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Should my car charger be backed up by my powerwalls or not?

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That's how I designed mine too. Seemed like the best price/performer.

Yeah, in my case I couldn’t really go any bigger without starting to put panels on my north facing roof and I’m not sure that’s a great idea in terms of cost/performance.

Additionally it’s already a pretty big system and I don’t know that I’m necessarily going to be in this house forever. I feel like it might make it a little harder to sell this house at some point (or at least try to recover some of my investment) if the system would produce twice as much power as a normal household would use.

So far, on paper at least, I’m pretty happy with the size.
 
We installed a 15.4 KW/4 PowerWall system a few months ago.

Our two Wall Chargers are on a separate breaker panel, connected to grid power - not to the TEG.

During installation of the solar/PowerWall system, the installers added a 14-50 outlet to one of the house breaker panels connected to the TEG.

Normally we charge our S & X (at 48A each) from the grid. But if we have an extended power outage (hurricane), we'll be able to get a small amount of charge for one vehicle from solar or PowerWalls.

Last week, we switched electric plans to a "free nights" plan - free electricity from 9PM to 9AM. The S & X are set to charge only overnight. The solar/PowerWalls provide power to the house during the peak 9AM to 9PM period - and so far, each day we're using less than 1KWh of grid power during peak time and anything we use between 9PM to 9AM is free.

So we don't worry about how much grid power we're using for EV charging - at least not until the utilities decide to exclude homes with battery storage for free nights plans...