On the potential of reduced order models for wind farm control: a Koopman dynamic mode decomposition approach

Abstract

The high dimensions and governing non linear dynamics in wind farm systems make the design of numerical optimal controllers computationally expensive. A possible pathway to circumvent this challenge lies in finding reduced order models which can accurately embed the existing non linearities. The work here presented applies the ideas motivated by non linear dynamical systems theory - the Koopman Operator - to an innovative algorithm in the context of wind farm systems - Input Output Dynamic Mode Decomposition - to improve on the ability to model the aerodynamic interaction between wind turbines in a wind farm and uncover insights into the existing dynamics. It is shown that a reduced order linear state space model can reproduce the downstream turbine generator power dynamics and reconstruct the upstream turbine wake. It is further shown that the fit can be improved by judiciously choosing the Koopman observables used in the IODMD algorithm without jeopardizing the models ability to rebuild the turbine wake. The extensions to the IODMD algorithm provide an important step towards the design of linear reduced order models which can accurately reproduce the dynamics in a wind farm.

A three-dimensional dynamic mode decomposition analysis of wind farm flow aerodynamics

“…After gaining a visual impression of the performance of the AP and SP methods, we further quantify the performance of the methods by determining the performance loss, which is defined as [47] P% = X − ΦD α V and F X F × 100 (17) In Fig. 15, we show that increasing the number of DMD modes reduces the performance loss, i.e., the accuracy becomes higher for both the AP and SP method.…”

Streaming dynamic mode decomposition for short‐term forecasting in wind farms

“…DMD, which initially showed success in the field of fluid dynamics, has been applied to a wide range of disciplines including neuroscience, economics, and epidemiology. In the field of wind energy, DMD is also showing increasing popularity 30‐32 . Annoni et al used the DMD methodology to perform sparse optimization of the location of wind sensors to reconstruct a wind farm wind field 30 .…”

“…Annoni et al used the DMD methodology to perform sparse optimization of the location of wind sensors to reconstruct a wind farm wind field 30 . Cassamo and van Wingerden show the potential benefits of using DMD for wake reconstruction in dynamic induction control 32 . Whereas these studies estimate the wind field, the present study takes a different approach by reconstructing the time series of interest directly from the high‐frequency SCADA data of each individual turbine in a wind farm environment.…”

“…In the field of wind energy, DMD is also showing increasing popularity. [30][31][32] Annoni et al used the DMD methodology to perform sparse optimization of the location of wind sensors to reconstruct a wind farm wind field. 30 Cassamo and van Wingerden show the potential benefits of using DMD for wake reconstruction in dynamic induction control.…”

“…30 Cassamo and van Wingerden show the potential benefits of using DMD for wake reconstruction in dynamic induction control. 32 Whereas these studies estimate the wind field, the present study takes a different approach by reconstructing the time series of interest directly from the high-frequency SCADA data of each individual turbine in a wind farm environment. In particular, we use a combination of the wind power output, wind speed, and wind direction of each turbine to forecast the power output of each turbine.…”