Wind turbines are often sited together in wind farms as it is economically advantageous. However, the wake inevitably created by every turbine will lead to a time-varying interaction between the individual turbines. Common practice in industry has been to control turbines individually and ignore this interaction while optimizing the power and loads of the individual turbines. However, turbines that are in a wake experience reduced wind speed and increased turbulence, leading to a reduced energy extraction and increased dynamic mechanical loads on the turbine, respectively. Neglecting the dynamic interaction between turbines in control will therefore lead to suboptimal behaviour of the total wind farm. Therefore, wind farm control has been receiving an increasing amount of attention over the past years, with the focus on increasing the total power production and reducing the dynamic loading on the turbines. In this paper, wind farm control-oriented modeling and control concepts are explained. In addition, recent developments and literature are discussed and categorized. This paper can serve as a source of background information and provides many references regarding control-oriented modeling and control of wind farms.

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.

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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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Currently, wind farms typically rely on greedy control, in which the individual turbine's structural loading and power are optimized. However, this often appears suboptimal for the collective wind farm. A promising solution is closed-loop wind farm control using state feedback algorithms employing a dynamic model of the flow. This control method is a novelty in wind farms, and has potential to provide a temporally optimal control policy accounting for time-varying inflow conditions and unmodeled dynamics, both often neglected in current methods. An essential building block for state feedback control is a state estimator (observer) that reconstructs the system states of the dynamic model using a small number of measurements. As computational efficiency is critical in real-time control, lower-fidelity models are proposed to be used. In this work, WindFarmObserver (WFObs) is introduced, which is a state estimator relying on the WindFarmSimulator (WFSim) model and an Ensemble Kalman Filter (EnKF). The states of WFSim form the two dimensional flow field in a wind farm. In WFObs, WFSim models large scale wake dynamics, while smaller scale and stochastic effects (often neglected by current models) can be picked up by sensors and incorporated using the EnKF. WFObs is tested in a two-turbine setup using a high fidelity simulation model. With a realistic sensor setup where only 1.1% of the to-be-estimated states are measured, WFObs reduces the rms error by 21% compared to open-loop simulation, at a low computational cost of 0.76 s. As WFObs is sampled at 1 Hz, this readily allows real-time closed-loop wind farm control.

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