OL., NO., FEBRUARY 7 ISSN 89-668 REDICTION OF ELECTRICAL RODUCTION FROM WIND ENERGY IN THE MOROCCAN SOUTH Elyaqouti Mustapha, Ezzaidi Asma, Bouhouch Lahoussine and Ihlal Ahmed ERTAIER, ESTA, Univesity Ibn Zoh, Agadi, Moocco LMER, FS d'agadi, B, Univesity Ibn Zoh, Agadi, Moocco E-Mail : elyaqouti@gmail.com ABSTRACT In this pape, we pesent the analysis and the statistical modeling of wind speed, duing 6 yeas (9-), in Ait Aiaaza egion of the Taoudant povince in southen Moocco. Futhemoe, we estimate the powe and the electical enegy, poduced by the wind tubine, ATB.. that we have poposed as electical aeogeneato fo the site unde study. In fact, the modeling of wind esouces consists of using two methods: fist, we use the diect statistical pocessing of wind data, aftewad; we apply a mathematical appoach to fequency distibutions of wind speed. As fo the estimation of the powe and the poduced electical enegy by the wind tubine unde test, we have modeled the powe cuve using polynomial intepolation of Lagange. Keywods: wind enegy, weibull distibution, estimation of powe, powe cuve. INTRODUCTION The enegy tanspoted by the wind is the diving foce of wind tubines, with a andom and intemittent chaacteistic. The vaiation of the wind speed can affect diectly the dynamic chaacteistic of the wind tubine []. Consequently, in the development of a poject of wind enegy, the high quality of the data of wind is necessay to estimate the wind esouces in a coect way []. The statistical appoach is one of the adequate methods fo the estimation of the impotant popeties in the wind poduction. In fact, these popeties ae the fequency and the value of the wind speed. Fo the peiod of 6 yeas going fom 9 till, this pape pesents the study, the analysis and the statistical modelling of the wind speed in the egion of Ait Aiaaza, povince of Taoudant in the South of Moocco. It also deals with the estimation of the powe and the poduced enegy by ATB.. wind tubine [3] that we have suggested fo the site unde test. This pape is subdivided as follows: afte this intoduction, the section pesents the chaacteistics of the site unde test situated in the povince of Taoudant in Moocco. Next, in the section 3, we model and estimate the wind esouces that is to say, the modelling of the wind of this site based pimaily on the technique using the law of and also the estimation by modelling the powe and the enegy poduced by the ATB..wind tubine. In the section we will pesent the vaious analyzed and contovesial esults. In the end of this pape, we will put up a conclusion and some pespectives. RESENTATION OF THE SITE UNDER STUDY The site of ou study is the village of Ait Aiaaza which is situated in the povince of Taoudant in the south of Moocco. The geogaphical coodinates of this site ae: 8.798 W of longitude, 3. N of latitude and 73 m of height, its geogaphical location is pesented in the Figue-. Figue-. Geogaphical location of the site of Ait Aiaaza. The meteoological data, such as the sola illumination, the ambient tempeatue, the humidity and the wind speed and its diection, ae collected though a meteoological station installed aound this site. MODELING AND EALUATION OF WIND RESOURCES Mathematical modeling of the wind Diect statistical teatment of the wind data The statistical teatment of the wind data depends on the natue and on the numbe of available measues. This teatment allows, in fact, the volume eduction of the data. This method epesents the data obseved by a numbe of limited paametes []. It povides inteesting infomation to the uses of the wind enegy on the fluctuation of the wind speed. This offes the possibility of detemining the wind potential of a given site and so allows the estimation of the wind enegy which we can poduce in this site. Concening the wind speed, it is expessed though its aveage value moy given by the equation (). This expession epesents the aveage aithmetic of all the 96
OL., NO., FEBRUARY 7 ISSN 89-668 statements i of the speed, made accoding to a fequent and egula sampling. N moy () i N i Whee i and N coesponds espectively to the aveage speed duing a peiod of sampling Δt and the measue numbes i. To teat statistically these speeds, we exploit the elation () which gives the expession of the standad deviation of the wind speeds. In fact, it will be a citeion allowing measuing the dispesal of the wind speeds aound its aveage value. The moe this citeion is low, the moe speeds ae gouped aound the aveage speed moy. () N i N i moy Mathematical modeling of the fequency distibutions of the wind speed The pupose of this pat is to find a mathematical function f() epesenting the distibution of the wind speed fequencies. This function will be useful fo the calculation of the pefomances of a wind system whee the estimation of the wind enegy at heights diffe fom those whee the measues ae taken. To know the speed vaiation of the wind, we use the distibution. The latte, allows us to chaacteize the fequency distibution of the wind speeds ove a given peiod, in ode to analyze the wind enegy potential of any given site. This distibution is defined by the density of pobability f() given by the equation (3) [] []: f K C C K e K C Whee the paametes of K, without dimension and C having the dimension of a speed (m/s), ae espectively: fo the fist one, it s the facto fom of the law. It chaacteizes the fom of the distibution fequency. The moe K is aised, the moe the distibution is naowed. Concening the second paamete, it is the scaling facto. This detemines the quality of the wind, the value of which is geneally high fo the windy sites and week fo the sites chaacteized by athe low winds. The accumulated fequency F() coesponding to the density of pobability f() is given by () []: F e K C (3) () b F f d () a b a The detemination of the paametes K and C allows the knowledge of the distibution of winds fo a given site. Fom the data of the wind of a site, thee ae seveal methods which lead to detemine these paametes [6]. One of the techniques stipulates that, K and C can be estimated fom the aveage speed and the aveage standad deviation of the wind speed. In fact, the paamete K is detemined by an empiical appoximation poposed by Justus in 978 [7]. This appoximation is given by the elation (6): K.86 (6) moy Afte the detemination of K, the facto of shape C is calculated by the equation (7): C Γx = moy K Whee Γ(x) is the function Gamma given by (8): + t x (7) t t (8) The aveage speed of the wind moy can be obtained by integating the function of density of pobability f(), accoding to (9): moy f ( ) d (9) Accoding to the paametes of, this aveage speed moy can be estimated by the equation () []: moy C () K As fo the standad deviation of the speeds of winds, it is expessed by the equation (): moy f d () By using the paametes of and afte some substitutions, is calculated by the equation (): C () K K Concening the pobability of a speed of the wind, occuing between a and b, can be calculated by (): 963
OL., NO., FEBRUARY 7 ISSN 89-668 Concening the most pobable speed of the wind, pp, coesponding to the most fequent speed of the wind in the studied site, it is calculated by the equation (3): K pp C (3) K Fo the wind speed poducing a maximal enegy, it is calculated by the equation (): énegie,max C K K () Fo the highest heights, an extapolation is necessay to calculate the wind speed accoding to the heights z. To make this extapolation, we have used the law of powe pesented in [6] [8]. This law is a simple model fo the detemination of the vetical pofile of the wind. This model takes into account influences of the oughness of the suface and the atmospheic stability. This law is descibed by the equation (): Z ( Z ) ( Z ) Z Z () Whee (z) is the wind speed fo the height z and (z ) is the value of this speed in height of the efeence z. With z, an empiical coefficient, epesenting the oughness of the gound and the atmospheic stability. its value depends essentially on the natue of the gound. Numeically z vaies between. fo a smooth gound, and, fo a bumped field. The value, most fequently adopted fo z, is aound, [6]. The detemination of the empiical fomulas of paametes extapolation equies the use of the model poposed by Mikhail and Justus [9] []. Indeed, the extapolation of the facto of fom K (z) at the height z is given by (6): K ( Z ) K ( Z ) Z.88ln Z (6) With K (z ) coesponding to the value of this facto of shape in height of the efeence z. As fo the extapolation of C (z), it is given by (7): Z C ( Z ) C ( Z ) Z n (7) With C (z ) epesenting the value of this scaling facto in height of the efeence z. As fo the exhibito n, it is given by (8):.88 C ( ) ln Z n Z g.88 6 ln Z (8) Whee z g is the geometic aveage of the height given by (9): Z g Z. Z (9) Estimation of the powe and the available wind enegy in a site Diect calculation The wind powe éol,d, available in a steam of wind elements which have speeds i that can be obtained by the elation (): N 3 éol, d s () i N i Whee =.3 Kg/m3 epesents the density of the ai and s is the suface which is swept by the blades of the wind tubine m². The aveage powe density of the wind d,éol,d, epesents the available aveage powe by suface unit, it is calculated by (): d, éol, d N 3 () i N i Fom the available powe éol,d, and fom the powe density d,éol,d, aveage, we calculate the available wind enegy E éol,d, duing a peiod of time T = NΔt and its density aveage E d,éol,d, by the equations () and (3): E T () éol, d éol, d E T (3) d, éol, d d, éol, d Use of the paametes of In this case, the aveage powe density of available wind by suface unit d, éol,w is given by (): 3 d, éol, w f d () Howeve, the integal coesponding to the cubic aveage speed can be calculated by using the paametes of, accoding to () [7]: 3 3 f d C 3 kweibull () Finally the powe density aveages d,éol,w can be expessed by (6) []: 96
OL., NO., FEBRUARY 7 ISSN 89-668 d, éol, w 3 3 C K (6) The density of enegy E d,éol,w duing a peiod of time T can be calculated by the fomula (7): E T (7) d, éol, w d, éol, w Estimation of the powe and the enegy poduced by a wind tubine Modelling of the powe cuve of a wind tubine The powe cuve of a wind tubine is a specification of pefomance supplied by the manufactue. It epesents the powe output of the wind tubine accoding to the wind speeds. This cuve is geneally used to conside the enegy poduction aveage in a paticula place fo a pofile of a given wind. In the case of ou study, the ATB.. wind tubine of the company ATB Riva Calzoni spa, in which we ae inteested, possesses the typical powe cuve epesented on the Figue- [3]. Si d Ls ( ) Si d n ( ) (8) n Si n a Si a Whee L () is a polynomial of the fifth degee given by the equation (9): 3 L a a a a a a (9) 3 owe and enegy poduced by a wind tubine The aveage powe g,éol geneated by a wind tubine can be diectly calculated as a function of the pobability density f() by integation given by the equation (3) : a d g, éol f d (3) We specify that, on one hand, the powe geneated by the wind tubine emains constant beyond the nominal speed n, and on the othe hand, this powe vaies only between the speed of stating up d and the nominal speed n. Accoding to these hypotheses, the expession (3) takes then the shape (3): n a n L f d f d g, éol d n (3) As a consequence, the electical enegy E g,éol poduced by a wind tubine, duing a peiod T is calculated by the elation (3): g, éol d n a n E T L f d T f d n (3) Figue-. ATB.. wind powe cuve [3]. Each powe cuve is chaacteized by a numbe of paametes which ae: d :Statup speed ; n :Nominal speed o the to which the tubine geneates its nominal powe ; a : Stop speed ; n : Nominal powe of the aeo geneato RESULTS AND DISCUSSIONS With the aim of consideing the wind esouces of the studied site, we exploited the data concening the wind speeds, aised at a cetain efeence height z, geneally m, by the weathe station above. Afte teatment, we epesent by the figues 3 and espectively, the vaiation of the daily aveage speed of the wind moy fom 9 to, the vaiation of the annual aveage speed A.moy and that of the standad deviation of the wind speeds in the site unde test. To model the powe cuve, we have opted fo two appoaches. The fist one coesponds to the exploitation of one of the models of the available powe cuves in the liteatue; such as the model of allabazze, o the linea model, etc. Wheeas the second, it coesponds to the use of the eal cuves which an intepolation method is applied []. We will adopt the last appoach fo ou modeling by using the polynomial intepolation of Lagange. The typical cuve of powe of the wind tubine unde test can be modelled by the system of equations (8): 96
Standad deviation OL., NO., FEBRUARY 7 ISSN 89-668 moy [m/s] A,moy [m/s] 8 6 Days (9-) Figue-3. The daily aveage speed vaiation moy of the wind fo 9 to. 3 A,moy Standad deviation 9 3 Yeas Figue-. The annual aveage speed vaiations A.moy of the wind and its deviation standad fo the yeas 9 till. Duing the peiod 9 till, the ecoded measues show that the wind speed vaies in a andom way, with an aveage annual speed A.moy vaying between.38 m/s and.86 m/s. Afte teatment of these 6 yeas of measues on the site of Ait Aiaaza, the aveage speed as well as its standad deviation is espectively moy = 3.73 m/s et =.33 m/s. To evaluate the wind distibution in this site, we pesent in Table-, the paametes K weibull and C weibull which ae deduced fom the wind data of this site by using the fomalism discussed ealie.,8,6,,,,8 Table-. paametes calculated fo the yeas 9 till. Yeas K C.87 3.9 3..9 3.69.86.9. 3..7 9.7.69 6 yeas 9 to.6.86 Fo the estimation of a aeo geneato poduction, we ae going to extapolate the measues of the wind speeds fo desied height, that is that of the hub of the tubine. To do it, we use the fomulated law highe. In the figue we have shown the vetical pofile of the aveage wind speed fo z =.. We notice that the moe z is aised, the moe the speed moy inceases. Indeed, in this case, fo example fo a wind speed moy = 3 m/s measued as high as efeence z = m, in 6 m above gound level, this speed amounts to 3.8 m/s. The wind powe available on this height is then. times highe than in m. moy [m/s],,,, 3, 3,,,,, 6 8 6 8 Height [m] Figue-. etical pofile of wind speed fo z =. by using the powe law. Taking into account what pecedes, fo the peiod 9 till, and with K (z ) =.6 and C (z ) =.86 m/s fo z = m, the Figue-6 pesents the vaiation of these paametes with the height z. Futhe to this study, we notice that the paametes of gow with the height z. 966
C [m/s] OL., NO., FEBRUARY 7 ISSN 89-668 K, 3, 3,,,,,, K C, - 6 8 6 8 Height [m] Figue-6. K and C vaiation with the altitude z. Following ou investigations, we estimate the aveage enegy poduction of the wind ATB.. tubine poposed fo the site unde test, by modelling its powe cuve thanks to the expessions (9) and (3). In fact, the coefficients of the polynomial of Lagange L () summaized in the Table-, ae identified by means of a pogam which we have developed unde Matlab whose oganization chat is epesented in the Figue-7. Table-. Lagange coefficients identified. 8 7 6 3 Figue-7. Flowchat of identification of coefficients Lagange polynomial L () unde Matlab. The validation of ou fomalisms exposed peviously is made by the plan of the Figue-8. On the latte we compae the cuves of powe simulated and measued by the manufactue. 6 x Stat Inputs : ( d, n, a, n, péiode T) Fo i = d To a Input i Calculate a To a (Lagange coefficient) Calculate g, éol, moy eq. () Calculate E g, éol, moy eq. (6) End a a a a 3 a a 799-3393 8-67. owe g,éol [W] 3 Measue of manufuctue Simulation 6 8 6 8 Wind speed [m/s] Figue-8. Compaison of intepolation cuves with measuement manufactue [3]. We notice that the cuve of simulation is pefectly coelated in the measues of the manufactue. It poves the validity of the model that is chosen. The densities of the available powe and enegy in the site unde test, duing 9 till, ae summaized in Table-3. Duing the same peiod, the Table- gives the powes and the available enegies in a suface s equal to the suface swept by the blades of the ATB.. aeo geneato. These latte magnitudes ae calculated by the espective poducts, the powe density and the enegy density to be fom the suface s is the peiod T. 967
OL., NO., FEBRUARY 7 ISSN 89-668 Yeas Table-3. The densities of the available powe and enegy in Ait Aiaaza site. owe density (W/m ) Enegy density (MWh/m ) Diect calculation (Eq. ) Using (Eq. 6) Diect calculation (Eq. 3) Using (Eq. 7) 33.9 33.8.9.97 3 7.97 8.37.7.6 67.38 6.96.9.78 9.76 9.6.36.38 68.86 6.99.968.68 9 63.98 6.96.7.78 6 yeas 9 to 9.77.9.3. Yeas Table-. The available powe and enegy in Ait Aiaaza site. Diect calculation (Eq. ) owe (kw) Using (Eq. ) x s Diect calculation (Eq. ) x T Enegy (MWh) Using (Eq. 7) x s 76.7 76.8 67.7 667.8 3..6 39.73 368.7.37.99 33. 33.6 3.9.76 998.9 988..86 6.96 366. 88. 9.8. 76. 33.6 6 yeas 9 to.7. 986.7 9.8 To detemine the elative eo committed on the estimation of the wind powe density d,éol,w that we have calculated by (33). In fact, this eo is evaluated by the atio of the diffeence between the densities of the wind powes d,éol,w and d,éol,d, elative to the powe density diectly calculated. E d, éol, d d, éol, w (33) d, éol, d The vaiations of the eo E, of the yea 9 till ae epesented on the figue-9. Duing this peiode is between. % and.7% and it is equalled to.7 % as the aveage value fo 6 yeas (9- ). This shows that the used appoach gives good esults allowing then its validity. E (%) 8 6 - - -6-8 - 9 3 Yeas Figue-9. Relative eo on the estimation of wind powe density. Finally, in the Table- we illustate the powes and the consideed enegies poduced by tubine of the ATB.. aeo geneato. In the same table, we also epesent the pecentage pp of the consideed powe poduced with egad to the available powe in the site unde test. This pecentage is always defined by the elation (3) fo the peiod 9 to : g, éol pp (3) éol, d 968
OL., NO., FEBRUARY 7 ISSN 89-668 Table-. The estimated powes and enegies poduced by the ATB.. aeogeneato and the pecentage pp. Yeas Estimated powe poduced g, éol (kw) Estimated enegy poduced E g, éol (MWh) ecentage pp (%). 3.3.7 3.7 7.8 9.9.73 79.73 3. 3. 99.78 3. 3.3 67.9 3. 9. 86.93 38.6 6 yeas 9 to 39.3 3. 3.9 Accoding to the esults of Tables, and 6, we notice that the site unde test, efeshed of a elatively aveage wind potential, because the maximal value of the powe density d,éol,d does not exceed 68.86 W/m. This is justified by the week measued values of the wind speed. It is thus obvious that a study of complementaily entes the wind enegy and desiable photovoltaic, because the peiods of the yea having a week peiod of sunshine, coespond to those having a bette wind potential. So the coupling of these two souces of enegy tuns out to be the safest and most adequate solution, fo autonomous systems of electification. CONCLUSION AND ERSECTIES In this pape, we have pesented the study and the modeling of the wind potential concening the Ait Aiaaza site, in Taoudant povince at Mooccan south. Based on the diect statistical analysis of the wind data, and mathematical modeling of wind speed fequency distibutions, we have poposed two pediction techniques of the electical enegy poduced by the ATB.. aeogeneato - ATB iveted CALZONI Spa Company - that we have poposed fo ou site. The analysis of the esults shows that the appoach used fo pediction of electical enegy fom the wind powe, yields good esults, since the elative eo E does not exceed.7%, as an aveage value fo 6 yeas. Likewise, these esults show that the unde test site has a elatively aveage wind enegy potential because the maximum value of the powe density does not exceed 68.86 W/ m. This is justified by the low measued values of the wind speed. The pespectives of this wok aim at pedicting the poduction of a wind plant, by taking into account in ou study the effect of the aeodynamic inteactions between wind tubines, to give a coect estimation of the electical poduction of the wind fam. It also aims at making a study of complementaity between the sola and wind enegy fo the unde test site, to estimate the electical powe poduction by combining the wind and sola enegies, in a hybid system composed of enewable enegy souces. REFERENCES [] Jianxiao Zou, Chao eng, Yan Yan, Hong Zheng, Yan Li.. A suvey of dynamic equivalent modeling fo wind fam. Renewable and Sustainable Enegy Reviews. : 96-963. [] C. Chancham, J. Waewsak, T. Chaichana, M. Landy, Y. Gagnon.. Assessment of onshoe wind enegy potential using egional atmospheic modeling system (RAMS) fo Thailand, 3 Intenational Confeence on Altenative Enegy in Developing Counties and Emeging Economies, Enegy ocedia. : 87-96. [3] http://www.atbivacalzoni.it/wp-content/uploads/ //ATB_Geenowe_Bochue.pdf. [] Ilhan Usta. 6. An innovative estimation method egading paametes fo wind enegy applications, Enegy. 6: 3-3. [] Can Ozay, Melih Sone Celiktas. 6. Statistical analysis of wind speed using two paamete distibutions in Alaçah egion. Enegy Convesion and Management. : 9-. [6] Cipian-Micea Nemeş. 3. Statistical Analysis of Wind Speed ofile: A Case Study fom Iasi Region, Romania. Intenational Jounal of Enegy Engineeing (IJEE). 3(6): 6-68. [7] Z.R. Shu, Q.S. Li,.W. Chan.. Investigation of offshoe wind enegy potential in Hong Kong based on distibution function. Applied Enegy. 6: 36-373. [8] amod Jain. 9. Wind Enegy Engineeing, McGaw-Hill companies, Fist edition mach. pp. 33-3. 969
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