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Induction Machine (Squirrel-Cage)

Purpose

Non-saturable induction machine with squirrel-cage rotor.

Library

Electrical / Machines

Description

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This model of a squirrel-cage induction machine can only be used with the continuous state-space method. If you want to use the discrete state-space method or if you need to take saturation into account, please use the Induction Machine with Saturation and short-circuit the rotor terminals.

The machine model is based on a stationary reference frame (Clarke transformation). A sophisticated implementation of the Clarke transformation facilitates the connection of external inductances in series with the stator windings.

The machine operates as a motor or generator; if the mechanical torque has the same sign as the rotational speed the machine is operating in motor mode, otherwise in generator mode. All electrical variables and parameters are viewed from the stator side. In the component icon, phase a of the stator winding is marked with a dot.

In order to inspect the implementation, please select the component in your circuit and choose Look under mask from the Edit menu.

Electrical System

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The rotor flux is computed as

Yr,d = L ′lri′r,d + Lm (is,d + i′r,d)

                (        )
Yr,q = L′lri′r,q + Lm is,q + i′r,q

The three-phase voltages vs,ab   and vs,bc   at the stator terminals are transformed into dq quantities:

[     ]   [        ] [      ]
  vs,d   =    23  13   ⋅  vs,ab
  vs,q       0   1√3-    vr,bc

Likewise, the stator currents in the stationary reference frame are transformed back into three-phase currents:

⌊    ⌋    ⌊           ⌋
  is,a     |  1    √0  |  [ i  ]
⌈ is,b ⌉  = ⌈ - 12   -32√- ⌉ ⋅  si,d
  is,c       - 12  - 23-     s,q

Electro-Mechanical System

Electromagnetic torque:

T  =  3 pL  (i  i′  - i i′ )
 e    2   m  s,q r,d   s,d r,q

Mechanical System

Mechanical rotor speed ωm  :

ω   =  1-(T  - Fω  - T )
 m     J  e     m    m

ω  = pωm

Mechanical rotor angle θm  :

θm  = ωm

θ = pθm

Parameters

Same as for the Induction Machine with slip-ring rotor.

Inputs and Outputs

Same as for the Induction Machine with slip-ring rotor.

Probe Signals

Most probe signals for the Induction Machine with slip-ring rotor are also available with this squirrel-cage machine. Only the following probe signal is different:

Rotor currents
The rotor currents i′r,d    and i′r,q    in the stationary reference frame in A, referred to the stator side.