It's not a tank, it's a machine.
The correct term, here, is Oxygen Concentrator. Details on its operation at Wiki(hah hah)pedia.
And yes, they run on electricity. No, they don't work when the electricity is cut off. Yes, I know more than I want to know about home medical oxygen due to personal experience with a relative.
Now you know something your didn't know this morning.
OBTW, the relative's home is complete with a stand-by generator. And I make sure her utility bill is paid on time.