12.1 Wind Energy, Part 2 Frank R. Leslie, B. S. E. E., M. S. Space Technology, LS IEEE 2/23/2010, Rev (321) Wind Energy Theory and Data Processing Oil ~$80/bbl 2/22/2010

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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 anemometer Statistical processing is required to estimate accurately for the long term

12.1 About This Presentation Anemometers Wind Data Processing Site Wind Variations Wind Power Wind Energy Grants and Assistance Advantages and Disadvantages 12.1 Conclusion

Anemometers Anemometers measure the speed and direction of the wind as a function of time  Spinning cups or propeller  Ultrasonic reflection (Doppler)  Sodar (Sound detection and ranging with a large horn)  Radar  Drift balloons  Etc. 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

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) format Specialized computer codes may read the data or an export function used to produce a txt output file Statistical 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 domain Graphic analysis displays the results for visual interpretation; excellent for a holistic view

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 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

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)

Speed and Energy

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,..., 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

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 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

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 Grey = total power Blue = useable power Red = turbine power output 0 to 25 m/s on abscissa

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

How to find the Total Wind Power Each speed range, say 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 mph Find all the products for all the ranges and add the resultant products in miles per hour to find the most likely wind speed

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

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

How to find the Wind Power Here the turbine power curve is used to estimate the power generated in each speed range The sum of the probable powers yields the kWh/h, so if over 8760 hours in a year, E = 8760 h/yr * 2027kWh/h = 17,756,520 kWh = 17 GWh/year

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

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

A really simple example For any site, the wind speed distribution varies with time  The 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

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

Wind Energy Derivation Equations (also applies to water turbines) Assume a “tube” of air the diameter, D, of the rotor  A = π D 2 /4(could be rectangular for a VAWT) A length, L, of air moves through the turbine in t seconds  L = u·t, where u is the wind speed The tube volume is V = A·L = A·u·t Air density, ρ, is kg/m 3 (water density ~1000 kg/m 3, or 832 times more than air) Mass, m = ρ·V = ρ·A·u·t, where V is volume Kinetic energy = KE = ½ mu

Wind Energy Equations (continued) Substituting ρ·A·u·t for mass, and A = π D 2 /4, KE = ½·π/4·ρ·D 2 ·u 3 ·t Theoretical power, P t = ½·π/4·ρ·D 2 ·u 3 ·t/t = ·ρ a ·D 2 ·u 3, 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 extracted P e = P t ·59.3%·ή r ·ή t ·ή g, where P e is the extracted power, ή r is rotor efficiency, ή t is mechanical transmission efficiency, and ή g is generator efficiency For example, 59.3%·90%·98%·80% = 42% extraction of theoretical power

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 cost Anemometers 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

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 energy  A 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:

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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References: Books Brower, Michael. Cool Energy. Cambridge MA: The MIT Press, , TJ807.9.U6B76, ’4’0973. Gipe, Paul. Wind Energy for Home & Business. White River Junction, VT: Chelsea Green Pub. Co., , TJ820.G57, 621.4’5 Patel, Mukund R. Wind and Solar Power Systems. Boca Raton: CRC Press, 1999, 351 pp. ISBN , TK1541.P , ’2136 Sørensen, Bent. Renewable Energy, Second Edition. San Diego: Academic Press, 2000, 911 pp. ISBN

References: Websites, etc. best choice for information _________________________________________________________________________________ _____________________ Wind Energy elist Wind energy home powersite elist rredc.nrel.gov/wind/pubs/atlas/maps/chap2/2-01m.html PNNL wind energy map of CONUS Elist for wind energy experimenters telosnet.com/wind/20th.html solstice.crest.org/ dataweb.usbr.gov/html/powerplant_selection.html