Pelican Parts Forums - Problem with charging system

Hi Pelican staff, I am having problem with my car 2010 Bmw 528i when I replaced the battery. I replaced the battery to the same capacities, and had it programmed and registered. However, once battery is installed, the voltage reading 12.2-12.5 while the engine is off, that's when the battery is fully charged but while the engine is idle, the voltage doesn't go up, it sits in that range, once I turned on the ac, it dropped sightly, once i turned on the headlight, it dropped down even more maybe between 11.9 to 12.1. I got a message "Increase battery discharged" I drove the car for maybe a good 40-50 minutes and 20 miles. I checked the voltage again while the engine is running, it's still sitting at 12.3 then somehow at some point, the whole modules lights up on the dash, DBS malfunction, passanger restraint seatbealt malfunction, tranmission malfunction, dynamic stability control malfunction, airbag malfunction, battery level is low signal, that's until the battery reached between 9v to 10v somewhere then the car dead. I replaced the battery, same things happened again. so I have the battery charged up. Take it to a shop where they perform a test at idle no load and under a load for free. Battery is good, starter is good, charging system is on low voltage. They said there is something wrong with the charging system. Is it high likely that it's the alternator that failed? It's on the original alternator with 120,000 miles on clock. One more things, sometime, the car goes in the "limp mode" I think that's what people called it. What I meant is that the car shift to "N" while the car in motion. Thanks