Friday, April 20, 2012

Will the Chevrolet Volt Save You Money?

EDIT 4/23/12: I made a pretty huge mistake here in not taking the relative efficiencies of gas vs. electric car motors into account and just assuming they were roughly equal.  In reality electric motors are about a factor of four better.  That completely changes the conclusion of the post, which originally had the Volt costing about as much as a regular car to drive around.  I've edited heavily to take all that into account.  

The Chevrolet Volt, and other plug-in hybrid vehicles like it, are marvels of engineering that should have all self-respecting nerds salivating for them to come down to normal-people prices.  Their genius is in the way they get around what's always been the main issue with electric cars: the energy density (the amount of energy you can store in a given weight or volume) of batteries, while it sucks less than it used to, has never been able to match the energy density of gasoline.  As a result, electric cars either need to carry several times the mass of a full gas tank in storage batteries (almost always impractical) or have their range drastically compromised.  The Volt and its ilk work around this by adding a gasoline engine to basically act as a battery charger on the road; it doesn't do much more than burn (high-energy-density) gasoline to keep the (low-energy-density) battery topped up, while the battery powers the drivetrain via electric motor.  This is different from parallel-hybrids like the Prius, which freely switch between using their gas and electric motors to power the drivetrain, and in principle should be able to seriously increase gas mileage to well above what even current hybrids are capable of.  It does in fact succeed in doing this, as this photo from James Fallows' blog shows:

For reference, that's approximately Philadelphia to Denver on a single tank of gas.

That's bananas, right?  Unfortunately it's not that simple.  The Volt ain't magic; it still takes the same amount of energy to push it that 1389.4 miles as it does a regular car of the same size.  The difference is that a lot of that energy is coming from electricity (via charge-ups between drives) rather than gasoline.  Since electricity isn't generated from nowhere and definitely isn't free, miles per gallon of gasoline is an extremely deceiving metric to use when evaluating the efficiency of plug-in hybrids; we need to think of a way to take that generated electricity into account too.  I decided to figure out a way to do this and, in the process, find out (roughly) how much money you'd actually save by driving a Volt vs. a regular, decently-efficient car.

I made a couple of simplifying assumptions in figuring all this out:
  •  I assumed the car usage summarized in the photo above was typical.  From the numbers I've heard thrown around for plug-in hybrids, it's probably close.
  • My "normal" car was assumed to have an average gas mileage of 30 mpg over the same 1389.4 miles that Volt drove.  That's a reasonable assumption for a well-built traditional car of the Volt's size.  I also assumed that it had roughly the same size, weight, drag coefficient, etc. as the Volt, so the energy used to move both of them would be close to identical.
  • I assumed that the efficiency of charging the Volt's battery with a gasoline motor is the same as the efficiency of moving the regular car with a gasoline motor. The Volt is probably slightly more efficient for various reasons. 
  • I assumed that all the electric power used to push the Volt came from charging it off a residential power grid.  In real life some of it will come from regenerative braking, but probably not enough to throw off our calculations by more than a couple of percentage points.  
We need to know a few numbers before we can get started:
  • The energy you get from burning gasoline is, according to Wikipedia, about 34 MJ/liter.  In American units, that converts to about 35.75 kW-hr/gallon
  • The average US price of a gallon of gas, at the time of this writing, was about $3.88.  We can calculate the energy cost of burning gasoline to be about 10.9 cents per kW-hr, using the previous number. 
  • Likewise, the average national cost of 1 kW-hr of electricity in 2010 (the most recent data I could find with a quick Google search) was about 11.5 cents.
  • The energy efficiency of a good internal combustion engine is about 20%; electric motors run closer to 80%.  In other words, you can get an electric motor to do the same amount of work as a gasoline motor for 1/4 the input energy.  

First we need to calculate the total energy used to move the car over our representative 1389.4 miles.  If we assume it's the same for both our Volt and normal car, and that our normal car can average 30 mpg efficiency, then we know the normal car will need 46.313 gallons of gas to go that distance.  Since we know how much energy is contained in a gallon of gas now, we can work out that the gas-powered car will use about 1656.16 kW-hrs of energy during the drive.  Since the engine is only 20% efficient, only about 331 kW-hrs of that were actually needed to move the car; the rest gets lost as heat, noise, etc.

All of that energy came from burning gasoline for the traditional car, so we can pretty easily calculate the total cost of the drive by using the price of gas and the energy density of gas: about $180.52.

For the Volt, things are slightly more complicated.  The electric motor powering the drivetrain is about 80% efficient, so dividing 331 kW-hrs by that gives us 414 kW-hrs, the input energy needed to move the car.  Since we know we burned 10.4 gal of gasoline during the trip, we can calculate that about 372 kW-hrs was used by the (20% efficient) gasoline engine.  If we assume all of that was used to charge the battery (in reality some would have been used to power the drivetrain, but we'll ignore that for simplicity) that's about 75 kW-hrs of battery charge from burning gasoline.  The rest of the battery's charge would have come from the power grid;; we can calculate that by subtracting the gas engine's contribution to charging the battery from the total 414 kW-hr charge.  The total energy cost can then be calculated as follows, by adding the battery-charging contributions of the gasoline engine and the power grid:

Cost = (372 kW-hrs)*($0.109/kW-hr) + (414-75 kW-hrs)*($0.115/kW-hr)

The total cost comes out to about $79.50, more than a factor of two less than the conventional car

So that's about 13 cents/mile to drive the conventional car, vs. 5.6 cents/mile for the Volt.  That's a pretty big difference; even with the money you're paying to charge the car, it's still costing you about half as much to drive your Volt around as it would a similarly-sized conventional car.  To put that in perspective, if you drive 20,000 miles in a year, the Volt will save you almost $1500 annually.  That's a long way from "paying for itself," at least at current prices (a Volt will run you almost twice as much as a similar conventional car), but if plug-in hybrids like the Volt are anything like the current generation of hybrids they should fall in price pretty quickly over the next few years. 

So yes, the Volt will save you quite a bit of gas money, even though it's far from the free lunch that the mpg numbers being thrown around make it look like.  From a cost standpoint, you could assume it's equivalent to a hypothetical gas car that got around 70 mpg; that's not exactly Philly to Denver on a tank of gas, but it's pretty good.   The cost savings will probably only get bigger, as gas prices continue to rise faster than electricity prices, and in places like Europe where gas isn't artificially cheap the Volt is already close to paying for itself in a couple of years.  

It's worth mentioning that this is only looking at raw fuel cost; there are a lot of other advantages (less pollution and reduced dependence on foreign oil are two big ones) to using centrally-generated electric power vs. burning gasoline to power our cars.  It's far from a perfect solution to the transportation problem the US is going to have to deal with when our current era of cheap gas ends, but it's one of the best things anybody's come up with so far.

2 comments:

  1. You forgot to consider wearout/consumption of batteries at .347$/w with about 3000 discharge cylcles to wearout -- i calc 5.5 cents / kwhr for lithium ion ... so u r at 11.1 cents mi saving 2 cents ... consider motor life for gas car and the 55 barrels of oil in the gas car tossed ---electric motors last a long time so u cant throw it away to get ur real savings

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  2. The standard warranty that comes with the Prius and such gives you one replacement battery, so if the serial-hybrids stick to that model the cost is mitigated a little. You're right though, battery cost is pretty nontrivial ($5K-ish a pop?) and I left it out of this mostly because there's no good data online on how long a Li-ion will last in a Volt-type motor configuration.

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