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Powerwall wiring and overload situation

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I previously had a 6.5kW Tesla solar system with a SE5000 inverter installed. I've moved up the queue enough that Tesla is is now ready to install a single Powerwall. My interest in the PW is primarily for backup use.
With a single PW I know and accept I will not be able to run the AC, oven or clothes dryer when using backup power.

Tesla installation plan calls for keeping the dryer breaker in the existing load panel which would be backed-up since moving the dryer load would be rather expensive. This strikes me as a strange way of handling it.

I can see two ways where this could be a problem:
1. Grids go off and PW takes over seamlessly, unaware the of this the dryer is used, overloading the PW causing it to shutdown.
2. Dryer is being used and the grid goes off, PW tries to take over but is overloaded causing PW to shutdown.

My questions are:
1. Does the PW/gateway make a notification that backup power is in use that you would reasonably know not to use the dryer? (assuming the PW is configured for backup use only)
2. If the PW is overloaded what does it take to get it back online when the grid is not available and capacity is >10% (I assume the availability of solar is not a factor in the PW restart)
3. Is the wiring suggested by Tesla reasonable to have loads that cannot really be supported be in a "backed up" load panel?

Thanks in advance.
 
I have a single powerwall. My entire house is in a 125 amp subpanel off of my 200 amp service panel. I have everything backed up except my Model 3 and my AC, however both are being measured by the CT clips so that the powerwall will provide them with power during my peak times during the day (since outages are rare here). My AC drains my powerwall during the summer but still helps overall. I have a 20% reserve threshold.

I also have my electric 30 amp dryer in that 125 amp panel. I haven't actually tried to run the dryer with a simulated grid outage (main breaker thrown) so I'm curious what the experts here say will happen. I know the powerwall can sustain 5kW out but peaks at 7kW.

I'd say it's mostly expected for you to know to not use the dryer during an outage, but that wouldn't help if your dryer is already running. If it's overloaded I assume you just flip the powerwall breaker off then flip the powerwall switch off, then breaker back on and switch back on.
 
I don't think an electric dryer by itself would overload a Powerwall. However, you could use a clamp meter to measure how many amps it's drawing while running. The startup amps also should not be a problem because the motor should start tumbling the load before the heating element turns on. Of course, if you have a bunch of other stuff running at the same time, it certainly could overload, especially at night when there is no solar output.
 
Just wanted to say thanks for the replies.

I ended getting the single Powerwall installed as outlined originally. So far over 2 summer months have managed to be self powered 92% of the time only time that breaks down is those 95degF+ days. Haven't had to use the backup yet but have been really pleased overall.