# Stochastic modelling of turbulence - with applications to wind energy

by Emil Hedevang
PhD Dissertations | December 2012

This thesis addresses stochastic modelling of turbulence with applications to wind energy in mind. The primary tool is ambit processes, a recently developed class of computationally tractable stochastic processes based on integration with respect to Lévy bases. The subject of ambit processes is still undergoing rapid development. Turbulence and wind energy are vast and complicated subjects. Turbulence has structures across a wide range of length and time scales, structures which cannot be captured by a Gaussian process that relies on only second order properties. Concerning wind energy, a wind turbine operates in the turbulent atmospheric boundary layer. In this respect, three regimes are of particular interest: modelling the turbulent wind before it interacts with the wind turbine (e.g. to be used in load simulations), modelling of the interaction of the wind with the wind turbine (e.g. to extract information about a wind turbine's production of power), and modelling the wake generated by the wind turbine so that its influence on other wind turbines further downstream in turn can be modelled (e.g. to be used in load simulations). The thesis makes the contributions listed below.

A spatial stochastic turbulence model based on ambit processes is proposed. It is shown how a prescribed isotropic covariance structure can be reproduced. Non-Gaussian turbulence models are obtained through non-Gaussian Lévy bases or through volatility modulation of Lévy bases. As opposed to spectral models operating in the frequency domain, the ambit process is formulated directly in the spatial domain. Anisotropy (e.g. in the atmospheric boundary layer flow) and inhomogeneity (e.g. the wake generated by a wind turbine) can therefore be modelled explicitly.

At the smallest scales the kinetic energy of the turbulent flow is dissipated into heat due to the internal friction caused by viscosity. An existing stochastic model, also expressed in terms of ambit processes, is extended and shown to give a universal and parsimonious description of the turbulent energy dissipation. The volatility modulation, referred to above, has previously been shown to be closely connected to the energy dissipation. The incorporation of the small scale dynamics into the spatial model opens the door to a fully fledged stochastic model of turbulence.

Concerning the interaction of wind and wind turbine, a new method is proposed to extract wind turbine power curves from low-frequency data. The method improves over the current IEC~61400-12-1 industry standard by being capable of incorporating the turbulence intensity into the estimation procedure.

Finally, three existing simple wake models for the average flow inside a wind farm are evaluated against measured wind power data at time scales from 15 sec to 10 min. The wake models are shown to be incapable of capturing the dynamics of wakes.

Format available: PDF (6 MB)
Thesis advisor: Jürgen Schmiegel and Martin Greiner