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Wind energy is one of the most promising energy technologies for today, for the 21st century, and beyond.

WIND ENERGY IS CLEAN

Wind turbines emit no pollutants.
A modern 600 kW wind turbine in an average location will annually displace 1,200 tones of carbon dioxide from other electricity sources, i.e. usually coal fired power stations. The energy produced by a wind turbine throughout its 20 year life-time (in an average location) is eighty times larger than the amount of energy used to build, maintain, operate, dismantle, and scrapping it again. In other words, on average it takes only two to three months for a wind turbine to recover all the energy required to build and operate it.

WIND ENERGY IS ABUNDANT

The energy in the wind is a truly sustainable resource. Wind will not run out.

Already, wind energy is covering 7 per cent of Danish electricity consumption, a figure that will increase to at least 10 per cent by 2005.
The wind resources above the shallow waters in the seas around Europe could theoretically provide all of Europe’s electricity supplies several times over.

WIND ENERGY MAKES A DIFFERENCE

Wind Turbines have grown dramatically in size and power output.

A typical Danish wind turbine of 1980 vintage had a 26 kW generator and a rotor diameter of 10.5metres. A modern wind turbine has a rotor diameter of 43 meters and a 600 kW generator. It will produce between 1 and 2 million kilowatt hours in a year. This is equivalent to the annual electricity consumption of 300 to 500 European households. The latest generation of wind turbines has a 1,000-1,500 kW generator and a 50-64 meter rotor diameter.

Europe’s largest wind park in Carno, Wales produces the equivalent of the electricity consumption of 20,000 homes. In Europe more than 3,000 megawatts of wind power is on-line as of 1997, covering the aver-age domestic electricity consumption of five million people.

WIND ENERGY IS INEXPENSIVE

Wind energy has become the least expensive renewable energy technology in existence.

Today, according to the Danish electrical power companies, the energy cost per kilowatthour of electricity from wind is the same as for new goal fired power stations fitted with smoke scrubbing equipment, i.e. around 0.05 USD per kWh for an average European site.

WIND ENERGY IS SAFE

Wind energy leaves no harmful emissions or residue in the environment. Wind Energy has a proven safety record. Fatal accidents in the wind industry have been related to construction and maintenance work only.

WIND PROJECTS MINIMIZE ECOLOGICAL IMPACT

Manufacturers and wind farm developers have by now substantial experience in minimizing the ecological impact of construction work in sensitive areas such as moors, or when building wind farms in offshore locations. Restoring the surrounding landscape to its original state after construction has become a routine task for developers. After the useful life of a wind farm has elapsed, foundations can be reused or removed completely. The scrap value of a wind turbine can normally cover the costs of restoring its site to its initial state. of the year.

WIND TURBINES WHISPER QUIETLY, NOW

Noise is no longer a major problem with advanced wind turbine technology. Modern turbines have far better aerodynamic and mechanical engineering than designs from 10 or 15 years ago, and two-speed generators with slow moving rotors at low wind speeds have done away with the problem of noise at low wind speeds.

At distances above 200 meters, the swishing sound of rotor blades is usually masked completely by wind noise in the leaves of trees or shrubs. The perception of noise is interestingly an extremely subjective phenomenon, and it depends to a large extent on the attitude of the listener:

A Danish scientific survey shows that people who find the sight of wind turbines unpleasant, also perceive that turbines are noisy, regardless of the actual sound level.

WIND ENERGY FITS WELL INTO THE ELECTRICAL GRID

The major drawback of wind power is variability.

In large electrical grids, however, consumers’ demand also varies, and electricity generating companies have to keep spare capacity running idle in case a major generating unit breaks down.

If a power company can handle varying consumer demand, it can technically also handle the »negative consumption« from wind turbines. The more wind turbines on the grid, the more short-term fluctuations from one turbine will cancel out the fluctuations from another.

In the Western part of Den-mark, more than 25 per cent of the electricity supply today comes from wind during windy winter nights.

WIND ENERGY IS A SCALEABLE TECHNOLOGY

Wind energy can be used in all sorts of applications -; from small battery chargers in lighthouses or remote dwellings to industrial scale turbines capable of supplying the equivalent of the electricity consumption of one thousand families.

Other interesting and highly economic applications include wind energy combination used in with diesel powered backup generators in several small, isolated electrical grids throughout the world. Desalination plants in island communities in the Atlantic and the Mediterranean Sea are another recent application.

1. History of windturbines

1.1 The Wind Energy Pioneer -;

Poul la Cour

Poul la Cour (1846-1908) who was originally trained as a meteorologist was the pioneer of modern electricity generating wind turbines.
La Cour was one of the pioneers of modern aerodynamics, and built his own wind tunnel for experiments. La Cour was concerned with the storage of energy, and used the electricity from his wind turbines for electrolysis in order to produce hydrogen for the gas light in his school. One basic drawback of this scheme was the fact that he had to replace the windows of several school buildings several times, as the hydrogen exploded due to small amounts of oxygen in the hydrogen

Two of his test wind turbines in 1897 at Askov Folk High School, Askov, Denmark

Charles F. Brush

Charles F. Brush (1849-1929) is one of the founders of the American electrical industry.

He invented e.g. a very efficient DC dynamo used in the public electrical grid, the first commercial electrical arc light, and an efficient method for manufacturing lead-acid batteries. His company, Brush Electric in Cleveland, Ohio, was sold in 1889 and in 1892 it was merged with Edison General Electric Company under the name General Electric Company (GE).

The Giant Brush Windmill in Cleveland, Ohio

During the winter of 1887-88 Brush built what is today believed to be the first automatically operating wind turbine for electricity generation. It was a giant - the World's largest - with a rotor diameter of 17 m (50 ft.) and 144 rotor blades made of cedar wood.. The turbine ran for 20 years and charged the batteries in the cellar of his mansion.

Despite the size of the turbine, the generator was only a 12 kW model. This is due to the fact that slowly rotating wind turbines of the American wind rose type do not have a particularly high average efficiency. Brush windmill is particularly noted for its fully automated electrical control system.

Its principles using solenoids does not change very much with future generations of wind turbines - until about 1980 when the wind turbine controllers become equipped with computers.

1.2. The Wind Energy Pioneers - 1940-1950

The F.L. Smidth Turbines

During World War II the Danish engineering company F.L. Smidth built a number of two- and three-bladed wind turbines.

Danish wind turbine manufacturers have actually made two-bladed wind turbines, although the so-called "Danish concept" is a three bladed machine. All of these machines (like their predecessors) generated DC (direct current)

Three-bladed F.L. Smidth machine from the island of Bogø, built in 1942, looks more like a "Danish" machine, was part of a wind-diesel system which ran the electricity supply on the island. This machine played an important role in the 1950s wind energy study programme in Denmark. In 1951 the DC generator was replaced with a 35 kW asynchronous AC (alternating current) generator, thus becoming the second wind turbine to generate AC

The Gedser Wind Turbine

The innovative 200 kW Gedser wind turbine was built in 1956-57 by J. Juul for the electricity company SEAS at Gedser coast in the Southern part of Denmark.

The three-bladed upwind turbine with electromechanical yawing and an asynchronous generator was a pioneering design for modern wind turbines, although its rotor with guy wires looks a bit old fashioned today.

The turbine was stall controlled , and J. Juul invented the emergency aerodynamic tip brakes which were released by the centrifugal force in case of over speed. Basically the same system is used today on modern stall controlled turbines.

The turbine, which for many years was the world's largest, was incredibly durable. It ran for 11 years without maintenance.

The Nibe Turbines

After the first oil crisis in 1973, interest in wind energy rekindled in several countries. In Denmark, the power companies immediately aimed at making large turbines, just like their counterparts in Germany, Sweden, the UK, and the USA.

In 1979 they built two 630 kW wind turbines, one pitch controlled, and one stall controlled. In many ways they suffered the same fate as their even larger colleagues abroad: The turbines became extremely expensive, and the high energy price subsequently became a key argument against wind energy.

The Riisager Turbine

A carpenter, Christian Riisager, however, built a small 22 kW wind turbine in his own back yard using the Gedser Wind Turbine design as a point of departure.

He used inexpensive standard components (e.g. an electric motor as generator, and car parts for gear and mechanical brake) wherever possible.

Riisager's turbine became a success with many private households around Denmark, and his success gave the present day Danish wind turbine manufacturers their inspiration to start designing their own wind turbines from around 1980

The Tvind 2 MW Machine

One important exception to the rule of small machines was the Tvind 2 MW machine, a fairly revolutionary machine. The machine is a downwind machine with 54 m rotor diameter running at variable speed with a synchronous generator, and indirect grid connection using power electronics. The machine is still running nicely.

Bonus 30 kW

The Bonus 30 kW machine manufactured from 1980 is an example of one of the early models from present day manufacturers

Nordtank 55 kW

The 55 kW generation of wind turbines, which were developed in-1980 - 1981, became the industrial and technological breakthrough for modern wind turbines.

The cost per kilowatt-hour (kWh) of electricity dropped by about 50 per cent with the appearance of this generation of wind turbines. The wind industry became much more professionalism, and the parallel development of the European Wind Atlas Method by Risoe National Laboratory was extremely important in lowering kWh costs.

The Micon 55 kW

Thousands of machines were delivered to the wind programme in California in the early eighties. The Micon 55 kW is one example, delivered to one huge park of more than 1000 machines in Palm Springs, California.

Having started series manufacturing of wind turbines about 5 years earlier, Danish manufacturers had much more of a track record than companies from other countries. About half of the wind turbines placed in California are of Danish origin.

The market for wind energy in the United States disappeared overnight with the disappearance of the Californian support schemes around 1985. Since then, only a tiny trickle of new installations has been commissioned, although the market seems to have been picking up, lately. Germany is now the world's main market, and the country with the largest wind power installation.

1.3 Offshore Wind Turbines

Vindeby

The Vindeby windfarm in the Baltic Sea off the coast of Denmark was built in 1991 by the utility company SEAS.

The wind farm consists of 11 Bonus 450 kW stall controlled wind turbines, and is located between 1.5 and 3 kilometers North of the coast of the island of Lolland near the village of Vindeby.

The turbines were modified to allow room for high voltage transformers inside the turbine towers, and entrance doors are located at a higher level than normally. These same modifications were carried over to the subsequent Tunø Knob project.

Two anemometer masts were placed at the site to study wind conditions, and turbulence, in particular. A number of interesting results on offshore wind conditions have been obtained through these studies which were carried out by Risø National Laboratory

The park has been performing flawlessly. Electricity production is about 20 per cent higher than on comparable land sites, although production is somewhat diminished by the wind shade from the island of Lolland to the South.

Tunø Knob

The Tunø Knob offshore wind farm in the Kattegat Sea off the Coast of Denmark was built in 1995 by the utility company Midtkraft. The construction work with a floating crane. The Wind farm consists of 10 Vestas 500 kW pitch controlled wind turbines.

The turbines were modified for the marine environment, each turbine being equipped with an electrical crane to be able to replace major parts such as generators without the need for a floating crane. In addition, the gearboxes were modified to allow a 10 per cent higher rotational speed than on the onshore version of the turbine. This will give an additional electricity production of some 5 per cent. This modification could be carried out because noise emissions are not a concern with a wind park located 3 kilometers offshore from the island of Tunø, and 6 kilometers off the coast of the mainland Jutland peninsula.

The park has been performing extremely well, and production results have been substantially higher than expected, cf. the page on offshore wind conditions.

The Future of Offshore Wind Energy

Offshore wind energy is an extremely promising application of wind power, particularly in countries with high population density, and thus difficulties in finding suitable sites on land. Construction costs are much higher at sea, but energy production is also much higher

The Danish electricity companies have announced major plans for installation of up to 4 000 megawatts of wind energy offshore in the years after the year 2000. The 4 000 MW of wind power is expected to produce some 13.5 TWh of electricity per year, equivalent to 40 per cent of Danish electricity consumption.

1.4 Megawatt-Sized Wind Turbines

Nordtank 1500

The prototype of the NEG Micon 1500 kW Turbine (35K JPEG) was commissioned in September 1995. The original model had a 60 metre rotor diameter and two 750 kW generators operating in parallel.

The most recent version is a 1,500/750 kW model (with two 750 kW generators) with a 64 metre rotor diameter.

Vestas 1.5 MW

The prototype of the Vestas 1500 kW Turbine) was commissioned in 1996. The original model had a 63 metre rotor diameter and a 1,500 kW generator. The most recent version has a 68 metre rotor diameter and a dual 1650/300 kW generator.

The Future for Megawatt-Sized Turbines

600 and 750 kW machines continue to be the "working horses" of the industry at present, but the megawatt-market took off in 1998.

Megawatt-sized machines will be ideal for offshore applications, and for areas where space for siting is scarce, so that a megawatt machine will exploit the local wind resources better.

1.5 Multi-Megawatt Wind Turbines

NEG Micon 2 MW

The prototype of the NEG Micon 2 MW turbine (1024 x 768 pixels, 132K JPEG) was commissioned in August 1999. It has a 72 m (236 ft.) rotor diameter. In this case it is mounted on a 68-m tower. The turbine is intended for offshore applications.
The difference to 1500 kW NEG Micon machine: The rotor blades are pitchable, since the machine has active stall power control, whereas its 1500 kW cousin has passive stall power control.

Bonus 2 MW

The prototype of the Bonus 2 MW turbine (88 K) was commissioned in the fall of 1998. It has a 72 m (236 ft.) rotor diameter. The turbine is intended for offshore applications, and has Combi Stall® power control (Bonus trademark for active stall power control). The machine resembles the Bonus 1 MW and 1.3 MW machines considerably.

Nordex 2,5 MW

The prototype of the Nordex 2,5 MW turbine (132 K) was commissioned in the spring of 2000. The rotor diameter of the wind turbine is 80 m. which has a 80 m tower. The turbine has pitch power control

2. Wind Energy Resources

2.1 Where does Wind Energy come From?

All renewable energy (except tidal and geothermal power), and even the energy in fossil fuels, ultimately comes from the sun. The sun radiates 174,423,000,000,000-kilowatt hours of energy to the earth per hour. In other words, the earth receives 1.74 x 1017 watts of power.
The power emission from the sun is 1.37 kW/m2 on the surface of the sphere, which has the sun as its centre and the average radius of the earth trajectory. The power hits a circular disc with an area of of 1.27 x 1014 m2. The power emitted to the earth is thus 1.74 x 1017W
About 1 to 2 per cent of the energy coming from the sun is converted into wind energy. That is about 50 to 100 times more than the energy converted into biomass by all plants on earth.
On average, plant net primary production is about 4.95 x 106 calories per square metre per year. This is global NPP, Global net primary production, i.e. the amount of energy available to all subsequent links in the food/energy chain. The earth's surface area is 5.09 x 1014 m2. The net power output stored by plants is thus 1.91 x 1013W, or 0.011% of the power emitted to earth.

2.2 Temperature Differences Drive Air Circulation

The regions around equator, at 0° latitude are heated more by the sun than the rest of the globe. These hot areas are indicated in the warm colours, red, orange and yellow in this infrared picture of sea surface temperatures (taken from a NASA satellite, NOAA-7 in July 1984).
Hot air is lighter than cold air and will rise into the sky until it reaches approximately 10-km (6 miles) altitude and will spread to the North and the South. If the globe did not rotate, the air would simply arrive at the North Pole and the South Pole, sink down, and return to the equator.

2.3 The Coriolis Force

Since the globe is rotating, any movement on the Northern hemisphere is diverted to the right, if we look at it from our own position on the ground. (In the southern hemisphere it is bent to the left). This apparent bending force is known as the Coriolis force. (Named after the French mathematician Gustave Gaspard Coriolis 1792-1843).
The Coriolis force to an object's mass (m), its velocity in a rotating frame (vr) and the angular velocity of the rotating frame of reference :

FCoriolis = -2 m (w x vr)

The Coriolis force is a visible phenomenon. Railroad tracks wear out faster on one side than the other. River beds are dug deeper on one side than the other. (Which side depends on which hemisphere we are in: In the Northern hemisphere moving particles are bent towards the right).

In the Northern hemisphere the wind tends to rotate counterclockwise (as seen from above) as it approaches a low pressure area. In the Southern hemisphere the wind rotates clockwise around low pressure areas.

2.3.1 How the Coriolis Force Affects Global Winds

The wind rises from the equator and moves north and south in the higher layers of the atmosphere. Around 30° latitude in both hemispheres the Coriolis force prevents the air from moving much farther. At this latitude there is a high pressure area, as the air begins sinking down again. As the wind rises from the equator there will be a low pressure area close to ground level attracting winds from the North and South. At the Poles, there will be high pressure due to the cooling of the air. Keeping in mind the bending force of the Coriolis force, we thus have the following general results for the prevailing wind direction:

Prevailing Wind Directions

Latitude 90-60°N 60-30°N 30-0°N 0-30°S 30-60°S 60-90°S
Direction NE SW NE SE NW SE

The size of the atmosphere is grossly exaggerated in the picture above (which was made on a photograph from the NASA GOES-8 satellite). In reality the atmosphere is only 10 km thick, i.e. 1/1200 of the diameter of the globe. That part of the atmosphere is more accurately known as the troposphere. This is where all of our weather (and the greenhouse effect) occurs.

The prevailing wind directions are important when siting wind turbines, since we obviously want to place them in the areas with least obstacles from the prevailing wind directions. Local geography, however, may influence the general results in the table above, cf. the following pages.

2.4 Wind

2.4.1 The Atmosphere (Troposphere)

The atmosphere around the globe is a very thin layer. The globe has a diameter of 12,000 km. The troposphere, which extends to about 11 km (36,000 ft.) altitude, is where all of our weather, and the greenhouse effect occurs. On the picture you can see at stretch of islands 300 km (200 miles) across, and the approximate height of the troposphere. To look at it at a different scale: If the globe were a ball with a diameter of 1.2 metres (4 ft.), the atmosphere would only be 1 mm (1/25") thick

2.4.2 The Geostrophic Wind

The winds we have been considering on the previous pages on global winds are actually the geostrophic winds. The geostrophic winds are largely driven by temperature differences, and thus pressure differences, and are not very much influenced by the surface of the earth. The geostrophic wind is found at altitudes above 1000 metres (3300 ft.) above ground level. The geostrophic wind speed may be measured using weather balloons

2.4.3 Surface Winds

Winds are very much influenced by the ground surface at altitudes up to 100 metres. The wind will be slowed down by the earth's surface roughness and obstacles, as we will learn in a moment. Wind directions near the surface will be slightly different from the direction of the geostrophic wind because of the earth's rotation (cf. the Coriolis force). When dealing with wind energy, we are concerned with surface winds, and how to calculate the usable energy content of the wind.

2.4.4 Local Winds: Sea Breezes

Although global winds are important in determining the prevailing winds in a given area, local climatic conditions may wield an influence on the most common wind directions. Local winds are always superimposed upon the larger scale wind systems, i.e. the wind direction is influenced by the sum of global and local effects. When larger scale winds are light, local winds may dominate the wind patterns

Land masses are heated by the sun more quickly than the sea in the daytime. The air rises, flows out to the sea, and creates a low pressure at ground level which attracts the cool air from the sea. This is called a sea breeze. At nightfall there is often a period of calm when land and sea temperatures are equal. At night the wind blows in the opposite direction. The land breeze at night generally has lower wind speeds, because the temperature difference between land and sea is smaller at night.

The monsoon known from South-East Asia is in reality a large-scale form of the sea breeze and land breeze, varying in its direction between seasons, because land masses are heated or cooled more quickly than the sea.

2.4.5 Local Winds: Mountin Winds

Mountain regions display many interesting weather patterns.

One example is the valley wind which originates on south-facing slopes (north-facing in the southern hemisphere). When the slopes and the neighbouring air are heated the density of the air decreases, and the air ascends towards the top following the surface of the slope. At night the wind direction is reversed, and turns into a downslope wind. If the valley floor is sloped, the air may move down or up the valley, as a canyon wind. Winds flowing down the leeward sides of mountains can be quite powerful: Examples are the Foehn in the Alps in Europe, the Chinook in the Rocky Mountains, and the Zonda in the Andes.

3. The Energy in the Wind: Air Density and Rotor Area

3.1 Density of Air
The kinetic energy of a moving body is proportional to its mass (or weight).

The kinetic energy in the wind thus depends on the density of the air, i.e. its mass per unit of volume. In other words, the "heavier" the air, the more energy is received by the turbine.
At normal atmospheric pressure and at 15° Celsius air weighs some 1.225 kilogrammes per cubic metre, but the density decreases slightly with increasing humidity. Also, the air is denser when it is cold than when it is warm. At high altitudes, (in mountains) the air pressure is lower, and the air is less dense.
The Ke kinetic energy of an object with total mass M and velocity V:
Ke = ½ *M*V
For determinating the Ke of wind we take a large air parcel this has the geometry of a collection of air molecules passing throught the plane of a wind turbine`s blades.
A- corss sectional area
D- thickness
T- time that is needed for the parcel to pass trough the plane of the wind energy turbine’s baldes
Vol- volume of the parcel
Vol = A*D
?- desity of air in this parcel
? = M/Vol
M =.?*Vol
V- velocity of the air parcel
T- time required for the parcel to move trought the plane of the wind turbine blades.
V = D/T
D = V*T
Ke = ½ *M*V2
Vol = A*D D = V*T M = ?*Vol

Ke = ½ *?*A*V*T*V2
Ke = ½ *?*V3*A*T

Pwr- .power from the air parcel

Pwr = Ke/T = (½ *?*V3*A*T)/T
= ½ *?*V3*A*

3.2 Rotor Area

A typical 600 kW wind turbine has a rotor diameter of 43-44 metres, i.e. a rotor area of some 1,500 square metres. The rotor area determines how much energy a wind turbine is able to harvest from the wind.

Since the rotor area increases with the square of the rotor diameter, a turbine which is twice as large will receive 22 = 2 x 2 = four times as much energy.

A wind turbine rotor converts part of the available wind power into mechanical power and then into electrical power according to:

where
Cp - is the power coefficient, l is the tip-speed ratio,
w s the wind speed, wr is the rotor speed, r s the rotor plane radius, r is the air density,
A is the area swept by the rotor and h(wr ) is the efficiency of the generator and gear-box.
Pmec is the mechanical power on the main shaft and
Pel is the electrical power.

The wind turbine rotor, gear-box and generator.

The mechanical power derived from the wind can be described, according to Eq. 1, as a function of the wind speed, w, or as a function of the rotor speed, wr, divided by the tip-speed ratio, l. The measured wind speed is not directly correlated to the mechanical power and therefore averaging procedures have to be used to find the correlation between them a9i.

The rotor efficiency curve, Cp(l), is a non-linear function of the tip-speed ratio, l. It is determined by the blade design and the pitch angle and it is sensitive to dirt etc. on the blade surface.

The efficiency of the generator and the gear-box, h(wr), is different for different rotor speeds. At 32 Rpm Eq. 4 becomes:

Pmec =Pel*1.12+1.5*1000 (5)

The output power does not only origin from the wind, there will also be an extra power contribution (power from the moment of inertia, Pi) from the system during a deceleration or acceleration of the rotor speed, wr, due to the change of rotational energy Wr, in the rotor.

where J is the rotor inertia, 12500 kgm 2 , Dt is the sample interval.

3.3 Wind Turbines Deflect the Wind

Wind turbine will deflect the wind, even before the wind reaches the rotor plane. This means that we will never be able to capture all of the energy in the wind using a wind turbine.

Wind Turbines are limited by what is called the Betz law. If you capture 100% of the energy available in the wind, you stop the wind. The wind will stop flowing through such a turbine. The opposite of that is that if you don't capture any energy in the wind, you don't need a turbine. The wind is able to flow around any major obstruction.
The Betz limit says that essentially, if you capture 59.6% of the energy in the wind, that is the best compromise between stopping the air and forcing it to go around your machine. You need to maintain the flow of air, that's the compromise any wind machine must make whether it is a horizontal axis (traditional style turbine) or vertical axis turbine, with many blades or few, or any such combination. It's covered by the Betz limit.
In the image we have the wind coming from the right, and we use a device to capture part of the kinetic energy in the wind. (In this case we use a three bladed rotor, but it could be some other mechanical device

3.3.1 The Stream Tube

The wind turbine rotor must obviously slow down the wind as it captures its kinetic energy and converts it into rotational energy. This means that the wind will be moving more slowly to the left of the rotor than to the right of the rotor.

Since the amount of air entering through the swept rotor area from the right (every second) must be the same as the amount of air leaving the rotor area to the left, the air will have to occupy a larger cross section (diameter) behind the rotor plane.

In the image above is shown an imaginary tube, a so called stream tube around the wind turbine rotor. The stream tube shows how the slow moving wind to the left in the picture will occupy a large volume behind the rotor.

The wind will not be slowed down to its final speed immediately behind the rotor plane. The slowdown will happen gradually behind the rotor, until the speed becomes almost constant.

As the wind approaches the rotor from the right, the air pressure increases gradually, since the rotor acts as a barrier to the wind. The air pressure will drop immediately behind the rotor plane (to the left). It then gradually increases to the normal air pressure level in the area.

Farther downstream the turbulence in the wind will cause the slow wind behind the rotor to mix with the faster moving wind from the surrounding area. The wind shade behind the rotor will therefore gradually diminish as we move away from the turbine. It is the so called park effect.

Why not a Cylindrical Stream Tube? The wind to the left of the rotor moves with a lower speed than the wind to the right of the rotor. But at the same time we know that the volume of air entering the tube from the right eachsecond must be the same as the volume of air leaving the tube to the left. We can therefore deduce that if we have some obstacle to the wind (in this case our rotor) within the tube, then some of the air coming from the right must be deflected from entering the tube (due to the high air pressure in the right ende of the tube).

3.4 The Power of the Wind: Cube of Wind Speed

The wind speed is extremely important for the amount of energy a wind turbine can convert to electricity:

The energy content of the wind varies with the cube (the third power) of the average wind speed, e.g. if the wind speed is twice as high it contains

23 = 2 x 2 x 2 = eight times as much energy.

The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object

Fnet = m * a

In the case of the wind turbine we use the energy from braking the wind, and if we double the wind speed, we get twice as many slices of wind moving through the rotor every second, and each of those slices contains four times as much energy, as we learned from the example of braking a car. The graph shows that at a wind speed of 8 metres per second we get a power (amount of energy per second) of 314 Watts per square metre exposed to the wind (the wind is coming from a direction perpendicular to the swept rotor area). At 16 m/s we get eight times as much power, i.e. 2509 W/m2.

3.4.1 Power of the Wind Formula

The power of the wind passing perpendicularly through a circular area is:
P= ½ *v3* *r2

Where

P = the power of the wind measured in W (Watt).

= (rho) = the density of dry air = 1.225 measured in kg/m3 (kilogrammes per cubic metre, at average atmospheric pressure at sea level at 15° C). v = the velocity of the wind measured in m/s (metres per second).

= (pi) = 3.1415926535... r = the radius (i.e. half the diameter) of the rotor measured in m (metres).

3.5 Wind Speed Measurement: Anemometers

The measurement of wind speeds is usually done using a cup anemometer, The cup anemometer has a vertical axis and three cups which capture the wind. The number of revolutions per minute is registered electronically. Normally, the anemometer is fitted with a wind vane to detect the wind direction. Instead of cups, anemometers may be fitted with propellers, although this is not common. Other anemometer types include ultrasonic or laser anemometers which detect the phase shifting of sound or coherent light reflected from the air molecules. Hot wire anemometers detect the wind speed through minute temperature differences between wires placed in the wind and in the wind shade (the lee side). The advantage of non-mechanical anemometers may be that they are less sensitive to icing. In practice, however, cup anemometers tend to be used everywhere, and special models with electrically heated shafts and cups may be used in arctic areas

Quality Anemometers are a Necessity for Wind Energy Measurement

For wind speed measurement in the wind energy industry quality of anemometers is very important. A poorly calibrated anemometer, with measurement errors of maybe 5 per cent or even 10 per cent.: if you have an anemometer which measures wind speeds with a 10% error, you may risk counting on an energy content of the wind which is 1.13 - 1 = 33% higher than than it is in reality. If you have to recalculate your measurements to a different wind turbine hub height (say, from 10 to 50 m height), you may even multiply that error with a factor of 1.3, thus you end up with a 75% error on your energy calculation.

The best way of measuring wind speeds at a prospective wind turbine site is to fit an anemometer to the top of a mast which has the same height as the expected hub height of the wind turbine to be used. This way one avoids the uncertainty involved in recalculating the wind speeds to a different height.

By fitting the anemometer to the top of the mast one minimises the disturbances of airflows from the mast itself. If anemometers are placed on the side of the mast it is essential to place them in the prevailing wind direction in order to minimise the wind shade from the tower.

4.1 Roughness and Wind Shear

High above ground level, at a height of about 1 kilometre, the wind is hardly influenced by the surface of the earth at all. In the lower layers of the atmosphere, however, wind speeds are affected by the friction against the surface of the earth. In the wind industry one distinguishes between the roughness of the terrain, the influence from obstacles, and the influence from the terrain contours, which is also called the orography of the area. We shall be dealing with orography, when we investigate so called speed up effects, i.e. tunnel effects and hill effects, later
Roughness
In general, the more pronounced the roughness of the earth's surface, the more the wind will be slowed down. Forests and large cities obviously slow the wind down considerably, while concrete runways in airports will only slow the wind down a little. Water surfaces are even smoother than concrete runways, and will have even less influence on the wind, while long grass and shrubs and bushes will slow the wind down considerably.
In the wind industry, people usually refer to roughness classes or roughness lengths, when they evaluate wind conditions in a landscape. A high roughness class of 3 to 4 refers to landscapes with many trees and buildings, while a sea surface is in roughness class 0.
Concrete runways in airports are in roughness class 0.5. The same applies to the flat, open landscape to the left which has been grazed by sheep.
The term roughness length is really the distance above ground level where the wind speed theoretically should be zero.
Wind Shear
Wind speeds vary in roughness class 2 (agricultural land with some houses and sheltering hedgerows with some 500 m intervals), if we assume that the wind is blowing at 10 m/s at a height of 100 metres. The fact that the wind profile is twisted towards a lower speed as we move closer to ground level, is usually called wind shear. Wind shear may also be important when designing wind turbines. If considered a wind turbine with a hub height of 40 metres and a rotor diameter of 40 metres, you will notice that the wind is blowing at 9.3 m/s when the tip of the blade is in its uppermost position, and only 7.7 m/s when the tip is in the bottom position. This means that the forces acting on the rotor blade when it is in its top position are far larger than when it is in its bottom position.

Wind Shear Formula

The wind speed at a certain height above ground level is: v = vref ln(z/z0) / ln(zref/z0) v = wind speed at height z above ground level. vref = reference speed, i.e. a wind speed we already know at height zref. ln(...) is the natural logarithm function. z = height above ground level for the desired velocity, v. z0 = roughness length in the current wind direction. Roughness lengths may be found in the Reference Manual. zref = reference height, i.e. the height where we know the exact wind speed vref.
The formula assumes so-called neutral atmospheric stability conditions, i.e. that the ground surface is neither heated nor cooled compared to the air temperature.
Average wind speeds are often available from meteorological observations measured at a height of 10 metres. Hub heights of modern 600 to 1,500 kW wind turbines are usually 40 to 80 metres, however. The spreadsheet will calculate average wind speeds at different heights and roughness classes. Just enter a wind speed measured at a certain height for a given roughness class and click the Submit button. Please note, that the results are not strictly valid if there are obstacles close to the wind turbine (or the point of meteorological measurement) at or above the specified hub height. a"close" means anything up to one kilometrei.

That there may be inverse wind shear on hilltops because of the hill effect, i.e. the wind speed may actually decline with increasing height during a certain height interval above the hilltop. You should consult the European Wind Atlas mentioned in the bibliography in the Reference Manual for further information on this phenomenon.

4.2 Wind Speed Variability

The wind speed is always fluctuating, and thus the energy content of the wind is always changing.
Exactly how large the variation is depends both on the weather and on local surface conditions and obstacles.

Energy output from a wind turbine will vary as the wind varies, although the most rapid variations will to some extent be compensated for by the inertia of the wind turbine rotor.

4.3 Turbulence

You have probably experienced how hailstorms or thunderstorms in particular, are associated with frequent gusts of wind which both change speed and direction.

In areas with a very uneven terrain surface, and behind obstacles such as buildings there is similarly created a lot of turbulence, with very irregular wind flows, often in whirls or vortexes in the neighbourhood. You can see an example of how turbulence increases the fluctuations in the wind speed in the image, which you may compare with the image on the previous page. Turbulence decreases the possibility of using the energy in the wind effectively for a wind turbine. It also imposes more tear and wear on the wind turbine, as explained in the section on fatigue loads. Towers for wind turbines are usually made tall enough to avoid turbulence from the wind close to ground level.

4.4 Wind Obstacles

Obstacles to the wind such as buildings, trees, rock formations etc. can decrease wind speeds significantly, and they often create turbulence in their neighborhood. The turbulent zone may extend to some three time the height of the obstacle. The turbulence is more pronounced behind the obstacle than in front of it. Therefore, it is best to avoid major obstacles close to wind turbines, particularly if they are upwind in the prevailing wind direction, i.e. "in front of" the turbine.

4.5 Shelter Behind Obstacles

Obstacles will decrease the wind speed downstream from the obstacle. The decrease in wind speed depends on the porosity of the obstacle, i.e. how "open" the obstacle is. (Porosity is defined as the open area divided by the total area of the object facing the wind).

A building is obviously solid, and has no porosity, whereas a fairly open tree in winter (with no leaves) may let more than half of the wind through. In summer, however, the foliage may be very dense, so as to make the porosity less than, say one third. The slowdown effect on the wind from an obstacle increases with the height and length of the obstacle. The effect is obviously more pronounced close to the obstacle, and close to the ground.

When manufacturers or developers calculate the energy production for wind turbines, they always take obstacles into account if they are close to the turbine - say, less than 1 kilometer away in one of the more important wind directions.

4.6 Turbine Hub Height

The higher you are above the top of the obstacle, the less wind shade. The wind shade, however, may extend to up to five times the height of the obstacle at a certain distance.

If the obstacle is taller than half the hub height, the results are more uncertain, because the detailed geometry of the obstacle,

4.7 Distance Between Obstacle and Turbine

The distance between the obstacle and the turbine is very important for the shelter effect. In general, the shelter effect will decrease as you move away from the obstacle, just like a smoke plume becomes diluted as you move away from a smokestack. In terrain with very low roughness (e.g. water surfaces) the effect of obstacles (e.g. an island) may be measurable up to 20 km away from the obstacle.
If the turbine is closer to the obstacle than five times the obstacle height, the results will be more uncertain, because they will depend on the exact geometry of the obstacle..

4.7 Roughness Length or Roughness Class

The roughness of the terrain between the obstacle and the wind turbine has an important influence on how much the shelter effect is felt. Terrain with low roughness will allow the wind passin outside the obstacle to mix more easily in the wake behind the obstacle, so that it makes the wind shade relatively less important.

4.8 Wake Effec

Since a wind turbine generates electricity from the energy in the wind, the wind leaving the turbine must have a lower energy content than the wind arriving in front of the turbine. This follows directly from the fact that energy can neither be created nor consumed.

Laboratory, Denmark
A wind turbine will always cast a wind shade in the downwind direction. In fact, there will be a wake behind the turbine, i.e. a long trail of wind which is quite turbulent and slowed down, when compared to the wind arriving in front of the turbine. (The expression wake is obviously derived from the wake behind a ship).

You can actually see the wake trailing behind a wind turbine, if you add smoke to the air passing through the turbine, as was done in the picture. (This particular turbine was designed to rotate in a counterclockwis direction which is somewhat unusual for modern wind turbines). Wind turbines in parks are usually spaced at least three rotor diameters from one another in order to avoid too much turbulence around the turbines downstream. In the prevailing wind direction turbines are usually spaced even farther apart.

4.9 Park Effect

Each wind turbine will slow down the wind behind it as it pulls energy out of the wind and converts it to electricity. Ideally, we would therefore like to space turbines as far apart as possible in the prevailing wind direction. On the other hand, land use and the cost of connecting wind turbines to the electrical grid would tell us to space them closer together.

4.10 Speed Up Effects: Tunnel Effect

The air becomes compressed on the windy side of the buildings or mountains, and its speed increases considerably between th obstacles to the wind. This is known as a "tunnel effect". So, even if the general wind speed in open terrain may be, say, 6 metres per second, it can easily reach 9 metres per second in a natural "tunnel".

Placing a wind turbine in such a tunnel is one clever way of obtaining higher wind speeds than in the surrounding areas. To obtain a good tunnel effect the tunnel should be "softly" embedded in the landscape. In case the hills are very rough and uneven, there may be lots of turbulence in the area, i.e. the wind will be whirling in a lot of different (and rapidly changing) directions.

4.11. Speed Up Effects: Hill Effect
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A common way of siting wind turbines is to place them on hills or ridges overlooking the surrounding landscape. In particular, it is always an advantage to have as wide a view as possible in the prevailing wind direction in the area. On hills, one may also experience that wind speeds are higher than in the surrounding area. Once again, this is due to the fact that the wind becomes compressed on the windy side of the hill, and once the air reaches the ridge it can expand again as its soars down into the low pressure area on the lee side of the hill.

You may notice that the wind in the picture starts bending some time before it reaches the hill, because the high pressure area actually extends quite some distance out in front of the hill. Also, you may notice that the wind becomes very irregular, once it passes through the wind turbine rotor. As before, if the hill is steep or has an uneven surface, one may get significant amounts of turbulence, which may negate the advantage of higher wind speeds.

5. The General Pattern of Wind Speed Variations

It is very important for the wind industry to be able to describe the variation of wind speeds. Turbine designers need the information to optimise the design of their turbines, so as to minimise generating costs. Turbine investors need the information to estimate their income from electricity.

If you measure wind speeds throughout a year, you will notice that in most areas strong gale force winds are rare, while moderate and fresh winds are quite common. The wind variation for a typical site is usually described using the so-called Weibull distribution, as shown in the image. This particular site has a mean wind speed of 7 metres per second, and the shape of the curve is determined by a so called shape parameter of 2.

5.1. Weibull Distribution

The Weibull distribution is one of the most commonly used distributions in reliability engineering because of the many shapes it attains for various values of (slope). It can therefore model a great variety of data and life characteristics a18i.

The 2-parameter Weibull pdf is given by:

where,

and,

· = scale parameter
· = shape parameter (or slope).

5.2 Weibull Statistical Properties Summary
The Mean or MTTF

The mean, of the 2-parameter Weibull pdf is given by:



where is the gamma function evaluated at the value of .

The Median
The median, , of the 2-parameter Weibull is given by:

(6)


The Mode
The mode, , of the 2-parameter Weibull is given by:

(7)


The Standard Deviation
The standard deviation, of the 2-parameter Weibull is given by:



The cdf and the Reliability Function
The cdf of the 2-parameter Weibull distribution is given by:



The Weibull reliability function is given by:

The Conditional Reliability Function
The Weibull conditional reliability function is given by:

(8) or,



Equation (8) gives the reliability for a new mission of t duration, having already accumulated T hours of operation up to the start of this new mission, and the units are checked out to assure that they will start the next mission successfully. (It is called conditional because you can calculate the reliability of a new mission based on the fact that the unit(s) already accumulated T hours of operation successfully).

The Reliable Life
For the 2-parameter Weibull distribution, the reliable life, , of a unit for a specified reliability, starting the mission at age zero, is given by:

(9)


This is the life for which the unit will function successfully with a reliability of . If = 0.50 then = , the median life, or the life by which half of the units will survive.

The Failure Rate Function
The 2-parameter Weibull failure rate function, (T), is given by:



This subchapter includes the following topics:

Statistical Description of Wind Speeds

The distribution of wind speeds is skewed, i.e. it is not symmetrical. Sometimes you will have very high wind speeds, but they are very rare. Wind speeds of 5.5 metres per second, on the other hand, are the most common ones. 5.5 metres is called the modal value of the distribution. If we multiply each tiny wind speed interval by the probability of getting that particular wind speed, and add it all up, we get the mean wind speed. The statistical distribution of wind speeds varies from place to place around the globe, depending upon local climate conditions, the landscape, and its surface. The Weibull distribution may thus vary, both in its shape, and in its mean value. If the shape parameter is exactly 2, as in the graph on this page, the distribution is known as a Rayleigh distribution. Wind turbine manufacturers often give standard performance figures for their machines using the Rayleigh distribution.

Balancing the Weibull Distribution

Another way of finding the mean wind speed is to balance the pile of blue bricks to the right, which shows exactly the same as the graph above. Each brick represents the probability that the wind will be blowing at that speed during 1 per cent of the time during the year. 1 m/s wind speeds are in the pile to the far left, 17 m/s is to the far right. The point at which the whole pile will balance exactly will be at the 7th pile, i.e. the mean wind speed is 7 m/s

6. Mean (Average) Power of the Wind

6.1 Balancing the Power Distribution
The reason why we care about wind speeds is their energy content, just like with the bottles on the previous page: We cared about their content in terms of volume. Now, the volume of a bottle varies with the cube of the size, just like wind power varies with the cube of the wind speed.

6.2 The Ideal Braking of the Wind
Betz' Law
The more kinetic energy a wind turbine pulls out of the wind, the more the wind will be slowed down as it leaves the left side of the turbine in the picture.
If we tried to extract all the energy from the wind, the air would move away with the speed zero, i.e. the air could not leave the turbine. In that case we would not extract any energy at all, since all of the air would obviously also be prevented from entering the rotor of the turbine.
In the other extreme case, the wind could pass though our tube above without being hindered at all. In this case we would likewise not have extracted any energy from the wind.
We can therefore assume that there must be some way of braking the wind, which is in between these two extremes, and is more efficient in converting the energy in the wind to useful mechanical energy. It turns out that there is a surprisingly simple answer to this: An ideal wind turbine would slow down the wind by 2/3 of its original speed.

7. Models of wind tubines

The possibilities of designing a wind turbine vary from choosing the axis and to the number of blades and orientation of the rotor.

7.1 Horizontal Axis Wind Turbines

Most of the technology described on these pages is related to horizontal axis wind turbines (HAWTs, as some people like to call them).

The reason is simple: All grid-connected commercial wind turbines today are built with a propeller-type rotor on a horizontal axis (i.e. a horizontal main shaft). The purpose of the rotor is to convert the linear motion of the wind into rotational energy that can be used to drive a generator. The same basic principle is used in a modern water turbine, where the flow of water is parallel to the rotational axis of the turbine blades.

We distinguish:

· Even Number Of Blades ( Wind Rose)
· Three-Bladed Concept
· Two-Bladed (Teetering) Concept
· One-Bladed Concept

7.1.1. Even Number of Blades

Modern wind turbine engineers avoid building large machines with an even number of rotor blades. The most important reason is the stability of the turbine. A rotor with an odd number of rotor blades (and at least three blades) can be considered to be similar to a disc when calculating the dynamic properties of the machine.

A rotor with an even number of blades will give stability problems for a machine with a stiff structure. The reason is that at the very moment when the uppermost blade bends backwards, because it gets the maximum power from the wind, the lowermost blade passes into the wind shade in front of the tower.

7.1.2 The Danish Three-Bladed Concept

Most modern wind turbines are three-bladed designs with the rotor position maintained upwind (on the windy side of the tower) using electrical motors in their yaw mechanism. This design is usually called the classical Danish concept, and tends to be a standard against which other concepts are evaluated. The vast majority of the turbines sold in world markets have this design. The basic design was first introduced with the renowned Gedser wind turbine. Another characteristic is the use of an asynchronous generator.

7.1.3 Two-Bladed (Teetering) Concept

Two-bladed wind turbine designs have the advantage of saving the cost of one rotor blade and its weight, of course. However, they tend to have difficulty in penetrating the market, partly because they require higher rotational speed to yield the same energy output. This is a disadvantage both in regard to noise and visual intrusion. Lately, several traditional manufacturers of two-bladed machines have switched to three-bladed designs.

Two- and one-bladed machines require a more complex design with a hinged (teetering hub) rotor as shown in the picture, i.e. the rotor has to be able to tilt in order to avoid too heavy shocks to the turbine when a rotor blades passes the tower. The rotor is therefore fitted onto a shaft which is perpendicular to the main shaft, and which rotates along with the main shaft. This arrangement may require additional shock absorbers to prevent the rotor blade from hitting the tower.

7.1.4. One-Bladed Concept

Yes, one-bladed wind turbines do exist, and indeed, they save the cost of another rotor blade! If anything can be built, engineers will do it. One-bladed wind turbines are not very widespread commercially, however, because the same problems that are mentioned under the two-bladed design apply to an even larger extent to one-bladed machines. In addition to higher rotational speed, and the noise and visual intrusion problems, they require a counterweight to be placed on the other side of the hub from the rotor blade in order to balance the rotor. This obviously negates the savings on weight compared to a two-bladed design.

7.1.5. Upwind Machines

Upwind machines have the rotor facing the wind. The basic advantage of upwind designs is that one avoids the wind shade behind the tower. By far the vast majority of wind turbines have this design.

On the other hand, there is also some wind shade in front of the tower, i.e. the wind starts bending away from the tower before it reaches the tower itself, even if the tower is round and smooth.

Therefore, each time the rotor passes the tower, the power from the wind turbine drops slightly. The basic drawback of upwind designs is that the rotor needs to be made rather inflexible, and placed at some distance from the tower (as some manufacturers have found out to their cost). In addition an upwind machine needs a yaw mechanism to keep the rotor facing the wind.

7.1.6. Downwind Machines

Downwind machines have the rotor placed on the lee side of the tower. They have the theoretical advantage that they may be built without a yaw mechanism, if the rotor and nacelle have a suitable design that makes the nacelle follow the wind passively. For large wind turbines this is a somewhat doubtful advantage, however, since you do need cables to lead the current away from the generator. How do you untwist the cables, when the machine has been yawing passively in the same direction for a long period of time, if you do not have a yaw mechanism? (Slip rings or mechanical collectors are not a very good idea if you are working with 1000 ampere currents).

A more important advantage is that the rotor may be made more flexible. This is an advantage both in regard to weight, and the structural dynamics of the machine, i.e. the blades will bend at high wind speeds, thus taking part of the load off the tower.

The basic advantage of the downwind machine is thus, that it may bebuilt somewhat lighter than an upwind machine.

The basic drawback is the fluctuation in the wind power due to the rotor passing through the wind shade of the tower. This may give more fatigue loads on the turbine than with an upwind design.

7.2. Vertical Axes

This category includes wind turbines where the axis direction is at a right angle to the wind direction. In practical terms, this virtually always involves a vertical axis. There is a wonderful bonus from this situation. It works identically well, no matter what direction the wind comes from. So no provision for aiming the mechanism is necessary.

We distinguish:

· Savonius Rotor
· Darrieus Rotor

7.2.1. Savonius Rotor

An early style is generally called a Savonius Rotor. The spinning part of a weatherman's windspeed device (anemometer) is a Savonius Rotor. Sideways mounted cups catch the wind and cause the vertical shaft to spin. A Savonius Rotor has an advantage over the farm windmill in that it does not have to be pointed into the wind. It works equally well with wind from any direction. However, a Savonius Rotor has a rather low maximum efficiency, around 14%. That efficiency does not drop off as rapidly as most other designs (only the propeller style has a wider range of windspeeds for high efficiency). In addition, the Savonius Rotor has tremendous starting torque where most other designs have very little torque at low rotational velocity.

This design is technically called a low-tip-speed (or slow speed) cross-wind-axis turbine. No airfoil shape is involved, which is part of the explanation for the very low efficiency.

However, the Savonius design is by far the simplest of these various mechanisms. Nearly all of the others involve advanced airfoil shapes and complicated structures. The economy and simplicity of a Savonius Rotor cannot be matched.

7.2.2. Darrieus Rotor

A very sophisticated cross-wind-axis turbine is the Darrieus Rotor. This design looks something like an egg-beater, with usually either two or three curved airfoils.

This design is technically called a high-tip-speed cross-wind-axis turbine. The airfoils and the high airfoil velocities allows this style to have efficiencies as high as about 32%, over a fairly wide range of wind speeds.

The Darrieus machine is characterised by its C-shaped rotor blades which make it look a bit like an eggbeater. It is normally built with two or three blades. The basic theoretic