Here are the technical specifications of the PSP 3000.
While the PlayStation Vita replaced the PSP in 2011, Sony didn’t discontinue PSP hardware production until 2014.
Ebay, Wal-Mart, and other retailers also carry PSP 3000 replacement batteries.

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Charge your PSP 3000 by plugging the included AC adapter into a wall outlet.
Alternatively, use a mini-USB cable connected to your gear.
Wal-Mart also sells a car charger that works with your PSP 3000.