For a project I'm working on, I want to use the Clarke Transform to detect faults in a power system. To do this, I already wrote a script in Python which returns the sine wave behavior of the Alpha, Beta and Zero components of the transform for an ABC system given in the form
$$s(t) = A\sin(\omega t + \phi)$$
Getting the amplitude and phase is easy enough to do from the ABC system. However, when I compute the Clarke transform, my program returns three numpy arrays: one for each component (\$\alpha\$, \$\beta\$, \$0\$). Since they are returned to me in the form of numpy arrays, getting the amplitude and phase of those waves is not so straightforward, since I don't have an equation in the form of
$$s(t) = A\sin(\omega t + \phi)$$
for these numpy arrays.
The first question I wanted to ask was if someone knows how I can get the amplitude and phase of the Clarke transform only with the numpy arrays I have.
The second and final question I wanted to ask is if someone knows of a way to plot the \$\alpha-\beta\$ plane in Python or MATLAB with the space vector in real time. For example, I would like to plot the \$\alpha-\beta\$ plane for the transform I just got.
Thanks so much for any information you can give me in advance.
