Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines

Models of synchronous induction machines

Information

This package contains models of synchronous induction machines, based on space phasor theory:

SM_PermanentMagnet: synchronous induction machine with permanent magnet excitation, with damper cage
SM_ElectricalExcited: synchronous induction machine with electrical excitation and damper cage
SM_ReluctanceRotor: induction machine with reluctance rotor and damper cage
i.e., a squirrel cage rotor with magnetic poles due to different airgap width

These models use package SpacePhasors.
Please keep in mind:

We keep the same reference system as for motors, i.e.:
Positive RotorDisplacementAngle means acting as motor,
with positive electric power consumption and positive mechanical power output.
ElectricalAngle = p * MechanicalAngle
real axis = d-axis
imaginary= q-axis
Voltage induced by the magnet wheel (d-axis) is located in the q-axis.

Extends from Modelica.Icons.VariantsPackage (Icon for package containing variants).

Package Content

Name Description

SM_PermanentMagnet Permanent magnet synchronous induction machine

SM_ElectricalExcited Electrical excited synchronous induction machine with damper cage

SM_ReluctanceRotor Synchronous induction machine with reluctance rotor and damper cage

Name	Description
SM_PermanentMagnet	Permanent magnet synchronous induction machine
SM_ElectricalExcited	Electrical excited synchronous induction machine with damper cage
SM_ReluctanceRotor	Synchronous induction machine with reluctance rotor and damper cage

Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_PermanentMagnet

Permanent magnet synchronous induction machine

Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_PermanentMagnet

Information

Model of a three phase permanent magnet synchronous induction machine.
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 ccordinate system. Permanent magnet excitation is modelled by a constant equivalent excitation current feeding the d-axis. 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

no-load voltage per phase 112.3 V RMS @ nominal speed

nominal current per phase 100 A RMS

nominal torque 181.4 Nm

nominal speed 1500 rpm

nominal mechanical output 28.5 kW

nominal rotor angle 20.75 degree

efficiency 95.0 %

power factor 0.98

stator resistance 0.03 Ohm per phase at reference temperature

reference temperature TsRef 20 °C

temperature coefficient alpha20s 0 1/K

stator reactance Xd 0.4 Ohm per phase in d-axis

stator reactance Xq 0.4 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

stator operational temperature TsOperational 20 °C

damper operational temperature TrOperational 20 °C

These values give the following inductances:

main field inductance in d-axis (Xd - Xss)/(2*pi*fNominal)

main field inductance in q-axis (Xq - Xss)/(2*pi*fNominal)

stator stray inductance per phase Xss/(2*pi*fNominal)

damper stray inductance in d-axis XDds/(2*pi*fNominal)

damper stray inductance in q-axis XDqs/(2*pi*fNominal)

Extends from Machines.Interfaces.PartialBasicInductionMachine (Partial model for induction machine).

Parameters

Type Name Default Description

Integer p Number of pole pairs (Integer)

Frequency fsNominal Nominal frequency [Hz]

Inertia Jr Jr(start=0.29) Rotor's moment of inertia [kg.m2]

Boolean useSupport false Enable / disable (=fixed stator) support

Inertia Js Stator's moment of inertia [kg.m2]

Boolean useThermalPort false Enable / disable (=fixed temperatures) thermal port

Current idq_ss[2] airGapR.i_ss Stator space phasor current / stator fixed frame [A]

Current idq_sr[2] airGapR.i_sr Stator space phasor current / rotor fixed frame [A]

Current idq_rs[2] airGapR.i_rs Rotor space phasor current / stator fixed frame [A]

Current idq_rr[2] airGapR.i_rr Rotor space phasor current / rotor fixed frame [A]

Voltage VsOpenCircuit Open circuit RMS voltage per phase @ fsNominal [V]

Operational temperatures

Temperature TsOperational Operational temperature of stator resistance [K]

Temperature TrOperational Operational temperature of (optional) damper cage [K]

Nominal resistances and inductances

Resistance Rs Stator resistance per phase at TRef [Ohm]

Temperature TsRef Reference temperature of stator resistance [K]

LinearTemperatureCoefficient20 alpha20s Temperature coefficient of stator resistance at 20 degC [1/K]

Inductance Lszero Lssigma Stator zero sequence inductance [H]

Inductance Lssigma.start 0.1/(2*pi*fsNominal) Stator stray inductance per phase [H]

Inductance Lmd Main field inductance in d-axis [H]

Inductance Lmq Main field inductance in q-axis [H]

DamperCage

Boolean useDamperCage Enable / disable damper cage

Inductance Lrsigmad Damper stray inductance in d-axis [H]

Inductance Lrsigmaq Lrsigmad Damper stray inductance in q-axis [H]

Resistance Rrd Damper resistance in d-axis at TRef [Ohm]

Resistance Rrq Rrd Damper resistance in q-axis at TRef [Ohm]

Temperature TrRef Reference temperature of damper resistances in d- and q-axis [K]

LinearTemperatureCoefficient20 alpha20r Temperature coefficient of damper resistances in d- and q-axis [1/K]

Losses

FrictionParameters frictionParameters frictionParameters(wRef(star... Friction losses

CoreParameters statorCoreParameters Stator core losses

StrayLoadParameters strayLoadParameters Stray load losses

Type	Name	Default	Description
Integer	p		Number of pole pairs (Integer)
Frequency	fsNominal		Nominal frequency [Hz]
Inertia	Jr	Jr(start=0.29)	Rotor's moment of inertia [kg.m2]
Boolean	useSupport	false	Enable / disable (=fixed stator) support
Inertia	Js		Stator's moment of inertia [kg.m2]
Boolean	useThermalPort	false	Enable / disable (=fixed temperatures) thermal port
Current	idq_ss[2]	airGapR.i_ss	Stator space phasor current / stator fixed frame [A]
Current	idq_sr[2]	airGapR.i_sr	Stator space phasor current / rotor fixed frame [A]
Current	idq_rs[2]	airGapR.i_rs	Rotor space phasor current / stator fixed frame [A]
Current	idq_rr[2]	airGapR.i_rr	Rotor space phasor current / rotor fixed frame [A]
Voltage	VsOpenCircuit		Open circuit RMS voltage per phase @ fsNominal [V]
Operational temperatures
Temperature	TsOperational		Operational temperature of stator resistance [K]
Temperature	TrOperational		Operational temperature of (optional) damper cage [K]
Nominal resistances and inductances
Resistance	Rs		Stator resistance per phase at TRef [Ohm]
Temperature	TsRef		Reference temperature of stator resistance [K]
LinearTemperatureCoefficient20	alpha20s		Temperature coefficient of stator resistance at 20 degC [1/K]
Inductance	Lszero	Lssigma	Stator zero sequence inductance [H]
Inductance	Lssigma.start	0.1/(2pifsNominal)	Stator stray inductance per phase [H]
Inductance	Lmd		Main field inductance in d-axis [H]
Inductance	Lmq		Main field inductance in q-axis [H]
DamperCage
Boolean	useDamperCage		Enable / disable damper cage
Inductance	Lrsigmad		Damper stray inductance in d-axis [H]
Inductance	Lrsigmaq	Lrsigmad	Damper stray inductance in q-axis [H]
Resistance	Rrd		Damper resistance in d-axis at TRef [Ohm]
Resistance	Rrq	Rrd	Damper resistance in q-axis at TRef [Ohm]
Temperature	TrRef		Reference temperature of damper resistances in d- and q-axis [K]
LinearTemperatureCoefficient20	alpha20r		Temperature coefficient of damper resistances in d- and q-axis [1/K]
Losses
FrictionParameters	frictionParameters	frictionParameters(wRef(star...	Friction losses
CoreParameters	statorCoreParameters		Stator core losses
StrayLoadParameters	strayLoadParameters		Stray load losses

Connectors

Type Name Description

Flange_a flange Shaft

Flange_a support Support at which the reaction torque is acting

PositivePlug plug_sp Positive stator plug

NegativePlug plug_sn Negative stator plug

Type	Name	Description
Flange_a	flange	Shaft
Flange_a	support	Support at which the reaction torque is acting
PositivePlug	plug_sp	Positive stator plug
NegativePlug	plug_sn	Negative stator plug

Modelica definition

model SM_PermanentMagnet 
  "Permanent magnet synchronous induction machine"
  extends Machines.Interfaces.PartialBasicInductionMachine(
      Lssigma(start=0.1/(2*pi*fsNominal)),
      final idq_ss = airGapR.i_ss,
      final idq_sr = airGapR.i_sr,
      final idq_rs = airGapR.i_rs,
      final idq_rr = airGapR.i_rr,
    redeclare final Machines.Thermal.SynchronousInductionMachines.ThermalAmbientSMPM
      thermalAmbient(final useDamperCage = useDamperCage, final Tr=TrOperational,
      final Tpm=TpmOperational),
    redeclare final Machines.Interfaces.InductionMachines.ThermalPortSMPM
      thermalPort(final useDamperCage = useDamperCage),
    redeclare final Machines.Interfaces.InductionMachines.ThermalPortSMPM
      internalThermalPort(final useDamperCage = useDamperCage),
    redeclare final Machines.Interfaces.InductionMachines.PowerBalanceSMPM
      powerBalance(final lossPowerRotorWinding = heatFlowSensorDamperCage.Q_flow,
                   final lossPowerRotorCore = 0,
                   final lossPowerPermanentMagnet = 0),
    statorCore(final w=statorCoreParameters.wRef));
  Machines.BasicMachines.Components.AirGapR airGapR(
    final p=p,
    final Lmd=Lmd,
    final Lmq=Lmq,
    final m=m);
  final parameter Modelica.SIunits.Temperature TpmOperational=293.15 
    "Operational temperature of permanent magnet";
  parameter Modelica.SIunits.Temperature TrOperational(start=293.15) 
    "Operational temperature of (optional) damper cage";
  parameter Modelica.SIunits.Voltage VsOpenCircuit(start=112.3) 
    "Open circuit RMS voltage per phase @ fsNominal";
  parameter Modelica.SIunits.Inductance Lmd(start=0.3/(2*pi*fsNominal)) 
    "Main field inductance in d-axis";
  parameter Modelica.SIunits.Inductance Lmq(start=0.3/(2*pi*fsNominal)) 
    "Main field inductance in q-axis";
  parameter Boolean useDamperCage(start = true) "Enable / disable damper cage";
  parameter Modelica.SIunits.Inductance Lrsigmad(start=0.05/(2*pi*fsNominal)) 
    "Damper stray inductance in d-axis";
  parameter Modelica.SIunits.Inductance Lrsigmaq=Lrsigmad 
    "Damper stray inductance in q-axis";
  parameter Modelica.SIunits.Resistance Rrd(start=0.04) 
    "Damper resistance in d-axis at TRef";
  parameter Modelica.SIunits.Resistance Rrq=Rrd 
    "Damper resistance in q-axis at TRef";
  parameter Modelica.SIunits.Temperature TrRef(start=293.15) 
    "Reference temperature of damper resistances in d- and q-axis";
  parameter Machines.Thermal.LinearTemperatureCoefficient20 alpha20r(
    start=0) "Temperature coefficient of damper resistances in d- and q-axis";
  output Modelica.SIunits.Current idq_dr[2](each stateSelect=StateSelect.prefer)=
    damperCage.spacePhasor_r.i_ if useDamperCage 
    "Damper space phasor current / rotor fixed frame";
protected 
  final parameter Modelica.SIunits.Current Ie=sqrt(2)*VsOpenCircuit/(Lmd*2*pi*fsNominal) 
    "Equivalent excitation current";
public 
  Machines.BasicMachines.Components.PermanentMagnet permanentMagnet(final Ie=Ie);
  Machines.BasicMachines.Components.DamperCage damperCage(
    final Lrsigmad=Lrsigmad,
    final Lrsigmaq=Lrsigmaq,
    final Rrd=Rrd,
    final Rrq=Rrq,
    final T_ref=TrRef,
    final alpha=Machines.Thermal.convertAlpha(alpha20r, TrRef),
    final T=TrRef,
    final useHeatPort=true) if useDamperCage;
  Modelica.Thermal.HeatTransfer.Sensors.ConditionalFixedHeatFlowSensor
                                                  heatFlowSensorDamperCage(final useFixedTemperature=
                          not useDamperCage);
equation 
  connect(airGapR.spacePhasor_r, damperCage.spacePhasor_r);
  connect(airGapR.spacePhasor_r, permanentMagnet.spacePhasor_r);
  connect(airGapR.support, internalSupport);

  connect(airGapR.flange, inertiaRotor.flange_a);
  connect(lssigma.spacePhasor_b, airGapR.spacePhasor_s);
  connect(damperCage.heatPort, heatFlowSensorDamperCage.port_a);
  connect(heatFlowSensorDamperCage.port_b, internalThermalPort.heatPortRotorWinding);
end SM_PermanentMagnet;

Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_ElectricalExcited

Electrical excited synchronous induction machine with damper cage

Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_ElectricalExcited

Information

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 ccordinate 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)/(2*pi*fNominal)

main field inductance in q-axis (Xq - Xss)/(2*pi*fNominal)

stator stray inductance per phase Xss/(2*pi*fNominal)

damper stray inductance in d-axis XDds/(2*pi*fNominal)

damper stray inductance in q-axis XDqs/(2*pi*fNominal)

Extends from Machines.Interfaces.PartialBasicInductionMachine (Partial model for induction machine).

Parameters

Type Name Default Description

Integer p Number of pole pairs (Integer)

Frequency fsNominal Nominal frequency [Hz]

Inertia Jr Jr(start=0.29) Rotor's moment of inertia [kg.m2]

Boolean useSupport false Enable / disable (=fixed stator) support

Inertia Js Stator's moment of inertia [kg.m2]

Boolean useThermalPort false Enable / disable (=fixed temperatures) thermal port

Current idq_ss[2] airGapR.i_ss Stator space phasor current / stator fixed frame [A]

Current idq_sr[2] airGapR.i_sr Stator space phasor current / rotor fixed frame [A]

Current idq_rs[2] airGapR.i_rs Rotor space phasor current / stator fixed frame [A]

Current idq_rr[2] airGapR.i_rr Rotor space phasor current / rotor fixed frame [A]

Operational temperatures

Temperature TsOperational Operational temperature of stator resistance [K]

Temperature TrOperational Operational temperature of (optional) damper cage [K]

Temperature TeOperational Operational excitation temperature [K]

Nominal resistances and inductances

Resistance Rs Stator resistance per phase at TRef [Ohm]

Temperature TsRef Reference temperature of stator resistance [K]

LinearTemperatureCoefficient20 alpha20s Temperature coefficient of stator resistance at 20 degC [1/K]

Inductance Lszero Lssigma Stator zero sequence inductance [H]

Inductance Lssigma.start 0.1/(2*pi*fsNominal) Stator stray inductance per phase [H]

Inductance Lmd Main field inductance in d-axis [H]

Inductance Lmq Main field inductance in q-axis [H]

DamperCage

Boolean useDamperCage Enable / disable damper cage

Inductance Lrsigmad Damper stray inductance in d-axis [H]

Inductance Lrsigmaq Lrsigmad Damper stray inductance in q-axis [H]

Resistance Rrd Damper resistance in d-axis at TRef [Ohm]

Resistance Rrq Rrd Damper resistance in q-axis at TRef [Ohm]

Temperature TrRef Reference temperature of damper resistances in d- and q-axis [K]

LinearTemperatureCoefficient20 alpha20r Temperature coefficient of damper resistances in d- and q-axis [1/K]

Losses

FrictionParameters frictionParameters frictionParameters(wRef(star... Friction losses

CoreParameters statorCoreParameters Stator core losses

StrayLoadParameters strayLoadParameters Stray load losses

BrushParameters brushParameters Brush losses

Excitation

Voltage VsNominal Nominal stator RMS voltage per phase [V]

Current IeOpenCircuit Open circuit excitation current @ nominal voltage and frequency [A]

Resistance Re Excitation resistance at TRef [Ohm]

Temperature TeRef Reference temperture of excitation resistance [K]

LinearTemperatureCoefficient20 alpha20e Temperature coefficient of excitation resistance [1/K]

Real sigmae Stray fraction of total excitation inductance

Type	Name	Default	Description
Integer	p		Number of pole pairs (Integer)
Frequency	fsNominal		Nominal frequency [Hz]
Inertia	Jr	Jr(start=0.29)	Rotor's moment of inertia [kg.m2]
Boolean	useSupport	false	Enable / disable (=fixed stator) support
Inertia	Js		Stator's moment of inertia [kg.m2]
Boolean	useThermalPort	false	Enable / disable (=fixed temperatures) thermal port
Current	idq_ss[2]	airGapR.i_ss	Stator space phasor current / stator fixed frame [A]
Current	idq_sr[2]	airGapR.i_sr	Stator space phasor current / rotor fixed frame [A]
Current	idq_rs[2]	airGapR.i_rs	Rotor space phasor current / stator fixed frame [A]
Current	idq_rr[2]	airGapR.i_rr	Rotor space phasor current / rotor fixed frame [A]
Operational temperatures
Temperature	TsOperational		Operational temperature of stator resistance [K]
Temperature	TrOperational		Operational temperature of (optional) damper cage [K]
Temperature	TeOperational		Operational excitation temperature [K]
Nominal resistances and inductances
Resistance	Rs		Stator resistance per phase at TRef [Ohm]
Temperature	TsRef		Reference temperature of stator resistance [K]
LinearTemperatureCoefficient20	alpha20s		Temperature coefficient of stator resistance at 20 degC [1/K]
Inductance	Lszero	Lssigma	Stator zero sequence inductance [H]
Inductance	Lssigma.start	0.1/(2pifsNominal)	Stator stray inductance per phase [H]
Inductance	Lmd		Main field inductance in d-axis [H]
Inductance	Lmq		Main field inductance in q-axis [H]
DamperCage
Boolean	useDamperCage		Enable / disable damper cage
Inductance	Lrsigmad		Damper stray inductance in d-axis [H]
Inductance	Lrsigmaq	Lrsigmad	Damper stray inductance in q-axis [H]
Resistance	Rrd		Damper resistance in d-axis at TRef [Ohm]
Resistance	Rrq	Rrd	Damper resistance in q-axis at TRef [Ohm]
Temperature	TrRef		Reference temperature of damper resistances in d- and q-axis [K]
LinearTemperatureCoefficient20	alpha20r		Temperature coefficient of damper resistances in d- and q-axis [1/K]
Losses
FrictionParameters	frictionParameters	frictionParameters(wRef(star...	Friction losses
CoreParameters	statorCoreParameters		Stator core losses
StrayLoadParameters	strayLoadParameters		Stray load losses
BrushParameters	brushParameters		Brush losses
Excitation
Voltage	VsNominal		Nominal stator RMS voltage per phase [V]
Current	IeOpenCircuit		Open circuit excitation current @ nominal voltage and frequency [A]
Resistance	Re		Excitation resistance at TRef [Ohm]
Temperature	TeRef		Reference temperture of excitation resistance [K]
LinearTemperatureCoefficient20	alpha20e		Temperature coefficient of excitation resistance [1/K]
Real	sigmae		Stray fraction of total excitation inductance

Connectors

Type Name Description

Flange_a flange Shaft

Flange_a support Support at which the reaction torque is acting

PositivePlug plug_sp Positive stator plug

NegativePlug plug_sn Negative stator plug

PositivePin pin_ep Positive excitation pin

NegativePin pin_en Negative excitation pin

Type	Name	Description
Flange_a	flange	Shaft
Flange_a	support	Support at which the reaction torque is acting
PositivePlug	plug_sp	Positive stator plug
NegativePlug	plug_sn	Negative stator plug
PositivePin	pin_ep	Positive excitation pin
NegativePin	pin_en	Negative excitation pin

Modelica definition

model SM_ElectricalExcited 
  "Electrical excited synchronous induction machine with damper cage"
  extends Machines.Interfaces.PartialBasicInductionMachine(
      Lssigma(start=0.1/(2*pi*fsNominal)),
      final idq_ss = airGapR.i_ss,
      final idq_sr = airGapR.i_sr,
      final idq_rs = airGapR.i_rs,
      final idq_rr = airGapR.i_rr,
    redeclare final Machines.Thermal.SynchronousInductionMachines.ThermalAmbientSMEE
      thermalAmbient(final useDamperCage = useDamperCage, final Te=TeOperational, final Tr=TrOperational),
    redeclare final Machines.Interfaces.InductionMachines.ThermalPortSMEE
      thermalPort(final useDamperCage = useDamperCage),
    redeclare final Machines.Interfaces.InductionMachines.ThermalPortSMEE
      internalThermalPort(final useDamperCage = useDamperCage),
    redeclare final Machines.Interfaces.InductionMachines.PowerBalanceSMEE
      powerBalance(final lossPowerRotorWinding = heatFlowSensorDamperCage.Q_flow,
                   final powerExcitation = ve*ie,
                   final lossPowerExcitation = -re.heatPort.Q_flow,
                   final lossPowerBrush = -brush.heatPort.Q_flow,
                   final lossPowerRotorCore = 0),
    statorCore(final w=statorCoreParameters.wRef));
  Machines.BasicMachines.Components.AirGapR airGapR(
    final p=p,
    final Lmd=Lmd,
    final Lmq=Lmq,
    final m=m);
  parameter Modelica.SIunits.Temperature TrOperational(start=293.15) 
    "Operational temperature of (optional) damper cage";
  parameter Modelica.SIunits.Inductance Lmd(start=1.5/(2*pi*fsNominal)) 
    "Main field inductance in d-axis";
  parameter Modelica.SIunits.Inductance Lmq(start=1.5/(2*pi*fsNominal)) 
    "Main field inductance in q-axis";
  parameter Boolean useDamperCage(start = true) "Enable / disable damper cage";
  parameter Modelica.SIunits.Inductance Lrsigmad(start=0.05/(2*pi*fsNominal)) 
    "Damper stray inductance in d-axis";
  parameter Modelica.SIunits.Inductance Lrsigmaq=Lrsigmad 
    "Damper stray inductance in q-axis";
  parameter Modelica.SIunits.Resistance Rrd(start=0.04) 
    "Damper resistance in d-axis at TRef";
  parameter Modelica.SIunits.Resistance Rrq=Rrd 
    "Damper resistance in q-axis at TRef";
  parameter Modelica.SIunits.Temperature TrRef(start=293.15) 
    "Reference temperature of damper resistances in d- and q-axis";
  parameter Machines.Thermal.LinearTemperatureCoefficient20 alpha20r(
    start=0) "Temperature coefficient of damper resistances in d- and q-axis";
  parameter Modelica.SIunits.Voltage VsNominal(start=100) 
    "Nominal stator RMS voltage per phase";
  parameter Modelica.SIunits.Current IeOpenCircuit(start=10) 
    "Open circuit excitation current @ nominal voltage and frequency";
  parameter Modelica.SIunits.Resistance Re(start=2.5) 
    "Excitation resistance at TRef";
  parameter Modelica.SIunits.Temperature TeRef(start=293.15) 
    "Reference temperture of excitation resistance";
  parameter Machines.Thermal.LinearTemperatureCoefficient20 alpha20e(
    start=0) "Temperature coefficient of excitation resistance";
  parameter Real sigmae(min=0, max=0.99, start=0.025) 
    "Stray fraction of total excitation inductance";
  parameter Modelica.SIunits.Temperature TeOperational(start=293.15) 
    "Operational excitation temperature";
  parameter Machines.Losses.BrushParameters brushParameters "Brush losses";
  output Modelica.SIunits.Current idq_dr[2](each stateSelect=StateSelect.prefer)=
    damperCage.spacePhasor_r.i_ if useDamperCage 
    "Damper space phasor current / rotor fixed frame";
  output Modelica.SIunits.Voltage ve = pin_ep.v-pin_en.v "Excitation voltage";
  output Modelica.SIunits.Current ie = pin_ep.i "Excitation current";
protected 
  final parameter Real turnsRatio = sqrt(2)*VsNominal/(2*pi*fsNominal*Lmd*IeOpenCircuit) 
    "Stator current / excitation current";
  final parameter Modelica.SIunits.Inductance Lesigma = Lmd*turnsRatio^2*3/2 * sigmae/(1-sigmae);
public 
  Machines.BasicMachines.Components.DamperCage damperCage(
    final Lrsigmad=Lrsigmad,
    final Lrsigmaq=Lrsigmaq,
    final Rrd=Rrd,
    final Rrq=Rrq,
    final T_ref=TrRef,
    final alpha=Machines.Thermal.convertAlpha(alpha20r, TrRef),
    final T=TrRef,
    final useHeatPort=true) if useDamperCage;
  Machines.BasicMachines.Components.ElectricalExcitation electricalExcitation(final turnsRatio=turnsRatio);
  Modelica.Electrical.Analog.Basic.Resistor re(
    final R=Re,
    final T_ref=TeRef,
    final alpha=Machines.Thermal.convertAlpha(alpha20e, TeRef),
    final useHeatPort=true,
    final T=TeRef);
  Modelica.Electrical.Analog.Basic.Inductor lesigma(final L=Lesigma);
  Modelica.Electrical.Analog.Interfaces.PositivePin pin_ep 
    "Positive excitation pin";
  Modelica.Electrical.Analog.Interfaces.NegativePin pin_en 
    "Negative excitation pin";
  Machines.Losses.DCMachines.Brush brush(final brushParameters=brushParameters);
  Modelica.Thermal.HeatTransfer.Sensors.ConditionalFixedHeatFlowSensor
                                                  heatFlowSensorDamperCage(final useFixedTemperature=
                          not useDamperCage);
equation 
  connect(airGapR.spacePhasor_r, damperCage.spacePhasor_r);
  connect(airGapR.spacePhasor_r, electricalExcitation.spacePhasor_r);
  connect(airGapR.support, internalSupport);
  connect(airGapR.flange, inertiaRotor.flange_a);
  connect(electricalExcitation.pin_en, pin_en);
  connect(pin_ep, brush.p);
  connect(brush.n, re.p);
  connect(re.n, lesigma.p);
  connect(lesigma.n, electricalExcitation.pin_ep);

  connect(lssigma.spacePhasor_b, airGapR.spacePhasor_s);
  connect(brush.heatPort, internalThermalPort.heatPortBrush);
  connect(re.heatPort, internalThermalPort.heatPortExcitation);
  connect(damperCage.heatPort, heatFlowSensorDamperCage.port_a);
  connect(heatFlowSensorDamperCage.port_b, internalThermalPort.heatPortRotorWinding);
end SM_ElectricalExcited;

Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_ReluctanceRotor

Synchronous induction machine with reluctance rotor and damper cage

Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_ReluctanceRotor

Information

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 ccordinate 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/(2*pi*fNominal)

rotor stray inductance in d-axis Xrds/(2*pi*fNominal)

rotor stray inductance in q-axis Xrqs/(2*pi*fNominal)

main field inductance per phase in d-axis (Xsd-Xss)/(2*pi*fNominal)

main field inductance per phase in q-axis (Xsq-Xss)/(2*pi*fNominal)

Extends from Machines.Interfaces.PartialBasicInductionMachine (Partial model for induction machine).

Parameters

Type Name Default Description

Integer p Number of pole pairs (Integer)

Frequency fsNominal Nominal frequency [Hz]

Inertia Jr Jr(start=0.29) Rotor's moment of inertia [kg.m2]

Boolean useSupport false Enable / disable (=fixed stator) support

Inertia Js Stator's moment of inertia [kg.m2]

Boolean useThermalPort false Enable / disable (=fixed temperatures) thermal port

Current idq_ss[2] airGapR.i_ss Stator space phasor current / stator fixed frame [A]

Current idq_sr[2] airGapR.i_sr Stator space phasor current / rotor fixed frame [A]

Current idq_rs[2] airGapR.i_rs Rotor space phasor current / stator fixed frame [A]

Current idq_rr[2] airGapR.i_rr Rotor space phasor current / rotor fixed frame [A]

Operational temperatures

Temperature TsOperational Operational temperature of stator resistance [K]

Temperature TrOperational Operational temperature of (optional) damper cage [K]

Nominal resistances and inductances

Resistance Rs Stator resistance per phase at TRef [Ohm]

Temperature TsRef Reference temperature of stator resistance [K]

LinearTemperatureCoefficient20 alpha20s Temperature coefficient of stator resistance at 20 degC [1/K]

Inductance Lszero Lssigma Stator zero sequence inductance [H]

Inductance Lssigma.start 0.1/(2*pi*fsNominal) Stator stray inductance per phase [H]

Inductance Lmd Main field inductance in d-axis [H]

Inductance Lmq Main field inductance in q-axis [H]

DamperCage

Boolean useDamperCage Enable / disable damper cage

Inductance Lrsigmad Damper stray inductance in d-axis [H]

Inductance Lrsigmaq Lrsigmad Damper stray inductance in q-axis [H]

Resistance Rrd Damper resistance in d-axis at TRef [Ohm]

Resistance Rrq Rrd Damper resistance in q-axis at TRef [Ohm]

Temperature TrRef Reference temperature of damper resistances in d- and q-axis [K]

LinearTemperatureCoefficient20 alpha20r Temperature coefficient of damper resistances in d- and q-axis [1/K]

Losses

FrictionParameters frictionParameters frictionParameters(wRef(star... Friction losses

CoreParameters statorCoreParameters Stator core losses

StrayLoadParameters strayLoadParameters Stray load losses

Type	Name	Default	Description
Integer	p		Number of pole pairs (Integer)
Frequency	fsNominal		Nominal frequency [Hz]
Inertia	Jr	Jr(start=0.29)	Rotor's moment of inertia [kg.m2]
Boolean	useSupport	false	Enable / disable (=fixed stator) support
Inertia	Js		Stator's moment of inertia [kg.m2]
Boolean	useThermalPort	false	Enable / disable (=fixed temperatures) thermal port
Current	idq_ss[2]	airGapR.i_ss	Stator space phasor current / stator fixed frame [A]
Current	idq_sr[2]	airGapR.i_sr	Stator space phasor current / rotor fixed frame [A]
Current	idq_rs[2]	airGapR.i_rs	Rotor space phasor current / stator fixed frame [A]
Current	idq_rr[2]	airGapR.i_rr	Rotor space phasor current / rotor fixed frame [A]
Operational temperatures
Temperature	TsOperational		Operational temperature of stator resistance [K]
Temperature	TrOperational		Operational temperature of (optional) damper cage [K]
Nominal resistances and inductances
Resistance	Rs		Stator resistance per phase at TRef [Ohm]
Temperature	TsRef		Reference temperature of stator resistance [K]
LinearTemperatureCoefficient20	alpha20s		Temperature coefficient of stator resistance at 20 degC [1/K]
Inductance	Lszero	Lssigma	Stator zero sequence inductance [H]
Inductance	Lssigma.start	0.1/(2pifsNominal)	Stator stray inductance per phase [H]
Inductance	Lmd		Main field inductance in d-axis [H]
Inductance	Lmq		Main field inductance in q-axis [H]
DamperCage
Boolean	useDamperCage		Enable / disable damper cage
Inductance	Lrsigmad		Damper stray inductance in d-axis [H]
Inductance	Lrsigmaq	Lrsigmad	Damper stray inductance in q-axis [H]
Resistance	Rrd		Damper resistance in d-axis at TRef [Ohm]
Resistance	Rrq	Rrd	Damper resistance in q-axis at TRef [Ohm]
Temperature	TrRef		Reference temperature of damper resistances in d- and q-axis [K]
LinearTemperatureCoefficient20	alpha20r		Temperature coefficient of damper resistances in d- and q-axis [1/K]
Losses
FrictionParameters	frictionParameters	frictionParameters(wRef(star...	Friction losses
CoreParameters	statorCoreParameters		Stator core losses
StrayLoadParameters	strayLoadParameters		Stray load losses

Connectors

Type Name Description

Flange_a flange Shaft

Flange_a support Support at which the reaction torque is acting

PositivePlug plug_sp Positive stator plug

NegativePlug plug_sn Negative stator plug

Type	Name	Description
Flange_a	flange	Shaft
Flange_a	support	Support at which the reaction torque is acting
PositivePlug	plug_sp	Positive stator plug
NegativePlug	plug_sn	Negative stator plug

Modelica definition

model SM_ReluctanceRotor 
  "Synchronous induction machine with reluctance rotor and damper cage"
  extends Machines.Interfaces.PartialBasicInductionMachine(
      Lssigma(start=0.1/(2*pi*fsNominal)),
      final idq_ss = airGapR.i_ss,
      final idq_sr = airGapR.i_sr,
      final idq_rs = airGapR.i_rs,
      final idq_rr = airGapR.i_rr,
    redeclare final Machines.Thermal.SynchronousInductionMachines.ThermalAmbientSMR
      thermalAmbient(final useDamperCage = useDamperCage, final Tr=TrOperational),
    redeclare final Machines.Interfaces.InductionMachines.ThermalPortSMR
      thermalPort(final useDamperCage = useDamperCage),
    redeclare final Machines.Interfaces.InductionMachines.ThermalPortSMR
      internalThermalPort(final useDamperCage = useDamperCage),
    redeclare final Machines.Interfaces.InductionMachines.PowerBalanceSMR
      powerBalance(final lossPowerRotorWinding = heatFlowSensorDamperCage.Q_flow,
                   final lossPowerRotorCore = 0),
    statorCore(final w=statorCoreParameters.wRef));
  Machines.BasicMachines.Components.AirGapR airGapR(
    final p=p,
    final Lmd=Lmd,
    final Lmq=Lmq,
    final m=m);
  parameter Modelica.SIunits.Temperature TrOperational(start=293.15) 
    "Operational temperature of (optional) damper cage";
  parameter Modelica.SIunits.Inductance Lmd(start=2.9/(2*pi*fsNominal)) 
    "Main field inductance in d-axis";
  parameter Modelica.SIunits.Inductance Lmq(start=0.9/(2*pi*fsNominal)) 
    "Main field inductance in q-axis";
  parameter Boolean useDamperCage(start = true) "Enable / disable damper cage";
  parameter Modelica.SIunits.Inductance Lrsigmad(start=0.05/(2*pi*fsNominal)) 
    "Damper stray inductance in d-axis";
  parameter Modelica.SIunits.Inductance Lrsigmaq=Lrsigmad 
    "Damper stray inductance in q-axis";
  parameter Modelica.SIunits.Resistance Rrd(start=0.04) 
    "Damper resistance in d-axis at TRef";
  parameter Modelica.SIunits.Resistance Rrq=Rrd 
    "Damper resistance in q-axis at TRef";
  parameter Modelica.SIunits.Temperature TrRef(start=293.15) 
    "Reference temperature of damper resistances in d- and q-axis";
  parameter Machines.Thermal.LinearTemperatureCoefficient20 alpha20r(
    start=0) "Temperature coefficient of damper resistances in d- and q-axis";
  Machines.BasicMachines.Components.DamperCage damperCage(
    final Lrsigmad=Lrsigmad,
    final Lrsigmaq=Lrsigmaq,
    final Rrd=Rrd,
    final Rrq=Rrq,
    final T_ref=TrRef,
    final alpha=Machines.Thermal.convertAlpha(alpha20r, TrRef),
    final T=TrRef,
    final useHeatPort=true) if useDamperCage;
  Modelica.Thermal.HeatTransfer.Sensors.ConditionalFixedHeatFlowSensor
                                                  heatFlowSensorDamperCage(final useFixedTemperature=
                          not useDamperCage);
equation 
  connect(airGapR.spacePhasor_r, damperCage.spacePhasor_r);
  connect(airGapR.support, internalSupport);

  connect(airGapR.flange, inertiaRotor.flange_a);
  connect(lssigma.spacePhasor_b, airGapR.spacePhasor_s);
  connect(damperCage.heatPort, heatFlowSensorDamperCage.port_a);
  connect(heatFlowSensorDamperCage.port_b, internalThermalPort.heatPortRotorWinding);
end SM_ReluctanceRotor;

Automatically generated Fri Nov 12 16:28:44 2010.

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 voltage per phase	112.3	V RMS @ nominal speed
nominal current per phase	100	A RMS
nominal torque	181.4	Nm
nominal speed	1500	rpm
nominal mechanical output	28.5	kW
nominal rotor angle	20.75	degree
efficiency	95.0	%
power factor	0.98
stator resistance	0.03	Ohm per phase at reference temperature
reference temperature TsRef	20	°C
temperature coefficient alpha20s	0	1/K
stator reactance Xd	0.4	Ohm per phase in d-axis
stator reactance Xq	0.4	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
stator operational temperature TsOperational	20	°C
damper operational temperature TrOperational	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)