A low-order model for wind farm control

Wind turbines in a wind farm are operated individually to maximize their own power regardless of the impact of aerodynamic interactions on neighboring turbines. There is the potential to increase power and reduce overall structural loads by properly coordinating the turbines. To perform control design and analysis, a model needs to be of low computational complexity but retain the necessary dynamics seen in high-fidelity models. This paper addresses a model reduction approach that computes the dominant modes of the flow that capture the energy and frequency characteristics of the system. Specifically, the paper uses the balanced proper orthogonal decomposition technique to construct the dominant input/output modes. Using these modes, a low-order model of a wind farm is constructed that can be used for control design.

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

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

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

[5]  Jan-Willem van Wingerden,et al.  SOWFA Super-Controller: A High-Fidelity Tool for Evaluating Wind Plant Control Approaches , 2013 .

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

[7]  L Y Pao,et al.  Control of Wind Turbines , 2011, IEEE Control Systems.

[8]  Robert Flemming Mikkelsen,et al.  Large-eddy simulations of the Lillgrund wind farm , 2013 .

[9]  Kathryn E. Johnson,et al.  Assessment of Extremum Seeking Control for Wind Farm Energy Production , 2012 .

[10]  Jason R. Marden,et al.  A Model-Free Approach to Wind Farm Control Using Game Theoretic Methods , 2013, IEEE Transactions on Control Systems Technology.

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

[12]  O. Zikanov Essential Computational Fluid Dynamics , 2010 .

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

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

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

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

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

[18]  Leonardo P. Chamorro,et al.  An experimental case study of complex topographic and atmospheric influences on wind turbine performance , 2013 .

[19]  J G Schepers,et al.  Improved modelling of wake aerodynamics and assessment of new farm control strategies , 2007 .

[20]  Fotis Sotiropoulos,et al.  On the predictive capabilities of LES-actuator disk model in simulating turbulence past wind turbines and farms , 2013, 2013 American Control Conference.

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

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

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

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

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

[26]  Milos Ilak,et al.  Model reduction and feedback control of transitional channel flow , 2009 .

[27]  Jan-Willem van Wingerden,et al.  A model-free distributed approach for wind plant control , 2013, 2013 American Control Conference.

[28]  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.

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

[30]  Jiarong Hong,et al.  Natural snowfall reveals large-scale flow structures in the wake of a 2.5-MW wind turbine , 2014, Nature Communications.

[31]  Kathryn E. Johnson,et al.  SOWFA + Super Controller User's Manual , 2013 .

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

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

[34]  Fernando Porté-Agel,et al.  Turbulent Flow Inside and Above a Wind Farm: A Wind-Tunnel Study , 2011 .

[35]  Eilyan Bitar,et al.  Coordinated control of a wind turbine array for power maximization , 2013, 2013 American Control Conference.

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

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

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

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

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

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

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