WOLFRAM SYSTEM MODELER
SM_ElectricalExcitedElectrical excited synchronous machine with damper cage |
SystemModel["Modelica.Electrical.Machines.BasicMachines.SynchronousMachines.SM_ElectricalExcited"]
This information is part of the Modelica Standard Library maintained by the Modelica Association.
Model of a three-phase electrical excited synchronous 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:
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) |
Jr |
Value: Type: Inertia (kg⋅m²) Description: Rotor's moment of inertia |
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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 |
m |
Value: 3 Type: Integer Description: Number of phases |
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 |
idq_ss |
Default Value: airGap.i_ss Type: Current[2] (A) Description: Stator space phasor current / stator fixed frame |
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idq_sr |
Default Value: airGap.i_sr Type: Current[2] (A) Description: Stator space phasor current / rotor fixed frame |
idq_rs |
Default Value: airGap.i_rs Type: Current[2] (A) Description: Rotor space phasor current / stator fixed frame |
idq_rr |
Default Value: airGap.i_rr Type: Current[2] (A) Description: Rotor space phasor current / rotor fixed frame |
phiMechanical |
Default Value: flange.phi - internalSupport.phi Type: Angle (rad) Description: Mechanical angle of rotor against stator |
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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 |
flange |
Type: Flange_a Description: Shaft |
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support |
Type: Flange_a Description: Support at which the reaction torque is acting |
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internalSupport |
Type: Support Description: Support/housing flange of a one-dimensional rotational shaft |
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plug_sp |
Type: PositivePlug Description: Positive stator plug |
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plug_sn |
Type: NegativePlug Description: Negative stator plug |
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thermalPort |
Type: ThermalPortSMEE Description: Thermal port of synchronous machine with electrical excitation |
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internalThermalPort |
Type: ThermalPortSMEE Description: Thermal port of synchronous machine with electrical excitation |
|
ir |
Type: RealOutput[2] Description: Damper cage currents |
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idq_dr |
Type: RealOutput[2] Description: Damper space phasor current / rotor fixed frame |
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pin_ep |
Type: PositivePin Description: Positive excitation pin |
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pin_en |
Type: NegativePin Description: Negative excitation pin |
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damperCageLossPower |
Type: RealOutput Description: Damper losses |
frictionParameters |
Type: FrictionParameters Description: Friction loss parameter record |
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inertiaRotor |
Type: Inertia Description: 1D-rotational component with inertia |
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inertiaStator |
Type: Inertia Description: 1D-rotational component with inertia |
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fixed |
Type: Fixed Description: Flange fixed in housing at a given angle |
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friction |
Type: Friction Description: Model of angular velocity dependent friction losses |
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statorCoreParameters |
Type: CoreParameters Description: Stator core loss parameter record; all parameters refer to stator side |
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strayLoadParameters |
Type: StrayLoadParameters Description: Stray load loss parameter record |
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powerBalance |
Type: PowerBalanceSMEE Description: Power balance |
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rs |
Type: Resistor Description: Ideal linear electrical resistors |
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lssigma |
Type: Inductor Description: Space phasor inductor |
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lszero |
Type: Inductor Description: Ideal linear electrical inductor |
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statorCore |
Type: Core Description: Model of core losses |
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spacePhasorS |
Type: SpacePhasor Description: Physical transformation: three-phase <-> space phasors |
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strayLoad |
Type: StrayLoad Description: Model of stray load losses dependent on current and speed |
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thermalAmbient |
Type: ThermalAmbientSMEE Description: Thermal ambient for synchronous machine with electrical excitation |
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airGap |
Type: AirGapR Description: Airgap in rotor-fixed coordinate system |
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brushParameters |
Type: BrushParameters Description: Brush loss parameter record |
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damperCage |
Type: DamperCage Description: Squirrel Cage |
|
electricalExcitation |
Type: ElectricalExcitation Description: Electrical excitation |
|
re |
Type: Resistor Description: Ideal linear electrical resistor |
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lesigma |
Type: Inductor Description: Ideal linear electrical inductor |
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brush |
Type: Brush Description: Model considering voltage drop of carbon brushes |
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