My psp version is 5.51, if I buy pandora battery

depends on the make of your psp 2001 can be downgraded depending on the motherboard....3000 and 3xxx cannot be downgraded....If your psp is a fat 1000 or 1xxx a pandora battery is the tool for you, you can use youtube for instructions on how to downgrade and also visit psphacks.com They go further into detail about what motherboards can be downgraded and what ones cant