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INTERNATIONAL ENERGY AGENCY
Implementing Agreement for Co-operation in the Research and Development of Wind Turbine Systems ANNExXI
IEA Joint Action
Wind Conditions for Wmd Turbine Design
2d. Symposium
RISO, Denmark, April 12.-13.,1999
Organized by : RISO National Laboratory
D-m Scientific Coordination:
B. Maribo Pedersen Dept. of Fluid Mechanics FITechnical University of Denmark
ISSN 0590-8809 .,; .
DISCLAIMER
Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. I
CONTENTS page
J@RGEN H@JSTRUP Introductory note 1
DANNY WINKELAAR Review of IEC Extreme Wind Conditions using Extreme Value Theory 3
A. CRAIG HANSEN Wind Characteristics for Wind Turbine Design 23
WIM BIERBOOMS Modelling of Extreme Gusts for Design Calculations 31
N.D. KELLEY A Case for Including Atmospheric Thermodynamic Variables in Wind Turbine Fatigue Loading Parameter Identification 57
GUNNER C. LARSEN, HANS E, J@RGENSEN Design Off-Shore Wind Climate 73
GUNNER C. LARSEN a.o. Fatigue Life Consumption in Wake Operation 77
J@RGEN L@VSETH, TORE HEGGEM Properties of the Maritime and Coastal Wind Field 83
R.P. LUIJENDIJK The Influence of Wind Conditions on Wind Turbine Design 99
GUNNER C. LARSEN, KURT S. HANSEN Database on Wind Characteristics 111
KURT S. HANSEN Determination of Wind Speed Accelerations 137
LIST OF PARTICIPANTS 143 1
IEA Symposium on Wind Conditions for Wind Turbine Design
INTRODUCTORY NOTE
by J@-genE?@trup, NEG Micon A/S
Wind energy is in a period of very rapid development, in which we are currently approaching the situation where the price of wind energy will be competitive to other energy sources. The development towards bigger, highly optimised and more efficient windturbines has put still greater emphasis on understanding the temporal and spatial variations of the mechanical loads created by the wind.
Today more windfarrns than ever before are being erected in very complex mountaneous terrain where our simple models for wind and turbulence become deficient, and at the same time under these circumstances, we see increased turbulence levels in the incoming flow, together with quite creative array geometries with closely spaced turbines, again increasing the need for knowledge of how the mean flow and turbulence react to this type of environment.
We are also very close to entering into massive offshore developments, where a whole new set of questions arises. Incoming turbulence levels are less than what we are used to, but this can in turn lead to problems with increased loads coming from more sharply defined wakes, changed stall characteristics of the blades. The interaction between the wave and wind fields is an important factor that amongst other effects also creates a strong variation of surface roughness (and turbulence) with wind speed.. We also have a suspicion that the generally lower turbulence levels at sea leads to a slower recove~ to the upstream wind speed downstream of a wind farm than what we are used to over land. This could lead us into two different directions, either increase the spacing between wind turbines/wind farms to optimise the energy yield or maybe decrease the spacing in order to increase local production of turbulence by the wind farm, in turn leading to more mixing causing retrieval of energy from a much thicker portion of the boundary layer. These two scenarios of course lead to quite different philosophies concerning the loads for which the turbines should be designed, smaIler loads than on land for the increased spacing situations or maybe much larger loads for the decreased spacings.
The IEA symposium in Hamburg in 1994 provided for a very fruitful discussion of the present state of the art in this area, raised a lot of questions, and initiated important work on some of this questions. Now five years later, it seems timely to review the iituation again, what have we learnt since then, what questions remained unanswered, which are the pressing questions of today and what tools are at our disposal for answering these questions.
One of the recurrent discussions that came up also in 1994 was the possibility of exploiting large amounts of data, and we were faced with the usual situation, most researchers in this area are willing to share their data in return for access to other data, but the practical implications in doing so seemed to raise insurmountable problems concerning documentation, data quality and data formats. This is one issue that was resolved by a JOULE project, started in 1996 and finalized 1998 by which a system for storage, access and quality control of the data was provided. The result was a large capacity Internet database with WEB access, documented data quality and standmdized data formats. A lot of effort went into that database, the result was a very good user-friendly tool using state-of-the-art software, and now the time has come to use 2
the tool. Now, finally we shall not be (as much) limited by the lack of availability of data as we so often were before, but we can just pick out all the data we need, need very little effort in checking and decoding the data, and use all of our energy where it should be used, doing the data analysis.
The basic question remains the same, and it is still relevant to quote from the last part of the introducto~ note from the first meeting (Nath & Matthies, 1994), what should constitute the basis for the design of wind turbines?
Several further questions are related to this general one ● Is the format of currently used design guidelines concerning wind, i.e. extreme conditions and turbulence, sufficient, is it too simple, does it cover all the relevant situations? ● Is our knowledge about extreme wind conditions sufficiently accurate, what do we learn from failures which are ultimately attributed to wind conditions? ● How important are extreme situations other than extreme windspeed, i.e. extreme gusts while operating, extreme gradients and shear flows, extreme directions changes, and how well are they covered in the present design guidelines? How sensitive is the wind turbine design to uncertainties relating to wind conditions? What is the most reliable values for turbulence descriptors to be used in modelling the turbulent wind fiels (intensity, spectra, coherence, a.o.), both in normal and complex terrain and for single turbines as well as turbines in wind farms?
Our main subject areas are related to the different situations in which we erect wind turbines:
● WAKES, what are the magnitude of loads resulting from closely spaced turbines (we have seen rows with 1.2-2 diameter spacings). Do we know what the most serious causes of damage are, shear from wakes, turbulence from wakes, other problems?
COMPLEX terrain, how do we properly describe the turbulence under such conditions, is the turbulence intensity sufficient or do we need a more detailed description because of the general differences in turbulence structure? And the loads resulting from flow coming at the turbine at angles other than horizontal in sloping terrain, are there easy ways of calculating the flow angle in complex terrain?
OFFSHORE. Despite the apparent simplicity of this type of ‘terrain’, we have some unanswered questions, relating to wake structure, and how do we design our offshore wind turbine? For low turbulence and moderate spacings or maybe for high wake induced turbulence and small spacings. Is the general level of understanding of wind-wave interaction sufficient or do we need more knowledge?
We have a new TOOL at our disposal for answering some of our questions, the WEB- DATABASE, how do we best utilize the data from the database for answering our questions. 2ndIEA Symposiumon Wind Conditionsfor WindTurbineDesign, R@, Denmark April 12-13,1999
Review of IEC Extreme Wind ConditionsUsing Extreme Value Theory
DannyWhkelaar NetherlandsEnergy ResearchFoundation(ECN) P.O.Box 1, 1755ZG Petten The Netherlands 4 5
1 INTRODUCTION
Since the Draft IEC 1400-1standard wasissued there continuesto be interestin reviewingthe modelsin the standardand their consequencesfor wind turbinedesign. Oneof thesereviewstudieswasthe Joule-2 Project “EuropeanWindTurbineStandards”[10]. This studyproposedmodificationsand recommended additionalresearchamong others on the models for extremewindconditions. This investigationon extremes was carried out in Part 1, Sub C of the Joule-3 Project “European Wind Turbine Standards II”, and is reported in [14], which, to date (June 1999),for unknownreasons, has not been publishedyet. This paper is an abridgedand improvedversionof that report.
The IEC 1400-1standard divides the wind regime for load and safety considerationsinto wind normal conditionswhich will occur frequently during normal operationof the wind turbine, and extreme wind condhionswhichare definedashavinga 1yearor50 yearrecurrenceperiod. The extremewindconditions are used to determine critical design loads which the turbine must withstandduring its lifetime. These extremeconditionsincludepeakwindspeedsdueto stormsandrapidchangesinwindspeedand direction. In orderto reviewthe modelsfor extremesit was decidednotto analysemeasurementsas for example was done by a revision working group (TC88/WG7)[2]. Althoughmeasurementsshouldultimately be decisive,it is obviouslydangerousto inferextremesfrom a ratherlimitedset of data. Besidesif we would perform exactly the same sort of investigationas the workinggroup TC88/WG7did, then it would be difficultto vaIidateor invalidatethe resultsof that group. Inspired by a report by Bergstrom [1] and papers by Cook [6] and Harris [8] it was decided to adopt a completely different and more theoretical approach, by using Extreme Value Theory. Assuming that the statistics of the wind climate is given (i.e. the Weibull distribution and the turbulence model) it is possible to derive the probability of occurrence of extreme wind climate events. An additional advantage of tlis mathematicaUstatistical approach is that the models for extremes and the models for normal turbulence are logically connected, making the results more “physical.”
Section 2 reviews the so-called Extreme Wind speed Model (EWM) of the IEC 1400-1 standard. Com- puted extreme 10-minute and 3-second average wind speeds with a certain probability of occurrence are compared with the values given by the IEC. In addition the sensitivity for the Weibull shape and location parameter is investigated.
Section 3 deals with the problem of deriving a pdf and cdf of the extreme 3-second average gust. The resulting distribution function is used to compute extreme gust magnitudes with a certain probability of occurrence and the values found are compared with the values given by the IEC in the so-called Extreme Operational Gust model (EOG) and Extreme Coherent Gust model (ECG).
Section 4 deals with the question whetherthere are extremewind eventswhichare not describedby the IEC standardbut should be included. One rare event is described,a so-called downburst,which may induceextremeloads on a wind turbine.
Section 5 gives a summary, some conclusions and recommendations.
Finally, Appendix A gives some background on extreme value theory and some statistical concepts hich are important for the present report. 6
2 REVIEW OF THE IEC EXTREME WIND SPEED MODEL (EWM)
In the IEC 1400-1 standard [9] the peak values of the wind speed are given in the so-called Extreme Wind Speed Model (EWM). This model must be applied in two design ultimate load cases (DLC 6.1 and 7.1) where the wind turbine is standing still or idling. One of the specified extreme wind speeds is also used for fatigue calculations in DLC 6.2.Three extreme wind speeds are defined 1. the 10-minute average reference wind speed V.,f;
2. the extreme 3-secondaveragewind speedV.50;
3. and the extreme 3-secondaveragewind speed V.l. The extreme 3-see average wind speeds V,l and V.50 are both based on the referencewind speedV,.f and have to be computed as a fimctionof height .zusing the followingequations:
ve~o(z) = 1.4vref(z/z~u~) o”ll, (2.1)
Vel(z) = 0.75V,50(Z), (2.2) where .?&bis the hub height. For each of the three extreme wind speeds a recurrence period is specified, so that, in principle, the probability of occurrence is known. In the following sections these wind speeds will be evaluated from a theoretical point of view. Using the Gumbel distribution for the 10-minute average extreme wind speed and the extreme distribution for 3-second averages, (A.21), the extreme wind speeds are determined according to the probability of occurrence (recurrence period) specified in the Extreme Whd Speed Model (EWM) of the IEC standard. The values obtained are compared with the values specified by that standard. Some conclusions are drawn and recommendations given.
2.1 Evacuation of V,ef in the IEC 1400-1 standard
The extreme wind speeds are given as a function of the reference wind speed Vr.f which is defined as : ‘the extreme 10-minute average wind speed at turbine hub height with a recurrence period of 50 years.’ This definition is here interpreted as : ‘the annual extreme lo-minute average wind speed at hub height with a confidencelimit of 9870’. In the IEC 1400-1standardthe ratio of V,.f to V,v, is constant for wind turbine class I through Iv —=Vref ~. vave The choice of this ratio is based on typical values found in the British building code. This ratio is probably characteristic of mid latitudes because in de Dutch building code the same ratio appears. This value is, to a large extent, based on a Gumbel type analysis of wind speed measurements. It is relatively easy to derive a theoretical expression for this ratio, assuming a Weibull parent and a Gumbel limit distribution.
CombiningEquations (A.12),(A.5),(A.7),(A.8)and (A.9)yields: v, — = &y’’:;k)[klnn - lrl{-ln(l - l/~)}] , (2.3) vave where V, denotes the amual extreme 10-minute average wind speed at hub height with a return period of T, years. Using Eq. (2.3) the ratio of V, to Vaveis computedas a function of the Weibullshapeparameter 7
k and presentedin Figure 2.1. To determinethe number n of independenteventsin a year,the effective frequencyvT givenby Bergstrom[1],see TableA.2, is used:
vT = 7.3 X 10-4 = vt “TP = 23037 (2.4) TP = 3.15576 X 107 n } It should be noted that the computed curve is not very sensitive for the precise choice of effective frequency in Table A.2: n is always so large that the extreme value curve has practically converged to the limit curve. For flat terrain sites at mid latitudes the value of the Weibull shape parameter k varies typically
Figure 2.1 The ratio of V,ef to VaVeas function of the Weibull shape pammeter k between 1.65 inland and 1.9 in coastal areas. Figure 2.1 shows that V,,f/V,v. <5 fork >1.77. Hence at mid latitudes the ratio V,.f/V.v. = 5 is acceptable for most inland flat terrain sites, and evenslightly conservativefor flatterraincoastal areas.
Figure 2.1 also makes clear that this ratio is too low for sites in complex terrain where k-values <1.5 are found. Taking k = 1.4 as a characteristic value for complex terrain then according to Figure 2.1 the ratio, V,ef/Vave, should be approximately 7.5. Hence, with respect to V,,f, a Class I wind turbine is only suitable for complex terrain sites with an annual average wind speed which is lower than 6.7 m/s (at hub height!).
2.2 Evaluation of V.l and V=50in the IEC 1400-1 standard The IEC 1400-1 standard [9] defines two extreme 3-second avemge wind speeds:
1. The 50-year extreme wind speed V,50, which is defined as the extreme 3-seconds average wind speed with a recurrence period of 50 years. 8
2. The one year extreme wind speed Vel, which is defined as the extreme 3-seconds average wind speed with a recurrence period of one year.
The definition of V,50 is OK but that of V.l seems a bit odd. An amual extreme wind speed with a nmu-renceperiod of one year has a 1OO$%probabilityof being exceeded (cf. Section A.6). This cannot be intended of course. It is thereforeassumedthat V,l is the characteristic largest value. This value gives an idea of the central location of the possible largest values, and corresponds to a confidence level of approximately 63.21 %, cf. Section A.7. To verify whether the values given by the IEC standard conespond to the definitions as we assume they should be, V.l and V.50 have been computed for various values of V,ve and k. The results are presented in Figures 2.2 and 2.3. For the purpose of comparison these figures also show the IEC values for the four wind turbine classes. From these Figures it is clear that the IEC values of V.l and V.50 are valid for sites where k >1.9 and k > 1.7, respectively. Hence the assumed confidence level for V.l is probably correct. That V.l is less conservative than V=50,in terms of k-values, seems appropriatebecause V.l should also be used in fatigue calculations (DLC 6.2). It can be concluded that the IEC values of V.l and V.50 are acceptable for most flat terrain sites at mid latitudes and certainly valid if the parent distribution is Rayleigh. But, with respect to these values, a Class I wind turbine is only suitable for complex terrain sites (k x 1.4) where V& <7.5 n-h at hub height.
2.3 Conclusions In the previous sections the theoretical values of V,,~, Vel and V=50have been derived as a function of the amual average wind speed V.v. and the Weibull shape parameter k. These theoretical values are compared to the values specified by the IEC 14001-1 standard in the so-called Extreme W]nd Speed Model (EWM). It is shown that according to these theoretical computations the IEC values are acceptable for flat terrain sites at mid latitudes. For sites with a Rayleigh parent distribution the IEC values are conservative. As was to be expected, the IEC values are definitively not v~ld for complex terrain sites. With respect to the survival wind speeds, V,l and V,~O,a Class I wind turbine is only suitable for complex terrain sites witi an annual average wind speed which is lower than 7.5 m/sat hub height. 9
o 1 1.0 1.5 2.0 2.5 Weibullshspe psrameter k
Figure 2.2 The annual characteristic largest 3-see average wind speed as function of the Weibull shape parameter k, for annual average wind speeds V~vevarying between 4 d.. and 12.5 m/s. Also shown are the values of Vel for the fourlEC wind turbine classes.
100
lj 20 e ~10 ...... "...... F=..??.E ...... I {+ OF 1.0 1.5 2.0 2.5 Weibullshspe pstameter k
Figure 2.3 The annual extreme 3-SW average wind speed with a confidence level of 98%, as fmction of the parent Weibull shape pa.mmeter k, for annual average wind speeds V.., varying between 4 mls and 12.5 m/s. Also shown are the values of V.SOfor the fourL5C wind turbine classes. 10
3 REVIEW OF THE IEC EXTREME GUST MODELS
The IEC 1400-1 standard specifies two gust models, the so-called Extreme Operating Gust model (EOG), and the Extreme Coherent Gust model (ECG). The values of the gusts and the gust shapes in these models are subject to considerable debate. What will be discussed here are the latest models, proposed in the final draft of edition 2 of the IEC 1400-1 standard. The hub height ‘Extreme Operating Gust’ magnitude V~U,tNfor a recurrence period of N years is given by the following relationship ~us’N=4+2%)) (3.5) where al is the standard deviation given by Eq. (A.23), Al a turbulence scale parameter, D the rotor diameter, ~ = 4.8 for N = 1 and P = 6.4 for N = 50. The wind speed for a recurrence period of N years is given by
V(z) – 0.37V&~N sin(37rt/2’)(1 – cos(2/ 2’)) for O < t < T V(z, t) = (3.6) { v(z) where T=10.5sfor N= land T=14sfor N = 50. The parameter values for both recurrence periods were selected to give the same maximum tise rate. As an example, the extreme operating gust with a recurrence period of 50 years, turbulence category A and Vhub= 14 m/s is shown in Figure ??.
To find the probability density function of gusts it is assumed that conditional pdf ~(u~l, ?@2 I ~) iS
t (See)
Figure 3.1 Example of extreme operating gust (N = 50, category A, Vhub= 14 ml.) 11
jointly normal, where U2’1and UTZare the short-term average wind speeds at the same location but at two instants il and tz. Then it can be shown that the pdf of (UTZ- UT1)given UT1is (see Chaviaropoulos [4]:
UTI)IUTI) = ,W ~((uT2– I t((uT2– d ]h), u)du w = ~[2@; (~ – UTI)(l – ~), ~T(l – ~2)1/2] o~[~; C, k] dZ7. (3.7) Jo In otherwords,~((~Tz – uT~) Iu~l) is the productof a normal distributionwith mean (U - VI)(l – p) and standarddeviation~T(l – p2)l/2 and a Weibulldistributionwith parametersC and k. The resulting pdf provides the probability of a wind increase (u2’z– UT1)in a given time interval T and a starting wind speedu2’1.It shouldbe noted that the pdf dependson the correlationfunctionp which is not only a iimct.ion of r but also of the integral time scale. As a consequence p cannot be entered as a constant in (3.7), as was incorrectly done in [4]. Under stationary conditions, one may obtain the correlation as function of the time lag T from the power spectrum of the longitudinal wind speed component. Here the Von Kdrmtin spectrum will be used. For @ the expression A.22 applies here as well. The number of independent events n is the same as for the extreme wind speeds, see [4]. A typical plot of ~(y2 \ gl) is presented in Figure 3.2. This figure shows that for decreasing annual average wind speed the negative gust portion increases and vice
0.5
0.4
;-0.3 i ~ % o~
0.1
0.0 -10 0 10 Vw=%2 - l+, (M/s)
Figure3.2 The pdf of gusts for a s-”ng (3s average) wind speed UT== 14 &s, and external conditions according to lEC wind turbine class I – IV versa. It can dsObe shownthat when Tdecreases(mOreCorrelation)the widthOf~((uTz – uTl) IuTl) iS reducedand the peak becomeshigher, sharper and more symmetricallycenteredaroundzero. When the str@ingvalue u2”lincreases, the peak of the distributionshifts to the left, indicatingthat the probability of findinglarge (positive)gusts becomes smaller. UsingEq. (3.7),the magnitudeof the extremeoperatinggustsis computed,assumingD = Oand the 12
probability of occurrence is the same as for the annual extreme wind speeds. The results are presented in Table 3.1. The table also contains the magnitude of the extreme coherent gust V.g. The IEC does not specify a probability of occurrence for this gust and therefore it is assumed that the probability of occurrence of this gust magnitude corresponds to that of the characteristic largest value. Hence V&~l and V& have the same assumed probability of occurrence, only the time lag is different (~=2.8sand~ = 10s, respectively).Based on Table3.1 the followingremarks can be made
Table 3.1 The extreme operational gust and extreme coherent gust for a starting wind speed?.@== 14 m/s and 25 rds and external conditions according to the lEC wind turbine class I – IV
IEC rev. 2 UTI = 14 ds UTI= 25 IIlh IEc vgu,t~ vg”,~~~Vcg vgu,~~vgu,t~(j Vcg vgwt~ vgwt~~ class (m/s) (m/s) (m/s) (In/s) (In/s) (m/s) (m/s) (m/s) I 18.72 24.96 15.0 25.8 34.7 31.0 17.7 25.3 II 18.72 24.96 15.0 19.8 27.1 24.5 12.2 18.3 III 18.72 24.96 15.0 16.0 22.2 20.1 8.8 13.7 IV 18.72 24.96 15.0 10.6 15.1 13.4 4.2 7.4
1. For a given probability the gust values are lower at a starting wind speed of 25 mk than at 14 m/s. The IEC model does not make that distinction. The IEC also does not make a distinction for the different turbine classes. The computed values for V~WtNare in good agreement with IEC turbine class I for a starting wind speed of 25 m/s. VC~apparently has a much higher probability of occumence than what here is assumed. 2. The IEC standard (and the proposed revision) is unclear about how to compute the standard deviation in the EOG model. It must be made clear that in all cases al should be computed for &b = VOUt, but this is nowhere stated.
3. Because the gusts should be applied with the turbine in operation it is probably better to restrict the range of U and to compute the extreme gusts using the density function ~((yz I yl) I U < VOUt). This will reduce the computed gust values. The extreme values given in Table 3.1 should serve as an upper limit, we do not need to evaluate the loads due to larger gusts.
4. The above derived gust distribution function can be used to construct gust time histories, because the pdf and cdf depend on the time lag ~. One may use of some kind of Markov chain simulation (random walk). 5. We are not so much interested in extreme gusts but in gusts which cause extreme loads in the various components of the wind turbine. It is quite possible that the extreme gust values found here do not induce the highest loads, simply because the wind turbine does not have time to respond to such large and rapid wind speed changes. When the gust is found that induces the highest loads (this may vary with the cross section that is considered) the above presented theory can be used to compute the number of occumences.
6. Due to their physically unrealistic nature, sinusoidal gust are not the most reliable means to compute extreme loads, see Wmkelaar [13]. It is recommended to use several realisations of a wind field which somehow contains the gust to compute the (hopefully) extreme loads. 13
4 OTHER EXTREME EVENTS
At mostsites,windspeedarisesfrom a variety of physicallydistinctmeteorologicalmechanisms,such as depressions,thunderstorms,tropical cyclones, etc. In the previoussectionsit is assumed,however,that all large wind speeds are produced by only one of these mechanisms. For sites at temperate latitudes, suchas mostsitesin Europe,this is a reasonableassumption,the dominantmechanismbeing depressions. In meteorologicaltermsit is assumedthat when the highestgustspeedsandthe highestaverage(over 10 min or 1 h) wind speed occur near the ground (say at 10 m) the lower boundarylayer is neutrally stratifiedand the gusts are caused solely by the vertical shearof the windand the resistanceof the rough ground. This condition of the boundary layer is usuaIIydefined(in meteorology)by the criterion that lh/L~ol <0.1, where h is the height above the boundary layer depth (typically 500-1000 m) and L~o is the Monin-Obukhov length. Typically in temperate climates this criterion is satisfied if the wind speed at 10 m above the ground UIOis greater than 10 m/s. However, even for mid-latitudes, where tropical cyclones do not occur, it has been recognized that there are exceptional meteorologicrd situations when mechanisms quite different to shear turbulence cause very high wind speeds. In particular, tornadoes are associated with high swirl velocities (< 100 m/s) and vertical upwardmotion, while downdrafts,produced by cold air formed in deep clouds well above the boundarylayer, descend and spread out rapidly on hitting the groundgivingrise to typical gust speeds <30 mh [7]. Althoughboth these phenomenaare mostfrequentin continentalclimates and the tropics, they are occasionfly observedeven in temperate climates, such of those of NorthWesternEurope,and need to be includedin the statisticsof extreme winds,see Collieret al. [5]. In this sectionwe will not concern ourselveswith tornadoes. To date, most tornado study is a post- disasteranalysisof structureswhich were victims of the storm,withthe darnageassessedby calculating the upperlimit of the failure load due to a straight limewind approximatedas 140mk. Judgingfrom the survivalwind speedsspecifiedin the IEC standard (70 m/s at the most)a wind turbine does not have to survivea tornado. Although it is sometimes difficult to distinguish a downbu~t from a tornado the associated wind speedsare generallynot that high. NO largemeasurementcampaigns(NIMRODandJAWS)in the USA (Fujita [7]) recorded gust speeds up to 30 nds and showedthat intense downburmscan leave a trail of darnage,like uprooted trees etc. For these reasons and the assumptionthat downburstsprobablyhappen much more often than tornadoes it seems a good idea to study the phenomenonmore closely, to see whetherit shouldbe included as a load case in the IEC standard. 14
5 CONCLUSIONS
Using extreme value theory it is shown that, given a certain knowledge of the climatology, it is possible to derive statistical characteristics of extreme wind conditions which are believed to be important for wind turbine design, e.g. the survival wind speed, extreme gusts and extreme wind direction changes. In the present report the limit distributions of the extreme wind speeds and extreme gusts have been investigated, assuming that the design external conditions (i.e. the climatology) is defined by the IEC 1400-1 standard wind turbine classes I-IV. Whh the assumptions given above the derivation of the probability density function (pdf) and cumu- lative distribution function (calf)for the 10-minute average and 3-second average extreme wind speeds is straightforward. It is shown that, given a certain confidence level or return period, the magnitude of the extreme wind speed strongly depends on the shape (k) and scale (C) pammeters of the parent Weibull distribution. Smaller shape parameters lead to higher extreme values and vice versa. The influence of k becomes pronounced when k <1.8. Comparison with the IEC values shows that the reference wind speed V,,f is acceptable for sites with k z 1.77, i.e. for most flat terrain sites in Western Europe. This is also the case for the 3-second average extreme wind speeds V.l and V.50(the so-called ‘survival wind speeds’) given in the IEC Extreme Wind speed Model (EWM). But it should be noted that the annual extreme wind speed with a recurrence period of one year, V.1, has been redefinedto the “annual characteristic largest wind speed.”
Assuming longitudinal wind speed fluctuations UT, and UT,at the same location but at different instants tl and tz to be jointly normal, the conditional pdf ~(~T, - U*I I uTl) is derived and the limit distribution function computed through numerical integration. For extreme gusts not only a strong dependence on the parameters of the parent Weibull dk.tribution is found but also on the assumed turbulence model, viz. Von K4rrnti or Kaimal, which determines the tempoml correlation as function of the time lag ~ = tz – tl and the integral time scale, which is equal to L/U when Taylor’s hypothesis of frozen turbulence applies. The magnitude of the extreme gust shows the same dependence on the Weibull parameters as the extreme wind speed. The gust speed increases for increasing time lag T until the time lag is greater than the integral time scale, from that point on the the gusts speed does not change very much. Given the same confidence level, gust values are greater for a starting wind speed at v,~t~dthan at VOut.Again, the extreme with a recurrence period of one year has been redefined to the amual characteristic largest value. Also the coherent gust, VC~,is assumed to be an annual characteristic largest gust (but then with a larger time lag).
The computed values for the extreme operating 3-see average gusts are in reasonable agreement with the values according to the EOG-model which is given in the final draft of the second revision of the IEC standard. Only the computations for a starting wind speed of 14 mk and wind turbine class I external conditions, predict somewhat higher values. The computations also suggest that there is a strong depen- dence on the annual average wind speed, V’v., and the starting wind speed. The EOG-model, however, does not make a distinction for different wind turbine classes and for different starting wind speeds. The analysis presented here could be refined in two ways. Firstly we should replace the single point gust by a so-called coherent gust. To compute the distribution function of coherent gust we have to take into account the spatial correlation function. Secondly the lo-minute average wind speed should be restricted to U s VOUt.In the present computations V vanes in theory between zero and infinity, but in practice computer accuracy limits that range to much lower values. Both refinements will lead to lower gust values. The gust values presented here should be regarded as upper limits; in design calculations we do not need to evaluate larger gusts. When the gust is found that induces the highest loads, the distribution 15
function could be used to compute the number of occurrences.
Finally some attention is given to some rare meteorologicalphenomena– tornadoes and downbursts– which quite likely will induce extreme wind loads, but which are not included in the extreme climate events described by the IEC standard. Given the high price it takes, it is questionablewhether wind turbines should be designed to survive a tornado, but it seems liiely that they should be designed to withstandan intense microbursc One of the main reasonsfor this assumptionis that, althoughmicroburstsare sometimesdifficultto distinguish from tornadoes, they are probably less rare and the associated wind speeds compare quite well withthe extremegust speedsestablishedhere. In additionit seemsquitelikelythat thisphenomenon induces extreme loads due to the combinationof a strong vertical wind speed, high gust speeds in all directionsand a vortexwith a horizontalaxis. It is thereforerecommendedto studythis phenomenonin more detail, both physicallyand statistically,and to determine what its impact on a wind turbine could be. 16
A NOTATION AND BACKGROUND
NO types of statistics are of interest those relating to the total population of wind speeds and second the properties of the extremes. In the following it is assumed that the statistics of the wind climate (i.e. Weibull distribution and turbulencemodel) at the site of the structure is established and what will be discussedis an attempt to find a relation between these statistics and the properties of extremes. In statisticaljargon: we assume that the parent dktribution is somehowknown and we want to find the extremevalue distributions. Some of the difficultiesin findingthese limit distributionsare addressed.
A.1 The Weibull distribution of averages The lo-minute or l-hour average wind speed is usually well described by the Weibull distribution k Pr{X
f(z)= ~(~)k-’exp [()]- ~ k; O
A.2 Order statistics from independent and identically distributed samples Consider a random variable X and let (Xl, X2,..., X.) be a sample of n independent and identically distributed observations from a parent population with cumulative distribution function l’(z). If the values of the sequence Xl, X2, ..., X. are rearranged in an increasing order Xl:. < X2. ~ . ..< X.:. of magnitude, then the r-th member of this new sequence is called the r-th order statistic of the sample. Note that the sample size n is incIuded in the notation Xr:n and that any order statistics must have an associated sample size, cf. Castillo [3][Chap. 2].
A.3 Extreme value distributions
The two members of the sample Xl:. = min (XI, X2,..., X.) and X.:. = max (Xl, X2,..., X.) are called the extremes. Now suppose that the members Xl, X2, ..., X. of the sample are independent and identically distributed and that they come from a parent population of samples with cumulative distribution function (calf)F(z). If we fit separate distributions for the smallest or largest values of the samples only the resulting distributions Fxl,m(z) and Fxm:~(z) arecalledtheextremevalue distributions for the smallest and largest value of X, respectively. It is possible to express the extreme value distributions Fxl:m(z) and Fx_ (z) in terms of the parent distribution Fx(z). To find the distribution of the largest value Xn:n, we use the relation
Fx=:n(z) = Pr{Xn:n < z} = Pr{all Xi ~ z} = Pr{Xl if all Xi are independent. This means that the probability of realizing X.:. less than equal to x is the same as the probability of realizing all X~, i = 1,2,... , n to be less than or equal to z. If the Xi is identically distributed with the distribution function F(z) then F~m,=(z) = [F(z)]n, (A.4) cf. Castillo [3][Chap.2] and Rao [1l][Chap. 4]. A.4 Limit distributions The shape of the distribution function of the extreme value becomes increasingly insensitive to the exact shape of the parent distribution function F(z) as n tends to infinity. The limiting forms of the extreme value distribution function as n + oo are known as asymptotic distributions. The asymtotic distribution, I’.(z), often describe the behaviour of the random variable X. reasonably well even when the exact shape of the parent distribution is not knwon precisely. The asymptotic forms of l?xm (z) are classified into three types based on general features of the tail part of the parent distribution F(z). The Fisher-Tippett type I asymptotic distribution forthemaximum values, betterlmown as the Gumbel distribution, is useful whenever the right tail of the parent distribution F(s) is unbounded (s + co) and is of an exponential type. Parent distributions such as normal, lognonnal and Weibull distributions belong to this category. The Gumbel distribution of the largest value is given by F.(z) = exp [–exp{-cx(z – j?)}] -cm< z < co; a >0, (A.5) where a and@ are known as the scale and Iocation parameters, respectively. The associated pdf is f(z) = ‘Xwwe+exdwl ; —Cc) (A.7) P = C(lnn)+, (A.8) c = “V’ (A.9) r (I + I/k). The main parameters of the GumbeI distribution are summarised in Table Al. A.5 The number of independent events per year It is important to note that the above presented extreme value theory assumes samples of n independent and identicallydistributedobservations.Thusin the caseof 10-minuteaveragewind speeds,if the values of each 10-minuteaverage were statisticallyindependentof those of neighboring ten minutes, then it wouldbe expectedthat n equalsthe numberof ten minutesin a year,i.e. n = 52596. Thk is not observed in practice, because values of adjacent ten minutes are not independent. More recent studies (Castillo [3]) have shown that, provided the data are statistically stationary, and hence have a finite correlation time, T, then n ~ T“/~ if T= is the record length. Following Bergstrom [1], a relatively simple and convenient way to determine r is to use the autocorrelation function p(~), where r is the time lag over which the comelation is calculated. If 18 we put p = 0.5 and solve for T, the solution maybe interpreted as a measure of the average time between two 50% correlated values in the time series. The solution of this particular case becomes, using spectral representation (see Rice [12]) : VT = ;“5’T f2S..(f) df/~:’T S..(f)df “2 , (A.1O) [J 1 where S.. (~) is the spectral density function, i the frequency and VT = l/~ is the sought effective frequency valid for averaging time T’. The lower integration limit, ~o, may be chosen to be about 1/(2” 3600) Hz to eliminate the synoptical part of the spectrum. The number of independent observations, averaged over a period of length 2’, within a time period TP, may then be estimated from the relation n = VT . TP. (A.11) Bergstrom [1] states that the effective frequency is rather insensitive to the specific choice of spectral density function. This is not confirmed by our own calculations, see Table A.2. The table shows that the estimated effmtive frequencies, using the IEC Von Kdrmdn spectrum with L/U = 10, are roughly four times greater than the corresponding values given by Bergstrom. It is possible that Bergstrom actually used a lower correlation. We will use Bergstrom values because he finds good agreement between measurements and com- putation, especially for l-hour and 10-minute avemges. However, note that for short term averages n btxomes so large that even a factor of 4 is not making much of a difference because the extreme value distribution is already close to the limit distribution. A.6 Return period The return period is defined as the average elapsed time between occurrences of an event with a specified magnitude or greater. If an exceedance occurs every 50 years, on the average, then the probability that the event occurs in any given year is 1/50 = 0.02 or 2 percent. Thus the return period T, and the probability of occurrence are related as . 1 (A.12) ‘r= 1 – F(z) Rather than choosing a return period it is better to state the risk r one considers acceptable that a certain value, ~fi~it say, is exceeded within Tp years. The corresponding return period T, then follows from the relation Tp l–r= 1–$ . (A.13) () r Note that the risk r that ~K~itis exceeded within 20 years is 33.2%, when a return period of 50 years is specified Note also that a return period of one year (as the IEC 1400-1 standard in some cases specifies) is rather difficult to understand unless we assume that the parent distribution and the limit distribution are based on a sample length which is shorter than one year. A.7 Characteristic largest value The particular value of the random variable X, denoted x., is called the characteristic largest value for a period of n units if the mean value of the number of exceedances of z. is unity. The characteristic largest 19 value gives an idea of the central location of the possible largest value. By definitionthe characteristic largestvalueis givenby the relation n [1– F(zn)] = 1 (A.14) If we consider n time periods, the distribution of the largest value of z. is given by Fj&(zn) = p’(q)]” =(1- :)” (A.15) Thus the probabilityof exceedingthe characteristiclargest value in n time periodswill be ~11 1–FX*(Z.)=1– 1–; (A.16) () As n tendsto infinity,Eq. (A.16)convergesto the value 1 – e-l = 0.6321. A.8 The cdf of the extreme 3-second average wind speed In the previoussectionsit hasbeen shownthat most practicalproblemsregardingextremescanbe solved if the parentdistributionand the sample size are known. For l-hour and 10-minuteaveragewind speeds the parentdistributionis generallywell describedby the Weibulldistribution. Toderivethe parentdistributionfor shorteraveragingtimes,2’(e.g.3-secondaverages),it is assumed that the wind speed, UT, is normally distributed around the lo-minute mean value U, with standard deviation @ ~[~”; U, OT]= 1 +;(UT;U)2], (A.17) ~T& where ~[t@; u, ~T]- f(t.t. I U) is shorthand notation for the Normal (Gaussian) probability density function. If U follows a Weibullpdf IV[U; C, k] ( cf. A.2) then thejoint pdf of u!r and U is givenby f(t@, ~) = ~[UT; ~,aT] “ ~[u; C,k], (A.18) from whichit followsthat ~(~=) = ]a j(~”, U) dU = ~~ ~[UT; U,@(U)] oW[U; C,k] dU. (A.19) o 0 The cumulative distribution function (calf)of?@ is then given by: (A.20) Assuming n independent observations, the extreme value distribution is then given by the distribution of the n’th order statistic: ~xmim(UT)= [~(UT)]n = “’ mN[uT; U,~T(17)]“W[U; C, k]dZ7dUT “ , (A.21) [1-m /o 1 where @is the part of the total turbulent standard deviation au which remains after having applied a low pass filterWithaVemgingtime T. The mt.io~. = a2’/~Ucan be computed(seeBergstrom[1])from: q~ % :“s’T S..(f) df/ ~: s..(f) dt . (A.22) [1 1 20 The lower integration limit ~0can be chosen to be about 1/(2. 3600) Hz, to eliminate the synoptical part of the spectrum, see Table A.2. The table shows that the values given by Bergstrom are quite close to the values found with the Kaimal spectrum given by the IEC 1400-1 standard. To compute the standard deviation a. the expression given by the IEC 1400-1 ed. 2 standard is used: CTu= 115(15+ (zv~uJ/(a + 1), (A.23) where category A turbulence characteristics will be used, i.e. 115= 0.18 and a = 2. Note, however, that it would probably be better if a distribution function is used for u.. Using (A.19) and (A.23), the pdf ~(u~) of the 3-see average wind speed is computed for IEC wind turbine class IA through IVA, and presented in Figure A. 1. The figure shows that the distribution of the 0.14 0.12 0.10 ;“ 0.08 R 0.08 0.04 0.02 0.00 -5 0 5 10 15 20 25 20 35 Figure A.1 The probability density function of the 3-second average wind speed for lEC 1400-1 ed. 2 wind turbine ckss IA through WA. 3-see average wind speed resembles a Weibull distribution but is somewhat flatter than the underlying Weibull distribution of 10-minute averages and has a more pronounced right tail towards higher wind speeds. Note however, that, contrary to the Weibull distribution, the left tail in theory extends to –co. 21 Table A.1 Some parametem of the Weibull and Gumbel dism”bution I I Weibull I Gumbel I I Mean cr (I + *) I Medkm I C (ln2)1ik I A - ln(ln(2))6 I I Mode A I 2 Variance czp(l+f)-rz(l+ f)]. q I I Kurtosis I I 1.1396 I I Euler’sconstant I ~ = 0.5772156649.. I Table A.2 The effective frequencyv~ and the ratio qT = @/~U fOrv~”ous averaging times T; accortig toBergs&tim [I]andaccordingtopresentca.lculations basedon thelEC VonKdrnulnandKaimaJspectrum withL/U = 10. T UT.B VT–VK VT_K !?T-B qT–VK !?T-K [s] [s-’] [s-’] [s-’] 600 0.00073 0.000526 0.000522 0.18 0.167 0.163 60 0.00100 0.004637 0.004456 0.48 0.541 0.482 10 0.00460 0.019240 0.020772 0.78 0.853 0.775 5 0.00790 0.030721 0.035490 0.85 0.909 0.852 3 0.01000 0.042996 0.051734 0.89 0.936 0.893 1 0.02400 0.088163 0.112265 0.95 0.970 0.948 22 References [1] Bergstrom, H. “DistributionofExtremeW lndS peed”. Wind Energy Report WE 92:2, Uppsala University, Department of Meteorology, Uppsala, Sweden, 1992. [2] Butterfield, S., B. Honey, P. Hauge Madsen, and C. Stork. “Report on 88/69/CIMWlnd Turbine Generator Systems Part 1: Safety Requirements, 2nd edition”. unpublished repom 1996. [3] CastilIo, E. IZrtreme Value ?%eoryin Engineering. Academic Press, Inc., 1988. [4] Chaviaropoulos, P.K. “Probabilistic Analysis of Extreme Wind Events”. Wind Engineering, 20(3):139–159, 1997. [5] Collier, C.G., J. Dixon, M.S.J. Harrison, J.C.R. Hunt, J.F.B. Mitchell, and D.S. Richardson. “Extreme surface winds in mid-latitude storms: forecastingand changes in climatology”. J. Wind Eng. M. Aerodyn., 52(Complete): 1–27, 1994. [6] Cook, N.J. “Towards better estimation of extreme winds”. J. Wind Eng. Ind. Aerodyn., 9:295-323, 1982. [7] Fujita, T.T. “The downburst”. SMRP Research Paper Number 210, Department of the Geophysical Sciences, The University of Chicago, Chicago, Illinois 60637, 1985. Published by Satellite and Mesometeorology Research Project (SMRP). [8] Harris, R.I. “Gumbel re-visited – a new look at extreme value statistics applied to wind speeds”. J. Wind Eng. Ind. Aerodyn., 59(1):1-22, 1996. [9] International Electrotechnical Commission. “International Standard IEC 1400-1; Wind turbine generator systems – Part 1: Safety requirements”, first edition, 1994. [10] Rademakers, L. and R. Hunter. “European Wind Turbine Standards, Project Results”. EUR 16898, European Commission, DG XII, B-1049 Brussels, Belgium, 1996. ISBN 92-827-7948-3. [11] Rae, S.S. Reliability-based design. McGraw-Hill, Inc., 1992. [12] Rice, S.0. “Mathematical Analysis of Random Noise”. Bell System Tech. J., 23:282-332, 1944, and 24.46-156, 1945. both of which are reprinted in N. Wax (cd.), Selected Papers on Noise and Stochastic Processes, Dover, New York, 1954. [13] Whkelaar, D. “Some Ideas on the Modelling of Atmospheric Turbulence”. In ZEAJoint Action on Wind Conditions for Wind Turbine Design; Ist Symposium, Hamburg, Germany, June 1994. [14] Winkelaar, D., I. Car16n J.W.M. Dekker, P. Chaviaropoulos, and G.C. Larsen. “European Wind Turbine Standards ~, PART 1 Load Spectra and Extreme Wind Conditions; Sub C Extreme Wind Climate Events”. unpublished repoti, 1998. 23 WindCharacteristicsfor Wind Turbine Design A. Craig Hansen WindwardEngineeringLC Salt Lake Cily, UT 84117 [email protected] Introduction The IEC guidelines and standards for wind turbine design have been a subject of constant attention, In this Specialists’ Meeting we have the improvemn~ and increasingimportance for many years. -. opportunityto reflecton our experienceswith, and our perceptionsof the strengthsand weaknessesOEthe wind characteristicsthat are used in the estimationof design loads for wind turbine structures. This is the subject of this paper. In particular, the paper discusses the author’s experience with wind characteristics as specified in IEC 61400-1, the large wind turbine safety standard. WindwardEngineeringis a small consulting firm founded in 1994by the author and one associate. ‘The foundersand employeesof WindwardEngineeringwere -alIinvolvedin the developmentof the YawDyn and AeroDyn turbine dynamicscodes while at the University of Utah. The company is engaged in development,validation,and application of wind turbine dynamic loads analysis soflware, wind turbine design, testing, and research. We have experiencein design load estimation for a wide variety of turbine systems; from megawatt scale, rigid rotor$ to large articulated (teetering or flapping) rotor> to small rotors. We have worked whh stiff systems and very soft systems, with active controls and passive controls, and whh variable-speed and constant speed rotors. We develop computer models of the rotor of intere% then estimate loads when the turbine is subjected to the IEC 61400-1 wind characteristics. It is this experience that we draw upon as the basis for the discussion and conclusions in this paper. Much of this work is pefiormed under confidentiality agreements with our clients that prevent this paper from being highly specific and detailed. Nonetheless, I hope there may be some benefit to describingour geneml observationsandsomethoughtsaboutfiturerevisionsofthedesignstandard. Articulated and Soft Rotor Systems The need to reduce turbine costs has provided incentive to reduce the structural loads on the systems. One method for achieving this goal has been to make the structure more compliant (or “softer”), either by use of teetering flapping,and/ornoddinghinges or by use of flexible blade spars, drive trains andor towers. It has been well establishedthat softer systems are successtid at reducing loads cyclic due to normal operation in turbulence. However, operational expedience and modeling indicate that the loads during extreme events may reduce or even eliminate the advantage gained in normal operation. Deflection limits (to avoid a bladeAower strike, for exampIe) may become the design limiting condition. This potential vulnerability to extreme events makes the design of a sofi system more challenging. Characterization of the extreme winds is made more difficult by the rare occurrence of extremes and the resulting lack of a data base. Table 1 compares the results of load estimation using an ADAMS model of a large turbine with flapping hinges and a sofl-soft tower. We estimated the maximum load at several location on the structure in normal operation in turbulence (24rnJsmean), and in all of the extreme gust conditions as specified in the second edition of IEC 61400-1. Note that in most locations the loads during the extreme events exceed those due to normal turbulence. Load locations should be generally evident flom the names, and coordinate systems are oriented as described in the IEC load measurement standart but the specific locations are not as important as the overall view of the range of the load ratios. The Extreme Coherent Gust with Direction Change (ECD) event is often the case that produces the highest Ioads. Most systems are unable to yaw quickly enough to stay aligned with the rapidly changing wind direction, so the rotor is placed at a large yaw error in high winds. This combination not only produces large blade loads, it also produces large rotor moments that in turn create high loads throughout the structure. 24 The Extreme Operating Gust (EOG) event is often the condition that places the greatest demand upon the rotor brake (if it is an emergency stopping brake). However, this gust alone seldom produces the highest loads in the structure. It is interesting and important to note that tower strikes of very sott blades are predicted and observed in wind conditions that are not extreme. For instance, Hansen (1999) discusses tower strikes in light and variable winds when a rotor is idling or free.-wheeling with no load. Though such conditions are not specifically enumerated in the IEC standard they should be considerecJ particularly in the design of very flexible rotor systems. Small, Furling Rotor Systems Most small wind turbines rely upon passive controls such as tiling (yawing or tilting) of the rotor to limit power output and rotor speed in high winds. Historically, tiling systems have been designed by testing and relatively simple design calculations. It is very difficult to develop a passive system that will limit rotor speeds in high wind during normal operationand whenthere is a loss of generatorload As a result, manysmall turbines occasionallyrun at veryhigh rotor speeds,creatinghigh loadsand noise. Methods are now available, though not thoroughly proven, for detailed design analysis of tiling rotors. These design calculations indicate that the ECD condition presents one of the greatest challenges to a furling rotor. The changing wind direction yaws the turbine and generates gyroscopic moments that tend to retard fhrling of the rotor. (Both positive and negative direction changes must be considered. One dmection will assist filing and result in low loads, the other will retard fi.n-lingand result in high loads.) The simultaneous increase in wind speed can generate very high rotor speeds and systems loads. Figure 1 shows a Synergy Power Corp. SL turbine at a test site operated by Windward Engineering in Utah. This turbine has an induction generator and operates at constant speed and fixed blade pitch. The rotor diameter is 12.8m and the nominal rotor speed is 67 RPM. The system is attached to a yoke arrangement at the tower top that allows the entire rotor and tail structure to tilt upwards under the influence of aerodynamic forces and moments on the tail and rotor. Figures 2 and 3 compare histograms of power output and rotor tilt angle measurements and predictions. The histograms were compiled from 1000 seconds of operation and predictions made using the measured wind time-series as an input to the ADAMS model. There is reasonable agreement between the model and test results in this high-wind condition. Figure 4 shows the predicted response of the SL system to an ECD @. In this case the rotor tilts up (the rotor axis of rotation becomes ahnost vertical)in responseto the increasing wind speed. If the wind had shitled in the opposite direction the power would have increased until the rotor shaft brake stopped the system. The passive tiling alone is not predicted to prevent an overspeed (or excess power) in this ECD event. This indicates the difficulty of designing a completely passive filing system that will give the desired in response in all wind and generator load conditions. Rigid Rotor Systems Stiff systems are generally designed by fhtigue loads during normal operation in turbulence and extreme winds (EWM) with the rotor parked Persistent yaw errors during normal operation can significantly increase fatigue loading and the load spectrum is also sensitive to the turbulence intensity. Deflections generally remain smal~ and the fatigue loading is high enoughthat the extremeloads due to discrete gusts do not often I.wcomethe load limiting case. This makes the system design much more straightfbnvard and is one reason fbr the commercial success of rigid rotorsystems. Two discrete gusts have not been found important in any of the designs that Windward Engineering has been involved in or aware of. These are the Extreme Wind Shear (EWS) and Extreme Direction Change (EDC) eases. Of course, there maybe some system architecture that is particularly sensitive to these types of wind events, but we have not encountered such a system in our experience. 25 Suggestions for Futwe Revisions We have seen three general areas where IEC 61400-1 might be improved to better represent design wind conditions: 1) There are currently two turbulemx categories in the standard. The turbulence intensity is slightly lower in category B than in category A. The refwence intensity differs by two percentage points in the two categories. Otherwise the two are identical. Large turbines are likely to be designed for a more specific type of site, e.g. smooth terrain or complex terra~ instead of designing one system that can be used in a wide variety of sites. The turbulence intensity specification is too rigorous for a smooth or otl%hore site, but it maybe too relaxed for a mountainous site. The standard could be strengthened by using turbulence categories that more closely represent the wide variety of sites that might be encountered. 2) Turbulence simulation% if they represent actual atmospheric turbulence, will contain extreme events. Simulations using such wind inputs should also predct extreme loads. However, the extremes will be observed only rarely, i.e., after an impractical number of lengthy simulations. l%is makes it advisable to implement one or both of the following in the next revision of the standard a) Use extreme value statistics techniques to extrapolate extreme loads from those observed in a practical number of turbulence simulations. This would not avoid the need fix many simulations to quali@ a desi~ but it wouId reduce the number of simulation required to achieve the same statistical confidence in the results. Some research in this area is showing promise, but much work must be done befme this technique alone can be assured of accurately predkting extreme loads (Mads~ et al, 1999). b) Embed the IEC extreme gusts in a turbulent flowfield. The gusts that are specified in the current editim of the standard do not include any turbulent fluctuations. However, we know that the broad frequency content of turbulence and rotational sampling effects excite structural modes of vibration more than simple laminar winds. For this reas~ we should expect that a discrete gust embedded in turbulence could generate higher loadsthan a similargust that doesnot excitethe naturalmodes. The extreme wind model is perhaps the easiest example of this latter concept to visualize. The current standard requires, for the most rigcrous turbine class a 70 mls wind from the worst direction within a 10° (horizontal) and 8° (vertical) range. ‘l%e design calculation can be performed with a steady wind. However, a turbulent wind with a peak (3sec) gust of 70 mh can be expected to generate highez loads (and to be more representative of the actual conditions where a 70 mk gust would be observed). A simulation of category A turbulence with a 50 mh mean wind results in a peak three-second gust near 70 IU/Sand a peak instantaneous gust near 80 mk. We have run simulations of f=thered rotors, fixed-pitch stall-controlled rotors, and Ike-and fixed-yaw rotors parked in such winds. l%e peak loads are consistently higher than those predicted with steady 70 m/s winds. Of course, this technique does introduce a random element in the loads, thus requiring longer simulations to have confidence that an extreme load has been observed. The advantage of this latter method is that the extreme event can be captured with far fewer turbulence simulations, but the simulations still contain the important effects of turbulence on the random component of the system loading. 3) The fatigue Ioadmg of a rotor is quite sensitive to the turbulence structure, not just the turbulence intensity. Atmospheric stability can influence tbe distribution of turbulence scales, hence the fatigue load spectrum. At present the IEC standard uses only neutral atmospheric stability. The t%tigue load spectra could be made more accurate by including stability efftxts in the wind specifications of IEC 61400-1. This may also improve the prediction of extreme deflections and loads in light wind conditions such as those that are known to result in tower strikes of soft blades. Conclusions IEC 61400-1 has been very helpful to designers and analysts when estimating the design loads fbr a wind turbine system. The standard represents the consensus of many people with diverse backgrounds and expertise, and is therefore superior to the design conditions that might be devised by any individual. This 26 paper reflects upon the experience of the author in applying the IEC standard to a wide variety of turbine configurations and sizes. Rigid rotor systems are generally found to have their structural design determined by normal operation in turbulence and the Extreme Wind Model (EWM). Soft systems have reduced cyclic loads in turbulence, but may be design limited by deflections or loads in extreme wind conditions. This means that softer (more compliant) structures are often designed by the extreme discrete gusts. This makes such designs more difficult because they are more dependent upon rare events and the computer simulations must be accurate in conditions of very high wind amlor deflections. Many soft systems are predicted to experiencetheir highest loads in the Extreme Coherent gust with Directionchange(ECD)event. This obviouslymakes it essentialthat this event be describedas accurately as possiblein the IEC standard. The Extreme Wmd Shear (EWS) and Extreme Drection Change (EDC) events have not been found to be design limiting for any of the rotors that Windward Engineering has analyzed. These two types of events could be de-emphasized in the research to improve IEC 61400-1. Two types of changes are proposed for the design standard with the intent of improving estimates of extreme loads. A third change, addtiion of atmospheric stability specifications, may help improve the estimates of t%tigueloads during normal operation in turbulence. References Hans% AC. and J.E. Minnema (1999). “Dynamics of Pultruded Blades on the PS Enterprises P16 Rotor”. To be published in the Proceedings of Windpower ’99, the annual meeting of the American Wind Energy Association held in Burlingto~ VT, June, 1999. Mads~ PM., K. Pierce, and M. Buhl. (1999) “Predicting Ultimate Loads for Wind Turbine Design”, Proceedings of the 1999 ASME Wmd Energy Symposium, 37th AI&4 Aerospace Sciences Meeting, Reno, N-v. 27 Table~L Ratio of maximum loads due to extreme gusts to those due to normal operation in turbulence. me values for turbulence are the peak value in ten, 10-minute simulations in 24 m/s winds. No load extmpolationwasptiormed Parameter Ratio Parameter Ratio r RotorR PM 1.08 MnfrmTrnMy 1.60 FlapAnglmax 1.42 YawFx 1.32 FtapAng2max 1.47 YawFy 2.09 ConHinFX 1.81 YawMx 3.03 ConHinFY 1.05 YawM y 1.55 ConHinFZ 1.09 YawMz 1.52 ConHinMX 2.03 YawAng 2.78 ConHinMZ 1.10 Power 1.24 FlapActl 1.39 GenTorq 1.13 1 -. )Act2 1.36 TwrX 1.05 ~Adl Edge 2.01 TwrY 2.13 Aftl Flan 2.65 TwSt6M y 1.46 1 BldAd 1MZ 1.10 1-Tw. ._6t24My 1.05 LSS2FX 1.07 TwSt42M y 1.03 Lss2Fy 1.46 Twst60My 1.01 LSS2FZ 1.49 Lss2My 1.08 LSS2MZ 1.63 28 Figure 1 ‘k Utah. 29 1 I 0.08 — Test Data [ — ADAMS prediction 0.06 0.04 0.02 Rotor Power (kMl) Figure2. Comparisonofmeasuredandpredictedpoweroutputhistogramsofthe SynergySLturbine operatinginhighwinds. I ~ O.IOJ I i I I .- Cn — Test Data Tilt Angle (deg) Figure3. Comparison of measured and pre&cted power output histograms of the Synergy SL turbine operating in high winds. 30 z ’00 I i I x ------~G 80 - Yaw ‘“., o \ \% ● ; 60 - 88 5 ~ 40 G g 20 - g) m o F z =.- + -20 1 1 I ‘‘cD-;i200 o 5 10 15 Time (see) Figure 4. Response of the Synergy SL to an ECD gust with an initial wind speed of 12 XII/S(IEC 61400-1, 1“ Ed.) 31 2nd IEA Symposium on IMnd Conditions for PWndTurbine Design Wim Bierbooms Modelling of extreme gusts for design calculations This presentation is based upon a Dutch project (’Uitbreiding en verificatie van methode voor extreme windbelastingen’; in cooperation with TNO-MEP) and the EU project ‘NewGust’ (JOR3-CT98-0239 in cooperation with RiseJand Vestas). An overview of the first results of the NewGust project has been presented at the EWEC ’99 conference in Nice. The background of the project is the rather arbitrariness in the shape and amplitude of extreme gusts as given in standards. In the present IEC code the extreme gust has a ‘mexican hat’ like shape; this is based on a few measurements only. The goal of the project is to come to a description of extreme gusts which is based on the stochastic properties of turbulence (as is the case for stochastic wind field generators for the determination of fatigue loads). According to theory the mean gust shape is a function of the correlation function of turbulence and as a consequence it is (very) sharp. Note: the shape around t=Os is connected to the behaviour of the power spectrum for very high frequencies. For turbulence the spectrum for high frequencies is given by a 5/3 power relation (’inertial subrange’). This implies a theoretically infinitely sharp peak in fact, infinitely high frequencies will not occur so the peak will be somewhat less sharp. For the verification of this sharp peak several analysis methods have been applied. The first one is standard available at the ‘database on wind characteristics’. A window is moved along the time series and the amplitude of the gust is defined by the difference between the maximum and minimum within the window. The second analysis method is more or less based on the theoretical work. All local extremes, with amplitude within a certain range, are localized within the time series. The mean gust shape is determined through averaging of the parts (say 10s for and after the extreme) around the found extremes. The analysis method is first applied on simulated turbulence. The advantage of simulated turbulence is that the autocorrelation function is known a priori. The resemblance between the determined mean gust shape from the simulated wind and the theoretical curves, turned out to be very good. Furthermore the influence on the mean gust shape due to sampling and the dynamics of the (cup) anemometer is investigated. For the preliminary verification the wind data of the Cabauw measurement mast have been used. The resemblance between measurements and theory is good; for the theoretical expression the estimated correlation function (from the wind data) is used. In order to obtain the extreme wind turbine loads, ‘constrained simulations’ will be performed in the future. The mean gust shape is combined with a stochastic wind time series in such a way that no distinction (in statistical sense) can be made with gusts from ‘real wind’. These kind of simulations have to be performed for several different amplitudes and for each amplitude several realisations must be performed (as it concerns a stochastic process). By combining these results with the chance of occurrence of gusts, the distribution of the extreme loading can be obtained. From literature an expression is found for the chance of occurrence of gusts. Depending on the bandwidth of the process the density function is in between a Rayleigh and a Gauss distribution. Finally the extreme loading due to a ‘50-years’ gust can be determined 32 applying the extreme value theory (e.g. as stated in the EWTS II study). For the moment it is assumed that the extreme loading correspond with a gust. From simulations and measurements it will be determined if this is correct; perhaps the slope of a gust is more decisive. Furthermore the sensitivity of several parameters (e.g. the exact gust shape) on the extreme loading will be determined. The theoretical mean gust shape has been determined by applying a general statistical method. This general method consist out of two steps. The first one is the determination of the mathematical operations which transform the original stochastic time series into a series of delta functions, at the time locations corresponding with the appropriate events (in our case: the local extremes). The second step is the mathematical treatment of the expression: a multi-dimensional integral with as integrand a multi-dimensional density function. For the first step it is not necessary that the stochastic process is normal; in practice, the second step can only be performed for a Gaussian process. Applying the same method it is possible to obtain an expression for the gust shape at height 2 which correspond with an extreme at height 1. This expression contains the crosscorrelation function. The expression is very useful for the verification of the spatial shape of an extreme gust. Note: in practice it will be impossible to determine the exact position of the peak of a wind gust, even in case several anemometers (in one plane) are available. The derived expression can be verified in case 2 anemometers only are available. Appendices 1) Wim Bierbooms et al., Modelling of extreme gusts for design calculations (NewGust), EWEC ’99, Nice. 2) The theoretical mean gust shape (this forms a part of an article submitted to the journal Wind Energy). 33 MODELLINGOFEXTREMEGUSTS FORDESIGNCALCULATIONS (iVewGust) WimBierbooms1,Po-WenCheng 1 Gumer Larsen 2 Bo Juul Pedersen 3 Kurt Hansen 4 ‘ Institute for Wind Energy, Delft University of Technology Stevinweg 1,2628 CN DeIft, The Netherlands tel. +31 152782097, fax+31 152785347, e-maik [email protected] 2Ris@National Laboratory, Roskilde, Denmark 3Vestas Wind Systems A/S, LenL Denmark 4Technical University of Denmark, Denmark ABSTRACT The mainobjective of the NewGust project is to come to a realistic and verified description of extreme gusts based on the stochastic properties of wind. In this paper the first resuhs of the project are presented. Theoretical considerations indicate that the shape of extreme gusts is very sharp. Based on simulated wind time series, mean gust shapes (for several amplitudes and mean wind speeds) are determined and compared with the theoretical curves. The resemblance turned out to be very good. Furthermore, the influence of the sampling rate and the dynamics of a cup anemometer on the empirical mean gust shape are examined. The promising results are contirmed by a (preliminary) verification based on measured wind time series, available from the database on wind characteristics. The mean shape of gusts, of certain amplitude, together with their probability of occurrence can be used to obtain the distribution of the extreme response of wind turbines to gust loading. Keywords: Gust Models, Extreme Wind Conditions, Turbulence, Wind Field Simulation 1. INTRODUCTION 2.1 Technical approach In essence the new method to be developed in the project, For design load calculations of wind turbines it is necessary describes a way to combme a stochastic turbulence field (as to determine the fatigue loads as well as the extreme loads. used for fatigue analysis) and a well defined deterministic Up to now simple deterministic and coherent gusts (e.g. a gust shape (which can betheoretically derived) in such a way cosine gust) have been used to determine the extreme that a realistic extreme gust is obtained. response. The shape, amplitude and duration specified for The project approach can redivided into the following steps these discrete events remain rather arbitrary and largely 1. “Experimentalverification of the shape of extreme gusts. invalidated. Thk is in contrast to the fatigue analysis, which From theory it follows that the gust shape resembles the conventionally rely on a synthetic stochastic wind field autocorrelation function of turbulence. This will be reflecting the stochastic properties of natural turbulence. verified by comparing with shapes extracted from an The main objective of the here presented NewGust project is existing database of wind measurements. to achieve a realistic and verified description of extreme gusts 2. Determination of the probability distribution function of based on the (stochastic) properties of wind. The basic ideas extreme gusts from a database of wind measurements of this advanced method are given in [1]. From theoretical and./orfrom theory (in case wind measurements are not considerations it has been demonstrated that the shape of available for a long enough period). extreme gusts is (very) sharp, which is in contrast with the 3. Development of an advanced method to determine the gust shapes given in present standards. A preliminary dynamic response of a wind turbine to extreme gusts. verification of the predicted mean gust shape can be found in The advanced method will generate wind time series [2] and [3]. This paper focus on the first results of the which can not, in a statistical sense, be distinguished NewGust project. from natural extreme wind gusts. OnIy the longitudinal turbulence component will be 4. Implementation of the advanced method in a number of considered, and consequently no account is given on wind existing design packages. direction changes. 5. Experimental verification of the predicted loading and response of a wind turbine to ex&eme gusts. - 2. THE NEWGUST PROJECT 2.2 Expected achievements The project will result in an advanced and verified method to In this section a global overview of the NewGust project is determine the extreme response to gusts. The method will be presented. The project is a cooperation between Delft worked out in a way that enables it to be implemented in University of Technology (coordinator), Ris@and Vestas. state-of-the-art design packages for wind turbine design as 34 used by the industry. interval (of say 5 s). The more accurate description of the extreme loading will enable wind turbine manufacturers to build more reliable and optimised wind turbines. 4. VERIFICATION OF THE MEAN GUST SHAPE WITH SIMULATED WIND 3. ANALYSIS METHOD FOR THE VERIFICATION For evaluation of the analytical expression for the mean gust shape, the autocorrelation function (ACT) should be known. For the determination of a mean gust shape, the primary task This implies that a comparison between the determined mean to address is the definition of gusts occurring in wind time gust shape as obtained from measurements and the theoretical series, One possibility is to consider a gust as the pm of the prediction may be affected by uncertainty in the ACF. In signal between a positive and a successive negative zero order to avoid this problem a preliminary verification is crossing. However, usually several (local) extremes may conducted based on a simulated wind field where the ACF occur between the two zero crossings, for a broad banded is known priori, as input of the wind field simulation. signal as it is the case for turbulence. Furthermore, it is Furthermore, possible influences on the determined mean difficult to attach a corresponding gust amplitude. gust shape originating from the measurement can easily be Therefore a different method has been applied. A gust is studied by computer simulations. interpret as the time period, say 20s, around a (local) extreme in the time series (mean subtracted) with a certain amplitude 4.1 Comparison gust shape predicted from theory and (e.g. between 2.7 and 3.3 times the standard deviation). The determined horn simulated wind mean gust shape, with a given amplitude, follows by With the aid of the wind field simulation package SWING4 straightforward averaging of the pieces of the wind time [4], time series Me generated for two mean wind speeds (10 series around all found extremes. In this method a (local) m/s and 20 rnls), for a height of 40 m. For each mean wind maximum is counted as +1 and a (local) minimum as -1. In speed 10 wind field realisations have been generated, each of such way a gust with a small dlp has about the same effect as a duration of more than 10 minutes (16384 time steps of 0.04 a gust without the dip, see Figure 1. Furthermore, a small s). disturbance, around a certain magnitude, in a flank of some In Figure 2 the mean gust shapes are given according to the higher peak will have a minor influence only on the mean theoretical expression (1) and compared with the mean gust shape of that specific magnitude. shapes determined from the simulated wind time series. ASit can-be seen the resemblance is very good...... I W2.llaal 2 1-5 ~ ~, . = ‘s s - 0.5 : % 0 0.51 I .5945 5945.5 5946 5946.5 5947 - [4 Figure 1: Originalwindsignal(solid line) with2 maxima and 1 minimumaroundt=5945.5s andthe corresponding Figure 2: The comparison of the mean gust shapes mean gust shape (dashed line) according to the applied (amplitude20) according to theory (solid lines) andfrom analysismethod. simulatedwind (dotted lines)for 2 wind speeds: 10 rds (uppercurves)and20 tis (lower curves). Surprisingly, it turned out to be possible to derive an analytical expression for the mean gust shape ;g~i(~) (with amplitude between A and A+dA), based on the 4.2 Influence of the sample frequency stochastic properties of turbulence This subsection deds with the infhrence of the sample frequency of the wind on the determined mean gust shape. The theoretical expression (1) has a (very) sharp peak, which can not be resolved in case the sampling rate is too small. This effect can easily be examined by first sampIing the where r denotes the normalized autocomelation function generated wind time series and afterwards determining the and u is the standard deviation. mean gust shape. The results are shown in F@ure 3 for two different sampling rates, 0.1 s and 1 s. As seen, the influence A full treatment of the analytical derivation of thk expression on the shape originating from the sampling rate may be is given in [2]. In the same mricle a preliminary verification substantial. can be found. There are of course alternative ways to define a gust. In section 5 a gust is regarded as a suitable large wind speed excursion from a (local) minimum inside a certain time 35 wind speed. Denoting the autocorrelationin space and in time by R, and R,,respectively, the following relation holds R$(ur) =R,(7) (2) where U denotes the advection speed The left hand side of relation (2) is directly determined from the frozen turbulence structure. The autocomelation in time is thus obtained fromthespatial autocorrelation by an affinity of the independent variable. The theoretical expression for the gust shape depends on the autocomelation coefficient in time and consequently on the mean wind speed. Two possible =10 -5 6 10 methods to compare experimental and theoretical gust shapes d [1] thus emerges. One is to apply a suitable detailed binning in Figure3: Themeangustshapes(uppercurves: amplitude the mean wind speed for the experimental data and base the 40; lower curves: 2tT)for two samplingrates: 1 s (&shed theoretical determination on an averaged autocorrelation lines)and0.1s [airsh-dotlines)comparedtothetheoretical coefficient associated with one particular bin which is thus ones(solLilines). subsequently compared with bin-averaged gust shapes. A second, and more consistent method, is to derive the spatial 4.3Influence of the dynamics of a cup anemometer autocorrelation coefficients from each measuring series The dynamics of a cup anemometer will also have an effect applying the scaling relation (2) and subsequently evaluate an on the empirical mean gust shape. In order to investigate that, average autocorrelation coefficient. Application of the a simple model for the cup anemometer has been applied a averaged normalised autocorrelation coefficient in the first order system with a ‘time constant’ which depends on theoretical expression should enable a comparison with a the momentary wind speed. The generated wind field is used mean of the identified experimental gusts, each with the as input to ttds dynamic model of a cup anemometer. The physical time axis multiplied by the associated mean wind results are shown in Figure 4 for two different distance speed. constants of the cup anemometer, i.e. 2 m and 15 m. The The theoretical gust shape is based on an assumption of effects are somewhat simdar to the smoothing effect caused statiomuy“parent” stochastic processes. In order to obtain a by sampling. In addition an asymmetry is introduced, which consistent comparison with experimental time series, it is is very modest for realistic distance constants of the cup necessary to remove possible (linear) trends in these. anemometer. 5.2 Application A number of high wind situations (mean wind speeds between 13 M/s and 17 rnls) from the Cabauw site, extracted from “Database on Wmd Characteristics” [5], has been selected. The measuring height was 40 m and the length of each run were converted to 600s with a sampling rate of 2 Hz. Thetotrd available data material consisted of 129 runs, of which 66 were associated with mean wind speeds between 13 M/s and 15 M/s and the remaining 63 related to mean wind speeds between 15 M/s and 17 MIS. The experimentally determined gusts were classified into 4 I ! groups depending on the ratio between the gust amplitude -!0 -5 5 10 d [$] and the (de-trended) standard deviation associated with the Figure4: Themeangustshapes(uppercurves:amplitude pruticular time series. The ratio intervals defining the classes 40; lowercurves:2u) for twodistanceparameters:15 m were 1.75-2.25,2.25-2.75, 2.75-3.25 and 3.25-3 .75.The gust (dashedlines) and 2 m (aksh-dotlines) comparedto the amplitude in this respect was defined as the difference theoreticalones (solidlines). between the maximum recorded wind speed and the minimum recorded wind speed within a centred time interval of 20s length around the gust maximum. It should be noted that this procedure deviates from the analysis method as 5. VERIFICATION OF THE MEAN GUST SHAPE WITH MEASURED WIND described in section 3. Two types of comparisons have been performed. In the first 5.1 Background place the investigated mean wind speed interval has been The present section deals with a preliminary experimental subdivided into two mean wind speed bins of equal size(13 M/s -15 M/s and 15 m/s -17 M/s). For each of these bin verification of the theoretical expression for the gust shape at a particular spatial point as presented in section 3. Assuming intervals the classification according to gust size is Taylor’s frozen turbulence hypothesis to be valid, the (frozen) performed, and within each resuking class the experimentally turbulences presumed to convect in the mean wind direction identified gusts are averaged and compared with the with the mean wind speed. Thus, the hypothesis enables us to theoretical expression (1) based on the related averaged convert temporaI measurements at a given point in space to autocorrelation coefficients and the mean standard deviation associated with each class. Autocorrelation coefficients and spatial patterns in space. The implication for the autocorrelation function is that it must depend on the mean standard deviations are evaluated nom the total time series, per class, in which gusts were identified. The results are 36 presented in Figure 5 and 6. Cabauw, M.igma=2.@, 13mkUc17m/s Cabauw ALsigma=2.S3; Lt=14mls 1 I I 1 I ... ----- —.> I A v4 I, I .I * . 1..J’ . I , . . . . . : 2 0 -1 ) 1 “K a o I I I I I I I n I I I [ -10 -5 0 5 10 Dbtama[m] tin-e@] Figure 5: Comparison between theory (line) and mean Figure 7: Comparisonbetween theo~ (line) and mean qerimental (dots) gust shape for the mean wind speed experimental(dots) gust shape in spatial representation; rangingbetween 13 mlsand 15 nA. includingtheconfidenceintervals,ZEG(&shed lines). Cabaq A/aigma~.40; &l 6nt/s 6. CONCLUSIONS AND OUTLOOK , According to presented theory a gust has a sharp peak in contradiction to standards. ‘llepredicted mean gust shape has been verified by comparison with simulated as well as measured wind data. These promising results demonstrates the viability of a new method to determine the extreme 4 loading of wind turbines (NewGust project). Further work, in the scope of this project, constitutes the determination of the probability densi~ function of gusts for 10 -5 0 5 10 a given mean wind speed. Combining the constrained time[s] simulation for wind turbine response [1] and the occurrence probability of extreme gusts, the distribution of extreme Figure 6: Comparison between theory (line) and mean response can be obtained. By applying the reliability method, eqenkxtal (dots) gust shape for the mean wind speed the failure probability due to gust loads can be determined. rangingbetween 15 mh and 17 tis. In the second place the mean wind speed binning is omitted. 7. ACKNOWLEDGEMENT Instead, a spatial normalised “time” axis, obtained from the physical time axis by multiplying with the mean wind speed, The work is partially financed by the European Commission is applied within each gust class. The resulting gusts are under the DG XII Non-Nuclear Energy Programme, contract averaged within each chss and subsequently compared with JOR3-CT138-0239. the theoretical expression based on a mean of the related autocomelation coefficients with time axes transformed in the same way as for the gust shape. The average standard 8. REFERENCES deviation associated with each gust class are applied as standard deviation in the theoretical determination of the gust [1] J.B. Dragt, W. Bierbooms, Modelling of extreme shape. Figure 7 shows the results of the above described gusts for design calculations, EUWEC ’96 (p. comparison for one of the gust classes (representing in total 842). 45 gusts). [2] Wlm Bierbooms, Jan B. Dragt, Hans Cleijne, The shape of the gusts are predicted well by the theoretical Verification of the mean shape of extreme gusts curves, although the measured wind speeds are not strictly (submitted to Wind Energy). Gaussian. The asymmetry in Figures 5-7 maybe due to the [3] W. Bierbooms,J.W. Cleijne, P. Cheng, Uitbreiding dynamics of the cup anemometer as explained in subsection en verificatie van methode voor extreme 4.3. windbelastingen [in Dutch; to be published], 1999. [4] Wlm Bierbooms, SWJNG4 (Stochastic WINd Generator) - User Guide, DUT, 1998. [5] K. Hansen and M. Courtney, Data Base on Wind Characteristics, Final Report (to be published). .. . 37 VERIFICATIONOF THE MEANSHAPEOF EXTREME GUSTS Wim Bierbooms Institute for Wind Energy, Delft University of Technology, The Netherlands Jan B. Dragt Emeritus professor of wind energy, Delft University of Technology, The Netherlands Hans Cleijne TNO-MEP, Apeldoom, The Netherlands (present: KEMA Sustainable, Arnhem, The Netherlands) Correspondence to: Wim Bierbooms Institute for Wind Energy, Delft University of Technology, Stevinweg 1,2628 CN Delft, The Netherlands. Email: w.bierbooms@ct.~delft.nl 38 Abstract For design load calculations for wind turbines it is necessary to determine the fatigue loads as well as the extreme loads. An advanced method has been presented previously to incorporate extreme turbulence gusts in wind field simulation; the so-called “NewGust” method. The gust generator works by constraining the random parameters of a stochastic wind field simulator. The present paper deals with the verification of the mean shape of extreme gusts. On the basis of a statistical analysis an expression of the mean gust shape is obtained. This theoretical gust shape is compared with the mean ~mst shape determined from both simulated and measured turbulence. The resemblance is remarkably good which demonstrates the viability of the NewGust method. Keywords: Extreme Wind Conditions, Gust Models, Turbulence, Wind Field Simulation Introduction The sophistication of the methods used to carry out wind turbine design calculations has increased enormously over the last two decadesl. A good example forms the treatment of fatigue loads. It is now common practice to consider for the fatib~e analysis a complete representation of both the temporal and spatial structure of the turbulence. The applied wind field simulation methods are based on a stochastic description of turbulence (i.e. spectral and coherence function). The situation for the determination of extreme loads is totally different. Up to now just simple deterministic gusts (e.g. a cosine gust) are used to determine the extreme response, instead of appIying a stochastic description of the wind (as is the case for fati=me analysis). Quoted from reference 1: “Turbulence models of the form described above are now widely used for the calculation of fati=me loads for design purposes. For calculation of extreme loads, however, it is standard practice to base calculations on deterministic descriptions of extreme wind conditions. Current design standards and certification rules specify extreme events in terms of discrete gusts, wind direction changes and wind shear transients. The form, amplitude and time period specified for these discrete events remain rather arbitrary and largely invalidated. The development of more reliable methods for the evaluation of extreme desi=m loads, based possibly on the use of probabilistic analysis, requires considerable effort but is crucially important in the context of refining wind turbine design analysis. ” Such a new method has been proposed by the Institute for Wind Energy and presented at the EUWEC ’96 conference. This method, which has been given the name ‘NewGust’, is based on constrained simulation and briefly described in2; a more comprehensive description of constrained simulation is under preparation. The present paper will focus on the gust shape and is partly based on the work performed during a Dutch project4. Please note that our prime goal is not the determination of the mean ~~st shape in a meteorological sense but with respect to the extreme loading on wind turbines. In the next section a general statistical method is presented in order to derive an analytical expression for the mean gust shape. The succeeding two sections will treat the comparison of the theoretical mean gust shape with the mean gust shape determined from simulated and measured wind respectively. 39 The theoretical mean gust shape General statistical method A general method to determine the statistical means of certain parameters of a stationary stochastic process has been given by Middleton5. In order to present this method it is inevitable to use a lot of equations. The reader is encouraged to put some effort in understanding them in order to grasp the elegance and strength of the statistical method. The method can be divided into the following steps: . Specify the events of interest (e.g. zero crossing or maximum). Determine a series of mathematical operations (differentiation, time shift, rectifier, step function, etc.; see also Figure 1) which transfers the original time series u(t)into a series of delta fhnctions at the time instants of the specific events: p(t) = ~ qt-ti) (1) i with p(t) a (possibly non-linear) function of u(t), u(t+ r), i(t) , etc. ● The number of events, for a specific time series, in the time interval T equals: T N = p(t).dt (2) J o The expectation value of the number of events equals: T T E[NJ = E[fp(t).dt]=@@].dt =T.E@(tO)] (3) o 0 for any to(due to the stationarity of the stochastic process) ● The sum of the signals in the neighborhood of the events is: T S(T) = ~ ‘(ti+z) = ~ j“”(t+z)-a(t-ti) -dt = ju(t+z).~(t).dt (4) i ‘o o for some range of r (both positive as well as negative values are allowed; the range must be small compared to T). The expectation value of this sum of the signals in the neighborhood of the events is: E[S(T)] = ;E[u(t+r).p(t)].dt=T.-Wto+Op(~o)l (5) o 40 Notice that this is a function of ~only. ● The mean signal in the neighborhood of the events equals (for one sample time series): ii(r) = —S(T) N (6) The expectation value equals: E[S(T)] = lzu(~+~).p(~)l Z(T) = (7) E[lVl E~(t)] The above given expectation values can be evaluated in case the (multi-dimensional) density function of u(t), u(t+ ~, i(t) ,etc. which occur in p(t), is known. Please note that, in principle, it is not required that the density function is Gaussian. In practice however, the expectation value can be analytically detefiined in case the density function is Gaussian and is of limited dimension only. It is subject of further research whether it is possible to determine the expectation value in case of a non-Gaussian (multi-dimensional) distribution function, if such function can be specified anyway, by means of Monte Carlo integration. Example application The above method will be illustrated by the determination of the expected number of (positive) zerocrossings in a stationary Gaussian (wind) signal. In Figure 2 it is shown by which operations the (positive) zerocrossings maybe selected from a (wind) signal u(t): p(t) = a(u(t)).g(zi(t)) (8) with g(t) the rectifier function The expected number of (positive) zerocrossings per time period equals, according to (3): ‘[M = E@(t)] = ffdu.dv.a(u).g(;-~(~,v) (9) T The multi-dimensional density function of u(t)and ti(t) is here denoted by F’(u,v) and assumed to be joint normal. The covariance matrix equals: 10 A=oz (lo) [)OJ. with 41 A = -t(o) (11) and r denotes the normalized autocorrelation function and othe standard deviation. The inverse of the covariance matrix equals: ~-llo (12) & (1o l/a and thUS ---L(U 2+V%) 1 . ~ 2A? P(u,v) = (13) 2.n.02.fl Substitution gives: * = jdv.g(v).P(o,v) = 1 ;v.e-*dv (14) -- 2.7c.ff2.fi () Note: the delta function in the integrand is evaluated by setting u equal to zero and g(v) may be replaced by v and setting the lower limit of integration equal to zero. By substitution ofi V2 z=— (15) 2.02.A we finally obtain: .,~ E[Nj @ ‘e-ZdZ _ G — =— .— (16) T 2.7CJ~ 2.7C with a. = +(o) (17) This is the famous formula of Rice6. Mean gust shape 42 We now direct the attention,to our topic of extremes. In an analogous manner the following expression for the mean shape of an extreme (maximum or minimum), between level A and level A+fl, maybe derived (see Figure 3 and Appendix I): ;(T) F(T) =4-(T)–:.[r(T)+— (18) 0 (3 A] Notice that local minima are also taken into account (but counted as -1). The advantage is the treatment of a peak with a small dip, which will reewlarly occur in a stochastic time series. In this way such a peak is counted as 2 maxima and 1 minimum thus in total as 2-1=1 extreme (instead of 2 maxima). In other words a peak with a small dip will have about the same effect on the average peak shape as a peak without a dip. Furthermore a dip (near the threshold A) in a flank of some higher peak, which is of no interest for our purpose, will have a minor effect only on the mean gust shape as it is treated as 1 maximum and 1 minimum thus as O extremes. The theoretical expression of the autocorrelation function of turbulence has a sharp peak at r = O.The second derivative at r= O,which is required for the evaluationof(18), is infinite; this is due to the fact that the turbulence spectrum, for large frequencies, is inversely proportional to the (5/3)* power of the frequency (’inertial subrange’). In the situation of measurements this will not be the case due to the involved rounding off. Firstly, the anemometer has some dynamic properties. Secondly, the measurements should have been filtered according to the applied sample frequency; e.g. in case of a 2 Hz sampled wind signal a filter of 1 Hz should have been applied. For the verification of the mean gust shape this may have a considerable influence in case the sample frequency is low. See Fiowre 4 for the theoretical mean gust shape for two filter time constants. This implies that for verification the filter time constant (or sampling frequency) should be taken into account. Our interest concerns extreme gusts, so large values of the amplitude A. III this case the first term of (18), A/cr.r( r), is dominating, which comesponds with the expression of NewGust* based upon constrained simulation. Note: it is not yet clear why the above given expression ‘(18) deviates from the expression of NewGust for small amplitudes caused by the second term; this deviation does however not have any practical consequence because it is restricted to small amplitudes. In literature, a similar expression as (18) can be found for the extreme loads on offshore platforms due to hydrodynamic excitation by means of waves’; this expression is based on the general work on extremes by Lindawens.The (small) difference between (18) and the expression given in reference 8 is due to the fact that there maxima only are considered without correction for small dips; both expressions converge again for large amplitudes. So far the (extreme) wind speed at one point in space has been considered. In fact an extreme ~~st has a spatial extension (thus non-uniform over the rotor plane) as is given in reference 2. In practice it will be difficult or even impossible to determine the position of the center of some gust with the aid of a limited number, say 6 to 8, of anemometers. This implies that a statistical analysis of a large number of ~mstsis the only way possible. For this purpose an analogous derivation as given in Appendix I has been carried out leading to the following (theoretical) expression for the ‘spatial gust shape’; this is the shape of the wind at height 2 around the time instant of an extreme at height 1 (with amplitude A): ‘gwx=)=4p(T) -;.[p(#@] (19) a o R(o) with p the cross correlation fimction. Equation (19) is a generalizationof(18). Verification of the gust shape by means of simulated wind Inthis section the mean gust shape from simulated wind will be compared with the theoretical expression given in the previous section. The advantage of simulated wind is that the correlation function, required in(18) is known, for it is used as input for the wind field simulation. With the aid of the wind field simulation package SWING3 9time series are generated for a mean wind speed of 10 rds and 20 mk, for two heights (40 and 80 m) with a duration of more than 10 minutes (16384 time steps of 0.04 s). For each of these situations 10 realizations have been generated in order to increase the number of gusts. The expressions according to the isotropic turbulence theory are used (see Appendix ~. The following steps, according to the analysis method described in the previous section, are applied in order to determine the mean ~wstshape: ● search in the simulated wind time series u(t) for time instants of local maxima or minima (thus no condition on the second derivative) and for which the wind speed u is between level A and A+GM. Four classes have been investigated: between 0.5a and 1.50, between 1.5oand 2.5cz between 2.5a and 3.5 sand larger than 3.50 c take the pieces of the wind time series around the extremes found (e.g. 10 seconds before until 10s after the extreme) ● average all found pieces; a maximum is counted as +1 and a minimum as -1 ,... As can be seen from Figure 5, the agreement between the theoretical ~gp.tshape and the ones derived from the time series is remarkably good. The fact that the mean gust shape from the time series is lower than the theoretical curve is due to the relative large width of the amplitude range: all gusts between 2.50 and 3.50 are counted as 30 gusts. The gusts with smaller amplitude will occur more often than larger gusts; this implies that averaging over all gusts will lead to a mean gust shape with a smaller amplitude. In Figure 6 the.mean gust shapes are given for two different mean wind speeds; it can be seen that it is necessary to do the verification for each mean wind speed separately. From a similar comparison (not shown here) the importance of the specific auto- and cross correlation functions can be demonstrated. 44 The theoretical method can also be applied to determine the spatial shape. The method is as follows: ● search in the simulated wind at height 1 for extremes ● determine the piece of the wind time series at height 2 around the found time instants ● average all these pieces The agreement between the mean spatial gust shape according to the time series and the theoretical curves is somewhat less (Fiegme 7). For the 4agust this is probably due to the limited number of extremes. In future work smaller distances will be examined. Verification of the gust shape by means of measured wind In this section the mean temporal and spatial gust shape are determined experimentally and compared with the theoretical expressions derived previously. The wind data analyzed here have been measured at the 240 m tall meteorological tower of Cabauw. Cabauw is situated near Utrecht in the Netherlands and surrounded by farmland with an average terrain roughness of 0.03 m. The data set contains approximately 700 hours data recorded at five different heights (20, 40,80, 140 and 200 m) measured at a sample frequency of 2 Hz. The measurements have been made during periods when wind speeds higher than 10 m/s were expected. The average wind speed of the complete data set is 10 m/s. For the verification process the wind data from 40 and 80 m height have been selected as these are relevant to wind turbine desi=m.The gust shape was derived from the measurements at 40 m height. The data from 80 m height have been used to verify the spatial gust shape, i.e. the wind signal at 80 m, given a wind maximum at 40 m height. For the data processing the following process was used: ● for every record of 10 minutes average properties were calculated: average wind speed and standard deviation ● the wind speed was normalized using these average properties; this implies that, just for convenience, no distinction was made between different mean wind speeds ● minima and maxima of the 40 m signal having an amplitude larger than 1.50 were extracted and stored, together with 30 seconds before and after the extreme ● for the same time peciod the 80 m wind sibwal was stored ● using ensemble averaging the average maximum gust an-dthe gust shape at 80 m were calculated The total number of gusts used for averaging was 1700, approximately. Figure 8 shows the gust shape at 40 m height for two different amplitudes, i.e. 30 and 40. The time axis has been normalized with the longitudinal length scale L (i.e. the ‘LUof ESDU12) and the average wind speed W 7 =0.747 V.r/L . Figure 9 shows the average gust shape of the wind speed at 80 m, measured simultaneously with the 40 m maximum. The maximum value is lower than that of the 40 m maximum gust reflecting the non-perfect lateral coherence. For comparison, the theoretical gust shapes have been plotted. The expressions for the auto-comelation and cross-correlation function were taken from ESDU 12. 45 The agreement between the measurements and the theoretical curves is remarkably good. Both the shape and the magnitude of the gusts are predicted well by the theoretical curves, although the real wind speeds are not strictly Gaussian. The existing small deviations between the theoretical and measured data might be partially due to the fact that for the theoretical curves the auto- and cross correlation functions from ESDU were taken rather than the ones derived from the actual site measurements. Note that the wind signal exhibits a time asymmetry. A possible explanation for this effect is the asymmetric behaviour of cup anemometers, which accelerate fast but decelerate much slower. The maximum of the 80m gust seems to have shifted to negative time values. This suggests that there is an effect of wind shear, which has not been accounted for in the theoretical expressions. Conclusions An analytical expression for the mean shape of extreme gusts is presented assuming that turbulence is a stationary stochastic process. According to this expression the gust has a rather sharp peak in contradiction to the gust shape given in standards. The theoretical mean gust shape has been verified by means of simulated and measured wind data. The resemblance between the theoretical and experimental curves is good, in particular for the shape in time. Some possible reasons have been indicated for still existing small deviations. This demonstrates the viability of a new advanced method (NewGust?) for the determination of the extreme response. In the framework of a European projectl”’ II this method will be extended and demonstrated for present wind turbines. It might be possible to apply the statistical method (for deriving means from a stochastic process) for other problems, e.g. rainflow counting in the frequency domain. Acknowledgements Many of the results in this article have been obtained through work supported by the Netherlands Agency for Energy and the Environment (no. 224.720-9740) and the Commission of the European Union under the Non-Nuclear Energy Programme (JOR3- CT98-0239). References 1. D.C. Quarton, ‘The evolution of wind turbine design analysis - A twenty year progress review’, Wind Energy, 1,5-24 (1998). 2. J.B. Dragt, W. Bierbooms, ‘Modelling of extreme gusts for design calculations’, European Union Wind Energy Conference, Goteborg, May 1996, pp. 842-845. 3. J.B. Dragt, W. Bierbooms, ‘Constrained simulation’ (to be published). 4. W. Bierbooms, J.W. Cleijne, P. Cheng, ‘Uitbreiding en verificatie van methode voor extreme windbelastingen’, Novem project 224.720-9740 (to be published). 46 5. D. Middleton, An Introduction to Statistical Communication l%eoq, McGraw-Hill, New York, 1960. 6. S.0. Rice, ‘Mathematical analysis of random noise’, Bell Syst. Techn. J., 23 (1944). [Reprinted in N.Wax (cd.), Selected papers on noise and stochastic processes, Dover Pub]. 1958]. 7. P.H. Taylor, P. Jonathan, LA. Harland, ‘Time domain simulation of jack-up dynamics with the extremes of a Gaussian process’, 119,624-628 (1997). 8. G. Lindgren, ‘Some properties of a normal process near a local maximum’, The Annals of iklathematical Statistics, 41, 1870-1883 (1970). 9. W. A.A.M. Bierbooms and J.B. Dragt, ‘The choice of atmospheric turbulence models for stochastic rotor load calculations’, European Wind Energy Conference, Thessaloniki, October 1994, pp. 648-653. 10. W. Bierbooms, ‘Determination of the loading due to extreme gusts for design calculations’, European Wind Energy Conference, Dublin, October 1997, pp. 622- 625. 11. W. Bierbooms et al., ‘Modelling of extreme gusts for design calculations (NewGust)’, European Wind Energy Conference, Nice, March 1999 (to be published). 12. ESDU engineering sciences data, Wind engineering; Volume la; wind speeds and turbulence, ESDU International Limited, London. 13. A. Heck, Introduction to Maple, Springer-Verlag, New York, 1993. Appendix 1: Peaks above some threshold A in a stationary Gaussian wind signal Inthis appendix peaks above some threshold A are investigated. For this situation the function p(t) is as follows (see also Figure 3): p(t) = -ti.5(ti(t)).e(tt(t) -A) (20) with e(t) the unit step function at t = O (Heaviside function) As remarked before the local minima are also taken into account (but counted as -l). The advantage is the treatment of a peak with a small dip, which ,,will- regularly occur in the stochastic time series. In this way such a peak is counted as 2 maxima and 1 minimum thus in total as 2-1=1 extreme (instead of 2). In other words a peak with a small dip will have about the same effect on the average peak shape as a peak without a dip. Furthermore a dip (near the threshold A) in a flank of some higher peak, which is of no interest for our purpose, will have a minor effect only on the mean gust shape as it is treated as 1 maximum and 1 minimum thus as O extremes. Another advantage of this approach is that it simplifies the analytical derivation. The expectation value of u around these peaks according (7) is: 47 .E[-u(t+r).ii(t).5(ti(t)).4dt) -A)] z (T) = (21) E[-ti(t).5(ti(t)).e(u(t) -A)] The multi-dimensional distribution function of u(t), i(t) , ii(t) and u(t+ @ will be denoted by P(u,v,W,Z). The shape of a gust above level A can now be expressed as: du.dv.dw.dz.(-z.w. ~(v).e(u -A)).Hu,v,w,z) ~(z) ‘ Mu (22) ddv.dw.dz.(-w.b( v).e(u -A)).Hu,v,wz) LIY.1 The delta function in the integrand can be evaluated by setting v equal to zero. Furthermore the Heaviside function can be eliminated by adapting the limits of integration, so we obtain: jdu ~ dw j d.z P(u,(),WyZ).W.Z (23) ‘~d+wfdz P(WO,W,Z).W . . The above expression gives the mean of all peaks above level A. In order to derive an expression for the mean shape of a peak between level A and level A+dA the denominator and numerator should be differentiated to A. ?dwjdz P(A>O>WX)W.Z (24) ~dwjdz P(A,O>W,Z).W -- -m The probability density fimction P(u,v,w,z) is a 4D normal distribution with zero means and covariance matrix: 48 10 -k r(~) Oao –f(T) A=CJz (25) -A o p Y(T) Lr(~) -t(~) Y(T) 1 In principle the required integrals can now be evaluated. In practice this will be difficult because the inverse of the covariance matrix is needed. For this purpose one may use special tools for formula manipulation like Maple13. After performing these mathematical derivations expression (18) will be obtained without further approximations. In reference 4 another route is followed by introducing conditional probabilities which reduces the dimension of the problem. In an analogous manner expression (19) can be derived for the ‘spatial’ mean gust shape. Appendix 11:Auto- and cross correlation functions based on the isotropic turbulence theory The (normalized) autocorrelation function for the longitudinal turbulence component equals *2: r(r) = 0.59271BKIJ7) (26) with K the modified Bessel function of the 2ndkind, and 7 the dimensionless time: (27) with V the mean wind speed and L the longitudinal length scale. The cross correlation function of the longitudinal velocity component (for a distance D perpendicular to the longitudinal velocity component) equalslz: As 2 p(ll,’c) = y(~) -g(T)] *— +g(t) Ar2 with (28) f(~) = 0.592 ?1nK1n(i) g(7) = 0.592 [71BK1B(7) - 0.574%Yz@] and 49 As = TV Ar = ~- (29) ? . 0.747 Ar L with V the mean wind speed and L the longitudinal length scale. The second derivatives of these functions maybe obtained in an analytical or numerical way. 50 u(t) A e(u(f)) *-?&j&& -$e(u(t)) = a(u(t)) .Zi(r) g(d (u(t)). ti(?)) = ~* a(u(r)) . g(ti(t)) ti_* ti t.1+1 Figure 2. The mathematical operations which select the (positive) zero crossingsfrom a stochastic signal. e(x) = $ g(x) g(x) 3(x) = ~e(x) .+LX +x +-x Rectifier Step function Delta function Figure I. Some basic mathematical operations. \ 1 1 e(ti(t)) m ! I I 1 –f e(ti(t)) = 1 ! I I 1 I 1 I 1 1 - ii(?) . a(ti(t)) II e(u(f) – A) I – ii(r).6 (K(t))-e(u(f) - A) 1,1 I t Figure 3. The mathematical operations which select the extremes above level A from a stochastic signal. 51 o~ -lo -5 0 5 10 time [s] Figure 4. The theoretical mean gust shapes for two di~erent time constants of the sampling filter (T=] s, dotted lines; T=O.1s, dashdotted lines) compared to the theoretical curves (solid lines); for 2 different gust amplitudes: 40 (upper curues) and 20 (lower curves). dimensionless wind speed [-] o A dimensionless wind speed [-] N @ p o 4 cn~ bl h) LICIJ bl$ul p . m A b N ( ul 8 c e. 3 (DC ‘7 .. . m d o 53 , ! I I -0.51 -lo -5 0 5 10 time [s] “’-’ Figure 6. The comparison of the mean gust shapes according to theory (solid lines) and derivedfrom the simulated wind (dotted lines), with amplitude of 2 crfor 2 difierent wind speeds: 10 m/s (upper curves) and 20 mh (lower curves). 54 1.1 I h , 1 - 0.9 - T :0.8 - al ~~ 0.7- .- : ~ 0.6- j$ .= 0.5- *4’ W c .e -g 0.4- .V u .:...-. 0.3- I 0.1I ! , -lo -5 0 5 10 time [s] 2.: t , , . -...... 1 . “... . 8..0 .*. 1.E *“W. - *4 . . .%.” .. “ .. ●. ..~.. “. <. : ●.:. .% ../#s - ..“” . . .. .0 . . . . . .. .‘R . . . -.. . .“ ...... a. .?..,- 0.6 .-...... -.....:... . .%.... 0.4 -...... :... ..“ . 1.. . 0.2 I “ , , 1 -10 -5 0 .5 10 time [s] Figure 7. (a) The comparison of ~he mean spatial gust shape according to theoty (solid line) and derivedfrom the simulated wind (dotted line), with amplitude of 3a (b) The comparison of the mean spatial gust shape according to theo~ (solid line) and derivedfrom the simulated wind (dotted line), with amplitude of 4cz 55 Cabauw 40m -1.5 -1 -0.5 0 0.5 1 1.5 dimensionless time tau [-] Figure 8. The comparison of the mean gust shapes according to theory (lines] and derived from measured wind (symbols), for the amplitudes 3~and 4a - Cabauw 40-80m -1.5 -1 -0.5 0 0.5 1 1.5 dimensionless time tau [-] Figure 9. The comparison of the mean spatial gust shapes according to theory (lines) and derived from measured wind (symbols), for the amplitudes 3c7and 40 57 IEA Annex Xl 2&!lymposiuq WindConditionsfor TurbineDesign NW NationalLabomto~ Roskilde,DK, 12-13April 1999 A CASE FOR INCLUDING ATMOSPHERIC THERMODYNAMIC VARIABLES IN WIND TURBINE FATIGUE LOADING PARAMETER IDENTIFICATION N.D. Kelley National Wind Technology Center National Renewable Energy Laboratory Golden, Colorado U.SJL ABSTRACT This paper makesthe case for establishing efficient predictor variabks for atmosphericthermodynamics that can be used to statistically correlate the fatigue accumulationseen on wind turbines. Recently, two approachesto this issue have been reported. One uses multiple linear-regressionanalysisto estabIishthe relative causalitybetween a number of predictors related to the turbulent inflow and turbine loads. The otherapproach usingmanyof the samepredictors, appliesthe techniqueof principal componentanalysis. An examinationof the ensemble of predictor variables revealed that they were all kinematic in natur% i.e., they were only related to the description of the velocity field. Boundary-layerturbulence dynamics dependsupona descriptionof the thermal field and its interactionwith the velocity distribution. We used a series of measurements taken within a multi-row wind f- to demonstrate the need to include atmospheric thermodynamic variables as well as velocity-related ones in the search for efficient turbulence loading predictors in various turbineoperating environments. Our results show that a combinationof vertical stability and hub-height mean shearing stress variables meet this need over a period of 10 minutes. INTRODUCTION A recent study has recently identified and modeled the dominant inflow turbulence-scaliig parameters responsible for the accumulation of fatigue in wind turbines operating in complex terrain environments. Called MONTURB, this international multi-laboratory effort analyzed measurements of both the inflow turbulence and wind turbine dynamic variables for several turbines in both relatively smooth and complex terrain sites in Greece, Denmarlq Spa~ and the United States (CaWornia) [1,2,3]. Using sensitivity 58 analysis, analysts concluded that the fatigue loads increased significantly with the standard deviation of the longitudinal wind speed (au), which was also considered as the primary fatigue driver. One part of the MONTURB study [4], which was incorporated in [2], applied multivariate regression to analyze the statistical response of turbine fatigue loads to a wide range of turbulence descriptors (including higher order statistical moments). These analyses were based on data from a substantial array of turbulence and load measurements taken for a single turbine installed at the crest of a hill in Greece. A similar study conducted in Spain used principal component analysis to examine the effect of several turbulence descriptor variables on fatigue-load factors [5]. The turbulence descriptors used as explanatory or predictor variables in [2, 4] included the following ● Mean wind speed (U) ● Power law wind-shear exponent (a) ● Inclination angle between the wind vector and the horizontal (v) ● Standard deviations of the longitudinal, lateral, and vertical wind components (OMa,, and a~) ● Longitudina~ latera~ and vertical turbulence length scales (L&L., and h) ● Skewness of U [aq(U)] ● Kurtosis of U [c@)] ● Davenport decay factor between two elevations (AA and A=) ● Ratios a&ru and o~cru. The cross-correlation of the longitudinal and vertical wind components (p~) and the U, OWcrs(U),04(U), da~ and crdau parameters was used by [5]. In both studies, the response variable chosen was the equivalent load parameter defined by —1 niL~ m Equivalent Load = L~ = z ~ [) eq where ~ is the number of cycles in the i* load range, Li is the maximum (conservative) value of each load level in a b~ Nw is the equivalent number of constant-amplitude cycles, and m is the slope of the material S-N curve. For these studies, record lengths of 10 minutes were used and a l-Hz equivalent load calculate~ which set N~ to 1200 half-cycles for that period. The effect of various materials was evaluated by applying S-N curve slopes in the range of 4 to 12. Using this defirdtiou L~ repeated Nq times is equivalent to the same fatiguedamagecontainedin the measuredload spectrum [2]. 59 A review of the abovementioned turbulence descriptors used as predictor variables results in the realization that they are all kinernatiq i.e., they are all related to the description of the inflow veloci~ field. In 1994, we reportedon the reds of a similar experiment involving the 10-minuteload response of tsvo side-by-sidewind turbines deep within a multi-row wind farm in San Gorgonio Pass, California [6]. We also applied multivariate regression and the analysis of variance (ANOVA) to assess the sensitivi~ of a range of turbulencedescriptorson the measured loading spectra. Our predictorvariable list although including many of the variables listed above, also contained the following kinematic variables and their highermomentsmeasuredat hub height: ● Mean horizontal windspee~ definedby U~ = ~ ● Standarddeviationof U~(cr~ ● Turbulence intensity(~flH) ● Mean longitudiml, lateral, and vertical wind components aligned with the mean shear vector (U, V, and W) ● Reynolds stress components(u’w’,u’v’,and v%’) where u’, V, and w’ are the zero-meau fluctuating componentsof U, V, and W ● Local frictionvelocity,definedby U*= – Inu’w’ ● Cross-correlationcoefficientsof u’w’,u’v’,and V’W’(p.w, P.V, W) ● Standard deviations of the instantaneous Reynolds stresses (G.w, CJ.V, G,W) ● Skewnesscoefficients of instantaneousvalues of u’w’,u’v’,and V’W’[css(u’w’),OS(U’V’),cr~(v’w’)] ● Kurtosiscoefficientsof instantaneousvalues of u’w’,u’v’,and V’W’[G4(u’w’),04u’v’),cn(vtw’)]. In addition to the kinematic variables and their derivations listed above, we also included the following parameters that are related to the thermodynamics of the planetaryboundary Iayer: . turbinelayer gradient Richardson number @i) stability parameter defined by Ri = (@m)[(amzy(mzr] where g is the gravity acceleratio~ z is the height in meters, & is the layer mean thermodynamic potential temperature (K) given by fiz) = T(z)[1000/p(z)]02M, and T(z) and p(z) are the temperature (K) and barometric pressure (hPa), respectively at height z. The turbine layer is defined as the 60 vertical distance between the sufiace and the maximum elevation of the wind turbine rotor. The over bars represent 10-minute averages. . Hub potential temperature (Qti) ● Cross-correlation coefficient of w’chub’(pti13’) . w’d’ covariance or vertical temperature flux (w’~hti’) . Standard deviatio~ skewness, and kurtosis of w’f?h~’. The response variable we used for most load parameters, except edgewise bending, was the slope ~) of the high-loading tail or low-cycle, high-amplitude portion of the loading spectral distribution. This tail region is a major contributor to the fatigue damage seen in materials with large S-N slopes. The loading spectral tails are fitted with an exponential distribution N=- #Oe-@l,-, , where M is the p~k-to-peak or alternating load range and N is the number of cycles. We also found that the slope A was most sensitive to the atmospheric stability expressed by the turbine layer Ri and the u’w’-component of the Reynolds stress or its square root u.. We observed that the slope varied indwectly with u. and KU e.g., higher values of u. and/or Ri produced a shallower slope and higher potential fatigue damage and vice versa. These results indicated that, at the minimum, both a kinematic and a thermodynamic turbulence-related descriptor are necewuy for a linear, multivariate regression model that can explain a high percentage of the observed variance. Finally, we found that more than 89% of the observed variance of the combined turbine flapwise loads could thus be explained. A CASE STUDY WITHIN A LARGE, MULTI-ROW WIND FARM In 1990, the National Renewable Energy Laboratory (NREL) operated two adjacent Micon 65/13 wind turbines deep within a very large wind farm in San Gorgonio Pass, Caltiomia. Both of the turbines were identical except that one used a rotor based on the NREL 7.9m Thin Airfoil Family; the other was an original AeroStar design. We will refer to the turbine using the NREL blades as Rotor 1 and the AeroStar-equipped turbine as Rotor 2. A total of 397 10-minute records were taken over a wide range of inflow conditions during late July and August, the latter half of the San Gorgonio wind season. Inflow measurements for the turbines were taken using a near-hub-height (21-m), three-axis sonic anemometer/thermometer and propeller-vane anemometers installed at three elevations. Temperature, 61 vertical temperature dfierence, and the barometric pressure were also recorded. The maximum height of the rotors was 31 meters above ground and the turbine hubs were located at 23 meters. The two test turbines were located downwin& with respect to the prevailing wind directio~ about mid-row in Row 37 of a 41-row wind farm that included nearly 1000 machines. The nearest rows of turbines were located approximately seven rotor diameters up and downwind. Although the terrain surrounding the farm was complex (there is a 3700-m mountain peak immediately to the south), locally it is relatively flat desert with a slight upgrade towards the prevailing wind direction. The dominant flow comes through the throat of the mountain pass to the west. However, once or twice during the nigh~ much of the wind f- (including Row 37) is influenced by COOLunstable gravity or drainage flows. These flows, which originate in the hi~ cold elevations of the mountains to the south spill out onto the desert floor after being fumeled down through steep canyons. Intense turbulent bursts are often observed with these drainage winds when they merge and interact with the flow being channeled through the pass to the west. A result of this merger is higher than normal maintenance on the wind turbines that operate in the region of their confluence. Stability Sensitivities We calculated the l-Hz equivalent loads (l&) from each of the bladewoot flapwise rainflow load spectra for each of the three blades of each turbine for S-N slopes of 4,6,8, 10, and 12. We then summarized the L~ loads born the three blades and determined the peaks and averages for each turbine. Ne@ we plotted the thre~blade peak and average l-Hz Lq Ioads for each rotor and S-N slope parameter m as a fimction of the turbine-layer gradient Richardson number stability parameter, Ri (see Figure 1). The Richardson number parameter indicates the ratio between turbulence production due to buoyancy and turbulence production caused by wind shear. Negative values represent unstable flow conditions, zero neutral, and positive stable. Unstable flows are characterized by large eddies with a positively buoyant circulation and turbulence energy peaks occurring at large wavelengths. The turbulence in truly neutral flows is generated solely by the action of wind shear and is usually associated with strong winds. Flows with just slightly positive Ri values are often referred to as weakly stable. Under such conditions, the influence of negative buoyancy can produce intense, transient shears at moderate to high wind speeds that are often characterized by bursts of temporally and spatially coherent turbulence whose peak energy is at small wavelengths. As Ri approaches the critical value of 0.25, increased buoyant damping decreases the turbulence levels, eventually reaching more or less Iaminar conditions at 0.25 and above. 62 The graphs of Figure 1 clearly distinguish a structural change in the load characteristics as the stability transitions from unstable to stable. The largest loads for all values of the S-N slope parameter occur in the weakly stable region. Furthermore, as the value of the S-N slope parameter increases, the fatigue damage also increases in this stability region. A distinct cluster of high-level peak Lw loads develops for values of m=l Oand m=12 in the Ri range of approximately -0.01 to +0.10. This suggests that under such conditions, rotor blades made of materials such as glass fiber and exhibiting high values of S-N slopes will sustain greater fatigue damage. This increased damage can be fiu-ther substantiated by noting that the cluster of peak Lq loads for m=l O and m=12 in Figure 1 occur at values exceeding 20 kNm. We determined that there are 16 10-minute records contained within this cluster, whose associated mean wind speed ranged from 12.25 to 15.09 m/s. Excluding the elements of this cluster, we searched the remaining database for records whose mean wind speeds fell within this range. We found that there were 49 records of the remaining381 available that met this criteria. We then summarized the individual load spectra associated with the records of the peak cluster and 49 other records from both turbine rotors into two composite spectra. Best-fit curves were regressed through each of these spectra and the results plotted as a fimction of cycles per hour (see Figure 2). These curves indicate why the Lw peaks with high values of the S-N slope parameter occurred. The inflow conditions associated with these 16 records contained elements that produced a greater number of high-amplitude cycles than were characteristic of the other 49 records measured within the same wind speed range. Because Figure 1 indicates a strong dependency on the Richardson number, we plotted the distributions of th~ parameter for each of the above cases in Figure 3. This figure shows that the Lq distribution associated with the high-damage cluster tends to be narrow and uni-modal. It is centered between 21 and 22 h with the bulk of the occurrences in the range of 20 to 22 h. The L~ distribution of the 49 records with lower peaks is much broader and hi-modal and is centered between 22 and 23 h with peaks at21 and 01 h. Therefore, the higher fatigue damage for materials with high S-N slopes occurred earlier in the transition from the daytime to the nocturnal boundary layer structure. Such damage is thereforestrongly diurnally related. Sensitivity to Hub-Heiqht Friction Velocity, u. The other parameter that we identified in our earlier work [6] as an efllcient predictor of low-cycle turbine load behavior was the hub-height fiction velocity, or u.. Figure 4 presents the variation of the three-blade averaged L~ loads for m=12 for each rotor and the corresponding hub-height u. values as a function of the turbine-layer Richardson number. Aga~ there is an abrupt change in both the Lq loads 63 on the rotors and u. as the stability transitions ftom unstable to stable. The high u. and LWload regime continues until an Ri value of approximately +0.10 is reache~ whereas much lower values are evident in the Ri down to -0.10. Thus, for the operating environment in this particular site, the number of operating hours within a critical Ri range of Oto +0.10 will see increased fatigue damage, particularly for blades made of high S-N expbnent material. This is consistent with the findings of a study by Sutherland and Kelley [7], who compared the measured load spectrum from Rotor 1 with the WISPER spectrum [8]. They found that the San Gorgonio load spectrum contains many more cycles than the WISPER spec~ and that the increased number of cycles results in more damage. The higher loads and damage at San Gorgonio are attributed to a combination of boundary-layer flows interacting with the complex terrain and upstream turbine wakes. Distributions of Richardson number and u* at Other Locations at this Site In 1989 we made extensive turbulence measurements from two 50-meter towers located upwind of Row 1 and downwind of the last turbines of Row 41 using similar but more sensitive instrumentation. The total records from each location are much more extensive than those that were available from Row 37 in 1990. The majority of the measurements were made earlier in the wind seaso~ covering a six-week period approximately from early June to mid July that was characterized by periods of strong winds. There were no turbines upwind of Row 1 and the closest operating row to Row 41 was approximately 14 rotor diameters (D) upstream. In Figures 5a and 5b we compared the distributions of the gradient Richardson number and the hub-height u. for the upstreanL downstream and Row 37 locations. respectively in Figures 5a and 5b. Figure 5a shows the predominance of operation in the weakly stable region for both the upwind (Row 1) and downwind locations. There is a smau secondary peak at the downwind station and 14-D spacing that coincides with the primary peak at Row 37. In genera~ the Ri distribution at Row 37 peaks at a slightly more stable value and is much broader than the distributions at the other two locations in the stable region. In comparison with the other hvo layers, the shallower depth of the Ri measurement layer at Row 37 may have more influence than the other two. The impact of the presence of upstream turbine wakes is clearly visible in the u. d~tributions. The median value for the upwind location is 0.771 mk, 1.106 m/s downwind of Row 41, and 1.161 rnk for Row 37, with the tail reaching values in excess of 1.800 m/s. Thus, from the Ri and u. dkributions shown in Figures 5a and 5b, one would expect the highest fatigue damage at Row 37 and the least from the turbines installed in Row 1. This scenario is essentially what the wind farm operator has observed. 64 DIURNAL VARIATION AS AN iMPORTANT PARAMETER One of most sensitive factors affecting thermodynamic-related turbulence descriptors is the time-of-day (or diurnal) variation (see Figure 3). The daily heating and cooling cycle of the earth’s boundary layer is a major source of variation. This is true in most locations except of course, in arctic regions during periods with little or no sunlight reaching the usually snow covered stuface. Even here thermodynamics may still be important because very strong inversions often exist with much warmer air aloft that is occasionally brought to the surface through some form of intrusion process. The diurnal heating and cooling of complex terrain features is known to alter the flow characteristics around such obstacles. In Figure 6 we plotted the diurnal variation of the thre~blade average 1-Hz Lw loads using m=12 for each of the two rotors in the San Gorgonio wind farm. The shaded region between 20 and 22 h corresponds to the period where the majority of the peak loads were observ@ as discussed earlier. The distribution of Lq loads is strongly diurnal and follows the hourly variation in mean wind speed. This profile is largely controlled by the large-scale dynamics of the regio~ which are modulated by the complex terrain fmtures (i.e., the mountains and the pass). The strongest winds tend to occur two or three hours after local sunset when the boundary layer is in the process of transitioning from the day to night boundary layer structure. Between 10 and 15 h the wind generally drops below power generation levels as (see Figure 6). The diurnal relationship between the thermal field and the hub-height mean shearing stress or u. is shown in Figure 7. We plotted the variation of u. (dotted circles) and the covariance of the fluctuating vertical velocity component and potential temperature, which is the vertical temperature flux (filled triangles). A positive temperature flux indicates that heat is being transported away from the surface. The period of sunrise is clearly visible between 06 and 08 h with a strong, positive temperature flux readily evident. Local sunset is between about 19 and 20 h on this diagram. At approximately 19 h the vertical temperature flux reaches a maximum for the day, at the same time the sun is setting. This indicates the presence of a strong positive, vertical velocity field transporting a net heat flow into the boundary layer. Immediately after this peak the u. increases rapidly as the temperature flux falls at more or less the same rate. It is during this approximately one-hour period that turbulence production changes from one dominated by buoyant plumes to shear production. Very intense, transient coherent turbulent structures exist in regions of strong vertical velocity fields and rapidly changing shears. The processes described here are tier documented by the diurnal variation of the Richardson number and u. plotted in Figure 8. Agai~ the transitions at sunrise and sunset are well characterized by the Ri 65 and u. variations. The strong vertical temperature (heat) flux after sunrise quickly destabilizes the boundary layer through positive buoyancy while the shear (u.) contribution falls, resulting in large negative Ri values. At sunset the inverse occurs with an increasingly stabilizing boundary layer and an increase in the shear which causes the value of Ri to become slightly positive. After about 21 ~ the shear becomes the dominant turbulence source damped by a small amount of negative buoyancy, as indicated by the small positive values of Ri. Early in the morning after about 02 h the Ri begins to rise and the turbulence becomes fbrther damped as the wind speed and shearing stress decrease before reaching a minimum just before sunrise. The diurnal variation of the 1-Hz L~ loads shown in Figure 6 closely mirrors the variation of RI and u. of Figure 8; i.e., a combination of negative RI and low u. values leads to low Lw Conversely, during the day-night transition when u. is high and the Ri weakly positive, the Lq are high and damaging. The variations in the velocity and thermodynamic fields of Figure 7 show why it is necessary to consider both when assessing the efficiency of turbulent load predictor variables. The processes d~cussed above are quantified by the turbulent kinetic-energybudget equation given by Panofs@ andDutton [9]: I II m I n III In this equatio~ the pressure correction term and the effects of moisture were ignored. E is the total kinetic energy given by E = (1/2) (u’*+ V’2+ w’*)ands is the dissipation rate of turbulent kinetic energy. The fwst term ~ of the terms on the right is the shear production term and is always positive. The second term (II) is the buoyancy production term and may be positive or negative depending on the sign of the vertical temperature flux -. The values of ~ shown in Figure 7 never go negative because of the high surface temperatures in July and August. The third term (III) defines the rate at which turbulence is transported into or out of the local volume by velocity fluctuations. This equation couples the importance of the velocity and thermodynamic fields and the related scaling quantities. In a wind f- environment the third term on the right maybe very important due to the transport of upwind turbine wakes. CONCLUSIONS In th~ paper we have underscoredthe need to include atmosphericthermodynamicvariables, such as a measureof verticalstability,when identifyingefilcient predictorsfor evaluatingturbulence-inducedwind 66 turbine loads. We also have demonstrated that the diurnal variation of these predictors needs to be established for particular site environments or classes of environments. In the United States these classes could include, for example, characteristic Great Plains, mountain passes, elevated ridges, and seashore sites. All exhibit varying degrees of terrain complexity and the large-scale dynamics defining the local wind regime can be quite different from location to location. It is also quite important that the turbulence simulations used in numerical simulations of wind turbine dynamics reproduce the characteristics as discussed here in order to fully appreciate the structural and fatigue impacts of such environments. ACKNOWLEDGEMENTS This work has been supported by the U.S. Department of Energy, Contract No. DE-AC36-83CH1OO93. REFERENCES 1. Mousakis, F., Morfiadaki& E., and Fragoulis, A. (eds.), November 1996, “MONTURB (JOU2-CT93-0378) Final Report – Volume ~“ Centre for Renewable Energy Sources, Pikermi, Greece, 182p. 2. Mousakis, F., Morfiadakis, E., and Fragoulis, A. (eds.), November 1996, “MONTURB (JOU2-CT93-0378) Final Report – Volume IL” Cmtre for Renewable Energ Sources, Pikermi, Greece, 245p. 3. Mousakis, F., Mofiadaki& E., and Fragoulis, A. (eds.), November 1996, “MONTURB (JOU2-CT93-0378) Final Report – Volume III,” Centre for Renewable Energy Sources, Pikermi, Greece, 42p. 4. Mousakis, F., Morfiadaki$ E., and Dellaportas, P., 1996, “Parameter Identification of Fatigue Loading of a Wind Turbine Operating in Complex Terra@” CRES.WE.MNTRB. 14, Centre for Renewable Energy Sources, Pikermi Greece. 5. Cuerva-Tejero, & L6pez-Die~ S-, and Bercebal-Weber, D., 1999, ” Higher Level Descriptions of Sites and Wind Turbines by Means of Principal Component Analysis,” l%c. -EWECS1999, Nice, France. 6. Kelley, N.D., 1994, “The Identification of Inflow Fluid Dynamics Parameters That Can Be Used To Scale Fatigue Loading Spectra of Wind Turbine Spectral Components,” NIUXITP-442-6008, National Renewable Energy Laboratory, Golden, CO. 7. Sutherlan& H.J. and Kelley, N.D., 1995, “Fatigue Damage Estimate Comparisons for Northern Europe and U.S. Wind Farm Loading Environments,” Proc. WindPower ’95, American Wind Energy Associatio~ Washington DC. 8. Ten Have, A.A., 1992, “WISPER and WISPERX: Final Definition of Two Standardized Fatigue Loading Sequences for Wind Turbine Blades,” NLR-TP-91476U, National Aerospace Laboratory NL~ Amsterdam, The Netherlands. 9. Panofiky, H.A. and Dutton, J.A., 1984, Atmospheric Turbulence, Wiley-Interscience, New York NY, p. 92. .. Three-Blade Avemge l-Hz Lq Thm!e-Blade Peak l-Hz L= ● Rc&rl t 0 -2 ~~1 I 1 22] nl=i $ Im=f$ 1 \——— w t 18 16 16 ,. 14 n 12 la 16 14 .88: ) . ’28 .0 tI [ 5,~ I :P,! 2! 24 24. i # 22M=8 2 1 1 I x. 24 I z. 72. m=lo w. ‘a. IS 18. 16 16 . M M 12 !2 to !0 . f 8 ‘4o 6 ! ‘ t I 2 *J % =. ns2 w- 18. M . 14 . 12 m . I a .0 1 6 .~ Fwure 1. Variation of three-blade peak and average l-Hz L- loads with the Richardson number stabtity parameter 68 40 35 5 0 1 [ I t 1 10 100 1000 10000 Cycles/h Figure 2. Comparison of peak load cases xl _ Peak Lqs 20 kNm 30 ~ Peak L- >20 kNm A 25 :,. [-’i 1 ,> 15 ,,.. .. ,.,,, 10 ..<... ~-It ..;. ,.. 5 .. ..>. y I t , i 9 B m o , i t 1 , 1 1516171819202122 2324123456 7 Local time (h) Fgure 3. Time distributions of peak loading groups 69 -1.C1 — 1.4 1.2 1.0 — I . . I n w Ii?!-1 Turbinelayer gradient Richardson number (1%) F~ure 4. Variation of hub u. and average 1-Hz Lq with stability 70 50 40 !111 30 LL n CL 20 i Ill:\: 10 0 -0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10 Gradient Richardson number (Ri) 2.5 2.0 -7 G 1.5 ~ IL n m 1.0 0.5 0.0 , , , , , , t # 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 F~ure 5. Probabtii distirbutions of (a) gradient Richardson numbe~ and (b) hubheight u. or fiction velocity 71 Local time (h) Figure 6. Diurnal variation of l-Hz Lq for Rotors 1 and 2 -n,y..:-->. 10 2.(),::::: ::::-.,.-.~ ‘~: -..,4-’+3.., ... :.,~ I 1 u i I I I I 1 0.0 ! 1 I t 1 I 8 20 22 24 O 2 4 6 8 ‘0 ‘2 ‘4 ‘6 ‘8 LOG!II time (h) F~ure 7. Diurnal variation of hub U*and vertid temperature flu% ~ 72 2.0 0.3 I 1.8 . 0.2 1.6 / -- Ri=O, neutral 1.4 0.1 _ 1.2 0.0 ‘cl) g 1.0 3“ -0.1 0.8 0.6 -0.2 0.4 -0.3 : .,..:‘,:.,:. : 0.2 :,:,. ,. . . ;..-..:.,...-. :..:.’..’:...... -1 0.0 1 I 1 I I I 1 I 1 1 -0.4 O 2 4 6 8 10 12 14 16 18 20 22 24 Local time(h) F~ure 8. Diurnal variation of Richardson number and EUROPEAFJ Wm ENERGY CONFERENCEANdkJBI’IION.NICEFRANCElWCH 1-5,1999 DESIGN OFF-SHORE WIND CLIMATE GunnerC. LarsenandHansE.&gensen Whd Energy and Atmospheric Physics Department Ris@National Laboratory DK-4000 Roskilde, DENMARK phomx +4546775056 [email protected] *1.. ABSTRAff. Specific recommendations on off-shore turbulence intensities, applicable for design purposes, ase lacking in the present IEC-code. The present off-shore wind climate analysis preserm tie diirnbution of the turbulence standard deviation around the mean turbulence standard deviation. conditioned on the mean wind speed. iMemureddiirriiutions, based on a huge amount of measuring data from two ddow water off-shore sires, are pamrnererized by fitting to a three parameter Weibull distribution. Combining a simple heuristic load model witff the parsmeterized probabilitydenshy functions of the turbulence srandasd deviations, rutempirical off-shore de.si~wturbulence imensiry is evaluated that in average yields the same fatigue damage as the distributed turbulence intensiw. The proposed off-shore design turbulence intensity is, within the tEC code framework, applicable for extreme as well as for fatigue load determination. KEYWORDS: Fatigue, Off-shore, Turbulence L INTRODLJCTION Due to the strongly non-linear relationship between wind loading and the farigue life time consumption in a wind An increasing part of wind turbines will be erected at off- turbine suucture, the design turbulence intensity can not be shore sites in the future due to environmental requirements taken as the mean of estimated probatiliv densities. Instead and the limited number of on-shore sites with favorable the mean fatigue life time consumption is estimated by wind potential. The wind load conditions are the primary combining the probaliliry density d~tributions of the external load concern for the srructumf integrity of a wind turbulence intensities with a (simple heuristic) general load turbine. Consequently, the off-shore design wind climate mcdel. The particular turbulence intensity resulting in the becomes of increasing importance. , mean fati=meIife time consumption, as determined from the conditioned probability distioutions, is defined as the According to the IEC-61400 design code proposal, the on- designturbulenceinfensip. shore desi=wwind cfimate may be classified into a limited number of wind categories reflecting differences .m wind potentials as weU as in varitilii~ of the turbulence 2. METHOD components. The ofl-skore design wind climate, however, is to be specified entirely based on information provided by At a given site and in a given height above tie .gound (or the manufacturer. One of the issue& that is of particular water surface), che standard deviation, mu, of the arbkrary importrmce in that re.spec~ is the turbulence intensity as wind speed, condkioned on the mean wind speed, will function of the mean wind speed. follow some probabii~ dstioution in the long term. This reflecrs a naturaf varialiliry over time owing to, e.g., At off-shore site&,the roughness length wiUdepend on the varying atmospheric stabii~ condkions, vasying wind mean wind speed, which in rum means that the description directions (and thusvarying roughness conditions) etc.. It is of the turbulence intensity, as function of mean wirtd speed, appropriate to consider the staI?darddeviation, &..T, of the becomes qualitatively different from the on-shore load arbitray wind speed in the short term - i.e. over some situation. However, where on-shore sites display large Iimited time span T. The mean wind $peed associated with differences in terrain topology, the off-shore sites ase fas this the time span T is denoted UT. more homogeneous as the majoriY of off-shore sites are Iiiely to be associated with shallow water areas. Thii in The variabilityof the turbulencestandard deviation, 17u.T, is turn opens for a simple and relative general description of approached empirically in the present analysis. Based on a the variabti~ of an off-shore design turbulence intensi!y as huge da~ ma[eri~, a sui~le &mn@ma~~ ~ tie me~ function of the mean wind speed. The present paper wind speed and in the standard deviation can provide an presents such a model. estimate of the probability density function (PD~ of the standard deviation, ~..T , condkioncd on the mean wind Based on a huge amount of 10-minute shallow water off- speed as expressed by shore wind statistics, originating from the Vindeby and the Gedser experiment, the variability of the startdard deviation of the horizontal wind speed is quantified in terms of a set of probaliliitic mudels conditioned on the mean wind speed. where P denotes probability. 74 The binning procedure results in PDF-estimates repr=ented as histo=ms. Provided that the number of bins in the (4) standard deviation is large, the resolution of the estimated PDFs are good. The se!ection of bin interval sizes is a compromise between sufficient resolution and a reasonable number of data within each bin - in the ores.entanalysis the mean wind speed has been binned u&g a bm ;nterval whereby the design standard deviation is expressed only in equal to 2 rnk. As for the binning “mthe standard deviation, terms of the conditional distributions of the standard a total OF 20 bin intemrds have been selected which is deviation of the horizontal turbulence component as somewhat more than the number of bin intervals proposed in (Conradsen, 1976). Having established estimates of the conditional probability densi~ functions of the turbulence standard deviation, U..T, ‘m terms of histograms, the results are pu-ar-neterizedby fitting a three parameter Weibuil PDF to these In case the fati=qe loading, in addirion co fie turbulence experimentally based estimates. The three parameter contribution, originates from a petiodic deterministic load Weibull PDF, which is known to be a very “flexible” component, it can be shown dl~t the de-sign standud distribution type, is expressed as deviation defined according to equ~tion (s) WN be consemative. Due to the non.fine~ weighring of the standard deviation perfomrerl in equation (5), the design standard deviations do not correspond to 5t)% quantiles (or mean values) in the associated empirical distributions conditioned on the me.zn wind speed. The qu~tile level %T’~xp[-(YY]-‘2) will depend on the value of the WOirIerexponent. where k is a shape parameter, a a position pmeter and fl 3. RESULTS a scaling parameter (k and ~ are required positive). Subsequent numerical testing has shown that it is suitable The ,analysis is based on a huge mount Of wind speed for repr=entation of the body of the distribution, however, sCNkkS originating from measuring C~p@ns conducted it has a tendency of underestimating the upper tail. at 2 different shallow water off-shore sites in Denmark - Gedserturd Vincleby.All the avtiiable statistics on the data The basic presumption, in the succeeding determination of mxteriai have been tmns formed to [()-minute statistics. a desi=w turbulence intensity} is that the fatigue load spectrum, in a fmt order approximmion, is proportional to .4[ the Vindeby site the investigated wind data originate the standard deviation of the horizontal w’krdfluctuations. from &meteoroiogica.1mmt erected wv close to the coast The physics behind the assumption is the following for a line. The data me recorded at level 37.5m and, depending given mean wind speed (expansion Pokt) the dynamic on the wind direction, a sea fetch, a l~d fetch and a mixed wind loadiig of a turbine can be approximated by a fetch are represented at this site. ~ the present investigation “gradlen t“ multiplied by the (horizontal) turbulence oniy the pure sea fetch is considered. The sea fetch is fluctuations. It is here further assumed that this “gradient” characterised by having more th~ Ij ~ of sea upstream is independent of the size of the fluctuations. (Bwthelmie, 1994). The data within the sea fetch, are selected in order to avoid mast- ~d b~m effects. !Mth the For a given mean wind speed, UT, the mean fatigue defined selection criteria the avtilable data material loading, IA(UT), of the is then syrnbohcdy determined constitutes 5566 10-minute time series wirh an overall from the expression mean wind speed equal to 7.92m/s. The meteorological mast at tie Cie&er site is also erected close to the coast liie providing tie possi~lfi~ of artalysing both l~d- and sea fetches. The present kv~rigation relates to (sea fetch) wind observations recorded at level 30.Om. Based on the available 21622 lo-minute rime series, the where C is a characteristic constant for the particular load overall mean wind speed, associated with the sea fetch, is on the pmticuhr wind turbine, and m is’ the }Vohler estimated to 7.87m/s. exponent for the panicular material. In the above formulation it is implicitly assumed that the fatigue loading 3. [ Vindeby is caused exclusively by the stochastic part of the wind The Vinrkby data material Covem l@minute mtim wind tleld. speeds ranging from 2rn/s to approximately 20m/s, The distribution of the wind speed st~d~d deviation is Detirring the design srandd deviation as [he standard cvahltited for ench mean wind speed bin ,m described in deviation, o-J._ @T) , giving rise to the above mean fatigue scctiun ~. AS & example the result, ;~sock}ted with [he loading we find mean wind speed bin ~.mging from Sm/s to 1em/s, is illustr.~tcd in Ftgurc 1. The do[[cd [inc in [he tigurc 75 represents the three pasameter Weibull fit, whereas the full estimated desi.~ standard deviation with the mm w~d line is the estimo.ted distribution determineddirectly from speed as illustrated in Figure 3. the measurements. Note, that the abscissa values relate to the shifted standard deviation m determined by the Weibull parametrization. I Vindeby (ad-shore) pdf 2.5, 2 I 3 ~=1.s a: ,, I .z 0.5. \ y .O.cuztr .O.MC9X, O,,?g 0. I 0 s 10 15 20 Mom WhdSp, ed[m/,J L_ ~ stdv [m/s] Figure 3: Polynomia[ least square>t of (m=12) design 0.5 1 1.5 standard deviation asfunction of [he mean windspeed. FigureY1: Measured and Jilted PDF’s representingthe 3.2 Getlser meun wind speed bin 8nr/s-IOrrA. The data material covers 10-minu[e mean wind speeds The design turbulence intensity, as defined in section 2, is ranging from 2rrr/s[0 approximately22rn/s. In analoe~-wirh subsequently determined by numerical integration of [he investigation of the Vindeby da~ the conditioned equation (5) applying the titted PDFs. Two different PDFs of the 10-minute standard deviation ase established VKMlerexponents -4 corresponding to loading on a steel for all mean wind speed bm irrtermls. The resuk for the component, and 12 corresponding to the loading of a GRP mean wind speed bin ranging from 8rn/s to 10rn/s is compunent - were applied. As expected, the design i[Iuscrated in F~gure 4. [urbulcncc intensity increases with increwing Wtihier exponent. However, the increase is moderate as shown in Pdf Fjgure 2. 2.5 ~~ t Vlndeby (Off-ShOr.3) 2 1 I 1.5 1 I \ 1 \ \ \ 0.5 A * z Scdv (m/s] 0.5 1 1.5 0 5 10 1s 20 M.sn Wlnd$p*.d[mls] Figure 4: Measured and fitted PDF’s represeruing[he I meanwindspeed bin &nls-IOrnk. Fib~re 2: Design turbulence intensitiesas computed Proceeding along the lines described in section 3.1, the based on m=4 andm=12, respectively. result presented in FI=Wre5 for the desi=gnturbtdence standard deviation, as based on Gedser data, is obtained. From a desi=~ point of view it is not practical to deal with design turbulence intensities that depend on the material properties. The off-shore design turbulence proposal will Gedsar (elf.*ore) therefore (conservatively) be based only on the past of the I I analysis related to the largest Wohler exponent (m=12). & a consequence the Vindeby analysis fimrdlyresults in the following empirical relationship between design turbulence intensi~ and the mean wind speed 0.1790 y .0.W$2XX+0.0199x-0.4226 TIV = 0.0031L/lo+ 0.0409+— (6) 0 II u 10 0 s 10 15 29 M.IJI Wad Sp..d [mI,] I where index V indicates [hat the result is breed on Vintleby dat~, lJl{)denotes a mean winclspeed bwed on a 10-minute ~lveraging pefiod. The result is obtained by applying a swoncl order polynomial tit to the dependence of {he -. lb The derived design turbulence intensity is thus expressed as Note, however, that [he present investigation only includes mean wind speed values up to approximately 22rn/s, and that the above specification of deign turbulence intensity 0.4326 (7) consequently should be used with care in wind regimes TIG = 0.0032 U,. +-0.0189 +—., “10 outside this range. However, compared to the conventiomd practice where off-shore conditions, according to the JEC where index G refers to Gedser data. 61400 standard must be considered as a “.S” class type situation (where the required parameters must be entirely 3.3 Synthesis supplied (and documented) by the designer), the present The results obtained from the two independent analyses ase proposal gives considerable guidance. in good agreement, as shown in F@re 6. 4. CONCLUS1ON m.12 Specific recommendations on off-shore design turbulence 25 intensities are lacking in the present IEC-code. A simple expression for a desi=n turbulence intensity, applicable for 2 shallow water off-shore siting of wind rurbkres, has been ● Vhdebf proposed. The proposal is based on extensive analyses of a huge da~ materi~ ori=fiaring from two D~ish off-shore nmGedsw sites situated in shallow water regions. 0.s o The analysis embraces quantification of the distribution of 0 s 10 Is 20 2s the horizontal turbulence standard deviation conditioned on Man WLad Sp..d fro/s] the mean wind speed and subsequent application of a simple heuristic load model. Figure 6: Design standard deviations based on Vindeby- and GeLrer data, respectively The application of the proposal will, until further analyses of other categories of water regions are available, be limited to shallow water regions. However, at present most off- The close agreement is interpreted as a com%rnation ot’the shore turbines are erected at such sites. conjecture that off-shore sites generally are relatively homogeneous. As a consequence, based on the available data material, it makes perfectly sense to determine a 5. ACKNOWLEDGEMENT “general” expression for the design turbulence intensity applicable for shallow water off-shore site conditions. The present work is partially tinancetl by the Commission of the European Union under the DG XII Non-Nuclear The resulting proposal for an off-shore design turbulence Energy Pro=gasnme,contract JOR3-CT95-0026, which is intensi~, TID, is based on a weighted mean of the results gratefully acknowledged. obtained from the NO investigated sites. The weighting factor is selected as the relative number of the total number of available data series associated with each site 6. REFERENCES (5566/27 188 for the Vindeby experiment and 21622/27 188 for the Gedser experiment). The final [1] Larsen, G.C. and Jorgensen, H.E. (1999). Variability of expression for the design turbulence intensity is Wind Speeds. Ris@-R-1078(EN). 0.3807 [2] Draft lEC 61400-1, Ed. 2 (1998). Wind Turbine “ TI* = 0.0032 U,. + 0.0234+ — (8) generator Systems - Past 1: Safety equirements. u 10 International ElectrotechnicaI Commission (unpublished). The above expression applies to extreme load design as wefl [3] Barthetile, R.J. eL al. (1594). The Vindeby Project A as to fari=~e desi=~ provided that the .wideliies in fEC Description. Ris@R-741, Risg National Laboratory, 64100 are adopted. Denmark. . [4] Conradsen, K. (1976). h Introduction to Stariirics (in Danish). IMSOR, DTU. 77 FATIGUE LIFE CONSUMPTION IN WAKE OPERATION Gunner Chr. Larsen*, Ingemar Cad6n**, and GeTard Schemers*** *Address: Wind Energy and Atmos. Phys. Dept., Risfl Nat’1 Lab., DK-~000 Roskilde, DenmaTk **Address: Teknikgruppen AB, P. O. BOX 211 S-191 21 Sollentuna, Sweden ***AddTess: Nethedands EneTgy Research Foundation EC’N, NL–1 755 ZG Petten, the Netherlands ABSTRACT When operating under wake conditions, an increase in fatigue life consumption on wind turbines has been observed. The changes in the load patterns originate both from modifications in the mean wind field and from modifications in the turbulence field. By performing a parameter study, the significant wind field parameters, in relation to the increased wind turbine fatigue life consumption in wakes, are identified. The analysis is based on a large number of aeroelastic simulations, and it has been performed for four significantly different wind turbine concepts. For each of these the effect on selected equivalent loads, originating from realistic variations in the selected load parameters, is determined by means of a two level factorial method. 1 INTRODUCTION bient situation. The modiiied turbulence field is char- acterized by an increased turbulence intensity, a de- creased turbulence length scale and an increase in the An increasing part of the future wind turbines will coherence decay. As no significant qualitative modifi- be erected in wind farms due to the diverted reduc- cations in the spectral shape have been observed, the tion in grid costs, the limited number of sites with turbulence description in the present study follows the optimal wind potential, and environmental require- traditional description of turbulence in fiat and ho- ments. Therefore, prediction of the wind induced loads mogeneous terrainl. Thus, the wind farm effects are in wind farms is of vital importance. condensed only in the modification of three parameters defining the turbulence field. The fatigue loads on a wind turbine is a combination of periodic deterministic loads and turbulence induced loads. The increase in fatigue life consumption in wind 2.1 Mean wind field farms originates both from modified mean wind field In the present investigation, only the modification of and from modified turbulence field. One possible strat- the mean wind field in the mean wind direction is taken egy, to account for increased wake loads, is to col- into account. The mean wake wind field is obtained lect the total impact from wake operation in only one by superimposing a bell-shaped velocity deficit on the parameter - often chosen as the turbulence intensity, mean shear wind field associated with the undisturbed which is a parameter experienced to be of sign&cant flow. The wake deficit in the mean wind direction, importance [1]. However, thk method has the draw- A~, md the wake extension, expressed in terms of back that its generality is ailected by the fact that it the wake radius, &, are estimated according to the is based on the choise of a specific fatigue evaluation following expressions [2] : model, and a limited number of predefine W6hler exponents and wind turbine concepts. Moreover, it excludes the detailed wind farm topology from being taken into account, and fails to reflect, that the in- duced load types respond individually on the different elements in the total wind load modification. - &(3c;cTA(z+ zo))-+}2 I (2) Therefore a more detailed description is required, not where z and r denote axial and radial directions, A is only for design approval of a specific site, but especially the rotor area, CT denotes the rotor thrust coefficient, for optimization of wind turbines suited for wake oper- ~. the ambient mean wind velocity at hub height, and ation. Consequently it is of importance to investigate c1 and xo are parmeters approximated by : in detail the impact arising from wake modtications of the individual parameters constituting the conven- 9.5D ZIJ= tional wind field description. (*)’ -~’ ~1_ D ‘+ (CTAZO)-~ , 2 WAKE WIND FIELD -(3-) where D is the diameter of the upstream rotor. De- When operating in a wake situation, the mean wind noting the ambient turbulence intensity by I= and the profile as well as the turbulence characteristics, expe- 1A Kaimal turbulence spectrum and a Davenport coher- rienced by a turbine, are modified compared to the am- ence model are applied in the analysis. 78 hub height by H, Rg.5 is determined from : R9.5 = ~ (&b + miW, &b)) > &b= max(l.08D, 1.08D + 21.7D(1. - 0.05)) where L: denotes the u–turbulence length scale in the undkturbed flow, and S. is defined as : 2.2 Turbulence intensity .4t down stream distances, - corresponding to tradi- & = 2’3.$+ (s – 2.)’34 for S>2. tional spacings in wind farms, it is assumed that only the surface and wake shear mechanisms contribute .Assuming local isotrophy in the inertial subrange for significantly to turbulence production. It is moreover sufficiently small eddies, the following relations can be assumed that the turbulence fluctuations originating derived for the wake turbulence length scales in the v- from these two sources are statistically independent, and w-directions : such that the turbulent energies are additive in the energy sense. Normalizing with respect to the undis- turbed mean wind velocity, %, the total turbulence L: = 0.33L; (8) intensity of the along wind turbulence component in L: = 0.14L: . (9) the wake, l&, is expressed as [2] : 2.4 Coherence (3) Only the modification of the uu-coherence decay fac- tor is considered important. Assuming a Davenport- formulation of the coherence, the uu-coherence decay where subscripts a and w refer to ambient and wake, factor related to wake turbulence, a~, is determined respectively. The specific wake contribution, 1~, de- according to : pends on both the down wind distance and the undis- turbed mean wind velocity and is (for spacings larger than two rotor diameters) determined as : (1+ IG)a= for 2~S <7.5 aW = , (lo) { a= for 7.5 ~ S 1.= 0.93(DS)-1’3/1 – m, (4) where a= is the coherence decay factor related to am- bient conditions, and the wake correction factor, K~, where S denotes the spacing expressed in rotor diam- is given by eters. Compared to ambient situations the wake turbulence tends to be more isotropic, and the energy in the transversal turbulence components, v and w, are de- termined from [4] : For vertical separation C, = 1, and for horizontal sep- CT;= o.81:tva, (5) aration C’, = 2. For spacings less than 2 rotor diam- u: = o.61:tv=, (6) et ers, the vslue of the wake coherence decay factor is assumed to equal the value related to a 2 diameter spacing. It should, however, be noted that the present where subscript “ w“ indicate wake-values. coherence model is based on a somewhat limited data material, and this might tiect its generality. 2.3 Turbulence length scale When the two shear turbulence contributions have 3 SIMULATIONS scales of comparable orders of magnitude, it is rea- sonable to expect the resulting spectral shape to be qualitatively invariant. However, the resulting length In order to cover a broad spectrum of wind tur- scale is modified. The modified length scale depends bine types, four fundamentally different horizontal axis on the rotor thrust coefficient, the spacing distance, wind turbine concepts have been considered - a stall the rotor diameter, and the undisturbed turbulence regulated three- bladed turbine, a pitch regulated length scale. three-bladed turbine, a three bladed variable speed turbine, and a large two-bladed pitch regulated tur- Referring to a Kaimal formulation of the turbulence bine. The main data, describing the investigated tur- spectrum, the length scale for the u turbulence com- bines, are summarized in the Appendix. To cover a ponent inside the wake, L;, is expressed as : broad spectrum of load situations, simulations have 79 been performed for each of the defined turbines op- lence intensity of the longitudinal turbulence compo- erating at (undisturbed) mean wind speeds 10 m/s, nent equal to 12 YO at hub height, and a logarithmic 14 m/s, and 18 m/s, corresponding to the regimes mean wind shear consistent with this choise. The mean “below stall”, “stall”, and “deep stall” for the stall wind speed at altitude z, ~=(z), is thus derived from regulated turbine. 1:7=(H) ~ z exp(l/O.12) The fatigue loads have been determined based on v=(z) = ~ SK (11) 10 minutes time series obtained from aeroelsstic cal- ( H’ ) culations using “state of the art” wind field genera- tors and the aeroelastic codes PHATAS, HAWC, and where the previously introduced notation is applied, VIDYN. In the simulations, the focus was put on and IGdenotes the von Karman constant. flapwise-, edgewise, yaw–, and tilt moments, as well as on the thrust force. The magnitude of the energy in the transversal turbu- lence components are determined from : The basic philosophy in the parameter investigation is to choose two sets of reference situations - one related Cr:= 0.751;7=(H), (12) to wind farms with 5D spacing, and an other related to wind farms with SD spacing. The choise of wind a: R 0.51; 17=(H) , (13) farm spacings is believed to be representative for most existing wind farms. Each set of reference situations where subscript “ a“ indicate ambient values. contains a (common) reference situation related to flat and homogeneous terrain, and a turbine dependant ref- The u-turbulence length scale, corresponding to the erence situation related to the wind farm situation (5D Kaimal formulation given in [6], is specified to 1000 m, or 8D spacing). and assuming local isotrophy in the inertial subrange, for sufficiently small eddies, results in the following For each reference set, the effect on the selected loads, relations for the ambient turbulence length scales in originating from variations in the investigated parame- the v- and w-dkections, L:, L: : ters, is subsequently determined. In the analysis a two-level factorial method has been applied [3], and consequently aeroelastic simulations with all possible combinations of the four parameter variations, con- tained within the same reference set, are required. Finally, the cross correlations between the Cartesiaa Thus, for each turbine, each reference set, and each turbulence components have been specified to zero, mean wind speed, the simulation matrix to be per- and the coherence decay constants, corresponding to formed appears from the table 2 below. the three autocorrelations, were specitied to 15 in a conventional Davenport formulation. Simulation AV IU’VVW LU*V*W a 1 A A A A The relevant wake situations have been determined 2 A A A w from the expressions given in section 2, and a con- 3 A A w A servative choise of the wake position has been adopted 4 A w A A for the wake deficit, as the wake center was situated at 5 w A A A the tip of a horizontal positioned blade (correspond- 6 A A w w ing to maximal induced horizontal shear) on the side 7 A w A w of the rotor giving the most unfavorable blade flap 8 A w w A loads. As the applied wind field generators are not 9 w A A w able to distinguish between vertical- and horizontal 10 w A w A separation, the average value C, = 1.5 is used in the 11 w w A A simulations for the modified coherence decay factor. 12 A w w w 13 w A w w 14 w w A w 4 ANALYSIS AND RESULTS 15 w w w A 16 w w w w In order to secure suitable robustness of the results from the analysis, a number of replicated runs have Table 1. Specification of aeroelastic calculations. been performed for one of the turbine concepts, in or- Within a given reference set, “A” denotes ambient wn- der to document that the choise of one single 10 min- ditions and “ W“ denotes wake conditions of a partic- utes simulated time serie, respresenting each of the rel- ular parameter. evant load situations, yields significant results. Based on the knowledge extracted from the above pre- analysis, the wake pmameter effects have tinally been The ambient situation has been defined with a turbu- determined for the four different turbine concepts. 80 4.1 Replicated runs Load Case 10 mjs 14 mfs 18 m/s ] In order to investigate the statistical significance of the results, based on one single aeroelastic calculation for each combination of parameters, some replicated sets of calculations were performed. By extending the set - of 16 combinations, specified in table 1, to a new set of 32 combinations, a fifth factor was hereby introduced - the random seed used as input for the turbulence field generator. A significant effect of this fifth factor would then indicate a need for averaging equivalent Table 3. Relative increase in equivalent ffap wise mo- loads from several 10 rnin load series, using different ment based on W5hler ezponent 12 and caused by mod- random seeds. The conclusion from this excercise was ified turbulence intensity. that for this specific study, the need for replicated runs was not found to be essential. 4.2 Wake effects . Load Case 10 mjs 14 mis 18 mfs The two-level factorial method [3] has been aplied in Pitch; 5D 6% 1% 2% the analysis of the simulated results. The method has Var.; 5D o% 1’% 070 the advantage that the main effects - an effect caused Stall; 5D 7% 470 5% by the isolated modification of only one parameter – 2-B1.; 5D 470 o% o% are determined with good significance as it is based Pitch; SD 4% 1% -1’% on 8 realisations of differens load series2. Moreover, Var.; SD 2% 1% 170 this type of analysis is able to detect whether the in- Stall; SD 3% 5% 3% dividual parameters act additively and if not, the in- 2-B1.: SD 3’% 4% 170 teractions between these can be quantified. To avoid influence from irrelevant parameter changes, the in- Table J. Relative increase in equivalent jiap wise mo- voved turbulence fields have been generated using the ment based on W6hler exponent 12 and caused by mod- same random seed. ified turbulence length scale. The analysis of the fatigue loads has been based on equivalent loads (refeering to 1 Hz) evaluated apply- ing the Wohler exponents 4, 8, 12. From the anal- Load Cue ysis it appears, that the effects of the investigated 10 mfs 14 mis 18 mfs parameters act approximately additively, and in the Pitch; 5D -2?70 -6% -3’% Var.: 5D tables below the relative changes in equivalent mo- I -4% -5% 37. Stall’; SD -2% -1% -2% ments/forces, originating from specified single parame- 2-B1.; 5D -1% -7% -4~o ter variations, are presented for a number of selected Pitch; SD 0% o% -1% loads and Wohler exponents. Var.; SD o% 0’70 070 Stall; SD o% o% o% 2-B1.; SD o% o% o% Table 5. Relative increase in equivalent flap wise mo- Load Case 10 I-n/s I 14 m/s m/s I 18 ment based on Wiihler ezponent 12 and caused by mod- ified coherence decay. REEEEl J var.;’ SD -9% Iv. o’% Stan;SD 070 870 2’70 Load Case 10 mJs 14 mis 18 m/s 2–B1.; SD 070 -6Y0 3% Pitch; 5D 2% o% 0’70 Var.; 5D -11’70 -1’% -170 Table 2. Relative increase in equivalent j7ap wise mo- Stall: 5D -2% 3% 2?70 ment based on W6hler ezponent 12 and caused by the deficit. Table 6. Relative increase in equivalent tilt moment based on Wiihler ezponent 4 and caused by the deficit. 2Effectively, it means that the an average effect is com- puted as the average of 8 grad]ent estimates corresponding to 8 different expansion points. 81 Load Case 10 mjs 14 mfs I 18 m/s Load Case 10 mfs 14 m/s 18 m/s Pitch; 5D 25% 16% 12% Pitch; 5D 31% 20% 13% Var.; 5D 40% 17% 8% Var.; SD 37% 16% 8% Stal~ 5D 24% 20% 13% Stall; 5D 27% 16’% 6% 2-B1.; 5D 6% 5% 3% 2-B1.; 5D 4% 6% 2% Pitch; 8D 18% 13% 9’% Pitch; 8D 24% 17% 11% var.; 8D 32% 14% 6% Var.; 8D 28% 12% 6% Stall; 8D 4% 15% 10% stall; 8D 3% 12% 4% 2-B1.; 8D 4% 3% %1 2-B1.; 8D 370 4~o 2?% Table 7. Relative increase in equivalent tilt moment Table 11. Relative increase in equivalent thrud force based on Wc7hler exponent J and caused by modified based on W6hler ezponent J and caused by modifkd turbulence intensity. turbulence intensity. Load Case 10 m/s 14 m/s 18 m/s Load Case 10 m/s I 14 m/s 18 m/s Pitch; 5D 10% 5% 2% Pitch; 5D 13% 570 2’% Var.; 5D 2% o% 1% Var.; 5D 270 170 1% Sta14 5D 13% 8% 6% Stall; 5D 11% 7% 3% 2-BI.; 5D 5% 3% 3% 2-B1.; 5D 270 270 1’70 Pitch; 8D 8% 3% -2% Pitch; 8D 9~o 3% 1% Var.; 8D 3% 2% 2% var.; 8D 3% 3’% 2’70 stall;8D 4% 6% 4% Stall; 8D 2% 2% 2% 2-B1.; 8D 4% 370 2’?70 2-B1.; 8D 270 1% 1’70 Table 8. Relative increase in equivalent tilt moment Table 12. Relative increase in equivalentthrust force based on Wiihler exponent ./ and caused by modified based on W6hler ezponent ~ and caused by modified turbulence length scale. turbulence length scale. Load C=e 10 m/s 14 m~s 18 m/s Load C=e 10 mfs 14 m/s 18 m/s Pitch; 5D 6% 9% 6% Pitch; 5D 6% 8?70 6% Var.; 5D 8% 8% 770 Var.; 5D -1% 12% 17% Stall; 5D 3% 4% 0’70 Stall: 5D -2% -4% -2?70 2-BI.; 5D -1% -2% -2% 2-B1.’; 5D 170 2% 4?70 Pitch; 8D o% o% -1% Pitctq 8D 0% o% -170 var.;8D o% o% o’% var.; 8D o% 070 0’7’0 stall; 8D o% o% o% stall;8D o% o% 0’70 2-B1.; 8D o% 070 o% 2-B1.; 8D 0’70 Oyo o% Table 9. Relative increase in equivalent tilt moment Table 13. Relative increase in equivalentthrust force based on W6hler ezponent J and caused by modified based on W6hler ezponent ~ and caused by modified coherence decay. coherence decay. A number of qualitative findings can be extracted from Load Case 10 m/s 14 mJs 18 m/s the analysis. The wind field modifications caused by Pitch; 5D 0% o% o% the wake, and quantified in section 2, all tend to di- Var.; 5D -31% 2% -276 minish with increasing wind turbine spacing. This be- Stalb 5D -1% 3% -7% haviour is also reflected in the life time consumption, 2-B1.; 5D -19~o -9% -5% as a general tendency of decreasing wake effects, from o% o% -1% Pitch 8D the 5D situation to the 8D situation, is observed. The var.; 8D -24% o% -2% turbulence intensity- and the length scale modifica- stall;8D -1070 -7% 3% 2-BI.; 8D -lo% -7% -2’% tions are seen to decrease for increasing wind speed, and this behaviour is also reflected in the investigated Table 10. Relative increase in equivalent thrust force equivalent moments. based on W6hler ezponent ~ and caused by the deficit. The fatigue load dependence of the mesa wind deficit with the mean wind speed is more involved, as three factors contribute simultaneously - decrease in mean 82 wind speed, introduction of horizontal shear, and mod- That the effect of incressed turbulence intensity ification of the vertical shear. In contradiction to the usually dominates the effects of the other investi- fatigue loading caused by wake turbulence intensity, gated parameters with a factor of 2-3. the fatigue loading associated with the wake deficit in- That different turbine concepts and different load dicates no general tendency with the mean wind speed types act differently with respect to parameter for the investigated turbine concepts and load types. sensitivity. Tilt- and yaw moments exhibit the same behaviour ex- cept for the two-bladed turbine, where the increased 6 ACKNOWLEDGEMENT’S wake coherence decay results in significant differences. The two-bladers are, however, born with distinct pe- riodic properties of the rotor inertia often introducing The work has been supported by the European Com- phase-shifts in the turbine loads, even for very modest mission under contract JOR-CT95-O0642. Stimulat- changes in the mechanical properties. These phase- ing discussions and assistance from our collegue Per shifts often ailect the loading in an unexpected way, VOlund is furthermore acknowledged. and the discrepancy between the tilt- and yaw loading, arising from an increased coherence in the turbulence field, is believed to originate from such a phenomenon. 7 REFERENCES All the four investigated parameters were demon- [1] Adarns, B.M. (1996). Dynamic loads in Wind strated to be significant in relation to fatigue life con- Farms 2. Final report of Joule project JOU2- sumption. However, in most of the investigated sit- CT92-0094. uations the effect originating from the turbulence in- [2] Larsen, G. C., HOjstrup, J., and Madsen, H.Aa. tensity dominates the other parameter effects with a (1996). Wind Fields in Wakes. EUVTEC’96, factor of 2-3. Goteborg 1996. [3] Box, G.E.P. et al (1978). Statistics for Experi- It is moreover evident that different turbine concepts menters - An Introduction to Design, Data Anal- act differently with respect to a particular parame- ysis, Data Analysis, and Model Building. John ter sensitivity, and that this also applies for different Wiley & Sons. load types. More specific it is seen that the induced wake deficit generally is favorable for the thrust force, [4] HOjstrup, J. and Nmg5rd, P. (1990). Tcendpipe whereas it, for the majority of the investigated turbine Wind Farm Measurements 1988. FW+M-2894. concepts, introduces increased blade- and rotor fatigue [5] Petersen, S.M. et al. (1997). EWTS II - loading. Load Spectra and Extreme Wind Conditions. EWEC’97, Dublin 1997. Finally, it is observed that the increased wake coher- [6] Danish Code of Practice DS472 (1992). Loads and ence decay is favorable for the flap root moment, Safety of Wind Turbine Structures (in Danish). whereas increased wake turbulence intensity is in gen- Teknisk Forlag. eral introducing higher fatigue loading. APPENDIX 5 CONCLUSIONS The main data, describing the investigated turbines of The main conclusions from the investigation are different sizes and concepts, are summarized below. Turbine Vestaa I WPS-30 I Danwin AEOLUS-11 ● That only one single 10-min. simulation time se- Type V27 180 kW (const. speed) ries is a sufficient representation of the individual Rated load situations to yield significant results with the power 225 kW 500 kW 180 kW 3000 kW applied analysis method. No. of blades 3 3 3 2 ● That the investigated parameters are shown to Rotor act additively, which imply that a simple approx- diameter 27.0 m 30.0 m 22.2 m 80.0 m imative method, involving only a very limited Hub number of aeroel~tic calculations, can be applied height 28.7 m 35.0 m 29.8 m 77.0 m for fatigue estimates taking into account the de- Control pitch variable stall pit ch tailed wind farm topology and the particular wind strategy regul. speed regul. regul. turbine concept [5]. Table 14. Main characteristics of the investigated tur- ● That all four investigated parameters were bine concepts. demonstrated to be significant in relation to fa- tigue life consumption. 83 PROPERTIES OF THE MARITIME AND COASTAL WIND FIELD J@gen L@vseth and Tore Heggem, Norwegian University of Science and Technology, Department of Physics, N-7491 Trondheim, Norway. E-mail: Jorgen.Lovseth @phys.ntnu.no Abstract During 15 years, detailed wind observations have been made on the coast of Mid-Norway. The main station with three masts is situated on the western tip of the island Fr$y~ which is bordering the Norwegian Sea. Approaching winds will have passed a length of land varying from 100 m to several tenths km depending on direction. A satellite station located on a small islet west of Fr@yahas one mast of 45 m and is exposed to nearly undisturbed maritime winds from the westerly half sector. A survey is given of general results. The turbulence description given in the Norwegian Petroleum Di- rectorate’s guidelines is based on measurements from the stations and is reviewed and compared to new data. Due to winter periods with a strongly convective boundary layer, the spectra genemlly indicate more turbu- lent energy for frequencies below 0.01 Hz than the conventional formulations. Some 12 hour spectra even have maxima in the one hour region, and long time spectra show no h-l gap. Coherence spectra of wind speed are shown to follow a modified Davenport formul~ with very short coherence lengths in the trans- versal directions. Gust factors and turbulence intensity are shown to exhibit a non Gaussian distribution, de- pendent on stability, for wind speeds below 20 mh. Keywords: Maritime wind turbulence, wind profile, turbulence spectra, coherence, gust factors 1 Introduction In off-shore and coastal areas, wind forces will often dominate in the determination of a sufficient survival strength of constructions. A parameterization of wind loads in such areas is therefore im- portant for design purposes. Our group did the field measurements, mostly during the 1988/89 sea- son, in the “Statoil Joint Industry Project: The Maritime Turbulent Wind Field, Measurements and Models’’[2][3][4] [5]. The project was co-ordinated by Dr. O.J. Andersen, Statoil, and financed by eight international oil companies. In collaboration with Dr. Andersen, the experimental data were compared to existing models, but in particular for the spectral data, new or modified models had to be developed. Based on the work, new guidelines for off-shore structures were proposed and lat- er issued by the Norwegian Petroleum Directorate [6]. Some of the results (except spectra) were discussed by Andersen and L@vseth[7]. The first 4 sections of this paper follows closely an account given by L@vsethand Heggem[l]. In the next section, a short description of the measurement stations and experimental facilities are given. A 15 year time series of 10 minute data exists, with some gaps, and in total some 4 years of 0.85 Hz data (512 leggings per 10 minute). In Sec. 3 a brief review of general data properties is given. In Sec. 4 the spectral distributions are discussed. The so-called spectral gap in the one hour region (0.3 mHz) is not seen in our data. This poses some particular problems for the modelling of the spectra, because the traditional separation between the region of ground generated turbulence, peaking around 10 mHz, and weather (synoptic) variations is not there, but filled by turbulence or fluctuations caused by long range structures (30-50 km) in the wind. The 2-point spectra are char- acterized by very short correlation lengths in the transversal directions. In Sec. 5, gust factors are defined and discussed. It is shown that their distribution is non-Gaussian. The same holds for tur- bulence intensity discussed briefly in Sec 6. In the final section, some conclusions are given. L@vsethand Heggem, page 1 of 16 84 2 Experimental setting The data analysed in this paper are collected at two measurement stations situated on or near the western part of the island of Fr@ya,located on the coast of Norway, approximately 100 km west of the city of Trondheim (63° 40’N). Fr@yais protruding like a wedge into the Norwegian sea. A branch of the Gulf stream flowing along the coast will in general contribute to unstable atmospher- ic conditions for NW winds during the cold season. The main station, Skipheia, situated on Fr@ya,has three masts and is surrounded by small hills covered with heather or moss - or having a bare rock face. The maximum heights are 20 m above MSL, and the horizontal spacing of the hills is 100 to 500 m. The wind pattern observed at the sta- tion is strongly dependent on the direction. In the maritime sector, 235°-500 (SW to NE through north), the wind is coming from the North-Atlantic, but has travelled over land for the last 1 to 3 km. It is in this sector we find the strong winds which are the main concern of this paper. In the complementary sector 50°-2350, the wind is coming from inland and has travelled across a mixture of land and sea. The Skipheia station has been operative since 1982. Two of the masts have a height of 100 m, the third one is 45 m. The masts are placed in a triangle, 80 to 150 m apart. Sea temperature is meas- ured near the station. Air temperature and wind speed are measured at 10 m, 40 m, 70 m, and 100 m. Wind direction sensors are located at 40 m and 100 m. The wind-speed sensors are placed on slender rods at a distance of 2.5 m from the mast and are duplicated (in the western and easterly direction) to avoid shading effects. During data analysis, the up-wind sensor is normally selected automatically. Until 1988 the system was only logging 10 min. mean values and 2 sec gust values. After 1988 the system was redesigned and has since been logging at a rate of 0.85 Hz for all sen- sors. The data acquisition system for the stations was developed at the department, and runs on a real time operating system, allowing control from Trondheim. A more detailed descriptions of the measurement station may be found in references [8] and [9]. Extensive discussions are given by Aasen [10] and Heggem [11]. A back-up battery operated system will measure 10-min. average wind speed, gust, and direction at 3 heights. The second station is located on the flat and barren islet Sletringen, approximately 400 m in diameter, 4 km to the west of the station at Skipheia. A single mast, 45 m high, is located 150 m from the shore line in the westerly half sector. The measurement system is of the same type as used at Skipheia. Temperature sensors are placed at 5 and 45 m, wind speed sensors at 5, 10, 20,42 and 46 m and wind direction sensor at 45 m. The speed sensors are placed on slender rods 3.0 m to the west of the mast. We assume that sensors from 10 m and up are exposed to true oceanic wind in the maritime sector as defined above. The Sletringen station has only been operated i selected years. The wind-speed sensors are cup-anemometers with a distance constant, C-l.5 m giving a time response that is fully adequate for the wind speeds and sampling frequency considered here. The sensors give a certain number of pulses (mostly 14) per revolution (corresponding to 1.4 m of wind way), and # pulses in the sampling period is recorded. The resulting resolution (sampling) noise in the spectra is negligible. The data are compared to models modified to reflect the way of recording, including the aliasing effect caused by the finite logging frequency. Details are dis- cussed by Heggem et al. [9]. 3 Mean wind speed and direction distribution The upper part of Fig. 1 shows the mean wind speed in 5° sectors vs. wind direction, demonstrating L@vseth and Heggem, page 2 of 16 85 14 f 1 1 i I I I — 1OOm 12 -. ..-. 40m ~ “—”- 20m g 10 — – 10m 3 8 - I I 1 t I I 4 I o 50 100 150 200 250 300 350 0.012 1 1 I I 1 1 1 g ...... a 0.01 — Alldata . . . . % . . b 0.008 -“”. ”u>8rn/s g .“ .. - j 0.006 u .“ 30.004 - ~ g 0.002 - & ...... I 1 I 0 I 1 ! I o 50 100 150 200 250 300 350 Wind direction (degree) Fig. 1 Mean wind speed as function of direction (upper), and frequency distribution of wind directions (lower) a clear peak in SW direction. The graph is based on hourly mean values. The lower part shows the direction distribution for all data, and for periods with mean wind speed greater than 8 m/sat 10 m height. The probability for maritime wind is very high for strong winds, thus the highest contribu- tion to the wind power spectra comes from this sector. The mean annual variation of the wind at Skipheia may be fitted to the formula (d+4) U(z,d) = i(z) + a(z)cos 2X= (1) {1. where d is the day number. In Table 1 the mean wind speed ~(z) and annual amplitude a(z) at several heights z at Skipheia are given. Table 1: Annual mean wind speed and amplitude versus height for Eq. (1) Height z (m) I 10 I 20 I 40 I 70 I 100 Mean wind speed ;(z) (m/s) 6.90 7.32 7.82 8.30 8.74 Mean amplitude a(z) (rnk) I 1.57 I 1.66 I 1.76 I 1.88 I 1.95 The height profile of the mean wind speed is for neutral atmospheric conditions well fitted by the L@vseth and Heggem, page 3 of 16 86 logarithmic law, which may be expressed as (2) ‘(z)=‘(4+4:)1 a=[’n(%)r where the height coefficients is expressed in terms of the standard aero-dynamical roughness length ZOand the reference height ~ - the standard choice is Zr= 10 m. To first order, a is equal to the exponent in the popular power law. At Sletringen ZOis to a good approximation given by the Charnock relation, Z. = (~h /g) U*2,where a fit to the data gives ~h = 0.017 for the Charnock con- stanc g is the gravitational constant and u* is the friction velocity. Thus the height coefficient in- creases with wind speed over the ocean. For practical purposes, Eq. (2) maybe used combined with the parameterization Cx= 0.035 + 0.004 u(zr)sm-l (3) for maritime wind and neutral atmospheric conditions. For U(ZQ>20 m/s, the approximation is val- id for all thermal stability regimes. But definitive stable or unstable conditions may persist over the ocean even in these cases of very strong winds, contrary to what textbooks generally are saying. Also at Skipheia, there is an observable Charnock effect in the maritime sector, and in general the effective value of a is dependent on direction and height. A typical value is u = 0.1, correspond- ing to a roughness length ZO= 0.45 mm. The surface of the small scale hilly terrain does not absorb much energy, but may create a large scale turbulent structure typical of slightly unstable thermal conditions, thus giving a wind speed height gradient corresponding to a very smooth terrain. For strong winds typically coming from the westerly sector, eqs. (2) and (3) may be used to estimate the wind speed profile also at Skipheia. As discussed by Heggem [11], a neutral or slightly stable intermediate boundary layer will be established to the height of the masts after a few km of wind way over land, regardless of the conditions at sea further upwind. 4 Turbulence spectra Details regarding the calculation of spectra maybe found in Heggem et al. [9]. We will first discuss the one point spectra, which do show some striking effects, and then briefly discuss the coherence between two different time series. 4.1 One point spectra The spectral function S(f) may be defined as the density of the variance of wind speed in the fre- quency space. The value of the variance C2 will depend on the length, T, and the number of terms, N, of the time series from which it is calculated. The relation to the Fourier coefficients is discussed in Sec. 4.2. To get the density with sufficient accuracy, an ensemble average over a number of time series must be done. In the continuous approximation, one has ~’=fymfj f,=;> f2=& (4) L@vseth and Heggem, page 4 of 16 87 S(f) is proportional to the density of turbulent energy at the frequency f, and thus the power to ex- cite vibrations at this frequency in a compliant structure. In Fig. 2 we show long term spectra for the two stations discussed. For periods when the sta- 10’ ,@ ! I ! I I 10-2‘ I 1 I A 104 1o~ 10= 10-’ 10° 10’ lIY 103 10’ 10s 10’ ~ .—. — 10° F 20m g $Q -- a ------10-’ T ,0.1 104 lo- 104 10° 10’ 1(Y 10’ 104 10’ Frequency (per day) Fig. 2 Long-term spectra from Sletringen and Skipheia. tions have been down, missing data have been substituted with data from nearby stations or from the Norwegian Meteorological Institute (DNMI) to provide a continuous time series. As standard, fS(j) is plotted, this quantity indicates the energy density in a graph versus log@. The annual var- iations have been filtered out of the spectrum. As one may observe, there is no gap in the h-l region. The Skipheia spectrum, based on 14 years of dat% goes nearly as~for frequencies below the syn- optic peak or weather maximum, which is located near (3 days)-1.In the high frequency (I@) part of the spectra there is a maximum around 0.01 Hz for the sensors nearest to the ground. The high level of turbulence in the one hour region is due to a cellular large scale convection pattern which appears for strongly unstable atmospheric condition during the winter season. During periods with lengths of the order of one day, one may observe quasi periodic oscillations with periods of the order of one hour. The wind speed is typically in the region 10-15 mk, meaning these structures have wavelengths in the region 30-60 km. A more detailed discussion with references to relevant literature is given by Gjerstad et al. [12] and Heggem et al. [9]. The existence of such fluctuations should be taken into account in short term weather forecasts, the amplitude of the wind speed var- iations are typically 20% of the mean value. The HF spectra calculated from the observed time series are in general flatter than e.g. the Kai- mal or ESDU parameterization (see e.g Panofsky and Dutton [13]) indicate. The parameterization proposed in NPD guidelines [6] is based on the relations [4] LOvserh and Heggem, page 5 of 16 88 f~(f) = A(uP z)~ 1 + ~~ ‘i A(ur, Z) = 0.0746u2 ~ [1 ,(0°”7’2(:10”21’ (5) ~ n = 0.468 ‘=fx ‘x= 00232Hz(;)””74’(:)-0”’77 U* = 20 mls Ur = ;(2,) 2, = 10m Here, ~Xis the abscissa of the maximum point of the fknction ~S~. Integrating SW defined by eq. (5) over all frequencies gives a total variance 02 = 0.238 A(uP z ), indicating a stronger in- crease with wind speed than normally assumed. In Fig. 3 spectra calculated from one hour time series from Sletringen for two wind speed regions and several heights are shown and compared to the parameterization. Linear trend has been removed from the time series prior to the spectrum cal- culation. The parameterization is approximately valid for all stability conditions when u,> U.. For u,< UO itwill apply for neutral conditions only. The fit is generally good. The observed spectrum is rather flat in the lower speed class for f e fx, in the upper speed class a spectral maximum is in- dicated, but only 8 time series are included in this selection. Fig. 2 gives the general picture. 4.2 Two point spectra or coherence The coherence is a measure of the correlation between the Fourier-components of two time series. From the cosine- and sine-coefficients of standard discrete Fourier transforms (DFT) of two time series, one may define the densities of the two spectra, the co-spectrum and quadrature spectrum in the following way S1U3= ~(a1n2+bl~’) S2~ = ~(a2n2 + b2n2) (6) T c(j) = ~(alna’n +blnb’n) Q(f) = ~(a1#2. -a2nbJ Here T is the time period, and the frequency f is approximately related to the coefficient index n as f= n/T. The averaging should be done over coefficients from several time series in a suitable in- terval in the variables that affect the spectra. For n >3 the spectra were averaged over intervals of frequency (range of n) corresponding to one third of an octave. The coherence is then defined as (also called coherence squared in some books) C(f)’+ Q(f)’ Q(f) coh~ = tan(p(f) = –— (7) Sl(fls’(fl cm q~ is the phase angle between the harmonic components of frequency f of the two time series. It can be shown that cob(f) correspond to the square of the ordinary correlation coefficient i.e. coh~ = O correspond to no correlation, or independent time series. cob(f) = 1 similarly cor- responds to full correlation. The traditional Davenport formulation of coherence, cob(f) = exp(–(a. f” d/u)) (see e.g. Panofsky and Dutton[13]), where d is the distance between the points of observation, has been re- L@vseth and Heggem, page 6 of 16 89 10’ I 1 1 r < Mod 44m * * Obs 44m ——. Mod 20m o 0 Obs 20m ...... Mod 10m -- ~lo” *+ i n-’ I I t 1 I ‘“104 104 10-2 10-’ 10° Frequency (Hz) 10’ I 1 Mod 44m * * Obs44m ——- Mod 20m o 0 Obs20m ...... Mod 10m + + ObslOm G=IJ 31 @lo !? : / .“ .- 10-’ 104 10-3 10-2 10-’ 10° Frequency (Hz) Fig. 3 One-point turbulence spectra for Sletringen. Wind speed is 15-20 mh (top) and 20-25 tis (bottom). Wind direction is from 180° via north to 40°. formulated to allow different damping coefficients, aN ay, aZ in the three directions (x-axis along the wind direction, y- lateral and z-direction vertical) as well as a dependence on stability as dis- cussed by Andersen et al. [3]. A simplified version for neutral conditions and a separation vector [h, Ay, Az] is givenas L@vseth and Heggem, page 7 of 16 90 1 CO~~ = eXP –~[(@-x)2 + (aYAY)2 + (aZ/AZl(l + ‘))2]2 { r ‘1 (8) 2122 (Zi = Ui “f ‘ri”z~-pi z~ = —r Zr = lom Zr where the parameters cti, i = x, y, z and the exponents ri, Pi>q were determined by a least square fit to the experimental data. The values shown in Table 2 correspond to those given in the NPD guidelines [6] based on the results of Andersen et al.[3]. Table 2: Parameters for the coherence model, Eq. (8) (S1 units understood). Direction (relative to wind) I Ui I ri I Pi I q x (parallel) 2.9 I 0.08 0.4 - y (lateral) 45 0.08 0.4 - z (vertical) 13 0.15 0.5 0.25 The original fit to eq. (8) for the x- and y-components was done using data from all directions and all combinations of sensors at the same level from the three masts at Skipheia. In Fig. 4, new and independent data from 1995-96 for wind speed 18-22 mls are compared to the model. The top graph shows “longitudinal” data from a 10° wide sector symmetric around the sensor-sensor con- necting lines at each height for the 100 m masts, the middle shows data in a 30° sector around the normal to the same lines, in both cases for 4 heights. Sensor distance is 75 m. The longitudinal co- herence of the new data is somewhat larger, the lateral coherence less than the model predicts. Data and model for vertical separations for Sletringen are shown in the bottom part of Fig. 4. Similarly modelling the phase ~ as defined by Eq. (7), it is found that the turbulence structures moves with a speed close to that of the wind. In the vertical direction, lines of constant phase are curved, and strongly forward inclined at the lower heights. 5 Gust factors In the project discussed in Sec. 1, the reference gust factor for a sub-interval ti and height z was defined as the ratio of the hourly maximum mean value of the wind speed over this sub-interval divided by a 60 minutes mean value of wind speed at the reference height, 10 m. The latter mean is calculated symmetrically in time around the interval of the maximum gust value. Thus trend ef- fects are minimized. (9) L@vseth and Heggem, page 8 of 16 91 1 . . @ . .. I I .. **** x .x. ..\.. ““. .X’. ..\\ ()* 0.8 - .x ** ““xx. \ o 0) : 0.6 - ““””; +\+”* g ‘.. ”~\+ * Mod 100 .- “:\ + 2 * Obs 100 * o 0.4 .* ——. o Mod 40 ““..+O * o 0 Obs 40 .—. — ““.&A+ Mod 20 -. \.; o 0.2 -+ + Obs 20 ...... “.. \ \ Mod 10 ..y$ x x Obs 10 m~%...... “x%. n . . ;04 10-3 10-2 10-’ 10° Fram mnrw (H7) 1 1 1 t Mod 100 * * Obs 100 0.8 - ——- Mod 40 o Q..”*X o 0 Obs 40 + .—. — Mod 20 + + Obs 20 ~ 0.6 - + ...... Mod 10 x al x x Obs 10 % .c o 0+4 - 0 x 0.2 - xx o 104 10+ 10-2 10-’ 10° Frcw mrmv (H7\ 1 + * Obs 46/42 “\ ——- 0.8 - ~ o ““. Mod 46/20 ~++ \ “.x o 0 Obs 46/20 ~.+ y)o .? “–”— Mod 46/10 a \+\ “-x + + Obs 46/1 O & 0.6 - “\ ‘o ..x ...... Mod 20/1 O g “. x x Obs 20/10 2 “>.+ ‘: x \ ~ 0.4 - ‘.+ Qp “x * \ “x * “* Q “x “+ 0.2 - I I o 104 104 10-2 10-’ 10° Frml mnrw (H7\ Fig. 4 Examples of two-point coherence spectra.Top - parallel, middle - lateral to wind direction, compared to Skipheiadata. Bottom,vertical separation,and data horn Sletringen. LOvseth and Heggem, page 9 of 16 92 Equation (2) and (3) can of course be used to relate this reference gust factor to the gust factor de- fined with respect to the mean wind at the same height as the gust is evaluated. Experimental data for the cumulative distribution of reference gust factors at 46 m height for the Sletringen station is shown in Fig. 5. Data from some 5 months during winter season in two speed ranges 14-18 and 18-22 m/s are included, in a “normal” plot, where a Gaussian distribution would have given a straight line. The non-Gaussian character is quite pronounced at the lower wind speeds, where there also is a clear lapse rate dependence, the non-Gaussian character being strong- est for thermally unstable situations. The curves shown in Fig, 5 is based on a parameterization of the frequency function for the gust factors of the form f(G) =Nexp “-( G2~~)2 G–a Here, N is a normalization factor. For small values, the distribution is Gaussian with a width c and peak value a, at large values the distribution is exponential, characterized by the parameter 6. The two sections are joined at the point D such that the function value and the first derivative is contin- uous. The parameters U, o, 6 have been expressed as functions of UP in (z/zr), In (ti/T). The ex- plicit parameterization is under revision. It will be given in a future paper and compared to a more extensive data material. The exponential “tail” of the distribution does allow an explicit expression to be found from eq. (10) for the (small) probability p that the reference gust factor will exceed a certain value GrP G = u + 02/(28)+ 81n((N3)/p) (11) v In Fig. 6 we show curves for the values of GrP with exceedance probabilities of one per cent and one per mine, respectively, as a function of height for a reference wind speed of 20 tis and gust length of 3.5 s, 15 s, 1 minute and 10 minutes. 6 Turbulence intensity Turbulence intensity is defined as the ratio between the standard deviation and the mean wind speed. Before comparing different measurements, one must make sure that the standard deviation is evaluated in the same way, i.e. the time periods must have the same length (crop. eq. 4), and trend elimination and other types of filtering prior to the calculation should be identical. According to Monin-Obukov similarity theory (see e.g. Panofsky & Dutton[13] p. 159), one would expect that the turbulence intensity for neutral and strong wind conditions are given as c ](z) = & = (12) u(z) ln(z/zO) where C is a constant close to one. Using Eq. (2) we obtain L@seth and Heggem, page 10 of 16 93 ii(zr) C(X I(z) = cct~ (13) u(z) = 1 + czln(z/z,) In Andersen & L@vseth[4] the standard deviation was calculated from one hour time series after turbulence components with periods greater than 10 minutes were filtered out by FFT-techniques. Data from Sletringen for reference wind speeds larger than 10 m/s were fitted to the ad hoc formula l(z) = [0.06+ 0.0026 ii(zr)] (14) (:)-””’’{w(:)-o”’’(%r””} where L is the Monin-Obukov length. The fit is shown in Fig. 7, and is quite good. The error bars on the experimental points indicate the standard deviation within the experimental sample. Ther- mal stability effects are seen to be of importance for reference wind speeds below 15 rrh. The reduction of turbulence intensity with height, indicated by the height exponent p = -0.22, is much stronger than implied by standard theory as expressed in Eq. (12). Looking back at the dis- cussion of the Charnock relation i Sec. 3, and the numerical result in Eq. (3), a value of the height exponent of p =+x = –O.1 is implied. In an earlier analysis of the same data material by Andersen et al. [3], the standard deviation was calculate from one hour time series as the root-mean-square (rms) deviation of the single values and the running mean value (in a one hour window symmetric around the point in question). This resulted in a 20% higher value of the turbulence intensity, but otherwise very similar results. The distribution of turbulence intensity values from hour to hour was found to depend on sta- bility and wind speed in a similar way as discussed for gust values. “Normal” plots for the cumu- lative distributions are shown in Fig, 8 for two wind speed classes, 14-18 and 18-22 m/s; and three classes of lapse rate. The non Gaussian behaviour is most noticeable for unstable conditions and lower wind speeds. 7 Conclusions Measurements of the temperature profile at the islet of Sletringen show that thermal profiles far from neutral may persist even for strong winds. The wind speed profile for oceanic winds is found to vary with wind speed as indicated by the Charnock relation. Stability effects are important below 15-20 mh. Long time series indicate that there is in generaI no gap in the one hour region in the maritime turbulence spectra, the reason is thought to be long wavelength convective activity. In some periods of the length of days, one may even find maxima in the time series with periods of the order of one hour. This should be taken into account for short term weather forecasts. The HF- spectra do not obey traditional Kaimal scaling, but increase more with wind speed than the Kaimal model indicate and have a flatter maximum than conventionally assumed. The coherence lengths (in two point spectra) are found to be short in the transversal directions. Thus turbulence compo- nents with periods below one minute will to a large extent even out over a structure with the di- mension of 50 m. Gust factors show anon Gaussian distribution, most evident for low wind speeds and unstable conditions, but clearly noticeable up to 20 rrds.The distribution of turbulence intensity values show a similar behaviour, and do otherwise decrease more strongly with increasing height at both sta- L@seth and Heggem, page 11 of 16 94 tions than conventional theory predicts. References 1 L@vseth, J and Heggem, T., (1998) Wind Description for Coastal and Off-Shore Structures. Proceedings of the COiVSEC’98 conference: Concrete under Severe Conditions. Ed. O.E. Gj@v et al., E & FiV S’pen, London pp. 1979-1988 2 Andersen, O.J. and J. L@seth: The Fr@yadatabase for gale force maritime wind. Part 1: Sites and instrumentation. Review of the database. J. Wind Engineering and Industz Aerodyn. 57, pp. 97-109, (1995). 3 Andersen, O.J., Heggem, T., L@vseth,J., Mollestad, K. and Aasen, S.E., (1991) The Maritime Turbulent Wind Field. Measurements and Models. Phuse 2. Statoil Joint Industry Project. Fi- nal report. Allforsk, Trondheim, 216 pp. 4 Andersen, O.J. and L@vseth,J. (1992) The Maritime Turbulent Wind Field. Measurements and Models. Extended Analysis of the Fr@ya Database, Allforsk, Trondheim, 154 pp. 5 Andersen, O.J. and L@vseth, J. (1994) The Maritime Turbulent Wind Field. Measurements and Models. Final Report to the Statoil Joint Industry Project, Phase 2, Extension 2. All forsk, Trondheim, 89 pp. 6 Norwegian Petroleum Directorate (1994) Acts, Regulations and Provisions for Petroleum Ac- tivi~, Vol. 2, pp. 669-71. 7 Andersen, O. J. and L@vseth, J. (1993) The Fr@yadatabase for gale force maritime wind. Structural Dynamics–EURODYN’93, Ed. T. Moan, Balkema, Rotterdam, pp. 1091-7 8 L@vseth,J., Aasen, S.E. and Lende, R. (1996) Measurement and Modelling of the Profile and Turbulence of Coastal Wind. Proc. EWECS 1996, pp. 548-551. 9 Heggem, T., Lende, R. and L@vseth J. (1998) Analysis of Long Time Series of Coastal Wind. J. Atmos. Sci. Vol. 55 pp 2907-2917. 10 Aasen S.E. (1995) The Skipheia Wind Measurement Station. Instrumentation, Wind Speed Profiles and Turbulence Spectra. Dr.scient. (Ph.D.) dissertation, Dept. of Physics, University of Trondheim. 11 Heggem T. (1997) Measurements of Coastal Wind and Temperature. Sensor Evaluation, Data Quality, and Wind Structures, Dr.scient. (Ph.D.) dissertation, Dept. of Physics, NTNU, Trondheim. 12 Gjerstad, J., Aasen, S.E., Andersson, H. I., Brevik, I. and L@vseth,J. (1994) An Analysis of Low-Frequency Maritime Atmospheric Turbulence. J. Atmos. Sci., 52, pp. 2663–9. 13 Panofsky, H.A. and Dutton, J.A. (1984) Atmospheric Turbulence, John Wiley& Sons, 397 pp L@vsethand Heggem, page 12 of 16 95 t * I , * , , t , 9 I I t I t i , Y I I I , 1 I , 1 , , , I I , , t I t t 0.99 - 0.95 - --15 s fit --lm fit .yJ0.90- ..--10 m fit i 2 , ~ 0.’70- G 0.50- . : ! 3 {. I v 0’30 ‘“ i @ + 0.10 - , 0.05 - 0.01 - iQ35*lo-a 7 I , I 7 0.99 -- .! 0.95 - ~ 0.90 - 3 ~ 0.70 - k ~ 0.30 - CO T-i 0.10 -“ 0.05 -- “ 0.01 - , , , 8 1.35’10-’ & , , , r , , , , 2.40 2.60 1.00 1.20 1.40 1.60 1.80 2.00- 2.20. Reference gust factor Fig.6.“Normal plots” of the cumulative distributions of gust factors at 46 m height, Sletringen, for two wind speed classes. All stability classes are included. L@vseth and Heggem, page 13 of 16 96 t , I 1, * , , 1,, , , , 1, , , [9,,1,,,1, , , 1, , 1 I 1 , J , I , I I I t,ttl, ,,l,,,J . : . . Legend .. . . —T=3.5sp=0.01 ; ...... T=15s p=O.01 . : . I: ‘.”: ;=1;: ;X:.:: . . .:.. ———--—. : :. ~. . : ...... : ...... “ . ., ...... “ ,. . : . .,.. . :“ :. . . : . ~. :...... : .. ... -...- ;.: ....- .:__ .: .: .. : ...... : ! ..1 . . .“ 1: I # # 1“’1’””1$:. ,. . .:..:. p=o;$l; ‘ .! ,.. ‘. ).001 . .: : ~ . . I. . . T=lftm.-— %=f).Ool , I ,.. r- . . :. . .:. !.. :. ., .,4 :.: . . . . . : “...... ,. .. ;. .. . . “. ..-...... “ .. . :.,.. ...-i . . . .. :.. ;. . .. -“. .’! 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.60 Reference gust factor Ug(Ti,z,p)/Ur Fig. 6. Estimate of the gust factor limit that have a probability of 1 per cent (top) and 1 per mine (bottom) of being exceeded.Referencewindspeed 20 m/s. The limits will decrease slowlywith windspeed. L@vseth and Heggem, page 14 of 16 97 I * t t 1 t 1 , 1 , , 1 I , f I I , t , I t , , I , , , I * , t Ei 0.12 0 . 0.10 4+-+BZ?Legend n m Ohs. S.Unst ———Fit S.Unst ~ 0.08 * Ohs. Unstab --- Fit. Unstab 2 @ 0.06 x Ohs. Neutrl — - Fit Neutrl 41 o Ohs. Stable , , I I I I I , I I i , , I & 1 8 I , I I 1...... 0.04 1 Fit Stable._ —.- -. G 0.12 ~ o 02 0.10- n ~ 0.08 ~ 0.06- 1 z , , , I a , , 1 1 , , 8 , 1 1 I 0.04 -“ s 8 , I , , I I I I I I ~ 0.12 : 02 + 0.10 - t-i ~ 0.08 ------. --- .#-#’$#”+# -- - -- ~-. .... a ...... ~ 0.06 - ..... ,... ~ i 48 i , I , 1 I , 1 , , , # * i , , , 1 0.04 1 I , I * # , 1 a , I I I i -1 ~$+#_$#-# Au- ---- ~... ------.~-...... ‘ 4 &*+++4 , , * , , ‘ , I 3 1 0.04 ; ‘t 8 I I I I I I 22.0 24.0 26.0 10.0 12.0 14.0 16.0 18.0 20.0 Wind speed (rniS) Fig. 7. Turbulence intensity vs. reference wind speed at Sletringen for 4 heights and 4 stability classes. Mod- el curves calculated from Eq. (14). L@vseth and Heggem, page 15 of 16 I I I I ...... —, . .-.. “Le&d ● 4i3m 090- ~ !“ 0.90- ! V42m / ,,...”””’... *20m 0.05- 0 lo% 0.05 .6” .“ o 1:: 1 E .“ cd \ ’390- .“ ~ Fit 46 m r’ ~ Fit 46 m g :0.70- --- Fit42m --- Fit 42 m Cm -- Fit20m -- Fit20m ~ ~ 0.50 - ..... Fit 10 m ..... Fit 10 m g $J 0.30- . .. Fit 5m —. . ——.Fit 5m— v @ 0.10- ~ 0.10- A 0.05 s+ 0.05 - ,,. I 0.01 0.01 - I L 1.35$ 10-$ //,’ /’, l’” I i # I.36*1O-’ 0.09- ~ .!’ 0.09 +. 1 I 0,06 ! ,, . . . . 0.06 SDO l.i . f! 0.00 ,0,0’:> .. -- ..---- . . . $>:.:: .“ ,, &0.70 .. ,-. guJ ~50 . . . i! .. . . ,, g :0,50 -...... - .- .- . ~ v &o - . .,,------f...... -. _ ...-.,-, .,. ,. . . . . ZI!3 ‘ g ~ 0.30 v ().10- ,.. .J . v 0.10 ., ,. @ 0,05-- .. . ..,.,.._;, ,------...... --- ~ 0.06 ., w i co 0,01 - ,{ . . . 0.01 \ 1.35” 10-’ 1 ili 1, I /! J, . . > 1.369104 0.00 - . . 0.90 .:, .“ F/ 0.95: :a . . . 0.06 ., >H 0!90 . . r+J * 0.70 ,.. OjJ ; 0.60 WI ~ 0’30 0 I ... . .,.. . - ~ 0.10 . . ,,. I 0.05 0.01 0.01 i I l.36*lo- ,. -,- ! I 1 I I b 1.35*1 O-’ -1 0.00 0.05 0.10 o.i6 0.20 0.25 0.30 0.00 0.06 0.10 0.15 0.20 0. Turbulence intensity Turbulence intensity . . .. . Fig. 8, “Normal plot” of the cumulative distribution of turbulence intensity at Sletringen for 4 heights and 3 stability classes. Left: Reference wind speed 14-18 rids, right 18-22 rrds, 99 .,-.-.-. ?i!r-.$,.. The influence of wind conditions on wind turbine design Experiences and suggestions from the designer point of view Ir. R.P. Luijendijk Stentec BV Hollingerstraat 14 8621 CA Heeg The Netherlands Tel: +31 515443515 Fax: +31 515442824 E-mail: [email protected] (Presentedat the Sympc6ium on Wind Condfions for Wind Tutine Design Risa, Denmark 12 snd13 April1999) Summary This paper describes some aspects of currently used wind field models and touches briefly on some solution techniques to improve these models. Some user experience is given with certification calculations for extreme wind conditions and also ideas are presented for new developments of pitch control algorithms to reduce the influence of wind conditions on the design of the wind turbines. Introduction On the basis of the material passed fonvard in the invitation of this meeting, some headlines are given by the author to form a basis for a discussion. These are summarised below and originate from the overhead sheets presented at the meeting. [t is important for the reader to know that Stentec is an engineering consultancy, specializing in wind energy technology. Over the years, Stentec has become known for its wide experience in designing and optimisation of wind turbines for a great number of national and international contractors. For this purpose, Stentec has developed several calculation and simulation programs. Our points of view are naturally centred around this work field. RL52.051007106.99 Stentec B.V. Page 1/11 100 IEA Symposium on Wind Conditions for Wind Turbine design Ir. R.P. Luijendijk ~- ‘“ >r-. % .. . Turbulence intensity The influence of the wind input, as prescribed in the current wind turbine design codes, on the design of pitch controlled wind turbines, is world-wide being evaluated. Relevant fatigue loading depends strongly on the stochastic wind field modelling, which has been evaluated during the last years. The turbine response on stochastic wind field input depends strongly on the pitch control system interacting with the tower dynamics. This in fact leads to the suggestion to define not only load sets with a varying average wind speed of 2 m/s, but also with a varying turbulence intensity. This can include killer turbulence with a once in a lifetime frequency of occurrence. [t is proposed to use at least three turbulence classes depending on the three atmospheric conditions, i.e. turbulence intensity for a stable, unstable and neutral atmosphere. For each turbulence class, the frequency of occurrence has to be defined. Probably the new WEB- DATABASE can deliver the frequency of occurrence of turbulence intensity. On the other hand, a suggestion is made to design pitch control algorithms, which effect load reduction during periods of high turbulence, strongly reducing fatigue loading. In 1998, Stentec investigated this concept in the UPC project funded by Novem. This project was a feasibility study for the design of an ultimate pitch control algorithm for the next generation of wind turbines. One of the concepts for the design of a new pitch control algorithm, is the use of adaptive peak shaving. In general, peak shaving is a method to reduce the axial force by opening the pitch angle before the nominal power has been reached (Figure 1 and Figure 2). Adaptive peak shaving is realised when the measured turbulence intensity is used to control a (tailored) pitch adjustment, so the axial force peak is shaved off and held constant. Naturally, this will also result in a certain reduction of the energy production. From the feasibility study it appears that normal peak shaving leads to an energy reduction of less than 3.3%. However, when adaptive peak shaving is used, depending on the measured turbulence intensity, then the total energy reduction can be reduced with a factor 2. It is obvious, that also for the design calculations, the frequency distribution of the turbulence intensity is necessary. Only in this way, it will be possible to design an optimum pitch algorithm which will result in a strong reduction of the tower fatigue loads in windward direction, to a level that is comparable to the sideward direction. The international standard for wind turbine generator systems (IEC 61400-1), defines only two characteristics of the turbulence intensity as a function of wind speed (Figure 3), which are limited usable for adaptive peak shaving. Furthermore, it is not clear to the author, which data these curves are based on (Figure 4). For extreme gusts it is also important to know the accompanying level of turbulence intensity and the frequency of occurrence of the gust. In the present lEC-standard, neither the turbulence intensity nor the frequency is prescribed for extreme gusts. RL52.051007106.99 Stentec B.V., 25-06-99 Page 2/1 1 101 _..- IEA Symposium on Wind Conditions for VVIndTurbine design k. R.P. Luijendijk ~---> -.. e . ...’ Wind field models w-component wind field For two different wind field models (EWS_4, made by Stentec, and Swift, made by ECN) the influence of the w-component of the wind speed on the fatigue load of wind turbines has been investigated. The conclusion is that for regular locations (flat terrain, on land) the fatigue damage of a wind turbine increases less than 5’?40,when a 3-dimensional wind field is used instead of a 2-dimensional. Future wind models It is strongly recommended to develop more sophisticated wind field models in the near future. The current mathematical wind field models are based on yearly averages of turbulence intensity, length scales and coherence, and are not satisfying physical models. Future design codes need probably more 3D physical correct wind field description, for instance to calculate the wake effects in offshore wind parks. Vortex Particle (Figure 5), or lifting Iine/surfaces based design codes also need a more realistic wind modelling, which probably could be done with stochastically generated vortex particles or line vortices. Extreme wind gust model Different standards define different extreme models, which have been accepted, among others, by Germanischer Lloyd and DIBt. One of the extreme gusts prescribed by the DIBt, is defined as load case E2.I (Figure 6). The turbine is parked and is being hit by an extreme gust with an occurrence of once in the 50 years and a simultaneous direction change of * 15°. Defined is a gust factor (relation between maximum gust amplitude and the mean wind speed) and a maximum wind acceleration of 5 m/s2. For the calculation of the tower loads, also an excitation factor has to be taken into account (of magnitude 2.5). This load case leads often to the maximum tower loads. The author was surprised to hear that nowadays other “descriptions” of extreme gusts are accepted by the well-known authorities. Hence, in stead of load case E2.I also the following description is allowed (Figure 7). Take a l-dimensional stochastic wind field from which only the longitudinal U-component will be used, because just a constant yaw misalignment has to be applied. Furthermore, a mean wind speed with a frequency of occurrence of once in 50-year has to be applied. The turbulence intensity has to be varied in such a way that somewhere in the time response, the extreme wind speed with the frequency of once in the 50 years for more than 3 seconds is exceeded. For the calculations being fully dynamic, the excitation factor for the calculation of the tower loads may be omitted. It is obvious that such a calculation method leads to arbitrary results. In the first place, there is no relation between the tuned turbulence intensity and the occurrence of the gust. In the second place, the use of longer time series will result in other extreme values. In the third place, the exclusion of the V- and W-component of the wind field has nothing to do with the reality. Finally, this method is not unique and will also lead to different results. RL52.051007106.99 Stentec B.V., 25-0%99 Page 3/1 1 102 E/4 Symposium on Wind Conditions for Wind Turbine design k. R.P. Luijendijk ~;~:~~ ~ % ..* Conclusion The designers have a need for . More information about the way of measurement of turbulence intensi~ . A better turbulence model, with varying turbulence intensity depending on e.g. atmospheric conditions; . Prescribed extreme gusts, with corresponding turbulence intens”~ . Development of a more physical wind field description. References 1. Kuik, W., U/tieme b/adhoek rege/ing (u/timate pitch control), Eindverslag van het UPC project, R052.01/01 .09.98, Stentec, Heeg, 1998 2. /EC 61400-7, Wind turbine generator systems – Part 1: Safety requirements, second edition, Switzerland, Geneva, Central OfYice of the IEC, 1998-10. 3. Germanischer L/oyd, Rules and Regulations, IV- Non-Marine Technology, Part 7 – Wind Energy, Hamburg, 1993 edition. RL52.051007106.99 Stentec B.V., 25-06-99 Page 4/1 1 103 . .. . IEA Symposium on Wind Conditions for Wind Turbine design [r. R.P. Luijendijk ‘----T a .— Responseh 0,000to400.000w.(dT=O.011 WW ...... -_-”_.-..,------...... ”-..-....-...-...-.-...... ------—------.-0-----0------W*- M= 5.W k= 15.(HI MaL=25M M.= 5J7 M M ------...... 6CmWJrPmm4 MIL=IOM5 kkn=81U2 Mw=975952 M.=2~J4 k~ MM ...... ”-- ...... -..._-.——..e...... ROtmjwlm UIL=13S35 lkal=2L26 ML=2293 m.= 249 m 265 Rclwlgbl m h = 0,00 Mm=12LKI l@L=27c60 INS= 9.65 t@ 2U4 llxbm=d ML =-249.73 Mm= 114,10 & =436059 RMS=202.74 ~ W .“..-..-...-——._ -———-— ----- ...... k!yllll]mm k= 26.15 Mm= 355,56 Ma= 799.51 Wd$.= 174M h 7L37 --. -— ~ .———— — --—- ...... Mxnmrsa -“”––––w&r-&–3j,35 Ma%=43(.42 RM’s.= 1- ~ 42U3 ...... - ....-. —--.—— .— ...... -...-..—....-...——...... FxQwkg@m ~~~~—ika = 63.a76 Max,= 145.67 W&S.= 2L66 H 7/./7 -. —.——--. . . ..-——------..-—...-....-”-...-.—------...... Stmsm)”xtlmf- ML=1131 Mm=62S0 h= 11137 RMS.=1938 Wa n~ ...... -.— . ...——______—------..... slress161Jtammm ML= -14.17 k= -3.53 Ma= 2863 m.= 3*11 ~~ -~oJ~ Figure 1: Stationary characteristics without peak shaving RL52.051007106.99 Stentec B.V., 25-06-99 Page 5/1 1 104 ... IEA Symposium on Wind Conditions for Wind Turbine design Ir. R.P. Luijendijk ‘--w .. % .*+,,.. Responsefrom 0,000to 400JOOsoc.[dT’=0.01) ..—..- .—..—- .— -~ II&L= 5(X) )l&xl=15,(KJ MalL=25JYl RMs.= 5.77 F@ Ijw Gera?mPow- k= 102.45 h= &15.74ftw=ww fw. =266~ kMf 9w7 —.-.—-..-—--—-.—— k= l&35 MWI=2L20 MalL=22J9 RM$.= 2847 m 2249 —-—--—.——--—-———.———-1..-—.. ..-.————..—...--.—.—--———.——————— ?i&M’@lm h= 0,# b= 12d8 Mm=27J8 W= 9.46 M XII .- Mh=-25L66 Mm=lR66 Mm=437M fW=m48- ~ MM — —..___ ._.. _____ —— .-.- ...... Ilyw- —-. --.—..—-. ——-.— ------—...———— ---—...... -”... Mxnm=l k= 78.63 MM= 368.49 Maxa= 43(L78 INS.= IU77 ~ 427.73 n \ -._-- ._. _--__ -_.__— .—...... —.— —.—...-....----- .----....-----..”------FxQMilgm4 ~-;~,~:––~z~~~ ~= ll#,og Mis.= 2020 M ?424 /—--. -.. -.- —..——.— ---... —. ——-—---. -—------———--—....-.....-..-...—— Strasslol-xtowarmsaML=t2J2 h= 6&L~-~l@---~$. = IW ~ 6t5J .- —____ ——... — __. ”-...... StreqolYtomr- h-.=-1w9 thIIIs w8 k= IN RW$= W Wa U3 Figure 2: Stationary characteristics with peak shaving RL52.051007106.99 Stentec B.V., 25-06-99 Page 6/1 1 IEA Symposium on Wind Conditions for Wind Turbine design Ir. R.P. Luijendijk <,&:~ . % 7...++ ao- 50- ~40- 1 & a z \ i = \ ~ 31- 0 : \ a5 5 \ i- ● zo- - . - 10- o-f o 10 20 30 40 wind spe@ Vhub(ds) Figure 3: Turbulence intensity as function of wind speed according to IEC 61400-1 RL52.051007106.99 Stentac B.V., 25-06-99 Page 7/1 1 IEA Symposium on Wind Condtions for Wind Turbine design I n6 Ir. R.P. Luijendijk ~--;- @ .. DATABASE ON WIND CHARACTERISTICS 70 60 50 a$ 0 40 s 30 20 m 0 4 8 12 16 20 24 28 Nominall wind speed [mls~ Figure 4: Database on wind characteristics (//database.afm. dtu.dk) RL52.051007106.99 Stentec B.V., 25-06-99 Page 8/1 1 107 .J.,..+. k. R.P. Luijendijk ‘~;“”. IEA Symposium on Wind Condtions for Wind Turbine design e -- E .!>.. Wake view 2s 20 ?! 1s 10 g& 1’irw OFcm issiml=CCJ s i Figure 5: Free wake modeling by NTUA (with Genuvp) Page 9/1 1 RL52.051007106.99 Stentec B.V., 25-06-99 108 IEA Symposium on Wmd Condtions for Wind Turbine design k. R.P. Luijendijk “~---;~ a >. .. Responsefrom&OOOto150.000sect{dT=O.01) 7MU MNiqlwl,lHimLm h = 28.28 lth = 4851 k = 72Z8 w.= 7.11 M/s 49,14 M1411fceQ!.m !&= 73903 Mea= 138$1 W =237.% ~.= 30.$$ ~ z31z? ) ...... wiiJl@W- I&L= 43.90 Mwl= 44095 Max= 56.10M.= 3.14 RI/$ M! ...... IW+OtWlijl?m! MkL= 117.94 Mean=125.05 k = 194,12 M$o = 18.96 M I192J ~ Figure 6: Stochastic and deterministic wind speed according to DIBt (Load case 2.1). RL52.051007106.99 Stentec B.V., 25-06-99 Page 10/1 1 109 IEA Symposium on Wind Conditions for Wind Turbine design k. R.P. Luijendijk ~:-~ % i. Responsefrom 0.000to 150,000sec. (dT=O,Ol) A$’,OJ —Ll% \...... -...-.”..L ...... -...... , Wm(;peed,huhm-m ML= 2818 Mean= 48.51 Miw= 7228 RMS.= 7.11 M/s 5607 I Figure R Enlargement of stochastic w“nd speed according to DIBt (E2.1). RL52.051007106.99 Stentec B.V., 250&99 Page 11/1 1 110 Database on Wind Characteristics http:/.www.winddata. corn/ Email: [email protected] by Gunner Chr. Larsen & Kurt S, Hansen Note: updated information are available on the web-server Database on Wind Characteristics http://www.winddata. corn/ 112 >x x 2 0 s c+ a n 4 x“ u .- c -6 0 .— a w c“ s CD a) 73 1- s — . . s c 3 cd C2 Lu — n OBJECTIVES ● to build a database consisting of a large number of time series from many different sources. ● to make available tools for efficiently searching through A4 w the data, to select the cases needed. ● to setup access to this database through Internet for online search and downloading of selected time series. Database tm Wind Characteristics http://wvvw.winddata.com/ 114 c 7s CD . a) E o .0 .-s . .-C CD E 0 C9 0 ; . a) Q .- UI m % . 0 .—s s 0 E 0 CO —.— (0 E .- .—CD Cn P .-a) Q a) .- ?5 s CD (n c1) Q x cd m c s 3 c1) co CD g -5 ~ .— u) E m“ c u) s .— .— 0 .—CD .- L m a) 5 .— CD -E co .-c CD % .—z E Q x cd g 0 .—E s w u) 7s ● ● ● SERVER ACCESS ftp server JUKEBOX . .., containing time series ———— mummnn ~ ‘R Illlllnlllull .,~!<~%.+h..:,.;!!, Web I &ver ● definitions Html ● documentation ● software ~hil~l!EEXl# ) ● user instructions Database server c site information c instrument information ● screening results ● basic statistics “’-”-”-”””------● indexed values Database bn Wind Characteristics http://www.winddata..!, corn/ 116 mal C6 CL m m—c as Q 0 Sites in Europe DATABASE ON WIND CHARACTERISTICS Sites in Europe [Norway I Sweden IDenmark IGermanyIThe Netherlands IBelgium] [ United Kingdom\ France I~ IGreece I Spain IPortuRal] Database on Wind Characteristics http://www.winddata. corn/ Database on Wind Characteristics http://www.winddata. ~om/ Database on Wind Characteristics http://www.winddata. corn/ .- . . . 120 s c o ■ — z m x.. 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T:...... ~.~ ...... 127 s 0 \ s 0 ■ — \ m z s m— E 3 c1) ■ - > 128 0 0 m ao o a co z 0 00 c) a) s 0 a) u) 2 c1) s m a) c s .— s x 3 .— c1) a . .— > .- 129 Off-line plot; T = O -600 sec Database on Wind Characteristics http://www.winddata.corn/ 131 ,, u) co E 0 m A cm 0 0 0 . s s’ c a) . . CD .-x u) u) > E JQ a) CG + ■ - CD cd Cn s co 0 ccl s II u CD co .— c co.- u 0 s s s .-+- ■- m- a) .- E E E 0 u s c co g G ● ● 132 133 134 s o 135 s 0 ‘b n 136 .C1 I I * I I I I I I 1 1 I I I i I I I I I I -0 I I m I I I I I I I do Q c) w a) .0 E 1 I I I I I I I o 1 I 1 I 8 -a z 0 0 0 0 0 o m =1- m 04 [/1‘o 137 Presented at the 2. IEA Symposium on Wind Turbine Conditions for Wind Turbine Design. April 12-13, 1999, Risa National Laboratory, Denmark. Determination of wind speed accelerations by Kurt S. Hansen Department of Energy Engineering Technical University of Denmark DK-2800 Lyngby HTTP://WWW.WINDDATA. COM/ 138 Introduction. The size of wind speed accelerations are very impottant when simulating extreme loads and blade deflections on wind turbines. This paper contains a wind speed acceleration distribution based on wind speed measurements from one site, downloaded from the Internet database [1]. Data. The time series used for this analysis are recorded at Cabauw in The Netherlands at 40 m height with a frequency of 2 Hz and consists of 485 hours of measurements. All time series are divided into 10 min. periods and trend corrected before use. The trend corrected turbulence intensity (TIK) are shown on figure 1 (average trend correction is 5%). Mean gust shape. The mean gust shape is determined as part of the /Veffiust project [2] using a windows averaging technique. The definitions refers to figure 2.: ● “moving window” size; T= 5 [see]. ● Gust rise time; T~s 5 [see]. ● Gust size; V~ [m/s]. ● Acceleration; Acc = V~/T~ [m/s/s]. ● Trend corrected standard variation; OK[m/s] Each gust is categorized in gust classes based on the normalised gust amplitude V@K (=Ns). Table1 definesthe gust classes together with the number of gusts. Table 1. vG/DK range number of gusts (gust classes) 1.5 1.25-1.75 3469 2.0 1.75-2.25 1659 2.5 2.25-2.75 763 3.0 2.75-3.25 315 3.5 3.25-3.75 106 >3.75 47 z 6359 The mean gust shapes representing gust classes 2-3.5 in the wind speed range [7-9 m/s] are shown on figure 3. Wind speed accelerations The wind speed acceleration is calculated for each gust and visualized as function of the nominal gust amplitude on Figure 4. The mean wind speed acceleration is 0.52 [m/s/s] with standard deviation of 0.30 [m/s/s]. Figure 5 shows the power density function for the wind speed accelerations for 5 different gust classes and table 2 contains the turbulence intensities (after trend correction). 139 Table 2. vG/cTK(=A/s) Conclusion The size of the mean wind speed acceleration depends on the gust size and this result is only validated for gust periods <5 seconds with a limited number of wind speed measurements. References [11 Database on Wind Characteristics Internet httm//www.winddata. corn/ [21 Wim Bierbooms et.al. Modelling of Extreme Gusts for design Calculations (~effiust) EWEC99, March 1-5, 1999, Nice, France -to be published. Trend corrected turbulence intensity 25”0- ~ 0 9nn — ------–------–------%---:- --z- ‘-”. ” -15.0 ------$ -/ k$~::~~~’ o 5 10 15 20 2( Figure 1: Trend corrected turbulence intensity. + Determination of mean gusts shape T ~ — mowing_, — window — > n a) 0 Q % v= .- ; T= ~“ T=5 S;c. ~ Time [see] b Figure 2: Determination of gust. 4 I 1 ...... ------i ...... : ~e~e-----...... _! ~ I l’I’1 ’1’ ii’ -12 -8 -4 0.4 8 1; time [see] Figure 3: Mean gust shapes for wind speed interval 7-9 mls 141 Wind speed acceleration 2EEEE1° ---- —--- ~e------—--—------0------———— ______ 00 0 *O 0 e .-t++l -Vo-w------wo-––0 0 0 0 0 --–------2------–---–-––– 00 * -- -_-_C_-–--– - I I I I I I I I I 1 I I I I I ‘1” I I 1 2 5 Normalise~ gustamplitud Cabauw, h=40m 50 -1 T Y I gust classes .. 40 +----"--k--:------+-""------"---i-"----Als=l .5 * AIS=2.O .. g 30 ...... AM-:.-.,...... ;------..--,,-.------...... ------6-- A/s=2.5 --e- /4/s=3.0 +/’ ; : : ; ----- :20 ------/,:--/--%/------,---.---..-----,...... + AIS=3.5, IY i ...... ---- ...... 10 ---A--"--R%k-:"---"-----"~ ~ — S_ 0 11’”i-’- i-’- i-’ i-’ o 3 3.5 4 0“5 ~ind sp~$d acc~eratio~”?m/s/s] Figure 5: Power densityjimction for windspeed acceleration in 5gust classes. 142 143 2d IEA Symposium on Wind Characteristics for Wkd Turbine Design RISO,Denmark, 12.-13. april 1999 List of Participants NAME ADDRESS PHONWFAXNUMBERS/ EMAIL WimBierbooms InstituteforWindEnergy Tel:(+31)152782097 DelftUniversityofTechnology Fax (+31)152785347 Stevinweg1 [email protected] 2628CNDelft TheNetherlands Teknikgruppen AB Tel: (#6) 84445120 Sweden Fax: (+46) 84445129 inca(?ha.chalmers.se Craig Hansen Windward Engineering Tel: (+1) 8012787852 4661 Holly Lane Fax: (+1) 8012724132 Salt Lake City windward@ sprynet.com UT 84117 U.S.A. Kurt S. Hansen DepL of Energy Engineering Tel: (+45) 45254318 DTU, Building 404 Fax: (+45) 45882421 2800 Lyngby [email protected] Denmark J@gen H@jstrup NEGMicon Tel: (+45) 87105262 Alsvej21 Fax: (+45) 87105001 8900Randers [email protected] Denmark Neil Kelley NREL. Tel: (+1) 3033846423 1617 Cole Boulevard Fax: (+1) 3033846901 Golden CO 80401 [email protected] U.S.A. GunnerLarsen Ris@National Laboratory Tel: (+45) 46775056 P.O.Box 49 Fax: (+45) 42372965 DK-4000 Roskilde [email protected] Denmark R.P.Luijendijk Stentec B.V. Tel: (+31) 515443515 Hollingerstraat 14 Fax (+31) 515442824 8621 CA Heeg [email protected] The Netherlands 144 J@gen L@seth NTNU, Dept. of Physics Tel: (+47) 73591856 N-7034 Trondheim Fax (+47) 73591852 Norway [email protected] B.Maribo Pedersen Dept. of Energy Engineering Tel: (+45) 45254312 Techn. University of Denmark Fax (+45) 45882421 Building 404,2800 Lyngby [email protected] Denmark Danny Winkelaar ECN Tel: (+31) 224564233 P.O.Box 1 Fax (+31) 224563214 1755 ZG Petten [email protected] The Netherlands