SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Figure 4.26 – Base SVs showing the states of a 180° inverter.
The values in Table 4.2 are for k 2/3 such that they will be magnitude invariant. Since the
values in Table 4.2 were computed from the voltages in Table 4.1 (which were peak line-neutral
voltages specified in terms of V DC ), the SVs have magnitude Si(4 / 3) VDC.
Now compare
Figure 4.26 with Figure 4.23. For state S1, S1
has a magnitude of S (4 / 3) V
i DC
and it is seen
that the phase-neutral voltage of phase-A has the same magnitude. This seems to make sense
because k 2/3 yields a magnitude-invariant SV. But the values in Table 4.2 (hence the
magnitude of the SVs in Figure 4.26) were computed from the pole voltages in Table 4.1, not the
phase voltages. Why then do the SV magnitudes match the phase voltages? The reason is that the
SV (the α- and β- components) cannot contain a ZS component. By definition (Equation 4.5 and
Appendix D) each pole voltage is composed of a phase voltage (which cannot contain a ZS
component) and the neutral voltage (which consists of only the ZS component). Since the SV can
only contain the non-ZS component, taking the SV transform of the pole voltages produces the
same result as taking the SV transform of the phase voltages; in either case, the resulting SV will
represent the phase voltages. Since the only difference is the ZS term, we should be able to see
this using the αβ0 transform. The αβ0 transform of the pole voltages were given as Table 4.2; the
ZS terms are clearly present. Now the αβ0 transform of the phase voltages is given below in
183