SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

First the self-flux-linkage of an individual winding is considered. The total flux is given by
Equation (B.1). We know the total flux produced splits between the magnetizing and leakage
paths as represented by Equation (B.2).
f Ni (B.1)
R R
mag (B.2)
Since the number of turns and the current are the same, the only difference must be the
reluctance. This is shown by combining these two results into Equation (B.3).
Ni Ni
R R
mag
Now the flux linkage can be found as shown in Equation (B.4).
2 2
N i N i
N
R R
mag
(B.3)
(B.4)
A self inductance is defined as the amount of flux linked per unit current, which for a simple
inductor is equal to the number of turns squared divided by the reluctance as shown by Equation
(B.4). These inductances are shown explicitly in Equation (B.5) and are called the magnetizing
inductance (or airgap inductance) and the leakage inductance.
2 2
N N
i i
R
R
mag
L iLi mag
(B.5)
Although they are separate components they are both a part of the self inductance of a winding.
Thus the self inductance could be defined as Equation (B.6) and each phase in a motor would
have this same self inductance.
L Lmag L (B.6)
Now the total flux linkage of a winding is considered. The flux linkage of a phase winding
consists of its own self flux linkage, mutual flux linkage between other windings, and the flux
linked by the rotor. In general terms these are given for each phase by Equation (B.7).
A LAAiALABiBLACiCAR B LBAiA LBBiB LBCiC BR
(B.7)
L i L i L i
C CA A CB B CC C CR
273