The Ergosphere
Saturday, March 13, 2004

Is the tide turning?

One of the more radical dreams of the true environmentalists (as opposed to the anti-humanists who use environmentalism as a cover) is to convert the world economy to renewable energy.  They will not be fulfilled until homes, factories and transport are using no fossil, nuclear or other unclean, depletable energy supplies.

This is a tall order, one that humanity has not met since the discovery of the useful properties of coal.  Yet it remains worthwhile to keep the goal in mind, if not for the environment, then for our political and economic defense in the war declared against us by the Islamofascists.  Randall Parker sets forth a standard by which we can measure our progress in one sense:  when the alternatives to oil are cheaper than oil, the economic power of the Middle East will be beaten.  Technology is unlikely to retreat, while depleted oil fields will never be more full than they are today.

The ideal scheme has always been the most expensive:  the solar-powered car versus the status quo.  Photovoltaic cells are one of the most expensive means of capturing energy from renewable sources, albeit also one of the simplest and lowest-maintenance.  If a car receiving power from solar PV cells can deliver transportation at a lower cost per mile than gasoline, the millennium will have arrived.  But could the millennium have sneaked in while we weren't looking?  Let's take a look at the figures.

The beauty of electric vehicles is that most of the required infrastructure is already in place; we need no filling stations for new fuels or new pipeline networks.  The new vehicle designs are ready to hand:  we already have plug-free hybrid cars which attain 60 MPG and upwards, and if we add bigger batteries to such a hybrid we can make a plug-in hybrid or CalCar.  More batteries does not just mean better acceleration and more efficient regenerative braking, it also means some operation without the need for any energy besides the stored electricity.  We can build these cars today; we could (and should) have been building them ten years ago (but the litany of the sins of the California Air Resources Board is a rant for another day).

Suppose for a moment that we built such cars with today's technology and tried to power them as much as possible with renewable energy.  How much would they cost to run?

The two major costs of the electric portion of such a vehicle are electricity and battery degradation.  Let's start with batteries.

The current price-leader technology for storage batteries is the old, reliable lead-acid chemistry.  It wins no prizes for energy density or lifespan, but it can be made for substantial power density and it is certainly cheap.  Lithium-ion or fuel cells may be the ultimate winner of the technology race forty years hence, but if we can make things work with lead-acid we can get started immediately.  We needed to get started in 1990, so we have no time to lose.

Depending on the chemistry and technology, batteries are limited by both cycle life and calendar life.  If we take 3 years as a reasonable period between battery replacements in a car and assume daily use, we need approximately 1100 cycles from the battery if it is charged once a day and 2200 cycles if it is charged twice a day (say, at home overnight and again at work).  If we refer to the cycle life vs. depth of discharge curve below, we see that if we want 2200 cycles of life we can discharge that model of battery by roughly 40%; if we only need 1100 cycles we can discharge the battery by roughly 50%.

Current electric vehicles consume roughly 200 watt-hours per mile.  This seems to be a reasonable figure for conventional vehicles as well.  If the vehicle is required to operate for 30 miles on electricity alone, it will require 6 KWH of electricity.  At 50% DoD the battery pack would have to store 12 KWH, or 15 KWH at 40% DoD.

A commercially-available deep-cycle battery storing a nominal 1.2 KWH costs approximately $70 US at retail.  If we assume that a battery equivalent to the Yellow Top can be built at this price, plus bulk discounts for production and purchase, we might see that drop to $60 or about $50 per KWH.  A 12 KWH battery would cost $600; a 15 KWH battery would cost $750.  The cost of energy storage for 2200 cycles to 40% DoD would be ($750/2200*6) = 5.7 cents/KWH; for 1100 cycles to 50% DoD, the cost would be ($600/1100*6) = 9.1 cents/KWH.  The corresponding per-mile costs are 1.1 cents/mile and 1.8 cents/mile.

That takes care of the battery costs.  What about the electricity to charge them?  Solar PV panels produce DC, so it seems reasonable to assume a very high potential efficiency if they are being used to charge batteries more or less directly.  Assume the net efficiency of battery plus charger is 80%, which yields 250 WH of PV output per vehicle-mile of travel.

The actual price of solar PV depends on too many factors to account for in an analysis this simple; however, the figure of $.25/KWH seems to be reasonable for the day.  If we assume values from $.30/KWH down to $.20/KWH and run numbers, we get this range of projections:

  • $.30/KWH and 1100 cycles/3 years:  9.3 cents/mile.
  • $.30/KWH and 2200 cycles/3 years:  8.6 cents/mile.
  • $.25/KWH and 1100 cycles/3 years:  8.1 cents/mile.
  • $.25/KWH and 2200 cycles/3 years:  7.4 cents/mile.
  • $.20/KWH and 1100 cycles/3 years:  6.8 cents/mile.
  • $.20/KWH and 2200 cycles/3 years:  6.1 cents/mile.
If we assume wind or hydro power may be available at $.10/KWH retail, the figures look even better:
  • $.10/KWH and 1100 cycles/3 years:  4.3 cents/mile.
  • $.10/KWH and 2200 cycles/3 years:  3.6 cents/mile.
At this writing the retail price of regular unleaded gasoline is pushing $2.20/gallon in California.  If the competition is a conventional internal-combustion engine vehicle burning regular gas at that price, I get the following energy costs for various levels of economy:
  • 12 MPG (typical big SUV):  18.3 cents/mile
  • 16 MPG (typical medium SUV):  13.8 cents/mile
  • 20 MPG (typical small SUV):  11 cents/mile
  • 27.5 MPG (CAFE limit for passenger cars):  8 cents/mile
  • 35 MPG (economy car):  6.3 cents/mile
  • 60 MPG (2004 Toyota Prius, city rating):  3.7 cents/mile
From the look of it, solar PV feeding plug-in hybrid cars can already deliver transportation to Californians more cheaply than any ICE-powered vehicle getting less than 20 MPG.  If solar PV costs 20 cents/KWH and the vehicle runs its batteries for 2200 cycles between replacements, the cost is already par with a 35-MPG economy car.  And if you assume the availability of wind or hydro power at 10 cents/KWH for charging, the plug-in hybrid can push energy-cost parity with the Prius.

It looks like the millenium may already be here.  It's time to wake up and smell the coffee.

Cycle life vs. depth-of-discharge diagram for Yellow Top batteries.
(Graphic courtesy Optima, via Commuter Cars Corp.  Copyrights NOT mine.)

Links and acknowledgements:

Costs of Oil Dependence: A 2000 Update
EPRI study on plug-in hybrid vehicles

Many thanks to the Institute for Analysis of Global Security, who compiled many of these links and did a fine job of documenting much of what I've been thinking about for the last several years before I found out about them.  Also thanks to Randall Parker, who brought them to my notice.

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A very informative and thought provoking article. How about using the same figures for homes, given a consumption of 600 KwH per month of a regular house hold with 5 days storage.

Would love to hear about it if you choose to post ant such information.

In the meanwhile, thanks for your work.
600 kwh = 20kwh/day

* 5 = 100kwh

100/6 = 16.666


= $12,750
The multiplication by 5 and the divison by 6 mean what, exactly?  What are the units of these numbers?  And why multiply by $750?

Go back to unit analysis if you have any questions.
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