su-wind turbines lecture notes

7/31/2019 SU-Wind Turbines Lecture Notes

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Physics and Astronomy Outreach Program at the University of British Columbia

RenewableAnd CleanEnergy

Wind Turbines

Lecture Notes


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1) How much energy is available inwind?

2) How is a useful amount of energy (or

power) extracted using wind turbinetechnology?



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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 togrind grain and pump water

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The question to ask in this early stageof 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 andpower.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 kineticenergy , but the rate at which thisenergy 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 ofenergy transformations from solarenergy (radiation) to wind energy

(kinetic). About 2% of the solar energy

absorbed by the earth goes into wind.

Solar radiation is absorbed by thesurface of the earth and heats itunevenly.

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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 temperatureacross the globe can create wind!

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Figure 1 . A wind energy map of Canada showing the average power(in W/m 2) that can theoretically be extracted from the wind.

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solar intensity at the top of the earth'satmosphere = 350 W/m 2.

Given that only 2% is converted to windthus ~ 7 W/m 2 goes into wind energy.

35% of wind energy (2.45 W/m 2) isdissipated in the first kilometre aboveEarth's surface and available forturbines.

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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/m 2) (5.1 x 10 14 m2) (3.2x10 7 s)= 4.0 x 10 22 J

...which is 200 times larger than our energy

consumption on Earth, estimated to be2 x 10 20 J.

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Calculate the power extracted fromwind.

Calculate kinetic energy, KE = mv 2 ofair passing through the rotor of the windturbine.

Measure mass of air travelling througharea of circle swept out by rotor bladesin time t .

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

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From this you can find the mass...mass

is the density of the air (1.2 kg/m 3 for standardtemperature and pressure)

v is the velocity of the air

t is the length of time for a unit of air to pass throughthe loop.

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

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density volume

Av t


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Therefore the kinetic energy, K , is foundto be:

while the power of the wind passingthrough our hoop is:

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K 1

2mv 2

1

2 A tv

3

P 12

A tv3

t 12

Av 3


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But turbines cant extract all of thekinetic energy of the wind.

Why not?

If this was the case the air would stopas soon as it passed through the bladesand no other wind would be able topass through.

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But you cannot capture more than59.3% (2/3) of winds energy (Betz,1919).

maximum ratio of P / P 0 = 2/3 is found atv 2 / v 1 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 Betzs conclusions that themaximum power output (of 59.3%) occurs when v 2 is 1/3 of v 1.

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Wind turbines are not 100% efficient:power = efficiency max power extracted

where d is the diameter of the circle coveredby the rotor.

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23

2

3

3

8

1

22

12

1

d v

d v

AvP


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This expression is true for a single windturbine 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 whenwind moves uniformly in the samedirection.

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

The edge of a continental shelf, highground and tundra have low turbulenceand are the best locations to build aturbine.

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Local wind speed is also an importantfactor since:power (wind speed) 3

The local wind speed should be, onaverage, at least 7 m/s at 25 m abovethe earths surface in order to make

harnessing wind from it worthwhile.

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Demand and dependability areimportant. Wind is not locally predictable in the

short term, and so its use should belimited to only fulfill 5 15% of the totalenergy demand of the area.

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Setting up turbines in several locationsmakes wind energy more reliable. The available power is averaged out.

Globally there is always a relativelyconstant amount of wind energy beingharnessed at any one moment.

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The machinery of a wind turbine alsolimits how much power can beextracted from wind.

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

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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 turnsthe generator to produce electricity. To maximize the power extracted, the

nacelle, which connects the rotor to thetower and houses the generator, can berotated 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 turbinedepends on: rotor area

air density wind speed

wind shear.

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Wind shear is a difference in windspeed and direction over a shortdistance 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 youget away from the ground. To maximize the power output of wind

turbines, rotors are tilted slightlyupwards.

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 windfarms to satisfy their energy needs. To optimize energy production in a wind

farm, turbines are spread 5 9 rotordiametres apart in the prevailing winddirection 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 isguaranteed to be slow. One common way of spacing them out is ensuring there isat 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 diametresbetween turbines.

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223

8

1

nd

d v

arealand power


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The average power of a wind turbinefarm is the product of the capacity ofthe farm and the fraction of the time

when the wind conditions are nearoptimal.

The capacity factor is usually around

15 30%.

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Now that it is established that wind is apossible source of power, the benefitsand drawbacks need to be considered.

Why use wind power in lieu of other energy sources?

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Harnessing wind power does not producehazardous wastes, use non-renewableresources or cause significant amounts ofdamage to the environment.

Some CO 2 is produced in themanufacturing of the turbines, but it ismuch less than the emissions fromburning an energy-equivalent amount ofcoal or natural gas.

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The use of wind power can reducehidden costs such as those related topollution and in the longer term, climatechange.

Since you can farm around them, windturbines 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 windturbines?

Arguments against include fears ofdamages from collapsing turbines, noise, aless attractive skyline, an unreliable power

source, unnecessarily high bird fatality, andsignificantly modifying the Earths windpatterns.

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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 anoffice or a home.

Reliability : the reliability of wind energyincreases depending on location andhow many farms are operating in avariety of sites within the area.

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DISCLAIMERS

Birds : in the US less than 40,000 are saidto die from turbine blades while hundredsof millions are said to die from domesticcats!

Earths climate : it is plausible that onewould see local climate changesurrounding areas with concentrated windfarms, but the large-scale climatic effectswill likely be negligible.

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DISCLAIMERS Earths climate : wind turbines would be

replacing coal-fired power plants, so if

anything, we anticipate a considerablereduction in CO 2 emissions.

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