WOLFRAM SYSTEM MODELER

SM_ReluctanceRotor

Synchronous induction machine with reluctance rotor and damper cage

Diagram

Wolfram Language

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SystemModel["Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_ReluctanceRotor"]

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Information

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

Model of a three phase synchronous induction machine with reluctance rotor and damper 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 rotor-fixed AirGap model. The machine models take the following loss effects into account:

heat losses in the temperature dependent stator winding resistances
optional, when enabled: heat losses in the temperature dependent damper cage resistances
friction losses
core losses (only eddy current losses, no hysteresis losses)
stray load losses

Whether a damper cage is present or not, can be selected with Boolean parameter useDamperCage (default = true).
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	50	A RMS
nominal torque	46	Nm
nominal speed	1500	rpm
nominal mechanical output	7.23	kW
efficiency	96.98	%
power factor	0.497
stator resistance	0.03	Ohm per phase at reference temperature
reference temperature TsRef	20	°C
temperature coefficient alpha20s	0	1/K
rotor resistance in d-axis	0.04	Ohm at reference temperature
rotor resistance in q-axis	same as d-axis
reference temperature TrRef	20	°C
temperature coefficient alpha20r	0	1/K
stator reactance Xsd in d-axis	3	Ohm per phase
stator reactance Xsq in q-axis	1	Ohm
stator stray reactance Xss	0.1	Ohm per phase
rotor stray reactance in d-axis Xrds	0.05	Ohm per phase
rotor stray reactance in q-axis Xrqs	same as d-axis
stator operational temperature TsOperational	20	°C
damper operational temperature TrOperational	20	°C
These values give the following inductances:
stator stray inductance per phase	Xss/(2pifNominal)
rotor stray inductance in d-axis	Xrds/(2pifNominal)
rotor stray inductance in q-axis	Xrqs/(2pifNominal)
main field inductance per phase in d-axis	(Xsd-Xss)/(2pifNominal)
main field inductance per phase in q-axis	(Xsq-Xss)/(2pifNominal)

Parameters (25)

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
TrOperational	Value: Type: Temperature (K) Description: Operational temperature of (optional) damper cage
Lmd	Value: Type: Inductance (H) Description: Stator main field inductance per phase in d-axis
Lmq	Value: Type: Inductance (H) Description: Stator main field inductance per phase in q-axis
useDamperCage	Value: Type: Boolean Description: Enable / disable damper cage
Lrsigmad	Value: Type: Inductance (H) Description: Damper stray inductance in d-axis
Lrsigmaq	Value: Lrsigmad Type: Inductance (H) Description: Damper stray inductance in q-axis
Rrd	Value: Type: Resistance (Ω) Description: Damper resistance in d-axis at TRef
Rrq	Value: Rrd Type: Resistance (Ω) Description: Damper resistance in q-axis at TRef
TrRef	Value: Type: Temperature (K) Description: Reference temperature of damper resistances in d- and q-axis
alpha20r	Value: Type: LinearTemperatureCoefficient20 (1/K) Description: Temperature coefficient of damper resistances in d- and q-axis

Inputs (4)

idq_ss	Default Value: airGapR.i_ss Type: Current[2] (A) Description: Stator space phasor current / stator fixed frame
idq_sr	Default Value: airGapR.i_sr Type: Current[2] (A) Description: Stator space phasor current / rotor fixed frame
idq_rs	Default Value: airGapR.i_rs Type: Current[2] (A) Description: Rotor space phasor current / stator fixed frame
idq_rr	Default Value: airGapR.i_rr Type: Current[2] (A) Description: Rotor space phasor current / rotor fixed frame

Outputs (8)

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: PowerBalanceSMR 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

Connectors (10)

	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: ThermalPortSMR
	internalThermalPort	Type: ThermalPortSMR
	ir	Type: RealOutput[2] Description: Damper cage currents
	idq_dr	Type: RealOutput[2] Description: Damper space phasor current / rotor fixed frame
	damperCageLossPower	Type: RealOutput Description: Damper losses

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: PowerBalanceSMR Description: Power balance
	rs	Type: Resistor
	lssigma	Type: Inductor
	lszero	Type: Inductor
	statorCore	Type: Core
	spacePhasorS	Type: SpacePhasor
	strayLoad	Type: StrayLoad
	thermalAmbient	Type: ThermalAmbientSMR
	airGapR	Type: AirGapR
	damperCage	Type: DamperCage