The storage capacity is the hard part. Batteries aren't really a viable option (we don't really have good enough batteries, limits on how many can be made with current resources, etc).

Dams would be good (pump water uphill when electricity is cheap and release when you need the energy back), but dams are not a viable option everywhere and also have a high environmental impact and are arguably not the safest thing for a community.

I read somewhere recently about the idea of putting smaller batteries in individual homes, basically distributing the power ahead of time to a certain number of places so they are not taking from the grid in peak times, but it would be hugely expensive still, and I also question if we have the ability to make so many batteries, much less get enough people to install them.