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Tidal and wind energy projects almost exclusively adopt horizontal axis turbines (HATs) due to their maturity. In contrast, vertical axis turbines (VATs) have received limited consideration for large-scale deployment, partly because of their earlier technology readiness level. This paper analyses the power density of turbine arrays comprising aligned and staggered configurations with decreasing turbine spacing of HATs and VATs with height-to-diameter aspect ratios from one to four at three real tidal sites. The VAT rotor has vertical blades extending over a portion of the water depth on a circular frame. Equivalent diameter is defined as $$D_0$$ D 0 = $$\sqrt{A}$$ A based on the projected rotor area for both VATs and HATs. The three-dimensional velocity field is computed using analytical wake models that capture cumulative wake effects. At highly energetic sites, e.g. Ramsey Sound (UK), HATs are the most suitable technology attaining power densities beyond 100 W m$$^{-2}$$ - 2 , whilst VATs provide higher power densities than HATs at those sites with low-to-medium velocities, e.g. Ría de Vigo (Spain) and Kobe Strait (Japan). At the latter site, VATs provided up to 35% larger energy yield than HATs over a 14-day tidal cycle. Our results show that VATs with height-to-diameter aspect ratios larger than three notably reduce wake effects even when deployed with a normalised turbine spacing of two $$D_0$$ D 0 , reaching an average power density capacity of 40.7 W m$$^{-2}$$ - 2 compared to HATs that attain 49.3 W m$$^{-2}$$ - 2 . This study outlines the higher efficiency of tidal stream energy compared to other renewable energy resources, e.g. offshore wind farms, reaching power densities at least one order of magnitude larger, and that VATs counterbalance their smaller individual performance with improved array synergy as wake effects are limited.

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.

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 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.

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 (Technical Report Risø-M; No. 2411, 1983), 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.

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.

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%.

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.

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.

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.

High-lift devices are commonly modelled using potential flow methods at the conceptual design stage. Often, these analyses require the use of prescribed wake shapes in order to avoid numerical stability issues. The wake type used, however, has an impact on the absolute aerodynamic load predictions, which is why, in general, these methods are used to assess performance changes due to configuration variations. Therefore, a study was completed that compared the predicted aerodynamic performance changes of such variations of high-lift configurations using different wake types. Lift and induced drag results are compared with the results that were obtained using relaxed wakes and various prescribed wake shapes. Specific attention is given to predictions of performance changes due to changes in geometry. It was found that models with wakes that are prescribed below the freestream direction yield the best results when investigating performance changes due to flap deflections and flap-span changes. The effect of flap-gap sizes is best evaluated using a fully-relaxed model. The numerically most stable approach of wakes that are prescribed leaving the trailing edge upwards seems to be least reliable in predicting performance changes. Keywords: potential flow; wake model; high-lift

[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.

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.

Presentation at Wakebench3 meeting of the final results fromthe Offshore Wind Accelerator (OWA) Wake Modelling Challenge on the prediction of array efficiency at 5 offshore wind farms.Evaluation scripts and additional results available at the GitHuband simulation data repositories.&nbsp

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.

We describe a generalization of the coupled wake boundary layer (CWBL) model for wind farms that can be used to evaluate the performance of wind farms under arbitrary wind inflow directions, whereas the original CWBL model (Stevens et al., J. Renewable and Sustainable Energy 7, 023115 (2015)) focused on aligned or staggered wind farms. The generalized CWBL approach combines an analytical Jensen wake model with a ‘top-down’ boundary layer model coupled through an iterative determination of the wake expansion coefficient and an effective wake coverage area for which the velocity at hub-height obtained using both models converges in the ‘deep-array’ portion (fully developed region) of the wind farm. The approach accounts for the effect of the wind direction by enforcing the coupling for each wind direction. Here, we present detailed comparisons of model predictions with large eddy simulation results and field measurements for the Horns Rev and Nysted wind farms operating over a wide range of wind inflow directions. Our results demonstrate that two-way coupling between the Jensen wake model, and a ‘top-down’ model enables the generalized CWBL model to predict the ‘deep-array’ performance of a wind farm better than the Jensen wake model alone. The results also show that the new generalization allows us to study a much larger class of wind farms than the original CWBL model, which increases the utility of the approach for wind farm designers.

A case study is presented, in which the authors compare several models against yet unpublished data from a large wind farm. The wind farm is in mostly flat and open farmland, with some settlements. Ten-minute SCADA data collected over three years has been filtered, cleaned, and processed, to be represented as flow cases. For each wind direction and wind speed the resulting observed power average, the standard deviation and min./max., and the number of underlying data points are presented. A range of different commercial models is used. These are implemented in the packages WindFarmer, WindPro, OpenWind, WAsP, and WakeBlaster. This case study shows that, if operated by an experienced engineer, the commercial models agree well with each other and with the corresponding data, overall. In the model verification, the differences between the models are highlighted and explored what differentiates them from one another. In the validation, the model results are compared for critical scenarios with the production data.

This study builds on recent analysis (Mifsud, et al., 2018) in which uncertainties in predicting long term wind speeds using different Measure Correlate Predict methodologies were compared. These included the Simple Linear Regression, Artificial Neural Networks, Decision Trees and Support Vector Regression. The current work focuses on the uncertainties resulting from the different MCP methods to predict the power and energy yield from a wind farm. The analysis is based on a case study that utilizes short-term data acquired from a LiDAR system deployed in a coastal site in the northern part of the island of Malta and long-term measurements from the island’s airport. LiDAR measurements at various heights, ranging from 10 to 200m are considered. A hypothetical offshore wind farm layout consisting of 50 turbines rated at 5-MW each is assumed. The wind farm faces the north-west direction, which is the prevailing wind direction for the island archipelago. The turbines are placed in rows of ten wind turbines each, with a cross-wind inter-turbine spacing set at five rotor diameters and a downwind spacing of eight rotor diameters between successive rows. The predicted power output from the various MCP methodologies is compared to the actual power output obtained directly from the input of LiDAR data to establish which MCP methodology best predicts the output power. The different MCP methods, that were implemented in Matlab®, are used to predict the absolute wind speed, while wind direction is predicted using the same regression methodology but, using the vector components of the wind. The wind direction is then calculated from the predicted vector components. The power output from the wind farm is predicted by inputting wind speed and direction into WindPro®, using a Risø/EMD (N.Ø. Jensen) wake model and a standard 5-MW wind turbine. The wake model introduces a more realistic value of the power output for the wind farm, as it includes the shadowing effects on the wind turbines and the wind direction. The power is predicted for a range of wind turbines (from 10 to 50, in steps of 10) and at hub heights of 30, 80, 100, 150 and 200m. The predicted power is compared to the power output generated from the actual wind and direction data by using the Mean Squared Error (MSE) and the Mean Absolute Error (MAE). This methodology will establish which combination of MCP methodology and wind farm configuration will have the least prediction error. &nbsp

Presentation at the Wind EnergyScience Conference in Cork, Ireland. The "Wakebench" framework for the evaluation of wind farm flow models is presented. This IEA-Wind Task gathers an international forum of researchers to define best practices for model evaluation through model intercomparison benchmarks. The modeling scope spans multi-scale models dealing with the atmospheric boundary layer, to predict wind conditions for site suitability assessment and numerical site calibration, as well as wind farm wake effects for the assessment of array efficiency and loads in connection to wind farm design. An overview of current activities is presented.&nbsp

In order to study the effect of vertical staggering in large wind farms, large eddy simulations (LES) of large wind farms with a regular turbine layout aligned with the given wind direction were conducted. In the simulations, we varied the hub heights of consecutive downstream rows to create vertically staggered wind farms. We analysed the effect of streamwise and spanwise turbine spacing, the wind farm layout, the turbine rotor diameter, and hub height difference between consecutive downstream turbine rows on the average power output. We find that vertical staggering significantly increases the power production in the entrance region of large wind farms and is more effective when the streamwise turbine spacing and turbine diameter are smaller. Surprisingly, vertical staggering does not significantly improve the power production in the fully developed regime of the wind farm. The reason is that the downward vertical kinetic energy flux, which brings high velocity fluid from above the wind farm towards the hub height plane, does not increase due to vertical staggering. Thus, the shorter wind turbines are effectively sheltered from the atmospheric flow above the wind farm that supplies the energy, which limits the benefit of vertical staggering. In some cases, a vertically staggered wind farm even produced less power than the corresponding non vertically staggered reference wind farm. In such cases, the production of shorter turbines is significantly negatively impacted while the production of the taller turbine is only increased marginally.

Wind turbine wake physics is by nature unsteady and highly sensitive to the local wind characteristics. While modern Computational Fluid Dynamic methods (eg: Large Eddy Simulation) allow to accurately capture the flow at the wind farm scale, they still come at a prohibitive computational cost, preventing their use for online control or Machine Learning schemes. This work aims at developing a computationally affordable yet robust wake meandering model. The latter is based on the commonly used passive tracer hypothesis which states that the wake is advected by the downstream background flow. Providing a robust wake characterization requires the knowledge of the upstream wind conditions, i.e. velocity and turbulence intensity. Following previous work of Bottasso et al.(2017), an Extended Kalman Filter was developed to estimate the wind profile upstream the wind turbine based on the blade loads. The flow characteristics as estimated by the filter are then fed to the wake model as input parameters. The present study assesses the performances of both the wind estimator and the wake model on the NREL 5MW wind turbine thanks to data recovered from high fidelity numerical simulations. An Immersed Lifting Line-enabled Vortex Particle-Mesh method is used for simulations at the scale of a single wind turbine, while windfarm simulations are performed by a fourth-order finite difference Large Eddy Simulation code.

Wind turbine wake physics is by nature unsteady and highly sensitive to the local wind characteristics. While Large Eddy Simulations (LES) allow to accurately capture the flow at the wind farm scale for a wide range of atmospheric conditions, they still come at a prohibitive computational cost when it comes to online control. Based on the Dynamic Wake Meandering model (Larsen, 2007), the presented model couples a meandering model and a wake speed deficit model in order to estimate the velocity field downstream the wind turbine. Focus is laid on limiting the number of input parameters by building on recent advances in flow sensing to feed the wake model with estimated inflow conditions. The remaining parameters are fine-tuned through online data assimilation techniques, thus adapting to inflow conditions. The performances of the resulting wake model are assessed using data recovered from high fidelity LES simulations.

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.

Wake models play a fundamental role in finding optimized solutions in wind farm control. In fact, they allow assessing how wakes develop and interact with each other with the agility required for real-time applications. In this paper, a Gaussian Wake Model (GWM) is implemented in the OpenFAST framework in a way such that its fidelity is increased with respect to previously implemented models, while enhancing its compatibility with control purposes. The OpenFAST tool is coupled with Floris, NREL’s software based on the GWM, in order to simulate the wake effect on downstream machines (in the case where the downstream rotor is fully covered by the wake, only partially covered by the wake, of the wake is generated by the interaction of more than one turbine), while the rotor aerodynamics is calculated using the BEMT on the actual rotor flow field. We intend this work as a starting point for developing and testing open/closed-loop control logics that will work in real wind farms. To show the suitability of the implementation, the entire model is then compared to Floris.

With the increasing size of wind farm, the impact of the wake effect on wind farm energy yields become more and more evident. The arrangement of the wind turbines’ (WT) locations will influence the capital investment and contribute to the wake losses which incur the reduction of energy production. As a consequence, the optimized placement of the wind turbines may be done by considering the wake effect as well as the components cost within the wind farm. In this paper, a mathematical model which includes the variation of both wind direction and wake deficit is proposed. The problem is formulated by using Levelized Production Cost (LPC) as the objective function. The optimization procedure is performed by Particle Swarm Optimization (PSO) algorithm with the purpose of maximizing the energy yields while minimizing the total investment. The simulation results indicate that the proposed method is effective to find the optimized layout, which minimizes the LPC. The optimization procedure is applicable for optimized placement of wind turbines within wind farms and extendible for different wind conditions and capacity of wind farms.

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.

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.

In the present work, a comparison between the results obtained by a panel code with a Reynolds-averaged Navier-Stokes (RANS) code is made to obtain a better insight on the viscous effects of the ducted propeller and on the limitations of the inviscid flow model, especially near bollard pull conditions or low advance ratios, which are important in the design stage. The analysis is carried out for propeller Ka4-70 operating inside duct 19A. From the comparison, several modelling aspects are studied for improvement of the inviscid (potential) flow solution. Finally, the experimental open-water data is compared with the panel method and RANS solutions. A strong influence of the blade wake pitch, especially near the blade tip, on the ducted propeller force predictions is seen. A reduction of the pitch of the gap strip is proposed for improvement of the performance prediction at low advance ratios.

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.

We present a methodology to process wind turbine wake simulations, which are closely related to the nature of wake observations and the processing of these to generate the so-called wake cases. The method involves averaging a large number of wake simulations over a range of wind directions and partly accounts for the uncertainty in the wind direction assuming that the same follows a Gaussian distribution. Simulations of the single and double wake measurements at the Sexbierum onshore wind farm are performed using a fast engineering wind farm wake model based on the Jensen wake model, a linearized computational fluid dynamics wake model by Fuga and a nonlinear computational fluid dynamics wake model that solves the Reynolds-averaged Navier–Stokes equations with a modified k-" turbulence model. The best agreement between models and measurements is found using the Jensen-based wake model with the suggested post-processing. We show that the wake decay coefficient of the Jensen wake model must be decreased from the commonly used onshore value of 0.075 to 0.038, when applied to the Sexbierum cases, as wake decay is related to the height, roughness and atmospheric stability and, thus, to turbulence intensity. Based on surface layer relations and assumptions between turbulence intensity and atmospheric stability, we find that at Sexbierum, the atmosphere was probably close to stable, although the stability was not observed.We support these assumptions using detailed meteorological observations from the Høvsøre site in Denmark, which is topographically similar to the Sexbierum region. © 2015 The Authors. Wind Energy published by John Wiley & Sons Ltd.

We describe a generalization of the Coupled Wake Boundary Layer (CWBL) model for wind-farms that can be used to evaluate the performance of wind-farms under arbitrary wind inflow directions whereas the original CWBL model (Stevens et al., J. Renewable and Sustainable Energy 7, 023115 (2015)) focused on aligned or staggered wind-farms. The generalized CWBL approach combines an analytical Jensen wake model with a "top-down" boundary layer model coupled through an iterative determination of the wake expansion coefficient and an effective wake coverage area for which the velocity at hub-height obtained using both models converges in the "deep-array" portion (fully developed region) of the wind-farm. The approach accounts for the effect of the wind direction by enforcing the coupling for each wind direction. Here we present detailed comparisons of model predictions with LES results and field measurements for the Horns Rev and Nysted wind-farms operating over a wide range of wind inflow directions. Our results demonstrate that two-way coupling between the Jensen wake model and a "top-down" model enables the generalized CWBL model to predict the "deep-array" performance of a wind-farm better than the Jensen wake model alone. The results also show that the new generalization allows us to study a much larger class of wind-farms than the original CWBL model, which increases the utility of the approach for wind-farm designers., Comment: 17 pages, 11 figures

This paper reports a novel frandsen generalized wake model and its variation model-frandsen generalized normal distribution wake model for off-shore wind farms. Two different new wake models in off-shore wind farms have been studied comparatively. Their characteristics have been analyzed through mathematical modeling and derivation. Meanwhile, simulation experiments show that the proposed two new wake models have different properties. Furthermore, the distributions of wind speed and wind direction are modeled by the statistical methods and Extreme Learning Machine through the off-shore wind farms of Yangshan Deepwater Harbor in the Port of Shanghai, China. In addition, the data of wind energy are provided to verify and test the correctness and effectiveness of the proposed two models. Wind power has been demonstrated by wind rose and wind resources with real-time data. These techniques contribute to enhance planning, utilization and exploitation for wind power of off-shore wind farms.

Recently attention has been paid to wind farm noise due to its negative health impact, not only on human beings, but also to marine and terrestrial organisms. The current work proposes a numerical methodology to generate a numerical noise map for a given wind farm. Noise generation from single wind turbines as well as wind farms has its basis in the nature of aerodynamics, caused by the interactions between the incoming turbulent flow and the wind turbine blades. Hence, understanding the mechanisms of airfoil noise generation, demands access to sophisticated numerical tools. The processes of modeling wind farm noise include three steps: (1) The whole wind farm velocity distributions are modelled with an improved Jensen’s wake model; (2) The individual wind turbine’s noise is simulated by a semi-empirical wind turbine noise source model; (3) Propagations of noise from all wind turbines are carried out by solving the parabolic wave equation. In the paper, the wind farm wake effect from the Horns Rev wind farm is studied. Based on the resulted wind speed distributions in the wind farm, the wind turbine noise source and its propagation are simulated for the whole wind farm.

The aim of the paper is to examine the nowadays well-known wind farm wake photographs taken on 12 February 2008 at the offshore Horns Rev 1 wind farm. The meteorological conditions are described from observations from several satellite sensors quantifying clouds, surface wind vectors and sea surface temperature as well as ground-based information at and near the wind farm, including Supervisory Control and Data Acquisition (SCADA) data. The SCADA data reveal that the case of fog formation occurred 12 February 2008 on the 10:10 UTC. The fog formation is due to very special atmospheric conditions where a layer of cold humid air above a warmer sea surface re-condensates to fog in the wake of the turbines. The process is fed by warm humid air up-drafted from below in the counter-rotating swirl generated by the clock-wise rotating rotors. The condensation appears to take place primarily in the wake regions with relatively high axial velocities and high turbulent kinetic energy. The wind speed is near cut-in and most turbines produce very little power. The rotational pattern of spiraling bands produces the large-scale structure of the wake fog.

Due to the increasing size of offshore wind farm, the impact of the wake effect on energy yields become more and more evident. The seafloor topography would limit the layout of the wind farm so that irregular layout is usually adopted in large scale offshore wind farm. However, the calculation for the energy yields in irregular wind farm considering wake effect would be difficult. In this paper, a mathematical model which includes the impacts of the variation of both wind direction and velocity on wake effect is established. Based on the wake model, a binary matrix method is proposed for the energy yields calculation for irregular wind farms. The results show that the proposed wake model is effective in calculating the wind speed deficit. The calculation framework is applicable for energy yields calculation in irregular wind farms.

We apply the 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 analyis mainly focuses on the question whether POD could be a useful tool to develop a simplified dynamic wake model. The extracted POD modes are used to obtain approximate descriptions of the velocity field. To assess the quality of these POD reconstructions, we define simple measures which are believed to be relevant for a sequential turbine in the wake such as the energy flux through a disk in the wake. It is shown that only a few modes are necessary to capture basic dynamical aspects of these measures even though only a small part of the turbulent kinetic energy is restored. Furthermore, we show that the importance of the individual modes depends on the measure 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 POD modes relating them to specific properties of the wake. For example the first mode is related to the horizontal large scale movement. Besides yielding a deeper understanding, this also enables us to view our results in comparison to existing dynamic wake models.

The present article proposes a framework for validation of stationary wake models that wind developers can use to predict the energy production of a wind power plant more accurately. The application of this framework provides a new way to quantify the uncertainty of annual energy production predictions. Additionally this methodology enables the fair comparison of different wake models. Furthermore the methodology enables the estimation of how much information can be obtain from a measurement dataset to quantify model inadequacy. In the present work the proposed framework is applied to the Horns Rev 1 offshore wind power plant. The model uncertainty of a modified N. O. Jensen wake model under uncertain undisturbed flow conditions was studied. Evidence of model inadequacy is found in terms of a bias in the predicted AEP distribution. It was found that the use of the official power curve compensates the errors in the wake model, as a consequence a larger uncertainty of the overall model is predicted. Furthermore a study of wake model benchmarking based on filtered flow cases indicates that measurement uncertainty in the wind speed and wind direction is large enough to obtain any evidence of model inaccuracy even for the simplest wake models.

A new two-dimensional (2D) wake model is developed and validated in this article to predict the velocity and turbulence distribution in the wake of a wind turbine. Based on the classical Jensen wake model, this model is further employing a cosine shape function to redistribute the spread of the wake deficit in the crosswind direction. Moreover, a variable wake decay rate is proposed to take into account both the ambient turbulence and the rotor generated turbulence, different from a constant wake decay rate used in the Jensen model. The obtained results are compared to field measurements, wind tunnel experiments, and results of an advanced k−ω turbulence model as well as large eddy simulations. From the comparisons, it is found that the proposed new wake model gives a good prediction in terms of both shape and velocity amplitude of the wake deficit, especially in the far wake which is the region of interest for wind farm development projects.

Particles with a size distribution in the range of 34 to 468 µm were fluidized in a three-phase bed using low liquid and gas velocities. Particle size distribution and pressure profile measurements were carried out at different locations in the bed in order to study the influence of fluid velocities on segregation and dispersion of particles in different size classes. The influence of gas velocity on particle mixing was analyzed in terms of internal solid fluxes, calculated by means of the wake model. Based on the experimental results, different particle distribution patterns were identified. Although no significant tendencies were observed for radial profiles, particles of different sizes have significantly different axial profiles, which are mainly affected by the velocity of the liquid phase. Thus, depending on the liquid velocity, smaller particles reach a maximum concentration at different bed heights.

Compared to horizontal-axis wind turbines (HAWTs), vertical-axis wind turbines (VAWTs) exhibit a different behaviour when built in tight arrays. In this research we build a model based on a free vortex model and empirical wake models, which are the Jensen wake model and multiple wakes combination models. The Jensen wake model and multiple wakes combination models are used to calculate the power production of wind farms, where the power output of single turbine is calculated using the free vortex model at a given wind speed and wind direction. The simulation results are compared with the field test results from a literature. The goal is to investigate the main factors impacting the power density of wind farms of VAWT pairs. The results indicate that the power density of wind farms using VAWTs could be much higher than existing wind farms, mainly because of enhanced power performance of closely-spaced counter-rotating VAWT pairs and because of large height-diameter-ratio of VAWTs. However, wind direction has a crucial influence on the power production of wind farms using turbine pairs.

The topic of this thesis is wind farm optimization. The goal is to be able to decide where to install wind turbines within a given region in order to maximize the power output in two different scenarios: For a fixed number of turbines with free placement, and for a limited number of possible locations and a variable number of turbines with a fixed cost associated with the installation of each turbine that is subtracted from the power output. These are referred to as "Problem 1" and "Problem 2". First, we develop a new, simple wake model. It is based on a model that was described by Katic et. al. in 1986, and then we make some improvements based on the authors' own comments and data. This is then further developed into complete mathematical models for Problem 1 and Problem 2. We consider a few heuristic methods for carrying out the optimization, including one that we have not seen in the literature. These are tried out on simple test cases. Finally, we try out exact optimization on two simple cases, and try out the heuristic methods on a larger sample of cases. We conclude that the new wake model, combined with the method that displays the best performance in the experiments, appears to be a useful tool in designing wind farms. Master i Informatikk MAMN-INF INF399

A hybrid Euler/full potential/Lagrangian wake method, based on single-blade simulation, for predicting unsteady aerodynamic flow around helicopter rotors in hover and forward flight has been developed. In this method, an Euler solver is used to model the near wake evolution and transonic flow phenomena in the vicinity of the blade, and a full potential equation (FPE) is used to model the isentropic potential flow region far away from the rotor, while the wake effects of other blades and the far wake are incorporated into the flow solution as an induced inflow distribution using a Lagrangian based wake analysis. To further reduce the execution time, the computational fluid dynamics (CFD) solution and rotor wake analysis (including induced velocity update) are conducted parallelly, and a load balancing strategy is employed to account for the information exchange between two solvers. By the developed method, several hover and forward-flight cases on Caradonna-Tung and Helishape 7A rotors are performed. Good agreements of the loadings on blade surface with available measured data demonstrate the validation of the method. Also, the CPU time required for different computation runs is compared in the paper, and the results show that the present hybrid method is superior to conventional CFD method in time cost, and will be more efficient with the number of blades increasing.

This article presents a continuously differentiable modification of the commonly used Jensen wake model. This property is con- served in the wake combination model and, by formulating the turbine's power curve as a set of constraints, also in the computation of a turbine's power output. The resulting objective function, maximizing the total power production, and optimizing the turbine positions, is thus continuously differentiable, and gradient based solution methods can be applied. Numerical experiments are conducted with simulated wind data of six offshore wind farm locations.