SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Equation 3.36). It further showed how the scalar quantity in υ can itself be assigned a vector
orientation in α in its own units (the voltage and current SVs of Equation 3.33 and Equation 3.38)
that when multiplied by the constant of proportionality produced the same result. The two
versions differ only by how the constant of proportionality is distributed in the equation thus they
are equivalent. The purpose of the discussion was to provide an interpretation for a voltage or
current space vector in the space α where they would otherwise not have a meaning, and this
understanding is the basis on which we assume the voltage and current SVs may be added
together.
In the case of voltage it isn’t hard to understand that the electron experiences force in two
orthogonal directions and that the sum of those forces could have been though of as being
imparted by a certain voltage applied to two plates aligned in the direction of resultant force, as
shown in Figure 3.24. This illustrates an important understanding of the space vector (voltage
space vector in this case): the effect of the voltage SV has a physical interpretation but the voltage
SV itself is an abstract quantity that does not exist and thus cannot be physically measured. The
same applies to the MMF and current SVs. The resulting MMF SV could have been produced by
a winding oriented along the axis of the resulting MMF. In that case, the MMF SV could be
described by the constant of proportionality multiplied by the resulting current SV, as shown in
Figure 3.27, for the general case of Equation (3.50).
Ne
f i
2
(3.50)
Ne
ˆ j ˆ j
f Ie Fe
2
102