transix.abc_to_ab0

transix.abc_to_ab0(a, b, c, variant: Literal['power_variant', 'power_invariant'] = 'power_invariant')

Compute Clarke alpha, beta and zero components from abc quantities.

Parameters:

a, b, carray_like

Signal a, b, c. These can be three phase signals in complex form.

variant{“power_invariant”,”power_variant”}, optional

Default is power_invariant

Returns:

alpha, beta, zerondarray

Alpha-, beta-, and zero components of three phase quantities.

See also

transix.ab0_to_abc()

Notes

Clarke’s transformation [1] converts three phase abc quantities to alpha-beta-zero quantities.

The power invariant type is computed by,

\[\begin{split}\begin{bmatrix} \alpha \\ \beta \\ zero \end{bmatrix} = \sqrt{\frac{2}{3}} \begin{bmatrix} 1 & -1/2 & -1/2\\ 0 & \frac{\sqrt{3}}{2} & -\frac{\sqrt{3}}{2}\\ \sqrt{\frac{1}{2}} & \sqrt{\frac{1}{2}} & \sqrt{\frac{1}{2}} \end{bmatrix} \begin{bmatrix} a\\ b\\ c \end{bmatrix}\end{split}\]

The power variant type is computed by,

\[\begin{split}\begin{bmatrix} \alpha \\ \beta \\ zero \end{bmatrix} = \frac{2}{3} \begin{bmatrix} 1 & -1/2 & -1/2\\ 0 & \frac{\sqrt{3}}{2} & -\frac{\sqrt{3}}{2}\\ \frac{1}{2} & \frac{1}{2} & \frac{1}{2} \end{bmatrix} \begin{bmatrix} a\\ b\\ c \end{bmatrix}\end{split}\]

References

[1]

E. Clarke, Circuit Analysis of A-C Power Systems: Symmetrical and Related Components. Wiley, 1943.

Examples

>>> import transix as tx
>>> a, b, c = tx.generate_abc(rms=230,f=50,t=0.1,fs=50000)
[ 0.      2.0437  4.0873 ... -4.0873 -2.0437 -0.    ]
[-281.6913 -282.7076 -283.7128 ... -279.6254 -280.6639 -281.6913]
[281.6913 280.6639 279.6254 ... 283.7128 282.7076 281.6913]
>>> alpha,beta,zero = tx.abc_to_ab0(a,b,c)
[ 0.      2.503   5.0059 ... -5.0059 -2.503   0.    ]
[-398.3717 -398.3638 -398.3403 ... -398.3403 -398.3638 -398.3717]
[ 0.      0.     -0.0001 ...  0.0001  0.      0.    ]