Introduction to Three-phase Circuits. Balanced 3-phase systems Unbalanced 3-phase systems

Transcription

1 Intrductin t Three-hse Circuits Blnced 3-hse systems Unblnced 3-hse systems 1

2 Intrductin t 3-hse systems Single-hse tw-wire system: Single surce cnnected t ld using tw-wire system Single-hse three-wire system: Tw surces cnnected t tw lds using three-wire system Surces hve EQUAL mgnitude nd re IN PHASE 2

3 Circuit r system in which AC surces erte t the sme frequency but different hses re knwn s lyhse. Blnced Tw-hse three-wire system: Tw surces cnnected t tw lds using three-wire system Surces hve EQUAL frequency but DIFFFERENT hses Tw Phse System: A genertr cnsists f tw cils lced erendiculr t ech ther The vltge generted by ne lgs the ther by 90. 3

4 Blnced Three-hse fur-wire system: Three surces cnnected t 3 lds using fur-wire system Surces hve EQUAL frequency but DIFFFERENT hses Three Phse System: A genertr cnsists f three cils lced 120 rt. The vltge generted re equl in mgnitude but, ut f hse by 120. Three hse is the mst ecnmicl lyhse system. 4

5 AC Genertin Three things must be resent in rder t rduce electricl current: ) Mgnetic field b) Cnductr c) Reltive mtin Cnductr cuts lines f mgnetic flux, vltge is induced in the cnductr Directin nd Seed re imrtnt

6 GENERATING A SINGLE PHASE S N Mtin is rllel t the flux. N vltge is induced.

7 GENERATING A SINGLE PHASE S N Mtin is 45 t flux. Induced vltge is f mximum.

8 GENERATING A SINGLE PHASE S x N Mtin is erendiculr t flux. Induced vltge is mximum.

9 GENERATING A SINGLE PHASE S N Mtin is 45 t flux. Induced vltge is f mximum.

10 GENERATING A SINGLE PHASE S N Mtin is rllel t flux. N vltge is induced.

11 GENERATING A SINGLE PHASE S N Ntice current in the cnductr hs reversed. Mtin is 45 t flux. Induced vltge is f mximum.

12 GENERATING A SINGLE PHASE S N Mtin is erendiculr t flux. Induced vltge is mximum.

13 GENERATING A SINGLE PHASE S N Mtin is 45 t flux. Induced vltge is f mximum.

14 GENERATING A SINGLE PHASE S N Mtin is rllel t flux. N vltge is induced. Redy t rduce nther cycle.

15 GENERATION OF THREE-PHASE AC S Three ltges will be induced crss the cils with 120 hse difference x x N

16 Prcticl THREE PHASE GENERATOR The genertr cnsists f rtting mgnet (rtr) surrunded by sttinry winding (sttr). Three serte windings r cils with terminls -, b-b, nd c-c re hysiclly lced 120 rt rund the sttr. As the rtr rttes, its mgnetic field cuts the flux frm the three cils nd induces vltges in the cils. The induced vltge hve equl mgnitude but ut f hse by 120.

17 THREE-PHASE WAEFORM Phse 1 Phse 2 Phse Phse 2 lgs hse 1 by 120. Phse 2 leds hse 3 by 120. Phse 3 lgs hse 1 by 240. Phse 1 leds hse 3 by 240.

18 WHY WE STUDY 3 PHASE SYSTEM? ALL electric wer system in the wrld used 3-hse system t GENERATE, TRANSMIT nd DISTRIBUTE One hse, tw hse, r three hse icn be tken frm three hse system rther thn generted indeendently. Instntneus wer is cnstnt (nt ulsting). thus smther rttin f electricl mchines High wer mtrs refer stedy trque Mre ecnmicl thn single hse less wire fr the sme wer trnsfer The munt f wire required fr three hse system is less thn required fr n equivlent single hse system. 18

19 3-hse systems Genertin, Trnsmissin nd Distributin 19

20 3-hse systems Genertin, Trnsmissin nd Distributin 20

21 Y nd cnnectins Blnced 3-hse systems cn be cnsidered s 3 equl single hse vltge surces cnnected either s Y r Delt () t 3 single three lds cnnected s either Y r SOURCE CONNECTIONS Y cnnected surce LOAD CONNECTIONS Y cnnected ld cnnected surce cnnected ld Y-Y Y- -Y - 21

22 Blnce Three-Phse ltges Tw ssible cnfigurtins: Three-hse vltge surces: () Y-cnnected ; (b) Δ-cnnected 22

23 Blnced 3-hse systems LOAD CONNECTIONS Y cnnectin cnnectin n Z 1 Z c Z b b c Z 2 Z 3 Z c b Blnced ld: Z 1 = Z 2 = Z 3 = Z Y Z = Z b = Z c = Z Y Z Z 3 Unblnced ld: ech hse ld my nt be the sme. 23

24 Phse Sequence The hse sequence is the time rder in which the vltges ss thrugh their resective mximum vlues. cn n + bn n b c v v v n bn cn (t) (t) (t) cs( t) cs( t 120 cs( t 120 ) ) n 0 bn 120 cn 120 RMS hsrs! n bn cn 24

25 Phse Sequence cn 120 cn n + n n 0 bn b c 120 bn 120 Phse sequence : n leds bn by 120 nd bn leds cn by 120 This is knwn s bc sequence r sitive sequence 25

26 Wht if different hse sequence? Phse Sequence v n (t) 2 cs( t) n 0 v cn (t) 2 cs( t 120 ) cn 120 v bn (t) 2 cs( t 120 ) bn 120 RMS hsrs! n cn bn 26

27 Phse Sequence Wht if different hse sequence? bn n 0 cn 120 Phse sequence : n leds cn by 120 nd cn leds bn by 120 This is knwn s cb sequence r negtive sequence 27

28 Exmle 1 Determine the hse sequence f the set f vltges. v v v n bn cn 200 cs( t 10) 200 cs( t 230) 200 cs( t 110)

29 Slutin: The vltges cn be exressed in hsr frm s n bn cn We ntice tht n leds cn by 120 nd cn in turn leds bn by 120. Hence, we hve n cb sequence.

30 c cn I I I b c n I n + 0 Z Y Z Y bn I b ZY I c I n b 0 I n I b I c I Blnced 3-hse Y-Y line currents Line current = hse current B b A N Z Y The wire cnnecting n nd N cn be remved! n 3 Z Y b nb Z Y 30 bc c C bn b 0 nc n 0 bn 120 n 3 90 cn n cn 120 n 60 Phse vltges mesured between the neutrl nd ny line (line t neutrl vltge) line-line vltges OR Line vltges 30

31 Blnced 3-hse systems Blnced Y-Y Cnnectin b n 0 nb

32 Blnced 3-hse systems Blnced Y-Y Cnnectin b n nb 0 60 cn 3 30 n bn 32

33 Blnced 3-hse systems Blnced Y-Y Cnnectin b n nb n nb 33

34 Blnced 3-hse systems Blnced Y-Y Cnnectin b n 0 nb n nb bn bc bn nc 3 90 nc 34

35 Blnced 3-hse systems Blnced Y-Y Cnnectin n b n 0 nb cn n nb bn bc bn nc 3 90 nc c cn n

36 Blnced 3-hse systems Blnced Y-Y Cnnectin b n 0 nb c 30 cn 30 b bn n bc bn nc c cn n bc L 3 where L b bc c nd n bn cn Line vltge LEADS hse vltge by 30 36

37 Blnced 3-hse systems Blnced Y-Y Cnnectin Fr blnced Y-Y cnnectin, nlysis cn be erfrmed using n equivlent er-hse circuit: e.g. fr hse A: I A n n + I n =0 N Z Y cn c bn b I b I c B Z Y Z Y C 37

38 Blnced 3-hse systems Blnced Y-Y Cnnectin Fr blnced Y-Y cnnectin, nlysis cn be erfrmed using n equivlent er-hse circuit: e.g. fr hse A: n n + I A N Z Y I Z n Y Bsed n the sequence, the ther line currents cn be btined frm: I b I 120 I c I120 38

39 Blnced 3-hse systems Blnced Y- Cnnectin c cn n n + bn b I b I c I B Z A I AB Z I BC Z C I CA n 0 bn 120 cn 120 b 330 AB bc 3 90 BC c 3150 CA I I I AB CA BC AB Z BC Z CA Z Using KCL, Phse currents I I I b I I I AB AB AB I I I BC BC BC I CA ( I AB ( c ICA ) )

40 Blnced 3-hse systems Blnced Y- Cnnectin I c I CA 30 I b IL 3I 30 I BC I b I 30 I I I AB AB AB I BC BC I CA ( I IBC 3 30 where IL I Ib Ic nd I IAB IBC ICA Ic ICA 3 30 Phse current LEADS line current by 30 I I AB AB I ( ) ) 40

41 c Blnced 3-hse - b I Z A Z Line-line vltge is the sme s hse vltge in - b 0 bc 120 c + bc b I b I c B I AB Z I BC C I CA cn 120 b AB bc BC I I AB BC AB Z BC Z Using KCL, Phse currents I I b I I I AB AB AB I I BC BC I CA ( I AB ( ) ) line currents c CA I CA CA Z I I BC 3 30 c ICA

42 Blnced 3-hse systems Blnced - Cnnectin c b I Z A Z b 0 bc 120 c + bc b I b I c B I AB Z I BC C I CA cn 120 Alterntively, by trnsfrming the cnnectins t the equivlent Y cnnectins er hse equivlent circuit nlysis cn be erfrmed. 42

43 Blnced 3-hse systems Blnced -Y Cnnectin I A b 0 c b L1 N Z Y bc 120 c 120 c + bc b I b I c B Z Y Z Y C Hw t find I? L1 - b Z Y I Z Y I b 0 I I b Z b Y Since circuit is blnced, I b = I -120 I I I (1 1 ( 120 )) b Therefre I 30 Z Y 3 I

44 Blnced 3-hse systems Blnced -Y Cnnectin I A b 0 c b N Z Y bc 120 c 120 c + bc b I b I c B Z Y Z Y C Hw t find I? (Alterntive) Trnsfrm the delt surce cnnectin t n equivlent Y nd then erfrm the er hse circuit nlysis 44

45 A blnced Y-Y system, shwing the surce, line nd ld imednces. Line Imednce Surce Imednce Ld Imednce Equivlent Circuit 45