WOLFRAM SYSTEM MODELER

AIM_SquirrelCage

Asynchronous induction machine with squirrel cage rotor

Diagram

Wolfram Language

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SystemModel["Modelica.Electrical.Machines.BasicMachines.AsynchronousInductionMachines.AIM_SquirrelCage"]

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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	0.29	kg.m2
rotor's moment of inertia	0.29	kg.m2
nominal frequency fNominal	50	Hz
nominal voltage per phase	100	V RMS
nominal current per phase	100	A RMS
nominal torque	161.4	Nm
nominal speed	1440.45	rpm
nominal mechanical output	24.346	kW
efficiency	92.7	%
power factor	0.875
stator resistance	0.03	Ohm per phase at reference temperature
reference temperature TsRef	20	°C
temperature coefficient alpha20s	0	1/K
rotor resistance	0.04	Ohm at reference temperature
reference temperature TrRef	20	°C
temperature coefficient alpha20r	0	1/K
stator reactance Xs	3	Ohm per phase
rotor reactance Xr	3	Ohm
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))/(2pifNominal)
rotor stray inductance	Xr * (1 - sqrt(1-sigma))/(2pifNominal)
main field inductance per phase	sqrt(XsXr (1-sigma))/(2pifNominal)

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 (7)

	flange	Type: Flange_a Description: Shaft
	support	Type: Flange_a Description: Support at which the reaction torque is acting
	internalSupport	Type: Support
	plug_sp	Type: PositivePlug Description: Positive stator plug
	plug_sn	Type: NegativePlug Description: Negative stator plug
	thermalPort	Type: ThermalPortAIMC
	internalThermalPort	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 (9)

	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_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

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