So far circuit analysis has been performed on single-

Transcription

1 Three phase systems

2 ntrdctn S far crct analyss has been perfrmed n sngle- phase crcts,.e. there has been ne crct wth a nmber f dfferent vltage and crrent srces whch were nt synchrnsed n any prpsefl way. n a three-phase system, three vltages are generated wth specfc relatnshp n ampltde, freqency and phase. The ampltde and freqency f the vltages are the same bt each vltage s dsplaced frm the ther by 120. Three phase systems are sed t delver pwer frm a pwer statn t a lcal sbstatn befre beng dstrbted t hme and factres. n the K, the vltage n the transmssn system s 250kV-440kV and at dstrbtn level t s 11kV-145kV.

3 Merts f three t phase systems s Wth same szes,3-phase generatrs and electrcal mtrs have hgh tpt pwer, smple n cnstrctn and better capacty than sngle phase systems. Transmssn f electrcty n three phases ecnmcally. Sngle phase nstantanes pwer s tme-varant whle hl ttal nstantanes pwer f three phase s tme-nvarant.

4 nstantanes expressn X Y ( t ) 2 cs( t ) ( t) 2 cs( t 120 ) ( ) 2 cs( 120 ) t t 0 t

5 Phasr expressn Phase Seqence: t refers t the rder n whch three-phase vltage generated Pstve phase seqence:

6 Y cnnectn f srce X Y The netral pnt s knwn as the star pnt.... Phase vltage,,... Lne vltage,, Phase crrent = lne crrent,, N Three-wre systems Fr-wre systems

7 Relatn between phase and lne vltages N N N N The phase relatn f three-phase vltages and crrents mst be clear.

8 Smmary fr symmetrc Y cnnectn Lne crrent s eqal t phase crrent Phase vltage s symmetrc,and lne vltage s als symmetrc 3 Lne vltage s tmes the phase vltage l 3 Lne vltage phase leads phase vltage by 30 p N N N

9 Delta cnnectn f srce Y X Lne vltage = phase vltage... Phase vltage,,... Lne vltage,, Lne crrent phase crrent,,?

10 Relatn between phase and lne crrents ab 0 bc 120 ca 120 ca 30 a b c ab b a bc ca c bc 30 ca ab ab bc ca ca ab bc 3 ab 30 3 bc 30 3 ca 30

11 Smmary fr delta cnnectn Lne vltage s dentcal t phase vltage Phase crrent s symmetrc and lne crrent s als symmetrc 3 Lne crrent s tmes the phase crrent l 3 p Lne crrent lags phase crrent by 30 Reference drectn, ab, bc, ca

12 alanced Y-Y Y cnnectn _ N n Y - Y Example: Gven n symmetrc 3-phase srce, lne vltage s 38030V,symmetrc lad = Slve lne crrents?

13 Vltage at the neral pnt The character f balanced The character f balanced three-phase vltage:

14 alanced Y-Y Y cnnectn - _ - N n Gven S N V V N - N n N ( ) ( )

15 alanced delta-delta cnnectn a ca c bc ab b Example: Gven n symmetrc 3-phase crct, lne vltage 380 0V,Symmetrc lad =10030 Slve lne crrents?

16 alanced delta-delta cnnectn hse phase t cmpte f 3800 V - ab a b ab ( ) ( ) ( )

17 alanced Y-delta cnnectn alanced Y delta cnnectn a _ N b c ab ca Y - b c bc n - Y n - Y

18 Y - cnnected systems s There are a nmber f methds fr dealng wth sch systems. One methd s t change the srces frm star cnnected t delta cnnected. t remember t add n the asscated phase dfference, ths as the phase and lne vltage relatnshps as derved fr the star cnnected system. N _

19 Y - cnnected systems s Star Vltages Delta Vltages The calclatn prceeds as nrmal.

20 - Y cnnected systems s Smlarly change the delta cnnected srces t star. Then prceed as sal. Delta Vltages Star Vltages

21 nbalanced three-phase systems S far, the analyss has been n balanced three-phase systems. Fr nbalanced three-phase systems, the lad n each f the phases s nt the same. The calclatns are smlar bt they need t be dne fr each phase f the lad. The analyss f nbalanced lads and the dsplacement f mddle pnt.

22 nbalanced Y-Y Y 4 wre cnnectn N N a _ N N N N' N b n 0 c a b c N N N a N b N a N b N c N c 0

23 nbalanced delta cnnected lad a b _ N ca a c c bc ab b The specfed lne vltage wll be acrss each phase. Take three phases and pt them nt 3 ndependent sngle phase systems wth vltage 120 apart n phase. / / ab b ca a ab ca

24 nbalanced 3 wre Y cnnected lad N N _ N N' N c a b Ths s a dffclt case. Wtht the netral cndctr, the vltage at n wll vary. The crrents n the lad sm t zer at n and then express the crrents as vltages and mpedances.

25 Three-phase pwer Three-phase ttal pwer: PP P P When Lads are balanced: P 3 p p cs P 3 l l cs

26 3 phase pwer The pwer per phase = V ph ph csφ Ths TOTL pwer (n a balanced) system = 3V ph ph cs φ Delta Star V L = V ph, L = 3 ph V L = 3V ph, L = ph P T = 3V L L cs φ P T = 3V L L cs φ pparent pwer: * S P jq V P = Real Pwer (W, kw, MW) Q = Reactve Pwer (var, kvar, Mvar) S = mplex pwer (V, kv, MV)

27 Measrement f sngle phase wattmeter Vltage lp * rrent lp * 1 2 lads n crct k 1 cs s the angle between 1 and Pnter Deflectn ngel)

28 3-phase fr-wre cnnectn Lads s Y cnnectn and se three pwer meters t measre. The ttal pwer s eqal t the sm f three wattcmeters. t ths tme each vltage lp measre the phase vltage f each phase N * W * W 1 * W * W 2 * * W W3 lads

29 three-wre system wth nly tw wattmeter * * W 1 * * W 2 The ttal pwer s the algebrac sm f the meter readngs

30 Prncpal f measre pwer sng the twwattmeter methd p wattmeter methd p Ntes:three-phase ttal pwer s eqal t Ntes:three phase ttal pwer s eqal t the sm f tw meter readngs. Jst a sngle meter readng has n meanng Jst a sngle meter readng has n meanng.