REDUCED-ORDER WAKE MODEL OF WIND TURBINES BASED ON STATE EXPANSION INPUT-OUTPUT DYNAMIC MODE DECOMPOSITION

Wei Shangshang; Li Zhihan; Chen Yikai; Xu Chang; Zhao Zhenzhou; Xu Bofeng

doi:10.19912/j.0254-0096.tynxb.2023-0975

PDF(1798 KB)

Acta Energiae Solaris Sinica ›› 2024, Vol. 45 ›› Issue (10) : 580-587. DOI: 10.19912/j.0254-0096.tynxb.2023-0975

REDUCED-ORDER WAKE MODEL OF WIND TURBINES BASED ON STATE EXPANSION INPUT-OUTPUT DYNAMIC MODE DECOMPOSITION

Wei Shangshang, Li Zhihan, Chen Yikai, Xu Chang, Zhao Zhenzhou, Xu Bofeng

Author information +

History +

Abstract

Based on the data and considering the influence of yaw control on wake model, this paper constructs a reduced-order wind turbine wake model with input and output. At the same time, to solve the inefficiency of the input-output dynamic mode decomposition （IODMD） method in reconstructing the local flow field, an extended state input-output dynamic mode decomposition （EIODMD） approach is proposed by integrating wind turbine speed, so that the characteristics of the wind turbines can be considered in the mode decomposition. The results show that compared with the rtaditional IODMD method, the proposed EIODMD can improve the flow field reconstruction and prediction accuracy, demonstrating the superiority of the reduced-order model based on the proposed EIODMD approach.

Key words

wind turbines / wakes / dynamic mode decomposition / state expansion / reduced-order model

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

Wei Shangshang, Li Zhihan, Chen Yikai, Xu Chang, Zhao Zhenzhou, Xu Bofeng. REDUCED-ORDER WAKE MODEL OF WIND TURBINES BASED ON STATE EXPANSION INPUT-OUTPUT DYNAMIC MODE DECOMPOSITION[J]. Acta Energiae Solaris Sinica. 2024, 45(10): 580-587 https://doi.org/10.19912/j.0254-0096.tynxb.2023-0975

References

[1] GOLAIT N, MOHARIL R M, KULKARNI P S.Wind electric power in the world and perspectives of its development in India[J]. Renewable and sustainable energy reviews, 2009, 13(1): 233-247.
[2] 许昌. 风电场微观尺度空气动力学: 基本理论与应用[M]. 北京: 中国水利水电出版社, 2018.
XU C.Micro-scale aerodynamics of wind farms: basic theory and application[M]. Beijing: China Water & Power Press, 2018.
[3] 侯亚丽, 汪建文, 王强, 等. 基于大涡模拟的风力机尾流湍流特征的研究[J]. 太阳能学报, 2015, 36(8): 1818-1824.
HOU Y L, WANG J W, WANG Q, et al.Study on wake turbulence characteristics of wind turbine base on large eddy simulation[J]. Acta energiae solaris sinica, 2015, 36(8): 1818-1824.
[4] ROLLET-MIET P, LAURENCE D, FERZIGER J.LES and RANS of turbulent flow in tube bundles[J]. International journal of heat and fluid flow, 1999, 20(3): 241-254.
[5] LÜBCKE H, SCHMIDT S, RUNG T, et al. Comparison of LES and RANS in bluff-body flows[J]. Journal of wind engineering and industrial aerodynamics, 2001, 89(14-15): 1471-1485.
[6] 田琳琳, 赵宁, 钟伟. 风力机尾流相互干扰的数值模拟[J]. 太阳能学报, 2012, 33(8): 1315-1320.
TIAN L L, ZHAO N, ZHONG W.Numerical simulation of wake interactions of wind turbines[J]. Acta energiae solaris sinica, 2012, 33(8): 1315-1320.
[7] 曹娜, 于群, 王伟胜, 等. 风电场尾流效应模型研究[J]. 太阳能学报, 2016, 37(1): 222-229.
CAO N, YU Q, WANG W S, et al.Research on wake effect model of wind farm[J]. Acta energiae solaris sinica, 2016, 37(1): 222-229.
[8] EMANUEL G, GAD-EL-HAK M. Analytical fluid dynamics, second edition[J]. Applied mechanics reviews, 2001, 54(4): B68.
[9] BOERSMA S, DOEKEMEIJER B, VALI M, et al.A control-oriented dynamic wind farm model: WFSim[J]. Wind energy science, 2018, 3(1): 75-95.
[10] LARSEN G, AAGAARD H M, BINGÖL F, et al. Dynamic wake meandering modeling[M]. Roskilde: Riso Natioual Laboratory, 2007.
[11] MODIN-EDMAN A K, ÖBORN I, SVERDRUP H. FARMFLOW: a dynamic model for phosphorus mass flow, simulating conventional and organic management of a Swedish dairy farm[J]. Agricultural systems, 2007, 94(2): 431-444.
[12] LUMLEY J L .The structure of inhomogeneous turbulent flows[C]//Atmospheric Turbulence and Radio Wave Propagation, Moscow, Russia, 1965.
[13] BERKOOZ G, HOLMES P, LUMLEY J L.The proper orthogonal decomposition in the analysis of turbulent flows[J]. Annual review of fluid mechanics, 1993, 25: 539-575.
[14] WANG Z, AKHTAR I, BORGGAARD J, et al.Proper orthogonal decomposition closure models for turbulent flows: a numerical comparison[J]. Computer methods in applied mechanics and engineering, 2012, 237: 10-26.
[15] ÖSTH J, NOACK B, KRAJNOVIĆ S, et al.On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high-Reynolds-number flow over an Ahmed body[J]. Journal of fluid mechanics, 2014, 747: 518-544.
[16] PERRIN R, BRAZA M, CID E, et al.Obtaining phase averaged turbulence properties in the near wake of a circular cylinder at high Reynolds number using POD[J]. Experiments in fluids, 2007, 43(2): 341-355.
[17] HALL K C.Eigenanalysis of unsteady flows about airfoils, cascades, and wings[J]. AIAA journal, 1994, 32(12): 2426-2432.
[18] DOWELL E H.Eigenmode analysis in unsteady aerodynamics - Reduced-order models[J]. AIAA journal, 1996, 34(8): 1578-1583.
[19] SCHMID P, ECOLE P.Dynamic mode decomposition of numerical and experimental data[J]. Journal of fluid mechanics, 2008, 656: 5-28.
[20] SCHMID P J.Dynamic mode decomposition of numerical and experimental data[J]. Journal of fluid mechanics, 2010, 656: 5-28.
[21] 寇家庆. 非定常气动力建模与流场降阶方法研究[D]. 西安: 西北工业大学, 2018.
KOU J Q.Reduced-order modeling methods for unsteady aerodynamics and fluid flows[D]. Xi’an: Northwestern Polytechnical University, 2018.
[22] MEZIĆ I.Spectral properties of dynamical systems, model reduction and decompositions[J]. Nonlinear dynamics, 2005, 41(1): 309-325.
[23] KOOPMAN B O.Hamiltonian systems and transformation in Hilbert space[J]. Proceedings of the national academy of sciences of the United States of America, 1931, 17(5): 315-318.
[24] MEZIĆ I.Analysis of fluid flows via spectral properties of the koopman operator[J]. Annual review of fluid mechanics, 2013, 45: 357-378.
[25] SUN C, TIAN T, ZHU X C, et al.Investigation of the near wake of a horizontal-axis wind turbine model by dynamic mode decomposition[J]. Energy, 2021, 227: 120418.
[26] CASSAMO N, VAN WINGERDEN J W. On the potential of reduced order models for wind farm control: a koopman dynamic mode decomposition approach[J]. Energies, 2020, 13(24): 6513.
[27] 刘鹏寅, 陈进格, 沈昕, 等. 深度动态失速流场的DMD分析[J]. 太阳能学报, 2018, 39(9): 2477-2485.
LIU P Y, CHEN J G, SHEN X, et al.Dmd analysis of flow field under deep dynamic stall condition[J]. Acta energiae solaris sinica, 2018, 39(9): 2477-2485.
[28] TIRUNAGARI S, KOUCHAKI S, POH N, et al.Dynamic mode decomposition for univariate time series: analysing trends and forecasting[OE/J]. https://hal.science/hal-01463744v12017.
[29] CHURCHFIELD M J, LEE S, MICHALAKES J, et al.A numerical study of the effects of atmospheric and wake turbulence on wind turbine dynamics[J]. Journal of turbulence, 2012, 13: 14.
[30] CASSAMO N, VAN WINGERDEN J W. Model predictive control for wake redirection in wind farms: a koopman dynamic mode decomposition approach[C]//2021 American Control Conference (ACC), New Orleans, LA, USA, 2021: 1776-1782.
[31] WILLIAMS M O, KEVREKIDIS I G, ROWLEY C W.A data-driven approximation of the koopman operator: extending dynamic mode decomposition[J]. Journal of nonlinear science, 2015, 25(6): 1307-1346.