12.1 Wind Energy, Part 2

Frank R. Leslie, B. S. E. E., M. S. Space Technology, LS IEEE

2/23/2010, Rev. 2.0.0

fleslie @fit.edu; (321) 674-7377

www.fit.edu/~fleslie

Wind Energy Theoryand Data Processing

Oil ~$80/bbl 2/22/2010

In Other News . . .

http://www.youtube.com/watch?v=myu2Dmv1mOQ

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12.1 Overview: Wind

Wind speed measurements provide local data to estimate wind power available“Local” means where the turbine will stand

(within a few feet)Wind power/energy computations yield estimates

of energy available at the anemometerStatistical processing is required to estimate

accurately for the long term

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12.1 About This Presentation

12.1.1 Anemometers12.1.2 Wind Data Processing12.1.3 Site Wind Variations12.1.4 Wind Power12.1.5 Wind Energy12.1.6 Grants and Assistance12.1.7 Advantages and Disadvantages12.1 Conclusion

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12.1.1 Anemometers

Anemometers measure the speed and direction of the wind as a function of timeSpinning cups or propellerUltrasonic reflection (Doppler)Sodar (Sound detection and ranging with a large horn)RadarDrift balloonsEtc.

Wind data are usually collected at ten-minute rate and averaged for recording

Gust studies are occasionally used, and require fast sampling at a higher rate to avoid significant information loss (4 pts/gust)

Spectral analysis indicates the frequency components of the wind structure and permits sampling frequency selection to minimize loss

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12.1.2 Wind Data Processing

Serial data from a datalogger must be validated to detect errors, omissions, or equipment malfunctions

These data are usually produced in a text (.TXT) formatSpecialized computer codes may read the data or an

export function used to produce a txt output fileStatistical analysis is used to detect anomalies, peaks

and nulls (lulls in wind jargon), and determine the distribution of the speeds and directions

Frequency analysis with the Fast Fourier Transform (FFT) will show where the energy lies and its probability

Cepstral analysis shows the periodicities in time domainGraphic analysis displays the results for visual

interpretation; excellent for a holistic view

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12.1.3.1 Local Site Wind Availability

Once a region of persistent winds is located, an area of interest is defined by local reconnaissance, land inquiries made, dissenters prospected, etc.

Since trees act to block the wind or cause turbulence, a distance to the nearest tree of less than 200-300 feet (500 ft is better) will significantly impact the free wind

A wind rose for that area will define the principal directions of arrival; seek local advice as to storm history as well; look for flagging of vegetation

Place an anemometer or small temporary turbine about 20 ft away from the intended tower site so that the anemometer can be retained there when the main turbine is installed; choose the direction of least likely wind from where the turbine would be placed

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12.1.3.2 Wind Variation

Since wind velocity (speed and direction) varies over a year and over many years, long-term data are required

The velocities may be estimated using one year’s data or climate (long-term weather data) may be obtained from climate agencies

While wind direction varies, most wind turbines will track in azimuth (yaw) to maximize the energy extracted, and wind arrival direction knowledge is more important in determining upwind blockage or obstruction

The wind speed, average, one-minute gust, and extreme, is sufficient for most energy assessment purposes

The top 30% of the wind speed regime will provide ~70% of the energy; (87.9% of statistics are made up on the spot)

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12.1.3.2.1 Speed and Energy

http://en.wikipedia.org/wiki/Wind_power

12.1.3.3 Wind Speed Variation

In a time series of wind speed data, there will be many different values of speed

For convenience, the speeds are usually divided into “bins”, or ranges of speed, e.g., 0-1 mph, 1+ to 4 mph, . . . , 60-65 mph, etc.

The ranges vary, but since there are many samples in a year, there can be many ranges in the process

The number of samples that fall within a bin can be plotted as a histogram versus the wind speed ranges

A line drawn through the top of the histogram bars approximates a continuous function that is similar to a Weibull Distribution Function, or in a more simple case, a Rayleigh Distribution Function

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12.1.3.3 Wind Speed Variation

This Weibull probability curve shows the variation for a site with a 6.5 m/s mean wind and a Weibull shape factor of 2; the higher the factor, the more peaked or pointed

Notice that the mean is not the most common; that is the mode, and the median is in the middle of the data

The shape factor of 2.0 reveals that this is the Rayleigh probability as well, which is easier to use for that case

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http://www.windpower.dk/tour/wres/weibull.htm Usually it’s a little windy, sometimes it’s calm, and in storms, the wind blows hard but not for long

A probability curve (p.d.f.) is just a way to express this mathematically

If the wind values are integrated, a distribution curve results

12.1.4.1 Wind Speed Power Density

Not all wind power can be extracted or the wind would stop The Betz Limit of 59.3% is the theoretical maximum Turbines approach 40% from the rotor, but the mechanical

and electrical losses may take 20% of the rotor output

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http://www.windpower.dk/tour/wres/powdensi.htm Grey = total power Blue = useable power Red = turbine power output 0 to 25 m/s on abscissa

12.1.4.2 Power Is Proportional to Wind Speed Cubed

Recall that the average wind power is based upon the average of the speed cubed for each occurrence

Don’t average the speed and cube it! Cube the various speeds and average those cubes to

estimate the power The Bergey wind turbine curve below indicates the energy

output in nonturbulent flow

Ref.: Bergey

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12.1.4.3 How to find the Total Wind Power

Each speed range, say 10-14 mph, has a probability of occurrence that has been estimated from some length of data

Suppose the mid-range speed (12 mph) is 5% probability of occurrence

The product is 12 mph times 5% = 0.6 mphFind all the products for all the ranges and add

the resultant products in miles per hour to find the most likely wind speed

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12.1.4.4 How to find the Wind Power

Each speed range is multiplied by the probability that the speed occurs

The sum of these products yields the mean effective speed

Wind Speed Range,

m/s

Mid-Range of

Wind Speed,

m/s

Probability of

Occurance

Product & Sum

Products, m/s

0-1 0.5 0.0069 0.0031-2 1.5 0.2426 0.3642-3 2.5 0.0485 0.1213-4 3.5 0.0624 0.2184-5 4.5 0.0762 0.3435-6 5.5 0.0832 0.4576-7 6.5 0.0693 0.4507-8 7.5 0.0624 0.4688-9 8.5 0.0589 0.5019-10 9.5 0.0554 0.52710-11 10.5 0.0347 0.36411-12 11.5 0.0277 0.31912-13 12.5 0.0208 0.26013-14 13.5 0.0139 0.18714-15 14.5 0.1178 1.70815-16 15.5 0.0069 0.10716-17 16.5 0.0049 0.08017-18 17.5 0.0055 0.09718-19 18.5 0.0014 0.026over 19 20 0.0007 0.014

Total 1.0000 6.615

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12.1.4.5 How to find the Wind Power

A turbine power curve is cubic to start, but becomes intentionally less efficient at very high wind speeds to avoid damage

At very high winds, the power output may fall to zero, usually by design to prevent damage

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12.1.5.1 A Turbine Power Example

Turbine power is essentially a cubic curve with respect to wind speed (up to a point)

The more measured points, the better the equation represents the performance

A regression curve fit allows use of the equation to estimate between points measured

The cubic fit is a model of the real variable data

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Turbine Power

y = 0.1382x3 - 2.2943x2 + 42.062x - 229.43

R2 = 1

0

500

1000

1500

2000

2500

3000

0 5 10 15 20 25 30 35

Wind Speed, mph

Po

wer

, kW

h

12.1.5.2 Simple Example of Energy

The wind in Zephyr, Wyoming varies as shown in the table The turbine doesn’t move until the wind speed reaches over 7 mph Most energy comes from the high storm winds that occur 10% of the time

Strange Weather in Zephyr, Wyoming

Wind Speed Range,

mph

Mid-Range of

Wind Speed,

mph

Probability of

Occurrence

Hours wind / year

Turbine Power at

speed, kW

Energy, kWh/ year

7 7 0.1 876 0 010 10 0.5 4380 100 43800020 20 0.3 2628 800 2102400

30 30 0.1 876 2700 2365200

Total 1.0 8760 4905600hours kWh

Note that the most energy comes from the least frequent wind speedThe wind doesn't overcome turbine bearing resistance until 7 mph

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12.1.5.3 A really simple example

For any site, the wind speed distribution varies with timeThe distribution is estimated from whatever data is

available --- the more, the better

Each turbine type has different operating characteristics, so the power curves will vary

The power multiplied by the time at that speed yields the energy for that speed

The sum of the various energies for the speeds yields the total energy over the time considered

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12.1.5.4 Effective Wind Speed

The effective wind speed is that value of steady wind that would have the same energy output as the variable wind regime

One can only find this for real data in a particular wind regime by cubing each of the wind speeds, summing them in proportion to their probability of occurrence, and taking the cube root

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12.1.5.5 Wind Energy Derivation Equations(also applies to water turbines)

Assume a “tube” of air the diameter, D, of the rotorA = π D2/4 (could be rectangular for a VAWT)

A length, L, of air moves through the turbine in t secondsL = u·t, where u is the wind speed

The tube volume is V = A·L = A·u·tAir density, ρ, is 1.225 kg/m3 (water density

~1000 kg/m3, or 832 times more than air)Mass, m = ρ·V = ρ·A·u·t, where V is volumeKinetic energy = KE = ½ mu2

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12.1.5.5 Wind Energy Equations (continued)

Substituting ρ·A·u·t for mass, and A = π D2/4 , KE = ½·π/4·ρ·D2·u3·t

Theoretical power, Pt = ½·π/4·ρ·D2·u3·t/t = 0.3927·ρa·D2·u3, ρ (rho) is the density, D is the diameter swept by the rotor blades, and u is the speed parallel to the rotor axis

Betz Law shows 59.3% of power can be extractedPe = Pt·59.3%·ήr·ήt·ήg, where Pe is the extracted

power, ήr is rotor efficiency, ήt is mechanical transmission efficiency, and ήg is generator efficiency

For example, 59.3%·90%·98%·80% = 42% extraction of theoretical power

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12.1.6 Grants and Assistance

In some cases, grants and/or anemometer loans from a state or the US Federal government may be approved to stimulate interest in wind energy systems

Some states provide a rebate of up to 50% of the costAnemometers for energy testing might consist only of a

wind distance indicator with a digital readout of miles of wind (difference the readings & divide by time elapsed)

The tower used should approximate the height of the turbine rotor, but the tower may be a temporary mast like a television antenna would be mounted on

Some experts advise that it is better to simply put up a substantial tower and mount a small wind turbine on it

Wind energy can be used from the small turbine before buying a larger size

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12.1.7 Advantages and Disadvantages of Wind Systems

Wind systems, more than solar, provide variable energy as the weather changes rapidly

Storage is required to have energy available when the wind isn’t blowing and smooth it somewhat; batteries now exist for this

This highly variable wind sends variable power to lines; each turbine has different outputs, reducing electrical line variability by the square root of the number of turbines

Large utility size turbines now produce energy at a cost competitive with fossil fuels, but it takes a lot of them to get comparable energyA typical utility plant may have nearly 1000 MW or 1 GW

peak power, while a “large” turbine might be rated at 4 MW at 25 mph wind --- that’s 250 turbines for rated wind speed!

Largest now is the Enercon E-126: 126 m diameter and 7+ MW nameplate rating at Emden, Germany

10 MW to come: http://www.cpi.umist.ac.uk/Eminent/publicFiles/brno/RISO_Future_10MW_Wind_Turbine.pdf

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12.1 Conclusion: Wind Theory

The theory of wind energy is based upon fluid flow, so it also applies to water turbines (water has 832 times the density)

While anemometers provide wind speed and usually direction, data processing converts the raw data into usable information

Because of the surface drag layer of the atmosphere, placing the anemometer at a “standard” height of 10 meters above the ground is important; airport anemometer heights often historically differ from 10 meters

For turbine placement, the anemometer should be at turbine hub height

The average of the speeds is not the same as the correct average of the speed cubes!

The energy extracted by a turbine is the summation of (each speed cubed times the time that it persisted)

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Olin Engineering Complex 4.7 kW Solar PV Roof Array

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Questions?

References: Books

Brower, Michael. Cool Energy. Cambridge MA: The MIT Press, 1992. 0-262-02349-0, TJ807.9.U6B76, 333.79’4’0973.

Gipe, Paul. Wind Energy for Home & Business. White River Junction, VT: Chelsea Green Pub. Co., 1993. 0-930031-64-4, TJ820.G57, 621.4’5

Patel, Mukund R. Wind and Solar Power Systems. Boca Raton: CRC Press, 1999, 351 pp. ISBN 0-8493-1605-7, TK1541.P38 1999, 621.31’2136

Sørensen, Bent. Renewable Energy, Second Edition. San Diego: Academic Press, 2000, 911 pp. ISBN 0-12-656152-4.

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References: Websites, etc.

http://www.windpower.dk/tour/wres/weibull.htm best choice for information

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awea-windnet@yahoogroups.com. Wind Energy elistawea-wind-home@yahoogroups.com. Wind energy home powersite elistrredc.nrel.gov/wind/pubs/atlas/maps/chap2/2-01m.html PNNL wind energy map of CONUS

windenergyexperimenter@yahoogroups.com. Elist for wind energy experimenterstelosnet.com/wind/20th.htmlsolstice.crest.org/dataweb.usbr.gov/html/powerplant_selection.html

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