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Low SOC = Terrible Supercharging

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The older 85 batteries will also limit supercharging to 3kw for first 5 mins or so when very low SOC, like in negative number. -3kwh out of a 4.2kwh buffer indicated between 0 km and batteryprotection.

Have been there 2 times.

True I have seen this as well, but they added that in a software update. I drove my car passed 0 many times and it always started charging fast. After a software update the behavior changed. Probably a good idea. That ramp up phase is just very long on the new batteries. It charges at a reduced rate all the way up to 14% before it reaches it's max.
 
True I have seen this as well, but they added that in a software update. I drove my car passed 0 many times and it always started charging fast. After a software update the behavior changed. Probably a good idea. That ramp up phase is just very long on the new batteries. It charges at a reduced rate all the way up to 14% before it reaches it's max.

Check out Bjorns video. The ramp up is even slower in a rate-limited situation:

Bjørn's Tesla Model S videos