WOLFRAM SYSTEM MODELER

SM_ElectricalExcited

Electrical excited synchronous induction machine with damper cage

Diagram

Wolfram Language

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

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Information

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

Model of a three phase electrical excited synchronous induction machine with damper cage.
Resistance and stray inductance of stator is modeled directly in stator phases, then using space phasor transformation and a rotor-fixed AirGap model. Resistance and stray inductance of rotor's squirrel cage is modeled in two axis of the rotor-fixed coordinate system. Electrical excitation is modelled by converting excitation current and voltage to d-axis space phasors. 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 excitation winding resistance
optional, when enabled: heat losses in the temperature dependent damper cage resistances
brush losses in the excitation circuit
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
no-load excitation current @ nominal voltage and frequency	10	A DC
warm excitation resistance	2.5	Ohm
nominal current per phase	100	A RMS
nominal apparent power	-30000	VA
power factor	-1.0	ind./cap.
nominal excitation current	19	A
efficiency w/o excitation	97.1	%
nominal torque	-196.7	Nm
nominal speed	1500	rpm
nominal rotor angle	-57.23	degree
stator resistance	0.03	Ohm per phase at reference temperature
reference temperature TsRef	20	°C
temperature coefficient alpha20s	0	1/K
stator reactance Xd	1.6	Ohm per phase in d-axis
giving Kc	0.625
stator reactance Xq	1.6	Ohm per phase in q-axis
stator stray reactance Xss	0.1	Ohm per phase
damper resistance in d-axis	0.04	Ohm at reference temperature
damper resistance in q-axis	same as d-axis
reference temperature TrRef	20	°C
temperature coefficient alpha20r	0	1/K
damper stray reactance in d-axis XDds	0.05	Ohm
damper stray reactance in q-axis XDqs	same as d-axis
excitation resistance	2.5	Ohm at reference temperature
reference temperature TeRef	20	°C
temperature coefficient alpha20e	0	1/K
excitation stray inductance	2.5	% of total excitation inductance
stator operational temperature TsOperational	20	°C
damper operational temperature TrOperational	20	°C
excitation operational temperature TeOperational	20	°C
These values give the following inductances:
main field inductance in d-axis	(Xd - Xss)/(2pifNominal)
main field inductance in q-axis	(Xq - Xss)/(2pifNominal)
stator stray inductance per phase	Xss/(2pifNominal)
damper stray inductance in d-axis	XDds/(2pifNominal)
damper stray inductance in q-axis	XDqs/(2pifNominal)

Parameters (33)

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
VsNominal	Value: Type: Voltage (V) Description: Nominal stator RMS voltage per phase
IeOpenCircuit	Value: Type: Current (A) Description: Open circuit excitation current @ nominal voltage and frequency
Re	Value: Type: Resistance (Ω) Description: Excitation resistance at TRef
TeRef	Value: Type: Temperature (K) Description: Reference temperature of excitation resistance
alpha20e	Value: Type: LinearTemperatureCoefficient20 (1/K) Description: Temperature coefficient of excitation resistance
sigmae	Value: Type: Real Description: Stray fraction of total excitation inductance
TeOperational	Value: Type: Temperature (K) Description: Operational excitation temperature
brushParameters	Value: Type: BrushParameters Description: Brush loss parameter record

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 (10)

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: PowerBalanceSMEE 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
ve	Default Value: pin_ep.v - pin_en.v Type: Voltage (V) Description: Excitation voltage
ie	Default Value: pin_ep.i Type: Current (A) Description: Excitation current

Connectors (12)

	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: ThermalPortSMEE
	internalThermalPort	Type: ThermalPortSMEE
	ir	Type: RealOutput[2] Description: Damper cage currents
	idq_dr	Type: RealOutput[2] Description: Damper space phasor current / rotor fixed frame
	pin_ep	Type: PositivePin Description: Positive excitation pin
	pin_en	Type: NegativePin Description: Negative excitation pin
	damperCageLossPower	Type: RealOutput Description: Damper losses

Components (22)

	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: PowerBalanceSMEE Description: Power balance
	rs	Type: Resistor
	lssigma	Type: Inductor
	lszero	Type: Inductor
	statorCore	Type: Core
	spacePhasorS	Type: SpacePhasor
	strayLoad	Type: StrayLoad
	thermalAmbient	Type: ThermalAmbientSMEE
	airGapR	Type: AirGapR
	brushParameters	Type: BrushParameters Description: Brush loss parameter record
	damperCage	Type: DamperCage
	electricalExcitation	Type: ElectricalExcitation
	re	Type: Resistor
	lesigma	Type: Inductor
	brush	Type: Brush

Used in Examples (5)

	SMEE_DOL Modelica.Electrical.Machines.Examples.SynchronousInductionMachines Test example: ElectricalExcitedSynchronousInductionMachine starting direct on line
	SMEE_Generator Modelica.Electrical.Machines.Examples.SynchronousInductionMachines Test example: ElectricalExcitedSynchronousInductionMachine as Generator
	SMEE_LoadDump Modelica.Electrical.Machines.Examples.SynchronousInductionMachines Test example: ElectricalExcitedSynchronousInductionMachine with voltage controller
	SMEE_Rectifier Modelica.Electrical.Machines.Examples.SynchronousInductionMachines Test example: ElectricalExcitedSynchronousInductionMachine with rectifier
	SMEE_Generator Modelica.Magnetic.FundamentalWave.Examples.BasicMachines Electrical excited synchronous machine operating as generator

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