My 2012 Chevy Cruze LT is making this noise, but I have never heard it before until after we had the turbocharger replaced. I hope this normal. It kept making the noise even after we took the battery cables off.
I had this after having the engine replaced. I found a Chevy service bulletin saying it was the HVAC relay being in an unknown state when the engine is shut off. The bulletin required having the computer being reprogrammed. One dealer wanted a full service hour to do this, and another was willing to do it for 1/2 service hour. Obviously I got it done for 1/2 hour!
It fixed the buzzing - AND - my outside temp. display is accurate, which it never has been before - AND - the car can retrieve my phone's contact list, which it never has been able to do.