SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

imparted by the definition of the inverse transform. This is made clear when an attempt is made to
take the real part of the phasor only to find that it yields a stationary quantity:
Re X Re j
X e X cos .
p p
In contrast, the inverse of the phasor transform is defined as
1
P X Re j jt X e e Re jt X e
p
j t
and it is seen that the e term is appended to the phasor as a part of the definition of the inverse
transform—the phasor does not contain any “frequency” information itself. The trajectory of the
j t
phasor (coupled to e ) is the same as the trajectory of the SV discussed above for the case of
balanced sinusoidal quantities in steady-state. In contrast, the “frequency” information of the SV
is contained in the SV itself. The SV can represent any 0 combination of the instantaneous
phase variables, whether those variables are changing, stationary, or switching between discrete
values. It is the instantaneous nature of the SV (along with its ability to capture each phase’s
contribution) that make it superior to the phasor for dynamic analysis.
142