# Simplified Induction Motor

Induction motor powered by ideal AC supply

**Library:**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:

*R*is the stator resistance._{1}*R*is the rotor resistance with respect to the stator._{2}*L*is the stator inductance._{1}*L*is the rotor inductance with respect to the stator._{2}*L*is magnetizing inductance._{m}s is the rotor slip.

$$\overline{V}$$ and $$\overline{I}$$ are the sinusoidal supply voltage and current phasors.

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

$$s=1-\frac{p{\omega}_{m}}{\omega}$$

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:

$$T=\frac{np{R}_{2}}{s\omega}\frac{{V}_{rms}{}^{2}}{{\left({R}_{1}+{R}_{2}+\frac{1-s}{s}{R}_{2}\right)}^{2}+{\left({X}_{1}+{X}_{2}\right)}^{2}}$$

where:

*V*is the line-neutral supply voltage for a star-configuration induction motor, and the line-to-line voltage for a delta-configuration induction motor._{rms}*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.

### Thermal Ports

The block has two optional thermal ports, one per winding, hidden by default. To expose the
thermal ports, right-click the block in your model, and then from the context menu select
**Simscape** > **Block choices** >
**Show thermal port**. This action displays the thermal ports on
the block icon, and exposes the **Temperature Dependence** and
**Thermal Port** parameters. These parameters are described further on
this reference page.

Use the thermal ports to simulate the effects of copper resistance losses that convert electrical power to heat. For more information on using thermal ports in actuator blocks, see Simulating Thermal Effects in Rotational and Translational Actuators.

## 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*is negligible, and the magnetizing inductance is not included in the simulated component._{m}

## Ports

### Output

### Conserving

## Parameters

## Model Examples

## References

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

## Extended Capabilities

## See Also

DC Motor | Motor & Drive (System Level) | Shunt Motor | Universal Motor

**Introduced in R2008a**