I believe your car is equipped with an A/C idle adjustment sensor...does what it says, adjusts the idle when it senses voltage at the compressor. Don't know much detail after that, location, cost, incidence of failure, etc.

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2009 ML350 (106K) - Family vehicle
2001 CLK430 Cabriolet (80K) - Wife's car
2005 BMW 645CI (138K) - My daily driver
2016 Mustang (32K) - Daughter's car