# Electric-Car Charging Stations Needed in U.S.

L. David Roper, http://www.roperld.com/personal/roperldavid.htm
13-Mar-2017

Question: If all cars in the U.S. were fueled by electricity (BEV) instead of fossil fuels (ICE), how many charging stations would be required?

Charging stations types: http://www.roperld.com/Science/ChargingStationsTypes.pdf
Here we only consider level-2 (240-volts) stations and level-3 (480-volts or higher) stations.

Let:

• d = average distance traveled in a year by a car (BEV or ICE)
• t = average capacity of the fuel tank in gallons for an ICE
• b = average capacity of the battery in kWh for a BEV
• m = average miles/gallon for an ICE (distance between refuels = tm)
• k = average miles/kWh for a BEV (distance between recharges = bk)
• f = fraction of BEVs that have capacity to charge at home base
• a = fraction of recharges that home-based BEVs charge away from home base (public recharges)
• g = number of gasoline stations in U.S. to refuel ICEs = ~115,000 (This number is very uncertain; it is steadily declining.)
• e = number of charging stations needed in U.S. to replace all ICEs by BEVs

The number of gasoline stations in the U.S. has been declining linearly:

Then:

• r = number of refuels in a year for an average ICE = d/(tm)
• c = number of recharges in a year for an average BEV = d/(bk)
• p = number of public recharges in a year for an average BEV = (1-f)c + afc = [1 - (1- a)f]c = p
• e = pg/r = 115,000[1 - (1 - a)]f]d/(bk)(tm/d)= 115,000[1 - (1 - a)f]tm/bk (The d cancels top and bottom.)

Let:

• d = 15,000 miles (Actually the value of d is not needed; it cancels out in the calculation of e.)
• t = 15 gallons
• b = 100 kWh
• m = 30 miles/gallon (distance between refuels = tm = 450 miles)
• k = 3.8 miles/kWh (distance between recharges = bk = 380 miles)
• f = 0.5 (Half of BEVs can charge at home base.)
• a = 0.1 (10% of the charges are done publicly of BEVs that can charge at home base.)

Then: e = 115,000[1 - (1 - a)f]tm/bk = 115,000[1 - (1 - 0.1)0.5 ](15 x 30)/(100 x 3.8) = 115,000 x 0.651 = 75,000

Of course, it will be a long time until all ICE cars are replaced by BEVs. Assume that 25% are replaced in 10 years; then the number of charging stations needed are 0.25 x 75,000 = 18,750 needed in 10 years.

Here are rough data of how many charging stations were available in the U.S. in 2016:

Gasoline stations have between 2 and 10 pumps. Tesla Superchargers have between 4 and 12 stations. So, it is difficult to compare gasoline stations to charging stations. However, the numbers given above indicate that there is now and will be in the future no problem with the number of charging stations.