The Modelling of Wind Farm Layout Optimization for the Reduction of Wake Losses

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1 Indan Jornal of Scence and Technology, Vol 8(7), DOI: /jst/05/v87/6987, Agst 05 ISSN (Prnt) : ISSN (Onlne) : The Modellng of Wnd Farm Layot Optmzaton for the Redcton of Wake Losses Raba Shakoor, Mohammad Ysr Hassan,*, Abdr Raheem, and Nada Rasheed Centre of Electrcal Energy Systems (CEES), Insttte of Ftre Energy, Unverst Teknolog Malaysa (UTM), 80 Johor Bahr, Johor, Malaysa Faclty of Electrcal Engneerng, Unverst Teknolog Malaysa (UTM), 80 Johor Bahr, Johor, Malaysa; ysrh@fke.tm.my Unversty College of Engneerng and Technology, The Islama Unversty of Bahawalpr, Bahawalpr Pakstan Abstract The objectve of the present research s to fnd ot the optmzed dmensons of the wnd farm area and trbnes layot to redce the overall cost per nt power. The velocty defcts cased by the wakes of each trbne were calclated by sng Jensen s wake model. The optmal postons of wnd trbne placement are evalated by sng genetc algorthm, whle sstanng the oblgatory space between adjacent trbnes for operaton safety. The research on the wnd farm area dmensons and flly tlzaton of pstream wnd velocty s crrently lackng n lteratre. The logcal applcaton of area dmensons and genetc algorthm mproved the overall effcency of the wnd farm. It s conclded that proposed del level optmzaton method otperforms the exstng ones. The total wnd farm area (km km) was dvded nto 00 dentcal cells, wth each cell havng dmensons 00m 00 m. The performance of the proposed method s compared wth the reslts from prevos stdes. The smlaton reslts showed that power otpt of the wnd farm was ncreased by sng same area wth dfferent dmensons. It was observed that by sng the same nmber of wnd trbnes, the total effcency of wnd farm was ncreased by 7 %. Keywords: Jensen s Wake Mode, Layot Optmzaton, Wnd Farm Area Dmensons, Wake Losses, Wnd Trbne Postonng. Introdcton Renewable energy system s an envronment frendly, consstent and economcal system that remarkably employs the local means. All types of sstanable energy systems (.e., ocean, geothermal, solar, wnd, hydroelectrc, and bomass energy) have ther own specfc benefts that make them dstnctvely stable for specfc applcatons. The nstallaton demand of wnd energy and the related research actvtes has experenced a tremendos ncrease n the past decade. The Global Wnd Energy Concl Report stated that wnd energy has become the most rapdly rsng sorce of energy n the world, havng a steep ncrease n development from 009. Sch prompt expanson of the wnd energy ndstry has led to many challenges for redcton the cost of prodcng power. The fndamental task of a wnd trbne s to extract the knetc energy from wnd and convertng t nto mechancal energy at the rotor axs, and then the converson of mechancal energy nto electrcal energy 4,5. In the prmary process, when wnd trbnes extract the energy from wnd, the rotaton of wnd trbne rotor can redced the wnd speed behnd t and swrls the ar flow, whch s known as Wake Effect of wnd trbne. Becase of ths effect, the area behnd the wnd trbne s experenced a modfed wnd flow both n terms of mean velocty and trblence ntensty. There have been several models developed amng for a better nderstandng on wake *Athor for correspondence

2 The Modellng of Wnd Farm Layot Optmzaton for the Redcton of Wake Losses dynamcs. These can be dvded nto two man categores, namely analytcal/explct wake models 6 9 and comptatonal/mplct wake models 0,. The world s movng towards the constrcton of wnd farms comprsng of many wnd trbnes nstead of sngle wnd trbne. Modern wnd farms consst of tens of wnd trbnes arranged on the stes for the prpose of maxmm tlzaton of wnd energy. As the sze and the nmber of trbnes ncreases n wnd farm, the cost wll also ncrease. Ths, the man challenge s to redce the cost per nt power of the wnd farm. The cost of wnd farm depends on the nmber of factors, for example, the ste layot desgn, the ste selecton, predctve mantenance, and optmal control system desgn. However, the aerodynamc behavor of wnd trbnes wll generate large scale wakes n the downwnd feld, whle excessve wnd dstrbance leads to low energy prodcton n wnd farms, and hgh trblence ntenstes lead to hgh level of velocty flctaton. Therefore, t s very mportant to optmze the wnd trbne postons n the wnd farm to redce the ncertanty n power otpt 4,5. There are several researchers that addressed the wnd farm layot optmzaton n the lteratre 6. Mosett et al. 6 sed a dscretzed solton space n the wnd farm area to optmze wnd trbnes locaton. The wnd trbne wake effect calclaton has been done by sng Jensen s analytcal wake model 6. The genetc algorthm n whch each row of the grd consdered as a bnary strng s tlzed for wnd trbne postonng. The framework developed n 6 has been contnosly sed for comparson prposes n the proceedng research, ncldng the wnd scenaro, the se of the Jensen s wake model, and objectve fncton. Grady et al. 7.attempted smlar bt mproved approach of genetc algorthm whch ntegrated herstc knowledge abot the layot of wnd farms for power optmzaton. Grady et al. 7 showed that the reslts obtaned by Mosett et al. s were not optmm. They sggested that the probable case, that the solton was not allowed to evolve for sffcent generatons (.e., t was not converged to the optmm pont). Marmds et al. 8 also attempted the same wnd farm layot optmzaton by Grady et al. 7 for analyzng constant drecton and speed of wnd. They sed the Monte Carlo algorthm for optmzaton; however, descrpton on ther method was not gven. Mttal 9 recommended the se of mcro stng technqe wth Genetc Algorthm (GA) n order to fnd more precse locatons of trbnes nsde a wnd farm. He smlates the wnd farm layot for three scenaros and proposed the ncreased sze of wnd farm eqal to km.km rather than km km as sed n 6,7. The spacng between the postons of wnd trbnes redced by sng condense grd sze wth each cell dmensons eqal to m m. The redcton of grd spacng reslted n the decrease of overall cost per nt power of wnd farm. The reference 9 compared the obtaned reslts wth the reslts from the stdes by Grady et al. 7 and Mosett et al. 6 for all three wnd scenaros. Emam et al. proposes an mprovement n wnd farm layot optmzaton wth the Jansens s wake model by modfcaton of the objectve fncton, whch takes nto accont the effcency of wnd trbnes and the wnd farm deployment cost. Reference show that ths amendment leads to mproved reslts than earler methods. Samna et al. employ the genetc algorthm and spread sheet to solved the same wnd farm layot optmzaton problem. In reference 4, the athors stded the nflence of the wnd trbnes wth dfferent hb heghts (50 m to 78 m) on the power prodcton of a wnd farm. Chen et al. 4 fond that the wnd farm wake losses can be mnmze and power otpt became better by nstallaton of varyng hb heghts wnd trbnes. Trner et al. 5 assmng a flat terran for wnd farm and develop a qadratc nteger program and a mxed nteger lnear program for layot optmzaton. The lteratre revew gves a clear vson that mostly research n the feld of wnd farm layot optmzaton focsed only on the wnd trbne postonng wthn the specfc area of wnd farm 6. However the research on the wnd farm area dmensons and flly tlzaton of pstream wnd velocty s crrently lackng n lteratre. The present research proposes a method to obtaned the best wnd farm area dmensons (maxmm wdth of area was become perpendclar to the domnant wnd drecton) for the gven wnd scenaro. After that, the frst 9 grd cells are flled by nstallaton of wnd trbnes to tlze the all avalable free-stream wnd velocty whle satsfyng the necessary dstance between the wnd trbnes. The placement of the remanng wnd trbnes has been done by sng the genetc algorthm 7 n the contnng porton of the wnd farm. For valdaton, the obtaned reslts n present stdy had been compared to the reslts of related prevos stdes. The remanng parts of ths paper are arranged as follows: Secton descrbes the proposed desgn models of the wnd farm. Secton descrbes optmzaton steps. Secton 4 presents the obtaned reslts and gves Vol 8 (7) Agst 05 Indan Jornal of Scence and Technology

3 Raba Shakoor, Mohammad Ysr Hassan, Abdr Raheem and Nada Rasheed a comparson wth prevos research. Fnally, Secton 5 presents the conclson.. Wnd Farm Modelng Ths secton descrbes power, cost and wake models of the wnd farm proposed n present research work. These models are based on some assmptons whch also gven n detal.. Power Model Avalable power n wnd farm for each trbne can be estmated by sng follows eqaton: P = h ra C () p o p where P p s the electrcal power prodced (W), η s the overall effcency of the wnd trbne, ρ s ar densty (kg/ m ), A s swept area of wnd trbne (m ), o s the free stream wnd velocty (m/s), and C p s the power coeffcent, ts vale wll be gven as; C p = ( ) P A ra o () Where P A represents the aerodynamc power otpt of a wnd trbne. In present stdy, by assmng that the wnd trbne effcency η s 40 %, the wnd trbne prodced power can be calclated as: P p 40 =. p 0 o kw () 00 P p = 0. 0 kw (4) The above eqaton shows that the prodced power s drectly proportonal to the cbe of avalable wnd velocty at the poston of wnd trbne. Therefore, n a wnd farm the wnd trbnes facng free-stream velocty wll gve the maxmm power otpt, however the downstream wnd trbnes wll gve the redced power otpt becase of the wake effect of pstream wnd trbnes. To determne the prodced power from a wnd trbne, t shold be ensred whether the wnd trbne nder consderaton les n the wake of other wnd trbne or not. law of conservaton of momentm 6. The near feld behnd the wnd trbne s neglected, makng t possble to model the resltng wake as a negatve jet. The mostly research n wnd farm layot optmzaton sed Jensen s wake model, becase of ts accracy of reslts. The velocty defct ( d ) n the wake of a wnd trbne can be gven as the fractonal redcton of free-stream wnd velocty. = o d (5) The rads of the wake jst behnd the wnd trbne wll be eqal to the rads of the wnd trbne rotor. Fgre shows the wake effect of a wnd trbne facng wnd speed o. The wake rads r depends on the downstream dstance, x, and ncreases lnearly, as the wake propagates downstream. The downstream wnd speed de to the wake effect of a sngle wnd trbne s gven by followng eqaton, a = 0 x + a r (6) The ndcton factor, α, can be calclated from thrst coeffcent, C T of the wnd trbne, C T = 4α(-α). The,α, n above eqaton s known as entranment constant and defned as rate of wake expanson. The vale of, α, s emprcally gven by eqaton. 05. a = ln H z 0 (7). Wake Model The calclaton of the redced wnd speed from each wnd trbne has been done by sng an alytcal wake model proposed by N.O. Jensen, whch s based on the Fgre. Wake behnd a wnd trbne. Vol 8 (7) Agst 05 Indan Jornal of Scence and Technology

4 The Modellng of Wnd Farm Layot Optmzaton for the Redcton of Wake Losses Where, H, s the wnd trbne s hb heght and, z 0, represents the srface roghness of wnd farm area. For present stdy t s 0. m. The wake rads jst behnd the wnd trbne, r d, s called the downstream rads of the trbne. It can be determne by sng eqaton 8, where, r r, s the rads of wnd trbne. r d = r r a a (8) The rads of wake at any dstance, x, from a wnd trbne s drectly depends pon the vale of r d and entranment constant, α, as gven n followng eqaton. r = r +a x (9) d In a wnd farm when a nmber of wakes occrs together, the resltant velocty can be calclated by eqatng the sm of the knetc energy defcts of each wake to the knetc energy defcts of the mxed wake at that pont, as gven n the followng eqatons; N t = (0) 0 = 0 Nt = 0 () = 0 Fgre shows a wnd farm of havng 7 wnd trbnes. The wnd trbnes T, T, T are facng free-stream velocty whle the wnd trbnes T4, T5, T6 are operatng n a sngle wake effect. The wnd trbne T7 faces the wake effect from two pstream trbnes T and T4. The calclaton of wnd speed defct at the poston of T7 has been done by sng Eqaton no ().. Cost Model The cost model sed n present stdy gves nondmensonal cost of the wnd farm as a fncton of the nmber of wnd trbnes 7,9. The total cost s calclated sng the followng expresson: Cost = Nt + e N t () Where N t s the nmber of wnd trbnes prchased. The objectve fncton sed to mnmze the total cost per nt power of the wnd farm and s gven as follows: cost objectve= mnmze power.4 Effcency Model () Effcency s determned as a rato between the amont of energy extracted from the wnd farm and the total energy wthot wake. The nmerator represents the actal energy extracted from the rotor of each wnd trbne, consderng the Betz lmt of aerodynamc theory. The wnd farm effcency can be formlated sng the eqaton dependng on the nmber of wnd trbnes. Total power prodced n wnd farm when consderng wake effect can be calclated by sng eqaton4: power total Nt = 0. (4) = 0 ( ) Eqaton 5 s sed to calclate the wnd farm total power wthot wake effect: ( ) power = p* N = N 0. (5) wf t t o Where, p, s the rated capacty of each wnd trbne. The overall effcency of the wnd farm s calclated by sng eqaton 6 and 7, as follows: powertotal Effcency = (6) power wf Fgre. Mltple wake effect of wnd farm. ( ) Nt Effcency = 0. * = 0 N 0. * t ( o ) (7) 4 Vol 8 (7) Agst 05 Indan Jornal of Scence and Technology

5 Raba Shakoor, Mohammad Ysr Hassan, Abdr Raheem and Nada Rasheed The wnd farm characterstcs sed n present research are gven n Table. The characterstcs of wnd dstrbton can be descrbed sng Webll probablty dstrbton. In order to compare the obtaned reslts the parameters of wnd farm were smlar as sed n prevos stdes 6 9,4.. Optmzaton In the wnd farm layot optmzaton problem the basc and the most mportant thng s the land avalablty and ts specfc area dmensons. The wnd farm layot optmzaton s a dscrete problem and solvng by sng classcal technqes makes t frther complex and also reqres sng more varables.. Ponts of Zero Wake Effect The overall power prodcton of a wnd farm can be ncreased by tlzng the whole avalable wnd resorce. Ths can be done by nstallng the maxmm nmber of wnd trbnes at the all possble pstream postons. The zero wake effect ponts n the wnd farm area can be calclated by sng the followng method. Fgre shows the two wnd trbnes, WT and WT located wthn the wnd farm wth an arbtrary orange, O. and the gven wnd drecton q. The vector OWT represents the poston of wnd trbne WT and the poston vector OWT represents the poston of wnd trbne WT. Let pont, B, s the frst cone vertex of the WT s wake n the drecton of wnd velocty. The angle, β, between the two vectors, orgnatng from the cone vertex B of the wnd trbne WT to the vector orgnatng from B to the wnd trbne WT. The vale of angle β s calclated as: ( )( ) b = cos BWT BWT L L BWT BWT (8) If the angle β between the the vectors BWT and BWT s grater than the angle, α, the wnd trbne WT wll be not lay n the wake effect of the wnd trbne WT (). For the mltple wake effect condton the angle β wll be calclated by sng the followng eqaton. b = cos j ( x xj) cosq+ ( y yj) snq+ R k (9) x x R j + cosq y k y R ( j k snq ) ( ) + +. Parameters of Genetc Algorthm Genetc Algorthm s based on the prncples of chromosome genetc process. It comprses of randomly generated poplaton (n ths case, farm layots). The steps n genetc algorthm nvolved for wnd farm layot optmzaton are descrbed below. The chromosome strng constttes a fxed wnd farm area and a fxed nmber of wnd trbnes. Usng the constrants gven n Table, the defned nmber of chromosomes s generated. In ths stdy, the nmber of chromosomes was set to 00, generatng 00 (0 x 0) ndvdals. Each ndvdal contaned (N t 9) randomly placed wnd trbnes, where N t s the total nmbers of wnd trbnes. To place ( N t 9) wnd trbnes n the aforementoned wnd farm area, the objectve fncton (cost per nt area) for each ndvdal s calclated sng Eqaton. Table. Parameters and characterstcs of wnd farm Hb heght 60m Rotor rads (r d ) 40 m Thrst coeffcent (C T ) 0.88 Swept area (m ) 5080 Wnd farm area (km ) km km Cell sze (m ) Length of Srface roghness (m) 0. Free stream velocty (m/s) Ar densty (kg/m ).5 Fgre. Wnd trbne otsde the wake effect of another wnd trbne. Vol 8 (7) Agst 05 Indan Jornal of Scence and Technology 5

6 The Modellng of Wnd Farm Layot Optmzaton for the Redcton of Wake Losses At least members of each ndvdal need to be set to be reprodced n the next generaton n ths case. Crossover s the man step n GA. It s responsble for the execton of crossover of replcated chromosomes n the form of parng. Crossover has many types. Two crossover methods tlzed n ths stdy were snglepont crossover and two-pont crossover, as shown n Fgre 4 and 5, respectvely. The ftness fncton s then compted for all ndvdals. Each generated ftness fncton wll be compared wth those of next generaton. If the next generaton ftness fncton s lower than the prevos ones, they wll be replaced by the last ones as new fncton. The prevos ftness fncton s retaned and ths process s contned ntl the last generaton. Fgre 6 presents the flowchart of the proposed process, where the objectve s to fnd the least cost per nt area for the aforementoned wnd farm dmensons. Fgre 7 shows the wnd farm wth proposed optmzed layot of total wnd trbnes. The frst 9 wnd trbnes was placed at pstream wnd postons and the genetc algorthm was sed n the wnd farm area left behnd for the nstallaton of remanng wnd trbnes. Table enlsts the power otpt of each trbne and shows the objectve fncton vales and the effcency of wnd farm, as well as addton of the wnd trbnes. It s Fgre 6. Flow chart of the process. Fgre 4. Sngle-pont crossover. Fgre 7. Proposed wnd farm layot. Fgre 5. Two-pont crossover. observed that as we ncrease the nmber of wnd trbnes after 9 th, the effcency wll decrease contnosly. The total effcency of wnd farm aganst the nmber of wnd trbnes s shown n Fgre 8. The frst 9 wnd trbnes faced the pstream wnd velocty operated at ther maxmm effcency (00%). After that, the wnd farm effcency decreases contnosly wth the placement of the wnd trbnes becase of the wake effect losses. 6 Vol 8 (7) Agst 05 Indan Jornal of Scence and Technology

7 Raba Shakoor, Mohammad Ysr Hassan, Abdr Raheem and Nada Rasheed Table. Power and effcency calclaton wth nmber of wnd trbnes No of wnd trbne Cost of trbne Power (kw) Cost per Effcency (%) nt power Reslts and Dscsson In ths secton, the obtaned reslts from present research for constant wnd speed m/s wth nform drecton are presented and compared to the reslts from earler stdes 6 8, 0,, 5, 8. In present stdy, we consdered a wnd farm of total area km km, smlar as n all prevos stdes, except Mttal s work who sed grd of dmensons of km.km. The wnd farm area s dvded nto 00 sqares wth each havng dmensons of 5D 5D, where D s the dameter of wnd trbne rotor. A wnd trbne can be placed at the center of each sqare, so that the dstance between the two adjacent trbnes wll not exceed 00 m. Fgre 9 shows the proposed wnd farm layot and the optmal layots proposed by 6 8, 0,, 5, 8. The athors of,5,8 are proposed the same layot as gven by Grady et al. 7. The black boxes ndcate the postons of wnd trbnes. The optmal layot descrbed by Mosett et al. 6 was not balanced, as shown n Fgre 9. Ths was becase the wnd was ndrectonal and had a fxed speed. Therefore, for all colmns, the wnd condtons were dentcal. They tlzed the frst three rows for the placement of the frst 9 wnd trbnes, whch showed that they cold not tlze the space correctly. By sng 6 wnd trbnes, Mosett obtaned a total power of,5 kw wth objectve fncton vale of , whle the proposed layot s able to extract,64.55 kw wth ftness fncton vale of by sng the same nmber of trbnes. The effcency dfference between the reslts from the present stdy and Mosett reslts s lsted n Table. The vales descrbed by 7,,5,8 were proportonal becase they optmzed a sngle colmn and nterpreted the otcomes to all the other colmns. The symmetrcal confgraton had an objectve fncton vale lower Fgre 8. Graph of effcency aganst nmber of trbnes. Fgre 9. Proposed optmal layots by earler stdes 6 8,0,,5,8 and present work. Vol 8 (7) Agst 05 Indan Jornal of Scence and Technology 7

8 The Modellng of Wnd Farm Layot Optmzaton for the Redcton of Wake Losses than that obtaned by Mosett et al. 6. Table 4 lsts the comparson between reslts obtaned by 7,,5,8 and present stdy. They sed a total of 0 wnd trbnes n the wnd farm, and obtaned a total power of 4,0 kw wth objectve fncton vale of and effcency of 9.05%. In comparson, present wnd farm layot wth 0 trbnes gave a total power of 5,.5 kw wth objectve fncton vale of and the effcency of the wnd farm 98.98%. Table 5 shows the optmzaton comparson between the reslts from the present research and Mttal 9 by sng nmber of wnd trbnes. Mttal s optmzed layot gave a total power of 5,8. kw wth effcency of Table. Effcency dfference between the present stdy and Mosett et al. 6 Mosett et al. Present reslts No. of wnd trbnes 6 6 Total power (kw) 5,64.55 Objectve fncton Effcency (%) Table 4. Effcency dfference between the present stdy and 7,,5,8 Reference (7,, 5, 8) Present stdy No. of wnd trbnes 0 0 Total power (kw) 4,0 5,.5 Objectve fncton Effcency (%) Table 5. Effcency dfference between the present stdy and Mttal 9 Mttal Present stdy No. of wnd trbnes Total power (kw) 5,8. 6,5.56 Objectve fncton Effcency (%) Table 6. Effcency dfference between the present stdy and Rahman et al. 0 Rahman et al. 0 Present stdy No. of wnd trbnes 6 6 Total power (kw),89,64.55 Objectve fncton Effcency (%) % and objectve fncton vale. The present stdy shows that by sng wnd trbnes, the 6,5.56 kw power can be obtaned wth effcency of % and an objectve fncton vale of The optmal layot of wnd farm proposed by Rahman et al. 0 shows that they dd not se wnd trbne n Colmn and, whch s dsptable, becase these colmns were not employed as the drecton of wnd was along the colmn. Moreover, the tenth and sxth colmns were flled by placng the trbnes back to back, whch mght have dstressed the power and effcency from these trbnes becase of great wake effect. By sng 6 wnd trbnes, they obtaned,89 kw of power wth objectve fncton vale and the effcency 95. %. Meanwhle, the proposed wnd farm layot s obtaned,64.55 kw power wth objectve fncton vale of 0.55 and % effcency wth the same nmber of wnd trbnes. 5. Conclson Wnd farm layot optmzaton s mportant for harnessng maxmm wnd energy. The present stdy proposed the modelng of wnd farm layot optmzaton for the redcton of wake effect losses to obtan optmzed layot for onshore as well as offshore wnd farms. The developed genetc algorthm programmng formlatons for the wnd trbne postonng problem was presented that consdered all nteractons between trbnes. The presented layot shows effectveness of the dmenson of the area sed for a wnd farm. The fxed placement of the wnd trbnes s assmed to be benefcal for the se of pstream wnd. Wth the help of two level optmzaton framework the obtaned reslts notceably mproved as compared to the mostly prevos research n terms of overall wnd farm effcency. The proposed wnd farm layot reqres placement of 9 trbnes where no wake effect shold affect the power otpt, whereas the remanng trbnes are placed sng GA algorthm. The effcency of the proposed wnd farm was fond to be 97.7 % and total power avalable was 6,5.56 kw for the placement of wnd trbnes. The objectve fncton (cost per nt power) was calclated to be References. Raheem A, Hassan M Y, Shakoor R. Pecnary optmzaton of bomass/wnd hybrd renewable system. Proceedngs of the st Internatonal Conference on Energes, Scform 8 Vol 8 (7) Agst 05 Indan Jornal of Scence and Technology

9 Raba Shakoor, Mohammad Ysr Hassan, Abdr Raheem and Nada Rasheed Electronc Conference Seres c006; 04 Mar 4. p Fred L, Shkla S, Sawyer S. Global Wnd Report: Annal market pdate 0. GWEC; 0. Avalable form: net/pblcatons/globalwnd-report-. Energy Agency I. Internatonal Energy Agency WIND 0 Annal Report [Onlne] Moskalenko N, Rdon K. Stdy of wake effects for offshore wnd farm plannng Vermeer LJ, Sorensen JN, Crespo A. Wnd trbne wake aerodynamcs. Progress n Aerospace Scences. 00; 9 (6 7): Jensen NO. A Note on Wnd Generator Interacton. 98. Techncal Report: Rso-M Ishhara T, Yamagch A, Fjno Y. Development of a new wake model based on a wnd tnnel experment. Global Wnd Power Frandsen S, Barthelme R, Pryor S, Rathmann O, Larsen S. Defct n large offshore wnd farms. 006 Jan; p Werle M. A new analytcal model for wnd trbne wakes Report No: FD Schepers J, Van der Pjl S, edtors. Improved modellng of wake aerodynamcs and assessment of new farm control strateges. Jornal of Physcs: Conference Seres; IOP Pblshng; Crasto G, Gravdahl AR, edtors. CFD wake modelng sng a poros dsc. Eropean Wnd Energy Conference & Exhbton; W Y-K, Lee C-Y, Chen C-R, Hs K-W, Tseng H-T. Optmzaton of the Wnd Trbne Layot and Transmsson System Plannng for a Large-Scale Offshore Wnd Farm by AI Technology. IEEE Transactons on Indstry Applcatons. 04; 50(): Mgoya E, Crespo A, Garca J, Moreno F, Manel F, Jmenez A, et al. Comparatve stdy of the behavor of wnd-trbnes n a wnd farm. Energy. 007; (0): Aytn Oztrk U, Norman BA. Herstc methods for wnd energy converson system postonng. Electrc Power Systems Research. 004; 70(): Sanderse B. Revew of comptatonal fld dynamcs for wnd trbne wake aerodynamcs. Wnd Energy. 0 Feb; p Mosett G, Polon C, Dvacco B. Optmzaton of wnd trbne postonng n large wndfarms by means of a genetc algorthm. Jornal of Wnd Engneerng and Indstral Aerodynamcs. 994; 5(): Grady SA, Hssan MY, Abdllah MM. Placement of wnd trbnes sng genetc algorthms. Renewable Energy. 005; 0(): Marmds G, Lazaro S, Pyrgot E. Optmal placement of wnd trbnes n a wnd park sng Monte Carlo smlaton. Renewable Energy. 008; (7): Mttal A. Optmzaton of the layot of large wnd farms sng genetc algorthm [MS thess]. Department of Mechancal and Aerospace Engneerng, Case Western Reserve Unversty; Rahman R, Kharddn A, Cherat SM, Mahmod Pesaran HA. A novel method for optmal placng wnd trbnes n a wnd farm sng Partcle Awarm Optmzaton (PSO). 00 Conference Proceedngs IPEC; 00. p Ksak A, Song Z. Desgn of wnd farm layot for maxmm wnd energy captre. Renewable Energy. 00; 5(): Emam A, Noghreh P. New approach on optmzaton n placement of wnd trbnes wthn wnd farm by genetc algorthms. Renewable Energy. 00; 5(7): Rajper S, Amn IJ. Optmzaton of wnd trbne mcrostng: A comparatve stdy. Renewable and Sstanable Energy Revews. 0; 6(8): Chen Y, L H, Jn K, Song Q. Wnd farm layot optmzaton sng genetc algorthm wth dfferent hb heght wnd trbnes. Energy Converson and Management. 0; 70: Trner SDO, Romero DA, Zhang PY, Amon CH, Chan TCY. A new mathematcal programmng approach to optmze wnd farm layots. Renewable Energy. 04; 6: Shakoor R, Hassan M Y, Raheem A, Rasheed N, Mohd Nasr MN, edtors. Wnd farm layot optmzaton by sng defnte pont selecton and genetc algorthm. 04 IEEE Internatonal Conference on Power and Energy (PECon 04); 04; IEEE Dgtal Explore. 7. Goldberg DE, Holland JH. Genetc algorthms and machne learnng. Machne learnng. 988; (): Gonzalez JS, Gonzalez Rodrgez AG, Mora JC, Santos JR, Payan MB. Optmzaton of wnd farm trbnes layot sng an evoltve algorthm. Renewable Energy. 00; 5(8):67 8. Vol 8 (7) Agst 05 Indan Jornal of Scence and Technology 9