2003 Ford Mustang Idling

My problem is my idling. It idles fine most of the time. I just cleaned my throttle body, put a new air filter in. And it has been idling fine, sometimes. There are times when I give it a little extra. Revving it too higher Rpms to 3000 or 3500, my idle drops down very low to 500 even below and one time it just completely cut out. I haven't been hard on it at all lately since I started realizing what was going on, and never even revved it over 4000 Rpms since I've had the car, so I haven't been that hard on it. I'm only revving it to 2000 or 2500 Rpms. But I would just like to know what could be wrong with it? FYI I have had battery and alternator problems since I got the car when it had 72000 miles on it. I put a brand new battery in it when I got it and have replaced my alternator twice. Not sure if that has anything to Do with it at all, but I figured I would include that.