Typical electric car consumes 35 kWh per 100km. (62 miles)
The Tesla Model S easily gets 400km out of 85kWh which puts it at ~20kWh per 100km.
Say it can drive 400km (250 miles). That's 140 kWh of energy.
85kWh for the Model S
Now, to pump 140 kWh in 15 mins, one needs electircity source of 560 kW.
Typical "big" power plants with several blocks are normally in 1-1.5GW area.
With about 2500 such vehicles you'd consume 100% of power generated by such power plant.
Only if all cars always simultaneously drive 400km in 15 minutes and also charge at full capacity during those 15 minutes, and they do this continuously 24/7. This is a practical impossibility for a number of reasons.
Even if you suppose that all cars drive 400km per day (which isn't the case) and so need a full charge every day, a smart grid would distribute those 2500 cars out such that 26 charge at a time (26 x 4 x 24 = ~2500 cars) and you only need a 9MW energy supply for the 2500 cars with the Model S 85kWh battery. (In practice cars drive a lot less than this and so when all is said and done you don't need a whole lot of electricity at all to keep them going.)