SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

n=1:
n=3:
n=5:
x1A() t X1cos1 t x1A() t X1cost
x1B() t X1cos1 t x1B() t X1cost
x1 () 1cos1
x1C() t X1cost C t X t
x3A() t X3cos3 t x3A() t X3cos3t
x3B( t) X3cos 3 t x3B( t) X3cos 3t
x3 () 3cos3
x3C() t X3cos3t C t X t
x5A() t X5cos5 t x5A() t X5cos5t
x5B() t X5cos5 t x5B() t X5cos5t
x5 () 5cos5
x5C() t X5cos5t C t X t
It is seen that the phase offsets follow the pattern 0, , ,
0,0,0 , 0, ,
(D.4)
(D.5)
(D.6)
. Only the
fundamental and the first two harmonics need be evaluated because the pattern repeats. If a set of
balanced phasors were used to describe the sets in Equations (D.4)-(D.6) they would look like
those in Figure D.1. 51 Note that the order of the phasors differs between the PS and NS diagrams.
Figure D.1 – Phasor diagrams for positive-, zero-, and negative- sequence sets.
Projecting the phasors of each set onto the real axis would show that the order in which the phase
variables peak. In the first set the order is ( A B C),
in the second set the variables are all
cophasal, and in the third set the order is ( AC B).
The first set is called a positive-sequence
(PS) set, the second a zero-sequence (ZS) set, and the third a negative-sequence (NS) set.
Sometimes the argument of the cosines in Equation (D.6) is negated, yielding phasors that have
51
Each phasor would be defined using a different ω (namely, n·ω) but this fact is not shown because the
emphasis is on the sequence rotation.
310