SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Figure 3.23 – Time relationships between flux linkages and induced voltages; lagging PF.
These relationships in Figure 3.23 are given by Equations (3.29), (3.30), and (3.31).
a S, a R, a
LI
s a R, a
G a j
a
jL I j
jL IE a R, a
s a R, a
s a
(3.29)
(3.30)
E j
(3.31)
Once again, the stator flux linkage is composed of two components: the rotor-stator flux linkage
and the self flux linkage. The bEMF is the time derivative of the former and the inductive voltage
drop is that of the latter. The total induced stator voltage is then the sum of the inductive voltage
drop and the bEMF. In reality, the flux due to stator currents (which produces the self flux
linkage) and the flux due to the rotor (which produces the bEMF) add together in the airgap to
produce a resultant flux (with corresponding flux density, MMF, and field strength), and the time
derivative of this resultant flux linkage is the total induced stator voltage ( a G ). That the rotor-
stator flux linkage induces the bEMF is familiar. That an inductor produces flux linkage with
itself as a result of the current through it is familiar. That the two act independently of one
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