A Generalized Framework for Reduced-Order Modeling of a Wind Turbine Wake

Nicholas Hamilton, Bianca Viggiano, Marc Calaf, Murat Tutkun, Raul Cal

Research output: Contribution to journalArticlepeer-review

29 Scopus Citations


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. 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.

Original languageAmerican English
Pages (from-to)373-390
Number of pages18
JournalWind Energy
Issue number6
StatePublished - 2018

Bibliographical note

Publisher Copyright:
Copyright © 2018 John Wiley & Sons, Ltd.

NREL Publication Number

  • NREL/JA-5000-71684


  • dynamical system
  • proper orthogonal decomposition
  • reduced-order model
  • wind turbine wake


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