Statistics of Local Extremes

The gust events described in the IEC-standard are formulated as coherent gusts of an inherent deterministic character, whereas the gusts experienced in real situation are of a stochastic nature with a limited spatial extension. This conceptual differencemay cause substantial differences in the load patterns of a wind turbine when a gust event is imposed. The Newgust method is a rational way of taking wind speed gust situations into account in a design process. A corner stone in the method is a cogentalgorithm to embed a wind speed gust of a prescribed appearance in a stochastic wind field [Dragt, 1996]. However, dealing with wind turbine design, not only detailed knowledge on the spatial/time structure of the gust event is required. The probabilityof occurrence of a gust event with a given wind speed amplitude/magnitude is equally important. This theme is addressed in the present report. A theoretical expression for the probability density function associated with local extremes of a stochasticprocess is presented. The expression is basically based on the lower four statistical moments and a bandwidth parameter. The theoretical expression is subsequently verified by comparison with simulated synthetic wave/wind fields as well as with measuredwind fields covering a broad range of mean wind speed situations and terrain conditions. The simulated wave fields represents narrow band processes, whereas the wind fields represent broad-banded processes. The work reported makes part of the project"Modelling of Extreme Gusts for Design Calculations " (NEWGUST), which is co-funded through JOULEIII on contract no. JOR3-CT98-0239.