The way home battery backup works with solar is quite simple. During the day, your solar panels produce energy and send it to your panel box. You’ll use some of this energy in your house, and if you have any excess energy, you’ll begin to charge your battery. Once your battery is charged, any additional energy will flow back out onto the grid. At night, since you won’t get power from solar, you draw power from the battery, then from the grid, reducing the amount of energy you actually take from the grid as much as possible.
New home battery technology would allow you to coordinate with these time of use rates. When the demand on the grid is high and the TOU rates are high, instead of paying the high rates from the grid, you will use the energy stored in your battery at no cost to you.
When the grid goes down, you can use the energy your solar system produces, as well as the energy stored in your home battery to power your home until the grid comes back. A battery is a giant step toward energy independence.