SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Figure 3.27 – Equivalent MMF produced by coil with axis aligned with resultant MMF
(c.f. Figure 3.24).
This explains part of the meaning of the statement above that said the MMF and current SVs are
cophasal (a fuller explanation is given in the next subsection). Figure 3.27 shows how the simple
additivity of the force and voltage SVs of the CRT example directly applies to the MMF and
current SVs of the machine.
The take-away from this subsection is that space vectors can be added and that the space vector
itself is not a physically-existing quantity. Although a SV (such as f ) may represent a
physically-distributed quantity, as SV (such as i ) may represent a quantity that cannot be
understood in physical terms; this is discussed next and is the additional “level of abstraction”
referred to in the quote that opened Part II.
The SV as a Distribution
The second facet of the SV to study is the manner in which it represents a distribution. The
previous section concentrated on the vector nature of MMF but ignored distribution, which will
be studied now. When a machine is modeled using SV theory all quantities (voltage, current,
MMF, flux linkage) will be space vectors. Although each SV could be interpreted as representing
a distribution, stator MMF is the only quantity whose physical distribution is equal to the
distribution represented by the SV. For the other quantities, the “distribution” represented by the
SV does not physically exist, or if it does, it is not exactly that described by the SV. This seems
an unwelcome artifact of the theory but it will be shown to be the meaning of reference frame
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