Is there a sort of cost function? And how the height of an electrical transmission tower affects the self-inductance, the capacity of the conductor to ground and the cost?
In short, yes.
Transmission implies moving significant power over a significant distance.
There are two competing issues.
First is current - you want the minimum current possible because transmission losses are I2R (note - current squared - twice the current gives four times the losses due to heat), so for a given power you want the highest voltage possible to minimize the current.
And to keep R down you want heavier cables.
One the other hand, capacitance losses go up linearly with voltage, so to minimize capacitance losses you want a lower voltage. And the greater the voltage, the higher above ground your transmission lines need to be.
To minimize capacitance losses, you can also lower the frequency; you're in 50Hz-ville so your capacitance losses are less than at 60Hz. Ideally you want to reduce capacitance losses to zero and thus you want to transmit power using DC. Transmit power using DC and you only need two wires not three. But sometimes the capacitance losses are sogreat that DC is the only answer.
And all this interacts with money. Cable weight versus tower costs versus I2R losses. Capacitance losses versus I2R losses. Go DC and you have to pay for converter stations, which cost huge.
So the answer is that the question of what voltage should my transmission be at is a really complicated question, and one of choosing how to optimise.
