STUDY OF SUBSYNCHRONOUS RESONANCE AND ANALYSIS OF SSR

Transcription

1 ISSN: Vol., Iue 7, July 03 STUDY OF SUBSYNCHRONOUS RESONANCE AND ANALYSIS OF SSR Rajit M. Zede, Suryakat H. Pawar P.. Studet, Departmet of Electrical Egieerig, ovt. College of Egg.Karad, Maharahtra, Idia Aociate Profeor, Departmet of Electrical Egieerig, ovt. College of Egg.Karad, Maharahtra, Idia Abtract: Sub-ychroou reoace (SSR) i the proce which lead to the turbie geerator haft damage. Thi work addree Cotributio of ychroou geerator rotor motio ad iductio geeratio to utaied ubychroou ocillatio. The defiitio regardig ub ychroou reoace pheomeo i preeted. For aalyi the IEEE ecod bechmark model ytem- i take ad dicued i detailed. Key Word: Capacitor Compeated Tramiio Lie, Sub-ychroou reoace, Iductio eerator Effect, Torioal Iteractio Effect, Traiet Torque Effect I. INTRODUCTION Serie capacitor compeatio ha bee widely ued i the AC tramiio ytem [] a a ecoomical alterative for differet purpoe uch a icreaig power trafer capability through a particular iterface, cotrollig load harig amog parallel lie, ad ehace Steady tate tability []. However, the ue of erie compeatio may brig about ome ew problem to power ytem operatio. Oe of the problem i poibility of Sub-Sychroou Reoace (SSR), which may lead to torioal ocillatio of turbie geerator haft ytem ad electrical ocillatio with frequecy below the ub ychroou frequecy. Turbie-geerator haft failure ad electrical itability at ocillatio frequecie lower tha the ormal ytem frequecy reult from SSR. The two haft failure at the Mohave eeratig Statio i Souther Nevada led to the advacemet i udertadig the SSR pheomeo a well a explaiig the iteractio betwee erie capacitor compeated lie ad the torio mode of team turbie-geerator [3]. Turbie-geerator electromechaical iteractio with erie capacitor ha hitorically bee kow a the pheomea of "Sub ychroou Reoace" (SSR). The iteractio betwee power cotrollig device, uch a HVDC coverter, tatic var ytem, ad power ytem tabilizer, ad turbie-geerator ha lead to a recogitio of a broad rage of' turbie-geerator torioal iteractio which i othig but the ub ychroou ocillatio. I thi regard, thi work preet a compreheive approach toward SSR ad IEEE ecod bechmark model. II. SUB-SYNCHRONOUS RESONANCE Sub-Sychroou Reoace i a electrical power ytem coditio where, electrical etwork exchage eergy with turbie geerator at oe or more atural frequecy of combied ytem, below the ychroou frequecy of the ytem []. The defiitio iclude ay ytem coditio that provide the opportuity for a exchage of eergy at a give ub ychroou frequecy. Thi iclude what might be coidered "atural" mode of ocillatio that are due to the iheret ytem characteritic, a well a "forced" mode of ocillatio that are drive by a particular device or cotrol ytem. The mot commo example of the atural mode of ub ychroou ocillatio i due to etwork that iclude erie capacitor compeated tramiio lie. Thee lie, with their erie LC combiatio, have atural frequecie w ad the coditio for occurrece of SSR i give a below. III. NATURAL FREQUENCY X L Ad L C w w X c So that oly atural radia frequecy i w w wxc w LC XL Copyright to IJIRSET 89

2 ISSN: Vol., Iue 7, July 03 I term of ytem frequecy f f w w Where i degree of erie compeatio varie betwee 0 ad i.e. (0 < S <) If S = 0, there i o erie compeatio. If =, we have 00% erie compeatio, the lie ha o reactace ad oly reitace predomiate. The power trafer, a with direct curret, oly by differece of voltage magitude, ot by phae differece, ad ytem i utable. For >, the et circuit reactace i capacitive, ad power curve i iverted. If 0 < <, the alo 0 < < ad f < f There exit a rik of SSR. Where i the atural frequecy aociated with a particular lie LC product, i the ytem bae frequecy, ad X L ad X C are the iductive ad capacitive reactace repectively. Thee frequecie appear to the geerator rotor a modulatio of the bae frequecy, givig both ub ychroou ad uper ychroou rotor frequecie. It i the ub ychroou frequecy that may iteract with oe of the atural torioal mode of the turbie-geerator haft, thereby ettig up the coditio for a exchage of eergy at a ub ychroou frequecy, with poible torioal fatigue damage to the turbie-geerator haft. The torioal mode (frequecie) of haft ocillatio are uually kow, or may be obtaied from the turbie-geerator maufacturer. The etwork frequecie deped o may factor, uch a the amout of erie capacitace i ervice ad the etwork witchig arragemet at a particular time. IV. TYPES OF SSR INTERACTION There are may way i which the ytem ad the geerator may iteract with ub ychroou effect. A few of thoe iteractio are baic i cocept ad have bee give pecial ame. We metio three of thoe that are of particular iteret: Iductio eerator Effect, Torioal Iteractio Effect, ad Traiet Torque Effect [5]. A] INDUCTION ENERATOR EFFECT Iductio geerator effect i caued by elf excitatio of the electrical ytem. The reitace of the rotor to ub ychroou curret, viewed from the armature termial, i a egative reitace. The etwork alo preet a reitace to thee ame curret that i poitive. However, if the egative reitace of the geerator i greater i magitude tha the poitive reitace of the etwork at the ytem atural frequecie, there will be utaied ub ychroou curret. Thi i the coditio kow a the "iductio geerator effect." B] TORSIONAL INTERACTION Torioal iteractio occur whe the iduced ub ychroou torque i the geerator i cloe to oe of the torioal atural mode of the turbie geerator haft. Whe thi happe, geerator rotor ocillatio will build up ad thi motio will iduce armature voltage compoet at both ub ychroou ad uper ychroou frequecie. Moreover, the iduced ub ychroou frequecy voltage i phaed to utai the ub ychroou torque. If thi torque equal or exceed the iheret mechaical dampig of the rotatig ytem, the ytem will become elf excited. Thi pheomeo i called "torioal iteractio." C] TRANSIENT TORQUES Traiet torque i thoe that reult from ytem diturbace. Sytem diturbace caue udde chage i the etwork, reultig i udde chage i curret that will ted to ocillate at the atural frequecie of the etwork. I a tramiio ytem without erie capacitor, thee traiet are alway dc traiet, which decay to zero with a time cotat that deped o the ratio of iductace to reitace. For etwork that cotai erie capacitor, the traiet curret will be of a form imilar to above equatio, ad will cotai oe or more ocillatory frequecie that deped o the etwork capacitace a well a the iductace ad reitace. I a imple radial R-L-C ytem, there will be oly oe uch atural frequecy, which i exactly the ituatio decribed i above equatio, but i a etwork with may erie capacitor there will be may uch Sub ychroou frequecie. If ay of thee ub ychroou etwork frequecie coicide with oe of the atural mode of a turbie-geerator haft, there ca be peak torque that are quite large ice thee torque are directly proportioal to the magitude of the ocillatig curret. Curret due to hort circuit, therefore, ca produce very large haft torque both whe the fault i applied ad alo whe it i cleared. I a real power ytem there may be may differet ub ychroou frequecie ivolved ad the aalyi i quite complex. Of the three differet type of iteractio decribed above, the firt two may be coidered a mall diturbace coditio, at leat iitially. The third type i defiitely ot a mall diturbace ad oliearitie of the ytem alo eter ito the aalyi. From the view poit of ytem aalyi, it i importat to ote that the iductio geerator ad Copyright to IJIRSET 893

3 ISSN: Vol., Iue 7, July 03 torioal iteractio effect may be aalyzed uig liear model, uggetig that Eige value aalyi i appropriate for the tudy of thee problem. V. ELECTRICAL NETWORK PRESENTATION Electrical Model for Aalyi of SSR: Here IEEE Secod Bechmark model i give for the Aalyi of SSR, which deal with o-called parallel reoace [6]. Oe lie diagram of IEEE ecod bechmark model i how i below figure. The electrical modal of the tudie ytem comprie the EN coected to a ifiite bu through tep up traformer ad two parallel tramiio lie, oe of which i erie compeated. The value of X C /X L of the compeated lie i fig. defie the erie compeatio ratio. The capacitive reactace X C ca be varied ad X C /X L i raged from 0% to 90%. The mechaical ytem comprie four mae, i.e. the HP, LP, EN, ad EXC, which are mechaically coupled o the ame haft. From the tructure of thi model ma prig ytem, there exit three torioal mode (mode, mode, ad mode 3) ad oe electromagetic mode (mode 0) i the ytem. Thee four-mode are called SSR mode or torioal mode ice there atural frequecie are all le tha ychroou frequecy or power frequecy (60Hz). The iheret atural frequecie for mode 0,, ad 3 are.35h z,.7 H z, 3.39H z ad 5. H z, repectively. The SSR mode i (i= 0,,, 3) tad for the umber of twit o the haft. For example mode 0 igifie the four mae ocillate i uio without a haft twit, mode ha oe haft twit, mode ha two haft twit, etc o o. All turbie torque proportioal, with each cotributig fractio. The fractio for both HP ad LP are 70% ad 30% repectively. Fig. IEEE Secod Bechmark Model Sytem- Expreio for Serie Capacitor Value at Which SSR Take Place: Expreio for erie capacitor value at which SSR take place ca be derived a follow. Bu 0 Bu X R Bu Kv / 500 Kv Rt + jxt X 3 R 3 /Y e# Ifiite bu X X c varied from 0% to 90% of X Fig. Modified IEEE Secod Bechmark Model Sytem - R r g + jx g Let R = r g + R t + R () Copyright to IJIRSET 89

4 ISSN: Vol., Iue 7, July 03 X x g t X 3 [ R j( X c)] [ R jx] ZT R jx [ R j( X c) R jx ] [ R j( X c)] [ R jx] ZT R jx [ R j( X )] Where R = R +R X =X +X By ratioalizig ad equatig imagiary part equal to zero ad implifyig [ R R R R ] c Xc [ X ] R R R R The above Equatio ca be writte a a X c +b X c + c=0 Where a = X b c [ R X R R [ R R R R R R R R R c ] R () (3) () ] Solvig equatio value X c ca be fid out. For F m =.67 value of capacitor at which SSR take place i 7.7 micro farad. R --- (5) SAMPLE MATLAB/SIMULINK RESULTS Thi Simulik model i a IEEE ecod bechmark model- ued to tudy ub ychroou reoace ad particularly torque amplificatio after a fault o a erie-compeated power ytem [6]. It coit a igle geerator (600 MVA/K V /60 H z /3600 rpm) coected to a ifiite bu via two tramiio lie, oe of which i eriecompeated. The ub ychroou mode itroduced by the compeatio capacitor after a fault ha bee applied ad cleared excite the ocillatory torioal mode of the multi-ma haft ad the torque amplificatio pheomeo ca be oberved. Fig. how the torque betwee the eerator-l. Fig 5 how the rotor peed ad the electrical power. Fig 6 how the voltage acro the erie capacitor. Fig 3. MATLAB/SIMULINK Model of the Sample Turbie-eerator ad Ifiite Bu Sytem with IEEE Secod Bechmark Model- Simulatio Reult at C=7. micro farad (55% erie compeatio of tramiio lie) Copyright to IJIRSET 895

5 ISSN: Vol., Iue 7, July 03 Torque i P u Time Fig. Torque betwee eerator-lp Fig 5. Rotor Speed ad electrical power Fig 6. Voltage acro Serie Capacitor VI. CONCLUSION The propoed work preeted a compreheive approach for ub-ychroou reoace (SSR). Thu with the help of IEEE Secod Bechmark Model we ca aalyze the Sub Sychroou Reoace (SSR) Pheomeo. The mai caue of the Productio of SSR i the Serie Compeatio. There are other ource repoible for excitatio of SSR are Power Sytem Stabilizer (PSS), HVDC Covertor, Static Var Compeator (SVC), Variable Speed Drive Covertor. Model have bee prepared for turbie-geerator ad ytem to compare elf-excitatio ad torque amplificatio aalytic techique. The ytem have oly bee made complex eough to provide for "parallel reoace" ad iteractio betwee turbie-geerator havig torioal mode. Copyright to IJIRSET 896

6 ISSN: Vol., Iue 7, July 03 REFERENCES [] J. Ballace ad S. oldberg, Subychroou reoace i erie compeated tramiio lie, Power Apparatu ad Sytem, IEEE Traactio o, vol. PAS-9, o. 5, pp , 973. [] N.. Higorai, L. yugyi, Udertadig FACTS, Cocept ad Techology of Flexible AC Tramiio ytem, Newyork IEEE Pre 000 [3] R. Farmer, A. L. Schwalb, ad E. Katz, Navajo project report o ubychroou reoace aalyi ad olutio, Power Apparatu ad Sytem, IEEE Traactio o, vol. 96, o., pp. 6 3, 977. [] Reader uide to Sub-Sychroou Reoace IEEE Committee Report, IEEE Traactio o Power Sytem, VOL. 7, No., Feb. 99. [5] Reader uide to Sub-Sychroou Reoace TERMS, DEFINITIONS AND SYMBOLS FOR SUBSYNCHRONOUS OSCILLATIONS IEEE Traactio o Power Apparatu ad Sytem, Vol. PAS-0, No. 6, Jue 985 [6] workig group of the dyamic ytem performace ubcommittee power ytem egieerig committee Secod bechmark model for computer imulatio of ubychroou reoace ieee ubychroou reoace, Power Egieerig Review, IEEE, vol. PER-5, o. 5, pp. 3 3, 985. Copyright to IJIRSET 897