In recent years, the relevance of the interaction between neighboring wind farms has grown steadily. As one farm extracts energy from the wind, a downstream one can systematically experience lower wind speeds which threatens the economic viability of the farm. Significant progress has been made in understanding these farm-farm wake interactions, but we still lack methodologies to mitigate their undesired effects. In this study, we introduce Active Cluster Wake Mixing (ACWM). This novel method aims to accelerate the recovery of the cluster wake using dynamic control actions: By exciting the thrust of the individual turbines depending on their relative location, we generate non-uniform patterns of energy extraction. Phase offsets between the individual excitation signals propagate these regions through the wind farm. This results in large-scale velocity gradients inside the farm, which also affect the flow in the cluster wake region. An in-depth exploration and optimization of ACWM requires significant computational effort. Therefore, we compare three different wind farm modeling approaches in Large Eddy Simulations (LES) that differ in their computational costs regarding their suitability for further exploration of ACWM. For this purpose, we use an unoptimized ACWM scheme with two different excitation frequencies. For the first time ever we successfully show that ACWM manipulates the flow inside the wind farm with favorable effects on the wake velocity. We also demonstrate that the modeling of cluster wakes is challenging and has a significant effect on the potential gain.

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In this work, we investigate a method to derive characteristic dynamic flow field behavior from field measurements. We further explore how these changes impact the performance of a wind farm flow control strategy. For a long time, hourly to 10-min averaged data has been the predominant form to store meteorological quantities such as wind speeds and wind directions. With the decreasing cost of digital storage and improvements in measurement technology, the assimilation of higher frequent data has become more feasible. We use one of these open-source datasets provided by the KNMI to explore what characteristic flow behavior is described in the high-frequency recordings of a Wind-LiDAR located in the North-Sea. To this end we employ a K-Means algorithm to cluster 10-min time series of wind direction changes sampled at 20 s. Our study finds that the majority of wind direction changes within this time window can be described by five main clusters with clock- and counterclockwise changes of the wind direction in the range of ±4 deg. Subsequently we investigate the implications for quasi-steady wind farm flow control. We employ look-up table yaw-steering control next to baseline control in selected cases in a turbulent Large Eddy Simulation to verify the predictions made by a dynamic parametric engineering wake model. We find good agreement between both simulation environments and use the engineering model to investigate all wind directions in 2 deg resolution. The results show that the identified wind direction changes can have a significant negative impact on the power generated by a 10 turbine wind farm. The study also shows that the fixed yaw-steering set-points are still favorable over baseline operation for wind direction changes in the range of ±1.6 deg, but can act detrimental for larger changes.@en

A variety of wind farm control strategies exist in order to reduce unfavorable wake effects in large wind farms. While strategies like wake steering already reached a high maturity level, it is interesting to compare them to more recently proposed strategies. Such a comparison can form the basis for the development of a symbiotic wind farm control toolbox, from which a control strategy is chosen and activated depending on the operating conditions. The present study compares wake steering with helix control across a wide range of turbine spacings and wind directions using large-eddy simulation (LES). The size of the search space is made computationally tractable for LES by adopting a setup based on one physical upstream turbine and a distribution of virtual downstream turbines which do not exert any thrust force. It is found that helix control is beneficial for full wake overlap and turbine spacing of less than six rotor diameters whereas wake steering proves to be optimal further downstream and for partial wake overlap. Furthermore, the results show that the helix control setpoint in the proximity of full wake overlap scenarios is less susceptible to wind direction variations. This finding indicates that the combination of wake steering and helix control has potential for the design of a wind farm controller which is more robust in full wake overlap scenarios and can reduce the need for large yaw offset adjustments.

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Dynamic wind farm flow control is the art and science to maximize the energy yield of large wind farms. In this paper we will address the problem of large time delays between control actions of the different turbines in the farm and the delayed impact on the downstream turbines. We propose and show how a time-shifted cost function approach can render the receding horizon optimization problem more efficient and can mitigate the unavoidable turn-pike effect. We further show how the resulting setup can be used to break the optimization problem apart into several smaller optimization tasks to reduce the computational load. We demonstrate that the proposed changes do allow an economic model predictive control strategy to engage into collaborative wind farm control for long term gains, while a more traditional cost function approach leads to greedy turbine behavior. As a result, we take a crucial step towards a mature implementation of dynamic model based wind farm flow control.

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A novel dynamic economic model-predictive control strategy is presented that improves wind farm power production and reduces the additional demands of wake steering on yaw actuation when compared to an industry state-of-the-art reference controller. The novel controller takes a distributed approach to yaw control optimisation using a free-vortex wake model. An actuator-disc representation of the wind turbine is employed and adapted to the wind farm scale by modelling secondary effects of wake steering and connecting individual turbines through a directed graph network. The economic model-predictive control problem is solved on a receding horizon using gradient-based optimisation, demonstrating sufficient performance for realising real-time control. The novel controller is tested in a large-eddy simulation environment and compared against a state-of-the-art look-up table approach based on steady-state model optimisation and an extension with wind direction preview. Under realistic variations in wind direction and wind speed, the preview-enabled look-up table controller yielded the largest gains in power production. The novel controller based on the free-vortex wake produced smaller gains in these conditions while yielding more power under large changes in wind direction. Additionally, the novel controller demonstrated potential for a substantial reduction in yaw actuator usage.@en

Dynamic Mode Decomposition (DMD) is a fully data-driven method to extract a linear system from experimental or numerical data. It has proven its suitability for modeling wind turbine wakes, particularly those generated with Dynamic Induction Control (DIC), a method to reduce the wake deficit by enhancing its mixing with the surrounding flow. In this context, DMD may be used to build computationally efficient aerodynamic models suitable for model-based wind farm control algorithms. However, these standard DMD models are only valid for the flow conditions of the training data. This paper presents a novel approach to generalize a DMD model for DIC wakes from the training wind speed to various wind speeds by scaling the DMD modes. For this purpose, we first extract the DMD modes from numerical simulations of a DIC wake at a constant, homogeneous wind speed. Then, we adapt the obtained modes to a different wind speed with a scaling law for the frequency and magnitude derived from the definition of the Strouhal number. This allows for a versatile, efficient application of the DMD model in heterogeneous wind conditions at low computational costs. For validating the presented method, we model a helix wake at 6 ms^-1 based on the DMD modes from Large Eddy Simulations (LES) at 9 ms^-1. The DMD model coincides at a high level with validation simulations, resolving even mid- to small-scale structures.

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This paper presents a new framework of the FLOw Redirection and Induction Dynamics (FLORIDyn) model. It is able to dynamically simulate the wake behaviour in wind farms under heterogeneous and changing environmental conditions at a low computational cost. The novelty of this work is the improved segregation of wake dynamics and wake influence: the framework creates Observation Points (OPs) at each turbine, which propagate wind field states and turbine states downstream and follow the wind direction of the free stream velocity. These observation points cover the dynamic aspects of the simulation. The OPs, along with the stored states, are now used to derive so-called Temporary Wind Farms (TWF), which approximate the effective intra-farm wind conditions at a given location. Within these TWF, the flow conditions are homogeneous and steady state. This way, arbitrary wake models can be used to calculate the farm influence on the location. The FLORIDyn framework also provides interfaces to flow field estimators, which is tested with an effective wind speed estimator. A nine turbine case is used to highlight the quality and performance of the simulation result. Compared to its predecessor, the new FLORIDyn framework decreases the computational cost by one to two orders of magnitude, which makes it a promising candidate for real-time model predictive dynamic wind farm control.

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In this paper, a new version of the FLOw Redirection and Induction Dynamics (FLORIDyn) model is presented. The new model uses the three-dimensional parametric Gaussian FLORIS model and can provide dynamic wind farm simulations at a low computational cost under heterogeneous and changing wind conditions.

Both FLORIS and FLORIDyn are parametric models which can be used to simulate wind farms, evaluate controller performance and can serve as a control-oriented model. One central element in which they differ is in their representation of flow dynamics: FLORIS neglects these and provides a computationally very cheap approximation of the mean wind farm flow. FLORIDyn defines a framework which utilizes this low computational cost of FLORIS to simulate basic wake dynamics. This is achieved by creating so-called observation points (OPs) at each time step at the rotor plane which inherit the turbine state.

In this work, we develop the initial FLORIDyn framework further considering multiple aspects. The underlying FLORIS wake model is replaced by a Gaussian wake model. The distribution and characteristics of the OPs are adapted to account for the new parametric model but also to take complex flow conditions into account. To achieve this, a mathematical approach is developed to combine the parametric model and the changing, heterogeneous world conditions and link them with each OP. We also present a computationally lightweight wind field model to allow for a simulation environment in which heterogeneous flow conditions are possible.

FLORIDyn is compared to Simulator for Offshore Wind Farm Applications (SOWFA) simulations in three- and nine-turbine cases under static and changing environmental conditions. The results show a good agreement with the timing of the impact of upstream state changes on downstream turbines. They also show a good agreement in terms of how wakes are displaced by wind direction changes and when the resulting velocity deficit is experienced by downstream turbines. A good fit of the mean generated power is ensured by the underlying FLORIS model. In the three-turbine case, FLORIDyn simulates 4 s simulation time in 24.49 ms computational time. The resulting new FLORIDyn model proves to be a computationally attractive and capable tool for model-based dynamic wind farm control.@en

Wind farm control methods allow for a more flexible use of wind power plants over the baseline operation. They can be used to increase the power generated, to track a reference power signal or to reduce structural loads on a farm-wide level. Model-based control strategies have the advantage that prior knowledge can be included, for instance by simulating the current flow field state into the near future to take adequate control actions. This state needs to describe the real system as accurately as possible. This paper discusses what state estimation methods are suitable for wind farm flow field estimation and how they can be applied to the dynamic engineering model FLORIDyn. In particular, we derive an Ensemble Kalman Filter framework which can identify heterogeneous and changing wind speeds and wind directions across a wind farm. It does so based on the power generated by the turbines and wind direction measurements at the turbine locations. Next to the states, this framework quantifies uncertainty for the resulting state estimates. We also highlight challenges that arise when ensemble methods are applied to particle-based flow field simulations. The development of a flow field estimation framework for dynamic low-fidelity wind farm models is an essential step toward real-time dynamic model-based closed-loop wind farm control.@en

Wind farm flow control (WFFC) is a topic of interest at several research institutes and industry and certification agencies worldwide. For reliable performance assessment of the technology, the efficiency and the capability of the models applied to WFFC should be carefully evaluated. To address that, the FarmConners consortium has launched a common benchmark for code comparison under controlled operation to demonstrate its potential benefits, such as increased power production. The benchmark builds on available data sets from previous field campaigns, wind tunnel experiments, and high-fidelity simulations. Within that database, four blind tests are defined and 13 participants in total have submitted results for the analysis of single and multiple wakes under WFFC. Here, we present Part I of the FarmConners benchmark results, focusing on the blind tests with large-scale rotors. The observations and/or the model outcomes are evaluated via direct power comparisons at the upstream and downstream turbine(s), as well as the power gain at the wind farm level under wake steering control strategy. Additionally, wake loss reduction is also analysed to support the power performance comparison, where relevant. The majority of the participating models show good agreement with the observations or the reference high-fidelity simulations, especially for lower degrees of upstream misalignment and narrow wake sector. However, the benchmark clearly highlights the importance of the calibration procedure for control-oriented models. The potential effects of limited controlled operation data in calibration are particularly visible via frequent model mismatch for highly deflected wakes, as well as the power loss at the controlled turbine(s). In addition to the flow modelling, the sensitivity of the predicted WFFC benefits to the turbine representation and the implementation of the controller is also underlined. The FarmConners benchmark is the first of its kind to bring a wide variety of data sets, control settings, and model complexities for the (initial) assessment of farm flow control benefits. It forms an important basis for more detailed benchmarks in the future with extended control objectives to assess the true value of WFFC.

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FLORIDyn is a parametric control-oriented dynamic model suitable to predict the dynamic wake interactions between wind turbines in a wind farm. In order to improve the accuracy of FLORIDyn, this study proposes to calibrate the tuning parameters present in the model by employing a probabilistic setting using the UQ4WIND framework. The strategy relies on constructing a surrogate model (based on polynomial chaos expansion), which is then used to perform both global sensitivity analysis and Bayesian calibration. For our analysis, a nine wind turbine configuration in a yawed setting constitutes the test case. The results of sensitivity analysis offer valuable insight into the time-dependent influence of the model parameters onto the model output. The model parameter tied to the turbine efficiency appear to be the most sensitive parameter affecting the model output. The calibrated FLORIDyn model using the Bayesian approach yield predictions much closer to the measurement data, which is equipped with an uncertainty estimate.

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