Is that at the fuse box or the power point on the wall? Sorry if this is a silly question, it's just that here in NZ it's nowhere near that at the wall as the fuses are 10 amp ish.
The 200A are at the fuse box (in new houses, old houses may have less).
The wall sockets usually have 110V-15/20A connections. But there are some especial sockets with 240V-30/50A for special applications, like clothes dryers and electric ovens.
In our old house some genius used paper clips instead of fused wire in the (very old) fuse box. Not sure how I didn't die when I draped and extension lead in a puddle and got a shock. After I recovered I looked in the fuse box to see why the fuse didn't blow and found one fat paper clip over the gap.
I'm not sure what current the box took, but I'm sure glad it wasn't 200Amps.
Seems pretty simple to me: You create a grid for your house, so it will always have electricity. You trickle charge a rack of graphine Supercaps for your house using mains. You dont need to send that power all at once.
The standard devices to handle passing from mains to battery should be able to be used.
By contrast the energy flux of a garden-variety gas pump is in the tens of megawatts.