With the previous ELI12 under control, let's ELI>12 overhead line catenary a little more. For instance, why do you need tension in the first place?

Fact of the matter is that using a rigid conductor is problematic with high voltage AC (skin effect and such), plus it's more visually intrusive than wires. Meanwhile, a wire will sag, regardless of how much tension you can practically apply. So you need a few devices to help keep the wire at height.

For one, the wire is supported every few dozen metres. Secondly, there's a second wire strung above the first one. And while both wires are pulled taut, there are dropper wires between the upper and lower wires, which vary in length. Longer near the poles, while at the shortest near the middle between two poles, which creates a structure similar to a suspension bridge to keep the contact wire within a tight margin of vertical space.