Wind turbine costs
I’ve been arguing with my associate Ben about the relative costs of wind turbines. (We work at a GreenMountain, a renewable energy engineering firm near Boston, so this is what we do for fun.) We’re both puzzled over the continued growth in the size of wind turbines.
Aldo da Rosa writes in Fundamentals of Renewable Energy Processes, Elsevier Academic Press, 2005 (pp. 599-600):
“For a given wind regimen, the amount of energy that can be abstracted from the wind is proportional to the swept area of the turbine. . . . The mass of the plant (in a first-order scaling) varies with the cube of the diameter. . . . Hence for the same amount of energy produced, the total equipment mass varies inversely with the diameter. Since costs tend to grow with mass, many small turbines ought to be more economical than one large one.”
This is exactly the argument that Ben came up with last week. The flaw, as best as I can tell, appears to be that cost does not actually track mass. Historically, it appears that costs are dropping as mass increases.
(Chart removed because javascript was screwing up other scripts. It was just a falling line–just imagine looking at the right side of a silhouette of a mountain.)
The data above comes from Gil Masters’ Renewable and Efficient Electric Power Systems, Wiley-Interscience, 2004 p. 372, with the 1981 data point added from an American Wind Energy Association paper, “The Economics of Wind Energy.” Masters states that, “taller towers increase energy faster than costs increase,” (p. 372), but he does not directly address mass scaling relative to area scaling. Masters also cites data from the Canadian Ministry of Natural Resources that estimates the annual operating and maintenance costs (~$2m) of a 60 MW windfarm at 3% of the capital costs (~$60m).
Let me add here (because I can hear fellow wind energy enthusiast Keith gnashing his teeth over TCP/IP) that if I had the data, I would prefer to see wind turbine values expressed as $/(kWh/year), rather than $/kW, where the kW rating calculated can be achieved at some high windspeed found only in Stillwater, Minnesota.
December 17th, 2006 at 4:23 pm
Thanks. At last a sense of reasonability in the never ending climb to develop the highest, most massive, most expensive, and in the most idiotic pursuit of the biggest wind turbine in pursuit of the biggest bucks.
Keep up the great work guys. Jack
December 17th, 2006 at 9:16 pm
Hi Jack,
I won’t speak for Ben, but I’m definitely baffled by the continued growth of wind turbines. I suspect that the historically decreasing costs as a function of size are actually an artifact of the maturation of the technology, and with that maturation I expect that smaller wind turbines will gain the advantage over the larger.
Ben and I have also been debating the role of two other factors– transportation and siting.
At some point, transporting towers and blades becomes difficult, with the gating threshold being whether they can fit under freeway overpasses.
In regard to siting, fewer, larger turbines may be easier from both a management complexity perspective and from a political standpoint
Ben also pointed out that in situations in which you are siting turbines linearly along a ridgeline, your potential swept area scales approximately linearly with rotor diameter, i.e. with you’ll get the length of your ridgeline with small or large blades, but the highest winds are accessible only by the largest towers. If suitable sites are scarce, higher quantities of power, expensive though it be, might be the optimal choice.
Brandon
February 2nd, 2007 at 1:52 am
Hi All,
There is one point that is missing in the original Aldo da Rosa argument - Brandon already touches on this but it is crucial I think - that is the importance of wind shear.
Wind velocity nearly always increases significantly the further away from the ground you go. And so large turbines see more wind than small ones. Since energy increases to the cubic of wind velocity, this surely has a big impact on the economics.
I myself like the small turbines but you have to admit their shortcomings.
Paul