Dynamic Modelling and Simulation of Five Phase Induction Motor
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1 ISSN (Pnt : ISSN (Onln: Intnatonal Jounal of Advancd Rsach n Elctcal, Elctoncs and Instuntaton Engnng (An ISO 397: 007 Ctfd Oganzaton ol. 4, Issu 4, Apl 05 Dynac Modllng and Sulaton of Fv Phas Inducton Moto Mtsh B. Astk Assstant Pofsso, Dpt. of EE, A.D. Patl Insttut of Tchnology, Nw.. Naga, Anand, Gujaat, Inda ABSTRACT: In ths pap, a dynac odllng of fv-phas nducton oto s dscd n a stp y stp appoach. A dq odl asd on tansfoaton thoy fo fv-phas nducton achn s psntd. A dtald plntaton of an nct-typ fv-phas fld ontd contol ncludng th hystss-typ pu wh odulaton (PWM cunt gulato s dscd. Sulatons hav n cad out fo dffnt load conons. KEYWORDS: Dynac Modl, Fv-Phas Inducton Moto, Inct cto Contol. I. INTRODUCTION Th advantags of fv-phas achns a found ov th-phas achns such as an ncas n cunt p phas wthout th nd to ncas th phas voltag, ducton n apltud and ncas n fquncy of puatng toqus, fault tolanc, stalty and low cunt ppl []. It has ao n shown that ncasng th nu of phass can sult n an ncas n th toqu/ap laton fo th sa volu achns []-[4]. Hnc th analyss, dsgn and applcaton of achns wth hgh phas nus qu adquat athatcal od to stahd, though whch th pfoanc and advantags can assssd. S. Booa t. al. [5] psntd pap on dynac d-q axs odl of th- phas asynchonous oto n synchonously otatng fa. In ths pap, authos hav tansfd th-phas voltag n to two-phas voltag axs usng dq tansfoaton. S. Gupta and S. Wadhwan [6] dscussd odlng of nducton oto usng synchonously otatng fnc fa. Mathatcal odlng of th-phas nducton oto was dscussd n ths pap. Th stady-stat and tansnt spons of th oto hav shown wth vayng load on oto. Fv-phas nducton oto pfoanc und sytcal and asytcal conncton hav dscussd n [7]-[8]. In ths paps, authos hav ntond that f on o two lgs of th nvt a opn ccutd thn ao oto wok satsfactoy wth th ncnt of fundantal and thd haonc cunts. Sulnk nducton achn od a avalal n th ltatu [9]-[0], ut thy appa to lack-oxs wth no ntnal dta. In ths pap ach lock solvs on of th odl quatons. Th ncssay dffntal quatons dscng th pfoanc of fv-phas nducton achns n d-q fa of fnc asd on tansfoaton thoy a psntd n ths pap. A dtald plntaton of an nct-typ fv-phas fld-ontaton contol ncludng th hystss typ of PWM cunt gulato s llustatd []. Sulatons hav n cad out fo dffnt load conons. II. DYNAMIC MODEING OF FIE-PHASE INDUCTION MOTOR Th fv-phas statonay fnc fa vaa a tansfod nto two-phas statonay fnc fa vaa and thn tansfo ths vaa nto synchonously otatng fnc fa and vc-vsa. Th voltag as-s-cs-s can solvd nto and coponnts and can psntd n th atx fo usng (. ns cos cos sn sn 5-5 cos sn cos 4 5 sn 4 5 cos 5 sn 5 as s cs s ( Copyght to IJAREEIE 0.566/ja
2 ISSN (Pnt : ISSN (Onln: Intnatonal Jounal of Advancd Rsach n Elctcal, Elctoncs and Instuntaton Engnng (An ISO 397: 007 Ctfd Oganzaton ol. 4, Issu 4, Apl 05 I I I ns cos sn 5 cos sn - 5 cos sn cos 4 5 sn 4 5 I cos 5 I sn 5 I I I as s cs s ( wh, as, s, cs, and s a stato phas voltags. and a th d s and q s axs stato fundantal voltags spctvly. ns s th zo squnc coponnt of th stato. It s convnnt to st 0, so that th q s axs s algnd wth th as-axs. Ignong th zo squnc coponnts, th tansfoaton latons can splfd usng (3-( a sn ( - cos ( c c cos ( sn ( d d cos ( 4 5 sn ( 4 5 sn ( cos ( 5 5 (4 (3 Th two-phas d s -q s wndng a tansfod nto th hypothtcal wndngs ountd on th d -q axs, whch otat at synchonous spd wth spct to th d s -q s axs and th angl t. th voltag on th d s -q s axs can convtd nto th d -q fa as follows[]-[3]: q d cos sn sn cos (5 Fo th two-phas achn, w nd to psnt oth d s -q s and d -q ccut and th vaa n a synchonously otatng d -q fa. Th d -q fa voltag xpssons a: d d (6 d R - ; d R - (7 Rs ; Rs - Snc th oto actually ovs at spd, th dq axs fxd on th oto whch ovs at a spd of ( - latv to th synchonously otatng fa. Th flux lnkag xpssons fo dq fa a: F X X ( ; F = ω Ψ = Xl + X ( + (8 F X X ( ; F = ω Ψ = Xl + X ( + (9 F q q X ( ; F d d X ( (0 wh X, X l l and X ( By susttutng (8-(9 n (6-(7, th voltag xpssons can wttn as: d d R s F F ; F - F R s ( d ( - d ( 0 R F F ; - 0 R F - F (3 Copyght to IJAREEIE 0.566/ja
3 ISSN (Pnt : ISSN (Onln: Intnatonal Jounal of Advancd Rsach n Elctcal, Elctoncs and Instuntaton Engnng (An ISO 397: 007 Ctfd Oganzaton ol. 4, Issu 4, Apl 05 By susttutng ( n (8-(9, th flux lnkag quatons can wttn as F ( F (l F ; ( F ; ( l (4 (5 By susttutng (4 n (, w gt (6-(7. d ( d - - Rs - ( (6 d - - Rs - ( (7 Slaly, w can wt anng cunt quatons as gvn n (8-(0. d - - Rs ( (8 l l - - d d - R - R - ( - (l (9 ( - ( (0 Now, th flux lnkag xpssons n ts of cunts can wttn as follows: ( ; ( l l ( ; l ( ( q ( ; d ( (3 Now, th toqu xpsson can wttn as follows: 5 P T ( - (4 l Th spd and toqu a gvn y th followng laton: ( d J B T - T (5 III. CONTROER OF FIE-PHASE INDUCTION-MOTOR (INDIRECT ECTOR CONTRO METHOD Fg. shows th coplt lock daga of nct vcto contol thod. Copyght to IJAREEIE 0.566/ja
4 ISSN (Pnt : ISSN (Onln: Intnatonal Jounal of Advancd Rsach n Elctcal, Elctoncs and Instuntaton Engnng (An ISO 397: 007 Ctfd Oganzaton ol. 4, Issu 4, Apl 05 Fg. Coplt lock daga of nct vcto contol thod A. dq axs otatng cunt: Th fv-phas cunts can solvd nto and coponnts and can psntd n th atx fo fo (. B. Flux Ph: Th flux poducd n th stato wndng s gvn y * I Ph (6 T s wh T = / R. C. Roto poston: Now, th oto poston wh, (7 chancal spd and ω s oto fquncy (ad/sc R (8 Ph D. Fundantal fnc toqu (T*: Th fundantal fnc toqu (T * s otand y usng popotonal plus ntgal (PI contoll whos nput s th o twn th actual and fnc spd. E. Synchonous otatng dq-axs cunt: Th dq-axs synchonous otatng cunts a gvn y Ph T ; (9 5 P Ph d wh ph* s constant flux, and q a d and q axs synchonous otatng fnc cunts spctvly. F. Rotatng to statonay acd convson: Now, th otatng cunts a tansfod nto statonay fv-phas cunts ( acd * y takng nvs of (. Copyght to IJAREEIE 0.566/ja
5 ISSN (Pnt : ISSN (Onln: Intnatonal Jounal of Advancd Rsach n Elctcal, Elctoncs and Instuntaton Engnng G. Hystss Contol PWM: (An ISO 397: 007 Ctfd Oganzaton ol. 4, Issu 4, Apl 05 Wth th us of hystss contol PWM thod, actual and fnc fv-phas cunts a copad and th gat pus a gnatd to contol th fv-phas nducton oto [5]. Fg. shows th lock daga of hystss contol PWM. Fg. Block daga of Hystss Contol PWM Fg. 3 shows th sulaton of fv-phas voltags fo th gat pus. Ths fv-phas voltags appld to th stato wndng of fv-phas nducton oto. Fg. 3 Fv-phas voltags fo th gat pus I. SIMUATION RESUTS AND DISCUSSIONS Fv-phas nducton oto s sulatd n MATAB softwa fo dffnt load conons. No-load spd, cunt and toqu wavfos a shown n Fg. 4, 6 and 8 spctvly. oad toqu of N and 5 N a appld to th oto and th spd, cunt and toqu sponss of th oto a shown n Fg. 5, 7 and 9 spctvly. Fg. 4 shows th dynac sulaton sult of no-load spd of fv-phas nducton oto. Fg. 4 No-load spd Copyght to IJAREEIE 0.566/ja
6 ISSN (Pnt : ISSN (Onln: Intnatonal Jounal of Advancd Rsach n Elctcal, Elctoncs and Instuntaton Engnng (An ISO 397: 007 Ctfd Oganzaton ol. 4, Issu 4, Apl 05 Fg. 5 (a and ( show th dynac sulaton sult of spd at load toqu T = N and T = 5 N spctvly. Fg. 5 Spd spons at (a T = N ( T = 5 N It s osvd fo Fg. 4 and 5 that th oto achv atd spd of 60 ad/sc at aound sc and ao achv stady stat spd fo dffnt load wth appoxat zo stady stat o. Th spd of fv-phas nducton oto s 60 ad/sc fo th nt load and th spons of th oto s und dapd. Fg. 6 shows th dynac sulaton sult of no-load toqu of fv-phas nducton oto. Fg. 6 No-load toqu Fg. 7 (a and ( show th dynac sulaton sult of toqu spons at load toqu T = N and T = 5 N spctvly. Fg. 7 Toqu spons at (a T = N ( T = 5 N Fo Fgs. 6 and 7, w can s that th axu toqu dvlopd n fv-phas nducton oto s vad wth th load toqu vaatons ut ths vaatons a vy s. Th stady stat toqu s alost sa fo nt load. Fg. 8 shows th dynac sulaton sult of no-load cunt of fv-phas nducton oto. Copyght to IJAREEIE 0.566/ja
7 ISSN (Pnt : ISSN (Onln: Intnatonal Jounal of Advancd Rsach n Elctcal, Elctoncs and Instuntaton Engnng (An ISO 397: 007 Ctfd Oganzaton ol. 4, Issu 4, Apl 05 Fg. 8 No-load cunt Fg. 9 (a and ( show th dynac sulaton sult of cunt spons at load toqu T = N- and T = 5 N spctvly. Fg. 9 Cunt spons at (a T = N ( T = 5 N Th vaatons n tansnt as wll as stady stat cunt a s wth th chang n load toqu of fv-phas nducton oto. Th ffct of load toqu vaatons n oto pfoanc can sn n Tal. Tal- copaatv sulaton sults oad (N Spd (ad/sc Maxu Toqu (N Tansnt Cunt (A T = T = T = Tal shows th copaatv sulaton sults whn dffnt load toqu appld to fv-phas nducton oto. Th stady stat spd of th oto s constant fo nt load. Th vaatons n axu toqu and cunt a s dung load toqu vaatons.. CONCUSION Th spd of fv-phas nducton oto can contolld usng dffnt typs of tho such as / f thod, vcto contol thod tc. Th dynac odlng of fv-phas nducton oto s don n stp y stp appoach n ths pap. Th spd contol of th fv-phas nducton oto s achvd y nct vcto contol thod. Fo th sulaton sult, w can conclud that th actual spd succssfully tacks th fnc spd n oth tansnt as wll as stady stat conons. Th stady stat o n spd s alost zo. Th vaatons n actual toqu and n actual Copyght to IJAREEIE 0.566/ja
8 ISSN (Pnt : ISSN (Onln: Intnatonal Jounal of Advancd Rsach n Elctcal, Elctoncs and Instuntaton Engnng (An ISO 397: 007 Ctfd Oganzaton ol. 4, Issu 4, Apl 05 cunt a vy s n oth th tansnt as wll as stady stat pat vn f chang n load toqu. Th sulaton sults pov th ffctvnss of th contoll dsgn. APPENDIX Tal - paats of fv-phas nducton oto Pow 7.5 hp oltag 400 olt Po 4 Fquncy 50 Hz Stato Rsstanc 0. Ω Roto Rsstanc 0.6 Mutual nductanc 5.5 H Mchancal oton nta 0.04 Kg- REFERENCES [] H. Xu, H.A. Tolyat and.j. Ptson, Modlng and Contol of Fv-Phas Inducton Moto und Asytcal Fault Conons, Pocdngs of th Thd Naval Syposu on Elctc Machns, Phladlpha, pp. 4-7, 000. [] H.A. Tolyat, Analyss and Sulaton of Fv-phas aal Spd Inducton-Moto Dvs und Asytcal Connctons, IEEE Tansacton on Pow Elctoncs, ol. 3, No. 4, pp , 998. [3] H.A. Tolyat, T.A. po and J.C. Wht, Analyss of a concntatd wndng Inducton Machn fo adjustal Spd Dv Applcaton-pat I (Moto Analyss, IEEE Tansacton on Engy Convson, ol. 6, No. 4, pp , 99. [4] H.A. Tolyat, T.A. po and J.C. Wht, Analyss of a concntatd wndng Inducton Machn fo adjustal Spd Dv Applcaton-pat II (Moto Dsgn and Pfoanc, IEEE Tansacton on Engy Convson, ol. 6, No. 4, pp , 99. [5] S. Booa, S.K Agawal and K.S Sandhu, Dynac d-q Axs Modlng of Th-Phas Asynchonous Machn Usng Matla, Intnatonal Jounal of Advancd Rsach n Elctcal, Elctoncs and Instuntaton Engnng (IJAREEIE, ol., No. 8, pp , Aug. 03. [6] S. Gupta and S. Wadhwan, Dynac Modlng of Inducton Moto Usng Roto Rotatng Rfnc Fa, Intnatonal Jounal of Advancd Rsach n Elctcal, Elctoncs and Instuntaton Engnng (IJAREEIE, ol. 3, No. 6, pp , Jun 04. [7] M.B. Astk and D.R. Mhta, dq Modlng and Contol of Fv-phas Inducton Moto und Asytcal Connctons usng MATAB Sulaton, NUCONE 007, Na Unvsty, pp. 3-7, 007. [8] K. Thyagaajah and S. Mythl, cto Contol of Fv-Phas Inducton Moto und Asytcal Conncton, Intnatonal Jounal of Elctcal and Pow Engnng, ol., No. 5, pp. 88-9, 008 [9] Atf Iqal, Sk Mon Ahd, Md Af Khan, Mohd. Rzwan Khan and Hatha Au-Ru, Modlng, Sulaton and Iplntaton of a Fv-Phas Inducton Moto Dv Syst, Jont Intnatonal Confnc on Pow Elctoncs, Dvs and Engy Systs (PEDES-00, Pow Inda, pp. -6, 00. [0] u s Alto Pa, C sa Cataldo Schalau, u s Fnando Alvs Pa and Jos Flp Haffn, Gnal Modl of a Fv-Phas Inducton Machn Allowng fo haoncs n th A Gap Fld, IEEE Tansacton on Engy Convson, ol., No. 4, pp , 006. [] Buak Ozpnc and on M. Tolt, Sulnk Iplntaton of Inducton Machn Modl A Modula Appoach, Elctc Machns and Dvs Confnc, IEMDC'03. IEEE Intnatonal, ol., pp , 003. [] B.K. Bos, Modn Pow Elctoncs and AC Dvs, Pason Educaton Pvt. td., Dlh, Inda, 3 d on, 003. [3] Ch-Mun Ong, Dynac Sulaton of Elctc Machny Usng Matla/Sulnk, Pntc Hall PTR, Nw Jsy, 998. Copyght to IJAREEIE 0.566/ja
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