Abstract

Wind power generation is growing fast as one of the most promising renewable energy sources that can serve as an alternative to fossil fuel-generated electricity. When the wind turbine generator (WTG) extracts power from the wind, the wake evolves and leads to a considerable reduction in the efficiency of the actual power generation. Furthermore, the wake effect can lead to the increase of turbulence induced fatigue loads that reduce the life time of WTGs. In this work, a pulsed coherent Doppler lidar (PCDL) has been developed and deployed to visualize wind turbine wakes and to characterize the geometry and dynamics of wakes. As compared with the commercial off-the-shelf coherent lidars, the PCDL in this work has higher updating rate of 4 Hz and variable physical spatial resolution from 15 to 60 m, which improves its capability to observation the instantaneous turbulent wind field. The wind speed estimation method from the arc scan technique was evaluated in comparison with wind mast measurements. Field experiments were performed to study the turbulent wind field in the vicinity of operating WTGs in the onshore and offshore wind parks from 2013 to 2015. Techniques based on a single and a dual Doppler lidar were employed for elucidating main features of turbine wakes, including wind velocity deficit, wake dimension, velocity profile, 2D wind vector with resolution of 10 m, turbulence dissipation rate and turbulence intensity under different conditions of surface roughness. The paper shows that the PCDL is a practical tool for wind energy research and will provide a significant basis for wind farm site selection, design and optimization.

© 2016 Optical Society of America

1. Introduction

Wind power generation is rapidly growing as one of the most promising renewable energy sources. When the turbine extracts power from the wind, the vortex evolves and moves downwind to form the turbine wake. The power output of the whole wind farm operating inside the turbulent wake will be decreased as compared to the turbines operating in the free wind. For a wind park, it is desirable to place the wind turbines as close together as possible to maximize power generation. However, if wind turbines are too closely spaced, wake interference effects could lead to a considerable reduction in the efficiency of the gross actual power generation. According to the study by Frandsen et al. [1], with spacing between the turbines of 4-8 D (D is the Diameter of turbine scanning plane), power dissipation due to wind turbine wakes can be 5%–15%. Spacing of turbines beyond 8-10 D is unlikely due to the high cost of installing cables. Furthermore, the wake effect can lead to the increase of turbulence induced stress and reduce the life time of wind turbines and their components. Precise evaluation of turbulent wake effects is indispensable for optimizing the turbine arrangement and power output in a wind farm [2].

Turbulent wake characteristics of wind turbines have been studied since 1980s. Current industry standard for wind turbine wake measurements is the use of an in situ meteorological mast with wind cup and vane anemometers on it [3], but high cost and complexity often hinders building such a must system. Because of the global growth of wind energy industry, techniques such as ultrasonic anemometer, profilers and SODAR (Sonic Detection and Ranging) are increasingly being used to measure wind wake [4]. The measurement range is dependent on relative air humidity, and their sensitivity is typically lower than that of a lidar, leading to much reduced data rates.

As compared with the techniques mentioned above, the coherent Doppler Lidar (Light Detection and Ranging), CDL, has enabled high spatial and temporal resolution measurements of wind fields [5]. Krishnamurthy et al. presented the utilization of a commercial WindTracer lidar, manufactured by Lockheed Martin, to calculate spatially varying wind power density distribution in an ongoing wind assessment study [6]. A CDL isan optical remote sensing system that transmits a laser beam into the atmosphere and the backscattered signal is detected. The1.5-μm wavelength all-fiber pulsed CDL with high resolution takes advantage of the fact that the frequency of the echo signal is shifted from the local-oscillator light because of the Doppler effect which occurs from backscattering of aerosols [7]. The Doppler shift in the frequency of the backscattered signal is analyzed to obtain the line-of-sight (LOS) velocity component of the air motion. From the LOS velocities the characteristics of the turbulent wake can be retrieved. The research of wind turbine wake detected by a continuous-wave (CW) CDL was done by Bingöl et al. [8] and Trujillo et al. [9]. A CW CDL system of QinetiQ was put into turbine control study to examine the requirements for a lidar system at Postlow in 2005 [10]. Kasler et. al. modified a 2 μm pulsed coherent Doppler lidar, WindTracer transceiver unit, with the data range resolution of 154 m and the laser pulse length of approximately 400 m, and applied it to calculate the velocity deficit of the WTGs wake [11]. Jungo et. al. used scanning lidars to analyze the velocity components over the vertical symmetry plane of the wind turbine wake with the relatively high spatial resolution of 18 m and the maximum sampling frequency of 0.77 Hz [12]. A high peak power coherent Doppler lidar, the VALIDAR from NASA, was applied for offshore wind energy applications [13]. Banta et al. studied the 3D structure of turbine wake using 3D volume scan patterns by a 2-μm wavelength high peak power laser system with effective measurement updating rate of 2 Hz and pulse duration of 30 m [14], which was a part of a field campaign generally reported by Smalikho et al. [2].

This paper is a substantially extended study of the selected conference presentations at OSA’s Light, Energy and the Environment Congress recently held in Suzhou, China [15]. The objective of this paper is to use a pulsed CDL (PCDL) with relatively high spatial resolution and sampling rate to visualize the WTGs wakes and to characterize the geometry and dynamics of wakes. The pulsed Doppler lidar specifications are described in section 2. Section 3 presents the retrieval methods of wind from arc scan techniques and the evaluation of lidar measurement uncertainties compared to the wind mast measurements. Field experiments to visualize and characterize WTG wakes are described in section 4, including the actual implementation of the Doppler lidar method and data processing. A brief conclusion is given in section 5.

2. Pulsed coherent Doppler wind lidar

Lidar is one of the most accurate optical remote sensing techniques that transmit a laser beam into the atmosphere and the backscattered signal is detected. The 1.5-μm wavelength all-fiber PCDL with high resolution takes advantage of the fact that the frequency of the echo signal is shifted from the local-oscillator light because of the Doppler effect which occurs from backscattering of aerosols. The Doppler shift in the frequency of the backscattered signal is analyzed to obtain the radial velocity or LOS velocity along the lidar beam direction. From the LOS velocities the characteristic of the turbulent wake can be deduced.

The PCDL is based on the heterodyne technique, consisting of a single frequency seed laser source, an acousto-optic modulator (AOM), an Erbium doped fiber amplifier (EDFA), optical isolators (ISO) and amplified spontaneous emission noise filters, an optical switch, a transceiver telescope, a balanced detector and an analog-to-digital converter (A\D) and a Fast Fourier Transform (FFT) signal processor as shown in Fig. 1. The specifications of the PCDL are listed in Table 1. The seed laser has a linewidth (FWHM from Lorentzian) of 1.6 kHz. The pulsed 1550 nm fiber laser source is based on the MOPA architecture with a large core fiber. Achieved pulsed energy is approximately 150 µJ with a pulse repetition frequency of 10 kHz. The spatial resolution can be varied in a range of 15 - 60 m by changing the gate pulse width of the AOM in a range of 100 - 400 ns. The shift frequency of the AOM is 80 MHz that is the intermediate frequency of the heterodyne signal. The real-time analysis based on FFT is carried out with a Field Programmable Gate Array (FPGA). The detection range of 4000 m (maximum 6000 m at a proper aerosol concentration) enables the system to monitor the wind field and multiple wakes interactions in a wind park. In order to capture turbine wakes, different scan strategies are used to scan horizontal or vertical sections back and forth to track the wake.

 

Fig. 1 The pulsed coherent Doppler Lidar setup.

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Tables Icon

Table 1. Component Parameters of the CDL System

The highlights of the lidar include the flexible range resolution from 15 to 60 m and relatively high sampling rate. The finest resolution of 15 m is useful for the detection of small scale wakes. The duration of measurement of one LOS velocity (FFT spectrum) equaled 0.25 s, which increases the temporal sampling rate up to 4 Hz and therefore reduces uncertainty in an averaged wind measurement.

3. Retrieval method, data quality control and uncertainty evaluation using wind mast

The Doppler wind lidar can only detect the velocity component along the laser beam. Therefore, to retrieve the wind velocity vector (ie. wind speed and direction) from a scanning lidar data, it is necessary to conduct measurement at three or more different directions of the probing beam. In the validation test and the subsequent turbine wake observation, it was proposed to change the azimuth angle of the probing beam at the fixed elevation angle. This scanning geometry is known as the Velocity-Azimuth-Display technology (VAD) [16] and the Plane-Position Indicator (PPI), the measurement procedures of which has been presented using a direct detect Doppler wind lidar, developed by lidar group of the Ocean University of China, Qingdao, for wind profile and the sea surface wind measurements [17–20].

In the case of statistically homogeneous wind field at certain altitude and in a limited region, the mean value of the LOS velocity has a sine wave dependence on the azimuth angle. In order to estimate the wind velocity vector from the VAD scanning measurement, a sine wave fitting method is applied to the LOS velocity on the azimuth angle based on the least-squares techniques. Due to the inhomogeneous wind by turbulence and the low SNR induced error, the obtained dependence of the lidar estimate of the radial velocity on the azimuth angle differs from the sine wave one. A full circular radial velocity scan at the same height enables the retrieval of wind speed and direction by the sine wave fitting. Another modified form of VAD technique is the arc scan (i.e. sector scan), in which lidars scan its laser beam over a small sector of azimuth angle at the fixed elevation angle. In comparison with a full 360° azimuthal scan, the constraints of horizontally homogeneous wind field can be made less strict with arc scans. By utilizing the VAD fitting technology, wind speed and direction can be retrieved from an arc scan as shown in Fig. 2.

 

Fig. 2 The LOS velocity estimation by an arc scanning lidar and sine wave fitting.

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According to the very different scales of unperturbed free streams and turbulent wakes, we use combined retrieval methods that is a VAD method with quality control and the Dual-Doppler-Lidar method, to retrieve the wind vector in a turbulent wind field in the vicinity of operating wind turbines. To avoid turbulence introduce errors in the process of least squares fitting in VAD technique, two quality control methodologies are taken into account, including a SNR threshold filter and a vertical velocity threshold screening. Before performing the sine wave fitting to obtain the wind vector, the SNR threshold filter eliminates the LOS velocities from a group of LOS velocities measured in one scan with an SNR threshold of less than 40. Several wind vectors calculated from corresponding scans performed in 10 minutes are averaged to generate a 10-min wind vector. Then the vertical velocity threshold screening is used to filter out the 10-min wind vector if the simultaneous mean vertical velocity is larger than 3 ms−1. The advantage of VAD technique is that it is not sensitive to small scale turbulence along the azimuth, which is used to retrieve the background wind (i.e. free stream) in a wind park. On the contrary, the Dual-Doppler-Lidar method is able to retrieve wind speed consisting of small scale turbulence in the local detection volume. A case study of wind field retrieval using this method is introduced in section 4.

The PCDL’s performance was evaluated with the purpose of quantitative analysis for wind turbine wake. This was done by performing an ordinary least squares linear regression of the concurrent scanning wind lidar and wind mast speed and checking whether the values for the slope, offset and correlation coefficient are within the acceptable limits.

The evaluation tests were undertaken at SgurrEnergy’s test facility in Glasgow, Scotland referred to as Carrot Moor Test Facility. The test facility consists of an 80 m meteorological mast located in moderately complex terrain with associated test beds for the deployment of remote sensing systems. Wind measurements were performed with two PCDLs, produced by Seaglet Environmental Technology, including a wind profiler lidar WindPrint V300 and a scanning 3D wind lidar WindPrint S4000. The latter was deployed for the subsequent 2D turbine wake measurements introduced in section 4. The Vector A100L2 anemometry and Vector W200P wind vane at height of 80 m and 78 m, respectively, on the meteorological mast are calibrated systems with configuration and instrumentation traceable to international standards for wind measurement, IEC 61400-12-1 guidelines (International Electrotechnical Commission, 2014).

The pulsed coherent Doppler lidar and wind mast observation results are compared at the height of 80 m to evaluate whether accord with the standard. In the experiment carried out for 40 days from May 31, 2015 to July 9, 2015, the results of PCDL measurement at the height of 80 m were compared with those of the wind mast assumed as a standard. The Scanning lidar was placed at a distance of 270 m from the mast and ran in a an arc scan mode conducting a scan at an elevation of 20.8° to coincide with the measurement volumes around the 80 m anemometry. Each arc consisted of seven points over an azimuth range of 59° to 119° to allow accurate measurements when the wind was in the crosswind orientation. Figure 3 shows the measured wind speed and wind direction by scanning wind lidar and mast (in red and blue lines, respectively).

 

Fig. 3 Comparison of wind speed (a) and wind direction (b) measured by scanning wind lidar and mast.

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Figure 4 shows a linear correlation comparing ten-minute averaged wind speed and wind direction data from both the scanning wind lidar and the mast at 80 m represented by the scatter plot. The trend line plotted through these points represents an ordinary linear least square regression. The two equations presented are for each fit, the first a free fit with a recorded offset and the second a constrained fit with the fit forced to pass through the origin. The wind speed linear regression shows the correlation coefficient of 0.995 (the coefficient of determination of 0.99019) and standard deviation of 0.54 ms−1. The wind direction linear regression shows the correlation coefficient of 0.9989 (the coefficient of determination of 0.99789) and standard deviation of 5.19°.

 

Fig. 4 Horizontal wind speed correlation (a) and wind direction correlation (b) at 80m for ten-minute data measured by 3D wind lidar and anemometer.

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The data were then binned and a regression performed in the same manner as above with the results displayed in Fig. 5. The wind speed data is binned by the lidar and the mast wind speed in to bins 0.5 ms−1 wide centered on multiple integers of 0.5 ms−1. The wind direction data is binned with bins 5° wide centered on multiple integers of 5°. The bin averaged wind speed linear regression shows the correlation coefficient of 0.9996 (the coefficient of determination of 0.99952) and standard deviation of 0.16 ms−1. The wind direction linear regression shows the correlation coefficient of 0.9999 (the coefficient of determination of 0.99988) and standard deviation of 4.16°. Linear regressions show that the scanning wind lidar is operating within acceptable limits.

 

Fig. 5 Horizontal wind speed correlation (a) and wind direction correlation (b) at 80m for Bin Averaged Data.

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4. Field campaigns to characterize the wind turbine wake

As introduced above, when the wind turbine generator extracts power from the wind, a trailing vortex evolves and moves downwind to form the turbine wake corridor with the central axis at the height of the hub. Along with its forwarding, wake also has an axisymmetric expansion, which increases the radius of it. The power output of the whole wind farm operating within the turbulent wake will be decreased comparing with the turbines operating in the free stream. In order to understand the wake characteristics in a real ambient, we performed field experiments with different topographies and surface roughness to study the turbulent wind field in the vicinity of operating WTGs in the onshore and offshore wind parks from 2013 to 2015. From measurements by a scanning PCDL, the WTG wake was visualized and analyzed to evaluate the velocity deficits along the wake trajectory, wake length, wake width, vertical profile of the wake, turbulence intensity and turbulence energy dissipating rate.

In the first field campaign, we positioned the lidar at a wind park surrounded by complex terrain in the Longgang Wind Power, Shandong Peninsula, East China in the winter of 2013, as shown in Fig. 6. The complex terrain can cause inhomogeneous flow conditions and disturb turbine wakes with more complicated behaviors.

 

Fig. 6 Map of the test site in Longgang Wind Power with the positions of the wind turbines (denoted by turbine blade) and the lidar locations (denoted by the pins and balloons for the wake detection and alternative wind profile measurement, respectively). The red circle indicates the region for wake study where the PCDL scan was made over turbine wakes and ambient atmosphere (lower right).

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The lidar was located from a sufficient distance from wind turbines so as to observe the upwind and leeward of the turbine. To visualize the 2D structure of wake, two scanning modes were applied. One of those is PPI scanning mode that is introduced in section 3, and the other scanning mode is Range-Height Indicator (RHI), that is, by scanning the laser beam with a fixed azimuthal angle and by varying its elevation angle over vertical planes.

Taking into account the high accuracy of the spatial resolution of PCDL, LOS velocity measurements of the wind turbines are shown below: one PPI scan as seen in Fig. 7 on January 3rd, 2014 and one RHI scan as shown in Fig. 8 on December 26th, 2013. The position of the wind turbines and the wind direction are indicated in the figure. The red and blue colors indicate positive (away from lidar) and negative (towards lidar) movement, respectively, of the atmospheric parcels along the laser beam. Figure 7 shows a PPI scan through the rotor blades at foothills area. The background wind was blowing from north to south. Wind direction and position of the different wind turbines are indicated in the figure. WTG b submerged under the turbulent wake of WTG a. The scanning speed was 1°/s and the elevation was 2° for this measurement. The turbulence caused by complex terrain can also be seen in Fig. 7.

 

Fig. 7 LOS wind velocity by lidar with PPI scanning at the wind park with foothills topography. Three of wind turbine generators are denoted as a, b and c.

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Fig. 8 LOS velocity detected by RHI scanning mode through two rotor blades at the wind park with foothills topography. Two wind turbine generators are denoted as d and e.

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Figure 8 shows the vertical profile of wakes from two WTGs, WTG d and e, by using RHI scanning mode. The wind was blowing from the northwest (from left to right in this figure). Low Signal Noise Ratio (SNR) made the data unavailable beyond the range of 3 km. The position of the WTG d and WTG e were at a range of 700 m and 1200 m respectively. The foothills are located approximately 1.8 km from the lidar to the southeast. The hard target returns when the laser pulse hit foothills resulted in a zero velocity zone in the RHI LOS velocity plot. The scanning speed was 1°/s and the elevation varied from 0° to 20° and the azimuth was 150° for this measurement.

4.1. Velocity deficit characteristics using single scanning Doppler wind lidar

We define the velocity deficit δ in a wake as:

δ=v¯amb(z)vwake(z)v¯amb(z)×100%,
Where v¯amb(z) is the mean ambient wind velocity outside of the wake, and vwake(z) is the mean wind velocity within the wake downstream. The initial velocity deficit depends on the amount of momentum extracted by the turbine from the ambient flow.

The rotor diameter was 80 m (1D) and hub height was 110 m in the first field test. The width of downwind turbulence was about 2D at the distance of 1D downwind of the rotor. In this observation, turbine wake lengths were from 3D to 10D depending on atmospheric conditions. Figure 9(a) and (b) show the velocity deficit behind the WTG c and WTG e, respectively, due to the wake vortices of turbine blades (derived from the PPI scanning mode in Fig. 7 and RHI scanning mode in Fig. 8). For WTG c in Fig. 7, two rotor diameter range downwind of the LOS velocity at 50 m high was reduced about 54% in comparison with the maximum LOS velocity values. After 9D downwind distance the deficit was about 14%. For wind WTG e in Fig. 8, one rotor diameter range downwind of the LOS velocity at height of 80 m was reduced about 52%. After 5D downwind (10% reduction of the LOS velocity at 80 m high), the wind field recovered slowly. For WTG d in Fig. 8, because of the limited distance between two WTGs, the maximum range of wake of WTG d recorded in this measurement was only 3D. The wakes of the WTG a and WTG d cause turbulences and flow distortions that can be a source of potential dangerous fatigue loads for the WTG b and WTG e downstream.

 

Fig. 9 Velocity deficit downwind behind the WTG c (a) and WTG e (b) as the function of the blade diameter D.

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The second and the third field campaign were performed in the spring and winter of 2014 respectively at the Longyuan Jiangsu Rudong wind park, the first intertidal wind farm in the world, stretching from a temporary dry coast to the sea horizon, filled with both offshore and onshore wind turbine generators. Map of the lidar test site is shown as Fig. 10. The water-covered surface and mud flat in the intertidal zone produced a more homogeneous surface with lower roughness, hence producing distinct turbine wakes with extended its longitudinal dimensions, as shown in Fig. 11.

 

Fig. 10 Map of the lidar test site at the Rudong intertidal wind farm in spring and winter of 2014 with the positions of wind turbine generators (denoted by red dots) and locations of two 3D scanning PCDLs (denoted by the balloon A and B) and a wind profiler lidar (denoted by the balloon C).

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Fig. 11 LOS wind field at the intertidal zone by lidar PPI scan.

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During the measurements, the sea surface temperature was 14°C - 15.4 °C along the coastline, higher than the air temperature around 13°C in the nighttime. This temperature gradient may bring in surface turbulence created by thermal convection within which the wake dissipates faster than in a stable boundary layer.

The fourth field experiment was performed at the Hami wind park, Xinjiang Province with at a flat desert topography from September to November of 2014. The Hami wind park is one of the largest and fastest growing wind energy facilities in China, expected that by 2015, 6 GW of wind power will be installed in this region. In the lidar measurements at Gobi plain area, turbines formed wide and long wakes extending for 2 km (ie. Approximately 25 D for a WTG with the rotor diameter of 80 m) as shown in Fig. 12. As shown in Fig. 12(b), at low wind speed (4-6 ms−1), the lateral size of turbine wakes are bigger that leads to the merging of neighboring wakes downwind (as indicated in the grey circle). On the other hand, as shown in Fig. 12(a), wakes are constantly constrained near the wake axis with smaller horizontal size when the wind speed is bigger (8-10 ms−1).

 

Fig. 12 Turbulent wind field in the vicinity of operating wind turbines in Hami Gobi plain wind park at high wind speed of 8 −10 ms−1 (a) and relatively low wind speed of 4 - 6 ms−1 (b).

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4.2. Wind shear over the vertical plane of wake

Wind profiles retrieved from the lidar RHI scanning measurement in Fig. 8 have much higher vertical spatial resolution compared with the measurement by a vertical pointing lidar, the spatial resolution of which is limited to the laser pulse width. To analyze the wind shear intensity within wakes, wind profile series around wind turbine WTG d and WTG e are shown in Fig. 13, illustrating the wind velocity varying with the height at difference distances.

 

Fig. 13 Wind speed profile series around two wind turbines retrieved form the Fig. 8’s RHI measurement.

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Because the dominant wind direction is nearly parallel to the PCDL pointing direction, the wind profiles illustrated in the Fig. 13 are depicting the wind velocity varying with height at different distance. The wind velocity at different height represents the horizontal wind velocity retrieved from the LOS wind velocity, taking LOS angle into consideration. The positive and negative values shown in the Fig. 13 indicate the wind direction toward or away the lidar. The rotating WTG blades are hard targets that scatter laser with the intensity several orders of magnitude larger than that from aerosol scattering. The velocity retrieved from these signal would be anomalous in adjacent range gates ahead of or behind wind turbine location [14]. The negative values illustrated in the Fig. 13, for example the profiles No.3, No.4, No.9 and No.10, show these influences. These effects are under further investigation to explore methods to eliminate these artifacts.

The profiles No.5- No.8 represent the wind speed profiles between two wind turbines. The wind speed decreased to the minimum of 3 ms−1 near ground at No. 5 profile and the mean wind speed is approximately 6 ms−1, lower than the freestream before WTG d. The wind speed is nearly 6 ms−1 when it encounters the second wind turbine WTG e. This amounts to 75 percent of the wind speed at the front of the upstream one. From the present analysis of the wind profiles series, it is likely that the second wind turbine is influenced by the turbulent wake generated by the first wind turbine.

4.3. Wake visualization using 2 synchronously scanning lidars

As discussed in Section 3 and 4, because the Doppler wind lidar can only detect the LOS velocity, to retrieve the 2D wind velocity a hypothesis of horizontally homogeneity is needed. To investigate the inhomogeneous nature of a turbulent wind field, synchronous measurements with two scanning lidars were performed in the intertidal wind park in December 2014 in order to retrieve 2D velocity fields.

The experimental setup is shown in Fig. 10, in which the positions of WTGs are denoted by red dots and two scanning WindPrint S4000 PCDLs locations are denoted by the balloon A and B, respectively). Another lidar wind profiler, Windcube V2, produced by the Leosphere, was deployed for the background wind profile observation (denoted by balloon C in Fig. 10). Two scanning PCDLs were placed at the WTG Ta and Tb respectively with a spacing of 912 m. For these tests the full 360° PPI scan mode was used with the azimuthal scanning speed of 2°/s at the elevation angle varying from 0 to 4°, better known as the Constant Altitude Plan Position Indicator (CAPPI) that gives a horizontal cross-section of data at constant altitude. The laser pulse width for this measurement is adjusted to 100 ns, with regard to the physical range resolution of 15 m along the radial direction of detection. Then two 3D meshes of the LOS velocity were established with a spatial resolution of 10 m from two lidars’ CAPPI measurements, in which each sampling volume has two radial velocity components obtained from the dual lidar measurement from different directions so that we can retrieve the wind vector from simple trigonometric functions.

The 2D wind field, wind velocity within the turbine wake and in the free stream parallel to the wake corridor, and the velocity deficit rate are shown in Fig. 14, Fig. 15 and Fig. 16, respectively. The selected zone of the wake and the reference wind velocity is marked in black and red rectangles, respectively, in Fig. 14. The velocity inside the wake induced by WTG T1 and the reference wind velocity scatter plot is shown in Fig. 15. In the distance of 0.5 km, the background wind velocity is influenced by the airflow of wake from turbines in the vicinity from the upwind direction and the velocity is slightly smaller than that in the distance of about 0.4 km. The tendency can be seen clearly in triangle and rectangle points which are calculated by bin average strategy. The velocity deficit as a function of distance is shown in Fig. 16 and gradually decreases as distance increasing. Due to the influence of reference velocity by the wake induced by the other WTGs, the velocity deficit in the distance of 0.5 km is higher than that in the distance of about 0.4 km. When velocity deficit decreases to 10%, the wake distance is about 0.56 km.

 

Fig. 14 The wind speed obtained by the 2 synchronously scanning lidars at the intertidal wind farm in December 2014 with the positions of lidars (denoted by red squares A and B). A wake induced by wind turbine generator WTG T1 is denoted by a rectangle in dash black line. The free stream region outside the wake is marked as a reference wind field by a rectangle in solid red line.

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Fig. 15 Wind velocity at the free stream region as a reference velocity and the wind velocity in the wake region. The tendency of reference velocity and wake velocity are plotted by a red triangle in solid red line and a black rectangle in dash black line, respectively.

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Fig. 16 Velocity deficit downwind behind the wind turbine generator WTG 1 as the function of the distance.

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The main uncertainties for this measurement are from the pointing accuracy of the lidar beam scanner and the temporal difference at which two lidars detect the same detection volume. The latter can be optimized by programing the scan script for a specific wake region.

4.4. Velocity structure function and turbulence dissipation rate

To analyze the influence of atmospheric turbulence on the turbine wake using coherent wind lidar, we use the 2D wind field by arc PPI scanning measurements to retrieve the longitudinal velocity structure function of the turbulence in a wind park. The turbulence energy dissipation rate (TEDR) is retrieved based on the structure function of 2D LOS wind velocity. Several methods of TEDR estimation are known, for instance, the methods based on measurements of velocity structure function (VSF method) and the Doppler spectrum width (DSW method) [2,21,22], herein the VSF method is used to retrieve the TEDR. This method has been described in detail by Frehlich and Cornman [23]. Sathe and Mann [24] gave a comprehensive review of turbulence measurement using ground-based wind lidar by combining an isotropic turbulence model with raw lidar data.

From the measured data, if the fluctuations of the radial velocity are homogeneous and isotropic over the plane defined by the fixed elevation angleθ, ϕ1<ϕ<ϕ2 and R1<r<R2, the spatial statistics of the longitudinal velocity are described by the longitudinal structure function,

DLL(s)=Draw(s)E(s),
Draw(kΔs)=1NT(NRk)l=1NTj=1NRk{v'[R1+(j1)Δs,ϕ1+(l1)Δϕ,θ]v'[R1+(j+k1)Δs,ϕ1+(l1)Δϕ,θ]}2,
where Draw(s) is the raw estimate of the velocity structure function, v'(R,ϕ,θ)=v(R,ϕ,θ)<v(R,ϕ,θ)> is the fluctuations from the mean LOS velocity <v(R,ϕ,θ)> that is retrieved from an arc VAD scan at the range of R, the separation s=kΔs=R1R2, Δs is the range gate of PCDL, NT is the number of velocity measurements for the given VAD scan, NR is the number of range gates for each azimuth angle, and E(s) is an unbiased correction for the contribution from the estimation error e(R,ϕ,θ) of the velocity estimates. Here, the correction term E(s) is calculated using the technique of velocity differencing [23].

A common model for isotropic turbulence is the von Kármán model [25,26] defined by

DLL(s)~=2σ2Λ(sL0),
Λ(x)=122/3x1/3Γ(1/3)K1/3(x)=10.5925485x1/3K1/3(x),
where σ2 is the variance of each velocity component, Γ(x) is the gamma function,Kn(x) is the modified Bessel function of order n, and the outer scale L0 is proportional to the integral length scale Li,

Li=πΓ(5/6)Γ(1/3)L0=0.7468343L0.

For finite L0, the TEDR ε can be described as

ε=[21/3π3Γ(1/3)Γ(4/3)]σ3L0=0.933668σ3L0.

Considering the volume average effect of lidar detection, instead of a fixed point measurement (i.e. ultra-sonic anemometer), Frehlich et al. [27] showed that the simple model given in Eq. (4) can be described as

Dwgt(s,σ,L0)=2σ2G(sΔs,2ln2ΔsΔr,ΔsL0),
where

G(m,μ,χ)=F(x,μ)[Λ(χ|mx|)Λ(χ|x|)]dx.

F(x,μ) is the transfer function of the Gaussian lidar pulse in the atmosphere. The turbulent parameters (ε andLi) are determined by minimizing the weight error χLL2 between the longitudinal structure function DLL(s) and the corrected von Kármán modelDwgt(s,σ,L0), that is,

χLL2=1Nsk=1Ns[DLL(kΔs)Dwgt(kΔs,σ,L0)]2[kDwgt(kΔs,σ,L0)]2.

Similarly, the structure function of the velocity perturbations in the azimuth direction for each range-gate distance is described by the transverse structure function [28].

Following the method described above, and using the lidar measurements taken on January 3rd, 2014 at Longgang, data on April 10th, 2014 at Rudong, and observations on November 15th, 2015 at Hami, the corrected von Kármán model Dwgt(s,σ,L0) was calculated from Eq. (8). Figure 17 shows the calculation of the longitudinal structure functionDraw(s), and the corrected dataDLL(s). Using Eq. (3), the structure function for the von Kármán model DLL(s)~ was calculated, and following this the corrected von Kármán model Dwgt(s,σ,L0) was calculated from Eq. (8). From the fit to the corrected von Kármán modelDwgt(s,σ,L0), the values for σv2 and L0 can be derived. Then using Eq. (6) and Eq. (7), the values for Li and ε can be calculated, respectively.

 

Fig. 17 Longitudinal structure function for (a) Jan 3 2014 at Longgang, (b) April 10 2014 at Rudong, (c) Nov 15 2015 at Hami. Curves show calculations of the structure function for Draw(s) (blue closed circle), the corrected structure function DLL(s) (black closed circle), the von Kármán model DLL(s)~ (black solid line) and the corrected von Kármán model Dwgt(s,σ,L0)(red solid line).

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It can be seen that there is a large difference in the turbulence characteristics with different topographies and surface roughness. The Longgang wind park has the largest ε andσ, 0.026 m2s−3, 2.206 m2s−2, respectively, owning to the complex terrain, causing inhomogeneous flow conditions and disturbing the turbine wake more frequently. The Rudong intertidal wind park has approximately one order smaller ε of 0.003 m2s−3 and smaller σof 1.241 m2s−2, respectively, because it lies in the flat intertidal zone with more homogeneous surface, making turbine wakes more distinct and therefore extending its longitudinal dimensions. The Hami wind park with the topography of flat sand ground has the least ε andσ, 0.0022 m2s−3, 0.923 m2s−2, respectively, which is corresponding to the longest wake length shown before. In general, the decrease in ε and σ corresponds to the increase in the turbine wake length and the complex wind-wakes interactions in larger wind parks.

εandσare essential for the wind energy assessment, location selection and turbine generator selection. The traditional method to analyze εand σin a wind park using the hot-line or ultra-sonic anemometer technique is impractical for commercial wind masts. In this respect, the scanning PCDL provides a promising technique for retrieving turbulence parameters.

5. Conclusions

Wind power is growing fast as one of the most promising renewable energy sources that can serve as an alternative to fossil fuel-generated electricity. Traditionally, meteorological models and wind masts have been used to assess the large scale wind resource. However, when the wind turbine generator extracts power from the wind, the wake evolves, leading to a considerable reduction in the efficiency of the gross actual power generation. Furthermore, the wake effect can lead to the increase of turbulence induced fatigue loads and reduce the life time of wind turbine generators.

A pulsed Doppler lidar has been developed and optimized to visualize wind turbine wakes and to characterize the geometry and dynamics of wakes. The pulsed coherent Doppler lidar in this work has, to our knowledge, the highest updating rate of 4 Hz, the shortest physical spatial resolution of 15 m (extendable to 60 m) and the finest 2 D wind grid with resolution of 10 m, which improve its capability to observation in observing the instantaneous turbulent wind field with acceptable measurement accuracy for wind energy industry. The wind speed estimation method from arc scan technique was evaluated by the comparison with the wind mast measurements. By utilizing the lidar technique, we performed four field experiments with different topographies and surface roughness to study the turbulent wind field in the vicinity of operating wind turbine generators in the onshore and offshore wind parks from 2013 to 2015. The LOS velocity measurements by a single lidar and the wind vector field by the Dual-Doppler-Lidar technique are proved to be effective for homogeneous wind field and turbulent wind field respectively. The turbine wake was revealed by PPI, RHI and CAPPI scanning techniques, main features revealed including: wind velocity deficit along the longitudinal dimension, wake dimension, turbulence energy dissipation rate and turbulence intensity and their impacts on turbine wake length.

The paper shows that the pulsed coherent Doppler lidar with high accuracy is a practical tool for wind energy research and a powerful technique for the wind energy industry, especially in the offshore and complex terrain wind farms. The subsequent significance is to improve the power output efficiency of the wind turbines and reduce dissipation. Currently, studies on the lateral structure function of a turbulence wind field and wind veer in the plane of turbine disk are underway in order to evaluate the gross power output of wind parks and to further investigate the abnormal vibration of turbine generators operating in a high turbulent wind condition.

Acknowledgments

We thank our colleagues for their kind support during the field experiments, including Kailin Zhang and Xiaoquan Song from Ocean University of China (OUC) for preparing and conducting the experiment; Dongxiang Wang for operating the lidar in Rudong; Yilin Qi from Seaglet Environment Technology for preparing and operating the lidar in the Gobi desert; Ian Irvine, Craig McDonald, Peter Clive and Cathryn Chu from SgurrEnergy for initializing and support the lidar validation test in Glasgow; Chris Lawrence from SgurrEnergy for maintaining the validation device in Glasgow; Ji Zhang, Qiusheng Zhang from China Longyuan Power Group Corporation for organizing the wake test in Rudong; Hongdong Zhu from Envision Energy for discussion on turbine technology; Xiaoming Li from the Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences for insightful discussion on wake behavior over sea surface. This work was partly supported by the National Natural Science Foundation of China (NSFC) under grant 41471309 and 41375016.

References and links

1. S. Frandsen, R. Barthelmie, S. Pryor, O. Rathmann, S. Larsen, J. Højstrup, and M. Thøgersen, “Analytical modelling of wind speed deficit in large offshore wind farms,” Wind Energy A 9(1-2), 39–53 (2006). [CrossRef]  

2. I. N. Smalikho, V. A. Banakh, Y. L. Pichugina, W. A. Brewer, R. M. Banta, J. K. Lundquist, and N. D. Kelley, “Lidar investigation of atmosphere effect on a wind turbine wake,” J. Atmos. Oceanic Technol. A 30(11), 2554–2570 (2013). [CrossRef]  

3. F. B. Amar, M. Elamouri, and R. Dhifaoui, “Energy assessment of the first wind farm section of Sidi Daoud, Tunisia,” Renew. Energy A 33(10), 2311–2321 (2008). [CrossRef]  

4. R. J. Barthelmie, G. C. Larsen, S. T. Frandsen, L. Folkerts, K. Rados, S. C. Pryor, B. Lange, and G. Schepers, “Comparison of wake model simulations with offshore wind turbine wake profiles measured by sodar,” J. Atmos. Oceanic Technol. A 23(7), 888–901 (2006). [CrossRef]  

5. U. Högström, D. N. Asimakopoulos, H. Kambezidis, C. G. Helmis, and A. Smedman, “A field study of the wake behind a 2MW wind turbine,” Atmos. Environ. A 22(4), 803–820 (1988). [CrossRef]  

6. R. Krishnamurthy, A. Choukulkar, R. Calhoun, J. Fine, A. Oliver, and K. Barr, “Coherent Doppler lidar for wind farm characterization,” Wind Energy (Chichester Engl.) 16(2), 189–206 (2013). [CrossRef]  

7. S. Kameyama, T. Ando, K. Asaka, Y. Hirano, and S. Wadaka, “Compact all-fiber pulsed coherent Doppler lidar system for wind sensing,” Appl. Opt. 46, 1953–1962 (2007). (P. Artaxo, “Changes in Atmospheric Constituents and in Radiative Forcing,” https://www.ipcc.ch/pdf/assessment-report/ar4/wg1/ar4-wg1-chapter2.pdf.)

8. F. Bingöl, J. Mann, and G. C. Larsen, “Light detection and ranging measurements of wake dynamics, part I: one-dimensional scanning,” Wind Energy A 13(1), 51–61 (2010). [CrossRef]  

9. J. Trujillo, F. Bingol, G. Larsen, J. Mann, and M. Kuhn, “Light detection and ranging measurements of wake dynamics. Part II: Two-dimensional scanning,” Wind Energy A 14(1), 61–75 (2011). [CrossRef]  

10. H. Jørgensen, T. Mikkelsen, J. Mann, D. Bryce, A. Coffey, M. Harris, and D. Smith,“Site wind field determination using a CW Doppler Lidar- comparison with cup anemometers at Risø,” in The Science of Making Torque from Wind (European Wind Energy Association, 2004), pp. 261–266.

11. Y. Käsler, S. Rahm, R. Simmet, and M. Kuhn, “Wake measurements of a multi-MW wind turbine with coherent long-range pulsed Doppler wind lidar,” J. Atmos. Ocean. Technol. 27(9), 1529–1532 (2010). [CrossRef]  

12. G. Iungo, Y. Wu, and F. Porteagel, “Field Measurements of Wind Turbine Wakes with Lidars,” J. Atmos. Ocean. Technol. 30(2), 274–287 (2013). [CrossRef]  

13. G. Koch, J. Beyon, E. Modlin, P. Petzar, S. Woll, M. Petros, J. Yu, and M. Kavaya, “Side-scan Doppler lidar for offshore wind energy applications,” J. Appl. Remote Sens. 6(1), 063562 (2012). [CrossRef]  

14. R. M. Banta, Y. L. Pichugina, W. A. Brewer, J. K. Lundquist, N. D. Kelley, S. P. Sandberg, R. J. Alvarez II, R. M. Hardesty, and A. M. Weickmann, “3D volumetric analysis of wind turbine wake properties in the atmosphere using high-resolution Doppler lidar,” J. Atmos. Ocean. Technol. 32(5), 904–914 (2015). [CrossRef]  

15. S. Wu, J. Yin, B. Liu, and J. Liu, “Wind Turbine Wake Visualization by Doppler Lidar,” in Light, Energy and the Environment 2015, OSA Technical Digest (online) (Optical Society of America, 2015), paper EM3A.4. [CrossRef]  

16. R. L. Schwiesow, F. Köpp, and C. Werner, “Comparison of CW-lidar-measured wind values obtained by full conical scan, conical sector scan and two-point techniques,” J. Atmos. Ocean. Technol. 2(1), 3–14 (1985). [CrossRef]  

17. Z. S. Liu, W. B. Chen, T. L. Zhang, J. W. Hair, and C. Y. She, “An incoherent Doppler Lidar for ground-based atmospheric wind profiling,” Appl. Phys. B 64(5), 561–566 (1997). [CrossRef]  

18. Z. S. Liu, B. Y. Liu, S. H. Wu, Z. G. Li, and Z. J. Wang, “High spatial and temporal resolution mobile incoherent Doppler lidar for sea surface wind measurements,” Opt. Lett. 33(13), 1485–1487 (2008). [CrossRef]   [PubMed]  

19. Z. S. Liu, Z. J. Wang, S. H. Wu, B. Y. Liu, Z. G. Li, X. Zhang, D. C. Bi, Y. B. Chen, R. Z. Li, and Y. Q. Yang, “Fine-measuring technique and application for sea surface wind by mobile Doppler wind lidar,” Opt. Eng. 48(6), 066002 (2009). [CrossRef]  

20. Z. Wang, Z. Liu, L. Liu, S. Wu, B. Liu, Z. Li, and X. Chu, “Iodine-filter-based mobile Doppler lidar to make continuous and full-azimuth-scanned wind measurements: data acquisition and analysis system, data retrieval methods, and error analysis,” Appl. Opt. 49(36), 6960–6978 (2010). [CrossRef]   [PubMed]  

21. V. Banakh, V. Bodaruev, and I. Smalikho, “Estimation of the turbulence energy dissipation rate from the pulsed Doppler lidar data,” Atmos. Oceanic Opt. 10, 957–965 (1997).

22. R. Frehlich, “Effects of wind turbulence on coherent Doppler lidar performance,” J. Atmos. Ocean. Technol. 14(1), 54–75 (1997). [CrossRef]  

23. R. Frehlich and L. Cornman, “Estimating spatial velocity statistics with coherent Doppler lidar,” J. Atmos. Ocean. Technol. 19(3), 355–366 (2002). [CrossRef]  

24. A. Sathe and J. Mann, “A review of turbulence measurements using ground-based wind lidars,” Atmos. Meas. Tech. 6(11), 3147–3167 (2013). [CrossRef]  

25. J. O. Hinze and J. Hinze, Turbulence: an introduction to its mechanism and theory (McGraw-Hill New York, 1959).

26. D. H. Lenschow and L. Kristensen, “Applications of dual aircraft formation flights,” J. Atmos. Ocean. Technol. 5(6), 715–726 (1988). [CrossRef]  

27. R. Frehlich, S. M. Hannon, and S. W. Henderson, “Coherent Doppler lidar measurements of wind field statistics,” Bound. -Layer Meteor. 86(2), 233–256 (1998). [CrossRef]  

28. R. Frehlich, Y. Meillier, M. L. Jensen, B. Balsley, and R. Sharman, “Measurements of boundary layer profiles in an urban environment,” J. Appl. Meteorol. Climatol. 45(6), 821–837 (2006). [CrossRef]  

References

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  1. S. Frandsen, R. Barthelmie, S. Pryor, O. Rathmann, S. Larsen, J. Højstrup, and M. Thøgersen, “Analytical modelling of wind speed deficit in large offshore wind farms,” Wind Energy A 9(1-2), 39–53 (2006).
    [Crossref]
  2. I. N. Smalikho, V. A. Banakh, Y. L. Pichugina, W. A. Brewer, R. M. Banta, J. K. Lundquist, and N. D. Kelley, “Lidar investigation of atmosphere effect on a wind turbine wake,” J. Atmos. Oceanic Technol. A 30(11), 2554–2570 (2013).
    [Crossref]
  3. F. B. Amar, M. Elamouri, and R. Dhifaoui, “Energy assessment of the first wind farm section of Sidi Daoud, Tunisia,” Renew. Energy A 33(10), 2311–2321 (2008).
    [Crossref]
  4. R. J. Barthelmie, G. C. Larsen, S. T. Frandsen, L. Folkerts, K. Rados, S. C. Pryor, B. Lange, and G. Schepers, “Comparison of wake model simulations with offshore wind turbine wake profiles measured by sodar,” J. Atmos. Oceanic Technol. A 23(7), 888–901 (2006).
    [Crossref]
  5. U. Högström, D. N. Asimakopoulos, H. Kambezidis, C. G. Helmis, and A. Smedman, “A field study of the wake behind a 2MW wind turbine,” Atmos. Environ. A 22(4), 803–820 (1988).
    [Crossref]
  6. R. Krishnamurthy, A. Choukulkar, R. Calhoun, J. Fine, A. Oliver, and K. Barr, “Coherent Doppler lidar for wind farm characterization,” Wind Energy (Chichester Engl.) 16(2), 189–206 (2013).
    [Crossref]
  7. S. Kameyama, T. Ando, K. Asaka, Y. Hirano, and S. Wadaka, “Compact all-fiber pulsed coherent Doppler lidar system for wind sensing,” Appl. Opt. 46, 1953–1962 (2007). (P. Artaxo, “Changes in Atmospheric Constituents and in Radiative Forcing,” https://www.ipcc.ch/pdf/assessment-report/ar4/wg1/ar4-wg1-chapter2.pdf .)
  8. F. Bingöl, J. Mann, and G. C. Larsen, “Light detection and ranging measurements of wake dynamics, part I: one-dimensional scanning,” Wind Energy A 13(1), 51–61 (2010).
    [Crossref]
  9. J. Trujillo, F. Bingol, G. Larsen, J. Mann, and M. Kuhn, “Light detection and ranging measurements of wake dynamics. Part II: Two-dimensional scanning,” Wind Energy A 14(1), 61–75 (2011).
    [Crossref]
  10. H. Jørgensen, T. Mikkelsen, J. Mann, D. Bryce, A. Coffey, M. Harris, and D. Smith,“Site wind field determination using a CW Doppler Lidar- comparison with cup anemometers at Risø,” in The Science of Making Torque from Wind (European Wind Energy Association, 2004), pp. 261–266.
  11. Y. Käsler, S. Rahm, R. Simmet, and M. Kuhn, “Wake measurements of a multi-MW wind turbine with coherent long-range pulsed Doppler wind lidar,” J. Atmos. Ocean. Technol. 27(9), 1529–1532 (2010).
    [Crossref]
  12. G. Iungo, Y. Wu, and F. Porteagel, “Field Measurements of Wind Turbine Wakes with Lidars,” J. Atmos. Ocean. Technol. 30(2), 274–287 (2013).
    [Crossref]
  13. G. Koch, J. Beyon, E. Modlin, P. Petzar, S. Woll, M. Petros, J. Yu, and M. Kavaya, “Side-scan Doppler lidar for offshore wind energy applications,” J. Appl. Remote Sens. 6(1), 063562 (2012).
    [Crossref]
  14. R. M. Banta, Y. L. Pichugina, W. A. Brewer, J. K. Lundquist, N. D. Kelley, S. P. Sandberg, R. J. Alvarez, R. M. Hardesty, and A. M. Weickmann, “3D volumetric analysis of wind turbine wake properties in the atmosphere using high-resolution Doppler lidar,” J. Atmos. Ocean. Technol. 32(5), 904–914 (2015).
    [Crossref]
  15. S. Wu, J. Yin, B. Liu, and J. Liu, “Wind Turbine Wake Visualization by Doppler Lidar,” in Light, Energy and the Environment 2015, OSA Technical Digest (online) (Optical Society of America, 2015), paper EM3A.4.
    [Crossref]
  16. R. L. Schwiesow, F. Köpp, and C. Werner, “Comparison of CW-lidar-measured wind values obtained by full conical scan, conical sector scan and two-point techniques,” J. Atmos. Ocean. Technol. 2(1), 3–14 (1985).
    [Crossref]
  17. Z. S. Liu, W. B. Chen, T. L. Zhang, J. W. Hair, and C. Y. She, “An incoherent Doppler Lidar for ground-based atmospheric wind profiling,” Appl. Phys. B 64(5), 561–566 (1997).
    [Crossref]
  18. Z. S. Liu, B. Y. Liu, S. H. Wu, Z. G. Li, and Z. J. Wang, “High spatial and temporal resolution mobile incoherent Doppler lidar for sea surface wind measurements,” Opt. Lett. 33(13), 1485–1487 (2008).
    [Crossref] [PubMed]
  19. Z. S. Liu, Z. J. Wang, S. H. Wu, B. Y. Liu, Z. G. Li, X. Zhang, D. C. Bi, Y. B. Chen, R. Z. Li, and Y. Q. Yang, “Fine-measuring technique and application for sea surface wind by mobile Doppler wind lidar,” Opt. Eng. 48(6), 066002 (2009).
    [Crossref]
  20. Z. Wang, Z. Liu, L. Liu, S. Wu, B. Liu, Z. Li, and X. Chu, “Iodine-filter-based mobile Doppler lidar to make continuous and full-azimuth-scanned wind measurements: data acquisition and analysis system, data retrieval methods, and error analysis,” Appl. Opt. 49(36), 6960–6978 (2010).
    [Crossref] [PubMed]
  21. V. Banakh, V. Bodaruev, and I. Smalikho, “Estimation of the turbulence energy dissipation rate from the pulsed Doppler lidar data,” Atmos. Oceanic Opt. 10, 957–965 (1997).
  22. R. Frehlich, “Effects of wind turbulence on coherent Doppler lidar performance,” J. Atmos. Ocean. Technol. 14(1), 54–75 (1997).
    [Crossref]
  23. R. Frehlich and L. Cornman, “Estimating spatial velocity statistics with coherent Doppler lidar,” J. Atmos. Ocean. Technol. 19(3), 355–366 (2002).
    [Crossref]
  24. A. Sathe and J. Mann, “A review of turbulence measurements using ground-based wind lidars,” Atmos. Meas. Tech. 6(11), 3147–3167 (2013).
    [Crossref]
  25. J. O. Hinze and J. Hinze, Turbulence: an introduction to its mechanism and theory (McGraw-Hill New York, 1959).
  26. D. H. Lenschow and L. Kristensen, “Applications of dual aircraft formation flights,” J. Atmos. Ocean. Technol. 5(6), 715–726 (1988).
    [Crossref]
  27. R. Frehlich, S. M. Hannon, and S. W. Henderson, “Coherent Doppler lidar measurements of wind field statistics,” Bound. -Layer Meteor. 86(2), 233–256 (1998).
    [Crossref]
  28. R. Frehlich, Y. Meillier, M. L. Jensen, B. Balsley, and R. Sharman, “Measurements of boundary layer profiles in an urban environment,” J. Appl. Meteorol. Climatol. 45(6), 821–837 (2006).
    [Crossref]

2015 (1)

R. M. Banta, Y. L. Pichugina, W. A. Brewer, J. K. Lundquist, N. D. Kelley, S. P. Sandberg, R. J. Alvarez, R. M. Hardesty, and A. M. Weickmann, “3D volumetric analysis of wind turbine wake properties in the atmosphere using high-resolution Doppler lidar,” J. Atmos. Ocean. Technol. 32(5), 904–914 (2015).
[Crossref]

2013 (4)

G. Iungo, Y. Wu, and F. Porteagel, “Field Measurements of Wind Turbine Wakes with Lidars,” J. Atmos. Ocean. Technol. 30(2), 274–287 (2013).
[Crossref]

I. N. Smalikho, V. A. Banakh, Y. L. Pichugina, W. A. Brewer, R. M. Banta, J. K. Lundquist, and N. D. Kelley, “Lidar investigation of atmosphere effect on a wind turbine wake,” J. Atmos. Oceanic Technol. A 30(11), 2554–2570 (2013).
[Crossref]

R. Krishnamurthy, A. Choukulkar, R. Calhoun, J. Fine, A. Oliver, and K. Barr, “Coherent Doppler lidar for wind farm characterization,” Wind Energy (Chichester Engl.) 16(2), 189–206 (2013).
[Crossref]

A. Sathe and J. Mann, “A review of turbulence measurements using ground-based wind lidars,” Atmos. Meas. Tech. 6(11), 3147–3167 (2013).
[Crossref]

2012 (1)

G. Koch, J. Beyon, E. Modlin, P. Petzar, S. Woll, M. Petros, J. Yu, and M. Kavaya, “Side-scan Doppler lidar for offshore wind energy applications,” J. Appl. Remote Sens. 6(1), 063562 (2012).
[Crossref]

2011 (1)

J. Trujillo, F. Bingol, G. Larsen, J. Mann, and M. Kuhn, “Light detection and ranging measurements of wake dynamics. Part II: Two-dimensional scanning,” Wind Energy A 14(1), 61–75 (2011).
[Crossref]

2010 (3)

Y. Käsler, S. Rahm, R. Simmet, and M. Kuhn, “Wake measurements of a multi-MW wind turbine with coherent long-range pulsed Doppler wind lidar,” J. Atmos. Ocean. Technol. 27(9), 1529–1532 (2010).
[Crossref]

F. Bingöl, J. Mann, and G. C. Larsen, “Light detection and ranging measurements of wake dynamics, part I: one-dimensional scanning,” Wind Energy A 13(1), 51–61 (2010).
[Crossref]

Z. Wang, Z. Liu, L. Liu, S. Wu, B. Liu, Z. Li, and X. Chu, “Iodine-filter-based mobile Doppler lidar to make continuous and full-azimuth-scanned wind measurements: data acquisition and analysis system, data retrieval methods, and error analysis,” Appl. Opt. 49(36), 6960–6978 (2010).
[Crossref] [PubMed]

2009 (1)

Z. S. Liu, Z. J. Wang, S. H. Wu, B. Y. Liu, Z. G. Li, X. Zhang, D. C. Bi, Y. B. Chen, R. Z. Li, and Y. Q. Yang, “Fine-measuring technique and application for sea surface wind by mobile Doppler wind lidar,” Opt. Eng. 48(6), 066002 (2009).
[Crossref]

2008 (2)

F. B. Amar, M. Elamouri, and R. Dhifaoui, “Energy assessment of the first wind farm section of Sidi Daoud, Tunisia,” Renew. Energy A 33(10), 2311–2321 (2008).
[Crossref]

Z. S. Liu, B. Y. Liu, S. H. Wu, Z. G. Li, and Z. J. Wang, “High spatial and temporal resolution mobile incoherent Doppler lidar for sea surface wind measurements,” Opt. Lett. 33(13), 1485–1487 (2008).
[Crossref] [PubMed]

2007 (1)

2006 (3)

S. Frandsen, R. Barthelmie, S. Pryor, O. Rathmann, S. Larsen, J. Højstrup, and M. Thøgersen, “Analytical modelling of wind speed deficit in large offshore wind farms,” Wind Energy A 9(1-2), 39–53 (2006).
[Crossref]

R. J. Barthelmie, G. C. Larsen, S. T. Frandsen, L. Folkerts, K. Rados, S. C. Pryor, B. Lange, and G. Schepers, “Comparison of wake model simulations with offshore wind turbine wake profiles measured by sodar,” J. Atmos. Oceanic Technol. A 23(7), 888–901 (2006).
[Crossref]

R. Frehlich, Y. Meillier, M. L. Jensen, B. Balsley, and R. Sharman, “Measurements of boundary layer profiles in an urban environment,” J. Appl. Meteorol. Climatol. 45(6), 821–837 (2006).
[Crossref]

2002 (1)

R. Frehlich and L. Cornman, “Estimating spatial velocity statistics with coherent Doppler lidar,” J. Atmos. Ocean. Technol. 19(3), 355–366 (2002).
[Crossref]

1998 (1)

R. Frehlich, S. M. Hannon, and S. W. Henderson, “Coherent Doppler lidar measurements of wind field statistics,” Bound. -Layer Meteor. 86(2), 233–256 (1998).
[Crossref]

1997 (3)

V. Banakh, V. Bodaruev, and I. Smalikho, “Estimation of the turbulence energy dissipation rate from the pulsed Doppler lidar data,” Atmos. Oceanic Opt. 10, 957–965 (1997).

R. Frehlich, “Effects of wind turbulence on coherent Doppler lidar performance,” J. Atmos. Ocean. Technol. 14(1), 54–75 (1997).
[Crossref]

Z. S. Liu, W. B. Chen, T. L. Zhang, J. W. Hair, and C. Y. She, “An incoherent Doppler Lidar for ground-based atmospheric wind profiling,” Appl. Phys. B 64(5), 561–566 (1997).
[Crossref]

1988 (2)

U. Högström, D. N. Asimakopoulos, H. Kambezidis, C. G. Helmis, and A. Smedman, “A field study of the wake behind a 2MW wind turbine,” Atmos. Environ. A 22(4), 803–820 (1988).
[Crossref]

D. H. Lenschow and L. Kristensen, “Applications of dual aircraft formation flights,” J. Atmos. Ocean. Technol. 5(6), 715–726 (1988).
[Crossref]

1985 (1)

R. L. Schwiesow, F. Köpp, and C. Werner, “Comparison of CW-lidar-measured wind values obtained by full conical scan, conical sector scan and two-point techniques,” J. Atmos. Ocean. Technol. 2(1), 3–14 (1985).
[Crossref]

Alvarez, R. J.

R. M. Banta, Y. L. Pichugina, W. A. Brewer, J. K. Lundquist, N. D. Kelley, S. P. Sandberg, R. J. Alvarez, R. M. Hardesty, and A. M. Weickmann, “3D volumetric analysis of wind turbine wake properties in the atmosphere using high-resolution Doppler lidar,” J. Atmos. Ocean. Technol. 32(5), 904–914 (2015).
[Crossref]

Amar, F. B.

F. B. Amar, M. Elamouri, and R. Dhifaoui, “Energy assessment of the first wind farm section of Sidi Daoud, Tunisia,” Renew. Energy A 33(10), 2311–2321 (2008).
[Crossref]

Ando, T.

Asaka, K.

Asimakopoulos, D. N.

U. Högström, D. N. Asimakopoulos, H. Kambezidis, C. G. Helmis, and A. Smedman, “A field study of the wake behind a 2MW wind turbine,” Atmos. Environ. A 22(4), 803–820 (1988).
[Crossref]

Balsley, B.

R. Frehlich, Y. Meillier, M. L. Jensen, B. Balsley, and R. Sharman, “Measurements of boundary layer profiles in an urban environment,” J. Appl. Meteorol. Climatol. 45(6), 821–837 (2006).
[Crossref]

Banakh, V.

V. Banakh, V. Bodaruev, and I. Smalikho, “Estimation of the turbulence energy dissipation rate from the pulsed Doppler lidar data,” Atmos. Oceanic Opt. 10, 957–965 (1997).

Banakh, V. A.

I. N. Smalikho, V. A. Banakh, Y. L. Pichugina, W. A. Brewer, R. M. Banta, J. K. Lundquist, and N. D. Kelley, “Lidar investigation of atmosphere effect on a wind turbine wake,” J. Atmos. Oceanic Technol. A 30(11), 2554–2570 (2013).
[Crossref]

Banta, R. M.

R. M. Banta, Y. L. Pichugina, W. A. Brewer, J. K. Lundquist, N. D. Kelley, S. P. Sandberg, R. J. Alvarez, R. M. Hardesty, and A. M. Weickmann, “3D volumetric analysis of wind turbine wake properties in the atmosphere using high-resolution Doppler lidar,” J. Atmos. Ocean. Technol. 32(5), 904–914 (2015).
[Crossref]

I. N. Smalikho, V. A. Banakh, Y. L. Pichugina, W. A. Brewer, R. M. Banta, J. K. Lundquist, and N. D. Kelley, “Lidar investigation of atmosphere effect on a wind turbine wake,” J. Atmos. Oceanic Technol. A 30(11), 2554–2570 (2013).
[Crossref]

Barr, K.

R. Krishnamurthy, A. Choukulkar, R. Calhoun, J. Fine, A. Oliver, and K. Barr, “Coherent Doppler lidar for wind farm characterization,” Wind Energy (Chichester Engl.) 16(2), 189–206 (2013).
[Crossref]

Barthelmie, R.

S. Frandsen, R. Barthelmie, S. Pryor, O. Rathmann, S. Larsen, J. Højstrup, and M. Thøgersen, “Analytical modelling of wind speed deficit in large offshore wind farms,” Wind Energy A 9(1-2), 39–53 (2006).
[Crossref]

Barthelmie, R. J.

R. J. Barthelmie, G. C. Larsen, S. T. Frandsen, L. Folkerts, K. Rados, S. C. Pryor, B. Lange, and G. Schepers, “Comparison of wake model simulations with offshore wind turbine wake profiles measured by sodar,” J. Atmos. Oceanic Technol. A 23(7), 888–901 (2006).
[Crossref]

Beyon, J.

G. Koch, J. Beyon, E. Modlin, P. Petzar, S. Woll, M. Petros, J. Yu, and M. Kavaya, “Side-scan Doppler lidar for offshore wind energy applications,” J. Appl. Remote Sens. 6(1), 063562 (2012).
[Crossref]

Bi, D. C.

Z. S. Liu, Z. J. Wang, S. H. Wu, B. Y. Liu, Z. G. Li, X. Zhang, D. C. Bi, Y. B. Chen, R. Z. Li, and Y. Q. Yang, “Fine-measuring technique and application for sea surface wind by mobile Doppler wind lidar,” Opt. Eng. 48(6), 066002 (2009).
[Crossref]

Bingol, F.

J. Trujillo, F. Bingol, G. Larsen, J. Mann, and M. Kuhn, “Light detection and ranging measurements of wake dynamics. Part II: Two-dimensional scanning,” Wind Energy A 14(1), 61–75 (2011).
[Crossref]

Bingöl, F.

F. Bingöl, J. Mann, and G. C. Larsen, “Light detection and ranging measurements of wake dynamics, part I: one-dimensional scanning,” Wind Energy A 13(1), 51–61 (2010).
[Crossref]

Bodaruev, V.

V. Banakh, V. Bodaruev, and I. Smalikho, “Estimation of the turbulence energy dissipation rate from the pulsed Doppler lidar data,” Atmos. Oceanic Opt. 10, 957–965 (1997).

Brewer, W. A.

R. M. Banta, Y. L. Pichugina, W. A. Brewer, J. K. Lundquist, N. D. Kelley, S. P. Sandberg, R. J. Alvarez, R. M. Hardesty, and A. M. Weickmann, “3D volumetric analysis of wind turbine wake properties in the atmosphere using high-resolution Doppler lidar,” J. Atmos. Ocean. Technol. 32(5), 904–914 (2015).
[Crossref]

I. N. Smalikho, V. A. Banakh, Y. L. Pichugina, W. A. Brewer, R. M. Banta, J. K. Lundquist, and N. D. Kelley, “Lidar investigation of atmosphere effect on a wind turbine wake,” J. Atmos. Oceanic Technol. A 30(11), 2554–2570 (2013).
[Crossref]

Calhoun, R.

R. Krishnamurthy, A. Choukulkar, R. Calhoun, J. Fine, A. Oliver, and K. Barr, “Coherent Doppler lidar for wind farm characterization,” Wind Energy (Chichester Engl.) 16(2), 189–206 (2013).
[Crossref]

Chen, W. B.

Z. S. Liu, W. B. Chen, T. L. Zhang, J. W. Hair, and C. Y. She, “An incoherent Doppler Lidar for ground-based atmospheric wind profiling,” Appl. Phys. B 64(5), 561–566 (1997).
[Crossref]

Chen, Y. B.

Z. S. Liu, Z. J. Wang, S. H. Wu, B. Y. Liu, Z. G. Li, X. Zhang, D. C. Bi, Y. B. Chen, R. Z. Li, and Y. Q. Yang, “Fine-measuring technique and application for sea surface wind by mobile Doppler wind lidar,” Opt. Eng. 48(6), 066002 (2009).
[Crossref]

Choukulkar, A.

R. Krishnamurthy, A. Choukulkar, R. Calhoun, J. Fine, A. Oliver, and K. Barr, “Coherent Doppler lidar for wind farm characterization,” Wind Energy (Chichester Engl.) 16(2), 189–206 (2013).
[Crossref]

Chu, X.

Cornman, L.

R. Frehlich and L. Cornman, “Estimating spatial velocity statistics with coherent Doppler lidar,” J. Atmos. Ocean. Technol. 19(3), 355–366 (2002).
[Crossref]

Dhifaoui, R.

F. B. Amar, M. Elamouri, and R. Dhifaoui, “Energy assessment of the first wind farm section of Sidi Daoud, Tunisia,” Renew. Energy A 33(10), 2311–2321 (2008).
[Crossref]

Elamouri, M.

F. B. Amar, M. Elamouri, and R. Dhifaoui, “Energy assessment of the first wind farm section of Sidi Daoud, Tunisia,” Renew. Energy A 33(10), 2311–2321 (2008).
[Crossref]

Fine, J.

R. Krishnamurthy, A. Choukulkar, R. Calhoun, J. Fine, A. Oliver, and K. Barr, “Coherent Doppler lidar for wind farm characterization,” Wind Energy (Chichester Engl.) 16(2), 189–206 (2013).
[Crossref]

Folkerts, L.

R. J. Barthelmie, G. C. Larsen, S. T. Frandsen, L. Folkerts, K. Rados, S. C. Pryor, B. Lange, and G. Schepers, “Comparison of wake model simulations with offshore wind turbine wake profiles measured by sodar,” J. Atmos. Oceanic Technol. A 23(7), 888–901 (2006).
[Crossref]

Frandsen, S.

S. Frandsen, R. Barthelmie, S. Pryor, O. Rathmann, S. Larsen, J. Højstrup, and M. Thøgersen, “Analytical modelling of wind speed deficit in large offshore wind farms,” Wind Energy A 9(1-2), 39–53 (2006).
[Crossref]

Frandsen, S. T.

R. J. Barthelmie, G. C. Larsen, S. T. Frandsen, L. Folkerts, K. Rados, S. C. Pryor, B. Lange, and G. Schepers, “Comparison of wake model simulations with offshore wind turbine wake profiles measured by sodar,” J. Atmos. Oceanic Technol. A 23(7), 888–901 (2006).
[Crossref]

Frehlich, R.

R. Frehlich, Y. Meillier, M. L. Jensen, B. Balsley, and R. Sharman, “Measurements of boundary layer profiles in an urban environment,” J. Appl. Meteorol. Climatol. 45(6), 821–837 (2006).
[Crossref]

R. Frehlich and L. Cornman, “Estimating spatial velocity statistics with coherent Doppler lidar,” J. Atmos. Ocean. Technol. 19(3), 355–366 (2002).
[Crossref]

R. Frehlich, S. M. Hannon, and S. W. Henderson, “Coherent Doppler lidar measurements of wind field statistics,” Bound. -Layer Meteor. 86(2), 233–256 (1998).
[Crossref]

R. Frehlich, “Effects of wind turbulence on coherent Doppler lidar performance,” J. Atmos. Ocean. Technol. 14(1), 54–75 (1997).
[Crossref]

Hair, J. W.

Z. S. Liu, W. B. Chen, T. L. Zhang, J. W. Hair, and C. Y. She, “An incoherent Doppler Lidar for ground-based atmospheric wind profiling,” Appl. Phys. B 64(5), 561–566 (1997).
[Crossref]

Hannon, S. M.

R. Frehlich, S. M. Hannon, and S. W. Henderson, “Coherent Doppler lidar measurements of wind field statistics,” Bound. -Layer Meteor. 86(2), 233–256 (1998).
[Crossref]

Hardesty, R. M.

R. M. Banta, Y. L. Pichugina, W. A. Brewer, J. K. Lundquist, N. D. Kelley, S. P. Sandberg, R. J. Alvarez, R. M. Hardesty, and A. M. Weickmann, “3D volumetric analysis of wind turbine wake properties in the atmosphere using high-resolution Doppler lidar,” J. Atmos. Ocean. Technol. 32(5), 904–914 (2015).
[Crossref]

Helmis, C. G.

U. Högström, D. N. Asimakopoulos, H. Kambezidis, C. G. Helmis, and A. Smedman, “A field study of the wake behind a 2MW wind turbine,” Atmos. Environ. A 22(4), 803–820 (1988).
[Crossref]

Henderson, S. W.

R. Frehlich, S. M. Hannon, and S. W. Henderson, “Coherent Doppler lidar measurements of wind field statistics,” Bound. -Layer Meteor. 86(2), 233–256 (1998).
[Crossref]

Hirano, Y.

Högström, U.

U. Högström, D. N. Asimakopoulos, H. Kambezidis, C. G. Helmis, and A. Smedman, “A field study of the wake behind a 2MW wind turbine,” Atmos. Environ. A 22(4), 803–820 (1988).
[Crossref]

Højstrup, J.

S. Frandsen, R. Barthelmie, S. Pryor, O. Rathmann, S. Larsen, J. Højstrup, and M. Thøgersen, “Analytical modelling of wind speed deficit in large offshore wind farms,” Wind Energy A 9(1-2), 39–53 (2006).
[Crossref]

Iungo, G.

G. Iungo, Y. Wu, and F. Porteagel, “Field Measurements of Wind Turbine Wakes with Lidars,” J. Atmos. Ocean. Technol. 30(2), 274–287 (2013).
[Crossref]

Jensen, M. L.

R. Frehlich, Y. Meillier, M. L. Jensen, B. Balsley, and R. Sharman, “Measurements of boundary layer profiles in an urban environment,” J. Appl. Meteorol. Climatol. 45(6), 821–837 (2006).
[Crossref]

Kambezidis, H.

U. Högström, D. N. Asimakopoulos, H. Kambezidis, C. G. Helmis, and A. Smedman, “A field study of the wake behind a 2MW wind turbine,” Atmos. Environ. A 22(4), 803–820 (1988).
[Crossref]

Kameyama, S.

Käsler, Y.

Y. Käsler, S. Rahm, R. Simmet, and M. Kuhn, “Wake measurements of a multi-MW wind turbine with coherent long-range pulsed Doppler wind lidar,” J. Atmos. Ocean. Technol. 27(9), 1529–1532 (2010).
[Crossref]

Kavaya, M.

G. Koch, J. Beyon, E. Modlin, P. Petzar, S. Woll, M. Petros, J. Yu, and M. Kavaya, “Side-scan Doppler lidar for offshore wind energy applications,” J. Appl. Remote Sens. 6(1), 063562 (2012).
[Crossref]

Kelley, N. D.

R. M. Banta, Y. L. Pichugina, W. A. Brewer, J. K. Lundquist, N. D. Kelley, S. P. Sandberg, R. J. Alvarez, R. M. Hardesty, and A. M. Weickmann, “3D volumetric analysis of wind turbine wake properties in the atmosphere using high-resolution Doppler lidar,” J. Atmos. Ocean. Technol. 32(5), 904–914 (2015).
[Crossref]

I. N. Smalikho, V. A. Banakh, Y. L. Pichugina, W. A. Brewer, R. M. Banta, J. K. Lundquist, and N. D. Kelley, “Lidar investigation of atmosphere effect on a wind turbine wake,” J. Atmos. Oceanic Technol. A 30(11), 2554–2570 (2013).
[Crossref]

Koch, G.

G. Koch, J. Beyon, E. Modlin, P. Petzar, S. Woll, M. Petros, J. Yu, and M. Kavaya, “Side-scan Doppler lidar for offshore wind energy applications,” J. Appl. Remote Sens. 6(1), 063562 (2012).
[Crossref]

Köpp, F.

R. L. Schwiesow, F. Köpp, and C. Werner, “Comparison of CW-lidar-measured wind values obtained by full conical scan, conical sector scan and two-point techniques,” J. Atmos. Ocean. Technol. 2(1), 3–14 (1985).
[Crossref]

Krishnamurthy, R.

R. Krishnamurthy, A. Choukulkar, R. Calhoun, J. Fine, A. Oliver, and K. Barr, “Coherent Doppler lidar for wind farm characterization,” Wind Energy (Chichester Engl.) 16(2), 189–206 (2013).
[Crossref]

Kristensen, L.

D. H. Lenschow and L. Kristensen, “Applications of dual aircraft formation flights,” J. Atmos. Ocean. Technol. 5(6), 715–726 (1988).
[Crossref]

Kuhn, M.

J. Trujillo, F. Bingol, G. Larsen, J. Mann, and M. Kuhn, “Light detection and ranging measurements of wake dynamics. Part II: Two-dimensional scanning,” Wind Energy A 14(1), 61–75 (2011).
[Crossref]

Y. Käsler, S. Rahm, R. Simmet, and M. Kuhn, “Wake measurements of a multi-MW wind turbine with coherent long-range pulsed Doppler wind lidar,” J. Atmos. Ocean. Technol. 27(9), 1529–1532 (2010).
[Crossref]

Lange, B.

R. J. Barthelmie, G. C. Larsen, S. T. Frandsen, L. Folkerts, K. Rados, S. C. Pryor, B. Lange, and G. Schepers, “Comparison of wake model simulations with offshore wind turbine wake profiles measured by sodar,” J. Atmos. Oceanic Technol. A 23(7), 888–901 (2006).
[Crossref]

Larsen, G.

J. Trujillo, F. Bingol, G. Larsen, J. Mann, and M. Kuhn, “Light detection and ranging measurements of wake dynamics. Part II: Two-dimensional scanning,” Wind Energy A 14(1), 61–75 (2011).
[Crossref]

Larsen, G. C.

F. Bingöl, J. Mann, and G. C. Larsen, “Light detection and ranging measurements of wake dynamics, part I: one-dimensional scanning,” Wind Energy A 13(1), 51–61 (2010).
[Crossref]

R. J. Barthelmie, G. C. Larsen, S. T. Frandsen, L. Folkerts, K. Rados, S. C. Pryor, B. Lange, and G. Schepers, “Comparison of wake model simulations with offshore wind turbine wake profiles measured by sodar,” J. Atmos. Oceanic Technol. A 23(7), 888–901 (2006).
[Crossref]

Larsen, S.

S. Frandsen, R. Barthelmie, S. Pryor, O. Rathmann, S. Larsen, J. Højstrup, and M. Thøgersen, “Analytical modelling of wind speed deficit in large offshore wind farms,” Wind Energy A 9(1-2), 39–53 (2006).
[Crossref]

Lenschow, D. H.

D. H. Lenschow and L. Kristensen, “Applications of dual aircraft formation flights,” J. Atmos. Ocean. Technol. 5(6), 715–726 (1988).
[Crossref]

Li, R. Z.

Z. S. Liu, Z. J. Wang, S. H. Wu, B. Y. Liu, Z. G. Li, X. Zhang, D. C. Bi, Y. B. Chen, R. Z. Li, and Y. Q. Yang, “Fine-measuring technique and application for sea surface wind by mobile Doppler wind lidar,” Opt. Eng. 48(6), 066002 (2009).
[Crossref]

Li, Z.

Li, Z. G.

Z. S. Liu, Z. J. Wang, S. H. Wu, B. Y. Liu, Z. G. Li, X. Zhang, D. C. Bi, Y. B. Chen, R. Z. Li, and Y. Q. Yang, “Fine-measuring technique and application for sea surface wind by mobile Doppler wind lidar,” Opt. Eng. 48(6), 066002 (2009).
[Crossref]

Z. S. Liu, B. Y. Liu, S. H. Wu, Z. G. Li, and Z. J. Wang, “High spatial and temporal resolution mobile incoherent Doppler lidar for sea surface wind measurements,” Opt. Lett. 33(13), 1485–1487 (2008).
[Crossref] [PubMed]

Liu, B.

Liu, B. Y.

Z. S. Liu, Z. J. Wang, S. H. Wu, B. Y. Liu, Z. G. Li, X. Zhang, D. C. Bi, Y. B. Chen, R. Z. Li, and Y. Q. Yang, “Fine-measuring technique and application for sea surface wind by mobile Doppler wind lidar,” Opt. Eng. 48(6), 066002 (2009).
[Crossref]

Z. S. Liu, B. Y. Liu, S. H. Wu, Z. G. Li, and Z. J. Wang, “High spatial and temporal resolution mobile incoherent Doppler lidar for sea surface wind measurements,” Opt. Lett. 33(13), 1485–1487 (2008).
[Crossref] [PubMed]

Liu, L.

Liu, Z.

Liu, Z. S.

Z. S. Liu, Z. J. Wang, S. H. Wu, B. Y. Liu, Z. G. Li, X. Zhang, D. C. Bi, Y. B. Chen, R. Z. Li, and Y. Q. Yang, “Fine-measuring technique and application for sea surface wind by mobile Doppler wind lidar,” Opt. Eng. 48(6), 066002 (2009).
[Crossref]

Z. S. Liu, B. Y. Liu, S. H. Wu, Z. G. Li, and Z. J. Wang, “High spatial and temporal resolution mobile incoherent Doppler lidar for sea surface wind measurements,” Opt. Lett. 33(13), 1485–1487 (2008).
[Crossref] [PubMed]

Z. S. Liu, W. B. Chen, T. L. Zhang, J. W. Hair, and C. Y. She, “An incoherent Doppler Lidar for ground-based atmospheric wind profiling,” Appl. Phys. B 64(5), 561–566 (1997).
[Crossref]

Lundquist, J. K.

R. M. Banta, Y. L. Pichugina, W. A. Brewer, J. K. Lundquist, N. D. Kelley, S. P. Sandberg, R. J. Alvarez, R. M. Hardesty, and A. M. Weickmann, “3D volumetric analysis of wind turbine wake properties in the atmosphere using high-resolution Doppler lidar,” J. Atmos. Ocean. Technol. 32(5), 904–914 (2015).
[Crossref]

I. N. Smalikho, V. A. Banakh, Y. L. Pichugina, W. A. Brewer, R. M. Banta, J. K. Lundquist, and N. D. Kelley, “Lidar investigation of atmosphere effect on a wind turbine wake,” J. Atmos. Oceanic Technol. A 30(11), 2554–2570 (2013).
[Crossref]

Mann, J.

A. Sathe and J. Mann, “A review of turbulence measurements using ground-based wind lidars,” Atmos. Meas. Tech. 6(11), 3147–3167 (2013).
[Crossref]

J. Trujillo, F. Bingol, G. Larsen, J. Mann, and M. Kuhn, “Light detection and ranging measurements of wake dynamics. Part II: Two-dimensional scanning,” Wind Energy A 14(1), 61–75 (2011).
[Crossref]

F. Bingöl, J. Mann, and G. C. Larsen, “Light detection and ranging measurements of wake dynamics, part I: one-dimensional scanning,” Wind Energy A 13(1), 51–61 (2010).
[Crossref]

Meillier, Y.

R. Frehlich, Y. Meillier, M. L. Jensen, B. Balsley, and R. Sharman, “Measurements of boundary layer profiles in an urban environment,” J. Appl. Meteorol. Climatol. 45(6), 821–837 (2006).
[Crossref]

Modlin, E.

G. Koch, J. Beyon, E. Modlin, P. Petzar, S. Woll, M. Petros, J. Yu, and M. Kavaya, “Side-scan Doppler lidar for offshore wind energy applications,” J. Appl. Remote Sens. 6(1), 063562 (2012).
[Crossref]

Oliver, A.

R. Krishnamurthy, A. Choukulkar, R. Calhoun, J. Fine, A. Oliver, and K. Barr, “Coherent Doppler lidar for wind farm characterization,” Wind Energy (Chichester Engl.) 16(2), 189–206 (2013).
[Crossref]

Petros, M.

G. Koch, J. Beyon, E. Modlin, P. Petzar, S. Woll, M. Petros, J. Yu, and M. Kavaya, “Side-scan Doppler lidar for offshore wind energy applications,” J. Appl. Remote Sens. 6(1), 063562 (2012).
[Crossref]

Petzar, P.

G. Koch, J. Beyon, E. Modlin, P. Petzar, S. Woll, M. Petros, J. Yu, and M. Kavaya, “Side-scan Doppler lidar for offshore wind energy applications,” J. Appl. Remote Sens. 6(1), 063562 (2012).
[Crossref]

Pichugina, Y. L.

R. M. Banta, Y. L. Pichugina, W. A. Brewer, J. K. Lundquist, N. D. Kelley, S. P. Sandberg, R. J. Alvarez, R. M. Hardesty, and A. M. Weickmann, “3D volumetric analysis of wind turbine wake properties in the atmosphere using high-resolution Doppler lidar,” J. Atmos. Ocean. Technol. 32(5), 904–914 (2015).
[Crossref]

I. N. Smalikho, V. A. Banakh, Y. L. Pichugina, W. A. Brewer, R. M. Banta, J. K. Lundquist, and N. D. Kelley, “Lidar investigation of atmosphere effect on a wind turbine wake,” J. Atmos. Oceanic Technol. A 30(11), 2554–2570 (2013).
[Crossref]

Porteagel, F.

G. Iungo, Y. Wu, and F. Porteagel, “Field Measurements of Wind Turbine Wakes with Lidars,” J. Atmos. Ocean. Technol. 30(2), 274–287 (2013).
[Crossref]

Pryor, S.

S. Frandsen, R. Barthelmie, S. Pryor, O. Rathmann, S. Larsen, J. Højstrup, and M. Thøgersen, “Analytical modelling of wind speed deficit in large offshore wind farms,” Wind Energy A 9(1-2), 39–53 (2006).
[Crossref]

Pryor, S. C.

R. J. Barthelmie, G. C. Larsen, S. T. Frandsen, L. Folkerts, K. Rados, S. C. Pryor, B. Lange, and G. Schepers, “Comparison of wake model simulations with offshore wind turbine wake profiles measured by sodar,” J. Atmos. Oceanic Technol. A 23(7), 888–901 (2006).
[Crossref]

Rados, K.

R. J. Barthelmie, G. C. Larsen, S. T. Frandsen, L. Folkerts, K. Rados, S. C. Pryor, B. Lange, and G. Schepers, “Comparison of wake model simulations with offshore wind turbine wake profiles measured by sodar,” J. Atmos. Oceanic Technol. A 23(7), 888–901 (2006).
[Crossref]

Rahm, S.

Y. Käsler, S. Rahm, R. Simmet, and M. Kuhn, “Wake measurements of a multi-MW wind turbine with coherent long-range pulsed Doppler wind lidar,” J. Atmos. Ocean. Technol. 27(9), 1529–1532 (2010).
[Crossref]

Rathmann, O.

S. Frandsen, R. Barthelmie, S. Pryor, O. Rathmann, S. Larsen, J. Højstrup, and M. Thøgersen, “Analytical modelling of wind speed deficit in large offshore wind farms,” Wind Energy A 9(1-2), 39–53 (2006).
[Crossref]

Sandberg, S. P.

R. M. Banta, Y. L. Pichugina, W. A. Brewer, J. K. Lundquist, N. D. Kelley, S. P. Sandberg, R. J. Alvarez, R. M. Hardesty, and A. M. Weickmann, “3D volumetric analysis of wind turbine wake properties in the atmosphere using high-resolution Doppler lidar,” J. Atmos. Ocean. Technol. 32(5), 904–914 (2015).
[Crossref]

Sathe, A.

A. Sathe and J. Mann, “A review of turbulence measurements using ground-based wind lidars,” Atmos. Meas. Tech. 6(11), 3147–3167 (2013).
[Crossref]

Schepers, G.

R. J. Barthelmie, G. C. Larsen, S. T. Frandsen, L. Folkerts, K. Rados, S. C. Pryor, B. Lange, and G. Schepers, “Comparison of wake model simulations with offshore wind turbine wake profiles measured by sodar,” J. Atmos. Oceanic Technol. A 23(7), 888–901 (2006).
[Crossref]

Schwiesow, R. L.

R. L. Schwiesow, F. Köpp, and C. Werner, “Comparison of CW-lidar-measured wind values obtained by full conical scan, conical sector scan and two-point techniques,” J. Atmos. Ocean. Technol. 2(1), 3–14 (1985).
[Crossref]

Sharman, R.

R. Frehlich, Y. Meillier, M. L. Jensen, B. Balsley, and R. Sharman, “Measurements of boundary layer profiles in an urban environment,” J. Appl. Meteorol. Climatol. 45(6), 821–837 (2006).
[Crossref]

She, C. Y.

Z. S. Liu, W. B. Chen, T. L. Zhang, J. W. Hair, and C. Y. She, “An incoherent Doppler Lidar for ground-based atmospheric wind profiling,” Appl. Phys. B 64(5), 561–566 (1997).
[Crossref]

Simmet, R.

Y. Käsler, S. Rahm, R. Simmet, and M. Kuhn, “Wake measurements of a multi-MW wind turbine with coherent long-range pulsed Doppler wind lidar,” J. Atmos. Ocean. Technol. 27(9), 1529–1532 (2010).
[Crossref]

Smalikho, I.

V. Banakh, V. Bodaruev, and I. Smalikho, “Estimation of the turbulence energy dissipation rate from the pulsed Doppler lidar data,” Atmos. Oceanic Opt. 10, 957–965 (1997).

Smalikho, I. N.

I. N. Smalikho, V. A. Banakh, Y. L. Pichugina, W. A. Brewer, R. M. Banta, J. K. Lundquist, and N. D. Kelley, “Lidar investigation of atmosphere effect on a wind turbine wake,” J. Atmos. Oceanic Technol. A 30(11), 2554–2570 (2013).
[Crossref]

Smedman, A.

U. Högström, D. N. Asimakopoulos, H. Kambezidis, C. G. Helmis, and A. Smedman, “A field study of the wake behind a 2MW wind turbine,” Atmos. Environ. A 22(4), 803–820 (1988).
[Crossref]

Thøgersen, M.

S. Frandsen, R. Barthelmie, S. Pryor, O. Rathmann, S. Larsen, J. Højstrup, and M. Thøgersen, “Analytical modelling of wind speed deficit in large offshore wind farms,” Wind Energy A 9(1-2), 39–53 (2006).
[Crossref]

Trujillo, J.

J. Trujillo, F. Bingol, G. Larsen, J. Mann, and M. Kuhn, “Light detection and ranging measurements of wake dynamics. Part II: Two-dimensional scanning,” Wind Energy A 14(1), 61–75 (2011).
[Crossref]

Wadaka, S.

Wang, Z.

Wang, Z. J.

Z. S. Liu, Z. J. Wang, S. H. Wu, B. Y. Liu, Z. G. Li, X. Zhang, D. C. Bi, Y. B. Chen, R. Z. Li, and Y. Q. Yang, “Fine-measuring technique and application for sea surface wind by mobile Doppler wind lidar,” Opt. Eng. 48(6), 066002 (2009).
[Crossref]

Z. S. Liu, B. Y. Liu, S. H. Wu, Z. G. Li, and Z. J. Wang, “High spatial and temporal resolution mobile incoherent Doppler lidar for sea surface wind measurements,” Opt. Lett. 33(13), 1485–1487 (2008).
[Crossref] [PubMed]

Weickmann, A. M.

R. M. Banta, Y. L. Pichugina, W. A. Brewer, J. K. Lundquist, N. D. Kelley, S. P. Sandberg, R. J. Alvarez, R. M. Hardesty, and A. M. Weickmann, “3D volumetric analysis of wind turbine wake properties in the atmosphere using high-resolution Doppler lidar,” J. Atmos. Ocean. Technol. 32(5), 904–914 (2015).
[Crossref]

Werner, C.

R. L. Schwiesow, F. Köpp, and C. Werner, “Comparison of CW-lidar-measured wind values obtained by full conical scan, conical sector scan and two-point techniques,” J. Atmos. Ocean. Technol. 2(1), 3–14 (1985).
[Crossref]

Woll, S.

G. Koch, J. Beyon, E. Modlin, P. Petzar, S. Woll, M. Petros, J. Yu, and M. Kavaya, “Side-scan Doppler lidar for offshore wind energy applications,” J. Appl. Remote Sens. 6(1), 063562 (2012).
[Crossref]

Wu, S.

Wu, S. H.

Z. S. Liu, Z. J. Wang, S. H. Wu, B. Y. Liu, Z. G. Li, X. Zhang, D. C. Bi, Y. B. Chen, R. Z. Li, and Y. Q. Yang, “Fine-measuring technique and application for sea surface wind by mobile Doppler wind lidar,” Opt. Eng. 48(6), 066002 (2009).
[Crossref]

Z. S. Liu, B. Y. Liu, S. H. Wu, Z. G. Li, and Z. J. Wang, “High spatial and temporal resolution mobile incoherent Doppler lidar for sea surface wind measurements,” Opt. Lett. 33(13), 1485–1487 (2008).
[Crossref] [PubMed]

Wu, Y.

G. Iungo, Y. Wu, and F. Porteagel, “Field Measurements of Wind Turbine Wakes with Lidars,” J. Atmos. Ocean. Technol. 30(2), 274–287 (2013).
[Crossref]

Yang, Y. Q.

Z. S. Liu, Z. J. Wang, S. H. Wu, B. Y. Liu, Z. G. Li, X. Zhang, D. C. Bi, Y. B. Chen, R. Z. Li, and Y. Q. Yang, “Fine-measuring technique and application for sea surface wind by mobile Doppler wind lidar,” Opt. Eng. 48(6), 066002 (2009).
[Crossref]

Yu, J.

G. Koch, J. Beyon, E. Modlin, P. Petzar, S. Woll, M. Petros, J. Yu, and M. Kavaya, “Side-scan Doppler lidar for offshore wind energy applications,” J. Appl. Remote Sens. 6(1), 063562 (2012).
[Crossref]

Zhang, T. L.

Z. S. Liu, W. B. Chen, T. L. Zhang, J. W. Hair, and C. Y. She, “An incoherent Doppler Lidar for ground-based atmospheric wind profiling,” Appl. Phys. B 64(5), 561–566 (1997).
[Crossref]

Zhang, X.

Z. S. Liu, Z. J. Wang, S. H. Wu, B. Y. Liu, Z. G. Li, X. Zhang, D. C. Bi, Y. B. Chen, R. Z. Li, and Y. Q. Yang, “Fine-measuring technique and application for sea surface wind by mobile Doppler wind lidar,” Opt. Eng. 48(6), 066002 (2009).
[Crossref]

Appl. Opt. (2)

Appl. Phys. B (1)

Z. S. Liu, W. B. Chen, T. L. Zhang, J. W. Hair, and C. Y. She, “An incoherent Doppler Lidar for ground-based atmospheric wind profiling,” Appl. Phys. B 64(5), 561–566 (1997).
[Crossref]

Atmos. Environ. A (1)

U. Högström, D. N. Asimakopoulos, H. Kambezidis, C. G. Helmis, and A. Smedman, “A field study of the wake behind a 2MW wind turbine,” Atmos. Environ. A 22(4), 803–820 (1988).
[Crossref]

Atmos. Meas. Tech. (1)

A. Sathe and J. Mann, “A review of turbulence measurements using ground-based wind lidars,” Atmos. Meas. Tech. 6(11), 3147–3167 (2013).
[Crossref]

Atmos. Oceanic Opt. (1)

V. Banakh, V. Bodaruev, and I. Smalikho, “Estimation of the turbulence energy dissipation rate from the pulsed Doppler lidar data,” Atmos. Oceanic Opt. 10, 957–965 (1997).

Bound. -Layer Meteor. (1)

R. Frehlich, S. M. Hannon, and S. W. Henderson, “Coherent Doppler lidar measurements of wind field statistics,” Bound. -Layer Meteor. 86(2), 233–256 (1998).
[Crossref]

J. Appl. Meteorol. Climatol. (1)

R. Frehlich, Y. Meillier, M. L. Jensen, B. Balsley, and R. Sharman, “Measurements of boundary layer profiles in an urban environment,” J. Appl. Meteorol. Climatol. 45(6), 821–837 (2006).
[Crossref]

J. Appl. Remote Sens. (1)

G. Koch, J. Beyon, E. Modlin, P. Petzar, S. Woll, M. Petros, J. Yu, and M. Kavaya, “Side-scan Doppler lidar for offshore wind energy applications,” J. Appl. Remote Sens. 6(1), 063562 (2012).
[Crossref]

J. Atmos. Ocean. Technol. (7)

R. M. Banta, Y. L. Pichugina, W. A. Brewer, J. K. Lundquist, N. D. Kelley, S. P. Sandberg, R. J. Alvarez, R. M. Hardesty, and A. M. Weickmann, “3D volumetric analysis of wind turbine wake properties in the atmosphere using high-resolution Doppler lidar,” J. Atmos. Ocean. Technol. 32(5), 904–914 (2015).
[Crossref]

Y. Käsler, S. Rahm, R. Simmet, and M. Kuhn, “Wake measurements of a multi-MW wind turbine with coherent long-range pulsed Doppler wind lidar,” J. Atmos. Ocean. Technol. 27(9), 1529–1532 (2010).
[Crossref]

G. Iungo, Y. Wu, and F. Porteagel, “Field Measurements of Wind Turbine Wakes with Lidars,” J. Atmos. Ocean. Technol. 30(2), 274–287 (2013).
[Crossref]

D. H. Lenschow and L. Kristensen, “Applications of dual aircraft formation flights,” J. Atmos. Ocean. Technol. 5(6), 715–726 (1988).
[Crossref]

R. Frehlich, “Effects of wind turbulence on coherent Doppler lidar performance,” J. Atmos. Ocean. Technol. 14(1), 54–75 (1997).
[Crossref]

R. Frehlich and L. Cornman, “Estimating spatial velocity statistics with coherent Doppler lidar,” J. Atmos. Ocean. Technol. 19(3), 355–366 (2002).
[Crossref]

R. L. Schwiesow, F. Köpp, and C. Werner, “Comparison of CW-lidar-measured wind values obtained by full conical scan, conical sector scan and two-point techniques,” J. Atmos. Ocean. Technol. 2(1), 3–14 (1985).
[Crossref]

J. Atmos. Oceanic Technol. A (2)

I. N. Smalikho, V. A. Banakh, Y. L. Pichugina, W. A. Brewer, R. M. Banta, J. K. Lundquist, and N. D. Kelley, “Lidar investigation of atmosphere effect on a wind turbine wake,” J. Atmos. Oceanic Technol. A 30(11), 2554–2570 (2013).
[Crossref]

R. J. Barthelmie, G. C. Larsen, S. T. Frandsen, L. Folkerts, K. Rados, S. C. Pryor, B. Lange, and G. Schepers, “Comparison of wake model simulations with offshore wind turbine wake profiles measured by sodar,” J. Atmos. Oceanic Technol. A 23(7), 888–901 (2006).
[Crossref]

Opt. Eng. (1)

Z. S. Liu, Z. J. Wang, S. H. Wu, B. Y. Liu, Z. G. Li, X. Zhang, D. C. Bi, Y. B. Chen, R. Z. Li, and Y. Q. Yang, “Fine-measuring technique and application for sea surface wind by mobile Doppler wind lidar,” Opt. Eng. 48(6), 066002 (2009).
[Crossref]

Opt. Lett. (1)

Renew. Energy A (1)

F. B. Amar, M. Elamouri, and R. Dhifaoui, “Energy assessment of the first wind farm section of Sidi Daoud, Tunisia,” Renew. Energy A 33(10), 2311–2321 (2008).
[Crossref]

Wind Energy (Chichester Engl.) (1)

R. Krishnamurthy, A. Choukulkar, R. Calhoun, J. Fine, A. Oliver, and K. Barr, “Coherent Doppler lidar for wind farm characterization,” Wind Energy (Chichester Engl.) 16(2), 189–206 (2013).
[Crossref]

Wind Energy A (3)

S. Frandsen, R. Barthelmie, S. Pryor, O. Rathmann, S. Larsen, J. Højstrup, and M. Thøgersen, “Analytical modelling of wind speed deficit in large offshore wind farms,” Wind Energy A 9(1-2), 39–53 (2006).
[Crossref]

F. Bingöl, J. Mann, and G. C. Larsen, “Light detection and ranging measurements of wake dynamics, part I: one-dimensional scanning,” Wind Energy A 13(1), 51–61 (2010).
[Crossref]

J. Trujillo, F. Bingol, G. Larsen, J. Mann, and M. Kuhn, “Light detection and ranging measurements of wake dynamics. Part II: Two-dimensional scanning,” Wind Energy A 14(1), 61–75 (2011).
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Other (3)

H. Jørgensen, T. Mikkelsen, J. Mann, D. Bryce, A. Coffey, M. Harris, and D. Smith,“Site wind field determination using a CW Doppler Lidar- comparison with cup anemometers at Risø,” in The Science of Making Torque from Wind (European Wind Energy Association, 2004), pp. 261–266.

S. Wu, J. Yin, B. Liu, and J. Liu, “Wind Turbine Wake Visualization by Doppler Lidar,” in Light, Energy and the Environment 2015, OSA Technical Digest (online) (Optical Society of America, 2015), paper EM3A.4.
[Crossref]

J. O. Hinze and J. Hinze, Turbulence: an introduction to its mechanism and theory (McGraw-Hill New York, 1959).

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Figures (17)

Fig. 1
Fig. 1 The pulsed coherent Doppler Lidar setup.
Fig. 2
Fig. 2 The LOS velocity estimation by an arc scanning lidar and sine wave fitting.
Fig. 3
Fig. 3 Comparison of wind speed (a) and wind direction (b) measured by scanning wind lidar and mast.
Fig. 4
Fig. 4 Horizontal wind speed correlation (a) and wind direction correlation (b) at 80m for ten-minute data measured by 3D wind lidar and anemometer.
Fig. 5
Fig. 5 Horizontal wind speed correlation (a) and wind direction correlation (b) at 80m for Bin Averaged Data.
Fig. 6
Fig. 6 Map of the test site in Longgang Wind Power with the positions of the wind turbines (denoted by turbine blade) and the lidar locations (denoted by the pins and balloons for the wake detection and alternative wind profile measurement, respectively). The red circle indicates the region for wake study where the PCDL scan was made over turbine wakes and ambient atmosphere (lower right).
Fig. 7
Fig. 7 LOS wind velocity by lidar with PPI scanning at the wind park with foothills topography. Three of wind turbine generators are denoted as a, b and c.
Fig. 8
Fig. 8 LOS velocity detected by RHI scanning mode through two rotor blades at the wind park with foothills topography. Two wind turbine generators are denoted as d and e.
Fig. 9
Fig. 9 Velocity deficit downwind behind the WTG c (a) and WTG e (b) as the function of the blade diameter D.
Fig. 10
Fig. 10 Map of the lidar test site at the Rudong intertidal wind farm in spring and winter of 2014 with the positions of wind turbine generators (denoted by red dots) and locations of two 3D scanning PCDLs (denoted by the balloon A and B) and a wind profiler lidar (denoted by the balloon C).
Fig. 11
Fig. 11 LOS wind field at the intertidal zone by lidar PPI scan.
Fig. 12
Fig. 12 Turbulent wind field in the vicinity of operating wind turbines in Hami Gobi plain wind park at high wind speed of 8 −10 ms−1 (a) and relatively low wind speed of 4 - 6 ms−1 (b).
Fig. 13
Fig. 13 Wind speed profile series around two wind turbines retrieved form the Fig. 8’s RHI measurement.
Fig. 14
Fig. 14 The wind speed obtained by the 2 synchronously scanning lidars at the intertidal wind farm in December 2014 with the positions of lidars (denoted by red squares A and B). A wake induced by wind turbine generator WTG T1 is denoted by a rectangle in dash black line. The free stream region outside the wake is marked as a reference wind field by a rectangle in solid red line.
Fig. 15
Fig. 15 Wind velocity at the free stream region as a reference velocity and the wind velocity in the wake region. The tendency of reference velocity and wake velocity are plotted by a red triangle in solid red line and a black rectangle in dash black line, respectively.
Fig. 16
Fig. 16 Velocity deficit downwind behind the wind turbine generator WTG 1 as the function of the distance.
Fig. 17
Fig. 17 Longitudinal structure function for (a) Jan 3 2014 at Longgang, (b) April 10 2014 at Rudong, (c) Nov 15 2015 at Hami. Curves show calculations of the structure function for D raw (s) (blue closed circle), the corrected structure function D LL (s) (black closed circle), the von Kármán model D LL (s) ~ (black solid line) and the corrected von Kármán model D wgt (s,σ, L 0 ) (red solid line).

Tables (1)

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Table 1 Component Parameters of the CDL System

Equations (10)

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δ= v ¯ amb (z) v wake (z) v ¯ amb (z) ×100%,
D LL (s)= D raw (s)E(s),
D raw (kΔs)= 1 N T ( N R k) l=1 N T j=1 N R k { v ' [ R 1 +(j1)Δs, ϕ 1 +(l1)Δϕ,θ] v ' [ R 1 +(j+k1)Δs, ϕ 1 +(l1)Δϕ,θ]} 2 ,
D LL (s) ~ =2 σ 2 Λ( s L 0 ),
Λ(x)=1 2 2/3 x 1/3 Γ(1/3) K 1/3 (x)=10.5925485 x 1/3 K 1/3 (x),
L i = π Γ(5/6) Γ(1/3) L 0 =0.7468343 L 0 .
ε=[ 2 1/3 π 3 Γ(1/3)Γ(4/3) ] σ 3 L 0 =0.933668 σ 3 L 0 .
D wgt (s,σ, L 0 )=2 σ 2 G( s Δs , 2ln2 Δs Δr , Δs L 0 ),
G(m,μ,χ)= F(x,μ) [Λ(χ| mx |)Λ(χ| x |)]dx.
χ LL 2 = 1 N s k=1 N s [ D LL (kΔs) D wgt (kΔs,σ, L 0 )] 2 [k D wgt (kΔs,σ, L 0 )] 2 .

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