Environmental Engineering Reference
In-Depth Information
Fig. 6.2
Induction machine
model in Clarke components
shows the model in
-components. It is assumed that the three-phase windings
are in Y-connection, and also that no neutral conductor is connected, so that the
zero-sequence component need not be considered.
The
αβ
0
transformation on the original stator components
abc
will be performed
in the power-variant form according to Tables 6.1 and 6.2. The same matrix is ap-
plied to voltages and currents, so that the transformation equation and its inverse is
given by:
αβ
u
abc
=
T
α
·
u
αβ0
;
i
abc
=
T
α
·
i
αβ0
.
u
αβ0
=
T
−
1
i
αβ0
=
T
−
1
·
·
u
abc
;
i
abc
(6.10)
α
α
In any moment the power in the three-phase system
P
abc
=
u
abc
i
abc
=
u
T
αβ0
(
T
T
α
·
T
)
i
αβ
(6.11)
α
0
As mentioned before, in the power-variant transformation
T
is not a unitary
α
matrix. The matrix (
T
T
) is diagonal and constant; for a system without zero-
sequence current it indicates a multiplying factor 3/2.
Same as this orthogonal transformation for the stator quantities, the rotor quanti-
ties for an assumed symmetrical three-phase winding system transform the original
components
klm
into modal components
AB0
, where the reference coordinate axis
A is rotated by the angle
α
·
T
α
γ
with respect to the stationary reference axis
α
.Inthe
following, zero-sequence components will not be considered.
The voltage equation of the four-winding model, not taking zero-sequence com-
ponents into account, and assuming short circuited rotor winding, equals the applied
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