The Powerwalls have about 13kWh of energy, that's not much considering that a gallon of gasoline has about 33kWh.
So, 20 gallons of gas = 660 kWh of energy for my small gas generators, or enough to keep critical things in my house running for a few days in an emergency. Not sure that the power walls would have enough energy to even keep something like a furnace going for more than a day.... even a high efficiency gas furnace pulls about 10 amps when it is operating, running the blower, etc.
True, 13kWh isn't a ton of energy, but a solar PV plus Powerwall setup can work better than many might expect. I think Tesla has a very large market opportunity with the Powerwall as word gets out. Here are some key points:
1. For whole-home backup, Tesla normally considers two Powerwalls to be the minimum. This gives you about 27kWh when full, and up to 10kW of discharge power.
2. On one of the coldest days of the year (maybe 14F/-10C for us), our high efficiency gas furnace may require 6 kWh in total. That's assuming 12 hours of running the blower at about 500W. It might be double that for a large house, or close to the capacity of a single Powerwall as you stated. Of course, this depends greatly on how well the home is insulated.
3. Solar panels will produce some energy even with lots of clouds. If necessary, particularly if there's a power outage, a snow rake can be used to clear the panels after a snowstorm.
4. In an outage, whether relying on a gas generator or on Powerwalls, we'd seek to conserve energy. The exception would be an outage occurring during spring or summer when we have far more daily PV generation than we ever use in the house (not including the EVs). Even during mid-winter, we have enough PV production to meet our basic needs, but outages often coincide with storms.
5. Gas generators aren't very efficient (pointed out by
docherf).
Since shortly after getting our Powerwalls installed, we've been entirely powered by PV and batteries between 8am and 10pm each day, and we export excess solar energy to the grid during the day in exchange for some peachy NEM credits. At night, during our utility's "super off peak" rate period, we switch to using the grid and the EVs get charged then. Economically, it only makes sense to charge an EV from our Powerwalls if we need a range boost during the utility's afternoon/evening "peak" rate period. We drive the EVs too much to be able to go off grid 24/7 anyway.