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We have solar panels and are considering having either 1 or 2 Powerwalls installed. Our main desire is for long term emergency power backup (more than a few days), although there are other benefits to the system as well, but not so important for this question.
The most our solar panels ever generate (peak efficiency, middle of summer) is about 17kWh per day. Given that the capacity of 1 Powerwall is about 13.5kWh, this matches relatively well with our system. If we installed 2, we'd have capacity that we could never charge, and we wouldn't even change the first one fully during the winter.
However, the power output of 1 Powerwall is 7kW peak / 5kW continuous... which is less than our peak usage on the rare days when we run the A/C, and have some other appliances on too.
So my question is what would happen if we have 1 Powerwall installed, and then the power grid went down at the exact time when we're using peak power (> 7kW)? The truth is that in this situation we'd quickly turn off the A/C and we'd be well below 5kW... but if we're not home or don't know the grid went down, doing this might take some time.
Note that I know some installers take the critical circuits and put them on a subpanel which is all the Powerwall powers. Honestly, this may be okay and would solve the peak power problem, but it's not our ideal. We'd rather the system be capable of powering the whole house and we choose what we want to use in that situation. Plus, installing a subpanel just costs more!