Detailed Analytical Modelling of Inductances and Electromagnetic Torque in Fractional-Slot Concentrated-Wound Interior Permanent Magnet Machines Under Healthy and Open-Phase Fault Conditions

  • Mohammad Farshadnia
Part of the Springer Theses book series (Springer Theses)


This chapter builds upon the modelling of the stator and rotor magnetic characteristics performed in Chaps.  2,  4 and  5, and proposes detailed novel analytical models for the machine self- and mutual inductances, field-alignment torque, reluctance torque and torque ripple in FSCW IPM machines operating under healthy and open-phase fault conditions. The proposed analytical models are a function of the machine geometrical parameters which are then substituted by the machine electrical parameters to obtain equations that can be readily used for real-time implementation on the machine. At first healthy operation of the machine is considered and the proposed models for the electromagnetic torque is used to obtain the optimum current angle that results in maximum average torque at different operating conditions. The obtained results are validated through FEA simulation of a FSCW IPM machine. In the next step, under an open-phase condition a four-leg inverter is considered and injection of custom currents with adjustable phase angles is assumed. An analytical model is first proposed for the stator MMF generated by such currents. This model is then used to derive the average field-alignment torque, reluctance torque, and their torque ripple under the open-phase fault condition. The derived analytical models are used to propose a maximum torque per ampere (MTPA) algorithm under an open-phase fault condition.


  1. 1.
    P.C. Krause, O. Wasynczuk, S.D. Sudhoff, S. Pekarek, Analysis of Electric Machinery and Drive Systems, vol. 75 (Wiley, 2013)Google Scholar
  2. 2.
    S. Jang Ho, C. Hong Soon, Analytical modeling for calculating cogging torque in interior permanent magnet machine with multi flux-barriers. IEEE Trans. Appl. Superconduct. 24, 1–4 (2014)Google Scholar
  3. 3.
    Z. Azar, Z.Q. Zhu, G. Ombach, Influence of electric loading and magnetic saturation on cogging torque, back-EMF and torque ripple of PM machines. IEEE Trans. Magn. 48, 2650–2658 (2012)CrossRefGoogle Scholar
  4. 4.
    H. Seok-Hee, T.M. Jahns, W.L. Soong, M.K. Guven, M.S. Illindala, Torque ripple reduction in interior permanent magnet synchronous machines using stators with odd number of slots per pole pair. IEEE Trans. Energy Convers. 25, 118–127 (2010)CrossRefGoogle Scholar
  5. 5.
    J.P. Karunadasa, A.C. Renfrew, Analysis of torque production in brushless DC and AC motor drives, in Fourth International Conference on Power Electronics and Variable-Speed Drives, 1991 (1990), pp. 451–456Google Scholar
  6. 6.
    B.A. Welchko, T.M. Jahns, S. Hiti, IPM synchronous machine drive response to a single-phase open circuit fault. IEEE Trans. Power Electron. 17, 764–771 (2002)CrossRefGoogle Scholar
  7. 7.
    A. Kontarcek, P. Bajec, M. Nemec, V. Ambrozic, D. Nedeljkovic, Cost-effective three-phase PMSM drive tolerant to open-phase fault. IEEE Trans. Ind. Electron. 62, 6708–6718 (2015)CrossRefGoogle Scholar
  8. 8.
    B.A. Welchko, T.A. Lipo, T.M. Jahns, S.E. Schulz, Fault tolerant three-phase AC motor drive topologies: a comparison of features, cost, and limitations. IEEE Trans. Power Electron. 19, 1108–1116 (2004)CrossRefGoogle Scholar
  9. 9.
    F. Meinguet, J. Gyselinck, Control strategies and reconfiguration of four-leg inverter PMSM drives in case of single-phase open-circuit faults, in Electric Machines and Drives Conference, 2009, IEMDC ‘09. IEEE International (2009), pp. 299–304Google Scholar
  10. 10.
    A. Mohammadpour, L. Parsa, Asymmetrical multi-lane multi-phase motor drives, in Proceedings of the APEC (2014), pp. 2482–2487Google Scholar
  11. 11.
    J.W. Bennett, G.J. Atkinson, B.C. Mecrow, D.J. Atkinson, Fault-tolerant design considerations and control strategies for aerospace drives. IEEE Trans. Ind. Electron. 59, 2049–2058 (2012)CrossRefGoogle Scholar
  12. 12.
    A. Gaeta, G. Scelba, A. Consoli, Sensorless vector control of PM synchronous motors during single-phase open-circuit faulted conditions. IEEE Trans. Ind. Appl. 48, 1968–1979 (2012)CrossRefGoogle Scholar
  13. 13.
    A. Gaeta, G. Scelba, A. Consoli, Modeling and control of three-phase PMSMs under open-phase fault. IEEE Trans. Ind. Appl. 49, 74–83 (2013)CrossRefGoogle Scholar
  14. 14.
    M. Fei, R. Zanasi, F. Grossi, Modeling of multi-phase permanent magnet synchronous motors under open-phase fault condition, in 2011 9th IEEE International Conference on Control and Automation (ICCA) (2011), pp. 59–64Google Scholar
  15. 15.
    L. Alberti, M. Barcaro, N. Bianchi, Design of a low-torque-ripple fractional-slot interior permanent-magnet motor. IEEE Trans. Ind. Appl. 50, 1801–1808 (2014)CrossRefGoogle Scholar

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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.School of Electrical Engineering and TelecommunicationsThe University of New South WalesSydneyAustralia

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