DYNAMIC STABILITY STUDY AND SIMULATION OF THE SYNCHRONOUS MACHINE COUPLED WITH THE NETWORK BY A LINE AND A LOAD IN PARALLEL

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1 IJRRAS 9 (2) Novembe 20 DYNAMIC STABILITY STUDY AND SIMULATION OF THE SYNCHRONOUS MACHINE COUPLED WITH THE NETWORK BY A LINE AND A LOAD IN PARALLEL Elahem A., Sboi A. & Haj Aballah H. Sax National Engineeing School, Electical Depatment. BP W, 3038 Sax Tnisia ABSTRACT This pape investigates the ynamic behavio o synchonos machine-netwok in tansitoy moe. In aition, simlation in ece time o the ynamic behavio o the machine will enable s to eine the limits o its stability ing seveal tansient states. Keywos: Synchonos Geneato, Netwok, Dynamic behavio, Tansient stability.. INTRODUCTION The se o a ece oe moel o synchonos geneato o simlation is inaeate o tansient stability sty o the machine. Conseently thee is a nee to analyse exclsively the moel o synchonos machine in powe system. This act the ome netwok o seveal inte-connecte machines is egae as a mlti vaiable nonlinea system. Its moeling becomes vey iiclt an complex then, owing to the act that each synchonos machine is escibe by a nonlinea state moel o oe seven an the eations o inteconnection o the netwok which ae also nonlinea nctions o sizes chaacteistic o the netwok.[7] A igoos sty o this pocess in tansitoy moe absoltely eies the taking into accont o the tansitoy moes o all the machines on the one han an a ine moeling on the othe han. Howeve, it wol be complicate to appoach the sty o this poblem in the total om. A soltion consists in consieing the case encontee eently in pactice whee the istbance occs in the vicinity o a synchonos machine which will be paticlaly aecte; the eect o this istbance on the othe machines which can be consiee negligible[6], []. Une these conitions, the netwok seen o the teminals o the machine consiee can be eplace by an invaiable thee-phase.é.m in amplite an eency, in seies with an impeance. This impeance can be assimilate as a esistance in seies with an inctance. [7] 2. MODELISATION OF SYNCHRONOUS MACHINE COUPLED TO THE NETWORK BY A LINE AND A LOAD By aopting a eeence ame (, ) speciic to the synchonos machine whose axis O is elate to the axis o the pimay cicit, the V voltage o the netwok noe have two components accoing to two axes' (O, O ) given by the ollowing eations [5 ]: V V sin () V V cos These expessions will be se late in the omlation o electic eations o the connection: synchonos geneato_ gi_ paallel loa (R ch, l ch ). i a A i R l X l i c Rch V a X ch V B Fige : synchonos machine connecte to the netwok by the intemeiay o a line an a loa 238

2 IJRRAS 9 (2) Novembe 20 Elahem & al. Synchonos Machine Cople with the Netwok To simpliy the sty an hanling, o the eations one by ecing the iagam o the ige to the ollowing iagam ne the conition which spposing that the eency o the netwok is constant: R e X e V V ' Fige2 : Thévenin eivalent Diagam o the synchonos machine connecte to the netwok by the intemeiay o a line an a paallel loa. Whee R e, X e et V' ae espectively; the esistance, the eactance an the Thévenin voltage obtaine by applying the theoem o Thévenin between points A an B o the ige. The aopte mathematical moel escibing the machine epens on the nate o the poblem to teat. Inee, in a sty concening the machine cople to an ininite powe netwok, it is possible to consie the moel o Pak complet[8] : ( Ra Re ) i V ' sin ' t ( Ra Re ) i V ' cos ' t R i V t k Rk ik t (2) k Rk ik t ' 0 t ( Cm Cem ) t J Cem i i With: le i (3) le i The system o eations obtaine epesents a esciption o the system by a nonlinea moel o state o oe 7 which has the ollowing om: X ( X ) BU t Whee: T X [ ] is the state vecto. U [C m k k T V ] is the comman vecto 239

3 IJRRAS 9 (2) Novembe 20 Elahem & al. Synchonos Machine Cople with the Netwok Calclation o the vaios vaiables o state in pemanent moe a calclation o the vaiables o state in pemanent moe is obligatoy to sty the state o the machine ate sch a petbation[3 ]. This calclation etns to solve: X t 0 3. SIMULATION OF A SERIES OF DISTURBANCES AND COMMENTS (4) Paametes o the machine which has Data o the netwok nominal appaent Powe S=88MVA l =.36 p. V =p. l =0.8 p. 0 l =.37 p. l a =.59 p. Line o tansmission l a =0.599 p. R l =0.0p. l k =.96 p. X l =0.2p. l k =295 p. R = p. Pemanent moe R a =0 P =p. R k = p. Q =0.4p. R k = p. J=2000 p. 3.. Calclation o the initial conitions: By the esoltion o the système : X 0 an om the vales speciie on the peceing table the vales o the pemanent moe ae the t ollowing: V p. i 0.926p p p p. k p. k p. Cm p Pesentation o the istbances simlate: one poposes to sty by simlation by means o Simlink, the stability o the machine ate the ollowing vaios types o istbances: -. Inlence impeance o the paallel loa with cosφ ch =C ste - 2. Inlence impeance o the line with cosφ l =C ste The sty compises the nmeical integation o the ieential eations o the nonlinea moel by the means o Simlink an tacing o the tempoal evoltion o the state vaiables. All this sty was caie ot with sotwae MATLAB (otineode4 (Rnge-Ktta)). 240

4 W(p) angle(p) Flx s(p) W(p) angle(p) IJRRAS 9 (2) Novembe 20 Elahem & al. Synchonos Machine Cople with the Netwok 3.3. Qalitative analysis o the eslts: the istbance Case Qality o stability. kept stability stability completely lost kept stability stability on bt no acceptable 3.4. Qantitative analysis o the eslts:./ Tansitoy evoltion o the vaiables o state ollowing the petbation in paallel loa :(Rch, Xch om 50p to p) Fig..a.oto spee ate a loa vaiation 0.5 Fig..b.oto angle ate a loa vaiation Fig..c. stato lx ate a loa vaiation Following this istbance, one sees that the system ins anothe stable moe (ate 3 secons)..2/ Tansitoy evoltion o the vaiables o state ollowing the petbation in paallel loa:(rch, Xch om 50p to 0.2p) Fig.2.a.oto spee ate a loa vaiation 0 Fig.2.b.oto angle ate a loa vaiation 24

5 angle(p) angle(p) Flx s(p) W(p) angle(p) Flx s(p) IJRRAS 9 (2) Novembe 20 Elahem & al. Synchonos Machine Cople with the Netwok Fig.2.c. stato lx ate a loa vaiation The minimal vale o the impeance which allows the instability o the system is Rch Xch 0. 2 p. It then constittes a citical limit o the loa. The ollowing iges show that the system stats to ivege stating om.8s. 2./ Tansitoy evoltion o the vaiables o state ollowing the petbation:(r l om 0.0p to 0.02p, X l om0.2p to 0.4p) Fig2..a.oto spee ate a line impeance vaiation Fig2..b.oto angle ate a line impeance vaiation Fig2..c.stato lx ate a line impeance vaiation 2.2/ Tansitoy evoltion o the vaiables o state ollowing the petbation:(r l om 0.0p to 0.25p, X l om0.2p to 4p) Fig2..b.oto angle ate a line impeance vaiation 0 Fig2.2.b.oto angle ate a line impeance vaiation 242

6 Flx s(p) IJRRAS 9 (2) Novembe 20 Elahem & al. Synchonos Machine Cople with the Netwok.25 X Fig2.2.c.stato lx ate a line impeance vaiation It is notice that o a geat incease in the line impeance (Rl=0.3p, Xl=2.6p) stability o the system is on bt ate an enomos time (the system caies ot seveal oscillations beoe joining its new pemanent moe). 4. DISCUSSION OF RESULTS Fist we wee paticlaly inteeste by the most signiicant phenomenon o tansitoy stability, i.e. the possible keeping o stability col be egae physically as acceptable; alitative jgment on the level o the maximm amplite o minimal attack by the vaiable consiee. As can be obseve o example cases whee stability is maintaine wheeas the impeance o the line eaches a vey low level, wheeas othe istbances, even weak, geneate the instability o the machine. By analyzing the cves (.,.2, 2., 2.2) one sees that the incease in the impeance o the line o the ection in the impeance o the loa (Rch, Xch) oten constittes a constaining istbance o the stability o the moe. Inee sch a istbance is pactically eivalent to a ection in the gi voltage V, which geneates a egaation o the machine voltage level an conseently a btal all o the electomagnetic intenal oce; this is tanslate by a ection in the esist electic toe an ths an honest ivegence o the oto o the machine compae with the synchonos axis o the netwok. 5. CONCLUSION In this aticle, one was inteeste in the sty o the stability o a synchonos machine cople with an ininite powe netwok by the intemeiay o a line an a loa. A sty was mae in a ist place has ine to lea to a physical moel o oe seven escibing the ynamics o the synchonos machine when it is cople with the ininite netwok by a line in paallel with a loa ( R ch, lch ). Then one was inteeste has to make a alitative an antitative analysis eslts o simlation obtaine by the means o sty o the tempoal vaiations o the vaios vaiables o state o vaios istbances on the paametes o the line an the paametes o the paallel loa. One always tie to limit the stable opeation ange o the machine while ixing the citical cases. 6. REFERENCES []. P.W.Sae, S.Ahme-Zai et P.V.Kokotovic: An integal maniol appoach to ece oe ynamic moelling o synchonos machines, IEEE Tansaction on Powe Systems, Vol. 4, No. 2, May 989 [2]. A.K.Behea, M.A.Pai, J.R.Winkelman et J.H.Chow: Tajectoy appoximations o iect enegy metho that se sstaine alts with etaile powe system moels, IEEE Tansaction on Powe Systems, Vol. 4, No. 2, 989 [3]. W.W.Lemmon, K. R. C. Maman, W. R. Bacelo : Tansient stability peiction an contol in eal-time by ep, IEEE Tansaction on Powe Systems, Vol. 4, No. 2, May 989 [4]. J. M. Feeia e Jess : A moel o satation in inction machines, IEEE Tansaction on Enegy Convesion, Vol. 3, No. 3, Septembe 989 [5]. Mohame Ben Ali Kamon : Notes e cos, les machines électies, cos Maste 2004 [6]. Masmoi Ahme : Notes e cos, commane es machines électies, cos Maste 2004 [7]. Ellech Mona : «Appoches paties e caactéisation es égimes e tansmission citie e l énegie n ésea électie.994 [8]. Jean-Pal Lois : «Moélisation es machines électies en ve e le commane» [9]. T. J Hammons, D. J. Winning, Compaisons o Synchonos Machine Moels in the Sty o the Tansient Behavio o Electical Powe Systems. IEE Poc, vol. 8, Pt. C. no. 0, Octobe 97. [0]. IEEE Committee. Excitation System Moels o Powe System Stability Sties. IEEE Tans. Powe Appa. Syst. pp , Feb