Wind Climate Modelling for Estimation of Along Wind Load

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1 The Eghth Asa-Pacc Coerece o Wd Egeerg, December 0 4, 03, Chea, Ida Wd Clmate Modellg or Estmato o Alog Wd Load Arab Sarar, Amt Kumar Sgh Assstat Proessor o mechacal egg.,iit(bhu),varaas,u.p.,ida,arab_xyz@yahoo.co. MTech studet o mechacal egg.,iit(bhu),varaas,u.p.,ida,umar.amtsgh06@gmal.com Abstract I ths scope o study, a ew method has bee desed or estmatg the parameters o Webull dstrbuto or alog wd load calculato. IS stadard computes square o the mea wd elocty recorded oer a perod o tme to calculate alog wd load. The Ida stadard code o practce o wd load (IS-875 (part-3), 987) s a bt outdated ad requres prompt amedmets to draw party wth other teratoal codes. Ths paper uses mea o the square wd elocty or better estmato o the alog mea wd load. Ths paper wll help to mproe exstg atoal code o stadard, as ad whe t taes up the reso o IS-875 (part-3) Keywords: Wd speed, Load patter actor, Alog wd load, Webull dstrbuto Itroducto Alog mea wd load has a proouced eect o most o the structures ad hece ts detaled aalyss s dspesble. Most teratoal codes ad stadards prode gudeles ad procedure or assessg the alog mea wd load eects o structures. IS-875 (part-3) suggests the ollowg relato to estmate the alog mea wd load. F z C Ae pzg () F z alog wd load o structure at ay heght Z correspodg to strp area A e C orce coecet or the structure A e eecte rotal area cosderd or the structure at heght Z p z desg pressure at heght Z due to mea hourly wd obtaed as (0.6 G gust actor I ths paper, mea o the square wd elocty has bee used or better estmato o p z ad hece alog wd load. The coetoal practce atoal code o stadard whch uses square o mea wd elocty wll lead to a possble uderestmato o p z especally or lower alues o Webull shape parameter whch wll be urther dscussed ths scope o research. ) Proc. o the 8th Asa-Pacc Coerece o Wd Egeerg Nagesh R. Iyer, Prem Krsha, S. Sel Raja ad P. Harrsha (eds) Copyrght c 03 APCWE-VIII. All rghts resered. Publshed by Research Publshg, Sgapore. ISBN: do:0.3850/

2 Proc. o the 8th Asa-Pacc Coerece o Wd Egeerg (APCWE-VIII) Methods or Estmatg Webull Parameters Wd s stochastc ature. Speed ad drecto o the wd at a locato ary radomly wth tme. Apart rom daly ad seasoal aratos, the wd speed patter may chage rom year to year. The wd speed s radom arable ad or deg the dstrbuto o wd elocty a regme oer ge perod o tme statstcal model s requred. I recet years, Webull dstrbuto has bee uersally accepted or deg the wd speed requecy dstrbuto. I Webull dstrbuto, the aratos wd elocty are characterzed by the two uctos; () The probablty desty ucto ad () The cumulate dstrbuto ucto. The probablty desty ucto ( ()) dcates the racto o tme (or probablty) or whch the wd s at a ge elocty. It s ge by ( ) s s exp s () Here, s the Webull shape actor ad s s scale actor. The cumulate dstrbuto ucto o the elocty ges us the racto o tme (or probablty) that the wd elocty s equal or lower tha. Thus the cumulate dstrbuto F() s the tegral o the probablty desty ucto. Thus, F( ) exp s Aerage wd elocty o a regme, ollowg the Webull dstrbuto s ge by s Γ + Seeral methods hae bee proposed or estmatg the Webull parameters. Here we wll dscuss see deret methods, cludg ew oe ad rstly preseted ths paper. Graphcal method I the graphcal method, we trasorm the cumulate dstrbuto ucto to a lear orm, adoptg logarthmc scales [Chag (0)]. The expresso or the cumulate dstrbuto o wd elocty ca be rewrtte as (3) 343

3 Proc. o the 8th Asa-Pacc Coerece o Wd Egeerg (APCWE-VIII) F( ) exp s Tag the logarthm twce, the ollowg relato s obtaed: l ( l( F() )) l l s (5) (6) Plottg the aboe relatoshp wth l() alog the X axs ad l{-l[-f()]} alog the Y axs, we get early a straght le. From Eq. (6), ges the slope o ths le ad l s represets the tercept. Maxmum lelhood method The Webull dstrbuto ca be tted to tme-seres wd data usg the maxmum lelhood method as suggested by Stees ad Smulders (979). The maxmum lelhood estmato method s dcult to sole, sce umercal teratos are eeded to determe the parameters o the Webull dstrbuto. I ths method, the parameters ad s are determed accordg to the equatos below [Ghosh (999)]: l l s (8) (7) Where s the wd speed tme step ad s the umber o ozero wd speed data pots. Eq. (7) must be soled usg a terate procedure ( s a sutable tal guess), ater whch Eq. (8) ca be soled explctly. Care must be tae to apply Eq. (7) oly to the ozero wd speed data pots. Moded maxmum lelhood method Whe wd speed data are aalable requecy dstrbuto ormat, a arato o the maxmum lelhood method ca be appled The Webull parameters are estmated usg the ollowg two equatos [Seguro et al. (000)]: 344

4 Proc. o the 8th Asa-Pacc Coerece o Wd Egeerg (APCWE-VIII) ( ) ( ) ( ) ( ) ( ) 0) ( l l (9) ( ) ( ) s 0 (0) Where s the wd speed cetral to b, s the umber o bs, ( ) s the requecy wth whch the wd speed alls wth b, ( 0) s the probablty that the wd speed equals or exceeds zero. Eq. (9) must be soled terately, ater whch Eq. (0) ca be soled explct. Momet method ad s are related to the ad σ by ollowg equatos [Justus et al. (978)]: + Γ s () + Γ + Γ s σ () + Γ + Γ σ (3) Where ad σ are the mea wd speed ad the stadard deato o the obsered data o the wd speed, respectely. Eq. (3) ca be soled umercally to d out Webull parameters. Emprcal method It s cosdered as a specal case o the momet method, where the shape () ad scale parameter (s) o the Webull dstrbuto s ge by the ollowg Eqs. [Adag et al. (009)]:.086 σ (4) + Γ s (5) 345

5 Proc. o the 8th Asa-Pacc Coerece o Wd Egeerg (APCWE-VIII) Eergy patter actor Method Eergy patter actor (E p ) s the rato betwee the total power aalable the wd ad the power correspodg to the cube o the mea wd speed [Rachle et al. (009)]. Thus E p s ge by: E p 3 3 Oce the eergy patter actor or a regme s oud rom the wd data, a approxmate soluto or s ge by [Garca et al. (998)]: (6) The scale parameter, s s ge by E p (7) s Γ + (8) Load actor method Ths ew method was deeloped the scope o ths artcle ad used or estmatg Webull parameters. It ca be easly dered. It s easy to mplemet ad requres less computatoal wor tha other methods. Load actor s ge by: Γ + L Γ + (9) Ths s the rato o the square mea elocty to the square o the mea elocty. Load actor s a ucto o oly. Oce the load actor orm the obsered data are ow, Webull parameters ca be estmated by solg Eq. (9) terately or approxmate soluto s ge by the ormula: L (0) 346

6 Proc. o the 8th Asa-Pacc Coerece o Wd Egeerg (APCWE-VIII) Comparso o Methods The deret methods were compared or wd speed data o the statos le Vshahapatam, Truchrapall, Kalauda ad Madras Harbour. The hourly mea wd speed data aalable by Ida Meteorologcal Departmet, Pue coerg the perod o , , ad respectely, were used or estmatg Webull parameters. For comparg the ececy o the aboe metoed methods, our statstcal tests le R (coecet o determato), (ch-square), K-S ad RMSE (root mea square error) were used. The parameters o these tests are deed by: R N N ( y x ) ( y y) () χ N ( y x ) y () N RMSE ( ( y x ) ) N (3) K-S max ( y x ) (4) Where, N s the umber o obseratos, y s the relate requecy o the obsered data ad x s the relate requecy o Webull dstrbuto. These tests ge the goodess o t result or deret methods. Fg. shows the graphs betwee the Webull probablty ucto (()) ad hourly mea wd speed or the Ida locatos (Truchrapall, Vshahapatam, Kalauda ad Madras Harbour) based o parameters calculated usg deret methods. From Fg., t may be erred that out o these see deret methods, whch oe s best tted to the hstogram obtaed rom actual data. 347

7 Proc. o the 8th Asa-Pacc Coerece o Wd Egeerg (APCWE-VIII) Relate Frequecy () actual e.p. emprcal M.o.m M.l.m M.m.l.m Load actor graphcal Relate Frequecy () actual e.p. emprcal M.o.m M.l.m M.m.l.m Load actor graphcal Hourly mea wd speed(m/s) Hourly mea wd speed(m/s) Relate Frequecy () actual e.p. emprcal M.o.m M.l.m M.m.l.m Load actor graphcal Relate Frequecy () actual e.p. emprcal M.o.m M.l.m M.m.l.m Load actor graphcal Hourly mea wd speed(m/s) Hourly mea wd speed(m/s) Fg.: Probablty desty dstrbuto o hourly wd speed data or Truchrapall (Top let), Vshahapatam (Top rght), Kalauda (Bottom let) ad Madras Harbour (Bottom rght) Table : Statstcal aalyss o wd data or stato Truchrapall χ crtcal 3.84 K-S crtcal 0.56 Methods S (m/s) % deato RMSE K-S E.p Emprcal M.o.m M.l.m

8 Proc. o the 8th Asa-Pacc Coerece o Wd Egeerg (APCWE-VIII) M.m.l.m Load actor Graphcal Table : Statstcal aalyss o wd data or stato Vshahapatam χ crtcal 3.84 K-S crtcal 0.85 Methods s (m/s) % deato RMSE K-S E.p Emprcal M.o.m M.l.m M.m.l.m Load actor Graphcal Table 3: Statstcal aalyss o wd data or stato Kalauda χ crtcal 3.84 K-S crtcal 0.75 Methods s (m/s) % deato RMSE K-S E.p Emprcal M.o.m M.l.m M.m.l.m Load actor Graphcal Table 4: Statstcal aalyss o wd data or stato Madras Harbor χ crtcal 3.84 K-S crtcal 0.53 Methods s (m/s) % deato RMSE K-S E.p Emprcal M.o.m M.l.m M.m.l.m Load actor Graphcal

9 Proc. o the 8th Asa-Pacc Coerece o Wd Egeerg (APCWE-VIII) These statstcal tests (Tables -4) help to determe the best method or ttg data wth Webull dstrbuto model. Howeer, these tests do ot esure the approprateess o the method or whch theoretcal alue o mea o square elocty wll be the closest to the obsered oe. For eryg ths, a array o 00x00 wd data were geerated by Mote-Carlo smulato, tag alues o shape ad scale parameters as ad 3 m/s respectely, rom Webull model. O the bass o RMSE ad Ch-square test, t ca be erred that load actor ad method o momet ge the mmum arato betwee obsered ad theoretcal alues o mea square elocty. Table 5: Ececy o methods based o radom smulato Method RMSE Ch-square E.p Emprcal M.o.m Load actor M.l.m M.m.l.m Graphcal Results ad Dscussos I ths study, the meas o square elocty hae bee estmated or our locatos metoed aboe, by Webull parameters whch were determed by ewly suggested load actor method ad method o momet. For comparg square o mea eloctes wth mea square eloctes, the ormers hae bee determed by Webull parameters whch were obtaed by the best method rederg mmum alues o RMSE. The percetage deatos rom the obsered alue o mea square elocty ad theoretcal alue calculated by the load actor ad method o momet ad square o mea elocty hae bee calculated whch are ge the tables below. Table 6: Webull model or wd data Truchrapall Method % deato rom M.o.m -0.6 Load actor -0.6 IS-875( V )

10 Proc. o the 8th Asa-Pacc Coerece o Wd Egeerg (APCWE-VIII) Table 7: Webull model or wd data Vshahapatam Method % deato rom M.o.m Load actor -0.5 IS-875( V ) -3.9 Table 8: Webull model or wd data Kalauda Method % deato rom M.o.m Load actor IS-875( V ) -3.7 Table 9: Webull model or wd data Madras Harbour Method % deato rom M.o.m -0.6 Load actor IS-875( V ) -4.5 For smaller alues o (shape parameter) load actor method s a preerable oe or determg Webull parameters o wd speed ad subsequet determato o mea wd load whch s proportoal to the square o wd elocty. At lower alues o, there s sgcat arato alues betwee square o the mea elocty ad mea square elocty ee or small chages the alue o whch s depcted Fg. show below. 35

11 Proc. o the 8th Asa-Pacc Coerece o Wd Egeerg (APCWE-VIII) 5 4 load actor Webull shape parameter () Fg. Varato o Load actor wth shape parameter () Though ths method s approprate at smaller alues o, at hgher alues o (>), load actor method does ot reder sutable results. For alues >, there s ery small arato alues o mea square elocty ad square o the mea elocty ee or ery large chages the alue o. So or hgher alues o, there would be a sgcat arato betwee the actual ad theoretcal alues o mea square elocty calculated by load actor method. For explag ths, 0 6 wd speed data hae bee geerated rom Webull dstrbuto by erse CDF method. The results are preseted Table 0 ge below: Table 0: Comparso o rom obsered data ad load patter actor method or deret S.No. Actual alues o shape ad scale parameters..5 s5.0 m/s. 3.5 s5.0 m/s s5.0 m/s Theoretcally estmated alues o shape ad scale parameters by l method.483 s m/s 3.49 s5.06 m/s s5.065 m/s obs l % o deato

12 Proc. o the 8th Asa-Pacc Coerece o Wd Egeerg (APCWE-VIII) Cocluso Load actor method ca be ewed as the most preerable method or wd load calculato o structures. Ths has bee ered by statstcal aalyss doe through a comparso o ths method wth other sx exstg methods. It has bee obsered that load actor method ges the smallest arato mea square eloctes whe compared wth the obsered alues most cases o actual wd data ad also rom smulated data. Load actor method ges the best estmate o mea square elocty or small alues o shape parameter. As the alue o shape parameter creases, deato rom the obsered alue o mea square elocty also creases. Reereces Chag, T.P. (0), Perormace comparso o sx umercal methods estmatg Webull parameters or Wd eergy applcato, Appled Eergy, 88, 7-8 Stees, M.J.M. ad Smulders, P.T. (979), The estmato o parameters o the Webull wd speed dstrbuto or wd eergy utlzato purposes, Joural o Wd Egeerg, 3, 3-45 Ghosh A. (999) A Fortra program or ttg Webull dstrbuto ad geeratg samples, Joural o Computers & Geosceces, 5, Seguro, J.V. ad Lambert, T.W. (000), Moder estmato o the parameters o the Webull wd speed dstrbuto or wd eergy aalyss, Joural o Wd Egeerg ad Idustral Aerodyamcs, 85, Justus, C.G., Hargraes, W.R., Mhal, A. ad Graber, D. (978), Methods o estmatg wd speed requecy dstrbutos, Joural Appled Meteorology, 7, Adag S.A. ad Dler A. (009), A ew method to estmate Webull parameters or wd eergy applcato, Joural o Eergy Coerso ad Maagemet, 50, Rachle B.W., Carso W.R (009), Wd resource assessmet o the Souther Appalacha Rdges the South-easter Uted States, Reewable ad Sustaable Eergy Reews, 3, 04-0 Garca A., Torres J.L., Preto E ad D.E. Fracsco A. (998), Fttg wd speed dstrbutos: a case study, Joural o Solar Eergy, 6(),