On The Speed Stability of Wind Driven Induction Generators Connected to Distribution Systems

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1 Issue, Volue, On he Speed Sabiliy of Wind Diven Inducion Geneaos Conneced o Disibuion Syses A. Kupean and R. Rabinovici Absac he oupu powe and echanical oque of a wind ubine diven inducion eneao, conneced o a disibued syse, chane wih he oaion speed. Fuheoe, in he eion coespondin o speeds above he one esulin in axiu oupu powe, he wind ubine oupu powe and oque decease in a dasic anne when he oaion speed inceases. Hence, he inducion eneao speed sabilizes even when he powe syse is heavily loaded and he eneao einal volae is uch lowe han he noinal value. Siulaion esuls ae pesened o pove he coecness of he enioned assupions. Keywods Disibuion, Geneaion, Speed Sabiliy, Wind ubine D I. INRODUCION ISRIBUED and ebedded eneaion has ecenly eceived a lo of aenion in he powe indusy. he peneaion of inducion eneaos (IG) in wind, hydo and heal powe plans has also apidly inceased. his fac is due o a elaively low pice of inducion achines, hei sipliciy, eliabiliy and obusness. Hence, i is ipoan o undesand he inducion eneao ipacs on sabiliy elaed pobles of disibued syses [-3]. Feias e al. [-] pesen a siulaion sudy eadin volae sabiliy of disibuion syses wih inducion eneaos. Behavio of powe syse pesened in Fi. is exained unde diffeen loadin condiions. I has been shown, ha IG einal volae, as well as volae a buses -5 would decease if syse load inceased. In addiion, i has been concluded ha he IG speed would incease in an unliied and onoonic anne when he syse loadin faco inceased above soe ciical value. his conclusion was based on pesupion of consan echanical oque applied o he IG, i.e. he pie Manuscip eceived May 9, 007: Revised vesion eceived uly 6, 007. A. Kupean was wih he Elecical and Copue Enineein Depaen, Faculy of Enineein, Ben-Guion Univesiy of he Neev, Bee-Sheva, 84000, Isael. He is now wih he Elecical and Eleconics Enineein Depaen, Sai Shaoon Collee of Enineein, Bee-Sheva, 84000, Isael (coespondin auho, phone: ; fax: ; e-ail: alonk@ sce.ac.il). R. Rabinovici is wih he Elecical and Copue Enineein Depaen, Faculy of Enineein, Ben-Guion Univesiy of he Neev, Bee-Sheva, 84000, Isael. ove dynaics was neleced. Howeve, his pesupion is no valid when he pie ove is a wind ubine, whose oupu oque does no eain consan wih he oaional speed incease. Accodin o [3], oo speed sabiliy efes o he abiliy of an inducion (asynchonous) achine o eain conneced o he elecic powe syse and unnin a a echanical speed close o he speed coespondin o he acual syse fequency afe bein subjeced o a disubance. his pape pesens an invesiaion eadin salldisubance speed sabiliy of wind-diven inducion eneaos unde vaious loadin condiions, akin pie ove dynaics ino accoun. I is clealy shown, ha he pie ove affecs he oveall syse sabiliy and pefoance. he pie ove sabilizin effec is deonsaed by exended siulaions. he pape is oanized as follows. Secions II IV descibe he odels used o epesen he ain syse coponens: secion II descibes he odel of wind ubine, used in he sudy; secion III conains a bief descipion of a coon ea dive ain; secion IV pesens he aheaical descipion of seady-sae opeaion of an inducion eneao. he ehodoloy of analyzin he speed sabiliy usin dynaic siulaions is pesened in Secion V. In secion VI, he esuls ae shown and discussed. he pape is concluded in Secion VII. II. HE WIND URBINE he powe capued by a fixed-pich wind ubine as a funcion of wind speed ay be pesened as [4-6] 3 P ( V ) ρπr C pv, () whee ρ - ai densiy (k/ 3 ) C p - powe coefficien of wind ubine V - wind velociy (/s) R - blade adius (). A wind ubine is chaaceized by is powe coefficien (C p ) o ip-speed aio (SR) cuve, whee powe coefficien is he aion beween he eney capued by a ubine and he eney

2 Issue, Volue, Fi. : Sinle phase diaa of he syse [] available in he wind; he ip-speed aio (SR) is he aio beween he linea speed of he blade ip and he wind speed. he SR is iven by whee - ubine oaional speed (ad/s) R - blade adius () V - wind velociy (/s). R SR, () V I is obvious fo () ha fo a fixed-speed ubine he SR is invesely popoional o he wind speed and vaies acoss a wide ane because he oo speed of inducion eneao conneced o a fixed-speed ubine is alos consan (dependin on slip) while he wind speed vaies sinificanly. A ypical C p (SR) cuve is shown in Fi.. Fo (), he wind speed is iven by Powe Coefficien, Cp R V SR. (3) Hence, subsiuin (3) ino (), he powe capued by a fixed-pich wind ubine can be ewien as a funcion of he ubine oaional speed: P 3 R 3 ( ) ρπr C p SR. (4) III. GEAR DRIVE RAIN MECHANICS he acceleaion and deceleaion of he eneao oo speed is descibed by he followin equaion [7], efeed o he eneao (hih-speed) side: whee + ) + D (, (5a) G G - eneao ineia - ubine ineia G - ea aio (Fi. 3) - eneao oque - ubine oque - eneao oaional speed D - oal dapin consan Eq. (5a) can be siplified o he followin fo: + D, (5b) ip-speed Raio Fi. : ypical powe coefficien C p vesus SR whee is he oal syse ineia and G is he ubine oque efeed o he eneao G side. +

3 Issue, Volue, aneizin eacance X. Leakae eacance and esisance of he oo ae efeed o he sao. Coe loss and effec of haonics in he achine ae neleced [8, 9]. he oo esisance is divided ino wo pas; one is epesenin he oo losses, he ohe one (a neaive esiso) is he eneaed powe equivalen. Boh pas su Fi.3: ypical ea (Inpu eneao side, Oupu ubine side) he ubine oupu oque is iven by P P, loss. (6) I is clea fo (5) ha when he powe exaced fo he wind is hihe han he powe deanded by he load, he oo acceleaes and vice-vesa. IV. INDUCION GENERAOR he pe-uni pe-phase seady sae equivalen cicui of he hee-phase self-excied squiel-cae inducion eneao (IG) is shown in Fi. 3, whee R, R, R - pe phase sao, oo (efeed o he sao), s and load esisances especively Xs, X, X - pe phase sao, oo (efeed o he sao) leakae, and load eacances especively X - pe phase sauaed aneizin eacance Xc - pe phase einal capaciance, F n - pe uni fequency and speed especively up o one neaive esiso. he powe ansfeed F n o he eneao is iven by (4) assuin lossless ubine and dive ain. Accodin o Fi. 3, he oo cuen is iven by I R V F, (7) R + jx F n and is squaed aniude is iven by I V F. (8) R + X F n Hence, he inpu and oupu powes ae, especively, and P in I n R F( F - n), (9) R Rs Pou Pin - ( I Is ) F + F. (0) he eneao oupu oque is iven by P ou. () Fi. 3: Pe Phase equivalen cicui of he IG In his cicui all he eneao paaees ae assued o be consans and ae independen of sauaion excep he he eneao losses vay wih eneao speed and should be consideed in any seady sae analysis of an inducion eneao. Deails can be found in [0]. he inducion achine, used in siulaions incopoaes ansien behavio as well. he oveall achine opeaion is hence odeled usin he followin equaions [], whee he elecical pa of he achine is epesened by a fouhode sae-space odel and he echanical pa by a second-ode syse. All elecical vaiables and paaees ae efeed o he sao. his is indicaed by he pie sins in he achine equaions iven below. All sao and oo quaniies ae in he abiay wo-axis efeence fae (dq fae):

4 () disd wkl ks wl u - i sd sd + i sq + i d + iq + d s Ls Ls Ls disq wkl wl ks usq - i q sd - i sq - i d + i + d Ls s Ls Ls did k wkls wl ks u i sd q sd - i sq - i d + i + d s Ls L L diq wkl s k wl i ku s sq sd + i d L sq + i q L d - i - L s 3 L ( i i - i i ) q sd d sq L L L s s + L L L + s - L LL Ls L s - L LL L L s s k s L L s s Rs L R k L Ls L whee isd, isd - insananeous values of diec- and quadaueaxis sao cuen coponens especively and expessed in he saionay efeence fae id, id - insananeous values of diec- and quadaue- axis oo cuen coponens especively and expessed in he saionay efeence fae Ls, L - self- and leakae inducances of he sao s especively L, L - self- and leakae inducances of he oo especively L - aneizin inducance s, - sao and oo ansien ie consans especively u sd, u sd - insananeous values of diec- and quadaue- axis sao volae coponens especively and expessed in he saionay efeence fae w - anula oo speed Issue, Volue, V. MEHOD PRESENAION he ehodoloy of analyzin he speed sabiliy usin dynaic siulaions is pesened in his secion. he speed sabiliy exisence is deived as follows. I is clea fo () and (4) ha wind ubine oupu powe depends on boh wind and oaion speeds. Fi. 4 pesens a ypical elaion beween wind ubine oupu powe and oaion speed fo diffeen wind speeds [5]. Fuheoe, i is clea fo obsevin Fi. 4, ha when he oaion speed inceases above he value esulin in axiu oupu powe a paicula wind speed, he ubine oupu powe educes dasically. his is also ue fo ubine oupu oque, accodin o (6). heefoe he assupion of consan echanical oque, iven in [], should be e-exained. Since he oque, applied o he IG by wind ubine, deceases wih he incease of he oaional speed on he descendin pa of he IG echanical oque chaaceisic, he IG speed sabiliy is achieved in his eion by he above enioned neaive feedback echanis accodin o (5b). Assuin no dupin wihou loss of enealiy, acceleaion ( > 0 ) is iediaely followed by he ubine oque educion ( ) and a new sable speed poin is achieved. he sabiliy poin is no feasible fo he case whee he sable speed is above he peied eneao/dive ain/ubine echanical speed. In such cases speed liiin usually exiss [7], [0], keepin he speed consan by educin he ubine capued powe and hence, he achieved oque. Powe, pu /s 9 /s /s /s 0 /s 0. 6 /s 7 /s 5 /s ubine speed efeed o eneao side, pu Fi. 4: Wind ubine powe vesus is oaion speed fo diffeen wind speeds VI. RESULS AND DISCUSSION he syse shown in Fi. was siulaed wih a wind ubine, whose chaaceisic is iven in Fi. 4, aken ino accoun. he wind speed was chosen o be 7/s, esulin in 0MW oupu powe a aed speed. he siulaions wee caied ou usin SiPoweSyses Blockse of Siulink []. SiPoweSyses exends Siulink wih ools fo odelin and siulain basic elecical cicuis and deailed elecical powe syses. hese ools le he use odel he eneaion, ansission, disibuion, and consupion of elecical powe, as well as is convesion ino echanical powe. SiPoweSyses is well suied o he developen of coplex, self-conained powe syses, such as hose in auoobiles, aicaf, anufacuin plans, and powe uiliy applicaions. Siulink solves ae well suied o coninuous-ie (analo), discee-ie, hybid, and ixed-sinal siulaions of any size. hey suppo alebaic consains

Issue, Volue, 007 6 and sae evens, includin disconinuiies such as insananeous chanes in plan dynaics. hey povide fas, eliable and accuae siulaion esuls.

5 Issue, Volue, and sae evens, includin disconinuiies such as insananeous chanes in plan dynaics. hey povide fas, eliable and accuae siulaion esuls. Wih SiPoweSyses, i is possible o use he vaiable-sep ineaos in Siulink o pefo hihly accuae siulaions of powe syse odels. Soe of hese ineaos handle he nueically siff syses ha ofen aise in odelin eal powe syses. he zeocossin deecion capabiliies of Siulink le he use deec and solve disconinuiies wih full achine pecision. oehe, SiPoweSyses and Siulink povide an efficien envionen fo ulidoain odelin and conolle desin. By connecin he elecical pas of he siulaion o ohe Siulink blocks, one can apidly daw he cicui opoloy and siulaneously analyze he cicui s ineacions wih echanical, heal, and conol syses. SiPoweSyses povides wo alenaives o coninuous siulaion of a powe syse []: disceizaion and phaso siulaion, as shown in Fi. 6. Disceizaion siulaes he syse wih fixed ie-sep apezoidal ineaion, and is especially effecive fo powe syse odels ha include powe eleconic devices. his ode also faciliaes he execuion of he odel in eal ie. Phaso siulaion eplaces he diffeenial equaions epesenin he newok wih a se of alebaic equaions a a fixed fequency. Phaso siulaion faciliaes ansien sabiliy sudies of uli achine syses. Phaso siulaion ode was incopoaed fo siulain he syse, since no powe eleconics devises wee involved and he eal ie behavio was no ipoan. he baseline fo he siulaion was loadin faco vaiaion. Loadin faco was vaied fo 0 o 0, ivin a wide opeaion ane fo no-load o heavy load condiions. he siulaions wee un fo 00 seconds in ode o each seady sae values fo all loadin facos. he ubine and dive ain wee assued lossless. he siulaion seup is shown in Fi. 5. he elecical newok and he inducion eneao ae odeled usin SiPoweSyses blockse, while he wind ubine is odeled usin Siulink. Fi. 6: Phaso vs. disceizaion (coninuous) siulaion [] Fi.5: Cobined Siulink and SiPowe syse odel

Bus 5 Volae, pu Issue, Volue, 007 6. 0.9 0.8 0.7 0.6 0.5 0.4 0.3 B 0. 0 5 0 5 0 5 30 35 40 Bus 5 Powe, MW Fi. 7: PV cuve of bus 5.

6 Bus 5 Volae, pu Issue, Volue, B Bus 5 Powe, MW Fi. 7: PV cuve of bus 5. Poin A coesponds o a loadin faco equal o, while poin B coesponds o a loadin faco equal o 0 Fis, a es siulaion was pefoed o veify he exisence of sae condiions as in [-]. Powe-volae (PV) cuve of bus 5 is shown in Fi. 7, whee poin A coesponds o loadin faco of, and poin B coesponds o loadin faco of 0. PV Cuves ae he poduc of paaeic analysis. ake ino consideaion he syse shown in Fi 8, powe is ansfeed fo he Sendin Aea o he Receivin Aea via a se of ansission lines foin an Ineface. A bin he cuve o a poin whee he syse collapses. he poin of collapse can likewise be desinaed as he Volae Collapse ansfe lii [3]. I is clea by copain he esuls wih esuls of [-], ha he siulaed syses ae siila. Speed, pu A Loadin Faco Fi. 9: Sable oo speed vesus loadin faco. Poin A coesponds o a loadin faco of, while poin B coesponds o a loadin faco of 0. oque, pu A B oque, pu B Speed, pu Fi. 8: PV cuve concep [3] As he ansfe inceases, he condiions on he lines and buses alon he ansfe pah, includin hose wihin he Sendin and Receivin aea, chane. he volaes ay dop; cuen flows on banches ay incease o decease. Monioin volae a a paicula bus and ploin his aains he powe ansfe poduces a failia diaa known as he PV Cuve. When he volae a he seleced bus oes below soe pedefined cieia, hen he ansfe a which his occus is he Low Volae ansfe lii fo ha bus. Inoin he low volae and coninuin o incease ansfe would evenually Fi. 0: oque-speed chaaceisics of he IG and he wind ubine, while he wind speed is 7 /sec and he wind ubine dynaics is also aken ino accoun. he syse loadin faco is: a) (poin A in Fis. 5 and 6); b) 0 (poin B in Fis. 5 and 6) he IG speed eached a sable value fo all he above enioned loadin facos, as shown in Fi. 9. I is clea, ha wih he incease of he loadin faco above soe value (abou 9, accodin o Fi. 9) he ae of chane in seady sae value of speed inceases, bu a sable speed sill exiss fo any loadin faco. he esuls ae quie easy o undesand by obsevin Fi. 0, whee elecoaneic oque of he IG and he ubine echanical oque fo loadin facos of and 0,

7 Issue, Volue, especively, ae ploed. I is obvious, ha if he pesupion of consan echanical oque applied o he IG is no valid, which is ue fo he wind ubine oupu oque, bu ahe has a ceain slope ( in Fi. 0), hee exiss a poin of inesecion beween he oque cuves. Fi. pesens he ansien behavio of he eneao speed fo he above enioned loadin facos. Aain, speed eaches a sable seady sae value fo boh exee cases. noinal value. Pacical sabiliy depends on he echanical consains of he syse eleens. Speed, pu; Loadin Faco Speed, pu; Loadin Faco e, Sec Fi. : Maxiu allowable speed consain REFERENCES Fi. : Chane of he IG oaion speed vesus ie fo loadin faco of a), b) 0 I is clea, ha fo any loadin faco hee an equilibiu poin exiss, whee boh oqueses ae equal and, hence, he speed eaches a sable value. Speed liiaion should be consideed ainly because of wo easons. Fis, a ceain level of acousic noise should no be eached. Second, physical liiaions of ubine and eneao oaional speed exis and us be aken ino accoun. If a speed lii coand would have been applied, he effec was equal o he effec of addiional loadin of he eneao and hence a sable poin would be eached. Howeve, if he sable speed poin is above he ubine allowable axiu speed, as shown in Fi., eihe he ubine us be shu down o he inpu powe us be educed by eans of pih eulaion if available. heefoe he fac, ha he ubine oupu oque does no eain consan wih he oaional speed incease, is cucial fo undesandin he speed sabiliy issue. VII. CONCLUSION When disibued syses wih wind ubine diven IGs ae sudied, i sees ha he coec assupion is ha he IG pie ove oupu powe and echanical oque chane wih he oaion speed. Fuheoe, in he eion coespondin o speeds above he one esulin in axiu oupu powe, he wind ubine oupu powe and oque decease in a ahe dasic anne when he oaion speed inceases. Hence, he IG speed sabilizes heoeically even when he powe syse is heavily loaded and he IG einal volae is lowe han he [] W. Feias, L. C. P. Da Silva, A. Moelao, "Sall-Disubance Sabiliy of Disibuion Syses Wih Iiducion Geneaos," IEEE ans. Powe Sys., vol. 0, no. 3, pp , 005 [] W. Feias,.C.M. Vieia, L.C.P. da Suva, C.M. Affonso and A. Moelao, "Lon-e volae sabiliy of disibuion syses wih inducion eneaos," IEEE Powe Enineein Sociey Geneal Meein, vol.3, pp , 005 [3] O. Sauelsson, S. Lindahl, "On speed sabiliy," IEEE ans. Powe Sys., vol. 0, no. 3, pp , 005 [4] A. Kupean, R. Rabinovici and G.Weiss, "A shun conneced invee based vaiable speed wind ubine eneaion," In. ou. of ELECROMOION, vol. 3, no., pp. 67-7, 006. [5] R. Ganon, B. Saulnie, G. Sybille, P. Gioux; "Modelin of a Geneic Hih-Peneaion No-Soae Wind-Diesel Syse Usin Malab/Powe Syse Blockse," Global Windpowe Confeence, Pais, Fance, Apil 00. [6] E. Muljadi, C. P. Buefield, "Pich-Conolled Vaiable Speed ubine Geneaion," IEEE ans. Ind. Appl., vol 37(), pp , 00 [7] N. Hoiuchi,. Kawahio, "oque and powe liiaions of vaiable speed wind ubines usin pich conol and eneao powe conol," IEEE Powe Enineein Sociey Sue Meein, vol., pp [8] A. Kh. abi, A. I. Alolah, Liis on he Pefoance of he hee- Phase Self-Excied Inducion Geneaos, IEEE ans. Eney Conv., vol. 5(), pp , 990 [9] A. Kh. abi, A. I. Alolah, Capaciance equieen fo Isolaed Self- Excied Inducion Geneao, IEE Poc., vol. 37(3), P. B, pp , 990 [0] A. Kupean, R. Rabinovici and G. Weiss, "oque and powe liiaions of a shun conneced invee based WECS," WSEAS ans. Cicuis and Syses, 7(4), 005 [] SiPoweSyses Use s Guide, anséneie echnoloies Inc., 006. [] P. Vas, Elecical Machines and Dives, New Yok: Oxfod Univesiy Pess, 99 [3]

8 Issue, Volue, Alon Kupean was bon in Republika Moldova, in 977. He eceived he B.Sc., M.Sc., Ph.D. and M.B.A. deees fo Ben-Guion Univesiy of he Neev, Bee-Sheva, Isael, and Ipeial Collee London in 999, 00, 00 and 006, especively. He was a Fellow of he Maie Cuie Conol ainin Sie wih he Conol and Powe Goup of Ipeial Collee, London, U.K. His fields of inees ae diial sinal pocessin and conol aloihs applied o he field of powe eleconics and elecic dives. Cuenly Alon is he Head of he aduae pojecs boad a he SCE, Isael. Raul Rabinovici (M83 SM 97) was bon in Roania in 950. He eceived he elecical enineein deee fo he Polyechnic Insiue of assy, Roania, in 97 and he Ph.D. deee in elecical enineein fo Ben- Guion Univesiy of he Neev, Bee-Sheva, Isael, in 987. He is cuenly an Associae Pofesso wih he Depaen of Elecical and Copue Enineein, Ben-Guion Univesiy of he Neev. He is a Mebe of he Edioial Boad of EE, he Inene ounal on Elecical Enineein. Ove he pas en yeas, his pincipal field of inees has been elecic dives, includin elecic achines, powe eleconic dives, diial sinal pocessin opeaion, and conol aloihs. Pof. Rabinovici is a Mebe of he Inenaional Seein Coiee of he Opiizaion of Elecical and Eleconic Equipen (OPIM) Confeence, Basov, Roania. He was a Mebe of he Edioial Boad of he IEEE RANSACIONS ON MAGNEICS beween 996 and 998.

4. Fundamental of A.C. Circuit

4. Fundamental of A.C. Circuit 4. Fundaenal of A.. icui 4. Equaion fo geneaion of alenaing induce EMF An A geneao uses he pinciple of Faaday s elecoagneic inducion law. saes ha when cuen caying conduco cu he agneic field hen ef induced