WOLFRAM SYSTEMMODELER

AIM_SquirrelCage

Asynchronous induction machine with squirrel cage rotor

Diagram

Wolfram Language

In[1]:=
SystemModel["Modelica.Electrical.Machines.BasicMachines.AsynchronousInductionMachines.AIM_SquirrelCage"]
Out[1]:=

Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

Model of a three phase asynchronous induction machine with squirrel cage.
Resistance and stray inductance of stator is modeled directly in stator phases, then using space phasor transformation. Resistance and stray inductance of rotor's squirrel cage is modeled in two axis of the rotor-fixed coordinate system. Both together connected via a stator-fixed AirGap model. The machine models take the following loss effects into account:

  • heat losses in the temperature dependent stator winding resistances
  • heat losses in the temperature dependent cage resistances
  • friction losses
  • core losses (only eddy current losses, no hysteresis losses)
  • stray load losses

Default values for machine's parameters (a realistic example) are:

number of pole pairs p 2
stator's moment of inertia 0.29kg.m2
rotor's moment of inertia 0.29kg.m2
nominal frequency fNominal 50Hz
nominal voltage per phase 100V RMS
nominal current per phase 100A RMS
nominal torque 161.4Nm
nominal speed 1440.45rpm
nominal mechanical output 24.346kW
efficiency 92.7%
power factor 0.875
stator resistance 0.03Ohm per phase at reference temperature
reference temperature TsRef 20°C
temperature coefficient alpha20s 01/K
rotor resistance 0.04Ohm at reference temperature
reference temperature TrRef 20°C
temperature coefficient alpha20r 01/K
stator reactance Xs 3Ohm per phase
rotor reactance Xr 3Ohm
total stray coefficient sigma 0.0667
stator operational temperature TsOperational 20°C
rotor operational temperature TrOperational 20°C
These values give the following inductances:
stator stray inductance per phase Xs * (1 - sqrt(1-sigma))/(2*pi*fNominal)
rotor stray inductance Xr * (1 - sqrt(1-sigma))/(2*pi*fNominal)
main field inductance per phase sqrt(Xs*Xr * (1-sigma))/(2*pi*fNominal)

Parameters (21)

Jr

Value:

Type: Inertia (kg·m²)

Description: Rotor's moment of inertia

useSupport

Value: false

Type: Boolean

Description: Enable / disable (=fixed stator) support

Js

Value: Jr

Type: Inertia (kg·m²)

Description: Stator's moment of inertia

useThermalPort

Value: false

Type: Boolean

Description: Enable / disable (=fixed temperatures) thermal port

frictionParameters

Value:

Type: FrictionParameters

Description: Friction loss parameter record

p

Value:

Type: Integer

Description: Number of pole pairs (Integer)

fsNominal

Value:

Type: Frequency (Hz)

Description: Nominal frequency

TsOperational

Value:

Type: Temperature (K)

Description: Operational temperature of stator resistance

Rs

Value:

Type: Resistance (Ω)

Description: Stator resistance per phase at TRef

TsRef

Value:

Type: Temperature (K)

Description: Reference temperature of stator resistance

alpha20s

Value:

Type: LinearTemperatureCoefficient20 (¹/K)

Description: Temperature coefficient of stator resistance at 20 degC

Lszero

Value: Lssigma

Type: Inductance (H)

Description: Stator zero sequence inductance

Lssigma

Value:

Type: Inductance (H)

Description: Stator stray inductance per phase

statorCoreParameters

Value:

Type: CoreParameters

Description: Stator core loss parameter record; all parameters refer to stator side

strayLoadParameters

Value:

Type: StrayLoadParameters

Description: Stray load loss parameter record

Lm

Value:

Type: Inductance (H)

Description: Stator main field inductance per phase

Lrsigma

Value:

Type: Inductance (H)

Description: Rotor stray inductance per phase (equivalent three phase winding)

Rr

Value:

Type: Resistance (Ω)

Description: Rotor resistance per phase (equivalent three phase winding) at TRef

TrRef

Value:

Type: Temperature (K)

Description: Reference temperature of rotor resistance

alpha20r

Value:

Type: LinearTemperatureCoefficient20 (¹/K)

Description: Temperature coefficient of rotor resistance at 20 degC

TrOperational

Value:

Type: Temperature (K)

Description: Operational temperature of rotor resistance

Inputs (4)

idq_ss

Default Value: airGapS.i_ss

Type: Current[2] (A)

Description: Stator space phasor current / stator fixed frame

idq_sr

Default Value: airGapS.i_sr

Type: Current[2] (A)

Description: Stator space phasor current / rotor fixed frame

idq_rs

Default Value: airGapS.i_rs

Type: Current[2] (A)

Description: Rotor space phasor current / stator fixed frame

idq_rr

Default Value: airGapS.i_rr

Type: Current[2] (A)

Description: Rotor space phasor current / rotor fixed frame

Outputs (9)

phiMechanical

Default Value: flange.phi - internalSupport.phi

Type: Angle (rad)

Description: Mechanical angle of rotor against stator

wMechanical

Default Value: der(phiMechanical)

Type: AngularVelocity (rad/s)

Description: Mechanical angular velocity of rotor against stator

tauElectrical

Default Value: inertiaRotor.flange_a.tau

Type: Torque (N·m)

Description: Electromagnetic torque

tauShaft

Default Value: -flange.tau

Type: Torque (N·m)

Description: Shaft torque

powerBalance

Type: PowerBalanceAIMC

Description: Power balance

vs

Default Value: plug_sp.pin.v - plug_sn.pin.v

Type: Voltage[m] (V)

Description: Stator instantaneous voltages

is

Default Value: plug_sp.pin.i

Type: Current[m] (A)

Description: Stator instantaneous currents

i_0_s

Default Value: spacePhasorS.zero.i

Type: Current (A)

Description: Stator zero-sequence current

ir

Default Value: squirrelCageR.i

Type: Current[2] (A)

Description: Rotor cage currents

Connectors (5)

flange

Type: Flange_a

Description: Shaft

support

Type: Flange_a

Description: Support at which the reaction torque is acting

plug_sp

Type: PositivePlug

Description: Positive stator plug

plug_sn

Type: NegativePlug

Description: Negative stator plug

thermalPort

Type: ThermalPortAIMC

Components (17)

frictionParameters

Type: FrictionParameters

Description: Friction loss parameter record

inertiaRotor

Type: Inertia

inertiaStator

Type: Inertia

fixed

Type: Fixed

friction

Type: Friction

statorCoreParameters

Type: CoreParameters

Description: Stator core loss parameter record; all parameters refer to stator side

strayLoadParameters

Type: StrayLoadParameters

Description: Stray load loss parameter record

powerBalance

Type: PowerBalanceAIMC

Description: Power balance

rs

Type: Resistor

lssigma

Type: Inductor

lszero

Type: Inductor

statorCore

Type: Core

spacePhasorS

Type: SpacePhasor

strayLoad

Type: StrayLoad

thermalAmbient

Type: ThermalAmbientAIMC

airGapS

Type: AirGapS

squirrelCageR

Type: SquirrelCage

Used in Examples (10)

AIMC_DOL

Modelica.Electrical.Machines.Examples.AsynchronousInductionMachines

Test example: AsynchronousInductionMachineSquirrelCage direct-on-line

AIMC_YD

Modelica.Electrical.Machines.Examples.AsynchronousInductionMachines

Test example: AsynchronousInductionMachineSquirrelCage Y-D

AIMC_Transformer

Modelica.Electrical.Machines.Examples.AsynchronousInductionMachines

Test example: AsynchronousInductionMachineSquirrelCage transformer starting

AIMC_Inverter

Modelica.Electrical.Machines.Examples.AsynchronousInductionMachines

Test example: AsynchronousInductionMachineSquirrelCage with inverter

AIMC_Conveyor

Modelica.Electrical.Machines.Examples.AsynchronousInductionMachines

Test example: AsynchronousInductionMachineSquirrelCage with inverter driving a conveyor

AIMC_InverterDrive

Modelica.Electrical.Machines.Examples.AsynchronousInductionMachines

Test example: AsynchronousInductionMachineSquirrelCage inverter drive

AIMC_Steinmetz

Modelica.Electrical.Machines.Examples.AsynchronousInductionMachines

AsynchronousInductionMachineSquirrelCage Steinmetz-connection

AIMC_withLosses

Modelica.Electrical.Machines.Examples.AsynchronousInductionMachines

Test example: AsynchronousInductionMachineSquirrelCage with losses

AIMC_Initialize

Modelica.Electrical.Machines.Examples.AsynchronousInductionMachines

Test example: Steady-State Initialization of AsynchronousInductionMachineSquirrelCage

AIMC_DOL

Modelica.Magnetic.FundamentalWave.Examples.BasicMachines

Direct on line (DOL) start of asynchronous induction machine with squirrel cage