Documentation Home Page OPAL-RT Schematic Editor Home Page
Pour la documentation en FRANÇAIS, utilisez l'outil de traduction de votre navigateur Chrome, Edge ou Safari. Voir un exemple.

Skip to end of metadata
Go to start of metadata

You are viewing an old version of this page. View the current version.

Compare with Current View Page History

Version 1 Next »

This block implements a doubly-fed induction machine (DFIM) with magnetizing inductance saturation in the stationary (stator) reference frame along with the temperature effects on the stator and rotor resistances.

The DFIM block implements a three-phase induction machine (asynchronous machine) with an accessible wound rotor model with resolvers and encoders. The machine can operate in both motoring mode, when the mechanical torque is positive, and generating mode when the mechanical torque is negative.

Model Formulation

Induction Machine Electrical Model


Fig.1. Implementation block diagram (Squirrel-cage/ Doubly-fed induction motor)

  1. Motor modelling equations

The stator and rotor voltage equations of a induction motor in the stationary (stator reference frame) reference frame can be written a equations (1)-(4).

Equations (1)-(4) can be represented as equation (5).

The stator and rotor flux linkages can be expressed as equation (6).

Note:- The stator and rotor flux linkages are calculated by using equation (5) and the stator and rotor currents are calculated by using equation (6).


2. Magnetizing flux linkage calculation

The magnetizing flux linkages are calculated from the stator and rotor flux linkages by using equations (7) and (8).

where

ψmq & ψmd = q & d-axis magnetizing flux linkages

Laq = q-axis inductance (= (Lm Lls Llr)/(Lm Lls + Lm Llr +Lls Llr))

Lad = d-axis inductance (= (Lm Lls Llr)/(Lm Lls + Lm Llr +Lls Llr)) 

Lls = Stator leakage inductance

Llr = Rotor leakage inductance (referred to stator side)

Lm = Magnetizing inductance

3. Thermal modelling of stator and rotor resistances

where

           Rsnom = stator resistance at temp ϴi

           Rrnom  = rotor resistance at temp ϴi

           Rs      = stator resistance at temp ϴf

           Rr      = rotor resistance at temp ϴf

           αcond   = temperature co-efficient of resistance of the material


abc  to dq0 (stator side)

Stationary reference frame (ϴe=0)

dq0  to abc (stator side)

Stationary reference frame (ϴe=0)

abc  to dq0 (rotor side)

Stationary reference frame (ϴe=0)

dq0  to abc (rotor side)

Stationary reference frame (ϴe=0)

Mechanical Model

The equation of the mechanical model in torque mode can be expressed as follows:


where ωm is the rotor speed, Te is the electromagnetic torque, Tm is the torque command, Fv is the viscous friction coefficient, J is the inertia and Ts the time step. There is a dead-zone implementation with the static friction torque, if the electromagnetic doesn't exceed the static friction torque, the speed remains zero.

In speed mode, the rotor speed is directly set to the speed command ωrc.

Resolver Encoder Model

The equations of the resolver encoder can be expressed as follows:



where θres is the resolver angle, θmec is the mechanical angle of the machine, θoffset is the angle offset, Rpp is the Number of pole pairs of the resolver and Rk are the resolver sine cosine gains.

Parameters and Measurements

The DFIM with Saturation's parameters and measurements are separated in 4 different tabs, Electrical, Mechanical, Resolver and Encoder.

Electrical Parameters and Measurements

Symbol

Name

Description

Unit

Type

RsnomStator resistanceStator winding resistance of phase a, b, and cΩInput
Rrnom'Rotor resistanceEquivalent rotor winding resistance referred to the stator of phase a, b, and cΩInput

Δθ

Temperature differenceTemperature difference w.r.t the initial temperature of stator and rotor windings°CInput
αcondstatorStator temperature coefficient of resistanceTemperature coefficient of resistance of stator winding°C-1Input
αcondrotor Rotor temperature coefficient of resistanceTemperature coefficient of resistance of rotor winding°C-1Input
LlsStatorleakage inductance Stator winding leakage inductance of phase a, b, and cHInput
Llr'Rotor leakage inductance Equivalent rotor winding leakage inductance referred to the stator of phase a, b, and cHInput
EsatElectrical saturation profile input

Choose your saturation profile between (More details)

  • Stator Voltage Line to Line vs. Stator Current
  • Magnetizing Inductance vs. Magnetizing Flux
N/ADropdown
VsllStator voltage line to line tableNo Load saturation curve parametersVFile
LmMagnetizing inductance tableStator-rotor mutual (magnetizing) inductance of phase a, b, and cHFile
NsrTurns ratioStator to rotor windings turns ratioN/AInput
ppNumber of pole pairsNumber of pole pairsN/AInput
isStator phase currentsStator currents measured at phases a, b and cAMeasurement
irRotor phase currentsRotor equivalent phase a, b, and c currents, referred to the statorAMeasurement
iβStator αβ currentsStator currents in αβ frameAMeasurement
isqdStator qd currentsStator currents in qd frame (αβ frame)AMeasurement
iβRotor αβ currentsRotor currents in αβ frame, referred to the statorAMeasurement
irqdRotor qd currentsRotor currents in qd frame, referred to the stator (αβ frame)AMeasurement
Vsαβ Stator αβ voltagesStator voltages in αβ frameVMeasurement
ΦsαβStator αβ fluxesStator fluxes in αβ frameWbMeasurement
ΦrαβRotor αβ fluxesRotor fluxes in αβ frame, referred to the statorWbMeasurement
RsnSnubber resistanceResistances of the snubber on phase A, B and CΩInput
CsnSnubber capacitanceCapacitance of the snubber on phase A, B and CFInput

Mechanical Parameters and Measurements

Symbol

Name

Description

Unit

Type

JRotor inertiaMoment of inertia of the rotorkg*m2Input
FvViscous friction coefficientViscous frictionN*m*s/radInput
FsStatic friction torqueStatic frictionN*mInput
ctrlMechanical control modeControl mode of the mechanical model. Has two possible values: speed or torque. In speed mode, the mechanical model is bypassed and the speed command is sent directly. In torque mode, the torque command is used to measure the speed using the mechanical parameters of the machine.
Input
TTorque commandTorque command sent to the mechanical modelN*mInput
ωrcRotor speed commandSpeed command sent to the mechanical modelrpmInput
ωrRotor speedSpeed of the rotorrpmMeasurement
TeElectromagnetic torqueTorque measured at the rotorN*mMeasurement
θ0Initial rotor angleRotor position at time t = 0°Input
θRotor angleRotor position from 0 to 360 degrees°Measurement

image2019-12-4_14-40-39.png

Resolver Parameters and Measurements

Symbol

Name

Description

Unit

Type

RenEnable resolverWhether or not to enable the resolverN/AInput
RscResolver feedback signalsThe two two-phase windings producing a sine and cosine feedback current proportional to the sine and cosine of the angle of the motorN/AMeasurement
RppNumber of resolver pole pairsNumber of pole pairs of the resolverN/AInput
RdirDirection of the sensor rotationDirection in which the sensor is turning, either clockwise or counterclockwiseN/AInput
RθAngle offset Δθ ( Sensor-  Rotor )Angle offset between the resolver and the rotor position from 0 to 360 degrees°Input
RkResolver sine cosine gainsThe sine/cosine modulation output sine/cosine component amplitude. Default value are 1, 0, 0 and 1N/AInput
EtypeExcitation source typeThe source from which the excitation of the resolver is generated. Can either be AC, which is generated inside the FPGA with the specified frequency, DC, which is generated with a 90° from the rotor and External, which is generated from outside the modelN/AInput
EfExcitation frequencyFrequency of the excitation when in AC modeHzInput
EsrcExcitation sourceSource of the external excitation source when in External modeN/AInput
EtsExcitation time shiftThis parameter is used to compensate the time offset between the carrier generation's input in the system and modulated signals' outputsInput

image2020-7-15_15-33-44.png

Encoder Parameters and Measurements

Symbol

Name

Description

Unit

Type

EncenEnable encoderWhether or not to enable the encoderN/AInput
EnctypeEncoder typeEncoder type, either Quadrature or Hall EffectN/AInput
QABZA B Z encoder signalsA B and Z signals of the encoderN/AMeasurement
QpprNumber of pulses per revolutionNumber of pulses in one full revolution of the encoderN/AInput
QdirDirection of the sensor rotationDirection in which the sensor is turning, either A leads B or B leads AN/AInput
QθAngle offset Δθ ( Sensor - Rotor )Angle offset between the encoder and the rotor position from 0 to 360 degrees°Input
QratEncoder speed ratio ( sensor to mechanical position )

Mechanical to encoder ratio. Angle of Encoder = Qrat * machine mechanical angle. 

N/AInput
HθHall effect sensor positionPosition of sensor phases A, B and C in Hall effect mode°Input

Visualization of Resolver Encoder Parameters Effects

Number of resolver pole pairs affects the number of electrical turns per mechanical turns. On the left figure, the number of resolver pole pairs is 2, on the right figure, the number of resolver pole pairs is 4.

Resolver sine cosine gains affect the sine ( first axe ) and cosine ( second axe ) modulation output. Default values set to 1, 0, 0, 1 make it so the sine modulation has a sine form and the cosine modulation has a cosine form. If set to 0, 1, 1, 0, the sine modulation would have a cosine and the cosine modulation would have a sine form.

Excitation frequency, in AC excitation source type, affects the frequency of the carrier signal. We can see the time step highlighted in red. ( Figure 3 is a zoomed in view of Figure 2 )

Number of pulses per revolution (Qppr) defines how many times signals A and B pulse between two Z pulses ( one full rotation ).

Direction of the sensor rotation describes if A leads B ( Clockwise ) or if B leads A ( Counterclockwise )

  • No labels