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Grappling with gusts

The recent blade failures in a Welsh wind farm have put the spot light on the importance of forecasting extreme gusts and perhaps caused some concern amongst developers monitoring wind strengths at about 50 prospective wind farm sites in the region. The failures (Windpower Monthly, January 1994) came at a crucial time, with many developers also about to submit bids for the next round of the Non-Fossil Fuel Obligation, now extended to include Scotland and Northern Ireland. Not only are these the windiest regions of the British Isles, but also of the whole of Europe. Are the winds there so furiously unpredictable that the risk of developing Europe's windiest sites becomes unacceptably high?

Extreme winds do not, perhaps, receive as much attention as they deserve -- out of the two hundred plus papers presented at the European Wind Energy Conference in Germany a year ago there were no papers discussing the topic. Although literature abounds on the calculation of energy yield there is relatively little on the topic of extreme winds, possibly because wind energy's largest testing ground, California, has not had to cope with severe gusts. Whether this means the wind industry has researched the subject to its satisfaction, is complacent, or simply daunted by the sheer complexity of the mathematical concepts is a matter of conjecture.

Fortunately, however, we can look to civil engineering practice to discover the underlying science and, to be fair, this is reflected in the certification rules for wind turbines. The need to predict extreme winds is not new -- any large and complex structures are subject to the fury of the elements and the design of such structures has evolved over a number of years. In some respects wind turbines are actually at an advantage compared with buildings, bridges, and the like, since loads can be reduced in extreme winds by feathering blades or turning rotors out of the wind. However, it is vital to be able to predict the relevant gust strengths and be assured that wind turbines can survive them.

Do gusts matter?

Yes. Although considerable attention is paid -- and quite rightly -- to wind turbulence, the design of a wind turbine is also influenced to a considerable degree by the need to withstand extreme gusts. The balance depends on the relative fatigue strengths and ultimate tensile strengths of the materials concerned. If wood blades are used then extreme gust loads are more important than if steel blades are used. In broad terms, the size of wood blades is mainly influenced by the need to withstand the "extreme wind" loads; with steel it is the fatigue calculations which are likely to be the more crucial. However, whatever the material, the designer must ensure that blades can withstand the worst the wind can throw at them.

The wind is a very capricious beast and although many attempts have been made to describe its behaviour by the use of neat equations, it is rare that these are able to account for all its possible antics. For example, the probability distribution functions used to calculate wind turbine energy yields are at best a reasonable fit which describes the variation of wind. Although these functions (such as the Rayleigh) have been used to predict extreme winds there are more accurate methods of doing so. It is here that wind energy enters into the world of "extreme value statistics," which is a branch of mathematics in itself. Some of the concepts are rather daunting.

Tackling the statistics

Gust data take longer to assemble than energy yield data simply because, by definition, they need to be accumulated over a period of years if they are to have any relevance. Extreme gust data cannot generally be derived from mean wind speed data. Maps showing the 50 year return period levels for gusts are available. Locations as far apart as Britain, Germany and Australia all show relevant speeds around 45 m/s in the centre of the country, reaching 50 m/s nearer the coast and 60 m/s in a few very exposed locations.

Although there is a weak correlation (gust levels rise with increase of site mean wind speed) there is a very wide spread and, even for a specific site, the ratio of the gust values to the mean wind speed can vary from year to year. This is illustrated at Lowther Hill in Scotland (fig 1), 750m sea above level. This site, which features in the European Wind Atlas, is one of the windiest in the British Isles.

The three second gust at a height of 10 m is widely, but not universally, used as a starting point in the design of structures such as wind turbines. The reasoning behind the use of a three second averaging period is quite simple; it is the gust most likely to damage the structure. If the averaging period were longer, the averaged values are likely to conceal higher velocity gusts; if the averaging period were shorter, the gust would probably be insufficiently large to envelop the whole of a structure. However, some design codes use two or five second gusts and the national building code of Canada uses peak mean hourly speeds for a 30 year return period from which peak gust speeds are derived by multiplying by a factor of 1.4.

The first step in assembling gust data into a usable form is to analyse extreme wind data over a period of many years -- at least ten and preferably 20 or more. The data are smoothed and a characteristic "probability of exceedance curve" is drawn (fig 2). The next stage in the process -- which intuitively seems simple but in practice takes a whole page of mathematics -- is to quantify the gust return periods, using the probability exceedance data. The curve shown (fig 3) was derived for a location in central England but is also typical for large areas of Australia, Canada Denmark, Germany and the Netherlands. The three second gust with a 50 year return period has in this case a value of about 46 m/s. We need, however, to stop here and think precisely what this means. There are three key issues:

¥ the 46m/s gust has a 63% probability of being exceeded in 50 years so that a structure, if designed to withstand this velocity -- and no more -- has a 63% chance of failure.

¥ the gust is sustained for a period of three seconds

¥ most gust data are based on measurements at a height of ten metres and corrections must be applied to allow for the height of the structure and the nature of the terrain.

This last point is important. Corrections need to be applied to the baseline values shown on the maps to allow for the height of the structure, the degree of exposure and the topography. The corrections are complicated and leave room for error, but for most wind power sites, gusts with a 63% probability of recurring within 50 years are likely to be stronger than 46 m/s. There are several correction techniques to establish likely gust strength at wind sites, but there is general agreement that the highest gusts will be found near the edge of steep escarpments, where they may be up to 30% or more above the baseline values. Higher up, however, the amplification is generally less and wind turbines, designed for strong winds, are therefore less vulnerable than structures near the ground. For a wind turbine on a hill top, with a hub height of 30 m, an extreme correction factor would be about 1.2. In other types of terrain, gust levels at turbine hub heights around 30 m will be about 10% higher than the reference values, say 50 m/s.

Safety Margins

A 63% chance of failure at 50 m/s seems too high and the next step in the design process is to reduce the risk to an acceptable level. The most common -- but by no means the only way forward -- is to design structures on the basis of 50 year return period for three second gusts and then to build in a safety factor. This ensures that failure does not occur until the stresses in the structure reach, say, 1.2 times the stresses appropriate to the 50 year gust level. Since wind loads increase as the square of wind velocity this is equivalent to raising design gust levels by about 15%. Hence, if the design process started with a gust speed of 50 m/s this would be implicitly raised to 57.5 m/s and actually reduces the risk quite dramatically. Another page of maths enables gust return periods to be linked to risk (fig. 4) and, using the data plotted in the diagram, the use of a gust level of 57.5 m/s instead of 50 m/s would effectively raise the return period from 55 years to around 300 years and reduce the risk level from 0.3 to around 0.07.

It must be emphasised that these are typical values only and design codes vary. Early machines designed for the Californian passes -- where the winds are less severe -- were made for survival wind speeds around 50 m/s, but most medium size machines are now designed for survival speeds of 55-70 m/s. Moreover, wind turbine designers are free to build in additional safety margins if they so wish. Wind turbines can be designed for 100 m/s gusts if necessary, but would be very heavy -- and hence costly. There is a balance between acceptable risk and cost -- just as there is with buildings, aircraft and all civil and mechanical plant. In areas of the world beset by tornadoes, it is unlikely wind turbines will be designed to withstand these, but to be lowered before being struck by wind speeds which are believed to reach around 135 m/s in the centre of a vortex. This approach is being tried in Japan.

The term "survival wind speed" is used in connection with extreme winds. The definition in the glossary of terms issued by the International Energy Agency does not make it clear whether or not this is the speed at which a turbine finally snaps. The definition reads: "The maximum speed a WT in automatic, unattended mode can sustain and still remain operable." In the Netherlands's, the type-certification criteria of the national laboratory, ECN, links survival speed to a gust with a probability of 0.01 (about 58 m/s, using the sample data discussed earlier). Hopefully the new European Safety Standard will clarify this point, but it must be emphasised that the survival wind speed is not necessarily the speed at which a wind turbine fails.

It should also be remembered that unlike many structures, to a certain extent wind turbines can escape from the worst excesses of the elements. The blades of variable pitch machines can be "feathered" (turned edge-on to the wind) which reduces the loads by a factor of about 40. However, there is no escape for the tower, which must always be designed to withstand the full fury of the worst winds. Certification rules, though, do not necessarily allow the benefits of feathering to be taken into account as it is possible that a failure of the pitch change mechanism might occur which would leave the blades in their running position and hence exposed to the higher loads.

Gust data -- no need for undue concern

Detailed data in Britain are logged by over 100 wind measuring stations. Significantly, though, there are only 13 recorded measurements of gusts over 50 m/s during the ten year period from 1982 to 1991 (see map and table). Perhaps this indicates, after all, that there is no need for undue concern. An analysis of the data in the table shows:

¥ five of the sites, and eight of the gusts over 50 m/s, were in Scotland, but only two at low level (Fair Isle and Fraserburgh)

¥ five sites are located at an altitude over 300 m

¥ at the hilltop sites, none of the measured gusts exceeds the baseline levels by more than 20% -- this confirms the importance of topographical effects, but indicates that they may not be unduly severe

¥ only three locations (Fraserburgh, Fair Isle and Rhoose) are in regions likely to be suitable for wind turbines and the gusts at these sites all exceeded the baseline levels for the locations concerned. The remaining sites listed are too high and/or remote for wind power development.

Although gusts at higher levels than the standard anemometer height of 10 m may exceed the measured values at level sites, the indications are that wind turbines designed for survival speeds around 60 m/s -- provided safety factors are built in -- should, in most locations, survive the rigours of the British climate, since most of the inland sites are less exposed than the stations at Cairngorm and Lowther Hill. Coastal sites in Scotland and its islands will, however, need to be examined very carefully, but the 55 kW machine which has operated on Fair Isle for about ten years shows that even the most severe sites need not be a deterrent to a well-engineered machine.

The greenhouse effect

As the measured gusts at three sites in the table exceed the reference levels, this raises the question as to whether gusts are generally becoming more severe. Accepting that the greenhouse effect is fact and not supposition, its seems probable that stronger winds could also be a symptom of global warming. There is some evidence to support this.

Modelling by the University of East Anglia has produced conflicting estimates -- one model says, yes, the evidence is there, the other says, no, it is not. An examination of recent wind records yielded a similar conclusion; two sites reported higher mean winds (by 0.1 m/s) for the decade 1980-89, compared with 1970-79; one site reported a lower mean, by 0.2 m/s. However, when ten annual peak hourly gust levels for three coastal sites (south, west and east facing) were averaged for each decade, each one yielded a higher average for 1980-89, by 7%, 7% and 1%, respectively. Data for two of these sites are shown in fig 5.

If gusts are getting stronger -- and only time will tell -- the reference maps will need to be redrawn and the machines now operating may need to withstand more extreme gusts -- over 50 m/s, say. This should not present problems for most machines, but developers should be aware of this potential trend.

The blade failures in Wales may trigger a resurgence of interest in the estimation and prediction of extreme gusts. Since most of the meteorological records -- from the UK and elsewhere -- are derived from measuring stations at relatively low level, there may be a case for looking carefully at data on increases of gust strengths with altitude. An examination of UK records seems to indicate that gust strengths increase with altitude -- a correction factor for altitude was advocated at one stage in both the UK and New Zealand -- and a more explicit method of taking into account this important parameter may be required.

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