Large-eddy simulation of a 15 GW wind farm: Flow effects, energy budgets and comparison with wake models

Large-eddy simulation of a 15 GW wind farm: Flow effects, energy budgets and comparison with wake models Oliver Maas

Planned offshore wind farm clusters have a rated capacity of more than 10 GW. The layout optimization and yield estimation of wind farms is often performed with computationally inexpensive, analytical wake models. As recent research results show, the flow physics in large (multi-gigawatt) offshore wind farms are more complex than in small (sub-gigawatt) wind farms. Since analytical wake models are tuned with data of existing, sub-gigawatt wind farms they might not produce accurate results for large wind farm clusters. In this study the results of a large-eddy simulation of a 15 GW wind farm are compared with two analytical wake models to demonstrate potential discrepancies. The TurbOPark model and the Niayifar and Porté-Agel model are chosen because they use a Gaussian wake profile and a turbulence model. The wind farm has a finite size in the crosswise direction, unlike as in many other large-eddy simulation wind farm studies, in which the wind farm is effectively infinitely wide due to the cyclic boundary conditions. The results show that new effects like crosswise divergence and convergence occur in such a finite-size multi-gigawatt wind farm. The comparison with the wake models shows that there are large discrepancies of up to 40% between the predicted wind farm power output of the wake models and the large-eddy simulation. An energy budget analysis is made to explain the discrepancies. It shows that the wake models neglect relevant kinetic energy sources and sinks like the geostrophic forcing, the energy input by pressure gradients and energy dissipation. Taking some of these sources and sinks into account could improve the accuracy of the wake models.
3 27 2023 1108180 10.3389/fmech.2023.1108180 1 10.3389/crossmark-policy frontiersin.org true https://creativecommons.org/licenses/by/4.0/ 10.3389/fmech.2023.1108180 https://www.frontiersin.org/articles/10.3389/fmech.2023.1108180/full https://www.frontiersin.org/articles/10.3389/fmech.2023.1108180/full J. Fluid Mech. Allaerts 814 95 2017 Boundary-layer development and gravity waves in conventionally neutral wind farms 10.1017/jfm.2017.11 J. Fluid Mech. Allaerts 862 990 2019 Sensitivity and feedback of wind-farm-induced gravity waves 10.1017/jfm.2018.969 J. Phys. Conf. Ser. Allaerts 1037 072006 2018 Annual impact of wind-farm gravity waves on the Belgian-Dutch offshore wind-farm cluster 10.1088/1742-6596/1037/7/072006 Renew. Energy Bastankhah 70 116 2014 A new analytical model for wind-turbine wakes 10.1016/j.renene.2014.01.002 Entwurf flächenentwicklungsplan 2022 J. Phys. Conf. Ser. Centurelli 1934 012021 2021 Evaluating global blockage engineering parametrizations with LES 10.1088/1742-6596/1934/1/012021 J. Wind Eng. Indust. Aerodyn. Crespo 61 71 1996 Turbulence characteristics in wind-turbine wakes 10.1016/0167-6105(95)00033-X Energies Dar 15 5345 2022 An analytical model for wind turbine wakes under pressure gradient 10.3390/en15155345 Boundary-Layer Meteorol. Deardorff 18 495 1980 Stratocumulus-capped mixed layers derived from a three-dimensional model 10.1007/BF00119502 Wind Energy Sci. Devesse 7 1367 2022 Including realistic upper atmospheres in a wind-farm gravity-wave model 10.5194/wes-7-1367-2022 J. Wind Eng. Indust. Aerodyn. Dörenkämper 144 146 2015 The impact of stable atmospheric boundary layers on wind-turbine wakes within offshore wind farms 10.1016/j.jweia.2014.12.011 Turbulence and turbulence-generated structural loading in wind turbine clusters Frandsen 2007 The esbjerg declaration Frederiksen 2022 Definition of the IEA wind 15-megawatt offshore reference wind turbine Gaertner 2020 10.2172/1603478 Eur. wind energy Assoc. Conf. Exhib. Katic 1 407 1987 A simple model for cluster efficiency J. Atmos. Sci. Klemp 35 78 1978 Numerical simulation of hydrostatic mountain waves 10.1175/1520-0469(1978)035<0078:NSOHMW>2.0.CO;2 Wind Energy Sci. Krüger 7 323 2022 Validation of a coupled atmospheric-aeroelastic model system for wind turbine power and load calculations 10.5194/wes-7-323-2022 Wind Energy Sci. Lanzilao 6 247 2021 Set-point optimization in wind farms to mitigate effects of flow blockage induced by atmospheric gravity waves 10.5194/wes-6-247-2021 J. Phys. Conf. Ser. Lanzilao 2265 022043 2022 Effects of self-induced gravity waves on finite wind-farm operations using a large-eddy simulation framework 10.1088/1742-6596/2265/2/022043 J. energy Lissaman 3 323 1979 Energy effectiveness of arbitrary arrays of wind turbines 10.2514/3.62441 Wind Energy Sci. Maas 7 715 2022 Wake properties and power output of very large wind farms for different meteorological conditions and turbine spacings: A large-eddy simulation case study for the German Bight 10.5194/wes-7-715-2022 LES of a 15 GW wind farm Maas Wind Energy Sci. Discuss. Maas 2022 1 Preprint: From gigawatt to multi-gigawatt wind farms: Wake effects, energy budgets and inertial gravity waves investigated by large-eddy simulations 10.5194/wes-2022-63 Boundary-Layer Meteorol. Maronga 148 1 2013 Derivation of structure parameters of temperature and humidity in the convective boundary layer from large-eddy simulations and implications for the interpretation of scintillometer observations 10.1007/s10546-013-9801-6 Geosci. Model Dev. Maronga 13 1335 2020 Overview of the PALM model system 6.0 10.5194/gmd-13-1335-2020 Q. J. R. Meteorol. Soc. Miller 107 615 1981 Radiation conditions for the lateral boundaries of limited-area numerical models 10.1002/qj.49710745310 J. Atmos. Sci. Moeng 45 3573 1988 Spectral analysis of large-eddy simulations of the convective boundary layer 10.1175/1520-0469(1988)045<3573:SAOLES>2.0.CO;2 Phys. Fluids Munters 28 025112 2016 Shifted periodic boundary conditions for simulations of wall-bounded turbulent flows 10.1063/1.4941912 Energies Niayifar 9 741 2016 Analytical modeling of wind farms: A new approach for power prediction 10.3390/en9090741 J. Phys. Conf. Ser. Nygaard 2265 022008 2022 Large-scale benchmarking of wake models for offshore wind farms 10.1088/1742-6596/2265/2/022008 J. Comput. Phys. Orlanski 21 251 1976 A simple boundary condition for unbounded hyperbolic flows 10.1016/0021-9991(76)90023-1 DTUWindEnergy/PyWake: PyWake Pedersen 2019 J. Phys. Conf. Ser. Pedersen 2265 022063 2022 Turbulence Optimized Park model with Gaussian wake profile 10.1088/1742-6596/2265/2/022063 Boundary-Layer Meteorol. Porté-Agel 174 1 2020 Wind-turbine and wind-farm flows: A review 10.1007/s10546-019-00473-0 Boundary-Layer Meteorol. Saiki 95 1 2000 Large-eddy simulation of the stably stratified planetary boundary layer 10.1023/A:1002428223156 Wind Energy Smith 13 449 2009 Gravity wave effects on wind farm efficiency 10.1002/we.366 promet - Meteorol. Fortbild. Steinfeld 39 163 2015 Hochauflösende Large-Eddy-Simulationen zur Untersuchung der Strömungsverhältnisse in Offshore-Windparks Wind Energy Stevens 19 359 2016 Effects of turbine spacing on the power output of extended wind-farms 10.1002/we.1835 J. Fluid Mech. Taylor 590 331 2007 Internal gravity waves generated by a turbulent bottom Ekman layer 10.1017/S0022112007008087 Mon. Weather Rev. Wicker 130 2088 2002 Time-splitting methods for elastic models using forward time schemes 10.1175/1520-0493(2002)130<2088:TSMFEM>2.0.CO;2 J. Phys. Conf. Ser. Witha 555 012108 2014 Large-eddy simulation of multiple wakes in offshore wind farms 10.1088/1742-6596/555/1/012108 Boundary-Layer Meteorol. Wu 138 345 2011 Large-eddy simulation of wind-turbine wakes: Evaluation of turbine parametrisations 10.1007/s10546-010-9569-x Energies Wu 10 2164 2017 Flow adjustment inside and around large finite-size wind farms 10.3390/en10122164 Wind Energy Zhang 22 189 2019 Large eddy simulations of the effect of vertical staggering in large wind farms 10.1002/we.2278