The problem with running an air conditioner using a battery backup system is not the energy it takes to run your AC. The problem is the energy it takes to start the air conditioner (it requires an energy spike that’s higher than the normal operating energy current).
So chances are that if you only have 1 Powerwall, your battery backup system won’t be able to start your air conditioner. You’ll probably need at least 2 Powerwalls connected together. (You can connect up to 10 Powerwalls together.)
The Powerwall’s Storage Capacity vs Air Conditioner
Another thing to consider is that, even if you can start your air conditioner with a Powerwall system, each Powerwall only has 13.5 kWh (kilowatt-hours) of storage capacity.
13.5 kWh may seem like a lot at first!
However, on those hot summer nights, while you’re running your air-conditioner, it turns out that 13.5 kWh isn’t that much. The Powerwall most likely won’t power your house through the entire night since the average air conditioner uses around 1 kilowatt an hour (or more).
If your air conditioner isn’t running all night, 13.5 kWh could actually be enough to power your house until morning.
Conclusion: Will Tesla Powerwall Run an Air Conditioner?
Depending on how many Powerwalls you have, that will determine how much you can back up.
Most people I know only have 1 Powerwall. As a result, their air conditioning and things like their oven are not backed up by the Powerwall. But everything else in their house is typically backed up by the Powerwall.
If you had 2 or 3 Powerwalls, maybe you could back up your air conditioner and other bigger, electricity-guzzling appliances like that.