I am working on an application of conformal mapping to the computation of the magnetic field in motors based on this paper, but I have trouble understanding how to compute the instantaneous current of each phase winding.
The paper describes the winding as: "9-phase semi-symmetric double-layer full-pitch concentrated windings" (paragraph III.B) which is quite the description, but I have no idea what half of these words actually mean since I never worked with motor winding standards. From the RMS equivalent current I_a, the paper just states that "it is easy to obtain the value of instantaneous current i_a of each phase winding at any time t" with no further explanation...
My exact question would be: what is the value of the instantaneous equivalent currents i_a(k) and i'_a(k) in the k-th slot at t=0?
At first, I thought of just switching the sign of I_a, but I realized that it doesn't make sense to use the RMS eq. current like this, then I thought about using a sine, but it doesn't seem to line up with the current directions on the image below (from the paper) when having: $$i_{a(k)} = \sqrt{2}\cdot I_a sin(\theta-k\cdot 2\cdot\pi/9)$$ maybe the equivalent points with the same color (in the image) have the same phase? I have no idea, I couldn't match any information about motor winding notation I found on the internet to apply to this case. So now I'm at a loss as to what exactly does "9-phase" mean in this paper...
The ultimate goal would be to understand this well enough to generalize the model I am making to any winding configuration, but I am losing hope seeing how complex motor windings are, so I'll be happy if I can reproduce this exact application.
Edit: fixed LaTeX formatting
