Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines

Models of synchronous induction machines

Information


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

These models use package SpacePhasors.

Please keep in mind:

Extends from Modelica.Icons.Library (Icon for library).

Package Content

NameDescription
Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_PermanentMagnet SM_PermanentMagnet Permanent magnet synchronous induction machine
Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_ElectricalExcited SM_ElectricalExcited Electrical excited synchronous induction machine with damper cage
Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_ReluctanceRotor SM_ReluctanceRotor Synchronous induction machine with reluctance rotor and damper cage


Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_PermanentMagnet 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. Only losses in stator and damper resistance are taken into account.
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 0.29kg.m2
rotor's moment of inertia 0.29kg.m2
nominal frequency fNominal 50Hz
nominal voltage per phase 100V RMS
no-load voltage per phase 112.3V RMS @ nominal speed
nominal current per phase 100A RMS
nominal torque 181.4Nm
nominal speed 1500rpm
nominal mechanical output 28.5kW
nominal rotor angle 20.75degree
efficiency 95.0%
power factor 0.98
stator resistance 0.03Ohm per phase in warm condition
stator reactance Xd 0.4Ohm per phase in d-axis
stator reactance Xq 0.4Ohm per phase in q-axis
stator stray reactance Xss 0.1Ohm per phase
damper resistance in d-axis 0.04Ohm in warm condition
damper resistance in q-axis same as d-axis
damper stray reactance in d-axis XDds 0.05Ohm
damper stray reactance in q-axis XDqs same as d-axis
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

TypeNameDefaultDescription
InertiaJrJr(start=0.29)rotor's moment of inertia [kg.m2]
BooleanuseSupportfalseenable / disable (=fixed stator) support
InertiaJs stator's moment of inertia [kg.m2]
Integerp number of pole pairs (Integer)
FrequencyfsNominal nominal frequency [Hz]
Currentidq_ss[2]airGapR.i_ssstator space phasor current / stator fixed frame [A]
Currentidq_sr[2]airGapR.i_srstator space phasor current / rotor fixed frame [A]
Currentidq_rs[2]airGapR.i_rsrotor space phasor current / stator fixed frame [A]
Currentidq_rr[2]airGapR.i_rrrotor space phasor current / rotor fixed frame [A]
Nominal resistances and inductances
ResistanceRs warm stator resistance per phase [Ohm]
InductanceLssigma.start0.1/(2*pi*fsNominal)stator stray inductance per phase [H]
InductanceLmd main field inductance in d-axis [H]
InductanceLmq main field inductance in q-axis [H]
Excitation
VoltageVsOpenCircuit open circuit RMS voltage per phase @ fNominal [V]
DamperCage
BooleanuseDamperCage enable / disable damper cage
InductanceLrsigmad damper stray inductance in d-axis [H]
InductanceLrsigmaqLrsigmaddamper stray inductance in q-axis [H]
ResistanceRrd warm damper resistance in d-axis [Ohm]
ResistanceRrqRrdwarm damper resistance in q-axis [Ohm]

Connectors

TypeNameDescription
Flange_aflange 
Flange_asupportsupport at which the reaction torque is acting
PositivePlugplug_sp 
NegativePlugplug_sn 

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);
  Components.AirGapR airGapR(            final p=p, final m=3, final Lmd=Lmd, final Lmq=Lmq);
  parameter Modelica.SIunits.Voltage VsOpenCircuit(start=112.3) 
    "open circuit RMS voltage per phase @ fNominal";
  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) 
    "warm damper resistance in d-axis";
  parameter Modelica.SIunits.Resistance Rrq=Rrd 
    "warm damper resistance in 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(Ie=Ie);
  Components.DamperCage damperCage(
    final Lrsigmad=Lrsigmad,
    final Lrsigmaq=Lrsigmaq,
    final Rrd=Rrd,
    final Rrq=Rrq) if useDamperCage;
equation 
  connect(airGapR.spacePhasor_r, damperCage.spacePhasor_r);
  connect(airGapR.spacePhasor_r, permanentMagnet.spacePhasor_r);
  connect(spacePhasorS.spacePhasor, airGapR.spacePhasor_s);
  connect(airGapR.support, internalSupport);

  connect(airGapR.flange, inertiaRotor.flange_a);
end SM_PermanentMagnet;

Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_ElectricalExcited 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. Only losses in stator, damper and excitation resistance are taken into account.
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 0.29kg.m2
rotor's moment of inertia 0.29kg.m2
nominal frequency fNominal 50Hz
nominal voltage per phase 100V RMS
no-load excitation current
@ nominal voltage and frequency
10A DC
warm excitation resistance 2.5Ohm
nominal current per phase 100A RMS
nominal apparent power -30000VA
power factor -1.0ind./cap.
nominal excitation current 19A
efficiency w/o excitation 97.1%
nominal torque -196.7Nm
nominal speed 1500rpm
nominal rotor angle -57.23degree
stator resistance 0.03Ohm per phase in warm condition
stator reactance Xd 1.6Ohm per phase in d-axis
giving Kc 0.625
stator reactance Xq 1.6Ohm per phase in q-axis
stator stray reactance Xss 0.1Ohm per phase
damper resistance in d-axis 0.04Ohm in warm condition
damper resistance in q-axis same as d-axis
damper stray reactance in d-axis XDds 0.1Ohm
damper stray reactance in q-axis XDqs same as d-axis
excitation stray inductance 2.5% of total excitation inductance
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

TypeNameDefaultDescription
InertiaJrJr(start=0.29)rotor's moment of inertia [kg.m2]
BooleanuseSupportfalseenable / disable (=fixed stator) support
InertiaJs stator's moment of inertia [kg.m2]
Integerp number of pole pairs (Integer)
FrequencyfsNominal nominal frequency [Hz]
Currentidq_ss[2]airGapR.i_ssstator space phasor current / stator fixed frame [A]
Currentidq_sr[2]airGapR.i_srstator space phasor current / rotor fixed frame [A]
Currentidq_rs[2]airGapR.i_rsrotor space phasor current / stator fixed frame [A]
Currentidq_rr[2]airGapR.i_rrrotor space phasor current / rotor fixed frame [A]
Nominal resistances and inductances
ResistanceRs warm stator resistance per phase [Ohm]
InductanceLssigma.start0.1/(2*pi*fsNominal)stator stray inductance per phase [H]
InductanceLmd main field inductance in d-axis [H]
InductanceLmq main field inductance in q-axis [H]
DamperCage
BooleanuseDamperCage enable / disable damper cage
InductanceLrsigmad damper stray inductance in d-axis [H]
InductanceLrsigmaqLrsigmaddamper stray inductance in q-axis [H]
ResistanceRrd warm damper resistance in d-axis [Ohm]
ResistanceRrqRrdwarm damper resistance in q-axis [Ohm]
Excitation
VoltageVsNominal nominal stator RMS voltage per phase [V]
CurrentIeOpenCircuit open circuit excitation current @ nominal voltage and frequency [A]
ResistanceRe warm excitation resistance [Ohm]
Realsigmae stray fraction of total excitation inductance

Connectors

TypeNameDescription
Flange_aflange 
Flange_asupportsupport at which the reaction torque is acting
PositivePlugplug_sp 
NegativePlugplug_sn 
PositivePinpin_ep 
NegativePinpin_en 

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);
  Components.AirGapR airGapR(            final p=p, final m=3, final Lmd=Lmd, final Lmq=Lmq);
  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) 
    "warm damper resistance in d-axis";
  parameter Modelica.SIunits.Resistance Rrq=Rrd 
    "warm damper resistance in 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) 
    "warm excitation resistance";
  parameter Real sigmae(min=0, max=1, start=0.025) 
    "stray fraction of total excitation inductance";
  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 
  Components.DamperCage damperCage(
    final Lrsigmad=Lrsigmad,
    final Lrsigmaq=Lrsigmaq,
    final Rrd=Rrd,
    final Rrq=Rrq) if useDamperCage;
  Components.ElectricalExcitation electricalExcitation(final turnsRatio=
        turnsRatio);
  Modelica.Electrical.Analog.Basic.Resistor re(
    final R=Re,
    final T_ref=293.15,
    final alpha=0,
    final useHeatPort=false,
    final T=re.T_ref);
  Modelica.Electrical.Analog.Basic.Inductor lesigma(final L=Lesigma);
  Modelica.Electrical.Analog.Interfaces.PositivePin pin_ep;
  Modelica.Electrical.Analog.Interfaces.NegativePin pin_en;

equation 
  connect(electricalExcitation.pin_en, pin_en);
  connect(pin_ep, re.p);
  connect(lesigma.p, re.n);
  connect(lesigma.n, electricalExcitation.pin_ep);
  connect(airGapR.spacePhasor_r, damperCage.spacePhasor_r);
  connect(airGapR.spacePhasor_r, electricalExcitation.spacePhasor_r);
  connect(spacePhasorS.spacePhasor, airGapR.spacePhasor_s);
  connect(airGapR.support, internalSupport);
  connect(airGapR.flange, inertiaRotor.flange_a);
end SM_ElectricalExcited;

Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_ReluctanceRotor 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. Only losses in stator and rotor resistance are taken into account.
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 0.29kg.m2
rotor's moment of inertia 0.29kg.m2
nominal frequency fNominal 50Hz
nominal voltage per phase 100V RMS
nominal current per phase 50A RMS
nominal torque 46Nm
nominal speed 1500rpm
nominal mechanical output 7.23kW
efficiency 96.98%
power factor 0.497
stator resistance 0.03Ohm per phase in warm condition
rotor resistance in d-axis 0.04Ohm in warm condition
rotor resistance in q-axis same as d-axis
stator reactance Xsd in d-axis 3Ohm per phase
stator reactance Xsq in q-axis 1Ohm
stator stray reactance Xss 0.1Ohm per phase
rotor stray reactance in d-axis Xrds 0.1Ohm per phase
rotor stray reactance in q-axis Xrqs same as d-axis
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

TypeNameDefaultDescription
InertiaJrJr(start=0.29)rotor's moment of inertia [kg.m2]
BooleanuseSupportfalseenable / disable (=fixed stator) support
InertiaJs stator's moment of inertia [kg.m2]
Integerp number of pole pairs (Integer)
FrequencyfsNominal nominal frequency [Hz]
Currentidq_ss[2]airGapR.i_ssstator space phasor current / stator fixed frame [A]
Currentidq_sr[2]airGapR.i_srstator space phasor current / rotor fixed frame [A]
Currentidq_rs[2]airGapR.i_rsrotor space phasor current / stator fixed frame [A]
Currentidq_rr[2]airGapR.i_rrrotor space phasor current / rotor fixed frame [A]
Nominal resistances and inductances
ResistanceRs warm stator resistance per phase [Ohm]
InductanceLssigma.start0.1/(2*pi*fsNominal)stator stray inductance per phase [H]
InductanceLmd main field inductance in d-axis [H]
InductanceLmq main field inductance in q-axis [H]
DamperCage
BooleanuseDamperCage enable / disable damper cage
InductanceLrsigmad damper stray inductance in d-axis [H]
InductanceLrsigmaqLrsigmaddamper stray inductance in q-axis [H]
ResistanceRrd warm damper resistance in d-axis [Ohm]
ResistanceRrqRrdwarm damper resistance in q-axis [Ohm]

Connectors

TypeNameDescription
Flange_aflange 
Flange_asupportsupport at which the reaction torque is acting
PositivePlugplug_sp 
NegativePlugplug_sn 

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);
  Components.AirGapR airGapR(            final p=p, final m=3, final Lmd=Lmd, final Lmq=Lmq);
  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) 
    "warm damper resistance in d-axis";
  parameter Modelica.SIunits.Resistance Rrq=Rrd 
    "warm damper resistance in q-axis";
  Components.DamperCage damperCage(
    final Lrsigmad=Lrsigmad,
    final Lrsigmaq=Lrsigmaq,
    final Rrd=Rrd,
    final Rrq=Rrq) if useDamperCage;
equation 
  connect(airGapR.spacePhasor_r, damperCage.spacePhasor_r);
  connect(spacePhasorS.spacePhasor, airGapR.spacePhasor_s);
  connect(airGapR.support, internalSupport);

  connect(airGapR.flange, inertiaRotor.flange_a);
end SM_ReluctanceRotor;

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