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## Symmetrical Components

by: Fredy Okuneva

38

0

38

# Symmetrical Components ECE 523

Fredy Okuneva
UI
GPA 3.81

Staff

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COURSE
PROF.
Staff
TYPE
Class Notes
PAGES
38
WORDS
KARMA
25 ?

## Popular in ELECTRICAL AND COMPUTER ENGINEERING

This 38 page Class Notes was uploaded by Fredy Okuneva on Thursday October 22, 2015. The Class Notes belongs to ECE 523 at University of Idaho taught by Staff in Fall. Since its upload, it has received 38 views. For similar materials see /class/227739/ece-523-university-of-idaho in ELECTRICAL AND COMPUTER ENGINEERING at University of Idaho.

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Date Created: 10/22/15
AZ 39OU NOISSEIS SiNElNOdIAIOI 39IVDIEILEIIAIIAIAS 25 332 Universityofldaho osmvtob thn s ocmntobm g n z ozwnte azc E osmuteb LchD E 053298335223 5 osmniob LQED E Ozmvto hg n a osmvtebm chb i ozmvtob ggEn a egmntebm gfz s osmvio m gmcn i osmviobmmgt3 i osmut tmhmgtED 5 osmvgb hgfz E osmulob bzcz i osmuteb gg a E EEO 3 555cr 3 Tyo8us Power System Model for Parallel Lines with Mutual Coupling ngn2mcd First 2 12 a es a ts not calculations JL 8191 System Configuration i51 1R1 VS gt VFl ltr VR zzc1 m21m 1 m ZlLl IS IFl ICCl IR gt I I lt ES ZS mz12 ZFl zcc 1 m Z12 Z RER I ICC2 ZZC2 leLZ 1 m21L2 gt IFZ VFZ lt I52 IRZ ZFZ The Three Phase abc Equations are IS 151 182 IR IRl IRZ ICCl 151 IRl IFl ICC2 ISZ IRZ IFZ 5 0 ZF1IF1 VFl 6 0 ZF2IF2 VFZ 7 o zcc151 1R1 IFl VFl VFZ 8 0 ZCCISZ IRZ IFZ VFl VFZ Equations 5 and 7 combined yield equation 5 below Equations 639 and 8 combined yield equation 5 below 1 E5 ZSISl ZSISZ ZZC1ISl mZLlISl mZ12ISZ VFl 2 2 ES ZSI52 ZSISl ZZC2ISZ mZL2ISZ mZ12ISl VFZ 3 2 ER ZRIR1 ZRIR2 1 mZL1IR1 1 mZ12IR2 VFl 4 ER ZRIR2 ZRIR1 1mZL2IR2 l mZlZIR1 VFZ 5 39 O 151 IRl ZFl ZCC VF1 ZCC VFZ l 1 1 6 39 0 152 IRZ ZCC VFl ZFZ ZCC VF2 Z Equations 1 to 6 yield a 6 x 6 matrix the 3 X 3 elements of which are H11 ZS ZZC1 mZL1 H33 ZR 1 m ZLl 1 391 H55 ZF1 ZCC The matrix is thus ES H11 H12 ES H12 H22 ER 0 0 ER 0 0 0 I 0 0 0 I H11 H12 H12 H22 K 0 0 0 0 The fault impedance matrix is thus 1 T ZFLTK LH L ES and ER are known H12 H22 H34 H44 H56 H66 I II II II H21 ZS ZZCZ mZL2 H43 ZS 111212 ZR 1 mZ12 ZR 1m 139rzm H65 ZCC l ZF2 then YFLT ZF LT ZCC 3 The currents are obtained as IS1SZ Z12 Z21 1 0 O I 0 1 0 0 0 1 0 151 I ISZ 0 IRl X I IRZ H56 VFl H66 VFZ 3 elements I 0 O I I 0 O I H55 H56 H56 H66 YFLT E og shunt Fault Impedance Configurations ZFILABCG ZFZABCG T1 B1 C1 IIXZ B2 3922 FTLA FZlB FZlC FTZA FZZB FZZC FZlG FZZG I I quotCross Countryquot Fault Impedance ZCC Configuration A1 l LINE 1 Bl I I I Q l l AIM A132 AlCZ BlAZ B182 BlC2 ClAZ C1132 C1C2 l A2 I quot l I 32 I I I l LINE 2 c2 Global Definitions CALCULATIONS Caution avoid singular matrix via ZFl or ZFZ data Inputs 3 S39deg m E 04 S E 100 as 80e er 70 Source 5 ZOS o j Z15 0 j Source R ZOR 0 j Z1R o j Line 1 ZOLl 3 24j ZlLl 1 Bj ZM 06 323 Line 2 20L2 3 24j Zle 1 8j Caps Line 1 ZZC1 05j Caps Line 2 ZZC2 0Sj Z Fault 1 FZlA FZlB 1 1 Z Fault 2 FZZA 1 FZZB 1 1 Z Cross A1A2 3 A132 1 1 BlAZ 1 B182 3 1 ClAZ 1 C182 1 3 Convert 0 to phase impedances 2z1 20 20 zl zszOzl zmz0zl 3 3 zszOzl zmz0zl zm20z1 Zzoz1 zmzOz1 zszOzl zmzOzl zmz0zl zmzOzl zszOzl 25 ZZOSZlS ZR ZZORZlR ZL1 ZZOL1Z1L1 ZLZ ZZDL2ZlL2 Source and line impedances to the fault ZCl ZZC1I ZC2 ZZC2I Z12 ZM II H11 2 ZS m39ZLl ZC1 H12 ZS mZlZ H22 ZS mZLZ ZC2 H33 ZR l mZL1 H341 ZR 1 mZ12 H44 ZR 1 mZL2 Prefault Currents and Voltages ES esBAL ER erBAL ZDENOM 2 ZL1 ZCl ZL2 ZC2 1 MONEDZ ZDENOM ZPRE ZS ZR ZL1 ZC1ZL2 ZC2MONEDZ 1 ISPRE ZPRE ES ER VSPRE ES zs ISPRE ISlPRE ZLZ ZCZMONEDZISPRE pg 4 56 Build the Fault Impedance Matrix ZFLT A1A2 A1B2 AlCZ ZCC B1A2 BlBZ B1C2 C1A2 C1B2 C1C2 FZlAG FZ1A FZ1G FZlBG FZlB FZlG FZlCG FZlC FZlG FZZAG FZZA FZZG FZZBG FZZB FZZG FZZCG FZZC FZZG FZlAG F216 F216 FZZAG FZZG FZZG FlABCG FZlG FZlBG FZ1G FZABCG FZZG FZZBG FZZG FZ1G FZlG F21CG FZZG FZZG F22CG 1 1 1 H55 F1ABCG ZCC H66 F2ABCG ZCC H56 2 ZCC M1 augmentH55H56 M2 augmentH56H66 M augmentM1TM2T K1 augmentH11augmentH12augmentZERZER K2 augmentH12augmentH22augmentZERZER K3 augmentZERaugmentZERaugmentH33H34 K4 2 augmentZERaugmentZERaugmentH34H44 39K augmentK1TaugmentK2TaugmentK37K4T L1 augmentIaugmentZERaugmentIZER L2 augmentZERaugmentIaugmentZERI L augmentL1TL27 1 ZFLT K LM 39LT YFL39I ZFLT Calculate the Relay Currents and Voltages TSl augmentIaugmentZERaugmentZERZER T52 augmentZERaugmentIaugmentZERZER E augmentESTaugmentESTaugmentERTERTT ISlSZ YFLT39E 151 TSl ISISZ 152 TSZ15182 IS 2 151 ISZ VS 2 ES ZS39IS VCAPl VS ZZClISl Outputs Prefault ISlPRE VSPRE A IVSPREI Outputs During Fault IS I51 I52 VS VCAPl Induction Machine Performance ECE523 Symmetrical Components with Neg Seq Session 24e Performance of an Induction Machine given a Slip with Negative Sequence Excitation Present Unbalanced Phase Voltages j 3 F Va 29098eJ390v J39122395439degv vb 27047e vc 27047eJ39122395439degv V0 Va v1 A 1 vb V2 V0 Odeg Odeg Odeg 7701 x 10 5 p 3 4 Prop 2950W 0186ohm rr3 0079ohm 21 J39 T 2 a e A 1 a a 1 a a2 v0 00049v argV0 v1 2771295v argV1 v2 138456V argV2 M M Evl 48000V o05 1 M M Slip sl 3 00333 52 3 2 7 51 52 19667 d System Parameters 08 37701 V11 480V V51 V1 sec Machine Parameters v52 V2 rS 01ohm X15 0205ohm X1r3 v51 2771295v Xmi 71501 v52 138456 v Calculations39 a P we a 7188 5 d 71 39 syn 397 syni ra sec rad 00m 1 7 sl1syn 00m1822229 NegativeSeqmcd Page 1 of4 ECE523 Symmetrical Components Induction Machine Performance Session 24e with Neg Seq 1quotr Zr13 J39X1r S1 1quotr 22 Jx1 r 2751 r Zfl r r jX1r Xm S1 Rfl ReZ fr J39Xm39 J39X1r S2 ZQ 1quotr JXlr xm S2 Rf ReZf2 Zin13 Zfl 1quots j39qs Zin2 3 23 1quots Ji39Xls rr J39Xm39 J39X1r S1 zrl 23724 0186i ohm zr1 23797 ohm argzr1 4483 deg zr2 00402 0186i ohm Izrgl 01903 ohm argzr2 778135 deg lzr2 lzrll 008 Zfl 20402 08411iohm IZflI 22068 ohm argZf1 224035 deg Rfl 20402 ohm ZQ 00382 01815iohm IZf2 01855 ohm argZf2 781272 deg Ra 00382 ohm zinl 21402 10461iohm zin1 23822 ohm argZin1 260478 deg zinz 01382 03865i ohm zin2 04104 ohm argZin2 7033 deg NegativeSeqmcd Page 2 of 4 ECE523 Induction Machine Performance Session 24e Symmetrical Components with Neg Seq I 7 Vsl 51quot Zinl 1511045175 e 5108451A 151 1163337A argISl 7260478 deg 01 eerg151 01 260478 deg pf1 00591 52 92 iarg152 pf2 00592 Sin13 MelE P1111 ReSin1 2 P1055513 339Isll 39rs 81112 aveQ P1112 ReSin2 P105552 3 339152 239rs pfl 08984 152 113547 7 3176481A 152 337332A arg152 77033 deg 92 7033 deg pf2 03366 1s2 029 1s1 kVA kw Sim 868947 4247111kVA Pinl 868947 kw P105551 40601 kw Sm 04716 13194ikVA P1112 04716kW P105552 03414kW NegativeSeqmcd Page 3 of 4 ECE523 Induction Machine Performance Session 24e Symmetrical Components with Neg Seq P105552 00841 Plosssl P105553 Plosssl P105552 Pin 3 Pinl Pin2 Pgapl 339151 Z39R Plossrl 3 Sl39Pgapl Pem131 S139Pgap1 Pgap2 3 339152 Z39R Plossr2 3 S239Pgap2 Pem23 1 S239Pgap2 Pem3 Peml Pem2 P gapl Teml 3 msyn 1 S239Pgap2 179mg 1 S1quot syn 17cm 17em14r 17em2 Pout 3 Peru Prot Flosss 44014kW Pin 873663 kw Pgapl 828346 kw Flossrl 27584kW Peml 800762 kw Pgapg 01303 kw Flossrg 02562 kw Pemg 701259kW reml 4394408Nm remz 70691Nm Tem2 00016 1763ml rem 4387498Nm Pout 770003 kw rout 4225609Nm n 08814 NegativeSeqmcd Page 4 of 4 ECE523 TLines Session 29a Input Dimensions Parameters resistivity and frequency m 5 40m11609 p100Qm f 60 m1 sec 2 9 0278 0278 ra 0278 rb ml rc m1 m1 m m 1609 1609 m1 m1 7 Q 7 Q ra173gtlt10 4 rb173gtlt10 4 001668ft D5 3 ft 3281 m D12 3 lOft D23 3 lOft Calculate Line Parameters 7 9 rd 986910 7 fsec Anderson 438 m De 2160ft Anderson 443 Q rc173gtlt10 4 m D31 3 20ft 759 rd592gtlt 10 m 9 rd 00953 m1 De 84995 In De279gtlt103ft Page 1 of 2 ECE523 TLines Session 29a Q D 7 7 Q 2 rardj27Efsec210 7 1 e zaa232gtlt10 4907jgtlt10 4 m DS m o 7 D 7 7 2 21313 rardj27Efsec 210 71 e zbb232gtlt10 4907jgtlt10 4 m DS m 9 7 D 7 7 Q zccz ra rd j27Esec f210 71n e zcc 7 232gtlt10 4 907jx10 4 m s m Q 7 7 De 7 5 7 4 Q zab3 rd J27Efsec 210 1 zab 592X 10 425 X 10 m D12 m Q 7 7 De 7 5 7 4 Q 2130 rd27Efsec 210 1 zbc592gtlt 10 425gtlt 10 m D23 m o 7 D 7 7 o 2 rdj27Efsec 210 71 e zac592gtlt 10 5372jgtlt 10 4 m D31 m Zba3 Zab an 3 Zac Zcb 3 Zbc Zaa Zab 2amp0 1493 5836j 381 2732j 381 2396j zabc 7 s zba zbb zbc zabc 7 381 2732j 1493 5836j 381 2732j Q Zea Zeb ch 381 2396j 381 2732j 1493 5836j Convert Line Parameters to Symmetrical Component Line Parameters quot1 111 3 a e A 1a2 a CA71 laa2 z 7 02 A 012 abc 2255 11077j 097 7 056j 7097 7 056j 2012 70977056j 11123216j 7194112j o 0977056j 194112j 11123216j Page 2 of 2 mm Nu HQ 99 oongoE f au NZ IIII39 Na lt86 J H90 H90 mo id ltuoo zo ltnoo Na lt00 I v Ha 2 2 L 2 6 z ltm Nu ltoam I HON HON mm sum mm 2m Kn P 135573 V1 100nm 102 V3 20 2b Zb VOO39O w Vrquot I00 00 FOr 4L 0FO39 0 V90 No V3 0 26 awm Ems 1 Zb 439 Voa39l v Vrquot39 Ia I1 H q aFl39 Us 239 41 El 3m zc39rz 3 ZF F Zb Voo392 quot39 I02 02 F21L V 4gtF239 I 2 TZZ 2 sz F39FZ ZFF Z ZF39F2 92 N2 i92 quot quot 50 E552 1 lt c 7 B MC K CasiquotC39C 57LMc 74 MM p 245 3 C05 Lu r 0 m K Hex 1quot Ewan m r f Wa 623 Z CcswCT 7 5 2 39ZWa Foo7 We FlaL Fm 513 W5 Va C 392 iii T L Q Uz FMSb Q F S 5 5r C Zquot m WV ewt TYZ7or 3 uwJl Kai O a i C a 3 Fmsz cogtAvm cospgm T I 1 Osalf7 2 C0Kdulz IZTZW54 cosanti 7Zrc r2rogtw 7 1 2 v5 4n V a 3 1 xz f I j 2 S O n An g J7 62 r Fm 1 E C0gt Zng NJH Z chIWzcrb a C05 Zng 7Cyl 5191 05 7yzor ZTYN3J1L C05 Zwt 7yzoffz T 05 OK 3392 39 r yquot391 39 l I Co5Zuf yz TowFL L3 ms 2 5n2w f r 122 555273 3 C A J 1 V lQi 7 LlL amp 7 V0 TC 4 p 30 43 7 Viaf2 1393 V21 amp Jo q A V gt gwf C Z 7 0 quot MHZ 41 a W i7W10C 75 RF Kgf 9 KO nc 7lc 4 gran formo 75 W179 A vrm ampc VIQKL ic 7L0 erc LgZ 39W C v f a fe 5 Wm 70er w CM 39 3quot 6941 72 quotPO71V 14 quot CPD AMI 7 Zu A 39 9 Piw 3741 a V39Q O fQZ 1 Ba jal 5 5 Is A arc 127 5 C 3 gt rig 0 Cou K 777939617 O fBFa 3239 Q w e r 7 r aaawv C O 59 quot H F 1 A f T Ly Q ZC f G ZU M0wngt I M Law We 7 9p B062 7 Amjl 7 AmyCF Br 3 r39 l I I I 6 I LVMJ J 1 L DD f L F 2 O y 07H 3 w quotL7w1 AFZ LmrJ 39 Lp jquot LF F O JUFl 51 339 Ewe2 3 5me Cog3 MC 7 C0503 72 W 2w xbj y I m my 1 6 5 ws yC lt a 41 6 iro Rms 7 E wn 6473 1quot 33V 6 3 r If jn 6 1 5 5 lt6 75 11 175 r V3 r e w Fz FF 2 t Frn51 54AM 2 igl insZ 5M ZVT ZJK339Z r P 39L V3 Emsz Cosltzw4dch2 4 Fri 2551 A frI Isz 1 5 FrUz 5605L914rdw g J39 5mZwd 15 A IK39 ZNi J7 r2 OIZ 3 findZ L 1 7 r39 r 39J w a 7 a W2 quot 4 5 W C a 39 3 M mag viz F vanJAM Call 1 r rquot 2 lt1 15 a5 1 E5583 1 5C T 7 WW LP L YCZ7 3 gt775 hale L La 4 g caJ LO J r f irr L FL Q Cgz L52 gt772 39 LQ v cil h u i L 7 39 L 21139 592 W L 4 5 A7 LQ L6 L L 391 7 z i quot ZZ 415 M La 96 Lha L15 quot7 gt W M a 49 7Equot 1 M A L 1 394 0 7 5 2 Z uxf F I 7 v zz fw v e f an 4 2 9 K quot7 1 1ft lt 11 In rm J v jAw7 C 77 4 VIZ 47 377 UT 7 af7ldfiir7 6 7 7 7 F7 72 23 7 FEE 471 7 gt f7 57 gawg z 7 72 327 I 2 994 f7 Yl L71lV7 1 We 7PW7 T fmzy7 k7 O IN 47747 229

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