CALCULATION OF A TORQUE RIPPLE A THREE-PHASE ASYNCHRONOUS MOTOR SUPPLIED BY A PWM CONTROLLED INVERTER

Transcription

1 Zszyty Problow Maszyny Eltryczn Nr 2/24 (2) Pavl Zásalicý Tchnical nivrsity of Košic, Slovaia CALCLATION OF A TORQE RIPPLE A THREE-PHASE ASYNCHRONOS MOTOR SPPLIED BY A PWM CONTROLLED INVERTER METODA OBLICZEŃ PLSACJI MOMENT W TRÓJFAZOWYM SILNIK ASYNCHRONICZNYM ZASILANYM Z PRZEKSZTAŁTNIKA PWM Abstract: Th papr dals with stady stat analysis of lctroagntic torqu rippls of a thr-phas induction achin, which is supplid by an IGBT transistors bridg connctd invrtr Th invrtr s output voltag is controlld by a PWM of th input DC voltag Th coplx Fourir sris analysis of th invrtr s output voltag was ad, to obtain a spctru of th haronic supply voltags Th diffrnt voltag haronic was applid to th two-phas asynchronous achin odl to obtain th lctroagntic torqu wavfors for various opration conditions Kywords: torqu rippl, thr-phas otor, asynchronous otor, PWM controlld invrtr Introduction A thr phas voltag sourc invrtr prits to product an altrnativ thr-phas voltag of variabl or constant frquncy on th basis of continuous input sourc voltag Th load of th invrtr can b ithr passiv, which dos not contains any sourc of th voltag, or activ containing so sourc of voltag Th applications of th thr-phas invrtrs ar various and thir utilisations ar incrasing or and or Thy ar usd in ost cass as a supply dvic for asynchronous and synchronous otors whr frquncy and voltag ar controlld Th invrtrs ar oftn usd in scurity supplid dvics In this application th invrtr is supply fro accuulator, which is constantly loadd fro th ain In a cas of a ain disruption, th accuulator guarants alintation during shortr or longr ti Th invrtrs ar vry oftn st in th board ains of th airplans, traction ngins and train wagons Hr ar thir supplis by accuulators and convrts DC voltag on AC voltag of constant frquncy Thr hav bn dvlopd two typ circuits of th invrtrs Thr ar th cntr-tapd circuit and bridg circuit Th cntr-tappd circuit rquirs transforr for its opration This on prsnts so inconvnincy, spcially in th low frquncy ara For this rasons, th cntr-tappd circuit is vry sldo usd Earlir th invrtrs wr built using convntional thyristors as switching lnts In this cas th circuits rquir xtnsiv nt-wors coutation using capacitors and inductors for turning off Mor rcnt dvlopnts in dvic tchnology hav a nubr of nw switching dvics for invrtr application Th transistor faily of dvics is now vry widly usd In th Fig thr is illustratd th thr-phas bridg connctd invrtr using th insulatd gat bipolar transistor (IGBT) This dvic is bing incrasingly usd in th both th singl-phas and thr-phas invrtrs 2 Mathatical odl of th supply convrtr For invrtr s opration study at stady stat w considr following idalizd conditions: Powr switch, that ans th switch can handl unliitd currnt and blocs unliitd voltag Th voltag drop across th switch and laag currnt through switch ar zro Th switch is turnd on and off with no ris and fall tis Sufficintly good siz capacity of th input voltag capacitors dividr, to can suppos convrtr input DC voltag to by constant This assuption hlps us to analyz a powr circuit and hlps us to build a athatical odl for th invrtr at stady stat If th dsird rfrnc voltag is sin-wav, two paratrs dfin th control: Cofficint of th odulation - qual to th ratio of th odulation and rfrnc frquncy

2 4 Zszyty Problow Maszyny Eltryczn Nr 2/24 (2) + T T T C T4 T6 T2 - u u2 u 2 Fig Thr-phas bridg connctd invrtr Voltag control cofficint r - qual to th ratio of th dsird voltag aplitud and th DC supply voltag Gnrally to control th invrtr nuric control dvic is usd Th turn on and turn off ( ) angls ar calculatd by th discrdit of th rfrnc sin-wav That ans th rfrnc sin-wav is by a valus discrt rplacd If th cofficint of odulation is sufficintly grat, th diffrnc btwn ral valus and discrt valus is ngligibl Th phas s branchs ar control to crat th output voltags: u = + r sin( θ ) 2 2 2π u2 = + r sin θ 2 2 2π u = + r sin θ () whr: -is a DC invrtr s input voltag valu To calculat a turn on and turn off ( ) angls w copar th DC ipuls ara with th rqustd voltag ara Th invrtr s output voltag of th first branch can b athatically xprssd as a coplx Fourir sris of th for: j u c n θ = (2) Whr th Fourir cofficints ta a for: jn jn cn ( ) for j2π c 2π n n n = for = Siilarly for th othr two u2 = c2n phass: u = c n () Th lin voltags ar givn by a diffrnc btwn two voltags of th branchs as follow: u = u u = c c 2 2 n 2n u = u u = c c 2 2 2n n u = u u = c c n n (4) For th balancd load and insulatd nutral nod, following rlations btwn lin and phas voltags ar valid:

3 Zszyty Problow Maszyny Eltryczn Nr 2/24 (2) u = ( 2 u u2 u ) = ( 2c n c2n cn ) u2 = ( 2 u2 u u ) = ( 2c2n cn c n ) u = ( 2 u u u2 ) = ( 2cn c n c2n ) () Th Fig 2 dpicts wavfors of a phas voltags, calculatd on basis of quation () Th wavfors on th Fig2 wr calculatd for supply voltag of = 6V, output frquncy f = Hz and r = ; = 2; Thr-phas to two-phas transforation In lctrical nginring, th,, athatical transforation is ployd This transforation is nown as th Clar transforation It ploynt vry oftn siplifis th analysis of thr-phas circuits Concptually th Clar transforation prsnt particular part of Par transforation On of vry usful application of th Clar transforation is th gnration of th rfrnc signal usd for spac vctor odulation control of th thrphas invrtrs Th Clar transforation applid to th thrphas quantitis is shown blow in a atrix for 2 2 x xa 2 x = x b 2 2 (6) x x c u u 2 u Fig 2 Th phas voltags wavfor u u Fig Th wavfors of th transford voltags u,u Not also, that x is just a scald vrsion of th zro squnc tr fro sytrical coponnts W can also writ

4 6 Zszyty Problow Maszyny Eltryczn Nr 2/24 (2) x = 2 x x x x = ( x2 x ) 2 (7) Thn for transford phas voltags (8) u = ( 2c n c2n cn ) u = ( c2n cn ) Th Fig shows th cours of th transford voltag coponnts u,u vrsus ti, calculatd on th basis of quation (8) Fig 4 shows th trajctory of th spac vctor of th phas transford voltags u u Fig Trajctory of th spac vctor of th phas voltags 4 Haronic analysis Phasor of ach of voltag haronics is givn by a product of su of coplx Fourir s cofficint and DC input voltag 2 = ( 2c n c2n cn ) n= 2 = ( c2n cn ) for =, 2, n= With aplituds and phass ( ) ( ) ( ) ( ) A = abs ; P = angl ; A = abs ; P = angl ; (9) () For practical application w ar intrstd only for significant haronics Thrfor w nglct th haronics which aplitud is lss thnv On th Fig4 and Fig ar shown th aplituds and phass th significant haronics of th voltags u and u A d ) (ra P haronics haronics Fig 4 Aplituds and phass of u voltag A d ) (ra P haronics haronics Fig Aplituds and phass of u voltag On th bas of th haronic analysis ad abov, wr calculatd th wavfors of th voltags u and u

5 Zszyty Problow Maszyny Eltryczn Nr 2/24 (2) 7 u (N i u Fig 6 Calculatd wavfors of th voltags u and u Fig 8 Calculatd lctroagntic torqu for no loadd otor Asynchronous otor torqu and currnts calculation To calculat th phas currnts and torqu wavfor, th su of dtrind voltag haronics wr as a supply voltags to th dynaic odl of asynchronous otor attachd V u a u a (A i a - - (A i a Fig 7 Calculatd phas voltag and currnt wavfors for no loadd otor Fig 9 Calculatd phas voltag and currnt wavfors for 2N loadd otor To calculat th currnts and torqu wavfors following paratrs of asynchronous otor was usd: P = 4, 4W, = 8V / Hz,n = 8rv / in, n n n R = Ω,R =, 47Ω,X = 2, Ω,X =, 6Ω, 2 σ 2σ X = 47, 2Ω, 2p = 4,a = 6, In th Fig 7 ar givn th wavfors of th phas voltag and currnt for no loadd achin Fig8 dpicts rspondnt lctroagntic torqu wavfor

6 8 Zszyty Problow Maszyny Eltryczn Nr 2/24 (2) Fig 9 shows th wavfors of phas voltag and currnt for loadd achin Motor was loadd by constant load of M = 2N In th Fig is shown rspondnt lctroagntic torqu wavfor (N i Fig Calculatd lctroagntic torqu for 2N loadd otor Conclusion In papr a thod of coplx Fourir sris to invstigat a torqu rippl wavfor of a thrphas asynchronous otor was prsntd Th lctroagntic torqu wavfor shows, that th gratst influnc to th output torqu rippl has a haronic which is cratd by odulation frquncy In practical ralization of th invrtr it s ncssary to hav a odulation frquncy highst possibl p Acnowldgnt Th financial support of th Slova Rsarch and Dvlopnt Agncy undr th contract N : APVV -8- is acnowldgd Bibliography [] Zásalicý, P, Dobrucý, B: Coplx Fourir sris athatical odl of a thr-phas invrtr with Iprovd PWM output voltag control; Eltronia ir Eltrotchnia, 22, Nr7 (2), pp6-68, Kaunas, KT, Lithuani [2] Frová, Ž,: Two-Phas Asynchronous Motor - Siulation in ANSYS Maxwll and MATLAB- Siulin; EDPE 2 : 7th Intrnational Confrnc on Elctrical Drivs and Powr Elctronics : 6th joint Croatian-Slova Confrnc : Octobr 2-4, 2, Dubrovní, Croatia [] Zásalicá M, Zásalicý P, Bňová M, Mahud AR, Dobrucý B: Analysis of coplx ti function of convrtr output quantitis using coplx Fourir transfor/sris; Counications- Scintific lttrs of th nivrsity of Žilina, pp 2-, vol2, No 2, Žilina [4] Frová Ž, Kaňuch J: Two-Phas Asynchronous Motor - Siulation and Masurnt; Kol- Zszyty Problov - Maszyny Eltryczn Vol, no 4 (2), p 2-, Katowic, Poland Author Prof Ing Pavl Zásalicý, PhD, is with Dpartnt of Elctrical Enginring and Mchatronic, Faculty of Elctrical Enginring and Inforatics, Tchnical nivrsity of Košic, Ltná 9, 4 Košic, Slovaia E-ail: pavlzasalicy@tus tl: