The power supply is a specialized version of the miniature fusion reactor, that is surgically implanted into Alexandra, replacing the entire space of her lungs. It also removes her windpipe, vocal cords, and larynx with the vocal cords removal. The removal of all of this, makes Alexandra completely mute, unable to create even the slightest sound, due to the missing vocal cords and windpipe.
It supplies all the devices and systems within Alexandra and which are part of her Bane system with power. As the collection of all the devices doesn’t require a lot of energy, and it being a fusion reactor, it has enough fuel given on its initial implantation for over 10 millennia of runtime for Alexandra.