Great tip Gary! I would say this inverter could be used with any 12V DC source. If a car battery is too heavy for your cart, a motorcycle battery should also work--but for a shorter period of time. I once played my BK-7m and Tyros 5 combo off of a computer backup power supply ("UPS") during a power outage. Supposedly my UPS was rated at 450 watts, but that's a peak rating and it only lasted 40 minutes. I would guess that my total current draw was 2 1/2 amps. I feel like they might have lasted longer powered directly from a battery, instead of going through the DC -> AC -> DC process of the UPS and in-line transformers. Obviously you would need the correct voltage and polarity. Also, NEVER try to save, edit, or do firmware updates when using this type of power. If you get a low voltage condition you could scramble the board!
Paul, Roland is my favorite brand. But the Casio CT-X3000 has a much better spec than the little E-X30 discussed here. It has Casio's newest acclaimed AiX sound engine. Rated to run 10 hours on D batteries, and probably more if you play sounds through a JBL Charge 3 or another battery-powered amplifier (and turn off the on-board speakers.)
Kabinopus, I don't know anything about Medeli. But I agree that this board wasn't developed by the Roland I'm familiar with. Even its chord recognition system is Yamaha's, not Roland's excellent Chord Intelligence. As you said, most likely "badge engineering."