SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

different triplen signal would be injected. Such a scheme could obviously be implemented
without a microprocessor, either in entirely in analog or as naturally-sampled PWM [128], [137].
However, the advantage of a SV-input command is lost and a switching algorithm is no longer
used, thus it is different from the SVM discussed here. In other words, such a scheme produces
pole and ZS waveforms that look like those produced using SVM but the control method is
different. The reader is simply cautioned that “SVM” does not always indicate the modulation of
base vectors as presented here.
Now, exactly why the switching algorithm discussed earlier produces a triangular ZS component
is beyond the author’s present understanding but that detail is not important here. On the contrary,
it is important that the reader understand the discussion above. We should always be aware that
any output produced by the SVM inverter will contain this average ZS component, which can
only be represented as αβ0 components. However, the ZS component is not present in the phase
voltages (indeed, we rely on this fact) and the SV cannot represent the ZS component. Therefore,
we can choose to ignore the ZS component, draw the two-dimensional SV diagrams of the
inverter output (such as Figure 4.26), and work with only the SV (only the αβ components) when
we use a SVM inverter in a control system.
Modulation Index
The modulation index was previously developed for the SPWM inverter. It was mentioned that
the modulation index could be defined with respect to the THI limit or to the fundamental
produced in six-step squarewave mode. The modulation index of a SVM inverter can be defined
in the same manner. Since SVM by definition uses SVs, it is also common to reference the SVM
modulation index relative to the magnitude of the active base SVs. Therefore the modulation
index may be referenced to three different SVs (representing the amplitudes of sinusoidal
components) or to the magnitude of a SV. However, it was shown that the “magnitude” of a SV
plotted in the αβ plane can be specified in different ways and it became apparent how important
that definition is when examining inverter output. Thus, when the modulation index of a SVM
inverter is discussed, the same considerations apply.
Recall that Table 4.4 gave the modulus of the space vector representation of different three-phase
waveforms. The first column corresponds to the largest sinusoid produced via regular SPWM (R),
the second column corresponds to the largest sinusoid produced via THI (T), and the third column
corresponds to the amplitude of the fundamental produced in squarewave mode (F). Each of these
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