Basic Electrical Engineering for Welding [ ] --- Introduction ---

Transcription

1 Basc Elctrcal Engnrng for Wldng [] --- Introducton --- akayosh OHJI Profssor Ertus, Osaka Unrsty Dr. of Engnrng VIUAL WELD CO.,LD OK 15 Ex. Basc A.C. crcut h fgurs n A-group show thr typcal A.C. crcuts and th fgurs n B-group show th rlatons btwn oltag() and currnt() n ths A.C. crcuts. Slct th bst cobnaton btwn th and put th appropratnubrs n th parnthss A-group B-group t C-crcut t -crcut t L-crcut

2 Basc crcut lnts An lctrc crcut s ford by an ntrconncton of arous crcut lnts. h basc crcut lnts ar: rsstanc, ; capactanc, C;nductanc, L; oltag sourc, ; and currnt sourc, ; hs ar shown graphcally n Fg.1. Fg.1 Basc crcut lnts h oltag-currnt rlatonshp for th rsstanc n Fg.1-(a) s gn by Oh's Law as = (1-1) h unt of rsstanc s th oh (). h oltag for th capactanc C n Fg.1-(b) s gn by th followng quaton, = qc (1-) whr q s charg n coulob. h unt of capactanc s th farad (F). Usng th dfnton of currnt,th nxt xprsson s obtand. = dq (1-3) = C or = C d (1-4) Inductanc, L n Fg.1-(c) has th - rlatonshp = L d (1-5) h unt of nductanc s th hnry (H). [J.J.Cathy and S.A.Nasar, Basc Elctrcal Engnrng, McGraw-Hll,1997 ] Elntary A.C. crcut Stady stat rsponss of, L and C to snusodal nputs 1 Snusodal wa Many lctrcal qupnts of practcal portanc ar xctd by ac sourcs, whr ac s an abbraton for altrnatng currnt, plyng a prodcal chang of drcton of currnt or oltag. Most portant ac wafor s of snusodal typ as shown n th followng fgur, whr th oltag s xprssd by th sn functon. (s Eq.(-1)). Fg. 1 Snusodal wafor = V snt (-1) In Eq.(-1), V s known as th apltud and as th angular frquncy (n rad/s), and th frquncy of th wa s xprssd by th nxt quaton, f = 1 = (-)

3 Stady stat rsponss of,l and C (1) rsstanc E = = E sn ωt = sn ωt h currnt s n phas wth th appld oltag, and th apltud s 1/ ts th apltud of th oltag. () L nductanc d = L I sn ωt = ωli cosωt h currnt lags wth th appld oltag. E cosωt (3) C capactanc q = E sn ωt q = CE snωt C h currnt lads wth th appld oltag. dq = = ωce cosωt Elntary A.C. crcut Induct actanc and Capact actanc 1 Induct ractanc For an nductanc L, wth appld oltag, th followng rlaton (1) s obtand btwn E and I n stady stat, as dscrbd prously. E = LI (1) Equaton (1) s sa n for as Oh s Law and L corrsponds to th rsstanc n th Law. Accordngly, X L =L s calld as nduct ractanc, asurd n ohs. Capact ractanc For a capactanc C, th followng rlaton () s obtand btwn E and I n stady stat. E = (1 C I () Slarly to th cas of nductanc, Xc = 1 C s calld as capact ractanc and th unt s oh.

4 Vctor rprsntaton of snusodal wa Anothr way of rprsntng snusodal wa s gn by th rotatng ctor. Fgur 1 shows an xapl of th rotatng ctor xprsson of snusodal wa, whr th ctor V.s rotatng around th orgnal pont wth angular locty n th countrclockws drcton. V sn V sn V t t (a) otatng ctor (b) Snusodal wa Fg.1 otatng ctor xprsson of snusod Vctor rprsntaton of snusodal wa Fgur shows th cas that th currnt and oltag ar out of phas, whr s known as th phas angl btwn &. V I, V sn I sn( phas angl btwn and Fg. Vctor xprsson of phas dffrnc It s connnt to rprsnt such snusods by coplx nubrs. Accordng to Eulr s forula, Eqs.(1) & () ha bn obtand. costj snt jt (1) cost( ), snti( ) () Iagnary snt sn al cost Fg.3 prsntaton of snusodal wa by coplx nubr OK 91

5 Vctor rprsntaton of snusodal wa In th coplx syst, th currnt s gn as follows, (3) As an xapl, lt us consdr a -L crcut whr th rlaton btwn and s xprssd n Eq.(4). L Fg.4 -L crcut = + L d w Fgur 5 s a ctor dagra of th -L crcut, whr th ral part of th oltag: s and th agnary part of s jl, as gn by Eq.(5). jl jl h coplx pdanc: Z s dfnd as Z = = jl h ral part of th pdanc s th rsstanc and th agnary part of Z s th ractanc. Fg.5 Vctor dagra of -L crcut Elntary A.C. crcut Powr and Powr Factor n AC crcuts L d = + L I sn ωt = I sn ωt + ωli cosωt = + ( ω L) sn( ωt + θ ) I Fg.1 An xapl of AC crcut tanθ = ωl / Fg. Voltag and currnt wafor n th AC crcut

6 Powr and Powr Factor n AC crcuts h nstantanous powr, p, s xprssd by p = = V I snt sn(t+) V = I + ( ωl) (3-1) If s th prod of th wafor, thn th arag powr, P, s gn by 1 1 P = p V Icosθ VI cosθ = = (3-) whr V and I ar th rs (root an squar) oltag and rs currnt, so calld th ffct alu, dfnd by Eq.(3-3). V = V / Elntary A.C. crcut = 1/ Fro th abo xprssons, th followng dfntons of powr ar gn: VI : apparnt powr (VA) P = VI cos: act or ral powr (W) Q = VI sn: ract powr (ar) cos: powr factor. (3-3) [J.J.Cathy and S.A.Nasar, Basc Elctrcal Engnrng, McGraw-Hll,1997 ] Ex. Effct alu of snusodal wa In AC crcut, th nstantanous oltag: s xprssd by Eq.(1). = V snt, (V : Maxu alu of th oltag) (1) Show that th ffct alu of th oltag: V s gn by Eq.(). V = V / () OK 15

7 Elntary A.C. crcut --hr-phas crcuts-- Most lctrc powr systs ar thr-phas whr thy nol thr oltag sourcs hang th sa apltud and frquncy but dsplacd n t fro ach othr by 1. a = V sn ωt (1) b = V sn( ωt 1 ) () c = V sn( ωt 4 ) = Vsn( ϖt + 1 ) (3) Fg. 1 hr-phas powr and ts xprsson by coplx ctors For a thr-phas powr sourc, th followng xprssons of powr ar gn: 3 V apparnt powr (VA) l I l P = 3 V l I act or ral powr (W) l cosθ Q = 3 V l I ract powr (ar) l snθ whr V l ln oltag (ffct alu), I l ln currnt (ffct alu). [J.J.Cathy and S.A.Nasar, Basc Elctrcal Engnrng, McGraw-Hll,1997 ]