HUGE problem with this theory.
The power grid operates on incredibly tight tolerances with regard to frequency...
FTA: "It found fundamental differences in the structure of the harmonics of the 50 Hz which could be detected because Total Harmonic Distortion was strongly affected by local factors and had as a result little geographical consistency."
Not that any of this is likely to matter. Even if they had a unique spectrum capture of a specific location at a specific time for comparison purposes, turning one computer on, (or off), would totally change the harmonic signature appearing on the local wiring, thereby making the reference capture useless. And a vacuum cleaner running would really mess things up.
For anyone worried about this, running a randomly-swept audio generator through a frequency range of, say, 20 to 150 Hz, and injecting the signal into the audio capture at a level that is just audible without being too annoying, should seriously reduce any chances of the 'power line signature' being traced.
Now if someone is actually injecting a unique signal into the grid for a defined geographic area, countermeasures would be more involved. Recording in a very good Faraday cage, using battery power only, with no cables entering the Faraday cage from outside, would probably thwart any such attempts at tracking. The sweep-generator technique mentioned above would provide additional insurance. But now we're very far into tin-foil-hat territory.