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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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

The wake of wind turbine in a complex terrain site is investigated by a modified delayed detached eddy simulation (MDDES) and a hybrid framework to predict the wind turbine wake effects in a real wind farm are presented. The wind field and turbine wake flows over the real terrain are simulated for different directions and validated by comparing with those measured by a LiDAR in the wind farm. Subsequently, the wake characteristics over the escarpment are systematically investigated by numerical simulations and the terrain effects on the turbine wake flow are clarified. A hybrid framework is then utilized for a wind farm over complex terrain. In this framework, the effects of local terrain and surface roughness on the wind speed, wind direction and turbulence intensity are taken into account by the numerical simulation, while the wind turbine wakes are represented by a new Gaussian-based analytical wake model. Finally, the applicability of the proposed framework is verified by comparison with the numerical simulation results of wake over the escarpment. • Numerical simulations on the wind turbine wake over complex terrain are conducted and validated by the field measurement. • The wind turbine wake characteristics over the escarpment with different elevation are systematically investigated. • A hybrid framework is utilized for wind turbine wake prediction over complex terrain and its applicability is verified. [ABSTRACT FROM AUTHOR]

• A novel method based on the characteristics of all commercial turbines is proposed. • The self-organizing map is a powerful means to perform a comprehensive analysis. • Maximising capacity factor and minimising levelized cost of energy generally match. • Installed power or rated speeds should be reduced, while rotor diameters maximised. • Mere maximisation of wind farm energy production is a misleading target. A novel method was developed to detect the optimal onshore wind farm layout driven by the characteristics of all commercially-available wind turbines. A huge number of turbine combinations (577) was processed, resulting in 22,721 generated layouts. Various assumptions and constraints were considered, mostly derived from the literature, including site features, wind conditions, and layout design. For the latter, an irregularly staggered turbine array configuration was assumed. Wake effects were simulated through the Jensen's model, while a typical turbine thrust coefficient curve as a function of wind speed was originally developed. A detailed cost model was used, with levelized cost of energy selected as primary and capacity factor as secondary objective function. The self-organizing maps were used to address a thorough analysis, proving to be a powerful means to straightforwardly achieve a comprehensive pattern of wind farm layout optimization. In general, the two optimization functions basically match, while for higher wind potential sites, increasing capacity factor did not necessarily result in decreasing levelized cost of energy. The latter may be minimised by reducing the total number of turbines or the overall wind farm capacity, as well as maximising rotor diameters or minimising rated wind speeds; increasing rated power or hub height is only beneficial for mid-potential sites. The mere maximisation of wind farm energy production is a misleading target, as corresponding to mid-to-high values of levelized cost of energy. In contrast to previous studies, the use of turbines with different rated power, rotor diameter or hub height should be avoided. [ABSTRACT FROM AUTHOR]

One of the current major challenges in wind energy is to maximize energy production of wind farms. One approach in this effort is through control of wind turbine wake interactions, since undesirable wake interactions can introduce additional mechanical stresses on turbines, leading to early failures and reduce overall energy production of wind farms. To develop control strategies that can minimize wake interactions, it is essential to simulate wake behaviors accurately and quickly. In this work, a fast and accurate turbine wake model capable of modeling turbine wakes under yaw is presented. This model builds upon the work of existing wake models and is capable of producing results comparable to that of conventional full CFD simulations using a fraction of the computational cost. The accuracy and speed of the proposed model allows for the development of real-time turbine control strategies to maximize power output. The results of the proposed model are validated with previous numerical and experimental data. • A fast and accurate wake model for simulating wakes of yawed turbines is proposed. • The accuracy of the model has been validated with full CFD simulations and experimental data. • The model solves at least 2 orders magnitude faster than full CFD simulations. [ABSTRACT FROM AUTHOR]

• A new wake model is proposed to predict the turbine wake in yawed conditions. • The wake model can be applied for both wind turbines and hydrokinetic turbines. • The skew distribution is employed to express the spanwise velocity asymmetry. • The wake model is validated by the wind tunnel and open channel flow. • measurements. Predicting the spatial evolution of horizontal-axis turbine wakes is a key factor to enhance the performance of wind and hydrokinetic power plants. The yaw angle misalignment is not only important to account for the uncertainty of the wind direction, but also a control strategy to improve the energy production averaged over the turbine array. In this paper, a new wake model, based on the skew-normal distribution and conservation of mass and momentum, is proposed to predict the turbine wake velocity distribution for given yaw angles. The new model is experimentally validated through wake measurements of yawed miniature wind and hydrokinetic turbines, in wind tunnel and open channel flows, respectively. Predictive capabilities extend from the spatial distribution of the maximum velocity deficit at hub height, to the spanwise asymmetry of the velocity distribution about the wake center. [ABSTRACT FROM AUTHOR]

Previous studies on wake of horizontal-axis wind turbines (HAWTs) mainly focus on the spatial distribution but ignore the time-varying characteristics of the wake profile which highly affect the operation strategy of the downstream HAWTs to ensure the high-efficiency and low-fatigue load. This paper proposed a mathematical method for studying the spatial-temporal inhomogeneity of wake profiles. Considering the anisotropy of wake expansion, the turbulence intensity was modified to avoid repeated experimental calculation of empirical parameters such as wake expansion coefficient. In addition, the super-Gaussian function was used to modify the near wake model, and the modified near wake model was combined with four typical far wake models to obtain four temporal wake models that can express the time-varying characteristics of the wake. The accuracy of the improved four temporal wake models were verified by wind tunnel test, and the relative errors were analyzed. Results show that the prediction errors of the modified two-dimensional temporal wake model are basically within 4%, which is smaller than the other three wake models. The method presented in this paper can effectively describe the spatial distribution and time-varying characteristics of wake expansion, and can provide a reference for optimizing the control strategy of HAWTs. • The spatial-temporal inhomogeneity characteristic of wake is discussed. • Four temporal wake models are proposed to express spatial-temporal profile of the wake. • These four temporal wake models are based on four typical far wake models. • The temporal wake models are verified using measured data of wind tunnel test. • The temporal wake models have good accuracy. [ABSTRACT FROM AUTHOR]

The benchmarking optimization of a wind farm layout was applied to the offshore wind farm on Jeju Island, Korea. This work focused on optimizing not only the annual energy production (AEP), but also the electrical grid cost and foundation cost. The benchmark wind farm will be installed on the west coast of Jeju. Ten turbines will be constructed in a simple straight line. To predict the aerodynamic loadings of the wind turbines, the Larsen model was used in combination with the unsteady vortex lattice method. The cost models developed by Larsen were used. In order to optimize the wind farm layout, the total optimization framework developed by the Technical University of Denmark, TOPFARM, was used. The results showed that the objective function values, which included the AEP and cost models, were increased, and an irregular layout was produced compared to the baseline layout. [ABSTRACT FROM AUTHOR]

In this work, large eddy simulation data is analysed to investigate a new stochastic modeling approach for the wake of a wind turbine. The data is generated by the large eddy simulation (LES) model PALM combined with an actuator disk with rotation representing the turbine. After applying a proper orthogonal decomposition (POD), three different stochastic models for the weighting coefficients of the POD modes are deduced resulting in three different wake models. Their performance is investigated mainly on the basis of aeroelastic simulations of a wind turbine in the wake. Three different load cases and their statistical characteristics are compared for the original LES, truncated PODs and the stochastic wake models including different numbers of POD modes. It is shown that approximately six POD modes are enough to capture the load dynamics on large temporal scales. Modeling the weighting coefficients as independent stochastic processes leads to similar load characteristics as in the case of the truncated POD. To complete this simplified wake description, we show evidence that the small-scale dynamics can be captured by adding to our model a homogeneous turbulent field. In this way, we present a procedure to derive stochastic wake models from costly computational fluid dynamics (CFD) calculations or elaborated experimental investigations. These numerically efficient models provide the added value of possible long-term studies. Depending on the aspects of interest, different minimalized models may be obtained. [ABSTRACT FROM AUTHOR]

The improved analytical wake model named as 2D_k Jensen model (which was proposed to overcome some shortcomes in the classical Jensen wake model) is applied and validated in this work for wind turbine multi-wake predictions. Different from the original Jensen model, this newly developed 2D_k Jensen model uses a cosine shape instead of the top-hat shape for the velocity deficit in the wake, and the wake decay rate as a variable that is related to the ambient turbulence as well as the rotor generated turbulence. Coupled with four different multi-wake combination models, the 2D_k Jensen model is assessed through (1) simulating two wakes interaction under full wake and partial wake conditions and (2) predicting the power production in the Horns Rev wind farm for different wake sectors around two different wind directions. Through comparisons with field measurements, results from Large Eddy Simulations (LES) as well as results from other commercial codes, it is found that the predictions obtained with the 2D_k Jensen model exhibit good to excellent agreements with experimental and LES data. [ABSTRACT FROM AUTHOR]

With the increased installation of wind farm in complex terrain, the wake expansion of large-scale wind turbine under real conditions downstream a hill is an elusive target and one of the main challenges in the optimization of the layout, operation, and control of wind farm. However, previous studies based on CFD simulations and typical commercial software have controversial descriptions about the wake expansion downstream a hill (Wei et al., 2021) [1]. Research of this paper focus on the velocity deficits detections in real complex wind farm conditions though LiDAR-based observation with an analytical wake model been proposed and validated which can describe the velocity distributions down of a turbine on the top of a real hill. The previous three-dimensional Jensen-Gaussian (3DJG) wake model of our team is improved with the Coanda effect (wall attachment effect) been considered. The altitude sink, Δ h of wind turbine is substituted into the new wake model. In addition, the wind shear effect is also considered, and the wake expansion rate k is modified in the new model. Two types of Doppler LiDARs, WindMast WP350 and Wind3D 6000, were used to measure the inflow wind profile and the wake expansion in the three-dimensional (3D) space downstream two wind turbines on the top of a hill in one complex wind farm in northern Hebei Province, China. The accuracy of the improved 3DJG wake model is compared with the field measured data and other typical wake models. Results show that the improved 3DJG wake model performance better in sank wake descriptions in both horizontal and vertical plane for wake in wind turbine on the top of a hill. The proposed model and observed wake expansion data in real conditions in this paper can provide theoretical and data support for wind farm micro-siting, the downstream turbine's control strategy adjustment as well as wind power prediction of for wind turbine on the top of a hill. • An improved 3DJG wake model for turbines on the top of a hill is proposed. • Conada effects is considered in the derivation of the model. • Wake and terrain superposition method of 'D-line' succeeds in field-measured. • The actual wind farm data measured by LiDAR are used to verify wake model. • Performance of 3DJG is better on wake prediction considering the wake sinking. [ABSTRACT FROM AUTHOR]

To further understand the spatiotemporal inhomogeneity characteristics of wake profile caused by the inflow change of upstream wind turbine and reduce the influence of wake expansion on the power output and fatigue load of downstream wind turbine, a three-dimensional full wake model (3DJGF model) and a three-dimensional temporal wake model (3DJGF-T model) are proposed and verified in this paper. Assuming that the downstream wake distribution of wind turbine is double-Gaussian distribution, a new 3DJGF model is derived based on the law of conservation of mass and considering the wind shear effect. Based on the 3DJGF model, the time variable is introduced to calculate the delay time, and the 3DJGF-T model of the whole flow field is obtained. The accuracy of the proposed 3DJGF model and 3DJGF-T model is verified by wind field measurement and wind tunnel test, and the relative error of the 3DJGF-T model is analyzed: under the time-varying characteristics of different incoming wind speeds, the error of the newly proposed 3DJGF-T model is basically within 4%. The results show that the 3DJGF-T model can effectively describe the spatiotemporal inhomogeneity distribution and expansion characteristics of wake, which can provide a reference for the dynamic load analysis of downstream wind turbine considering the dynamic adjustment process of wind turbine control strategy, further improve the wake model and optimize the control strategy of wind turbine. • The spatiotemporal inhomogeneity of wake profile is proposed. • The delay time of the wake expansion is defined and considered. • 3D full wake model and 3D temporal wake model are proposed. • Both field measurement in wind farm and wind tunnel test are conducted. • The accuracy of 3D full wake model and 3D temporal wake model is verified. [ABSTRACT FROM AUTHOR]

The grouping of turbines in large farms introduces that a wind turbine operating in the wake of another turbine and has a reduced power production because of a lower wind speed after rotor. The flow field in the wake behind the first row turbines is characterized by a significant deficit in wind velocity and increased levels of turbulence intensity. Consequently, the downstream turbines in a wind farm cannot extract as much power from the wind as the first row turbines. Therefore modeling wake effect is necessary because it has a great influence on the actual energy output of a wind farm. In this study, the adaptive neuro-fuzzy inference system (ANFIS) is designed and adapted to estimate wake effect in a wind farm according to wind turbine positions in wind farm, distances between turbines in the wind farm and rotor radius as well. [ABSTRACT FROM AUTHOR]

Dissection of the power output in a row of working turbines and the reliance on wind course in respect to the column heading is examined. The point is to portray the extent of the wake impacts and give a sign of the indication of wind bearing. The target is to delineate whether the uniting of wakes inside extensive wind homesteads can be depicted by basic direct models or whether the consideration of the two-route collaboration between the wind turbines and the limit layer is a fundamental essential for precise models of wakes to be utilized within future wind farm plan. Soft computing methodologies may be utilized as substitute for analytical approach since they provides some benefits such as no need to information of internal system parameters, compact solution for multi-variable problems. This investigation dealt with application of ANFIS (adaptive neuro-fuzzy inference system) for predicting the wake power and wind speed deficit. To provide statistical analysis, RMSE (root mean square error), coefficient of determination ( R 2 ) and Pearson coefficient ( r ) were utilized. The study results suggested that ANFIS would be an efficient soft computing methodology to offer precise predictions of wake wind speed deficit and power deficit ratio in wind farms. According to the achieved results, the best prediction was observed for free wind speed of 8 m/s. The RMSE, R 2 and r were computed as 0.0763, 0.9893 and 0.9946 for ANFIS prediction of wake wind speed deficit and as 0.0128, 0.9967 and 0.9984 for ANFIS prediction of power deficit ratio. [ABSTRACT FROM AUTHOR]

We apply a modified proper orthogonal decomposition (POD) to large eddy simulation data of a wind turbine wake in a turbulent atmospheric boundary layer. The turbine is modeled as an actuator disk. Our analysis mainly focuses on the pragmatic identification of spatial modes, which yields a low order description of the wake flow. This reduction to a few degrees of freedom is a crucial first step for the development of simplified dynamic wake models based on modal decompositions. It is shown that only a few modes are necessary to capture the basic dynamical aspects of quantities that are relevant to a turbine in the wake flow. Furthermore, we show that the importance of the individual modes depends on the relevant quantity chosen. Therefore, the optimal choice of modes for a possible model could in principle depend on the application of interest. We additionally present a possible interpretation of the extracted modes by relating them to the specific properties of the wake. For example, the first mode is related to the horizontal large-scale movement. [ABSTRACT FROM AUTHOR]

Production losses and increased turbine loadings are observed in wind farms, when wind turbines interact with each other. If a wind turbine is located in the wake of another one, its incoming flow is disturbed, slowed down, and its potential wind power is decreased. It is therefore necessary to study the wind turbine wakes and their interactions. It is important to consider these wake effects in the design of a wind farm in order to maximize the energy output and lifetime of the machines. The exact modeling of the wind speed distribution within a wind park is a fairly complicated task and many of the necessary parameters are not routinely available. A large number of studies have been established concerning the calculation of wake effect. Even though a number of mathematical functions have been proposed, there are still disadvantages of the models like very demanding in terms of calculation time. Artificial neural networks (ANN) can be used as alternative to analytical approach as ANN offers advantages such as no required knowledge of internal system parameters, compact solution for multi-variable problems and fast calculation. In this investigation adaptive neuro-fuzzy inference system (ANFIS), which is a specific type of the ANN family, was used to predict the wake power deficit. Neural network in ANFIS adjusts parameters of membership function in the fuzzy logic of the fuzzy inference system (FIS). This intelligent algorithm is implemented using Matlab/Simulink and the performances are investigated. The simulation results presented in this paper show the effectiveness of the developed method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Using the random forest (RF) algorithm, this study presented a key parameter to characterize the mean wake of H-rotor VAWTs while modelling the wake. First, the RF algorithm was used to establish the regression relationship between the average wake velocity distribution and the rotor features. Next, the feature crosses method was combined with the RF algorithm to analyze the interaction and importance of the inputs. It was found that the normalized importance of a synthetic feature in wake modelling occupied a considerable significance, reaching 0.884 out of 1. The RF wake model with this parameter as the only input feature could successfully reconstruct the wake. It was found that this feature may reflect the ability of incident wind passing through the operating rotor and played a decisive role in the wake velocity distribution, including initial velocity deficit and wake recovery rate. The universality of this parameter was proved through cases analysis of wind turbines under different sizes and operating conditions. The study of the wake field is important for the modelling of the H-rotor VAWT wake field, and hence affects the optimal configuration of the wind farm. • Random forest is used to model the mean wake of vertical axis wind turbines. • A hybrid method is used to analyze the importance of rotor features in wake flow. • A synthetic parameter is found to have a decisive effect on turbine wake. • A case study is provided to illustrate the universality of such key parameter. [ABSTRACT FROM AUTHOR]

Reducing wake losses and improving the overall power output of wind farms have become a research focus in attempts to optimize wind farm power generation. A cooperative multiagent optimization method (CMAOM) for wind farm power delivery maximization has been proposed in this paper. In the CMAOM, a wind farm wake distribution calculation model, based on the Jensen wake model, was constructed, and each turbine was then assigned as an agent; the CMAOM was used to reduce wake losses and improve the overall wind farm power output. The agent, multiagent objective function and grid environment were defined in this study using wind turbine characteristics, and the CMAOM, including the neighborhood competition operator, mutation operator, and self-learning operator, were calibrated using wind turbine aerodynamic correlation characteristics. The Danish Horns Rev wind farm was selected as a case study, and the CMAOM and particle swarm optimization (PSO) algorithm were used to conduct analyses there. The results showed that the CMAOM proposed in this paper was more effective than the PSO algorithm and that the wind farm overall power output was increased by 7.51% for a 270° incoming wind direction and an incoming wind speed of 8.5 m/s. • A cooperative multiagent optimization method was proposed for power maximization. • Agent, objective function and grid environment were defined. • Competition operator, mutation operator, and self-learning operator, were calibrated. • A wind farm wake calculation model, based on the Jensen wake model, was constructed. [ABSTRACT FROM AUTHOR]

Abstract: In the design of a wind farm, the placement of turbines is an important factor that affects the efficiency and profit, but automatic placement of turbines is still a challenging problem. This study reveals the “submodular” property of the wind turbine positioning problem based on Jensen wake model. Based on this property, a “lazy greedy” algorithm is used to optimize the placement. This method can obtain solutions with theoretical guarantee of quality. It can also estimate the lower bound of the optimal value of the objective function. This method is tested on three types of wind scenarios. Compared to previous research, this algorithm takes much less time, and always gains a better solution. To enlarge the application scope, the wake model is extended to the large scale complex terrain in this study. The present algorithm and some other algorithms are tested in the simulation of the complex terrain. The experimental results demonstrate the present method’s superior performance. [Copyright &y& Elsevier]

District of Namaacha in Maputo Province of Mozambique presents a high wind potential, with an average wind speed of around 7.5 m/s and huge open fields that are favourable to the installation of wind farms. However, in order to make better use of the wind potential, it is necessary to evaluate the operating conditions of the turbines and guide the independent power producers (IPPs) on how to efficiently use wind power. The investigation of the wind farm operating conditions is justified by the fact that the implementation of wind power systems is quite expensive, and therefore, it is imperative to find alternatives to reduce power losses and improve energy production. Taking into account the power needs in Mozambique, this project applied hybrid optimisation of multiple energy resources (HOMER) to size the capacity of the wind farm and the number of turbines that guarantee an adequate supply of power. Moreover, considering the topographic conditions of the site and the operational parameters of the turbines, the system advisor model (SAM) was applied to evaluate the performance of the Vestas V82-1.65 horizontal axis turbines and the system's power output as a result of the wake effect. For any wind farm, it is evident that wind turbines' wake effects significantly reduce the performance of wind farms. The paper seeks to design and examine the proper layout for practical placements of wind generators. Firstly, a survey on the Namaacha's electricity demand was carried out in order to obtain the district's daily load profile required to size the wind farm's capacity. Secondly, with the previous knowledge that the operation of wind farms is affected by wake losses, different wake effect models applied by SAM were examined and the Eddy–Viscosity model was selected to perform the analysis. Three distinct layouts result from SAM optimisation, and the best one is recommended for wind turbines installation for maximising wind to energy generation. Although it is understood that the wake effect occurs on any wind farm, it is observed that wake losses can be minimised through the proper design of the wind generators' placement layout. Therefore, any wind farm project should, from its layout, examine the optimal wind farm arrangement, which will depend on the wind speed, wind direction, turbine hub height, and other topographical characteristics of the area. In that context, considering the topographic and climate features of Mozambique, the study brings novelty in the way wind farms should be placed in the district and wake losses minimised. The study is based on a real assumption that the project can be implemented in the district, and thus, considering the wind farm's capacity, the district's energy needs could be met. The optimal transversal and longitudinal distances between turbines recommended are 8Do and 10Do, respectively, arranged according to layout 1, with wake losses of about 1.7%, land utilisation of about 6.46 Km2, and power output estimated at 71.844 GWh per year. [ABSTRACT FROM AUTHOR]

The arrangement of wind turbines in clusters presents two noteworthy issues: (1) diminished power generation brought about by wake wind speed deficits and (2) expanded unique loads on the blades caused by higher turbulence levels. The drop in power generation of downstream wind turbines can reach up to 46% of the upstream wind turbines in entirely created wake conditions. Thus, wind farm layout optimisation is an essential design criterion of a wind farm. Focusing on optimising the micro-position of the turbines within the wind farm to minimise the wake effects can maximise the expected power output. There are several crucial aspects in designing a wind farm layout, and most of the previous studies have been focusing on maximising the overall energy yield and minimise the initial investment. Several optimisation methods based on heuristic techniques have successfully found optimal solution to these challenges. However, far too little attention has been paid on comparing these methodologies to each other. Therefore, this work aims to survey the existing approaches used to-date in solving the wind turbine positioning within the wind farm. This work firstly briefs the historical background of the conventional development of a wind farm. Then, key features and basic components of a wind farm modelling are discussed and categorised into the following: wind farm siting, layout design, wake models and objective functions. Several research gaps and suggestion of future research areas in this field are highlighted which shall enable to guide researchers to explore further in the upcoming studies. • Review the recent approaches in wind turbine arrangement optimisation. • Highlight major challenges on wind turbine micrositing optimisation. • Artificial intelligence integration as promising optimisation strategies. • Focus review on three wind scenarios as performance benchmarking measurement. [ABSTRACT FROM AUTHOR]

An appropriate yaw angle misalignment of the wind turbines in a wind farm has been found to improve the average energy production of the turbine array. Predicting the spatial evolution of the yawed turbine wakes is a key factor in optimizing the yaw angles. In this study, a new three-dimensional yawed wake model is proposed to estimate the non-centrosymmetric cross-sectional shape of the yawed wake velocity distribution, and the model is experimentally validated. Then, a yaw angle optimization strategy that optimizes the wind farm yaw angle distribution and maximizes the power output using the proposed wake model is described. The covariance matrix adaptation evolution strategy is employed as an intelligent algorithm to implement the optimization. The results indicate that yaw angle optimization improves the power of an offshore wind farm by up to 7%, and the optimization yields better results for a small streamwise spacing between turbines than for a large streamwise spacing. Wind farm yaw angle optimization shows great promise for the development of smart wind farms because it has the potential to enable real-time optimization of the yaw angles in response to changes in the incoming wind direction. • A new 3-D wake model is proposed to predict the yawed turbine wake velocity. • The wake model can predict the curled cross-section shape of the wake velocity. • The yaw angle misalignment is adopted to improve the wind farm power production. • An optimization strategy is proposed to adjust the wind farm yaw angles. • The optimization strategy is based on the wake model and an intelligent algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a review on wind farm (WF) layout optimization with multiple types of wind turbines (WTs). Compared with uniform WF layout optimization, the three key research points of this topic are WT type selection, wake modelling and optimization algorithm design. Firstly, a series of WT power curves are demonstrated with a WT type selection method to choose the most suitable ones. When calculating the WF power output, a one-dimensional (1D) and a two-dimensional (2D) wake models are briefly introduced and a newly-developed three-dimensional (3D) wake model is described in detail for the application in the nonuniform WF layout optimization. The objective functions, constraints and optimization algorithms used in the literature are reviewed and the optimization framework is built. Case studies are carried out on two real-world WFs. One is the Greater Gabbard offshore WF, on a flat area with an irregular shape and the other is Huade II onshore WF, on a mountainous area with a square shape. The aim of this paper is to shed light on the most significant aspects in the nonuniform WF optimization design based on the summary of the latest works. In addition, future works have been pointed out in the conclusion. • Optimization frameworks of nonuniform wind farm design are reviewed. • A three-dimensional wake model is used in the wind farm nonuniform optimization. • Two real wind farms are optimized with mixed-installation of wind turbines. • Wind farms are suggested to be designed with multiple types of wind turbines. [ABSTRACT FROM AUTHOR]

• A parallel framework for wind farm optimization is developed using six wake models. • Framework accounts for terrain elevation and wake-terrain interaction. • Four turbine specific cost models are developed. • Wind farm area model is developed as the area of convex hull. • Optimization of a realistic wind farm is performed for maximum power generation. A new framework for Wind Farm Layout Optimization (WindFLO) is developed to accelerate the design of wind farms. The framework provides a large set of analytical wake models and wake superposition schemes. It is able to take into account terrain elevation and the ambient wind velocity profile. The schemes in the WindFLO model were validated against experimental data from a wind tunnel to within 1% relative error. A turbine rotor diameter and height dependent cost model was also developed using data from 250 different wind turbines. A land usage model was also developed using the convex hull approach. The framework was used to optimize a wind farm layout for maximum annual energy production using real wind farm terrain and conditions. The nonlinear optimization problem was solved using a robust Single-Objective Hybrid Optimizer. The wind farm layout and wind turbine (rotor diameter and tower height) were optimized and resulted in increased annual energy production, reduced cost and reduced land usage. The WindFLO framework is made publicly available to accelerate and advance the techniques for wind farm optimization. 1 1 WindFLO can be downloaded from https://github.com/sohailrreddy/WindFLO. [ABSTRACT FROM AUTHOR]

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

• The machine learning framework achieves favorable accuracy and efficiency in the wake prediction. • ADM-R/RANS coupling model can efficiently produce big wake datasets for machine learning model. • For an aligned turbine row, power drops at the second turbine and gradually stabilizes afterwards. • Turbulence model plays an important role in accurate power prediction of wind farm. In the paper, a novel framework that employs the machine learning and CFD (computational fluid dynamics) simulation to develop new wake velocity and turbulence models with high accuracy and good efficiency is proposed to improve the turbine wake predictions. An ANN (artificial neural network) model based on the back-propagation (BP) algorithm is designed to build the underlying spatial relationship between the inflow conditions and the three-dimensional wake flows. To save the computational cost, a reduced-order turbine model ADM-R (actuator disk model with rotation), is incorporated into RANS (Reynolds-averaged Navier-Stokes equations) simulations coupled with a modified k - ε turbulence model to provide big datasets of wake flow for training, testing, and validation of the ANN model. The numerical framework of RANS/ADM-R simulations is validated by a standalone Vestas V80 2 MW wind turbine and NTNU wind tunnel test of double aligned turbines. In the ANN-based wake model, the inflow wind speed and turbulence intensity at hub height are selected as input variables, while the spatial velocity deficit and added turbulence kinetic energy (TKE) in wake field are taken as output variables. The ANN-based wake model is first deployed to a standalone turbine, and then the spatial wake characteristics and power generation of an aligned 8-turbine row as representation of Horns Rev wind farm are also validated against Large Eddy Simulations (LES) and field measurement. The results of ANN-based wake model show good agreement with the numerical simulations and measurement data, indicating that the ANN is capable of establishing the complex spatial relationship between inflow conditions and the wake flows. The machine learning techniques can remarkably improve the accuracy and efficiency of wake predictions. [ABSTRACT FROM AUTHOR]

This paper presents a method for reconstructing the wake wind field of a wind turbine based on planar light detection and ranging (LiDAR) scans crossing the wake transversally in the vertical and horizontal directions. Volumetric measurements enable the study of wake characteristics in these two directions. Due to a lack of highly resolved wind speed measurements as reference data, we evaluate the reconstruction in a synthetic environment and determine the reconstruction errors. The wake flow of a multi-megawatt wind turbine is calculated within a 10-min large-eddy simulation (LES) for high-thrust loading conditions. We apply a numerical LiDAR simulator to this wake wind field to achieve realistic one-dimensional velocity data. We perform a nacelle-based set-up with combined plan position indicator and range height indicator scans with eight scanning velocities each. We temporally up-sample the synthetic LiDAR data with a weighted combination of forward- and backward-oriented space–time conversion to retrospectively extract high-resolution wake characteristic dynamics. These dynamics are used to create a dynamic volumetric wake deficit. Finally, we reconstruct the dynamic wake wind field in three spatial dimensions by superposing an ambient wind field with the dynamic volumetric wake deficit. These results demonstrate the feasibility of wake field reconstruction using long-range LiDAR measurements. [ABSTRACT FROM AUTHOR]

In the design of wind energy farms, the loss of power should be seriously considered for the second wind turbine located inside the wake region of the first one. The rotation of the first wind-front rotor generates a high-vorticity wake with turbulence, and a suitable model is required in computational fluid dynamics (CFD) to predict the deficit of energy of the second turbine for the given configuration. A simplified numerical model based on the classical momentum theory is proposed in this study for multiple wind turbines, which is proposed with a couple of tuning parameters applied to Reynolds-averaged Navier-Stokes (RANS) analysis, resulting in a remarkable reduction of computational load compared with advanced methods, such as large eddy simulation (LES) where two parameters reflect on axial and rotational wake motion, simply tuned with the wind-tunnel test and its corresponding LES result. As a lumped parameter for the figure of merit, we regard the normalized efficiency on the kinetic power output of computational domain, which should be directed to maximize for the optimization of wind farms. The parameter surface is plotted in a dimensionless form versus intervals between turbines, and a simple correlation is obtained for a given hub height of 70% diameter and a fixed rotational speed tuned from the experimental data in a wide range. [ABSTRACT FROM AUTHOR]