本研究利用大渦漩模擬 (Large-eddy simulation) 在中性邊界層下，不同的風機流向間距對於大型風電場的功率輸出以及尾流效應，其中我們引進了風機模組以及風機的相關參數來將風通過風機後所產生的力作用導入到流場的動量方程式當中，並藉由計算得到的速度場資料以及葉片元素理論 (Blade element theory) 來計算大型風電場中整體的功率輸出，在這項研究中，我們進行30個風電場模擬，每個風電場模擬由4行30列共120支風力渦輪機組成。另外，這些風電場模擬分別具有不同的渦輪機陣列配置（即，對齊、橫向交錯和垂直交錯）、風機流向間距（即，7d、9d、12d、15d和18d）和入流的紊流強度大小（即，7%以及11%），其中，入流的速度則定為9 m/s。而模擬結果表明，透過增加風機流向間距，風機產生的功率有顯著改善。隨著風機流向間距從7d增加到18d，對於使用風機為2MW效能之風電場的整體功率輸出提高了約27％~38％，特別是對於具有對齊渦輪機陣列配置的風電場有顯著的影響。此外，在地表粗糙度為0.5公尺的入流條件下，風機流向間距為18d的橫向交錯排列風電場的整體風機功率輸出平均達到80％以上。然而，即使增加的流向渦輪機間距可以有效地提高動力性能，但是單位面積內所產生的功率確有降低趨勢。而在風電場對於邊界層影響分析中，較大的風機流向間距能降低有效粗糙度和摩擦速度。具有對齊的渦輪機陣列配置的風電場比橫向交錯和垂直交錯的渦輪機陣列配置更快地達到穩定且接近三個模型。

A Large-eddy simulation framework is used to quantify the power production of the large wind farm and to investigate the effect of increasing streamwise turbine spacing on the overall power performance of the wind farm. In this study, thirty wind farm cases are considered and consist of 120 wind turbines which are arranged into 30 turbine rows along the streamwise direction with different turbine configurations (i.e., aligned, laterally-staggered, and vertically-staggered), increasing streamwise turbine spacing (i.e., 7d, 9d, 12d, 15d, and 18d), and incoming turbulence intensity level (i.e., 7% and 11%). The simulated results show the turbine power production has a significant improvement by increasing the streamwise turbine spacing. With increasing the streamwise turbine spacing from 7 to 18 rotor diameters, the overall averaged power outputs are raised by about 27% in the staggered wind farms and about 38% in the aligned wind farms. The wind farm scenarios with the turbine spacing of 12d or greater in a large wind farm can lead to an increasing trend in the power production from the downstream turbines in the high-turbulence inflow condition, or also avoids the degradation of the power output on the turbines with the low-turbulence inflow condition. The effective analysis shows the larger streamwise turbine spacing leads to a lower effective roughness and friction velocity. The wind farm cases with aligned turbine configuration reach to stable and close to the three models more quickly than laterally-staggered and vertically-staggered turbine configurations.

1. Castellani, F., et al. Analysing wind farm efficiency on complex terrains. in Journal of Physics: Conference Series. 2014. IOP Publishing.
2. Barlas, E., S. Buckingham, and J. van Beeck, Roughness effects on wind-turbine wake dynamics in a boundary-layer wind tunnel. Boundary-layer meteorology, 2016. 158(1): p. 27-42.
3. Stevens, R.J., D.F. Gayme, and C. Meneveau, Large eddy simulation studies of the effects of alignment and wind farm length. Journal of Renewable and Sustainable Energy, 2014. 6(2): p. 023105.
4. Parada, L., et al., Assessing the energy benefit of using a wind turbine micro-siting model. Renewable Energy, 2018. 118: p. 591-601.
5. Hansen, K.S., et al., The impact of turbulence intensity and atmospheric stability on power deficits due to wind turbine wakes at Horns Rev wind farm. Wind Energy, 2012. 15(1): p. 183-196.
6. Santhanagopalan, V., M. Rotea, and G. Iungo, Performance optimization of a wind turbine column for different incoming wind turbulence. Renewable Energy, 2018. 116: p. 232-243.
7. Barthelmie, R.J., et al., Modelling and measuring flow and wind turbine wakes in large wind farms offshore. Wind Energy: An International Journal for Progress and Applications in Wind Power Conversion Technology, 2009. 12(5): p. 431-444.
8. Barthelmie, R.J., et al., Quantifying the impact of wind turbine wakes on power output at offshore wind farms. Journal of Atmospheric and Oceanic Technology, 2010. 27(8): p. 1302-1317.
9. Barthelmie, R.J. and L. Jensen, Evaluation of wind farm efficiency and wind turbine wakes at the Nysted offshore wind farm. Wind Energy, 2010. 13(6): p. 573-586.
10. Tian, W., A. Ozbay, and H. Hu, An experimental investigation on the wake interferences among wind turbines sited in aligned and staggered wind farms. Wind Energy, 2018. 21(2): p. 100-114.
11. Adaramola, M. and P.-Å. Krogstad, Experimental investigation of wake effects on wind turbine performance. Renewable Energy, 2011. 36(8): p. 2078-2086.
12. Ali, N., et al., Assessing spacing impact on coherent features in a wind turbine array boundary layer. Wind Energy Science (Online), 2018. 3(NREL/JA-5000-72521).
13. Stevens, R.J., D.F. Gayme, and C. Meneveau, Effects of turbine spacing on the power output of extended wind‐farms. Wind Energy, 2016. 19(2): p. 359-370.
14. Draper, M., et al., A Large Eddy Simulation-Actuator Line Model framework to simulate a scaled wind energy facility and its application. Journal of Wind Engineering and Industrial Aerodynamics, 2018. 182: p. 146-159.
15. Calaf, M., C. Meneveau, and J. Meyers, Large eddy simulation study of fully developed wind-turbine array boundary layers. Physics of fluids, 2010. 22(1): p. 015110.
16. Sedaghatizadeh, N., et al., Modelling of wind turbine wake using large eddy simulation. Renewable Energy, 2018. 115: p. 1166-1176.
17. Churchfield, M.J., Y. Li, and P.J. Moriarty, A large-eddy simulation study of wake propagation and power production in an array of tidal-current turbines. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2013. 371(1985): p. 20120421.
18. Nilsson, K., et al., Large‐eddy simulations of the Lillgrund wind farm. Wind Energy, 2015. 18(3): p. 449-467.
19. Meyers, J. and C. Meneveau, Optimal turbine spacing in fully developed wind farm boundary layers. Wind Energy, 2012. 15(2): p. 305-317.
20. Stevens, R.J., Dependence of optimal wind turbine spacing on wind farm length. Wind energy, 2016. 19(4): p. 651-663.
21. Yang, X., S. Kang, and F. Sotiropoulos, Computational study and modeling of turbine spacing effects in infinite aligned wind farms. Physics of Fluids, 2012. 24(11): p. 115107.
22. Sharma, V., et al., Evolution of flow characteristics through finite-sized wind farms and influence of turbine arrangement. Renewable Energy, 2018. 115: p. 1196-1208.
23. Stoll, R. and F. Porté‐Agel, Dynamic subgrid‐scale models for momentum and scalar fluxes in large‐eddy simulations of neutrally stratified atmospheric boundary layers over heterogeneous terrain. Water Resources Research, 2006. 42(1).
24. Wu, Y.-T. and F. Porté-Agel, Modeling turbine wakes and power losses within a wind farm using LES: An application to the Horns Rev offshore wind farm. Renewable Energy, 2015. 75: p. 945-955.
25. Wu, Y.-T. and F. Porté-Agel, Atmospheric turbulence effects on wind-turbine wakes: An LES study. energies, 2012. 5(12): p. 5340-5362.
26. Wu, Y.-T. and F. Porté-Agel, Large-eddy simulation of wind-turbine wakes: evaluation of turbine parametrisations. Boundary-layer meteorology, 2011. 138(3): p. 345-366.
27. Wu, Y.-T. and F. Porté-Agel, Simulation of turbulent flow inside and above wind farms: model validation and layout effects. Boundary-layer meteorology, 2013. 146(2): p. 181-205.
28. Colmenar-Santos, A., J. Perera-Perez, and D. Borge-Diez, Offshore wind energy: A review of the current status, challenges and future development in Spain. Renewable and Sustainable Energy Reviews, 2016. 64: p. 1-18.
29. Drew, D., et al., The impact of future offshore wind farms on wind power generation in Great Britain. Resources, 2015. 4(1): p. 155-171.
30. Nygaard, N.G. Wakes in very large wind farms and the effect of neighbouring wind farms. in Journal of Physics: Conference Series. 2014. IOP Publishing.