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Permanent Magnet Synchronous Machine

Purpose

Synchronous machine excited by permanent magnets.

Library

Electrical / Machines

Description

pict

This machine is modeled in the rotor reference frame. The machine operates as a motor or generator; if the mechanical torque has the same sign as the rotational speed the machine is operating in motor mode, otherwise in generator mode. All electrical variables and parameters are viewed from the stator side. In the component icon, phase a is marked with a dot.

Electrical System

pict

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Stator flux linkages:

φq = Lqiq

φd = Ld id + φ′m

Electromagnetic torque:

    3
Te =- p (φd iq - φqid)
    2

Mechanical System

Mechanical rotor speed ωm  :

       1-
ωm  =  J (Te - Fωm - Tm)

θm  = ωm

Parameters

Stator resistance
Armature or stator resistance Rs   in _O_  .
Stator inductance
A two-element vector containing the combined stator leakage and magnetizing inductance. Ld   is referred to the d-axis and Lq   to the q-axis of the rotor. The values are in henries (H).
Flux induced by magnets
Constant flux linkage   ′
φ m    in Vs induced by the magnets in the stator windings.
Inertia
Combined rotor and load inertia J   in Nms2  .
Friction coefficient
Viscous friction F   in Nms.
Number of pole pairs
Number of pole pairs p  .
Initial rotor speed
Initial mechanical rotor speed ωm,0    in radians per second (s-1  ).
Initial rotor position
Initial mechanical rotor angle θm,0   in radians.
Initial stator currents
A two-element vector containing the initial stator currents ia,0   and ib,0   of phase a and b in amperes (A).

Inputs and Outputs

Mechanical torque
The input signal Tm   represents the mechanical torque at the rotor shaft, in Nm.

The output vector “m” contains the following 3 signals:

(1) Rotor speed
The rotational speed ωm    of the rotor in radians per second (s-1  ).
(2) Rotor position
The mechanical rotor angle θm   in radians.
(3) Electrical torque
The electrical torque Te   of the machine in Nm.