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Duo to fluctuations in atmospheric turbulence and yaw control strategies, wind turbines are often in a yaw state. To predict the far wake velocity field of wind turbines quickly and accurately, a wake velocity model was derived based on the method of momentum conservation considering the wake steering of the wind turbine under yaw conditions. To consider the shear effect of the vertical incoming wind direction, a two-dimensional Gaussian distribution function was introduced to model the velocity loss at different axial positions in the far wake region based on the assumption of nonlinear wake expansion. This work also developed a "prediction-correction" method to solve the wake velocity field, and the accuracy of the model results was verified in wake experiments on the Garrad Hassan wind turbine. Moreover, a 33-kW two-blade horizontal axis wind turbine was simulated using this method, and the results were compared with the classical wake model under the same parameters and the computational fluid dynamics (CFD) simulation results. The results show that the nonlinear wake model well reflected the influence of incoming flow shear and yaw wake steering in the wake velocity field. Finally, computation of the wake flow for the Horns Rev offshore wind farm with 80 wind turbines showed an error within 8% compared to the experimental values. The established wake model is less computationally intensive than other methods, has a faster calculation speed, and can be used for engineering calculations of the wake velocity in the far wakefield of wind turbines. [ABSTRACT FROM AUTHOR]

In this paper, a supervisory control concept for wind farms is proposed based on the neighboring wind turbines control functions in localized areas for power optimization considering wake effects. The flow control in wind farms to maximize power production is a challenging problem due to its time-varying nonlinear wake dynamics. Hence, we develop a method that authorizes coordination in a wind farm for a squarely payoff-based scenario where the turbines have access only to measurements from their neighbors via repeated interactions. Therefore, in order to maximize output power in a wind farm, an Adaptive Learning Game Theory (ALGT) method is introduced. This control scheme provides an interaction framework that constructs a series of common control functions. Here, in every iteration, each turbine chooses an independent decision according to a localized control law. The control objective of wind turbine i determines how each turbine adjusts a decision at each iteration by processing available information. [ABSTRACT FROM AUTHOR]

In this article, we present an investigative study on the often-overlooked partial wake phenomenon in previous studies concerning wind farm configurations. A partial wake occurs when a portion of the actuator disk of a downstream wind turbine is affected by the wake of another upstream turbine. This phenomenon occurs in addition to the full wake, where the entire upstream turbine is affected by the wake of the frontal turbine, also leading to a decrease in wind speed and consequently a reduction in power production. The proposed study is based on measuring the power generated by the area swept by the wake of an array of turbines in a wind farm. To accomplish this, we integrate the linear wake model of Jensen, the specifications of the ENERCON E2 wind turbine, and the wind farm data into Matlab-developed software (version 18) to perform the calculations. In a concrete application, this proposed method is validated by reproducing the previous works that neglected the partial wake in wind farm configurations. The simulation results obtained are analyzed, compared, and discussed under similar operational conditions. [ABSTRACT FROM AUTHOR]

Fog conditions at the offshore wind farm Horns Rev 2 were photographed on 16 April 2018. In this study, we present the results of an analysis of the meteorological conditions on the day of the photographs. The aim of the study was to examine satellite images, meteorological observations, wind turbine data, lidar data, reanalysis data, and wake and blockage model results to assess whether wind farm blockage was a likely cause for the formation of fog upstream of the wind farm. The analysis indicated the advection of warm and moist air mass from the southwest over a cool ocean, causing cold sea fog. Wind speeds at hub height were slightly above cut-in, and there was a strong veer in the shallow stable boundary layer. The most important finding is that the wake and blockage model indicated stagnant air mass arcs to the south and west of the wind farm. In the photographs, sea fog is visible in approximately the same area. Therefore, it is likely that the reduced wind triggered the sea fog condensation due to blockage in this area. A discrepancy between the blockage model and sea fog in the photographs appears in the southwest direction. Slightly higher winds might have occurred locally in a southwesterly direction, which may have dissolved sea fog. The wake model predicted long and narrow wind turbine wakes similar to those observed in the photographs. The novelty of the study is new evidence of wind farm blockage. It fills the gap in knowledge about flow in wind farms. Implications for future research include advanced modeling of flow phenomena near large offshore wind farms relevant to wind farm operators. [ABSTRACT FROM AUTHOR]

This paper proposes a control strategy to achieve minimum wake-induced power losses in a wind farm. At first, the axial-induction-based wake model is developed to consider the aerodynamic wake interactions among wind turbines. To optimize the generated power of the whole wind farm, the axial induction factor of each wind turbine is calculated by the genetic algorithm. As a supervisory controller, each wind turbine's optimal axial induction factor calculated by the genetic algorithm is implemented as a setpoint of each wind turbine's internal controller. In the internal control loop, a comprehensive controller is designed to track the commanded axial induction factor. In the partial load region, the commanded axial induction factor was attained by tuning the generator torque. In the transient and full load regions, the blade pitch angle is tuned to keep the generator speed and torque at the rated values. The performance of the proposed control strategy is investigated through case studies, including three different wind speeds and a time-varying wind speed case in a 3 × 3 wind-farm layout. The simulation results show the satisfactory performance of the proposed approach. [ABSTRACT FROM AUTHOR]

In the wind farm control field, wind turbines are normally manipulated to maximize the individual power production which is named the greedy control. However, this greedy control method can lead to massive losses of total wind farm power production, mainly caused by the wake interference between multiple wind turbines. To this end, the cooperative wake control, which seeks the maximum total power production by coordinating each individual wind turbine at the global optimum operation point, can greatly improve the wind farm output performance. In this paper, we investigate the effectiveness of two different cooperative wake control strategies, i.e., instantaneous control and wind-interval based (WIB) control under variable wind speeds/directions scenario. These two cooperative control strategies are achieved based on the power de-rating operation to the upstream wind turbines. Taking three in-line wind turbines as an example, the control parameters of the two upstream wind turbines are cooperatively optimized while the downstream third wind turbine operates at the maximum power coefficient. To account for the multiple wind turbines wake interference, an artificial neural network (ANN) wake model characterized by the fast computational efficiency and great accuracy, in combination with the best wake superposition model chosen to quantify multiple wake effect, is proposed for the control optimization. By comparing to the baseline greedy control, it shows that both cooperative control strategies are effective in improving the power production of the wind farm. More specifically, the WIB control can maintain the power production at the same level of instantaneous control with a maximum difference less than 3%, while it reduces the operating difficulty to a large extent which greatly facilitates its application under realistic more complex wind scenarios. [ABSTRACT FROM AUTHOR]

To decrease the power deficit of a wind farm caused by wake effects, the layout optimization is a feasible way for the wind farm design stage. A suitable optimization algorithm can significantly improve the quality and efficiency of the optimization process. For exploring the high-performance algorithms under different layout densities, a comparison is conducted by optimizing the layout of a real offshore wind farm with five algorithms, namely two population-based algorithms and three single-point algorithms. Wake effects are considered by a full-field wake model. A penalty function is proposed for the population-based algorithms to handle the constraint violations. Different iterations and constraints of the layout density are applied in the optimization. The random search has the best optimization results in all the cases and the control of the feasibility check is necessary for this algorithm. More iterations can advance the optimization results. The density constraint greatly affects the computational cost of the random search, which is significantly increased under the strict constraint. Except under the strict constraint, the random search has the best performance of optimization efficiency. A combination of the pattern search and random search is recommended when the strict constraint is applied in the layout optimization. [ABSTRACT FROM AUTHOR]

Porous discs are the experimental counterparts of the numerical actuator disc concept and are frequently used in wind tunnel studies to reproduce the far-wake characteristics of wind turbines. The potential of using porous discs instead of wind turbines comes with the benefits such as operational easiness and design simplicity. This paper presents the results of an experimental study focusing on the wake development characteristics of a single porous disc and a single wind turbine under different freestream turbulence intensities but at similar Reynolds number conditions. The measurements are performed using two-dimensional two-component particle image velocimetry (2D2C PIV) technique up to seven diameters downstream distance in the wake of the models. The wake flows are analyzed in terms of the development of mean wake velocity deficit, wake decay, and wake turbulence characteristics. The results show that the wake recovery occurs faster for both the porous disc and the turbine with increasing freestream turbulence intensity. The wake width increases with the freestream turbulence intensity, indicating faster diffusion of the wake for both models. On the other hand, the wake width of the porous disc and the turbine is similar at the same turbulence intensity conditions, although they operate with slightly different thrust coefficients. Turbulent kinetic energy profiles in the far wake of the porous disc and the turbine, which are significantly different for the low turbulence intensity conditions, become similar for the high turbulence intensity case. The comparison of the turbulent kinetic energy, decay rate and production characteristics points to different turbulence mechanisms in the wake of the porous disc and the turbine. In the near wake, the wake decay rate and turbulent kinetic energy levels are higher in the porous disc case due to enhanced mixing levels associated with the grid-generated turbulence. In the far wake, the decay rate of the turbine wake is higher, most probably due to the breakdown of the tip vortices. When the freestream turbulence is increased, the differences in the turbulent wake flow characteristics diminish in the far wake, particularly after a 4.5-diameter downstream distance. [ABSTRACT FROM AUTHOR]

In this article, we present an investigative study on the often-overlooked partial wake phenomenon in previous studies concerning wind farm configurations. A partial wake occurs when a portion of the actuator disk of a downstream wind turbine is affected by the wake of another upstream turbine. This phenomenon occurs in addition to the full wake, where the entire upstream turbine is affected by the wake of the frontal turbine, also leading to a decrease in wind speed and consequently a reduction in power production. The proposed study is based on measuring the power generated by the area swept by the wake of an array of turbines in a wind farm. To accomplish this, we integrate the linear wake model of Jensen, the specifications of the ENERCON E2 wind turbine, and the wind farm data into Matlab-developed software (version 18) to perform the calculations. In a concrete application, this proposed method is validated by reproducing the previous works that neglected the partial wake in wind farm configurations. The simulation results obtained are analyzed, compared, and discussed under similar operational conditions.

This paper conducts a comparative analysis of three wind farm simulators, examining the influence of wake on the local wind speed and power output for downstream turbines using experimental data. The study features experiments in three distinct scenarios, evaluating differences among the simulators by calculating the local wind speed and power for each. Each simulator employs a unique wake model, which substantially affects the local wind speed experienced by downstream turbines. Furthermore, the experiment involves adjusting parameter values for each simulator to assess their respective impacts on wind farm performance. The findings of this research are expected to play an important role in investigations related to power optimization and wake effects in the wind farm control. [ABSTRACT FROM AUTHOR]

Abstract An anisotropic double Gaussian (DG) model for analytical wake modeling to predict the streamwise wake velocity behind an isolated non‐yawed horizontal‐axis wind turbine is proposed. The proposed model is based upon the conservation of mass and momentum inside a streamtube control volume. The wake growth rate parameters to distinguish the wake expansion rate between lateral and vertical directions were tuned based on numerical and measurement data of utility‐scale turbines. It was found that the proposed model can give feasible predictions within the full‐wake region under different inflow conditions. In addition, the other analytical models based on top‐hat shape and single Gaussian approaches were evaluated for comparison. The root‐mean‐square error statistical analysis was used to evaluate the performance of each examined model under different flow conditions. In general, the proposed model outperformed the other examined models in all wake region categories, particularly within the near‐wake region and the onset of the far‐wake region, which are beyond the scope of the conventional approach for analytical wake modeling. This advantage gives the potential for the proposed model to provide a better prediction for the wake flow estimation within tightly packed wind farms.

This paper discusses how the incorporation of high-resolution ground coverage dataset ESA WorldCover into a wind flow field and wake simulation calculation, as well as the use of the coupled wake model for wind farm output simulation, can improve the accuracy of wind resource assessment using engineering examples. In the actual case of grid-connected wind farms in central China, SCADA wind speed data is reconstructed to the free flow wind speed in front of the wind turbine impeller using the transfer function of the nacelle, and the wind farm is modeled using OpenWind software, simulating the wind speed at the height of each wind turbine hub and each wind turbine output. The results show that when other initial data are consistent, using ESA's high-precision land cover dataset WorldCover 10 m to make roughness lengths which improves the wind farm output simulation accuracy by 8.91%, showing that it is worth trying to apply WorldCover 10 m to the wind farm simulation design. At the same time, this case is used to compare and analyze the application of the Eddy-Viscosity wake model and the two coupled wake models based on the Eddy-Viscosity wake model. The results show that the coupled wake model will have higher accuracy than the Deep Array Eddy Viscosity wake model and it is 1.24% more accurate than the Eddy Viscosity wake model, and the ASM Eddy Viscosity wake model is 5.21% more accurate than the Eddy Viscosity wake model. [ABSTRACT FROM AUTHOR]

Wind tunnel experiments are performed to investigate the wake characteristics of a model wind turbine using Particle Image Velocimetry (PIV) and Hot-wire velocimetry. Results show that the velocity deficit at the hub height is the largest, and the stratification of the velocity shear layer at the blade tip is obvious. The instantaneous turbulence kinetic energy (T K E) level is much larger than the mean T K E , especially downstream of the blade tip. In the x / d T = 4 position of the wake region, the mean T K E increased by two times due to the blade tip disturbance. The Reynolds stresses also increase and the instantaneous value is the highest along the blade's tip. A thin vortex band appears at the root and tip of the blade, the vortex core expands and diffuses with the development of the wake along the downstream direction. The two-dimensional distributions of velocity spectra f Φ u reveal that the velocity fluctuation at x / d T = 2 location is small and that at x / d T = 4 position is the largest. Based on Jensen's wake model, a new theoretical wake model is proposed to predict the velocity distribution in the wind turbine wake. The calculated results of the wake model are in good agreement with the experimental data. • Particle image velocimetry and Hotwire are used to study the wake characteristics. • Velocity meandering and turbulence characteristics in the wake are captured. • Blade's tip vortex and velocity fluctuation in the wake are explored. • A new theoretical wake model is proposed to predict the velocity distribution. [ABSTRACT FROM AUTHOR]

Wake models play a fundamental role in predicting loads and power generated by wind farms. Using them, it is possible to assess how wakes develop and interact with each other and what are the effects generated in the context of a real operating farm. In this paper, a Gaussian Wake Model implemented in OpenFAST is validated against experimental data gathered in wind tunnel GVPM @ Politecnico di Milano in the context of the European CL-Windcon project. The software used to reproduce the mechanical dynamics of the G1 wind turbines is OpenFAST. It is coupled with FLORIS, a NREL's software based on the Gaussian Wake Model, that allows to simulate the wake and partial wake conditions. The rotor aerodynamics is calculated using the BEMT on the actual rotor flow field. However, to properly use OpenFAST and the coupled GWM, eight parameters have to be estimated. Thus, a Least Squares Minimization procedure is performed using the available experimental data. [ABSTRACT FROM AUTHOR]

Fog conditions at the offshore wind farm Horns Rev 2 were photographed on 16 April 2018. In this study, we present the results of an analysis of the meteorological conditions on the day of the photographs. The aim of the study was to examine satellite images, meteorological observations, wind turbine data, lidar data, reanalysis data, and wake and blockage model results to assess whether wind farm blockage was a likely cause for the formation of fog upstream of the wind farm. The analysis indicated the advection of warm and moist air mass from the southwest over a cool ocean, causing cold sea fog. Wind speeds at hub height were slightly above cut-in, and there was a strong veer in the shallow stable boundary layer. The most important finding is that the wake and blockage model indicated stagnant air mass arcs to the south and west of the wind farm. In the photographs, sea fog is visible in approximately the same area. Therefore, it is likely that the reduced wind triggered the sea fog condensation due to blockage in this area. A discrepancy between the blockage model and sea fog in the photographs appears in the southwest direction. Slightly higher winds might have occurred locally in a southwesterly direction, which may have dissolved sea fog. The wake model predicted long and narrow wind turbine wakes similar to those observed in the photographs. The novelty of the study is new evidence of wind farm blockage. It fills the gap in knowledge about flow in wind farms. Implications for future research include advanced modeling of flow phenomena near large offshore wind farms relevant to wind farm operators.

Planned offshore wind farm clusters have a rated capacity of more than 10 GW. The layout optimization and yield estimation of wind farms is often performed with computationally inexpensive, analytical wake models. As recent research results show, the flow physics in large (multi-gigawatt) offshore wind farms are more complex than in small (sub-gigawatt) wind farms. Since analytical wake models are tuned with data of existing, sub-gigawatt wind farms they might not produce accurate results for large wind farm clusters. In this study the results of a large-eddy simulation of a 15 GW wind farm are compared with two analytical wake models to demonstrate potential discrepancies. The TurbOPark model and the Niayifar and Porté-Agel model are chosen because they use a Gaussian wake profile and a turbulence model. The wind farm has a finite size in the crosswise direction, unlike as in many other large-eddy simulation wind farm studies, in which the wind farm is effectively infinitely wide due to the cyclic boundary conditions. The results show that new effects like crosswise divergence and convergence occur in such a finite-size multi-gigawatt wind farm. The comparison with the wake models shows that there are large discrepancies of up to 40% between the predicted wind farm power output of the wake models and the large-eddy simulation. An energy budget analysis is made to explain the discrepancies. It shows that the wake models neglect relevant kinetic energy sources and sinks like the geostrophic forcing, the energy input by pressure gradients and energy dissipation. Taking some of these sources and sinks into account could improve the accuracy of the wake models.

Aiming at the problem where the current engineering wake model does not describe the wind speed distribution of the wake in the complex terrain wind farm completely, based on the three-dimensional full wake model (3DJGF wake model), this paper proposed a wake model that can predict the three-dimensional wind speed distribution of the entire wake region in the complex wind farm, taking into account the Coanda effect, wind shear effect, and wake subsidence under the Gaussian terrain. Two types of Doppler lidar were used to conduct wind field experiments, and the inflow wind profile and three-dimensional expansion of the wake downstream of the wind turbine on the Gaussian terrain were measured. The experimental results showed that the wake centerline and terrain curve showed similar variation characteristics, and the near wake profile was similar to a super-Gaussian shape (asymmetric super-Gaussian shape) under low-wind-speed conditions, while the near wake profile presented a bimodal shape (asymmetric bimodal shape) under high-wind-speed conditions. The predicted profiles of the Gaussian terrain wake model were compared with the experimental data and the three typical wake models. The comparison results showed that the newly proposed Gaussian terrain wake model fit well with the experimental data in both near wake and far wake regions, and it had better performance in predicting the wake speed of the Gaussian terrain wind farm than the other three wake models. It can effectively predict the three-dimensional velocity distribution in the whole wake region of complex terrain. [ABSTRACT FROM AUTHOR]

The wake management of offshore wind farms (OWFs) mainly considers the wake effect. Wake effects commonly occur in offshore wind farms, which cause a 5–10% reduction in power production. Although there have been many studies on wake management, many methods are not accurate enough; for instance, look-up table and static wake model control methods do not consider the time-varying wake state. Dynamic wake management is based on the real-time dynamic wake, so it can increase the energy of the OWFs effectively. For OWFs, dynamic wake control is the main method of dynamic wake management. In this paper, the existing wake model and control progress are discussed, mainly emphasizing the dynamic wake model and the dynamic wake control method, solving the gap of the review for dynamic wake management. This paper presents a digital twins (DT) framework for power and fatigue damage for the first time.. The structure of this paper is as follows: (1) the mechanism of wind farm wake interference is described and then the dynamic wake model is reviewed and summarized; (2) different control methods are analyzed and the dynamic wake management strategies for different control methods are reviewed; (3) in order to solve the problems of dynamic wake detection and real-time effective control, the technology of DT is applied to the dynamic wake control of OWFs. This new DT frame has a promising application prospect in improving power and reducing fatigue damage. [ABSTRACT FROM AUTHOR]

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.

To decrease the power deficit of a wind farm caused by wake effects, the layout optimization is a feasible way for the wind farm design stage. A suitable optimization algorithm can significantly improve the quality and efficiency of the optimization process. For exploring the high-performance algorithms under different layout densities, a comparison is conducted by optimizing the layout of a real offshore wind farm with five algorithms, namely two population-based algorithms and three single-point algorithms. Wake effects are considered by a full-field wake model. A penalty function is proposed for the population-based algorithms to handle the constraint violations. Different iterations and constraints of the layout density are applied in the optimization. The random search has the best optimization results in all the cases and the control of the feasibility check is necessary for this algorithm. More iterations can advance the optimization results. The density constraint greatly affects the computational cost of the random search, which is significantly increased under the strict constraint. Except under the strict constraint, the random search has the best performance of optimization efficiency. A combination of the pattern search and random search is recommended when the strict constraint is applied in the layout optimization.

Recently, wind farms consisting of clusters of closely spaced vertical-axis wind turbines (VAWTs) have attracted the interest of many people. In this study, a method using a wake model to predict the flow field and the output power of each rotor in a VAWT cluster is proposed. The method uses the information obtained by the preliminary computational fluid dynamics (CFD) targeting an isolated single two-dimensional (2D) VAWT rotor and a few layouts of the paired 2D rotors. In the method, the resultant rotor and flow conditions are determined so as to satisfy the momentum balance in the main wind direction. The pressure loss of the control volume (CV) is given by an interaction model which modifies the prepared information on a single rotor case and assumes the dependence on the inter-rotor distance and the induced velocity. The interaction model consists of four equations depending on the typical four-type layouts of selected two rotors. To obtain the appropriate circulation of each rotor, the searching range of the circulation is limited according to the distribution of other rotors around the rotor at issue. The method can predict the rotor powers in a 2D-VAWT cluster including a few rotors in an incomparably shorter time than the CFD analysis using a dynamic model. [ABSTRACT FROM AUTHOR]

An anisotropic double Gaussian (DG) model for analytical wake modeling to predict the streamwise wake velocity behind an isolated non‐yawed horizontal‐axis wind turbine is proposed. The proposed model is based upon the conservation of mass and momentum inside a streamtube control volume. The wake growth rate parameters to distinguish the wake expansion rate between lateral and vertical directions were tuned based on numerical and measurement data of utility‐scale turbines. It was found that the proposed model can give feasible predictions within the full‐wake region under different inflow conditions. In addition, the other analytical models based on top‐hat shape and single Gaussian approaches were evaluated for comparison. The root‐mean‐square error statistical analysis was used to evaluate the performance of each examined model under different flow conditions. In general, the proposed model outperformed the other examined models in all wake region categories, particularly within the near‐wake region and the onset of the far‐wake region, which are beyond the scope of the conventional approach for analytical wake modeling. This advantage gives the potential for the proposed model to provide a better prediction for the wake flow estimation within tightly packed wind farms. [ABSTRACT FROM AUTHOR]

The development of new wake models is currently one of the key approaches envisioned to further improve the levelized cost of energy of wind power. While the wind energy literature abounds with operational wake models capable of predicting in fast-time the behavior of a wind turbine wake based on the measurements available (e.g., SCADA), only few account for dynamic wake effects. The present work capitalizes on the success gathered by the Dynamic Wake Meandering formulation and introduces a new operational dynamic wake modeling framework aimed at capturing the wake dynamic signature at a low computational cost while relying only on information gathered at the wind turbine location. In order to do so, the framework brings together flow sensing and Lagrangian flow modeling into a unified framework. The features of the inflow are first inferred from the turbine loads and operating settings: a Kalman filter coupled to a Blade Element Momentum theory solver is used to determine the rotor-normal flow velocity while a Multi-Layer Perceptron trained on high-fidelity numerical data estimates of the transverse wind velocity component. The information recovered is in turn fed to a Lagrangian flow model as a source condition and is propagated in a physics-informed fashion across the domain. The ensuing framework is presented and then deployed within a numerical wind farm where its performances are assessed. The computational affordability of the proposed model is first confirmed: 7 × 10−4 wall-clock seconds per simulation second are required to simulate a small 12 turbines wind farm. Large Eddy Simulations of wind farm using advanced actuator disks are then used as a baseline and a strong focus is laid on the study of the wake meandering features. Comparison against the Large Eddy Simulation baseline reveals that the proposed model achieves good estimates of the flow state in both low and high Turbulence Intensity configurations. The model distinctly provides additional insight into the wake physics when compared to the traditional steady state approach: the wake recovery is consistently accounted for and the wake meandering signature is captured as far as 12D downstream with a correlation score ranging from 0.50 to 0.85.

This paper conducts a comparative analysis of three wind farm simulators, examining the influence of wake on the local wind speed and power output for downstream turbines using experimental data. The study features experiments in three distinct scenarios, evaluating differences among the simulators by calculating the local wind speed and power for each. Each simulator employs a unique wake model, which substantially affects the local wind speed experienced by downstream turbines. Furthermore, the experiment involves adjusting parameter values for each simulator to assess their respective impacts on wind farm performance. The findings of this research are expected to play an important role in investigations related to power optimization and wake effects in the wind farm control.

This paper presents some results from a computational fluid dynamics (CFD) model of a multi-megawatt crosswind kite spinning on a circular path in a straight downwind configuration. The unsteady Reynolds averaged Navier-Stokes equations closed by the k − ω SST turbulence model are solved in the three-dimensional space using ANSYS Fluent. The flow behaviour is examined at the rotation plane, and the overall (or global) induction factor is obtained by getting the weighted average of induction factors on multiple annuli over the swept area. The wake flow behaviour is also discussed in some details using velocity and pressure contour plots. In addition to the CFD model, an analytical model for calculating the average flow velocity and radii of the annular wake downstream of the kite is developed. The model is formulated based on the widely-used Jensen's model which was developed for conventional wind turbines, and thus has a simple form. Expressions for the dimensionless wake flow velocity and wake radii are obtained by assuming self-similarity of flow velocity and linear wake expansion. Comparisons are made between numerical results from the analytical model and those from the CFD simulation. The level of agreement was found to be reasonably good. Such computational and analytical models are indispensable for kite farm layout design and optimization, where aerodynamic interactions between kites should be considered. [ABSTRACT FROM AUTHOR]

This study employs a UAV anemometry system to assess the wind field around a yawed wind turbine, particularly focusing on its wake during operational conditions. The research findings reveal that the evolution of wind turbine wakes follows distinct patterns at various downstream distances. Turbulence intensity notably amplifies within regions characterized by significant fluctuations in mean wind speed. Specifically, in yawed conditions, the areas with the highest turbulence generated by the rotor coincide with zones exhibiting pronounced variations in mean wind speed. The heightened turbulence within the wake region to some extent constrains the safety and economic viability of wind farms. Turbulence intensity increases significantly in the region where the average wind speed changes greatly, that is, under the yaw state of the wind turbine, this region is characterized with the strongest turbulence generated by the rotor. The UAV anemometry system's wind speed assessment closely matches predictions from the Y-3DJGF model, accounting for wake experience coefficient adjustments. Furthermore, in yaw conditions, the wind turbine's wake trajectory exhibits some deviation from the incident flow's direction, with an initial increase in slope followed by gradual stabilization. As the downstream distance increases, the trajectory will eventually establish a consistent trend with the incident flow. The cost-effective and flexible UAV anemometry system enhances wind field measurements, offering an innovative approach for wind energy sector research and engineering. • Development of a UAV-based anemometry system for wake measurement of yawed wind turbines. • Investigation of wake characteristics under yawed conditions, revealing significant reductions in wake wind speed and increased turbulence intensity, especially at 2D downstream. • Experimental validation of wake trajectory deviations under yaw conditions, highlighting changes in slope and eventual alignment with incident flow downstream. • Validation of wind speed measurements using the UAV anemometry system against predicted results from the Y-3DJGF model. • Application of the UAV anemometry system in wind resource assessment, layout optimization, and power generation efficiency forecasting for wind farms. [ABSTRACT FROM AUTHOR]

This paper discusses how the incorporation of high-resolution ground coverage dataset ESA WorldCover into a wind flow field and wake simulation calculation, as well as the use of the coupled wake model for wind farm output simulation, can improve the accuracy of wind resource assessment using engineering examples. In the actual case of grid-connected wind farms in central China, SCADA wind speed data is reconstructed to the free flow wind speed in front of the wind turbine impeller using the transfer function of the nacelle, and the wind farm is modeled using OpenWind software, simulating the wind speed at the height of each wind turbine hub and each wind turbine output. The results show that when other initial data are consistent, using ESA’s high-precision land cover dataset WorldCover 10 m to make roughness lengths which improves the wind farm output simulation accuracy by 8.91%, showing that it is worth trying to apply WorldCover 10 m to the wind farm simulation design. At the same time, this case is used to compare and analyze the application of the Eddy-Viscosity wake model and the two coupled wake models based on the Eddy-Viscosity wake model. The results show that the coupled wake model will have higher accuracy than the Deep Array Eddy Viscosity wake model and it is 1.24% more accurate than the Eddy Viscosity wake model, and the ASM Eddy Viscosity wake model is 5.21% more accurate than the Eddy Viscosity wake model.

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. [ABSTRACT FROM AUTHOR]

Oscillating wave surge converter (OWSC) is widely utilized to exploit energy from waves. Due to the wake effects, the layout of OWSCs will significantly affect the energy output of an OWSC farm. However, up to now the layout of OWSC farm was only determined empirically, and there was no quantitative layout optimization method for OWSC farm. The quantitative layout optimization needs analytical wake model for OWSC to conduct fast optimization iterations. However, there was still no analytical wake model for OWSC. Therefore, in this study, we proposed an analytical wake model regarding regular waves, based on which a quantitative method for optimizing the layout of OWSC farm was also proposed. It was found that the total energy outputs of the optimized layouts using the proposed method are significantly larger than those of the empirical ones, and increasing the spacing between the OWSCs in the bi-direction of wave propagation can greatly increase the total energy output. The proposed OWSC analytical wake model can predict the wave height changes with an accuracy of 94.73%. Innovatively, GPU-acceleration technology was utilized, and the GPU-based codes can run at least 1479 times faster than the CPU-based ones. Those implemented codes are opened for other researchers. • A novel analytical wake model is proposed to predict wave height changes in OWSC wakes. • An array optimization method is proposed for OWSCs to maximize their energy outputs quantitatively. • Staggered layouts of the OWSCs are recommended. • Increasing spacing between the OWSCs in the bi-direction of wave propagation can greatly increase total energy output. • GPU-based codes can run at least 1479 times faster than the CPU-based ones and are opened. [ABSTRACT FROM AUTHOR]

This paper investigates the optimal layout of wind turbines (WTs) within a wind farm. Finding the best placement of WTs in a wind farm is a challenging process due to the existence of multiple wake effects. A biogeography based optimization (BBO) algorithm method is proposed to search for the optimal location of WTs in a wind farm (WF), to maximize the power produced by the WF and improve the annual economic performance of the WF. A wind turbine (WT) that operates in the wake of one or more other turbines is subject to lower flow and therefore produces less power. When designing a wind project, the arrangement of the turbines with each other in a wind farm is a very important factor. The best layout of a wind farm is to achieve the optimal placement of the turbines in relation to each other in a given area to maximize the efficiency of the whole wind farm and reduce its cost. A dense configuration would result in considerable power losses. Each turbine must have a sufficient distance from other turbines in the WF where the optimal number of turbines should be placed. The BBO approach is conducted on a 2 km x 2 km wind farm assuming a constant wind speed of 12 m/s with a fixed wind direction, for solving the wind farm layout optimization problem in two different configurations which include 26 and 30 WTs respectively. A comparison of the results obtained with the previous studies shows that the BBO is more efficient in terms of maximizing power output and economic profitability of the same wind farm model, which validates that BBO performs effectively in optimizing WTs placement within WF. BOO provides the greatest improvement in the optimal layout, for example, in the case of the layout for 30 WTs. The power output reaches 15,383 KW, the agreement between the ideal and the optimal layout is more favorable. The difference in output power is only 169 KW (1%). Knowing that the ideal layout is reached if all WTs receive a wind flow with a maximum wind speed of 12 m/s. Furthermore, a case study of wind turbine layout optimization using the BBO program on the Alta X wind farm has been performed under variable wind speed and variable wind direction. The results indicate that the optimized layout of the Alta X wind farm achieves a 12% increase in the power output for a similar cost when compared to the original layout of Alta X. It is also more appropriate for evaluating the wind farm layout in the Wind Power Project (WPP). [ABSTRACT FROM AUTHOR]

In the wind industry, power prediction of wind farm is commonly implemented by analytical wake models, which is low-cost but insufficient in accuracy for high-turbulent wake modelling. In this study, a novel machine-learning-based wake model is developed to improve the power prediction of wind farms. The presented model can reproduce the velocity and turbulence fields in turbine wakes commensurate to the high-fidelity Computational Fluid Dynamics (CFD) simulations while achieving good computational efficiency. Driven by massive CFD simulation dataset, the implicit relationship between inflows and wake flows is established using the Artificial Neural Networks (ANN) technique based on back-propagation algorithm. The reduced-order method Actuator Disk Model with Rotation (ADM-R) and modified k − ε turbulence model are implemented into RANS simulations to save the computational costs dramatically in producing the big-data of wake flows. The ANN wake model is deployed in the Horn Rev wind farm, and validated against LES, onsite measurement, and analytical wake models. The conclusions show that the ANN model can appreciably improve the power predictions compared with the existing analytical models and match the LES and measurement data well. The validated model is also adopted to investigate the influence of wind direction and turbine layout on power production of wind farms. • The machine learning-based wake model is competitive in both efficiency and accuracy for wind farm power prediction. • Turbulence modeling dominates the recovery speed of turbine wake, which is critical for accurate power prediction. • Comprehensive predictions of power output and losses inside Horns Rev wind farm under various wind directions are discussed. • In the Horns Rev wind farm, aligned layout performs better than staggered layout due to the local dominated wind directions. [ABSTRACT FROM AUTHOR]

The wake management of offshore wind farms (OWFs) mainly considers the wake effect. Wake effects commonly occur in offshore wind farms, which cause a 5–10% reduction in power production. Although there have been many studies on wake management, many methods are not accurate enough; for instance, look-up table and static wake model control methods do not consider the time-varying wake state. Dynamic wake management is based on the real-time dynamic wake, so it can increase the energy of the OWFs effectively. For OWFs, dynamic wake control is the main method of dynamic wake management. In this paper, the existing wake model and control progress are discussed, mainly emphasizing the dynamic wake model and the dynamic wake control method, solving the gap of the review for dynamic wake management. This paper presents a digital twins (DT) framework for power and fatigue damage for the first time.. The structure of this paper is as follows: (1) the mechanism of wind farm wake interference is described and then the dynamic wake model is reviewed and summarized; (2) different control methods are analyzed and the dynamic wake management strategies for different control methods are reviewed; (3) in order to solve the problems of dynamic wake detection and real-time effective control, the technology of DT is applied to the dynamic wake control of OWFs. This new DT frame has a promising application prospect in improving power and reducing fatigue damage.

Recently, wind farms consisting of clusters of closely spaced vertical-axis wind turbines (VAWTs) have attracted the interest of many people. In this study, a method using a wake model to predict the flow field and the output power of each rotor in a VAWT cluster is proposed. The method uses the information obtained by the preliminary computational fluid dynamics (CFD) targeting an isolated single two-dimensional (2D) VAWT rotor and a few layouts of the paired 2D rotors. In the method, the resultant rotor and flow conditions are determined so as to satisfy the momentum balance in the main wind direction. The pressure loss of the control volume (CV) is given by an interaction model which modifies the prepared information on a single rotor case and assumes the dependence on the inter-rotor distance and the induced velocity. The interaction model consists of four equations depending on the typical four-type layouts of selected two rotors. To obtain the appropriate circulation of each rotor, the searching range of the circulation is limited according to the distribution of other rotors around the rotor at issue. The method can predict the rotor powers in a 2D-VAWT cluster including a few rotors in an incomparably shorter time than the CFD analysis using a dynamic model.

A recently proposed analytical wake model for a horizontal axis utility scale wind turbine is revisited, and revised and improved. The model is based upon conservation of momentum in the context of actuator disc theory, and the assumption of a distribution of the double-Gaussian type for the velocity deficit in the wake. The model is developed and improved and reveals characteristics of the wind turbine wake velocity deficit for the full wake, including the near-wake to within close proximity of the wind turbine rotor. Full 2-dimensional model fitting to lidar wake measurement data obtained from a 5 MW utility scale wind turbine is carried out for the full range of inflow wind velocities of primary interest. Such a full wind turbine wake model has the potential to facilitate analytic calculations within the wind turbine wake region, and the potential to improve understanding of wind turbine aerodynamics. • Double-Gaussian analytical wake model for a horizontal axis wind turbine. • Wake model validation for utility scale wind turbine. • Characteristics of wind turbine wake velocity deficit modelled. [ABSTRACT FROM AUTHOR]

Most existing analytical wake models have been designed to represent the velocity distribution of the far wake region behind a wind turbine, but fail to reproduce the trend of the near wake. In order to meet the demand for both near and far wake velocity predictions, a concise three-dimensional dual-cosine shape (3D-COU) model is proposed. Moreover, by taking into account the wind shear and ground effects in the vertical direction, this model is capable of describing the anisotropic property of the 3-D wake field and is much closer to the reality. The proposed model is then calibrated and validated through a series of test cases, including different scales of turbines that are operating under a wide range of inflow conditions, and meanwhile the reference data resource is diverse. Overall, the results demonstrate that the 3D-COU model can accurately predict the variations of the wake velocity in both the vertical and horizontal directions throughout the whole wake region. Given its good accuracy, simplicity and applicability, this model provides the potential to effectively address practical problems in wind energy projects. [ABSTRACT FROM AUTHOR]

An analytical yawed wake model for wind turbine, which predicts the streamwise velocity distribution within the wake of a yawed wind turbine, is proposed in this study. The model applies mass and momentum conservation and uses a self-similar Gaussian shape to depict the transverse distribution of the streamwise velocity deficit and skew angle. Unlike existing yawed wake models, this model introduces additional equations to predict the transverse locations of maximum velocity deficit at different heights. What's more, a novel formula to calculate the expansion rate of wake width is proposed by the friction velocity, inflow velocity and the thrust coefficient. The measured data of wind tunnel experiment are used to investigate the validity of this model, as well as the other existing models firstly. Then, for validating the velocity distribution in the curled cross-section, the numerical simulations of wake under different yaw angles were carried out to provide the wake data. Comparisons between model predictions, experimental data and numerical results demonstrate that the model can satisfactorily predict the yawed wake deformation, as well as the velocity distribution at different heights. Due to its high accuracy and cost-effectiveness, this yawed wake model is advantageous for the application of yaw angle control. • The Gaussian-shape analytical model is proposed to describe the distribution of wake velocity. • This model considers the curled deformation of yawed wake with height. • A novel formula to compute the expansion rate of wake is introduced through the friction velocity. • The predictions of analytical model give outstanding performance in comparisons with CFD results and experimental data. [ABSTRACT FROM AUTHOR]

[Introduction] The paper aims to obtain the optimal layout of offshore wind farm and gain the maximum profit in the project life-cycle, it is high necessary to analyze its impact factors. [Method] The own developed application was used to compare the wake models between Jensen and Larsen, different superposition algorithm among wind turbines and the interannual variability of wind direction, this disquisition had combined the practical offshore wind farm case to analyse and provide the optimal layout. [Result] The results we obtained demonstrate that the interannual variability of wind direction is the most key factor to layout, followed by the different wake model, with superposition algorithm least. [Conclusion] This work provides some guidance for further project on choosing the optimal layout, thus the billions of dollars in losses caused by interannual variability of wind direction can be avoided in life-cycle of 25 years.

This paper presents some results from a computational fluid dynamics (CFD) model of a multi-megawatt crosswind kite spinning on a circular path in a straight downwind configuration. The unsteady Reynolds averaged Navier-Stokes equations closed by the k−ω SST turbulence model are solved in the three-dimensional space using ANSYS Fluent. The flow behaviour is examined at the rotation plane, and the overall (or global) induction factor is obtained by getting the weighted average of induction factors on multiple annuli over the swept area. The wake flow behaviour is also discussed in some details using velocity and pressure contour plots. In addition to the CFD model, an analytical model for calculating the average flow velocity and radii of the annular wake downstream of the kite is developed. The model is formulated based on the widely-used Jensen’s model which was developed for conventional wind turbines, and thus has a simple form. Expressions for the dimensionless wake flow velocity and wake radii are obtained by assuming self-similarity of flow velocity and linear wake expansion. Comparisons are made between numerical results from the analytical model and those from the CFD simulation. The level of agreement was found to be reasonably good. Such computational and analytical models are indispensable for kite farm layout design and optimization, where aerodynamic interactions between kites should be considered.

By optimizing the positions of wind turbines in a wind farm, the power loss caused by wake effects can be reduced maximally. A new methodology of layout optimization is proposed utilizing a full-field wake model that integrates the near-field and far-field wake models after modifications, and a random search (RS) algorithm improved with a scale factor for acceleration in high-density layouts. The methodology is applied to a floating wind farm composed of modular platforms, which have a novel configuration and the ability to face toward the wind direction. The applicability and efficiency of the methodology and the improved RS algorithm are validated. The power production of optimized layouts shows a flat crest with an increased number of wind turbines. There is a layout with maximal output power in the wind farm. The real optimal layout should be determined in consideration of both output power and cost. Two sizes of platforms with different number of modules are compared in the application. The wind farm with smaller platforms produces more power. For comparison, a pattern search (PS) algorithm is also implemented in the application. The improved RS algorithm shows outperformance compared with the original RS and the PS algorithm.

Analyzing or optimizing wind farm layouts often requires reduced-order wake models to estimate turbine wake interactions and wind velocity. We propose a wake model for vertical-axis wind turbines in streamwise and crosswind directions. Using vorticity data from computational fluid dynamic simulations and cross-validated Gaussian distribution fitting, we produced a wake model that can estimate normalized wake velocity deficits of an isolated vertical-axis wind turbine using normalized downstream and lateral positions, tip-speed ratio, and solidity. Compared with computational fluid dynamics, taking over a day to run one simulation, our wake model predicts a velocity deficit in under a second with an appropriate accuracy and computational cost necessary for wind farm optimization. The model agreed with two experimental studies producing percent differences of the maximum wake deficit of 6.3% and 14.6%. The wake model includes multiple wake interactions and blade aerodynamics to calculate power, allowing its use in wind farm layout analysis and optimization. [ABSTRACT FROM AUTHOR]

Huaneng Rudong 300 MW offshore wind farm project is located in eastern China. The wake effect is one of the major concerns for wind farm operators, as all 70 units are plotted in ranks, and the sea surface roughness is low. This paper investigated the wake intensity by combining a field test and a numerical simulation. To carry out further yaw optimization, a Gaussian wake model was adopted. Firstly, a 3D Light Detection and Ranging device (LiDAR) was used to capture the features in both horizontal and vertical directions of the wake. It indicated that Gaussian wake model can precisely predict the characteristics under time average and steady state in the wind farm. The predicted annual energy production (AEP) of the whole wind farm by the Gaussian model is compared with the calculation result of the actuator line (AL)-based LES method, and the difference between the two methods is mostly under 10%.

Accurate wake model in wind farm layout optimization can help extracting maximum power generation, minimizing cost of energy and prolonging wind turbines' lifetime as well. With the development of different wake models, the wind farm layout optimization results based on the models should be updated. This paper investigates the performances of four wake models in wind farm layout optimization using multi-population genetic algorithm (MPGA) with the wind farm power generation, COST/AEP and wind farm efficiency been reported. Comparison of results between typical wake models' performance shows that Jensen's wake model reported a higher wind farm power generation and efficiency because it underestimates the velocity deficit in the wake, and to the contrary, in the Frandsen wake model, the velocity in the wake is underestimated, resulting in a deceased power generation. The expression of 2D_k model shall be out of work in complicated wind condition. The 2D Jensen–Gaussian wake model performed better in the wind farm layout optimization using the MPGA program which can be promoted in real-world wind farm micrositing. [ABSTRACT FROM AUTHOR]

The operational security of power systems for wind farm (WF) integration becomes more important as the penetration of wind generation increases. A WF may contain hundreds of wind turbines (WT) and thus the power system simulations based on the complex model of a WT consume much time. This article proposes an equivalent WF model with the frequency-regulation function. The main research works include the establishment of the generic model of a WT, the development of single- and multimachine equivalent models for a large WF, the clustering of WTs based on the developed nonlinear wake model and the fuzzy C-means (FCM) clustering algorithm, the integration of the frequency-regulation function into the equivalent WF model, and the validation of the developed equivalent WF model by various operating scenarios. The results demonstrate that the proposed multimachine equivalent method based on the FCM clustering provides a more accurate model than a single-WT equivalent model. Consequently, the research results provide a solution for simulating a large-scale wind power integration, providing efficient, accurate, and fast steady-state and dynamic analyses. [ABSTRACT FROM AUTHOR]

Wake effects increase the fatigue loads on wind turbines in operation. However, the wake flow is considerably different from the traditional boundary layer flow, and poses many challenges in determining the fatigue loads on wind turbines operating in a wake. Therefore, in the present study, the actuator‐line model was adopted to numerically simulate the wake flow and an in‐house code named AOWT, which is based on a generalized coordinate method, was developed for analyzing the dynamics of wind turbines under an arbitrary distribution of the turbulent flow field varying in time and space. Using the numerically modeled instantaneous wake flow fields and AOWT, the dynamic response of a wind turbine, located at specified positions in both tandem and staggered arrangements in a wake, was examined, and the fatigue loads were determined. Furthermore, to determine the major contributions to the fatigue loads, the loads induced by the spatial variation of the mean flow fields were predicted. To the best of the authors' knowledge, no such analysis has been conducted thus far. Importantly, it was found that in the near‐wake region, the mean flow field had a significant influence on the fatigue loads, especially in the staggered layout. However, there is no analytical wake model available in the literature capable of predicting the near‐wake mean flow fields. Therefore, in this study, a near‐wake model was proposed, which yielded satisfactory predictions of the mean velocities in the near‐wake region. [ABSTRACT FROM AUTHOR]

The downwind rotor configuration provides a structural advantage compared with an upwind design. However, tower shadow has long been a concern for downwind systems. The tower shadow negatively affects the blade by introducing a load impulse during the wake passage. An aerodynamic fairing could shroud the tower reducing the wake. However, there is no clear consensus on the importance of a tower shadow for utility‐scale wind turbines. Simulations were conducted in FAST to determine the general parameters that influence the importance of the tower shadow effect for the differently sized wind turbines. The lock number of the blade was a significant driving quantity. Lower lock numbers (typical of small‐scale wind turbines) lead to greater relative fatigue damage from tower shadow effects. It was determined that a fairing is very helpful for small‐scale wind turbines operating in a low‐turbulence environment (such as a subscale wind tunnel test). However, the tower shadow increased the damage equivalent loading on an extreme scale blade by less than 5% in a turbulent environment. These results indicate that the cost of a tower fairing is likely unnecessary for utility‐scale wind turbines in operation. [ABSTRACT FROM AUTHOR]

This paper presents a data-driven wind farm layout optimization framework that uses a machine learning wake model that considers physical control stages. The machine learning wake model is trained using well-validated Computational Fluid Dynamics (CFD) simulation data, and consists of thousands of sub-models, each of which is an artificial neural network (ANN) wake model. The ANN wake models are trained separately for low-speed and high-speed inflows to ensure high accuracy of the predictions, with less than 2% error compared to CFD simulations. The accuracy and efficiency of the framework are validated, and the results show better agreement with CFD simulation than an analytical wake model developed in recent years. A parametric study on the number of wind turbines in the Horns Rev wind farm demonstrates that more wind turbines can be added with a minor decrease in average power, with more even and staggered layouts. Under full-wake uniform inflow, the selected analytical wake model exhibits a power prediction error of 5%–8%, while the differences between optimal layouts searched by different wake models range from 2% to 8%. When introducing a wider range of inflow direction sectors, the discrepancy between optimal layout performances decreases. [ABSTRACT FROM AUTHOR]

Wind power production is strongly affected by wake, and wake analysis is particularly important for wind farm layout optimization. The purpose of this study is to establish a multi-dimensional analysis wake model (3DJSG-M model) which can describe the wake region of multiple wind turbines perfectly to analyze the three-dimensional spatial distribution characteristics of the wake of multiple wind turbines. Firstly, considering the wind speed difference between wind shear inflow and uniform inflow, a three-dimensional wake model based on super-Gaussian function (3DJSG model) is derived by using the flow conservation theorem; Secondly, the influence of wind shear is introduced into the energy deficit theory, and the 3DJSG-M model is derived; Finally, wind field experiments are carried out with two high-precision LIDARs to verify the accuracy of 3DJSG model and 3DJSG-M model respectively. The results show that 3DJSG model and 3DJSG-M model fit well with the experimental data and can better predict the three-dimensional distribution characteristics of the whole wake region after a single wind turbine and multiple wind turbines. This study can provide optimization strategies for wind farm layout, reduce energy costs, and improve wind farm benefits. [ABSTRACT FROM AUTHOR]

This study aims to show the application of stochastic optimization for efficient and robust parameter calibration of engineering wake models. Standard values of the wake effect parameters are generally used to predict power using engineering wake models, but some recent studies have shown that these values do not result in accurate prediction. The proposed approach estimates the wake effect parameters using operational data available from actual wind farms to minimize the prediction error of the wake model by using trust-region optimization. To further improve computational efficiency, we implement stratified adaptive sampling. We employ decision trees to stratify the data and propose two ways of adapting the sampling budget to the constructed strata: budget allocation with dynamic weights and fixed weights. We extend our analysis to determine the functional relationship between the turbulence intensity and wake decay coefficient. Our experiments suggest that wake parameters or a functional relationship between turbulence intensity and wake decay coefficient may need adjustments (from assumed standard values) for a particular wind farm using its operational data to characterize the wake effect better. • Engineering wake models have parameters that crucially affect their performance. • Wake parameters can be calibrated as constants or functions of other wind variables. • Stochastic optimization (SO) provides accurate and reliable wake calibrations. • Both point and functional calibration of wake parameters can be done well with SO. • A derivative-free trust-region SO method provides robust wake calibration. • Efficiently implemented trust-region SO uses adaptive sampling and variance reduction. • Stratifying data based on wind characteristics effectively reduces variance during SO. • Choosing strata of wind data and dynamically sampling from each expedites calibration. • Robust wake calibration helps understanding power deficit patterns in wind farms. • Good prediction of power deficit due to wake enables optimal design of new wind farms. [ABSTRACT FROM AUTHOR]