Well two days after the new battery, the CCC seems to be back to normal. It was not good at first, but got gradually better to the point where it is now working as it should. I guess it took some time for the car to stabilize the voltage level and adjust to the new battery. You would think it's a living thing adjusting to a transplanted organ.

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2014 BMW 328i Xdrive
2011 BMW 335i M-Sport
2008 BMW X5 4.8i Sport
2000 BMW 528i 5sp