Superconducting coils are even in the best case something of the future.
There might be some experimental setup active somewhere, but just the proof of concept is a far cry from a commercially attractive, mature and proven method. It might well be, but not today. So we can leap over it in considering today's HVDC multi-terminal schemes.
Again, try to look the technical things up in publications. There are literally thousands of sources and papers out there.
Just because we can over here: let's do a back-of-the-envelope or
bierviltjesberekening.
Assume we have an imaginary island with a complex multi-terminal DC-grid without significant inertia and not interlinked to foreign inertia by a converter link to the AC supergrid. The DC-grid is there all at its own. It is loaded with (say) 300 MW of power. It is not relevant how we produce power in this grid as long as the method is static. We just assume it is balanced and it runs without any buffer. (Don't you even dare to touch anything bigger than a light switch!) Now we trip off a large solar park, separating 50 MW of production. Since there is no significant inertia and no storage, the grid will immediately collapse.
Avoiding this collapse can be done by a pack of big batteries. Static components, no startup-time. Using batteries is a common method for uninterruptable power supplies (UPS) like we see in hospitals and other critical applications. If the grid collapses and the subgrid has no own production (or just lacking sufficient mass and scale for FCC), a UPS is capable of powering the grid for a short brief in which auxiliary power units like diesel generators can be started to take over for the long run. For hospitals, the UPS installations usually have the size of half a sea container and they are capable of running the load for five to ten minutes before they are exhausted.
For our DC-island, the trip of the solar farm requires big batteries to buy significant time - and with big, I mean
big. The biggest battery arrays in the world at this moment, such as
Jardelund, are capable of about 60 MWh. If our island has such a 60 MWh battery (which in practice would be an absolute must just for balancing the time lags in demand and production anyway) and if it was fully loaded, it will buy us just an hour of time to desperate get 50 MW from somewhere and hook it up to the grid. That's shivering, but technically feasible.
Now assume we want to do the same trick with high voltage grid capacitors instead of batteries.
Big capacitor banks as we see them today in AC-grid are there for power quality and stabilizing purposes of the sine wave form, not in any way for storing bulk power such as batteries do. But let's assume we pick one of those stacks and use them for storage purposes anyway. We hook them up to a DC source and just 'fill them'. Now we place them at our island in the place where our battery just was and we trip the solar park again.
For this case, I did not look up the exact characteristics of such a stack of capacitors, but also with a proper guesstimation we will get the order of magnitude right. (Man, I love
Fermi estimations.
)
The capacitors are designed for AC, applied to compensate deformation of the sine characteristic of the AC waveform. This means, they will never have to store more energy than a single period of the AC can carry. (And probably just a fraction of it, but since we don't have numbers, I assume the worst case scenario which is the energy wrapped in 1/50'th of a second of a loaded grid.)
Now our grid is loaded with 300 MW (ignore AC or DC here and ignore the proper way by Joule as well, and assume this results in 300 MWh.) We just want to know how much energy is in the grid in 1/50'th of a second. Devide 300 MWh through 3600 and then 50. Result is 1.666 Wh.
The result is disappointing: the total stored energy in watt-hour is barely sufficient to run a single coffee machine for an hour. Even if you give or take a factor ten, or even hundred, you see it buys us barely a few seconds.
To conclude: superconducting is, just like the abbrevative
nano, not the solution for all of our problems today. For instant static power backup in a big grid without inertia, batteries are at this moment the only way to go.