SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Figure D.1 show that the PS and NS phasors vectorially sum to zero but the ZS phasors sum to a
cophasal phasor whose magnitude is three times that of the ZS phasors. Since the PS and NS
components sum to zero we will call them 0 components. Since the ZS component does not
sum to zero it could be called the 0 component but since only the ZS component has this
property it will be called the ZS component. The consequence of this is that in analyzing
symmetrical three-phase systems we can group the harmonic components into 0 components
and a ZS component. As will be shown, the reason for the separate treatment is that ZS
component affects three-phase systems differently than do 0 components.
The ZS component has been defined in the traditional manner using phasors. From Figure D.3 it
is seen that in three-phase systems the ZS component is composed of the odd multiples of three;
these are called the triplen harmonics. But also, any common-mode component among the phase
variables in a set is a ZS component. If a common mode component were plotted against time it
would be found to have a spectra consisting of only triplens and/or a DC component. Thus, this
report defines the ZS component to be the common-mode component; this is commonly implied in
the literature but is often unstated.
that ZS current would flow, the current would produce zero net MMF, which obviously cannot rotate.
Third, the SV cannot capture ZS terms even if they were present (this is true for any space vector).
312