Twenty megawatts in your hands

I needed to buy more gasoline for the car today, and I decided to see how long it took to fill the tank. I bought ten and a half gallons of gas, and it took 70 seconds to fill it up. Although filling up a gas tank is something that millions of Americans do every day, it’s really remarkable when you stop and think about the energy transfer going on.

Gasoline has, approximately, 113,000 BTUs per gallon.¹ One BTU is 1055 Joules. So I transferred 1.25 Billion Joules in those 70 seconds, which is a rate of 17.9 megawatts. When you consider that you spend less than two minutes pumping the same amount of energy you burn in four hours of driving, it’s not surprising that you end up with such a high power. What’s more interesting, I think, is to contemplate the rather fundamental limits this puts on plug-in electric cars.

Internal combustion engines, according to Wikipedia, are only about 20% efficient, which is to say, for every 100 BTUs of thermal energy consumed by the engine, you get 20 BTUs of mechanical energy out. This is, in large part, a consequence of fundamental thermodynamics. Although electric motors can be pretty close to perfectly efficient, a similar thermal-to-electric efficiency hit would be taken at the power plant.

Let’s consider, then, that we want a similar car to mine, but electric. Instead of 1.25 gigajoules, we need to have 250 megajoules. Battery charging can be pretty efficient, at 90% or so, which means we’d supply 280 megajoules. If we expect the filling-up time to be comparable to that of gasoline cars–call it 100 seconds for simplicity–then we’d need to supply 2.8 megawatts of power. At 240 Volts, which is the voltage we get in our homes, this would require 11700 amps; if you used 1000 Volts, it would take 2800 amps. Although equipment exists² to handle these voltage and current levels, it is an understatement to say that it cannot be handled as casually as gasoline pumps are handled. Nor is it clear that any battery system would actually be able to accept this much power.

A linear relationship exists between the power requirement for filling, and the vehicle range, the vehicle power, and the time for a filling. If you’re satisfied with half the range of a regular vehicle, for example, you could use half the filling power. Let’s imagine that you’d be happy for the filling to take ten times as long as with gasoline, or 1000 seconds, just under 17 minutes. At this level, you’d need 280 kilowatts of power. If battery charging is 90% efficient, that means 10% of the power is going to be dissipated as heat, which in this case would be 28 kilowatts.

For comparison, a typical energy consumption rate for a home furnace is 100,000 BTU per hour, about 28 BTU per second, or 29.3 kilowatts. Which means that the waste heat dissipated during charging for the example–of a 1000 second fill for a vehicle with similar range and power as a modest gasoline powered sedan, at 90% charging efficiency–is as much as the entire output of a home furnace.

No wonder overnight charges are the standard.

1. Summer and winter blends have slightly more and less, respectively. [↩]
2. think about how large the wires would need to be [↩]