AC Circuits Three-Phase Circuits

Transcription

1 AC Circuits Thr-Phs Circuits

2 Contnts Wht is Thr-Phs Circuit? Blnc Thr-Phs oltgs Blnc Thr-Phs Connction Powr in Blncd Systm Unblncd Thr-Phs Systms Aliction Rsidntil Wiring

3 Sinusoidl voltg sourcs A siml AC gnrtors Singl-hs systm Whn conductor rotts in constnt mgntic fild sinusoidl wv is gnrtd. Mor ol ics? Mor coils? Whn th loo is moving rndiculr to th lins of flux th mximum voltg is inducd. Norml houshold: Singl-hs thr-wir Singl-hs two-wir Whn th conductor is moving rlll with th lins of flux no voltg is inducd. nutrl

4 Polyhs Thr-hs circuit: A systm roducd by gnrtor consisting of thr sourcs hving th sm mlitud nd frquncy but out of hs with ch othr by 10. Thr sourcs with 10 out of hs Four wird systm 4

5 Advntgs of thr-hs circuit Most of th lctric owr is gnrtd nd distributd in thr-hs: Lss/mor thn -hs rquird tkn from -hs Th instntnous owr in thr-hs systm cn b constnt (not ulsting): uniform owr trnsfr nd lss vibrtion of thr-hs mchin Th mount of owr th thr-hs systm is mor conomicl tht th singl-hs. n fct th mount of wir rquird for thr-hs systm is lss thn tht rquird for n quivlnt singl-hs systm. 5

6 Blnc Thr-Phs oltgs A thr-hs gnrtor consists of rotting mgnt (rotor) surroundd by sttionry winding (sttor). t cn suly owr to both singlhs nd thr-hs lod A thr-hs gnrtor Th gnrtd voltgs 6

7 Blnc Thr-Phs oltgs Two ossibl configurtions: Four wirs Thr wirs Phs voltg Thr-hs voltg sourcs: () Y-connctd ; (b) Δ-connctd Blncd voltgs: n n 0 bn bn cn cn 7

8 Blnc Thr-Phs oltgs Blncd hs voltgs r qul in mgnitud nd r out of hs with ch othr by 10. n bn cn n bn cn j 4 j Th hs squnc is th tim ordr in which th voltgs ss through thir rsctiv mximum vlus. j bc/ositiv squnc cb/ngtiv squnc bc/ositiv squnc cb/ngtiv squnc n cn bn j 4 j j A blncd lod is on in which th hs imdncs r qul in mgnitud nd in hs Trnsform: Y 1 Y b c 8

9 Exml Exml 1 Dtrmin th hs squnc of th st of voltgs. Solution: Th voltgs cn b xrssd in hsor form s v v v n bn cn 00 cos( t 10) 00 cos( t 0) 00 cos( t 110) n bn cn W notic tht n lds cn by 10 nd cn in turn lds bn by 10. Hnc w hv n cb squnc. 9

10 Blnc Thr-Phs Connction Four ossibl connctions 1. Y-Y connction (Y-connctd sourc with Y- connctd lod). Y-Δ connction (Y-connctd sourc with Δ- connctd lod). Δ-Δ connction 4. Δ-Y connction 10

11 11 Blnc Y-Y systm A blncd Y-Y systm is thr-hs systm with blncd y-connctd sourc nd blncd y-connctd lod. c bc b L cn bn n L whr L l S Y j j j j bn n nb n b Lin voltg: 4 j j j c Y n Y bn b Y n Lin currnt (KL): 0-0 c b n c b 0 nn oltg cross th nutrl lin is zro: th nutrl lin cn b rmovd (rth cting s th nutrl lin). Th sm s th hs currnt in Y-Y Phsor digrm?

12 Blncd Y-Y connction Exml Clcult th lin currnts in th thr-wir Y-Y systm shown blow: Ans b c A A A 1

13 Blnc Y- Connction A blncd Y-Δ systm is thr-hs systm with blncd y-connctd sourc nd blncd Δ-connctd lod. Lin currnt Phs currnt Lin voltg = th voltg cross th lod Phs currnt Lin currnt b CA Δ 4 j 1 j 6 L whr L b c BC CA 1

14 Blnc Y- Connction: Exml Exml A blncd bc-squnc Y-connctd sourc with n is connctd to Δ-connctd lod (8+j4) r hs. Clcult th hs nd lin currnts. Solution Using singl-hs nlysis n / A Othr lin currnts r obtind using th bc hs squnc 14

15 Blnc - Connction A blncd Δ-Δ systm is thr-hs systm with blncd Δ -connctd sourc nd blncd Δ -connctd lod. Lin voltg = th hs voltg b Phs currnt Δ b Δ Lin currnt CA 1 j 6 4 j L 15

16 Blnc - Connction: Exml Exml 4 A blncd Δ-connctd lod hving n imdnc 0-j15 is connctd to Δ-connctd ositiv-squnc gnrtor hving ( b 00 ). Clcult th hs currnts of th lod nd th lin currnts. Ans: Th hs currnts A; BC A; A Th lin currnts A; b A; c A 16

17 Blnc -Y Connction A blncd Δ-Y systm is thr-hs systm with blncd Y-connctd sourc nd blncd Y-connctd lod. Cn you work out th rltionshi btwn lin currnt nd hs currnt? 17

18 Blnc -Y Connction: Exml Exml 5 A blncd Y-connctd lod with hs imdnc 40+j5 is sulid by blncd ositiv-squnc Δ-connctd sourc with lin voltg of 10. Clcult th hs currnts. Us b s rfrnc. Answr Th hs currnts AN BN CN.57 6 A; A;.5758 A; 18

19 Blncd thr-hs: Summry of hs nd lin /

20 0 Powr in Blncd Systm nstntnous owr (Y-lod Y = ) Comring th owr loss in () singl-hs systm nd (b) thr-hs systm - hs singl ' L L loss P R P hs thr - ' ' L L loss P P R f sm owr loss is tolrtd in both systm thr-hs systm us only 75% of mtrils of singl-hs systm cos cos cos t v t v t v CN BN AN cos cos cos t i t i t i c b cos c CN b BN AN c b i v i v i v θ Q P jq P sin cos hs : on For * S Tim indndnt

21 Unblncd Thr-Phs Systms An unblncd systm is du to unblncd voltg sourcs or n unblncd lod. n AN A b b c BN B c CN C To clcult owr in n unblncd thr-hs systm rquirs tht w find th owr in ch hs. Th totl owr is not simly thr tims th owr in on hs but th sum of th owrs in th thr hss. 1

22 Unblncd Thr-Phs Systms: Exml Exml 6 Dtrmin th totl vrg owr rctiv owr nd comlx owr t th sourc nd t th lod Ans At th sourc: S s = -(087 + j84.6) A P = -087W P r = -84.6AR At th lod: S L = (19 + j111) A P = 19W P r = 111AR

23 Aliction Rsidntil Wiring A 10/40 houshold owr systm

24 Aliction Rsidntil Wiring () Singl-hs thr-wir rsidntil wiring A tyicl wiring digrm of room 4