# 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:

- National Renewable Energy Laboratory (NREL), Golden, CO (United States)
- Portland State University
- University of Utah
- Institute for Energy Technology (IFE); University of Oslo

- Publication Date:

- Research Org.:
- National Renewable Energy Lab. (NREL), Golden, CO (United States)

- Sponsoring Org.:
- National Science Foundation (NSF); Research Council of Norway

- OSTI Identifier:
- 1441172

- Report Number(s):
- NREL/JA-5000-71684

- DOE Contract Number:
- AC36-08GO28308

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Wind Energy; Journal Volume: 21; Journal Issue: 6

- 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. doi: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.
doi:10.1002/we.2167.
```

```
@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. 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}

}