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Detailed model of a brushless DC machine excited by permanent magnets.
Electrical / Machines
A brushless DC machine is a type of permanent magnet synchronous machine in which the back electromotive force (EMF) is not sinusoidal but has a more or less trapezoidal shape. Additionally, the variation of the stator inductance with the rotor position is not necessarily sinusoidal.
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.
The back EMF voltages are determined by a shape function and the mechanical
rotor speed
. The shape function in turn is expressed as a fourier series of the
electrical rotor angle
:
The stator self inductance is also expressed as a fourier series of the
electrical rotor angle. The mutual inductance between the stator phases
is assumed to be constant. Since the stator windings are star connected,
the mutual inductance can simply be subtracted from the self inductance:
The electromagnetic torque is a superposition of the torque caused by the permanent magnet and a reluctance torque caused by the non-constant stator inductance:
The cogging torque is again expressed as a fourier series of the electrical rotor angle:
Mechanical rotor speed:
Mechanical and electrical rotor angle:
The output vector "m" contains the following 7 signals: