1 Introduction

With advances in technology associated with the use of wind energy, the latest wind turbine generators—with high wheel hubs and long blades—have the ability to work under conditions of small beginning wind speeds and are highly efficient in wind energy utilization. However, the design of such wind turbine generators requires considerable accuracy when judging the ranges over which surface layer winds and turbulent parameters vary. Banta et al. (2013) proposed the need for high-quality wind information aloft in the layer occupied by turbine rotors (30–150 m above ground level) as one of many significant challenges facing the wind energy industry. Kalvig et al. (2014) believed that an accurate estimation of the wind profile is important for design purposes, wind energy assessment, operational production, and for day-to-day power output estimations. Rajewski et al. (2013) measured air temperature, surface fluxes, and other variables at an Iowa wind farm as part of the Crop/Wind-Energy Experiment campaign.

Presently, a document entitled, Wind turbines—Part 1: Design requirements, which was compiled by the International Electro-technical Commission (hereinafter referred to as IEC61400-1; IEC, 2005), is the most widely applied text in the field of wind energy worldwide. The relevant documents adopted in China, such as Requirements of Wind Turbine Design (National Technical Committee for Wind Machinery Standardization, 2001; General Administration of Quality Supervision, Inspection and Quarantine of the People’s Republic of China and China National Standardization Management Committee, 2012) and Appraisal Method of Wind Energy Resource (China Water Conservancy and Hydropower Engineering Consulting Company, 2004), have all been improved and compiled according to the IEC61400-1 standard. In these standards, the wind speed and turbulence parameters are the basis for the classification of wind turbine generators, and different wind speed and turbulence parameters represent the differences in site conditions. Moreover, because the calculations of wind speed and turbulence parameters are simple and convenient, these calculations are widely adopted in the field of wind energy.

A considerable amount of research has been conducted on the characteristics of turbulent structures and transport phenomena in the boundary layer. Rozenn et al. (2010) used aerodynamic simulations to investigate the influence of the turbulence intensity on the power output of a multi-megawatt turbine. Niu et al. (2012) examined the Monin–Obukhov similarity for describing the turbulent fluctuations of 3D winds under all stability conditions and to obtain the turbulence characteristics under different weather conditions. Abkar and Porté-Agel (2013) used large-eddy simulations to study the influence of free-atmosphere stratification on the structure of atmospheric boundary-layer flow inside and above very large wind farms, as well as the power extracted by the wind turbines. Zhang and Hu (2017) studied the diurnal variation of turbulence intensity and wind power under different turbulence intensities. Huang et al. (2016) used the computation method for extreme wind speeds recommended by the IEC61400-1 standard and found that the results in China were mostly smaller than those of the standard. However, few studies have examined the surface-layer wind shear exponent and turbulence parameters in the IEC61400-1 standard.

In this paper, observational data from three 100-m wind towers in Xilinhot in Inner Mongolia (from May 2009 to April 2010; grassland region), Huanghua in Hebei Province (from September 2009 to August 2010; coastal flat region), and Xingzi County in Jiangxi Province (from November 2010 to October 2011; mountain–lake region) are used to analyze the variations in the surface-layer wind shear exponent and turbulence parameters over different underlying surfaces. The results of this study provide a reference for feasibility studies on the development of low-wind-speed wind energy resources and the selection, design, and operational maintenance of wind turbines.

2 Observational sites and data processing 2.1 Observational sites and instrumentation

The observational experiments were conducted at three sites in China: Xilinhot in Inner Mongolia, Huanghua in Hebei Province, and the Poyang Lake area of Jiangxi Province. Figure 1 shows the locations of the three 100-m wind towers and corresponding topographic maps. The height changes of the terrain surrounding the Xilinhot wind tower (44.12°N, 116.30°E; hereafter referred to as T1) in Inner Mongolia are gentle, and the elevation heights are generally greater than 1100 m. This wind tower is 100 m high, and the elevation height at the site location of the tower is 1159 m. The terrain in the western and northwestern parts of the area is relatively high, and there is a gentle slope of approximately 3°–6°. The underlying surface is grassland, the height of the grass in summer can reach 30–40 cm, and the coverage is approximately 70%–80%. The withered grass in winter has a height of approximately 5 cm. The height changes of the terrain surrounding the Huanghua wind tower (38.33°N, 117.67°E; hereafter referred to as T2) in Hebei Province are gentle. The Bohai Sea lies in the north-northeast to south-southeast direction, and farmland and residential areas are found in other directions. The wind tower is approximately 1500 m from the closest coastline, and the underlying surface is a shrimp pond that does not experience considerable changes over the four seasons of the year. The east side of the Xingzi wind tower in Jiangxi Province (29.37°N, 116.01°E; hereafter referred to as T3) is approximately 500 m from Poyang Lake. The ground is covered with low vegetation throughout the year. According to the aforementioned characteristics, we use the Xilinhot site to represent grassland region, the Huanghua site as a representative of a coastal flat region, and the Poyang Lake site as representative of a mountain–lake region to analyze the characteristics of surface layer winds over different underlying surfaces in China.

The observational instruments used for recording the wind speed, temperature, and humidity are all manufactured by Jiangsu Radio Scientific Institute Co. Ltd., China. The observational heights are 10, 30, 50, 70, and 100 m. Details of the instrumental setups are shown in Table 1. We also adopt the CSAT3 three-dimensional sonic anemometer/thermometer (SAT) manufactured by the Campbell Company, USA at heights of 10, 30, 50, and 70 m, and the sampling frequency is 20 Hz. The observational instruments used at the different sites are all the same. The time periods for the wind speed observational data used in this paper are from May 2009 to April 2010 for Xilinhot, September 2009 to August 2010 for Huanghua, and November 2010 to October 2011 for Xingzi.

2.2 Data processing 2.2.1 Basic quality control

Due to the influences of instrument malfunctions, overhauls, weather factors, and power supplies, there will be data gaps and anomalies. Thus, in this paper, we first undertake quality control on the observational data as follows:

(1) Eliminate the data beyond horizontal wind speeds [–20, 20] m s^–1, vertical wind speeds [–10, 10] m s^–1, and temperatures [–50, 50] °C that are inconsistent with common physical sense, and those data that are inconsistent with the general statistical characteristics of the climate.

(2) Eliminate random pulses generated by the data receiving system and data transmission system caused by water vapor condensation on the sensors. Values of $\left| {{X_{i + 2}}} - {X_{i}} \right| > 5\sigma $ are regarded as random pulses and therefore eliminated, where X is the time sequence and σ is the variance (Højstrup, 1993; Vickers and Mahrt, 1997).

2.2.2 Rotational coordinates

By referring to Kaimal and Finnigan (1994), and Foken (2008) for the convenience of analysis and calculation, we rotate the x-axis of the coordinate system to the predominant wind direction and make the average speed $\bar v$ in the y-direction zero. We establish the coordinate system according to the right-hand rotation rule. Upon rotation, the instantaneous wind speeds in the three directions of u, v, and w, derived by the observation of the turbulent gradient, are multiplied by the rotation matrix, as shown in Eq. (1), where $\bar u$ and $\bar v$ are the average values of u and v, respectively. After the rotation, the wind speed in the x-direction is u₁, and the wind speed in the y-direction is v₁, which satisfies $\bar v{_1} = 0$ ; the wind speed in the z-direction is w₁.

$(u\;\;v\;\;w) \times \begin{bmatrix} {\dfrac{{\bar u}}{{\sqrt {{{\bar u}^2} + {{\bar v}^2}} }}}&{\dfrac{{ - \bar v}}{{\sqrt {{{\bar u}^2} + {{\bar v}^2}} }}}&0 \; \\[6mm] {\dfrac{{\bar v}}{{\sqrt {{{\bar u}^2} + {{\bar v}^2}} }}}&{\dfrac{{\bar u}}{{\sqrt {{{\bar u}^2} + {{\bar v}^2}} }}}& 0 \; \\[6mm] 0 & 0 & 1 \; \end{bmatrix} = \left({{u_1}\;{v_1}\;{w_1}} \right).$

(1)

To eliminate the error caused by the non-horizontal installation of the instrument, we can make the average vertical speed ${\bar w} $ zero through the rotation of coordinates. The wind speeds in the three directions of u₁, v₁, and w₁, obtained with Eq. (1), are multiplied by the rotation matrix, as shown in Eq. (2). After rotation, the wind speed in the x-direction is u₂, and the wind speed in the y-direction is v₂, which satisfies $\bar v{_2} = 0$ ; the wind speed in the z-direction is w₂, which satisfies $\bar w{_2} = 0$ .

$\left({{u_1}\;{v_1}\;{w_1}} \right) \times \begin{bmatrix} {\dfrac{{\bar u}}{{\sqrt {{{\bar u}^2} + {{\bar w}^2}} }}} &0 &{\dfrac{{ - \bar w}}{{\sqrt {{{\bar u}^2} + {{\bar w}^2}} }}}\\[6mm] 0 &1 & 0\\[2mm] {\dfrac{{\bar w}}{{\sqrt {{{\bar u}^2} + {{\bar w}^2}} }}} & 0 &{\dfrac{{\bar u}}{{\sqrt {{{\bar u}^2} + {{\bar w}^2}} }}} \end{bmatrix}= \left({{u_2}\;{v_2}\;{w_2}} \right).$

(2)

2.3 Calculation of important turbulent parameters

According to surface-layer similarity theory (Monin and Obukhov, 1954),

$\!\!\!\!\!{\rm{Speed}}\;{\rm{scale}}:{u_*} = {\left({{{\overline {u'w'} }^2} + {{\overline {v'w'} }^2}} \right)^{\frac{1}{4}}}, $

(3)

${\rm{Temperature}}\;{\rm{scale}}:{T_*} = - \frac{{\overline {w'T'} }}{{{u_*}}}, \quad {\rm{and}}$

(4)

${\rm{Length}}\;{\rm{scale}}:L = - \dfrac{{u_*^3}}{{\kappa \dfrac{g}{T}\overline {w'T'} }}, \quad\quad\quad\!\!$

(5)

where the speed scale u_* is the frictional speed; the length scale is the Monin–Obukhov length L (hereinafter referred to as L); u', v', w', and T' are the three-dimensional wind speed fluctuations and temperature fluctuation, respectively;κ is the Karman constant (0.4); g is the gravitational acceleration; T is the average temperature; and z is the observation height.

The turbulence intensity (IEC, 2005) is the manifestation of the fluctuating characteristics of wind, and the turbulence intensity is calculated as follows:

${I_i} = \frac{{{\sigma _i}}}{{\bar U}} \quad \left({i = u, v, w} \right), $

(6)

where σ_i is the standard deviation of the average wind speed over 10 min, $\bar U$ is the modulus of horizontal wind speed, and the time interval is 10 min.

The turbulence integral scale expresses the mean spatial scale and mean life of turbulent vortices. Taylor introduced the correlation coefficient integral to characterize the overall characteristic length of a turbulent field (Kaimal, 1973; Stull, 1988; Sheng et al., 2003; Song et al., 2005):

${L_i} = U \mathop \int \limits_0^\infty \frac{{{R_i}\left({\tau } \right)}}{{\sigma _i^2}}{\rm d} \tau \quad \;\; $

(7)

${R_i}({\rm{\tau }}) = E \left[ {i \left(t \right)i \left({t + \tau } \right)} \right], $

(8)

where i(t) is the stationary random signal, and R_i(τ) is the autocorrelation function of i(t).

The turbulent power spectral density function S_i (Höbbel et al., 2018) can more accurately describe the characteristics of fluctuating winds, as well as the proportions of turbulent kinetic energy at different scale levels. The total integrals in the frequency domain are equal to the turbulent kinetic energy in the corresponding direction of fluctuation:

$\mathop \int \limits_0^\infty i{S_i}\left(n \right){\rm d}n = \sigma _i^2, $

(9)

where n is frequency. Turbulence spectrum calculations can be classified into the period graph and autocorrelation methods. In this paper, we adopt the period graph method (Xue, 2008). That is, we directly calculate the Fourier transform of a random signal X_N(n) of length N, calculate the square of the amplitude, and divide by N to obtain an estimate of the turbulent power spectrum as follows:

${{P(w)}} = \frac{1}{N}{\left| {{X_N}\left(w \right)} \right|^2}, $

(10)

where P(w) is the estimate of the power spectrum, and X_N(w) is the Fourier transform of signal X_N(n).

The turbulence scale parameter Λin IEC61400-1 is the wavelength when the dimensionless longitudinal turbulent power spectral density is equal to 0.05:

$\frac{{n{S_u}\left(n \right)}}{{{\sigma _u}^2}} = 0.05, $

(11)

$\varLambda = \frac{{\bar U}}{n},\quad\quad\quad\!$

(12)

where $\bar U$ is the modulus of horizontal wind speed, and the time interval is 1 h.

Moreover, for the standard grade of wind power generators, at the hub height location z, the value ofΛis determined as follows:

$\varLambda = \left\{ {\begin{array}{*{20}{c}} {0.7 z\;\;\;\;\;\;\;\;\;\;\;\;\;z < 60 \;{\rm m}}\\ {42 z\;\;\;\;\;\;\;\;\;\;\;\;\;z \geqslant 60 \;{\rm m}} \end{array}} \right..$

(13)

3 Analysis of the observational data 3.1 Variation in the wind shear exponent

The wind shear exponent is used to describe the vertical distribution of surface-layer wind speeds, and the wind shear exponent mainly depends on the characteristics of the underlying surface and atmospheric stratification state (Smedman-Högström and Högström, 1978; Irwin, 1979; Zoumakis, 1993; Petersen, 1998; van den Berg, 2008). Currently, the wind turbine development trend is towards higher towers and longer blades. When the wind shear between the upper and lower layers is too large, uneven forces are easily created on the blade and increase the load of the tower, which will reduce the lifetime of the wind turbine. While using fluid dynamics software to simulate the motion of the wind field, we also need to set the vertical wind speed profile as the initial boundary condition for the calculation. In this paper, we study the characteristics of the variation in the wind shear exponent for different underlying surfaces and different atmospheric stabilities in China.

Table 2 shows the distributions of Lvalues for 1 yr at a 100-m height for different locations, as calculated by adopting Eqs. (3)–(5) during the observational experiment period. In particular, the stability classification refers to the studies of Gryining et al. (2007) and Alfredo (2009). The occurrence frequencies of very stable stratifications (0 < L < 50) and very unstable stratifications (–100 < L < 0) in Europe are very small, and because there is a certain occurrence frequency in our country, we must consider these two situations. Gong et al. (2014) compared the classification of atmospheric stability in different regions, not shown here. We can see that the differences among the variations in atmospheric stability are very large at the three wind tower locations. The frequencies for the occurrence of very unstable and very stable stratifications both exceed 30% for T1, the stable stratification accounts for 12%, and the frequency for the occurrence of other stabilities is comparable. The occurrence frequency of very unstable stratifications is the highest (41%) for T2, followed by those for very stable, stable, and neutral stratifications (all above 10%), and the frequency of occurrence for other stabilities is not considerably different. The frequencies for the occurrences of very unstable, neutral, and very stable stratifications all exceed 20% for T3 and are followed by that of stable stratification, whereas the occurrence frequencies for unstable, slightly unstable, and slightly stable stratifications are relatively low.

Figure 2 shows the distribution variation of different stabilities with time. According to Peña et al. (2016), during the daytime, especially at noon, solar radiation is strong, the temperature increase at the ground surface is rapid, atmospheric motion is violent, and the proportion of unstable stratifications increases. At night, however, the proportion of stable stratifications is relatively large. The surface underlying T1 is an inland gentle slope of 3°–6° with a uniform underlying surface that is subject to the small influences of dynamic and thermodynamic effects. Therefore, these conditions essentially comply with the rule of diurnal variation in the atmospheric stability described by classical similarity theory. Although the terrain of T2 is flat, this area is 1.5 km from the coastline and will be subject to the actions of local sea–land circulations (Miao et al., 2015). The exchanges between the atmosphere over the continent and the atmosphere over the ocean slightly increase the stability of the nighttime atmospheric stratification. The terrain on which T3 is located is a mix of lacustrine and montane land, and the horizontal distance of this location from the water surface of Poyang Lake is approximately 500 m. The dynamic effects of terrain and local lake–land circulations will both affect the observations at the wind tower, I_w for T3 is much larger than that of T1 and T2, and the proportion of the appearance of nighttime neutral atmospheric stratification is increased.

Figure 3 shows the frequency distributions of the wind shear exponent α under different stabilities. The abscissae values are very unstable, unstable, slightly unstable, neutral, slightly stable, stable, and very stable from left to right, and the ordinates represent the frequency of the wind shear exponent α from 10–100 m. The wind speed is observed at heights of 10–100 m and fitted by the least square method to calculate wind shear exponent α. The frequency of α for T1 is the highest under the very unstable and very stable states, while for T2, the frequency is the highest under the very unstable state, and the frequency under other stabilities is comparable. The frequency of α for T3 is high under the very unstable, neutral, and very stable states.

T1 is located on an inland, hilly, gentle-slope topography, where α is small, and the proportion of α > 0.3 is 6%. Moreover, most frequencies appear under the stable and very stable states, which is because under the stable state of atmospheric stratification, the exchange between the upper and lower layers of the atmosphere is small. T2 is located in a coastal area, where the probability of α > 0.3 is high (13%). As the terrain around T2 is flat, if the atmospheric stratification is stable, α is more likely to exhibit large values. T3 is located in the mountains along the shores of inland lakes, and under the action of local terrain, the mountain flow is accelerated, neutral conditions increase, and the frequency of occurrence for small shear indices increases. Under stable stratification, the frequency of α > 0.3 is 10% because there are large wind accelerations within 30–50 and 70–100 m throughout the year. The aforementioned results indicate that the variation ranges of α for different underlying surfaces and different stabilities are not the same, while the unified assumption of a wind shear exponent cannot satisfy the actual demand (Hu et al., 2013).

3.2 Variation in turbulent intensity 3.2.1 Characteristics of turbulent intensity

Turbulence is the main form of atmospheric motion and plays a key role in momentum transfer, heat transfer, water vapor exchange, and material transfer between the ground surface and atmosphere. The phenomenon of turbulence will cause the instantaneous wind speed to fluctuate around the average wind speed and the output power of a wind turbine unit will change.

The IEC61400-1 standard provides two kinds of turbulence models that are used for calculating design loads: (1) the Mann uniform shear model (Mann, 1994, 1998), which presumes that the isotropic von Karman energy spectrum (von Kármán, 1948) is rapidly deformed by a uniform average speed shear and the relationship between the standard deviation of turbulence is derived in three directions through integration: ${\sigma _v} \approx 0.7{\sigma _u}, {\sigma _w} \approx 0.5$ $ {\sigma _u}$ ; and (2) the Kaimal spectrum and exponential coherence model (Kaimal, 1972), which uses three-dimensional ultrasonic observation data (20 Hz) from a 1968 experiment in Kansas (Kaimal and Wyngaard, 1990) and derives the relationships of ${\sigma _v} = 0.8{\sigma _u}\;{\rm{and}}\;{\sigma _w} = 0.5{\sigma _u}$ . In addition, for the standard grade of wind turbine generators, the turbulence model presumes that σ_u does not change as the altitude varies, ${\sigma _v} = 0.8{\sigma _u}\;{\rm{and}}\;{\sigma _w} = 0.5{\sigma _u}$ ; namely, ${I_v} = 0.8{I_u}\;{\rm{and}}\;{I_w} = 0.5{I_u}$ . These conclusions were obtained based on atmospheric boundary layer experiments in flat, open areas of Europe and America. However, the terrain in China is complicated, and there are various kinds of underlying surfaces. Niu et al. (2012) gave dimensionless standard deviations of velocity components (I_v/I_u and I_w/I_u) in near-neutral stratifications for different areas. Thus, whether the IEC61400-1 standard can be equally applied and what the specific situation in China would be are important questions to answer.

Figures 4 and 5 show the frequency distributions of I_v/I_u and I_w/I_u at heights of 10, 30, 50 and 70 m for T1 (17–30 April 2010), T2 (17–30 April 2010) and T3 (17–30 April 2011). The abscissa represents the values of I_v/I_u and I_w/I_u, the value range between [0.5, 2] and [0, 1], respectively, and the ordinate is the amount. The frequency distributions ofI_v/I_u and I_w/I_u at different heights at the same site are approximately the same, and the frequency distribution forms of I_v/I_u and I_w/I_u at the different sites differ slightly. The frequency of I_v/I_u at the four heights for T1 is the largest at approximately 0.8, and 90% of the I_v/I_u values are smaller than 1.97. The frequency of I_w/I_u in the range of 0.35–0.5 is relatively large, and 90% of the I_w/I_u values are smaller than 0.59. The frequency of I_v/I_u at the four heights for T2 is the largest at 0.8, and the frequencies decrease for larger ratios, with 90% of the I_v/I_u being smaller than 1.66. The frequency of I_w/I_u at a height of 10 m is relatively large in the range of 0.45–0.5, and the frequency for other heights is the largest at 0.5, with 90% of the I_w/I_u being smaller than 0.58. The frequency of I_v/I_u for the four heights for T3 is the largest at 0.8, and 90% of the I_v/I_u values are smaller than 1.72; the frequency of I_w/I_u at a height of 10 m is large in the range of 0.4–0.55, and 90% of the I_w/I_u values for the four heights are smaller than 0.75. Therefore, the situations for different underlying surfaces in China differ, and the proportion that is greater than the rated value in the IEC61400-1 standard is considerable. If the frequency is neglected, inadequate risk estimations can result when designing wind turbine loads, thus affecting the lifetimes of wind turbines.

For the situations in which the frequency is much larger than the rated value in the IEC61400-1 standard, we need to commence a separate discussion. Figure 6 shows the frequency distributions of I_v/I_u > 1.2 and I_w/I_u > 0.6 for different wind directions at height of 50 m for T1 (17–30 April 2010), T2 (17–30 April 2010), and T3 (17–30 April 2011). The abscissa represents eight wind directions with intervals of 45°, and the ordinate represents the amount. At different sites, the trends of the frequency distributions for I_v/I_u > 1.2 and I_w/I_u > 0.6 for different wind directions are not consistent, and the occurrence probability in the predominant wind direction is high. The east, southeast, and west sides of T1 are obstructed by mountains, the frequencies of occurrence for these three wind directions are relatively low, and the frequencies of I_v/I_u > 1.2 and I_w/I_u > 0.6 are also low. The predominant wind directions at T2 are easterly and northwesterly, and the frequencies of I_v/I_u > 1.2 and I_w/I_u > 0.6 are high. The predominant wind direction at T3 is northeasterly, which accounts for 34%; under the impact of terrain, air flow climbs and wind speed increases, the frequencies of I_v/I_u > 1.2 and I_w/I_u > 0.6 for the northeast wind direction are the highest. Moreover, the east side is approximately 500 m from the water area of Poyang Lake, and the local lake–land circulation causes the frequency of I_w/I_u > 0.6 to be higher on the water side than that for the non-water side. That is, regardless of the kind of underlying surface, more large values of I_v/I_u and I_w/I_u appear in the predominant wind direction. If the underlying surface is close to the water area, the frequency at which large values of I_w/I_u appear is higher in the predominant wind direction on the water side. The phenomena of I_v/I_u > 1.2 and I_w/I_u > 0.6 have local characteristics, which are not necessarily caused by external causes but are likely to be local turbulence characteristics.

3.2.2 Relationship between turbulent intensities calculated with different observation instruments

The sonic anemometer is more accurate than the ordinary wind cup. However, considering the high price, when an accuracy requirement is not high, wind farms still generally adopt wind cup observations, but the data need to be corrected. Figure 7 shows the relationship between the turbulence intensity calculated with two observational instruments at heights of 10, 30, 50, and 70 m for T1 (17–30 April 2010). The abscissa represents the results calculated from the wind cup observations, and the ordinate represents the results calculated from the sonic anemometer/thermometer (SAT) observations. The results of the two observations at heights of 10 and 70 m differ considerably, and the correlation is close to 0.6. The results for 30 and 50 m are relatively close, and the correlation is as high as 0.8. Figure 8 shows the relationship between the turbulence intensities calculated with these two kinds of observations at heights of 10, 30, and 50 m for T2 (17–30 April 2010). During this period, a wind speed (observed by wind cup) at a 70-m height is partly missing because of instrument failure. Figure 9 shows the same result but for T3 (17–30 April 2011). The difference in the results for the two kinds of observations at a height of 10 m is large, and the results for the heights of 30, 50, and 70 m are close. Generally, the results calculated by using the SAT observations are slightly larger than the wind cup results, primarily because the higher frequency of observations can acquire some of the smaller turbulences. According to the discussion above, the turbulence intensities calculated from the wind cup observational data should be multiplied by 1.13–1.29 in the T1 region, 1.33–1.47 in the T2 region, and 0.87–1.18 in the T3 region to ensure a reliable wind turbine unit design.

3.3 Variation of turbulence scale parameters

Figure 10 shows the turbulent power spectra at heights of 50 m (lower than the hub height) and 70 m (close or equal to the hub height) for T1 (17–30 April 2010), T2 (17–30 April 2010), and T3 (17–30 April 2010). The abscissa is the frequency, and the ordinate is the dimensionless longitudinal turbulent power spectral density. The dots represent that the dimensionless longitudinal turbulent power spectral density at every hour is equal to 0.05 and the corresponding frequency (n).

Table 3 shows the values of the turbulence scale parameter Λ for T1, T2, and T3. Based on the hub height of a wind-driven generator at 50 m, according to the IEC61400-1 standard, the value of Λ is 35 m, while the average values for T1, T2, and T3 are 48.17, 35.05, and 30.83 m, respectively. If the generator’s hub height is 70 m, according to the IEC61400-1 standard, the value ofΛ is 42 m, while the average values for T1, T2, and T3 are 48.47, 37.55, and 36.15 m, respectively. T1 is on inland, hilly terrain where the wind speed during spring is large (Ma et al., 2015), and the values ofΛ at heights of 50 and 70 m are not considerably different, with both being larger than the standard value. The terrain of T2 is flat, which is comparable to the observational conditions in other countries (Peña et al., 2016). The value of Λ at a 50-m height is comparable to the standard value, while the value at a 70-m height is smaller than the standard value. Moreover, the difference in the scale parameters between 50 and 70 m is obviously smaller than the IEC61400-1 standard. The terrain for T3 is complicated, and the wind speed is small (approximately 5 m s^–1). The values of Λat both 50 and 70 m are smaller than the standard value, which is comparable to the IEC61400-1 standard. Generally, as the hub height increases, the wind speed increases, and the value of Λ increases; the changes in Λ in the upper and lower layers are not large for different flat terrain heights, while the differences in the Λvalues at different heights over complicated terrain are large. Therefore, the calculation in this paper is reasonable, while the IEC61400-1 standard needs to be refined and improved.

Furthermore, Table 4 provides the ratios between the turbulence scale L_i and turbulence scale parameter Λ for T1, T2, and T3 at 70-m height. According to the IEC61400-1 standard, the L_u/Λ , L_v/Λ and L_w/Λ ratios are 8.1, 2.7, and 0.66, respectively. The L_u/Λ, L_v/Λ , and L_w/Λ ratios for T1 are 9.6, 9.4, and 0.81, respectively, while those for T2 are 9.4, 7.7, and 0.9, and those for T3 are 7.7, 7.7, and 1.13, respectively. At the T1 and T3 sites, L_v/Λ is close to L_u/Λ , which is also considerably different from the IEC61400-1 standard.

4 Conclusions

In this paper, observational data collected for 100-m wind towers in Xilinhot in Inner Mongolia, Huanghua in Hebei Province, and Xingzi County in Jiangxi Province are used to analyze the variations in the wind shear exponent and turbulence parameters from the ground surface to 100 m. The situation is different for various underlying surfaces in China.

(1) The probability of occurrence for a wind shear exponent exceeding 0.3 for the grassland region is 6%, while for the coastal flat region, the probability is 13%, and for the mountain–lake region, the probability is 10%.

(2) The frequency of I_v/I_u < 0.8 for the grassland region is 23%–29%, and 90% of the I_v/I_u values are smaller than 1.97; the frequency of I_w/I_u < 0.5 is 45%–75%, and 90% of the I_w/I_u values are smaller than 0.59. The frequency of I_v/I_u < 0.8 for the coastal flat region is only 32%–38%, and 90% of the I_v/I_u values are smaller than 1.66; the frequency of I_w/I_u < 0.5 is 52%–70%, and 90% of the I_w/I_u values are smaller than 0.58. The frequency of I_v/I_u < 0.8 for the mountain–lake region is only 30%–37%, and 90% of the I_v/I_u values are smaller than 1.72; the frequency of I_w/I_u < 0.5 is 43%–53%, and 90% of the I_w/I_u values are smaller than 0.75.

(3) At a 50-m height, the value of the turbulence scale parameterΛ for the grassland region exceeds the IEC61400-1 standard value, while the value for the coastal flat terrain is comparable to the standard value and that for the mountain–lake region is smaller than the standard value. At a 70-m height, the value ofΛ for the grassland region is greater than the IEC61400-1 standard value, while the values for the coastal flat region and mountain–lake region are smaller than the IEC61400-1 standard value. At the T1 and T3 sites, L_v/Λ is close to L_u/Λ .

Notably, this paper represents a preliminary study and more data should be obtained for further examination. In addition, it is necessary to investigate the wind characteristics over the complex terrain of China, including how the wind characteristics change under the atmospheric boundary layer (especially the height range from the surface layer to 300 m), with the aim of providing a scienti-fic basis for the design of large wind turbines and locations of wind farms.