SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

3
v v v v v v v
AM BM CM AM BM BM ZS
3
v v v v
(D.13)
AM BM CM ZS
The currents in the load must sum to zero. Since there are no voltage sources in the load, the sum
of the line-neutral load voltages must also sum to zero (Equation D.14).
Z s IA s IB s IC s
V s V s V s
() () () () 0
() () () 0
AN BN CN
v v v 0
(D.14)
AN BN CN
Applying the results of Equations (D.13)-(D.14) to Equation (D.11) gives Equation (D.15).
3v 0 3v
ZS NM
vNM vZS
(D.15)
Thus the ZS component of source voltage will always appear at the neutral in a passive load with
an isolated neutral. That v NM is a common-mode voltage should have already been clear from
Equation (D.10) and that the neutral voltage is exactly the common-mode voltage should be clear
from a general knowledge of circuit theory. To emphasize the latter, examine Figure D.5 in light
of Equation (D.12). There is no difference between the two circuits in Figure D.5 and it is seen
that the “balanced portion” of the source is v ZS above ground.
Figure D.5 – Equivalent source showing that ZS is common-mode.
By using Equation (D.15) the same perspective can be used to examine the load, as shown in
Figure D.6. The voltage v ZS is drawn as a square because it is not a real source (just as the point
of zero potential does not physically exist); the v ZS voltage against the zero potential simply
represents the effect of v ZS on the load; no current can be driven through it.
314