SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

produced by an equivalent (Ne-turn) sinusoidally-distributed coil whose magnetic axis is aligned
at the angular position of the current SV and driven by a current equal to the magnitude of the
current SV.
Figure 3.28 – Axis of rotating amp-turn distribution cophasal with current and MMF SVs.
Torque production is of critical interest and torque production is directly related to the amplitudes
and angular positions of the stator and rotor fields relative to one another, thus the stator MMF is
of interest. Since the magnitude and angle of the stator MMF are directly related to the magnitude
and angle of the current SV, even for arbitrary currents, it is clear that the current SV can be used
to describe the torque of the machine; this will be developed in Part III.
The take-away from this subsection is that each SV represents a cosinusoidal distribution relative
to the phase-A axis. For the MMF SV this distribution coincides with the actual distribution in the
machine but for all other quantities the “distribution” is an abstract concept described by
reference frame theory and this is the connection between the physical phenomena in the machine
and its SV representation. Surprisingly, most texts offer only a mathematical treatment and make
no distinction between the physical distribution represented by the MMF SV and the abstract
distributions represented by the SVs of transformed quantities. However, one text [73]—which
attempts (and does well) to look beyond the mathematical definition—explicitly states that no
attempt will be made in the book to assign a physical meaning to the SVs of transformed
quantities, indicating that only the MMF distribution is represented by the SV. Nonetheless, the
discussion in this report is a simplification of the full theory (which is not often used to its fullest
extent) in which the SV analysis treats a distributed-parameter machine [103] instead of the
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