Renewable And Clean Energy Wind Turbines

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Lecture Notes

Wind Turbines

1) How much energy is available in wind?

2) How is a useful amount of energy (or power) extracted using wind turbine technology?

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Wind energy:

• Proposed alternative energy source

• Is in the early stages of large scale development

• Used in Persia as early as 500 AD to grind grain and pump water

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• The question to ask in this early stage of large scale development:

Is it possible to extract a useful amount of raw energy from the wind?

• We will consider constraints of time, location and machinery.

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• Is there enough energy in wind?

• First, it is important to make the distinction between kinetic energy and power.Kinetic energy: The energy resulting from the movement of masses.

Power: The rate of doing useful work.

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• Wind possesses a lot of kinetic energy, but the rate at which this energy can be extracted limits the amount of useful power available.

• How much power can be harnessed from wind?

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• Wind energy comes from a series of energy transformations from solar energy (radiation) to wind energy (kinetic).

• About 2% of the solar energy absorbed by the earth goes into wind.

• Solar radiation is absorbed by the surface of the earth and heats it unevenly.

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• Uneven heating:o Intensity of solar energy varies due to

the angle of the Sun (the equator vs. the poles).

o Land heats up faster than water does, but also loses heat faster (inland vs. coast).

• These differences in air temperature across the globe can create wind!

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Figure 1. A wind energy map of Canada showing the average power (in W/m2) that can theoretically be extracted from the wind.

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• solar intensity at the top of the earth's atmosphere = 350 W/m2.

• Given that only 2% is converted to wind thus ~ 7 W/m2 goes into wind energy.

• 35% of wind energy (2.45 W/m2) is dissipated in the first kilometre above Earth's surface and available for turbines.

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Over a period of one year, the wind energy (E) is approximately...

E = intensity ∙ Earth's SA ∙ seconds per year

= (2.45 W/m2) (5.1 x 1014 m2) (3.2x107 s)

= 4.0 x 1022 J

...which is 200 times larger than our energy consumption on Earth, estimated to be 2 x 1020 J.

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• Calculate the power extracted from wind.

• Calculate kinetic energy, KE = ½mv2 of air passing through the rotor of the wind turbine.

• Measure mass of air travelling through area of circle swept out by rotor blades in time Δt.

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Figure 2. At time t = 0, the mass of air is just about to pass through the hoop, but Δt later, the mass of air has passed through the hoop. The mass of this piece of air is the product of its density ρ, area A, and length v ∙ Δt.

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From this you can find the mass...

mass

ρ is the density of the air (1.2 kg/m3 for standard temperature and pressure)

v is the velocity of the air

Δt is the length of time for a unit of air to pass through the loop.

A is the area swept by the blades, not the blade area.

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densityvolumeAvt

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Therefore the kinetic energy, K, is found to be:

while the power of the wind passing through our hoop is:

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K 12mv 2

12Atv 3

P 12

Atv 3

t12Av 3

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• But turbines can’t extract all of the kinetic energy of the wind.

Why not? • If this was the case the air would stop

as soon as it passed through the blades and no other wind would be able to pass through.

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• But you cannot capture more than 59.3% (2/3) of wind’s energy (Betz, 1919).

• maximum ratio of P/P0 = 2/3 is found at v2/v1 ≈ 1/3.

• Ideally you want the turbine to slow the wind down by 2/3 of its original speed.

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Figure 3.The plot agrees with Betz’s conclusions that the maximum power output (of 59.3%) occurs when v2 is 1/3 of v1.

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Wind turbines are not 100% efficient:

power = efficiency ∙ max power extracted

where d is the diameter of the circle covered by the rotor.

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23

23

3

81

22121

dv

dv

AvP

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• This expression is true for a single wind turbine in constant wind conditions.

• In real life, however, wind conditions change.

What local conditions must be satisfied in order to make the use of wind

turbines feasible?

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• Wind turbines are most efficient when wind moves uniformly in the same direction.

• Turbulence is caused by buildings, trees, and land formations.

• The edge of a continental shelf, high ground and tundra have low turbulence and are the best locations to build a turbine.

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• Local wind speed is also an important factor since:

power α (wind speed)3

• The local wind speed should be, on average, at least 7 m/s at 25 m above the earth’s surface in order to make harnessing wind from it worthwhile.

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• Demand and dependability are important.

• Wind is not locally predictable in the short term, and so its use should be limited to only fulfill 5 – 15% of the total energy demand of the area.

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• Setting up turbines in several locations makes wind energy more reliable.

• The available power is averaged out.

• Globally there is always a relatively constant amount of wind energy being harnessed at any one moment.

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• The machinery of a wind turbine also limits how much power can be extracted from wind.

• Some terminology: foundation, tower, nacelle and rotor. (See Figure 4 on next slide)

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Figure 4. A turbine is composed of a foundation, a tower, a nacelle and a rotorconsisting of 3 blades.

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• The wind turns the rotor, which turns the generator to produce electricity.

• To maximize the power extracted, the nacelle, which connects the rotor to the tower and houses the generator, can be rotated into the direction of the wind.

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Figure 5. The dimensions and characteristics of a typical smaller

sized turbine.

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• The power produced by a wind turbine depends on:

• rotor area

• air density

• wind speed

• wind shear.

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• Wind shear is a difference in wind speed and direction over a short distance and is caused by mountains, coastlines and weather patterns.

• Air density increases with colder temperatures, decreased altitude, and decreased humidity.

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• Wind speed increases the farther you get away from the ground.

• To maximize the power output of wind turbines, rotors are tilted slightly upwards.

Why do you think this is?

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Figure 6. As you get higher off the ground, the air speed increases, correspondingto a longer arrow. The rotors are tilted slightly upwards so that each part of therotor is exposed to the same speed.

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• Cities and countries need huge wind farms to satisfy their energy needs.

• To optimize energy production in a wind farm, turbines are spread 5 – 9 rotor diametres apart in the prevailing wind direction and 3 – 5 rotor diameters apart in the perpendicular direction (Fig. 7).

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Figure 7. On a wind farm, turbines must be spaced out enough so that they do notinterfere with each other. As the wind passes through the turbine it slows down,and so there is no point in putting a turbine in the region where the air is guaranteed to be slow. One common way of spacing them out is ensuring there is at least 5 rotor diametres between each turbine.

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When the turbines are placed on a square grid, the power per unit land area is:

where n is the number of turbine diametres between turbines.

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223

81

nd

dv

arealandpower

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• The average power of a wind turbine farm is the product of the capacity of the farm and the fraction of the time when the wind conditions are near optimal.

• The capacity factor is usually around

15 – 30%.

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• Now that it is established that wind is a possible source of power, the benefits and drawbacks need to be considered.

Why use wind power in lieu of other energy sources?

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• Harnessing wind power does not produce hazardous wastes, use non-renewable resources or cause significant amounts of damage to the environment.

• Some CO2 is produced in the manufacturing of the turbines, but it is much less than the emissions from burning an energy-equivalent amount of coal or natural gas.

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• The use of wind power can reduce hidden costs such as those related to pollution and in the longer term, climate change.

• Since you can farm around them, wind turbines use less space than traditional power stations.

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So why, in light of these positive elements, is there so much resistance against wind

turbines?

•Arguments against include fears of damages from collapsing turbines, noise, a less attractive skyline, an unreliable power source, unnecessarily high bird fatality, and significantly modifying the Earth’s wind patterns.

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DISCLAIMERS

• Noise: the noise of a typical turbine is 45 dB at 250 m away. This level is lower than the background noise at an office or a home.

• Reliability: the reliability of wind energy increases depending on location and how many farms are operating in a variety of sites within the area.

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DISCLAIMERS

• Birds: in the US less than 40,000 are said to die from turbine blades while hundreds of millions are said to die from domestic cats!

• Earth’s climate: it is plausible that one would see local climate change surrounding areas with concentrated wind farms, but the large-scale climatic effects will likely be negligible.

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DISCLAIMERS

• Earth’s climate: wind turbines would be replacing coal-fired power plants, so if anything, we anticipate a considerable reduction in CO2 emissions.

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