Barthelmie, R. J., Hansen, K., Frandsen, S. T., Rathmann, O., Schepers, J., Schlez, W., Phillips, J., Rados, K., Zervos, A., and Politis, E.: Modelling and measuring flow and wind turbine wakes in large wind farms offshore, Wind Energy, 12, 431–444, 2009. a
Bastankhah, M. and Porté-Agel, F.: A new analytical model for wind-turbine
wakes, Renew. Energy, 70, 116–123, 2014.
a,
b,
c
Bastankhah, M. and Porté-Agel, F.: Experimental and theoretical study of
wind turbine wakes in yawed conditions, J. Fluid Mech., 806,
506–541, 2016.
a,
b,
c
Bastankhah, M. and Porté-Agel, F.: Wind tunnel study of the wind turbine interaction with a boundary-layer flow: upwind region, turbine performance, and wake region, Phys. Fluids, 29, 065105,
https://doi.org/10.1063/1.4984078, 2017.
a
Bastankhah, M. and Porté-Agel, F.: Wind farm power optimization via yaw angle control: A wind tunnel study, J. Renew. Sustain. Ener., 11, 023301,
https://doi.org/10.1063/1.5077038, 2019.
a,
b
Basu, S., Holtslag, A. A., Van De Wiel, B. J., Moene, A. F., and Steeneveld,
G.-J.: An inconvenient “truth;; about using sensible heat flux as a
surface boundary condition in models under stably stratified regimes, Acta
Geophy., 56, 88–99, 2008. a
Boersma, S., Doekemeijer, B., Gebraad, P. M., Fleming, P. A., Annoni, J.,
Scholbrock, A. K., Frederik, J., and van Wingerden, J.-W.: A tutorial on
control-oriented modeling and control of wind farms, in: 2017 Amer. Cont. Conf. (ACC), IEEE, Piscataway, New York, USA, 1–18, 2017. a
Boersma, S., Doekemeijer, B., Vali, M., Meyers, J., and van Wingerden, J.-W.: A control-oriented dynamic wind farm model: WFSim, Wind Energ. Sci., 3, 75–95,
https://doi.org/10.5194/wes-3-75-201, 2018.
a
Bossuyt, J., Howland, M. F., Meneveau, C., and Meyers, J.: Measurement of unsteady loading and power output variability in a micro wind farm model in a wind tunnel, Exp. Fluids, 58, 1,
https://doi.org/10.1007/s00348-016-2278-6, 2017.
a
Burton, T., Jenkins, N., Sharpe, D., and Bossanyi, E.: Wind Energy Handbook, John Wiley & Sons, Wiley, New York, 2011.
a,
b,
c
Calaf, M., Meneveau, C., and Meyers, J.: Large eddy simulation study of fully developed wind-turbine array boundary layers, Phys. Fluids, 22, 015110,
https://doi.org/10.1063/1.3291077, 2010.
a
Campagnolo, F., Petrović, V., Bottasso, C. L., and Croce, A.: Wind tunnel testing of wake control strategies, in: 2016 Amer. Cont. Conf. (ACC), IEEE, Piscataway, New York, USA, 513–518, 2016. a
Cleary, E., Garbuno-Inigo, A., Lan, S., Schneider, T., and Stuart, A. M.: Calibrate, Emulate, Sample, arXiv [preprint]
arXiv:2001.03689, 2020.
a
Doekemeijer, B., Boersma, S., Pao, L. Y., and van Wingerden, J.-W.: Ensemble Kalman filtering for wind field estimation in wind farms, in: 2017 Amer. Cont. Conf. (ACC), IEEE, IEEE, Piscataway, New York, USA, 19–24, 2017.
a,
b
Doekemeijer, B. M., Boersma, S., Pao, L. Y., Knudsen, T., and van Wingerden, J.-W.: Online model calibration for a simplified LES model in pursuit of real-time closed-loop wind farm control, Wind Energ. Sci., 3, 749–765,
https://doi.org/10.5194/wes-3-749-2018, 2018.
a
Evensen, G.: The ensemble Kalman filter: Theoretical formulation and practical implementation, Ocean Dynam., 53, 343–367, 2003. a
Fleming, P. A., Scholbrock, A. K., Jehu, A., Davoust, S., Osler, E., Wright, A. D., and Clifton, A.: Field-test results using a nacelle-mounted lidar for improving wind turbine power capture by reducing yaw misalignment, J. Phys. Conf. Ser., 524, 012002,
https://doi.org/10.1088/1742-6596/524/1/012002, 2014.
a
Fleming, P., Gebraad, P. M., Lee, S., van Wingerden, J.-W., Johnson, K., Churchfield, M., Michalakes, J., Spalart, P., and Moriarty, P.: Simulation comparison of wake mitigation control strategies for a two-turbine case, Wind Energy, 18, 2135–2143, 2015. a
Fleming, P., Annoni, J., Shah, J. J., Wang, L., Ananthan, S., Zhang, Z., Hutchings, K., Wang, P., Chen, W., and Chen, L.: Field test of wake steering at an offshore wind farm, Wind Energ. Sci., 2, 229–239,
https://doi.org/10.5194/wes-2-229-2017, 2017.
a
Fleming, P., Annoni, J., Churchfield, M., Martinez-Tossas, L. A., Gruchalla, K., Lawson, M., and Moriarty, P.: A simulation study demonstrating the importance of large-scale trailing vortices in wake steering, Wind Energ. Sci., 3, 243–255,
https://doi.org/10.5194/wes-3-243-2018, 2018.
a
Fleming, P., King, J., Dykes, K., Simley, E., Roadman, J., Scholbrock, A., Murphy, P., Lundquist, J. K., Moriarty, P., Fleming, K., van Dam, J., Bay, C., Mudafort, R., Lopez, H., Skopek, J., Scott, M., Ryan, B., Guernsey, C., and Brake, D.: Initial results from a field campaign of wake steering applied at a commercial wind farm – Part 1, Wind Energ. Sci., 4, 273–285,
https://doi.org/10.5194/wes-4-273-2019, 2019.
a,
b,
c
Fleming, P. A., Ning, A., Gebraad, P. M., and Dykes, K.: Wind plant system engineering through optimization of layout and yaw control, Wind Energy, 19, 329–344, 2016.
a,
b
Frederik, J. A., Doekemeijer, B. M., Mulders, S. P., and van Wingerden, J.-W.: The helix approach: using dynamic individual pitch control to enhance wake mixing in wind farms, arXiv [preprint],
1912.10025, 2019.
a
Frederik, J. A., Weber, R., Cacciola, S., Campagnolo, F., Croce, A., Bottasso, C., and van Wingerden, J.-W.: Periodic dynamic induction control of wind farms: proving the potential in simulations and wind tunnel experiments, Wind Energ. Sci., 5, 245–257,
https://doi.org/10.5194/wes-5-245-2020, 2020.
a
Gebraad, P., Teeuwisse, F., Van Wingerden, J., Fleming, P. A., Ruben, S., Marden, J., and Pao, L.: Wind plant power optimization through yaw control using a parametric model for wake effects–a CFD simulation study, Wind Energy, 19, 95–114, 2016a.
a,
b,
c,
d,
e
Gebraad, P. M., Churchfield, M. J., and Fleming, P. A.: Incorporating atmospheric stability effects into the FLORIS engineering model of wakes in wind farms, J. Phys. Conf. Ser., 753, 052004,
https://doi.org/10.1088/1742-6596/753/5/052004, 2016b.
a
Gebraad, P., Thomas, J. J., Ning, A., Fleming, P., and Dykes, K.: Maximization of the annual energy production of wind power plants by optimization of layout and yaw-based wake control, Wind Energy, 20, 97–107, 2017.
a,
b,
c
Ghaisas, N. S., Ghate, A. S., and Lele, S. K.: Effect of tip spacing, thrust coefficient and turbine spacing in multi-rotor wind turbines and farms, Wind Energ. Sci., 5, 51–72,
https://doi.org/10.5194/wes-5-51-2020, 2020.
a
Ghate, A. S. and Lele, S. K.: Subfilter-scale enrichment of planetary boundary layer large eddy simulation using discrete Fourier–Gabor modes, J. Fluid Mech., 819, 494–539, 2017.
a,
b
Gottlieb, S., Ketcheson, D. I., and Shu, C.-W.: Strong stability preserving Runge-Kutta and multistep time discretizations, World Scientific, 188 pp.,
https://doi.org/10.1142/7498, 2011.
a
Grant, I., Parkin, P., and Wang, X.: Optical vortex tracking studies of a horizontal axis wind turbine in yaw using laser-sheet, flow visualisation, Exp. Fluids, 23, 513–519, 1997. a
Hansen, K. S., Barthelmie, R. J., Jensen, L. E., and Sommer, A.: The impact of turbulence intensity and atmospheric stability on power deficits due to wind turbine wakes at Horns Rev wind farm, Wind Energy, 15, 183–196, 2012. a
Hess, G.: The neutral, barotropic planetary boundary layer, capped by a low-level inversion, Bound.-Lay. Meteorol., 110, 319–355, 2004. a
Hoskins, B. J.: The geostrophic momentum approximation and the semi-geostrophic equations, J. Atmos. Sci., 32, 233–242, 1975. a
Howland, M. F., Bossuyt, J., Martínez-Tossas, L. A., Meyers, J., and Meneveau, C.: Wake structure in actuator disk models of wind turbines in yaw under uniform inflow conditions, J. Renew. Sustain. Ener., 8, 043301,
https://doi.org/10.1063/1.4955091, 2016.
a
Howland, M. F., Ghate, A. S., and Lele, S. K.: Influence of the horizontal component of Earth's rotation on wind turbine wakes, J. Phys. Conf. Ser., 1037, 072003,
https://doi.org/10.1088/1742-6596/1037/7/072003, 2018.
a
Howland, M. F., Lele, S. K., and Dabiri, J. O.: Wind farm power optimization through wake steering, P. Natl. Acad. Sci. USA, 116, 14495–14500, 2019.
a,
b,
c,
d,
e,
f,
g,
h,
i,
j,
k,
l,
m
Howland, M. F., Ghate, A. S., and Lele, S. K.: Coriolis effects within and trailing a large finite wind farm, in: AIAA Scitech 2020 Forum, p. 0994, Aerospace Research Central (ARC), Reston, VA, 2020a.
a,
b,
c
Howland, M. F., Ghate, A. S., and Lele, S. K.: Influence of the geostrophic wind direction on the atmospheric boundary layer flow, J. Fluid Mech., 883, A39,
https://doi.org/10.1017/jfm.2019.889, 2020b.
a,
b,
c,
d,
e
Howland, M. F., Ghate, A. S., Lele, S. K., and Dabiri, J. O.: Supporting data for ”Optimal closed-loop wake steering, Part 1: Conventionally neutral atmospheric boundary layer conditions”, Stanford Digital Repository, available at:
https://purl.stanford.edu/py769sx2667, last access: 19 February 2020c. a
Kanev, S.: Dynamic wake steering and its impact on wind farm power production and yaw actuator duty, Renew. Energy, 146, 9–15, 2020. a
Kheirabadi, A. C. and Nagamune, R.: A quantitative review of wind farm control with the objective of wind farm power maximization, J. Wind Eng. Ind. Aerod., 192, 45–73, 2019. a
King, J., Fleming, P., King, R., Martínez-Tossas, L. A., Bay, C. J., Mudafort, R., and Simley, E.: Controls-Oriented Model for Secondary Effects of Wake Steering, Wind Energ. Sci. Discuss.,
https://doi.org/10.5194/wes-2020-3, in review, 2020.
a
Kingma, D. P. and Ba, J.: Adam: A method for stochastic optimization, arXiv [preprint]
arXiv:1412.6980, 2014.
a,
b
Leibovich, S. and Lele, S.: The influence of the horizontal component of Earth's angular velocity on the instability of the Ekman layer, J. Fluid Mech., 150, 41–87, 1985. a
Liew, J., Urbán, A. M., and Andersen, S. J.: Analytical model for the power–yaw sensitivity of wind turbines operating in full wake, Wind Energ. Sci., 5, 427–437,
https://doi.org/10.5194/wes-5-427-2020, 2020.
a,
b
Lin, M. and Porté-Agel, F.: Large-eddy simulation of yawed wind-turbine wakes: comparisons with wind tunnel measurements and analytical wake models, Energies, 12, 4574,
https://doi.org/10.3390/en12234574, 2019.
a
Lissaman, P.: Energy effectiveness of arbitrary arrays of wind turbines, J. Energy, 3, 323–328, 1979. a
Lukassen, L. J., Stevens, R. J., Meneveau, C., and Wilczek, M.: Modeling space-time correlations of velocity fluctuations in wind farms, Wind Energy, 21, 474–487, 2018. a
Medici, D.: Experimental studies of wind turbine wakes: power optimisation and meandering, PhD thesis, KTH, Stockholm, Sweden, 2005.
a,
b
Miao, W., Li, C., Yang, J., and Xie, X.: Numerical investigation of the yawed wake and its effects on the downstream wind turbine, J. Renew. Sustain. Ener., 8, 033303,
https://doi.org/10.1063/1.4953791, 2016.
a
Mikkelsen, R.: Actuator disc methods applied to wind turbines, PhD thesis, Technical University of Denmark, Denmark, 2003. a
Mühle, F., Schottler, J., Bartl, J., Futrzynski, R., Evans, S., Bernini, L., Schito, P., Draper, M., Guggeri, A., Kleusberg, E., Henningson, D. S., Hölling, M., Peinke, J., Adaramola, M. S., and Sætran, L.: Blind test comparison on the wake behind a yawed wind turbine, Wind Energ. Sci., 3, 883–903,
https://doi.org/10.5194/wes-3-883-2018, 2018.
a
Munters, W. and Meyers, J.: Dynamic strategies for yaw and induction control of wind farms based on large-eddy simulation and optimization, Energies, 11,
177,
https://doi.org/10.3390/en11010177, 2018.
a
Munters, W., Meneveau, C., and Meyers, J.: Turbulent inflow precursor method with time-varying direction for large-eddy simulations and applications to wind farms, Bound.-Lay. Meteorol., 159, 305–328, 2016. a
Nicoud, F., Toda, H. B., Cabrit, O., Bose, S., and Lee, J.: Using singular values to build a subgrid-scale model for large eddy simulations, Phys. Fluids, 23, 085106,
https://doi.org/10.1063/1.3623274, 2011.
a
Önder, A. and Meyers, J.: On the interaction of very-large-scale motions in a neutral atmospheric boundary layer with a row of wind turbines, J. Fluid Mech., 841, 1040–1072, 2018. a
Park, J. and Law, K. H.: A data-driven, cooperative wind farm control to maximize the total power production, Appl. Energ., 165, 151–165, 2016. a
Raach, S., Doekemeijer, B., Boersma, S., van Wingerden, J.-W., and Cheng, P. W.: Feedforward-Feedback wake redirection for wind farm control, Wind Energ. Sci. Discuss.,
https://doi.org/10.5194/wes-2019-54, 2019.
a
Schreiber, J., Bottasso, C. L., Salbert, B., and Campagnolo, F.: Improving wind farm flow models by learning from operational data, Wind Energ. Sci., 5, 647–673,
https://doi.org/10.5194/wes-5-647-2020, 2020.
a
Senoner, J.-M., García, M., Mendez, S., Staffelbach, G., Vermorel, O., and Poinsot, T.: Growth of rounding errors and repetitivity of large eddy simulations, AIAA J., 46, 1773–1781, 2008. a
Shapiro, C. R., Meyers, J., Meneveau, C., and Gayme, D. F.: Dynamic wake modeling and state estimation for improved model-based receding horizon control of wind farms, in: 2017 Amer. Cont. Conf. (ACC), IEEE, Piscataway, New York, USA, 709–716, 2017.
a,
b
Shapiro, C. R., Gayme, D. F., and Meneveau, C.: Modelling yawed wind turbine wakes: a lifting line approach, J. Fluid Mech., 841, R1,
https://doi.org/10.1017/jfm.2018.75, 2018.
a,
b,
c,
d,
e,
f
Shapiro, C. R., Starke, G. M., Meneveau, C., and Gayme, D. F.: A Wake Modeling Paradigm for Wind Farm Design and Control, Energies, 12, 2956,
https://doi.org/10.3390/en12152956, 2019.
a
Stevens, R. J. and Meneveau, C.: Flow Structure and Turbulence in Wind Farms, Annu. Rev. Fluid Mech., 49, 311–339, 2017.
a,
b
Subramaniam, A., Ghate, A. S., Ghaisas, N. S., and Howland, M. F: PadeOps, GitHub, available at:
https://github.com/FPAL-Stanford-University/PadeOps, last access: 19 February 2020. a
Taylor, G. I.: The spectrum of turbulence, P. Roy. Soc. Lond. A Mat., 164, 476–490, 1938. a
Wiser, R., Lantz, E., Mai, T., Zayas, J., DeMeo, E., Eugeni, E., Lin-Powers, J., and Tusing, R.: Wind vision: A new era for wind power in the United States, The Electricity Journal, 28, 120–132, 2015. a
Wyngaard, J. C.: Turbulence in the Atmosphere, Cambridge University Press, United Kingdom, 2010. a
