Why does the Tesla PowerWall operate at 350v - 450v?
The Powerwall is/will be based on the lithium ion battery technology used in the Tesla cars, so instead of a few large lead acid batteries (like in PV battery banks) it will contain a zillion tiny 18650 cells, which work better if you put them in series and let the voltage soar.  This keeps the current low while still allowing the same amount of power output (good old ohms law).  The hardware to turn the current into a sine wave for consumption (called an inverter) also becomes simpler to design because it has high voltage to start with, so it doesn't need a boost circuit or a transformer to generate 120/208/240v RMS.