Magnetic Rotor

Air gaps between stator teeth and rotating permanent magnet rotor

Since R2023b

• 

Libraries:
Simscape / Electrical / Electromechanical

Description

The Magnetic Rotor block represents the magnetic and mechanical characteristics of a rotor component in a permanent magnet synchronous machine (PMSM). In particular, this block models the air gaps between the stator teeth and a rotating permanent magnet rotor as an array of Rotating Air Gap blocks.

The Number of stator teeth parameter specifies the number of Rotating Air Gap blocks that comprise the Magnetic Rotor block. This figure shows the equivalent circuit of the block when you set the Number of stator teeth parameter to 9:

If the rotor angle is zero, one of the rotor magnets perfectly aligns with the middle of the first stator tooth. The orientation of this permanent magnet opposes the flux flow from port N to port S.

The magnetic port N is an array of magnetic ports with a length equal to the value of the Number of stator teeth parameter. To connect the individual magnetic ports corresponding to each stator tooth, you need a Magnetic Demux block. You can write your own Magnetic Demux block using Simscape code, or use the block from the Faulted PMSM example model.

This figure shows the relationship between the parameters of the Magnetic Rotor block and their physical values inside a permanent magnet motor.

• r is the value of the Rotor radius parameter.

• g is the value of the Air gap parameter.

• l_m is the value of the Permanent magnet length (in direction of flux) parameter.

• l is the value of the Tooth depth (in direction of shaft) parameter.

The rotor circumference is equal to $$2\pi r$$. Then, the width of a permanent magnet on the rotor is equal to $$\frac{2\pi r}{2N}$$, where N is the Number of rotor pole pairs.

Faults

To model a fault in the Magnetic Rotor block, in the Faults section, click the Add fault hyperlink next to the fault that you want to model. In the Add Fault window, specify the fault properties. For more information about fault modeling, see Fault Behavior Modeling and Fault Triggering.

The Magnetic Rotor block supports faulting the rotor poles. This faulted behavior corresponds to one or more magnets (poles) in the rotor having a weakened magnetic field. You can apply a reduction factor to the flux density of any of the rotor poles by specifying the Flux multipliers for faulted rotor poles parameter.

The transition to the faulted values linearly interpolates over the time period that you specify in the Duration of transition to faulted parameter. Use this parameter to emulate how an overheated permanent magnet gradually loses its magnetization over time.

Examples

Faulted PMSM

Model a faulted permanent magnet synchronous motor (PMSM) using Simscape™ Electrical™. Normally when modeling a PMSM, you can represent each winding as a single entity with associated inductance, induced back electromotive force (EMF), and mutual inductive coupling to adjacent windings. However, when a winding fault occurs, the single entity assumption breaks down. To correctly capture the resulting dynamics, you have to model the motor at a winding slot level. This requires modeling in the magnetic domain.

• Open Model

Assumptions and Limitations

The Magnetic Rotor block assumes that the rotor magnets are surface-mounted and that the associated induced voltage is sinusoidal.

Ports

Conserving

N — Magnetic stator connection

magnetic | array

Magnetic conserving port associated with the stator.

The value at this port is an array of magnetic ports with a length equal to the value of the Number of stator teeth parameter.

S — Magnetic rotor connection

magnetic | array

Magnetic conserving port associated with the rotor.

The value at this port is an array of magnetic ports with a length equal to the value of the Number of stator teeth parameter.

C — Motor case

mechanical

Mechanical rotational conserving port associated with the motor case.

R — Motor rotor

mechanical

Mechanical rotational conserving port associated with the motor rotor.

Parameters

Main

Number of rotor pole pairs — Rotor pole pairs

5 (default) | positive scalar

Number of pole pairs of the rotor. This parameter must be equal to or greater than 1 and less than the value of the Number of stator teeth parameter.

Number of stator teeth — Number of stator teeth

9 (default) | positive scalar

Number of teeth of the stator. This parameter must be equal to or greater than 2.

Peak magnet flux density — Peak flux density of magnet rotor

0.4 T (default) | positive scalar

Peak flux density associated with the permanent magnet rotor. The flux density is sinusoidal with the rotor angle.

Permanent magnet length (in direction of flux) — Magnet length in radial machine direction

5 mm (default) | positive scalar

Length of the magnet in the radial machine direction or, equivalently, in the direction of the magnetic flux. This parameter must be less than the value of the Rotor radius parameter.

Permanent magnet relative permeability — Permanent magnet relative permeability

1.05 (default) | scalar

Relative permeability of the permanent magnets. Typically, you set this parameter to a value a little greater than 1 to reflect that the magnetic dipoles are already aligned in a permanent magnet.

Air gap — Air gap in radial direction

1 mm (default) | positive scalar

Length of the air gap in the radial direction.

Rotor radius — Rotor radius

65 mm (default) | positive scalar

Radius of the rotor.

Tooth depth (in direction of shaft) — Stator tooth depth

50 mm (default) | positive scalar

Length of a stator tooth in the direction of the rotating shaft.

Faults

Rotor poles fault — Option to fault rotor poles

Add fault (default)

Option to add a fault to the rotor poles.

To add a fault, click the Add fault hyperlink.

Flux multipliers for faulted rotor poles — Multipliers to reduce rotor pole flux

ones(1,10) (default) | vector

Multipliers used to reduce the rotor pole magnetic density when the rotor poles are faulted. The value of this parameter must be a vector with length equal to twice the value of the Number of rotor pole pairs parameter. Each element of the vector corresponds to one rotor pole.

The default value of ones(1,10) results in the same behavior as the unfaulted scenario.

Dependencies

To enable this parameter, add a fault to the Magnetic Rotor block by clicking the Add fault hyperlink in the Rotor poles fault parameter.

After you create the fault, you can change the properties in the Fault Inspector window. When you open a block that has a fault, the Open Fault Inspector hyperlink appears instead of the Add fault hyperlink. For an example that shows how to include faults, see Analyze a DC Armature Winding Fault.

Duration of transition to faulted — Duration after which block fully faults

100 s (default) | positive scalar

Duration after which the block applies the full effect of the faulted multipliers on the peak magnet flux density of each rotor pole. When the block enters the faulted state, the software gradually modifies the peak magnetic flux densities of each rotor pole using the faulted multipliers.

Dependencies

To enable this parameter, add a fault to the Magnetic Rotor block by clicking the Add fault hyperlink in the Rotor poles fault parameter.

After you create the fault, you can change the properties in the Fault Inspector window. When you open a block that has a fault, the Open Fault Inspector hyperlink appears instead of the Add fault hyperlink. For an example that shows how to include faults, see Analyze a DC Armature Winding Fault.

Trigger fault at time — Time before entering faulted state

0 s (default) | nonnegative scalar

Simulation time at which the block enters the faulted state.

Dependencies

To enable this parameter, in the Fault Inspector window, set Trigger Type to Timed.

This parameter appears in the Trigger section of the Fault Inspector window. For more information, see Set Fault Triggers.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2023b