International Journal of Scientific Engineering and Science Volume 2, Issue 4, pp , ISSN (Online):

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1 Iteratoal Joural of Scetfc Egeerg ad Scece Volume, Issue 4, pp. 5-6, 8. ISSN (Ole): How to Use the Data to Fd the Approprate Ste for Best Wd Speed Geerato? Applcatos o Data Obtaed from Three Dfferet Ctes of Cameroo Marette G. Jeutho, Fabe Kemoge *, Dad Yemélé Laboratore de Mécaque et de Modélsato des Systèmes Physques (LMSP), Faculté des Sceces, Uersté de Dschag, B.P. 67, Dschag, Cameroo, Lab. of Modellg ad Smulato Egeerg, Bommetcs ad Prototype, Faculty of Scece, Uersty of Yaoudé I, Po Box 8, Yaoudé, Cameroo * Correspodg author; phoe: (+7) 67556; emal: kefabe@yahoo.fr Abstract I order to proe that temperature data ca be used to fd the adequate ste leadg to the best wd eergy producto, the temperature ad wd characterstcs are aalyzed for three meteorologcal statos of Cameroo, submtted to dfferet clmates: The hot ad the cool oes. The data was collected for the perod gog to 7 to 6. Assessmet of the wd power potetal was carred out usg the Webull dstrbuto parameters, whch are ealuated by fe umercal techques: The mea stadard deato method, the momet s method, the eergy patter factor method, the Least squares regresso method ad the maxmum lkelhood method (MLM). Results of the study show that the aerage aual wd speeds at m aboe groud for, ad are.,, ad.4 m/s, respectely, leadg to the fact that s ot sutable for wd eergy producto at m alttude. Next, we use the data of temperatures for each cty ad the correspodg wd speed to dere the emprcal fucto goerg the depedecy of ambet temperature ad wd speed, whch lead to the fact that temperature data from umercal weather predcto models ca replace -stu wd speed measuremets. Keywords Assessmet; Wd Eergy; Webull Dstrbuto; estmato. I. INTRODUCTION Eergy plays a sgfcat role huma ad ecoomc deelopmet. Demad for eergy s growg expoetally whle coetoal eergy resources are lmted ad ther use cotrbutes major proporto to erometal polluto [].Sce more tha oe cetury ago, electrcty supply has bee hghly due to the dscoery of fossl fuels such as coal ad ol. Nowadays the use of fossl fuels s remaed growth ad they cotue to make up a large part of the global supply cha for electrcty. Due to depleto of fossl fuels ad loomg clmate chages, the deelopmet of sustaable eergy has receed cosderable atteto oer the last two decades. The rsg cocers oer global warmg, erometal polluto, ad eergy securty hae creased terest deelopg reewable ad erometally fredly eergy sources such as wd, solar, hydropower, geothermal, hydroge, ad bomass as the replacemets for fossl fuels[]. Reewable eergy resources are sustaable. Ths meas that they ca be replaced ad wll ot ru out. They are clea ad fredly to the eromet. Wd eergy ca prode sutable solutos to the global clmate chage ad eergy crss. The utlzato of wd power essetally elmates emssos of CO, SO, NOx ad other harmful wastes as tradtoal coal-fuel power plats or radoacte wastes uclear power plats. By further dersfyg the eergy supply, wd eergy dramatcally reduces the depedece o fossl fuels that are subjected to prce ad supply stablty, thus stregtheg global eergy securty. Durg the recet three decades, tremedous growth wd power has bee see all oer the world.[] There are three basc steps to detfy ad characterze the wd resource a ge rego. I geeral, they are prospectg, aldato ad optmzato. I prospectg, oe usually make the detfcato of potetal wdy stes wth a farly large rego, ad geerally, ths s carred out by meteorologsts who deped o arous sources of formato such as topographcal maps, clmatologcal data from meteorologcal statos, ad satellte mageres[]. A ste st s also coducted at ths stage ad a represetate locato for wd measuremet s detfed. Valdato process oles a more detaled leel of estgato lke wd measuremets ad data aalyss [4-6]. The ma objecte of ths mauscrpt s to detfy the approprate cty of Cameroo where the best testy of wd power eergy ca be foud, ad adequate for wd turbe stallato. It s mportat to meto that ther preous studes M. G. Jeutho et al. [7] estmated the wd potetal eergy of cty. As a result they foud that s a lower wd potetal eergy area. I the preset mauscrpt, we compare the area of lower temperature to the area of hgher temperature, ad propose the emprcal mathematcal relato betwee temperature ad wd speed, leadg to the fact that temperature data ca be used place of speed data to choose the approprate ste for wd turbe stallato. Thus, the rest of the paper s orgazed as follow: I Secto, we preset materals ad tools for the data 5

2 Iteratoal Joural of Scetfc Egeerg ad Scece Volume, Issue 4, pp. 5-6, 8. ISSN (Ole): aalyss, followg Secto by the presetato of the ma results of the preset mauscrpts ad the prodg of some dscussos. Fally, cocludg remarks are deoted to Secto4. II. MATERIALS AND TOOLS FOR THE DATA ANALYSIS. Wd speed data The wd ad temperature data used ths paper were obtaed from NASA meteorologcal serces for three meteorologcal statos of Cameroo:, ad. The elocty measuremets of the wd were made at m heght, whle the geographcal coordates of the selected stes are ge Table. TABLE. Geographcal coordates of selected locatos. Stato Logtude Lattude Alttude 5 58 Est Est 5 Est 7 Nord 5 7 Nord Nord 6 m 46 m 48 m.. Statstcal aalyss of wd speed aratos; Webull dstrbuto fucto The Webull dstrbuto fucto s usually used, accepted ad recommeded the lterature. It proed ot oly adapted for the descrpto of the statstcal propertes of the wd but ges a good agreemet wth the expermetal data [5]. The fucto of Webull dstrbuto wth two parameters for a place at a partcular tme s ge by [5-] k k k f exp, () c c c where (expressed m/s) s the speed of the wd, whle s a admesoal factor of form whch characterzes the frequecy dstrbuto ad c s the scale factor whch has the dmeso speed. The determato of k ad c called parameters of Webull leads to the kowg of the dstrbuto of the wds for a ge ste. I order to fd these Webull dstrbuto s parameters, oe usually use oe of the followg fe methods:.. Mea stadard deato method or emprcal method (MSDM) Oe ca use the MSDM to estmate the Webull parameters ad whe the mea wd speed ad stadard deatos are aalable [6-7]. I ths method, k ad c are expressed as:.86 k, c k where shows stadard deato ad s the aerage speed, wth, ().. Method of momet (MOM) The MOM, well kow as the emprcal method s the mperate techques uersally used for estmatg Webull shape ad scale parameters by aeragg wd speed ad stadard deato Followg ths method, k ad c ca be estmated as ().9874 k wth.98, c k, k k where by we mea the Gamma fucto of.. Eergy patter factor method (EPFM) The EPFM s related to the aerage data of wd speed ad s defed by the followg equato [9-] N k EPF (6) I N V k Where (espressed m / s) s the wd speed for the obserato. N beg the total umber of wd speed data ad s the mea wd speed. The Webull shape ad scale parameters ca be calculated by usg the followg equatos:.69 V k, c (7) EPF k..4 Least squares regresso method or graphcal method (LSRM) LSRM, also kow as a graphcal method mplemeted by plottg a graph such a way that the wd speed data are terpolated by a straght le. The equato ge the probablty desty fucto, after trasformato through the logarthm fucto ges the followg equato [8, -]: l l f kl klc, (8) whch ca be ftted usg the least square regresso y=ax+b wth y l l f, x l, b= klc, (9) ad b k a=k ad c e ()..5 Maxmum lkelhood method (MLM) The MLM s soled through umercal teratos to determe the parameters of the Webull dstrbuto k ad c, whch are estmated by the followg equatos [4-5]: k l k l k, c k k (4) (5) (). Determato of the Degree of Accuracy of the Webull dstrbuto model results To estmate the degree of accuracy of the Webull results, arous estmato statstcs were employed, These are the coeffcet of determato, COD, the root mea square error (RMSE) ad the Nash-Sutclffe model coeffcet of effcecy (COE). They are mathematcally expressed as [5]: 54

3 Iteratoal Joural of Scetfc Egeerg ad Scece Volume, Issue 4, pp. 5-6, 8. ISSN (Ole): y ym y c y COD Χ y y m, () RMSE yc y COE y y y c c y m () where s the actual data, s the Webull result, s the mea of the actual data ad s the umber of obseratos. It s mportat to meto that the closer the alues of ad COE are to oe, the more accurate the result, whle the closer to zero the alues of RMSE the better results..4. Statstcal Aalyss of Maxmum Etropy Prcple I order to study the Maxmum etropy prcple, the probablty desty fucto of speed has bee troduced the followg form: M j f exp α j (4) j Where are the Lagraga multplers, whle M s the umber of the low order momets used. Ths desty fucto s obtaed by mmzg the Shao s etropy, the wellkow Carla et al prcples [4], suggestg the followg costrats: max( ) max( ) ' f d, f d m. (5) beg the M-low statstcal orders, obtaed emprcally as N ' m []. N.5. Effect of ambet temperature o the wd speed predctos By studyg the method to parameterze the physcal depedecy of temperature ad releat meteorologcal parameters, Kurtz at al [6] used the followg relato to calculate the module temperature : Tc Ta I.exp( a b f ), a.44, b=.4 9 (6) Here Ta ad T c are the ambet ad module temperatures, respectely, whle I s the -plae rradace ad the wd speed measured at meters aboe the groud. As shall be proed the followg secto, a smlar equato ca be used to estmate the wd speed data, just by kowg the temperature data, whch ca help to select the approprate ste for wd eergy, wthout use the data of speed. III.. Prelmary: I stu data MAIN RESULTS AND DISCUSSION Wd s a atural pheomeo, ad s oe of the ulmted reewable eergy resources whch ca be a better alterate eergy resource Cameroo. The wd data for, ad, ot show here used ths study were obtaed from the NASA meteorologcal serces.. Webull dstrbuto fucto aalyss The Webull dstrbuto parameters hae bee calculated for daly wd speed data for 7-6 for, ad. The shape ad scale parameters (k ad c) for each rego are estmated by the fe methods metoed aboe. As show Table, a comparso of shape parameter (k) ad scale parameter (c) reeals that: The alues of scale parameters for, ad foud by MSDM, MOM, EPFM, ad MLM are good agreemet; Except LSRM whch fds slghtly dfferet alues of scale parameter rage of.. The alue of scale parameter s less tha for the rego of lower temperature ad hgher tha for the rego of hgh temperature, whle the LSRM estmatg the alue of shape parameter s less tha measured alue of the other methods. For the rego of lower temperature (that s ), the alue of shape parameter s hghest tha the rego of hgh temperature, ad respectely. The comparso of measured ad predcted mea wd speeds s preseted Table, showg that the estmated alue of mea wd speeds foud by MSDM, MOM, EPFM are detcal wth measured oe. The correlato coeffcet betwee measured ad predcted mea wd speeds s ge Table4 whch we ca that they are more adequate for the rego of hgh temperature, ad respectely, tha the rego of lower temperature,. Table 5 summarzes the predcto accuracy results for the preseted models. The actual data ad the theoretcal probablty dstrbuto fucto (PDF) geerated wth the help of shape ad scale parameters are plotted for each rego Fgure, whch we ca see that the Webull shape ad scale parameters calculated by usg the EPFM show ery fe agreemet tha the other Webull shape ad scale parameters estmated usg the other fourth methods.. Effects of temperature: Basc equato to predct the relatoshp betwee wd speed ad temperature data I order to study the relatoshp betwee temperatures ad wd speed, the temperature data hae bee also collected, leadg by plottg both the wd speed ad the temperature ersus tme as show Fgures ad to the followg remarks: The Ctes hag hgher temperature, that s ad Garoua respectely hae hgher wd speed tha that of the cty of the lower temperature,. Therefore hgher the temperatures, hgher the wd speeds ad lower the temperatures, lower wd speed. The plots of speed deped of days s globally the lear fucto of tme, leadg by usg the mea square regresso to the followg expresso [7]: N t t at b, a b t, b (7) N t t Where s the mea alue of ( replacg or ), wth. It s mportat to meto that ths form of mea square lear approxmato hae bee already used by E. Kapla ad S. Kaplas [8] for the Thermal modellg 55

4 Iteratoal Joural of Scetfc Egeerg ad Scece Volume, Issue 4, pp. 5-6, 8. ISSN (Ole): ad expermetal assessmet of the depedece of PV module temperature o wd elocty ad drecto, module oretato ad clato. The plots of temperature deped of days ge the radom arato, meag that temperature s a arbtrary fucto of tme. I order to fd the depedecy of temperature ad tme, we hae made dfferet tests ad we foud, as appeared Fgure that the plot of l T T as a fucto of tme leads to a cure whch globally appears to be a straght le. By usg aga the mea square lear regresso method, oe ca fd two parameters ad so that T l T at b T T l bt a,,, (8) N T T l l T T b N t t Equatos (5) ad (6) wll be combed to l T a T a equato showg the depedecy of speed ad temperature: ge b b, leadg to the followg emprcal a T Texp b b (9) a Ths result s ery mportat sce t meas that oe ca check the adequate ste for wd eergy geerato by usg ether the wd speed or temperature data. Fgure 6 shows the aually arato of Webull, maxmum etropes ad maxmum etropes fucto of temperature dstrbuto... Computed MEP based wd speed dstrbuto ad effects of temperature The Lagraga parameters of Eq.(4) subjected to costrats (5) are obtaed by usg the Newto-Raphso terate method for the mothly dstrbutos, leadg to the probablty desty fucto plotted Fg. 4 wth the collected data. I order to check the effect of temperature o the wd speed dstrbuto, let us cosder here the wd as a stochastc eet, meag that wd s upredctable ad wthout a stable patter or order (It has bee proed that all atural eets are stochastc pheomeo). Let us ow cosder that wd s goered by two collecte arables, the temperature, ad the wd speed. Whe the wd speed part s cosdered to act aloe, the MEP based wd speed dstrbuto s ge by Eq.(4), satsfyg the costrats (5). Whe the temperature s takg aloe to accout, the wd speed probablty dstrbuto ca be ge by the followg expresso m m g exp () kt kt B B where m s the effecte mass of ar, k B m kg s K s the Boltzma costat. Whe we cosder both the temperature ad speed to act together, the wd speed probablty dstrbuto ca be ge by f g( T ), leadg to M j, T 4 exp α j T T () j wth m/k B. The -D plot of ths probablty dstrbuto s show Fgure 4, obtaed for β?????. From where, t appears that the probablty dstrbuto s farly seste to temperature arato. TABLE. The estmated alues of Webull parameters by fe umercal methods. Method MSDM MOM EPFM LSRM MLM Ste k c k c k c k c k c IV. GENERAL CONCLUSION The temperature ad the wd characterstcs hae bee aalyzed for three meteorologcal statos, amely: Both ad the Far North Rego of Cameroo, ad the West rego, these regos beg submtted to dfferet clmates. The studes hae bee performed by usg fe umercal methods (MSDM, MOM, EPFM, LSRM ad MLM) for the determato of the Webull dstrbuto parameters, that s the scale ad shape oes, whch are used to geerate the probablty dstrbuto fucto. From these obous results, RMSE ad Χ tests are performed gg alues the recommeded rage suggestg relablty of the methods used for estmatg Webull parameters ad cosequetly a better approxmato of measured wd speed data dstrbuto. Next, by plottg both the speed ad temperature aratos ersus the tme, we foud the fucto gg the depedecy of the temperature ad the speed, whch s terestg sce the ste for wd turbes stallato ca be studed by usg ether the temperature or the wd speed data. Next, the Maxmum etropes fucto of temperature dstrbuto s ftted to measure wd speed dstrbuto. The agreemet betwee the obsered wd speed dstrbutos, maxmum etropes dstrbuto ad Maxmum etropes fucto of temperature dstrbuto was aalyzed by performg statstcal tests, such as RMSE ad Χ tests. The tests dcated good agreemet betwee the obsered ad ftted dstrbuto fucto. 56

5 Probablty Desty Dstrbuto Probablty Desty Dstrbuto Probablty Desty Dstrbuto Iteratoal Joural of Scetfc Egeerg ad Scece Volume, Issue 4, pp. 5-6, 8. ISSN (Ole): TABLE. The mea wd speed (actual ad predcted). Moths Mea Wd Speed Measured MSDM MOM EPFM LSRM MLM TABLE 4. The aually R aalyss. R MSDM MOM EPFM LSRM MLM TABLE 5. Comparate statstcs of the wd speed probablty dstrbuto models. Webull dstrbuto MEP dstrbuto MEP Fucto of temperature dstrbuto COD RSME Χ COD RSME Χ COD RSME Χ Yaguoa MSDM MOM EPFM LSRM MLM.5..5 MSDM MOM EPFM LSRM MLM Wd speed [m/s] Wd speed [m/s] MSDM MOM EPFM LSRM MLM Wd speed [m/s] Fg.. Plot of PDF of actual ad predcted data obtaed from fe methods MSDM, MoM, EPFM, LSRM, ad MLM. (a), (b), (c). 57

6 Speed(m/s) Speed(m/s) Speed(m/s) Speed(m/s) Speed(m/s) Iteratoal Joural of Scetfc Egeerg ad Scece Volume, Issue 4, pp. 5-6, 8. ISSN (Ole): Fg.. Speed ersus tme. The radom form s the smply plot, whch ted globally to the straght le, whle the straght le s ts least square lear regresso for ad ctes of Cameroo wth the 5-year teral. 58

7 Iteratoal Joural of Scetfc Egeerg ad Scece Volume, Issue 4, pp. 5-6, 8. ISSN (Ole):

8 Probablty Desty Dstrbuto Probablty Desty Dstrbuto Iteratoal Joural of Scetfc Egeerg ad Scece Volume, Issue 4, pp. 5-6, 8. ISSN (Ole): Fg.. Left had sde: ersus tme, whch teds to the straght le for the cty of lower temperature ( blue). Otherwse, the form s arbtrary for the ctes of hgher temperatures ( red ad mageta). Rght had sde: l T ersus tme, whch ted globally to the straght le, whch s approxmated by T.9.8 mea of the least square lear regresso method. MEP dstrbuto Webull dstrbuto ew dstrbuto.5. MEP dstrbuto Webull dstrbuto ew dstrbuto Wd speed [m/s] Wd speed [m/s] 6

9 probablty desty dstrbuto probablty desty dstrbuto probablty desty dstrbuto Probablty Desty Dstrbuto Iteratoal Joural of Scetfc Egeerg ad Scece Volume, Issue 4, pp. 5-6, 8. ISSN (Ole): MEP dstrbuto Webull dstrbuto ew dstrbuto Wd speed [m/s] Fgure 4: Wd speed frequecy dstrbutos for ad regos, Cameroo for year wd speed [m/s] wd speed [m/s] wd speed [m/s] Fgure 6: -D plot of the MEP dstrbutos ersus temperature ad wd speed, for ad regos, Cameroo for year 6. 6

10 Iteratoal Joural of Scetfc Egeerg ad Scece Volume, Issue 4, pp. 5-6, 8. ISSN (Ole): REFERENCES [] V. Nelso, Wd Eergy Reewable Eergy ad the Eromet, CRC Press, 9. [] P. Gpe, Wd Eergy Comes of Age, Joh Wley & Sos, 995. [] H. Lud, Reewable eergy strateges for sustaable deelopmet, Eergy, ol., ssue 6, 7. [4] A. K. Azad, M. G. Rasul, ad T. Yusaf, Statstcal Dagoss of the Best Webull Methods for Wd Power Assessmet for Agrcultural Applcatos, Eerges, ol. 7, pp , 4. [5] M. R. Islama, R, Sadura, ad N. A. Rahma, Assessmet of wd eergy potetalty at Kudat ad Labua, Malaysa usg Webull dstrbuto fucto, Eergy, ol. 6, ssue, pp ,. [6] T. P. Chag, Performace comparso of sx umercal methods estmatg Webull parameters for wd eergy applcato, Appled Eergy, ol. 88, pp. 7 8,. [7] G. M. Jeutho, F. Kemoge, ad D. Yemélé, Statstcal estmato of mea wd eergy aalable Wester Rego of Cameroo: Case of the cty, J. Harmoz. Res. Eg., ol. 5, ssue, pp. 5-7, 7. [8] S. A. Ahmet Shata ad R. Hatsch, Ealuato of wd eergy potetal ad electrcty geerato o the coast of Medterraea Sea Egypt, Reewable Eergy, ol., pp. 8, 6. [9] P. A. Costa Rocha, R. Coelho de Sousa, C. Fretas deadrade, ad M. Vera da Sla, Comparso of see umercal methods for determg Webull parameters for wd eergy geerato the ortheast rego of Brazl, Appled Eergy, ol. 89, pp. 95 4,. [] E. G. Paa ad J. JO Bra, Webull statstcs of wd speed oer the ocea, Joural of Clmate ad Appled Meteorology, Amerca Meteorologcal Socety, ol. 5, pp. 4, 986. [] F. C. Odo ad G. U. Akubue, Comparate Assessmet of Three Models for Estmatg Webull Parameters for Wd Eergy Applcatos a Ngera Locato, Iteratoal Joural of Eergy Scece (IJES), ol., ssue, pp. -5,. [] Partosh Bhattacharya, A study o Webull dstrbuto for estmatg the parameters, Joural of Appled Quattate Methods, ol. 5, ssue, pp. 4-4,. [] N. L. Johso ad S. Kotz, Cotuous uarate dstrbutos, ol.. Houghto Mffl, 97. [4] P. A. C. Rocha, R. C. D. Sousa, C. F. D. Adrade, ad M. E. V. D. Sla, Comparso of seeumercal methods for determg Webull parameters for wd eergy geerato the ortheast rego of Brazl, Appled Eergy, ol. 89, pp. 95 4,. [5] C. F. D. Adrade, H. F. M. Neto, P. A. C. Rocha, M. E. V. D. Sla, A effcecy comparso of umercal methods for determg Webull parameters for wd eergy applcatos: A ew approach appled to the ortheast rego of Brazl, Eergy Coerso ad Maagemet, ol. 86, ssue, pp. 8 88, 4. [6] S. Kurtz, K. Whtfeld, D. Mller, J. Joyce, J. Wohlgemuth, M. Kempe, et al., Ealuato of hgh-temperature exposure of rackmouted photooltac modules, 4 th IEEE Photooltac Specalsts Coferece (PVSC), pp , 9. [7] F. Red, The Mathematca o the Bakote: Carl Fredrch Gauss, Parabola, ol. 6, ssue, pp. -9,. [8] E. Kapla ad S. Kaplas, Thermal modellg ad expermetal assessmet of the depedece of PV module temperature o wd elocty ad drecto, module oretato ad clato, Solar Eergy, ol. 7, pp , 4. 6