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

January 2011 Category: Modelization

**Authors**: Duro Basic, Al Kassem Jebai, François Malrait, Philippe Martin, Pierre Rouchon in ADVANCES IN THE THEORY OF CONTROL, SIGNALS AND SYSTEMS WITH PHYSICAL MODELING, Lecture Notes in Control and Information Sciences, Vol 407, pp. 41-48, 2011 DOI: 10.1007/978-3-642-16135-3_4

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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**BibTeX**:

@Incollection{,

author = {Duro Basic, Al Kassem Jebai, François Malrait, Philippe Martin, Pierre Rouchon},

title = {Using Hamiltonians to Model Saturation in Space Vector Representations of AC Electrical Machines},

booktitle = {ADVANCES IN THE THEORY OF CONTROL, SIGNALS AND SYSTEMS WITH PHYSICAL MODELING},

editor = {J. Lévine, P. Müllhaupt},

publisher = {Springer Verlag},

address = {Berlin Heidelberg},

pages = {41-48},

year = {2011},

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.},

keywords = {}}