WOLFRAM SYSTEMMODELER

SM_PermanentMagnet

Permanent magnet synchronous induction machine

Diagram

Wolfram Language

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SystemModel["Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_PermanentMagnet"]
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Information

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

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 coordinate 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
  • permanent magnet 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
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 at reference temperature
reference temperature TsRef 20°C
temperature coefficient alpha20s 01/K
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 at reference temperature
damper resistance in q-axis same as d-axis
reference temperature TrRef 20°C
temperature coefficient alpha20r 01/K
damper stray reactance in d-axis XDds 0.05Ohm
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)

Parameters (28)

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

TpmOperational

Value: 293.15

Type: Temperature (K)

Description: Operational temperature of permanent magnet

TrOperational

Value:

Type: Temperature (K)

Description: Operational temperature of (optional) damper cage

VsOpenCircuit

Value:

Type: Voltage (V)

Description: Open circuit RMS voltage per phase @ fsNominal

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

permanentMagnetLossParameters

Value:

Type: PermanentMagnetLossParameters

Description: Permanent magnet 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 (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: PowerBalanceSMPM

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: ThermalPortSMPM

ir

Type: RealOutput[2]

Description: Damper cage currents

idq_dr

Type: RealOutput[2]

Description: Damper space phasor current / rotor fixed frame

Components (19)

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: PowerBalanceSMPM

Description: Power balance

rs

Type: Resistor

lssigma

Type: Inductor

lszero

Type: Inductor

statorCore

Type: Core

spacePhasorS

Type: SpacePhasor

strayLoad

Type: StrayLoad

thermalAmbient

Type: ThermalAmbientSMPM

airGapR

Type: AirGapR

permanentMagnetLossParameters

Type: PermanentMagnetLossParameters

Description: Permanent magnet loss parameter record

permanentMagnet

Type: PermanentMagnetWithLosses

damperCage

Type: DamperCage

Used in Examples (6)

SMPM_NoLoad

Modelica.Electrical.Machines.Examples.SynchronousInductionMachines

SMPM at no-load

SMPM_Inverter

Modelica.Electrical.Machines.Examples.SynchronousInductionMachines

Test example: PermanentMagnetSynchronousInductionMachine with inverter

SMPM_CurrentSource

Modelica.Electrical.Machines.Examples.SynchronousInductionMachines

Test example: PermanentMagnetSynchronousInductionMachine fed by current source

SMPM_VoltageSource

Modelica.Electrical.Machines.Examples.SynchronousInductionMachines

Test example: PermanentMagnetSynchronousInductionMachine fed by FOC

SMPM_Braking

Modelica.Electrical.Machines.Examples.SynchronousInductionMachines

Test example: PermanentMagnetSynchronousInductionMachine acting as brake

SMPM_Inverter

Modelica.Magnetic.FundamentalWave.Examples.BasicMachines

Starting of permanent magnet synchronous machine with inverter

Used in Components (1)

MotorWithCurrentControl

Modelica.Blocks.Examples.NoiseExamples.Utilities.Parts

Synchronous induction machine with current controller and measurement noise