PMSM (Single-Phase)

Single-phase permanent magnet synchronous motor

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Description

The PMSM (Single-Phase) represents a single-phase permanent magnet synchronous motor (PMSM), a type of DC motor that is useful for automation applications.

The figure shows the topology of the single-phase PMSM drive.

The figure shows the motor construction with a single pole-pair on the rotor. Single-phase PMSMs are not self-starting unless the air gap is asymmetrical.

The figure shows the equivalent circuit for the PMSM (Single-Phase) block.

Equations

The motor voltage equations are

$v_s=Ri+L\frac{di}{dt}+e$

and

$v_s=V_m\text{sin}({\omega }_{s}t+\epsilon ),$

where:

• v_s is the supply voltage.

• i is the instantaneous motor current.

• R is the resistance of the windings.

• L is the self-inductance of the windings.

• e is the back-electromotive force (BEMF).

• ɷ_s is the angular frequency of the supply voltage.

• ε is the angle of the supply voltage.

The back electro-motive force (BEMF) is

$e=k_e{\omega }_e\text{sin}({\theta }_e),$

where:

• ɷ_e is the rotor electrical angular velocity.

• θ_e is the rotor electrical angle.

• k_e is the BEMF constant.

Due to the large low-permeability gaps between the stator and rotor, the saturation can be neglected. Therefore, the electric torque equations are

$T_e=pi{\psi }_m\text{sin}({\theta }_e)$

and

${\psi }_m=\frac{k_e}{p},$

where:

• T_e is the electric torque.

• ψ_m is the permanent magnet flux linkage.

• p is the number of pole pairs.

The mechanical equation is

$J_m\frac{d{\omega }_r}{dt}=T_e-T_L-B_m{\omega }_r,$

where:

• J_m is the rotor inertia.

• T_L is the torque load.

• B_m is the friction coefficient.

• ɷ_r is the rotor mechanical angular velocity.

Model Thermal Effects

You can expose thermal ports to simulate the effects of generated heat and motor temperature. To expose the thermal ports and the Thermal parameters, set the Modeling option parameter to either:

• No thermal port — The block does not contain thermal ports.

• Show thermal port — The block contains thermal conserving ports for the stator and the rotor.

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

Variables

To set the priority and initial target values for the block variables before simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. You can specify nominal values using different sources, including the Nominal Values section in the block dialog box or Property Inspector. For more information, see System Scaling by Nominal Values.

Examples

Single-Phase PMSM Control

Control the rotor speed in an electrical drive based on a single-phase permanent magnet synchronous motor by using open loop control. An ideal torque source provides the load. The Commutation subsystem uses a Hall signal to compute the gate signals. An H-Bridge feeds the SPPMSM.

• Open Model

Limitations and Assumptions

• The machine air gap is free of saliency effects.

• The stator current has negligible effect on the flux distribution under normal operating conditions.

• The hysteresis, saturation effects, and eddy currents are neglected.

Ports

Conserving

R — Machine rotor

mechanical rotational

Mechanical rotational conserving port associated with the machine rotor.

C — Machine case

mechanical rotational

Mechanical rotational conserving port associated with the machine case.

+ — Negative

electrical

Electrical conserving port associated with the supply positive terminal.

- — Positive

electrical

Electrical conserving port associated with the supply negative terminal.

HS — Stator thermal port

thermal

Thermal conserving port associated with the stator.

Dependencies

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

HR — Rotor thermal port

thermal

Thermal conserving port associated with the rotor.

Dependencies

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

Parameters

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 generated heat and motor temperature.

Main

Number of pole pairs — Rotor pole pairs

2 (default) | positive integer

Number of permanent magnet pole pairs on the rotor.

Permanent magnet flux linkage parameterization — Parameterization method

Specify flux linkage (default) | Specify back EMF constant

Method for parameterizing the stator.

Dependencies

Selecting Specify flux linkage exposes the Permanent magnet flux linkage parameter.

Selecting Specify back EMF constant exposes the Back EMF constant parameter.

Permanent magnet flux linkage — Flux linkage

0.2 Wb (default) | positive scalar

Peak permanent magnet flux linkage.

Dependencies

Selecting Specify flux linkage for the Permanent magnet flux linkage parameterization parameter exposes the Permanent magnet flux linkage parameter.

Back EMF constant — Back-electromotive force constant

0.4 V/(rad/s) (default) | positive scalar

Back-electromotive force constant.

Dependencies

Selecting Specify back EMF constant for the Permanent magnet flux linkage parameterization parameter exposes the Back EMF constant parameter.

Inductance of stator coil — Inductance

1.15 H (default) | positive scalar

The direct-axis inductance.

Resistance of stator coil — Resistance

150 Ohm (default) | positive scalar

Resistance of each of the stator windings.

Rotor position at standstill due to asymmetric airgap — Rotor angular position at standstill

45 deg (default) | positive scalar in the interval [0, 360] deg

Rotor angular position at standstill due to asymmetric air gap.

Mechanical

Rotor inertia — Rotor moment of inertia

1e-6 kg*m^2 (default) | positive scalar

Inertia of the rotor attached to mechanical translational port R.

Rotor damping — Rotor damping

0 N*m/(rad/s) (default) | positive scalar

Damping of the rotor.

Thermal

To enable these parameters, set Modeling option to Show thermal port.

Measurement temperature — Rated temperature

298.15 K (default) | real scalar

Temperature for which motor parameters are quoted.

Resistance temperature coefficient — Temperature coefficient

3.93e-3 1/K (default) | positive scalar

Coefficient α in the equation relating resistance to temperature for all three windings, as described in Thermal Model for Actuator Blocks. The default value, 3.93e-3 1/K, is for copper.

Permanent magnet flux temperature coefficient — Permanent magnet flux temperature coefficient

-0.001 1/K (default)

Fractional rate of change of permanent magnet flux density with temperature. Use this parameter to linearly reduce the torque and the induced back EMF as temperature rises.

Thermal mass for each stator winding — Winding thermal mass

100 J/K (default) | positive scalar

Thermal mass value for each stator winding. The thermal mass is the energy required to raise the temperature by one degree.

Rotor thermal mass — Rotor thermal mass

200 J/K (default) | positive scalar

Thermal mass of the rotor. The thermal mass is the energy required to raise the temperature of the rotor by one degree.

References

[1] Ertugrul, N. and C. Doudle. “Dynamic analysis of a single-phase line-starting permanent magnet synchronous motor.” Proceedings of International Conference on Power Electronics, Drives and Energy Systems for Industrial Growth. Vol. 1, 1996, pp. 603–609.

Extended Capabilities

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

Version History

Introduced in R2018b