You've got the compressor line issue, more than likely. Once they fixed mine, it stopped doing this insane nonsense completely. It also cooled more effectively, and consumption with the AC on went way down. I'd push them on it, if you haven't already.
I deleted my post after realizing my issue is in a new style Model S and yours are Model X in the X forum. I will see if I can ask an SC about this. I'm due for my tire rotation now.
It was loud until I commanded my car to "report bug", and a minute later it quieted down. I even turned on the A/C after, and it stayed quiet. Is this a manual software fix? I'd be surprised if they worked on my issue that quickly.
The noise is back:
First time I went to the SC they said the loud AC was normal. I brought it back again to have them check for the swapped hoses and sure enough mine were swapped. They fixed up the car and the AC is definitely quieter than before, but I wouldn't say it's quiet, it's more on the loud end of normal now, compared to being a jet engine before. I'm very happy with the current sound levels. Previously it was impossible to have a conversation at all, now you can have a conversation, but you just need to speak slightly louder than normal.
This is the before fix and after fix with the AC at "LO".
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On my Model S, I tried an iPhone app called "DecibelMeter", and I think it's very uncalibrated, since it reported my "jet" fan noise in my Model S as around 91dB-93dB. It's loud, but you indicate that yours is not that loud on your X which is supposed to be worse than an S.
Mine sounds like a fan, not a compressor.
There are a dozen Model S and Model X's charging here at the SC and the wall chargers, and none of them are making any type of loud noise except mine. This is only the third time I've experienced loud fan noise. It always happens while charging for me. Right now, it is 78ºF in Hawthorne, but where I'm from it is often in 40's and 50's right now (much colder than here!).
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I moved it to a SuperCharger in the shade, and getting 52kW now, no fan noise. This seems related to the onboard AC -> DC converter that was converting 208VAC 48Amp to DC. But, I can't be sure. Driving 40 feet to the SuperCharger caused the outside temp reader to show "87º", and it's definitely not 87º. 78º I could have believed more readily, but not 87º.