The Application of U.S. Upper Wind Data in One Design of ... · SERI/TR-211-1400 UC Category: 60 The Application of U.S. Upper Wind Data in One Design of Tethered Wind Energy Systems

SERI/TR-211-1400UC Category: 60

The Application of U.S.Upper Wind Data in OneDesign of Tethered WindEnergy Systems

R.J. O'DohertyB. W. Roberts

, February 1982

Prepared under Task No. 1067.10WPA No. 172-81

Solar Energy Research InstituteA Division of Midwest Research Institute

1617 Cole BoulevardGolden. Colorado 80401

Prepared for theU.S. Department of EnergyContract No. EG-77-C-01-4042

Printed in the United States of AmericaAvailable from:National Technical Information ServiceU.S. Department of Commerce5285 Port ROfa1 RoadSpringfield, VA 22161Price:

Microfiche $3.00Pri nted Copy $ 7.25

NOTICE

This report was prepared as an account of work sponsored by the UnitedStates Government. Neither the United States nor the United States Depart..;ment of Energy, nor any of their employees, nor any of their contractors,subcontractors, or their employees, makes any warranty, express or implied,or assumes any 1ega1·liabi1ity or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or processdisclosed, or represents that itslse would not infringe privately ownedrights.

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FOREWORD

The work summarized in this report was supported through theAdvanced and Innovative Wind Energy Concepts task at the SolarEnergy Research Institute (SERI) within the Federal Wind EnergyProgram of the Department of Energy (DOE). Richard L. Mitchellwas the technical project manager.

This report was prepared to support SERI subcontractors working inthe field of Tethered Wind Energy Concepts. Data from theNational Genter for Atmospheric Research in Boulder, Colo. werereduced and analyzed by Robert J. O'Doherty (SERI) and Bryan v7.Roberts (Visiting Professor from the University of Sydney, Sydney,Australia). Specific sites are described in detail. Additionalsites were also analyzed, and results are available from SERI uponrequest.

R~chard L. MitchellSERI Project Manager

Approved for

SOLAR ENERGY RESEARCH INSTITUTE

Program Office .

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SUMMARY

Objective:

This report assesses the upper atmospheric wind resource for the continentalUnited States, Hawaii, and Alaska.

Discussion:

lhe document is intended for Solar Energy Research Institute contractorsinterested in tethered wind energy systems. The raw data were obtained fromthe National Center for Atmospheric Research, Boulder, Colo.

Conclusion:

The probability distributions of velocity are presented for 54 sites, anddetailed calm wind analyses have been undertaken for five of these locations. On the average, the wind lulls about one day per week for a period inexcess of about 30 hours.

The report shows that the average power density of this wind resource can beas high as 16 kW/m2 at northeastern U.S. sites. This power density is at amaximum around the 300-mb pressure level.

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TABLE OF alNTENTS

1.0 Introduction ••••.••••••....•.••.............•••..••..••••••..••..•. 1

2.0 Background of the COncept•••••••••••••••••••••••••••••••••••••••••• 3

2.12.2

2.32.42.52.62.72.8

Theoretical Foundations •••••••••••••••••••••••••••••••••••••••Numerical Techniques ••••••••••••••••••••••••••••••••••••••••••2.2.1 Average Wind Speed •••••••••••••••••••••••••••••••••••••2.2.2 Average Power Density ••••••••••••••••••••••••••••••••••2.2.3 Cumulative Velocity Distribution •••••••••••••••••••••••2.2.4 Calm Wind Analysis •••••••••••••••••••••••••••••••••••••2.2.5 Procedures for Missing Data ••••••••••••••••••••••••••••2.2.6 Sampling Periods •••••••••••••••••••••••••••••••••••••••2.2.7 Annual and Monthly Average Values of Velocity

and Power Density ••••••••••••••••••••••••••••••••••••Detailed Probability Analysis of the U.S. Upper Winds •••••••••Power-Duration Curves •••••••••••••••••••••••••••••••••••••••••The Annual Calm Period Analysis •••••••••••••••••••••••••••••••The Monthly Calm Period Analysis ••••••••••••••••••••••••••••••Lightning Conditions ••••••••••••••••••••••••••••••••••••••••••Conclusions •••••••••.••••.....•.•••••••••••••••..•.•..•••.••••

34555566

6131516192021

3.0 References .••••••.•••••••••.•.•••••••••.•.•••••••••••.•••••..•••••• 23

Appendix A - Average Values of Velocity and Power •••••••••••••••••••••••• 25

Appendix B - Application of U.S. Upper Wind Data in Pre-DesignTethered Wind Energy Systems •••••••••••••••••••••••••••••••• 55

Appendix C - Annual Calm-Period Charts ••••••••••••••••••••••••••••••••••• III

Appendix D - Use of the Annual Probability Distributionof Velocity Charts •••••••••••••••••••••••••••••••••••••••••• 123

vii

TR-1400S5~1'_'- --------------

LIST OF FIGURES

2-1

2-2

2-3

2-4

2-5

2-6

2-7

2-8

2-9

2-10

2-11

2-12

2-13

Time-Series Wind Data at a Pressure Altitude of p ••••••••••••••••••

Isopleths of Mean Power Density (kW/m2) at 300 mb ••••••••••••••••••




Monthly Average Power Density: Portland, ME •••••••••••••••••••••••

Annual Probability Distribution of Velocity: Portland, ME •••••••••

Annual Power-Duration Curve: Portland, ME •••••••••••••••••••••••••

Annual Calm-Period Analysis: Portland, ME •••••••••••••••••••••••••

Annual Calm-Period Analysis: Portland, ME •••••••••••••••••••••••••

Number of Occasions per Month Wind Speed is Below 15 m/s:Portland, ~ •••...••..••..•.....•....•••.•......•..••...•......•.

Average Period Wind Speed is Below 15 m/s: Portland, ME •••••••••••

Annual Average Number of Thunderstorm Days •••••••••••••••••••••••••

Page

4

9

10

11

12

13

14

15

17

18

19

20

21

LIST OF TABLES

2-1

2-2

Annual Average Values of Velocity and Power: Portland, ME ••••••••••

u.S. Sites Considered for Annual Average Values of Velocityand Power •••••••••••••••••••••••••••••••••••••••••••••••••••••••••

Page

7

8

ix

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SECTION 1.0

INTRODUCTION

The Solar Energy Research Institute (SERI) has recently awarded study contracts to assess and to recommend ways to harness the energy in the earth 'supper atmospheric wind system.

Jet streams flow continually in mid-latitudes in both hemispheres due to theeffect of both solar radiation on the tropics and cooling in the arcticregions with the rotation of the earth on its axis. Reiter, in his classictext on meteorology of the jet streams [1], describes the subtropical andpolar-front jet stream systems. Both these jets flow over the United States,but their confluence and meandering patterns lead to a variability in thestrength and persistence of the winds at anyone fixed site. The variabilityin the strength and location of these jets is the subject of this report.

Note that an assessment of the winds aloft is integral to the decision aboutthe siting, viability, and practicality of the various types of tethered windenergy systems.

This report is restricted to a statistical assessment of the U.S. upper windresource. It has been compiled from "Time Series Upper Wind Data," suppliedto SERI by the National Center for Atmospheric Research (NCAR), located inBoulder, Colo. These wind data are available for a variety of sites throughout the world, but this study is limited to the continental United States,Hawaii, and Alaska.

1

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SECTION 2.0

BACXGROUND OF THE ffiNCEPT

The current statistical survey uses wind energy conversion platforms, if theycan be located at sites remote from the earth's surface.

~~e will show that the availability of this wind energy resource increases withaltitude up to around 200 mb. In addition, at favorable u.s. sites, the powerdensity can be as high as 17 kW/m2, while at sites in the southern hemispherethe power density can be around 19 kW/m2 [2].

Note that the conversion of mechanical energy from winds invariably producesaerodynamic drag forces. In addition, the conversion of kinetic energy willgenerate a drag force that will be collinear with the free-stream velocityvector. This drag force must be balanced if a useful energy conversion is tobe produced.

These drag loads may be resisted by a tethering cable or cables. One end ofthe cable would be attached to the platform, and the other end would be fixedto the earth's surface. Subsystems other than a tethering cable might be usedto balance the drag load.

Finally, the means by which the converted energy will be transmitted to theearth's surface are left undefined. One can, however, assert that the averagepower density in the upper atmosphere is highly concentrated when compared toother renewable resources, such as direct solar radiation or wind energy nearthe surface.

2.1 THEORETI CAL FOUNDATIONS

By using standard wind energy techniques, we want to represent the cumulativeprobability distribution of the wind speed V by an integrated Weibull model:

p(V)p(V)

-(V/V )<lo= 1 - e for V ) 0= 0 elsewhere,

(1)

where Va and <l are two constants that give a good fit to the data.

The use of the Weibull distribution is common [3-6] in wind energy applications. Furthermore, the Rayleigh model is a special case of the Iveibull modelwhere a = 2. The application of these Rayleigh/Weibull models has become anestablished wind energy practice for the analysis of near-surface winds and isalso satisfactory for modeling upper wind data.

However, conventional meteorological techniques represent upper wind data witha bivariant normal distribution [7,8] so that the wind components in the zonal(E-W) and meridional (N-S) directions can be represented by suitable averagesand standard deviations. E~is model allows meteorologists to introduce windconstancy, vector means, and various wind components. However, in this report

3

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it is more appropriate to fit a vleibull distribution to the scalar winddistribution.

These raw rawinsonde data have been used to define the distributions. Thestandard pressure altitudes of 950, 850, 750, 700, 600, 500, 400, 300, 250,and 200 mb are used to define the various vertical sectors.

In summary, the probability distributions of velocity will be compiled for aseries of altitudes at 54 sites selected across the United States and its territories. Then probability distributions can be plotted on a log-log scale.(This graph paper will be referred to as ~-leibull paper , ) Further details ofthis type of representation can be found in a report by Takle and Brown [3 J •On this class of graph paper, the Weibull distribution plots a straight linewith a slope of a/2, which passes through point V = Va' p(V) = 1 - lie. Thistreatment (see Fig. 2-7) allows one to easily evaluate a by use of the sidenomogram. The magnitude of Vo is given by the intersection of appropriatedistribution with the 63.2% ordinate (shown as a dotted line in thefigures). More details on the use of these charts are given in Appendix D.

2.2 NUMERICAL TEOINIQUES

These raw rawinsonde data were obtained from NCAR. These tapes contained,among other information, a series of one-half day samples of wind velocity andair temperature at the standard pressure altitudes. These data were collectedfrom balloon soundings launched at 0000 and 1200 hours GMT from fixed sites.

The numerical analysis can bes t be described by reference to Fig. 2-1, whichis a segment of the time-series wind data at a pressure altitude p. Yne dataextend from day n to day (n + 4).

vPressure Level (p)

Day (n) • I" I .. I. '"Day(n + 1) Day(n + 2) Day(n+~) Day(I1-+ 4)

Time (h)

Figure 2-1. Time-Series Wind Data at a Pressure Altitude of p

4

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2.2.1 Average Wind Speed

The average wind speed is the summation of the observations divided by thetotal number of observations:

NV = I Vi/N

c=i(2)

2.2.2 Average Power Density

The average power density is defined as

NP = 1/2 I Pi Vi

3/Ni=l

(3)

The air density Pi has been derived from the equation of state as

Pi ~ 0.35 p/(Ti + 273) (4)

where Ti is the ith observation of the air temperature.

2.2.3 CUmulative Velocity Distribution

The cumulative velocity distribution at the velocity V is physically the percentage probability for which the wind velocity will be less than or equal tothe value of V:

p(V) = 100 n(V)/N (5)

where n(V) is the number of observations when the velocity is less than orequal to V. The total number of observations N is approximately 5100 per sitein this study.

2.2.4 calm Wind Analysis

A calm wind survey is important in the design and operation of any tetheredsystem.* Although it is important to know the cumulative probability P(V

I),

it is equally significant to know how long, on the average, the wind is be owthe threshold velocity VT• Also we would like to know on how many occasionsin a given period the winds will fall below the threshold value. In mathematical form, this implies that:

(6)

*The importance of the calm wind analysis will be discussed at length inSees. 8.0 and 9.0.

5

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1- - - - - - - - - - - - - - - - - - - - - - -

where

P(VT) is the probability the velocity will be equal to or below aspeed of VT;

H(VT) is the average number of times per year that the wind fallsbelow the threshold speed; and

T(VT) is the average period in hours that the wind speed is belowthreshold.

If N(VT) were compiled monthly, then the denominator in Eq. 6 will be 730.

In Fig. 2-1, for example, the first downtime is T1(VT) hours. Therefore, avalue of unity is accumulated into the c~unt of N(VT), while a value of T1(VT)is counted into the running average of T(V_T). A linear interpolation schemehas been used to compute the downtimes. rurthermore, the standard deviationof T(VT) has been computed and will be discussed later.

2.2.5 Procedures for Missing Data

Of approximately five thousand samples at each site and altitude, we foundthat about 1% to 2% of data were missing for two reasons.

First, occasionally, the rawinsonde sounding was completely missing due toradar breakdown or poor weather conditions. In this case, the data wereeffectively moved to the left, on Fig. 2-1, by one day. Thus, no gaps wereintroduced into the string of soundings. On other rare occasions, three orfour soundings were taken in one day. Under these circumstances, the information in Fig. 2-1 was moved to the right to receive the extra data.

Secondly, on some occasions, the rawinsonde flight was abandoned too early,perhaps because of a premature bursting of the balloon. In this case, weassumed the missing data (shown as the open square symbol in Fig. 2-1) were ofthe same value as those from the previous sounding at the same altitude.

We believe this treatment of the missing data is reasonable. However, othertechniques are possible, but the technique used should not significantlyaffect the result.

2.2.6 Sampling Periods

We have evaluated parameters in Sees. 2.2.1 to 2.2.5 for each month in aseven-year period. We have also assembled annual statistics for the 54 sitesin the United States.

2.2.7 Annual and Monthly Average Values of Velocity and Power Density

The average velocity and power density can be determined from the raw data bythe use of Eqs. 2 to 4. Average values of both of these variables are given

6

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in Table 2-1. This figure uses Portland, Maine, as an example, and nine altitudes are listed.

Table 2-1. Annual Average Valuesof Velocity and Power:Portland, ME

Altitude(mb)

Velocity(V, m/s)

Power(p, kl-1/m2)

900850700600500400300250200

9.4210.414.818.422.527.632.833.931.2

1.111.362.844.677.53

11.414.112.97.90

The same calculations have been performed for 53 other U.S. sites. The relevant values are given in Appendix A as Tables A-I through A-54. The appendixconsiders the sites alphabetically (see Table 2-2).

From the annual average power-density figures given in Appendix A, one candraw resource maps showing the isopleths of power density at the variousaltitudes. Figures 2-2 to 2-5 show these charts for the 300, 400, 500, and700 mb levels, respectively.

In the United States, the wind energy resource is primarily concentrated inthe Northeast, where the average power density can ~e in excess of 16 k\v/m2•

At 300 mb , the power densitY2 falls to about 8 klv/m in the Midwest, and itfalls further to about 4 kW/m in equatorial regions.

Note that the jet stream is the dominant influence in the upper airresource. The power density essentially reflects the average residence timethat a jet spends above a site as the jet "meanders" over the continent.

Finally, monthly values of power density can be calculated from the rawdata. This can be completed for all stations if required, but typical resultscan be seen in the output for Portland, Maine. Figure 2-6 shows the monthlyaverage power densities for Portland; the results were derived from a sevenyear sample.

Figure 2-6 shows that the power density is at a maximum of about 30 kW/m2 inJanuary and falls to 7 kW/m2 in July. The maximum and minimum values occurabout one month after the winter and summer solstices, respectively [1].

7

Table 2-2. U.S. Sites Cbnsidered for AnnualAverage Values of Velocity and Power

Albany, NY

Albuquerque, NM

Bismarck, ND

Boise, In

Brownsville, TX.

Buffalo, NY

Caribou, ME

Charleston, SC

Dayton, OR

Del Rio, TX.

Denver, CO

Dodge City, KS

Ely, NV

Fairbanks, AK

Fort Worth, TX.

Glasgow, MT

Great Falls, MT

Green Bay, WI

Greensboro, NC

Guadalupe Island, Mexico

Hilo, HI

Huntington, WV

International Falls, MN

Lander, WY

Little Rock, AR

Medford, OR

Hidland, TX.

Montgomery, AL

Nashville, TN

New York, NY

North Platte, NE

Oakland, CA

Oklahoma City , OK

Omaha, NE

Peoria, IL

Pittsburgh, PA

Portland, ME

Rapid City, SD

St. Cloud, MN

Salem, IL

Salem, OR

Salt Lake City, UT

San Nichols Island, CA

Sault Ste. Marie, HI

Shreveport, LA

Spokane, WA

Tampa, FL

Topeka, KS

Tucson, AZ

Wallops Island, VA

Waycross, GA

Winnemucca, NV

IHnslow, AZ

Yucca Flats, NV

8

TR-1400S=~II.I-----------------

'"'"'"so

300 rnb

E 30-.....~:.:.

:::IJlc:(1)

0.... 20(1)

:1:0

Mean 14.2 kW/m 2CL(1)Q)(\3....(1)

>< 10

J F M A o N o

Month

Figure 2-6. Monthly Average Power Density: Portland, ME

2.3 DETAILED PROBABILITY ANALYSIS OF THE n.s, UPPER WINDS

A typical, cumulative probability distribution of velocity is shown inFig. 2-7 for Portland, Maine. Here distributions for the pressure levels of700, 500, 400, 300, and 200 mb are approximated by straight-line Weibull distributions. In all cases, the actual distributions are closely modeled by theWeibull distributions. The intersection of the approximating straight linewith the dotted line gives the value of Va in Eq, 1. The slope of thestraight line gives the value of the exponent a which is also in Eq. 1. Moredetails of the distributions for the 54 sites are given in Appendix B asFigs. B-1 through B-54. These figures are relevant to the design of tetheredwind energy conversion systems. For example, it is conventional to usefigures similar to Figs. B-1 to B-54 in the design of a typical windmill.From the probability distribution of velocity, it is simple to derive the

13

TR-1400S5~1!_'---------------~":';;:';;:

power-duration curve for that location. These charts may then be used to complete the well-known cost-of-energy calculation. Presumably, an optimalarrangement would minimize this energy cost. An important aspect of thisoptimization procedure is the manipulation of the probability distributionfunctions given earlier.

2.4 P<JmR-DURATION aJRVES

The power-duration curve for any of the listed sites, at the relevant altitude, may be determined from the appropriate figure in Appendix B. It issimple to select a series of velocities, form the product 1/2 p V3, and plotthis function against B760 P(V), the effective duration period. The value ofp can be determined from standard tables or by use of Eq. 4.

A typical annual power-duration calculation is shown in Fig. 2-8 for Portland,Maine, at the altitude of 300 mb. One can determine a similar curve for anyother site and altitude.

300 mb

1 Year

~I8 9

Mean 14.1 kW/m2

765432

.....Q)

~aa.. 10

40r---~-------------------------------'

~JiJ

Q)

o

Hours x 103

']00557

Figure 2-8. Annual Power-Duration Curve: Portland, ME

IS

TR-1400

2.5 THE ANNUAL CALM PERIOD ANALYSIS

The economic and pragmatic conversion of wind energy at an altitude that isremote from the earth's surface is critically dependent on calm periods in thetropopause. A velocity (referred to as the threshold velocity) will be usedto define the onset of a calm period aloft. Tnis velocity could be equal tothe stalling speed of some fixed wind energy conversion platforms. However,it might be the minimum auto-rotative speed of some rotary wing device. Also,it might be the speed at which a balloon is deployed from a hybrid, fixedwing-balloon platform. This minimum, or threshold, speed will be, in principle, the threshold condition that defi~es a change in the operating modes ofa tethered platform. Furthermore, this report is not intended to discuss themerits of an operating mode in any particular system. This report will stressthat low-wind periods are an important variable that can be extracted from thetime series wind data.

In Eq , 6 we defined the parameters N(VT) and T(VT). The former is the totalnumber of individual occasions in a typical year or month that the wind speeddrops below the threshold speed. The companion parameter is T(VT); i.e., thenumber of hours, on the average, that the wind stays below the thresholdvelocity. The average can be taken over a month or a year, whichever isdesired. Note that the product of Nand T, relative to the number of hours ina year or month, is the cumulative probability at the velocity VT•

A large value for N and a small value for T may be an unfavorable combinationfor tethered systems. The inverse situation may be more attractive. Then thecalms would be as long as possible on relatively few occasions.

The current data have been analyzed to evaluate the functions Nand T througha ra~ge of the parameter VT from 5 to 40 m/s. The annual average values of Nand T are given in Figs. 2-9 and 2-10. These charts refer to Portland,Maine. Further charts for Denver, Colo.; Guadalupe Island, Mexico; Midland,Texas; and Oakland, Cal.Lf , , are given in Appendix C as Figs. C-1 throughC-10. Curves are given for the pressure levels of 600, 500, 400, 300, and200 mb, Data for additional locations and levels are available on requestfrom SERIo

Figure 2-9 and other charts in Appendix C show that the value of N decreaseswith increasing altitude for the velocity in the range 0 < VT < 25 m/s.Beyond 25 mis, the situation is reversed.

In Fig. 2-10 the average time T increases steeply with increasing velocity,which occurs at all altitudes. Conversely, as the altitude increases, thetime period decreases. One might conclude that at a typical U.S. site thewind lulls approximately below 20 mls weekly. In addition, the annual averagetime T below 20 mls is always greater than 30 hours, regardless of thealtitude or site location. Furthermore, from the statistical analysis, wehave ~bserved that the standard deviation in T(VT) is of the same order as themean T(VT), indicating the variation one might expect for T(VT) in any practical situation.

16

TR-14005=",11,------------------2.6 THE MONTHLY CALM PERIOD ANALYSIS

Data Eor the 54 stations have been analyzed at the monthly level. However, itis impossible to present all data now. Therefore, we suggest that Portland,Maine, might be considered an optimistic U.S. site.

The results of the monthly analysis at 300 mb with VT = 15 mls for Portlandare shown in Figs. 2-11 and 2-12. Scrutiny of the figures indicates thatJuly, one month past the summer solstice, has the least wind. In July, for athreshold of 15 mis, the winds will calm on about 6 occasions for about 30hours each. In the windiest month, January, the wind will fall below 15 mlson about 1.3 occasions per month for a period of about 10 hours on eachoccasion.

In summary, if 15 mls is the stalling speed of a certain aerodynamic platform,then the system will tend to collapse whenever the wind lulls below thisspeed. In other words, collapse situations will occur according to Fig. 2-11,and the downtime will last for the period indicated in Fig. 2-12.

If the platform's stalling speed is in excess of 15 mis, the collapse occasions and periods will generally increase. However, the inverse situationwill occur for stalling speeds less than 15 m/s.

300 mb

~

I I

Mean 3.6/mo.- -- --I I

"'"

I

I 1 I I I I I I 1 I

8

6

(J)

c0IJl(1J

UU0a 4"-Q).cE::lZ

2

o J F M A M J J A s o N o

Month

Figure 2-11. NumbecofOccasions Per Month Wind Speed Falls Below 15 m/s:Portland, ME

19

TR-1400S=~II_I--------------~"":::"':':':

40 r--------------------------------.300 mb

•s: 30sn'-E •l(),...~ •0aico 20 Mean 19.1(I)

Ei=(I)

OJell....(I)>-c

10

•a

J F M A M J J A S 0 N 0

Time of Year

Figure 2-12. Average Period Wind is Below 15 m/s: Portland, ME

2.7 T..IGHTNI~ OONDITIONS

Possible lightning conditions are also important in the design of tetheredwind energy systems. The average number of lightning days is essentially theaverage number of thunder days (which can be found in published charts) [91.Our report notes that lightning conditions will be important. The occurrenceof thunderstorm days is shown in Fig. 2-13.

20

TR-14005a'l,�fl---------------=--=-...;,.;;,..;:

..----------------------------------.. ~U1

'"s

Source: Dodd. C W. 1977 (Oct.) "lightning Protection for a Vertrcal-Axis Wind Turbine" Sand77-1241: Sandia Labs.

Figure 2-13. The Annual Average Number of Thunderstorm Days

2.8 <DNCLUSIONS

This report has attempted to analyze the relevant meteorological data thataffect the design of tethered wind energy conversion systems. The UnitedStates, as we have shown, is a favorable site for this renewable energyresource. At fixed sites, the annual average power density is 10 to 16 kW!m2,and over 30% of the continent.

21

22

TR-1400

SECTION 3.0

REFERENCES

1. Reiter, E. R. 1963. Jet Stream Meteorology. Chicago:Chicago Press.

University of

2. Atkinson, J. D. et al. The Use of Australian Upper Wind Data in theDesign of an Electrical Generating Platform. Charles Kolling Laboratory,Tech, Note D-17. Sydney, Australia: University of Sydney.

3. Takle, E. S.; Brown, J. M. 1978 (Apr.). "Note on the Use of Weibull Sta-tistics to Characterize H'ind Speed Data." J. Appl. Met. Vol. 17:pp , 556-559.

4. Hennessey, J. P. 1977 (Feb.). "Some Aspects of Hind Power Statistics."J. Appl. Met. Vol. 16: pp , 119-128.

5. Hennessey, J. P. 1978. "Comparison of Weibull and Rayleigh Distributionsfor Estimating Wind Power Potential." Wind Eng. Vol. 2 (No.3):pp , 156-164.

6. Cliff, W. C.; Justus, C. G.; Elderkin, C. E. Simulation of Hourly WindSpeeds for Randomly Dispersed Sites. Rep. PNL-2523. Richland, WA: Battelle-Pacific Northwest Laboratory.

7. Davenport, A. G.; Baynes, C. J. 1972 • "An Approach to the Mapping of theStatistical Properties of Gradient TN'inds (over Canada)." Atmosphere.Vol. 10 (No.3): pp. 80-92.

8. Maher, J. V.; Lee, D. M. 1977 (Apr.). "Upper Air Statistics - Aus-tralia." Bureau of Met. Department of Science.

9. Dodd, C. W. 1977 (Oct.). Lightning Protection for a Vertical-Axis \-JindTurbine. SAND 77-1241. Albuquerque, NM: Sandia Laboratories.

23

S-~I *=~il_1

24

TR-14005=~1 rill-------------------

APPENDIX A

AVERAGE VALOES OF VELOCITY AND POWER

25

S-~I /.·= ·'_ III I- .~~

26

TR-14005='li_I----------------.--

Table A-I. Annual Average Values ofVelocity and Power

Albany, NY

Altitude V!.locity Power(mb) (V, m/s) (P, kW/m2)

900 10.1 1.19850 11.3 1.63700 15.2 3·.10600 18.7 5.04500 22.6 7.78400 27.0 10.9300 31.9 13 .4250 33.1 12.2200 31.4 8.13

Table A-2. Annual Average Values ofVelocity and Power

Albuquerque, NH

Pressure Mean MeanAltitude Velocity Power

(mb) (V, m/s) (p, kiV/m2)

900850 2.50 0.01700 8.19 0.53600 11.4 1.31500 15.1 2.91400 18.8 4.85300 23.4 6.73250 26.0 7.31200 26.7 5.80

27


Bismarck, ND

TR-1400

Altitude(mb)

900850700600500400300250200

Velocity(V, m/s)

8.789.52

12.214.918.322.627.628.726.5

0.750.971.592.504.046.519.178.495.08


Boise, ID

Altitude Velocity Power(mb) (V, m/s) (p, kH/m2)

900 4.37 0.11850 6.05 0.29700 9.56 0.77600 13.2 1.72500 17.1 3.29400 21.6 5.70300 27.0 8.71250 28.6 8.69200 26.1 5.16

28

Table &-6. Annual Average Values ofVelocity and Power

Buffalo, NY

Altitude Velocity Power(mb) (V, mls ) (El, kvllm 2)

900 9.79 1.20850 10.7 1.44700 14.5 2.60600 17 .5 4.04500 21.1 6.39400 25.3 9.39300 29.8 11.2250 31.6 10.8200 29.6 6.8

29

TR-1400

TR-14005=~1 i_I---------------~----=;....,;:;,..;....:...:..


Caribou, ME

Altitude(mb)

Velocity(V, mls )

Power- 2(P, kW/m )

900850700600500400300250200

10.411.214.617.721.626.532.533.930.8

1.221.522.574.166.72

10.514.714.18.35


Charleston, SC

Altitude Velocity Power(mb) (V, m/s) (p, kH/m2)

900 8.15 0.77850 8.67 0.89700 11.6 1.79600 13.9 2.77500 16.8 4.30400 20.3 6.19300 25.2 8.86250 28.5 10.3200 30.9 9.96

30

TR-140055~1'_'-------------------


Dayton, OR

Altitude(rnb)

Velocity(V, rn/s)

900850700600500400300250200

8.919.85

13 .716.920.625.130.532.932.2

0.951.242.373.876.339.84

13.113.19.47

Table frIO. Annual Average Values ofVelocity and Power

Del Rio, TX

Altitude ~locity Power(mb) (V, m/s) (El, kW/m2)

900 8.09 0.50850 7.91 0.47700 8.44 0.61600 10.9 1.24500 13 .9 2.32400 17.8 3.94300 23.4 6.58250 26.7 7.98200 28.4 7.43

31

Table A-ll. Annual Average Values ofVelocity and Power

Denver, CO

TR-1400

Altitude(mb)

900850700600500400300250200

Velocity(V, m/s)

7.0110.714.518.623.925.925.5

0.411.082.183.986.406.484.60


Dodge City, KS

Altitude Velocity Power(mb) (V, ml s ) (p, k\.J/m2)

900 8.58 0.59850 10.3 1.21700 10.8 1.20600 13.1 1.90500 16.3 3.30400 20.6 5.66300 25.9 8.52250 28.5 9.11200 28.7 6.93

32

TR-1400S5~li_'----------------

Table A-l3. Annual Average Values ofVelocity and Power

Ely, NV

Altitude(mb)

Velocity(V, m/s)

Power(p, kW/m2)

900850700600500400300250200

7.2910.814.618.823.425.324.6

0.521.122.414.346.286.244.30

Table A:-14. Annual Average Values ofVelocity and Power

Fairbanks, AK

Altitude Velocity Power(mb) (V, m/s ) (p, kW/m2)

900 5.72 0.28850 6.40 0.38700 8.31 0.63600 9.72 0.88500 12.0 1.58400 15.4 2.76300 18.3 3.90250 17.3 s.n200 14.3 1.23

33

TR-1400S=~I i_I -----------------------

Table 1115. Annual Average Values ofVelocity and Power

Fort Worth, TX

Altitude(mb)

Velocity(V, m/s)

900850700600500400300250200

9.269.20

10.813.116.220.326.029.431.5

0.950.901.282.093.435.589.04

10.710.0

Table k-16. Annual Average Values ofVelocity and Power

Glasgow, MT

Altitude Velocity Power(mb) (v, m/ s ) (p, kW/m2)

900 7.61 0.48850 8.73 0.80700 11.7 1.42600 14.5 2.23500 17.8 3.58400 22.3 6.07300 27.1 8.41250 28.0 7.69200 25.1 4.31

34

5a'II.1


Great Falls, MT

Altitude Velocity Power(mb) ('i, m/s ) (p, kW/m2)

900 3.13 0.30850 .8.40 0.72700. 10.7 . 1.31600 13 .7 2.08500 17.3 3.43400 22.0 6.11300 27.3 8.99250 28.2 8.20200 25.2 4.53

Table ko18. Annual Average Values ofVelocity and Power

Green Bay, WI

Altitude Velocity Power(mb) (v, m/s) (p, k~-l/m2)

900 9.25 0.92850 9.67 0.99700 13 .0 1.81600 16.0 3.00500 19.4 4.85400 24.0 7.97300 30.0 11.53250 31.1 10.87200 28.8 6.71

35

TR-1400

TR-1400S=~li.I-----------------


Greensboro, NC

Altitude(mb)

Velocity(V, m/s)

Power(p, kW/m2 )

900850700600500400300250200

8.349.13

13.015.819.323.327.930.330.8

0.761.022.233.485.488.03

10.210.78.61


Guadalupe Island, Mexico

Altitude Velocity Power(mb) (v, m/s) CP, kW/m2)

900 4.81 0.15850 5.48 0.21700 7.45 0.45600 9.00 0.75500 10.7 1.08400 12 .8 1.50300 16.1 2.25250 17.9 2.69200 19.0 2.63

36

TR-140055'1,_1 -----------------------------

Table A-2I. Annual Average Values ofVelocity and Power

Hilo, HI

Altitude(mb)

Velocity(V, m/s)

900850700600500400300250200

4.274.165.646.027.58

10.917.221.725.0

0.0960.08B0.1910.2420.4130.9002.473.954.80


Huntington, WV

Altitude Velocity Power(mb) (V, m/s ) - 2(P, kW/m )

900 8.18 0.77850 9.32 1.06700 13 .6 2.37600 16.9 3.96500 20.5 6.32400 24.7 9.13300 30.3 12.8250 32.9 13 .1200 32.8 10.1

37

Table ~24. Annual Average Values ofVelocity and Power

Lander, WY

Altitude Velocity Power(mb) (V, m/s) (p, kW/m2)

900850700 6.83 0.42600 12.3 1.56500 15.9 2.87400 20.0 4.72300 25.4 7.49250 27.0 7.31200 25.5 4.79

38

TR-1400


Medford, OR

Altitude Velocity Power(mb) (v, m/s) (p, klv/m2)

900 3.63 0.087850 4.87 0.19700 ,10.9 1.42600 14.2 2.49500 18.0 4.25400 22.3 6.70300 26.8 9.05250 28.1 8.56200 26.1 5.19

39

TR-1400

TR-1400S=~II_I ---------------------------


:1idland, TX

Altitude(mb)

Velocity(V, m/s)

900850700600500400300250200

6.638.779.42

12.415.519.424.927.929.1

0.250.630.871.723.125.147.989.188.03


Montgomery, AL

Altitude Velocity Power(mb) (V, m/s) CP, kW/m2)

900 7.57 0.60850 8.28 0.74700 11.1 1.59600 13.4 2.52500 16.4 3.96400 19.9 5.83300 24.7 8.44250 27.8 9.80200 30.1 9.48

40

TR-1400S=~I ,;11 - - - - - - - - - - - - - - - - - - - - - - - - -


Nashville, TN

Altitude(mb)

Velocity(V, m/s)

PowerCP, k~.J/m2)

900850700600500400300250200

8.489.31

13 .015.819.223.328.831.332.5

0.891.092.203.595.638.33

11.612.510.4


New York, NY

Altitude Velocity Power(mb) (V, m/ s ) (p, kW/m2)

900 9.94 1.28850 10.7 1.46700 15.0 3.03600 18.5 1.85500 22.4 7.98400 27.5 12.3300 33.2 16.2250 35.5 16.3200 34.6 11.6

41

TR-1400S=~II_I------------------------


North Platte, NE


900 6.20 0.25850 9.74 0.96700 11.4 1.34600 13 .9 2.05500 16.9 3.24400 20.9 5.51300 26.1 8.29250 28.3 8.55200 27.6 6.04

..,


Oakland, CA

Altitude Velocity Power(mb) (V, ml s ) (p, k'oJ/m2)

900 6.18 0.33850 6.80 0.43700 9.99 loll600 13.0 2.12500 16.3 3.54400 20.3 5.43300 25.1 7.62250 27.0 7.57200 26.3 5.44

42

S=~I'_I


Oklahoma City, OK

Altitude Velocity Power(mb) (V, m/s) (p, k~~/m2)

900 10.0 1.21850 9.9 1.18700 11.2 1.49600 13.6 2.41500 16.5 3.84400 20.4 5.80300 25.6 8.04250 27.8 8.59200 27.8 6.94


Omaha, NE


900 10.3 1.67850 10.5 3.12700 12.6 1.78600 15.4 2.96500 18.6 4.72400 22.8 7.66300 28.1 10.8250 30.1 10.5200 29.0 6.96

43

TR-1400

TR-140055'1;_1-----------------


Peoria, IL


900 9.33 1.00850 9.87 1.12700 13.4 2.13600 16.5 3.59500 19.9 5.72400 24.3 8.86300 29.8 12.31250 32.1 12.35200 31.4 8.83


Pittsburgh, PA


900 8.57 0.79850 9.89 1.15700 14.5 2.640600 17.8 4.30500 21.6 6.91400 26.3 10.8300 32.2 14.9250 34.4 14.8200 33.1 10.0

44

TR-1400S=~I i_I ----------------------


Portland, ME

Altitude(mb)

Velocity(V, ml s)

Power(p, kH/m2)

900850700600500400300250200

9.4210.414.818.422.527.632.833.931.2

1.111.362.844.677.53

11.3814.112.97.9


Rapid City, SD

Altitude Velocity Power(mb) (ii, m/s) (p, kW/m2)

900 5.27 0.22850 8.31 0.73700 12.3 1.23600 19.4 1.94500 17.1 3.17400 21.3 5.23300 26.2 7.74250 27.7 7.60200 26.1 4.82

45

TR-1400S=~II_I ----------------------------


St. Cloud, MN

Altitude(mb)

Velocity(V, m/s)

Power(p, kt-J/m2)

900850700600500400300250200

9.199.66

12.715.418.722.928.329.827.5

0.880.981.692.704.296.829.889.425.61


Salem, IL

Altitude Velocity Power(mb) (V, ml s ) (p, kFllm2)

900 9.24 1.02850 9.86 1.16700 13.4 2.19600 16.2 3.56500 19.5 5.55400 23.6 8.24300 28.0 10.2250 30.0 10.1200 29.4 7.39

46

TR-1400S=~I i_I-----------------.,;:.:.:.-.;;"".;.~


Salem, OR

Altitude(mb)

Velocity(V, m/s)

900850700600500400300250200

6.917.96

11.915.018.823.227.828.325.3

0.630.891.632.594.447.159.318.054.40


Salt Lake City, UT


900850 4.79 0.15700 7.65 0.41600 11.6 1.15500 15.6 2.61400 20.0 4.87300 24.8 7.32250 26.7 7.50200 25.6 4.94

47

TR-14005=~11_1-----------------------


San Nichols Island, CA

Altitude(mb)

Velocity(V, m/s)

Power(p, kW/m2)

900850700600500400300250200

5.055.728.50

10.713.016.020.622.723.4

0.230.290.751.412.163.164.535.004.14


Sault Ste. Harie, HI

Altitude Velocity Power(mb) (1f, m/s) (p, kW/m2)

900 9.13 0.85850 9.82 1.00700 13.2 1.92600 16.0 2.99500 19.4 4.81400 23.8 7.87300 29.5 1l.70250 31.1 11.29200 28.7 6.95

48

TR-1400S=~II.I ---------------------------


Shreveport, LA

Altitude(mb)

Velocity(V, m/s)

900850700600500400300250200

8.449.03

11.313 .816.720.525.428.429.9

0.840.991.492.443.1345.998.249.528.62


Spokane, WA


900 6.32 0.34850 7.34 0.61700 10.0 0.98600 13.7 2.05500 17.7 3.77400 22.8 6.78300 28.7 10.6250 29.6 10.0200 26.3 5.57

49

TR-1400S=~I '_1--------------------...:.:.:......:....:....:


Tampa, FL

Altitude(mb)

Velocity(fi, m/s)

PowerCP, k\v/m2)

900850700600500400300250200

6.436.577.769.56

12.115.219.422.425.2

0.350.390.671.081.742.704.245.265.58


Topeka, KS

Altitude Velocity Power(mb) (fi, mls ) CP, kW/m2)

900 9.70 1.08850 9.96 1.14700 12.4 1.75600 15.0 2.76500 13.0 4.30400 22.0 6.80300 26.9 9.25250 29.0 9.24200 28.6 6.55

50

TR-1400S=~I '_I ---'-------------------------


Tucson, AZ

PressureAltitude

(mb)

HeanVelocity(v, m/s)

MeanPower

(p, kW/m2)

900850700600500400300250200

4.475.127.68

10.714.017 .922.825.626.7

0.130.190.501.232.544.436.447.496.37

Table h-50. Annual Average Values ofVelocity and Power

Hallops Island, VA

Altitude Velocity Power(mb) (v, m/s) (p, kH/m2)

900 9.71 1.20850 10.2 1.24700 14.0 2.43600 17.2 4-.08500 20.7 6.37400 24.9 9.24300 29.7 12.1250 32.0 12.2200 32.1 9.67

51

TR-1400S=~I '_I----------------=.:.:~


lvaycross, GA

Altitude(mb)

Velocity(V, m/ s )

Power(p, kW/m2)

900850700600500400300250200

7.507.92

10.412.515.318.823.526.629.2

0.600.711.412.233.455.207.318.548.58

Table h-52. Annual Average Values ofVelocity and Power

lHnnemucca, NV

Altitude Velocity Power(mb) (V, m/ s ) (p, kl-l/m2)

900850 4.52 0.11700 8.21 0.64600 12.2 1.57500 16.1 3.08400 19.9 4.84300 24.9 7.22250 26.1 6.76200 24.6 4.28

52

TR-1400S=~I '_I ---------'----------------


Winslow, AZ

Altitude(mb)

Velocity(V, m/s)

Power(p, kW/m2)

900850700600500400300250200

3.138.31

10.714.018.123.325.625.8

0.050.681.222.324.296.597.005.27


Yucca Flats, NV

Altitude Velocity Power(mb) (V, m/s) (p, k~.Jlm2)

900850 5.06 0.19700 7.81 0.50600 10.4 1.11500 14.1 2.39400 17.9 3.97300 22.4 5.47250 24.3 5.48200 24.1 4.17

53

S-~I ·?.;;;.= "_ III I- ,~~

54

APPENDIX B

APPLICATION OF U.S. UPPER WIND DATA INPRE-DESIGN TETHERED WIND ENERGY SYSTEMS

55

TR-1400

56

TR-1400S=~II_I---------------=~

APPENDIX C

ANNUAL CALM-PERIOD CHARTS

111

112

TR-1400S=~II_I-------------------

APPENDIX D

USE OF THE ANNUAL PROBABILITYDISTRIBUTION OF VELOCITY CHARTS

123

124

TR-1400

APPENDIX D

USE OF THE ANNUAL PROBABILITY DISTRIBUTION OF VELOCITY CHARTS

The Annual Probability Distribution of Velocity charts are given in Figs. B-1through B-54 in App. B. In each of the charts the actual cumulative probabilities P(V) are plotted against V for various pressure levels between 700 mband 200 mb.

Furthermore the charts have been plotted on special paper known as ~.Jeibull

paper [3]. On this paper the two-parameter Weibull distribution, given as

(1)

will appear as a straight-line plot. In this manner, ~ straight line may bedrawn to.represent the actual distribution formed from the NCAR data.

The probability distribution given in Eq. 1 uses two parameters, Vo and a. Inorder to reduce this. distribution to a straight-line plot on 'I.Jeibull graphpaper, one needs to compute the natural logarithm of both sides of Eq , 1.Hence it follows that

If Eq. 2 is plotted on log-log graph paper,

«t: = log(~{l/D - P(V)] f)/log(V/V o)

(2)

(3)

In this way the slope of the straight-line plot of Fig. 2-7 is exactly «n .In addition the value of Vo is found from V = Vo when P(V) = (1 - lie)= 0.633.

Finally a is approximately 2 in our work, so that the slope of the straightline is approximately 45 0 because a/2 ~ 1.

Figure 2-7 of the text gives the Weibull probability distributions for Portland, Me., at altitudes of 700, 500, 400, 300, and 200 mb. The intersectionof the appropriate Weibull straight line with the dotted horizontal line atp(V) = 63.3% gives the corresponding value of Vo ' as read on the abscissa ofthe chart. The values of Va are tabulated in Table D-l as read from Fig. 2-7to an accuracy of :0.5 m/s.

To determine the value of a, first choose the required straight-line distribution. Then draw another straight line parallel to this line so that it passesthrough the center of the target symbol near the top right corner of thefigure. Next extend this parallel line to cross the vertical line at theextreme left side of the figure. This latter intersection gives the value ofa. The relevant values of a from Fig. 2-7 are given in Table D-l to a readingaccuracy of about ±C.Ol.

125

TR-1400S=~I'_I-----------------

Table 0-1. Values of Vo inPortland, Maine

Pressure V(mb) (mts)

ex

700 16.5 1.98500 25.5 2.07400 31.5 2.07300 37.0 2.22200 35.5 2.21

It is possible to show from the Weibull distributionaverage annual wind speed V and the average annualfollowing functions of Vo and a:

given in Eq. 1 that thepower density P are the

(4)and

P = 1/2 PV3r ( 1 + 3/a)o

(5)

where r(x) is the gamma function that is widely tabulated.

Next, compare the mean velocities and power densities using Table D-1 with theactual computed values of V and P using the NCAR data. The comparison inTable D-2 verifies the validity or otherNise of our Weibull model. The firstof the columns V and P are for the 1;-leibull model, while the second columnsof V and P are formed from the NCAR data.

According to the results in Table D-2, the Weibull model gave good estimatesof the mean wind speeds and the mean power densities.

We feel that the two-parameter Weibull model is generally satisfactory, whichis in line with other wind energy results from workers such as Justus, Hennessey, and others.

126

Table D-2. Veibull Model vs , Actual Data for Values of V and P in Portland. Maine

InIIIN-.

~- '

I I

"- .

Pressure(mb)

700500400300200

r(l + 1/0.)

0.8860.8860.8860.8860.886

r(l + 3/0.)

1.3481.2851.2851.2031.210

1/2 PV~Weibull Model Actnal Data

p

(kg/m3) (kW/m2) V P V P(m/s) (kW/m2) (m/s) (k\,y/m2) -

0.913 2.05 It••6 2.76 14.8 2.840.695 5.76 22.6 7.40 22.5 7.530.580 9.06 27.9 1l.6 27.6 11.40.460 1l.65 32.8 14.0 32.8 14.10.323 7.23 31.5 8.74 31.2 7.90

H

~I-'~oo

Document Control 11. SERI Report No.

Page TR-211-1400\2. NTIS Accession No. 3. Recipient's Acceeston No.

4. Title and Subtitle

The Application of U.S. Upper Wind Data in the Designof Tethered Wind Energy Systems

7. Authorts)

R. J. 0' Doherty9. Performing Organization Name and Address

Solar Energy Research Institute1617 Cole BoulevardGo1den, Colorado 80401·

12. Sponsoring Organization Name and Address

15. Supplementa ry Notes

5. PUblication Date

February 19826.

8. Performing Organization Rept. No.

10. Project/Task/Work Unit No.

1067.1011. Contract (C) or Grant (G) No.

(C)

(G)

13. Type of Report & Period Covered

Technical Report14.

16. Abstract (Limit: 200 words) Th i s report assesses the upper atmospheric wlnd resource forthe continental United States, Hawaii, and Alaska. The document is intended forSolar Energy Research Institute contractors interested in tethered wind energysystems. The raw data were obtained from the National Center for AtmosphericResearch, Boulder, Colo. The probability distributions of velocity are presentedfor 54 sites, and detailed calm wind analyses have been undertaken for five ofthese locations. On the average, the wind lulls about one day per week for aperiod in excess of about 30 hours. The report shows that the average powerdensity of this wind resource can be as high as 16 kW/m2 at northeastern U.S.sites. This power density is at a maximum around the 300-mb pressure level.

17. Document Analysisa. Descriptors wind ; earth atmosphere ; altitude ; wind power ; velocity ; statistics ;

numerical analysis; power density; statistical data

b. Identifiers/Open-Ended Terms

c. UC Categories

60

19. No. of Pages

13918. Availa,bility Sta.tflm~nt. 1

Natlonal lecnnlca Information ServiceU.S. Department of Commerce5285 Port Royal Road$prinqfield, Virginia 22161

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