Simplified Induction Motor

Induction motor powered by ideal AC supply

Libraries:
Simscape / Electrical / Electromechanical / Asynchronous

Description

The Simplified 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 Simplified 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.
$\bar{V}$ and $\bar{I}$ are the sinusoidal supply voltage and current phasors.

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

$s = 1 - \frac{p ω_{m}}{ω}$

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:

$T = \frac{n p R_{2}}{s ω} \frac{V_{r m s}^{2}}{{(R_{1} + R_{2} + \frac{1 - s}{s} R_{2})}^{2} + {(X_{1} + X_{2})}^{2}}$

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.

Model Thermal Effects

You can expose thermal ports to model the effects of losses that convert power to heat. To expose the thermal ports, set the Modeling option parameter to either:

No thermal port — The block does not contain thermal ports.
Show thermal port — The block contains multiple thermal conserving ports.

For more information about using thermal ports in actuator blocks, see Simulating Thermal Effects in Rotational and Translational Actuators.

Examples

Motor Torque-Speed Curves

A comparison of the torque-speed characteristics for five different motor types. To select the motor type, right-click on the Electric Motor block and select Block Parameters (Subsystem) from the context menu. In the new window, specify the desired motor using the Label mode active choice parameter. All motors have been sized for roughly the same mechanical power rating.

Open Model

Washing Machine Fault Analysis

Model a washing machine and introduce a fault in its operation. The machine water supply faults at a specific time and this example models the system response under this scenario. The electric motor switches off and the machine operation is aborted by discharging the partially filled outer drum.

Open Model

Assumptions and Limitations

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 effect of the magnetizing inductance L_m is negligible, and the magnetizing inductance is not included in the simulated component.

Ports

Output

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W — Real power
physical

Physical signal port associated with the motor real power.

wm — Mechanical speed
physical

Physical signal port associated with the motor mechanical speed.

VAR — Imaginary power
physical

Physical signal port associated with the motor imaginary power.

s — Motor slip
physical

Physical signal port associated with the motor slip.

Conserving

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R — Rotor
mechanical

Mechanical rotational conserving port associated with the rotor.

C — Case
mechanical

Mechanical rotational conserving port associated with the motor case.

H1 — Rotor
thermal

Stator thermal port.

Dependencies

To enable this port, set Modeling option to Show thermal port.

H2 — Rotor
thermal

Rotor thermal port.

Dependencies

To enable this port, set Modeling option to Show thermal port.

Parameters

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Modeling option — Whether to enable thermal ports
`No thermal port` (default) | `Show thermal port`

Whether to enable the thermal ports of the block and model the effects of losses that convert power to heat.

Electrical Torque

Model parameterization — Block parameterization
`By motor ratings` (default) | `By equivalent circuit parameters`

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 effect of the magnetizing inductance L_m is negligible.
By equivalent circuit parameters — Provide electrical parameters for an equivalent circuit model of the motor.

Stator resistance R1 — Stator winding resistance
`1` `Ohm` (default)

Resistance of the stator winding. The default value is 1 Ω.

Dependencies

This parameter is visible only when you set the Model parameterization parameter to By equivalent circuit parameters.

Rotor resistance R2 — Rotor resistance
`1` `Ohm` (default)

Resistance of the rotor, specified with respect to the stator.

Dependencies

This parameter is visible only when you set the Model parameterization parameter to By equivalent circuit parameters.

Stator inductance L1 — Stator winding inductance
`0.02` `H` (default)

Inductance of the stator winding.

Dependencies

This parameter is visible only when you set the Model parameterization parameter to By equivalent circuit parameters.

Rotor inductance L2 — Rotor inductance
`0.02` `H` (default)

Inductance of the rotor, specified with respect to the stator.

Dependencies

This parameter is visible only when you set the Model parameterization parameter to By equivalent circuit parameters.

Magnetizing inductance Lm — Stator magnetizing inductance
`0.5` `H` (default)

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.

Dependencies

This parameter is visible only when you set the Model parameterization parameter to By equivalent circuit parameters.