On the Potential of Reduced Order Models for Wind Farm Control: A Koopman Dynamic Mode Decomposition Approach

Nassir Cassamo,Jan-Willem Van Wingerden

doi:10.3390/en13246513

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 presented here 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 (IODMD)—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.

Highlights

Renewable energy production has increased substantially over recent years, with a 5 to 6 fold increase since the 1960s [1]
The extensions to the Input Output Dynamic Mode Decomposition (IODMD) algorithm provide an important step towards the design of linear reduced order models which can accurately reproduce the dynamics in a wind farm
The results found show similarities with the ones in [34], where using the observables u2 + v2 and u2 + v2 + w2 yielded increases in fit of the downstream generator power output-albeit smaller for the case of Wake Redirection Control (WRC) by yaw misalignment, another wind farm control strategy-in the order of 1% when compared to the best performing IODMDu model

Summary

Introduction

Renewable energy production has increased substantially over recent years, with a 5 to 6 fold increase since the 1960s [1]. The total installed wind power capacity in Europe has been steadily increasing since 2009 [2]. Statistics indicate an increase from 77 GW (75 onshore and 2 offshore) of cumulative wind power capacity in 2009 to 205 GW (183 onshore and 22 offshore) in 2019. As wind turbines are sited together in wind farms, the aerodynamic interaction between turbines may have a negative effect on the total electrical power production. These effects are caused by the wakes, which are flow structures that form behind each turbine and are characterized by reduced flow velocity and increased turbulence intensity

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Conclusion