EUROPEAN WIND ENERGY CONFERENCE AND EXHIBITION, NICE, FRANCE, MARCH 1-5, 1999
VARIABILITY OF EXTREME FLAP LOADS DURING TURBINE OPERATION Knut O. Ronold Det Norske Veritas P.O. Box 300 N-1322 Høvik, NORWAY phone: +47-67577311 e-mail:
[email protected]
Gunner C. Larsen Wind Energy and Atmospheric Physics Dept. Risø National Laboratory DK-4000 Roskilde, DENMARK phone: +45-46775056 e-mail:
[email protected]
ABSTRACT: The variability of extreme flap loads is of utmost importance for design of wind-turbine rotor blades. The flap loads of interest consist of the flapwise bending moment response at the blade root whose variability in the short-term, for a given wind climate, can be represented by a stationary process. A model for the short-term bending moment process is presented, and the distribution of its associated maxima is derived. A model for the wind climate is given in terms of the probability distributions for the 10-minute mean wind speed and the standard deviation of the arbitrary wind speed. This is used to establish the distribution of the largest flapwise bending moment in a specific reference period, and it is outlined how a characteristic bending moment for use in design can be extracted from this distribution. The application of the presented distribution models is demonstrated by a numerical example for a site-specific wind turbine. KEYWORDS: Wind climate − wind speed variability − extreme response
1. INTRODUCTION The verification of the structural integrity of a wind turbine involves analyses of fatigue loading as well as extreme loading of the different structural components. With the trend of persistently growing turbines, the extreme loading seems to become relatively more important. Hence, also the natural variability of such extreme loads gain in importance as a topic that needs thorough attention to ensure an acceptably low failure probability. Several extreme failure modes need consideration, of which the extreme loading under turbine operation is one of significant importance. During operation, the turbine loading consists of a periodic deterministic part and a superimposed stochastic part. The mean wind field and gravity cause the deterministic part. The stochastic part originates from the natural variability of the wind turbulence components. A methodology for representation of the extreme flapwise loading of a rotor blade and its natural variability is proposed. The procedure is based on extensive measurements on a turbine sited in a flat and homogeneous terrain, and it provides probabilistic models for the wind loading and its transfer to extreme responses, conditional on the wind climate. The wind climate is parameterized by only two wind field characteristics - the 10-minute mean wind speed and the standard deviation of the wind speed, both referring to the hub height of the wind turbine. The distribution of the global extreme in a 1-year reference period is finally established by assuming the mean wind speed to be Weibull-distributed in the long term with parameters as given in the IEC−61400 code.
2. THEORY The wind climate that governs the loading of a wind turbine and its rotor blades is commonly described by the 10minute mean wind speed U10 at the site in conjunction with the standard deviation σU of the wind speed. The
long-term distribution of the 10-minute mean wind speed can be taken as a Weibull distribution u FU10 (u ) = 1 − exp(−( ) k ) A
(1)
in which k and A are site- and height-dependent coefficients. Only normal operation of the wind turbine is considered. The turbine will stop whenever the cut-out wind speed uC is exceeded. For analysis of failure in ultimate loading in the normal operating condition, it is therefore of interest to represent the 10-minute mean wind speed by a Weibull distribution, whose upper tail is truncated at the cut-out speed, u 1 − exp(−( ) k ) A FU10 (u ) = ; uC k 1 − exp(−( ) ) A
0
