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Actuators & Drivers
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.
Lm 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:
Vrms 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.
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 Lm is very large compared to L1 and L2.
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.
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.
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.
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.
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 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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Total number of pole pairs for the motor. The default value is 1.
Number of supply phases. The default value is 3.
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.
The line-to-line voltage that supplies the motor. The default value is 200 V.
Frequency of the AC supply voltage. The default value is 60 hertz.
Rotor inertia. The default value is 0.1 kg*m2. The value can be zero.
Rotor damping. The default value is 2e-06 N*m/(rad/s). The value can be zero.
Speed of the rotor at the start of the simulation. The default value is 0 rpm.
The block has the following ports:
Real power.
Mechanical speed.
Imaginary power.
Motor slip.
Mechanical rotational conserving port.
Mechanical rotational conserving port.
[1] S.E. Lyshevski. Electromechanical Systems, Electric Machines, and Applied Mechatronics, CRC, 1999.
DC Motor, Servomotor, Shunt Motor, and Universal Motor.
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