Optimal Power Planning of Wind Turbines in a Wind Farm

Transcription

1 Amecan Jounal o Eleccal owe and Eney Sysems 7; 6(): 7-5 hp:// do:.648/j.epes.76. ISSN: 36-9X (n); ISSN: 36-9 (Onlne) Opmal owe lannn o Wnd ubnes n a Wnd Fam unee Vshwakama Yunjun Xu * Kuo-Ch Ln Mechancal and Aeospace Enneen Depamen Unvesy o Cenal Floda Olando USA Emal adde: pvkama@mal.com (. Vshwakama) yunjun.xu@uc.edu (Yunjun Xu) ku.ln@uc.edu (Kuo-Ch Ln) * Coespondn auho o ce hs acle: unee Vshwakama Yunjun Xu Kuo-Ch Ln. Opmal owe lannn o Wnd ubnes n a Wnd Fam. Amecan Jounal o Eleccal owe and Eney Sysems. Vol. 6 No. 7 pp do:.648/j.epes.76. Receved: Decembe 5 6; Acceped: Mach 7; ublshed: Apl 4 7 Absac: Wnd eney s aacve n he pesence o clmae concens and has he poenal o damacally educe he dependency on nonenewable eney esouces. Wh he ncease n wnd ams hee s a need o mpove he ecency n powe allocaon and powe eneaon amon wnd ubnes. In hs pape a heachcal alohm ncludn a coopeave level and an ndvdual level s developed o powe coodnaon and plannn n a wnd am. In he coopeave level a consaned quadac poammn poblem s omulaed and solved o allocae he powe o wnd ubnes consden he aeodynamc eecs o wake neacon and he powe eneaon capables o wnd ubnes. In he ndvdual level a mehod based on he local pusu saey s suded o connec he coopeave level powe allocaon and he ndvdual level powe eneaon usn a vual leade-ollowe scheme. he sably o ndvdual wnd ubne powe eneaon s analyzed. Smulaons ae used o show he advanaes o he mehod. Keywods: Wnd ubne Coodnaed Conol Wnd Fam. Inoducon Wnd eney s consdeed o be an mpoan playe n he enewable eney make enabln a educon n cabon polluon om convenonal eney wh a apd owh a he ae o aound 7% pe yea beween 5-9 [] []. he US ovenmen has plans o poduce % o he couny s eney va wnd by 3 [3]. Alhouh pomsn n s poenal wnd ams aaned n aays sue n powe oupu due o aeodynamc neacon beween he wnd ubnes. hs ues wnd am conol schemes ha can mpove he powe poducon oupu and handle he aeodynamc neacons bee [4]. I s shown ha aound % o 4% o wnd eney oupu and po s los as a esul o he neacon amon wnd ubnes paculaly due o wake neacons [5] [6]. Wnd eney conol eseach s nomally ocused on ehe ndvdual wnd ubne conol o wnd am coopeave conol. In ndvdual wnd ubne conols wok has been done on usn lnea/nonlnea eedback conol echnques o ack he powe o be poduced. An example o hs can be seen n [7] whee he eseaches poposed an adapve conol saey usn neual newok o conol oo speed and blade pch anle. Anohe popula decon s he sudy o wnd avalably and he sably analy o he sysem whle swchn beween deen opeaon emes [8]. he appoach o maxmzn he powe o an ndvdual ubne endes subopmal n ems o wnd am powe poducon due o coupled aeodynamc eecs and mechancal loadns [9]. hs beckons a scheme o coodnaon o ndvdual wnd ubne acons o ncease he oveall ecency o he plan and educe aue and loads on wnd ubnes []. Wh an nceased esponsbly n powe eneaon wnd ams have ohe asks o peom such as eulaon and sablzaon o powe plans and may no be ued o un a a ull capacy a all mes [9]. Many eseaches have ackled coopeave wnd am conol poblems. he wo boad caeoes o appoaches nclude () maxmzn he oal powe oupu and () powe opmzaon schemes o dsbue he powe demand n ems o load educon e.. n []. In [5] wnd am oupu s maxmzed by ndn opmal combnaon o yaw anles and nducon aco usn a seepes decen mehod. In [] powe demand s me by dynamcally coodnan and vayn wnd ubne powe such ha he adon o he powe oupus maches he oal uemen. Alhouh hee have been many woks n ecen yeas

2 8 unee Vshwakama e al.: Opmal owe lannn o Wnd ubnes n a Wnd Fam ocusn on he coopeave conol o wnd ubnes hee s sll pleny o oom o mpovemen n hs eld. Fo example mos o he ecen wok ocuses on he use o lneazed wnd ubne models [] o opmzaon puposes; hs can lead o eos as some wnd ubne opean modes n lneazed models do no mach well wh eal nonlnea phenomena. Fuhemoe he wok n coodnaed wnd am conol oen noes sucual delecon consans o ndvdual wnd ubnes [3]. In some wnd am coopeave conol wok as seen n [4] he alohm has a hh compuaonal cos when appled o lae wnd ams and s no scalable wh ncease n he numbe o wnd ubnes. he opmal coopeave powe plannn n hs wok s dvded no a heachcal sucue whch cons o wo levels coopeave and ndvdual. he coopeave level alohm handles he objecve o opmally allocan powe o he wnd ubnes whle consden he coupled consan o wake neacon beween wnd ubnes as well as uncoupled consans o powe poducon lms o ndvdual wnd ubnes based on wnd ubne popees and avalable wnd speeds. he ndvdual level alohm s o mnmze he deences beween he acual powe eneaed and he allocaed powe demand whle consden ndvdual wnd ubne consans such as hus and oque on he oo he oo speed and he owe delecon. A leade ollowe aanemen s used n connecn he coopeave and ndvdual level alohms. he ecenly suded coopeave conol saey [5] movaed by he local pusu phenomenon seen n oan ans [6] wll be uhe enhanced o oven he elaonshp beween he powe eneaon n vual leade powe and ndvdual wnd ubne. he ollown aspecs o alohm ae suded: () he asympoc sably o powe allocaon omulaon ) he ulbum pon and he sably o wnd ubne oo speed dynamcs 3) he ably o handle nonlnea wnd ubne dynamcs and 5) he scalably o alohm wh ncease n wnd am sze. he pape pesened s dvded no he ollown pas. Secon noduces he adoped ndvdual wnd ubne model and he wake neacon model. In Secon 3 he coopeave level and ndvdual level opmzaon poblems ae dened. Secon 4 descbes he local pusu based ndvdual wnd ubne opmal powe conol and Secon 5 dscues he coodnaed wnd am powe allocaon alohm. Smulaon esuls ae shown n Secon 6. Lasly concluson s dawn n Secon 7.. Indvdual Wnd ubne Model he nonlnea wnd ubne model adoped om [7] cons o he blade pch acuao dynamcs and he oo dynamcs as ( ) ( ) u R C ( λ β ) xɺ = x + x 3 ρπ ω V anb bnb J ω J J = + β β / β β Hee he sae vaables x = [ ω β ] ae he oo anula velocy and he collecve blade pch anle and he conol vaable β s he blade pch anle eeence npu. ( ) C λ β s he oo powe coecen. λ = ωr / V s he () p speed ao. ρ R V n b J = J + nbj and β ae he a densy oo adus aveae wnd speed he uvalen sha nea ea box ao and me consan o he pch sevo sysem especvely. J and J ae he nea o he oo and eneao. he daa and coecens used n hs model ae seleced om a 3 blade hozonal axs 5 MW capacy oshoe wnd ubne [7]. he consans a and b ae he paamees n he lneazed eneao oque model = aω + b [7] n whch he eneao speed s ω = n ω. I s woh non ha he npu max n Eq. () b s non-squae. he oupus o he model ( ) h x nclude he powe exaced om he wnd he oque expeenced by he low speed sha and he hus expeenced by he oof as ollows ( λ β ) ( λ β ) ( λ β ) 3.5 ρπrv C 3 y = h ( x) = =.5 ρπrv CQ F.5 ρπ RV C In he above uaon CQ ( ) C ( ) ( ) () λ β = λ β / λ and C λ β ae he oo oque coecen and he oo hus coecen especvely [7]. he cu-n and aed wnd speeds o such a wnd ubne ae 8 m/s and.4 m/s [7] especvely. Fo he smulaon o wnd ubne dynamcs sa up and shu down scenaos ae no ncluded. he lmaons o oo speed oo oque and husoce ae ω ω ω F F (3) mn max max max o make he exacon o pch anle easy om known C and λ an uaon s adoped om [8] as c5 λk ( λ β ) ( / λk 3β 4 ) 6λk C = c c c c e + c (4).35 = λ λ + β β + k ( ) 3.8 whee c =.576 c = 6 c 3 =.4 c 4 = 5 c 5 = and c 6 =.68. he Cvalue calculaed usn Eqs. (4) and (5) (5)

3 Amecan Jounal o Eleccal owe and Eney Sysems 7; 6(): maches well wh he values obaned om he FAS and Aeo Dyn packaes o NREL [7]. he Jensen wake model [9] s used o calculae he downseam velocy beween wnd ubnes n he am whch pems as calculaons and s commonly used n commecal wake calculaon poams. he wnd speed a a dsancexs ven as ollows. ( C ) Vw ( x) = V x + k R Hee V and k ae he ncomn wnd speed and he enanmen consan and R s oo adus. he husoce acn on he oo plane o he wnd ubne causes he oscllaon o he owe and he owe delecon n he oe-a decon s depced n he second ode sysem [] as (6) mz ɺɺ + dzɺ + cz = F (7) n whch z s he dsplacemen o owe op alon he decon o he wnd he husoce F s aumed o be concenaed n he cene o he oo hub. In Eq. (7) paamee m s he modal ma d s he modal dampn and c s he modal sne o he owe. he dsplacemen o he owe op s consaned by z zmax. 3. Coopeave Opmal owe Conol owe Fomulaon 3.. owe Geneaon Opmzaon n Indvdual Wnd ubne he peomance ndex o be opmzed n each wnd ubne s ( ) J = W d WF W = (8) We aume ha hee ae N w wnd ubnes n he am and Wk k = 3 ae use dened wehs o each componen n he peomance ndex. and d ae he acual and allocaed powe o he h wnd ubne n he plannn hozon. F and ae he husoce acn n he oo plane and he hus oque o he h wnd ubne. he desn vaable (opmzable vaable) n he peomance ndex s he speed conol paamee (SC) n he acual powe em and wll be dscued n Secon 4. he ualy consans nclude he nonlnea dynamcs β ; whle Eq. Eq. () and nal conon ω ( ) and ( ) (3) and he owe delecon lmaons ae eaded as he nualy consans. 3.. owe Allocaon n Wnd Fams In he wnd am coopeave level powe allocaon he wnd speed avalable o upwnd ubnes and he dsances beween he upwnd and downwnd wnd ubnes ae known. A a pacula me he powe d newok needs a oal o o om hs am and he peomance ndex n he coopeave level s N w o (9) = J = he powe allocaed o wnd ubne s lmed by s powe eneaon capably mn max whch depends on he anes o s ncomn wnd pch anle and p speed ao. 4. Local usu Based Indvdual Wnd ubne Opmal Conol 4.. owe Oupu Reulaon he powe oupu o each wnd ubne s poposed o be dven by a moded local pusu saey [5] ( ) ɺ = v + v + ɺ = N () w n whch s he powe oupu o leade ha can be a vual wnd ubne and he value can be he aveae powe eneaed by N wnd ubnes n he am as ( ) / w = o. he consan em n a plannn hozon s he powe oupu bas o wnd ubne om. hee ae deen appoaches o dve he powe o each wnd ubne owads s allocaed value. Follown Eq. () s jus one appoach. In hs appoach he acual wnd ubne powe wll ollow a s ode ajecoy whou an oveshoo. Adonally he speed conol paamee (SC) v deemnes how as he powe oupu wll convee o s desed value +. Le us dene he oupu powe ackn eo o wnd ubne o be = = N () w Lemma : As he powe oupu o wnd ubne wll asympocally convee o s allocaed value v >. Also unde hs udance law he powe oupu s v = ( ) + + = w e N () oo: I s poven n [5] ha he eo snal wll v >. hus asympocally convee o zeo as ( ) he poo o hs pa o Lemma s omed. Accodn o Eq. () and Eq. () ɺ = v. heeoe

4 unee Vshwakama e al.: Opmal owe lannn o Wnd ubnes n a Wnd Fam whch leads o Eq. (). ( ) v = e (3) 4.. Equlbum on and Sably o Roo Lemma : I he powe eneaon ollows Eq. () he ulbum pons o he oo speed ω ae ( ) ( ) ω = c ± c + 4 c + / c = (4) n whch he coecens ae dened n he ollown poo. Hee a neave oo speed epesens he case ha he oo wll spn n he oppose decon allowed. oo: he oo dynamcs om Eq. () can be wen as ( λ β ) 3 ρπrv C an bω bn b ɺ ω = (5) J ω J J Le us dene c an > and c bn < and b 3 also because.5 ρπrv C ( λ β ) can be ewen as b = he oo dynamcs c c ɺ ω = ω = J ω J J c c v ω + ( + + J J J ω heeoe he ulbum pon ω when ɺ ω = ves ω = c ± c + 4c ( c ) ( + + v (6) (7) As he seady sae ulbum pon o he oo speed s deved as Eq. (7). Remak : In ealy a wnd ubne may only have one ulbum pon accodn o s wnd blade pch anle nsallaon. Lemma 3: I he powe eneaon o each wnd ubne ollows he moded local pusu uaon (Eq. ) he ulbum pon o he oo speed n Eq. (7) s asympocally sable he peubaon om s ulbum pon ω sases ω < ω. oo: Le us aume he oo speed s peubed o be ω = ω + ω whee ω s he eo aound he ulbum pon. hen Eq. (7) can be ewen as c c ɺ ω + ɺ ω = ω + ω ( ω ω ) ( ) J J v + ( + + J + whch can be smpled as c c c ɺ ω + ɺ ω = ω ω J J J ω + ω ω ω ω ( + ) v ( + + J (8) (9) Remove he ulbum pa n Eq. (9) he eo dynamcs s deved o be ω ω ω v ( ) e c = ω ( ω + ω ) J J + + () Fo anyv > v ( ) + + e v ( ( ) ) = e + + = e + + e > v v ( ) ( ) () I ω < ω ω ( ω + ω ) >. Snce c > he coecens n boh ems o he eo dynamcs ae neave whch means he oo speed eo wll decay o zeo as and he eo s bounded by s nal eo. heeoe accodn o [] he oo speed ulbum pon s asympocally sable. Lemma 4: he eons o aacon o posve and neave ω n Eq. (7) ae ( ) and ( ) especvely. oo: Le us dene v c c ( ω = + () J J J ω + + hee s a snula value a ω =. Fo he posve ω case ω = ω + Eq. () can be smpled as ω

5 Amecan Jounal o Eleccal owe and Eney Sysems 7; 6(): 7-5 c c = ( ω + ω ) J J v + ( + + / J ( ω + ω ) (3) Noe ha he ulbum conon s appled n devn Eq. (3). heeoe < < > and ω wll ω ω ncease unl eaches ω. I ω > > and ω wll decease unl eaches ω. hus he eon o aacon o he posve ω wll be ( ). Smlaly can be poven hao he neave ω he eon o aacon s ( ). Remak : based on Lemma 3 when he powe oupu eneaed ollows he moded local pusu uaon he nal oo anula velocy s posve (neave) wll convee o he posve (neave) ulbum pon. Remak 3: based on Lemma Lemma 3 and Remak he powe oupuollows Eq. () he oo speed n he ndvdual wnd ubne wll each s ulbum pon dependn on s nal conon whch s asympocally sable. Remak 4: Based on Eq. (3) ( ) = ( ) hus ( ) ( ) = ( ) v e. ln / v (4) hs uaon can povde nomaon on how as ouhly he powe eneaed by wnd ubne wll appoach he allocaed powe. Remak 5: I s woh non he asympocally sably o he ulbum oo speed aumes ha he model s peecly known and hee s no senso o acuao noses o unceanes. When he nose and/o unceanes canno be neleced o he wnd ubne s no peecly modeled he plannn alohm poposed hee can be pu n a ecedn hozon amewok and he powe eneaon n ndvdual wnd ubne wll be eplanned a he bennn o each plannn hozon Dynamc Model opaaon o solve he opmzaon poblem o ndvdual wnd ubne lsed n Secon 3. we need o know he sae and conol vaables a each nsance. Snce he npu max o model Eq. () s non-squae nsead o ndn hose vaables houh as collocaon mehods such as hose used n [5] we wll decly popaae he dynamc model hee. Snce ou oal s o plan ndvdual level wnd ubne s powe eulaon opmzaon aumpon s made ha he elaon beween oo speed collecve blade pch anle p speed ao coecen o powe and allocaed wnd ubne powe ae peecly modeled. he dealed seps nvolved ae lsed n he ollown alohm. Sep Sep able. Alohm - Model opaaon. Based on he allocaed powe o he h wnd ubne usn Eq. () he oo powe coecen C( λ β ) can be calculaed usn Eq. (). he esulom sep can be used o popaae he anula speed dynamcs ω usn he s uaon n Eq. (). Sep 3 he p speed ao s hen calculaed by λ = ω R / V he p speed ao calculaed n he pevous sep alon wh Sep 4 he known C( λ β) can help us evesely solve o he pch anle β usn Eqs. (4) and (5) he conol vaable (. e. he eeence pch anle β ) can be calculaed usn he devave o β and he second uaon Sep 5 n Eq. (). he devave o β can be appoxmaed usn he Eule scheme. he oupu vaables. e. he hus and oque on he oo can be calculaed usn Eq. (). he owe delecon ( z ) s Sep 6 popaaed usn Eq. (7) based on he calculaed hus F on he oo Indvdual Wnd ubne owe Geneaon Opmzaon he opmzaon o he powe eneaon n each wnd ubne s shown n Alohm lsed below. he mncon solve n MALAB s appled hee. As poven n Lemma 3 he closed-loop sysem s asympocally sable. Sep Sep Sep 3 Sep 4 able. Alohm - owe Geneaon Opmzaon. Usn he known vual leade powe and he allocaed powe bas ue he opmzable vaable (. e. he speed conol paamee v ) a each me node. he powe o be eneaed s popaaed usn he ueed v. Alohm s ollowed and he esuls ae used n evaluan he peomance ndex as dened n Eq. (8) and he ualy and nualy consans as descbed n Secon 3.. I he peomance ndex does no convee o he mnmum o a easble soluon o back o Sep. Else he opmzaon s accomplshed. Wnd ubnes n a wnd am can be opmzed usn Alohm n a decenalzed manne. 5. Coodnaed owe Allocaon n Wnd Fams 5.. owe Geneaon Allocaon n Coopeave Level he peomance ndex n he coopeave level s ven n Eq. (9). Expandn hs peomance ndex we e N w o o = = J = + (5) Mnmzn Eq. (5) s uvalen o mnmzn J =. Expandn he s em n (5) o = =

6 unee Vshwakama e al.: Opmal owe lannn o Wnd ubnes n a Wnd Fam N w = j = + j = = j= = j = j = + j (6) heeoe he peomance ndex can be wen as he om o a quadac poammn as J = mn H + (7) whee he opmzable paamees = w N ae he powes o be allocaed. he maces H and ae dened as H = and = o (8) he consan n he opmal powe allocaon s [ mnmax ]. o know he ane o he avalable powe o each wnd ubne he ane o poble wnd speed needs o be calculaed. he alohm o calculae he lowe and uppe bounds o he avalable powe [ mnmax ] s lsed nex as Alohm 3. able 3. Alohm 3 - Rane o Avalable owe o each Wnd ubne. Sep Receve he oal wnd am powe demand ( o ) Sep Follow Alohm 3 o nd and mn max Sep 3 Solve he omulaed quadac poammn poblem (Eqs. 7 and 8 and [ mn max ]) Sep 5 Compue he vual leade powe ( = / N and ɺ = ) Sep 6 o w Send he allocaed powe ( = + ) vual leade powe ( ) and bas nomaon ( ) o Alohm o lowe level opmzaon. hs sep s decenalzed. he MALAB quadac poammn solve quadpo s used o solve he omulaed powe allocaon poblem (Eqs. 7 and 8 and [ mn max ]). he alohm used o opmally allocae he powe o each wnd ubne s summazed n he ollown able. Sep Sep Sep 3 able 4. Quadac oammn o Coodnaed owe Allocaon. Receve he oal wnd am powe demand ( ) o Follow Alohm 3 o nd and mn max Solve he omulaed quadac poammn poblem (Eqs. 7 mn max ) and 8 and [ ] Sep 5 Compue he vual leade powe ( = / N and ɺ = ) Sep 6 o w Send he allocaed powe ( = + ) vual leade powe ( ) and bas nomaon ( ) o Alohm o lowe level opmzaon. hs sep s decenalzed. 5.. Coodnan owe Allocaon and lannn Alohm Alohms houh 4 ae pu oehe n Alohm 5 as he oveall powe allocaon and opmal powe plannn alohm o a wnd am. Sep Sep Sep 3 Sep 4 able 5. Alohm 5 - Summay o he Alohm. he d sends a oal desed powe oupu ( ) n he o bennn o each plannn hozon. Alohm 4 (ncludn Alohm 3) s used o nd and n he coopeave level whch wll be sen o ndvdual wnd ubne (cenalzed). Alohm (ncludn Alohm ) s used o nd he opmzed v and he opmal eeence pch anle β (decenalzed). Send he oveall opeaon and powe poducon nomaon back o he cenal compue. Indvdual wnd ubne wll execue he β command. 6. Smulaon and Dscuon 6.. Smulaon Sens he smulaon s caed ou on a lapop unnn Inel Coe 7-6M wh a poceo speed o.7 GHz and a 6 GB RAM. he consaned nonlnea poammn poblem n Alohm s solved usn he MALAB mncon uncon; whle he consaned lnea quadac poammn poblem n Alohm 4 s solved by he quadpo uncon. he popees o he wnd ubne ae adoped om [3] as shown n able 6. I s woh menonn ha alhouh all he wnd ubnes n he smulaed wnd am ae aumed o be he same non-homoenous dynamcs models can be used n he poposed coopeave conol alohm. able 6. opees o he chosen Wnd ubne Model. aamee Denon Gea box ao ( n b ) 97 Numbe Geneao nea ( J ) 534. k m Roo nea ( J ) 59 k m Equvalen sha nea ( J = J + n J ) b 5.4 k / m 6 3 A densy ( ρ ).4 k / m Roo adus (R ) ch acuao me consan ( β ) Modal ma o wnd ubne owe (m) 63 m. sec k Modal dampn o he wnd ubne owe (d ) N / ( m / s ) Modal sne o he wnd ubne owe ( c ) N / m owe heh (h ) 87.6 m he oleances o boh he consans and uncon evaluaons ae se o. he uppe and lowe bounds o he opmzable paamee (. e. he speed conol paamee) ae se o be beween 4 and 8. he consans on he oo speed oque and oce ae lmed by pm ω 5pm N m and F N especvely [3]. he maxmum owe delecon ( z max ) consan s kep a 5% o he owe heh. As one case he wehs n

7 Amecan Jounal o Eleccal owe and Eney Sysems 7; 6(): peomance ndex Eq. (8) ae se o W = W = and W 3 =. All he quanes n he opmzaon ae nondmensonalzed o help he opmzaon conveence. I s woh menonn hao bevy only he plos o he sae and conol vaables n Case A ae shown snce all he ohe cases have smla sae and conol vaable peomance. 6.. Indvdual Wnd ubne Opmzaon hee scenaos ae smulaed o es he obusne o Alohm. e. he powe plannn opmzaon o ndvdual wnd ubne: A) vayn wnd speed B) vayn allocaed powe and C) vayn nal powe conon. Dun he plannn hozon s pesumed ha he wnd speed emans consan Vayn Wnd Speeds (Case A) he able below summazes he opmzaon esuls o vayn wnd speeds o a xed se o allocaed and nal wnd ubne powe as well as an nvaan vual leade powe. he obaned seady sae values o oo speed pch anle oo oque and oo hus ae n aeemen wh hose n smla scenaos on a 5 MW NREL wnd ubne [7]. he mno deences n hose peomances ae due o ac ha he eneao oque values (. e. he values o a and b) chosen o he smulaon ae deenom he daa n NREL. Ou saey s o une he eneao oque o keep he p speed ao beween 7 and 8 nea he opmal p speed ao o 7.55 [7] Opmum soluons ae able o be aaned n easonable me as shown n able VII ann beween.8 and.8 seconds. (a) oque (b) hus (c) Roo Speed Case V (m/s) able 7. Case A - Vayn Wnd Speed. CU me (sec) β ω F (MN) (de) (pm) (MN-m) A A A A A he ollown ue shows he me hsoy o he wnd ubne sae and oupu vaables o hose ve vayn wnd speed cases. In Fue (a) Fue (b) he oque and husoce ae whn he lm. he oo speed (Fue (c)) s sablzed a s ulbum pon based on s powe oupu and blade pch anle. In all he cases he powe eneaon eaches s allocaed numbe MW (Fue (d)). he pch anle (Fue (e)) ollows well wh he commanded eeence pch anle (Fue ()). I s woh non ha all ve cases have deen nal pch anle due o he ac ha hee ae only wo ndependen vaables amon he nal powe nal blade pch anle and nal oo speed sens. (d) owe (e) ch Anle Fue. Resuls o Case A.

8 4 unee Vshwakama e al.: Opmal owe lannn o Wnd ubnes n a Wnd Fam 6... Vayn Allocaed owe (Case B) Fo he cases n able VIII he allocaed powe s chann and he wnd speed s kep consan. As expeced wh an ncease n powe demand he pch anle deceases. he maxmum owe delecon oce and hus expeenced by he ubne ae nceasn n a eneal end. he CU me s beween.79 and.8 seconds. he oo speed s mananed a s ulbum pon accodn o s powe oupu wnd speed and blade pch anle. able 8. Case B - Vayn Allocaed owe. CU me β V (m/s) ω F (MW) (sec) (de) (pm) (MN-m) (MN) Vayn Inal owe (Case C) Fo all ve C cases he nal powe conon s vaed whle he wnd speed and he allocaed powe ae kep a he aed value. Fo he same commanded powe a he same (aed) wnd speed he seady sae values o all 5 cases acheve he same value as expeced. he maxmum owe delecon s deen due o s deen nal powe oupu whch aecs he ansen sae o he powe eneaon; howeve s whn he lm. Fue. A x wnd am conuaon A 4 by 4 Wnd Fam Aay In he second case a be aay s used (Fue 3). Hee aan a aed wnd speed o.4 m/s s avalable n he s ow o wnd ubnes. Fo a oal powe demand o 3 MW he coopeave level alohm could apdly allocae powe o each wnd ubnes. he calculaed veloces a he nd 3d and 4h ows ae 9.83 m/s 8.74 m/s 7.54 m/s. he CU me o he coopeave powe allocaon s.35 sec. able 9. Case C - Vayn Inal owe Conon. CU me (sec) β ω (MNm) F (MN) (MW) (de) (pm) Coodnaed Wnd ubne Opmzaon he oveall coopeave opmal powe plannn alohm (Alohm 5) s esed on hee oshoe wnd ams wh deen szes A by Wnd Fam Aay In hs case an aay conn o 4 wnd ubne aay s seleced (Fue ). he dsance beween each ow o wnd ubnes s 54 m. A oal powe demand o MW s uesed om he am. A aed wnd speed o.4 m/s s avalable a he s ow o wnd ubnes. Follown Alohm 5 and subsuen alohms whn he downwnd wnd speed a he second ow s.3 m/s and he CU me used n allocan he powe o he wnd ubnes s.33 sec. he ndvdual level alohm s hen mnmzn he peomance ndex n Eq. (8) and deemnes he pch anle eeences o he ndvdual wnd ubnes. Fue 3. A 4x4 wnd am conuaon A 5 by 5 Wnd Fam Aay Fo smla upwnd conons n hs case wh 5 wnd ubnes (Fue 4) he oal powe demand om he wnd am s 45 MW. he calculaed wnd speeds based on he coopeave level alohm a he downwnd ows 3 4 and 5 ae 9.84 m/s 8.75 m/s 7.55 m/s and 5.9 m/s especvely. he CU me o he coopeave powe allocaon s.36 sec. Fue 4. A 5x5 Wnd Fam Aay.

9 Amecan Jounal o Eleccal owe and Eney Sysems 7; 6(): he able below demonsaes he scalably o he coopeave powe plannn alohm poposed n hs pape. Fo an ncease n he am sze he compuaonal cos emans a a smla level. he CU me o he coopeave level only nceases slhly om.33 seconds o.36 seconds. he CU me ncease o he ndvdual level s elavely vey low. he powe allocaon and plannn opmzaon n a ypcal wnd am s a mos. Hz [7]; heeoe he CU me acheved hee mees he need. Fuhemoe wh a moe ecen C poammn solve he CU me s expeced o be much lowe. able. CU me o 3 Wnd ubnes wh Deen Sze. Wnd am conuaon x aay 4x4 aay 5x5 aay Coopeave level CU me (sec) eomance ndex Indvdual level Mnmum CU me (sec).94.. Maxmum CU me (sec) Oveall CU me (sec) Concluson In hs pape a new heachcal mehod o coopeave conol o wnd ubnes n a wnd am s pesened. he powe allocaon amon wnd ubnes s obaned by solvn a omulaed quadac consaned poammn poblem akn no accoun coupled and uncoupled consans. he local pusu saey s cusomzed o each wnd ubne o opmally ack he allocaed powe command akn no accoun ealsc wnd ubne consans. Some benes o he alohms ae: he wnd ubne oo dynamcs unde he planned powe eneaon saey s uaaneed o be asympocally sable; he compuaonal cos s low; and he alohm s scalable n ems o he CU me. Reeences [] L. Y. ao and K. E. Johnson Conol o wnd ubnes: appoaches challenes and ecen developmens IEEE Conol Sysems Maazne vol. 3 no. pp [] Oshoe wnd eney hp:// [3] S. Scheck J. Lundqus and W. Shaw Reseach needs o wnd esouce chaacezaon Bullen o he Amecan Meeoolocal Socey 8 vol. 9 no. 4 pp [4] K. E. Johnson and N. homas Wnd am conol: adden he aeodynamc neacon amon wnd ubnes n Amecan Conol Con. 9. ACC 9 pp. 4-9 Jun. 9. [5] J. ak S. Kwon and K. H. Law Wnd am powe maxmzaon based on a coopeave sac ame appoach n oc. SIE Sma Sucues/NDE Con. vol pp. -5 Ma. 3. [6] Sanda Labs news eleases SWF commoned o sudy wnd am opmzaon hps://shae.sanda.ov/news/esouces/ news_eleases/swwnd-am-opmzaon/#. UzebldWSp. [7] Z. Wan C. Ca and K. Ja Neual Newok adapve conol o consan oupu powe o vaable pch wnd ubne n IEEE In. Con. on Vehcula Eleconcs and Saey IEEE Donuan Chna pp July 3. [8] G. Semau S. Rmkus and. Das Nonlnea sysems analy and conol o vaable speed wnd ubnes o muleme opeaon ASME Jounal o Dynamc Sysems Measuemen and Conol 5 vol. 37 no. 4 pp [9] V. Spudc M. Baoc and N. ec Wnd am load educon va paamec poammn based conolle desn n oc. 8 h IFAC Wold Cone Mlano Ialy pp Au.. []. Knudsen. Bak and M. Svensup Suvey o wnd am conol powe and aue opmzaon n Wnd Eney 5 Wley Onlne Lbay John Wley & Sons Ld. pp May 4. [] D. Madjdan M. Ksalny A. Ranze Dynamc powe coodnaon o load educon n dspachable wnd powe plans n 3 Euopean Conol Con. Zuch Swzeland pp July 3. [] L. Muneanu N. A. Cuululs A. I. Bachu and E. Ceana Opmzaon o vaable speed wnd powe sysems based on a LQG appoach Conol Enneen acce vol. 3 no. 7 pp July 5. [3] V. Spudc M. Jelavc M. Baoc and N. ec Heachcal wnd am conol o powe/load opmzaon n oc. Con. Sc. Makn oque om Wnd pp [4] M. Solemanzadeh A. J. Band and R. Wsnewsk A wnd am conolle o load and powe opmzaon n a am n IEEE In. Sym. Compue-Aded Conol Sysems Desn Denve CO pp. -7 Sep.. [5] Y. Xu C. Remekas and K. ham Local pusu saey nsped coopeave ajecoy plannn alohm o a cla o nonlnea consaned dynamcal sysems Inenaonal Jounal o Conol vol. 87 no. 3 3 pp [6] D. Hsu-Vasakels and C. Shao Bolocally-nsped opmal conol: leann om socal nsecs Inenaonal Jounal o Conol 4 vol. 77 no. 8 pp [7] J. Jonkman S. Bueeld W. Musal and G. Sco Denon o a 5-MW eeence wnd ubne o oshoe sysem developmen echncal Repoom Naonal Renewable Eney Lab. U. S. Dep. o Eney Feb. 9. [8] J. Hu and A. Bakhsha A new adapve conol alohm o maxmum powe pon ackn o wnd eney conveson sysems n oc. IEEE owe Eleconcs Specalss Con. 8 pp [9] D. J. Renkema Valdaon o wnd ubne wake models: usn wnd am daa and wnd unnel measuemens M. S. he Del Unv. o echnoloy 7. [] V. Spudc M. Jelavc M. Baoc and M. Vasak Dsbued conol o lae-scale oshoe wnd ams AEOLUS echncal Repo Unv. o Zaeb 8. [] J. J. Slone and W. L Appled Nonlnea Conol ence Hall Enlewood Cls NJ 99.