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Supercharger Charging Rate on Model 3 ?

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I usually charge my Model 3 at home on Tesla wall charger, but today I charged it on a Supercharger for the 1st time to check out that it would charge ok.
I used the new Superchargers at Wokingham, sixteen bays, and I was the only one there !
The charging went without a hitch but I was surprised how low the charging rate was. While driving there I got amessage in the car telling me it was preheating the battery ready for supercharging.
I have Model 3 SR+ and when I arrived the battery was showing 37% which I charged up to 60%
On plugging into Supercharger, the initial charge rate was 67KW which reduced to 58KW by the end of session.
This charging rate was lower than I expected. Can anyone enlighten me as to whether this is the rate to be expected ?
Thanks
 
From personal experience I'd expect to get a much higher rate, at least at the start. Could be reasons that the rate is limited, eg. the charger is overheating and limits itself, grid limits or something
 
I usually don’t get much above 80-90. I think it’s because the preheating takes a lot longer than I thought. I precondition for 30 mins, maybe it needs longer?

Would be useful to know what others are experiencing
 
If you use the nav to get to your destination it will try to make sure you get to the supercharger with a lower state of charge.
That optimizes the charge rate.
With a low charge you should be able to see >140kW depending on the supercharger.
 
We don't have those in the UK [AFAIK], only Superchargers and destination/wall chargers.

While driving there I got a message in the car telling me it was preheating the battery ready for supercharging.

Two key bits of info which will help us.
  1. what was the temperature outside - it's been 8-13ºC most mornings - 13ºC is cold enough to bring on limited regen and an even slower recharge speed
  2. how long was your drive from a cold start to the supercharger - even after a 70 minute motorway drive, preconditioning still comes on when I'm ~15 mins from a supercharger, i.e. it must want to pack in an awful lot of heat into the battery for preconditioning to have the desired effect if 70 mins motorway driving isn't enough on its own
 
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Thanks for the replies. As I said, I usually charge at home, and this was an experiment to test out Supercharging on my car, which is why battery charge was not very low.
I had just met a friend in a pub in Bracknell for lunch ‘ The peacock farm ‘ , and decided to try out Wokingham Superchargers on the way home to Maidenhead. Outside temperature was 15C and distance from pub to Supercharger was about 8 miles ( I went the wrong way ) so the time to preheat the battery was short.
 
Here is our supercharge at Wokingham - 42% to 95% - looking at minute deltas we started out at ~130kW and around 60% we were still at ~93kW. SR+ will be slower. Outside temp was 15C and we pre conditioned.

wokinghamCharges.png
 
You might well get more kW if you arrive at lower SOC - closer to 10%

I agree with others, worth changing stall if it doesn't ramp up as expected after a minute or two, and if the car has been parked overnight, at this time of year, the battery may well be cold.

Yes, I've not needed to do many Supercharger sessions with my own SR+ but I did charge from 10% and saw a solid 100kW ...