POST ISSUE 4 of 2016_11_18
Hi Glen,
As the other members say, you need a battery and and inverter to convert the battery direct voltage to an alternating voltage of 220V to 240V alternating.
One question that needs to be resolved is the wave shape required for the alternating voltage.
(1) Square wave
(2) Pseudo sine wave
(3) Sine wave
My feeling is that the Sony PlayStation is liable to have the type of power supply that will tolerate a square wave (off line switch mode power supply [SMPS]. This would be good because a square wave inverter is the most efficient and would thus give you the longest duration for a particular battery.
According to the label in the image that you posted the Sony PlayStation takes 10W but that wattage is according to the international standard and may not mean that the PlayStation actually takes 10W continuously, 10W is liable to be the maximum wattage that the PlayStation will ever take under all circumstances. My feeling is that the PlayStation will probably consume about 7.5W average.
About the battery. There are two main options I would suggest:
(1) Lead/acid as Mike says.
(2) Lithium/Ion (LiIon).
Lead/acid batteries have many advantages, but I will leave Mike to cover that approach, while I will cover the LiIon approach.
A reasonably priced 18650 LiIon rechargeable battery would have a capacity of 3AH (3,000 mAH), Which means a single LiIon battery would power the PlayStation for one hour. But a single LiIon battery would only have a terminal voltage of 3.6V which is not very convenient for an off-the-shelf inverter. So I would suggest four LiIon batteries in series.
A four way battery protection board would also be required, unless you bought protected batteries, that is. A suitable protection board is available off-the-shelf.
Four LiIon batteries would give a duration of (4 * 3.6V *3A)/ 7.5W= 5.76 Hours. But if you assume an overall efficiency of 70%, the achieved duration would be 5.76 * 0.7 = 4Hrs.
A four-bay LiIon battery charger is available off-the-shelf. Just unclip the the individula batteries and place them in the charger.
A suitable inverter is also available off-the shelf.
spec
PS: which county are you at? If you put it next to 'Location' on your user page it will show in the box at the left of your posts. Knowing where you are helps us answer your questions. In this case which component distributors you can easily buy from.
LINKS
(1) 18650 LiIon battery (4 of) (only buy top line manufacturer's batteries from a reliable source, or you will be ripped off: Panasonic, Sanyo, Samsung, LG, Sony):
https://batteriesplus.co.uk/acatalog/copy_of_Lithium_Ion__Li-Ion___3.7V_Batteries-1.html
The following items are just to give an indication of typical products at this stage:
(2) 18650 battery holder (4 of):
https://www.ebay.co.uk/itm/Batterie...721376?hash=item1a1c3a2160:g:c5kAAOSw8w1X4NGD
(3) Battery protector: **broken link removed**
(4) Battery charger (4 of): **broken link removed**
(5) Inverter: **broken link removed**