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Simple Brushless DC Machine

Purpose

Simple model of a brushless DC machine excited by permanent magnets.

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Machines

Description

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The Simple Brushless DC Machine is a model of a permanent magnet synchronous machine with trapezoidal back EMF.

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). In the component icon, phase a of the stator winding is marked with a dot.

Electrical System

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The back EMF voltages are determined by a shape function ke   and the mechanical rotor speed ωm  . The shape function is an ideal trapezoidal function scaled with the back EMF constant KE  .

ex(θe,ωm) = ke,x(θe)⋅ωm

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Electromechanical System

The electromagnetic torque is:

T  =  ∑    k  i
 e   x=a,b,c e,xx

Mechanical System

Mechanical rotor speed:

       1-
ωm  =  J (Te - F ωm - Tm)

Mechanical and electrical rotor angle:

θm  = ωm

θ =  p⋅θ
 e      m

Parameters and Dialog Box

[Picture]

Back EMF constant
The back EMF constant KE   in Vs.
Stator resistance
The stator resistance R   in ohms (_O_  ).
Stator inductance
The stator inductance L - M   in henries (H).
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 speed ωm,0   in radians per second (s- 1  ).
Initial rotor angle
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 6 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.
(4-6) Back EMF voltages
The back EMF voltages ea  , eb  , ec   in volts (V).

References

D.  Hanselman, "Brushless permanent magnet motor design, 2nd ed.", The Writers' Collective, Mar. 2003.
P. Pillay, R. Krishnan, "Modeling, simulation, and analysis of permanent-magnet motor drives, Part II: The brushless DC motor drive", IEEE Trans. on Ind. App., Vol. 25, No. 2, Mar./Apr. 1989.