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Direct Eigen Control for Induction Machines and Synchronous Motors by Jean Claude Alacoque

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1

Induction Machine

The three-phase induction machine with non-salient poles is the most widespread electric motor because of its simple and robust construction; it is perhaps the electrical machine that has the least intuitive operation (Caron and Hautier, 1995). It has been the subject of very many technical publications.

1.1 Electrical Equations and Equivalent Circuits

Starting from the equivalent three-phase electrical circuit of the induction machine without neutral current, let us establish initially the relations between the various electrical variables.

1.1.1 Definitions and Notation

Definitions and notation of motor parameters:

  • stator resistance

Rs

  • rotor resistance

Rr

  • stator leakage inductance

ls

  • rotor leakage inductance

lr

  • mutual inductance

Lm

  • stator inductance

Ls = Lm + ls

  • rotor inductance

Lr = Lm + lr

  • stator time constant

image
  • rotor time constant

image
  • pole pair number

Np

  • dispersion coefficient

image

Definitions and notations of mechanical and electrical angular frequencies:

  • mechanical angular frequency of the rotor        Ω
  • polar mechanical angular frequency1          ω = Np ⋅ Ω
  • stator electrical angular frequency                ωs
  • rotor electrical angular frequency                 ωr
  • relative slip                                                 ...

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