Gas prices, fuel economy, electricity prices, etc.

Last night, I posted a simple calculation to Twitter.  Based on gasoline energy content of 32.2 MJ/l LHV, and a conversion of 3.6 MJ/kWh, I calculated 8.94 kWh/l of gasoline, and thus stated that $1.30/l gasoline was approximately equivalent to 14.4c/kWh electricity.  This had, in a sense, the desired result.  Many of my followers followed up with questions on my assumptions and provided alternative calculations, so I thought I would open this space and allow them to do so in more than 140 characters.

So, here’s the question.  At $1.30 per liter gasoline, take us through the decision of Leaf vs. Corolla or similar.  What’s the break-even price of electricity if gas is$1.30/l (the price we paid yesterday in BC)?  At 14c/kWh electricity delivered to your home, assuming you have a 30amp feed to your garage for a charger, what’s the NPV of an electric car at $1.30/l gas?

Thanks for your contributions!

Andrew

10 responses to “Gas prices, fuel economy, electricity prices, etc.”

  1. Jesse

    To get the fuel costs the leak is rated at 765 kj/km from wikipedia. This would need to be devided by the charging efficiency to get to the meter to wheels energy cosnumption. This works out to 76.5 MJ/100km (or 21.25 kWh/100km). At 32.2 MJ/L gasoline, this is 2.4 L/100 km equivalent efficiency.

    A corolla is aprox 6.6 L/100km combined. At a gas cost of $1.30/L this is
    $8.57 / 100km.

    For the leaf ellectricity would need to cost $8.57/21.25 kWh = $0.40 / kWh to be even on a energy cost per 100 km basis. At your assumed $0.14/kWh, the energy cost is $2.95 / 100 km.
    If the NPV of the car is Purchase price + NPV (distance * driving cost, years, discount rate) + NPV(mtce per year, years, discount) + Insurance, we can fill in the rest when we finish the assumptions on number of years, driving profile, and dsicount rate to use.

  2. Joel Wood

    No responses yet?

    I am not going to do any math this week, so I am going to ignore the actual calculation debate. However, I will comment on the Leaf vs. Corolla consumer decision.

    From a consumers perspective, I would think that we will need to account for an uncertain depreciation rate for the Leaf. I would guess that the risk of having to fork over excessive amounts of cash in the future to repair your Leaf needs to be factored in, whereas with the Corolla there is a repair track record and lots of friends with Corollas you can get repair info from. I am not saying that it would actually have a higher depreciation rate (i.e., higher risk of expensive repairs), just that it has zero repair track record and risk averse consumers would put some value on depreciation rate information.

    On the other hand, some consumers may get a non-monetary benefit from either the appearance that they are eco-friendly (e.g., the South Park Prius Effect!) or tech savvy (i.e. an early adopter). But these things would probably be much more difficult to measure.

    Anyways, those are just my two cents.

    Joel

  3. Jesse

    In terms of inusrance, mtce and depreciation, I don’t have any real data other than the headline available. I’m not an expert, just doing the engineering calculation. (And you happened to ask the question at the same time as I am car shopping). As I understand insurance costs are basically (car value * (accident rate + theft rate)).

    The problem is that it really comes down to each persons driving pattern and insurance rate (especially with two cars with drsitically different $/km and purchase prices).

    That is one thing that makes electric cars a hard sell, is that you need to sit down with a real spreadsheet to figure out if it is a good deal, and can’t just guestimate.

    For my own case an electric would work for daily driving, but fail for fairly freqent long distance trips. Only 1 car in household so 2nd car is not an option either. I do more highway than city and average or less km / year. The front runners are between deisel and gas. Hybrids come distantly, and eletric cannot meet the minimum criteria.

  4. Dan Wolfe

    I’m too late to the game to share my Leaf vs Corola calcs, but suffice it to say, I get the same result as Jesse. What I also find interesting is the relative inefficiency of gasoline usage in a vehicle engine. Since most of our electricity is fossil-derived, you are essentially powering your Leaf with coal or methane, burned at a distance, at a much higher efficiency than what a piston engine is capable of.

    Now some numbers: assuming the drivetrain losses in a Leaf are relatively modest at 15% (I have no idea what they actually are), we can then say that of the 22.6kWh/100km power usage, 85% or 19.2kWh is actually motive power. A Corolla weighs only 81% as much as a Leaf, so it will require 15.6 kWh of motive power to do the same 100km. Given the mileage of 6.6L/100km, the Corolla will use 59 kWh of fuel at 8.94kWh/L. So, if the Leaf is 85% efficient, this would put the Corolla engine at about 22.5% efficient, which is a little high, but fairly close to the 18-20% range usually quoted for gasoline engines. A combined cycle natural gas power plant will have an efficiency of 50-60%, and on top of that, the fuel cost of $4/GJ vs about $40/GJ of gasoline (if I did my math correctly), and it quickly becomes clear why the fuel cost for a Leaf is so much lower than for a Corolla.

    For home heat though, different ballgame entirely. Gas at $4 and 95% efficiency gives you $4.21/GJ, while electricity at $0.15/kWh will cost you $41.67 for the same 1GJ of heat.

    So, run your car on electricity if you can, but use natural gas to heat your home!

    1. George

      I want to add a couple of comments for anyone else who is looking through this discussion at this late date.

      A lot of the operational cost discussion centred on gasoline cost vs. electricity cost and relative operational efficiencies. Gasoline costs include imbedded taxes which typically come close to 50% (in BC probably higher) of the pump cost. The gasoline engine is less efficient than the electricity cycle in most of Canada but most of the cost difference is the fuel taxes which will almost certainly at some future point be placed on the electric car operation as well if they become popular enough.

      The second point I would like to make is that in most of Canada you need to consider the winter operaton scenario as well. If you are operating the car heater/defroster you are draining the electricity in one of the less efficient ways (similar to the home electricity heating) at a time when the battery is much less efficient at holding the charge. During the same time the internal combustion engine powered car is using a waste product for vehicle comfort so there is no additional cost for cold weather operation that is not also faced by the electric powered car.

      I have found this to be an interesting discussion. It is always good to be better informed when considering an issue such as electricity vs. conventionally powered vehicles.

  5. Jesse

    Dan,

    Good points on what the relative costs show, but the frontal area of teh car and coefficient of drag have a very large impact at higher (highway) speeds. Weight is more dominant at city speeds with more acceleration.

    If your marginal electic kWh is coal, the electric probably hasn’t saved any green house gasses. With an electric car you are transferring the inneffcient heat engine step to an external location, but it is still there. The coal plant is more efficient (if I recall correctly 40-50% vs 25-40% for a gas engine), but there is more CO2 per fuel BTU than gasoline. The cost savings as Dan pointed out is in the cost difference of the source fuel.
    In North America the marginal electric BTU is almost always going to be some mix of coal and natural gas, as Hydro is run to produce essentially 100% of the resivour availability, and Nuclear is run flat out, since in both cases the marginal cost once you have built and staffed a plant is nearly 0. For fossil fuel plants the largest cost is fuel (mroe so with natual gas than coal).

  6. Mike

    Jesse, you raise a great point on marginal generation. It seems to me that a person with an electric vehicle is a perfect candidate for time of use pricing and should be charging in the middle of the night when they can take advantage of the lowest marginal price.

    If you can turn that 14c/kwh into 2c/kwh, the economics become very different.

    1. Mitchell

      Thanks for writing such an easy-to-underatnsd article on this topic.

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