I have one of those systems. It generates more than I use. It is tied into the grid. When the grid goes down, the system is shut down. Including battery charging into the system is expensive, and not so easy to do. Not impossible, but currently, residential systems which are tied into the grid are shut down when the grid goes down, so as to prevent repair crews from being fried.
So when they go down and my generator kicks in, they disconnect me, shut me down? Then what's the point of a generator?