We have some line reactors in some of the labs at work. Use them for some tests or as loads in 3ph inverter development. I am not sure what inductance values (they have taps I think) but physically, the steel cabinet housing them is a cube a little over a meter per side. 0000 cables are used for 3-400A RMS.
That'll be pretty low actually. Remember that for given voltage, current goes inversely with inductance. Let's see -- if that's 480V, and ignoring phasing for ballpark figures, 480V/360A = 4/3 ohm, L = (4/3) / (2 pi (60)) = 1 / (90 pi) = 3.5mH.
Meanwhile, the peak current might be over 500A, or 0.5 (3.5mH) (500A)^2 = 453.6J, no small amount of energy storage.
Let me see... something the size of a microwave oven transformer can store almost a J; this should need to be cuberoot(450) or 7.7 times larger on each side, or a core of say 15" stacked, 40" wide, 48" tall... or, yeah, a bit over a meter.
Likewise, EHV feeders don't need to be too crazy, though I haven't seen any datasheets and can only estimate. For example, say a transformer for 500kV 100A, a modest 50MVA substation tapping off long distance lines. Say magnetizing current is 1% or 500kV/1A = 500kohm at 60Hz, L = 1.3kH. Big, but not up there.
500kohm is also well above what you would need for most tube amplifier input (including phono) and interstage transformers, even if it drops to 1/3 that impedance at 20Hz. So like I said, not many applications that go higher; that's some serious choking!
Tim