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.