The main objective of the study was to investigate spatial and temporal characteristics of the wind speed and direction in complex terrain that are relevant to wind energy assessment and development, as well as to wind energy system operation, management, and grid integration. Wind data from five tall meteorological towers located in Western Nevada, USA, operated from August 2003 to March 2008, used in the analysis. The multiannual average wind speeds did not show significant increased trend with increasing elevation, while the turbulence intensity slowly decreased with an increase were the average wind speed. The wind speed and direction were modeled using the Weibull and the von Mises distribution functions. The correlations show a strong coherence between the wind speed and direction with slowly decreasing amplitude of the multiday periodicity with increasing lag periods. The spectral analysis shows significant annual periodicity with similar characteristics at all locations. The relatively high correlations between the towers and small range of the computed turbulence intensity indicate that wind variability is dominated by the regional synoptic processes. Knowledge and information about daily, seasonal, and annual wind periodicities are very important for wind energy resource assessment, wind power plant operation, management, and grid integration.
Wind energy represents a nonpolluting, never-ending source of energy able to meet increasing energy needs domestically and around the world. Wind power is replenished daily by the sun, due to the uneven heating of the Earth’s surface. Furthermore, the wind is accelerated by major land forms, so that entire regions may be very windy while others are relatively calm. A feasibility study of any wind energy project should certainly include a study of the spatial, temporal, and directional variations of wind velocity. On the other hand, the development of predictive models in order to supervise and operate wind-based electricity generation requires knowledge of the wind vector characteristics. This is a very difficult task because of the extreme transitions in the speed and direction of wind at most sites. In order to optimize wind energy conversion systems and maximize the energy extraction, annual, monthly, daily, hourly, and even by-minute frequency distributions of wind data are required. In the last few years, increasing attention has been paid to analyses of wind speed and direction statistics and to mathematical representations of wind speed and direction as being essential to wind engineering and wind energy industry. Knowledge of the wind characteristics and variability in the lower few hundred meters of the atmosphere is important to, for example, exploitation of wind energy, planning of tall buildings, and monitoring of dispersion of trace substances. For example, in the field of energy production, knowledge of the wind characteristics where wind turbine installations are planned is critical. Moreover, the development of prediction models in order to supervise and optimize the electricity generation and planning requires knowing the wind vector characteristics. An extensive review of the main issues related to the assessment and forecasting of the wind and wind energy has been shown by Koracin et al. [
Time series of meteorological conditions are of special interest to understanding, analyzing, and modeling atmospheric phenomena, determining the climate of a geographical area, and forecasting the possibilities of occurrence of some extreme situations. Several mathematical distribution functions have been suggested to represent the wind speed, and different methods have also been developed to estimate the parameters of these distribution functions. However, the Weibull distribution is the most appropriate and most commonly used for representing the wind speed, and a great deal of work related to wind speed statistics has been reported [
In this study, we analyze the wind speed, wind direction, diurnal, seasonal, and annual periodicities, and turbulence intensities at five sites located near Tonopah in Western Nevada (one 80 m tower and four 50 m meteorological towers; see Figure
Names, coordinates, and elevations of the instrumented meteorological towers used in this wind energy analysis.
Site name | Lat. (deg) | Long (deg) | Alt. (m) | Distance to Tonopah 24NW Tower (km) |
---|---|---|---|---|
Luning 5N | 38.57 | 118.18 | 1523 | 80.52 |
Luning 7W | 38.54 | 118.29 | 1354 | 91.80 |
Tonopah 24NW | 38.37 | 117.47 | 1535 | 0.00 |
Kingston 14SW | 39.05 | 117.00 | 1780 | 85.60 |
Stone Cabin | 38.11 | 116.74 | 2012 | 85.20 |
Topographical map showing the locations of the four 50 m towers near Tonopah, Nevada (Luning 5N, Luning 7W, Kingston 14SW, and Tonopah 24NW), and the 80 m tower (Stone Cabin).
The data analyzed in this work were collected during an experiment conducted by the Desert Research Institute near Tonopah in Western Nevada from August 2003 to March 2008 (Figure
Wind direction
Assessment of the wind energy potential at a particular site or area involves analyzing the wind characteristics, the distribution of the measured wind speed and direction, the maximum wind speed, the wind variability and seasonality, and the diurnal variations of the wind speeds. Wind characteristics were studied by using cumulative frequencies of the observed wind velocities and the Weibull and the von Mises probability distributions. To understand the diurnal, seasonal, and annual variations of the wind speeds and direction, a comprehensive statistical and spectral analysis was performed.
First, we performed a meteorological analysis of the composite 2003–2008 50 m tower datasets for the four 50 m meteorological towers and of the 14-month data measured at the 80 m tower. We analyzed the measured wind and meteorological data using statistical descriptors (mean and variance) and the relative and cumulative frequencies at each tower and measurement level. The air density was calculated using pressure and temperature measurements. The monthly and annual averages of the wind speed, temperature, pressure, and air density are summarized in Table
Monthly average wind speed and air density based on 2003 to 2008 composite datasets for the 50 m towers and February 2007 to March 2008 Stone Cabin Tower data.
Tower parameter | Jan. | Feb. | Mar. | Apr. | May. | Jun. | Jul. | Aug. | Sep. | Oct. | Nov. | Dec. | Annual average |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Tonopah 24NW | |||||||||||||
|
4.97 | 5.44 | 5.85 | 6.52 | 6.22 | 6.35 | 5.25 | 5.08 | 5.30 | 5.41 | 5.04 | 4.53 | 5.49 |
|
4.69 | 5.09 | 5.50 | 6.13 | 5.83 | 5.94 | 4.90 | 4.79 | 5.01 | 5.12 | 4.79 | 4.33 | 5.17 |
|
4.33 | 4.73 | 5.11 | 5.73 | 5.45 | 5.56 | 4.62 | 4.48 | 4.69 | 4.75 | 4.43 | 4.04 | 4.82 |
|
1.084 | 1.071 | 1.053 | 1.038 | 1.016 | 0.997 | 0.985 | 0.994 | 1.015 | 1.039 | 1.081 | 1.086 | 1.036 |
Kingston 14SW | |||||||||||||
|
3.73 | 4.21 | 4.81 | 5.51 | 4.93 | 5.27 | 4.69 | 4.66 | 4.35 | 4.22 | 3.45 | 3.99 | 4.53 |
|
3.25 | 3.71 | 4.30 | 4.95 | 4.44 | 4.78 | 4.26 | 4.11 | 3.80 | 3.64 | 2.98 | 3.48 | 4.01 |
|
2.81 | 3.20 | 3.81 | 4.34 | 3.94 | 4.22 | 3.80 | 3.69 | 3.44 | 3.29 | 2.70 | 3.06 | 3.56 |
|
1.059 | 1.045 | 1.029 | 1.015 | 0.995 | 0.977 | 0.964 | 0.972 | 0.992 | 1.015 | 1.013 | 1.058 | 1.055 |
Luning 7W | |||||||||||||
|
3.74 | 4.14 | 3.68 | 4.30 | 4.48 | 4.45 | 3.81 | 3.32 | 3.51 | 3.94 | 3.69 | 4.75 | 3.96 |
|
4.02 | 4.12 | 4.09 | 4.53 | 4.33 | 4.23 | 3.66 | 3.52 | 3.59 | 4.01 | 3.80 | 4.68 | 4.03 |
|
3.51 | 3.63 | 3.69 | 4.03 | 3.82 | 3.73 | 3.21 | 3.13 | 3.20 | 3.48 | 3.27 | 4.00 | 3.54 |
|
1.108 | 1.092 | 1.072 | 1.057 | 1.033 | 1.015 | 1.000 | 1.010 | 1.032 | 1.067 | 1.093 | 1.105 | 1.055 |
Luning 5N | |||||||||||||
|
3.11 | 3.77 | 4.14 | 4.63 | 4.50 | 4.40 | 3.69 | 3.51 | 3.41 | 3.63 | 3.26 | 3.81 | 3.81 |
|
2.80 | 3.46 | 3.83 | 4.33 | 4.20 | 4.10 | 3.42 | 3.24 | 3.15 | 3.25 | 2.91 | 3.43 | 3.49 |
|
2.52 | 3.00 | 3.48 | 3.88 | 3.73 | 3.60 | 2.99 | 2.06 | 2.86 | 2.90 | 2.70 | 3.05 | 3.12 |
|
1.080 | 1.067 | 1.048 | 1.036 | 1.015 | 1.000 | 0.983 | 0.991 | 1.011 | 1.043 | 1.068 | 1.079 | 1.033 |
Stone Cabin | |||||||||||||
|
5.123 | 5.562 | 5.525 | 5.752 | 5.883 | 5.667 | 5.061 | 3.985 | 4.514 | 6.463 | 4.536 | 4.988 | 5.255 |
|
6.034 | 6.243 | 5.945 | 6.125 | 6.287 | 5.955 | 5.461 | 3.935 | 5.208 | 6.757 | 4.542 | 5.619 | 5.676 |
|
5.652 | 5.908 | 5.661 | 5.751 | 5.883 | 5.673 | 5.163 | 3.793 | 4.683 | 6.255 | 4.197 | 5.352 | 5.445 |
|
4.460 | 4.875 | 4.588 | 4.717 | 4.918 | 4.338 | 3.919 | 2.517 | 3.004 | 4.468 | 3.236 | 4.201 | 4.104 |
|
0.982 | 0.962 | 0.945 | 0.936 | 0.941 | 0.962 | 0.984 | 0.997 | 1.025 | 1.025 | 1.014 | 1.008 | 0.982 |
The multiannual monthly means of wind speed and direction are in very good agreement with the climatologic values for Nevada found in the literature [
Monthly values are for the 2003–2008 composite datasets for the 50 m towers and for 2007-2008 for the 80 m towers. The use of probability distribution functions to define, characterize, and fit the field data has a long history. It is established that the Weibull distribution [
The Weibull parameters and wind characteristics derived from the Weibull distribution. Monthly values are for the 2003–2008 composite datasets for the 50 m towers and for 2007-2008 for the 80 m tower.
Tower (50 m level) parameter | Jan. | Feb. | Mar. | Apr. | May. | Jun. | Jul. | Aug. | Sep. | Oct. | Nov. | Dec. | Annual average |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Tonopah 24NW | |||||||||||||
|
1.505 | 1.630 | 1.730 | 1.748 | 1.919 | 1.939 | 1.924 | 1.932 | 1.830 | 1.721 | 1.600 | 1.487 | 1.703 |
|
5.389 | 5.977 | 6.431 | 7.221 | 6.881 | 7.017 | 5.764 | 5.569 | 5.810 | 6.007 | 5.537 | 4.953 | 6.041 |
|
4.86 | 5.35 | 5.73 | 6.43 | 6.10 | 6.22 | 5.11 | 4.94 | 5.16 | 5.36 | 4.96 | 4.48 | 5.39 |
Kingston 14SW | |||||||||||||
|
1.231 | 1.404 | 1.474 | 1.588 | 1.631 | 1.654 | 1.610 | 1.583 | 1.481 | 1.403 | 1.280 | 1.211 | 1.415 |
|
3.913 | 4.519 | 5.182 | 5.988 | 5.350 | 5.754 | 5.103 | 4.994 | 4.698 | 4.506 | 3.973 | 4.228 | 4.821 |
|
3.66 | 4.12 | 4.69 | 5.37 | 4.79 | 5.14 | 4.57 | 4.48 | 4.25 | 4.11 | 3.68 | 3.97 | 4.39 |
Luning 7W | |||||||||||||
|
1.248 | 1.361 | 1.182 | 1.298 | 1.475 | 1.506 | 1.550 | 1.365 | 1.315 | 1.304 | 1.297 | 1.409 | 1.346 |
|
4.353 | 4.609 | 4.120 | 4.853 | 4.855 | 4.854 | 4.177 | 3.737 | 3.803 | 4.303 | 4.095 | 5.256 | 4.385 |
|
4.06 | 4.22 | 3.97 | 4.48 | 4.39 | 4.38 | 3.76 | 3.42 | 3.51 | 3.98 | 3.78 | 4.79 | 4.02 |
Luning 5N | |||||||||||||
|
1.229 | 1.278 | 1.274 | 1.347 | 1.410 | 1.397 | 1.445 | 1.406 | 1.278 | 1.236 | 1.236 | 1.195 | 1.335 |
|
3.166 | 3.945 | 4.306 | 4.900 | 4.746 | 4.668 | 3.958 | 3.672 | 3.552 | 3.736 | 3.348 | 3.949 | 3.992 |
|
2.96 | 3.66 | 3.99 | 4.50 | 4.32 | 4.26 | 3.59 | 3.35 | 3.29 | 3.49 | 3.13 | 3.72 | 3.67 |
Stone Cabin (60 m level) | |||||||||||||
|
1.369 | 1.271 | 1.877 | 1.814 | 2.298 | 1.990 | 2.049 | 2.041 | 1.956 | 1.897 | 1.996 | 1.273 | 1.812 |
|
7.386 | 5.451 | 4.822 | 5.527 | 4.847 | 4.969 | 4.916 | 4.861 | 5.125 | 4.849 | 3.345 | 5.981 | 5.177 |
|
7.39 | 5.45 | 4.83 | 5.53 | 4.85 | 4.97 | 4.92 | 4.86 | 5.13 | 4.85 | 3.35 | 5.98 | 5.29 |
Wind speed frequency distributions for the Tonopah 24NW Tower (a) at 50 m, for 2003–2008 composite datasets, and the Stone Cabin Tower (b) at 60 m for 2007-2008 composite dataset.
The wind rose diagrams and wind direction frequency histograms provide useful information on the prevailing wind direction and availability of directional wind speed in different wind speed bins. The wind roses were constructed using the composite datasets of measurements of wind velocities, and they are shown in Figure
Wind rose diagrams for the composite 2003–2008 datasets at 50 m for the Tonopah 24NW Tower (a) and the Kingston 14SW Tower (b).
The wind direction was analyzed using a continuous variable probability model to represent distributions of directional wind speeds. The model is comprised of a finite mixture of the von Mises distributions (vM-PDFs), following the approaches given in [
Frequency histograms of wind directions and the fitted von Mises distribution functions at the Tonopah 24NW Tower (a) and the Kingston 14SW Tower (b) at 50 m using the composite 2003–2008 datasets.
Turbulence intensity (TI), defined as the ratio of the standard deviation over the wind speed, is an indicator of turbulence and not an absolute value, a very useful indicator in wind turbine operation and design. Notice that the maximum distance between the 50 m towers is about 200 km. Each site is situated in a complex terrain area, but we expect to see similar synoptic wind conditions. However, the comparative analysis of the values in Table
Overall wind speed and direction characteristics, turbulence intensity, and coefficient of variations for the wind speed for time scales larger than one month.
Tower | Mean wind speed (m/s) | Mean wind direction |
|
|
|
|
|
---|---|---|---|---|---|---|---|
Kingston 14SW | 4.48 | 162 | 3.37 | 0.20 | 0.75 | 1.415 | 4.82 |
Tonopah 24NW | 5.49 | 223 | 3.41 | 0.17 | 0.62 | 1.703 | 6.04 |
Luning 7W | 3.96 | 191 | 3.06 | 0.25 | 0.77 | 1.346 | 4.39 |
Luning 5N |
3.77 |
185 |
3.03 |
0.25 |
0.80 |
1.335 |
3.99 |
Stone Cabin (60 m) | 5.24 | 165 | 3.66 | 0.18 | 0.66 | 1.667 | 5.92 |
Coefficient of variations for the wind speed for time scales larger than one month.
Tower | Coefficient of variation |
---|---|
Kingston 14SW | 0.30 |
Tonopah 24NW | 0.26 |
Luning 7W | 0.36 |
Luning 5N | 0.35 |
Stone Cabin (60 m) | 0.27 |
To put in evidence the dynamical behavior of the wind speed for time scales larger than one month, a low-pass filter was applied to the measured wind speed signal. We use here the simplest one, that is, the moving average calculation:
Moving average time series of the wind speed for the Tonopah 245NW Tower, at 50 m, 30 m, and 10 m levels, and for the composite 2003–2008 datasets.
Wind speed moving average for the four 50 m towers; the averaging time is equal to 4032 hours (4 weeks), and at 10 m level.
The computed values of the cross-correlation coefficients of the four 50 m towers for smaller time lags are around 0.6, showing quite similar wind climatology, for this area. This is another very strong indication of the stability and uniformity of the wind characteristics in Western Nevada. This is a very important characteristic for wind energy assessment, as well as wind power plant operation, management, and grid integration. The coefficient of variation over time scales larger than one month is given by
Figure
Autocorrelation functions for 10 min wind speed, for all 50 m towers, and for 50 m level; the 2003–2008 composite datasets, with 95% confidence intervals, are also shown on the graph.
Autocorrelation of 10 min wind direction, for all 50 m towers and for 50 m level; the 2003–2008 composite datasets, with 95% confidence intervals, are also shown on the graph.
Two facts are immediately apparent in all of the autocorrelation data analyzed. First, the presence of a strong sinusoidal component at diurnal frequency which is almost constant as the lag value increases indicates that it is derived from a deterministic period component. The second feature is that the centerline of the diurnal component is not the zero datum line, but it is offset above the lag axis. This offset cannot be due to a zero mean (which is removed by the autocorrelation algorithm), suggesting the presence of another periodic component of a much lower frequency. The obvious candidate for investigation was an annual cycle. This is also in agreement with the presence of a spring maximum and a fall minimum in the wind speed moving average time series (Figures
Autocorrelation of the daily mean, using the 2003–2008 composite datasets, for all 50 m Towers, and at 50 m level, with 95% confidence intervals, is shown on the graph.
We decided to compute the power spectra by the standard and well-proven method of Blackman and Tukey [
Power density spectra of wind speed variations with time scales smaller than 1 week, the Kingston 14W Tower.
Following the approach of Harris [
Macrometeorological spectrum of the Tonopah 24NW, 50 m level dataset.
The annual mean wind speeds for the four towers’ wind observations at 50 m height were calculated as 5.49 m/s (Tonopah 24NW), 4.53 m/s (Kingston 14SW), 3.96 m/s (Luning 7W) and 3.81 m/s (Luning 5N). For the Stone Cabin Tower at the 60 m level, this value was found to be 5.68 m/s. The observed data show that the maximum seasonal wind speeds for all sites are during spring. The highest potential in terms of wind energy was estimated at the Tonopah 24NW and the Stone Cabin sites, with mean wind speeds above 5.5 m/s during the peak period of every year. The same pattern of the monthly mean wind speeds was found at all other towers, but with lower values, being less suited for wind energy generation. The fitted Weibull and von Mises distributions for the observed wind speed and wind direction datasets at all towers and heights are in very good agreement with the observed wind speed distributions.
The analysis of the wind speed variations at each of the instrumented towers in Western Nevada shows the following: (i) there is a strong coherence between wind speed and direction; (ii) for time scales smaller than 24 hours, the wind speed is statistically independent, thus indicating the possibility of smoothing the total available wind power for small time scales; (iii), there is a strong diurnal periodicity in the wind speed signals, for all towers and all heights, with a maximum during the late afternoon, as found in the power spectra and diurnal variations of the wind speeds, almost coincidental with the daily peak-load demand [
Although the mean wind speeds show differences due to specifics of the measurement location, the coefficients of variation of the turbulence intensity are quite similar for all five sites. This confirms that the regional synoptic processes are dominant for the variability of the wind speed on the scale of the tower locations within a domain ranging more than
One of the authors (D. Koracin) acknowledges support from the DOE-NREL, Grant no. NDO 5-4431-01. The authors are grateful to Greg McCurdy for assistance in obtaining data and to Travis McCord for editorial assistance.