The most easily available power source on the Moon is solar power. This has the obvious drawback that the night is two weeks long, during which you would probably still need power for a base to operate.
While there are countless other ways to work around this, ranging from a plethora of proposed ways to store energy, to alternative energy sources...
..how does a simple transmission line from the "day" side compare?
I'm primarily interested in what mass such an installation would have.
- It's long. The exact length would depend on location, with bases close to the pole merely needing to "flip" over the pole point. This question is not about finding clever base locations though, like the peaks of eternal light, so half the circumference of the Moon ~5000km, is the right order of magnitude.
- It's not affected by air, weather, surface water, vegetation, animals or human activities.
- There's likely some trade-off transmission voltage. The voltage will affect the required conductor cross section and transmission losses, but also be limited by how much the cable can be insulated from the ground.
I don't expect it to be a practical solution, but as even coming up with an order of magnitude estimation is difficult to me, there's no way to know for sure.