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

The growth in the number and size of wind energy projects in the last decade has revealed structural limitations in the current approach adopted by the wind industry to assess potential wind farm sites. These limitations are the result of neglecting the mutual interaction of large wind farms and the thermally stratified atmospheric boundary layer. While currently available analytical models are sufficiently accurate to conduct site assessments for isolated rotors or small wind turbine clusters, the wind farm's interaction with the atmosphere cannot be neglected for large-size arrays. Specifically, the wind farm displaces the boundary layer vertically, triggering atmospheric gravity waves that induce large-scale horizontal pressure gradients. These perturbations in pressure alter the velocity field at the turbine locations, ultimately affecting global wind farm power production. The implication of such dynamics can also produce an extended blockage region upstream of the first turbines and a favorable pressure gradient inside the wind farm. In this paper, we present the multi-scale coupled (MSC) model, a novel approach that allows the simultaneous prediction of micro-scale effects occurring at the wind turbine scale, such as individual wake interactions and rotor induction, and meso-scale phenomena occurring at the wind farm scale and larger, such as atmospheric gravity waves. This is achieved by evaluating wake models on a spatially heterogeneous background velocity field obtained from a reduced-order meso-scale model. Verification of the MSC model is performed against two large-eddy simulations (LESs) with similar average inflow velocity profiles and a different capping inversion strength, so that two distinct interfacial gravity wave regimes are produced, i.e. subcritical and supercritical. Interfacial waves can produce high blockage in the first case, as they are allowed to propagate upstream. On the other hand, in the supercritical regime their propagation speed is less than their advection velocity, and upstream blockage is only operated by internal waves. The MSC model not only proves to successfully capture both local induction and global blockage effects in the two analyzed regimes, but also captures the interaction between the wind farm and gravity waves, underestimating wind farm power by about only 2ĝ€¯% compared with the LES results. Conversely, wake models alone cannot distinguish between differences in thermal stratification, even if combined with a local induction model. Specifically, they are affected by a first-row overprediction bias that leads to an overestimation of the wind farm power by 13ĝ€¯% to 20ĝ€¯% for the modeled regimes.

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As offshore wind farms grow in size, the blockage effect associated with the atmospheric gravity waves they trigger is expected to become more important. To model this, recent research has produced an Atmospheric Perturbation Model (APM), which simulates the mesoscale flow in the atmospheric boundary layer at a low computational cost compared to traditional methods. However, as a simplified reduced-order model, it can not resolve individual turbine wakes, and has to be coupled to an engineering wake model to predict farm power output. Over the years, three coupling methods have been developed, and been combined into the open-source framework WAYVE. This paper compares them, discussing both their theoretical validity and their performance. For the latter, we validate the velocities and power outputs predicted by WAYVE against 27 LES simulations. We find that the velocity matching (VM) and the pressure-based (PB) methods perform the best. Of these two, the VM method is more consistent with the APM output, while the PB method has a significantly lower computational cost.

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Wind Farm Flow Control (WFFC) is the discipline of manipulating the flow between wind turbines to achieve a farm-wide goal, like power tracking, load mitigation, or power maximization. Specifically, steady-state control approaches have shown promising results in both theory and practice for power maximization. But how are they expected to perform in a dynamically changing environment? This paper presents an open-source wake modeling framework called OFF. It allows the approximation of the performance of WFFC strategies in response to environmental changes at a low computational cost. It is rooted in previously published dynamic parametric engineering models and offers a flexible and adaptable platform to explore these models further. The presented study tests the modeling framework by investigating the performance of different wake steering controllers in a 10-turbine wind farm case study based on a subset of the Dutch wind farm Hollandse Kust Noord (HKN). The case study uses a 24-hour wind direction time series based on field data and verifies subsets of the time series in LES. The results highlight how dependent yaw travel is on the controller settings and suggest where users can strike a balance between power gains and actuator usage. They also show the structural differences and similarities between steady-state and dynamic engineering models. The comparison to LES shows what time scales the surrogate models cover and how accurately. While steady-state models capture turbine power signal dynamics up to ≈ 1/570 Hz, the dynamic wake description can predict dynamics up to ≈ 1/360 Hz with a better correlation and normalized root-mean-square-error. Further results show that the dynamic wake description is mainly advantageous over steady-state wake models for shorter periods (< 20 min). The paper also opens up the discussion about the effectiveness of wind farm flow control in a time-marching manner as opposed to a steady-state viewpoint.@en

Accurately predicting wind turbine wake effects is essential for optimizing wind-farm performance and minimizing maintenance costs. This study explores the applicability of the Sparse Regression of Turbulent Stress Anisotropy (SpaRTA) framework to develop a simple yet robust Reynolds-averaged Navier-Stokes (RANS) model for wake prediction in wind energy contexts. The framework introduces two correction terms into two-equation models, with k - ϵ model being utilized in the current study. One correction term resembles the residual of the Turbulent Kinetic Energy (TKE) equation, and the other corrects the deviatoric part of the Reynolds Stress Tensor (RST). The terms are calculated from high-fidelity measurement or simulation data, and symbolic regression is used to determine the model for these terms. In this study, Large Eddy Simulation (LES) data from a single turbine is used as the training dataset, and a sample pre-selection process is employed to discover a correction model efficiently. The derived model incorporates two terms based on Pope's basis tensors and their invariants. The expression of the obtained model shows that it functions as a modification to the constant Cμ in the k - ϵ model. The model is evaluated by comparing its predicted velocity and TKE fields with the LES data used for the training. The model showed satisfactory performance in predicting both fields. Additionally, its generalizability is evaluated by testing it against a more complex six-turbine unseen case. The results indicate that the model effectively captures the velocity field and power output, but it tends to overpredict TKE, especially in the wake region.

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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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The growing number and growing size of wind energy projects coupled with the rapid growth in high-performance computing technology are driving researchers toward conducting large-scale simulations of the flow field surrounding entire wind farms. This requires highly parallel-efficient tools, given the large number of degrees of freedom involved in such simulations, and yields valuable insights into farm-scale physical phenomena, such as gravity wave interaction with the wind farm and farm–farm wake interactions. In the current study, we introduce the open-source, finite-volume, large-eddy simulation (LES) code TOSCA (Toolbox fOr Stratified Convective Atmospheres) and demonstrate its capabilities by simulating the flow around a finite-size wind farm immersed in a shallow, conventionally neutral boundary layer (CNBL), ultimately assessing gravity-wave-induced blockage effects. Turbulent inflow conditions are generated using a new hybrid off-line–concurrent-precursor method. Velocity is forced with a novel pressure controller that allows us to prescribe a desired average hub-height wind speed while avoiding inertial oscillations above the atmospheric boundary layer (ABL) caused by the Coriolis force, a known problem in wind farm LES studies. Moreover, to eliminate the dependency of the potential-temperature profile evolution on the code architecture observed in previous studies, we introduce a method that allows us to maintain the mean potential-temperature profile constant throughout the precursor simulation. Furthermore, we highlight that different codes do not predict the same velocity inside the boundary layer under geostrophic forcing owing to their intrinsically different numerical dissipation. The proposed methodology allows us to reduce such spread by ensuring that inflow conditions produced from different codes feature the same hub wind and thermal stratification, regardless of the adopted precursor run time. Finally, validation of actuator line and disk models, CNBL evolution, and velocity profiles inside a periodic wind farm is also presented to assess TOSCA’s ability to model large-scale wind farm flows accurately and with high parallel efficiency.@en

In the context of large off-shore wind farms, power production is influenced greatly by the turbine array's interaction with the atmospheric boundary layer. One of the most influencing manifestations of such complex interaction is the increased level of shear stress observed within the farm. This leads to higher momentum fluxes that affect the wind speed at the turbine locations and in the cluster wake. At the wind farm entrance, an internal boundary layer (IBL) grows due to the change in effective roughness imposed by the wind turbines, and for large enough clusters, this can reach the unperturbed boundary layer height in what is referred to as the fully developed regime. Downwind, a second IBL starts growing, while the shear stress profile decays exponentially to its unperturbed state. In the present study, we propose a simple analytical model for the vertical profile of the horizontal shear stress components in the three regions identified above. The model builds upon the top-down model of Meneveau (J. Turbul., vol. 13, 2012, N7), and assumes that the flow develops in a conventionally neutral boundary layer. The proposed parametrization is verified successfully against large-eddy simulations, demonstrating its ability to capture the vertical profile of horizontal shear stress, and its evolution both inside and downwind of the wind farm. Our findings suggest that the developed model can prove extremely useful to enhance the physical grounds on which new classes of coupled wind farm engineering models are based, leading to a better estimation of meso-scale phenomena affecting the power production of large turbine arrays.@en

The interaction of large wind farm clusters with the thermally stratified atmosphere has emerged as an important physical process that impacts the productivity of wind farms. Under stable conditions, this interaction triggers atmospheric gravity waves (AGWs) in the free atmosphere due to the vertical displacement of the atmospheric boundary layer (ABL) by the wind farm. AGWs induce horizontal pressure gradients within the ABL that alter the wind speed distribution within the farm, influencing both wind farm power generation and wake development. Additional factors, such as the growth of an internal boundary layer originating from the wind farm entrance and increased turbulence due to the wind turbines, further contribute to wake evolution. Recent studies have highlighted the considerable computational cost associated with simulating gravity wave effects within large-eddy simulations (LESs), as a significant portion of the free atmosphere must be resolved due to the large vertical spatial scales involved. Additionally, specialized boundary conditions are required to prevent wave reflections from contaminating the solution. In this study, we introduce a novel methodology to model the effects of AGWs without extending the LES computational domain into the free atmosphere. The proposed approach addresses the wave reflection problem inherently, eliminating the need for these specialized boundary conditions. We utilize the recently developed multi-scale coupled (MSC) model of Stipa et al. (2024b) to estimate the vertical ABL displacement triggered by the wind farm, and we apply the deformation to the domain of an LES that extends only to the inversion layer. The accuracy in predicting the AGW-induced pressure gradients is equivalent to the MSC model. The AGW modeling technique is verified for two distinct free-atmosphere stability conditions by comparing it to the traditional approach in which AGWs are fully resolved using a domain that extends several kilometers into the free atmosphere. The proposed approach accurately captures AGW effects on the row-averaged thrust and power distribution of wind farms while demanding 12.7 % of the computational resources needed for traditional methods. Moreover, when conventionally neutral boundary layers are studied, there is no longer a need to solve the potential temperature equation, as stability is neutral within the boundary layer. The developed approach is subsequently used to compare the global blockage and pressure disturbances obtained from the simulated cases against a solution characterized by zero boundary layer displacement, which represents the limiting case of very strong stratification above the boundary layer. This approximation, sometimes referred to as the “rigid lid”, is compared against the full AGW solution using the MSC model. This is done for different values of inversion strength and free atmosphere lapse rate, evaluating the ability of the “rigid lid” to predict blockage, wake effects, and overall wind farm performance.

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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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The Mesoscale to Microscale Coupling team, part of the U.S. Department of Energy Atmosphere to Electrons (A2e) initiative, has studied various important challenges related to coupling mesoscale models to microscale models for the use case of wind energy development and operation. Several coupling methods and techniques for generating turbulence at the microscale that is subgrid to the mesoscale have been evaluated for a variety of cases. Case studies included flat-terrain, complex-terrain, and offshore environments. Methods were developed to bridge the terra incognita, which scales from about 100ĝ€¯m through the depth of the boundary layer. The team used wind-relevant metrics and archived code, case information, and assessment tools and is making those widely available. Lessons learned and discerned best practices are described in the context of the cases studied for the purpose of enabling further deployment of wind energy.

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Reproducing realistic date- and site-specific unsteady wind conditions in large-eddy simulations is becoming increasingly useful in wind energy. How to run a large-eddy simulation to match observed conditions, however, remains an open research question. One approach that has received considerable attention is mesoscale-to-microscale coupling, in which information about the mesoscale weather, most commonly acquired from a mesoscale numerical weather model, is passed on to a microscale model. In this paper, we demonstrate how the recently developed profile-assimilation technique, a form of mesoscale-to-microscale coupling, can be used to drive large-eddy simulations solely based on observed mean-flow profiles at a single location, bypassing the need for auxiliary mesoscale simulations. The new approach is evaluated for a diurnal cycle at the Scaled Wind Farm Technology site. Observed mean-flow profiles from the ground up to a height of 2 km are reconstructed by aggregating measurements from multiple instruments, and gaps in the data are infilled with natural neighbor interpolation. We perform nine simulations using various forcing approaches to deal with data limitations. The results show that it is indeed possible to drive microscale large-eddy simulation with observations using the profile-assimilation technique, notwithstanding large gaps in virtual potential temperature measurements. However, profile assimilation with vertical smoothing of the error between the desired and actual profiles is required. Without that smoothing, the microscale simulations develop unrealistically high turbulence levels under many situations. Finally, we show that simulated mesoscale data can account for missing observations, although care is needed as both data sources are not necessarily compatible.

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Vertical temperature profiles influence the wind power generation of large offshore wind farms through stability-dependent effects such as blockage and gravity waves. However, numerical tools that are used to model these effects are often computationally too expensive to cover the large variety of atmospheric states occurring over time. Generally, an informed decision about which representative nonidealized situations to simulate is missing because of the lack of easily available information on representative vertical profiles, taking into account their spatiotemporal variability. Therefore, we present a novel framework that allows a smart selection of vertical temperature profiles. The framework consists of an improved analytical temperature model for the atmospheric boundary layer and lower troposphere, a subsequent clustering of these profiles to identify representatives, and last, a determination of areas with similar spatiotemporal characteristics of vertical profiles. When applying this framework on European ERA5 data, physically realistic representatives were identified for Europe, excluding the Mediterranean. Two or three profiles were found to be dominant for the open ocean, whereas more profiles prevail for land. Over the open ocean, weak temperature gradients in the boundary layer and a clear capping inversions are widespread, and stable profiles are absent except in the region of the East Icelandic Current. Interestingly, according to the ERA5 data, at its resolution, coastal areas and seas surrounded by land behave more similar to the land areas than to the open ocean, implying that a larger set of model integrations are needed for these areas to obtain representative results for offshore wind power assessments in comparison with the open ocean.

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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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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

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

To simulate the airflow through a wind farm across a wide range of atmospheric conditions, microscale models (e.g., large-eddy simulation, LES, models) have to be coupled with mesoscale models, because microscale models lack the atmospheric physical processes to represent time-varying local forcing. Here we couple mesoscale model outputs to a LES solver by applying mesoscale momentum- and temperature-budget components from the Weather Research and Forecasting model to the governing equations of the Simulator fOr Wind Farm Applications model. We test whether averaging the budget components affects the LES results with regard to quantities of interest to wind energy. Our study focuses on flat terrain during a quiescent diurnal cycle. The simulation results are compared with observations from a 200-m tall meteorological tower and a wind-profiling radar, by analyzing time series, profiles, rotor-averaged quantities, and spectra. While results show that averaging reduces the spatio-temporal variability of the mesoscale momentum-budget components, when coupled with the LES model, the mesoscale bias (in comparison with observations of wind speed and direction, and potential temperature) is not reduced. In contrast, the LES technique can correct for shear and veer. In both cases, however, averaging the budget components shows no significant impact on the mean flow quantities in the microscale and is not necessary when coupling mesocale budget components to the LES model.

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Mesoscale-to-microscale coupling (MMC) aims to address the limited scope of traditional large-eddy simulations by driving the microscale flow with information concerning large-scale weather patterns provided by mesoscale models. We present a new offline MMC technique for horizontally homogeneous microscale flow conditions, in which internal forcing terms are computed based on mesoscale time–height profiles of mean-flow quantities. The advantage of such an approach is that it can be used to drive a microscale simulation with either mesoscale or observational data, and that it does not rely on specific terms in the mesoscale budget equations, which are typically not part of the default output of a mesoscale solver. The performance of the proposed profile assimilation technique is assessed based on the simulation of a typical diurnal cycle over the Scaled Wind Farm Technology site in west Texas. Results indicate that simple data assimilation techniques lead to unphysically high levels of shear and turbulence caused by the algorithm’s inability to cope with inaccuracies in the mesoscale time–height profiles. Modifying the algorithm to account for vertical coherence in the mesoscale source terms gives the microscale solver a greater ability to correct the provided mesoscale time–height profiles, leading to improved predictions of shear and turbulence statistics. The resulting turbulence statistics are in good agreement with meteorological tower observations and simulation results obtained with state-of-the-art coupling techniques using mesoscale budget components.

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