Designing of Closed Loop Controller for 3 Phase to 3 Phase Power Conversion Using Matrix Converter

Transcription

1 Intnational Jounal of Scintific Engining an Tchnology Volum No.5 Issu No., pp: ISSN: Fb.1 Dsigning of Clos Loop Contoll fo Phas to Phas Pow Convsion Using Matix Convt 1 B.Muthuvl, K.C.Balaji, D.T.S.nanhi, M.Janani aj 1 Dpatmnt of EEE, KT Mmoial collg of Engining an Tchnology, Villupuam. Dpatmnt of EEE, S Sastha Institut of Engining an Tchnology, Chmbaampakkam, Chnnai Elctonics & Instumntation Engining, nnamalai Univsity, nnamalai Naga, Cualo Dt. Dpatmnt of EEE, Vivkanana Polytchnic Collg, Vaalu, Cualo Dt. 1 muthuvl.bmv7@yahoo.co.in balaji.kc.8@gmail.com ans_shakthi@yahoo.co.in jaanu.tkm7@gmail.com bstact: This pap poposs a simulation of signing an implmntation of a PI contoll with incasing an casing RL loa valus fo a phas to phas pow convsion using matix convt. Clos loop PI contoll is us to achiv al tim contol fo phas to phas matix convt. Th nti matix convt cicuits a vlop by Mathmatical mol so as to achiv lss computational tim an pfomancs of th contoll a valuat using MTLB fo iffnt RL Loa valu. Th mathmatical xpssions of th th phas matix convt a implmnt by using simulink block st. Th uty cycls of th matix convt biictional switchs a calculat using moifi vntuini algoithm fo maximum (.8) voltag tansf atio. Inx Tms: Matix convt, phas to phas convt, phas C pow convsion, Clos Loop Contoll, Clos loop Matix convt. I. INTRODUCTION Th matix convt (MC) is a on stag pow convt, capabl of fing an m-phas loa fom an n-phas souc without using ngy stoag componnts. It is a ict fquncy convsion vic that gnats vaiabl magnitu vaiabl fquncy output voltag fom th ac lin. It has high pow quality an fully gnativ. Rcntly, ict ac/ac convts a aliz fo high fficincis, long liftim, siz uction, an unity pow factos. Th bnfits of using ict ac/ac convts a vn gat fo mium voltag convts as ict ac/ac convts o not qui lctolytic capacitos, which account fo most of th volum an cost of miumvoltag convts. Matix convts hav som avantags whn compa to convntional back to back Puls with moulation voltag-souc convts. Th MC may b consi mo liabl an is small bcaus th bulky c capacito is liminat fom th topology. Thfo, whn MCs a us in ac ac pow convsion, th siz an wight of th whol gnation systm is uc. Fo a common mo voltag uction an th pow quality of matix convts fo a low-voltag tansf atio of lss than.5, a ict spac vcto moulation mtho has bn popos [1]. To intfac a MCbas gnation systm to an unbalanc th-phas stanalon loa, a fou-lg MC is qui to povi an lctical path fo th zo-squnc loa cunt. Hnc th application of sonant Contolls to fou-lg matix convts fing unbalanc o nonlina loas has bn vlop []. nw tchniqu impov spac vcto moulation using amplitu cofficint on a capacito-clamp multilvl matix convt. Th MMC utilizs a multilvl stuctu on a convntional matix convt, which allows ict ac-ac convsion without lag ngy sto lmnts has bn vlop []. Fo vaious inustial ajustabl sp ac ivs an applications, vaious analysis an mathmatical mol is intouc in matix convt. By vaying th Moulation Inx (MI), th outputs of th matix convt a contoll an in ac ivs, sps of th iv w contoll. To uc th computational tim an low mmoy quimnt, a mathmatical mol has bn popos []-[11]. Fig.1. Block iagam of pas to phas Matix convt. To achiv al tim contol with quick sp an fast spons, nw signs of contolls a n. PI contolls a th on to sns th output continuously an coct th output at th instant if any istubanc occu. In this pap, PI contolls a sign an implmnt fo th phas to phas matix convt in clos loop configuation an th pow cicuit in clos loop a implmnt by th mathmatical moling along with th PI contolls. Th uty cycl calculation is takn into account fo Maximum voltag tansf atios an th mathmatical mol is aliz with th RL loa. Th nti pow cicuit is mol with MTLB/SIMULINK. Implmntation of PI contoll in mathmatical moling inclus th moling of pow cicuit, switching algoithm, loa an th contoll. Mits of Mathmatical mol ov convntional pow cicuit a lss oi : /ijst/v5s/1 Pag 11 Phas Input Switching lgoith m Matix Convt Contoll Loa

2 Intnational Jounal of Scintific Engining an Tchnology Volum No.5 Issu No., pp: ISSN: Fb.1 computation tim an low mmoy quimnt. Fig. 1 fs th Basic block iagam of th popos pas to phas Matix convt. Th popos mol is vy simpl, flxibl an can b accommoat with any typ of loa. II. PHSE MTRIX CONVERTER Th Matix convt (MC) is a on stag ict ac to ac convt, which has an aay of m x n bi-ictional switchs that can ictly connct m phas voltag souc into n phas loa. phas matix convt consists of x switchs aang in matix fom. Th aangmnt of bi-ictional switchs is such that any of th input phass R, Y, B is connct to any of th output phass, y, b at any instant. Th avag output voltag with si fquncy an amplitu can b contoll by th bi-ictional switchs. Th biictional x switchs ( 9 ) givs 51 combinations of th switching stats. But only 7 switching combinations a allow to pouc th output lin voltags an input phas cunts. Input filts a n in o to liminat th hamonic componnts of th input cunt an uc th input voltag istotion suppli to th Matix Convt as shown in fig.. Th siabl chaactistics of a Matix convt a as follows: Sinusoial input an output wavfoms with minimal high o hamonics Contollabl input pow facto Biictional ngy flow capability an Minimal ngy stoag quimnts Long lif u to absnc of a bulky capacito Phas Input R Inp ut Matix Convt S R S Ry S Rb Y Filt S Y S Yy S Yb B To 9 Switchs S B S By S Bb Duty cycl Contoll y b Fig.. cicuit schm of phas to phas matix convt Th Matix convt has th following limitations Th voltag tansf atio limitation has a maximum valu of.8 Snsitiv to th pow souc istotion u to th ict connction btwn input an output sis. III. SWITCHING LGORITHM Phas RL Loa Whil opating phas to phas convt with 9 biictional switchs, th following two basic uls hav to b satisfi. o input lins shoul not b connct to th sam output lin to avoi shot cicuit t last on of th switchs in ach phas shoul b connct to th output to avoi opn cicuit. Th switching function of singl switch as M Kj = { 1, switch MKj clos, switch MKj opn Wh, K = {, y, b), j = {R, Y, B} Th abov constaints can b xpss by Mj + Myj + Mbj = 1, j = {R, Y, B} () Th input o souc voltag vcto of th phas to phas Matix convt is V V im cos(ω i t) R V i = V Y = V im cos (ω i t + π ) () V B V im cos (ω i t + π ) Th output voltag vcto of th phas to phas Matix convt is V V om cos(ω o t) V o = V y = V om cos (ω o t + π ) () V b V om cos (ω o t + π ) Similaly, th output cunt vcto of th phas to phas Matix convt is I I om cos(ω o t) I o = I y = I om cos (ω o t + π ) (5) I b I om cos (ω o t + π ) Wh, ω i - fquncy of input voltag an ω o - fquncy of output voltag Th lationship btwn output an input voltag is givn as V o (t) = M (t). V i (t) () Th input cunt is givn by I in = M T I o (7) Duty cycl must satisfy th following conition in o to avoi shot cicuit on th input si. M R + M Y + M B = 1 M Ry + M Yy + M By = 1 (8) M Rb + M Yb + M Bb = 1 Th abov conition is fulfill by calculation of uty cycl using moifi vntuini algoithm. In vntuini switching algoithm, th maximum voltag tansf atio is stict to.5.this limit can b ovcom by using moifi vntuini algoithm. Th maximum possibl output voltag can b achiv by injcting thi hamonics of th input an output fquncis into th output wavfom. This will incas th availabl output voltag ang to.75 of th input whn thi hamonics has a pak valu of V i /. Futh incasing of th tansf atio can b achiv by subtacting a thi hamonic at th output fquncy fom all tagt output voltags. Hnc th maximum tansf atio of.75/.8 =.8 of V i whn this (1) oi : /ijst/v5s/1 Pag 111

3 Intnational Jounal of Scintific Engining an Tchnology Volum No.5 Issu No., pp: ISSN: Fb.1 thi hamonic has a pak valu of V o /.Thfo th output voltag bcoms V oγ =qv im cos(ω o t + ψ γ ) q V im cos(ω o t)+ 1 q m V im (ω i t) (9) Wh, ψ γ =, π/, π/ cosponing to th output phas, y, b. IV. PROPORTIONL PLUS INTEGRL CONTROLLER (PI) Th contoll output m(t) is popotional to a lina combination of actuating signal (t) an its tim ivativ is call PI contoll. m = Wh, t Kp Ti. + Kp t = at of chang of with spct to tim (1) Kp = popotional snsitivity Ti = intgal tim In intgal fom, Kp m = ʃ t + K p + M (11) Ti In opational fom, m = Kp ( 1 + 1) (1) TiS Figu shows th tansf function block iagam of a PI contoll with positiv fback. Th tansf function of PI contoll is M(S) R(S) Kp (1 + 1 E(S) Fig. Tansf function of PI contoll. Th popotional plus intgal contoll poucs an output signal, u(t) consisting of two tms-on popotional to input signal, (t) an th oth popotional to th intgal of input signal, (t). Th PI contoll ucs th Stay stat o. In PI contoll, u(t) α [(t) + ʃ (t) t] (1) u(t) = K p (t) + K i ʃ (t) t (1) Wh, K i is th popotional gain = -ω 1 sin θ / 1 an K p is th intgal constant o gain = cos θ / 1 On taking Laplac tansfom of quation (1) with zo initial conition w gt, U(s) = K p E(s) + K E(s) i Tansf function of PI Contoll is G c (s) = U(s)/E(s) = K p + Ki S S = E(s) (K P + Ki S ) (15) (1) Th PI contoll ucs th stay stat o. Th intouction on PI contoll incass th o an typ numb of th systm by on V. MTRIX CONVERTER DESIGN TiS ) Th actual MTLB/SIMULINK mol of phas to phas Matix convt is shown in fig.. It compiss nomally sctions. 5.1 Contol lgoithm Dsign ph as In put Phas Dut y Cyc l calc ulat ion M R*V im cos ω it M Y*V im cos (ω it+π/) M B*V im cos (ω it+π/) M Ry*V im cos (ω it+π/) M Yy*V im cos ω it M By*V im cos (ω it+π/) M Rb*V im cos (ω it+π/) M Yb*V im cos (ω it+π/) M Bb*V im cos ω it Contoll Fig.. Mathmatical Moling of phas to phas Matix convt. Th qui voltag tansf atio (q), output fquncy (f o ) an switching fquncy (f s ) a th inputs qui fo calculation of uty cycl. Th uty cycl calculations fo voltag tansf atio of.5 an.8 a aliz in th fom of m-fil in Mat lab. Th a two moulation tchniqus to b consi fo matix convt sign. ω m = ω o ω i & ω m = ω o + ω i (17) Fo ω m = ω o ω i, th phas isplacmnt is in fowa squnc i.. R, Y, B M t is th Tansf matix an is givn by M R M Y M B M (t) = M Ry M Yy M By (18) M Rb M Yb M Bb Wh, M R = t R / T s, uty cycl switch S R, Ts is th sampling pio. Duty cycls fo maximum voltag tansf atio a; Fo ω m = ω o + ω i, th phas isplacmnt is in vs squnc i.. R, B, Y. Wh, ω m = ω o ω i = moulation fquncy, θ = lativ phas of output, q =voltag tansf atio. Switching tim fo voltag tansf atio of.8 a; T βγ = T s 1 + V oγ V iβ V + q sin ω im q i t + ψ β sin(ω i t) (19) m Phas Loa oi : /ijst/v5s/1 Pag 11

4 Intnational Jounal of Scintific Engining an Tchnology Volum No.5 Issu No., pp: ISSN: Fb.1 Wh, ψ β =, π/, π/ cosponing to th input phass R, Y, B, q m = maximum voltag tansf atio, q = qui voltag atio, V im =input voltag vcto magnitu, T s = sampling pio. 5. Pow Cicuit Dsign Th moling of pow cicuit is iv fom basic output voltag quations. V (t) = M R V R (t) + M Y V Y (t) + M B V B (t) V y (t) = M Ry V R (t) + M Yy V Y (t) + M By V B (t) () V b (t) = M Rb V R (t) + M Yb V Y (t) + M Bb V B (t) Fig.5 shows th alization of moling block of pow cicuit of phas in phas to phas Matix convt. Th switching pulss fo th bi-ictional switchs a aliz by compaing th uty cycls with a saw tooth wavfom having vy high switching fquncy =5.V in Phass. Th avag Output Voltag an Cunt wavfoms in y b Phass fo I f = amps as shown in Fig.7&8. Fig.9&1 shows th vag Output Voltag an Cunt wavfom fo R=1 Ω an L=mH of loa. Fig.11&1 shows th vag Output Voltag an Cunt wavfom fo R= Ω an L=1mH of loa. Fig.1&1 shows th vag Output Voltag an Cunt wavfom fo R=5 Ω an L=mH of loa. Fig.15&1 shows th vag Output Voltag an cunt wavfom fo R= Ω an L=mH of loa. Fig.17&18 shows th vag Output Voltag an Cunt wavfom fo R=1 Ω an L=5mH of loa. Fig.19& shows th vag Output Voltag an Cunt wavfom fo R=5 Ω an L=mH of loa M R Sawtooth cai wav Compaato V im cos ω it x Fig.. Input wavfom fo I f = amps an mplitu =5.V in Phas 1 M Y Sawtooth Cai wav M B Sawtooth Cai wav Dlay cicui t Dlay cicui t Compaato V im cos (ω it+π/) Compaato V im cos (ω it+π/) x x Fig.7. Output Voltag fo I f = amps in y b Phass Fig.8. Output Cunt fo I f = amps in y b Phass Fig.5. Moling block of pow cicuit of phas in phas to phas Matix convt. 5. RL Loa Dsign Th tansf function of mathmatical moling of RL loa is I(S) = 1 V(S) Ls+R (1) 5. Contoll Dsign Th PI contoll mol was vlop using Simulink Blockst. In PI contoll, u(t) = K p (t) + K i ʃ (t) t () Tansf function of PI Contoll is = U(s)/E(s) = K p + K i /s () G c (s) VI.SIMULTION OUTPUT RESULTS ND DISCUSSION Simulations sults a pfom fo a fnc cunt of mps an mplitu =5.V an tim limit is.1 m.sc. Th output is aliz with phas passiv RL loa fo R= 1 Ω an L= mh. Th fnc cunt is st to mps. Th output is again fback to th input of th matix convt though PI contoll to achiv th al tim contol. Fig. shows th Input wavfom fo I f = amps an mplitu Fig.9. Output Voltag wavfom fo phas to phas Matix convt fo R=1 Ω & L=mH loa Fig.1. Output Cunt wavfom fo phas to phas Matix convt fo R=1 Ω & L=mH loa Fig.11. Output Voltag wavfom fo phas to phas Matix convt fo R= Ω & L=1mH loa Fig.1. Output Cunt wavfom fo phas to phas Matix convt fo R= Ω & L=1mH loa oi : /ijst/v5s/1 Pag 11

5 Intnational Jounal of Scintific Engining an Tchnology Volum No.5 Issu No., pp: ISSN: Fb Fom th abov vaious simulation outputs, it is cla that th R valu shoul b chosn lss an L valu shoul b chosn mo fo smoothning th output cunt Fig.1. Output Voltag wavfom fo phas to phas Matix convt fo R=5 Ω & L=mH loa Fig.1. Output Cunt wavfom fo phas to phas Matix convt fo R=5 Ω & L=mH loa Fig.15. Output Voltag wavfom fo phas to phas Matix convt fo R= Ω & L=mH loa Fig.1. Output Cunt wavfom fo phas to phas Matix convt fo R= Ω & L=mH loa Fig.17. Output Voltag wavfom fo phas to phas Matix convt fo R=1 Ω & L=5mH loa Fig.18. Output Cunt wavfom fo phas to phas Matix convt fo R=1 Ω & L=5mH loa Fig.19. Output Voltag wavfom fo phas to phas Matix convt fo R=5 Ω & L=1mH loa Fig.. Output Cunt wavfom fo phas to phas Matix convt fo R=5 Ω & L=1mH loa VII CONCLUSION Simulation of mathmatical moling an implmntation of clos loop PI contoll fo phas to phas pow convsion using matix convt has bn psnt in this pap. mathmatical mol is vlop fo Matix convt using MTLB/Simulink which is also utiliz fo clos loop PI contoll configuation. In clos loop configuation, a al tim contol has bn achiv fo PI contoll with lss computational tim. Th output was aliz by iffnt RL loa valus an th simulation sults a takn fo maximum voltag tansf atio. Th simulation output sults a satisfactoy an th futu xtnsion of this pap is possibl fo clos loop Fuzzy logic contol in th phas to n phas Matix convt with iffnt voltag tansf atio an vaious passiv loas. REFERENCES i. Moling an simulation of singl-phas C-C matix convt using SPWM, Stunt confnc on Rsach an Dvlopmnt pocings, Malaysia,, pp ii. Kiwoo Pak, Kyo-Bum L an F Blaabjg, Impoving output pfomanc of a Z-souc spas matix convt un unbalanc input-voltag conitions, IEEE Tansactions on Pow Elctonics, Vol.7, No., pil 1. iii. Xu Li, Li Yongong, Wang Kui, Jon C.Cla an Patick W.Whl, Rsach on th amplitu cofficint fo multilvl matix convt spac vcto moulation, IEEE Tansactions on Pow Elctonics, Vol.7, No.8, ugust 1. iv. Imayavaamban, K.Latha an G.Uma, nalysis of iffnt schms of matix convt with maximum voltag convsion atio, IEEE MELECON'MY1-15,, pp v.. lsina an M.G.B. Vntuini, nalysis an sign of optimum amplitu nin-switch ict C-C convts, IEEE Tans. Pow Elcton., vol., pp.11-11, Jan vi. P.W.Whl, J. Cla an.winstin, Matix Convts: Tchnology Rviw, IEEE Inustial ElctonicsVol.9, No., pil, pp vii. Zuckbg,., Wingstock, D. an lxanovitz, Singl - phas matix convt, IEE pocings Elctic Pow pplication,vol1(), July 1997, pp5-. viii. Sat Sunt an Tata Y, Pspic moling an sign of a snubb cicuit fo th matix convt, Intnational Jounal of Engining Mol 1,, pp.1. ix. Zuckbg,., Winstock, D. an lxanovitz, Simulation of - phas loa matix convt, Elctic Pow pplications, IEE Pocings, Vol. 1, Issu:, July199, pp.9. x. B.Muthuvl, T.S.nanhi, P.Sivagnanam an K.Ramash kuma, Simulation of Phas to Phas Pow Convsion Using Matix Convt with Maximum an Minimum Voltag Tansf Ratio, Intnational Jounal of Engining Rsach an applications (IJER) ISSN: 8-9, Vol. 5, Issu 11, (Pat - ) Novmb 15. Pap ID: xi. B.Muthuvl, T.S.nanhi an M.Jananiaj, Simulation of Clos Loop Fuzzy Logic Contoll fo a Phas to Phas Pow Convsion Using Matix Convts, Intnational Jounal of Scintific Engining an Rsach (IJSER) ISSN (Onlin): 7-878,Volum-,Issu1,Januay 1(PP5-11), Pap ID: IJSER15 oi : /ijst/v5s/1 Pag 11

6 Intnational Jounal of Scintific Engining an Tchnology Volum No.5 Issu No., pp: B.Muthuvl was bon in 198 in Chiambaam, Tamilnau, Inia. H has obtain Diploma in EEE (Honous) fom Muthiah Polytchnic, Chiambaam in H civ th B.Tch g in EEE fom Ponichy Univsity in an th M.Tch g in Pow Elctonics an ivs fom SSTR Univsity in. H is pusuing Ph.D in nnamalai Univsity. H is psntly woking as an ssociat pofsso in th Dpt. of EEE, KT Mmoial Collg of Engg &Tch., Kallakuichi. His fil of intst is ac-ac convt, ac-c convt, c-c convt, c-ac convt, matix convt, ac ivs, PCB sign. ISSN: Fb.1 T.S.nanhi obtain th B.E. (Elctonics an Instumntation) an M.E (Pocss Contol an Instumntation) gs fom nnamalai Univsity in 199 an 1998 spctivly. Sh is psntly woking as an ssociat Pofsso in th Dpatmnt of Elctonics an Instumntation Engining, nnamalai Univsity wh sh has put in a total svic of 1 yas. H sach intsts a in moling an contol of pow convts, mb contolls an nwabl souc applications. K.C.Balaji was bon in 198 in Thiukkouilu, villupuam Dist, Tamilnau. H has obtain Diploma in EEE fom Kumaan Polytchnic, Tiuvanamalai. H civ th B.Tch g fist class with istinction in EEE fom Ponichy Univsity in an M.Tch at Sathyabama Univsity in 1. H is psntly woking as ssistant pofsso in th Dpt. of EEE at S Sastha Institut of Engining an Tchnology, Chnnai. His fil of intst is acac convts, Invts, Rctifis & ivs. M.Jananiaj was bon in 1989 in Chiambaam, Tamilnau, Sh civ th B.E g Fist Class with Distinction an Gol mal in Elctical an Elctonics ngining fom nna Univsity in 11. Sh is psntly woking as a Lctu in th patmnt of Elctical an Elctonics ngining, Vivkananha Polytchnic Collg, Vaalu, Cualo Distict, Tamilnau. H fil of intst is ac-ac convt, ac-c convt, c-ac convt, matix convt, ac ivs, oi : /ijst/v5s/1 Pag 115