Brushless DC Machine (Simplified)
Purpose
Simple model of brushless DC machine excited by permanent magnets
Library
Electrical / Machines
Description
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



Electromechanical System
The electromagnetic torque is:
Mechanical System
Mechanical rotor speed:
Mechanical and electrical rotor angle:
Parameters
- Back EMF shape
- Choose between sinusoidal and trapezoidal back EMF.
- Back EMF constant
- The back EMF constant
in Vs.
- Stator resistance
- The stator resistance
in ohms (
).
- Stator inductance
- The stator inductance
in henries (H).
- Inertia
- Combined rotor and load inertia
in
.
- Friction coefficient
- Viscous friction
in Nms.
- Number of pole pairs
- Number of pole pairs
.
- Initial rotor speed
- Initial mechanical speed
in radians per second (
).
- Initial rotor angle
- Initial mechanical rotor angle
in radians.
- Initial stator currents
- A two-element vector containing the initial stator currents
and
of phase a and b in amperes (A).
Inputs and Outputs
- Mechanical torque
- The input signal
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
of the rotor in radians per second (
).
- (2) Rotor position
- The mechanical rotor angle
in radians.
- (3) Electrical torque
- The electrical torque
of the machine in Nm.
- (4-6) Back EMF voltages
- The back EMF voltages
,
,
in volts (V).
Probe Signals
- Stator phase currents
- The three-phase stator winding currents
,
and
, in A. Currents flowing into the machine are considered positive.
- Back EMF
- The back EMF voltages
,
,
in volts (V).
- Stator flux (dq)
- The stator flux linkages
and
in the stationary reference frame in Vs.
- Rotational speed
- The rotational speed
of the rotor in radians per second (
).
- Rotor position
- The mechanical rotor angle
in radians.
- Electrical torque
- The electrical torque
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 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:
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 is independent of the rotor angle: