Inverse Symmetrical-Components Transform
Convert from +-0 to the abc coordinate system.
Description
Block Inverse Symmetrical-Components Transform implements the inverse symmetric transformation of forward, inverse and zero vector sequences. The transformation decomposes a symmetric sequence of three vectors into an equivalent asymmetric sequence of vectors , and .
Use this conversion to reproduce a three-phase signal from a system that has been converted using the block Symmetrical-Components Transform.
Use the Power invariant parameters to choose between the Fortescue transform and an alternative power invariant version.
Equations
The inverse symmetric component transform reconstructs an asymmetric three-phase signal from the components of a symmetric vector sequence [ ] defined in the region +-0:
where is the complex rotation operator:
and is a constant defining the type of transformation:
-
- Fortescue transformation.
-
- power invariant transformation.
If a power invariant transformation has been performed, select the Power invariant checkbox so that the inverse transformation will also be power invariant and the signal will be recovered correctly.
Symmetric component transformation
The symmetrical component transform divides an asymmetrical three-phase signal, represented in phase magnitudes, into three symmetrical magnitude sequences:
where
-
is the initial asymmetric set of vectors;
-
make a forward sequence of vectors;
-
make an inverse sequence of vectors;
-
make the null sequence of vectors.
The symmetric component transformation computes the symmetric -phase as:
Since the remaining two sequences are not often used in calculations, the transformation generates only the first set. However, - and - sets can be computed in terms of simple rotations of the first set:
и
Principle of operation
The three sequences of vectors obtained by symmetric component transformation have the following properties:
-
The forward sequence has the same order as the asymmetric set of phase vectors .
-
The inverse sequence has the opposite order as the asymmetric set of phase vectors .
-
The null sequence has no order because all three phase angles are equal.
This diagram visualises the separation performed by the transformation.
In the diagram, the upper axis shows an unbalanced three-phase signal with components , and . The lower set of axes divides the three-phase signal into symmetrical forward, reverse and zero sequences.
Note that in each case the components , and are symmetrical and separated:
-
+120 degrees for the forward sequence.
-
-120 degrees for reverse sequence.
-
0 degrees for the zero set.