Word of warning: Just like solar inverters, not every home battery system is made to be grid independent. For instance, the Tesla Powerwall does, but the Sessy home battery does not and needs an active AC sinus on the grid.
Even if you do have a home battery system that can generate its own sinusoidal AC wave, you still need an (automatic) transfer switch to disconnect your home from the failed grid, otherwise your home battery might be attempting to power the entire (local) grid which of course doesn't work.
Even if you do have a home battery system that can generate its own sinusoidal AC wave, you still need an (automatic) transfer switch to disconnect your home from the failed grid, otherwise your home battery might be attempting to power the entire (local) grid which of course doesn't work.