp. 84-86.

  18. Anan'ev S.S., Golubev A.N. Materialy XII regionalnoi nauchno-tekhnicheskoi konferentsii studentov i aspirantov “Elektroenergetika”, Ivanovo, IGEU, 2006, pp. 26-27.

  19. Babaev M.B., Golubev A.N., Ignatenko C.B. II Mezhdunarodnaya konferentsiya po elektromekhanike i elektrotekhnologiyam (Krym, 1-5 October 1996), Moscow, MEI. Part 2, pp. 150-152.

  20. Golubev A.N., Ignatenko C.B. Mezhvuzovskii sbornik nauchnykh trudov po elektrotekhnike, Ivanovo, IGEU, 1998, pp. 3-9.

  21. Elektrovoz gruzovoi postoyannogo toka 2ES10 (Granit) s asinkhronnymi tyagovymi elektrodvigatelyami: Rukovodstvo po ekspluatatsii (DC 2ES10 electric cargo locomotive (Granite) with asynchronous traction motors: manual), Moscow, STM, 2009, 694 p.

  22. Tereshkin V.M., Grishin D.A., Makulov I.A. Elektronika i elektrooborudovanie transporta, 2017, no. 1, pp. 19-26.

  23. Tereshkin V.M., Grishin D.A. Elektrotekhnika, 2017, no. 2, pp. 46-51.

  24. Tereshkin V.M., Grishin D.A., Makulov I.A. Elektrotekhnika, 2018, no. 5, pp. 60-67.

  25. Tereshkin V.M., Grishin D.A., Tereshkin V.V. Materialy mezhdunarodnoi nauchno-prakticheskoi konferentsii “Elektrotekhnicheskie kompleksy i sistemy”, Ufa, UGATU, 2016, pp. 49-55. URL: — informational site of MAI

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