Terawatts of Windpower, Global Calming, and a New Role for Meteorologists

Presented May 1, 2008: Here is the abstract.

Total Available Solar and Wind Power

EnergyCubes_sm.png

The above figure is from the Wikipedia, but with an additional annotation indicating the flux density derived using the total surface area of the Earth, 5.1 x 1014 m2.

Most of us could easily calculate the numbers for solar power using knowledge of the solar constant and the fraction of solar radiation reaching the surface. Deriving the number for available wind power might require more effort. Before we attempt such a derivation, notice that global consumption is 4% of the available wind power. This fact alone implies that powering a large portion of human energy needs with wind power could alter weather and climate, and not just within certain regions near where the extraction is occurring.

Derivation of Available Wind Power

Here is a simple way to estimate wind power availability:

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A Very Large Wind Turbine

Here is an image of a 5 MW wind turbine being erected. The rotor diameter is 2R=126 meters.

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Imagine a tube of air of radius R approaching the turbine. The rate of kinetic energy moving through the tube is ½ π R2 ρ V3. A wind turbine can capture up to 40% of this kinetic energy, at the ideal windspeed for which it was designed. This amount of power defines the capacity or nameplate of the wind turbine. In operation, windspeed is not ideal all the time, so production is typically about 30% of capacity.

This 5 MW example turbine will produce at capacity in 12.5 m/s windspeed (using ρ=1 kg m-3). In practice, it will produce about 1.66 MW. When operating at peak capacity, this wind turbine will be removing 388 W m-2 from the disc intercepted by the blades. Coincidently, the most efficient (and expensive) photovoltaics can also extract power at a similar flux density of 400 W m-2. But despite all the structural mass and strength of a wind turbine, wind power is cheaper than photovoltaic power.

A Very Large Wind Array

Imagine a slightly smaller turbine with 3 MW capacity and 1 MW production. Suppose we construct an array with spacing of 1 km. That allows for 1 W m-2 extraction from the wind. (A denser array would decrease the windspeed too much; the investment in more wire and access roads to produce 1 km spacing is worthy). Suppose we want to produce 16 TW. We need 16 million wind turbines, and an array 4000 km by 4000 km.

A Very Large Wind Hole

The atmosphere has a column mass density close to 104 kg m-2. Using the typical windspeed of U=10 m s-1, the column kinetic energy density is 5.0 x 105 J m-2. In 105 seconds, or just over one day, 1.6 x 1018 Joules would be extracted from the atmosphere if the extraction rate is 16 TW. That is equivalent to extracting all the wind, in the entire depth of atmosphere, in an area 1800 km by 1800 km - every day.

Resource needs

steel

Company documents for the Vestas V90-3.0 MW cite a combined weight of 256 tons for the tower, nacelle and rotor. Most of this weight is steel, and more steel will be needed for the foundation. Let's work with an easy number of 0.1 kg of steel per Watt of generation capacity, and also assume a 25 year lifetime for the wind turbine and tower. To produce 16 TW we need 50 TW capacity in operation, and about 2 TW of capacity demolished, recycled and installed every year. We therefore need 2x1011 kg of steel per year. Current annual global steel production is 8x1011 kg (requiring .5 TW for production). Thus we anticipate needing 1/4 of the world steel production, and at least .125 TW to produce that steel, to sustain 16 TW of wind power production.

As an American you will need about 30 kW capacity to supply your total power needs of 10 kW. That works out to be 3000 kg of steel comitted in wind turbines, on your behalf. This weight is equivalent to that of the Hummer automobile.

copper

Life cycle assessment of a wind turbine devulges that the Vestas V90-3.0 MW has as 8.5 ton generator, of which 35% is copper. This gives a number very close to 1 gram of copper per Watt of generating capacity (from the generator alone). 50 TW of wind power capacity requires 50 Tg of copper just for generators. Metal stocks and sustainability states that the USGS estimates total recoverable copper on Earth to be 1000 Tg. (400 Tg has been mined so far, and presumably most is in use). So 5% of all the world's copper, currently in use and potentially mined, is needed just for the generator component. (Yes, we do have a copper supply problem looming: peak copper).

money

According to Table B-11 in "20% Wind Energy by 2030" (US), in 2010 the capital cost for a shallow offshore installation in class 5 winds would be $2,300 per kW capacity. The capacity factor is stated to be .45 (too good to be true?). So the cost is $5,100 per kW of production. An American's total energy needs are 10 kW or 88 MWh per year. A turbine typically lasts 25 years. So an American can purchase their entire energy needs, both direct and indirect for $51,000 capital investment, every 25 years. Or, if your are paying 7.5% interest on the investment, you would be paying $3825 per year on interest. Table B-11 also implies fixed O&M costs of $333 and variable O&M costs of $1494, for a total of $5652. This implies a cost $0.064 per kWh. This is slightly lower than the $0.080 per kWh on a typical electric bill.

So the calculation here is consistent with the statement that wind energy is competitive with the cheapest source of electricity: coal power. The $5652 per year implies you are using wind generated electricity to heat your home, which is not cost-effective. You would probably rather use solar thermal energy for that purpose. But keep in mind your $5652 buys all your energy needs, both direct and indirect. Examples of indirect energy use are: mining and food production done for you, the energy needed for your steel and concrete production and transport, and so on. Though $5652 is lot of money, keep in mind that you currently pay a lot for indirect energy costs in all your purchases.

Projections for Wind Power 2020-2050

These projections are more modest than the 16 TW examples above. Keep in mind that, in generating electricity, fossil fuel energy consumption is 2 to 3 times the electrical energy production (the rest of the energy being lost as waste heat). So, coincidently, the fossil fuel offset provided by wind energy is close to the capacity of the wind turbine.

The following figure shows various production projections; capacity would need to be about 3 times as large:

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Environmental Impacts of Wind Farms

Traditional Environmental Impact Concerns

Not everybody thinks wind farms are desirable (and for some very good reasons):

Weather impacts of a simulated 10 GW wind farm within Oklahoma

Somnath Baidya Roy, Steve Pacala and Robert L. Walko (2004) Can Large Windfarms Affect Local Meteorology? J. Geophys. Res.-Atmos. VOL. 109, D19101.

This article emphasizes the effects within the wind farm itself.

Climate impacts of 10 TW of wind farms in a GCM

David W. Keith, Joseph F. DeCarolis, David C. Denkenberger, Donald H. Lenschow, Sergey L. Malyshev, Stephan Pacala and Phillip J. Rasch (2004):The influence of large-scale wind-power on global climate. Proceedings of the National Academy of Sciences, 101, p. 16115-16120.

Simulations with WRF

Three years after this page was constructed, at last, with help from my colleagues, we have completed our Windfarm Precip Project.