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. High-fidelity computational fluid dynamic models provide accurate characterizations of complex flow dynamics in a wind farm, but are not suitable for control design due to their prohibitive computational complexity. A variety of methods, including proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), can be used to extract the dominant flow structures and obtain reduced-order models. This paper introduces an extension to DMD that can handle problems with inputs and outputs. The proposed method, termed input-output dynamic mode decomposition (IODMD), uses a subspace identification technique to obtain models of low-complexity. Using this information, a low-order model of a wind farm is constructed that can be used for control design.