abc_to_alphabetagamma

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

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

If the input signals are symmetrical, the result represents its projection in alpha-beta stationary reference frame, while the gamma component equals to zero. There are three methods of this transformation, which can be chosen by setting the ‘method’ argument to appropriate value:

  • Amplitude invariant - with this method, amplitudes of the input signals are preserved. It is implemented by following equations:
    alpha = 2/3 * (a * cos(-theta) + b * cos(2*pi/3 - theta)  + c * cos(4*pi/3 - theta))
    beta = 2/3 * (a * sin(-theta) + b * sin(2*pi/3 - theta) + c * sin(4*pi/3 - theta))
    gamma = 1/3 * ( a + b + c)
  • Uniform - Clarke’s original. The calculation of alpha and beta is the same as before, but gamma axis is not
    squashed, so its output is the same as the zero sequence obtained from the symmetrical components trasformation:
    alpha = 2/3 * (a * cos(-theta) + b * cos(2*pi/3 - theta)  + c * cos(4*pi/3 - theta))
    beta = 2/3 * (a * sin(-theta) + b * sin(2*pi/3 - theta) + c * sin(4*pi/3 - theta))
    gamma = sqrt(2)/3 * (a + b + c)
  • Power invariant - this transformation preserves the power of the new equivalent, two phase system. Because of that, amplitudes of the signals are sqrt(3/2) times bigger then the original signals a,b,c. The equations for this method are:
    alpha = sqrt(2/3) * (a * cos(-theta) + b * cos(2*pi/3 - theta)  + c * cos(4*pi/3 - theta))
    beta = sqrt(2/3) * (a * sin(-theta) + b * sin(2*pi/3 - theta) + c * sin(4*pi/3 - theta))
    gamma = 1/sqrt(3) * ( a + b + c)

    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 every signal of the three-phase abc input.

  • method (string) – The chosen method of the transformation. It can have one of the following values: “Amplitude invariant’, ‘Uniform’ or ‘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 output signals. Labels for output signals are alpha, beta and gamma, respectively.

Return type:

pandas.DataFrame

Examples

>>> from typhoon.test.signals import pandas_3ph_sine
>>> from typhoon.test.transformations import abc_to_alphabetagamma
>>> abc_frame = pandas_3ph_sine(frequency=50)
>>> alpha_beta_frame = abc_to_alphabetagamma(abc_frame, method="Amplitude invariant")
>>> alpha = alpha_beta_frame["alpha"]
>>> beta = alpha_beta_frame["beta"]
>>> gamma = alpha_beta_frame["gamma"]