Is there some napkin math available on the net for a transmission line with a nitrogen-cooled high-temp superconductor (Tc > 90K) and thick thermal insulation? I mean for the energy required per km too keep it cooled below Tc.
Big high voltage transmission lines lose ~200 watts per meter in resistive losses when under full load.
The electrical energy to keep something 1 meter long at liquid nitrogen temperatures is also ~200 watts, assuming 8 inches of insulation.
The resistive losses go down with the square of the power transmitted - so they fall to zero rapidly when not under full load. Cooling losses stay approximately constant.
Therefore, I suspect a liquid nitrogen cooled superconducting cable wouldn't work out financially.
This is my own ignorance, but what determines the power carrying capacity of a wire besides melting from the resistance? Could you transmit a lot more wattage through that same line when superconducting?
The energy loss (in the sense of where the heat ends up) is at the refrigeration plant. The cable itself extracts heat from the environment. So SC cables make sense for underground cables, where heat buildup is a problem.
