The implantation of wind turbines generally follows a wind potential study which is made using specific numerical tools; the generated expenses are only acceptable for great projects. The purpose of the present paper is to propose a simplified methodology for the evaluation of the wind potential, following three successive steps for the determination of (i) the mean velocity, either directly or by the use of the most occurrence velocity (MOV); (ii) the velocity distribution coming from the single knowledge of the mean velocity by the use of a Rayleigh distribution and a Davenport-Harris law; (iii) an appropriate approximation of the characteristic curve of the turbine, coming from only two technical data. These last two steps allow calculating directly the electric delivered energy for the considered wind turbine. This methodology, called the SWEPT approach, can be easily implemented in a single worksheet. The results returned by the SWEPT tool are of the same order of magnitude than those given by the classical commercial tools. Moreover, everybody, even a “neophyte,” can use this methodology to obtain a first estimation of the wind potential of a site considering a given wind turbine, on the basis of very few general data.
At the end of 2010, the global capacity of wind electricity power has reached 200 MW. Consequently, the electric production was about 430 TWh, that is, 2.5% of the global electricity consumption [
Nowadays, wind turbine implementation is an activity which is clearly controlled. Wind farms are obviously built to produce the greatest quantity of energy on the site. However, it has been shown that the efficiency of wind turbines is not the major criteria for the use of wind turbine [
The reason of these facts is clear. Wind energy production has become an industrial activity, which is now mature. Many studies have been made to attest this reality, for example, [
This profitability is different depending on the site. Then it is necessary to predict the delivered energy for a given project before the equipment of a place. To do that, developers generally use specific software such as Wasp [
In fact, no wind can be correctly estimated without measurements. The height of the wind turbine must be taken into account, such as its aerodynamic and electric performances. The geographic configuration of the site around the wind turbine must be known and studied; the ground must be perfectly known in order to consider the surface roughness. The wind velocity must be measured so that the wind distribution can be correctly estimated. When it is impossible, a statistical distribution can be used, such as the Weibull distribution [
An alternative solution for such project is to simplify the previous methodology with the aim of obtaining an estimation of the delivered wind energy with an acceptable accuracy.
The present study presents a simplified (S) approach to estimate the wind potential of a place. This approach can be described in few steps based on three general characteristics: the wind estimation (WE) must be made; that is, the wind distribution is known; the place (P) must be known; that is, the local geography and the roughness surface are known; the turbine (T) is completely defined; that is, its characteristics are known.
Let us notice that each of the previous points is in fact essential. The last one is according to us very important; however, it is regularly forgotten because in many cases the choice of the wind turbine is made
The proposed methodology is not so different from the classical ones and is not in essence new. The real difference between the present methodology and the one used in different software is the simplification of the prediction process with the aim of a predesign project. Consequently the results will only consist in giving an “acceptable” order of magnitude to the designer or installer before using more conventional tools.
This approach is here called the SWEPT methodology. It has been recently presented, but the software was not realized and completely tested [
In the following, the methodology is exposed on the basis of each step of the present approach, that is, the wind estimation step (WE, coming from estimation of the wind velocity distribution), the P step (place configuration), and the T step (choice of the turbine). Preliminary results are presented and discussed. Then perspectives are given to improve the methodology.
Each step of the methodology must be carefully developed with an objective of extreme simplification.
The first step consists of the calculation of the wind distribution curve. If wind velocity measurements are available, this distribution curve can be deduced from the data using a Rayleigh distribution, which is a particular case of the two-parameter Weibull distribution, with a single parameter [
The probability density of the wind for a Weibull distribution, which represents the probability to obtain the velocity
Figure
Example of Weibull modeling for
The mean velocity
In the Rayleigh distribution,
In the present paper, a third approach is given. We propose to use a subjective data: the most occurrence velocity (MOV). This method consists in an estimation of the MOV, using a scale derived of the Beaufort scale for example. Table
On-shore Beaufort scale.
Beaufort number | Estimated Velocity (m/s) | International description | Observed conditions |
---|---|---|---|
0 | <1 | Calm | Smoke rises vertically |
1 | 1 | Light air | Direction of wind shown by smoke drift but not by wind vanes |
2 | 2 | Light brise | Wind felt on face: leaves rustle, vanes move by wind |
3 | 4 | Gentle breeze | Leaves and small twigs in constant motion; wind extends light flag |
4 | 7 | Moderate | Raises duct, loose paper; small branches move |
5 | 10 | Fresh | Small trees in leaf begin to sway; crested wavelets form on inland waters |
6 | 12 | Strong | Large branches in motion; whistling heard in telephone wires; umbrellas used with difficulty |
7 | 15 | Near gale | Whole trees in motion; resistance felt walking against wind |
8 | 18 | Gale | Breaks, twigs off trees; impedes walking |
9 | 20 | Strong gale | Slight structural damages occurs |
10 | 26 | Storm | Trees uprooted; considerable damage |
11 | 30 | Violent storm | Widespread damage |
For a Rayleigh distribution, the mean velocity
Rayleigh distribution (%) for a given value of
Using this method, it is possible to estimate not only the mean velocity
In fact, the velocity distribution described in part 2.1 must be adapted because of the supposed height of the wind turbine. Numerous authors propose empirical law to estimate the wind velocity at different heights (see, e.g., [
The wind velocity
The common value of the parameter
Estimation of the velocity from the ground roughness knowledge.
Ground type |
|
---|---|
Ice | 0.07 |
Snow on a flat ground | 0.09 |
Calm sea | 0.09 |
Short cut grass | 0.14 |
Meadow | 0.16 |
Cereal cultures | 0.19 |
Hurdles | 0.21 |
Trees and scattered hurdles | 0.24 |
Trees and dense hurdles | 0.29 |
Suburban or urban site | 0.31 |
Forest | 0.43 |
All these calculations lead to the estimated wind distribution at the wanted height
Let us notice that the surrounded wind configuration coming from the wind rose is not considered here.
As seen above, wind turbines are generally chosen
In fact, installers have generally an idea of the rotor and they “just” use the electrical curve (electric power versus wind velocity) to calculate the energy production from the velocity distribution on a given site.
Commercial software proposes many wind turbines to be “tried” directly in the modeling. But this methodology is time dependant. Besides, these data are not systematically available, especially for micro- and small turbines installation on “unknown sites.” The present methodology aims to use a simplified definition of the turbine.
Let us consider that a wind turbine is in fact essentially given by two data (see Figure the starting point is the one where the wind turbines runs on; that is, there is no power under the velocity the nominal point corresponds to the generated power
After the nominal point, the curve is around a horizontal line. Sometimes, a third point is given: the “breaking point” where the velocity is so high that the wind turbine must be stopped. But this third point is situated for high velocity values which are very rare, so that the corresponding energy during a year is very small. Under these considerations, the power curve of the wind turbine can easily be approximated by two lines (in blue in Figure
Example of a power curve for a given wind turbine.
This step is in fact very easy to put in a simple numerical worksheet. Let us notice that the present methodology will probably overestimates the wind potential in a way that should be clarified. In fact, it is possible to propose other curves than a simple line to estimate the power curve between the
The proposed software can be a single numerical worksheet and the user has just to answer several questions which are easy to understand.
First the user must put the mean velocity at a height of 10 m, because this data is currently known. If this quantity is not known, it is possible to put the value of the MOV variable, or to choose a mean value coming from a standard wind atlas (see, e.g., [
Estimated mean velocity range at 10 m high (in France) (source:
Then the estimated height
The two previous steps permit to plot the wind distribution according to relations (
Finally, the user must enter the three values
SWEPT organization chart.
The software has been realized following the SWEPT methodology; it has been first developed in a single worksheet and then was implemented in a specific numerical tool, easy to use by everybody. Figure
Some questions proposed to the user by the software (in French).
The software has been tested for a few standard wind turbines. The results returned by the “calculator” have been compared to few commercial tools. In the present study, we just present the results for a typical wind machine, the characteristics of which are known: Enercon 33–49 [
Main characteristics of the chosen wind turbine: Enercon 33–49.
Nominal power (kW) | 330 |
Height of the shaft (m) | 49 |
Rotor diameter (m) | 33.4 |
|
3 |
|
13 |
Power curve for the chosen wind turbine (Enercon 33–49).
The results coming from the SWEPT software have been compared to the ones given by the software [
Comparisons of the annual delivered energy for the Enercon 33–49 turbine (kWh) on a given place located on a calm sea (France).
Use of the software (8) | Present study : SWEPT methodology |
---|---|
370 MWh | 385 MWh |
Let us notice that the differences between the results were expected because some uncertainties have been made, but on the other hand, the commercial tools themselves can introduce some differences with the reality.
In fact, the real interest of the SWEPT methodology and of the corresponding software (which can be a single worksheet) is not the reduction of the uncertainty, but the simplicity of use; the remarkable time of “calculation” (corresponding to the filling of the worksheet and the results).
Considering the 2nd point, only few seconds are necessary to achieve the “calculation.”
The proposed methodology permits a “neophyte” to predict in few seconds an estimation of the electric energy production for a wind turbine on a site. The idea is to use very few data to obtain a first order of magnitude of the estimated delivered energy. This approach has been called the “SWEPT methodology.” A specific tool has been developed to estimate the wind potential. This tool, based on very simplified hypotheses, is very easy to use. An appropriate knowledge of the geography and of the velocity (mean velocity or MOV) on the site is necessary, which is probably a condition of acceptability if the local population is concerted. We have shown that the difference between the results returned using the SWEPT tool and the ones given by different commercial software do not exceed 20% in most cases. This is in good agreement with the main objective of present study: to give quickly an acceptable estimation of the delivered energy of a wind turbine. In a following step of the study, the power curve is to be approached by another curve that two lines and the “subjective” knowledge of the wind will be verified by more case studies. Finally, a profitability calculation will be proposed.
The author declares that there is no conflict of interests regarding the publication of this paper.