SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

The load line-neutral voltages are given by Equation (D.17), where IZ , A, IZ , C , IZ , C
voltage drops across the impedances.
v e v
v
e v
v
e v
AN A IZ, A
BN B IZ , B
CN C IZ , C
v v v are the
(D.17)
Similar to Equation (D.14), the drops across the impedances must sum to zero, thus Equation
(D.18).
Z() s I () s I () s I () s 0
A B C
V () s V () s () s V () s 0
IZ , A IZ , B IZ , C
vIZ A vIZ B vIZ
C
(D.18)
, , , 0
Summing Equation (D.17) and substituting Equation (D.18) gives Equation (D.19).
v v v v v v e e e
AN BN CN IZ, A IZ, B IZ, C A B C
v v v e e e
(D.19)
AN BN CN A B C
In order to examine the impact of a ZS component in the bEMF, the assumptions in Equation
(D.12) for source voltage are now applied to the bEMF. We assume (Equation D.20) that there is
a ZS component e ZS in addition to the 0 components e xM .
e
ee
e
ee
e
ee A A ZS
B B ZS
C C ZS
Substituting the result into Equation (D.19) gives Equation (D.21).
v v v e e e 3e
AN BN CN A B C ZS
3
AN BN CN ZS
(D.20)
v v v e
(D.21)
The KVL result is the same as before (Equation D.10) and since we still make the assumptions of
Equation (D.12) for the source voltages, Equation (D.13) still holds.
(D.10):
v
v v
v
v v
v
v v
AM AN NM
BM BN NM
CM CN NM
v v v v
(D.13): 3
AM BM CM ZS
Summing Equation (D.10) and substituting Equations (D.13) and (D.21) gives Equation (D.22).
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