) 3. 3 i. 2π ) 3. sin(

Size: px

Start display at page:

Download ") 3. 3 i. 2π ) 3. sin("

Jeffrey Nelson Murphy
6 years ago
Views:

1 Fl Ont Contol of An Inucton Moto Sp Snol wth Cunt Vcto Contoll, ct-quaatu Cunt Copnato an Full O Obv In ct-quaatu Ax Rwan Gunawan 1,F Yuva, Zuhal A. Ka 1 Dpatnt Elctcal Engnng, Unvty of Inona, Dpok Mb of IEEE, Dpatnt Elctcal Engnng, Unvty of Inona, Dpok Pofo Dpatnt Elctcal Engnng, Unvty of Inona, Dpok Abtact h Obv u to tat th-pha nucton oto p nol, uually n alfa-bta ax, n th tuaton an xta tanfoaton n to a copnato bcau th flux ol la n q-ax. In th pap, a nw tho to tat th p of nucton oto v wth obv la n q-ax popo. h actual oto ol u alfa-bta ax, but th obv u th oto ol n oto flux ont contol -RFOC, an alo th ffnt ol of oto v that b abl to u btwn th actual an tat on. h ulaton ult n C-MEX S-functon Matlab/Sulnk 6.5 how that full o obv gv btt pfoanc an n uch btt than uc o obv. Kywo : Cunt vcto, nucton oto,full o obv q-ax an q cunt copnato I. INRODUCION Fo th oto u, that all th clacal oto (DC, pannt agnt ynchonou, an nucton oto (IM hav bn put nto opaton. A wll known, IM poc gat avantag ov oth kn of oto, naly, pl contucton, all z, low antnanc, btt lablty, latvly chap, tc.[1]. h cucal facto n vy oto v how to contol th p of th oto. h oto p can b au by th tachot o anoth no, but th not ffctv nc t cot o xpnv an any no not abl to tct at vy low an vy hgh p. Nowaay, whn th knowlg of huan bng an th tchnology a nca aply, th cunt of oto v a contoll by vcto contoll an th oto p tat by th obv. h Obv u to tat th p of oto v uually n alfa-bta ax, an th tuaton wll b o coplcat f want to a a copnato, bcau th flux ol, contoll, an th couplng quaton a n q-ax. h n Inonan Japan Jont Scntfc Sypou 006. h pap popo a nw tho to ov th obv to q-ax. h oto v uually n th-pha yt, an th athatc ol that vlop n two-pha bcau th calculaton an analy wll b pl []. h Clak tanfoaton u fo tanfoaton fo th-pha ol nto tatonay two-pha ol, o alfa-bta ax α a 1 1 β 0 = b c (1.1 anfoaton fo tatonay two-pha α-β ax nto otatng two-pha ol q ax u Pak tanfoaton hown n Eq. (1. coθ nθ α = q nθ coθ β (1. h atc tanfoaton fo th-pha ol nto otatng two-pha ol : q 0 coθ = nθ 1 π co( θ π n( θ 1 II. MEHODOLOGY A. h Actual Mol of Inucton Moto π co( θ + a π n( θ + b 1 c (1. h gnal quaton fo nucton oto v a [] : V = R + ψ + jωψ (.1 t

2 V = R + ψ + j( ω ω ψ (. t ψ = L + L (. ψ = L + L (.4 Equaton (.1 untl (.4 a u to gt th athatc ol of nucton oto v n alfa-bta ax,, o that ω zo. h oto typ qul cag, thn oto voltag V zo. h athatc ol of nucton oto v n alfa-bta ax a : 1 R (1 σ L Lω α = V α + ( α + ψα + ψ β t σl σl στ σl L τ σl L ( L ( L Lω β = V β + R β + ψ β ψ α t σl σl τ L σlτ L σl L L L L L wth σ = an τ = L L R h tato voltag quaton : (.6 (.7 (.8 v = R + Lσ ωlσ q + L(1 σ t t (.9 vq = R q + Lσ q +ωlσ + L(1 σ ω t (.10 h PI contoll u to contol th cunt vcto, but th contoll can only contol a lna yt, o quaton (.9 an (.10 ut b lnaz ft by th couplng. v = u + vc (.11 v = u + v (.1 q q cq R R ψ = ψ + L ωψ t L L R R ψ = ψ + L + ωψ t L L α α α β β β β α u = R + Lσ t (.1 uq = Rq + Lσ q t (.14 vc = ωlσ q + L (1 σ (.15 t v =ωl σ + L (1 σω (.16 cq v c an v cq a th couplng voltag, u an u q a th tato voltag aft couplng poc. h flux ol quaton a : R = ( (.17 t L R * q ω = p ω + (.18 L t θ = ω (.19 an th oto p quaton [8] : t ( l ω = (.0 J h toqu quaton : L L = N q N q N(1 L q L ψ = L = σ (.1 B. PI Contoll an PWM h -ax tato cunt, * f to th yt contant at ap an th q-ax tato cunt, q * ha vaaton n th valu, wth axu valu ap, nu valu -1 ap an tabl n 0. ap. h PI contoll u n th ulaton. Fo th couplng voltag quaton an gnal quaton of PI contoll, w gt th quaton fo th ct ax : Lσ R kp = k = (. an fo th quaatu ax : Lσ R kqp = kq = (. h gnal fo PI contoll wll b gvn to Pul Wth Moulaton (PWM bfo f th actual nucton oto ol. PWM u to tanfo nuo wav nto ct pul wth wth of th pul ffnt btwn on anoth pn on th nuo wav a an nput.

3 C. Full O Obv n q-ax h Obv u to tat th valu of cunt, flux an p of th oto. h obv ov to q-ax, o th ω valu not a a zo anyo. h fnc fa can b vw n th Fg. 1 blow : q = q ψ ψ q y = C x (.7 o gt th obv gan, th oto ol n q-ax wth tat pac quaton u an hown n th followng quaton : x = Ax + Bu + G ( (.8 t gi 1 + gj G= gi + gj ; I = an J = 1 0 Wth Fg. 1 fnc fa αβ, q an γδ Mol of th yt cb n tat pac quaton a: x& = Ax + Bu y = Cx (.4 Matc A an C a obvabl, o fo th output, th tat of th yt can b known [4]. h obv quaton a : x & = Ax + Bu + G( y y y = Cx (.5 h ^ gn ncat th tat valu. A th oto ol atc n q-ax that can b gottn fo quaton (.1 (.4, bcau th oto ol n qax, th ω valu not zo. h oto ol n tat pac : R (1 σ L Lω ω σl στ σll τ σll 1 0 R (1 σ Lω L σl ω q L σ q 1 στ σll σll τ V = + 0 t ψ L 1 ψ σl 0 ( ω ω Vq ψ 0 0 q τ ψ τ q L ( ω ω τ τ x& = A x + B u (.6 h gn valu fo oto ol µ an th gn valu fo obv ol λ an tak au that obv ol gn valu k t hgh than gn valu fo oto ol. Wth ntty quaton, to gt th obv gan wth aupton that ω =ω : ( k 1 R R g1 = k σl σl k ωτ ; g ( k 1 = ( ω (.9 k ( k 1 RR τ + LR στll ω g = (.0 ( + 1 L g ( k 1 ( RL τ + RL τ + σ LL ω = (.1 ( ωτ + 1 L 4 k h quaton of nucton oto ol wth full o obv a : 1 R (1 σ L Lω ( = V + + ψ + ψq + ω q + g 1( g ( q q t σl σl στ σll τ σll (. 1 1 L L Lω ( q = V q + R q+ ψq ψ ω + g ( + g 1( q q t σl σl τl σl τl σll (. R R ψ ( = ψ + L + ω ω ψq + g( g4( q q t L L (.4 R R ψ ( q = ψq + L q ω ω ψ + g4( + g( q q t L L (.5 o tat th p, th Lyapunov thoy u. h Lyapunov functon canat cb a [8] :

4 ( ω ω V = + (.6 δ Accong to th Lyapunov thoy, th yt wll b tabl f Lyapunov functon canat, V, a Eq. (.6 [5], an th vaton of V hown n Eq. (.7 alo ngatv fnt to. V = [( A GC + ( A GC ] t (.7 ω ( ψ q ψ q c ω + ω δ t h. G atc ngatv fnt, thn th [( A GC + ( A GC] atc alo ngatv fnt. So th vatv of V wll b ngatv fnt f th con an th ow of th quaton (.46 a zo, th tat p hown n Eq. (.8. h ulaton ult fo : k obv : 0,75, k p : 8 an k : 650 Fg. Stato cunt -ax, ω = K ( ( p ψq ψ + K q ψq ψ t (.8 q h popotonal coponnt P a to uc th tay tat o. III. RESULS Fg 4. Stato cunt q-ax, q A. Syt wth full o obv : h paat oto that u n th ulaton a blow [8] : L = 0,79 H, L = 0,49 H,L 0,49 H; P = 750 watt R =,76 Ω, R =,90 Ω,pol = 4, Saplng t = 10-4 Block aga of th yt wth full o obv hown n Fg : Fg 5. Roto flux -ax, ψ Fg 6. Roto flux q-ax, ψ q Fg. Block aga wth full o obv

5 btwn t a cau by th ffnc of th θ, bcau n q-ax, θ bco a cucal facto. Fg 7. Roto p, ω In th bgnnng of th agntzng cunt Fg. 8, an ovhoot that cau by th chaacttc of th oto can b n, an θ btwn th actual an th tat ffnt. h ffnt btwn θ actual an tat foun untl con, an aft con th ovhoot not xt anyo. h oto p o btwn th actual an th tat 0.97 % an th toqu.1488 %. B. Copnato n Full O Obv h copnato quaton a : cop R cop = ( + k o (.1 t L * ( q o q cop R k p cop L ω = ω + (. Fg 8. Magntzng cunt, Block aga of th yt hown a blow : Fg 9. oqu, Fg. 11. Block aga wth copnato n full o obv h ulaton ult a hown n th followng Fgu: k obv : 0,75, k o : 0,7, k p : 8 an k = 650, Fg 10. Synchonou oto poton, θ h all gaphc, cb that btwn th actual an th tat valu a alot th a, although n o gaphc o ppl a foun h ffnc Fg 1. Roto flux -ax,

6 CONCLUSIONS Fg 1. Roto flux q-ax, q Fg 14. Magntzng cunt, Syt wth copnato cb that th n t ovhoot n agntzng cunt anyo an th ttlng t of th yt to b hot than bfo. h oto p o btwn th actual an th tat % an fo th toqu %. o analyz th o, th q-ax nput cunt * q chang nto tp, wth axu valu 0.8 ap an th nu valu zo an th -ax nput cunt, * a a bfo. An th ult a hown a bllow : Fg 15. Roto p o, 1. h ffnc nucton oto ol btwn actual an tat abl to b u.. Wth obv n q-ax, th q cunt copnato can b u l coplcat.. All th valu of tat paat a affct by θ, o that θ an potant facto n th whol yt. 4. Wth obv n q-ax, full o obv gv wll pfoanc. 5. h p taton can follow p actual bgn 100 p untl 1150 p, aft that th p ha vy all fluctuat, oto p o 0.97 % 6. h q cunt copnato n full o obv gv a gnfcant ult, th oto p o btwn actual an tat %. 7. h toqu o btwn actual an tat %. 8. If th nput cunt * q chang nto tp, th copnato o n full o obv bco bgg. REFERENCES [1] Cao-Mnh a, Mb, IEEE, Chanan Chakaboty, Sno Mb, IEEE, Yoch Ho, Sno Mb, IEEE, Effcncy Maxzaton of Inucton Moto Dv fo Elctc Vhcl Ba on Actual Maunt of Input Pow, Dpatnt of Elctcal Engnng, Unvty of okyo, Japan [] Va, Pt, Elctc Machn an Dv: A Spac Vcto hoy Appoach, Oxfo Unvty, Nw Yok, 199. [] Khnan, R., Elctc Moto Dv, Pntc Hall, USA, 001. [4] P. Albto an A. Sala, Multvaabl Contol Syt : An Engnng Appoach, Spng-Vlag Lonon Lt, Valnca, 004, hal. 70 [5] Wbowo, Anal Ktablan St Ln Dngan Mto Lyapunov, uga Akh, Fakulta knk Inut, Juuan knk Elkto, Inttut knolog Inona, 199 [6] Pa, Lu F A, an Jo F. Haffn, Evaluaton of a Nw Statgy fo Contollng Inucton Moto Wthout ung p no, n IECON 001, th 7 th annual confnc of th IEEE Inutal Elctonc Socty. [7] Ch-Mun Ong, Dynac Sulaton of Elctc Machny, Pntc Hall, Nw Jy, [8] Fy, Pngnal Vkto Au Dan Pbakan Kalahan Kalahan Eta Paa Moto Inuk anpa Sno Kcpatan, Skp, Dpatn Elkto, Fakulta knk Unvta Inona, Jul 004. Fg 16. oqu o,

Applications of Lagrange Equations

Applications of Lagrange Equations Applcaton of agang Euaton Ca Stuy : Elctc Ccut ng th agang uaton of oton, vlop th athatcal ol fo th ccut hown n Fgu.Sulat th ult by SIMI. Th ccuty paat a: 0.0 H, 0.00 H, 0.00 H, C 0.0 F, C 0. F, 0 Ω, Ω