For a few years, now, I've been running my plastic piano off batteries when I took it out on gigs. Likewise, with the desk light I built for it. I have a battery attached to the piano with adhesive velcro, and another attached to the stand with the light. I also have a second velcro patch on the stand, so that both batteries can be fitted there.
Running off the mains has its problems (being tethered to a wall socket, unreliable multi-way mains power boards, horrible noises when plugging and unplugging audio leads, and the potential to damage equipment when doing so). Battery powering them, and attaching them directly to the equipment, makes it very convenient when you have to move things around.
This was very simple to do with this piano, since it runs from 12 volts DC, around 1 amp maximum. Rechargeable batteries come in that voltage, and there's plenty to choose from with enough capacity. All that I had to do was attach a suitable lead, through a protective fuse, to a battery.
Be aware that some parts of the piano are directly powered from the 12 volt supply input and expect it to be externally regulated (that means two things—voltage stability, and being very close to 12 volts).
The piano needs up to 1 amp (in my tests), and the supplied plug pack is 1.5 amps, so the fuse should be rated for close to that. If the battery and cable is more than capable of supplying 2 amps, then a 2 amp fuse ensures you won't get nuisance blows, and that it will still definitely will blow if the connection is shorted.
I used a self-resetting polyswitch. They get hot when too much current passes through, go high-resistance, and stay that way until power is disconnected. Then they cool down and reset (it only takes moments). Considering that these DC plugs easily get shorted out, it's far more convenient, and economical, than having to replace fuses (and having to take spare ones with you).
My piano requires + on the plug tip, and the equipment is negative ground. But always make sure of what polarity your equipment uses before making your own power cabling. Make sure you get the polarity right, and fuse the supply side. In the above picture you can see that I've put red and black sleeving on the wiring to show the correct polarity for my equipment, and marked the connectors with T for tip and S for sleeve.
You should always use a protective fuse when using high current sources (and batteries are), particularly when the type of DC connector used can be easily shorted out (and these can). And the fuse should be as close to the battery terminal as possible, to protect against any wiring problems.
During my bench tests, a plug and socket both turned out to be badly manufactured and the socket shorted out the plug, and came close to setting the wiring (and other things) on fire. In the few seconds before I managed to disconnect the battery, there was smoking and melting insulation dripping off orange-glowing wiring, which then started shorting together as well. Also be aware that wiring that's thin enough to fit into these DC connectors can be all-too-easily sliced into, as well.
On some of these plugs, the insulation between the tip and sleeve is too small, the sleeve can overlap the insulation going right to the end of the barrel, the external diameter of the tip connector can be too wide and not recessed into the insulation, and can short out against other things while being carried, or plugged into some sockets. During my tests I had a socket where the pin that goes into the tip had a wide flange on it inside the socket, and it shorted out the tip to the sleeve of the plug.
When using these types of connectors you always have to check a variety of mechanical aspects of them. The width of the barrel, its length, the internal diameter of the tip connection, and whether the insulator between them is well formed. Quite apart from badly manufactured ones, they come in a variety of sizes and you need a connector that is a good fit. It should plug in and work, reliably, even if bumped. If you have to fiddle with it to make it work, you have mismatched connectors.
Although it was tempting to fit the battery somewhere inside the piano, that would bring about its own problems. There probably is enough space, but it means removing a lot of screws to disassemble the piano (since there is no battery hatch). Batteries inside equipment get forgotten about, and can cause damage if they fail. And there's the issue of how to connect them to a charger.