It may be just noise, but is it different noise between different power lines (and if so, consistently different)? If so, it's a fingerprint. Noise can be information if you're looking for a specific kind of noise. Not all noise is identical, and if you can fingerprint that noise, you can use it to determined the source.
Granted, that's a pretty big "if". I have no idea if powerline noise is consistent enough to be fingerprinted, different enough for a useful comparison, or strong enough to be picked up by standard recording devices. But it could be possible, in theory.