The Azimuth Project
Wind power



Wind can serve as a source of source of sustainable energy. According to the Renewables 2012 Global Status Report, global wind power capacity reached 238 gigawatts in 2011. Note however that ‘capacity’ is not equal to the average amount of power actually produced, since wind power is highly variable.

Wind power capacity is growing rapidly, as shown in the following chart taken from the Renewables 2010 Global Status Report. Over the five-year period from the end of 2004 to 2009, annual growth rates for cumulative wind power capacity averaged 27%. However, the percentage increase has been dropping since then. From 2009 to 2010 wind power capacity grew 25%, from 159 gigawatts to 198. From 2009 to 2011 it grew 20%, to 238 gigawatts.

  • REN21, [Renewables 2012 Global Status Report, page 17.]

  • REN21, Renewables 2010 Global Status Report, page 16.

Quoting the 2010 report:

China was the top installer in 2009, representing more than one-third of the world market. By comparison, China accounted for only about 2 percent of the market in 2004, when annual global installations were just over 8 GW. China’s installed wind power capacity reached nearly three times the country’s installed nuclear capacity in 2009, with just over 13.8 GW added to reach a total of 25.8 GW. This means that China doubled its existing wind power capacity for the fifth year running in 2009.

The United States added just over 10 GW of wind power capacity in 2009, enabling it to maintain its lead in existing capacity with a total of 35 GW. As of the end of 2009, 14 U.S. states had more than 1 GW each of installed capacity. Texas remained the leader with nearly 10 GW of cumulative capacity, enabling the state to reach its 2025 renewable energy target 15 years early.

Germany continued to lead in Europe in existing capacity, adding 1.9 GW and ending the year slightly behind China with a total installed capacity just under 25.8 GW. But Spain topped the European market for new installations, adding 2.5 GW. Other major European players included Italy, France, and the United Kingdom, all installing more than 1 GW each. India added 1.3 GW to maintain its fifth place position for existing capacity.

Canada experienced a record year, adding 950 megawatts (MW), and for the first time all provinces (although not all territories) were generating electricity from wind.

Wind farms

Wind power is often produced in large plants known as wind farms. For more details turn to this page:

The mathematics of wind

Wind power per square metre of of rotor swept area is proportional to the cube of the wind speed. So a doubling of wind speed results in eight times as much power. The map below shows the wind power density at 80 metres above sea level, per square metre of rotor swept area for UK offshore waters. (Adapted from UK government PDF file.)

Map of UK offshore wind power density

Conference talk by Julie Lundquist

Julie Lundquist gave an interesting talk on the mathematics of wind power at this conference:

Here is a summary of some points in her talk:

With increased reliance on wind, the power grid will need to be redesigned to handle fluctuating power sources. In the US, currently, companies aren’t paid for power they generate in excess of the amount they promised to make. So, accurate prediction is a hugely important game. Being off by 1% can cost millions of dollars! Europe has different laws, which encourage firms to maximize the amount of wind power they generate.

If you had your choice about where to build a wind turbine, you’d build it on the ocean or a very flat plain, where the air flows rather smoothly. Hilly terrain leads to annoying turbulence - but sometimes that’s your only choice. Then you need to find the best spots, where the turbulence is least bad. Complete simulation of the Navier-Stokes equations is too computationally intensive, so people use fancier tricks. There’s a lot of math and physics here.

For weather reports people use “mesoscale simulation” which cleverly treats smaller-scale features in an averaged way - but we need more fine-grained simulations to see how much wind a turbine will get. This is where “large eddy simulation” comes in.

A famous Brookhaven study suggested that the power spectrum of wind has peaks at 4 days, 1/2 day, and 1 minute. This perhaps justifies an approach where different time scales, and thus length scales, are treated separately and the results then combined somehow. The study is actually a bit controversial. But anyway, this is the approach people are taking, and it seems to work.

Night air is stable — but day air is often not, since the ground is hot, and hot air rises. So when a parcel of air moving along hits a hill, it can just shoot upwards, and not come back down! This means lots of turbulence.

The wind turbines at Altamont Pass in California kill more raptors than all other wind farms in the world combined! Old-fashioned wind turbines look like nice places to perch, spelling death to birds. Cracks in concrete attract rodents, which attract raptors, who get killed. The new ones are far better.

For more, see:


from Wikipedia:

Betz’s law is a rule of thumb about the maximum possible energy to be derived from a “hydraulic wind engine”, or a wind turbine such as the Éolienne Bollée (patented in 1868), the Eclipse Windmill (developed in 1867), and the Aermotor (first appeared in 1888 to pump water for cattle, and is still in production). Decades before the advent of the modern 3-blade wind turbine that generates electricity, Betz’s law was developed in 1919 by the German physicist Albert Betz. According to Betz’s law, no turbine can capture more than 59.3 percent of the kinetic energy in wind. The ideal or maximum theoretical efficiency n max (also called power coefficient) of a wind turbine is the ratio of maximum power obtained from the wind to the total power available in the wind. The factor 0.593 is known as Betz’s coefficient (from the name of the man who first derived it). It is the maximum fraction of the power in a wind stream that can be extracted.

Wind power and the electrical grid

Since wind power is highly variable, it can create greater challenges for the electrical grid. There is a lot of controversy about this, with proponents of nuclear power arguing that the role of wind is inherently limited by this fact, while proponents of wind arguing the other side. The following article relates to onshore wind-power in the mid-western United States.

Here is the abstract:

Wind is the world’s fastest growing electric energy source. Because it is intermittent, though, wind is not used to supply base-load electric power today. Interconnecting wind farms through the transmission grid is a simple and effective way of reducing deliverable wind power swings caused by wind intermittency. As more farms are interconnected in an array, wind speed correlation among sites decreases and so does the probability that all sites experience the same wind regime at the same time. The array consequently behaves more and more similarly to a single farm with steady wind speed and thus steady deliverable wind power. In this study, benefits of interconnecting wind farms were evaluated for 19 sites, located in the midwestern United States, with annual average wind speeds at 80 m above ground, the hub height of modern wind turbines, greater than 6.9 m s1 (class 3 or greater). It was found that an average of 33% and a maximum of 47% of yearly averaged wind power from interconnected farms can be used as reliable, baseload electric power. Equally significant, interconnecting multiple wind farms to a common point and then connecting that point to a far-away city can allow the long-distance portion of transmission capacity to be reduced, for example, by 20% with only a 1.6% loss of energy. Although most parameters, such as intermittency, improved less than linearly as the number of interconnected sites increased, no saturation of the benefits was found. Thus, the benefits of interconnection continue to increase with more and more interconnected sites.

This article has been criticised by Bill Hannahan:

The (Archer and Jacobson) paper makes this claim; “It was found that an average of 33% and a maximum of 47% of yearly averaged wind power from interconnected farms can be used as reliable, baseload electric power.”

This claim is not supported by the analysis.

If wind is to be a major source of energy, most arrays will be on locations where conditions are not as good. The study should have used an average area, for its conclusion to be applicable to our energy problem.

The study looks at wind power supplying baseload, but the above statement is only applicable if wind power is currently designed and located to compete with baseload generators. Is this the case?

The authors have redefined reliability. First they use the term, “Firm capacity,” ( “Firm capacity” is the fraction of installed wind capacity that is online at the same probability as that of a coal-fired power plant ) and then when they write their conclusion it is “reliable”. Reliability and capacity factor are two separate and distinct parameters. Maintenance and refueling outages scheduled long in advance reduce a plants capacity factor, not its reliability. The report compares the scheduled down time of conventional power plants with the unscheduled unpredictable downtime of wind power.

The study states that coal was shut down to scheduled maintenance 6.5% of the year and unscheduled maintenance or forced outages 6% of the year. Is it reasonable to compare unscheduled maintenance and forced outages that are by their nature unpredictable to declines in wind farm output that can be somewhat predictable through short term forecasting?

Treating a large array of wind farms as if they are a single fossil plant, or even as an array of independent fossil plants, is not realistic. The possibility of common mode failure due to widespread meteorological conditions resulting in a large drop in generation dramatically increases the spinning reserve required to assure grid reliability.

Intermittent sources like wind and solar can contribute energy to the grid but they do not contribute stability or reliability, in fact they suck up the stability provided by conventional power plants, reducing grid stability and reliability. For this reason it is misleading to say that wind and solar can replace any fraction of baseload power plants.

One of the biggest drawbacks of wind power is the daily and seasonal variation in power output. Wind power is very low in the summer when electrical demand peaks, and high during spring and fall when demand is lowest.

Is electrical demand always highest in the summer, or does this depend on region? With respect to this critique, what areas have wind resources that increase and decrease with seasonal demand and what areas don’t have wind resources with this characteristic?

It should also be noted that this only becomes a problem when the wind power share of the total production is more than 10–20% - See T Wizelius in the references).

A moderate share of wind power in a system does not need any backup capacity at all, since it already exists in the system.

He gives an example of how it works in Sweden, where the power operator could use saved hydro power. For He further addresses seasonal and diurnal variations:

In a power system power consumption varies continually during each day as well as during seasons. Every power system has a regulating capacity? to adapt production to actual consumption. This can be used to adapt the system to variations in the wind - and the output in the wind turbines as well.

When the wind power penetration increases to 10-20%, it maybe necessary to regulate the wind power as well, by reducing by reducing power from the wind turbines with situations with low load and high production, or by keeping a power reserve to be used to balance power production with consumption at short notice. Few countries have yet reached such penetration levels (2007).

So when we reach that wind power penetration it becomes relevant.In chapter 26 of his book Without the hot air David MacKay lists some options how to deal with the variable electrical power from wind farms.

The two issues are short-time changes in electric power (expressed by slew rates) and long-term lulls. The maximal slew rate for British wind power (scaled up to 10 GW average) could be about 4 GW/h. (btw, every morning, British demand climbs by 6,5 GW/h) Assuming a 5 day lull, 1200 GWh would have to be stored.

There are two solutions preferred by MacKay. The first solution is pumped storage. The second uses the batteries of the electric vehicles discussed by MacKay. The first solution is a centralized solution and stores up energy, then copes with fluctuations by turning on and off a source powered from the energy store. The second solution is decentralized and works by turning on and off a piece of demand.

MacKay discusses how many pumped-storage facilities would be needed to store 1200 Gwh with a capacity of 20 GW. Ideally, these facilities should be located close to the wind farms.

He proposes some ideas to cope with the slew rate of wind power: have on-off-turnable renewable energy power stations (waste incinerators and hydroelectric stations, for example), and varying demand (e.g. by charging batteries of electric vehicles cleverly, or by smart electric devices like fridges that react to signals of the grid).

For seasonal variations MacKay proposes thermal storage.

Wind power can also present challenges from too much electricity production that manifests itself as negative pricing, when generators end up paying grid operators to take the power they are generating because demand is lower than supply.

This can be remedied by better local transmission capacity, access to other markets (eg the WECC-west in the previous source), or an alternative economic use for the excess wind power like the creation of hydrogen to power generators when demand is higher, or the creation of anhydrous ammonia.

Capacity factor of wind power

The capacity factor of a wind power generator, or any generator, refers to the average generation compared to it’s nameplate rating, generally in the form of a decimal.



category: energy