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Squirrel-cage Induction Motor - Introduction

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Squirrel-cage Induction Motor - Introduction

Mar 06, 2023

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This courseware allows the students to test virtually (using real-time simulation) the operation of a squirrel-cage induction motor, henceforth designated IM, when a speed control is required.
The mechanical load of the IM consists of a direct current machine, henceforth designated DCM, operating as a generator and feeding a variable load resistance (see figure 1).


Figure 1: Basic Configuration of the Simulated Circuit for the IM Drive

 Two main control strategies are implemented for the squirrel-cage induction motor: the well-known indirect field-oriented control (IFOC) and the V/F control.

Indirect Field Oriented Control (IFOC)

The IFOC method can be defined as follows:

  • Use of the Concordia transformation which transforms three-phase quantities (a, b, c) into two-phase quantities (

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    ,

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    ) in a stationary reference frame.

  • Use of the Park transformation, which transforms the two-phase quantities (

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    ,

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    ) in a rotating reference frame.

  • Write the equations of the IM in the rotating reference frame.

  • Choose the d-axis so that it is aligned with the rotor flux.
    This goal is achieved by ensuring that a set of equations is verified.

  • The speed control of the IM required the three following steps:

    1. Magnetizing the machine through flux control.

    2. Torque control.

    3. Speed control.

Practical Implementation of the IFOC for IM Drive

First, let define the list of symbols and parameters that are going to be used throughout this document.

IM parameters

Rs : Stator resistance

Rr : Rotor resistance

Ls : Stator self-inductance

Lr : Rotor self-inductance

Msr : Stator-Rotor mutual inductance

s : Dispersion coefficient,

Ts : Stator electrical time constant, Ts = Ls / Rs

Tr :Rotor electrical time constant, Tr = Lr / Rr

DC machine characteristics

Pun : Nominal power.

Van : Armature nominal voltage.

Vfn : Field nominal voltage.

Ifn : Field nominal current.

Nn : Nominal speed in RPM.

Inverter characteristics

Uin : Nominal line to line output voltage.

Udcn : DC nominal input voltage.

fs : Switching frequency.

Other symbols

f : Stator voltages frequency

ω : Stator voltages angular frequency.

Ω : Rotor angular mechanical speed.

ωe : Rotor angular electrical speed, ωe = PΩ

Tem : Electromagnetic torque.

fv : Viscous friction factor.

J : Total inertia (IM and mechanical load).

RL : Load resistance connected to the DC generator.

TL : Total load torque.

TL0 : Load torque due to the mechanical load only, proportional to the speed, TL0 = kL.W

Tf : Viscous friction torque, Tf = fv.W

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m0 : Mechanical time constant at no load,

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m0 = J / fv

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mL : Mechanical time constant at load,
mL = J / (fv + kL)

 : Angle between the d-axis of the rotating reference frame and the a-axis of the stationary reference frame (e.g., Phase “a” of the stator).

ωmr : Angular speed of the rotating reference frame d-q,

imr : Rotor magnetizing current.

vsα, vsβ, isα, isβ : Stator voltages and currents expressed in the stationary reference frame.

vsd, vsq, isd, isq : Stator voltages and currents expressed in the rotating reference frame.

vsdc, vsqc : Decoupling stator voltages expressed in the rotating reference frame.

vsdref, vsqref : Reference stator voltages expressed in the rotating reference frame.

vsαref, vsβref : Reference stator voltages expressed in the stationary reference frame.

tTCL : Desired time constant of the torque closed loop.

tTr : Torque response time.

ΦCL : Time constant of the regulated flux.

The values of the parameters previously described are summarized in tables 1, 2, and 3.
It should be noted that a three-phase, two-level inverter has been considered for the IM drive.

DC Input

Voltage DC

1000 V

Maximum Current

13.5 A

AC Output

3-phase

Voltage LL RMS

460 V

Maximum Current

24 A

Power

13.5 kW