Engineering Wake Models Research Articles

Wind turbine load validation in wakes using wind field reconstruction techniques and nacelle lidar wind retrievals

Abstract. This study proposes two methodologies for improving the accuracy of wind turbine load assessment under wake conditions by combining nacelle-mounted lidar measurements with wake wind field reconstruction techniques. The first approach consists of incorporating wind measurements of the wake flow field, obtained from nacelle lidars, into random, homogeneous Gaussian turbulence fields generated using the Mann spectral tensor model. The second approach imposes wake deficit time series, which are derived by fitting a bivariate Gaussian shape function to lidar observations of the wake field, on the Mann turbulence fields. The two approaches are numerically evaluated using a virtual lidar simulator, which scans the wake flow fields generated with the dynamic wake meandering (DWM) model, i.e., the target fields. The lidar-reconstructed wake fields are then input into aeroelastic simulations of the DTU 10 MW wind turbine for carrying out the load validation analysis. The power and load time series, predicted with lidar-reconstructed fields, exhibit a high correlation with the corresponding target simulations, thus reducing the statistical uncertainty (realization-to-realization) inherent to engineering wake models such as the DWM model. We quantify a reduction in power and loads' statistical uncertainty by a factor of between 1.2 and 5, depending on the wind turbine component, when using lidar-reconstructed fields compared to the DWM model results. Finally, we show that the number of lidar-scanned points in the inflow and the size of the lidar probe volume are critical aspects for the accuracy of the reconstructed wake fields, power, and load predictions.

Verification of induction zone models for wind farm annual energy production estimation

Fast engineering wake models are the backbone of wind farm annual energy production (AEP) estimators, whereas the addition of induction zone models in existing tools is a more recent response to rising concerns over wind farm blockage associated losses. Here, “blockage” describes the combined induction fields of all wind turbines inside a farm. Unlike the term might suggest, blockage not only reduces flow speeds, but also increases them; for instance along the outer edges of wind farms. Evaluating the overall impact on AEP of these gains and losses necessitates accurate wind farm induction models. Whilst engineering wake models are tuned to predict wind farm performance, existing induction zone models are all derived for accurately predicting the near field induction not the far field value—important for wind farm simulations. This paper presents the induction models implemented in the wind farm simulation tool PyWake, as well as results from novel analytical models and compares their far field predictions to RANS-AD simulations of different turbines. We demonstrate that when including blockage in AEP simulations, the downstream speed-ups need to be included to avoid an unrealistic bias toward AEP loss and that wake expansion significantly impacts induction at rated thrust levels.

Application of the Townsend-George wake theory to field measurements of wind turbine wakes

As wind turbines are usually clustered in wind farms, knowledge of the evolution of the wind turbine wakes is important because downstream turbines will be exposed to them, causing higher loads and maintenance times. For that reason, wind turbine wakes have been studied intensively and different engineering wake models were derived. However, none of them is constructed from a few basic and robust assumptions, while such a formalism already exists for the axisymmetric turbulent wake. Therefore, we will apply these models to data obtained in a wind farm using a scanning LiDAR. The wakes of two wind turbines are analyzed in four different wind directions chosen so that their wakes will have different degrees of interaction. The axisymmetric wake models are found to perform better than the Jensen wake model, and the main source of improvement is shown to be the presence of a virtual origin. Indeed, a virtual origin is shown to also improve the Jensen wake model significantly. Overall, our results indicate that a view from classical axisymmetric wake theory can help to improve the understanding of the evolution of wind turbine wakes in the atmospheric boundary layer.

Doppler Lidar Investigations of Wind Turbine Near-Wakes and LES Modeling with New Porous Disc Approach

Many bottom-mounted offshore wind farms are currently planned for the coastal areas of Japan, in which wind speeds of 6.0–10.0 m/s are extremely common. The impact of such wind speeds is very relevant for the realization of bottom-mounted offshore wind farms. In evaluating the feasibility of these wind farms, therefore, strict evaluation at wind speeds of 6.0–10.0 m/s is important. In the present study, the airflow characteristics of 2 MW-class downwind wind turbine wake flows were first investigated using a vertically profiling remote sensing wind measurement device (lidar). The wind turbines used in this study are installed at the point where the sea is just in front of the wind turbines. A ground-based continuous-wave (CW) conically scanning wind lidar system (“ZephIR ZX300”) was used. Focusing on the wind turbine near-wakes, the detailed behaviors were considered. We found that the influence of the wind turbine wake, that is, the wake loss (wind velocity deficit), is extremely large in the wind speed range of 6.0–10.0 m/s, and that the wake loss was almost constant at such wind speeds (6.0–10.0 m/s). It was additionally shown that these results correspond to the distribution of the thrust coefficient of the wind turbine. We proposed a computational fluid dynamics (CFD) porous disk (PD) wake model as an intermediate method between engineering wake models and CFD wake models. Based on the above observations, the wind speed range for reproducing the behavior of the wind turbine wakes with the CFD PD wake model we developed was set to 6.0–10.0 m/s. Targeting the vertical wind speed distribution in the near-wake region acquired in the “ZephIR ZX300”, we tuned the parameters of the CFD PD wake model (CRC = 2.5). We found that in practice, when evaluating the mean wind velocity deficit due to wind turbine wakes, applying the CFD PD wake model in the wind turbine swept area was very effective. That is, the CFD PD wake model can reproduce the mean average wind speed distribution in the wind turbine swept area.

Power fluctuations in high-installation- density offshore wind fleets

Abstract. Detailed simulation of wind generation as driven by weather patterns is required to quantify the impact on the electrical grid of the power fluctuations in offshore wind power fleets. This paper focuses on studying the power fluctuations of high-installation-density offshore fleets since they present a growing challenge to the operation and planning of power systems in Europe. The Belgian offshore fleet is studied because it has the highest density of installation in Europe by 2020, and a new extension is expected to be fully operational by 2028. Different stages of the future installed capacity, turbine technology, and turbine storm shutdown technologies are examined and compared. This paper analyzes the distribution of power fluctuations both overall and during high wind speeds. The simulations presented in this paper use a new Student t-distributed wind speed fluctuation model that captures the missing spectra from the weather reanalysis simulations. An updated plant storm shutdown model captures the plant behavior of modern high-wind-speed turbine operation. Detailed wake modeling is carried out using a calibrated engineering wake model to capture the Belgium offshore fleet and its tight farm-to-farm spacing. Long generation time series based on 37 years of historical weather data in 5 min resolution are simulated to quantify the extreme fleet-level power fluctuations. The model validation with respect to the operational data of the 2018 fleet shows that the methodology presented in this paper can capture the distribution of wind power and its spatiotemporal characteristics. The results show that the standardized generation ramps are expected to be reduced towards the 4.4 GW of installations due to the larger distances between plants. The most extreme power fluctuations occur during high wind speeds, with large ramp-downs occurring in extreme storm events. Extreme ramp-downs are mitigated using modern turbine storm shutdown technologies, while extreme ramp-ups can be mitigated by the system operator. Extreme ramping events also occur at below-rated wind speeds, but mitigation of such ramping events remains a challenge for transmission system operators.

Axial induction controller field test at Sedini wind farm

Abstract. This paper describes the design and testing of an axial induction controller implemented on a row of nine turbines on the Sedini wind farm in Sardinia, Italy. This work was performed as part of the EU Horizon 2020 research project CL-Windcon. An engineering wake model, selected for its good fit to historical SCADA data from the site, was used in the LongSim code to optimise turbine power reduction setpoints for a large matrix of steady-state wind conditions. The setpoints were incorporated into a dynamic control algorithm capable of running on-site using available wind condition estimates from the turbines. The complete algorithm was tested in dynamic time-domain simulations using LongSim, using a time-varying wind field generated from historical met mast data from the site. The control algorithm was implemented on-site, with the wind farm controller toggled on and off at 35 min intervals to allow the performance with and without the controller to be compared in comparable wind conditions. Data were collected between July 2019 and early February 2020. The results have been analysed and indicate a positive increase in energy production resulting from the induction control, in line with LongSim model predictions, although a larger volume of valid data would be necessary to provide statistically robust conclusions. The measurements also provide a validation of the LongSim model, proving its value for both steady-state setpoint optimisation and time-domain simulation of wind farm performance.

Influence of Wake Model Superposition and Secondary Steering on Model-Based Wake Steering Control with SCADA Data Assimilation

Methods for wind farm power optimization through the use of wake steering often rely on engineering wake models due to the computational complexity associated with resolving wind farm dynamics numerically. Within the transient, turbulent atmospheric boundary layer, closed-loop control is required to dynamically adjust to evolving wind conditions, wherein the optimal wake model parameters are estimated as a function of time in a hybrid physics- and data-driven approach using supervisory control and data acquisition (SCADA) data. Analytic wake models rely on wake velocity deficit superposition methods to generalize the individual wake deficit to collective wind farm flow. In this study, the impact of the wake model superposition methodologies on closed-loop control are tested in large eddy simulations of the conventionally neutral atmospheric boundary layer with full Coriolis effects. A model for the non-vanishing lateral velocity trailing a yaw misaligned turbine, termed secondary steering, is also presented, validated, and tested in the closed-loop control framework. Modified linear and momentum conserving wake superposition methodologies increase the power production in closed-loop wake steering control statistically significantly more than linear superposition. While the secondary steering model increases the power production and reduces the predictive error associated with the wake model, the impact is not statistically significant. Modified linear and momentum conserving superposition using the proposed secondary steering model increase a six turbine array power production, compared to baseline control, in large eddy simulations by 7.5% and 7.7%, respectively, with wake model predictive mean absolute errors of 0.03P1 and 0.04P1, respectively, where P1 is the baseline power production of the leading turbine in the array. Ensemble Kalman filter parameter estimation significantly reduces the wake model predictive error for all wake deficit superposition and secondary steering cases compared to predefined model parameters.

Optimal tuning of engineering wake models through lidar measurements

Abstract. Engineering wake models provide the invaluable advantage to predict wind turbine wakes, power capture, and, in turn, annual energy production for an entire wind farm with very low computational costs compared to higher-fidelity numerical tools. However, wake and power predictions obtained with engineering wake models can be insufficiently accurate for wind farm optimization problems due to the ad hoc tuning of the model parameters, which are typically strongly dependent on the characteristics of the site and power plant under investigation. In this paper, lidar measurements collected for individual turbine wakes evolving over a flat terrain are leveraged to perform optimal tuning of the parameters of four widely used engineering wake models. The average wake velocity fields, used as a reference for the optimization problem, are obtained through a cluster analysis of lidar measurements performed under a broad range of turbine operative conditions, namely rotor thrust coefficients, and incoming wind characteristics, namely turbulence intensity at hub height. The sensitivity analysis of the optimally tuned model parameters and the respective physical interpretation are presented. The performance of the optimally tuned engineering wake models is discussed, while the results suggest that the optimally tuned Bastankhah and Ainslie wake models provide very good predictions of wind turbine wakes. Specifically, the Bastankhah wake model should be tuned only for the far-wake region, namely where the wake velocity field can be well approximated with a Gaussian profile in the radial direction. In contrast, the Ainslie model provides the advantage of using as input an arbitrary near-wake velocity profile, which can be obtained through other wake models, higher-fidelity tools, or experimental data. The good prediction capabilities of the Ainslie model indicate that the mixing-length model is a simple yet efficient turbulence closure to capture effects of incoming wind and wake-generated turbulence on the wake downstream evolution and predictions of turbine power yield.

Comparison of modular analytical wake models to the Lillgrund wind plant

Efficient and accurate wake models are required for wind plant performance modeling and the suite of engineering processes that support wind plant layout, control, and monitoring. Although many analytical and engineering wake models with low computational costs have been proposed, their ability to represent the power production of large wind plants in a wide range of atmospheric conditions is not completely understood. The following validation study reviews the underlying theory for analytical wake models, outlines quality control procedures for observational data, and compares model results with observational data from the Lillgrund Wind Plant. Lillgrund makes a valuable case study for wake modeling because of its regular arrangement and the relatively close spacing of constituent wind turbines, which lead to regular and significant wake interactions within the wind plant and the development of deep array flow conditions. Formulations for the velocity deficit, wake-added turbulence, and wake superposition methods are considered in a modular sense, yielding many possible configurations to represent wind turbine wakes, of which seven are examined in detail. Velocity deficit models that account for flow conditions in the near wake are better able to reproduce power production for wind turbines in the transitional region of the wind plant, where wind turbines experience as many as five wakes from upstream turbines. In the deep array, where power production reaches asymptotic values and wake statistics become quasi-periodic, wake superposition schemes become the largest driver in error reduction; using the linear or maximum wake superposition methods can reduce the relative root mean square error by as much as 40% in the deep array.

Wind farm layout optimization with special attention on noise radiation

This work presents a new wind farm layout design methodology that calculates the noise radiation using an advanced sound propagation model. Firstly, the wake velocity in wind farm is calculated via an improved engineering wake model. Then, the aero-acoustic noise source of wind turbine is obtained using the BPM method. To simulate the noise level at far field, the basis of propagation model is built on the parabolic wave equation (PE) method. The cost of energy for wind farm is assessed via an engineering model. Finally, based on the genetic algorithm (GA) optimization method, and taking the noise radiation level into account, a new wind farm layout design methodology is developed to solve a trade-off between cost and noise for wind farm.

Adaptation of Engineering Wake Models using Gaussian Process Regression and High-Fidelity Simulation Data

This article investigates the optimization of yaw control inputs of a nine-turbine wind farm. The wind farm is simulated using the high-fidelity simulator SOWFA. The optimization is performed with a modifier adaptation scheme based on Gaussian processes. Modifier adaptation corrects for the mismatch between plant and model and helps to converge to the actual plan optimum. In the case study the modifier adaptation approach is compared with the Bayesian optimization approach. Moreover, the use of two different covariance functions in the Gaussian process regression is discussed. Practical recommendations concerning the data preparation and application of the approach are given. It is shown that both the modifier adaptation and the Bayesian optimization approach can improve the power production with overall smaller yaw misalignments in comparison to the Gaussian wake model.

A New Wind Turbine CFD Modeling Method Based on a Porous Disk Approach for Practical Wind Farm Design

In this study, the new computational fluid dynamics (CFD) porous disk (PD) wake model was proposed in order to accurately predict the time-averaged wind speed deficits in the wind turbine wake region formed on the downstream side by the 2-MW wind turbine operating at a wind speed of 10 m/s. We use the concept of forest canopy model as a new CFD PD wake model, which has many research results in the meteorological field. In the forest canopy model, an aerodynamic resistance is added as an external force term to all governing equations (Navier–Stokes equations) in the streamwise, spanwise, and vertical directions. Therefore, like the forest model, the aerodynamic resistance is added to the governing equations in the three directions as an external force term in the CFD PD wake model. In addition, we have positioned the newly proposed the LES using the CFD PD wake model approach as an intermediate method between the engineering wake model (empirical/analytical wake model) and the LES combined with actuator disk (AD) or actuator line (AL) models. The newly proposed model is intended for use in large-scale offshore wind farms (WFs) consisting of multiple wind turbines. In order to verify the validity of the new method, the optimal model parameter CRC was estimated by comparison with the time-averaged wind speed database in the wind turbine wake region with fully resolved geometries, combined with unsteady Reynolds-averaged Navier–Stokes (RANS) equations, implemented using the ANSYS(R) CFX(R) software. Here, product names (mentioned herein) may be trademarks of their respective companies. As a result, in the range from x = 5D of the near wake region to x = 10D of the far wake region, by selecting model parameter CRC, it was clarified that it is possible to accurately evaluate the time-averaged wind speed deficits at those separation distances. We also examined the effect of the spatial grid resolution using the CFD PD wake model that is proposed in the present study, clarifying that the spatial grid resolution has little effect on the simulation results shown here.

Comparison of Rotor Wake Identification and Characterization Methods for the Analysis of Wake Dynamics and Evolution

Optimal wind power plant design requires understanding of wind turbine wake physics and validation of engineering wake models under wake-controlled operating conditions. In this work, we have developed and investigated several different wake identification and characterization methods for analyzing wake evolution and dynamics. The accuracy and robustness of these methods, based on Gaussian function fitting and adaptive contour identification, have been assessed by application to a large-eddy simulation data set. A new contour-based method based on downstream momentum deficit has been considered. Uncertainties arising from wake-identification errors result in characterizations of the wake expansion, recovery, and meandering motion that differ by 19% of the rotor area, 4% of the freestream, and 15% rotor diameter, respectively.

A new wake model and comparison of eight algorithms for layout optimization of wind farms in complex terrain

Layout optimization of wind farms constitutes an important and challenging task in complex terrain. This is especially due to the complex interactions of the boundary layer flows in complex terrain and wind turbine wakes, which renders wake modelling in complex terrain difficult. This study tackles this challenge with a new engineering wake model, which is developed by superposing a Gaussian shape wake model on top of the background flow field, assuming that the centerlines of wind turbine wakes follow the streamlines of the background flow field. The model is found to predict wind turbine wakes in complex terrain with good accuracy and at the same time it is computationally cheap to run for optimization applications. Comparisons with high fidelity simulations and field measurements for a real wind farm with 25 turbines in complex terrain demonstrate its effectiveness. A systematic comparison of eight optimization algorithms, which includes two gradient-based and six gradient-free algorithms, is also carried out for the layout optimization problem in complex terrain. To accelerate the optimization process, a double-stage approach is proposed, which optimizes the objective function first neglecting wake effects and then, in the second stage, including them. While all the tested optimization algorithms can improve the original wind farm layout, random search, local search, and pattern search are found to be the top three algorithms in terms of optimization results and computational cost.

Modeling of the atmospheric boundary layer under stability stratification for wind turbine wake production

The assessment of climatological site conditions, airflow characteristics, and the turbulence affecting wind turbines is an important phase in developing wake engineering models. A method of modeling atmospheric boundary layer structure under atmospheric stability effects is crucial for accurate evaluation of the spatial scale of modern wind turbines, but by themselves, they are incapable to account for the varying large-scale weather conditions. As a result, combining lower atmospheric models with mesoscale models is required. In order to realize a reasonable approximation of initial atmospheric inflow condition used for wake identification behind an NREL 5-MW wind turbine, different vertical wind profile models on equilibrium conditions are tested and evaluated in this article. Wind farm simulator solvers require massive computing resources and forcing mechanisms tendencies inputs from weather forecast models. A three-dimensional Flow Redirection and Induction in Steady-state engineering model was developed for simulating and optimizing the wake losses of different rows of wind turbines under different stability stratifications. The obtained results were compared to high-fidelity simulation data generated by the famous Simulator for Wind Farm Applications. This work showed that a significant improvement related to atmospheric boundary layer structure can be made to develop accurate engineering wake models in order to reduce wake losses.

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.