An engineering model for 3-D turbulent wind inflow based on a limited set of random variables

Abstract

Emerging stochastic analysis methods are of potentially great benefit for wind turbine power output and loads analysis. Instead of requiring multiple (e.g. 10min) deterministic simulations, a stochastic approach can enable a quick assessment of a turbine's long-term performance (e.g. 20-year fatigue and extreme loads) from a single stochastic simulation. However, even though the wind inflow is often described as a stochastic process, the common spectral formulation requires a large number of random variables to be considered. This is a major issue for stochastic methods, which suffer from the curse of dimensionality leading to a steep performance drop with an increasing number of random variables contained in the governing equations. In this paper a novel engineering wind model is developed which reduces the number of random variables by 4-5 orders of magnitude compared to typical models while retaining proper spatial correlation of wind speed sample points across a wind turbine rotor. The new model can then be used as input to direct stochastic simulations models under development. A comparison of the new method to results from the commercial code TurbSim and a custom implementation of the standard spectral model shows that for a 3-D wind field, the most important properties (cross-correlation, covariance, auto- A nd cross-spectrum) are conserved adequately by the proposed reduced-order method.