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Permanent Magnet Synchronous Machine

Purpose

Synchronous machine excited by permanent magnets.

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Machines

Description

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This machine is modeled in the rotor reference frame. The machine operates as a motor or generator; the sign of the mechanical torque determines the mode of operation (positive for motoring, negative for generating). All electrical variables and parameters are viewed from the stator side. In the component icon, phase a is marked with a dot.

Electrical System

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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 and Dialog Box

[Picture]

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 θ
m,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 ω
 m    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.