We examine the spatio-temporal interactions of widespread electric vehicle (EV) charging with a future, 100% renewable electricity system in Australia. More specifically, we use a GIS-based electricity supply-demand model simulating an hourly competitive-bidding process over an entire year. We obtain least-cost grid configurations that include both renewable energy (RE) generators and EVs, the latter under both uncontrolled and controlled charging, and adoption rates between 0 and 100%. We characterise the vehicle-to-grid interaction in terms of overall installed capacity, hourly generation and spillage, levelized cost of electricity (LCOE), as well as transmission network expansion topology. We show that supplying 100% renewable electricity to cover current electricity needs in Australia, as well as powering all Australian passenger vehicles as controlled-charged EVs, requires 205 GW of installed capacity at an LCOE of 14.7 AUD¢/kWh. This 100% RE supply with EV charging leads to an additional electricity cost of 1710 AUD/capita annually, comparing to the current annual expenditure for electricity and conventional vehicle fuel.