Analysis Of Symmetrical Short-Circuit Current And Performance Of Synchronous Generators

Transcription

1 Analysis Of Symmerical Shr-Circui Curren An Perfrmance Of Synchrnus Generars Oyela. J.B Dep. f lecricallecrnics ngineering Schl f ngineering, Lags Sae Plyechnic, kru, Lags, Nigeria Absrac This paper fcuses n he ransien behaviur an perfrmance f a synchrnus machine because hese cniins may have minan effec n he applicain f synchrnus machine an may eman special aenin in is esign. The general prblem herefre, requires knwlege f he sluin f he sub-ransien, ransien an synchrnus reacances an heir assciae ime cnsans. The abve sae parameers are esimae by analysing he curren wavefrms f a faul applie a he generar erminals as presene in his paper. Keywrs: Transien, Sub-ransien, synchrnus machines, shr-circui. nrucin The evens wihin a generar subjece a suen shr-circui epen n several facrs, incluing (i) he insan in he cycle a which shr-circui is iniiae (ii) he la an exciain f he machine a his ime (iii) he exen f he faul (i.e. he number f phase winings invlve an he isance f he faul frm he machine erminals) an (iv) he cnsrucinal feaures f he machine ha affec flux leakage an amping.. Shr-Circui Time nerval The ime immeiaely fllwing a shr circui may be ivie in hree successive inervals:. A very shr ime (e.g. ne r w peris f he supply frequency) uring which he cniins are largely epenen upn he flux linking he sar an rr winings a he insan f faul iniiain.. A subsequen inerval f ransien ecay f curren ampliues cnsequen upn amping an he rise f armaure reacin.. A final peri which is seay sae shr circui cniins. A machine will nrmally be pencircuie befre his peri is reache.. Shr-Circui Curren nvelpe On a hree-phase ea shr-circui, he a.c cmpnens f he phase currens (i.e. he currens ha remain afer he.c ransien cmpnens have been exrace) ccupy ienical envelpe shapes, f which fig. belw is ypical. A he beginning, hwever, here is a much rapi rae f ecay wih a ime cnsan f 0.s r less. xraplain f he main par f he envelpe back zer ime wul give a peak curren f given by : he acual curren peak a zer ime,, is in fac cnsierably greaer.. Simplifie Machine Mel s Fig : curren envelpe curve Fr a erminal shr-circui, all he effecive reacances (sub-ransien, ransien an seay-sae r synchrnus reacances) are -axis quaniies. f he shr-circui ccurs a a pin reme frm he generar erminals in he cnnece newrk, he phase angle may be less an quaraure reacin effecs may appear geher wih sme increase in he resisance an inucance parameers cncerne in he shrcircui pahs. Fr a seay-sae perain, generars are represene wih a cnsan e.m.f behin a synchrnus reacance, s uner ransien cniins. The machine reacance changes ue he effec f he armaure (ransfrmer) reacin an ey currens in he amping circuis.

2 Fr analysis, i is useful imagine he synchrnus reacance as hree cmpnens; (i) Direc axis sub-ransien reacance (ii) Direc axis ransien reacance (iii) Direc axis seay-sae reacance ach f hese reacances has is assciae ime cnsan.. Mel Visualisain A generar has hree winings separae by 0 0 ; each phase will have a ifferen.c cmpnen epening n he pin f he vlage cycle a which he shr-circui ccurs x sin c a c x x x a e e sin The curren f phase-a is given by cmbining he a.c an.c cmpnens using superpsiin. This is given by he expressin e sin sin The expressin fr he sar curren fr he simplifie machine mel es n inclue he effec f he ecaying expnenial uniirecinal curren. The.c cmpnen is a funcin f he machine s rr psiin, which is inicae by δ when he shr circui is applie a = 0. The ime cnsan assciae wih he ecay f he.c cmpnen is knwn as he armaure shr circui ime cnsan, τ. Typical ime cnsans range frm s. 4. Daa Preparain Fr he purpse f his analysis, n-la r pencircui erminal vlage, = 4.6kV. The curren wavefrm is ivie in hree peris. These are subransien, ransien an seay-sae peris. Firs eermine he synchrnus reacance, using he curren value, where he wavefrm envelpe becmes cnsan, i.e. (rms) ; Secn, using he par f he envelpe beween he subransien ime peri an he seay-sae ime peri. - The seay-sae curren is subrace frm he ransien curren. - The lgarihmic curve f he envelpe is ple wih respec linear ime as a sraigh line. - The y-inercep an he slpe are baine frm he graph, i.e. Where r an e i Take naural lgarihm f bh sies n i n c c m n c e m m r where c = inercep n he verical axis m = slpe f he graph Thir, using he w cycles f he faul curren envelpe, he seay-sae an ransien currens are subrace frm he subransien curren. - The lgarihmic curve f he envelpe is ple wih respec linear ime as a sraigh line - The y-inercep an he slpe are baine frm he graph, i.e. Where r an e i Take naural lgarihm f bh sies n i n c c n e c m m

3 r m where c = inercep n he verical axis m = slpe f he graph 5. Resul The able shws he aa baine frm he scillgram fr he phase-a f a generar erminal uner a hree-phase faul. The curren envelpe has an asymmery. The.c cmpnen is exrace an ple separae agains ime an he ime cnsans baine frm he urain beween he iniial value an 0.68 f his value. The remaining symmerical envelpe is ple as in he upper par f fig an res f he cnsans baine. Fr his purpse, he fllwing clumns are ae x scillgraph scale he able: ac p facr gives he a.c cmpnen in amps, an x scillgraph scale facr yiels he c p n ampliue (abve an belw curren zer) f he.c cmpnen in amps. The resuls are: The fllwing relain can be use fin he rae curren S( VA) rae x Where S = machine raing = n-la vlage Fr he purpse f his wrk, S = 56MVA an = 4.6kV. Tha is, he r.m.s value f he rae curren is 56x0 rae 4.6x = 7.0kA. Bu he peak value f he rae curren is peak rms x n = 7.0 x.44 = 9.94kA r.0pu. As shwn n he aache graph shee an he able f values in he appenix f his wrk. The iniial peak a.c cmpnen is 6.8A Bu 4.6x0 Hence, =.68Ω 6.8 xraplaing he pl gives he ransien cmpnen peak as 68A. Bu Hence, 4.6x0 = 7.6Ω 68 Similarly, he seay-sae shr-circui curren is 0.5A peak. Bu 4.6x0 Hence, =.5Ω 0.5 The ifference = 94.8A beween he subransien an ransien currens is shwn fall 94.8 x 0.68 = 4.88A in 0.08sec. Similarly, he ifference = 7.5A beween he ransien an seay-sae currens fall 7.5 x 0.68 = 50.6A in 0.4 sec. A separae pl f he.c cmpnen agains ime is als aache. By reaing i in like manner, he inercep n he verical axis n he graph f he.c cmpnen agains ime is 4A. Hence, 0.68 x 4 = 5.5A which gives sec. The parameers require are herefre 6. 8A 68. 0A 0. 5A. 68 an 7. 6 an sec. 0.4 sec. 6. Cnclusin sec. This paper has analyse a -phase curren envelpe an has shwn he require parameers (he reacances an he assciae ime cnsans) fr a hree-phase shr-circui n he erminals f he synchrnus generar. 7. References [] B. Akins, General Thery f lecrical Machines, Chapman & Hall, 975 []. R. Smih an S. Sriharan, Transien Perfrmance f nucin Machines. Prc.,, 7,

4 [] M. G. Say, Alernaing Curren Machine, Piman Publishing L, 4 h iin, 976. [4] P. J. Lawrence an J. M. Sevensn, nucin Machine Perfrmance wih a Variable Frequency Supply, Prc.,, 67, 966. [5] R. H. Park, Tw-Reacin Thery f Synchrnus Machines, Trans. A, 48, 76, 965. [6] T. J. Lewis, Transien Behaviur f Laer Newrks Represening Transfrmer an Machine Winings. Prc., 0, 54, 954. [7] Y. K. Ching an B. Akins, Transien Thery as Synchrnus Generar uner Unbalance Cniins, Mngraph N. 85,

5 Table : npu Daa SN (sec) ( cm ) ( cm ) max min Appenix max 6x max ( A) min 6x min max min max min ( A) ac ( A) c ( A) 5

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8 Vl. ssue 9, Nvember a.c (A) Fig : A.C graph ime (s) 8

9 .c cmpnen (A) (A) Vl. ssue 9, Nvember ime (s) Fig : DC GRAPH 9

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