Using Hamiltonians to Model Saturation in Space Vector Representations of AC Electrical Machines

  • Duro Basic
  • Al Kassem Jebai
  • François Malrait
  • Philippe Martin
  • Pierre Rouchon

Abstract

An Hamiltonian formulation with complex fluxes and currents is proposed. This formulation is derived from a recent Lagrangian formulation with complex electrical quantities. The complexification process avoids the usual separation into real and imaginary parts and notably simplifies modeling issues. Simple modifications of the magnetic energy underlying standard (α,β) models yield new (α,β) models describing machines with magnetic saturation and saliency. We prove that the usual expression of the electro-mechanical torque (wedge product of fluxes and currents) is related to a rotational invariance characterizing sinusoidal machines.

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Duro Basic
    • 1
  • Al Kassem Jebai
    • 2
  • François Malrait
    • 1
  • Philippe Martin
    • 2
  • Pierre Rouchon
    • 2
  1. 1.STIESchneider ElectricPacy-sur EureFrance
  2. 2.Mathématiques et SystèmesMines ParisTech, Centre Automatique et SystèmesParis cedex 06France

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