WOLFRAM SYSTEMMODELER

SM_ReluctanceRotor

Synchronous induction machine with reluctance rotor and damper cage

Diagram

Wolfram Language

In[1]:=
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 0.29kg.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 at reference temperature
reference temperature TsRef 20°C
temperature coefficient alpha20s 01/K
rotor resistance in d-axis 0.04Ohm at reference temperature
rotor resistance in q-axis same as d-axis
reference temperature TrRef 20°C
temperature coefficient alpha20r 01/K
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 0.05Ohm 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)

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 (7)

flange

Type: Flange_a

Description: Shaft

support

Type: Flange_a

Description: Support at which the reaction torque is acting

plug_sp

Type: PositivePlug

Description: Positive stator plug

plug_sn

Type: NegativePlug

Description: Negative stator plug

thermalPort

Type: ThermalPortSMR

ir

Type: RealOutput[2]

Description: Damper cage currents

idq_dr

Type: RealOutput[2]

Description: Damper space phasor current / rotor fixed frame

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

Used in Examples (3)

SMR_DOL

Modelica.Electrical.Machines.Examples.SynchronousInductionMachines

Test example: SynchronousInductionMachineReluctanceRotor direct-on-line

SMR_Inverter

Modelica.Electrical.Machines.Examples.SynchronousInductionMachines

Test example: SynchronousInductionMachineReluctanceRotor with inverter

SMR_Inverter

Modelica.Magnetic.FundamentalWave.Examples.BasicMachines

Starting of synchronous reluctance machine with inverter