With a large enough flywheel and enough renewable energy generation, efficiency wouldn't be a major problem.  It wouldn't even need to be made only of steel.  You could have something filled with heavy stone or concrete if need be.  If you have a cylinder or disk of several hundred tons spinning at a few hundred rpm fed by a green energy system that is capable of producing 115-130% of the nations average peak power requirements, it could probably handle that few minutes of heavy load until one of the other systems could take over.