Three-Phse Systems Prt 2 Prfessr Rmzy R. Oid HW: Ch.8 # 6, 10, 11, nd 12
With mny thnks nd ppreitin t Prfessr Mhmed A. El-Shrkwi
3 Y-Cnnetin Sure nd Ld Sure Trnsmissin Line Line urrent Ld n Phse urrent n n n n
Fr lned system n n n n n n Single-Phse Representtin 4
5 120 120 0 n n n ) ( ) ( 120 120 120 120 0 Fr lned system n n n n n n
6 Fr lned system n n n Referene n n n n 0 120 120 ( 120 ( 120 ) )
7 Neutrl Current f Blned Ld Fr lned system n 0 120 120 0
8 Delt () Cnnetin Sure nd Ld Sure Phse urrent - Trnsmissin Line - - - Line urrent - Ld Phse urrent -
Delt () Cnnetin: Sure _ is line urrent is phse urrent 9
10 Kirhhff s Current lw t nde _ n Referene ltge Digrm is hsen referene
11 Line Currents n 30 0 Refere - (120 ) 3 ( 30 )
12 Let 30 10 A Exmple Clulte the phse urrent f delt iruit 30 3 30 3 10 30 17.32 20 30 0 A 10 0 Referene
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 ) 30 0 3
14 Mixed Cnnetin Sure Phse urrent Trnsmissin Line Line urrent Ld Phse urrent - n
15 Mixed Cnnetin Sure Trnsmissin Line Line urrent Ld n - Phse urrent n n - n - n -
Y- Trnsfrmtin Y Y Y 16
Y- Trnsfrmtin Y Y n Y 2 Y 2 3 // 2 17
Y- Trnsfrmtin 2 3 // 2 Y Y Y 2 Y THEN 1 Y 3 18
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 n Prt 1: 312030 537 41.57 7 Prt 2: 5 37 Y 1.67 37 3 3 A Prt 3: The phse urrent in Y ld is equl t 3 30 3 41.57 7 30 72 37 A
Exmple Clulte the line urrent 1 = 4 j 3 2 = 12 - j 9 n = 120 v 21
Chnge delt t Y 1 = 4 j 3 2y = 4 - j 3 n = 120 v 22
23 eq = 25/8 n = 120 v 120 0 25 / 8 38.4 A
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
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
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
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
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
Clulte the ld pwer Exmple n = 120 v = 4 j 3 36
37 n 3 3 3 30 120 0 30 208 30 20830 537 30 n 41.57 7 72 37 A 30 0 A 30 0 n
38 Methd #1 P 3 phse phse s P 30 ( 7) 20. kw 3 s 3 20841.57s 736 Methd #2 P 3 line line s P 30 ( 7) 20. kw 3 s 3 20872 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
3 phse trnsfrmer nk 39
3-phse trnsfrmer 40
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 1 2 41
3-phse trnsfrmer ( -) A N 1 N 2 C B AC N 1 N 2 42 Rti f Phse ltge nd line vltge
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 2 1 43
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