Engineering Wake Models Research Articles

Efficient wind farm layout optimization with the FLOWERS AEP model and analytic gradients

Wind farm layout optimization (WFLO) studies often aim to maximize the annual energy production (AEP) of a wind farm by choosing an arrangement of turbines that minimizes wake interactions. One way to reduce the cost of WFLO studies is by using more computationally efficient AEP models. The cost of standard AEP modeling approaches, based on the numerical integration of low-fidelity engineering wake models, scales poorly with the number of simulated discrete wind conditions. A second way to reduce cost when using a gradient-based algorithm is to supply exact gradient information instead of finite-difference estimates. However, analytical functions for the derivatives of AEP with respect to turbine positions are not always available in the conventional modeling approach. FLOWERS is a computationally inexpensive, analytical model for wind farm AEP that is specifically developed for WFLO applications. In this paper, we analyze the performance of the FLOWERS AEP model with analytic gradients in a layout optimization study compared with a reference optimization framework across three wind farm case studies. We find that the FLOWERS-based approach reduces computation time by a factor of 50–4000 and improves optimal AEP by about 0.3% with less than half of the variability in AEP across instances with randomized initial conditions. We also find the optimal layouts to be insensitive to model parameter tuning, making FLOWERS-based layout optimization a streamlined, user-friendly approach.

A diffusion-based wind turbine wake model

Describing the evolution of a wind turbine's wake from a top-hat profile near the turbine to a Gaussian profile in the far wake is a central feature of many engineering wake models. Existing approaches, such as super-Gaussian wake models, rely on a set of tuning parameters that are typically obtained from fitting high-fidelity data. In the current study, we present a new engineering wake model that leverages the similarity between the shape of a turbine's wake normal to the streamwise direction and the diffusion of a passive scalar from a disk source. This new wake model provides an analytical expression for a streamwise scaling function that ensures the conservation of linear momentum in the wake region downstream of a turbine. The model also considers the different rates of wake expansion that are known to occur in the near- and far-wake regions. Validation is presented against high-fidelity numerical data and experimental measurements from the literature, confirming a consistent good agreement across a wide range of turbine operating conditions. A comparison is also drawn with several existing engineering wake models, indicating that the diffusion-based model consistently provides more accurate wake predictions. This new unified framework allows for extensions to more complex wake profiles by making adjustments to the diffusion equation. The derivation of the proposed model included the evaluation of analytical solutions to several mathematical integrals that can be useful for other physical applications.

The future of offshore wind power production: Wake and climate impacts

Rapid deployment of offshore wind is expected within the coming decades to help meet climate goals. With offshore wind turbine lifetimes of 25–30 years, and new offshore leases spanning 60 years, it is vital to consider long-term changes in potential wind power resource at the farm planning stage. Such changes may arise from multiple sources, including climate change, and increasing wake-induced power losses. In this work, we investigate and compare these two sources of long-term change in wind power, for a case study consisting of 21 wind farms within the German Bight. Consistent with previous studies, we find a small but significant reduction in wind resource due to climate change by the end of the 21st century under the high-emission RCP8.5 scenario, compared with a historical period, with a mean power reduction (over an ensemble of seven climate models) of 2.1%. To assess the impact of wake-induced losses due to increasingly dense farm build-out, we model wakes within the German Bight region using an engineering wake model, under various stages of (planned) build-out corresponding to the years 2010–2027. By identifying clusters of wind farms, we decompose wake effects into long-range (inter-cluster), medium-range (intra-cluster) and short-range (intra-farm) effects. Inter-cluster wake-induced losses increase from 0 for the 2010 scenario to 2.5% for the 2027 scenario, with intra-cluster losses also increasing from 0 to 4.3%. Intra-farm losses are relatively constant, at around 13%. While the evolution of wake effects therefore outweighs the climate effect, and impacts over a shorter timescale, both factors are significant. We also find evidence of an interaction between the climate and wake effects. Both climate change and evolving wake effects must therefore be considered within resource assessment and wind farm planning.

Wind Turbine Wake Regulation Method Coupling Actuator Model and Engineering Wake Model

The wake effect is one of the main factors affecting the power generation of wind farms. Wake regulation is often used to reduce the wake interference between wind turbines. Accurate assessment of the wake flow of wind turbine is essential to wake regulation. Engineering wake models are widely used for rapid evaluation of the wake at present due to lower computational resource cost. However, the selection of empirical parameters of the wake model has significant influence on the prediction accuracy, especially in the case of yaw. The actuator model based on CFD simulation has less dependence on empirical parameters and higher simulation accuracy. However, the computational cost is too high for wake regulation for large wind farms. This paper proposed an improved wake regulation method that combines the advantages of the actuator line model (ALM) method and the engineering wake mode. The simulation results of the ALM is used to calibrate the empirical parameters of the engineering wake model. The calibrated wake model can be used to optimize the yaw angle of wind turbines during wake regulation. The accuracy of two models is compared using wind tunnel experimental data. The ALM results give better agreement to the experimental data. The Horns Rev wind farm case is used for the coupled method verification. The power generation increase using the engineering wake model is obviously greater than that of the ALM. After calibrating the wake model, the gap between the two power predictions is greatly narrowed, which proves the effectiveness of the proposed method. The proposed coupling method can be used to improve the credibility of the wake regulation with affordable computational cost.

Graph network heterogeneity predicts interplant wake losses

Wind plants generate large-scale wakes, which can affect the performance of neighboring installations. Such wakes are challenging to estimate due to the inherent complexity in modeling wake interactions between large quantities of turbines at various distances. Weighted directed graph networks can inform complex models by linking turbine pairs into chains of upstream and downstream neighbors for a given wind direction. A novel interpretation of the graph network adjacency matrix is proposed where each element of the matrix represents the cumulative impact of upstream turbines on an individual. In this study, wake losses were estimated with an engineering wake model across a range of inflow conditions for nine parametric variations of a system containing two neighboring wind plants. The parametric nature of the study isolates turbine spacing within the plant, separation distance between plants, and wind direction as the main drivers of wake losses. Spatial heterogeneity is computed from the weighted average adjacency matrix of each plant arrangement. The proposed method is orders of magnitude faster than wake modeling and does not require detailed turbine information or atmospheric conditions. The weighted average adjacency matrix provides insight on the spatial organization of wake losses at various scales. Plant heterogeneity is correlated with wake losses within and among plants. Framing wind plant wake interaction in terms of graph network spatial heterogeneity provides an efficient approach for predicting wake losses within and among neighboring wind plants with applications to other complex systems where wake interactions are key factor.

FLOWERS AEP: An Analytical Model for Wind Farm Layout Optimization

ABSTRACTAnnual energy production (AEP) is commonly used in objective functions for wind farm layout optimization. AEP is proportional to wind farm power production integrated over an annual distribution of free‐stream wind conditions. Physics‐based estimates of wind farm power production typically rely on low‐fidelity engineering wake models that approximate the steady‐state wind farm flow field. AEP estimates are then obtained by performing independent simulations for discrete wind conditions and using rectangular quadrature to account for each condition's expected frequency of occurrence. Depending on the number of simulated discrete wind conditions, this numerical integral could be hampered by poor accuracy or high computational costs. The FLOWERS AEP model instead poses an analytical integral of the engineering wake model over the variable wind conditions, yielding a closed‐form, analytical function for wind farm AEP. This paper derives the analytical functions for FLOWERS AEP and its derivatives with respect to turbine position, which are useful for gradient‐based wind farm layout optimization, in nondimensional form. We then analyze the benefits of the FLOWERS AEP model over conventional reference models, focusing on its low cost, adequate wake loss predictions, and smooth design space. Although the FLOWERS approach is found to predict the exact value of AEP with some error relative to the reference model (within 14% on average), it dramatically reduces computation time by an order of magnitude, produces a qualitatively similar design space at relatively low resolution, and yields comparable optimal layouts. This significant speed improvement is critical in layout optimization applications, where determining an optimal layout in an efficient manner is more important than precise AEP prediction.

A Nonlinear Wind Turbine Wake Expansion Model Considering Atmospheric Stability and Ground Effects

This study investigates the influence of atmospheric stability and ground effects on wind turbine wake recovery, challenging the conventional linear relationship between turbulence intensity and wake expansion coefficient. Through comprehensive field measurements and numerical simulations, we demonstrate that the linear wake expansion assumption is invalid at far-wake locations under high turbulence conditions, primarily due to ground effects. We propose a novel nonlinear wake expansion model that incorporates both atmospheric stability and ground effects by introducing a logarithmic relationship between the wake expansion coefficient and turbulence intensity. Validation results reveal the superior prediction accuracy of the proposed model compared to typical engineering wake models, with root mean square errors of wake wind speed predictions ranging from 0.04 to 0.063. The proposed model offers significant potential for optimizing wind farm layouts and enhancing overall wind energy production efficiency.

Site-specific production forecast through data-driven and engineering models

The present study investigates the predictive capabilities of two site-specific wind power forecasting models. The two approaches make use of a machine learning ensemble model that combines forecasts from several numerical weather predictions (NWP) to match local observations. In the first approach, the training data consists of historical site power production recordings. This yields a black-box model that includes the wind farm behaviour. The second approach is a combination of data-driven and explicit modelling. In the first step, the machine learning ensemble model forecasts the site wind conditions. Then, this input is fed to a site-specific engineering wake model. This hybrid ”grey-box” approach explicitly resolves some farm flow effects.The study shows that the performance of both methods differs over the wind speed range. The purely data-driven model performs better at medium wind speeds, which also occur more often. The hybrid method predictions agree better during periods of higher wind speeds. In the last part, the study showcases the capabilities of the forecasting methods when participating in the energy market. Additionally, the engineering wake model allows for power maximisation through wind farm control.

Toward ultra-efficient high-fidelity predictions of wind turbine wakes: Augmenting the accuracy of engineering models with machine learning

This study proposes a novel machine learning (ML) methodology for the efficient and cost-effective prediction of high-fidelity three-dimensional velocity fields in the wake of utility-scale turbines. The model consists of an autoencoder convolutional neural network with U-Net skipped connections, fine-tuned using high-fidelity data from large-eddy simulations (LES). The trained model takes the low-fidelity velocity field cost-effectively generated from the analytical engineering wake model as input and produces the high-fidelity velocity fields. The accuracy of the proposed ML model is demonstrated in a utility-scale wind farm for which datasets of wake flow fields were previously generated using LES under various wind speeds, wind directions, and yaw angles. Comparing the ML model results with those of LES, the ML model was shown to reduce the error in the prediction from 20% obtained from the Gauss Curl hybrid (GCH) model to less than 5%. In addition, the ML model captured the non-symmetric wake deflection observed for opposing yaw angles for wake steering cases, demonstrating a greater accuracy than the GCH model. The computational cost of the ML model is on par with that of the analytical wake model while generating numerical outcomes nearly as accurate as those of the high-fidelity LES.

Wind pattern clustering of high frequent field measurements for dynamic wind farm flow control

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.

RANS wake surrogate: Impact of Physics Information in Neural Networks

Artificial Neural Networks (ANNs) are being applied as a faster alternative to Computational Fluid Dynamics (CFD) for wind turbine engineering wake models. Unfortunately, ANNs can fail to generalize if the data is insufficient. Physics-Informed Neural Networks (PINNs) can improve convergence while lowering the required data amounts. This paper investigates the PINN methodology systematically by considering varying amounts of data and physics collocation points. This work considers the rotationally symmetric Reynolds Averaged Navier-Stokes (RANS) formulation. Initially, a baseline fully data-driven ANN is studied to determine a suitable network size. Then, multiple PINN-based wake surrogates are trained with continuity and momentum conservation knowledge, varying amounts of data, and physics collocation points. It was found that including physics information under the best circumstances could improve accuracy by 18% at the cost of increasing the training time by a factor of 116. The findings imply that physics information can improve neural network based wake surrogates.

Profit-optimal data-driven operation of a hybrid power plant participating in energy markets

An energy management system (EMS) is formulated for a hybrid power plant (HPP), consisting of a wind power plant and battery storage plant, participating in bidding stages in the German energy market. The EMS utilizes supervisory control and data acquisition (SCADA) measurements from the site to improve power forecast from the wind power plant. First, the measurement data are used together with numerical weather prediction data to accurately forecast local wind conditions. Second, the measurement data are used to adapt a baseline engineering wake model that gives the total wind power generation for a given input wind condition. The EMS also uses an online cyclic damage minimization approach to accurately balance the battery damage cost against the revenue obtained by market bidding. An HPP controller is formulated to ensure proper tracking of optimal set-points. When compared with standard formulations, the proposed approach shows an accurate estimation and balancing of revenue and costs and a significant reduction in the power deviation penalty, which leads to significantly higher overall profit.

Wind Turbine Loads in the Near Wake

This work is analyzing the the engineering wake models Frandsen and TNO for small inter-turbine distances. Therefore, loads generated by actuator line LES (AL-LES) wind fields will be compared with the loads generated by the mentioned engineering models. The results are checked for plausibility by comparing the current results with the available literature. Load comparisons for non-dimensional distances x/D ranging from 1.75 to 4 and for seven different wind speeds in order to consider the influence of the thrust coefficient were made. For each speed a low and a high turbulence intensity case is considered. Two latest generation turbines are investigated (one with a diameter of 138 m and one with a diameter of 175 m).Our studies reveal that the fatigue loads computed with the Frandsen and TNO model are conservative compared to the loads generated by AL-LES wind fields. The Wöhler averaged (m=10 and a sector of 120°) flap wise blade root bending moments are at least 150% higher for the TNO and Frandsen model compared to the loads generated by AL-LES wind fields for distances lower than 2.3D and C T values higher than 0.7. This indicates that current sector management rules applied by means of the results of the Frandsen and TNO model are too restrictive. A possible way to decrease the conservatism without posing at risk the structural integrity of the turbines is the following: The wake added turbulence intensity can be kept constant for regions in the parameter space with very high conservatism (e.g. for distances smaller than 2.3D and C T values higher than 0.7).

Benchmarking engineering wake models for farm-to-farm interactions

Inter-farm wakes between offshore wind farms can cause a significant production loss at the downstream wind farm. We compare the power production at two wind farms that are separated by approximately 20 km to engineering model results provided by three different wind farm developers. Model inflow conditions were derived from the nacelle anemometry of the wake-creating wind farm and a mesoscale simulation. The comparison reveals that the model results show in general a good approximation of the wake losses, but underestimate the increase of losses in stable stability conditions. Here, specifically the measured wakes appear to be much wider than the modelled wakes.

Floating wind farm design using social and environmental constraints

This work proposes a wind farm design methodology, integrating several design variables from different design aspects into an optimization problem, such as turbine power, number of turbines, cable types, wind farm layout and site location. A mixed integer genetic algorithm is employed to combine discrete and continuous design variables to find the design with minimum Levelized Cost of Energy (LCoE). The wind farm LCoE is calculated using a wind farm model, which combines detailed cost functions for different cost elements and engineering wake models to estimate Annual Energy Production. The design is constrained not only by technical aspects such as total power, farm area, but also by environmental and social constraints. These include the wind farm visibility, which is a popular concern among the people living along the coast of nearby wind farms, and availability, implying the compliance with the designated exclusion zones. To demonstrate the sensitivity of design constraints, two floating wind farms are sited and optimized as a case study, using different visibility constraints. The developed design tool within this study aims to bridge the gap between wind farm developers and local authorities who are responsible for permitting and zoning of development areas.

Wake Modelling Based on the Stokes Stream Function and the Toroidal-Poloidal Decomposition

The Stokes stream function and its generalisation, the Toroidal-Poloidal decomposition, are well-suited for the derivation of axisymmetric engineering wake models, as they are solenoidal and fulfil conservation of mass of an incompressible fluid by construction. The presented model consists of a time-independent contribution based on Laguerre basis functions with a simple parametrisation that is well-suited for the diffusion-dominated far wake. A time-dependent part can be added based on a poloidal component that can model either helical or toroidal vortex structures, and its parametrisation can be closed towards the total thrust force on the rotor. Despite requiring an external solver, the presented model shows potential as a drop-in replacement for the Ainslie wake model that is widely used in the Wind Energy industry as part of the Dynamic Wake Meandering model.

Evaluating wind-farm power generation using a new direct integration of axisymmetric turbine wake

Engineering wake models enable fast calculation of wind-farm power generation including wake-turbine interactions, which is critical for annual energy yield calculations and for farm optimisation either at the design phase or during operation. The operating point of a turbine is determined based on its rotor-averaged wind speed, which is impacted by upstream wakes. The rotor-averaged deficit is typically calculated numerically by using a set of averaging points across the rotor disk, for which a Gaussian shape function is commonly evaluated. This numerical approach can have uncertainty based on the distribution of the averaging points. Also, a large number of averaging points can increase computational cost, which is detrimental for studies that rely on many individual calculations of farm power generation, e.g. layout optimisation. To avoid these drawbacks, we present a novel analytical solution to the circular-disk integration of a two-dimensional axisymmetric Gaussian function depicting upstream wakes for an arbitrary lateral offset between the rotor and the wake source. The analytical expression is compared against numerical averaging of an upstream wake, and is applied to the Horns Rev 1 wind farm showing excellent accuracy. Wind-farm layout optimisation models, especially methods based on gradient-descent optimisation, can benefit from the presented expression significantly, as this provides an analytically differentiable formulation for the rotor-averaged wind speed.

Comparing methods for coupling wake models to an atmospheric perturbation model in WAYVE

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.

Wake characteristics and vortex structure evolution of floating offshore wind turbine under surge motion

Offshore wind energy is booming and floating offshore wind has been proved to be a promising clean energy. Wake effect is one of the biggest challenges in large-scale floating wind farm which results in power loss and increased fatigue load. In this paper, actuator line model (ALM) coupled with unsteady Reynolds-averaged Navier-Stokes (URANS) is adopted to investigate the wake characteristics and evolution of floating wind turbine under motion. Besides, modal analysis is adopted to extract typical features of turbine wake. Velocity fluctuation is the prominent characteristic of floating turbine wake. The increase of surge frequency results in the decrease of velocity fluctuating region and large surge amplitude leads to bigger velocity deficit fluctuations. In addition, the surge motion brings a faster recovery rate than fixed wind turbine. The induced velocity field generated by vortex ring structure is the key to understanding complex evolution of turbine wake and the vortex ring structure is analyzed in this paper. With the deep understanding of FOWT wake, an innovative vortex ring structure model is proposed in this paper. This work is the basic work of developing the engineering wake model of floating wind turbine, to cope with the wake effect challenge in the large-scale floating wind farm.

Measurement-driven large-eddy simulations of a diurnal cycle during a wake-steering field campaign

Abstract. High-fidelity flow modeling with data assimilation enables accurate representation of the wind farm operating environment under realistic, nonstationary atmospheric conditions. Capturing the temporal evolution of the turbulent atmospheric boundary layer is critical to understanding the behavior of wind turbines under operating conditions with simultaneously varying inflow and control inputs. This paper has three parts: the identification of a case study during a field evaluation of wake steering; the development of a tailored mesoscale-to-microscale coupling strategy that resolved local flow conditions within a large-eddy simulation (LES), using observations that did not completely capture the wind and temperature fields throughout the simulation domain; and the application of this coupling strategy to validate high-fidelity aeroelastic predictions of turbine performance and wake interactions with and without wake steering. The case study spans 4.5 h after midnight local time, during which wake steering was toggled on and off five times, achieving yaw offset angles ranging from 0 to 17°. To resolve nonstationary nighttime conditions that exhibited shear instabilities, the turbulence field was evolved starting from the diurnal cycle of the previous day. These background conditions were then used to drive wind farm simulations with two different models: an LES with actuator disk turbines and a steady-state engineering wake model. Subsequent analysis identified two representative periods during which the up- and downstream turbines were most nearly aligned with the mean wind direction and had observed yaw offsets of 0 and 15°. Both periods corresponded to partial waking on the downstream turbine, which had errors in the LES-predicted power of 4 % and 6 %, with and without wake steering. The LES was also able to capture conditions during which an upstream turbine wake induced a speedup at a downstream turbine and increased power production by up to 13 %.