alphabetagamma_to_abc

typhoon.test.transformations.alphabetagamma_to_abc(signals, method='Amplitude invariant', alignment='alpha')

Calculates alpha-beta-gamma to abc transformation, also known as Clarke’s inverse transformation.

This transformation projects the two stationary (alpha-beta) axis onto the three-phase axis. It has the same three forms as abc to alpha-beta-gamma transformation:

• Amplitude invariant:

  a = alpha * cos(-theta) + beta * sin(-theta) + gamma

  b = alpha * cos(2*pi/3 - theta) + beta * sin(2*pi/3 - theta) + gamma

  c = alpha * cos(4*pi/3 - theta) + beta * sin(4*pi/3 - theta) + gamma
• Uniform - Clarke’s original:

  a = alpha * cos(-theta) + beta * sin(-theta) + 1/sqrt(2) * gamma

  b = alpha * cos(2*pi/3 - theta) + beta * sin(2*pi/3 - theta) + 1/sqrt(2) * gamma

  c = alpha * cos(4*pi/3 - theta) + beta * sin(4*pi/3 - theta) + 1/sqrt(2) * gamma
• Power invariant:

  a = sqrt(2/3) * (alpha * cos(-theta) + beta * sin(-theta) + 1/sqrt(2) * gamma)

  b = sqrt(2/3) * (alpha * cos(2*pi/3 - theta) + beta * sin(2*pi/3 - theta) + 1/sqrt(2) * gamma)

  c = sqrt(2/3) * (alpha * cos(4*pi/3 - theta) + beta * sin(4*pi/3 - theta) + 1/sqrt(2) * gamma)

  parameter theta is defined by function argument alignment: if it is set to alpha, theta angle is zero; otherwise, it is -pi/2

Parameters:

• signals (pandas.DataFrame) – DataFrame with three columns, one for alpha, beta and gamma signal.

• method (string) – The string for selecting the one of three possible methods: “Amplitude invariant’, ‘Uniform’, ‘Power invariant’

• alignment (string) – Defines axis of the alpha-beta reference frame which is aligned with a-axis of the original reference frame. Valid values are “alpha” and “beta”.

Returns:

result – DataFrame containing three columns - one for each output signal. The labels for selection of the signals are a, b and c, respectively

Return type:

pandas.DataFrame

Examples

>>> from typhoon.test.signals import pandas_sine
>>> from typhoon.test.transformations import alphabetagamma_to_abc
>>> import pandas as pd
>>> alpha = pandas_sine() # sine with amplitude 1 and phase 0
>>> beta = pandas_sine(phase=-90) # sine with amplitude 1 and phase -90
>>> gamma = pandas_sine(amplitude=0) # constant with zeros
>>> alpha_beta_frame = pd.DataFrame(data={"alpha":alpha, "beta":beta, "gamma":gamma}, index=alpha.index)
>>> abc_frame = alphabetagamma_to_abc(alpha_beta_frame, method="Amplitude invariant")
>>> a = abc_frame["a"]
>>> b = abc_frame["b"]
>>> c = abc_frame["c"]

See also

typhoon.test.transformations.abc_to_alphabetagamma, typhoon.test.transformations.alphabetagamma_to_dq0