I think your calcs might be a bit out V.
I live in an urban area and have a 5kw system on my roof. My partner and I use a third of what we generate, the rest is sold to the power company. If we could store what we sell to the power company and use it at night then we'd just about be self sufficient. Couldn't say for sure though as it would depend on how many heaters, computers, TV'S etc we had going.
I think the storage capacity of the battery is the thing.
Solar panels still generate on cloudy days, I've heard they'll even generate from street lamps if they're sited near enough.
