Engineering Wake Models Research Articles

Wind Turbine Wake Modeling in Accelerating Wind Field: A Preliminary Study on a Two-Dimensional Hill

Complex terrain can influence wind turbine wakes and wind speed profiles in a wind farm. Consequently, predicting the performance of wind turbines and energy production over complex terrain is more difficult than it is over flat terrain. In this preliminary study, an engineering wake model, that considers acceleration on a two-dimensional hill, was developed based on the momentum theory. The model consists of the wake width and wake wind speed. The equation to calculate the rotor thrust, which is calculated by the wake wind speed profiles, was also formulated. Then, a wind-tunnel test was performed in simple flow conditions in order to investigate wake development over a two-dimensional hill. After this the wake model was compared with the wind-tunnel test, and the results obtained by using the new wake model were close to the wind-tunnel test results. Using the new wake model, it was possible to estimate the wake shrinkage in an accelerating two-dimensional wind field.

Physics-induced graph neural network: An application to wind-farm power estimation

We propose a physics-inspired data-driven model that can estimate the power outputs of all wind turbines in any layout under any wind conditions. The proposed model comprises two parts: (1) representing a wind farm configuration with the current wind conditions as a graph, and (2) processing the graph input and estimating power outputs of all the wind turbines using a physics-induced graph neural network (PGNN). By utilizing the form of an engineering wake interaction model as a basis function, PGNN effectively imposes physics-induced bias for modelling the interaction among wind turbines into the network structure. simulation study shows that the combination of a graph representation of a wind farm and PGNN produce not only accurate and generalizable estimations but also physically explainable estimations. That is, the computing and reasoning procedures of PGNN can be understood by analyzing the intermediate features of the model. We also conduct a layout optimization experiment to show the effectiveness of PGNN as a differentiable surrogate model for wind farm power estimations.

Why curved wind turbine rows are better than straight ones

Wind turbine wake effects in wind farms not only reduce the wind farm power production but also influence the wind farm power dependency on wind direction. In this paper, the wake effects in wind farm layouts consisting of curved and straight wind turbine rows are studied using engineering wake models and a Reynolds-averaged Navier-Stokes model. These models predict a similar annual energy production for both wind farm layouts, but show stronger wake losses in the aligned wind directions for a rectangular wind farm layout, while the wake losses for a curved wind farm layout are more spread out over a larger wind direction sector. An energy system level simulation predicts that the enhanced spreading of wake losses over wind directions results in less hourly variability in energy generation on a Danish energy system level. Thus, our results show that a curved wind farm layout is more favorable compared to a wind farm layout with straight rows.

Engineering models for turbine wake velocity deficit and wake deflection. A new proposed approach for onshore and offshore applications

An engineering wake model based on the Ainslie model is proposed. The eddy viscosity term associated with momentum diffusivity is modified to take into account the effects of atmospheric stability. The parameters used are typically available from high-quality on-site measurement campaigns and the effects of atmospheric stability are based on empirical models for the estimation of the Monin-Obukhov length. The dependence on physical quantities only is particularly advantageous for fast wake modelling, since no further parametrical tuning is needed for each specific case. The proposed wake model is initially compared to wind tunnel data and CFD simulations to test the chosen Obukhov lengths for specific flow conditions. Wind farm production data and concurrent meteorological data at one onshore site are then used to validate the model for specific on-site flow conditions, obtaining good results. Two offshore wind farms are also used to assess the model in a large-scale wind farm scenario: results look promising although some reservations are expressed on the effect of the wake superposition model. Models for the prediction of wake centreline deflection due to yaw are compared at different yaw angles using wind tunnels data and CFD simulations. Although the EPFL model showed some advantage, especially in non-neutral conditions, both models give satisfactory results. Furthermore, it was showed that the wake deflection caused by the rotating wake for non-yawed turbines can have a large impact on the predictions of the centreline deflection.

Fast Control-Oriented Dynamic Linear Model of Wind Farm Flow and Operation

The aerodynamic interaction between wind turbines grouped in wind farms results in wake-induced power loss and fatigue loads of wind turbines. To mitigate these, wind farm control should be able to account for those interactions, typically using model-based approaches. Such model-based control approaches benefit from computationally fast, linear models and therefore, in this work, we introduce the Dynamic Flow Predictor. It is a fast, control-oriented, dynamic, linear model of wind farm flow and operation that provides predictions of wind speed and turbine power. The model estimates wind turbine aerodynamic interaction using a linearized engineering wake model in combination with a delay process. The Dynamic Flow Predictor was tested on a two-turbine array to illustrate its main characteristics and on a large-scale wind farm, comparable to modern offshore wind farms, to illustrate its scalability and accuracy in a more realistic scale. The simulations were performed in SimWindFarm with wind turbines represented using the NREL 5 MW model. The results showed the suitability, accuracy, and computational speed of the modeling approach. In the study on the large-scale wind farm, rotor effective wind speed was estimated with a root-mean-square error ranging between 0.8% and 4.1%. In the same study, the computation time per iteration of the model was, on average, 2.1 × 10 − 5 s. It is therefore concluded that the presented modeling approach is well suited for use in wind farm control.

An Optimization Framework for Wind Farm Design in Complex Terrain

Designing wind farms in complex terrain is an important task, especially for countries with a large portion of complex terrain territory. To tackle this task, an optimization framework is developed in this study, which combines the solution from a wind resource assessment tool, an engineering wake model adapted for complex terrain, and an advanced wind farm layout optimization algorithm. Various realistic constraints are modelled and considered, such as the inclusive and exclusive boundaries, minimal distances between turbines, and specific requirements on wind resource and terrain conditions. The default objective function in this framework is the total net annual energy production (AEP) of the wind farm, and the Random Search algorithm is employed to solve the optimization problem. A new algorithm called Heuristic Fill is also developed in this study to find good initial layouts for optimizing wind farms in complex terrain. The ability of the framework is demonstrated in a case study based on a real wind farm with 25 turbines in complex terrain. Results show that the framework can find a better design, with 2.70% higher net AEP than the original design, while keeping the occupied area and minimal distance between turbines at the same level. Comparison with two popular algorithms (Particle Swarm Optimization and Genetic Algorithm) also shows the superiority of the Random Search algorithm.

Data-driven Wake Modelling for Reduced Uncertainties in short-term Possible Power Estimation

One of the ancillary services the wind farms are required to provide to the system operators is reserve power, which is achieved by down-regulating the wind farm from its possible power. In order to estimate the reserves, the possible power needs to be calculated by correcting the reduced wake effects behind the down-regulated turbines. The most recent grid codes dictate the quality of the possible power at the wind farm level to be assessed within 1-min intervals for offshore wind power plants. Therefore, the necessity of a fast and reliable wake model is more prominent than ever.Here we investigate the performance of two engineering wake models with 1-sec resolution SCADA data on three different offshore wind farms, given the quantified input uncertainty. The preliminary results show that, even wind farm specific training of the model parameters might fail to comply with the strict criteria stated in the grid codes, especially for the layouts with significant wake losses. In order to tackle the inadequacy of the engineering wake models to capture some of the dynamics in the wind farm flow due to the embedded assumptions, purely data-driven techniques are evaluated. The flexibility of such an on-line model enables ‘site-turbine-time-specific’ modelling, in which the parameters are defined per turbine and updated with each time-step in a specific wind farm.

Validation of wind turbine wake models with focus on the dynamic wake meandering model

This analysis compares current wake models, such as the Sten Frandsen turbulence model, an engineering wind speed deficit and turbulence model developed by G. Chr. Larsen, the N. O. Jensen wind speed deficit description and three variations of the dynamic wake meandering (DWM) model to measurements from onshore wind farms. Special attention is given to the dynamic wake meandering model. Today different versions or implementations of the dynamic wake meandering model exist. These versions differ among others in the calculation of the quasi-steady wake deficit in the meandering frame of reference. The influence of these calculation methods on loads and yield is analysed in this work. The validation of the mentioned wake models is based on turbine load, power and wind measurements from two onshore wind farms. One key result of this work is that the DWM model in most cases coincides superiorly with the measurement results compared to the other engineering wake models commonly used in industry.

On wake modeling, wind-farm gradients, and AEP predictions at the Anholt wind farm

Abstract. We investigate wake effects at the Anholt offshore wind farm in Denmark, which is a farm experiencing strong horizontal wind-speed gradients because of its size and proximity to land. Mesoscale model simulations are used to study the horizontal wind-speed gradients over the wind farm. From analysis of the mesoscale simulations and supervisory control and data acquisition (SCADA), we show that for westerly flow in particular, there is a clear horizontal wind-speed gradient over the wind farm. We also use the mesoscale simulations to derive the undisturbed inflow conditions that are coupled with three commonly used wake models: two engineering approaches (the Park and G. C. Larsen models) and a linearized Reynolds-averaged Navier–Stokes approach (Fuga). The effect of the horizontal wind-speed gradient on annual energy production estimates is not found to be critical compared to estimates from both the average undisturbed wind climate of all turbines' positions and the undisturbed wind climate of a position in the middle of the wind farm. However, annual energy production estimates can largely differ when using wind climates at positions that are strongly influenced by the horizontal wind-speed gradient. When looking at westerly flow wake cases, where the impact of the horizontal wind-speed gradient on the power of the undisturbed turbines is largest, the wake models agree with the SCADA fairly well; when looking at a southerly flow case, where the wake losses are highest, the wake models tend to underestimate the wake loss. With the mesoscale-wake model setup, we are also able to estimate the capacity factor of the wind farm rather well when compared to that derived from the SCADA. Finally, we estimate the uncertainty of the wake models by bootstrapping the SCADA. The models tend to underestimate the wake losses (the median relative model error is 8.75 %) and the engineering wake models are as uncertain as Fuga. These results are specific for this wind farm, the available dataset, and the derived inflow conditions.

3-D shear-layer model for the simulation of multiple wind turbine wakes: description and first assessment

Abstract. The number of turbines installed in offshore wind farms has strongly increased in the last years and at the same time the need for more precise estimations of the wind farm efficiency too. In this sense, the interaction between wakes has become a relevant aspect for the definition of a wind farm layout, for the assessment of its annual energy yield and for the evaluation of wind turbine fatigue loads. For this reason, accurate models for multiple overlapping wakes are a main concern of the wind energy community. Existing engineering models can only simulate single wakes, which are superimposed when they are interacting in a wind farm. This method is a practical solution, but it is not fully supported by a physical background. The limitation to single wakes is given by the assumption that the wake is axisymmetric. As an alternative, we propose a new shear-layer model that is based on the existing engineering wake models but is extended to also simulate non-axisymmetric wakes. In this paper, we present the theoretical background of the model and four application cases. We evaluate the new model for the simulation of single and multiple wakes using large-eddy simulations as reference. In particular, we report the improvements of the new model predictions in comparison to a sum-of-squares superposition approach for the simulation of three interacting wakes. The lower deviation from the reference considering single and multiple wakes encourages the further development of the model and promises a successful application for the simulation of wind farm flows.

An analysis of offshore wind farm SCADA measurements to identify key parameters influencing the magnitude of wake effects

Abstract. For offshore wind farms, wake effects are among the largest sources of losses in energy production. At the same time, wake modelling is still associated with very high uncertainties. Therefore current research focusses on improving wake model predictions. It is known that atmospheric conditions, especially atmospheric stability, crucially influence the magnitude of those wake effects. The classification of atmospheric stability is usually based on measurements from met masts, buoys or lidar (light detection and ranging). In offshore conditions these measurements are expensive and scarce. However, every wind farm permanently produces SCADA (supervisory control and data acquisition) measurements. The objective of this study is to establish a classification for the magnitude of wake effects based on SCADA data. This delivers a basis to fit engineering wake models better to the ambient conditions in an offshore wind farm. The method is established with data from two offshore wind farms which each have a met mast nearby. A correlation is established between the stability classification from the met mast and signals within the SCADA data from the wind farm. The significance of these new signals on power production is demonstrated with data from two wind farms with met mast and long-range lidar measurements. Additionally, the method is validated with data from another wind farm without a met mast. The proposed signal consists of a good correlation between the standard deviation of active power divided by the average power of wind turbines in free flow with the ambient turbulence intensity (TI) when the wind turbines were operating in partial load. It allows us to distinguish between conditions with different magnitudes of wake effects. The proposed signal is very sensitive to increased turbulence induced by neighbouring turbines and wind farms, even at a distance of more than 38 rotor diameters.

Study on methods to determine rotor equivalent wind speed to increase prediction accuracy of wind turbine performance under wake condition

A downstream wind turbine located within the reach of the wake region of an upstream wind turbine experiences a decrease in power output due to wake effects. For this reason, when designing a wind farm, various engineering wake models are used to predict the power deficit and wind farm layout is designed in the optimal way to minimize the wake losses. Generally, in the process of calculating the loss of wind farm AEP, in most cases the single point-measured wind speed is used. However, this results in an error when predicting the loss of AEP under wake conditions. When predicting the AEP of a wind turbines affected by wakes, the rotor equivalent wind speed (REWS), which considers the effect of wake wind shear, should be applied. This research examined REWSpower converted from the power output of a wind turbine to demonstrate the need of rotor equivalent wind speed under upstream turbine's wake condition and furthermore suggested a method to calculate REWSspws using the nacelle-measured wind speed. By analyzing 48months collected data of Supervisory Control and Data Acquisition (SCADA) system from a wind farm, error percentages among REWSpower, REWSspws, and the nacelle-measured wind speed were compared.

Neighborhood Effects in Wind Farm Performance: A Regression Approach

The optimization of turbine density in wind farms entails a trade-off between the usage of scarce, expensive land and power losses through turbine wake effects. A quantification and prediction of the wake effect, however, is challenging because of the complex aerodynamic nature of the interdependencies of turbines. In this paper, we propose a parsimonious data driven regression wake model that can be used to predict production losses of existing and potential wind farms. Motivated by simple engineering wake models, the predicting variables are wind speed, the turbine alignment angle, and distance. By utilizing data from two wind farms in Germany, we show that our models can compete with the standard Jensen model in predicting wake effect losses. A scenario analysis reveals that a distance between turbines can be reduced by up to three times the rotor size, without entailing substantial production losses. In contrast, an unfavorable configuration of turbines with respect to the main wind direction can result in production losses that are much higher than in an optimal case.

Wind-farm layout optimisation using a hybrid Jensen–LES approach

Abstract. Given a wind farm with known dimensions and number of wind turbines, we try to find the optimum positioning of wind turbines that maximises wind-farm energy production. In practice, given that optimisation has to be performed for many wind directions, and taking into account the yearly wind distribution, such an optimisation is computationally only feasible using fast engineering wake models such as the Jensen model. These models are known to have accuracy issues, in particular since their representation of wake interaction is very simple. In the present work, we propose an optimisation approach that is based on a hybrid combination of large-eddy simulation (LES) and the Jensen model; in this approach, optimisation is mainly performed using the Jensen model, and LES is used at a few points only during optimisation for online tuning of the wake-expansion coefficient in the Jensen model, as well as for validation of the results. An optimisation case study is considered, in which the placement of 30 turbines in a 4 km by 3 km rectangular domain is optimised in a neutral atmospheric boundary layer. Optimisation for both a single wind direction and multiple wind directions is discussed.

Shear layer approximation of Navier-Stokes steady equations for non-axisymmetric wind turbine wakes: Description, verification and first application

The number of turbines installed in offshore wind farms has strongly increased in the last years and at the same time the need for more precise estimation of the wind farm efficiency. For this reason, the wind energy community could benefit from more accurate models for multiple wakes. Existing engineering models can only simulate single wakes, which are superimposed if they are interacting in a wind farm. This method is a practical solution, but it is not fully supported by a physical background. The limitation to single wakes is given by the assumption that the wake is axisymmetric. As alternative, we propose a new shear model which is based on the existing engineering wake models, but is extended to simulate also non- axisymmetric wakes. In this paper, we present the theoretical background of the model and two application cases. First, we proved that for axisymmetric wakes the new model is equivalent to a commonly used engineering model. Then, we evaluated the improvements of the new model for the simulation of a non-axisymmetric wake using a large eddy simulation as reference. The results encourage the further development of the model, and promise a successful application for the simulation of multiple wakes.

An analysis of offshore wind farm SCADA measurements to identify key parameters influencing the magnitude of wake effects

Atmospheric conditions have a clear influence on wake effects. Stability classification is usually based on wind speed, turbulence intensity, shear and temperature gradients measured partly at met masts, buoys or LiDARs. The objective of this paper is to find a classification for stability based on wind turbine Supervisory Control and Data Acquisition (SCADA) measurements in order to fit engineering wake models better to the current ambient conditions. Two offshore wind farms with met masts have been used to establish a correlation between met mast stability classification and new aggregated statistical signals based on multiple measurement devices. The significance of these new signals on power production is demonstrated for two wind farms with met masts and validated against data from one further wind farm without a met mast. We found a good correlation between the standard deviation of active power divided by the average power of wind turbines in free flow with the ambient turbulence intensity when the wind turbines were operating in partial load.

Toward efficient optimization of wind farm layouts: Utilizing exact gradient information

The Wind Farm Layout Optimization (WFLO) problem has attracted a lot of attention from researchers and industry practitioners, as it has been proven that better placement of wind turbines can increase the overall efficiency and the total revenue of a wind farm. Although the engineering wake models are commonly used for layout optimization, the literature seems to have settled on using metaheuristics and stochastic optimization methods. In the present study, we show the effectiveness of non-linear mathematical programming in solving continuous-variable WFLO problems by utilizing exact gradient information of the problem’s objective and constraints. Moreover, mathematical models for handling land-use constraints are developed to solve highly constrained practical problems. For demonstration purposes, the results were compared with those obtained by a genetic algorithm, using a set of test cases that have been frequently used in the WFLO literature. Additional test cases with higher dimensionality, significant land-availability constraints and higher wind farm turbine densities (i.e., turbines per square kilometer) are devised and solved to show the merits of the proposed approach. Our results show the superiority of mathematical programing in solving this problem, as evidenced by the resulting wind farm efficiency and the computational cost required to obtain the solutions.

Investigation into the wake aerodynamics of a five-straight-bladed vertical axis wind turbine by wind tunnel tests

Wake characteristics have significant effects on the performance design of standalone turbines and the optimal placement of multiple turbines. In the literature to date, little experimentation has been done on the wake of vertical axis wind turbines (VAWTs), and understanding of such wake is far from adequate. In this work, systematic measurements are presented of both the near and mid-range wake of a five-straight-bladed VAWT in a wind tunnel. The blockage ratio of the VAWT was 1.8%, and no correction of the measured data was required. The wake flow fields were measured up to 10 turbine diameters (10D) to the downstream. The wake exhibited high asymmetry in the horizontal direction. In addition, the wake expanded more in the horizontal direction than in the vertical direction. The causes of the asymmetry were analyzed and discussed through the experimental results. An engineering wake model was proposed to characterize the wake edges and the average velocities. The existence of a pair of counter-rotating vortical structures in the wake was detected. Moreover, the integral length scale was found to steadily grow with the downstream distance. This work contributes to the knowledge of the VAWTs׳ wake and the application of VAWTs in wind farm layout design.

Comparison and verification of wake models in an onshore wind farm considering single wake condition of the 2 MW wind turbine

Wind turbines installed in a wind farm can be affected by wake from neighboring wind turbines, which reduces power production and shortens turbine life due to mechanical fatigue. Therefore, careful consideration of the wake effects is necessary before establishing an optimum layout design for wind farms. Until now, various numerical models have been developed and applied to evaluate the wake effects, but comparison among (and verification of) the measurement results conducted at numerous wind farms have been few and insufficient. To verify the prediction accuracy of engineering wake models, namely, eddy viscosity, Larsen, Jensen, and Frandsen models, which are widely used in wind energy business, the current study presents the results of the comparative analysis of the values measured at a commercially operated onshore wind farm. The results demonstrate that the Jensen model is the best model in predicting the wake-centered velocity deficit under a specific wind-speed condition, and the eddy viscosity and Larsen models are relatively accurate in predicting the width of the wake and its profile. In conclusion, we need to carefully apply a model for wake-effect assessment based on the spacing between wind turbines because the prediction accuracy of the wake models varies with the downstream distance condition.

Another engineering wake model variant for horizontal axis wind turbines

AbstractAn engineering model is presented for predicting the performance of a single turbine located in an incoming turbulent, sheared, wind velocity field. The approach used is a variant of the well‐known and documented Ainslie eddy viscosity approach as also employed in the Direct Wake Meandering model. It incorporates a new and simple means of representing the rotor's loading profile, initializing the calculations, simplifying the wakes' shear layer mixing model and accounting for wind shear effects. Additionally, two figures of merit are employed for assessing the reliability of all data used and predictions provided. The first, a wake momentum‐flux/thrust parameter, is used for quantitatively assessing the accuracy and utility of both measured and/or computational wake data. The second, a rotor swept area wake‐averaged velocity, is employed as a single quantitative measure of a turbine's impact on its downstream neighbor. Through detailed comparisons with three independent state‐of‐the‐art Computational Fluid Dynamic generated datasets and a field‐measured dataset, the current model is shown to be accurate for turbine rated power levels from 100 kW to 2.3 MW, wind speeds of 6 to 22 m s−1 (corresponding to turbine thrust coefficient levels of 0.14 to 0.8) and free‐stream turbulence levels from 0% to 16%. Copyright © 2015 John Wiley & Sons, Ltd.