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Single-phase permanent magnet synchronous motor

**Library:**Simscape / Electrical / Electromechanical / Permanent Magnet

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.

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*is the supply voltage._{s}*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*is the angular frequency of the supply voltage._{s}*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*is the rotor electrical angular velocity._{e}*θ*is the rotor electrical angle._{e}*k*is the BEMF constant._{e}

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

${T}_{e}=i{\psi}_{m}\text{sin}({\theta}_{e})$

and

${\psi}_{m}=\frac{{k}_{e}}{p},$

where:

*T*is the electric torque._{e}*ψ*is the permanent magnet flux linkage._{m}*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*is the rotor inertia._{m}*T*is the torque load._{L}*B*is the friction coefficient._{m}*ɷ*is the rotor mechanical angular velocity._{r}

The block has two optional thermal ports, 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 **HS** and
**HR** on the block icon, and exposes the
**Thermal** parameters.

Use the thermal port to simulate the effects of generated heat and motor temperature. For
more information on using thermal ports and on the **Thermal**
parameters, see Simulating Thermal Effects in Rotational and Translational Actuators.

Use the **Variables** settings to specify the priority and initial target
values for the block variables before simulation. For more information, see Set Priority and Initial Target for Block Variables.

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.

[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.