Why is Kona 64kwh only charging at 3.5kw when plugged into 11kw point

Is it the new 2020 with 11kW charger, or the older one with 7kW?
Which country are you in ?
Did the car have a high state of charge when you plugged in ?

 

I never heard of stations markes in KW.. Sometimes, I see the AMP rating but not the kw rating.. It sounds to me like you were on a power shared station. Some charging stations share the power between the charging spots.. If one car is connected, you get 7 kw and if 2 cars are connected, you get 3.5 kw each..That's very common to have power shared stations..

 

You might check to see what level your Kona is set at for AC charging. The car can be set at Maximum, Reduced or Minimum. If it is set an Reduced or Minimum it will limit the amount of charge the car can take. The settings can be found on the center display under battery management, just be low the percentage of charge settings. If set at Maximum it should charge at around 7 kwh. Also have you tried different public level 2 chargers some work better than others but in any case your car should be capable of a 7 kwh charge on an AC charger.

 

I expect if these are Type 2 the EVSEs are marked with a rating pertaining to 3-phase and you are only using single phase. 11kW is 16 amps per phase, 3.6 kW. Or, the power limiter is set, as mentioned.
The ABB public charger near me has an AC cord marked 43 kW, about 63 amps per phase.

 

I believe also it is possible that you have the car set lower on maximum AC charging or someone could have limited the charging station output. Finally and maybe most likely, they hooked up a 3 phase charger to 2 phase power. The car charging system, confused only is using 1 leg of the 3 phase or 3 kwh.

 

OK, that's cleared things up more.
The likely possibility is that you are using a single phase Type 2 to Type 2 cable that is rated at 16 amps and supports only one phase.
It's extremely likely you have a 3-phase 11kW charger in the car, lift the plastic cover under the hood, it's aluminium coloured on the metal cover instead of black.
If you do have the 3-ph unit you should have a 32 amp rated, 3-phase capable cable. The info is written on the cable itself. 6.0mm2 x 5 or such.
EDIT: actually all public EVSEs will be 3-phase so if you do have a 3-ph on-board charger a 16-amp 3-ph cable is all that is required to reach 11kW max.