Not as much as people think. The existing grid, in the UK at least, can cope with only minor changes, so long as cars are smart enough to react to pricing signals as they charge. This is quite simple to do as the grid already implements a market system with prices available in real time.

The big challenge will be providing charging for people (in the UK about 40% of the population) who do not have the opportunity to park their car off road. Quite a lot of this demand could be met by simply providing normal domestic sockets with RFID controlled breakers on posts at 6 m intervals along urban streets and in every public parking space. This is relatively simple and scalable and does not need large capital expenditure to get started.