Analytical Wake Model Research Articles

A physically interpretable data-driven surrogate model for wake steering

Abstract. Wake steering models for control purposes are typically based on analytical wake descriptions tuned to match experimental or numerical data. This study explores whether a data-driven surrogate model with a high degree of physical interpretation can accurately describe the redirected wake. A linear model trained with large-eddy-simulation data estimates wake parameters such as deficit, center location and curliness from measurable inflow and turbine variables. These wake parameters are then used to generate vertical cross-sections of the wake at desired downstream locations. In a validation considering eight boundary layers ranging from neutral to stable conditions, the far wake's trajectory, curl and available power are accurately estimated. A significant improvement in accuracy is shown in a benchmark study against two analytical wake models, especially under derated operating conditions and stable atmospheric stratifications. Even though the results are not directly generalizable to all atmospheric conditions, locations or turbine types, the outcome of this study is encouraging.

Design and Stability Analysis of an Offshore Floating Multi-Wind Turbine Platform

The multi-wind turbine platform technology has the potential to harness the significant source of offshore wind energy in deep waters. However, the wake interference between the turbines on the multi-wind turbine platform can cause a reduction in power production; hence, it is important to study the wake effects in the initial phase of the design. This paper studies the effects of wake interference between the wind turbines on three different platform configurations to find a suitable configuration for the wind turbines on a multi-turbine platform. The analytical Larsen wake model and computational fluid dynamics (CFD) simulations are used for evaluating the wake effects. The platform configuration required for the wind turbines is determined based on the results of wake effects, and then a novel platform is designed. The free-floating stability behavior of the multi-wind turbine platform is analyzed using the hydrostatic analysis of the modeled platform. The wave-body interaction between the platform and the waves is predicted using the hydrodynamic analysis. A preliminary cost analysis of the multi-turbine platform concept is evaluated and compared with a single wind turbine floating concept. The results showed that the presented design is a promising concept that can enhance the offshore wind industry.

A physics-based model for wind turbine wake expansion in the atmospheric boundary layer

Analytical wind turbine wake models are widely used to predict the wake velocity deficit. In these models, the wake growth rate is a key parameter specified mainly with empirical formulations. In this study, a new physics-based model is proposed and validated to predict the wake expansion downstream of a turbine based on the incoming ambient turbulence and turbine operating conditions. The new model utilises Taylor diffusion theory, the Gaussian wake model, turbulent mixing layer theory and the analogy between wind turbine wake expansion and scalar diffusion. These components ensure that the model conserves mass and momentum in the far wake and accounts for the ambient turbulence and turbine-induced turbulence effects on the wake expansion. To account for the turbulence relevant scales that contribute to the wake expansion, the model uses the root-mean-square of the low-pass filtered radial velocity component. A simplified version that only requires the unfiltered velocity standard deviation and turbulence integral scale is also proposed. In addition, a new relation for the near-wake length is derived. The model performance is validated using large-eddy simulation data of a wind turbine wake under neutral atmospheric conditions with a wide range of incoming turbulence levels. The results show that the proposed model yields reasonable predictions of the wake width, maximum velocity deficit and near-wake length. In the case with a relatively low incoming streamwise turbulence intensity of 0.05, the ambient and turbine-induced terms in the model contribute almost equally to the wake width, rendering them both crucial for reasonable wake predictions.

Cooperative yaw control of wind farm using a double-layer machine learning framework

An appropriate cooperative yaw control strategy, in which the accurate power prediction and efficient optimization method play an essential role, can mitigate the significant power loss owing to the wake interference. The present study develops a novel double-layer machine learning framework, which combines an artificial neural network (ANN) yawed wake model and a Bayesian machine learning algorithm. The former undertakes the power prediction as the 1st layer, which is fed to the 2nd layer of the optimization system. Using computational fluid dynamics (CFD) simulation result as a reference, the performance of the proposed framework is evaluated compared with the framework based on a Gaussian-based analytical wake model by Qian and Ishihara. Furthermore, parametric studies have been conducted on the inflow conditions to explore its applicability. The results show that the proposed framework can realize more accurate power prediction with a mean error of 1.13% and 0.96% for different inflow velocities and turbulence intensities respectively, in contrast with the one based on the analytical model, 7.61% and 1.66%. Moreover, more notable power improvements can be achieved by the proposed framework, seeing a mean rise of 5.59% and 2.22% under four inflow velocities and turbulence intensities respectively, compared with 3.55% and 1.02% based on the analytical model. Specifically, its superiority becomes more obvious under relatively low inflow velocity and turbulence intensity.

Tailoring wind turbine wake models to incoming free-stream turbulence

Analytical wake models describe the main wake statistics using a reduced number of parameters: for instance, the Gaussian wake model relies on the single parameter k ∗ to predict the mean wake velocity. However, the robustness of these models to different inflows has been seldom tested and the effects of ambient turbulence on these coefficients are reported only in a limited number of studies.With this objective, we measured the wake generated by a model-scale wind turbine operating in a wind tunnel at a ReD ⋍ 105 under different ambient conditions, with turbulence intensities between 3% and 12% and integral time scales between 1/10 and 10 times the convective time-scale. The wake generated by the turbine has been measured by means of planar PIV in a region spanning between 1.25 and 8.75 rotor diameters downstream of the turbine.The results show that a description of the turbine wake with the single parameter k ∗ is not sufficient to obtain accurate predictions, while the quality of the wake estimations can be dramatically improved by introducing a virtual origin x 0. Analysis of the higher-order wake statistics shows how the former can be related to the intensity of the Reynolds shear stress in the wake, and the latter to the erratic motion of the tip-vortices.

Turbulence Optimized Park model with Gaussian wake profile

A new analytical wake model for wind farm design is presented. The new model, TurbOPark, is based on the Park model but features non-linear wake expansion and a Gaussian deficit profile. The modelled wake expansion depends on the intensity of the local turbulence, which is a combination of ambient atmospheric turbulence and wake-generated turbulence. Moving downstream from the rotor, the intensity of the wake-generated turbulence decreases, and the wake expansion slows down. This leads to more persistent wakes in wind farms and clusters of wind farms with large distances between turbines. In the present study, we focus on the London Array wind farm and show examples of how results from Park and TurbOPark compare to SCADA data. We look at the array efficiency of the wind farm, the production of individual turbines, and the impact of neighbouring wind farms. We find that predictions from TurbOPark generally are closer to observations than predictions from the Park model.

Wind tunnel experiments for investigating wake effects in atmospheric boundary layers using a simplified miniature model wind turbine

The clustering of wind turbines within a prospective site is prone to significant wake interactions, which have a negative impact in terms of loads and plant performance. Further improvements in the design and control of wind farms can be achieved through a detailed assessment of wake effects under site-specific conditions. The aim of this paper was to investigate wake effects in atmospheric boundary layer (ABL) flows using a simplified model wind turbine. First, we performed experiments under smooth- and turbulent-uniform inflows to highlight the wake features of the model. Second, we evaluated the interactions with two different neutrally stratified ABL: i) ABL Type-I (α = 0.11, TI = 6 %), ii) ABL Type-II (α = 0.23, TI = 13 %), where α is the incident wind shear and TI is the turbulence intensity. For each case, hot-wire anemometry was used to obtain wake mean velocity, turbulence intensity and power spectrum profiles at four different downstream positions. We also included a comparison with three analytical wake models to get further indications on the experimental measurements. First results showed that the simplified model is well-suited for its intended purpose. The largest discrepancies between experiments and model predictions were in the near-wake region and in cases with lower background turbulence. We also corroborated a strong influence of the incoming wind profile on how fast the wake recovers to the undisturbed conditions. Furthermore, this study provided an initial framework to explore the ABL wind tunnel at Universidade Federal do Rio Grande do Sul (UFRGS) as a viable tool for research in wind energy.

Analytical all-induction state model for wind turbine wakes

Analytical wind turbine wake models are prone to failure when the turbine induction factor increases, as they do not account for the increasingly important effects of low wake pressure. This work proposes a novel analytical wake model which incorporates the effect of wake pressure in its predictions. Comparison with high-fidelity wind turbine simulations shows that the newly developed model is comparable to conventional ones at low induction factors, but continues to be accurate at higher induction factors where existing models break down.

A 3D analytical model for predicting horizontal‐axis wind turbines wake based on a 2D analytical wake model

AbstractThe development of easy‐to‐implement 3D analytical models of the wake is highly desirable, due to the critical role played by the prediction of the wake velocity profile in the estimation of power generation and the layout optimization of wind turbines in wind farms. Herein, a 3D analytical model of the wake (based on a 2D analytical model) has been proposed, which is easy to implement thanks to using the Gaussian function for the description of the velocity profile and assuming an isotropic value for the wake decay coefficient. Validation of the model was carried out using six cases of wind tunnel, field measurement, and simulation data in horizontal and vertical planes, where the model was compared with three 3D analytical models of the literature. The predictions of the model for the normalized wind velocity typically exhibited mean absolute percentage error (MAPE) values of MAPE ≤3 at downwind distances of x ≥ dt (dt is the rotor diameter), which are the economically‐ and power harvesting‐optimized inter‐turbine spacing in wind farms. In addition to its theoretical significance, the model bears utility potentials in applications concerning solving practical problems in wind farms.

Combining shallow-water and analytical wake models for tidal array micro-siting

For tidal-stream energy to become a competitive renewable energy source, clustering multiple turbines into arrays is paramount. Array optimisation is thus critical for achieving maximum power performance and reducing cost of energy. However, ascertaining an optimal array layout is a complex problem, subject to specific site hydrodynamics and multiple inter-disciplinary constraints. In this work, we present a novel optimisation approach that combines an analytical-based wake model, FLORIS, with an ocean model, Thetis. The approach is demonstrated through applications of increasing complexity. By utilising the method of analytical wake superposition, the addition or alteration of turbine position does not require re-calculation of the entire flow field, thus allowing the use of simple heuristic techniques to perform optimisation at a fraction of the computational cost of more sophisticated methods. Using a custom condition-based placement algorithm, this methodology is applied to the Pentland Firth for arrays with turbines of 3.05,hbox {m}/hbox {s} rated speed, demonstrating practical implications whilst considering the temporal variability of the tide. For a 24-turbine array case, micro-siting using this technique delivered an array 15.8% more productive on average than a staggered layout, despite flow speeds regularly exceeding the rated value. Performance was evaluated through assessment of the optimised layout within the ocean model that treats turbines through a discrete turbine representation. Used iteratively, this methodology could deliver improved array configurations in a manner that accounts for local hydrodynamic effects.

Improved Evaluation of The Wind Power Potential of a Large Offshore Wind Farm Using Four Analytical Wake Models

The objective of this paper is to investigate the ability of analytical wake models to estimate the wake effects between wind turbines (WTs). The interaction of multiple wakes reduces the total power output produced by a large offshore wind farm (LOFWF). This power loss is due to the effect of turbine spacing (WTS), if the WTs are too close, the power loss is very significant. Therefore, the optimization of turbine positions within the offshore wind farm requires an understanding of the interaction of wakes inside the wind farm. To better understand the wake effect, the Horns Rev 1 offshore wind farm has been studied with four wake models, Jensen, Larsen, Ishihara, and Frandsen. A comparative study of the wake models has been performed in several situations and configurations, single and multiple wakes are taken into consideration. Results from the Horns Rev1 offshore wind farm case have been evaluated and compared to observational data, and also with the previous studies. The power output of a row of WTs is sensitive to the wind direction. For example, if a row of ten turbines is aligned with the 270° wind direction, the full wake condition of WTs is reached and the power deficit limit predicted by Jensen model exceeds 70%. When a wind direction changes only of 10° (260° and 280°), the deficit limit reduces to 30%. The obtained results show that a significant power deficit occurs when the turbines are arranged in an aligned manner. The findings also showed that all four models gave acceptable predictions of the total power output. The comparison between the calculated and reported power output of Horns Revs 1 showed that the differences ranged from - 8.27 MW (12.49%) to 15.27 MW (23.06%) for the Larsen and Frandsen models, respectively.

Analytical Modeling for Prediction of Horizontal-Axis Wind Turbines Power Generation in Wind Farms Based on an Analytical Wake Model

The development of models that predict power production of wind farms (WFs) by considering the interacting wakes is important; because wakes of the turbines exert a significant influence on power production of turbines, and hence on the layout of wind turbines in WFs. Thus, the purpose of present study was to provide an innovative analytical method for the prediction of power generation of the WFs that have a flat terrain and are consisted of horizontal-axis wind turbines (HAWTs) with the same hub height. The methodology employed utilized an analytical Gaussian model of HAWT wake to develop an analytical model that calculates the effective wind velocity acting on the downstream HAWT(s), which is further used for reading its generated power from the turbine’s catalog; thus, providing the generated power of the WF as the output. The results of presented model were validated by the field measurements data of Horns Rev WF and also were compared to two analytical models for predicting the generated power. The results were compared with two numerical simulations of the literature, and the output data of three commercial software. Moreover, the error analysis revealed that the presented model mostly showed superior accuracy in predicting the field measurements data.

A data-driven analytical model for wind turbine wakes using machine learning method

To reduce the wake effect by means of layout optimization or cooperative control, it is significant to modeling wind turbine wakes in an accurate and efficient way. However, existing analytical wake models still have large errors in actual wind farms due to the inadequate consideration of various inflow factors and local environmental characteristics. To satisfy this accuracy requirement, a data-driven analytical wake model is proposed in this paper. In the model, the local inflow information and wake expansion feature are extracted from measured data of wind farms, and a machine learning model is trained to establish the relationship between the two. In this way, the model can be well adapted to the local environment and inflow conditions. Verifications in two actual wind farm cases illustrate that there is a good agreement with the measured velocity and power data. Compared with traditional analytical models, the wake prediction performance of the new model has improved more than 20%. Therefore, the proposed model can serve as a reliable tool for wind farm control and optimization.

Evaluation of three potential machine learning algorithms for predicting the velocity and turbulence intensity of a wind turbine wake

In this paper, three machine learning (ML) algorithms, Support Vector Regression (SVR), Artificial Neural Networks (ANN), and Extreme Gradient Boosting (XGBoost), are validated to estimate the velocity and turbulence intensity of a wind turbine's wake at distinct downstream distances. To this end, a series of high-fidelity numerical simulations for the NREL Phase VI wind turbine is carried out to generate training and test datasets for the three machine learning algorithms. The predicted wake velocity and turbulence intensity from the ML models are also contrasted with significant existing analytical wake models. Machine learning algorithms estimate velocity and turbulence intensity in the wake in a way commensurate to the Computational Fluid Dynamics (CFD) simulations while running at a similar pace as low-fidelity wake models. The results demonstrate that machine learning-based algorithms can predict velocity and turbulence intensity better with higher precision than the traditional analytical wake models.

Operation assessment of analytical wind turbine wake models

Wind turbine wakes have a strong impact on wind farms as they affect the power output and the turbulence level. These factors have a determinant impact on turbines lifetime. Thus, wake modelling is of critical importance to the wind energy industry, playing a central role in the optimization of wind farm layouts. This work aims at assessing some of the available analytical wake models that modify the computed wind field by CFD as a post-processing correction tool. Such validation was done with recourse to experimental SCADA data obtained in an onshore wind farm with eight wind turbines distributed by two rows. Conclusions were drawn for the Jensen, Jensen2D, Larsen, Gaussian BPA and Gaussian Ishihara models, by analyzing the computed velocity ratio relative to the upstream leading turbine, both in a single wake and in multiple wake situations.

The Effect of Using Different Wake Models on Wind Farm Layout Optimization: A Comparative Study

Abstract The accuracy of analytical wake models applied in wind farm layout optimization (WFLO) problems is of great significance as the high-fidelity methods such as large eddy simulation (LES) and Reynolds-averaged Navier–Stokes (RANS) are still not able to handle an optimization problem for large wind farms. Based on a variety of analytical wake models developed in the past decades, Flow Redirection and Induction in Steady State (FLORIS) have been published as a tool that integrated several widely used wake models and their expansions. This paper compares four wake models selected from FLORIS by applying three classical WFLO scenarios. The results illustrate that the Jensen wake model is the fastest, but the issue of underestimating the velocity deficit is obvious. The multi-zone model needs additional tuning on the parameters inside the model to fit specific wind turbines. The Gaussian-curl hybrid (GCH) wake model, as an advanced expansion of the Gaussian wake model, does not provide a significant improvement in the current study, where the yaw control is not included. The Gaussian wake model is recommended for the WFLO projects implemented under the FLORIS framework and has similar wind conditions with the present work.

Wind farm layout optimization for levelized cost of energy minimization with combined analytical wake model and hybrid optimization strategy

Wind farm layout optimization is a crucial stage for wind farm projects. Most of previous studies aim to maximize the power generation by optimizing turbine locations using analytical wake models and heuristic optimization techniques. However, the performance of analytical wake models was not properly evaluated before being applied on the layout optimization, which may lead a large discrepancy. The efficiency of strategies to solve this optimization problem also needs to be improved with the increasing scale of wind farm. Moreover, the minimization of levelized cost of energy of wind farm is considered to be a more appropriate optimization objective than the power maximization. In this study, the combined analytical wake model considering wake loss, added turbulence and wake superposition model is presented and evaluated by comparing with numerical simulation data. A hybrid optimization strategy assembling genetic algorithm and particle swarm optimization is proposed and used to minimize the levelized cost of energy under different scenarios. The results show that the power generation is underestimated by up to 31% if neglecting the added turbulence model and the combined analytical wake model has an averaged error of 3%. The levelized cost of energy is decreased by 1.9% and the annual energy production, capacity factor and efficiency are improved by 2.3%, 2.3% and 1.3% respectively after the layout optimization for the full various wind scenario with 49 wind turbines. The proposed hybrid optimization strategy increases the optimization effect by up to 0.9% compared with the individual genetic algorithm strategy and improves the efficiency by up to 26% than the individual particle swarm optimization strategy.

An entrainment‐based model for annular wakes, with applications to airborne wind energy

AbstractSeveral novel wind energy systems produce wakes with annular cross‐sections, which are qualitatively different from the wakes with circular cross‐sections commonly generated by conventional horizontal‐axis wind turbines and by compact obstacles. Since wind farms use arrays of hundreds of turbines, good analytical wake models are essential for efficient wind farm planning. Several models already exist for circular wakes; however, none have yet been proposed for annular wakes, making it impossible to estimate their array performance. We use the entrainment hypothesis to develop a reduced‐order model for the shape and flow velocity of an annular wake from a generic annular obstacle. Our model consists of a set of three ordinary differential equations, which we solve numerically. In addition, by assuming that the annular wake does not drift radially, we further reduce the problem to a model comprising only two differential equations, which we solve analytically. Both of our models are in good agreement with previously published large eddy simulation results.

LiDAR and SCADA data processing for interacting wind turbine wakes with comparison to analytical wake models

This study is a follow up on a previous one carried out within the frame of the French project SMARTEOLE, during which, a ground-based scanning LiDAR measurement campaign was conducted in the onshore wind farm of Sole du Moulin Vieux. That previous study focused on the wakes of two wind turbines that experienced different degrees of interaction depending on the incoming wind direction, through the processing of LiDAR measurements. The measurement duration (7 months) ensured the statistical convergence of the ensemble-averaged flow fields obtained after holding a categorisation process based on the wind speed at hub height, wind direction, and atmospheric stability, where only near-neutral stability conditions were considered. The present study focuses on integrating the operational data of the wind turbines through SCADA processing to complement the LiDAR wake field observations and to be used as an input for analytical wake models. First, the correlation between the atmospheric stability, deduced from MERRA-2 dataset, and the free-stream turbulence intensity, measured by the wind turbines’ anemometers, is studied for different wind speed ranges. It is observed that the turbulence intensity tends towards a consistent value as the atmospheric stability approaches near-neutral stability conditions, giving confidence into the applied strategy of data categorisation based on MERRA-2 outputs. The influence of the degree of wake interaction on the wake added turbulence, the velocity and power deficits between both turbines is assessed. Clear trends between the wake added turbulence and both the velocity and power deficits are detected. Consequently, two fitting laws are proposed. Then, different analytical wake models and wake superposition methods are fed with the operational data deduced from the processed SCADA data, and are used for predicting the evolution of the velocity deficit within the wake. Some statistical metrics are used for error quantification of the different engineering wake models compared to the scanning LiDAR measurements, used as reference, and Blondel and Cathelain produces the closest results to the field measurements.

A Numerical Investigation of the Geometric Characteristics of Floating Wind Turbine Wakes under Axial and Yawed Rotor Conditions

The physics of wind turbine wakes on fixed foundations have been extensively studied through numerical modelling and measurements over the recent decades. While research initiatives in the field of floating wind turbines have increased significantly, various aspects characterising floating turbine wakes are still not well understood. This paper applies a free-wake vortex model to derive the geometric characteristics of the wake of a surging rotor under axial and yawed rotor conditions. The study examines the influence of platform motion on the wake boundaries and centreline up to four rotor diameters downstream. It is shown that floating turbine wakes experience a higher degree of perturbation as compared to those of fixed turbines. This is highly dependent on the sea state and suggests the need to develop new analytical wake models for the wind industry that are able to account the effect of platform motion on wake behaviour.