Synchronous Machine Modelling

  • Ahmed Masmoudi
Part of the SpringerBriefs in Electrical and Computer Engineering book series (BRIEFSELECTRIC)


The chapter deals with the modelling of the synchronous machines (SMs). Following the introduction of the continuous development of the SMs, their a-b-c model is established considering the case of salient pole machines. Then, the Park transform is applied to the established a-b-c model, leading to the Park one. A special attention is paid to the formulation and analysis of the electromagnetic torque with an investigation of the variations of its synchronizing and reluctant components in terms of the torque angle. Then, a characterization of the operation at (i) maximum torque and (ii) unity power factor is carried out before focusing the flux-weakening approaches that could be implemented in SMs considering both smooth and salient pole topologies. The chapter is achieved by a case study dealing with an investigation of the main features of the electric drive unit of a hybrid propulsion system and the possibility of their improvement with emphasis on the extension of the flux-weakening range.


Synchronous machines Modelling A-B-C model Park model Electromagnetic torque Smooth/salient pole Flux weakening 


  1. 1.
    M. Lajoie-Mazenc, Ph. Viarouge, Power Supply of Synchronous Machines (in French) (Technique de l’Ingenieur, D3630, Paris, 1991)Google Scholar
  2. 2.
    G. Grellet, G. Clerc, Electrical Acuators: Principles/Models/Control (in French) (Eyrolles, Paris, 1997). ISBN: 2-212-09352-7Google Scholar
  3. 3.
    B. Multon, J. Lucidarme, L. Prévond, Analysis of the possibilities of the flux weakening of permanent magnet machines (in French). J. Phys. III 5, 623–640 (1995)Google Scholar
  4. 4.
    A.M. El-Refaie, T.M. Jahns, P.J. McCleer, J.W. McKeever, Experimental verification of optimal flux weakening in surface PM machines using concentrated windings. IEEE Trans. Ind. Appl. 42(2), 443–53 (2006)CrossRefGoogle Scholar
  5. 5.
    D. Ishak, Z.Q. Zhu, D. Howe, Eddy-current loss in the rotor magnets of permanent-magnet brushless machines having a fractional number of slots per pole. IEEE Trans. Magn. 41(9), 2462–2469 (2005)CrossRefGoogle Scholar
  6. 6.
    K. Yamazaki, Y. Fukushima, M. Sato, Loss analysis of permanent-magnet motors with concentrated windings-variation of magnet eddy-current loss due to stator and rotor shapes. IEEE Trans. Ind. Appl. 45(4), 1334–1342 (2009)CrossRefGoogle Scholar
  7. 7.
    As. Masmoudi, Ah. Masmoudi, 3-D analytical model with the end effect dedicated to the prediction of PM eddy-current loss in FSPMMs. IEEE Trans. Magn. 51(4), 8103711(1-8) (2015)Google Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Sfax Engineering National SchoolUniversity of SfaxSfaxTunisia

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