Comparison and Evaluation of Induction Generator Models in Wind Turbine Systems for Transient Stability of Power System

Transcription

1 Comparion an Ealuation of Inuction enerator oel in Win urbine Sytem for ranient Stability of Power Sytem H. Li, Z. Chen, Senior ember, IEEE an L. Han Abtract-- In orer to analyze the tranient tability of griconnecte uiel cage inuction generator (SCI) in win power generating ytem, ariou mathematical moel, incluing the etaile an reuce generator moel a well a the one-ma an two-ma haft ytem moel, are tuie in thi paper. ae on the ifferent win turbine ytem moel, the ynamic behaior are imulate an compare by uing atlab/simulink, uner the conition that the generator tator terminal i ubjecte to a three-phae hort-circuit fault. In aition, the critical clearing time (CC) i calculate an compare by uing a irect metho with critical clearing lip of inuction generator an a metho of trial an eor by imulation, for ifferent ytem moel at the ariou operation conition. he moel an metho uitable to analyze the tranient tability of the win turbine ytem bae on SCI are icue in etail. Seeral comparatie reult hae hown that the ali tranient tability moel of SCI in win turbine ytem ha to incorporate the two-ma haft ytem moel, the irect metho of CC etimation bae on critical clearing lip i incompatible to etermine the tranient tability limit, owing to the large multi-ocillation of the generator rotor pee uring the fault perio. Inex erm Win turbine; inuction generation; critical clearing time; tranient tability; moel I. INRODUCION ri-connecte uiel cage inuction generator (SCI) are an important alternatie for large-cale win farm becaue of it rotor tructure, implicity of contruction an maintenance-free operation. A the penetration of win power in electrical power ytem increae, win turbine may begin to influence oerall power ytem operation [][2]. So it i ery neceary an important to tuy the tranient tability of the win farm with SCI [-4]. It i well known that a eere oltage ag ue to a fault in the connecting network may caue a ignificant pee increae of the turbine an generator rotor. After oltage recoery, the rotor pee of the SCI may be o H. Li i with the chool of Electrical Engineering, Chonging Unierity, Chongng, 444 China ( culh@63.com). Z. Chen. i with the iniitute of Energy echnology, Aalborg Unierity, DK-922 Aalborg Eat, Denmark( zch@iet.aau.k). L. Han i with the chool of Electrical Engineering, Chonging Unierity, Chongng, 444 China ( hanli@cu.eu.cn). high that it oe not return to a table alue. A efinition i gien which refer to the ability of an inuction machine to remain the connection to the electric power ytem an running at a mechanical pee cloe to the pee coeponing to actual ytem freuency after being ubjecte to a large iturbance. he efinition of the tranient tability i ifferent from rotor angle tability of conentional ynchronou generator an oltage tability of power ytem [5]. With the large-cale win power integration into the tranmiion electric power network, how to ae effectiely the tranient tability limit of SCI bae on win turbine ytem i increaingly attraction in power ytem ecurity an reliability. A general, the critical clearing time (CC) i etermine a a criterion for tranient tability of power ytem. etho of tranient tability etimation may be iie into numerical analyi techniue (e.g. time omain imulation) an irect metho [6][7]. In the former cae, tranient tability analyi i performe by utilitie excluiely by mean of the numerical integration of nonlinear ifferential euation ecribing the on-fault an pot-fault ytem, which i extremely inefficient for on-line etimation of tability limit of large power ytem an it nonlinear nature [7]. In the latter cae, the poible range of ytem tranient tability i etimate by uing a limite alue (threhol). So trial an eor proceing i unneceary in the irect metho, it i efficient to achiee fater computational tability limit, to obtain ualitatie information on ytem tability behaior, an to ientify the critical generator that are eerely affecte by the iturbance. Due to thee promiing feature, it ha become an effectie online tranient tability etimation metho in conentional power ytem. In orer to tuy the ynamic tability an it impact to the gri, there are a few literature to preent ome moel an metho of tranient tability analyi of inuction generator [3][4][8-4]. Howeer, the conentional tep-by-tep timeomain imulation metho i common choice for the tranient tability analyi of SCI. ae on the firt-orer generator moel, the imple metho of CC calculation i preente in [9], but it i epenent on the characteritic of teay tate toue-lip. Coniering the pee contribution of the haft tiffne of the win turbine rie train, a irect metho by calculating the generator pee with the on-fault trajectory an

2 2 compare with critical clearing pee of SCI i preente in [4], but thi metho i alo bae on the teay tate touelip characteritic. So it i worthy of ealuating an etermining the tranient tability limit of SCI in win turbine ytem. In orer to compare an analyze the aliity of the aement of the tranient tability limit of win turbine ytem bae on SCI, ome ifferent ytem moel incluing the etaile an reuce generator tranient moel, the one-ma an twoma haft moel are preente in thi paper. When the generator tator terminal i ubjecte to a three-phae hortcircuit fault, the ynamical behaior for ifferent ytem moel are imulate an compare by uing atlab/simulink. he CC i calculate an compare for ifferent win turbine ytem moel in the ariou initial operation conition, by uing the irect metho bae on critical clearing lip of inuction generator an the conentional tepby-tep time-omain imulation metho. he moel uitable to tranient tability analyi of win turbine ytem bae on SCI i obtaine; the irect metho of etermining the tranient tability limit i ealuate by ariou comparatie reult. II. SAILIY LII OF SCI IN WIND URINE SYSES In orer to theoretically analyze the tranient tability limit of gri-connecte SCI, a three-phae hort-circuit fault at the generator tator terminal i coniere a a large electrical iturbance, the teay tate toue-lip characteritic i ue. he firt-orer motion euation can be ecribe a 2 H = e m () t Where H i the um of contant inertia of the rotating ma in per unit; i the lip of SCI; e i the electromagnetic toue of SCI; m i the input mechanical toue from the win turbine. At the teay-tate conition, the electromagnetic toue, e, i eual to the mechanical toue, m, an the machine i operating at the lip, a hown in Fig.. Immeiately after e m ime t cr 3 e -lip cure cr 2 lip t t cr 2 lip Fig. Configuration of oue-lip an time-lip cure for threephae hort-circuit fault 2 the fault occur, e woul be zero (if the electrical tranient are ignore), while the lip remain at. hu, there i a net accelerating toue an the lip graually increae accoring to the aboe euation. If the fault i cleare at a lip, then e i aume to increae intantaneouly (auming the pot-fault oltage i the ame a the pre-fault). Howeer, the lip remain the ame, at thi operating point, the electrical toue i higher than the mechanical toue, the rotor ecelerate (cure- of the lip-time cure in Fig..) an return back to the original lip.intea of clearing the fault at lip, if the fault i cleare at a lip 2, then een the e increae from zero, it will be le than m an the machine continue to accelerate, o the SCI will become intable for it oer pee, which i hown a cure-2 of lip-time cure in Fig.. Similar ynamic behaiour can be expecte, if the fault i cleare at any point beyon the lip cr in Fig.. herefore, the lip cr can be calle a the critical clearing lip for thi operating point; an it coeponing pee i critical clearing pee [9][4]. hi implie that the fault i cleare before the lip reache cr, the generator will not be oer-pee an not be iconnecte gri. It i noticeable that the obtaine concluion i completely epenent on the teay tate toue-lip cure of inuction generator. Incorporating the generator electrical tranient an the low haft tiffne feature of the win turbine mechanical ytem, it may be incapable of etermining the tranient tability limit of win turbine ytem. Unlike the team an the hyro unit, apart from the ifference in the ource of conentional energy, the inuction generator in win turbine ytem i feature by haing high turbine inertia by comparion with generator rotor an low tiffne of the haft between the turbine an generator. During the power ytem fault conition, e collape an the tore potential in the win turbine haft i releae an tranforme into kinetic energy of the generator. y uing the law of coneration of mechanical energy, the pee change of the generator rotor after a fault inception can be expree [4] = (2) H K Where H i per unit inertia contant of SCI; K i the win turbine haft tiffne. It i imple that the effect of the low haft tiffne to tranient tability limit of win turbine ytem i the pee change of the generator rotor in euation (2), the implementation of thi irect metho of the CC etimation i ecribe in [4]. ut thi metho i alo epenent on the critical clearing lip of SCI bae on the teay tate touelip cure, o it aliity nee to be icue in etail. III. DIFFEREN ODELS OF WIND URINE SYSES A. Different Inuction enerator oel Accoring to a tanar per-unit notation [3], in the ynchronouly rotating frame, the inuction generator can be

3 3 repreente by the etaile ifferential euation of the flux linkage. r = Ri ψ (3) = Ri + ψ (4) = Rrir ψ r (5) = Rri + ψ r (6) Where i the ynchronou pee (in per-unit, = ); i the ytem bae freuency which i eual to the ynchronou freuency, = 2πf ; p i the /t operator. he electromagnetic toue, e, can be expree a e = L i i i i ) (7) m ( r he contitutie flux linkage-cuent relationhip are = L i L i ψ (8) m r ψ = L i L i (9) r = L i L m m i ψ () m r ψ = L i L i () Coniering generator are uually repreente a a oltage ource behin tranient impeance in power ytem tability tuie, the etaile tranient moel of SCI can be etablihe a (where the an component of rotor oltage are zero, repectiely). X pi X X = ( R + ) i (2) + ( ) E E + X i X X X pi = ( R + ) i X i (3) + ( ) E + E = ( E ( X X ) i ) + E = ( E + ( X X ) i ) E (4) (5) = E i + E i (6) e Where 2 ( ) Lm X = L = Lσ + Lm ; X = ( L ) ; L = L E m ; Rr L L Lm = ψ ; E = ψ r L If the tator tranient are ery fat, when compare with the rotor one, it i poible to neglect them. Upon neglecting the tator flux linkage tranient, the reuce tranient moel of SCI are obtaine by taking euation (3) an (4) a algebraic euation = R i + X i + E (7) = R i X i + E (8) e = ( E ( X X ) i ) + E = ( E + ( X X ) i ) E (9) (2) = E i + E i (2). Different mechanical rie train ytem moel Coniering the feature of low tiffne of the haft between the turbine an generator, the two-ma rie train moel can be expree a t θ 2 H = m K (22) 2 H K e (23) θ t Where t = θ = ( ) (24) H, H are the inertia contant of the win turbine rotor an the generator rotor, repectiely., are the win turbine an generator pee, repectiely. K i the haft tiffne; θ i the haft tenional twit angle. If the win turbine, gearbox, haft an generator are lumpe together into an euialent ma, the rie train moel of win turbine i ecribe a the one-ma moel, which i preente in euation (), here, the lumpe inertia contant i the um of the turbine rotor an the generator rotor.

4 4 IV. RANSIEN EHAVIOR ANALYSIS AND COPARISON FOR DIFFEREN SYSE ODELS In orer to analyze the tranient behaiour of ifferent ytem moel, an tetify the aliity of the irect metho of CC calculation bae on the critical clearing lip, the tranient tability of SCI in win turbine ytem i compare an analyze for the ifferent generator moel an the win turbine rie train moel at the ariou initial ytem operation conition. he four ifferent ytem moel are aopte an ecribe in ALE I. ALE I DESCRIPION OF DIFFEREN SYSE ODELS Symbol Electrical euation echanical moel DD Detaile tranient moel (2)-(6) wo-ma moel (22)-(24) RD Reuce tranient moel (7)-(2) wo-ma moel (22)-(24) RS Reuce tranient moel (7)-(2) One-ma moel () SS Steay tate moel One-ma moel () he ytem coniere i a ingle SCI euialent win farm connecte to an infinite bu through a ouble circuit tranmiion line a hown in Fig.2. he main ata of SCI an ytem parameter are ecribe in ALE II. gearbox Win turbine SCI Fault ranformer Fig.2 Configuration of SCI in win turbine ytem Stiff gri ALE II SCI DAA AND SYSE PARAENS ain parameter Value Rate power P N (W) 3 Rate oltage U N (V) 575 Rate freuency f N (Hz) 6 Stator reitance R (p.u.).4843 Rotor reitance R r (p.u.).4347 Stator leakage inuctance X σ (p.u.).248 Rotor leakage inuctance X rσ (p.u.).79 utual inuctance X m (p.u.) 6.77 enerator rotor inertia contant H () in per unit.5 Win turbine rotor inertia contant H () in per unit 4.54 Shaft tiffne K (p.u./el.ra).3 ranformation reactance X tr (p.u.).25 A ingle tranmiion line reactance X l (p.u.).3 A. ranient behaior imulation In the following imulation, auming the initial input mechanical toue m i normal toue. he three-phae hortcircuit fault at the tator terminal of SCI occur at the time t=2, the generator rotor pee, tator oltage an actie power are imulate for the cae of the critical table an an untable cae, repectiely. he tranient behaior of ifferent ytem moel are hown in Fig. 3. Where tcf an tcr are faultclearing time. he tcr i critical clearing time, obtaine by the trial an eor metho. A it can be een that the generator rotor pee an actie power preent large ocillation uring the on-fault an potfault for the cae of the two-ma haft ytem moel, o that the tability region i reuce in comparion with the one-ma a) DD ytem moel b) RD ytem moel c) RS ytem moel ) SS ytem moel Fig.3 ranient behaior of win turbine ytem for ifferent ytem moel

5 haft moel. he tranient behaior are imilar between the DD moel an RD moel, een though the obtaine CC of RD moel i maller than the cae of DD moel. In aition, the behaior are alo imilar between RS moel an SS moel, howeer, the SS moel i o imple that the actie power elom occur ocillation at the moment of clearing fault, an the CC i too optimitic. Comparion with SS moel, the actie power an pee occur ome ocillation in RS moel, owing to coniering with the rotor electrical tranient. ALE III. CC etimation HE CALCULAION RESULS OF CC FOR DIFFEREN SYSE ODELS ae on the irect metho of CC etimation with the critical clearing lip of generator toue-lip cure in teay tate conition, CC i calculate an compare for ifferent ytem moel on the conition of ariou initial input mechanical toue. Detaile reult are hown in ALE III. Where CS enote the irect metho bae on the critical clearing lip; E enote the trial an eor metho by imulation. Initial input CC () mechanical toue DD moel RD moel RS moel SS moel m (p.u.) CS E CS E CS E CR E.58,.3,.57,.97, ,.296,.568,.965, ,.32,.578,.985, ,.32,.574,.983, ,.35,.62,.2,..64.9,.33,.592,.2, ,.464,.64,.594, ,.454,.632,.58, ,.26, ,.4, ,.684, ,.654, From the reult in ALE III, ome cenario are obtaine a () At the ame conition of input mechanical toue, the CC calculation with the two- ma haft moel i maller than that of the one-ma haft moel by uing E metho. Furthermore, with the input mechanical toue increae, the ifference of CC calculation i more an more obiou, epecially at the normal operation conition, the CC i almot. with the two-ma haft moel, howeer, it i about.36 with the onema haft moel. (2) It i noticeable that eeral ifferent time alue are obtaine in DD moel an RD moel by uing CS metho at the ame initial input mechanical toue, an all of them aren t cloe to CC alue obtaine by E metho. hat i to ay, the CS metho i inali to calculate the CC in DD moel an RD moel. In orer to explain the multi-alue of the twoma haft moel, the repone of generator pee of RD moel an RS moel uring the fault perio are hown in Fig. 4, where the initial input mechanical toue i normal alue. Fig.4 generator rotor pee cure of RD moel an RS moel uring the fault perio A it can be een from Fig.4, the electromechanical interaction i een a tenional ocillation in the haft ytem euippe with gearboxe, the generator rotor pee cure of RD moel appear large multi-wing uring the fault perio, o that there are ome ifferent time alue coeponing to the ame critical clearing pee wcr. In aition, the generator rotor pee repone of RD moel i almot a line, therefore there i an only cro point between the cure of pee change an the critical clearing pee. (3) here are alo a few icrepancie of CC calculation in RS moel by uing the two metho; een though only coniering with the rotor electrical tranient, the CC calculation i almot compatible to the SS moel by uing the two metho. C. Dicuion () From the comparatie reult of the tranient behaior imulation an CC etimation, it can be een that the moel of tranient tability analyi of fixe-pee win turbine ytem houl be repreente with the two-ma haft moel of win turbine rie train ytem. A far a the inuction generator tranient moel are concerne, the reuce moel neglecting the tator electrical tranient can be ue to analyze the tranient tability, een though the calculate CC of RD i maller than in the cae of DD moel. (2) he metho of CC calculation bae on the teaytate critical clearing lip of SCI i incapable of etermining the tranient tability limit of the win turbine ytem, becaue the generator rotor pee may preent multi-wing uring the fault perio. So the uitable metho of tranient tability analyi of win turbine ytem nee to be tuie. V. CONCLUSIONS In orer to inetigate the moel an metho for the tranient tability analyi of win turbine ytem with SCI,

6 6 ome metho of etermining the tability limit bae on the critical clearing lip of SCI are preente. Seeral ytem moel incluing the ifferent generator moel an rie train moel of win turbine are etablihe in thi paper. ae on the four ifferent ytem tranient moel, the tranient behaior are imulate an compare when the tator terminal of SCI i ubjecte to the three-phae hortcircuit fault. he CC i calculate an compare by uing the CS an E metho. he moel an metho of tranient tability analyi of win turbine ytem bae on SCI are icuion in etail. he obtaine reult hae hown that the win turbine ytem moel incorporating the two-ma haft moel i uitable to the tranient tability analyi; the irect metho of calculation CC bae on the critical clearing lip i incapable of etermining the tranient tability limit, ue to the multi-ocillation of generator rotor pee uring the fault perio. VI. REFERENCES [] Z.Chen, "Iue of connecting win farm into power ytem," in 25 IEEE/PES ranmiion an Ditribution Conference& Exhibition: Aia an Pacific, Dalian,China, pp [2] C. C. Inwai, W. J. Lee, P. Fuangfoo, etal, "Sytem impact tuy for the interconnection of win generation an utility ytem," IEEE ran. on Inutry Application, ol. 4, no., 25, pp [3] D. J. runowki, A. entile, J.. Khan, E.. Petritz, "Fixe-pee win-generator an win-park moelling for tranient tability tuie," IEEE ran. on Power Sytem, ol. 9, no. 4, 24, pp [4] V.Akhmato an A.H. Nielen, "Fixe-pee actie-tall win turbine in offhore application," European ran. on Electrical Power, ol. 5, 25, pp. -2. [5] O. Samuelon an S. Linahl, "On pee tability," IEEE ran. on Power ytem, ol. 2, no. 2, 25, pp [6] P. Kunur an J. Paerba, "Definition an claification of power ytem tability," IEEE ran. on Power Sytem, ol. 9, no. 2, 24, pp [7] A. A. Foua an Vijay Vittal, Power Sytem ranient Stability Analyi Uing the ranient Energy Function etho, Prentice Hall Englewoo Cliff, NJ 7632, 992 [8] L. Holworth, X.. Wu, J.. Ekanayake, N. Jenkin, "Comparion of fixe pee an oubly-fe inuction win turbine uring power ytem iturbance," IEE Proc. eneration, ranmiion an Ditribution, ol. 5, no. 3, 23, pp [9] K. C. Diya an P. S. Nagenra Rao "Stuy of ynamic behaiour of gri connecte inuction generator," in 24 IEEE Power Engineering Society eneral eeting, pp [] Z. F. Quang,. Joo,. O. oon, "AC power tranmiion from remote large-cale win park bae on uiel-cage inuction generator," in 24 Internation Conference on Power Sytem echnology- POWERCON 24, Singapore, pp []. Francoie an C. P. ikah, "oelling an mall-ignal analyi of a gri connecte oubly fe inuction generator," in 25 IEEE Power Engineering Society eneral eeting, pp [2].. Nomiko an C. D. Vourna, "Inetigation of inuction machine contribution to power ytem ocillation," IEEE ran. on Power ytem, ol. 2, no. 2, 25, pp [3] W. S. ota, L. S. ao, F.. P. Pamplona, A. N. Epaminona, E. R.. Filho, A. A. F. Santo, "Win generation ynamic imulation connecte to an electric power ytem," in 24 IEEE/PES ranmiion & Ditribution Conference & Expoition: Latin America, pp [4] S. K. Salman an A. L. J. eo, "Inetigation into the etimation of the critical clearing time of a gri connecte win power bae embee generator," in 22 IEEE/PES ranmiion an Ditribution Conference an Exhibition, Aia Pacific, pp VII. IORAPHIES H. Li receie the.eng. egree an Ph. D egree in electrical engineering from Chonging Unierity, Chonging, China, in 2 an 24, repectiely. He wa a Lecturer an then an aociate profeor of Electrical achinery an Apparatu at Chonging Unierity, China, ince 22. Cuently, he i a iiting reearcher in the Intitute of Energy echnology, Aalborg Unierity, Denmark. Hi main reearch area are renewable energy an itribute generation Zhe Chen ( 95-S 98) receie the.eng. an.sc. egree from Northeat China Intitute of Electric Power Engineering, Jilin City, China, an the Ph.D. egree from he Unierity of Durham, Durham, U.K. He wa a Lecturer an then a Senior Lecturer with De ontfort Unierity, U.K. Since 22, Dr. Chen ha been a Reearch Profeor with the Intitute of Energy echnology (IE), Aalborg Unierity, Aalborg, Denmark. He i the coorinator of the Win urbine Reearch Program at IE. Hi main reearch area are renewable energy an itribute generation, power electronic, power ytem an protection. He ha more than publication in hi fiel. Dr. Chen i an Aociate Eitor of the IEEE ranaction on Power Electronic, a member of the Intitution of Electrical Engineer (Lonon, U.K.), an i a Chartere Engineer in the U.K. L. Han receie the.eng. egree in electrical engineering from Chonging Unierity, Chonging, China in 986. He wa a iiting cholar of Unierity of echnology, Syney, Autralia in 24. He i now an aociate profeor an ice ean of the College of Electrical Engineering, Chonging Unierity, China. Hi main reearch interet are optimal eign of electric machine an numerical computation of electromagnetic fiel in electric machine.