Smoothing turbulence-induced power fluctuations in large wind farms by optimal control of the rotating kinetic energy of the turbines

In the current study, we use a large-eddy simulation of a wind-farm boundary layer to generate the fluctuating wind fields that are observed at different turbines in the wind farm. Using these wind fields as inputs, we focus on the development of a benchmark framework in which we explore the trade-off between high energy extraction and low variability using optimal control of multiple turbines subject to a turbulent wind field. The controls variables that are optimized are the electric torque and the pitch angles of the individual turbines over time horizons of 10 minutes. Moreover, both optimal control of individual turbines and coordinated optimal control of groups of turbines are investigated. Optimal control results are presented in terms of Pareto fronts that show optimal trade-offs between energy extraction and power smoothing. We find that power variations can be significantly reduced with limited loss of extracted energy. Moreover, coordinated control can effectively reduce fluctuations over longer time scales. For instance, considering 24 optimally coordinated turbines, variability at a time scale of 50 seconds is reduced 4 times more than the normal statistical reduction of 24 uncoordinated turbines. © Published under licence by IOP Publishing Ltd.