On the application of the Jensen wake model using a turbulence‐dependent wake decay coefficient: the Sexbierum case

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‐ε 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.     

Impact of different forest densities on atmospheric boundary‐layer development and wind‐turbine wake

The aim of this work is to investigate the atmospheric boundary‐layer (ABL) flow and the wind turbine wake over forests with varying leaf area densities (LAD). The forest LAD profile used in this study is based on a real forest site, Ryningsnäs, located in Sweden. The reference turbine used to model the wake is a well‐documented 5‐MW turbine, which is implemented in the simulations using an actuator line model (ALM). All simulations are carried out with openFOAM using the Reynolds averaged Navier‐Stokes (RANS) approach. Twelve forest cases with leaf area index (LAI) ranging from 0.42 to 8.5 are considered. Results show that the mean velocity decreases with increasing LAI within the forest canopy, but increases with LAI above the hub height. Meanwhile, the turbulent kinetic energy (TKE) varies nonmonotonically with forest density. The TKE increases with forest density and reaches to its maximum at an average LAI of 1.70, afterwards, it decreases gradually as the density increases. It is also observed that the forest density has a clear role in the wake development and recovery. Comparisons between no‐forest and forest cases show that the forest characteristics help in damping the added turbulence from the turbine. As a consequence, the forest with the highest upstream turbulence has the shortest wake downstream of the turbine.     

Offshore wind farm wake recovery: Airborne measurements and its representation in engineering models

We present an analysis of wind measurements from a series of airborne campaigns conducted to sample the wakes from two North Sea wind farm clusters, with the aim of determining the dependence of the downstream wind speed recovery on the atmospheric stability. The consequences of the stability dependence of wake length on the expected annual energy yield of wind farms in the North Sea are assessed by an engineering model. Wakes are found to extend for significantly longer downstream distances (>50 km) in stable conditions than in neutral and unstable conditions (  15 km). The parameters of one common engineering model are modified to reproduce the observed wake decay at downstream distances  30 km. More significant effects on the energy yield are expected for wind farms separated by distances  30 km, which is generally the case in the North Sea, but additional data would be required to validate the suggested parameter modifications within the engineering model. A case study is accordingly performed to show reductions in the farm efficiency downstream of a wind farm. These results emphasize not only the importance of understanding the impact of atmospheric stability on offshore wind farms but also the need to update the representation of wakes in current industry models to properly include wake‐induced energy losses, especially in large offshore clusters.     

A linearized numerical model of wind‐farm flows

A fast and reasonably accurate numerical three‐dimensional wake model able to predict the flow behaviour of a wind farm over a flat terrain has been developed. The model is based on the boundary‐layer approximation of the Navier–Stokes equations, linearized around the incoming atmospheric boundary layer, with the assumption that the wind turbines provide a small perturbation to the velocity field. The linearization of the actuator‐disc theory brought additional insights that could be used to understand the behaviour, as well as the limitations, of a flow model based on linear methods: for instance, it is shown that an adjustment of the turbine's thrust coefficient is necessary in order to obtain the same wake velocity field provided by the actuator disc theory within the used linear framework. The model is here validated against two independent wind‐tunnel campaigns with a small and a large wind farm aimed at the characterization of the flow above and upstream of the farms, respectively. The developed model is, in contrary to current engineering wake models, able to account for effects occurring in the upstream flow region, thereby including more physical mechanisms than other simplified approaches. The conducted simulations (in agreement with the measurement results) show that the presence of a wind farm affects the approaching flow far more upstream than generally expected and definitely beyond the current industrial standards. Despite the model assumptions, several velocity statistics above wind farms have been properly estimated providing an insight into the transfer of momentum inside the turbine rows. Copyright © 2016 John Wiley & Sons, Ltd.     

Assessing atmospheric stability and its impacts on rotor‐disk wind characteristics at an onshore wind farm

As the average hub height and blade diameter of new wind turbine installations continue to increase, turbines typically encounter higher wind speeds, which enable them to extract large amounts of energy, but they also face challenges due to the complex nature of wind flow and turbulence in the planetary boundary layer (PBL). Wind speed and turbulence can vary greatly across a turbine's rotor disk; this variability is partially due to whether the PBL is stable, neutral or convective. To assess the influence of stability on these wind characteristics, we utilize a unique data set including observations from two meteorological towers, a surface flux tower and high‐resolution remote‐sensing sound detection and ranging (SODAR) instrument. We compare several approaches to defining atmospheric stability to the Obukhov length (L). Typical wind farm observations only allow for the calculation of a wind shear exponent (α) or horizontal turbulence intensity (I_U) from cup anemometers, whereas SODAR gives measurements at multiple heights in the rotor disk of turbulence intensity (I) in the latitudinal (I_u), longitudinal (I_v) and vertical (I_w) directions and turbulence kinetic energy (TKE). Two methods for calculating horizontal Ifrom SODAR data are discussed. SODAR stability parameters are in high agreement with the more physically robust L,with TKE exhibiting the best agreement, and show promise for accurate characterizations of stability. Vertical profiles of wind speed and turbulence, which likely affect turbine power performance, are highly correlated with stability regime. At this wind farm, disregarding stability leads to over‐assessments of the wind resource during convective conditions and under‐assessments during stable conditions. Copyright © 2011 John Wiley & Sons, Ltd.     

Variable‐sized wind turbines are a possibility for wind farm optimization

The potential benefits associated with harnessing available momentum and reducing turbulence levels in a wind farm composed of wind turbines of alternating size are investigated through wind tunnel experiments. A variable size turbine array composed of 3 by 8 model wind turbines is placed in a boundary layer flow developed over both a smooth and rough surfaces under neutrally stratified thermal conditions. Cross‐wire anemometry is used to capture high resolution and simultaneous measurements of the streamwise and vertical velocity components at various locations along the central plane of the wind farm. A laser tachometer is employed to obtain the instantaneous angular velocity of various turbines. The results suggest that wind turbine size heterogeneity in a wind farm introduces distinctive flow interactions not possible in its homogeneous counterpart. In particular, reduced levels of turbulence around the wind turbine rotors may have positive effects on turbulent loading. The turbines also appear to perform quite uniformly along the entire wind farm, whereas surface roughness impacts the velocity recovery and the spectral content of the turbulent flow within the wind farm. Copyright © 2013 John Wiley & Sons, Ltd.     

Large‐eddy simulations of wind‐farm wake characteristics associated with a low‐level jet

In this study, we performed a suite of flow simulations for a 12‐wind‐turbine array with varying inflow conditions and lateral spacings, and compared the impacts of the flow on velocity deficit and wake recovery. We imposed both laminar inflow and turbulent inflows, which contain turbulence for the Ekman layer and a low‐level jet (LLJ) in the stable boundary layer. To solve the flow through the wind turbines and their wakes, we used a large‐eddy simulation technique with an actuator‐line method. We compared the time series for the velocity deficit at the first and rear columns to observe the temporal change in velocity deficit for the entire wind farm. The velocity deficit at the first column for LLJ inflow was similar to that for laminar inflow. However, the magnitude of velocity deficit at the rear columns for the case with LLJ inflow was 11.9% greater because of strong wake recovery, which was enhanced by the vertical flux of kinetic energy associated with the LLJ. To observe the spatial transition and characteristics of wake recovery, we performed statistical analyses of the velocity at different locations for both the laminar and LLJ inflows. These studies indicated that strong wake recovery was present, and a kurtosis analysis showed that the probability density function for the streamwise velocity followed a Gaussian distribution. In a quadrant analysis of the Reynolds stress, we found that the ejection and sweep motions for the LLJ inflow case were greater than those for the laminar inflow case.     

Error features and their possible causes in simulated low‐level winds by WRF at a wind farm

The WRF model is applied to simulate the low‐level wind field for a wind farm located in a typical arid region in northwest China for February 2008. The selected region has complex terrain with sparse vegetation. Overall, the WRF model reproduced the variation features of wind speeds and wind directions. However, the model overestimated the observed low‐level wind speeds, and there were large discrepancies for the low wind velocity (i.e. the errors of simulated winds increase with height and will be larger when the observed wind speeds are lower than 2.5 m/s). The features of the simulated errors and the possible causes in the model were analysed. The simulated low‐level wind in the afternoon is more accurate than that in early morning, which is usually unstable. Copyright © 2013 John Wiley & Sons, Ltd.     

Comparison of the atmospheric stability and wind profiles at two wind farm sites over a long marine fetch in the North Sea

A comparison of the atmospheric stability and wind profiles using data from meteorological masts located near two wind farm sites in the North Sea, Egmond aan Zee (up to 116 m) in the Dutch North Sea and Horns Rev (HR; up to 45 m) in the Danish North Sea, is presented. Only the measurements that represent long marine fetch are considered. It was observed that within a long marine fetch, the conditions in the North Sea are dominated by unstable [41% at Egmond aan Zee Offshore Wind Farm (OWEZ) and 33% at HR] and near‐neutral conditions (49% at OWEZ and 47% at HR), and stable conditions (10% at OWEZ and 20% at HR) occur for a limited period. The logarithmic wind profiles with the surface‐layer stability correction terms and Charnock's roughness model agree with the measurements at both sites in all unstable and near‐neutral conditions. An extended wind profile valid for the entire boundary layer is compared with the measurements. For the tall mast at Egmond aan Zee, it was found that for stable conditions, the scaling of the wind profiles with respect to boundary‐layer height is necessary, and the addition of another length scale parameter is preferred. At the lower mast at HR, the effect was not noticeable. Copyright © 2011 John Wiley & Sons, Ltd.     

Wind turbine boundary layer arrays for Cartesian and staggered configurations‐Part I,flow field and power measurements

Model wind turbine arrays were developed for the purpose of investigating the wake interaction and turbine canopy layer in a standard cartesian and row‐offset turbine array configurations. Stereographic particle image velocimetry was used to collect flow data upstream and downstream of entrance and exit row turbines in each configuration. Wakes for all cases were analyzed for energy content and recovery behavior including entrainment of high‐momentum flow from above the turbine canopy layer. The row‐offset arrangement of turbines within an array grants an increase in streamwise spacing of devices and allows for greater wake remediation between successive rows. These effects are seen in exit row turbine wakes as changes to statistical quantities including the in‐plane Reynolds stress, , and the production of turbulence. The recovery of wakes also strongly mitigates the perceived underperformance of wind turbines within an array. The flux of kinetic energy is demonstrated to be more localized in the entrance rows and in the offset arrangement. Extreme values for the flux of kinetic energy are about 7.5% less in the exit row of the cartesian arrangement than in the offset arrangement. Measurements of mechanical torque at entrance and exit row turbines lead to curves of power coefficient and demonstrate an increase in efficiency in row‐offset configurations. Copyright © 2014 John Wiley & Sons, Ltd.     

An investigation of in‐field blockage effects in closely spaced lateral wind farm configurations

A method of increasing the performance of wind farms has been established by limiting the lateral separation between neighbouring wind turbines. The close proximity of the wind turbines creates a beneficial in‐field blockage effect that results in a core of increased speed that is accelerated through the gap between the turbines. A preceding study indicated that the performance of three wind turbines can be increased by over 10% with tip‐to‐tip separation of 0.5 diameters (D) compared with the power output of the respective turbines in isolation. A corresponding flow‐mapping study has been completed in the current work using a single‐normal hot‐wire anemometer to characterize the increased flow speed through a narrow lateral gap, leading to the observation of a region of increased speed that occurs between 0D and 2.5D downstream of the gap between laterally spaced wind turbines. The experimental results were confirmed by conducting a series of computational simulations with the generalized unsteady vortex particle discrete vortex method code. The simulations were conducted with three rotors arranged in five different configurations, and the increase in power generated by the multi‐rotor configurations closely followed the observed experimental trends. The closely spaced lateral wind turbine configurations may have the ability to increase the annual capacity factor of wind farms while reducing wind farm land use requirements. Copyright © 2014 John Wiley & Sons, Ltd.     

An experimental investigation on the wake interferences among wind turbines sited in aligned and staggered wind farms

An experimental investigation was conducted for a better understanding of the wake interferences among wind turbines sited in wind farms with different turbine layout designs. Two different types of inflows were generated in an atmospheric boundary layer wind tunnel to simulate the different incoming surface winds over typical onshore and offshore wind farms. In addition to quantifying the power outputs and dynamic wind loads acting on the model turbines, the characteristics of the wake flows inside the wind farms were also examined quantitatively. After adding turbines staggered between the first 2 rows of an aligned wind farm to increase the turbine number density in the wind farm, the added staggered turbines did not show a significant effect on the aeromechanical performance of the downstream turbines for the offshore case. However, for the onshore case, while the upstream staggered turbines have a beneficial effect on the power outputs of the downstream turbines, the fatigue loads acting on the downstream turbines were also found to increase considerably due to the wake effects induced by the upstream turbines. With the same turbine number density and same inflow characteristics, the wind turbines were found to be able to generate much more power when they are arranged in a staggered layout than those in an aligned layout. In addition, the characteristics of the dynamic wind loads acting on the wind turbines sited in the aligned layout, including the fluctuation amplitudes and power spectrum, were found to be significantly different from those with staggered layout.     

Large eddy simulations of the effect of vertical staggering in large wind farms

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.     

Combining economic and fluid dynamic models to determine the optimal spacing in very large wind farms

Wind turbine spacing is an important design parameter for wind farms. Placing turbines too close together reduces their power extraction because of wake effects and increases maintenance costs because of unsteady loading. Conversely, placing them further apart increases land and cabling costs, as well as electrical resistance losses. The asymptotic limit of very large wind farms in which the flow conditions can be considered ‘fully developed’ provides a useful framework for studying general trends in optimal layouts as a function of dimensionless cost parameters. Earlier analytical work by Meyers and Meneveau (Wind Energy 15, 305–317 (2012)) revealed that in the limit of very large wind farms, the optimal turbine spacing accounting for the turbine and land costs is significantly larger than the value found in typical existing wind farms. Here, we generalize the analysis to include effects of cable and maintenance costs upon optimal wind turbine spacing in very large wind farms under various economic criteria. For marginally profitable wind farms, minimum cost and maximum profit turbine spacings coincide. Assuming linear‐based and area‐based costs that are representative of either offshore or onshore sites we obtain for very large wind farms spacings that tend to be appreciably greater than occurring in actual farms confirming earlier results but now including cabling costs. However, we show later that if wind farms are highly profitable then optimization of the profit per unit area leads to tighter optimal spacings than would be implied by cost minimization. In addition, we investigate the influence of the type of wind farm layout. © 2016 The Authors Wind Energy Published by John Wiley & Sons Ltd     

Uncertainty quantification of infinite aligned wind farm performance using non‐intrusive polynomial chaos and a distributed roughness model

Uncertainty of wind farm parameters can have a significant effect on wind farm power output. Knowledge of the uncertainty‐produced stochastic distribution of the entire wind farm power output and the corresponding uncertainty propagation mechanisms is very important for evaluating the uncertainty effects on the wind farm performance during wind farm planning stage and providing insights on improving the performance of the existing wind farms. In this work, the propagation of uncertainties from surface roughness and induction factor in infinite aligned wind farms modeled by a modified distributed roughness model is investigated using non‐intrusive polynomial chaos. Stochastic analysis of surface roughness indicates that 30% uncertainty can propagate such that there is up a 8% uncertainty in the power output of the wind farm by affecting the uncertainty in the position of the individual wind turbines in the vertical boundary layer profile and uncertainty in vertical momentum fluxes which replenish energy in the wake in large wind farms. Induction factor uncertainty of the wind turbines can also have a significant effect on power output. Not only does its uncertainty substantially affect the vertical boundary layer profile, but the uncertainty in turbine wake growth which affects how neighboring turbine wakes interact. We found that optimal power output in terms of reduction of uncertainty closely correlates with the Betz limit and is dependent on the mean induction factor. Copyright © 2016 John Wiley & Sons, Ltd.     

Comparison of the near‐wake between actuator‐line simulations and a simplified vortex model of a horizontal‐axis wind turbine

The flow around an isolated horizontal‐axis wind turbine is estimated by means of a new vortex code based on the Biot–Savart law with constant circulation along the blades. The results have been compared with numerical simulations where the wind turbine blades are replaced with actuator lines. Two different wind turbines have been simulated: one with constant circulation along the blades, to replicate the vortex method approximations, and the other with a realistic circulation distribution, to compare the outcomes of the vortex model with real operative wind‐turbine conditions (Tjæreborg wind turbine). The vortex model matched the numerical simulation of the turbine with constant blade circulation in terms of the near‐wake structure and local forces along the blade. The results from the Tjæreborg turbine case showed some discrepancies between the two approaches, but overall, the agreement is qualitatively good, validating the analytical method for more general conditions. The present results show that a simple vortex code is able to provide an estimation of the flow around the wind turbine similar to the actuator‐line approach but with a negligible computational effort. Copyright © 2015 John Wiley & Sons, Ltd.     

De‐trending of wind speed variance based on first‐order and second‐order statistical moments only

The lack of efficient methods for de‐trending of wind speed resource data may lead to erroneous wind turbine fatigue and ultimate load predictions. The present paper presents two models, which quantify the effect of an assumed linear trend on wind speed standard deviations as based on available statistical data only. The first model is a pure time series analysis approach, which quantifies the effect of non‐stationary characteristics of ensemble mean wind speeds on the estimated wind speed standard deviations as based on mean wind speed statistics only. This model is applicable to statistics of arbitrary types of time series. The second model uses the full set of information and includes thus additionally observed wind speed standard deviations to estimate the effect of ensemble mean non‐stationarities on wind speed standard deviations. This model takes advantage of a simple physical relationship between first‐order and second‐order statistical moments of wind speeds in the atmospheric boundary layer and is therefore dedicated to wind speed time series but is not applicable to time series in general. The capabilities of the proposed models are discussed by comparing model predictions with conventionally de‐trended characteristics of measured wind speeds using data where high sampled time series are available, and a traditional de‐trending procedure therefore can be applied. This analysis shows that the second model performs significantly better than the first model, and thus in turn that the model constraint, introduced by the physical link between the first and second statistical moments, proves very efficient in the present context. © 2013 The Authors. Wind Energy Published by John Wiley & Sons Ltd.     

Observability of the ambient conditions in model‐based estimation for wind farm control: A focus on static models

Wind farm control (WFC) algorithms rely on an estimate of the ambient wind speed, wind direction, and turbulence intensity in the determination of the optimal control setpoints. However, the measurements available in a commercial wind farm do not always carry sufficient information to estimate these atmospheric quantities. In this paper, a novel measure (“observability”) is introduced that quantifies how well the ambient conditions can be estimated with the measurements at hand through a model inversion approach. The usefulness of this measure is shown through several case studies. While the turbine power signals and the inter‐turbine wake interactions provide information on the wind direction, the case studies presented in this article show that there is a strong need for wind direction measurements for WFC to sufficiently cover observability for any ambient condition. Further, generally, more wake interaction leads to a higher observability. Also, the mathematical framework presented in this article supports the straightforward notion that turbine power measurements provide no additional information compared with local wind speed measurements, implying that power measurements are superfluous. Irregular farm layouts result in a higher observability due to the increase in unique wake interaction. The findings in this paper may be used in WFC to predict which ambient quantities can (theoretically) be estimated. The authors envision that this will assist in the estimation of the ambient conditions in WFC algorithms and can lead to an improvement in the performance of WFC algorithms over the complete envelope of wind farm operation.     

Computational Fluid Dynamics model of stratified atmospheric boundary‐layer flow

For wind resource assessment, the wind industry is increasingly relying on computational fluid dynamics models of the neutrally stratified surface‐layer. So far, physical processes that are important to the whole atmospheric boundary‐layer, such as the Coriolis effect, buoyancy forces and heat transport, are mostly ignored. In order to decrease the uncertainty of wind resource assessment, the present work focuses on atmospheric flows that include stability and Coriolis effects. The influence of these effects on the whole atmospheric boundary‐layer are examined using a Reynolds‐averaged Navier–Stokes k‐ ε model. To validate the model implementations, results are compared against measurements from several large‐scale field campaigns, wind tunnel experiments, and previous simulations and are shown to significantly improve the predictions. Copyright © 2013 John Wiley & Sons, Ltd.