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Squirrel-Cage Induction Machine with Saturation

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

The SCIM block implements a three-phase induction machine (asynchronous machine) with a squirrel-cage 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

The SCIM electrical model formulation is described in the sections below.

Parameters and Measurements

The SCIM with Saturation's parameters and measurements are separated in 4 different tabs, ElectricalMechanicalResolver and Encoder.

Electrical Parameters and Measurements

Symbol

Name

Description

Unit

Type

Symbol

Name

Description

Unit

Type

Rsnom

Stator resistance

Stator winding resistance of phase a, b, and c

Ω

Input

Rrnom'

Rotor resistance

Equivalent rotor winding resistance referred to the stator of phase a, b, and c

Ω

Input

Δθ

Temperature difference

Temperature difference w.r.t the initial temperature of stator and rotor windings

°C

Input

αcondstator

Stator temperature coefficient of resistance

Temperature coefficient of resistance of stator winding

°C-1

Input

αcondrotor 

Rotor temperature coefficient of resistance

Temperature coefficient of resistance of rotor winding

°C-1

Input

Lls

Stator leakage inductance 

Stator winding leakage inductance of phase a, b, and c

H

Input

Llr'

Rotor leakage inductance 

Equivalent rotor winding leakage inductance referred to the stator of phase a, b, and c

H

Input

Esat

Electrical saturation profile input

Choose your saturation profile between (more details)

  • Stator Voltage Line to Line vs. Stator Current

  • Magnetizing Inductance vs. Magnetizing Flux

N/A

Dropdown

Vsll

Stator voltage line to line table

No Load saturation curve parameters

V

File (more details)

Lm

Magnetizing inductance table

Stator-rotor mutual (magnetizing) inductance of phase a, b, and c

H

File (more details)

FcLm

Cut-off frequency magnetizing inductance

Cut-off frequency associated with the frequency response of the magnetic coil, which acts as a filtering element. The default value is 3 kHz.

Hz

Input

Nsr

Turns ratio

Stator to rotor windings turns ratio

N/A

Input

pp

Number of pole pairs

Number of pole pairs

N/A

Input

is

Stator phase currents

Stator currents measured at phases a, b and c

A

Measurement

ir

Rotor phase currents

Rotor equivalent phase a, b, and c currents, referred to the stator

A

Measurement

iβ

Stator αβ currents

Stator currents in αβ (alpha-beta) reference frame

A

Measurement

isqd

Stator qd currents

Stator currents in dq reference frame

A

Measurement

iβ

Rotor αβ currents

Rotor currents in αβ reference frame, referred to the stator

A

Measurement

irqd

Rotor qd currents

Rotor currents in dq reference frame, referred to the stator

A

Measurement

Framesel

Synchronous reference frame orientation

Selection of the synchronous reference frame among:

  • Stator flux-oriented reference frame (default value);

  • Rotor flux-oriented reference frame;

  • Air gap flux-oriented reference frame.

N/A

Dropdown

Frameoffset

Synchronous reference offset

Offset Angle for Synchronous Reference Frame

degree

Input

θest

Synchronous angle

Estimated Synchronous angle

degree

Measurement

Vsαβ

Stator αβ voltages

Stator voltages in αβ reference frame

V

Measurement

Φsαβ

Stator αβ fluxes

Stator fluxes in αβ reference frame

Wb

Measurement

Φrαβ

Rotor αβ fluxes

Rotor fluxes in αβ reference frame, referred to the stator

Wb

Measurement

Rsn

Snubber resistance

Resistances of the snubber on phase a, b and c

Ω

Input

Csn

Snubber capacitance

Capacitance of the snubber on phase a, b and c

F

Input

Mechanical Parameters and Measurements

Symbol

Name

Description

Unit

Type

Symbol

Name

Description

Unit

Type

J

Rotor inertia

Moment of inertia of the rotor

kg*m2

Input

Fv

Viscous friction coefficient

Viscous friction

N*m*s/rad

Input

Fs

Static friction torque

Static friction

N*m

Input

ctrl

Mechanical control mode

Control 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

T

Torque command

Torque command sent to the mechanical model

N*m

Input

ωrc

Rotor speed command

Speed command sent to the mechanical model

rpm

Input

ωr

Rotor speed

Speed of the rotor

rpm

Measurement

Te

Electromagnetic torque

Torque measured at the rotor

N*m

Measurement

θ0

Initial rotor angle

Rotor position at time t = 0

°

Input

θ

Rotor angle

Rotor position from 0 to 360 degrees

°

Measurement

Resolver Parameters and Measurements

Symbol

Name

Description

Unit

Type

Symbol

Name

Description

Unit

Type

Ren

Enable resolver

Whether or not to enable the resolver

N/A

Input

Rsc

Resolver feedback signals

The two two-phase windings producing a sine and cosine feedback current proportional to the sine and cosine of the angle of the motor

N/A

Measurement

Rpp

Number of resolver pole pairs

Number of pole pairs of the resolver

N/A

Input

Rdir

Direction of the sensor rotation

Direction in which the sensor is turning, either clockwise or counterclockwise

N/A

Input

Rθ

Angle offset Δθ ( Sensor-  Rotor )

Angle offset between the resolver and the rotor position from 0 to 360 degrees

°

Input

Rk

Resolver sine cosine gains

The sine/cosine modulation output sine/cosine component amplitude. Default value are 1, 0, 0 and 1

N/A

Input

Etype

Excitation source type

The 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 model

N/A

Input

Ef

Excitation frequency

Frequency of the excitation when in AC mode

Hz

Input

Esrc

Excitation source

Source of the external excitation source when in External mode

N/A

Input

Ets

Excitation time shift

This parameter is used to compensate the time offset between the carrier generation's input in the system and modulated signals' output

s

Input

Encoder Parameters and Measurements

Symbol

Name

Description

Unit

Type

Symbol

Name

Description

Unit

Type

Encen

Enable encoder

Whether or not to enable the encoder

N/A

Input

Enctype

Encoder type

Encoder type, either Quadrature or Hall Effect

N/A

Input

QABZ

A B Z encoder signals

A B and Z signals of the encoder

N/A

Measurement

Qppr

Number of pulses per revolution

Number of pulses in one full revolution of the encoder

N/A

Input

Qdir

Direction of the sensor rotation

Direction in which the sensor is turning, either A leads B or B leads A

N/A

Input

Qθ

Angle offset Δθ ( Sensor - Rotor )

Angle offset between the encoder and the rotor position from 0 to 360 degrees

°

Input

Qrat

Encoder speed ratio ( sensor to mechanical position )

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

N/A

Input

Hθ

Hall effect sensor position

Position 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 )

 

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