I'm actually now designing software which calculates the parameters for the hardware that supports the power lines.
It's amazingly precise and complicated. Even at 200km/h tracks, the tolerances where the line should be in the sky are in millimeters. For example, there should be enough tension to hold the line almost straight, but not quite straight. You have to let it hang just enough so the that the weight of the line holds it firmly to the receiver on the train.
You have to account for tilted rails in turns. You have to move the line over the rails in a zig-zag so as not to stress the receiver from one point only. Then you have to account for turns, where the train goes on a nice radial track, but the line moves straight from pole to pole.
Etcetc... It is very interesting and perhaps the most math and physics hard project I have ever been involved in in my +10 year development career.
Anyway, it makes my mind boggle to even think how precise the electricity feed line has to be installed in some 500m/h tracks.