alphabetagamma_to_dq0

typhoon.test.transformations.alphabetagamma_to_dq0(signals, theta, alignment='d')

Implements the alpha-beta-gamma to dq0 transformation, also known as Clarke to Park angle transform.

The Clarke to Park Angle Transform block converts the alpha, beta, and zero components in a stationary reference frame to direct, quadrature, and zero components in a rotating reference frame. For balanced three-phase systems, zero component is equal to zero. There are two possible forms, as alpha-axis of stationary reference frame can be aligned with q- or d-axis of the rotating reference frame. These methods are implemented by following equations:

  • alpha-axis and d-axis are aligned:
    d = cos(theta) * alpha + sin(theta) * b
    q = -sin(theta) * alpha + cos(theta) * b
    zero = gamma
  • alpha-axis and q-axis are aligned:
    d = sin(theta) * a - cos(theta) * b
    q = cos(theta) * a + sin(theta) * b
    zero = gamma

    Variable theta represents the angle between two reference frames; it is measured between alpha-axis of alpha-beta reference frame, and the axis from d-q reference frame which is initially aligned with alpha.

Parameters:

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

  • theta (pandas.Series) – The angle in time between the two reference frames; it is measured between alpha-axis of alpha-beta reference frame, and the axis from d-q reference frame which is initially aligned with alpha.

  • alignment (string) – It has two valid values: ‘d’ or ‘q’. That is the way to chose which axis in rotating reference frame is initially aligned with alpha-axis from stationary reference frame.

Returns:

result – DataFrame with three columns, one for every output signal. The labels to select columns are d, q and zero, respectively.

Return type:

pandas.DataFrame

Examples

>>> from typhoon.test.signals import pandas_sine
>>> from typhoon.test.transformations import alphabetagamma_to_dq0
>>> from scipy.signal import sawtooth
>>> import numpy as np
>>> import pandas as pd
>>> alpha = pandas_sine(frequency=50) # sine with amplitude 1 and phase 0
>>> beta = pandas_sine(frequency=50, phase=-90) # sine with amplitude 1 and phase -90
>>> gamma = pandas_sine(frequency=50, amplitude=0) # constant with zeros

>>> # create pandas.Series which represents dq reference frame angle
>>> t = np.arange(0, 1, 1e-4) # time axis for the angle
>>> index = pd.TimedeltaIndex(t, unit='s')
>>> angle = sawtooth(2 * np.pi * 50 * t) # create sawtooth signal from -1 to 1
>>> angle = (angle + 1) * np.pi # make sawtooth go from 0 to 2pi
>>> theta = pd.Series(data=angle, index=index)

>>> alpha_beta_frame = pd.DataFrame(data={"alpha":alpha, "beta":beta, "gamma":gamma}, index=alpha.index)
>>> dq0_frame = alphabetagamma_to_dq0(alpha_beta_frame, theta, alignment='q')
>>> d = dq0_frame["d"]
>>> q = dq0_frame["q"]
>>> zero = dq0_frame["zero"]

See also

typhoon.test.transformations.alphabetagamma_to_abc, typhoon.test.transformations.dq0_to_alphabetagamma