SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

composed of three component space vectors corresponding to each phase as shown in Equation
(3.48). 23
Ne Ne j Ne
j
f iA()1 t i B() t e iC() t e
2
2
2
j j
fA()1 t fB() t e fC() t e
f f f f
(3.48)
A B C
It is clear that the magnitude of each component is proportional to the current in that phase and
that each component acts in the direction of its magnetic axis. This matches the description of the
MMF components given earlier in the chapter: the distribution is fixed in space, has a peak
aligned to the magnetic axis, and has a magnitude that scales with the phase current. The
definition of the MMF and current space vectors does not require the currents to be balanced
sinusoids but for the moment we will consider this case. The instantaneous values of the
component MMF SVs are shown directed along their respective axes in Figure 3.25 for threephase
currents at electrical positions of 0° and 30°. Figure 3.25 corresponds directly to Figure
3.11, and both figures correspond to Figure 3.7 and Figure 3.8.
Figure 3.25 – Instantaneous values of component and total MMF space vectors; (c.f. Figure 3.11).
23 Throughout this report it will be emphasized that the space vector describes the combined action of the
phases. That emphasis cannot be placed on the space vectors associated with each phase and perhaps this
terminology should not be used but it is found throughout the literature so it is adopted here.
100