Vortex Currents in High Voltage AC Power Grids

Geographical formations such as mountain ranges or big lakes and inland seas often result in large closed loops in high voltage AC power grids. Sizable circulating power flows have been recorded around such loops, which take up transmission line capacity and dissipate but do not deliver electric power. Power flows in high voltage AC transmission grids are dominantly governed by voltage phase differences between connected busses, much in the same way as Josephson currents depend on phase differences between tunnel-coupled superconductors. From this previously overlooked similarity between Josephson junction arrays and AC power systems, we argue that these circulating power flows are analogous to supercurrents flowing in superconducting rings and in rings of Josephson junctions. AC power systems however differ from superconducting systems in at least two significant ways. First, in superconductors, vortices couple to magnetic fluxes so that it is easy to create them by simply applying an external magnetic field. Second, superconductors are dissipationless systems and it is not at all clear if the above analogy still holds in dissipative AC power grids. We investigate how circulating power flows can be created and how they persist in the presence of ohmic dissipation. We show how changing operating conditions generates vortices, how significantly more power is ohmically dissipated in their presence and how they are topologically protected, even in the presence of dissipation, so that they persist when operating conditions are returned to their original values.