SCALAR CONTROL FOR A MATRIX CONVERTER

Transcription

1 8 Aca Elecrechnca e Infraca l. 9, N., 9, 8 4 SCAAR CONRO FOR A ARIX CONERER Ghale BACHIR, Azeddne BENDIABDEAH Unery f cence and he echnlgy f Oran "haed BOUDIAF" (USO), BP 55 El nauer Oran, Algera, Fax: , e-al: bachr@unu.dz,bendazz@yah.fr ABSRAC he auhr cpare w cnrl raege fr drec AC-AC arx cnerer; naely he enurn ehd and he calar raegy cnrl ehd. he perfrance cparn f he w raege ade under unbalanced dred rque, rr peed and ar curren peran. he ulan f he hree-phae arx cnerer feedng an nducn r wa accplhed by ean f he "alab /Sulnk " fware. h package ake pble ulae he dynac ye n a ple way and n graphc enrnen. eywrd: arx cnerer, enurn ehd, Scalar cnrl raegy, ceffcen f dulan, nducn r.. INRODUCION he perfrance f an nducn r dre fed by a cnennal nerer are lar he f a arx cnerer bu he an adanage f he la ne are: Elnan f he neredae age (recfer, DC-lnk capacr) B-drecnal pwer flw capably Snudal npu/upu curren and adjuable npu pwer facr. Furherre, becaue f a hgh negran capably and hgher relably f he ecnducr rucure, he arx cnerer plgy recended fr exree eperaure and crcal lue/wegh applcan. aru echnque f dulan hae been deelped be appled he arx cnerer cnrl [,4]. Se f hee echnque ake ue f he calar apprach (enurn and Ry), her are baed n he ecr apprach uch a he drec and ndrec pace ecr dulan (S and IS) [7,8]. he a f h paper preen a dealed cparae udy beween he w dfferen calar apprache naely, enurn and Ry, when appled he cnrl f an nducn r. he udy deal wh he r (curren, peed and rque) perfrance repne wh repec bh echnque. h wll enable u denfy he er f each f he n rder ake a judcu chce fr her ue n arx cnerer cnrl applcan.. HEORY OF HE ARIX CONERER he bac dagra f a arx cnerer can be ha repreened by Fg.. he ybl S j repreen he deal bdrecnal wche, where repreen he ndex f he upu lage and j repreen he ndex f he npu lage. [ ] e [ ] be he ecr f he npu lage gen a: c( ω c( ω + π /) c( ω + 4π /) and he ecr [ ] f he dered upu lage. [ ] c( ω c( ω + π / ) c( ω + 4π / ) he prble cn n fndng a arx knwn a he dulan arx, uch ha [ ] []. [ ] () and [I] []. [I] (4) [] repreen he ranped arx f []. he deelpen f he equan () ge: () () S j (5) where j are he dulan ceffcen. Fg. Bac crcu f a arx cnerer Durng cuan, he bdrecnal wche u funcn accrdng he fllwng rule: ISSN FEI UE

2 Aca Elecrechnca e Infraca l. 9, N., 9 9 A eery nan, nly ne wch S j (,,) wrk n rder ad hr-crcu beween he phae. A eery nan, a lea w wche S j (j,,) wrk enure a cled lp lad curren. he wchng frequency f ω /π u hae a alue weny e hgher he axu f f,f (f >>> ax (f,f )). Durng he perd knwn a equenal perd whch equal /f, he u f he e f cnducn beng ued ynheze he ae upu phae, u be equal. Nw a e j ; called e f dulan, can be defned a: j j. S (6). ENURINI EHOD Fr a e f hree-phae npu lage wh cnan aplude and frequency f ω /π, h ehd calculae he duy cycle f each f he nne bdrecnal wche. he reul when pleened allw he generan f a e f hree-phae upu lage by equenal pecewe aplng f he npu waefr. he hree phae upu lage hu baned huld derably rack a predefned reference waefr and when a hree phae lad cnneced, he npu curren f agnude I and angular frequency ω huld be n-phae wh he npu lage. aan he abe feaure, a aheacal apprach eplyed. he relanhp beween he npu and upu lage and ha f he upu and npu curren are wren repecely a: ( ( ( ( ) ( ) where j ( (,j,,) repreen he duy cycle f a wch cnnecng upu phae npu phae j whn ne wchng aple neral. j A any e, j ( and (7) (,,) (8) j ban axu upu npu lage ra, a reference hree phae lage defned a where and are he agnude f upu and npu fundaenal lage, repecely, and ω and ω crrepnd, he upu and npu angular frequence. When ( /) he funcnal lun fr he duy cycle j ( can be deerned and he general frula gen a: π + c( ( ) ) c( ( ) π j Q ω j ω ) c(ω + c( ) 6 ω Q π c(4ω ( j ) ) π c(ω ( j) where, j,, and Q /. () Cuan f j ( carred u a a aple frequency f wch al defne he cnerer wchng frequency[], [], []. 4. HE SCAAR CONRO SRAEGY A aed n [4], a raghfrward apprach generae he ace and zer ae f arx wche n Fg. cn f ung he nananeu lage ra f pecfc npu phae lage. e u defne he fllwng phae lage preen a npu pr: A B C c( ω π c( ω ) 4π c( ω ) () A he upu pr f he cnerer, he alue f any nananeu upu phae lage ay be expreed by he eq, where -- are arable ubcrp, any f whch ay be agned A, B r C accrdng he rule belw. [ + + ] () + + () c( ω c( ω π / ) 6 c( ω 4 / π c(ω + c(ω 4 c(ω c(ω c(ω c(ω (9) Rule : A any nan, he npu phae lage whch ha a plary dfferen fr bh her agned. Rule : he w npu phae lage whch hare he ae plary, are agned and, he alle ne f ISSN FEI UE

3 4 Scalar Cnrl fr a arx Cnerer he w, n ablue alue, beng. hen and are chen uch ha: ( ) (),5 ρ (4) fr he neral where: (5) Expren gen n eq and are lar ha ne rgnally prped by []. Eq4 defne he ace e ra beween w u f he hree wche, n ne cuang leg f he upu pr (ee Fg. ); h e ra ( / ) prprnal he nananeu lage ra ( / ) f her acaed npu phae. he ra u be eablhed wh he aller nananeu lage dded by he larger ne, a aed n eq5. he cnerer wchng paern depend nly n he SCAAR cparn f npu phae lage and he nananeu alue ( ) f he dered upu lage. he fllwng ge he prper prcedure ban he repece alue f, and durng ne perd f he equence (r he carrer) frequency f. Fr a pecfc neral where /, he nananeu phae lage ra ρ : ρ (6) + () he duy cycle f cuar and prprnal he nananeu alue f he crrepndng npu phae lage and ulpled by he lage dfference beween he dered upu lage and he npu phae lage. I huld be ned a h pn ha he upu lage, (.e a, b, c ), can be any knd f waefr, ncludng DC alue... Slng Eq, and fr a gen lage ra. / Q.5, wll yeld pe alue fr e k, and a n he cae f enurn cnrl algrh. Fr a hgher lage ranfer ra, e negae e alue ar appear becaue f he nananeu lage lan a he npu pr f he DFC. Hweer, dulan echnque prped by ayu [6] wrk well wh he calar raegy. Hence, by dfyng he wchng e f he bac calar cnrl law, pble add bh he upply neural pn dulan a ω and he lad neural pn dulan a ω ban an erall lage ranfer ra f Q /. Eq hen dfed by changng he er by he fllwng expren: ' + c(ω c(ω (4) 4 6 And he ace e fr hree wche acaed wh he dered upu lage bece: ( ) (7) ρ + ( + ρ) ρ (8) ( + ρ ) (9) Ung agan he curren alue f ρ. Eq7 can be furher deelped uch a: 5. SIUAIONS RESUS Sulan wa carred u, by keepng fxed he upply lage f he nducn r (he upu f he arx cnerer) and aryng nly he frequency f n rder be able cpare he r perfrance fr bh raege preened abe. he arx cnerer decrbed abe ulaed fr hree dfferen dered upu frequence (f 5 Hz, 5 Hz and Hz), wh a wchng frequency f 5Hz. Bh cnerer are fr feedng a 5HP, 46 nducn r drng a N. ree rque. ( ) () [ + + ( + + ) ] In a balanced hree phae ye, he uan f he hree nananeu phae lage zer. S he fllwng relanhp can be baned: ( ) ( ) () + +,5 Fg. Blck Sulnk f he nducn r ISSN FEI UE

4 Aca Elecrechnca e Infraca l. 9, N., 9 4 _ Ou k l _ k l k l.5*^ /f Fg. he arx cnerer ulnk /alab dagra (enurn ehd) Fg. 5 he arx cnerer ulnk /alab dagra (Scalar raegy cnrl) 5.. Reul f enurn ehd (f 5 Hz) 5.. Reul f Scalar cnrl raegy (f 5 Hz) Sar curren (A) 5-5 Sar Curren (A) 5-5 Rr Speed (r/n) rque (N.) x Z Fg. 4 Sar curren, rr peed, and rque fr a arx cnerer fed nducn r (f 5 Hz) Rr Speed (r/n) rque (N.) x Z Fg. 6 Sar curren, rr peed, and rque fr a arx cnerer fed nducn r (f 5 Hz) ISSN FEI UE

5 4 Scalar Cnrl fr a arx Cnerer 5.. Reul f enurn ehd (f 5 Hz) 5.5. Reul f Scalar cnrl raegy (f 5 Hz) Sar Curren (A) 5-5 Sar Curren (A) 5-5 Rr Speed (r/n) rque (N.) Fg. 7 Sar curren, rr peed, and rque fr a arx cnerer fed nducn r (f 5 Hz) Rr peed (r/n) rque (N.) Fg. 9 Sar curren, rr peed, and rque fr a arx cnerer fed nducn r (f 5 Hz) 5.4. Reul f enurn ehd (f Hz) 5.6. Reul f Scalar cnrl raegy (f Hz) Sar Curren (A) 5-5 Sar Curren (A) Rr Speed (r/n) Rr Speed (r/n) rque (N.) 5 rque (N.) Fg. 8 Sar curren, rr peed, and rque fr a arx cnerer fed nducn r (f Hz) Fg. Sar curren, rr peed, and rque fr a arx cnerer fed nducn r (f Hz) ISSN FEI UE

6 Aca Elecrechnca e Infraca l. 9, N., CONCUSION In h arcle, a cparae udy f w dfferen cnrl raege preened; he enurn and he Ry raege. Bh echnque were appled a hreephae arx cnerer fed nducn r n he purpe llurae he perfrance f each ne, and pn u he lare and dfference beween he. Fr he ulan reul, wh reference he ar curren, rr peed and rque paern baned fr he aru alue f frequency, ne can deduce ha chce f he raegy ue predeerned by he cparn beween he npu upply frequency and he upu (r dered) frequency f he arx cnerer. If he npu upply frequency equal he upu frequency f he arx cnerer, ne can generally cnclude ha bh echnque ge al larly reul. Hweer, f he upu frequency lwer han he upply newrk frequency, he chce fr he enurn raegy and f he upu frequency uperr he upply newrk frequency, he Ry raegy preferred. REFERENCES [] enurn, :A New Sne Wae n Sne Wae Ou, echncal Cnern Whch Elnae Reace Eleen. Prceedng Pwercn 7, pp.e_-e_5, 989hAnnual IEEE,-4 Apr 988.l.. [] Azeddne,Bendabdellah Ghane Bachr: A cparae perfrance udy beween a arx cnerer and a hree leel nerer fed nducn r. aca Elecrechnca & nfraca N, l 6, 6. [],Zhang C,wahanaar W,Shepherd : Analy and cparan f cnrl echnque fr AC-AC cnerer. IEE Prc-Elecr. Pwer Appl.l 45, J998. [4] G,Ry,Duguay S,ana G.A,Aprl.: Aynchrnu Operan f Cyclcnerer wh Iprd lage Gan by Eplyng a Scalar Cnrl Algrh.. Prc. 87CH499-. IEEE-IAS nd annual eeng. Alana. Oc pp [5] G,Ry and G.E,Aprl : Cyclcnerer peran under a new calar cnrl algrh. n Prc. IEEE PESC 89, 989, pp [6].J,ayu D,Clan : he Ipleenan and Fuure Penal f he enurn Cnerer. Prc. Of Dre, r and Cnrl, 98, pp [7] Yanhu,Xe Yngde,Ren: Ipleenan f DSP Baed hree-phae Ac-Ac arx Cnerer. (C) 4 IEEE. pp [8] E.H,lan D,Deperne J.,auffann: DSP Ipleenan f a Naurally Cuaed arx Cnerer Open p Cnrl. IEEE ISIE 5, June -, 5, Dubrnk, Craa pp Receed Jun, 8, acceped Aprl, 9 BIOGRAPHIES Ghale BACHIR wa brn n January, 6, 969 n Oran Algera. He receed h Engneerng Degree and aer Degree fr Unery f (USO), Algera n 995 and repecely. He currenly a lecurer and preparng h Dcrae he n arx Cnerer. Azeddne BENDIABDEAH wa brn n January,, 958 n Sada Algera. He receed h Bachelr Engneerng degree wh hnr and h Ph.D degree fr he Unery f Sheffeld, England, n 98, and 985 repecely. Fr he wa a ng prfer a ky Inue f echnlgy (.I.), Japan. He currenly Prfer f Elecrcal Engneerng a he Unery f Scence and echnlgy f Oran, (USO) Algera. H reearch nere nclude: Elecrcal achne Degn and Dre Cnrl and Cnerer; Nuercal ehd fr Feld Calculan, a well a Elecrcal achne Faul Dagn. ISSN FEI UE