SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Figure 3.8 – Developed view at thirty electrical degrees.
To recapitulate, a phase current will produce a component of airgap MMF that is cosinusoidally
distributed in space. The amplitude of this space-cosinusoid scales linearly with the phase current.
Since a phase current is itself cosinusoidal with time, the amplitude of the component MMF due
to a phase will be cosinusoidally modulated in time; for each phase alone, this creates a standing
MMF wave in space. When balanced cosinusoidal currents are forced into the stator, the
component MMFs from the phase windings will sum to produce a total airgap MMF that is
cosinusoidally distributed in space along the periphery of the airgap, just as the component
MMFs were. But unlike the component MMFs, this resulting distribution is a traveling wave that
rotates around the stator periphery with time. Figure 3.9 shows two traces of the resulting airgap
MMF at two different times: one corresponds to three-phase current at 0° (Figure 3.7) and the
other corresponds to three-phase current at 30° (Figure 3.8). The figure is the developed view,
thus the abscissa represents the angle around the stator and the figure is a snapshot of the
traveling MMF wave at two different times.
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