SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

indeed defined such that common-mode components are simply not contained in the PS & NS or
α & β components; there is obviously good reason for defining the transforms this way. There is a
very meaningful graphical understanding of the ZS component that the interested reader can
pursue [106], [105], [62, p.83], [70, p.25] but for brevity it is not presented here. However, a
simplified and insightful result is shown: if the 0 axis is taken to be orthogonal to the α and β
axes, we can draw a three-dimensional vector (although this does not fit our technical definition
of an SV since it only has two components). From the inverter chapter, the eight base SVs of a
180° inverter were projected onto the αβ plane as shown in Figure D.10. The magnitude of each
4
SV is k2 VDC,
which for k 2/3 is equal to
3 DC
S V .
Figure D.10 – Projection of base SVs of 180° inverter onto AB plane.
If the thee-dimensional vectors were plotted they would be as shown in Figure D.11 ( k 2/3),
where the cross section is that shown in Figure D.10. This shows a graphical interpretation of the
ZS component of the output voltage. (Be aware that in Figure D.11, only 0 S
, 1 S
, 4 S
, and 7 S
are in the αγ plane; S2
and S3
are behind the plane in the β direction. The cross-section
S
but these are omitted for clarity.)
should show a truncated portion of 5 S
and 6
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