Investigation on the Excitation Capacitor for a Wind Pumping Plant Using Induction Generator

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1 Sat id and Renewable Enegy doi:1.4236/ge Publihed Online ay 211 ( Invetigation on the Excitation Capacito fo a Wind Puping Plant Uing Induction eneato anel Ouali ohaed Ben Ali Kaoun ahe Chaabene Univeity of Sfax Unité de Coande de achine et Réeaux de Puiance CERP-ENIS Sfax Tuniia. Eail: anel_zouhi_ouali@yahoo.f; ahechaabane@gail.co; ba.kaoun@eni.nu.tn Received Febuay 27 th 211; evied ach 28 th 211; accepted Apil 2 nd 211. ABSTRACT Thi pape peent a SEI-I yte uing a elf excited induction geneato diven by wind tubine and upplying an induction oto which i coupled to a centifugal pup. A ethod to decibe the teady tate pefoance baed on nodal analyi i peented. Futheoe a dynaic analyi and pefoance chaacteitic ae exained. The popoed ethodology i dicued in ode to optiize the quantity of the puped wate. Theefoe an optial excitation capacito fo a given wind oto peed i deteined and a uitable opeation ode of the yte i etablihed. Keywod: SEI I Centifugal Pup Optial Excitation Capacito Wind Roto Speed 1. Intoduction Owing the inceae of the depletion of conventional enegy and the degadation of envionental condition the developent of uitable iolated powe geneato diven by enewable enegie a ola geotheal bioa hydo and wind enegy eouce ae enviaged to eplace conventional eouce [1]. Wind enegy i conideed the ot adopted attactive and pactical of all enewable enegie a it i available in ot ite. It conit of the conveion of kinetic enegy into a ueful fo of enegy uch a echanical o electical [2]. The ain application i the wind wate puping uing tubine [3]. any type of geneato ae ued fo tand alone powe geneation in eote and windy aea uch a peanent agnet buhle ynchonou aynchonou vaiable eluctance. Self Excited Induction eneato (SEI) i the ot ued fo low and ediu powe geneation thank to it lowe cot eay opeation buhle contuction and eay aintenance. It can utain elf excitation and upply electic powe while an appopiate value of a capacito banc i popely connected aco it tato teinal [45]. SEI diven by egulated o unegulated tubine and upplying a tatic o dynaic load ha been undetaken by any eeache and i well dicued in liteatue [67]. Invetigation in teady tate opeation ae eentially baed on the analyi of the pe phae equivalent cicuit of the thee phae induction achine and on eithe the loop ipedance [8] o the nodal adittance concept [9]. A fo the dynaic and tanient opeation it wa teated fo no load and fo diffeent load: eitive [1] inductive [11] capacitive [12] induction oto [13] DC load etc. In thi context thi wok peent an invetigation on a wind puping plant (SEI-I) uing a SEI diven by wind tubine and upplying an Induction oto (I) which i coupled to a centifugal pup. A SEI-I pefoance analyi i developed o a to deteine the optial excitation capacito which offe axiu puped wate fo a given wind oto peed. Thi pape i oganized a follow: ection two give the yte odeling in tatic and a dynaic tate. Section thee how the coputation pocedue which povide the optial excitation capacito that axiize the volue of the puped wate. Siulation eult ae dicued in ection fou. Finally a concluion eue the developed wok and it featue. 2. Syte odeling 2.1. Syte Configuation The puping unit hown by Figue 1 i copoed of a wind tubine which convet wind kinetic enegy into electicity by ean of SEI. The poduced powe i ued to upply an induction oto coupled to a centifugal wate pup. A the SEI equie eactive powe fo Copyight 211 SciRe. SRE

2 Invetigation on the Excitation Capacito fo a Wind Puping Plant Uing Induction eneato 117 Wind tubine SEI a b c Capacito Bank Figue 1. Wind electic puping yte. it excitation a thee phae capacito bank i connected aco it tato teinal. The I cannot be upplied unle the SEI tato voltage build up poce occu. Fo thi eaon an opeating ode witche elect fit the no load condition ( S O FF ) until the voltage build up poce i accoplihed. Subequently the witche i tuned on ( S ON ) o a to connect the I to the SEI. In ode to analyze the pefoance of elf excited induction geneato witch upplie an induction oto diving wate pup a yte odeling i equied. Following a teady tate and dynaic odeling ae peented Steady State odeling Fo a given excitation capacitance and wind oto peed the teady tate of SEI-I can be tudied unle the tato angula fequency the I angula velocity and the agnetizing inductance of the induction geneato L ae known. By exaining pe phae equivalent cicuit (Figue 2) and conideing the agnetization chaacteitic of both induction achine two equation ae deteined. A thid equation i deduced fo the yte powe balance. All cicuit paaete except the agnetizing inductance L and L ae aued to be contant and inenitive to atuation. In addition coe loe and effect haonic in the achine have been S I Centifugal pup ignoed. The loop equation involving the tato voltage V i witten a: YV V (1) whee Y i the total loop adittance giving by: Y Yot YC Y en (2) The expeion of adittance capacitive Y C i giving by: jc (3) YC The induction geneato adittance a: Y en Y Y ' Y Yen Y Y ' Y 1 1 Y ; Y' jl R ' jl' 1 Y R jl i expeed A a conequence of the yety of pe phae equivalent cicuit the expeion of induction oto adittance Yot can be deduced fo that of Yen by eplacing the index by and by. Since unde teady tate excitation V it iplie that Y o both eal and iaginay pat of Y ae equal to zeo: F1 Re Y F2 I Y While the otational lo toque the windage loe and daping facto ae ignoed the echanical powe of induction oto i equal to that of centifugal pup P ec _ pup P ec _ ot (4) (5) and it can be expeed a a function of Y ot Y C Y en j L' R j L R j L j L' I R' j L V j L R' Figue 2. Pe phae equivalent cicuit of elf excited induction geneato feeding an induction pup oto. Copyight 211 SciRe. SRE

3 118 Invetigation on the Excitation Capacito fo a Wind Puping Plant Uing Induction eneato the equivalent cicuit paaete: F P P (6) 3 ec ot ec pup 1 R ' P R I I 2 2 ec _ 3 ' ' 3 ' ot 2 ec _ pup pup (7) The echanical powe of the centifugal pup i giving by [14]: P T K (8) whee the T pup i the load toque of the pup and K i a coefficient coputed by: Tp ax K (9) ax Tp i the axiu ated toque and i the ax ax axiu ated echanical oto peed. The I oto cuent expeion can by obtained by the application of voltage divide theoe to the oto cicuit odel: ' // V ' I' V (1) ' // The tato voltage can alo be expeed by the application of voltage divide theoe to the geneato cicuit odel: ' V V ' (11) whee 1 ' Y ' 1 Y 1 Y V I. The oto ipedance expeion ' ae calculated by the ae way a above by eplacing the index by and by in expeion of '. ' ' I' I ' ' ' (12) The I agnetizing cuent I i foulated a a function of I ' : ' I I ' (13) Equation (5) and (6) ae nonlinea whee C L and ae unknown vaiable. Theefoe in ode to olve thee equation two of thee vaiable ut be pecified. Two appoache ae conideed in liteatue [8915]: To deteine the teady tate pefoance of the SEI-I yte and C ut be pecified and the equation ut be olved fo L. To deteine the iniu cap acito value equied fo the onet of elf-excitation poce C in SEI I L and ut be pecified and the equation ut be olved fo C. The above entioned equation can be olved by adopting the ethod of Newton Raphon and calculating the coeponding Jacobian atix. Since atuation phenoenon i a ignificant facto in the pocee of elf excited induction geneato the vaiation of agnetic geneato inductance L hould be taken into conideation to find the coect voltage build up. Theefoe at each apling tep the value of the agnetic geneato cuent I i adjuted accoding to L thank to a pline intepolation of the geneato agnetization eaued chaacteitic. Then I i coputed uing Equation 12 and 13. Finally L i adjuted accoding to the I value thank to a pline intepolation of the oto agnetizing ea- ued chaacteitic Dynaic State odeling In ode to analyze the tanient epone of SEI-I a dynaic yte odeling of the SEI the I and the centifugal pup i neceay Induction achine odel Uing the geneato convention the voltage equation of the SEI ae expeed a: d V R I dt (14) d ' R' I' ' j dt whee the fluxe of the SEI ae giving by: L I L ' I o (15) ' L I L' ' I o o epeent the initial eidual flux. The geneato agnetizing flux i coputed by: L L' L L ' L L' o 2 L L' L (16) In the ae way and by adopting the oto convention the voltage equation and fluxe of I ae epectively Copyight 211 SciRe. SRE

4 Invetigation on the Excitation Capacito fo a Wind Puping Plant Uing Induction eneato 119 given by: d V R I dt d ' R' I' j ' dt L I L I ' L' I' L I The oto agnetizing flux i coputed by: L L' L L 2 L L' L ' The tato voltage of both achine i expeed a: (17) (18) (19) 1 V V V I C dt C (2) I C epeent the capacity cuent. It i given by: I I I (21) C To take account of the non lineaity of the agnetic ateial the agnetization cuve of both achine SEI and I ae ipleented in thei odel: at each apling tep the value of L and L ae adjuted. The echanical equation that decibe thi yte i: d p Te T pup (22) dt J whee Te and Tpup epeent epectively the elec- toagnetic toque poduced by I and the load toque of the pup Centifugal Pup odel Due to echanical loe the ueful powe of centifugal pup coupled to the haft of I i: P P g H Q (23) u pup w whee Ppup i the echanical powe given by Equation (8) epeent the pup efficiency w i the wate denity ( Kg ) g i the gavity acceleation 2 3 ( S ) H i the height of ie ( ) and Q i the flow 3 ( S ). Fo a puping peiod T the volue of 3 pu ped wate ( ) i coputed by: V Q T (24) 3. Deteination of the Optial Capacito The wok ai to axiize the aount of the puped wate by iniizing the excitation capacitance value. Refeing to Equation 8 23 and 24 the volue of the puped wate inceae while aiing the I echanical powe (oto peed). Thi i enued by iniizing the excitation capacitance value. Theefoe the citeion defined by iniize C o that i axiu ut be checked uing an iteative pocedue. Fit it i neceay to deteine the iniu excitation capacitance value fo which the SEI tato voltage build upoccu at I load opeation ( C in ). Then the SEII axiu excitation capacitance ( Cax ) i calcu- SEII lated conideing the liitation of the cuent tato at 12% of it noinal value to avoid detuctive ove cuent which caue eiou daage to the yte equipent. Finally the following tep ae to poceed: 1) Fo a given wind oto peed the excitation capacitance i aued equal to C in SEII fo which the paaete of the centifugal pup the paaete of the two achine and thei agnetization chaacteitic ae defined. 2) The Newton Raphon iteative ethod i ued a follow: a) The initial condition ae fixed and the ubtitution of paaete adopted in the eolution of Equation 1-13 ae calculated. b) The F F1 F2 F3 vecto the coeponding Jacobian a tix and the X L vecto ae deteined. c) The L value i etiated uing L value agnetic chaacteitic of both achine and Equation d) Uing the new obtained value epeat tep a b and c until the eo on the vecto X i le than a given peciion. In thi cae the convegence i conideed eached. 3) The obtained value of i aved and then the excitation capacitance i inceented by 5 F. 4) Repeat tep 2 and 3 until C va lue i equal o geate then Cax SEI I. Thu fo each value of a databae i etablihed in ode to tudy the I wind oto vaiation function of the excitation capacitance. The iniu value of C fo which becoe axiu and ubtantially con- and tant i choen. Thi value i conideed a the optial capacito. 4. Reult Dicuion The popoed ethod of evaluating the teady and dy- naic tate chaacteitic of a SEI-I i teted efeing to a thee-phae induction geneato: 4.4 Kw 22 / 38 V 16.8 / 9.7 A 5 Hz. Thi late upplie an induction oto: 1.5 Kw 22 / 38 V 8 / 5.6 A 5 Hz. The fixed paaete of both induction achine ued Copyight 211 SciRe. SRE

5 12 Invetigation on The Excitation Capacito fo a Wind Puping Plant Uing Induction eneato in iulation ae: RS 5 R' 5.7 P 2 L L.34H RS 1.2 R' P 2 L L'.56H The agnetizing inductance of the both induction achine ae eaued a a function of the agnetizing cuent by pefoing an open cicuit tet fo which the achine ae diven at ynchonou peed and a vaiable voltage ouce i applied to the tato (Figue 3) Steady State Reult The behaviou of the tato v oltage V the I tato cuent I the I tato cuent I and the fequency ae plotted a a function of the excitation capacitance and the wind oto peed. The cuve netwok fo n 1 d and diffeent value of u (a tep of wn.25 i conideed) ae hown by Figue 4 and 5. It i noticed that the inceae in C caue a gadually inceae of V I and I. A fo the fequency f it inceae then eain contant. A iila cuve et of Ppup C fo diffeent value of u i hown by Figue 6. Fo each cuve it i clea that by inceaing C fo Cin SEII to Cax SEI I Ppup inceae gadually. Nevethele ince a cetain value of C Ppup becoe axiu and ubtantially contant. At thi functional point the obtained value of C i conideed a optial C. opt.2.18 L en (I en ) L ot (I ot ) L (H) I (A) Figue 3. agnetization chaacteitic of both induction. Vg(C) V (C) u u=1.1 = u u=.9 = C(µF) Ig(C) I (C) u u=1.1 u u=.9= C(µF) Figue 4. V I vaiation function of excitation capacitance fo vaiou value of u. Copyight 211 SciRe. SRE

6 Invetigation on the Excitation Capacito fo a Wind Puping Plant Uing Induction eneato 121 I I (C) (C) 1 u u=1.1 = 5 u u=.9= C(µF) 6 55 u u=1.1 = Figue 5. f f(c) I f vaiation function of excitation capacitance fo vaiou value of u u u=.9 = C(µF) Copt u u=1.1 = P pup (C) Ppup (C) u u=.9 = Figue 6. C C( (µf) F ) Ppup ( C ) chaacteitic fo vaiou Dynaic Reult In ode to deteine the uitable opeation ode of SEI-I yte diven by wind tubine at n the effect of the capacitance value on the tato voltag e wavefo i tudied. Fitly C i equal to Cin SEI I. It i hown that the elf excitation poce doe not occu (Figue 7). Thi pove the neceity of functioning in two tage. The induction geneato i elf excited at no load ( S OFF in fit tage) V a i etablihed and eache it tead y tate value; then the oto pup tat opeation afte a delay of about 1.5 (S ON in econd tage). Secondly when C i equal to C inat no load duing the two tage the tato voltage i etablihed in fit tage and deceae apidly to be eliinated duing the econd tage (at I opeation) (Figue 8). Subequently C i equal to C duing the insei I two tage (Figue 9(a) and 9(b)). The elf excitation poce i well etablihed and aintained but V a and I a can each peak at no load opeation. Thi phenoenon i epecially ipotant when woking at high wind oto peed. Hence the value of C i fixed at C in at no load duing the fit tage and epectively at Cin SEI I C C duing the econd tage (Figue 1 ax SEII and opt Copyight 211 SciRe. SRE

7 122 Invetigation on the Excitation Capacito fo a Wind Puping Plant Uing Induction eneato C = C insei SEII I 1.5 Va V a Va V a Figue 7. Vaiation with tie at V a C C in. SEII C = C in at no atload no duing load duing the two the two tage of opeation tage of opeation Figue 8. Va() t chaacteitic at C C duing the two tage of opeation. insei I (a) 4 2 V a fo C = C in at no load fo two tage of opeation V a fo C= C in at no load fo two tage of opeation 2-2 (b) Figue I a fo C = C in at no load fo two tage of opeation Va tand Ia I a fo C= C n at no loa fo two tage of opeation i d t chaacteitic at C C duing the two tage. in SEII Copyight 211 SciRe. SRE

8 Invetigation on the Excitation Capacito fo a Wind Puping Plant Uing Induction eneato 123 (a) 5 V a fo C =f it C in at no load then V a fo C=f it C in at no load then C Cin SEII (b) VV a a fo C=fC =f it it C in in at at no load then C Cax SEII SEII 5 (c) V a Vfo a C fo =f C=f it it C in C in at no at load no then load Copt then Copt Figue 1. V a Vaiation with tie at diffeent ode of opeation w ω 15 1 C=C C C inseii SEII C=C C C axseii C=C C C opt Figue vaiation with tie at diffeent ode of opeation. Ia Ia Ia Ia Figue 12. I a and I a vaiation with tie at adequate opeation ode. Copyight 211 SciRe. SRE

9 124 Invetigation on The Excitation Capacito fo a Wind Puping Plant Uing Induction eneato 2 15 I I L Figue 13. I and L vaiation with tie at adequate opeation ode. 3 2 Ia Ia Ia Figue 14. Ia and Ia vaiation with tie at adequate opeation ode. (a)-1(c)). The elf excitation poce i conequently etablihed and aintained. Fo the ae cenaio of capacitance value the vaiation a a function of tie i peented ented (Figue 11) and thei teady tate value duing the econd p hae noted by ae exained. It how that ax SEII in SEI I. ax SEI I and in SEII opt opt opt a a Thi pove the jutification of the choice of the value C opt calculated in the tatic tate teady. Theefoe the appopiate opeation ode of SEI i that fo which C i equal to C inat no load duing the fit tage and equal to C opt duing the econd tage. Figue how the vaiation of I a I a I L I and I a a function of tie. The con- tinuou line cuve ae the cuve obtained in dynaic ode and thoe in boken line ae obtained in tatic ode. ood ageeent between the two eult a e con- fi ed. 5. Concluion In ode to optiize the quantity of the puped wate an effect of an excitation capacito on the teady tate behaviou of the SEI-I plant i tudied to enable elecvalue fo a giving wind oto. tion of optial capacitance A teady tate analyi i exained uing the nodal adittance concept and the pe phae equivalent cicuit which epeent the odel of thi plant. The tanient pefoance of SEI-I yte i oeove peented and exained to deteine the uitable opeation ode of thi yte. Copyight 211 SciRe. SRE

10 Invetigation on the Excitation Capacito fo a Wind Puping Plant Uing Induction eneato 125 REFERENCES [1] A.. Oe Enegy Envionent and Sutainable Developent Renewable and Sutainable Enegy Review Vol. 12 No pp doi:1.116/j.e [2] B.. ite Electic Wind Puping fo eeting Off- id Counity Wate Deand uelph Engineeing Jounal Vol pp [3]. S. ianda R. O. Lya and S. R. Silva An Altenative Iolated Wind Electic Puping Syte Uing Induction achine IEEE Tanaction on Enegy Conveion Vol. 14 No. 4 Decebe 1999 pp doi:1.119/ [4] N. H. alik and A. H. AI-Bahani Influence of the Teinal Capacito on the Pefoance Chaacteitic of a Self Excited Induction eneato IEE Poceeding C: eneation Taniion and Ditibution Vol. 137 No. 2 ach 199 pp [5] K. Idjdaene D. Rekioua T. Rekioua and A. Tounzi Vecto Contol of Autonoou Induction eneato Taking Satuation Effect into Account Enegy Conveion and anageent Vol. 49 No pp doi:1.116/j.enconan [6] R. C. Banal Thee-Phae Self-Excited Induction eneato: An Oveview IEEE Tanaction on Enegy Conveion Vol. 2 No. 2 June 25 pp doi:1.119/tec [7]. K. Singh Self-Excited Induction eneato Reeach A Suvey Electic Powe Syte Reeach Vol. 69 No pp doi:1.116/j.ep [8]. H. Haque Copaion of Steady State Chaacteitic of Shunt Shot-Shunt and Long-Shunt Induction eneato Electic Powe Syte Reeach Vol. 79 No pp doi:1.116/j.ep [9] K. A. Nigi.. A. Salaa and. Kazeani Identifying achine Paaete Influencing the Opeation of the Self-Excited Induction eneato Electic Powe Syte Reeach Vol. 69 No pp doi:1.116/j.ep [1] I.. Katinioti.. Ioannide and P.. Venado Opeation of Induction eneato in the agnetic Satuation Region a a Self-Excited and a a Double Output Syte Jounal of ateial Poceing Technology Vol. 161 No pp doi:1.116/j.jatpotec [11] L. Wang and Ch.-H. Lee A Novel Analyi on the Pefoance of an Iolated Self Excited Induction eneato IEEE Tanaction on Enegy Conveion Vol. 12 No. 2 June 1997 pp doi:1.1 19/ [12]. H. Salaa and P.. Hole Tanient and teady State Load Pefoance of a Stand Alone Self Excited Induction eneato IEE Poceeding Electic Powe Application Vol. 143 No. 1 Januay 1996 pp doi:1.149/ip-epa:19962 [13] B. Singh L. Shidha and C. S. Jha Tanient Analyi of Self-Excited Induction eneato Supplying Dynaic Load Electic achine And Powe Syte Vol. 27 No pp doi:1.18/ [14] S. Salle. Chaabene and. B. A. Kaoun Enegy anageent Algoith fo an Optiu Contol of a Photovoltaic Wate Puping Syte Applied Enegy Vol. 86 No pp doi:1.116/j.apenegy [15] R. J. Haington and F... Baiouny New Appoach to Deteine the Citical Capacitance fo Self- Excited Induction eneato IEEE Tanaction on Enegy Conveion Vol. 13 No. 3 Septebe 1998 pp doi:1.119/ Noenclatue R R : Stato and oto eitance L L : Stato and oto leakage inductance L : Cyclic tato utual inductance C : Excitation capacito : Stato angula fequency : Roto electical angula peed : echanical oto peed tand fo induction geneato and induc- : Induction oto lip p : Nube of pole pai of induction oto J : Inetia oent of I j : Iaginay opeato Supecipt ' denote the tanfoed oto quantitie baed on the tato. Indice and tand fo tato and oto epectively while and tion oto epectively. Copyight 211 SciRe. SRE