Induced currents in an HVDC loop due to solar magnetic disturbances

I recently calculated the induced currents in an HVDC loop due to past (and therefore expected future) solar magnetic disturbances. This is important for me to consider because I have been loudly advocating the desirability of HVDC loops as the unit cell of a future supergrid, due to the intrinsic redundancy of such a loop (as long as there are circuit breakers between each next-neighbor pair of power taps on the loop). The loop morphology favors redundancy, but also makes the system prone to induced DC currents, as could occur due to EMP from nuclear detonations in space or due to "space weather." I reported on this in more detail on this in my presentation to HST 2012 recently (see especially slides #23-31).

I calculated the inductance of a simplified system comprising a 1000 km diameter elpipe HVDC loop where two continuous conductive loops (one +, one -) form the circuit (there would be 10-20 power taps on this loop system connecting it to the AC grid). I used the vacuum magnetic permeability within the loop to make my estimate (not a bad estimate for a subcontinental scale HVDC loop that would make sense as a component part of a supergrid), and at first I used the worst case superconductive loop (this implies complete exclusion of magnetic effects within the loop, no ground currents: all the changing magnetic field is cancelled by the induced loop current). I looked at the worst historical solar magnetic disturbance (1859 Carrington event) which is estimated to have involved a 2.0 microtesla geomagnetic field change over about an hour. What I calculated was ~one trillion amps current induced in the two loops. I was astounded by this worst case calculation. I was amazed that the loop current due to a geomagnetic storm could be that large, even in the case of a superconducting loop. Magnetic storms that are one tenth as intense as the 1859 event are fairly common, so there is clearly a need for a mechanism in the HVDC loop design to quench the induced currents. It turns out that this is actually not a problem for a real HVDC loop.

A real loop of wire will have less induced amperage because part of the induced current will circulate in the Earth, and because the loop current will decay as an ordinary resistive inductor would decay, proportional to exp[-t(R/L)] (so the inductor loop current is constantly decaying as the magnetic field changes, which takes around an hour typically, at the least). For a 24 GW elpipe loop that is 1000 km in diameter:

R = 1.67 ohms (circumferential resistance)

L = 9.9 henries

R/L = 0.17/second (that means the induced current decays to 1/e its original value in 5.93 seconds)

Therefore the current cannot build up as it would in the case of a superconducting loop. The loop current would be substantial during the height of a magnetic storm as severe as 1859 (about 17 kA), but not enough to damage or overheat the conductors per se.

New York Times post based on this discussion (March 19, 2013):
The disturbance at the Earth's surface is far to weak to harm auto electronics, I think. The grid effects come about because of small local changes in the local magnetic field that are amplified because of the great distances involved. The changing magnetic field induces currents to flow in both metallic loops (pipelines as well as the grid) and in the Earth as well. The flowing current in the earth causes the local ground potential to change with position, which causes most of the damage.

In principle, a region can be protected by a superconductive loop around the region (this implies complete exclusion of magnetic effects within the loop, no ground currents: all the changing magnetic field is cancelled by the induced loop current). The 1859 Carrington event is estimated to have involved a 2.0 microtesla geomagnetic field change (out of a total field of ~65 microteslas in the normal gweomagnetic field), over about an hour. What I calculated for the induced current on a 1000 km diameter superconducting loop is ~one trillion amps induced in the loop. This is not practical, but it gives an idea about how much magnetic energy is sloshing around in such an event.