"Example: 20 kW, charge time 5 minutes, lasting for 4 hours of driving:
The recharge power P needed is 20x(4/5)x60 = 960 kW.
At 3x400 V, each Ampère delivers 1.2 kW. Meaning that for a recharge power P one needs a current I of P/1.2 Ampère. For a paltry 960 kW as above, 960/1.2 = 800 Ampère are needed.
For those weaklings in math, here is the combined formula for the current needed:
I = 20x(4/5)x60/1.2 (in Ampère). Good luck!"
Well, lets skip the 3ph, and use just 1ph.
30KW is a better average to use for continuous power with all the electrical stuff now a days.
4 hours is a reasonable driving time (350KM), recharge is 10 minutes to 80% and use the 80% to provide 350KM (that is, ignore the 20% final charge that takes a long time, and one cannot use on a long trip anyway w/o waiting more than 10 min to recharge).
P = (30KW)((4hr)(60min/hr)/(10min)) = 720KW (rate for 10 min, or in energy, 120KW-hr).
So, for a 240 mains, for 720KW, I=3000A (for a 10min recharge)
For a 7700 feed (pretty common), I=94A, reasonably low
Out of curiousity, a typical house with 200A service (about 50KVA) would take around 2.4hr to charge the runabout at 100% utilization. Don't everyone in the neighborhood plug in together, or the area will go dark due to overload....
More reasonably, at 240v/50A (12KW), it would take 10hr to recharge 120KW-hr (100% efficient recharging etc.).
As for refueling stations, we don't know now what the best architecture for power conversion is-- but it probably is not a high current feed with expensive thick metal cables, and we certainly don't want more mass in the runabout for thick intermediate cabling. More likely is a long multicontact rod or maybe a multicontact slide in plate with multiple taps that mates closely to the battery pack (minimise mass in the vehicle, protects the contacts from electrocuting bystanders, has multiple taps to reduce the weight of the multiplicity of converters (lower voltage differential, lighter converters, vs. more then one of them), etc.). Indeed, the bulk of the converter mass ought to be off vehicle so that the (generally unused) mass isn't toted around while driving...