Module 8. Three-phase Induction Motor. Version 2 EE IIT, Kharagpur

Transcription

1 Module 8 Thee-phae Induction Moto Veion EE IIT, Khaagpu

2 Leon 31 Equivalent Cicuit and Powe Flow Diagam of IM Veion EE IIT, Khaagpu

3 Intuctional Objective detemine the induced emf, and the cuent, pe phae in the tato and oto winding, find the elation between the oto input, oto coppe lo and oto output, in tem of lip, calculate the vaiou loe ion, coppe and mechanical, in an IM, and find whee do the loe occu. Intoduction In the peviou, i.e. econd, leon of thi module, the contuction (the tato and two type of oto quiel cage and wound (lip-ing one, of the thee-phae induction moto (IM, ha been decibed. Then, the pinciple of opeation, i.e. poduction of toque, with the tato upplied fom balanced thee-phae upply and the oto winding teminal hot-cicuited, i dicued. In thi leon, the equivalent cicuit pe phae of IM will be deived fit, to be followed by the peentation of powe flow diagam, wheein the vaiou loe, and alo whee do they occu, ae decibed. Keywod: The induced voltage (emf in tato winding and oto ba/winding, the equivalent cicuit pe phae of IM, the fictitiou eitance in the cicuit, input powe to tato and oto, loe ion lo, tato and oto coppe lo, mechanical loe, output powe. The induced emf pe phae, in the moto winding The induced emf pe phae in the tato winding i nealy equal to the input voltage pe phae, and i given by V E =. k w f φ Z = k w f φ T whee, V = Input voltage (V pe phae, to the tato winding E = Induced emf (V pe phae, in the tato winding φ = Flux (Wb pe pole f = Fequency (Hz o c/ of the input voltage Z = T = No. of tato conducto in eie pe phae T = No. of tato tun o coil in eie pe phae k w = kd k p = Stato winding facto k d = Ditibution facto of tato winding k p = Pitch facto of tato winding The above fomula, not deived hee, i a tandad one available in any textbook. It i imila to the fomula fo the induced emf in a tanfome, deived in the ealie module. A the winding in thi cae i tationay, with the otating magnetic field otating at a Veion EE IIT, Khaagpu

4 peed of n = f /( p / = ( f / p (alo temed a the ynchonou peed, the fequency of the induced emf in the tato winding i ame a that of input fequency ( f = ( p /, whee, n n = Speed of the otating magnetic field (ev/ec p = No. of pole fo which the tato winding of IM i deigned The induced emf pe phae at tandtill ( ω = 0. 0, o = 1. 0 in the oto winding (auming a wound o lip-ing one, i given by E =. k w f φ Z = k w f φ T whee, E = Induced emf (V pe phae, in the oto winding at tandtill ( = 1. 0 f = f = f = Fequency (Hz in the oto winding at tandtill ( = 1. 0 Z = T = No. of oto conducto in eie pe phae T = No. of oto tun o coil in eie pe phae k = k k = Roto winding facto w k d d p = Ditibution facto of oto winding k p = Pitch facto of oto winding It may be noted fo the wound oto, the numbe of pole in the oto winding mut be the ame a thoe in the tato winding, which ha been explained in the peviou leon (#30. The quiel cage oto can be conideed a equivalent to a wound one. The fequency of the induced emf in the oto winding with the oto otating at any peed, i popotional to the elative peed between the peed of the otating magnetic field, and that of the oto, and i given by f = ( p / ( n n = ( p / n = f whee, n = (1 = Speed of the oto (ev/ec n ( n n / n = 1 ( n / n = = lip in IM The atio of the induced emf pe phae, in the tato and oto winding, with the oto at tandtill, i given by, E / E T / T = Z / Z auming that the winding facto in both winding ae ame. It may be noted that the induced voltage pe phae in the winding i popotional to the effective tun pe phae, of the winding ( = k w T. The fomula i imila to that obtained in a tanfome, whee the induced voltage pe tun ( E t = E / T i the ame in the two (pimay/econday winding. The induced emf in the oto winding with the moto unning at any peed i popotional to the oto fequency ( f = f, and i given by E =. k w f φ Z The cuent in the balanced thee-phae winding of the tato poduce a eultant mmf, otating at the ynchonou peed ( n elative to tato conducto, which i tationay. Similaly, the cuent in the balanced thee-phae winding of the oto (taken Veion EE IIT, Khaagpu

5 a a wound one poduce anothe eultant mmf, otating at the peed of ( n n = n elative to oto conducto in the ame diection a that of the oto, which otate at a peed ( n = (1. Hence, the peed of the eultant oto mmf elative to tato n conducto i ( n + n = n. The axe of the eultant oto mmf otate at the ame peed a thoe of the eultant tato mmf, o that the mmf ae tationay elative to each othe. The equivalent cicuit pe phae, of the oto The cuent pe phae in the oto winding (Fig. 31.1a i given by I = E ( + ( x whee, = Reitance ( Ω pe phae, of the oto winding x = π f l = Leakage eactance ( Ω pe phae, of the oto winding at tandtill ( = 1.0 o ω = 0. 0 The leakage eactance pe phae of the oto winding at any othe peed n, i popotional to the oto fequency ( f = f, and i given by x = x. The tem in the denominato of the expeion i the magnitude of the oto impedance pe phae at any othe peed, which i ( z ( + ( x =, with it phae angle a φ = tan [( x / ]. It may be noted that the ubcipt i ued hee, intead of ealie. Similaly, the ubcipt 1 may be ued, intead of, i.e. tato. In the expeion fo the oto cuent pe phae, if both numeato and denominato i divided by the tem, I i E I = ( / + ( x The cicuit of the oto (Fig. 31.1a can now be dawn a hown in Fig. 31.1b, fom the equation given ealie. It may be noted hee the input voltage pe phae to the cicuit i contant, i.e. E and the leakage eactance pe phae i alo contant, x, both being ame a at tandtill, with the oto fequency being ame a line o input fequency. Alo the phae angle of the impedance, whoe magnitude i the tem in the denominato, emain ame a φ = tan [ x /( / ] = tan [( x / ], a obtained ealie. Veion EE IIT, Khaagpu

6 The cicuit of Fig. 31.1b can be edawn a hown in Fig. 31.1c, with the eitance ( / now being hown a um of two eitance, oto eitance, and fictitiou eitance, ( ( / = (1 /. The fit pat of the cicuit conit of the oto impedance at tandtill, which i ( z φ = + j, whoe magnitude and phae angle ae ( ( x x z = + and φ = tan ( x / epectively. The elation between oto input, oto coppe lo and oto output Fom the equivalent cicuit (Fig. 31.1c pe phae of the oto winding, the total input (W to the oto i Pi = 3 E I co φ = 3 ( I ( /. Pleae note that the phae angle, φ i the angle between the induced voltage and cuent (both in the oto. The total input to the oto i the powe tanfeed fom the tato via ai gap. The total coppe lo in the oto winding i 3 ( I. The total output of the oto i the total powe lo in the fictitiou eitance, (1 / of the oto cicuit (Fig, 31.1c, and i given by 3 ( I (1 /. The total oto output i obtained alo a the diffeence of the total oto input and the total oto coppe lo. Altenatively, Total input to the oto = Total oto coppe lo + Total oto output It may be hown that Total oto coppe lo = Total oto input, o, Total oto input = ( 1/ Total oto coppe lo In tem of total oto output, the elationhip ae a follow, Total oto coppe lo = [ / (1 ] Total oto output, o, Total oto output = {( 1 / ] Total oto coppe lo The elation between total oto output and total oto input i Total oto output = ( 1 Total oto input o, Total oto input = [ 1/(1 ] Total oto output In the above dicuion, total oto output i the output in electical tem, alo temed a go one, which include mechanical, o fiction and windage loe. The expeion fo go powe and toque developed, and the toque-peed o toque-lip chaacteitic of Induction moto along with othe elevant point, will be peented in the next leon. Powe flow diagam In the induction moto, efficiency i Output Output Efficiency (η = = Input Output + loe a Input = output + loe The total loe ae loe in both tato and oto, and mechanical loe. The tato loe ae ion o coe lo and coppe lo, i.e. lo in the tato winding eitance. The coe lo i the um of hyteei and eddy cuent loe, with the fequency in the tato Veion EE IIT, Khaagpu

7 being line fequency of 50 Hz. Both the above loe ae elated to fequency. It may be noted hee that the flux in the ai gap i ated, a the input o upply voltage fed to the tato winding i ated with the fequency i alo ated. The coppe lo i popotional to the quae of the cuent in the tato winding. The lo in the oto i only coppe lo a hown ealie, with the ion lo being low due to low fequency in the oto coe. Fo example, the oto fequency ( f = f i only Hz, if the lip i aumed a 4%, the peed being 1,440 pm fo a 4-pole moto. The line (input fequency i 50 Hz. The ion lo i elated to the fequency a tated ealie. The net output available at the haft i the go output minu the mechanical loe. Befoe coming to the powe flow diagam in an Induction moto, total input powe fed to the moto via tato (winding i Pi = 3 V I coφ i = 3 V I co( V, I whee, V and I ae the input voltage and cuent pe phae, to the moto. Total input powe to the moto (tato = Stato loe (ion & coppe + Total input powe to the oto (o Powe tanfeed via ai gap Total input powe to the oto = Roto coppe lo + Total output powe (go Total output powe (go = Mechanical loe + Total output powe (net [o Powe available at the haft] It may be noted that all the loe, excluding mechanical one, ae total fo all thee phae, and a given ealie, ion loe in the oto ae vey low.. In thi leon the thid one of thi module, the equivalent cicuit pe phae of an IM ha been deived, tating with the fomula fo the induced emf pe phae, in both tato and oto winding. The vaiou loe and whee do they occu, ae decibed next, followed by peentation of powe flow diagam fo IM. In the next leon a given ealie, the expeion fo go powe o toque developed, and the toque-peed o toque-lip chaacteitic of an IM, along with othe elevant point, will be peented in detail. Veion EE IIT, Khaagpu