W.A.A.M. Bierbooms

Stochastic gust model for design calculations of wind turbines

Abstract A new probabilistic method has been developed in order to determine the long-term distribution of the extreme response of wind turbines. The probabilistic method relies on the quick determination of the response to a single gust, with a given amplitude, by means of the so-called constrained simulation. A constrained simulation corresponds to the addition, in a special manner, of turbulence and a deterministic part (which resembles the autocorrelation function of turbulence). The stochastic gusts produced in this way has been denoted NewGust and are, in a statistical sense, not distinguishable from gusts selected from a (very long) stochastic time series, with the same amplitude.

Influence of different wind profiles due to varying atmospheric stability on the fatigue life of wind turbines

Offshore wind energy is being developed on a very large scale in the European seas. The objective of developing wind energy offshore is to capture greater wind speeds than are encountered onshore and as a result more energy. With this also come more challenges in the design of wind turbines due to the hostile offshore environment. Currently the standards for offshore wind turbines prescribe a site specific design for the support structures and the design for the rotor nacelle assembly according to onshore standards. Wind turbines are designed to withstand fatigue and ultimate loads. For the fatigue loading several input conditions have been prescribed, amongst which wind profile is one of them. Wind profile is represented by power law or logarithmic law as given in the standards. A neutral stability of the atmosphere is considered while obtaining the wind profile using the logarithmic law. In this paper the atmospheric stability is varied in order to estimate different wind profiles and simulations are run in Bladed to check its influence on the fatigue damage at the blade root. The variations in the atmospheric stability has been taken into account by using some typical values of Obukhov length. From steady state simulations it has been found that atmospheric stability is important for fatigue damage. The analysis showed that variation in the distribution of atmospheric stability causes large variations in the fatigue damage for different sites. Thus, it is worthwhile to carry out a full scale study using the turbulent winds and real data for wind turbine and environmental conditions.

A comparison between unsteady aerodynamic models

Abstract This paper describes two methods to deal with unsteady aerodynamics. The results of the methods are compared with dynamic wind tunnel measurements on a NACA 0012 aerofoil. Furthermore simulations of the dynamic behaviour of a flexible rotor are presented using both methods.

Verification of the mean shape of extreme gusts

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 article 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 gust shape determined from both simulated and measured turbulence. The resemblance is remarkably good, which demonstrates the viability of the NewGust method. Copyright

Distribution of extreme gust loads of wind turbines

Extreme gust loading of wind turbines has been treated deterministically as prescribed in the design codes, without taking into account the stochastic property of the wind turbulence. In this paper a rational approach to quantify the variability of the gust loading of a wind turbine is presented and a new approach on the simulation of the extreme gusts with constrained simulations is proposed. The results from simulations with deterministic gusts and stochastic gusts are compared. The distribution of the extreme response due to extreme gust is derived using the constrained gust approach. The influence on response of a spatial gust and a point gust is studied. The effect of the gust centre on the turbine response has also been taken into account. The response distribution at a certain mean wind speed is determined with full-scale time domain simulation and compared to the distribution derived with constrained gusts. The method is demonstrated using the turbine model of a prototype wind turbine; for this reason the result is preliminary and generalization should be made with care.

Definition of the equivalent atmospheric stability for wind turbine fatigue load assessment

In this paper the dependence of wind turbine fatigue loads on atmospheric stability is assessed. It is shown that fatigue loads depend strongly on stability, and highest loads occur for very unstable conditions. For a given hub height wind speed one can dene an equivalent atmospheric stability that corresponds to the same cumulative loads as if one performs an infinite amount of simulations for all stability conditions that may occur. It is shown that stability, conditionalised to hub height wind speed, is approximately normally distributed and the equivalent stability corresponds well to the mean stability for a given hub height wind speed. If one follows the IEC guidelines for offshore sites, neglecting atmospheric stability, one will compute higher cumulative lifetime fatigue loads (~ 10%). This overestimation is caused by conservatism in both wind shear and turbulence levels, which is explicitly shown for the turbulence levels analyzed in this paper

Specific gust shapes leading to extreme response of pitch- regulated wind turbines

Via so-called constrained stochastic simulation gusts can be generated which satisfy some specified constraint. Constrained stochastic simulation is based on conditional densities of normal random variables and it has previously been applied to generate maximum amplitude gusts and velocity jumps. In this paper it is used in order to generate specific wind gusts which will lead to local maxima in the response of (pitch-regulated) wind turbines. The method is demonstrated on basis of a linear model of a wind turbine, inclusive pitch control. The mean gust shape as well as the mean shape of the response, for some gust amplitude, is shown. By performing many simulations (for given gust amplitude) the conditional distribution of the response is obtained. By a weighted average of these conditional distributions over the probability of the gusts the overall distribution of the response can be obtained. Analytical expressions for the conditional distribution of the response (for given gust amplitude) as well as the overall distribution are specified. These form an ideal test case of tools (e.g. fitting to an extreme value distribution) to be used for non-linear wind turbine models. The application of the above method on a non-linear model of a wind turbine has still to be done.

Modelling of Gusts for the Determination of Extreme Loads of Pitch Regulated Wind Turbines

A probabilistic method has been applied to determine the extreme response of pitch regulated wind turbines caused by wind speed gusts. It is assumed that the extreme loading for pitch regulated turbines is caused by gusts with an extreme rise time rather than an extreme gust amplitude. A special kind of wind field simulation, so-called constrained stochastic simulation, is dealt with in order to generate the desired gusts. It can be stated that the stochastic gusts produced in this way are, in a statistical sense, not distinguishable from gusts selected from a (very long) time series. The theoretical mean gust shape, as well as the probability of occurrence of gusts, has been verified by measurements for modest gusts; but not, as yet, severe gusts. For the reference turbine the 50-year blade root flapping moment turned out to be much higher than the response on the IEC operating gust; this should be verified for commercial turbines. The method is formulated in such a way that it can easily be implemented in state-of-the-art design packages for wind turbine design as used by the industry. It should be possible to extend the method to a spatial gust. The proposed more accurate description of extreme loading will enable wind turbine manufacturers to build more reliable and optimised wind turbines.

Assessing the Severity of Wind Gusts with Lidar

Lidars have gained a lot of popularity in the field of wind energy, partly because of their potential to be used for wind turbine control. By scanning the oncoming wind field, any threats such as gusts can be detected early and high loads can be avoided by taking preventive actions. Unfortunately, lidars suffer from some inherent weaknesses that hinder measuring gusts; e.g., the averaging of high-frequency fluctuations and only measuring along the line of sight). This paper proposes a method to construct a useful signal from a lidar by fitting a homogeneous Gaussian velocity field to a set of scattered measurements. The output signal, an along-wind force, acts as a measure for the damaging potential of an oncoming gust and is shown to agree with the rotor-effective wind speed (a similar control input, but derived directly from the wind turbine’s shaft torque). Low data availability and the disadvantage of not knowing the velocity between the lidar beams is translated into uncertainty and integrated in the output signal. This allows a designer to establish a control strategy based on risk, with the ultimate goal to reduce the extreme loads during operation.

Estimating atmospheric stability from observations and correcting wind shear models accordingly

Atmospheric stability strongly influences wind shear and thus has to be considered when performing load calculations for wind turbine design. Numerous methods exist however for obtaining stability in terms of the Obukhov length L as well as for correcting the logarithmic wind profile. It is therefore questioned to what extend the choice of adopted methods influences results when performing load analyses. Four methods found in literature for obtaining L, and five methods to correct the logarithmic wind profile for stability are included in the analyses (two for unstable, three for stable conditions). The four methods used to estimate stability from observations result in different PDFs of L, which in turn results in differences in estimated lifetime fatigue loads up to 81%. For unstable conditions hardly any differences are found when using either of the proposed stability correction functions, neither in wind shear nor in fatigue loads. For stable conditions however the proposed stability correction functions differ significantly, and the standard correction for stable conditions might strongly overestimate fatigue loads caused by wind shear (up to 15% differences). Due to the large differences found, it is recommended to carefully choose how to obtain stability and correct wind shear models accordingly.