The last time my alternator (regulator) went south on my 300E, the battery was venting sulphuric acid gas (you could smell and see the cloud emanating from the hood!!!). Voltage readings were 17+ volts as you have confirmed with yours.

Time for a new regulator as others have posted...

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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