Home battery backup question: My PV generates up to 120 kwh a day, can I run my AC from a single 10 kwh battery pack?

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Far as I can tell, I need 2 powerwalls to power my 5T AC, but hear me out:

My PV is effectively dead if it isn’t connected to the grid. What I’m thinking is, if the PV is generating power, the grid is down, and I have a single powerwall (or equivalent), can the excess power the PV generates (which would be far beyond what my AC would consume) go directly into the AC? Or does the PV power always go into the battery and I have the limits of the battery to contend with?

submitted by /u/y90210
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