PLECS 3.7 Online Help

Brushless DC Machine (Simple)

Purpose

Simple model of brushless DC machine excited by permanent magnets

Library

Electrical / Machines

Description

pict

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

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

Electrical System

pict

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

ex(θe,ωm) = ke,x(θe)⋅ωm

pict

pict

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

Back EMF shape
Choose between sinusoidal and trapezoidal back EMF.
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).

Probe Signals

Stator phase currents
The three-phase stator winding currents ia  , ib   and ic  , in A. Currents flowing into the machine are considered positive.
Back EMF
The back EMF voltages ea  , eb  , ec   in volts (V).
Stator flux (dq)
The stator flux linkages Yd   and Yq   in the stationary reference frame in Vs.
Rotational speed
The rotational speed ωm   of the rotor in radians per second (s-1  ).
Rotor position
The mechanical rotor angle θ
 m   in radians.
Electrical torque
The electrical torque Te   of the machine in Nm.

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.

See also

For back EMF shapes other than sinusoidal or trapezoidal, and/or if the stator inductance L   is angle dependent please use the sophisticated model of the Brushless DC Machine. The sophisticated BLDC machine can be configured as a simple BLDC machine with sinusoidal back EMF if the parameters are converted as follows:

Kc,n = [0]

Ks,n = [- KE]

L0- M = L - M

Lc,n = [0]

Ls,n = [0]

For machines with sinusoidal back EMF you may also consider to use the Permanent Magnet Synchronous Machine. The parameters can be converted as follows provided that the stator inductance L   is independent of the rotor angle:

[Ld Lq] = [L- M L- M ]

φ′m = KE ∕p