A generalized framework for reduced-order modeling of a wind turbine wake
Abstract
A reduced-order model for a wind turbine wake is sought from large eddy simulation data. Fluctuating velocity fields are combined in the correlation tensor to form the kernel of the proper orthogonal decomposition (POD). Proper orthogonal decomposition modes resulting from the decomposition represent the spatially coherent turbulence structures in the wind turbine wake; eigenvalues delineate the relative amount of turbulent kinetic energy associated with each mode. Back-projecting the POD modes onto the velocity snapshots produces dynamic coefficients that express the amplitude of each mode in time. A reduced-order model of the wind turbine wake (wakeROM) is defined through a series of polynomial parameters that quantify mode interaction and the evolution of each POD mode coefficients. The resulting system of ordinary differential equations models the wind turbine wake composed only of the large-scale turbulent dynamics identified by the POD. Tikhonov regularization is used to recalibrate the dynamical system by adding additional constraints to the minimization seeking polynomial parameters, reducing error in the modeled mode coefficients. The wakeROM is periodically reinitialized with new initial conditions found by relating the incoming turbulent velocity to the POD mode coefficients through a series of open-loop transfer functions. The wakeROM reproduces mode coefficients to within 25.2%,more »
- Authors:
-
- Portland State Univ., Portland, OR (United States); National Renewable Energy Lab. (NREL), Golden, CO (United States)
- Portland State Univ., Portland, OR (United States)
- Univ. of Utah, Salt Lake City, UT (United States)
- IFE, Kjeller (Norway); Univ. of Oslo, Oslo (Norway)
- Publication Date:
- Research Org.:
- National Renewable Energy Lab. (NREL), Golden, CO (United States)
- Sponsoring Org.:
- National Science Foundation (NSF); Research Council of Norway; USDOE
- OSTI Identifier:
- 1441172
- Report Number(s):
- NREL/JA-5000-71684
Journal ID: ISSN 1095-4244
- Grant/Contract Number:
- AC36-08GO28308
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Wind Energy
- Additional Journal Information:
- Journal Volume: 21; Journal Issue: 6; Journal ID: ISSN 1095-4244
- Publisher:
- Wiley
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 17 WIND ENERGY; 42 ENGINEERING; dynamical system; proper orthogonal decomposition; reduced-order model; wind turbine wake
Citation Formats
Hamilton, Nicholas, Viggiano, Bianca, Calaf, Marc, Tutkun, Murat, and Cal, Raul Bayoan. A generalized framework for reduced-order modeling of a wind turbine wake. United States: N. p., 2018.
Web. doi:10.1002/we.2167.
Hamilton, Nicholas, Viggiano, Bianca, Calaf, Marc, Tutkun, Murat, & Cal, Raul Bayoan. A generalized framework for reduced-order modeling of a wind turbine wake. United States. https://doi.org/10.1002/we.2167
Hamilton, Nicholas, Viggiano, Bianca, Calaf, Marc, Tutkun, Murat, and Cal, Raul Bayoan. Wed .
"A generalized framework for reduced-order modeling of a wind turbine wake". United States. https://doi.org/10.1002/we.2167. https://www.osti.gov/servlets/purl/1441172.
@article{osti_1441172,
title = {A generalized framework for reduced-order modeling of a wind turbine wake},
author = {Hamilton, Nicholas and Viggiano, Bianca and Calaf, Marc and Tutkun, Murat and Cal, Raul Bayoan},
abstractNote = {A reduced-order model for a wind turbine wake is sought from large eddy simulation data. Fluctuating velocity fields are combined in the correlation tensor to form the kernel of the proper orthogonal decomposition (POD). Proper orthogonal decomposition modes resulting from the decomposition represent the spatially coherent turbulence structures in the wind turbine wake; eigenvalues delineate the relative amount of turbulent kinetic energy associated with each mode. Back-projecting the POD modes onto the velocity snapshots produces dynamic coefficients that express the amplitude of each mode in time. A reduced-order model of the wind turbine wake (wakeROM) is defined through a series of polynomial parameters that quantify mode interaction and the evolution of each POD mode coefficients. The resulting system of ordinary differential equations models the wind turbine wake composed only of the large-scale turbulent dynamics identified by the POD. Tikhonov regularization is used to recalibrate the dynamical system by adding additional constraints to the minimization seeking polynomial parameters, reducing error in the modeled mode coefficients. The wakeROM is periodically reinitialized with new initial conditions found by relating the incoming turbulent velocity to the POD mode coefficients through a series of open-loop transfer functions. The wakeROM reproduces mode coefficients to within 25.2%, quantified through the normalized root-mean-square error. Furthermore, a high-level view of the modeling approach is provided as a platform to discuss promising research directions, alternate processes that could benefit stability and efficiency, and desired extensions of the wakeROM.},
doi = {10.1002/we.2167},
journal = {Wind Energy},
number = 6,
volume = 21,
place = {United States},
year = {Wed Jan 31 00:00:00 EST 2018},
month = {Wed Jan 31 00:00:00 EST 2018}
}
Web of Science
Works referenced in this record:
Polynomial identification of POD based low-order dynamical system
journal, January 2006
- Perret, Laurent; Collin, Erwan; Delville, Joël
- Journal of Turbulence, Vol. 7
Wind plant power optimization through yaw control using a parametric model for wake effects-a CFD simulation study: Wind plant optimization by yaw control using a parametric wake model
journal, December 2014
- Gebraad, P. M. O.; Teeuwisse, F. W.; van Wingerden, J. W.
- Wind Energy, Vol. 19, Issue 1
Dynamic mode decomposition of numerical and experimental data
journal, July 2010
- Schmid, Peter J.
- Journal of Fluid Mechanics, Vol. 656
Equation-free/Galerkin-free POD-assisted computation of incompressible flows
journal, August 2005
- Sirisup, Sirod; Karniadakis, George Em; Xiu, Dongbin
- Journal of Computational Physics, Vol. 207, Issue 2
Investigation of the incoming wind vector for improved wind turbine yaw-adjustment under different atmospheric and wind farm conditions
journal, February 2017
- Cortina, G.; Sharma, V.; Calaf, M.
- Renewable Energy, Vol. 101
Low-Dimensional Representations of Inflow Turbulence and Wind Turbine Response Using Proper Orthogonal Decomposition
journal, July 2005
- Saranyasoontorn, Korn; Manuel, Lance
- Journal of Solar Energy Engineering, Vol. 127, Issue 4
Feedback shear layer control for bluff body drag reduction
journal, July 2008
- Pastoor, Mark; Henning, Lars; Noack, Bernd R.
- Journal of Fluid Mechanics, Vol. 608
PIPs and POPs: The reduction of complex dynamical systems using principal interaction and oscillation patterns
journal, January 1988
- Hasselmann, K.
- Journal of Geophysical Research, Vol. 93, Issue D9
Identification strategies for model-based control
journal, July 2013
- Cordier, Laurent; Noack, Bernd R.; Tissot, Gilles
- Experiments in Fluids, Vol. 54, Issue 8
A hierarchy of low-dimensional models for the transient and post-transient cylinder wake
journal, December 2003
- Noack, Bernd R.; Afanasiev, Konstantin; MorzyŃSki, Marek
- Journal of Fluid Mechanics, Vol. 497
REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems
journal, March 1994
- Hansen, Per Christian
- Numerical Algorithms, Vol. 6, Issue 1
Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models
journal, August 2008
- Bergmann, M.; Cordier, L.
- Journal of Computational Physics, Vol. 227, Issue 16
Large eddy simulation study of fully developed wind-turbine array boundary layers
journal, January 2010
- Calaf, Marc; Meneveau, Charles; Meyers, Johan
- Physics of Fluids, Vol. 22, Issue 1
On Low-Dimensional Galerkin Models for Fluid Flow
journal, June 2000
- Rempfer, D.
- Theoretical and Computational Fluid Dynamics, Vol. 14, Issue 2
Large eddy simulation study of the kinetic energy entrainment by energetic turbulent flow structures in large wind farms
journal, February 2014
- VerHulst, Claire; Meneveau, Charles
- Physics of Fluids, Vol. 26, Issue 2
Time-adaptive wind turbine model for an LES framework: Time-adaptive wind turbine model for an LES framework
journal, July 2015
- Sharma, V.; Calaf, M.; Lehning, M.
- Wind Energy, Vol. 19, Issue 5
Optimizing the arrangement and the selection of turbines for wind farms subject to varying wind conditions
journal, April 2013
- Chowdhury, Souma; Zhang, Jie; Messac, Achille
- Renewable Energy, Vol. 52
Low-order representations of the canonical wind turbine array boundary layer via double proper orthogonal decomposition
journal, February 2016
- Hamilton, Nicholas; Tutkun, Murat; Cal, Raúl Bayoán
- Physics of Fluids, Vol. 28, Issue 2
Low-dimensional analysis, using POD, for two mixing layer–wake interactions
journal, June 2004
- Braud, Caroline; Heitz, Dominique; Arroyo, Georges
- International Journal of Heat and Fluid Flow, Vol. 25, Issue 3
Unrestricted wind farm layout optimization (UWFLO): Investigating key factors influencing the maximum power generation
journal, February 2012
- Chowdhury, Souma; Zhang, Jie; Messac, Achille
- Renewable Energy, Vol. 38, Issue 1, p. 16-30
Low-order dynamical system model of a fully developed turbulent channel flow
journal, June 2017
- Hamilton, Nicholas; Tutkun, Murat; Cal, Raúl Bayoán
- Physics of Fluids, Vol. 29, Issue 6
Anisotropic character of low-order turbulent flow descriptions through the proper orthogonal decomposition
journal, January 2017
- Hamilton, Nicholas; Tutkun, Murat; Cal, Raúl Bayoán
- Physical Review Fluids, Vol. 2, Issue 1
Data-driven Reduced Order Model for prediction of wind turbine wakes
journal, June 2015
- Iungo, G. V.; Santoni-Ortiz, C.; Abkar, M.
- Journal of Physics: Conference Series, Vol. 625
Quantifying the Impact of Wind Turbine Wakes on Power Output at Offshore Wind Farms
journal, August 2010
- Barthelmie, R. J.; Pryor, S. C.; Frandsen, S. T.
- Journal of Atmospheric and Oceanic Technology, Vol. 27, Issue 8, p. 1302-1317
Variational assimilation of POD low-order dynamical systems
journal, January 2007
- D'adamo, Juan; Papadakis, Nicolas; Mémin, Etienne
- Journal of Turbulence, Vol. 8
Application of artificial neural network to predict the friction factor of open channel flow
journal, May 2009
- Yuhong, Zeng; Wenxin, Huai
- Communications in Nonlinear Science and Numerical Simulation, Vol. 14, Issue 5
Wind Speed Estimation and Parametrization of Wake Models for Downregulated Offshore Wind Farms within the scope of PossPOW Project
journal, June 2014
- Bozkurt, Tuhfe Göçmen; Giebel, Gregor; Poulsen, Niels Kjølstad
- Journal of Physics: Conference Series, Vol. 524
POD Analysis of a Wind Turbine Wake in a Turbulent Atmospheric Boundary Layer
journal, June 2014
- Bastine, D.; Witha, B.; Wächter, M.
- Journal of Physics: Conference Series, Vol. 524
The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
journal, March 1998
- Huang, Norden E.; Shen, Zheng; Long, Steven R.
- Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 454, Issue 1971
Closed-Loop Turbulence Control: Progress and Challenges
journal, August 2015
- Brunton, Steven L.; Noack, Bernd R.
- Applied Mechanics Reviews, Vol. 67, Issue 5
A method to construct reduced-order parameter-varying models: REDUCED-ORDER PARAMETER-VARYING MODELS
journal, July 2016
- Annoni, Jennifer; Seiler, Peter
- International Journal of Robust and Nonlinear Control, Vol. 27, Issue 4
Reduced order model of the inherent turbulence of wind turbine wakes inside an infinitely long row of turbines
journal, December 2014
- Andersen, S. J.; Sørensen, J. N.; Mikkelsen, R.
- Journal of Physics: Conference Series, Vol. 555
Calibrated reduced-order POD-Galerkin system for fluid flow modelling
journal, July 2005
- Couplet, M.; Basdevant, C.; Sagaut, P.
- Journal of Computational Physics, Vol. 207, Issue 1
On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high-Reynolds-number flow over an Ahmed body
journal, April 2014
- Östh, Jan; Noack, Bernd R.; Krajnović, Siniša
- Journal of Fluid Mechanics, Vol. 747
Natural integration of scalar fluxes from complex terrain
journal, November 1999
- Albertson, John D.; Parlange, Marc B.
- Advances in Water Resources, Vol. 23, Issue 3
Wind turbine boundary layer arrays for Cartesian and staggered configurations: Part II , low-dimensional representations via the proper orthogonal decomposition : Description of turbine array wake recovery via POD
journal, February 2014
- Hamilton, Nicholas; Tutkun, Murat; Cal, Raúl Bayoán
- Wind Energy, Vol. 18, Issue 2
A grey-box modeling approach for the reduction of nonlinear systems
journal, October 2008
- Romijn, Reinout; Özkan, Leyla; Weiland, Siep
- Journal of Process Control, Vol. 18, Issue 9
Statistical analysis of kinetic energy entrainment in a model wind turbine array boundary layer
journal, November 2012
- Hamilton, Nicholas; Suk Kang, Hyung; Meneveau, Charles
- Journal of Renewable and Sustainable Energy, Vol. 4, Issue 6
Model reduction for compressible flows using POD and Galerkin projection
journal, February 2004
- Rowley, Clarence W.; Colonius, Tim; Murray, Richard M.
- Physica D: Nonlinear Phenomena, Vol. 189, Issue 1-2
A Large-Eddy-Simulation Model for the Study of Planetary Boundary-Layer Turbulence
journal, July 1984
- Moeng, Chin-Hoh
- Journal of the Atmospheric Sciences, Vol. 41, Issue 13
Wind turbine condition monitoring by the approach of SCADA data analysis
journal, May 2013
- Yang, Wenxian; Court, Richard; Jiang, Jiesheng
- Renewable Energy, Vol. 53
Experimental study of the horizontally averaged flow structure in a model wind-turbine array boundary layer
journal, January 2010
- Cal, Raúl Bayoán; Lebrón, José; Castillo, Luciano
- Journal of Renewable and Sustainable Energy, Vol. 2, Issue 1
Tikhonov Regularization and Total Least Squares
journal, January 1999
- Golub, Gene H.; Hansen, Per Christian; O'Leary, Dianne P.
- SIAM Journal on Matrix Analysis and Applications, Vol. 21, Issue 1
Reduced-order models for closed-loop wake control
journal, April 2011
- Tadmor, Gilead; Lehmann, Oliver; Noack, Bernd R.
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 369, Issue 1940
Large-Eddy Simulation of Wind-Turbine Wakes: Evaluation of Turbine Parametrisations
journal, December 2010
- Wu, Yu-Ting; Porté-Agel, Fernando
- Boundary-Layer Meteorology, Vol. 138, Issue 3
Turbulence and the dynamics of coherent structures. I. Coherent structures
journal, January 1987
- Sirovich, Lawrence
- Quarterly of Applied Mathematics, Vol. 45, Issue 3
Black-box system identification for reduced order model construction
journal, May 2014
- Polifke, Wolfgang
- Annals of Nuclear Energy, Vol. 67
Wind turbine wake aerodynamics
journal, August 2003
- Vermeer, L. J.; Sørensen, J. N.; Crespo, A.
- Progress in Aerospace Sciences, Vol. 39, Issue 6-7, p. 467-510
A proper-orthogonal-decomposition–based model for the wall layer of a turbulent channel flow
journal, January 2009
- Podvin, Bérengère
- Physics of Fluids, Vol. 21, Issue 1
A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows
journal, February 2005
- Bou-Zeid, Elie; Meneveau, Charles; Parlange, Marc
- Physics of Fluids, Vol. 17, Issue 2
Calibrated POD Reduced-Order Models of Massively Separated Flows in the Perspective of Their Control
conference, September 2008
- Favier, J.; Cordier, L.; Kourta, A.
- ASME 2006 2nd Joint U.S.-European Fluids Engineering Summer Meeting Collocated With the 14th International Conference on Nuclear Engineering, Volume 2: Fora
Balanced Model Reduction via the Proper Orthogonal Decomposition
journal, November 2002
- Willcox, K.; Peraire, J.
- AIAA Journal, Vol. 40, Issue 11
Balanced model reduction via the proper orthogonal decomposition
journal, January 2002
- Willcox, K.; Peraire, J.
- AIAA Journal, Vol. 40
Balanced model reduction via the proper orthogonal decomposition
conference, August 2001
- Willcox, K.; Peraire, J.
- 15th AIAA Computational Fluid Dynamics Conference
On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high Reynolds number flow over an Ahmed body
text, January 2013
- Östh, Jan; Noack, Bernd R.; Krajnović, Siniša
- arXiv
Works referencing / citing this record:
Dynamic mode decomposition analysis for Savonius wind turbine
journal, November 2019
- Naderi, Mohammad Hossein; Tahani, Mojtaba; Esfahanian, Vahid
- Journal of Renewable and Sustainable Energy, Vol. 11, Issue 6
Characterizing the Coherent Structures Within and Above Large Wind Farms
journal, August 2019
- Zhang, Mengqi; Stevens, Richard J. A. M.
- Boundary-Layer Meteorology, Vol. 174, Issue 1