WOLFRAM SYSTEMMODELER

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 0.29kg.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 at reference temperature
reference temperature TsRef 20°C
temperature coefficient alpha20s 01/K
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 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
excitation resistance 2.5Ohm at reference temperature
reference temperature TeRef 20°C
temperature coefficient alpha20e 01/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)

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 (9)

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: 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

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)

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