The idea for the when-part is that people will have electric cars at home, which can double as a big battery, or as the other guy already said, you can buy dedicated storage, too.

You could also hook these storages up to the grid, and then have an algorithm decide to sell to the grid when electricity is expensive, or to charge from the grid while electricity is cheap, possibly even taking the weather forecast into account.
Definitely still lots of details to figure out, but I expect things to head that way…