Potential Eolian

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RECENT, Vol. 8, no. 2 (20), July, 2007 91

O METODSIMPLDEEVALUARE A POTENIALULUI

EOLIAN AL UNEI REGIUNI

A SIMPLE METHOD TO

ESTIMATE THE WIND

POTENTIAL OF A REGION

Mariana DELIU, Gheorghe DELIU

"Transilvania" University of Brasov, Romania

Rezumat. Pornind de la convingerea c problemautilizrii energiei eoliene ar merita mai mult atenie nRomnia, autorii prezinto metodsimplde evaluare apotenialului eolian.

Se propune o modalitate de apreciere i comparare apotenialului din diverse zone geografice, precum i ometod de estimare a cuantumului utilizabil din acestpotenial. Exemplificarea se face prin prelucrarea datelorfurnizate de INMH, pentru 23 de staii meteorologice, pedurata unei luni (martie 2007).

Abstract.Starting from the conviction that the problemof wind power conversion should deserve a greaterattention in Romania, the authors present a simplemethod to estimate the wind potential of a region.

An evaluation and comparison modality for thewind power potential on different geographical zones isproposed, as well as a method to estimate the useful partof this potential. The illustration is made by processingmeasured data, supplied by INMH, for 23 meteorologicalstations, during a month (march, 2007).

Cuvinte cheie:energie eolian, potenial, estimare Key words:wind energy, potential, estimation

1. Introduceren contextul actualei crize energetice,

preocuparea pentru gsirea i utilizarea unor sursealternative de energie este mai mult dect necesar.Una dintre sursele cele mai ieftine este energiaeolian, utilizat din vechime, dar cu o dezvoltaredeosebitn ultimul timp

Energia eolian este larg rspndit, esteregenerabil, curat, reducnd indirect emisiile de

gaze toxice produse la obinerea energiei electriceprin arderea combustibililor fosili.La sfritul lui 2006, producia pe plan mondial

a generatoarelor electrice antrenate de vnt a fost de74,223 MW; dei acestea produc n mod curent maipuin de 1% din consumul mondial de energieelectric, aportul acestei surse de energie este de20% n Danemarca, 9% n Spania i 7% nGermania. Pe plan global, cantitatea de energieelectricobinutdin generatoare eoliene a crescutde mai mult de patru ori ntre 2000 i 2006 [1].

Fundamentarea investiiilor privind utilizarea

energiei vntului n gospodriile individuale, nferme sau n baterii (reele) de turbine necesitnscunoaterea potenialului eolian pentru fiecareamplasament, respectiv gen de utilizator.

n prezent, dei exist hri ale vitezelorvntului n Romnia [2], nu sunt publicate nliteratur modalitile de evaluare folosite pentru

ntocmirea lor. De aceea, autorii propun o metodde evaluare a potenialului eolian pe baza datelorfurnizate de INMH privind viteza vntului ladiverse staii meteorologice, care poate fi utilizatuor pentru a decide asupra oportunitii amplasrii

unor turbine n zone geografice concrete.

1. IntroductionIn the present conditions of energetic crisis, the

concern to find new unconventional energy sourcesbecomes more than necessary. One of the cheapersources is wind energy, which is used for centuries,but having a huge development in the last timeonly.

Wind energy is plentiful, renewable, widelydistributed, cleans and reduces toxic atmospheric

gas emissions when it is used to replace fossil-fuel-derived electricity.At the end of 2006, world-wide capacity of

wind powered generators was 74,223 MW;although it currently produces less than 1% ofworld-wide electricity use, it accounts forapproximately 20% of electricity use in Denmark,9% in Spain, and 7% in Germany. Globally, windpower generation was more than quadrupledbetween 2000 and 2006 [1].

The investment decision of individual users or

firms on wind power utilities installation demandsan appropriate knowledge of wind potential forevery site and/or customer type.

At the present time, although there are somemaps of wind velocities in Romania [2], there is noavailable literature concerning the estimationmethods used in drawing them. For this reason, theauthors propose here an estimation method of windpotential, starting from the online available datasupplied by INMH for different meteorologicalstations. This method may easily be used in order tomake a decision on the opportunity of wind power

utilities placement on a given site.


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O metodsimplde evaluare a potenialului eolian al unei regiuni

92 RECENT, Vol. 8, nr. 2 (20), Iulie, 2007

2. Metodologia de evaluare a potenialuluieolian

2.1. DefiniiiCantitatea de energie care traverseaz unitatea

de suprafa normal pe direcia vntului, n

unitatea de timp, se numete densitate a fluxului deenergie [3]:

2. Wind potential evaluating

methodology2.1. Definitions

The energy quant ity that passes by t he unit areanormal to the wind direction, in a second, is

denominated as energy flux density [3]:

2

3v

P = , (1)

unde este densitatea aerului, iar v este viteza vntului.Evident, aceast densitate a fluxului prezint

variaii mari, n timp i n spaiu. Pentru un anumitamplasament, media temporala densitii fluxului deenergie, pe un interval de timp T suficient de mare,definetepotenialul eolian al amplasamentului:

whereis the air density and v is the wind speed.This flux density evidently presents great

variations, in time and space. For a given location,the temporal mean value of the energy flux density,for a sufficient great time interval T, defines thewind potential of the site:

( )dttPT

T

T

=

0

1lim , (2)

Uneori se folosete termenul de potenial eoliani pentru energia medie anual care traverseazunitatea de suprafanormalpe direcia vntului:

Sometimes, one uses the term wind potentialfor the mean value of the wind energy passing in anyear through an unit area, normal to the winddirect ion, too:

( )dttPET

=0

, (3)

cu T= 1 an = 8760 ore.Din expresiile de mai sus, rezult c energia

posibil de captat este dependent de cubul vitezeivntului; de aici apare importana stabilirii ct mai

precise a vitezei i duratei vntului pentru un anumitamplasament.

2.2. Date de intrare i prelucrarea acestoraSe pleacde la date furnizate online de INMH

privind viteza vntului. Astfel, s-au descrcat dateprivind viteza vntului de-a lungul unei luni (martie2007), cu valori maxime, minime i mediiponderate, la 23 de staii meteo de pe cuprinsulRomniei [4]. Spre ilustrare, dm datele nregistratela staia Sulina (figura 1).

Avnd n vedere caracterul aleatoriu alfenomenului meteorologic numit vnt, se impune oprelucrare statistica datelor prezentate.

with T = 1 year = 8760 ours.From the above expressions we get that the

available energy is depending of the third power ofthe air speed; from this fact results the importance

of a precise determination of the wind speed andduration, for a given site.

2.2. Enter data and their processingWe were starting from the online data provided byINMH on wind speed. So, we have downloadeddata regarding the wind speed, meaning maximum,minimum and weighted mean daily values, during amonth (March 2007), at 23 meteorological stationsin Romania [4]. As an illustration, we give thestored data at Sulina (figure 1).

Taking into account the random character of thewind, a statistical processing of these discreet datais recommended.

Figura.1. Viteza vntului la Sulina, martie 2007Figure.1. Wind speed at Sulina, March 2007


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A Simple Method to Estimate the Wind Potential of a Region


n primul rnd, vom reine nu att valorilemaxime ale vitezei ct, mult mai important, valorilemedii ponderate ale vitezei (care sunt furnizate deINMH). Aceasta deoarece, pentru a surprindeaspectul energetic al fenomenului, conteaz foarte

mult durata vntului de o anumitintensitate.n al doilea rnd, datorit faptului co turbineoliannu drandament bun dect la viteze de vntmai mari de 3 m/s (turbinele Savonius), iar cele maimulte turbine Darrieus abia de la valori mai mari de5 m/s, valorile vitezei vntului se vor grupa nintervale convenabile (tabelul 1).

First, we shall retain not the maximum valuesof the speed, but the most important mean weightedvalues, also given by INMH. This because, in orderto consider the energetic aspect of this phenomenon,the wind duration at a given mean speed is more

important than the peak speed.Secondly, because a wind turbine gives a goodefficiency at speeds greater than 3m/s only(Savonius type), and the most middle powerturbines even at speeds greater than 5 m/s (Darrieusand other types), the wind durat ions will be groupedinto speed intervals (table 1).

Tabelul 1. Durata vntului (ore)Table 1. Wind duration (hours)

Site v > 3m/s

v > 6m/s

v > 9m/s

v > 12m/s

Site v > 3m/s

v > 6m/s

v > 9m/s

v > 12m/s

Arad 120 Deva 96Bacu 384 48 Drobeta Tr. Severin 48Botoani 336 48 Galai 432 24Bucureti 216 Iai 504 72Buzu 624 72 Miercurea Ciuc 192Clrai 432 24 Ocna ugatag 168

Caransebe 336 72 Rmnicu Vlcea 96Ceahlu Toaca 528 360 192 96 Roiorii de Vede 408 96Cluj Napoca 216 Sibiu 336 24Constana 264 Sulina 744 456 96Craiova 456 Tulcea 432 72 48

Vrful Omu 672 576 384 240

Din simpla citire a datelor din tabelul alturat sepoate vedea c exist unele zone cu potenialnesemnificativ, altele cu potenial mic, moderat saufoarte mare. Desigur, nu trebuie uitat cstudiul defa este demonstrativ; aceasta nu nseamn ns crezultatele sale nu pot avea caracter de semnal i deiniiere n problem. Urmeazca un astfel de studius fie amplificat i extins pe mai muli ani. Pentrumoment, autorii i propun doar s contureze ometodologie de evaluare, avnd certitudinea cdup un studiu cantitativ amnunit se va puteaspune cu precizie unde este util a se plasa turbineeoliene, de care tip sfie acestea i de ce putere.

Gruparea vitezelor pe intervale este necesarpentru determinarea unei funcii de corelaie ntretimpul Tct vntul bate cu o vitez egalsau maimare dect o vitezoarecare v i vitez, adic, ofuncie T= T(v).

Plecnd de la aspectul datelor din tabelul 1, sepoate presupune c cea mai potrivit form afunciei T= T(v) este cea exponenial. Prin urmare,se propune forma:

From the first reading of tabulated data, one cansee that there are zones of too low potential, otherzones having a middle or even great wind potential.Of course, one must remember that the presentstudy is a demonstrative one; but, even so, itsresults should be taken as a signal and in aninitiatory sense. The study must be amplified andextended on a longer duration (a year or many). Forthe time being, the authors intended to sketch onlyan evaluation methodology, keeping the convictionthat after a quantitative and detailed study one cansay with accuracy where will be useful to place awind turbine of an optimum gain.

This grouping of wind values into speedintervals is necessary in order to find a correlationfunction between the t ime Twhen t he wind speed isequal or greater than a given value v, meaning aT= T(v) function.

Start ing from the data aspect in table 1, we canpresume that the most suitable form of the T= T(v)function is the exponential one. Therefore, it cantake the form:

bv

eaT = (4)


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Coeficienii ai bpot fi determinai prin metodacelor mai mici ptrate, dup liniarizarea expresiei(4) prin logaritmare.

Spre exemplificare, dm mai jos expresiile (4)calculate pentru amplasamentele cu cele mai

semnificative poteniale din tabelul 1:

After linearization of the expression (4) takingits logarithm, and using the smallest squares method,we can get the values of a and b coefficients.

For example, we give bellow the calculatedexpressions (4) for five most significant sites from

table 1:veT 1155,01033 = , Vrful Omu (5a)

veT 1918,049,1022 = , Ceahlu Toaca (5b)

veT 3455,066,2537 = , Sulina (5c)

veT 366,049,1022 = , Tulcea (5d)

veT 648,02,3512 = , Iai (5e)

Graficele funciilor de mai sus sunt redate nfigura 2. Alura curbelor permite cu uurin s sefac o comparaie ntre diversele zone privitor la

viteza i durata vntului pentru perioada studiat.

The graphs of above mentioned functions aregiven in figure 2. Here, the curves aspect allows aneasy comparison between different zones regarding

the wind speed and durat ion, for the studied period.

Figura 2. Funcia T= T(v) pentru diferite locaiiFigure 2. Function T= T(v) for different locations

2.3. Evaluarea potenialului eolian i a energieiutilizabile

Calculul potenialului eolian se va face pentrucele cinci staii mai sus menionate, cu referire laperioada de timp martie 2007. Fr ndoial,modalitatea de calcul se va putea utiliza apoi pentruorice altperioadde timp sau zongeografic.

n baza relaiilor (1) (3), se poate scrie:

2.3. Evaluation of wind potential and usefulenergy

Wind potential evaluation will be made for thefive sites above mentioned, regarding the timeperiod March 2007. Undoubtedly, the same mannerof calculus will be usable for any other time periodand/or geographic zone.

In the base of relations (1) (3), can be written:

dtvET

=

0

3

2 (6)

n care se va introduce vit eza medie ponderat, cafuncie de timp.

Cum valorile vitezei de care se dispune au un

caracter aleatoriu discret, un calcul adecvat arpresupune prelucrarea statistic a datelor de

where we shall introduce the weighted mean speedas a time function.

As the speed values have a random discreet

character, a proper calculus would presume thestatistic processing of measured data. For the


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A Simple Method to Estimate the Wind Potential of a Region


msurtori. Pentru moment, autorii au preferat scalculeze integrala din relaia (6) prin transformareaacesteia n sumcu numr finit de termeni. n acestsens, s-a folosit expresia:

moment, the authors preferred to evaluate theintegral from the relation (6) by taking the sum of afinite number of terms. In this sense, the expressionused is:

=+

+

=

30

1

31

3

22 iii vv

E (7)

n care: - durata unei zile; vi - viteza medieponderata vntului n ziua i.

Dac n relaia de mai sus se introduce:= 1,255 kg/m3 i = 86400 s, rezult o valoare apotenialului n J/m2. Aceasta reprezint energia pecare o posedo vnde curent cu seciunea de 1 m2.Prin mprirea valorii de mai sus cu 3,6106,energia va fi exprimat n kWh/m2. Rezultateleacestui calcul sunt redate n tabelul 2.

where: - duration of a day; vi - weighted meanspeed of day i.

If in the above relation we introduce = 1.225kg/m3and = 86400 s, the wind potential will resultin J/m2. This will represent the energy possessed byan air stream having a cross section of 1 m2.Dividing the above value by 3.6106, the energywill result in kWh/m2. The results of t his calculusare presented in table 2.

Tabelul.2. Energia eolianspecificn luna martie 2007

Table 2. Specific wind energy in March 2007Site Vrful Omu Ceahlu Toaca Sulina Tulcea Iai

E(kWh/m2) 1784.9 654.39 229.8 45.138 43.53

Aa cum s-a mai spus, la viteze de vnt miciturbinele eoliene nu pot porni sau, chiar dacpornesc, au un randament foarte sczut. De aceea,valorile din tabelul 2 ale energiei eoliene trebuieamendate. Aceasta se poate face funcie deamplasament, de frecvena vnturilor mari i defelul turbinelor instalate. De pild, n zonele cuenergii specifice mici E100 kWh/m2, unde esteposibil utilizarea unor turbine Savonius carepornesc uor i dau randament ncepnd de la vitezede 3 m/s, se pot elimina din start zilele n carev < 3 m/s. Atunci, energia utilizabil se va calculacu relaia:

As we said before, at low wind speed the windturbines can not start or even if they do start theywould have a very poor efficiency. For this reason,the values given in table 2 for the wind energy mustbe amended. This can be made regarding thelocation, the high wind frequency and the type ofthe turbine. For example, in the zones with lowenergy levels, lets say E 100 kWh/m2, wherethere is still possible to use small turbines(Savonius) which start easily and are efficient forspeeds greater than 3 m/s, we can eliminate fromthe beginning the days when wind speed wassmaller than 3 m/s. Then, the useful energy will becalculated with the relation:

=k

ku vEE1

3

21 , (8)

n care: k- numrul zilelor n care v < 3 m/s;vk- viteza medie a vntului n ziua k.

Astfel, pentru locaia Iai, unde timp de 11 zile

vntul a fost mai slab de 3 m/s, energia utilizabilafost:

where: k the number of days in which v < 3 m/s;vk- mean wind speed in the day k.

So, for t he Iai zone, where during 11 days the

wind mean speed was less than 3 m/s, the usefulenergy was:

76.403.188242000

225,153.43 ==uE kWh/m

2.

Dup cum se poate observa, chiar dupeliminarea din calcul a zilelor cu vnt slab sau nulpotenialul nu a sczut dect cu 6,3%.

n zonele cu potenial mediu, de pildla Sulina,se pot utiliza att turbine de mic putere, ct iturbine de medie putere. Avnd n vedere faptul caici a existat o singurzi n care vntul a fost mai

slab de 5 m/s, diferena ntre energia pe care vntulo poseda i cea utilizabileste neglijabil.

As we can see, even after the elimination of thedays having small or null wind, the energy potentialwasnt reduced more than with 6.3%.

In the zones with middle level of potential, forexample at Sulina, it is possible to utilise both smalland middle turbines. So, because here was a singleday in which the wind speed was smaller than 3

m\s, the difference between the potential energyand the useful one was negligible.


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n zonele montane, de exemplu Ceahlu Toacasau Vrful Omu, problema se pune invers: aiciturbinele vor trebui s fie blocate n zilele cu vntmai tare de 20 m/s ! Dacn Ceahlu a fost numai osingurzi cu astfel de vnt (23 m/s), la Vrful Omu

au fost 4 zile cu astfel de condiii (din care o zi cu32 m/s !). Maniera de calcul a energiei utilizabilermne nsaceeai aici se vor elimina din calculzilele cu vnt mai tare dect indicaiile tehnice aleconstructorului turbinei.

Trebuie precizat cn cele de mai sus s-a artatcum se poate evalua potenialul eolian i nu putereaefectiv obinut de pe urma unei turbine. Se tie(teoria lui Betz, 1966) c puterea unei turbineeoliene variazntre 36% i 59% din puterea vneide curent care traverseazdiscul t urbinei [5].

3.ConcluziiLucrarea de fase vrea un semnal asupra unei

probleme care, dei cu 20 de ani n urmpreocupacercurile tiinifice romneti din domeniul surseloralternative de energie, a adus prea puine rezultateconcrete. La ora actual se presupune, frdemonstraie, cn Romnia potenialul eolian fiindprea slab, o investiie n acest domeniu nu esterentabil. Or, dupcum se aratn prezenta lucrare,un anume potenial eolian exist; el ateaptdoar sfie evaluat cu exactitate i utilizat cu maximum derandament.

Metoda propuspermite evaluarea, cu uurinicu suficient precizie, a potenialului eolian n oricezon, pe baza datelor furnizate de INMH sau a celorobinute prin msurri n chiar amplasamentul vizat.

Construirea curbelor T = T(v) pentru toatestaiile meteorologice, pe baza unor date peperioade lungi de timp, furnizeaz un instrumentrapid de apreciere a zonelor semnificative din punctde vedere al energiei eoliene.

Precizia evalurii potenialului eolian poate fi

mbuntitdacn relaia (6) se introduce expresiavitezei vntului rezultatprintr-o abordare statist ic,pentru gsirea formei adecvate a repartiieivitezelor. Aceasta este direcia n care autorii ipropun scontinue acest studiu.

In the mountain zones, for example at CeahluToaca or Vrful Omu, the problem becomesreversed: here, the turbines must be stopped in thedays with wind speed greater than 20 m/s. If atCeahlu there was a single day with such a wind

(23 m/s), at Vrful Omu there were 4 days withsuch conditions (from which, one day with 32m/s!). The calculus manner for useful energyremains the same here will be eliminated the dayspresenting a stronger wind than the turbinetechnical book indicates.

We have to point out that so far we presentedthe method to evaluate the wind energy potentialand not the effective mechanical power of theturbine. It is well known that th is one last parameterreaches only 36% - 59% from the power of the flowpassing through the turbine area [5].

3. ConclusionsThe present paper intents to be a signal on a

topic which, though 20 years ago was in the attentionof Romanian scientific circles from the alternativeenergy sources domain, so far has a few concreteresults. At the present, there are people whopresume, without demonstration, that in Romania thewind energy potential being to low there is no reasonto make an investment in this field. But, as we havepointed out in the paper, a certain potential doesexist; it is only waiting to be exactly evaluated andused with maximum efficiency.

The proposed method allows an easy and preciseevaluation of wind energy potential in every zone, onthe basis of data supplied by INMH or on the basis ofmeasurements made in the very specific site.

The curves T = T(v), made for all themeteorological stations and for longer periods oftime, represent a rapid instrument for evaluation ofsignificant zones from the point of view of windenergy.

The accuracy of the potential evaluation may

be improved if one replaces in the relation (6) thewind speed expression resulted from a statisticalapproach in data processing, in order to find anadequate form for the speed repartition. This is thedirection in which the authors intend to continue.

References1. ** *: http://en.wikipedi a.org/wiki/Wind_power. A ccessed: 2007-03-022. ** *: http://www.ibcoenerg.ro/eolian.html. Acc ess ed: 2007-05-043. Ili e, V., et al.: W ind energy usage. Editura Tehnic, Bucureti, 1984 (in Romanian)4.***: http://www.inmh.ro. Accessed: 2007-04-045.***: http://www.windpow er.org/en/tour/wres/betz.htm. Access ed: 2007-06-07

Lucrare primitn Mai 2007(i n formrevizuitn Iunie, 2007)

Received in May, 2007(and revised form in June, 2007)

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Potential Eolian