The Zedboard's input power supply needs to be 12V. Applying any more then that could cause unwanted damage. Please refer to the hardware user guide for more information.
As a follow up note, the reason 16V won't work is that we connect the 12V input directly to the FMC slot, which requires 12V for operation. The ZedBoard itself will power off of 16V in, but again that 16V would be passed to the FMC card header so connecting an FMC card could result in damage to the ZedBoard, the FMC or both.
