The UK grid company (who also run some of the US grid) put out a report on the impact which I'll summarise as "no big deal". They mapped out a few different scenarios, the most extreme of which got taken, then mangled and exagerrated and turned into scary headlines about EVs destroying the grid.

They then had to issue a second report pointing out that their first report said it wasn't going to be a big deal.

http://fes.nationalgrid.com/media/1264/ev-myth-buster-v032.p...