The OVP relay can be a source of problems as suggested above. They're not expensive to replace and are a VERY common failure item that will affect several parts of the car. If the car really is idling down around 500-550 RPM, it can cause low alternator output. The normal idle speed when in gear should be somewhere around 650 RPM.

If you want to diagnose low voltage, get a cheap voltmeter that plugs into the cigarette lighter and watch the voltage as you sit. If it heads down and keeps going, you have a charging system problem of some sort. At idle with everything in the car on, you should be 13V+ if the charging system is working correctly.

How old is your battery? Occasionally an old battery can misrepresent an alternator issue.

Has anyone checked the engine ground strap to the chassis and the chassis connection to the battery? Poor contact can trick the alternator into thinking that it is producing adequate voltage due to low load conditions caused by poor cable connections.

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Current stable:
1995 E320 157K (Nancy)
1983 500SL 125K (SLoL)

Gone but not forgotten:
1986 300SDL (RIP)
1991 350SD
1991 560SEL
1990 560SEL
1986 500SEL Euro (Rusted to nothing at 47K!)

Gone and wanting to forget:
1985 524TD 167K (TotalDumpster™) [Definitely NOT a Benz]