It's doable, but it requires a bunch of extra expensive equipment. Most people that want to accomplish that goal just install a battery array instead, since you

It's doable, but it requires a bunch of extra expensive equipment. Most people that want to accomplish that goal just install a battery array instead, since you're spending the money and it also gets you power coverage when the sun isn't shining. But the point stands that the typical grid-tied solar system just turns off when the grid goes down.