Abstract. Wind turbines are often sited together in wind farms as it is economically advantageous. Controlling the flow within wind farms to reduce the fatigue loads, maximize energy production and provide ancillary services is a challenging control problem due to the underlying time-varying non-linear wake dynamics. In this paper, we present a control-oriented dynamical wind farm model called the WindFarmSimulator (WFSim) that can be used in closed-loop wind farm control algorithms. The three-dimensional Navier–Stokes equations were the starting point for deriving the control-oriented dynamic wind farm model. Then, in order to reduce computational complexity, terms involving the vertical dimension were either neglected or estimated in order to partially compensate for neglecting the vertical dimension. Sparsity of and structure in the system matrices make this model relatively computationally inexpensive. We showed that by taking the vertical dimension partially into account, the estimation of flow data generated with a high-fidelity wind farm model is improved relative to when the vertical dimension is completely neglected in WFSim. Moreover, we showed that, for the study cases considered in this work, WFSim is potentially fast enough to be used in an online closed-loop control framework including model parameter updates. Finally we showed that the proposed wind farm model is able to estimate flow and power signals generated by two different 3-D high-fidelity wind farm models.

Abstract. This paper studies a closed-loop wind farm control framework for active power control (APC) with a simultaneous reduction of wake-induced structural loads within a fully developed wind farm flow interacting with the atmospheric boundary layer. The main focus is on a classical feedback control, which features a simple control architecture and a practical measurement system that are realizable for real-time control of large wind farms. We demonstrate that the wake-induced structural loading of the downstream turbines can be alleviated, while the wind farm power production follows a reference signal. A closed-loop APC is designed first to improve the power-tracking performance against wake-induced power losses of the downwind turbines. Then, the nonunique solution of APC for the wind farm is exploited for aggregated structural load alleviation. The axial induction factors of the individual wind turbines are considered control inputs to limit the power production of the wind farm or to switch to greedy control when the demand exceeds the power available in the wind. Furthermore, the APC solution domain is enlarged by an adjustment of the power set-points according to the locally available power at the waked wind turbines. Therefore, the controllability of the wind turbines is improved for rejecting the intensified load fluctuations inside the wake. A large-eddy simulation model is employed for resolving the turbulent flow, the wake structures, and its interaction with the atmospheric boundary layer. The applicability and key features of the controller are discussed with a wind farm example consisting of 3×4 turbines with different wake interactions for each row. The performance of the proposed APC is evaluated using the accuracy of the wind farm power tracking and the wake-induced damage equivalent fatigue loads of the towers of the individual wind turbines.

Abstract.Wind turbines are often sited together in wind farms as it is economically advantageous. Controlling the flow within wind farms to reduce the fatigue loads and provide grid facilities such as the delivery of a demanded power is a challenging control problem due to the underlying time-varying nonlinear wake dynamics. It is therefore important to use the closed-loop control paradigm since it can partially account for model uncertainty and, in addition, it can deal with unknown disturbances. State-5 of-the-art closed-loop dynamic wind farm controllers are based on computationally expensive wind farm models, which make these methods suitable for analysis though unsuitable for online control. The latter is important, because it allows for model adaptation to the time-varying atmospheric conditions using SCADA measurements. As a consequence, more reliable control settings can be evaluated.In this paper, a dynamic wind farm model suitable for online wind farm control will be presented. The derivation of the 10 control-oriented dynamic wind farm model starts with the three-dimensional Navier-Stokes equations. Then, terms involving the vertical dimension will be estimated in order to partially compensate for neglecting the vertical dimension or neglected such that a 2D-like dynamic wind farm model will be obtained. Sparsity of and structure in the system matrices make this model relatively computational inexpensive hence suitable for online closed-loop controller synthesis including model parameter updates. Flow and power data evaluated with the wind farm model presented in this work will be validated with high fidelity 15 flow data.

In this paper, a model predictive control (MPC) is proposed for wind farms to minimize wake-induced power losses. A constrained optimization problem is formulated to maximize the total power production of a wind farm. The developed controller employs a two-dimensional dynamic wind farm model to predict wake interactions in advance. An adjoint approach as an efficient tool is utilized to compute the gradient of the performance index for such a large-scale system.The wind turbine axial induction factors are considered as the control inputs to influence the overall performance by taking the wake interactions into account. A layout of a 2×3 wind farm is considered in this study. The parameterization of the controller is discussed in detail for a practical optimal energy extraction. The performance of the adjoint-based model predictive control (AMPC) is investigated with time-varying changes in wind direction. The simulation results show the effectiveness of the proposed approach. The computational complexity of the developed AMPC is also outlined with respect to the real time control implementation.

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