SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Figure 4.31 – Temporal limit of inverter output.
The α-projection of a SV tracing the hexagon is shown in Figure 4.32; it will be called the
“gambrel” waveform. In the figure, the degree markings are nonstandard (they are measured from
the negative imaginary axis).
Figure 4.32 – α-projection of hexagon trajectory.
This is the “maximum” for a continuously-changing output. Recall that the THI limit was the
circle inscribed in the hexagon (Figure 4.28). That limit is the maximum sinusoidal limit for any
180° inverter, whether it is an analog THI or a SVM implementation. Thus when the average SV
is tracing the THI limit and the commanded magnitude is increased, the resulting SV will trace
the THI limit tangentially but will enter the shaded regions shown in Figure 4.33 and harmonics
will be produced since the trajectory is not circular. The relationship between the magnitude of
the SV and the amplitude of its fundamental component becomes nonlinear. Operation in this
region is similar to overmodulation in the SPWM inverter. Increasing the magnitude of the
commanded SV to (S) will encounter the temporal hexagon limit and produce the gambrel
waveform.
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