Optimization of turbine design in wind farms with multiple hub heights,using exact analytic gradients and structural constraints

Wind farms are generally designed with turbines of all the same hub height. If wind farms were designed with turbines of different hub heights, wake interference between turbines could be reduced, lowering the cost of energy (COE). This paper demonstrates a method to optimize onshore wind farms with two different hub heights using exact, analytic gradients. Gradient‐based optimization with exact gradients scales well with large problems and is preferable in this application over gradient‐free methods. Our model consisted of the following: a version of the FLOw Redirection and Induction in Steady‐State wake model that accommodated three‐dimensional wakes and calculated annual energy production, a wind farm cost model, and a tower structural model, which provided constraints during optimization. Structural constraints were important to keep tower heights realistic and account for additional mass required from taller towers and higher wind speeds. We optimized several wind farms with tower height, diameter, and shell thickness as coupled design variables. Our results indicate that wind farms with small rotors, low wind shear, and closely spaced turbines can benefit from having two different hub heights. A nine‐by‐nine grid wind farm with 70‐meter rotor diameters and a wind shear exponent of 0.08 realized a 4.9% reduction in COE by using two different tower sizes. If the turbine spacing was reduced to 3 diameters, the reduction in COE decreased further to 11.2%. Allowing for more than two different turbine heights is only slightly more beneficial than two heights and is likely not worth the added complexity.     

Investigation of wind shear coefficients and their effect on electrical energy generation

Wind measurements are generally performed below wind turbine hub heights due to higher measurement and tower costs. In order to obtain the wind speed at the hub height of the turbine, the measurements are extrapolated, assuming that the wind shear is constant. This assumption may result in some critical errors between the estimated and actual energy outputs. In this paper wind data collected in Bal?kesir from October 2008 to September 2009, has been used to show the effects of wind shear coefficient on energy production. Results of the study showed that, the difference between wind energy production using extrapolated wind data and energy production using measured wind data at hub height may be up to 49.6%.     

A tall tower study of Missouri winds

This paper summarizes the results of a study of wind speeds observed at heights up to 150 m above ground level around Missouri. This is an amalgamation of four projects that allowed a total of eleven tall communication towers to be instrumented with wind observation equipment across the State of Missouri. This provided an assessment of the wind resource and the characteristics of the seasonal and diurnal cycles of wind in different areas of Missouri at the heights of utility scale wind turbines. Comparisons were also made to wind speeds predicted at these levels from a previously published wind map.The main finding was that the observed winds at each tower were smaller than those presented in the wind map. The discrepancy is most likely to be due to underestimation of the surface roughness and turbulence leading to an overestimation of near-surface wind shear. However, the wind shear, as expressed by the shear parameter was consistently greater than the ‘standard’ value of 1.4. The reconciliation of these two apparently contradictory findings is that the shear varies with the height at which it is measured. In wind resource assessment, wind shear is usually observed below 50 m and is tacitly assumed to be constant with height when used to extrapolate winds to higher levels. The author advocates the use of the friction velocity as a measure of shear in wind power applications in preference to the shear parameter that is usually used. This is because the shear parameter has a velocity bias that can also manifest as a bias with height or season. As wind power resource assessment is starting to use taller towers than the standard 50 m, intercomparison of site resources and extrapolation to turbine heights can be compromised if the shear parameter is used.     

Do we really need rotor equivalent wind speed?

The use of the rotor equivalent wind speed for determination of power curves and annual energy production for wind turbines is advocated in the second edition of the IEC 61400‐12‐1 standard. This requires the measurements of wind speeds at different heights, for which remote sensing equipment is recommended in addition to meteorological masts. In this paper, we present a theoretical analysis that shows that the relevance of the rotor equivalent wind speed method depends on turbine dimensions and wind shear regime. For situations where the ratio of rotor diameter and hub height is smaller than 1.8, the rotor equivalent wind speed method is not needed if the wind shear coefficient at the location of the wind turbine has a constant value between ?0.05 and 0.4: in these cases, the rotor equivalent wind speed and the wind speed at hub height are within 1%. For complex terrains with high wind shear deviations are larger. The effect of non‐constant wind shear exponent, ie, different wind shear coefficients for lower and upper half of the rotor swept area especially at offshore conditions is limited to also about 1%.     

Extrapolating wind speed time series vs. Weibull distribution to assess wind resource to the turbine hub height: A case study on coastal location in Southern Italy

Increasing knowledge on wind shear models to strengthen their reliability appears as a crucial issue, markedly for energy investors to accurately predict the average wind speed at different turbine hub heights, and thus the expected wind energy output. This is particularly helpful during the feasibility study to abate the costs of a wind power project, thus avoiding installation of tall towers, or even more expensive devices such as LIDAR or SODAR.The power law (PL) was found to provide the finest representation of wind speed profiles and is hence the focus of the present study. Besides commonly used for vertical extrapolation of wind speed time series, the PL relationship between “instantaneous” wind profiles was demonstrated by Justus and Mikhail to be consistent with the height variation of Weibull distribution. Therefore, in this work a comparison is performed between these two different PL–based extrapolation approaches to assess wind resource to the turbine hub height: (i) extrapolation of wind speed time series, and (ii) extrapolation of Weibull wind speed distribution. The models developed by Smedman–Högström and Högström (SH), and Panofsky and Dutton (PD) were used to approach (i), while those from Justus and Mikhail (JM) and Spera and Richards (SR) to approach (ii). Models skill in estimating wind shear coefficient was also assessed and compared.PL extrapolation models have been tested over a flat and rough location in Apulia region (Southern Italy), where the role played by atmospheric stability and surface roughness, along with their variability with time and wind characteristics, has been also investigated. A 3-year (1998–2000) 1–h dataset, including wind measurements at 10 and 50 m, has been used. Based on 10–m wind speed observations, the computation of 50–m extrapolated wind resource, Weibull distribution and energy yield has been made. This work is aimed at proceeding the research issue addressed within a previous study, where PL extrapolation models were tested and compared in extrapolating wind resource and energy yield from 10 to 100 m over a complex–topography and smooth coastal site in Tuscany region (Central Italy). As a result, wind speed time series extrapolating models proved to be the most skilful, particularly PD, based on the similarity theory and thus addressing all stability conditions. However, comparable results are returned by the empirical JM Weibull distribution extrapolating model, which indeed proved to be preferable as being: (i) far easier to be used, as z₀–, stability–, and wind speed time series independent; (ii) more conservative, as wind energy is underpredicted rather than overpredicted.     

The round robin site assessment method: A new approach to wind energy site assessment

Portability is one of the many potential advantages of utilizing ground-based measurement devices such as SODARs and LIDARs instead of meteorological towers for wind resource assessment. This paper investigates the use of a monitoring strategy that leverages the portability of ground-based devices, dubbed the “round robin site assessment method.” The premise is to measure the wind resource at multiple sites in a single year using a single portable device, but to discontinuously distribute the measurement time at each site over the whole year, so that the total measurement period comprises smaller segments of measured data. This measured data set is then utilized in the measure-correlate-predict (MCP) process to predict the long-term wind resource at the site. This method aims to increase the number of sites assessed in a single year, without the sacrifice in accuracy and precision that usually accompanies shorter measurement periods. The performance of the round robin site assessment method was compared to the standard method, in which the measured data are continuous. The results demonstrate that the round robin site assessment method is an effective monitoring strategy that improves the accuracy and reduces the uncertainty of MCP predictions for measurement periods less than 1 year. In fact, the round robin site assessment method compares favorably to the accuracy and uncertainty of a full year of resource assessment. While there are some tradeoffs to be made by using the round robin site assessment method, it is potentially a very useful strategy for wind resource assessment.     

The influence of the wind speed profile on wind turbine performance measurements

To identify the influence of wind shear and turbulence on wind turbine performance, flat terrain wind profiles are analysed up to a height of 160 m. The profiles' shapes are found to extend from no shear to high wind shear, and on many occasions, local maxima within the profiles are also observed. Assuming a certain turbine hub height, the profiles with hub‐height wind speeds between 6 m s^?1 and 8 m s^?1 are normalized at 7 m s^?1 and grouped to a number of mean shear profiles. The energy in the profiles varies considerably for the same hub‐height wind speed. These profiles are then used as input to a Blade Element Momentum model that simulates the Siemens 3.6 MW wind turbine. The analysis is carried out as time series simulations where the electrical power is the primary characterization parameter. The results of the simulations indicate that wind speed measurements at different heights over the swept rotor area would allow the determination of the electrical power as a function of an ‘equivalent wind speed’ where wind shear and turbulence intensity are taken into account. Electrical power is found to correlate significantly better to the equivalent wind speed than to the single point hub‐height wind speed. Copyright © 2008 John Wiley & Sons, Ltd.     

LiDAR measurements for an onshore wind farm: Wake variability for different incoming wind speeds and atmospheric stability regimes

Wind measurements were performed with the UTD mobile LiDAR station for an onshore wind farm located in Texas with the aim of characterizing evolution of wind‐turbine wakes for different hub‐height wind speeds and regimes of the static atmospheric stability. The wind velocity field was measured by means of a scanning Doppler wind LiDAR, while atmospheric boundary layer and turbine parameters were monitored through a met‐tower and SCADA, respectively. The wake measurements are clustered and their ensemble statistics retrieved as functions of the hub‐height wind speed and the atmospheric stability regime, which is characterized either with the Bulk Richardson number or wind turbulence intensity at hub height. The cluster analysis of the LiDAR measurements has singled out that the turbine thrust coefficient is the main parameter driving the variability of the velocity deficit in the near wake. In contrast, atmospheric stability has negligible influence on the near‐wake velocity field, while it affects noticeably the far‐wake evolution and recovery. A secondary effect on wake‐recovery rate is observed as a function of the rotor thrust coefficient. For higher thrust coefficients, the enhanced wake‐generated turbulence fosters wake recovery. A semi‐empirical model is formulated to predict the maximum wake velocity deficit as a function of the downstream distance using the rotor thrust coefficient and the incoming turbulence intensity at hub height as input. The cluster analysis of the LiDAR measurements and the ensemble statistics calculated through the Barnes scheme have enabled to generate a valuable dataset for development and assessment of wind farm models.     

Upwind preview to a horizontal axis wind turbine: a wind tunnel and field‐scale study

Data collected at the Eolos wind research facility and in the Saint Anthony Falls Laboratory atmospheric boundary layer wind tunnel are used to study the impact of turbulent inflow conditions on the performance of a horizontal axis wind turbine on flat terrain. The Eolos test facility comprises a 2.5MW Clipper Liberty C96 wind turbine, a meteorological tower and a WindCube LiDAR wind profiler. A second set of experiments was completed using particle image velocimetry upwind and in a wake of a miniature turbine in the wind tunnel to complement LiDAR measurements near the Eolos turbine. Joint statistics, most notably temporal cross‐correlations between wind velocity at different heights and turbine performance, are presented and compared at both the laboratory and field scales. The work (i) confirms that the turbine exerts a blockage effect on the mean flow and (ii) suggests a key, specific elevation, above hub height, where the incoming velocity signal is statistically most relevant to turbine operation and control. Wind tunnel measurements confirm such indication and suggest that hub height velocity measurements are optimal for wind preview and/or as input for active control strategies in aligned turbine configurations. Copyright © 2015 John Wiley & Sons, Ltd.     

A spinner‐integrated wind lidar for enhanced wind turbine control

A field test with a continuous wave wind lidar (ZephIR) installed in the rotating spinner of a wind turbine for unimpeded preview measurements of the upwind approaching wind conditions is described. The experimental setup with the wind lidar on the tip of the rotating spinner of a large 80 m rotor diameter, 59 m hub height 2.3 MW wind turbine (Vestas NM80), located at Tjæreborg Enge in western Denmark is presented. Preview wind data at two selected upwind measurement distances, acquired during two measurement periods of different wind speed and atmospheric stability conditions, are analyzed. The lidar‐measured speed, shear and direction of the wind field previewed in front of the turbine are compared with reference measurements from an adjacent met mast and also with the speed and direction measurements on top of the nacelle behind the rotor plane used by the wind turbine itself. Yaw alignment of the wind turbine based on the spinner lidar measurements is compared with wind direction measurements from both the nearby reference met mast and the turbine's own yaw alignment wind vane. Furthermore, the ability to detect vertical wind shear and vertical direction veer in the inflow, through the analysis of the spinner lidar data, is investigated. Finally, the potential for enhancing turbine control and performance based on wind lidar preview measurements in combination with feed‐forward enabled turbine controllers is discussed. Copyright © 2012 John Wiley & Sons, Ltd.     

Convertible wind energy based on predicted wind speed at hub-height

Support vector machine is proposed to find wind speed at higher heights using measurements at lower heights. The mean absolute percentage error between measured and the estimated wind speed at height 40 m is found to be satisfactory. After validation at 40 m, the model was used to calculate the wind speed at hub heights up to 100 m. Annual energy yield was found to be increasing with hub height and, hence, accurate estimation of wind speed at heights becomes essential for realistic wind energy assessment. Furthermore, the plant capacity factor was found to be increasing approximately 1% for each 10-m increase in hub height.     

Wind energy analysis based on turbine and developed site power curves: A case-study of Darling City

The observed wind at a given site varies continuously as a function of time and season, increasing hub heights, topography of the terrain, prevailing weather condition etc. The quality of wind resource is one of the important site factors to be considered when assessing the wind potential of any location for any energy project. In this study, two wind energy analysis techniques are presented: the use of direct technique where the electrical power outputs of the wind turbines at a time t are estimated using the turbine power curve(s) and the use of statistical-based technique where the power outputs are estimated based on the developed site power curve(s). The wind resource assessment at Darling site is conducted using a 5-min time series weather data collected on a 10 m height over a period of 24 months. Because of the non-linearity of the site's wind speed and its corresponding power output, the wind resources are modeled and the developed site power curve(s) are used to estimate the long term energy outputs of the wind turbines for changing weather conditions. Three wind turbines rating of 1.3 MW, 1.3 MW and 1.0 MW were selected for the energy generation based on the gauged wind resource(s) at 50, 60 and 70 m heights, respectively. The energy outputs at 50 m height using the 1.3 MW WT were compared to the energy outputs at 60 m to determine the standard height for utility scale energy generation at this site. An additional energy generation of 190.71 MWh was available by deploying the same rated turbine at a 60 m height. Furthermore, comparisons were made between the use of turbine and site power curve for wind energy analysis at the considered heights. The results show that the analysis of the energy outputs of the WTs based on the site power curve is an accurate technique for wind energy analysis as compared to the turbine power curve. Conclusions are drawn on the suitability of this site for utility scale generation based on the wind resources evaluation at different heights.     

Optimum turbine-site matching

This paper presents a new formulation for the turbine-site matching problem, based on wind speed characteristics at any site, the power performance curve parameters of any pitch-regulated wind turbine, as well as turbine size and tower height. Wind speed at any site is characterized by the 2-parameter Weibull distribution function and the value of ground friction coefficient (α). The power performance curve is characterized by the cut-in, rated, and cut-out speeds and the rated power. The new Turbine-Site Matching Index (TSMI) is derived based on a generic formulation for Capacity Factor (CF), which includes the effect of turbine tower height (h). Using the CF as a basis for turbine-site matching produces results that are biased towards higher towers with no considerations for the associated costs. The proposed TSMI includes the effects of turbine size and tower height on the Initial Capital Cost (ICC) of wind turbines. The effectiveness and the applicability of the proposed TSMI are illustrated using five case studies. In general, for each turbine, there exists an optimal tower height, at which the value of the TSMI is at its maximum. The results reveal that higher tower heights are not always desirable for optimality.     

Impact of low‐level wind maxima below hub height on wind turbine sound propagation

An analysis of the effect of low‐level wind maxima (LLWM) below hub height on sound propagating from wind turbines has been performed at a site in northern Sweden. The stably stratified boundary layer, which is typical for cold climates, commonly features LLWM. The simplified concept for the effects of refraction, based on the logarithmic wind profile or other approaches where the wind speed is continuously increasing with height, is often not applicable there. Long‐term meteorological measurements in the vicinity of a wind farm were therefore used to identify LLWM. Sound measurements were conducted simultaneously to the meteorological measurements. LLWM below hub height decrease the sound level close to the surface downwind of the wind farm. This effect increases with increasing strength of the LLWM. The occurrence of LLWM as well as strength and height of the LLWM are dependent on the wind direction.     

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.     

Redefinition power curve for more accurate performance assessment of wind farms

The lack of accurate methods for assessment of the productive capacity of wind power plants is becoming a bottleneck in an increasingly commercialized wind power industry. In this article the inherent components of performance assessment are identified and analysed and ways of minimizing uncertainties on the components are investigated. The main components are identified as ‘site calibration’, ‘wind turbine sensitivity to flow variables’, ‘plant blockage effects’ and ‘uncertainty analysis’. Site calibration is the action of estimating the flow variables at the wind turbine position from measurements of these quantities at another (reference) position. The purpose of sensitivity analysis is to clarify which and how flow variables influence power output. Plant blockage effects refer to the power plant's influence on the reference measurements of flow variables. Finally, the component uncertainties and in turn the integrated uncertainty on the average productive capacity of the wind power plant are investigated. It is found that uncertainties can be reduced (1) by including several more flow variables in addition to hub‐height wind speed, (2) by carrying out site calibration with utmost care and by inclusion of more variables, (3) by taking plant blockage into consideration, (4) by aiming at ‘plant‐average’ power instead of looking only at individual machines and, possibly, (5) by introduction of remote‐sensing anemometer techniques. Copyright © 2000 John Wiley & Sons, Ltd.     

Coherent Doppler lidar for wind farm characterization

Coherent Doppler lidar measurements are of increasing interest for the wind energy industry. Wind measurements are fundamental inputs for the evaluation of potential energy yield and performance of wind farms. Three‐dimensional scanning Doppler lidar may provide a new basis for wind farm site selection, design and optimization. In this paper, the authors discuss Doppler lidar measurements obtained for a wind energy development. The possibility of using lidar measurements to more fully characterize the wind field is discussed, specifically terrain effects, spatial variation of winds, power density and the effect of shear at different layers within the rotor swept area. Vector retrieval methods have been applied to the lidar data, and results are presented on an elevated terrain‐following surface at hub height. The vector retrieval estimates are compared with tower measurements, after interpolation to the appropriate level. Doppler lidar data are used to estimate the spatial power density at hub height (for the period of the deployment). An example wind farm layout is presented for demonstration purposes based purely on lidar measurement, even though the lidar data acquisition period cannot be considered climatological. The strength of this approach is the ability to directly measure spatial variations of the wind field over the wind farm. Also, because Doppler lidar can measure winds at different vertical levels, an approach for estimating wind power density over the rotor swept area (rather than only the hub height) is explored. Finally, advanced vector retrieval algorithms have been applied to better characterize local wind variations and shear. Copyright © 2012 John Wiley & Sons, Ltd.     

Properties of the offshore low level jet and rotor layer wind shear as measured by scanning Doppler Lidar

The atmospheric flow phenomenon known as the Low Level Jet (LLJ) is an important source of wind power production in the Great Plains. However, due to the lack of measurements with the precision and vertical resolution needed, particularly at rotor heights, it is not well‐characterized or understood in offshore regions being considered for wind‐farm development. The present paper describes the properties of LLJs and wind shear through the rotor layer of a hypothetical wind turbine, as measured from a ship‐borne Doppler lidar in the Gulf of Maine in July–August 2004. LLJs, frequently observed below 600 m, were mostly during nighttime and transitional periods, but they were also were seen during some daytime hours. The presence of a LLJ significantly modified wind profiles producing vertical wind speed shear. When the wind shear was strong, the estimates of wind power based upon wind speeds measured at hub‐height could have significant errors. Additionally, the inference of hub‐height winds from near‐surface measurements may introduce further error in the wind power estimate. The lidar dataset was used to investigate the uncertainty of the simplified power‐law relation that is often employed in engineering approaches for the extrapolation of surface winds to higher elevations. The results show diurnal and spatial variations of the shear exponent empirically found from surface and hub‐height measurements. Finally, the discrepancies between wind power estimates using lidar‐measured hub‐height winds and rotor equivalent winds are discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

测风塔选址对复杂地形风电场风资源评估的影响

为研究复杂地形条件下风电场测风塔的代表性及其对风资源评估的影响,以陕西省靖边县境内某风电场为例,选取3座测风塔资料,利用WindSim软件模拟分析了2011年风电场风能资源分布,并估算了风电场年发电量。结果表明,复杂地形风电场处测风塔数量较少时风资源评估结果的不确定性显著增加,而在考虑地形因素情况下测风塔数量增多,估算发电量更为准确。在地形较为复杂的风电场应根据地形条件布设适当数量测风塔,以得到风电场内较为精准的风资源分布,减少因测风塔位置选择而造成的风资源评估的不确定性。     

Investigating the possibility of using different hub height wind turbines in a wind farm

Many researchers have focused on the layout design of a wind farm using the computational methods. Most of previous researches focused on relevant large cell size and using same hub height wind turbines. In this paper, the authors investigate the possibility of using different hub height wind turbines in a wind farm. A limited area (2?km?×?2?km) with constant wind speed and direction is considered as the potential wind farm area, and a nested genetic algorithm is used as optimisation algorithm. Two different hub height wind turbines are introduced with two different cell sizes. Power output, cost, payback period, and total profit are selected as evaluation criteria when comparing the layouts with same hub height wind turbines with the layouts with different hub height wind turbines. The results demonstrate that it is feasible and possible to use different hub height wind turbines in a wind farm.