Permanent magnet synchronous motor#

The Permanent magnet synchronous motor block is a synchronous electric motor whose inductor consists of permanent magnets.

In order to calculate parameters, a replacement diagram of a synchronous motoris represented in dq-axes Fig. 1 :

The voltage equations applied to the stator are shown in the formulas below (1) :

\[ U_sd=U_d+\omega _el\cdot L_sq\cdot i_sq \]

(1)#\[ U_{sq}=U_{q}-\omega _{el}\cdot \left(L_{sd}\cdot i_{sd}+\psi _{PM}\right) \]

where:

\( \psi_{PM}\) - flux linkage generated by the rotor permanent magnets (set by user);

The currents are determined according to the following formulas (2) :

\[ I_{sd}=\left(U_{d}+U_{di}+L_{sd}\cdot \left(dI_{sd0}/dt\right)\right)/\left(R_{s}+L_{sd}/dt\right) \]

(2)#\[ I_{sq}=\left(U_{q}-U_{qi}+L_{sq}\cdot \left(dI_{sq0}/dt\right)\right)/\left(R_{s}+L_{sq}/dt\right) \]

The electromagnetic moment is determined according to the formula (3) :

(3)#\[ T_{e}=3/2\cdot 2p\cdot \left(i_{sq}\cdot \psi _{PM}+i_{sq}\cdot i_{sd}\cdot \left(L_{sd}-L_{sq}\right)\right) \]

where 2p - number of pole pairs.

1. Properties#

Property	Default value	Description	Units of measurement
Stator resistance	500e-3	–	Ohm
Stator inductance d axis	1e-3	–	H
Stator inductance q axis	1e-3	–	H
Magnets’ flux linkage	50e-3	Parameter that defines the amount of induced flux linkage in stator on one pole pair	Wb
Friction coefficient	100e-3	–	N·m·s
Inertia	1	Rotor inertia	kg\(\cdot\) m\(^2\)
Pole pairs	1	Number of pole pairs	–

Parametes	Input/Output	Description	Units of measurement	Port type
A	Input	Phase A	–	Electronics
B	Input	Phase B	–	Electronics
C	Input	Phase C	–	Electronics
Applied torque	Input	Torque applied to the shaft	N\(\cdot\) m	Automation
Angular velocity	Output	Shaft’s angular velocity	rad/s	Rotational motion
Electromagnetic torque	Output	Torque produced by electromagnetic field	N\(\cdot\) m	Automation
Current phase A	Output	I\(_a\)	A	Automation
Current phase B	Output	I\(_b\)	A	Automation
Current phase C	Output	I\(_c\)	A	Automation

In order to see the connection capabilities of the block, you need to go to page Description of block ports