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Induction Machine (Open Stator Windings)

Purpose

Non-saturable induction machine with squirrel-cage rotor and open stator windings

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. 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, the positive terminal of phase a of the stator windings 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,a  , vs,b   and vs,c   across the individual stator windings are transformed into dq0 quantities:

⌊     ⌋   ⌊              ⌋  ⌊     ⌋
  vs,d        23  - 13  - 13      vs,a
⌈ vs,q ⌉ = ⌈  0  √13- - √13-⌉ ⋅⌈ vr,b ⌉
  vs,0        13   13    13       vr,c

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

⌊     ⌋    ⌊             ⌋  ⌊     ⌋
  is,a      |  1   √0-  1 |    is,d
⌈ is,b ⌉ =  ⌈ - 12  -2√3  1 ⌉ ⋅⌈ is,q ⌉
  is,c        - 12 - -32- 1      is,0

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  :

       1-
ωm  =  J (Te - Fωm - Tm)

ω  = pωm

Mechanical rotor angle θ
 m  :

θ   = ω
 m     m

θ = pθm

Parameters

Most parameters for the Induction Machine with slip-ring rotor are also applicable for this machine. Only the following parameter differs:

Initial stator currents
A three-element vector containing the initial stator currents is,a,0  , is,b,0   and is,c,0   of phase a, b and c in amperes (A).

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 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.