SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

also correspond to six-step squarewave operation. The relative magnitudes of the circular
trajectories are given; these directly follow from the above discussion. It is crucial to understand
that the only reason a comparison of these magnitudes makes any sense is that each space vector
has been defined as describing the same type of quantity, relative to the same reference, in the
same unit of measurement. In this case, the quantity is a peak voltage, the reference is the bus
midpoint M (thus these are line-neutral voltages), and the unit of measurement is the fraction of
V DC . The relationships shown in the figure hold regardless of how we specify a SV, but it is clear
that all SVs must be defined in exactly the same way in order to compare them on the same
diagram. For this reason it is nearly impossible to decipher literature written in terms of space
vectors unless this concept is understood well. One does not have to look far in the literature to
find a surprising number of conventions used. Table 4.4 is provided to reconcile these different
definitions. The boldface lines show the definition used in this report (peak, L-N, V DC ). In this
report, k is often left explicit to aid understanding but when working with inverters, k 2/3 is
generally chosen.
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