SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Figure 4.27 – Transformed voltage waveforms for six-step 180° squarewave inverter.
From Appendix D we already know the SV cannot contain (encode) any ZS component; what has
been illustrated here is that when the output of the inverter is represented as a SV, that SV is only
showing us the non-ZS component—and for a wye-connected load, this is equal to the phase
(line-neutral) voltages. Since the ZS component adds in the neutral and does not affect the load
anyhow, this is particularly handy because it allows us to continue to use the two-dimensional SV
plots we normally work with. However, when we need to examine the details (such as this
discussion of the connection between SVM and six-step squarewave) it is obvious that we cannot
ignore the ZS component. We will return to dealing with the ZS component in a later subsection;
right now the study of the SV magnitude and trajectories will be resumed.
Chapter 3 derived the SV corresponding to balanced sinusoidal waveforms. Supposing those
sinusoidal waveforms are produced by an inverter, the corresponding SV would be given by
Equation (4.6). As with the above tables and SV diagram, our SV definition must take into
account that the inverter output is given as a peak, line-neutral voltage specified in terms of V DC .
3 j t
v k VDCe 2
For k 2/3 the SV has a constant magnitude of ˆ V V , which is the maximum amplitude
sinewave that can be generated using an SPWM inverter. Obviously the trajectory of this SV is a
circle of radius V DC ; its projection will give α- and β- components that are sinusoidal; the inverse
SV transform of those projections yield the original sinusoidal phase-variables, as we have
already seen. If THI is used the maximum possible amplitude of the fundamental is 2/ 3 times
DC
(4.6)
185