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# 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 rotor time constant pole pair number Np dispersion coefficient

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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