SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

the same order as the PS set (arranged A-C-B in the CCW direction) but rotate in the opposite
direction, as shown in Figure D.2. 52
Figure D.2 – An alternate (but equivalent) interpretation of sequence sets.
The sequence order of some low-order harmonics are summarized in Figure D.3.
Figure D.3 – Sequence order of some low-order harmonics.
The component of MMF that a current harmonic produces in a machine will rotate according to
its sequence. To see this it is not necessary to use SV theory but doing eases understanding. The
SVs corresponding to the harmonics of Equations (D.4)-(D.6) are given by Equations (D.7)-
(D.9), respectively, where k 2/3 has been used to achieve magnitude-invariance (a derivation
is given later in this appendix).
j t
x1 Xe 1
x3 0
j5t x X e
5 5
(D.7)
(D.8)
(D.9)
It is clear that PS harmonics would cause a positive rotation, NS harmonics would cause negative
rotation, and ZS harmonics do not cause any rotation. 53 More importantly the phasor diagrams in
52 In the method of symmetrical components (MSC) all phasors are at the fundamental frequency. These
sets discussed here are similar to those of MSC but since they have different frequencies they are not the
same. Therefore when “PS,” “NS,” and “ZS” are used in this report, they refer to general sets that have PS,
NS, and ZS rotation, not those sets particular to the MSC.
53 There are several simultaneous “reasons” why the third-harmonic SV is zero. First, we cannot force ZS
current into a winding when the neutral is isolated (KCL). Second, even if the neutral were grounded so
311