Uncertainty quantification of offshore wind farms using Monte Carlo and sparse grid

ABSTRACT

The power produced by an offshore wind farm is subject to multiple uncertainties, such as volatile wind, turbine performance wear, and availability losses. Knowledge about the propagation of these uncertainties and their effect on the produced power is crucial in the design stage of a wind farm. Due to the multitude of uncertainties, an analysis requires high-dimensional numerical integration to determine these parameter sensitivities. Such an analysis has not been done in the current literature for the full set of parameters. In this work, a thorough analysis of all uncertainties is provided, modeled from several years of collected data from the existing wind farms Horns Rev 1, DanTysk, and Sandbank. The analysis reveals four major parameters, allowing the other parameters to be neglected in future measurement data acquisitions and sensitivity analysis processes. Furthermore, the accuracy of several Uncertainty Quantification techniques is analyzed and a recommendation for future analysis is given.

KEYWORDS:

• Offshore wind farm
• Uncertainty Quantification
• Quasi-Monte Carlo
• Stochastic Collocation
• Sensitivity Analysis

Acknowledgments

The authors thank the Federal Ministry for Economic Affairs and Energy BMWi (Bundesministerium für Wirtschaft und Energie) and the Project Executing Organization PTJ (Projektträger Jülich) for making the FINO3 data available. The authors thank Adam Verhoeven-Mrosek from Vattenfall Europe Windkraft GmbH for making offshore wind farm data available.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Trying to approximate the volume of a unit sphere by drawing random samples from a unit cube and determining if the sampled point is inside the sphere works well in two or three dimensions, but for arbitrary dimension $d$ the ratio of points inside of the sphere to the total number of samples converges to the cube’s volume divided by $2^d$. This leads to the conclusion that the error constant, which has been omitted in the $\mathcal{O}(\cdot )$ notation, rapidly increases with dimension $d$.

² More information: https://powerplants.vattenfall.com/horns-rev

³ https://powerplants.vattenfall.com/dantysk

⁴ https://powerplants.vattenfall.com/sandbank

⁵ https://www.fino3.de/en/