# Wind Power (Technology and Economics)

By Barrie Lawson, UK
Adapted with the permission of the author from Electropaedia.com

The wind is a source of free energy which has been used since ancient times in windmills for pumping water or grinding flour. The technology of high power, geared transmissions was developed centuries ago by windmill designers and the fantail wheel for keeping the main sales pointing into the wind was one of the world’s first examples of an automatic control system.

Windmills at Kinderdijk in the Netherlands Dating from 1740 Used for Pumping Water from the Polder
Source – Birds As Art

Though modern technology has made dramatic improvements to the efficiency of windmills which are now extensively use for electricity generation, they are still dependent on the vagaries of the weather. Not just on the wind direction but on the intermittent and unpredictable force of the wind. Too little wind and they can’t deliver sufficient sustained power to overcome frictional losses in the system. Too much and they are susceptible to damage. Between these extremes, cost efficient installations have been developed to extract energy from the wind.

#### Available Power From the Wind

Theoretical Power
The power P available in the wind impinging on a wind driven generator is given by:
P = ½CAρv3
Where C is an efficiency factor known as the Power Coefficient which depends on the machine design, A is the area of the wind front intercepted by the rotor blades (the swept area), ρ is the density of the air (averaging 1.225 Kg/m3 at sea level) and v is the wind velocity.

Note that the power is proportional to area swept by the blades, the density of the air and to the cube of the wind speed. Thus doubling the blade length will produce four times the power and doubling the wind speed will produce eight times the power.
Note also that the effective swept area of the blades is an annular ring, not a circle, because of the dead space around the hub of the blades.

A similar equation applies to the theoretical power generated by a “run of river” and “tidal flow” hydro turbines.

#### Energy Conversion

Practical Power and Conversion Efficiency
German aerodynamicist Albert Betz showed that a maximum of only 59.3% of the theoretical power can be extracted from the wind, no matter how good the wind turbine is, otherwise the wind would stop when it hit the blades. He demonstrated mathematically that the optimum occurs when the rotor reduces the wind speed by one third.

In practical designs, inefficiencies in the design and frictional losses will reduce the power available from the wind still further. Converting this wind power into electrical power also incurs losses of up to 10% in the drive train and the generator and another 10% in the inverter and cabling. Furthermore, when the wind speed exceeds the rated wind speed, control systems limit the energy conversion in order to protect the electric generator so that ultimately, the wind turbine will convert only about 30% to 35% of the available wind energy into electrical energy.

Note that the power output from commercially available domestic wind turbines is usually specified at a steady, gust free, wind speed of 12.5 m/s. (Force 6 on the Beaufort scale corresponding to a strong breeze). In many locations, particularly urban installations, the prevailing wind will rarely reach this speed.

Blade Design for Optimum Energy Capture
Modern, high capacity wind turbines, such as those used by the electricity utilities in the electricity grid, typically have blades with a cross section similar to the aerofoils used to provide the lift in aircraft wings.

The direction of the apparent wind, that is the incident wind, relative to the chord line of the airfoil is known as the angle of attack. Just as with aircraft wings, the lift resulting from the incident wind force increases as the angle of attack increases from 0 to a maximum of about 15 degrees at which point the smooth laminar flow of the air over the blade ceases and the air flow over the blade separates from the airfoil and becomes turbulent. Above this point the lift force deteriorates rapidly while drag increases leading to a stall. See more about the angle of attack.

The tangential velocity S of any blade section at a distance r from the center of rotation (the root of the blade) is given by S = r Ω where Ω is the angular velocity of rotation in radians.
For a given wind speed the apparent wind will be different at the root of the blade from the apparent wind at the tip of the blade because the rotational relative wind speed is different.

For a given speed of rotation, the tangential velocity of sections of the blade increases along the length of the blade towards the tip, so that the pitch of the blade must be twisted to maintain the same, optimum angle of attack at all sections along the length of the blade. The blade twist is thus optimized for a given wind speed. As the wind speed changes however, the twist will no longer be optimum. To retain the optimum angle of attack as wind speed increases a fixed pitch blade must increase its rotational speed accordingly, otherwise, for fixed speed rotors, variable pitch blades must be used.

The number of blades in the turbine rotor and its rotational speed must be optimized to extract the maximum energy from the available wind.

While using rotors with multiple blades should capture more wind energy, there is a practical limit to the number of blades which can be used because each blade of a spinning rotor leaves turbulence in its wake and this reduces the amount of energy which the following blade can extract from the wind. This same turbulence effect also limits the possible rotor speeds because a high speed rotor does not provide enough time for the air flow to settle after the passage of a blade before the next blade comes along.

There is also a lower limit to both the number of blades and the rotor speed. With too few rotor blades, or a slow turning rotor, most of the wind will pass undisturbed through the gap between the blades reducing the potential for capturing the wind energy. The fewer the number of blades, the faster the wind turbine rotor needs to turn to extract maximum power from the wind.

The notion of the Tip Speed Ratio (TSR) is a concept used by wind turbine designers to optimise a blade set to the shaft speed required by a particular electricity generator while extracting the maximum energy from the wind.
The tip speed ratio  is given by:
TSR=ΩR/V
where Ω is the angular velocity of the rotor, R is the distance between the axis of rotation and the tip of the blade, and V is the wind speed.

A well designed typical three-bladed rotor would have a tip speed ratio of around 6 to 7.

Design Limits
For safety and efficiency reasons wind turbines are subject to operating limits depending on the wind conditions and the system design.

• Cut – in Wind Speed This is the minimum wind velocity below which no useful power output can be produced from wind turbine, typically between 3 and 4 m/s (10 and 14 km/h, 7 and 9 mph).
• Rated Wind Speed (also associated with the Nameplate Capacity.) This is the lowest wind velocity at which the turbine develops its full power. This corresponds to the maximum, safe electrical generating capacity which the associated electrical generator can handle, in other words the generator’s rated electrical power output. The rated wind speed is typically about 15 m/s (54 km/h, 34 mph) which is about double the expected average speed of the wind. To keep the turbine operating with wind speeds above the rated wind speed, control systems may be used to vary the pitch of the turbine blades, reducing the rotation speed of the rotor and thus limiting the mechanical power applied to the generator so that the electrical output remains constant. Though the turbine works with winds speeds right up to the cut-out wind speed, its efficiency is automatically reduced at speeds above the rated speed so that it captures less of the available wind energy in order to protect the generator. While it would be possible to use larger generators to extract full power from the wind at speeds over the rated wind speed, this would not normally be economical because of the lower frequency of occurrence of wind speeds above the rated wind speed.
• Cut – out Wind Speed This is the maximum safe working wind speed and the speed at which the wind turbine is designed to be shut down by applying brakes to prevent damage to the system. In addition to electrical or mechanical brakes, the turbine may be slowed down by stalling or furling.
• Stalling This is a self-correcting or passive strategy which can be used with fixed speed wind turbines. As the wind speed increases so does the wind angle of attack until it reaches its stalling angle at which point the “lift” force turning the blade is destroyed. However increasing the angle of attack also increases the effective cross section of the blade face-on to the wind, and thus the direct wind force and the associated stress on the blades. A fully stalled turbine blade, when stopped, has the flat side of the blade facing directly into the wind.
• Furling or Feathering This is a technique derived from sailing in which the pitch control of the blades is used to decrease the angle of attack which in turn reduces the “lift” on the blades as well as the effective cross section of the aerofoil facing into the wind. A fully furled turbine blade, when stopped, has the edge of the blade facing into the wind reducing the wind force and stresses on the blade.

The cut-out speed is specified to be as high possible consistent with safety requirements and practicality in order to capture as much as possible of the available wind energy over the full spectrum of expected wind speeds (See diagram of Wind Speed Distribution below). A cut-out speed of 25 m/s (90 km/h, 56 mph) is typical for very large turbines.

• Survival Wind Speed This is the maximum wind speed that a given wind turbine is designed to withstand above which it cannot survive. The survival speed of commercial wind turbines is in the range of 50 m/s (180 km/h, 112 mph) to 72 m/s (259 km/h, 161 mph). The most common survival speed is 60 m/s (216 km/h, 134 mph). The safe survival speed depends on local wind conditions are usually regulated by national safety standards.

Yaw Control
Windmills can only extract the maximum power from the available wind when the plane of rotation of the blades is perpendicular to the direction of the wind. To ensure this the rotor mount must be free to rotate on its vertical axis and the installation must include some form of yaw control to turn the rotor into the wind.

For small, lightweight installations this is normally accomplished by adding a tail fin behind the rotor in line with its axis. Any lateral component of the wind will tend to push the side of the tail fin causing the rotor mount to turn until the fin is in line with the wind. When the rotor is facing into the wind there will be no lateral force on the fin and the rotor will remain in position. Friction and inertia will tend to hold it in position so that it does not follow small disturbances.

Large turbine installations have automatic control systems with wind sensors to monitor the direction of the wind and a powered mechanism to drive the rotor into its optimum position.

Capacity Factor
Electrical generating equipment is usually specified at its rated capacity. This is normally the maximum power or energy output which can be generated in optimal conditions. Since a wind turbine rarely works at its optimal capacity the actual energy output over a year will be much less than its rated capacity. Furthermore there will often be periods when the wind turbine can not deliver any power at all. These occur when there is insufficient wind to power the turbine system, or other periods, fortunately only a few, when the wind turbine must be shut down because the wind speed is dangerously high and exceeds the system cut-out speed.

The capacity factor is simply the wind turbine generator’s actual energy output for a given period divided by the theoretical energy output if the machine had operated at its rated power output for the same period. Typical capacity factors for wind turbines range from 0.25 to 0.30. Thus a wind turbine rated at 1 Megawatt will deliver on average only about 250 kilowatts of power. (For comparison, the capacity factor of thermal power generation is between 0.70 and 0.90)

#### Wind Supply Characteristics

Wind speed
Though the force and power of the wind are difficult to quantify, various scales and descriptions have been used to characterize its intensity. The Beaufort scale is one measure in common use. The lowest point or zero on the Beaufort scale corresponds to the calmest conditions when the wind speed is zero and smoke rises vertically. The highest point is defined as force 12 when the wind speed is greater than 34 meters per second (122 km/h, 76 mph). as occurs in tropical cyclones when the countryside is devastated by hurricane conditions.

Small wind turbines generally operate between force 3 and force 7 on the Beaufort scale with the rated capacity commonly being defined at force 6 with a wind speed of 12 m/s.

Below force 3 the wind turbine will not generate significant power.

At force 3, wind speeds range from 3.6 to 5.8 m/s (8 to 13 mph). Wind conditions are described as “light” and leaves are in movement and flags begin to extend.

At force 7, wind speeds range from 14 to 17 m/s (32 to 39 mph). Wind conditions are described as “strong” and whole trees are in motion.

With winds above force 7 small, domestic wind turbines should be shut down to prevent damage.

Large turbines used in the electricity grid are designed to work with wind speeds of up to 25 m/s (90 km/h, 56 mph) which corresponds to between force 9 (severe gale, 23 m/s) and force 10 (storm, 27 m/s) on the Beaufort Scale.

Wind Consistency
Wind power has the advantage that it is normally available 24 hours per day, unlike solar power which is only available during daylight hours. Unfortunately the availability of wind energy is less predictable than solar energy. At least we know that the sun rises and sets every day. Nevertheless, based on data collected over many years, some predictions about the frequency of the wind at various speeds, if not the timing, are possible.

Wind Speed Distribution
Care should be taken in calculating the amount of energy available from the wind as it is quite common to overestimate its potential. You cannot simply take the average of the wind speeds throughout the year and use it to calculate the energy available from the wind because its speed is constantly changing and its power is proportional to the cube of the wind speed. (Energy = Power X Time). You have to weigh the probability of each wind speed with the corresponding amount of energy it carries.

Experience shows that for a given height above ground, the frequency at which the wind blows with any particular speed follows a Rayleigh Distribution. An example is shown below.

Important Notes
1. The modal wind speed, that is the speed at which the wind most frequently blows, is less than the average wind speed which is the speed often quoted as representing the typical wind conditions. For reference, the average wind speed across the UK quoted by the Department of Trade and Industry (DTI), is approximately 5.6 meters per second [m/s] at 10 meters above ground level (agl).”
2. Published average wind speeds are only reliable for open rural environments. Wind speeds just above roof level in urban environments will be considerably less than the quoted averages because of turbulence and shielding caused by buildings and trees. A wind turbine sited below the ridge of a building or at a similar height in the garden of an urban dwelling as often shown in the product sales literature is unlikely to provide the energy levels claimed in the specifications.
3. The distribution does not represent the energy content of the wind since this is proportional to the cube of the wind speed.
4. A distribution such as the one above is only valid for the prevailing wind conditions at a particular height above the ground. Average wind speeds usually tend to increase with height then level off which is why wind turbines are usually installed as high above ground as possible.
An empirical formula developed by D.L. Elliott of Pacific Northwest Labs gives the wind speed V at a height H above ground level as
V = Vref( H / Href
Where Vref is the reference wind speed at a reference height Hrefand the exponent α is a correction factor dependent on obstacles on the ground, the density of the air and wind stability factors. In wind resource assessments α is commonly assumed to be a constant 1/7th . The histogram below shows this relationship.

Wind Energy Distribution
The histogram below shows the resulting distribution of the wind energy content superimposed on the the Rayleigh wind speed distribution (above) which caused it. Unfortunately not all of this wind energy can be captured by conventional wind turbines.

Notes
1. The peak wind energy occurs at wind speeds considerably above both the modal and average wind speeds since the wind energy content is proportional to the cube of its speed.
2. Very little energy is available at low speeds and most of this will be needed to overcome frictional losses in the wind turbine. Energy generation typically does not cut in until wind is blowing at speeds of at least 3 m/s to 5 m/s.
3. High wind speeds cause high rotation speeds and high stresses in the wind turbine which can can result in serious damage to the installation. To avoid these dangerous conditions, wind turbines are usually designed to cut out at wind speeds of around 25 m/s either by braking or feathering the rotor blades allowing the wind to spill over the blades, though smaller domestic installations may have lower operating limits.
4. Because of the limitations of the generating system and also upper speed limit at which the wind turbine can safely be used, it may capture only half or less of the available wind energy.

For a given wind speed the wind energy also depends on the elevation of the wind turbine above sea level. This is because the density of the air decreases with altitude and the wind energy is proportional to the air density. This effect is shown in the following histogram.

Notes
5. For a given wind speed the wind energy density decreases with increases in altitude. However at the same time the actual wind speeds tend to increase with height above ground level. Since the wind energy is proportional to the cube of the wind speed, the net effect is that wind energy tends to increase with the height above ground level.
6. As the density of air decreases with altitude, the wind energy density also decreases. By contrast the available solar energy increases with altitude due to lower atmospheric absorption. See Solar Radiation and Insolation (Incident Solar Radiation).

Location Considerations
Generally marine locations and exposed hilltops provide the most favorable wind conditions with wind speeds consistently greater than 5 m/s.
Turbulent conditions will reduce the amount of energy which can be extracted from the wind reducing in turn the overall efficiency of the system. This is more likely to be the case over land than over the sea. Raising the height of the turbine above the ground effectively lifts it above the worst of the turbulence and improves efficiency.
Domestic wind turbines located between buildings in urban environments rarely operate at peak efficiency suffering from turbulence as well as being shielded from the wind by buildings and trees.

#### Practical Systems

Community/Grid Installations

Vesta 7 MW Wind Turbines with a Rotor Diameter of 164 m
(Source The IET)

Large scale wind turbine generators with outputs of up to 8 MWe or more with rotor diameters up to 164 meters are now functioning in many regions of the world with even larger designs in the pipeline..

A typical system employs a fixed speed rotor with three variable pitch blades which are controlled automatically to maintain a fixed rotation speed for any wind speed. The rotor drives a synchronous generator through a gear box and the whole assembly is housed in a nacelle on top of a substantial tower with massive foundations requiring hundreds of cubic metres of reinforced concrete.

Source US DOE (EERE)

Large rotor blades are necessary to intercept the maximum air stream but these give rise to very high tip speeds. The tip speeds however must be limited, mainly because of unacceptable noise levels, resulting in very low rotation speeds which may be as low as 10 to 20 rpm for large wind turbines. The operating speed of the generator is however is much higher, typically 1200 rpm, determined by the number of its magnetic pole pairs and the frequency of the grid electrical supply. Consequently a gearbox must be used to increase the shaft speed to drive the generator at its synchronous speed.

Grid connected systems are dimensioned for average wind speeds 5.5 m/s on land and 6.5 m/s offshore where wind turbulence is less and wind speeds are higher. While offshore plants benefit from higher sustainable wind speeds, their construction and maintenance costs are higher.

#### Wind Farms

Grouping 10 to 100 wind turbines together in so called “wind farms” can lead to savings of 10% to 20% in construction, distribution and maintenance costs.

According to NREL the “footprint” of land needed to provide space for turbine towers, roads, and support structures is typically between 0.1 and 0.2 hectares (0.25 and 0.50 acres) per turbine. With the typical capacity of wind turbines installed in existing wind farms being around 2 MW, it would take a wind farm with 2000 wind turbines covering 200 to 400 hectares (500 to 1000 acres) just to replace the 4000 MWe power generated by the UK’s Drax coal fired power station.

Unfortunately for the economics of wind turbines, the utility company needs to keep the equivalent capacity from other sources (conventional generating stations or batteries) just to keep the grid customers supplied when the wind is not blowing.

#### Domestic Wind Turbine Installations

1.6 kW Wind Turbine with 2.8 Metre Diameter Rotor by Cyclone Green Power Inc.

In a typical domestic system the wind turbine is coupled directly to a three phase asynchronous permanent magnet AC generator mounted on the same shaft. To save on capital costs, domestic installations do not have variable pitch rotor blades so the rotor speed varies with the wind speed. The generator output voltage and frequency are proportional to the rotor speed and the current is proportional to the torque on the shaft. The output is rectified and fed through a buck-boost regulator to an inverter which generates the required fixed amplitude and frequency AC voltage.

Note: There is possible confusion in the classification of the generator. It is actually a synchronous generator because the frequency of its output is directly synchronized with the rotor speed. In this application however it is called an asynchronous generator because the output frequency of the generator is not synchronized with the mains/utility frequency.

Urban Installations
Wind turbine blade sizes in urban applications are usually limited for practical reasons to less than about 1 metre (2 metres diameter) as well as by local planning ordinances and for similar reasons the height of the turbine above ground is limited to just above rooftop level but below treetop level.

• Economics
A typical domestic installation with a 1.75m swept diameter, (swept area of 2.4m2), costs around £1500 (\$2250). At the rated wind speed of 12.5m/s (28 mph) the wind power intercepted will be 2870 Watts, but after taking into account all the unavoidable system losses, the actual electrical output power will be around 1000 Watts. However this is at the upper end of the performance possibilities. Wind turbulence and shielding due to buildings and trees inhibits sustained strong, gust free wind flow and in any case, for most of the time, the wind speed will more likely be towards the lower end of the performance specification at 4 m/s (9 mph,) that is a light breeze. At this speed the power output of the system will be about 32 Watts – Not enough to power a single light bulb. For much of the time the power generated could be less than the quiescent power drain of the inverter.

Running with a constant power output of 32 Watts for a full year would generate only 280 kWh (280 Units) of electrical energy worth £28 at today’s price of £0.10 (\$0.15) per kWh. To put it into perspective, a typical UK household consumes about 5,000 kWh of electrical energy per year.

Because the system is connected directly to the grid there is no need for battery back-up and in any case the cost of the batteries would make an already weak economic case for the system even weaker. See also Grid Connected Systems

Thus small domestic rooftop wind turbine installations do not make a serious contribution to the household energy supply.

Self sufficiency and selling surplus energy back to the utility are out of the question and the payback period on the capital investment is out of sight.

• Carbon Footprints
As with solar power, if the investment fails the conventional economic tests, the notion of carbon footprints is often used to justify the expense, based on the potential for reducing the amount of greenhouse gases emitted by alternative methods of power generation.
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• Rural Installations
The economics of rural and remote locations make wind power more attractive than for urban locations. Because of the remoteness, connection to the electricity grid may be impossible or prohibitively expensive. Furthermore, larger, more efficient wind power installations are possible and the prevailing winds will also be higher. See also Stand Alone Systems
•

• Hybrid Installations
Hybrid systems combining wind and solar power provide energy diversity reducing the risk of power outages. Wind speeds are often high in the winter when the available solar energy is low and low in the summer when the available solar energy is high.

Hybrid systems are discussed in more detail in the section on Remote Area Power Systems

Wind power provides a valuable complement to large scale base load power stations. Where there is an economic back-up, such as hydro power or large scale storage batteries, which can be called upon at very short notice, a significant proportion of electricity can be provided from wind.

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