Batman: Except that if you go on your annual journey, then so would 1 million others. Or 10 million if you are from a metropolis. The queue to charge would be ... Sorry beyond my math ability.
I'm sure they will come up with something ...
It will be a problem and already is in some places. EVs that charge slowly make it worse....especially PHEVs with small batteries that are slow AND can't go very far....but the owners are trying to drive them like EVs. In the UK, the Mitsi Outlander PHEV is hated by many other EV drivers for this reason. That's been somewhat resolved by most of the chargers no longer being free......and the PHEV drivers have stopped charging every 40km at £6 a pop. :-)
But lets say in 5 years the average range of an EV is 400km. For all but the biggest trips people will charge at home or overnight in a motel or campground. Few people will drive that distance in large enough numbers on the same day so as to overwhelm the fast charging network of that time.
The Tesla Supercharger model is a good one. 8-12 (or more) charging stalls, each capable of (today) 120kw charging......so even the biggest Tesla battery can get to 80% in barely more than a half hour. If there are more of them and they go to the planned 350kw charging....then they will be charging cars with 100kw batteries in less than 20 minutes. Still longer than with petrol.......but without the background burden of supporting ALL other vehicles. They need only support the vehicles on road trips from several hundred kms away.
You just won't need as many of them. A tiny fraction.....and remember....an EV can charge up pretty much anywhere => homes, hotels, shopping malls, libraries....lamp posts (a new thing).


