SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

as large as that for regular SPWM, thus for k 2/3 the SV would have a magnitude of
Vˆ (2 / 3) VDCand
trace a circle just as in SPWM. Finally, in six-step squarewave mode we
saw that the “time history” of the SV consisted of discrete points (the SVs corresponding to the
six active inverter states). When the projections onto the αβ plane are plotted against time and
transformed back to phase variables the familiar six-step pattern appeared. But we know the
fundamental of the output voltage in this mode has an amplitude of (4 / ) VDC
thus the SV
representing this fundamental would have a magnitude of ˆ V (4 / ) VDCfor
k 2/3.
The
results of our investigation into magnitudes and trajectories are summarized by the diagram
shown in Figure 4.28.
Figure 4.28 – Magnitudes and trajectories of some important SVs.
There are three circular trajectories shown: the SPWM linear limit (R, blue), the THI linear limit
(T, black), and the maximum fundamental of six-step squarewave mode (F, red). In addition, the
magnitude of the base SVs (corresponding to the six active states of the inverter) is shown (S);
since six-step squarewave mode consists of stepping through these active states, the base SVs
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