A generalized framework for reducedorder modeling of a wind turbine wake
A reducedorder 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. Backprojecting the POD modes onto the velocity snapshots produces dynamic coefficients that express the amplitude of each mode in time. A reducedorder 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 largescale 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 openloop transfer functions. The wakeROM reproduces mode coefficients to within 25.2%,more »
 Authors:

^{[1]}
;
^{[2]};
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^{[2]}
 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:
 Report Number(s):
 NREL/JA500071684
Journal ID: ISSN 10954244
 Grant/Contract Number:
 AC3608GO28308
 Type:
 Accepted Manuscript
 Journal Name:
 Wind Energy
 Additional Journal Information:
 Journal Volume: 21; Journal Issue: 6; Journal ID: ISSN 10954244
 Publisher:
 Wiley
 Research Org:
 National Renewable Energy Lab. (NREL), Golden, CO (United States)
 Sponsoring Org:
 National Science Foundation (NSF); Research Council of Norway; USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 17 WIND ENERGY; 42 ENGINEERING; dynamical system; proper orthogonal decomposition; reducedorder model; wind turbine wake
 OSTI Identifier:
 1441172
Hamilton, Nicholas, Viggiano, Bianca, Calaf, Marc, Tutkun, Murat, and Cal, Raul Bayoan. A generalized framework for reducedorder modeling of a wind turbine wake. United States: N. p.,
Web. doi:10.1002/we.2167.
Hamilton, Nicholas, Viggiano, Bianca, Calaf, Marc, Tutkun, Murat, & Cal, Raul Bayoan. A generalized framework for reducedorder modeling of a wind turbine wake. United States. doi:10.1002/we.2167.
Hamilton, Nicholas, Viggiano, Bianca, Calaf, Marc, Tutkun, Murat, and Cal, Raul Bayoan. 2018.
"A generalized framework for reducedorder modeling of a wind turbine wake". United States.
doi:10.1002/we.2167.
@article{osti_1441172,
title = {A generalized framework for reducedorder modeling of a wind turbine wake},
author = {Hamilton, Nicholas and Viggiano, Bianca and Calaf, Marc and Tutkun, Murat and Cal, Raul Bayoan},
abstractNote = {A reducedorder 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. Backprojecting the POD modes onto the velocity snapshots produces dynamic coefficients that express the amplitude of each mode in time. A reducedorder 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 largescale 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 openloop transfer functions. The wakeROM reproduces mode coefficients to within 25.2%, quantified through the normalized rootmeansquare error. Furthermore, a highlevel 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 = {2018},
month = {1}
}
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