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Induction Motor - Model induction motor powered by ideal AC supply

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Actuators & Drivers

Description

The Induction Motor block represents the electrical and torque characteristics of an induction motor powered by an ideal AC supply. The following figure shows the equivalent circuit model of the Induction Motor block.

In the figure:

R₁ is the stator resistance.
R₂ is the rotor resistance with respect to the stator.
L₁ is the stator inductance.
L₂ is the rotor inductance with respect to the stator.
L_m is magnetizing inductance.
s is the rotor slip.
and are the sinusoidal supply voltage and current phasors.

Rotor slip s is defined in terms of the mechanical rotational speed , the number of pole pairs p, and the electrical supply frequency ω by

This means that the slip is one when starting, and zero when running synchronously with the supply frequency.

For an n-phase induction motor the torque-speed relationship is given by:

where:

V_rms is the line-neutral supply voltage for a star-configuration induction motor, and the line-to-line voltage for a delta-configuration induction motor.
n is the number of phases.

You can parameterize this block in terms of the preceding equivalent circuit model parameters or in terms of the motor ratings the block uses to derive these parameters.

This block produces a positive torque acting from the mechanical C to R ports.

Basic Assumptions and Limitations

The model is based on the following assumptions:

The block does not model the starting mechanism for a single-phase induction motor.
When you parameterize the block by motor ratings, the block derives the equivalent circuit model parameters by assuming that the magnetizing inductance L_m is very large compared to L₁ and L₂.

Dialog Box and Parameters

Electrical Torque Tab

Model parameterization

Select one of the following methods for block parameterization:

By motor ratings — Provide electrical torque parameters that the block converts to an equivalent circuit model of the motor assuming that the magnetizing inductance is very large compared to L₁ and L₂. This is the default method.
By equivalent circuit parameters — Provide electrical parameters for an equivalent circuit model of the motor.

Stator resistance R1

Resistance of the stator winding. The default value is 1 Ω. This parameter is only visible when you select By equivalent circuit parameters for the Model parameterization parameter.

Rotor resistance R2

Resistance of the rotor, specified with respect to the stator. The default value is 1 Ω. This parameter is only visible when you select By equivalent circuit parameters for the Model parameterization parameter.

Stator inductance L1

Inductance of the stator winding. The default value is 0.02 H. This parameter is only visible when you select By equivalent circuit parameters for the Model parameterization parameter.

Rotor inductance L2

Inductance of the rotor, specified with respect to the stator. The default value is 0.02 H. This parameter is only visible when you select By equivalent circuit parameters for the Model parameterization parameter.

Magnetizing inductance Lm

Magnetizing inductance of the stator. Its value is hard to estimate from motor parameters, but the effect is usually small. If you do not know its value, use a typical value of 25 times the Stator inductance L1 value. The default value is 0.5 H.

Rated mechanical power

Mechanical power the motor delivers when running at the rated speed. The default value is 825 W. This parameter is only visible when you select By motor ratings for the Model parameterization parameter.

Rated speed

Speed at which the motor delivers the specified Rated mechanical power value. The default value is 3.5e+03 rpm. This parameter is only visible when you select By motor ratings for the Model parameterization parameter.

Rated RMS line-to-line voltage

Line-to-line voltage at which the motor ratings are specified. The default value is 200 V. This parameter is only visible when you select By motor ratings for the Model parameterization parameter.

Rated supply frequency

Frequency of the AC supply voltage at which the motor ratings are specified. The default value is 60 hertz. This parameter is only visible when you select By motor ratings for the Model parameterization parameter.

Rated RMS line current

Line current at which the motor delivers the specified Rated mechanical power value. The default value is 2.7 A. This parameter is only visible when you select By motor ratings for the Model parameterization parameter.

L1+L2 parameterization

Select one of the following parameterizations for the equivalent circuit inductance, L₁+L₂, of the motor:

From starting current — Estimate the total equivalent circuit inductance from the motor starting current. This is the default method.
From maximum torque — Estimate the total equivalent circuit inductance from the motor maximum torque.

This parameter is only visible when you select By motor ratings for the Model parameterization parameter.

RMS starting (or locked rotor) line current

The current that flows when the motor starts, or when the rotor is locked so that it cannot turn. The default value is 7.5 A. This parameter is only visible when you select By motor ratings for the Model parameterization parameter and From starting current for the L1+L2 parameterization parameter.

Maximum torque

The maximum value of torque on the torque-slip curve. The default value is 3.3 N*m. This parameter is only visible when you select By motor ratings for the Model parameterization parameter and From maximum torque for the L1+L2 parameterization parameter.

R1 parameterization

Select one of the following parameterizations for the equivalent circuit resistance, R₁, of the motor:

From motor efficiency — Calculate R₁ from the motor efficiency. This is the default method.
From power factor — Calculate R₁ from the motor power factor.
Use measured stator resistance R1 — Measure R₁ directly.

This parameter is only visible when you select By motor ratings for the Model parameterization parameter.

Motor efficiency (percent)

the percentage of input power to the motor that gets delivered to the mechanical load when running at the Rated speed value. The default value is 95. This parameter is only visible when you select By motor ratings for the Model parameterization parameter and From motor efficiency for the R1 parameterization parameter.

Motor power factor

The cosine of the angle by which the supply current lags the supply voltage when running at the Rated mechanical power value. The default value is 0.93. This parameter is only visible when you select By motor ratings for the Model parameterization parameter and From power factor for the R1 parameterization parameter.

Measured stator resistance R1

the measured stator resistance. The default value is 1 Ω. This parameter is only visible when you select By motor ratings for the Model parameterization parameter and Use measured stator resistance R1 for the R1 parameterization parameter.

Number of pole pairs

Total number of pole pairs for the motor. The default value is 1.

Number of phases

Number of supply phases. The default value is 3.

Stator connections

Select one of the following motor configurations:

Delta configuration — Connect the motor stator windings in delta configuration. This is the default method.
Star configuration — Connect the motor stator windings in star configuration.

Power Supply Tab

Supply RMS line-to-line voltage: The line-to-line voltage that supplies the motor. The default value is 200 V.
Supply frequency: Frequency of the AC supply voltage. The default value is 60 hertz.

Mechanical Tab

Rotor inertia: Rotor inertia. The default value is 0.1 kg*m². The value can be zero.
Rotor damping: Rotor damping. The default value is 2e-06 N*m/(rad/s). The value can be zero.
Initial rotor speed: Speed of the rotor at the start of the simulation. The default value is 0 rpm.

Ports

The block has the following ports:

W: Real power.
wm: Mechanical speed.
VAR: Imaginary power.
s: Motor slip.
C: Mechanical rotational conserving port.
R: Mechanical rotational conserving port.

References

[1] S.E. Lyshevski. Electromechanical Systems, Electric Machines, and Applied Mechatronics, CRC, 1999.