Abstract
ABSTRACTThis study examines the various sources to the uncertainties in the application of two widely used extreme value distribution functions, the generalized extreme value distribution (GEVD) and the generalized Pareto distribution (GPD). The study is done through the analysis of measurements from several Danish sites, where the extreme winds are caused by the Atlantic lows. The simple extreme wind mechanism here helps us to focus on the issues mostly related to the use of limited wind measurements. Warnings are flagged and possible solutions are discussed. Thus, this paper can be used as a guideline for applying GEVD and GPD to wind time series of limited length. The data analysis shows that, with reasonable choice of relevant parameters, GEVD and GPD give consistent estimates of the return winds. For GEVD, the base period should be chosen in accordance with the occurrence of the extreme wind events of the same mechanism. For GPD, the choices of the threshold, the definition of independent samples and the shape factor are interrelated. It is demonstrated that the lack of climatological representativity is a major source of uncertainty to the use of both GEVD and GPD; the information of climatological variability is suggested to be extracted from global or mesoscale models. © 2013 The Authors. Wind Energy published by John Wiley & Sons, Ltd.
Highlights
In wind energy industry, the turbine design wind needs to be estimated in order to ensure that winds will not exceed the turbine’s design specification and to avoid turbine design being unrealistically over-specified
It is generally considered that numerically modeled climate data can reasonably provide such a climatological variability, but these data are troubled with the smoothing effect of models that leads to a lack of variability at strong winds, which is crucial for the extreme wind estimation.[5]
One of the sources of uncertainty that is common in both generalized extreme value distribution (GEVD) and generalized Pareto distribution (GPD) is the determination of the shape factor k as in equations (1) and (9)
Summary
The turbine design wind needs to be estimated in order to ensure that winds will not exceed the turbine’s design specification and to avoid turbine design being unrealistically over-specified. In order to compensate for the problems with insufficient extreme wind samples caused by short data series length, it is popular to lower the wind speed threshold for more exceedances in connection with the use of GPD or to shorten the basis period in order to get more periodic wind maxima in connection with the use of GEVD These simple attempts can, violate the pre-conditions for applying these distribution functions, and it is necessary to examine the extent to which the measurements of only a limited number of years can be used for estimating the 50 year wind. A list of variables and abbreviations is given in Table I for readability
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