Professor Ramzy R. Obaid HW: Ch.8 # 6, 10, 11, and 12

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1 Three-Phse Systems Prt 2 Prfessr Rmzy R. Oid HW: Ch.8 # 6, 10, 11, nd 12

2 With mny thnks nd ppreitin t Prfessr Mhmed A. El-Shrkwi

3 3 Y-Cnnetin Sure nd Ld Sure Trnsmissin Line Line urrent Ld n Phse urrent n n n n

4 Fr lned system n n n n n n Single-Phse Representtin 4

5 n n n ) ( ) ( Fr lned system n n n n n n

6 6 Fr lned system n n n Referene n n n n ( 120 ( 120 ) )

7 7 Neutrl Current f Blned Ld Fr lned system n

8 8 Delt () Cnnetin Sure nd Ld Sure Phse urrent - Trnsmissin Line Line urrent - Ld Phse urrent -

9 Delt () Cnnetin: Sure _ is line urrent is phse urrent 9

10 10 Kirhhff s Current lw t nde _ n Referene ltge Digrm is hsen referene

11 11 Line Currents n 30 0 Refere - (120 ) 3 ( 30 )

12 12 Let A Exmple Clulte the phse urrent f delt iruit A 10 0 Referene

13 13 Min Cnlusins fr Delt-Cnneted Line-t-line vltge is equl t phse vltge 3 ( 30 Line urrent is greter thn ld phse urrent y Line urrent lgs the ld phse urrent y )

14 14 Mixed Cnnetin Sure Phse urrent Trnsmissin Line Line urrent Ld Phse urrent - n

15 15 Mixed Cnnetin Sure Trnsmissin Line Line urrent Ld n - Phse urrent n n - n - n -

16 Y- Trnsfrmtin Y Y Y 16

17 Y- Trnsfrmtin Y Y n Y 2 Y 2 3 // 2 17

18 Y- Trnsfrmtin 2 3 // 2 Y Y Y 2 Y THEN 1 Y 3 18

19 Exmple 1. Clulte the phse urrent f the ld 2. Clulte the equivlent Y ld 3. Clulte the phse urrent f the equivlent Y ld n = 120 v = 4 j 3 19

20 20 n Prt 1: Prt 2: 5 37 Y A Prt 3: The phse urrent in Y ld is equl t A

21 Exmple Clulte the line urrent 1 = 4 j 3 2 = 12 - j 9 n = 120 v 21

22 Chnge delt t Y 1 = 4 j 3 2y = 4 - j 3 n = 120 v 22

23 23 eq = 25/8 n = 120 v / A

24 Pwer f 3-phse iruits phse phse MPORTANT P Q Fr Single phse phse phse phse phse s ( ) sin ( ) is the ngle etween phse vltge nd phse urrent. Use vltge s referene P Q Fr Blned 3-phse 3 3 phse phse phse phse s ( ) sin ( ) 31

25 32 Rel Pwer in Delt Ciruit phse phse line line P 3 _ 3 s ( ) 3 s ( ) phse phse P 3 s ( ) 3 s ( ) line line

26 33 Retive Pwer in Delt Ciruit phse phse line line Q 3 _ 3 sin ( ) 3 sin ( ) phse phse Q 3 sin ( ) 3 sin ( ) line line

27 Rel Pwer in Y Ciruit phse phse line line 3 P P 3 s ( ) 3 s ( ) phse phse 3 s ( ) 3 s ( ) line line 34

28 Retive Pwer in Y Ciruit phse phse line line 3 Q Q 3 sin ( ) 3 sin ( ) phse phse 3 sin ( ) 3 sin ( ) line line 35

29 Clulte the ld pwer Exmple n = 120 v = 4 j 3 36

30 37 n n A 30 0 A 30 0 n

31 38 Methd #1 P 3 phse phse s P 30 ( 7) 20. kw 3 s s 736 Methd #2 P 3 line line s P 30 ( 7) 20. kw 3 s s 736 Keep in mind The pf ngle is the ngle f the ld impedne. t is the sme s the ngle etween the phse vltge nd the phse urrent

32 3 phse trnsfrmer nk 39

33 3-phse trnsfrmer 40

34 Rti f Phse ltge 3-phse trnsfrmer Y-Y nnetin. Als knwn s str-str nnetin A N 1 N 2 n C B N Rti f Line ltge N n AN 1 N 2 AB 3 3 n AN N N

35 3-phse trnsfrmer ( -) A N 1 N 2 C B AC N 1 N 2 42 Rti f Phse ltge nd line vltge

36 Rti f Phse ltge 3-phse trnsfrmer (Y-) Als knwn s str-delt nnetin A N 1 n N 2 B C Rti f Line ltge N n AC 1 N 2 AC 3 AC n 3 N N

37 3-phse trnsfrmer nk (Y-) A N AB n 2 N 1 n N 1 N 2 AB B AB AB 3 n N 3 2 N 1 N 1 N 2 C N 1 N 2 44

Dorf, R.C., Wan, Z. T- Equivalent Networks The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000

Dorf, R.C., Wan, Z. T- Equivalent Networks The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000 orf, R.C., Wn,. T- Equivlent Networks The Eletril Engineering Hndook Ed. Rihrd C. orf Bo Rton: CRC Press LLC, 000 9 T P Equivlent Networks hen Wn University of Cliforni, vis Rihrd C. orf University of