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High input voltage and amperage makes for a fast charge. Any battery suitable for an EV (regardless of chemistry or pack voltage) will charge faster - Which is a good thing.
While some batteries take power in faster than others, at typical rates (i.e. the amount of power normally available in your garage or a street plug-in post) a 10kw 144v pick-your-favorite-chemistry pack would take about the same amount of time to charge as a 10kw 400v pick-your-second-favorite-chemistry battery pack - about an hour using a 50 amp, 220v RV plug (11kw) or a 27.5 amp, 400v exotic plug (11 kw).
Not sure if you've been in an RV recently... multi-air conditioning, microwave oven, plasma TV, outdoor lighting, hydraulic leveling, etc. can challenge even a 220 volt 50 amp circuit!
The same 220v, 50 amp RV plug will give about 40 miles or so charge (per hour plugged in) to a modern EV if they have an on-board charger that can use that much power. Would a higher voltage be better? Sure!
Problem here is that above 220, higher voltages (such as 440) are typically for industrial users. Probably not available in a suburban neighborhood or typical downtown street. Want more amperage out of a 220v circuit, say 100 or 200 amps? - Possible, but then the costs go up dramatically (bigger service wire, upgraded breaker panels, etc.)
Perhaps they might want to use a transformer to 'up' the voltage. Easy solution... But transformers have some amount of loss, cost a lot, and can only give out as much power as they get in. A 400v up converted charging station will only put out 27.5 amps (less transformer losses) if fed by the normally available 220v, 50 amp circuit that will probably be used upstream of the charging station. Anything more than ~30 amps/400v would probably require a much bigger plug and wires than they show in the teaser picture.
So, what exactly is the advantage of this 400v, proprietary, high-dollar plug in system?
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