Wind farm modeling and control using dynamic mode decomposition

The objective of this paper is to construct a low-order model of a wind farm that can be used for control design and analysis. There is a potential to use wind farm control to increase power and reduce overall structural loads by properly coordinating the turbines in a wind farm. To perform control design and analysis, a model of the wind farm needs to be constructed that has low computational complexity, but retains the necessary dynamics. This paper uses an extension of dynamic mode decomposition (DMD) to extract the dominant spatial and temporal information from computational fluid dynamic simulations. Specifically, this extension of DMD includes input/output information and relies on techniques from the subspace identification literature. Using this information, a low-order model of a wind farm is constructed that can be used for control design.

[1]  Maciej Balajewicz,et al.  A New Approach to Model Order Reduction of the Navier-Stokes Equations , 2012 .

[3]  J. Marsden,et al.  A subspace approach to balanced truncation for model reduction of nonlinear control systems , 2002 .

[4]  L. Silverman,et al.  Model reduction via balanced state space representations , 1982 .

[5]  D. Enns.  Model reduction with balanced realizations: An error bound and a frequency weighted generalization , 1984, The 23rd IEEE Conference on Decision and Control.

[6]  P. Luchini,et al.  Adjoint Equations in Stability Analysis , 2014, 2404.17304.

[7]  Luis Santos,et al.  Aerodynamic shape optimization using the adjoint method , 2007 .

[8]  Kathryn E. Johnson,et al.  Wind farm control: Addressing the aerodynamic interaction among wind turbines , 2009, 2009 American Control Conference.

[9]  Christina Freytag,et al.  Stability And Transition In Shear Flows , 2016 .

[10]  Mario A. Rotea,et al.  Data-driven Reduced Order Model for prediction of wind turbine wakes , 2015 .

[11]  P. Holmes,et al.  Turbulence, Coherent Structures, Dynamical Systems and Symmetry , 1996 .

[12]  Peter J Seiler,et al.  Gain scheduled active power control for wind turbines , 2014 .

[13]  G. Barbose,et al.  Renewable Portfolio Standards in the United States - A Status Report with Data Through 2007 , 2008 .

[14]  P. Schmid,et al.  Dynamic mode decomposition of numerical and experimental data , 2008, Journal of Fluid Mechanics.

[15]  N. Jensen.  A note on wind generator interaction , 1983 .

[16]  J. F. Ainslie,et al.  CALCULATING THE FLOWFIELD IN THE WAKE OF WIND TURBINES , 1988 .

[17]  B. Moore.  Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .

[18]  Niles A. Pierce,et al.  An Introduction to the Adjoint Approach to Design , 2000 .

[19]  Xiaolei Yang,et al.  Large‐eddy simulation of turbulent flow past wind turbines/farms: the Virtual Wind Simulator (VWiS) , 2015 .

[20]  Matthias Wachter,et al.  Towards a Simplified Dynamic Wake Model Using POD Analysis , 2014, 1409.1150.

[21]  H. Fernholz.  Boundary Layer Theory , 2001 .

[22]  Richard H. Bartels,et al.  Algorithm 432 [C2]: Solution of the matrix equation AX + XB = C [F4] , 1972, Commun. ACM.

[23]  N. Jenkins,et al.  Wind Energy Handbook: Burton/Wind Energy Handbook , 2011 .

[24]  Mario Garcia-Sanz.  Special Issue on ‘Wind Turbines: New Challenges and Advanced Control Solutions’ International Journal of Robust and Nonlinear Control , 2007 .

[25]  Clarence W. Rowley,et al.  Model Reduction for fluids, Using Balanced Proper Orthogonal Decomposition , 2005, Int. J. Bifurc. Chaos.

[26]  Steven L. Brunton,et al.  Dynamic Mode Decomposition with Control , 2014, SIAM J. Appl. Dyn. Syst..

[27]  L.Y. Pao,et al.  Control of variable-speed wind turbines: standard and adaptive techniques for maximizing energy capture , 2006, IEEE Control Systems.

[28]  J. Sørensen,et al.  Unsteady actuator disc model for horizontal axis wind turbines , 1992 .

[29]  Jens Nørkær Sørensen,et al.  A MODEL FOR UNSTEADY ROTOR AERODYNAMICS , 1995 .

[30]  H. Schlichting.  Boundary Layer Theory , 1955 .

[31]  Kathryn E. Johnson,et al.  Evaluating techniques for redirecting turbine wakes using SOWFA , 2014 .

[32]  Ervin Bossanyi,et al.  Wind Energy Handbook , 2001 .

[33]  P. Schmid,et al.  Stability and Transition in Shear Flows. By P. J. SCHMID & D. S. HENNINGSON. Springer, 2001. 556 pp. ISBN 0-387-98985-4. £ 59.50 or $79.95 , 2000, Journal of Fluid Mechanics.

[34]  J. Peraire,et al.  Balanced Model Reduction via the Proper Orthogonal Decomposition , 2002 .

[35]  Mats Viberg,et al.  Subspace-based methods for the identification of linear time-invariant systems , 1995, Autom..

[36]  Ian Postlethwaite,et al.  Multivariable Feedback Control: Analysis and Design , 1996 .