Modelling and measurements of power losses and turbulence intensity in wind turbine wakes at Middelgrunden offshore wind farm

Understanding of power losses and turbulence increase due to wind turbine wake interactions in large offshore wind farms is crucial to optimizing wind farm design. Power losses and turbulence increase due to wakes are quantified based on observations from Middelgrunden and state‐of‐the‐art models. Observed power losses due solely to wakes are approximately 10% on average. These are relatively high for a single line of wind turbines due in part to the close spacing of the wind farm. The wind farm model Wind Analysis and Application Program (WAsP) is shown to capture wake losses despite operating beyond its specifications for turbine spacing. The paper describes two methods of estimating turbulence intensity: one based on the mean and standard deviation (SD) of wind speed from the nacelle anemometer, the other from mean power output and its SD. Observations from the nacelle anemometer indicate turbulence intensity which is around 9% higher in absolute terms than those derived from the power measurements. For comparison, turbulence intensity is also derived from wind speed and SD from a meteorological mast at the same site prior to wind farm construction. Despite differences in the measurement height and period, overall agreement is better between the turbulence intensity derived from power measurements and the meteorological mast than with those derived from data from the nacelle anemometers. The turbulence in wind farm model indicates turbulence increase of the order 20% in absolute terms for flow directly along the row which is in good agreement with the observations. Copyright © 2007 John Wiley & Sons, Ltd.     

Effects of spatial and temporal resolution of the turbulent inflow on wind turbine performance estimation

The effects of spatial and temporal resolution of wind inflows generated using large eddy simulations (LES) on the scales of turbulence present in the wind inflow, and the resulting changes in wind turbine performance were investigated for neutral atmospheric boundary layer conditions. Wind inflows with four different spatial resolutions and five different temporal resolutions were used to produce different turbine responses. An aero‐elastic code assessed the dynamic response of two wind turbines to the different inflows. Auto‐spectral density functions (ASDF) of turbine responses, such as blade deflection and bending moment, that are representative of the turbine response were used to assess the effect of the inflow. The results indicated that, as additional turbulence scales were resolved, the wind turbines showed a similar increased response that was evident in both the ASDF and variance of the different wind turbine performance parameters. As a result, the amount to which turbulence is resolved in the inflow, particularly using tools such as LES, will be important to consider when using these inflows for wind turbine design and performance prediction. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Influence of inflow conditions on turbine loading and wake structures predicted by large eddy simulations using exact geometry

A large eddy simulation was performed on an National Renewable Energy Laboratory (NREL) phase VI wind turbine (10 m diameter), using the exact blade geometry, to determine the influence of different inflow conditions on the aerodynamic loadings and the near wake characteristics. The effects of the three inflow conditions, uniform inflow, linear wind shear and linear wind shear with turbulence, are investigated. Wind shear causes periodic variations in power and aerodynamic loading with an additional force component exerted along the lateral direction. Significant separation occurs in the high wind region on the suction side of the blades, resulting in unstable loading in off‐design inflow conditions. Because of the shear effect between the near‐blade tip vortex and ambient flow, the strong vortex core in the helical structure dissipates and transforms into a continuous vorticity sheet when x/D > 1.5. The combination of inflow turbulence and wind shear enhances the turbulence generation mechanism in the near wake, where energy is withdrawn from large wake structures and converted into energy of small‐scale structures. Copyright © 2015 John Wiley & Sons, Ltd.     

Benefits of collocating vertical‐axis and horizontal‐axis wind turbines in large wind farms

In this study, we address the benefits of a vertically staggered (VS) wind farm, in which vertical‐axis and horizontal‐axis wind turbines are collocated in a large wind farm. The case study consists of 20 small vertical‐axis turbines added around each large horizontal‐axis turbine. Large‐eddy simulation is used to compare power extraction and flow properties of the VS wind farm versus a traditional wind farm with only large turbines. The VS wind farm produces up to 32% more power than the traditional one, and the power extracted by the large turbines alone is increased by 10%, caused by faster wake recovery from enhanced turbulence due to the presence of the small turbines. A theoretical analysis based on a top‐down model is performed and compared with the large‐eddy simulation. The analysis suggests a nonlinear increase of total power extraction with increase of the loading of smaller turbines, with weak sensitivity to various parameters, such as size, and type aspect ratio, and thrust coefficient of the vertical‐axis turbines. We conclude that vertical staggering can be an effective way to increase energy production in existing wind farms. Copyright © 2016 John Wiley & Sons, Ltd.     

Effects of turbine spacing on the power output of extended wind‐farms

We present results from large eddy simulations of extended wind‐farms for several turbine configurations with a range of different spanwise and streamwise spacing combinations. The results show that for wind‐farms arranged in a staggered configuration with spanwise spacings in the range ≈[3.5,8]D, where D is the turbine diameter, the power output in the fully developed regime depends primarily on the geometric mean of the spanwise and streamwise turbine spacings. In contrast, for the aligned configuration the power output in the fully developed regime strongly depends on the streamwise turbine spacing and shows weak dependence on the spanwise spacing. Of interest to the rate of wake recovery, we find that the power output is well correlated with the vertical kinetic energy flux, which is a measure of how much kinetic energy is transferred into the wind‐turbine region by the mean flow. A comparison between the aligned and staggered configurations reveals that the vertical kinetic energy flux is more localized along turbine columns for aligned wind‐farms than for staggered ones. This additional mixing leads to a relatively fast wake recovery for aligned wind‐farms. Copyright © 2015 John Wiley & Sons, Ltd.     

Experimental verification of computational predictions in power generation variation with layout of offshore wind farms

The optimization of wind farms with respect to spatial layout is addressed experimentally. Wake effects within wind turbine farms are well known to be deleterious in terms of power generation and structural loading, which is corroborated in this study. Computational models are the predominant tools in the prediction of turbine‐induced flow fields. However, for wind farms comprising hundreds of turbines, reliability of the obtained numerical data becomes a growing concern with potentially costly consequences. This study pursues a systematic complementary theoretical, experimental and numerical study of variations in generated power with turbine layout of an 80 turbine large wind farm. Wake effects within offshore wind turbine arrays are emulated using porous discs mounted on a flat plate in a wind tunnel. The adopted approach to reproduce experimentally individual turbine wake characteristics is presented, and drag measurements are argued to correctly capture the variation in power generation with turbine layout. Experimental data are juxtaposed with power predictions using ANSYS WindModeller simulation suite. Although comparison with available wind farm power output data has been limited, it is demonstrated nonetheless that this approach has potential for the validation of numerical models of power loss due to wake effects or even to make a direct physical prediction. The approach has even indicated useful data for the improvement of the physics within numerical models. Copyright © 2014 John Wiley & Sons, Ltd.     

Estimation of turbulence intensity using rotor effective wind speed in Lillgrund and Horns Rev-I offshore wind farms

Turbulence characteristics of the wind farm inflow have a significant impact on the energy production and the lifetime of a wind farm. The common approach is to use the meteorological mast measurements to estimate the turbulence intensity (TI) but they are not always available and the turbulence varies over the extent of the wind farm. This paper describes a method to estimate the TI at individual turbine locations by using the rotor effective wind speed calculated via high frequency turbine data.The method is applied to Lillgrund and Horns Rev-I offshore wind farms and the results are compared with TI derived from the meteorological mast, nacelle mounted anemometer on the turbines and estimation based on the standard deviation of power. The results show that the proposed TI estimation method is in the best agreement with the meteorological mast. Therefore, the rotor effective wind speed is shown to be applicable for the TI assessment in real-time wind farm calculations under different operational conditions. Furthermore, the TI in the wake is seen to follow the same trend with the estimated wake deficit which enables to quantify the turbulence in terms of the wake loss locally inside the wind farm.     

Survey of modelling methods for wind turbine wakes and wind farms

This article provides an overview and analysis of different wake‐modelling methods which may be used as prediction and design tools for both wind turbines and wind farms. We also survey the available data concerning the measurement of wind magnitudes in both single wakes and wind farms, and of loading effects on wind turbines under single‐ and multiple‐wake conditions. The relative merits of existing wake and wind farm models and their ability to reproduce experimental results are discussed. Conclusions are provided concerning the usefulness of the different modelling approaches examined, and difficult issues which have not yet been satisfactorily treated and which require further research are discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

Data-driven modelling of turbine wake interactions and flow resistance in large wind farms

Turbine wake and local blockage effects are known to alter wind farm power production in two different ways: (1) by changing the wind speed locally in front of each turbine and (2) by changing the overall flow resistance in the farm and thus the so-called farm blockage effect. To better predict these effects with low computational costs, we develop data-driven emulators of the ‘local’ or ‘internal’ turbine thrust coefficient $C_T^{\ast }$ as a function of turbine layout. We train the model using a multi-fidelity Gaussian process (GP) regression with a combination of low (engineering wake model) and high-fidelity (large eddy simulations) simulations of farms with different layouts and wind directions. A large set of low-fidelity data speeds up the learning process and the high-fidelity data ensures a high accuracy. The trained multi-fidelity GP model is shown to give more accurate predictions of $C_T^{\ast }$ compared to a standard (single-fidelity) GP regression applied only to a limited set of high-fidelity data. We also use the multi-fidelity GP model of $C_T^{\ast }$ with the two-scale momentum theory (Nishino & Dunstan 2020, J. Fluid Mech. 894, A2) to demonstrate that the model can be used to give fast and accurate predictions of large wind farm performance under various mesoscale atmospheric conditions. This new approach could be beneficial for improving annual energy production (AEP) calculations and farm optimization in the future.     

Dynamic wind turbine output power reduction under varying wind speed conditions due to inertia

The inertia of wind turbines causes a reduction in their output power due to their inability to operate at the turbine maximum co‐efficient of performance point under dynamic wind conditions. In this paper, this dynamic power reduction is studied analytically and using simulations, assuming that a steady‐state optimal torque control strategy is used. The concepts of the natural and actual turbine time‐constant are introduced, and typical values for these parameters are examined. It is shown that for the typical turbine co‐efficient of performance curve used, the average turbine speed can be assumed to be determined by the average wind speed. With this assumption, analytical expressions for the power reduction with infinite and then finite turbine inertia are determined for sine‐wave wind speed variations. The results are then generalized for arbitrary wind speed profiles. A numerical wind turbine system simulation model is used to validate the analytical results for step and sine‐wave wind speed variations. Finally, it is used with real wind speed data to compare with the analytical predictions. Copyright © 2012 John Wiley & Sons, Ltd.     

Wind tunnel study on wind and turbulence intensity profiles in wind turbine wake

In recent years, there has been a rapid development of the wind farms in Japan. It becomes very important to investigate the wind turbine arrangement in wind farm, in order that the wake of one wind turbine does not to interfere with the flow in other wind turbines. In such a case, in order to achieve the highest possible efficiency from the wind, and to install as many as possible wind turbines within a limited area, it becomes a necessity to study the mutual interference of the wake developed by wind turbines. However, there is no report related to the effect of the turbulence intensity of the external flow on the wake behind a wind turbine generated in the wind tunnel. In this paper, the measurement results of the averaged wind profile and turbulence intensity profile in the wake in the wind tunnel are shown when the turbulence intensity of the external wind was changed. The wind tunnel experiment is performed with 500mm-diameter two-bladed horizontal axis wind turbine and the wind velocity in wake is measured by an I-type hot wire probe. As a result, it is clarified that high turbulence intensities enable to the entrainment of the main flow and the wake and to recover quickly the velocity in the wake.     

风切变对大直径风力机风轮输出功率影响的初探

以风切变幂指数为0．14的风廓线模型进行了风轮输出功率计算,并与以风轮中心风速计算风轮功率进行了对比分析,指出风切变对风轮输出功率的影响不容忽视。     

Exploring the benefits of vertically staggered wind farms: Understanding the power generation mechanisms of turbines operating at different scales

Wind farms are known to modulate large scale structures in and around the wake regions of the turbines. The potential benefits of placing small hub height, small rotor turbines in between the large turbines in a wind farm to take advantage of such modulated large‐scale eddies are explored using large eddy simulation (LES). The study has been carried out in an infinite wind farm framework invoking an asymptotic limit, and the wind turbines are modeled using an actuator line model. The vertically staggered wind turbine arrangements that are studied in the present work consist of rows of large wind turbines, with rows of smaller wind turbines (ie, smaller rotor size and shorter hub height) placed in between the rows of large turbines. The influence of the hub height of the small turbines, in particular, how it affects the interactions between the large and small turbines and consequently their power, along with the multiscale dynamics involved, has been assessed in the current study. It was found that, in the multiscale layouts, the small turbines at lower hub heights operate more efficiently than their homogeneous single‐scale counterparts. In contrast, the small turbines with higher hub heights incur a loss of power compared with the corresponding single‐scale arrangements.     

Optimal turbine spacing in fully developed wind farm boundary layers

As wind farms become larger, the asymptotic limit of the ‘fully developed’, or ‘infinite’, wind farm has been receiving an increased interest. This limit is relevant for wind farms on flat terrain whose length exceeds the height of the atmospheric boundary layer by over an order of magnitude. Recent computational studies based on large eddy simulation have identified various mean velocity equilibrium layers and have led to parameterizations of the effective roughness height that allow the prediction of the wind velocity at hub height as a function of parameters such as wind turbine spacing and loading factors. In the current paper, we employ this as a tool in making predictions of optimal wind turbine spacing as a function of these parameters, as well as in terms of the ratio of turbine costs to land surface costs. For realistic cost ratios, we find that the optimal average turbine spacing may be considerably higher than that conventionally used in current wind farm implementations. Copyright © 2011 John Wiley & Sons, Ltd.     

Self‐similarity and turbulence characteristics of wind turbine wakes via large‐eddy simulation

Mean and turbulent properties of the wake generated by a single wind turbine are studied in this paper with a new large eddy simulation (LES) code, the wind turbine and turbulence simulator (WiTTS hereafter). WiTTS uses a scale‐dependent Lagrangian dynamical model of the sub‐grid shear stress and actuator lines to simulate the effects of the rotating blades. WiTTS is first tested by simulating neutral boundary layers without and with a wind turbine and then used to study the common assumptions of self‐similarity and axisymmetry of the wake under neutral conditions for a variety of wind speeds and turbine properties. We find that the wind velocity deficit generally remains self similarity to a Gaussian distribution in the horizontal. In the vertical, the Gaussian self‐similarity is still valid in the upper part of the wake, but it breaks down in the region of the wake close to the ground. The horizontal expansion of the wake is always faster and greater than the vertical expansion under neutral stability due to wind shear and impact with the ground. Two modifications to existing equations for the mean velocity deficit and the maximum added turbulence intensity are proposed and successfully tested. The anisotropic wake expansion is taken into account in the modified model of the mean velocity deficit. Turbulent kinetic energy (TKE) budgets show that production and advection exceed dissipation and turbulent transport. The nacelle causes significant increase of every term in the TKE budget in the near wake. In conclusion, WiTTS performs satisfactorily in the rotor region of wind turbine wakes under neutral stability. Copyright © 2014 John Wiley & Sons, Ltd.     

Gaussian vs non‐Gaussian turbulence: impact on wind turbine loads

From large‐eddy simulations of atmospheric turbulence, a representation of Gaussian turbulence is constructed by randomizing the phases of the individual modes of variability. Time series of Gaussian turbulence are constructed and compared with its non‐Gaussian counterpart. Time series from the two types of turbulence are then used as input to wind turbine load simulations under normal operations with the HAWC2 software package. A slight increase in the extreme loads of the tower base fore‐aft moment is observed for high wind speeds when using non‐Gaussian turbulence but is insignificant when taking into account the safety factor for extreme moments. Other extreme load moments as well as the fatigue loads are not affected because of the use of non‐Gaussian turbulent inflow. It is suggested that the turbine thus acts like a low‐pass filter that averages out the non‐Gaussian behaviour, which is mainly associated with the fastest and smallest scales. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical simulations of wake characteristics of a wind turbine in uniform inflow

The wake of a wind turbine operating in a uniform inflow at various tip speed ratios is simulated using a numerical method, which combines large eddy simulations with an actuator line technique. The computations are carried out in a numerical mesh with about 8.4·10⁶ grid points distributed to facilitate detailed studies of basic features of both the near and far wake, including distributions of interference factors, vortex structures and formation of instabilities. Copyright © 2009 John Wiley & Sons, Ltd.     

An assessment of the impact of reduced averaging time on small wind turbine power curves,energy capture predictions and turbulence intensity measurements

The effect of varying the averaging time of measured data used to calculate wind turbine power curves is examined. The effects of reducing the averaging time from 10 to 1 min, as recommended for small wind turbines, are investigated using power performance data recorded using a 15 kW wind turbine. Test site data have been processed according to the relevant international standard, IEC 61400‐12‐1, to provide power curves and annual energy yield predictions. A number of issues are explored: the systematic distortion of the power curve that occurs as averaging time is decreased, the errors introduced by the use of 1 min averaged power curves to calculate energy yield and the reduction of turbulence intensity as averaging time is reduced. Recommendations for improved small wind turbine testing and energy yield calculation are given. Copyright © 2012 John Wiley & Sons, Ltd.     

Aerodynamic loads on wind turbine nacelles under different inflow turbulence conditions

The aerodynamic loads on wind turbine nacelles for range of inflow turbulence conditions are investigated. To this end, a series of wind tunnel experiments are conducted to investigate pressure field distributions over the surface of scaled models of rectangular and ellipsoidal nacelles. It is found that the mean pressure fields on the roof of the rectangular nacelle are similar for all the inflow turbulence cases for respective yaw angles. However, when yaw angle is around 90°, the mean pressure coefficient becomes more negative close to upstream edge with increasing inflow turbulence. For the ellipsoidal nacelle, the magnitude of the mean pressure coefficient increases with decreasing inflow turbulence in the adverse pressure gradient region, although the minimum peak pressure coefficient remains unaffected by inflow turbulence. The overall effect of wind‐induced load on the nacelle surfaces is evaluated by computing force coefficients from the pressure data. It is observed that the peak force coefficients for both rectangular and ellipsoidal nacelles increase with increasing inflow turbulence. The models for the estimation of peak aerodynamic loads on the nacelle surfaces are proposed as functions of inflow turbulence and mean force coefficients and show satisfactory agreement with measurements. Finally, the loads calculated by the GL guideline are compared against the measurements. It is found that the guideline estimation is conservative for design load case (DLC) 6.1, but it underestimates the load by about 35% for DLC 6.2 when the inflow turbulence intensity is 13.2%.