The PSP uses a 5V AC Adapter. If you plan to replace the adapter make sure that the voltage matches to avoid damaging your system.

Even if the proper setting is already turned on, the PSP must be powered on to use USB charging. Note: This method is NOT supported by the first generation PSP models (series 1000). [2] X Research source Games cannot be played while using USB charging.

The PSP uses a 5 pin Mini-B USB port. Any USB cable that fits this spec will work. [4] X Research source

If you are connecting your mini USB cord to your computer instead of an electrical outlet, then both the laptop and the PSP need to be powered on in order for the charge to take place.