transix.abc_to_sym

transix.abc_to_sym(a, b, c)

Compute symmetrical components using Fortescue transform from abc quantities.

Parameters:

a, b, carray_like of complex

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

Returns:

outSequenceABC

Zero-, positive-, and negative-sequence phase quantities in the abc frame.

out.zerotuple of complex

Zero-sequence phase quantities (a0, b0, c0), where a0 = b0 = c0.

out.postuple of complex

Positive-sequence phase quantities (a1, b1, c1).

out.negtuple of complex

Negative-sequence phase quantities (a2, b2, c2).

Other Parameters:

power_invariantbool, optional

(Planned) If True, use the power-invariant Fortescue formulation. Default is False (amplitude-invariant).

decimalsint, optional

(Planned) Number of decimal places to round complex outputs.

Notes

Uses the Fortescue symmetrical component transformation [1] with \(\alpha = e^{j2\pi/3}\).

The sequence components are computed by,

\[\begin{split}\begin{bmatrix} a_0\\ a_1\\ a_2 \end{bmatrix} = \frac{1}{3} \begin{bmatrix} 1 & 1 & 1\\ 1 & \alpha & \alpha^2\\ 1 & \alpha^2 & \alpha \end{bmatrix} \begin{bmatrix} a\\ b\\ c \end{bmatrix}\end{split}\]

Then the corresponding phase triples are formed.

\[\begin{split}\begin{aligned} \text{zero} &= (a_0,\; a_0,\; a_0) \\ \text{pos} &= \left(a_1,\; \alpha^2 a_1,\; \alpha a_1\right) \\ \text{neg} &= \left(a_2,\; \alpha a_2,\; \alpha^2 a_2\right) \end{aligned}\end{split}\]

References

[1]

Fortescue, C.L. Method of symmetrical co-ordinates applied to the solution of poly-phase networks (with discussion). Presented at the 34th Annual Convention of the AIEE (American Institute of Electrical Engineers), Atlantic City, NJ, USA, 28 June 1918; Volume 37, pp. 1027-1140.

[2]

Wagner, C.F.; Evans, R.D. Symmetrical Components as Applied to the Analysis of Unbalanced Electrical Circuits; Mc-Graw-Hill: New York, NY, USA, 1933.

Examples

The below example is taken from Wagner and Evans (1933) [2].

>>> import transix as tx
>>> Ea = 60+0j
>>> Eb = 45-75j
>>> Ec = -21+120j
>>> seq = tx.abc_to_sym(Ea, Eb, Ec)
>>> seq.zero
(28+15j, 28+15j, 28+15j)
>>> seq.pos
(72.29+11.55j, -26.14-68.38j, -46.15+56.83j)
>>> seq.neg
(-40.29-26.55j, 43.14-21.62j, -2.85+48.17j)

The original sequence can be constructed again by,

>>> seq.zero[0]+seq.pos[0]+seq.neg[0]
60+0j
>>> seq.zero[1]+seq.pos[1]+seq.neg[1]
45-75j
>>> seq.zero[2]+seq.pos[2]+seq.neg[2]
-21+120j