Zero sequence of transmission lines. I tried to figure it out once, and was overcome by the complexity. Most of what people use is referred to as Carson's equations, but if you pull up a copy of Carson's paper, it provids un-derived equations that jump to results that I have never seen proven. Furhter, what are typically called Carson's Equations appear to actually be equations out of 1930's text by Wagner and Evans, and which then ended up in the famous WH T&D reference text, but if you look at the equations in the latter 2 sources, I see no way to compare to the equations in the old Carson paper. I sometimes think people are adjusting the "ground resistivity" fudge factor in the Zo equations till they get answers that match what they see in real faults, and then say the equations are correct. Maybe the major T-line software mfrs (Cape, Aspen) have papers that somehow prove their equations, but I think they treat their equations as a trade secret. I think it would be good if someone could really prove for public domain some good Zo equations that can model the side issue of showing current distribution in the ground. I found a guy that said he could prove Carson's equations once using an infinite Fourier series, but when I looked his results, I was lost but it looked to me it has a problem with showing current distribution in the ground.
J. Horak, P-R Engineering, Colorado