IEEE PES Boston Chapter. Protection Engineering Course Series. Instructor: Dean V. Sorensen (National Grid)

Transcription

1 ymmetril Components EEE PE Boston Chpter Protetion Engineering Course eries Fll nstrutor: Den. orensen (Ntionl Grid)

2 ymmetril Components Disussion Topis History nd Desription The Generl ethod of ymmetril Components N-Phse ystems -Phse ystems Ciruit Element equene Representtions Fult Anlysis Using ymmetril Components J. Lewis Blkurn nd Thoms J. Domin, Protetive Relying Priniples nd Applitions, rd Ed., CRC Press, 7. John, A Hork, Derivtion of ymmetril Component Theory nd ymmetril Component Networks, Georgi Teh protetive e Relying Conferene, Atlnt, GA, April 5, mmomp pdf Fll Den. orensen ymmetril Components

3 ymmetril Components History nd Desription The method of symmetril omponents provides tool to study systems with unlned phsors. Developed y Chrles Fortesue in 9, who presented pper entitled ethod of ymmetril Co-ordintes Applied to the olution of Polyphse Networks. n mthemtis terms, it is liner trnsformtion 4 mpping quntities (ABC) from physil domin into quntities () in sequene domin. implifies iruit nlysis of three-phse mutully oupled iruit y trnsforming it into single phse iruits with no mutul oupling. Fortesue s pper is ville t from the University of Wterloo. 4 Rowlnd, Todd nd Weisstein, Eri W. "Liner Trnsformtion." From thworld A Wolfrm We Resoure th lf /Li f ti l Fll Den. orensen ymmetril Components

4 A Tool for implifying Fult Anlysis A lned system is esily nlyzed euse only one phse needs to e onsidered. Unlned systems require full iruit nlysis of ll three phses, neutrl nd ground elements. Therefore trnsforming n unlned system into lned systems promises to simplify our nlysis Fll Den. orensen ymmetril Components 4

5 The Generl ethod of ymmetril Components The use of symmetril omponents for three-phse power system nlysis is suset of more generl trnsformtion method. The generl method resolves N unlned phsors whih shre the sme referene plne into N sets of lned phsors, eh of whih h hs N memers. Within eh set, eh of the phsors hs the sme mgnitude nd suessive phses hve the sme phse ngle seprtion etween them. Let α e the ngle etween phses in n N-phse system. Then let s define useful opertor dued the opertor. The opertor is unit phsor (mgnitude ) with n ngle equl to α. ultiplying phsor y simply rottes tht phsor y α degrees in the ounterlokwise diretion. α 6 N α Rottion opertor Within eh sequene network, the ngulr displement of suessive phsors is -α n where n is the phse sequene network numer nd where n,,, N-. Fll Den. orensen ymmetril Components 5

6 -Phse ystem Exmple Note: All system rottion, even negtive-sequene phsors, is ounterlokwise! Fll Den. orensen ymmetril Components 6

7 4-Phse ystem Exmple Fll Den. orensen ymmetril Components 7

8 5-Phse ystem Exmple Fll Den. orensen ymmetril Components 8

9 6-Phse ystem Exmple Trivi Ftoid: When N is prime, eh set where n> will form regulr N-sided polygon. Consider n s eing -sided polygon. For N6, prime ftors re,, nd 6. Cn you find -sided, -sided, -sided nd 6-sided polygon mong these sets? Try this for ny vlue of N. A more detiled fult nlysis nd development of 6-phse sequene network pplitions n e found in the following pper: 5 Bhtt, Nvin B., ix-phse (ulti-phse) Power Trnsmission ystems: Fult Anlysis, EEE Trnstions on Power Apprtus nd ystems, ol. PA-96, No., y/june 977, Fll Den. orensen ymmetril Components 9

10 Bk to the -Phse ystem Exmple We n relte physil domin quntities to sequene domin quntities y superposition. This trnsforms quntities into totl of 9 quntities. We n then define quntities nd in the sequene implified? We n then define quntities, nd in the sequene domin using -phse (or speifilly ) s referene nd long with the opertor sustitute the new sequene quntities into nd -phses. Fll Den. orensen ymmetril Components

11 -Phse ystem Exmple Using trix Nottion Expressing the trnsformtion in mtrix nottion mkes the trnsformtion formt esier to rememer [ ] [ ] [ ] A to rememer. trix nottion lso lets us esily derive n inverse trnsform. [ ] [ ] [ ] A [ ] [ ] [ ] A Fll Den. orensen ymmetril Components

12 -Phse ystem Exmple Using trix Nottion Nturlly, urrent phsors will hve the sme trnsformtion form s voltge phsors. [ ] [ ] [ ] A [ ] [ ] [ ] A [ ] [ ] [ ] A Fll Den. orensen ymmetril Components

13 ymmetril Component Trnsformtion Worked Exmple 6 This exmple is from Wshington tte University s rh Hnds-On Rely hool Fll Den. orensen ymmetril Components

14 ymmetril Component Trnsformtion Worked Exmple (Continued) This exmple is from Wshington tte University s rh Hnds-On Rely hool Fll Den. orensen ymmetril Components 4

15 ymmetril Component Trnsformtion Worked Exmple (Continued) This exmple is from Wshington tte University s rh Hnds-On Rely hool Fll Den. orensen ymmetril Components 5

16 ymmetril Component Trnsformtion Worked Exmple (Continued) This exmple is from Wshington tte University s rh Hnds-On Rely hool Fll Den. orensen ymmetril Components 6

17 ymmetril Component Trnsformtion Worked Exmple (Continued) This exmple is from Wshington tte University s rh Hnds-On Rely hool Fll Den. orensen ymmetril Components 7

18 Ciruit Element equene Representtions Fll Den. orensen ymmetril Components 8

19 Ciruit Element equene Representtions -Phse ystem with ending nd Reeiving End oltges Fll Den. orensen ymmetril Components 9

20 Ciruit Element equene Representtions elf mpednes The voltge drop equtions in mtrix form for our system re A B C AR BR CR AA BA CA AB BB CB AC BC CC A B C trting ti with KL round the loop, the self impedne of loop A (i.e. the voltge drop in loop A resulting from the urrent in loop A) is A AR ( R A R G ) A j( X AA X AG ) A ( R R ) j( X X ) A AR AA A G AA A BB nd CC in the impedne mtrix re similrly defined. AG Fll Den. orensen ymmetril Components

21 Ciruit Element equene Representtions utul mpednes Agin, our voltge drop equtions in mtrix form re A B C AR BR CR AA BA CA AB BB CB AC BC CC A B C The mutul impedne from Loop A to Loop B (i.e. the voltge drop in loop A resulting from the urrent in Loop B) is ( X X ) A AR AB R G j AB B The X AG term might look like typo ut rell the following for flux linkge in Phse A: AG φ L i ( t ) L i ( t ) L i ( t ) L i ( t ) A AA where A i G AB ( t) i B A ( t) i B AC C ( t) i C ( t) AG G φ ( L L ) i ( t) ( L L ) i ( t) ( L L ) i ( t) A AA AG A AB AG B AC AG C Fll Den. orensen ymmetril Components

22 Ciruit Element equene Representtions ABC-to- Conversion the oltge Drop Expressions trt with our voltge drop equtions in mtrix form A B C AR BR CR AA BA CA AB BB CB AC BC CC A B C ultiply l oth sides of the expression y [A - ] whih h preserves the equlity nd multiply l [ ABC ] y [A - ] [A] whih is the sme s multiplying it y the identity mtrix []. A AR AA AB AC A [ A] [ A] [ A] [ A] [ A] B C BR CR This leves us with the voltge drop expressions in the sequene domin. BA R R R CA BB CB BC CC B C Fll Den. orensen ymmetril Components

23 Ciruit Element equene Representtions equene ndependene nd equene Coupling R Let s exmine eh of the impedne terms of. q p q p g R R ee how the digonl terms indite impednes with no oupling etween the sequene networks wheres the off-digonl terms indite impednes with oupling etween the sequene networks. R R R R R R R R R R R R Fll Den. orensen ymmetril Components

24 Cses of mpedne tries with High ymmetry Cse ymmetril Pssive Elements n the se of trnsmission lines, ommon ssumptions inlude symmetrilly sped phse ondutors with regulr ondutor trnsposition. This yields the following equlities: R X X P G R A X X AA AB AG R B X X BB R BC BG C X X X X X X CC CA CG X BA X CB X AC This in turn enles the introdution of new vriles representing ese self nd mutul impednes. R P AA R G BB CC j ( X X G ) G AB BC CA R j ( X X G ) G BA CB AC Fll Den. orensen ymmetril Components 4

25 Cses of mpedne tries with High ymmetry Cse ymmetril Pssive Elements y Now we sustitute for the self impedne nd for the mutul impednes in the ABC impedne mtrix CC CB CA BC BB BA AC AB AA ABC And onvert to. [ ] [ ] A A Notie tht ontins only digonl elements (i.e. no oupling etween sequene networks) nd tht. The more ommon form of expression is tht. Fll Den. orensen ymmetril Components 5 networks) nd tht. The more ommon form of expression is tht.

26 Cses of mpedne tries with High ymmetry Cse Rotting hines n the se of rotting mhines (motors nd genertors), mutul oupling etween phses inludes rottion s well s physil geometry. This differs from non-rotting iruit elements euse now AB BA, BC CB nd CA AC. R X X X X P G RA RB RC X AA X BB X X AB X BC X X BA X CB X X X X This in turn enles the introdution ti of new vriles representing self nd mutul impednes. R P AA AG R G BB BG j ( X CC CC CA AC CG X G ) AB BC CA BA CB R G j ( X X G ) RG j ( X X G AC ) Fll Den. orensen ymmetril Components 6

27 Cses of mpedne tries with High ymmetry Cse Rotting hines g Now we sustitute for the self impedne nd for the mutul impednes in the ABC impedne mtrix CC CB CA BC BB BA AC AB AA ABC And onvert to. CC CB CA [ ] [ ] A A Notie tht ontins only digonl elements (i.e. no oupling etween sequene networks) nd tht this time or the more ommon form of expression is tht. Fll Den. orensen ymmetril Components 7

28 Fll Den. orensen ymmetril Components 8

29 Ciruit Element equene Representtions equene Networks Elements of power system re represented y their impednes nd hrteristis in eh of sequene networks. For -phse power system: ero sequene - represents impednes of the system to equl (in-phse) urrents in ll three phses. Positive sequene - represents impednes of the system to norml (lned) urrents in ll three phses. Negtive sequene - represents impednes of the system to urrents with reversed phse sequene. Fll Den. orensen ymmetril Components 9

30 Ciruit Element equene Representtions equene Network ndependene Eh of the sequene networks is independent of the others. For lned network: equene urrents flowing in lned network produe only like sequene network voltge drops. Thus the sequene networks re not onneted to eh other. Unlned soures resolve to zero, positive nd negtive sequene soures. For unlned network: n generl, sequene urrents n produe ll three sequene network voltge drops. Thus, we model unlnes y setting up independent sequene networks nd interonneting them t the point of the unlne (i.e. the fult lotion). For these studies we ssume the rest of the system nd ll the soures re lned (i.e. no soures in the zero nd negtive sequene networks). Fll Den. orensen ymmetril Components

31 Ciruit Element equene Representtions ystem Equivlent oures (i.e. Non-rotting) hort iruit ka or A vlues re used to express the fult duty of n equivlent soure t point in the power system nd n e onverted to equivlent impednes. ometimes you my get driving point.k.. Thevenin impednes from short iruit progrm suh s CAPE or Aspen. Generlly they provide nd vlues nd you ssume. Alterntively you my e given fult duties expressed in A or ka sed on the driving ing point (i.e. se system) stem) voltge nd ville ille fult urrent. You need oth phse ( ph or A C ) nd LG ( ph or A GC ) fult duties to lulte sequene impednes (see next slide). With this method ssume impednes to e ll retive. For hnd lultions you n often ssume n idel voltge soure,.k.. n infinite us, (i.e. ). Fll Den. orensen ymmetril Components

32 Ciruit Element equene Representtions ystem Equivlent oures (i.e. Non-rotting) Following is lultion method for, nd from given ph ( ph ) nd LG ( ph ) fult duties in A. Resulting impednes re in per unit. Bse Bse g php ph g Bse ph Bse ph ee Blkurn Appendix 4. for detiled derivtion. Fll Den. orensen ymmetril Components

33 Ciruit Element equene Representtions ynhronous Genertors For sustined fult on the terminls of n unloded genertor, the rmture urrent hs derement s shown elow. This defines genertor impednes. Fll Den. orensen ymmetril Components

34 Ciruit Element equene Representtions ynhronous Genertors Retne inreses with time fter short iruit euse of the demgnetizing effet of the fult urrent on the ir-gp flux. For round rotor mhines, typil positive sequene impednes re s follows:.95 < X d <.45. < X d <.8 pu on genertor se.7 < X d <.7 Negtive-sequene impedne is often pproximted y equting it to the sutrnsient retne. X Xd Fll Den. orensen ymmetril Components 4

35 Ciruit Element equene Representtions Genertors ndution hines ndution mhines (motors or genertors) re not generlly onsidered ed soures of fult urrent for relying purposes. poses The fult urrent ontriution from n indution mhine deys in few yles. ndution mhine ontriution to fult urrent (sutrnsient retne) my e onsidered when performing mximum instntneous fult urrent studies for us nd swithger rting purposes. Fll Den. orensen ymmetril Components 5

36 Ciruit Element equene Representtions Blned -Phse oures ero-sequene impedne depends on the mnner in whih the genertor is grounded. Any impedne in the neutrl iruit ( n ) is represented s three times this vlue ( n ) in the zero-sequene model sine flows through the neutrl. E n REF REF REF Externl neutrl impedne. POTE NEGATE ERO For solidly EQUENCE EQUENCE EQUENCE grounded neutrl n. Fll Den. orensen For ungrounded neutrl n ymmetril Components 6

37 Ciruit Element equene Representtions Lod mpednes Positive nd negtive sequene impednes of lods re generlly equl. These re shown on referene phse sis in sequene networks. For synhronous motors, prtiulrly those tht re designed with slient poles, the negtive sequene impedne generlly lies etween X d nd X d. ero sequene impedne of lods depends on the mnner in whih they re onneted nd grounded s shown on the following pge. Fll Den. orensen ymmetril Components 7

38 Ciruit Element equene Representtions ero equene odels for Different Lod Connetions N N REF Connetion Arrngement N REF N ero equene Equivlent Ciruit N n n N REF Fll Den. orensen REF ymmetril Components 8

39 Ciruit Element equene Representtions Trnsmission Lines nd Cles n sequene network lultions, the per-phse vlues of line resistne, retne nd shunt pitive suseptne re used. These vlues n e found from ondutor tles or lulted y hnd using Crson s equtions. everl softwre pps re ville suh s ATP-ETP whih n derive the per-phse phse line onstnts from physil dimensions of the line or le. Rell from erlier expressions tht for lines nd les, L L while L > L. A [ A ] [ ] Fll Den. orensen ymmetril Components 9

40 Ciruit Element equene Representtions mple ATP-ETP Output for OH Trnsmission Lines Clulted impednes re for typil 45k trnsmission line (left-most tower onfigurtion shown elow) with two undled ondutors per phse. mpedne mtrix, in units of [ohms/mile ] for the system of equivlent phse ondutors. Rows nd olumns proeed in the sme order s the sorted input. AA.787E-.9986E BA BB.574E-.9487E E-.854E CA CB CC.8E-.575E-.788E- 4.46E E-.9986E mpedne mtrix, in units of [ohms/mile ] for symmetril omponents of the equivlent phse ondutor Rows proeed in the sequene (,, ), (,, ), et.; Columns proeed in the sequene (,, ), (,, ), et E- AA RA RG j X AA X AG.796E E E E E E E E E- 6.4E-.7469E- AB ( ) ( ) G ( X X ) R j AB AG Fll Den. orensen ymmetril Components 4

41 Ciruit Element equene Representtions L for Overhed Trnsmission Lines The zero sequene impedne, L, of n overhed line depends on severl lftors whih hn result ltin wide vrition. The use of overhed shield wires nd the type of tower grounding nd ounterpoise. Ground resistivity. ero-sequene impedne is usully to.5 times the positive-sequene impedne. Fll Den. orensen ymmetril Components 4

42 Ciruit Element equene Representtions L for Trnsmission Line Cles For les, the type of sheth or pipe used in the onstrution is mjor ftor in the zero-sequene impedne. n ddition, the plement of the phse ondutors reltive to eh other ffets the mount of urrent flow in the le sheths or pipe nd thus hs signifint impt on the zero-sequene impedne. Fll Den. orensen ymmetril Components 4

43 Ciruit Element equene Representtions Pipe-type Cles R nd X Things expnd when they het up so R nd X in pipe type les vry with urrent loding. ost fult studies will hoose urrent level t whih to study the le, usully level orresponding with the ville fult urrent R/R 5 5 X/X Totl Pipe Current - Amperes Totl Pipe Current - Amperes Fll Den. orensen ymmetril Components 4

44 Ciruit Element equene Representtions Trnsformers Positive nd Negtive equene The positive nd negtive-sequene impednes of trnsformer re equl nd re the lekge impedne of the trnsformer. Positive-sequene voltges nd urrents re shifted ± when pssing through Delt - Wye trnsformer nk. The sign of the phse shift is determined y the trnsformer onnetions. Negtive sequene voltges nd urrents re orrespondingly shifted y the opposite phse shift. No phse shift ours in the zero sequene network. Fll Den. orensen ymmetril Components 44

45 Ciruit Element equene Representtions Trnsformers ero equene Where three-phse trnsformer nk is rrnged without interlinking mgneti flux (tht is three-phse shell type, or three single-phse units) nd provided there is pth for zero sequene urrents, the zero sequene impedne is equl to the positive sequene impedne. n the se of three-phse ore type units, the zero sequene fluxes produed y zero sequene urrents n find high relutne pth, the effet eing to redue the zero sequene impedne to out 9% of the positive sequene impedne. hell-type However, in hnd lultions, it is usul to ignore this vrition nd onsider the positive nd zero sequene impednes to e equl. t is ommon when using softwre to perform fult lultions to enter vlue of zero-sequene impedne in ordne with the ove guidelines, if the mnufturer is unle to provide vlue. oure: Arev Network Protetion nd Automtion Guide, Chpter 5, pge 57. Core-type Fll Den. orensen ymmetril Components 45

46 Ciruit Element equene Representtions -Winding Trnsformers ero equene The onnetion from internl impedne to the referene nd the open onnetion to the externl terminl represents delt onnetion. You n lso refer to similr tle on p. in Blkurn. This represents solidly grounded neutrl (i.e. n ). Reple with n for n impedne grounded neutrl. Reple with n open (i.e. n ) for n ungrounded neutrl. Fll Den. orensen ymmetril Components 46

47 ero equene Network eries nd hunt Elements How They Relte to Neutrl Current Current ross shunt elements in the zero sequene representtion orresponds with neutrl urrent. f the zero sequene is open s for delt-delt trnsformer or ungrounded wye winding lerly there e is no neutrl urrent. When there e is only series es pth there e is zero sequene urrent flow ut not through the neutrl. Fll Den. orensen ymmetril Components 47

48 Ciruit Element equene Representtions -Winding nd Autotrnsformers -winding trnsformers n e represented with T-model. Rell tht the impednes derived from mesurements (i.e test reports) re those etween pirs of windings with the third winding eing n open iruit. Thus we n relte the vlues P, PT nd T to effetive individul winding impednes P, nd T s follows: Then with some lgeri mnipultion we n rrive t the following: Fll Den. orensen ymmetril Components 48

49 Ciruit Element equene Representtions -Winding nd Autotrnsformers Positive nd Negtive equene The positive nd negtive sequene representtions re the sme nd simply inlude solid onnetions from the internl impednes P, nd T to the externl terminls P, nd T s shown elow right. Ref. Fll Den. orensen ymmetril Components 49

50 Ciruit Element equene Representtions -Winding nd Autotrnsformers ero equene ero sequene representtions use the sme internl onnetion rules for eh winding onfigurtion s seen in the -winding exmple. You n lso refer to similr tle on p.4 in Blkurn. Note for N-Winding Trnsformers: Representtion of trnsformers with more thn windings (i.e. N-winding trnsformers) follow the sme proess nd onnetion rules s -winding trnsformers. Fll Den. orensen ymmetril Components 5

51 Fll Den. orensen ymmetril Components 5

52 Fult Anlysis Using ymmetril Components Exmple ystem (Fult t Bus C) Fll Den. orensen ymmetril Components 5

53 Fult Anlysis Using ymmetril Components -Phse (PH) Fult At the fult point nd ine From the definitions: ine From the definitions: nd As expeted, these reltionships suggest only the positive sequene network to e onneted t the fult point. ( ) ( ) ( ) REFERENCE EQUATON ( ) ( ) ( ) Fll Den. orensen ymmetril Components 5

54 Fult Anlysis Using ymmetril Components -Phse (PH) Fult Fll Den. orensen ymmetril Components 54

55 Fult Anlysis Using ymmetril Components -Phse (PH) Fult PO NEG Notie there is extr omponent of nd present euse of lod urrent nd soure impedne. ERO The ove fult reord is from Wshington tte University s rh Hnds-On Rely hool Fll Den. orensen ymmetril Components 55

56 Fult Anlysis Using ymmetril Components ingle-line-to-ground (LG) Fult g ( ) At the fult point nd ine ine nd These reltionships suggest tht ll three sequene networks re Whih simplifies to ll three sequene networks re onneted in series t the fult point. REFERENCE EQUATON ( ) ( ) ( ) ( ) ( ) ( ) Fll Den. orensen ymmetril Components 56

57 Fult Anlysis Using ymmetril Components ingle-line-to-ground (LG) Fult Fll Den. orensen ymmetril Components 57

58 Fult Anlysis Using ymmetril Components ingle-line-to-ground (LG) Fult PO Notie there is extr omponent of nd present euse of lod urrent nd soure impedne. NEG ERO The ove fult reord is from Wshington tte University s rh Hnds-On Rely hool Fll Den. orensen ymmetril Components 58

59 Fult Anlysis Using ymmetril Components Line-to-Line (LL) Fult ( ) At the fult point nd - nd ine ine Whih simplifies to ine - -( ) Whih simplifies to - p ine where - Whih simplifies to These reltionships suggest the positive nd negtive sequene networks re onneted in prllel t the fult point. REFERENCE EQUATON ( ) ( ) ( ) ( ) ( ) ( ) Fll Den. orensen ymmetril Components 59

60 Fult Anlysis Using ymmetril Components Line-to-Line (LL) Fult Fll Den. orensen ymmetril Components 6

61 Fult Anlysis Using ymmetril Components Line-to-Line (LL) Fult PO Notie there is extr omponent of nd present euse of lod urrent nd soure impedne. NEG ERO The ove fult reord is from Wshington tte University s rh Hnds-On Rely hool Fll Den. orensen ymmetril Components 6

62 Fult Anlysis Using ymmetril Components Doule Line-to-Ground (DLG) Fult ( ) At the fult point nd ine nd ine nd Whih simplifies to ine Or rewritten s -( ) These reltionships suggest the zero, positive nd negtive sequene networks re ll onneted in prllel t the fult point point. REFERENCE EQUATON ( ) ( ) ( ) ( ) ( ) ( ) Fll Den. orensen ymmetril Components 6

63 Fult Anlysis Using ymmetril Components Doule Line-to-Ground (DLG) Fult Fll Den. orensen ymmetril Components 6

64 Fult Anlysis Using ymmetril Components Doule Line-to-Ground (DLG) Fult PO ( ) NEG Notie there is extr omponent of nd present euse of lod urrent nd soure impedne. ERO The ove fult reord is from Wshington tte University s rh Hnds-On Rely hool Fll Den. orensen ymmetril Components 64

65 Fult Anlysis Using ymmetril Components Phse hifting Aross Delt-Wye Trnsformers For this exmple H leds L y. Let the system voltge rtio (N) equl. Consequently, the turns rtio (n) must e /. We know tht Beuse the sequene networks re independent, we n pply them individully dding the results y superposition. trting with positive sequene vlues we get the following for voltge nd urrent. Pitures nd equtions re from Appendix 4. in Blkurn. Fll Den. orensen ymmetril Components 65

66 Fult Anlysis Using ymmetril Components Phse hifting Aross Delt-Wye Trnsformers Rell from efore tht Next pplying negtive sequene vlues we get the following for voltge nd urrent. Pitures nd equtions re from Appendix 4. in Blkurn. Fll Den. orensen ymmetril Components 66

67 Fult Anlysis Using ymmetril Components Phse hifting Aross Delt-Wye Trnsformers Blkurn Appendix 4. provides seond trnsformer, Exmple (), whih hs high side delt, low side wye with the H side similrly leding the low side y. The proess for determining the positive nd negtive sequene shift ngles is the sme s Exmple () s re the tul shift ngles. Fll Den. orensen ymmetril Components 67

68 Fult Anlysis Using ymmetril Components Exmple ystem (Fult t Bus C) After interonneting the sequene networks to model the prtiulr fult type nd solving the network to determine the fult urrent, you likely wnt tto determine other internl vlues for prtiulr elements sy the urrent through Genertor GB nd the voltge ehind its retne. You simply determine the urrent through GB in eh network ( GB, GB nd GB ) s well s the voltges ross GB ( GB, GB nd GB ). Rell tht GBA GB GB GB, nd GBA GB GB GB. You similrly determine GBB nd GBC. Fll Den. orensen ymmetril Components 68

69 Questions? Fll Den. orensen ymmetril Components 69