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Stochastic Modelling of Wind Speed Power Production Correlations
Author(s) -
Gottschall Julia,
Anahua Edgar,
Barth Stephan,
Peinke Joachim
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610313
Subject(s) - langevin equation , wind speed , turbine , wind power , statistical physics , power (physics) , noise (video) , control theory (sociology) , physics , mathematics , computer science , meteorology , engineering , electrical engineering , quantum mechanics , thermodynamics , control (management) , artificial intelligence , image (mathematics)
Abstract Based on measurements we investigate the velocity‐power characteristic of a 2 MW wind turbine. We apply a stochastic analysis where we describe the evolution of the power output with a Langevin equation, with special respect to short‐time fluctuations in wind speed. Standard procedures, such as the IEC 61400‐12 standard, are limited due to the fact that only mean values over several minutes of wind speed and power output are considered. According to this, short‐time dynamics of wind and power fluctuations are usually not taken into account. We introduce an improved method which enables us to extract these dynamics of the power characteristic from the measured data. In particular, we get the response dynamics of the power L ( u ( t )) via the estimation of Kramers‐Moyal coefficients, describing its evolution in time $ \dot L $ ( t ) with a Langevin equation where we separate the power output into a relaxation and a noise part. A fixed‐point analysis provides the required power characteristic. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)