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I'm a bit skeptical of these measuring tools - if you posted a screenshot of you car's charging screen that sometimes said 32A and sometimes 16A, then I'd say to call Tesla for service.
FWIW, it is the pilot that is being recorded at 16A, meaning that the defect would be in your charging equipment. You don't mention what equipment that is.
I'm also getting this issue. I figure that it's the 14-50 receptacle my UMC's plugged into not making a good contact. I plan on getting some
WD-40 Specialist Electrical Contact Cleaner Spray to rectify this. Else, I'm going to buy a new receptacle.
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Not the same issue as the OP, but I have recently started using TM-Spy to monitor a lot more real-time info about the car, and noticed some very unexpected charging behaviour yesterday. I was connected to a 50kW DC fast charger, and I started charging at ~50% SoC. Most of the charge was at ~35kW. Near the end of the charge with SoC~97%, the charge power was ~11kw and the cell temperatures were ~53°C (which seems pretty hot to me), but the car was still trying to HEAT the battery. It was pouring 3.5kW into both the front and rear motors, with a reported stator temperature of 130°C, which was heating the coolant up to 60°C at the battery coolant inlet! I would have expected the car to be trying to cool the batteries down, not heat them up. It also seems like an awful waste to be using 7kW of the "charge" power just to make things hot. Outside temp ~15°C. Anyone have any thoughts on this??
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Specific to CHAdeMO I have a lot of complaints about what it does, which you can find in my post history or in yours if you start a thread on this and I dump my thoughts/observations