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Scientific Bulletin of the Politehnica University of Timisoara

Transactions on Mechanics Special issue

The 6th International Conference on Hydraulic Machinery and Hydrodynamics Timisoara, Romania, October 21 - 22, 2004

APPROXIMATE EVALUATION OF WIND POWER DATABASE FOR SITE SEMENIC

Adrian BEJ, Senior Scientific Researcher Wind Energy Research Center

"Politehnica" University of Timisoara

Francisc GYULAI, Prof. Department of Hydraulic Machinery “Politehnica” University of Timisoara

Bv Mihai Viteazu 1, 300222, Timisoara, Romania Tel.: (+40) 256 403696, Fax: (+40) 256 403682, Email: adibej@mec.utt.ro

ABSTRACT

Investments in wind farms or stand-alone wind turbine applications are based on information concern-ing the wind potential of the site that was chosen for a wind application. The investment efficiency depends mainly on how the wind harnessing technology (given by turbine type, rotor diameter, tower height etc.) match the site wind potential. Usually the pre-feasibility studies have as basis summary information about the wind speed regime. In the paper is shown a methodol-ogy, developed by Wind Energy Research Center from "Politehnica" University of Timisoara, meant for estimating the three Weibull constants used for wind speed frequency distribution function and wind speed cumulative distribution function, depending on the average wind speed estimated for a charac-teristic year. The proposed Weibull model with three parameters offers a certain frequency distribution function that further is used for pre-feasibility studies. The methodology given in the paper has as basis statistical data issued in two reference sources (Russian and American), and some measurements done in Romania on the site Semenic along 30 years, and also a global wind speed map made by ICEMENERG for the entire Romanian territory at 50 m height. The Weibull constants in this general shape, given in the paper, offers an evaluation methodology of wind speed potential more useful than that of average wind speeds evaluation. The paper shows finally an improved shape of wind speed database of site Semenic for extended elevations up to 100 m.

KEYWORDS Wind energy, Weibull function, database, assessment

NOMENCLATURE

alth [m] site altitude p [Pa] current barometric pressure

0bp [Pa] barometric pressure at sea level 287R = [J/(kg 0K)] gas (air) constant

t [0C] temperature T [0K] absolute temperature v [m/s] current wind speed

.extrv [m/s] extreme wind speed

mv [m/s] average wind speed

rmv [m/s] reference average wind speed z [m] current elevation

rz [m] reference elevation

0z [m] conventional terrain roughness

cT∆ [hours/year] windless duration ρ [kg/m3] air mass density

1. AIMS HAD IN VIEW Wind Energy Research Center from "Politehnica"

University of Timisoara has promoted through Prof. Preda's papers the Weibull model with three parameters used for characterizing the sites for future wind farms [6]. This research was focused on capitalizing the meteorological database of Semenic site from Caras-Severin County. The Weibull model used for the fre-quency distribution curve and cumulative distribution curve in this case has a rich database, the Weibull constants being identified on this basis.

In this paper the goal is to do a generalization with the purpose to identify the three Weibull parameters knowing or assessing the average wind speed of a certain site which has also associated a characteristic roughness.

The methodology given in the paper has as basis statistical data issued in two reference sources (Russian

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and American) [1, 2, 3] and some measurements done in Romania on the site Semenic along 30 years, and also a global wind speed map made by ICEMENERG for the entire Romanian territory at 50 m height [4, 5].

The Weibull constants in this general shape, offer an evaluation methodology of wind speed potential more useful than only that of average wind speeds.

The Weibull model usually approached in literature focuses the information on few constants which enables to build the frequency distribution curve and cumu-lative distribution curve directly into the frame of some application software meant for wind technology optimi-zation and output energy assessments.

2. REFERENCE DATA The methodology used in the paper starts with some

reference data: • the average wind speed given for a certain period

of time (usually for a characteristic year), evaluated on the basis of meteorological stations from the site area or near the site ( rmv )

• the site altitude from sea level ( alth ) • barometric pressure, usually recalculated at the sea

level ( 0bp ) • terrestrial surface feature of the site given by a

conventional roughness ( 0z ) • elevation from the ground for which the average

wind speed was evaluated ( rz ) • information concerning the air temperature( t ) and

eventually the air humidity (ϕ [%]) • other complementary information (white-frost de-

poses, atmospheric lightning discharges, extreme wind speeds).

3. TERESTRIAL BOUNDARY LAYER INFLUENCE Terrestrial boundary layer extends up to several hundreds meters. In this space the influence of friction forces with the terrestrial surface is present. Beyond the boundary layer the wind speed depends only on barometric gradients and Earth rotation. The wind speed profile into the boundary layer depends on the roughness of solid boundary. The wind turbine is placed in this space of terrestrial boundary layer. Thus, for al energetic analyses is essentially to know the profile of horizontal wind speed into the boundary layer.

Writing the current elevation from the ground with z , we selected the following relations:

α

⎟⎟⎠

⎞⎜⎜⎝

⎛=

rrm

zm

zz

vv

(1)

[ ]rm

2.0

r

0 vlog55.01zz

⋅−⋅⎟⎟⎠

⎞⎜⎜⎝

⎛=α (2)

Some guiding values for the roughness parameters are: • cities with tall buildings: m32.1z0 ÷= • cities with short buildings: m55.0z0 = • suburban areas: m4.0z0 = • areas with farms and vegetation (uneven terrain):

m002.03.0z0 ÷= • flat terrain (water, desert): m0001.0001.0z0 ÷=

For feasibility studies are used the conventional roughness classes between 0.001 and 0.3. The value

0z0 = must be avoided because that means the ab-sence of friction, and thus a constant wind speed inside the boundary layer. The roughness parameter has a constant value either for the reference data or for other wind speeds from boundary layer.

For extreme wind speeds (with return a period of 30 … 100 years) are used statistical methods suitable with rare phenomena: rme.extr vkv ⋅= (3)

10;2.9;7.8ke = for a return period of 30, 50 and 100 years.

In this extreme field are recommended:

77.0rmv55.0 −⋅=α ( for s/m20vr > ) (4)

4. AIR DENSITY The air mass density depends on the local atmos-

pheric pressure (p) and absolute temperature (T [0C]). For usually values can be used the relation for perfect gases:

TR

p⋅

=ρ (5)

The barometric pressure at sea level oscillates due to meteorological reasons being about:

torr)770(720 Pa ÷÷= 10232595680p 0b

For torr 760=0bp and )KC15t o o 288(T == the standard air density at sea level is 1.225 kg/m3.

The local relative air pressure depends on the local height (the altitude of the site and the elevation from the ground):

]m[zhalt + 0 200 400 600 800 1000 2000

][p

p

0b

−

1 0.976 0.953 0.931 0.909 0.887 0.784

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5. THE PROPOSED WEIBULL MODEL The model uses for frequencies the "bins method".

The bin represents a wind speed interval having a central value and an associated width, e.g.:

m/s etc. ; 0,53 ; 0,52 ; 0.51 ; ±±±+ 5.01 .

The wind speeds are considerate mean values for time periods of a few minutes corresponding on the meteorological station methodology.

In this way are identified statistically the frequencies or the periods correlated with the wind speed bins, which then are correlated with the central value of the bins allowing to draw two type of curves: • the frequency distribution curve (histograms) • the cumulative distribution curve.

The curves are linked by operations of derivation - integration.

When power analyses are done the statistical set-tings should be done for the term ( 3v⋅ρ ). For the first analyses are accepted distinct settings for air density and wind speed.

The above mentioned curves have the following Weibull shape: • Frequency distribution function:

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

−⋅⎟⎠⎞

⎜⎝⎛ −

⋅=− k1k

cavexp

cavk

c8760)v(FF (6)

• Cumulative distribution function:

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

−⋅=≥k

cavexp8760)v(FA (7)

The wind speed frequencies resulted using relation (3) are given in hours / years or if they are reported to 8760 in relative values.

The Weibull curves contain tree constants: k- the shape parameter, c - the scale parameter and a - the location parameter.

The aim of this paper is to assess these three con-stants depending on average multi-annual wind speed localized at a certain elevation.

Based on data taken from [1] and other references, there was finally found the following formulas: • for shape parameter:

mvk.constk ⋅= ;

73.005.1k.const ÷= (average value of 0,94) (8)

For sites from USA, NASA used values between 0,9144 and 0,9002. • for scale parameter:

k51928,0k68605.0k1236.009562.0

vc m

+⋅+⋅−−= (9)

• for location parameter (there was taken in view information from reference [3]):

k/1

0T8760lnca ⎥

⎦

⎤⎢⎣

⎡⋅−= (10)

where c0 T8760T ∆−= (11) and 65.1

mc v3050T −⋅=∆ (12)

Table 1 synthetically shows the values of the Weibull constants for different average wind speeds.

Table1. Weibull constants

]s/m[mv 4 6 8 10

05.1k.const = k 2.1 2.57 2.97 3.32 c 4.51 6.75 9.00 11.25 a -0.92 -1.42 -1.99 -2.61

94.0k.const = k 1.88 2.30 2.66 2.97 c 4.50 6.67 8.89 11.12 a -0.67 -1.19 -1.65 -2.17

73.0k.const = k 1.46 1.79 2.06 2.31 c 4.40 6.73 8.97 11.22 a -0.45 -0.71 -1,021 -1.37

Justus's paper [1] gives some information concern-ing the atmospheric stability caused by the buoyancy movements due to the soil warming. In the proposed model this perturbation, as well as the turbulence effects and the gusts were neglected. Thus, it was assumed a stable or neutral atmosphere. The issue of these phenomena will be reconsidered as subject of a future specific study.

6. CASE STUDY FOR SITE SEMENIC Assessments concerning the site Semenic were done

known by us in different research stages. More recent syntheses were shown in [4] and [5]. Here we show some completions aiming to verify the model. Reference data

As reference data there are available the measure-ments done by the meteorological station from Semenic site, gathered during 50 years, from which we have processed in energetic analyses those that refers to the period between the year of 1961 and 1990 [4], [6]. Averaging the data measured at 10 m height from the ground was found the reference average wind speed of 5.6 m/s. If computing the average on an extended database through the Weibull method, this average

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wind speed is higher (5.98 m/s). The study of global wind resource map developed by ICEMENERG for Romanian territory reveled for Semenic an average wind speed about 8÷10 m/s at 50 m height.

The conventional roughness is difficult to be choos-ing for the uneven terrain as Semenic site has it. This might be assumed somewhere for m 3.01.0z0 ÷= .

With these approximations the exponent of terrestrial boundary layer results as follows:

• )3.0)1.0228.0234.0

=÷=÷=

0

0

(z 0.2840.292 (z α

for the data measured

on site Semenic at m 10zr =

• )3.0)1.0129.0144.0

=÷=÷=

0

0

(z 0.1020.181 (z α

for the global data of

ICEMENERG ( m 50zr = ) Dealing with these exponents, elevations (heights)

and reference wind speeds, was computed the wind speed profile for the terrestrial boundary layer, as that is given in table 2. Table 2. Wind speed profile for site Semenic

rz [m]

10 50

rmv [m/s]

5.6 6.0 8.0 10.0

0z [m]

0.1 0.3 0.1 0.3 0.1 0.3 0.1 0.3

z [m]

zmv [m/s]

10 5.60 5.60 6.00 6.00 6.35 5.98 8.12 8.4920 6.59 6.86 7.03 7.31 7.01 6.78 8.80 9.1130 7.24 7.72 7.71 8.20 7.43 7.29 9.36 9.4940 7.75 8.39 8.23 8.90 7.75 7.68 9.72 9.7850 8.16 8.96 8.66 9.48 8.00 8.00 10.00 10.0060 8.52 9.45 9.03 9.98 8.21 8.27 10.24 10,1970 8.83 9.89 9.35 10.43 8.40 8.50 10.44 10.3580 9.11 10.28 9.46 10.83 8.56 8.71 10.63 10.4990 9.36 10.64 9.90 11.19 8.71 8.90 10.79 10.62

100 9.60 10.97 11.75 11.54 8.84 9.07 10.94 10.73α 0.234 0.292 0.228 0.284 0.144 0.181 0.129 0.102

The dispersion of the resulted values, caused by the reference data and the assumed roughness, could enhance the dispersions of the energetic evaluations. Hence, is required to be done some control measure-ments with state of the art wind speed devices. These measurements cannot refind the data gathered during a period of 50 years done sometimes with old-fashioned devices, but they are useful to select some probable values more real for the reference wind speed data, the exponent of boundary layer and the conventional roughness.

Through the Weibull constants assessed with the methodology shown in this paper, the information extends easily to the wind speed frequency distribution curves and further to realistically energetic assessments.

The results given in table 2 are useful for approxi-mate assessments done with certain precaution. In this way the multi-annual average wind speed of 10 m/s at elevation of 50 m height probably is too optimistic, but the value of 8 m/s at the same elevation can be certainly assumed.

Other details concerning the air density, temperature and other information regarding the site Semenic are shown in papers mentioned in the reference [4] and [5], as well as in other papers issued by Wind Energy Research Center from "Politehnica" University of Timisoara.

REFERENCES

1. Justus C.G. (1978) Wind and wind system perform-ance, The Franklin Institute Press

2. Spera D.A. (editor) (1994) Wind turbine technology, ASME PRESS, New York, USA

3. Martens L.K. (1949) Mashinostroienie -Tom 12, Moskva, URSS, pp.207-208

4. Bej A., Grarbacea A, (2002) Sites for wind farms in Romania, The World Wind Energy Conference, Berlin, Germany.

5. Gyulai F., Bej A. (2002) Wind Potential Informatics, Symposium "Hidroinformatica", Hidrotim SA, Timisoara, Romania

6. Preda I., Santau I. (1994) Experimental researches concerning the wind speed distribution in Semenic massif, The Fourth Conference on Hydraulic Ma-chinery and Hydrodynamics, Timisoara, Romania.