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.     

Effects of inflow turbulence intensity and turbine arrangements on the power generation efficiency of large wind farms

In this study, we conduct a series of large‐eddy simulations (LESs) to study the impact of different incoming turbulent boundary layer flows over large wind farms, with a particular focus on the overall efficiency of electricity production and the evolution of the turbine wake structure. Five representative turbine placements in the large wind farm are considered, including an aligned layout and four staggered layouts with lateral or vertical offset arrangements. Four incoming flow conditions are used and arranged from the LESs of the ABL flow over homogeneous flat surfaces with four different aerodynamic roughness lengths (i.e., z0 = 0.5, 0.1, 0.01, and 0.0001 m), where the hub‐height turbulence intensity levels are about 11.1%, 8.9%, 6.8%, and 4.9%, respectively. The simulation results indicate that an enhancement in the inflow turbulence level can effectively increase the power generation efficiency in the large wind farms, with about 23.3% increment on the overall farm power production and up to about 32.0% increment on the downstream turbine power production. Under the same inflow condition, the change of the turbine‐array layouts can increase power outputs within the first 10 turbine rows, which has a maximum increment of about 26.5% under the inflow condition with low turbulence. By comparison, the increase of the inflow turbulence intensity facilitates faster wake recovery that raises the power generation efficiency of large wind farms than the adjustment of the turbine placing layouts.     

Evaluation of log‐of‐power extremum seeking control for wind turbines using large eddy simulations

The extremum seeking control (ESC) algorithm has been proposed to determine operating parameters that maximize power production below rated wind speeds (region II). This is usually done by measuring the turbine's power signal to determine optimal values for parameters of the control law or actuator settings. This paper shows that the standard ESC with power feedback is quite sensitive to variations in mean wind speed, with long convergence time at low wind speeds and aggressive transient response, possibly unstable, at high wind speeds. The paper also evaluates the performance, as measured by the dynamic and steady state response, of the ESC with feedback of the logarithm of the power signal (LP‐ESC). Large eddy simulations (LES) demonstrate that the LP‐ESC, calibrated at a given wind speed, exhibits consistent robust performance at all wind speeds in a typical region II. The LP‐ESC is able to achieve the optimal set‐point within a prescribed settling time, despite variations in the mean wind speed, turbulence, and shear. The LES have been conducted using realistic wind input profiles with shear and turbulence. The ESC and LP‐ESC are implemented in the LES without assuming the availability of analytical gradients.     

Modeling space‐time correlations of velocity fluctuations in wind farms

An analytical model for the streamwise velocity space‐time correlations in turbulent flows is derived and applied to the special case of velocity fluctuations in large wind farms. The model is based on the Kraichnan‐Tennekes random sweeping hypothesis, capturing the decorrelation in time while including a mean wind velocity in the streamwise direction. In the resulting model, the streamwise velocity space‐time correlation is expressed as a convolution of the pure space correlation with an analytical temporal decorrelation kernel. Hence, the spatiotemporal structure of velocity fluctuations in wind farms can be derived from the spatial correlations only. We then explore the applicability of the model to predict spatiotemporal correlations in turbulent flows in wind farms. Comparisons of the model with data from a large eddy simulation of flow in a large, spatially periodic wind farm are performed, where needed model parameters such as spatial and temporal integral scales and spatial correlations are determined from the large eddy simulation. Good agreement is obtained between the model and large eddy simulation data showing that spatial data may be used to model the full spatiotemporal structure of fluctuations in wind farms.     

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.     

A comparison of methods for assessing power output in non‐uniform onshore wind farms

Wind resource assessments are used to estimate a wind farm's power production during the planning process. It is important that these estimates are accurate, as they can impact financing agreements, transmission planning, and environmental targets. Here, we analyze the challenges in wind power estimation for onshore farms. Turbine wake effects are a strong determinant of farm power production. With given input wind conditions, wake losses typically cause downstream turbines to produce significantly less power than upstream turbines. These losses have been modeled extensively and are well understood under certain conditions. Most notably, validation of different model types has favored offshore farms. Models that capture the dynamics of offshore wind conditions do not necessarily perform equally as well for onshore wind farms. We analyze the capabilities of several different methods for estimating wind farm power production in 2 onshore farms with non‐uniform layouts. We compare the Jensen model to a number of statistical models, to meteorological downscaling techniques, and to using no model at all. We show that the complexities of some onshore farms result in wind conditions that are not accurately modeled by the Jensen wake decay techniques and that statistical methods have some strong advantages in practice.     

Large‐eddy simulations of the Lillgrund wind farm

The power production of the Lillgrund wind farm is determined numerically using large‐eddy simulations and compared with measurements. In order to simulate realistic atmospheric conditions, pre‐generated turbulence and wind shear are imposed in the computational domain. The atmospheric conditions are determined from data extracted from a met mast, which was erected prior to the establishment of the farm. In order to allocate most of the computational power to the simulations of the wake flow, the turbines are modeled using an actuator disc method where the discs are imposed in the computational domain as body forces which for every time step are calculated from tabulated airfoil data. A study of the influence of imposed upstream ambient turbulence is performed and shows that higher levels of turbulence results in slightly increased total power production and that it is of great importance to include ambient turbulence in the simulations. By introducing ambient atmospheric turbulence, the simulations compare very well with measurements at the studied inflow angles. A final study aiming at increasing the farm production by curtailing the power output of the front row turbines and thus letting more kinetic energy pass downstream is performed. The results, however, show that manipulating only the front row turbines has no positive effect on the farm production, and therefore, more complex curtailment strategies are needed to be tested. Copyright © 2014 John Wiley & Sons, Ltd.     

Large‐eddy simulation of turbulent flow past wind turbines/farms: the Virtual Wind Simulator (VWiS)

A large‐eddy simulation framework, dubbed as the Virtual Wind Simulator (VWiS), for simulating turbulent flow over wind turbines and wind farms in complex terrain is developed and validated. The wind turbines are parameterized using the actuator line model. The complex terrain is represented by the curvilinear immersed boundary method. The predictive capability of the present method is evaluated by simulating two available wind tunnel experimental cases: the flow over a stand‐alone turbine and an aligned wind turbine array. Systematic grid refinement studies are carried out, for both single turbine and multi‐turbine array cases, and the accuracy of the computed results is assessed through detailed comparisons with wind tunnel experiments. The model is further applied to simulate the flow over an operational utility‐scale wind farm. The inflow velocities for this case are interpolated from a mesoscale simulation using a Weather Research and Forecasting (WRF) model with and without adding synthetic turbulence to the WRF‐computed velocity fields. Improvements on power predictions are obtained when synthetic turbulence is added at the inlet. Finally the VWiS is applied to simulate a yet undeveloped wind farm at a complex terrain site where wind resource measurements have already been obtained. Good agreement with field measurements is obtained in terms of the time‐averaged streamwise velocity profiles. To demonstrate the ability of the model to simulate the interactions of terrain‐induced turbulence with wind turbines, eight hypothetical turbines are placed in this area. The computed extracted power underscores the significant effect of site‐specific topography on turbine performance. Copyright © 2014 John Wiley & Sons, Ltd.     

Model‐based receding horizon control of wind farms for secondary frequency regulation

In this study, we propose the use of model‐based receding horizon control to enable a wind farm to provide secondary frequency regulation for a power grid. The controller is built by first proposing a time‐varying one‐dimensional wake model, which is validated against large eddy simulations of a wind farm at startup. This wake model is then used as a plant model for a closed‐loop receding horizon controller that uses wind speed measurements at each turbine as feedback. The control method is tested in large eddy simulations with actuator disk wind turbine models representing an 84‐turbine wind farm that aims to track sample frequency regulation reference signals spanning 40 min time intervals. This type of control generally requires wind turbines to reduce their power set points or curtail wind power output (derate the power output) by the same amount as the maximum upward variation in power level required by the reference signal. However, our control approach provides good tracking performance in the test system considered with only a 4% derate for a regulation signal with an 8% maximum upward variation. This performance improvement has the potential to reduce the opportunity cost associated with lost revenue in the bulk power market that is typically associated with providing frequency regulation services. Copyright © 2017 John Wiley & Sons, Ltd.     

Large eddy simulation study of the humidity variation in the shadow of a large wind farm

Numerous studies have shown that wind turbine wakes within a large wind farm bring about changes to both the dynamics and thermodynamics of the atmospheric boundary layers (ABL). Previously, we investigated the relative humidity budget within a wind farm via field measurements in the near‐wake region and large eddy simulations (LES). The effect of the compounding wakes within a large wind farm on the relative humidity was also investigated by LES. In this study, we investigate how the areas of relative humidity variation, that was observed in the near‐wake, develop downstream in the shadow region of a large wind farm. To this end, LES of a wind farm consisting of 8x6 wind turbines with periodic boundary condition in the lateral direction (inferring an infinitely wide farm) interacting with a stable ABL is carried out. Two wind farm layouts, aligned and staggered, are considered in the analysis and the results from both configurations are compared to each other. It is observed that a decrease of relative humidity underneath the hub height and an increase above the hub height build up within the wind farm, and are maintained in the downstream of the farm for long distances. The staggered farm layout is more effective in keeping a more elongated region of low relative humidity underneath the hub, when compared to the aligned layout.     

Large eddy simulations of the flow past wind turbines: actuator line and disk modeling

Large eddy simulations of the flow through wind turbines have been carried out using actuator disk and actuator line models for the turbine rotor aerodynamics. In this study, we compare the performance of these two models in producing wind turbine wakes. We also examine parameters that strongly affect the performance of these models, namely, grid resolution and the way in which the actuator force is projected onto the flow field. The proper choice of these two parameters has not been adequately addressed in previous works. We see that as the grid is coarsened, the predicted power decreases. As the width of the body force projection function is increased, the predicted power increases. The actuator disk and actuator line models produce similar wake profiles and predict power within 1% of one another when subject to the same uniform inflow. The actuator line model is able to generate flow structures near the blades such as root and tip vortices which the actuator disk model does not, but in the far wake, the predicted mean wakes are very similar. In order to perform validation against experimental data, the actuator line model output was compared with data from the wind tunnel experiment conducted at the Norwegian University of Science and Technology, Trondheim. Agreement between measured and predicted power, wake profiles, and turbulent kinetic energy has been observed for most tip speed ratios; larger discrepancies in power and thrust coefficient, though, have been found for tip speed ratios of 9 and 12. Copyright © 2014 John Wiley & Sons, Ltd.     

Economic feasibility of electricity generation from wind farms: A case study

Environmental problems, population growth, and the recent energy crisis have emphasized the need for zero-emission technologies while also ensuring economic feasibility. This work presents the economic advantages of using wind energy for power generation in Iran. A theoretical model is developed, which predicts the output power under various geographical and operating conditions. The wind data (speed and direction) of 2-h interval long-term period from December 2010 to October 2015 was adopted and analyzed to evaluate the levelized costs of electricity (COE) for power generation from wind farms (Arsanjan, Lamerd, and Abadeh) for the year 2018 per time. The influence of two important geographical factors namely winds speed and air humidity on output power also was studied. The results showed that the output power increases continuously when the wind speed varies from 2.0 to 2.6 m/s probably due to the compression of air passing through the wind turbine.     

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.     

Investigation of wind power density at different heights in the Gelibolu peninsula of Turkey

This study aims to determine the wind characteristics and wind power potential of the Gelibolu peninsula in the Çanakkale region of Turkey. For this purpose, hourly average wind data observed at the Gelibolu meteorological station were used. The Weibull probability density functions and Weibull parameters of time-series of wind speed, mean wind speed, and mean wind power potential were determined for different heights as 10, 20, 30, 40, and 50 m. According to the results obtained at 10- and 50-m heights above the ground level, the annual wind speed varied from 6.85 to 8.58 m/s in this region, respectively. The annual wind power potential of the site was determined as 407 and 800 W/m² for 10- and 50-m heights, respectively. These results indicate that the investigated site has a reasonable wind power potential for generating electricity.     

Application of a LES technique to characterize the wake deflection of a wind turbine in yaw

When a wind turbine works in yaw, the wake intensity and the power production of the turbine become slightly smaller and a deflection of the wake is induced. Therefore, a good understanding of this effect would allow an active control of the yaw angle of upstream turbines to steer the wake away from downstream machines, reducing its effect on them. In wind farms where interaction between turbines is significant, it is of interest to maximize the power output from the wind farm as a whole and to reduce fatigue loads on downstream turbines due to the increase of turbulence intensity in wakes. A large eddy simulation model with particular wind boundary conditions has been used recently to simulate and characterize the turbulence generated by the presence of a wind turbine and its evolution downstream the machine. The simplified turbine is placed within an environment in which relevant flow properties like wind speed profile, turbulence intensity and the anisotropy of turbulence are found to be similar to the ones of the neutral atmosphere. In this work, the model is used to characterize the wake deflection for a range of yaw angles and thrust coefficients of the turbine. The results are compared with experimental data obtained by other authors with a particle image velocimetry technique from wind tunnel experiments. Also, a comparison with simple analytical correlations is carried out. Copyright © 2009 John Wiley & Sons, Ltd.     

Statistical wind direction modeling for the analysis of large scale wind power generation

Understanding the effects of large‐scale wind power generation on the electric power system is growing in importance as the amount of installed generation increases. In addition to wind speed, the direction of the wind is important when considering wind farms, as the aggregate generation of the farm depends on the direction of the wind. This paper introduces the wrapped Gaussian vector autoregressive process for the statistical modeling of wind directions in multiple locations. The model is estimated using measured wind direction data from Finland. The presented methodology can be used to model new locations without wind direction measurements. This capability is tested with two locations that were left out of the estimation procedure. Through long‐term Monte Carlo simulations, the methodology is used to analyze two large‐scale wind power scenarios with different geographical distributions of installed generation. Wind generation data are simulated for each wind farm using wind direction and wind speed simulations and technical wind farm information. It is shown that, compared with only using wind speed data in simulations, the inclusion of simulated wind directions enables a more detailed analysis of the aggregate wind generation probability distribution. Copyright © 2016 John Wiley & Sons, Ltd.     

Statistical post‐processing of turbulence‐resolving weather forecasts for offshore wind power forecasting

Accurate short‐term power forecasts are crucial for the reliable and efficient integration of wind energy in power systems and electricity markets. Typically, forecasts for hours to days ahead are based on the output of numerical weather prediction models, and with the advance of computing power, the spatial and temporal resolutions of these models have increased substantially. However, high‐resolution forecasts often exhibit spatial and/or temporal displacement errors, and when regarding typical average performance metrics, they often perform worse than smoother forecasts from lower‐resolution models. Recent computational advances have enabled the use of large‐eddy simulations (LESs) in the context of operational weather forecasting, yielding turbulence‐resolving weather forecasts with a spatial resolution of 100 m or finer and a temporal resolution of 30 seconds or less. This paper is a proof‐of‐concept study on the prospect of leveraging these ultra high‐resolution weather models for operational forecasting at Horns Rev I in Denmark. It is shown that temporal smoothing of the forecasts clearly improves their skill, even for the benchmark resolution forecast, although potentially valuable high‐frequency information is lost. Therefore, a statistical post‐processing approach is explored on the basis of smoothing and feature engineering from the high‐frequency signal. The results indicate that for wind farm forecasting, using information content from both the standard and LES resolution models improves the forecast accuracy, especially with a feature selection stage, compared with using the information content solely from either source.     

Field-data-based reliability analysis of power converters in wind turbines: Assessing the effect of explanatory variables

Frequent failures of power converters affect the availability of wind turbines and cause considerable maintenance costs. To enhance the reliability of power converters in wind turbines, the prevailing causes and modes of failures have to be identified. This publication contributes to root-cause analysis of the power-converter failures in wind turbines from a statistical point of view. For this purpose, the failure behavior of power-converters is modeled via lifetime models as well as repairable-system models. By means of regression models, covariates are incorporated, including both design-related and site-specific covariates. The analysis is based on a worldwide extensive field-data collection covering more than 9000 turbines, including different turbine designs, sites, and ages. The results obtained by means of the applied regression models indicate that the location of the power converter within the turbine, the cooling system, the converter rated power, the DC-link voltage, the IGBT-module manufacturer, and the commissioning date of the turbine as design-related covariates have a significant effect on the phase-module failure behavior and with that on converter reliability. Among the site-specific covariates, the analysis results confirm humidity as a likely significant driver of failures.     

风电与燃气轮机互补系统发电成本敏感性分析

详细讨论了大型风电场与燃气轮机组成的互补发电系统发电成本的主要影响因子及其对系统的敏感性。通过对互补发电系统发电成本理论公式的研究,推导了互补系统中各项影响因子相对于发电成本的数学方程和影响尺度,得到了影响发电成本几个关键的影响因子。通过采用敏感性分析原理,对这些主要的影响因子在不同变化条件下对互补发电系统发电成本的影响进行了详细的分析与讨论,提出降低系统发电成本的可行性措施及其努力的方向,为在新疆地区实现这种互补发电系统提供经济分析上的基础。