It's not entirely clear from the article, and I can't find the Nature publication yet... but I think you're wrong.
It does carry it's own power supply and battery:
"Finally Barrett used a computer model to get the most out of every design element in the aircraft, from the thruster and electrical system designs to the wires that ran through the plane. “The power converter, the battery, the caps and fuselage—everything was optimized,” Barrett says. “The simulations failed all the time. We had to make hundreds of changes.” In the end, they had the triumphant Version 2."
It does carry it's own power supply and battery: "Finally Barrett used a computer model to get the most out of every design element in the aircraft, from the thruster and electrical system designs to the wires that ran through the plane. “The power converter, the battery, the caps and fuselage—everything was optimized,” Barrett says. “The simulations failed all the time. We had to make hundreds of changes.” In the end, they had the triumphant Version 2."
Here's the researchers earlier publication (2015) on the physics behind it: http://rspa.royalsocietypublishing.org/content/471/2175/2014...
Edit: found some more material. No video of the actual plane yet. But the professor has a website here.
http://electricaircraft.mit.edu/research/