Symmetrical-Components Transform
Convert from the abc coordinate system to +-0.
Description
The Symmetrical-Components Transform block implements a symmetrical transformation of vector sequences. The transformation splits an asymmetrical sequence of three vectors into three symmetrical vector sequences.
In an asymmetrical system with symmetrical impedances, use this block to divide the system into three independent networks. In a symmetrical system, use this block to simplify the sequence of three phase vectors to an equivalent single-line network. In this case, the direct sequence is a single-line network.
Use the Power invariant parameter to choose between the Fortescue transform and the alternative power invariant version.
Equations
The symmetric component transform divides an asymmetric three-phase signal, represented in phase magnitudes, into three symmetric magnitude sequences:
where
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is the initial asymmetric set of vectors;
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make a forward sequence of vectors;
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make an inverse sequence of vectors;
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make the null sequence of vectors.
The block calculates the symmetric -phase using the transformation:
where is the complex rotation operator:
and is a constant defining the type of transformation:
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- Fortescue transformation.
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- power invariant transformation.
To select a power invariant transformation and simplify the calculation of power in the area +-0, select the Power invariant checkbox.
Since the remaining two sequences are not often used in calculations, the block does not calculate them. However, they are given in terms of simple rotations of the first sequence:
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Principle of operation
The three sequences of vectors generated by the transformation have the following properties:
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The forward sequence has the same order as the asymmetric vector sequence .
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The inverse sequence has the opposite order as the asymmetric vector sequence .
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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 forward, reverse and zero sequence.
Note that in each case the components , and are symmetrical and separated:
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+120 degrees for the forward sequence.
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-120 degrees for reverse sequence.
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0 degrees for zero sequence.
Reverse conversion
The conversion of symmetrical components is unique and invertible:
Use the Inverse Symmetrical-Components Transform block to perform the inverse conversion.
Ports
Parameters
Power Invariant - conversion type
disabled (by default) | enabled
Selects between the Fortescue transform and the power invariant transform. Select this check box to use the power invariant transform.