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I've noticed, as many of you probably have, that when you first connect an EVSE to a Tesla with charging scheduled at a later time, the Tesla still asserts READY and ramps up to a few amps. Then it drops READY to de-energize the cable and waits for the scheduled charging time. The whole process...
Just being a little pedantic -- kWh (kilowatt-hour) is a unit of energy. kW (kilowatt) is a unit of power, i.e., the rate of energy flow.
I've often noticed varying supercharger power levels. I can think of several possible reasons aside from the obvious one (contention from the paired spot)...
This is what it looked like when I returned to my car after lunch. (That's my car on the left. It was undamaged.) The first responders cut power to the site, and I suspect it'll be down for a while.