Modelling of voltage transfer function of the three-phase hybrid transformers with voltage or current source matrix converter
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- Godfrey Phillips
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1 Zgew EDYZ Pweł ZZEŚ Jcek EW vey of Zelo Gó cly of Eleccl Egeeg ope cece d Telecoco e of Eleccl Egeeg do:.599/ Modellg of volge fe fco of he hee-phe hyd foe wh volge o ce oce x covee c. Th ppe del wh hee-phe powe ye wh hyd foe (HT). The HT co coveol hee-phe foe wh elecogec coplg d / covee eged wh he ecody wdg hogh elecc coplg. The HT e hee-phe Yy coeced foe wh ddol ecody wdg d hee-phe volge o ce oce x covee (VM o M) whch gve poly o chgg he vle d phe hfg of he op phe volge. The ppe gve decpo of ch powe ye wh pve lod well he odellg d copo of volge fe fco fo oh olo of he HT. The edy e ly el of powe ye wh plfed HT hecl odel e vefed y e of he lo d expeel e el oed fo he powe ye wh HT of o 6 kv. ezczee. ykł doyczy ójfzowego ye zl z fooe hyydowy (TH). TH zwe kowecjoly foo ójfzowy ze pzężee elekogeyczy pzekzłk eegoelekoczy yp / ze pzężee elekyczy zegowy z zwoje wóy foo. W TH je oowy foo zwoje yp Yy oz dodkowy zwoje ójfzowy pzekzłke ycowy (PM) pęc l pąd kóe ożlwją zę pzeęc fzowego pęc wyjścowego. W ykle opo dzłe kego ye zl z ocążee pywy oz jego odelowe poówe elcj pęcowych dl dwóch ozwązń TH (z PM pęc l pąd). Wyk lzy włścwośc w e loy ye zl z pozczoy odele eyczy ą weyfkowe z poocą dń ylcyjych ekpeyelych yee zl z TH o ocy ok. 6 kv. (Modelowe elcj pęcowych ójfzowego foo hyydowego z pzekzłke ycowy pęc l pąd). łow klczowe: Pzekzłk yp / Tfoo ójfzowy Pzekzłk ycowy pęc l pąd. eywod: / covee Thee-phe foe Volge o ce oce x covee. odco well kow h pd lod chge wchg effec d ophec dchge geee dele effec he powe ye ch volge g epo d well []. Thee effec Eope e oe h 6% of powe ly d elly eled pole []. he ce of pply volge chge oh dowwd d pwd hee hgh k of dge o devce whch e eve o volge chge d coeely lge fcl dge y e epeclly oove phcecl d ecodco de [] [5]. he kow plco hee e peeed vo ype of / volge g/well copeo h ge he wed effec o pply [6] []. Thee copeo co: () coveol foe (elecogec coplg) wh p chge [6] [7] () / hyo coolle [8] () PWM x choppe (M) d PWM x ecce choppe (MR) wh o who ee ddo foe [8]-[4] (v) /D/ covee he dyc volge coolle (DVR) wh D oge d ee ddo foe [5] []. ddo hee e (v) hyd foe (HT) wh coveol foe (elecogec coplg) d M o MR (eleccl coplg) whch hve ecely ee evely developed [] []. The HT povde glvc epo d wde ge of chge of volge ce (.5 H ). Th pclly e fo HT wh ck-oo MR [9]-[]. Wok o HT e cooly eg developed d ecely coce HT wh volge oce x covee (VM) h gve poly o fvole chge of op volge phe he HT []. The eo of he ho of h ppe o fhe develop he cocep of HT wh x covee y odcg ce oce x covee (M) whch h oewh ple opology wh lowe e of pve copoe []. Th ppe pee he el of he odellg d ly of he hee-phe HT wh hee-phe volge o ce oce x covee (VM o M). The ex eco dece he opology d opeo of he peeed HT. ollowg h e eco wh HT volge fe fco he lo d expeel e el fo c.. 6 kv looy odel d coclo. Hyd foe decpo plfed chee of he lyed HT how g. whee he chee of he VM d M ed he HT e how g. ) d ). geel fo op phe volge foed of he phe volge he op of he x covee (VM o M) poweed y volge dced ecody wdg of he TR d he phe volge dced ecody wdg of he TR deced fo he pply volge () y expeo () d lled g.. () / / () whee: - - d - pply op of he VM o M d op of he HT phe volge epecvely x volge φ l phe e of he ecody wdg. Deled decpo of he x covee (VM o M) op volge ed o expeo () d (4) h decg volge d ce elo fo VM d M epecvely hee e peeed [] [5]. () c c c c T PRZEGĄD EETROTEHZY -97 R. 9 R /5
2 4 PRZEGĄD EETROTEHZY -97 R. 9 R /5 (4) c c c c T whee: ope wch cloed wch j j j - wch e fco j = { c} = { } T eo fe x. g.. plfed dg of he HT; cool gl g.. Dg of he ) volge oce x covee ) ce oce x covee; cool cc OP ovevolge poecve cc Well kow cool ege c e ed o fog of he volge o ce elo [] [5] plfed ppoch fo TH wh VM led o phe volge elo deced y (5) [] whee fo TH wh M c e deced y (6). (5) O (6) O whee: O RM vle of pply volge op volge of he VM who fle d op volge of he VM wh fle epecvely volge elo coeffce O RM vle of pply d op ce of he M ce elo coeffce e of he ecody wdg. g.. llve e of HT volge pho; φ l phe of he V o M Tkg o cco (6) fo cc wh M we c o phe volge elo (7) whch fe egg d g h O d h fo (8). (7) (8) whee: O p d op volge plo of he M p ( ) d op ( ) phe ecce of he M / - eoce plo. Volge fe fco Tkg o cco e wvefo of op volge (5) (8) d expeo decg of wo od ype deved [6] he phe op volge expeo () h fo (9) whee coeffce d e deced y () d () fo HT wh VM d y () d () fo HT wh M. (9) () co co co co co co
3 PRZEGĄD EETROTEHZY -97 R. 9 R /5 5 () () co co co co co co () whee: φ l phe of he VM o M op phe volge / j e / g. 4. HT wh VM ) ) op phe volge e wvefo fo dffee (fo.866 o.5) d φ (fo o π) c) chcec of he elve vle of he op volge d d) hodogph of he pce veco of op phe volge ) Exple e wvefo of he HT op phe volge chcec of he elve vle d hodogph of pce veco of h volge deced y (4) fo HT wh VM o M fo dffee pee e how g. 4 d 5. (4). whee: =e jπ..5 / j e / g. 5. HT wh M ) ) op phe volge e wvefo fo dffee (fo.866 o.5) φ (fo o π) d ( /) =.5 c) chcec of he elve vle of he op volg e d d) hodogph of he pce veco of op volge ) o fge g. 4 d 5 vle h fo HT wh VM (g. 4) wold e expeced vle of he op volge c e foed oh y chge of he volge elo coeffce ( ) d y chge he phe of he VM op phe volge (φ ). heoe fo HT wh M hee ll oe degee of feedo y e of eoce plo ( / ) chge. po h h ddol degee of feedo fo HT wh M h llow og he gee op phe volge h vle fo g. 4 d lo vle fo g 6. lo d expeel e el The lo lk Ml cc odel how g. 7 whee decpo d vle of he lo d expeel cc pee hee e colleced he Tle. Exple of he lo e wvefo of he HT op phe volge chcec of he elve vle d hodogph of pce veco of h volge deced y fo HT wh VM o M fo dffee pee e how g. 8 d 9 whee exple of he expeel e el fo HT wh VM e how g..
4 ) / ) 4 / g. 6. Volge elo fo HT fco of he volge elo coeffce ( o ) d y chge he phe of he M op phe volge (φ ) ) fo VM ) fo M g. 7. lo cc odel Tle.c Pee Pee Vle e VM M lo Expee lo Volge o Volge o le dcce 5 H le cpcce 5 μ R od ece Ω f wchg khz feecy pply volge V geel e he HT lo e el fo cc how g. how fge g. 8 d 9 e l o clclo oe (g. 4 g. 6). vle fo g. 8 he vle of he op volge c e foed oh y chge of he volge elo coeffce ( ) d y chge he phe of he VM op phe volge (φ ) d hgh coply of he clclo d lo e el ocele. o HT wh M gee dffeece ewee clclo d lo e el c e oeved de o he plfyg po doped fo he hecl odel of he M op volge (8). The / covee ed o he x-ecce choppe (MR) c opee lo ecve powe copeo. The h powe copeo ed o Ćk MR deced [4] (g. 5). g.. Expeel e wvefo fo HT wh M 6 PRZEGĄD EETROTEHZY -97 R. 9 R /5
5 / / j / e 4 j / e - g. 8. HT wh VM ) ) op phe volge e wvefo fo dffee (fo.866 o.5) d φ (fo o π) c) chcec of he elve vle of he op volge d d) hodogph of he pce veco of op phe volge ) oclo h ppe he hecl odel of he volge fe fco he hee-phe hyd foe (HT) wh volge o ce oce x (VM o M) covee hve ee peeed. oh cc olo he phe op volge plde d phe c e chged y e of he VM o M volge o ce elo coeffce ( ) o ( ) d he phe of he VM o M op phe volge (φ ) epecvely. o HT wh M hee ll oe degee of feedo y e of he eoce plo ( ) chge. geel e he lo d expeel e el cofed he heoecl oe. he vego wll e foced o developg hecl odel epeclly HT wh M d expeel pleeo of he dced foe g. 9. HT wh M ) ) op phe volge e wvefo fo dffee (fo.866 o.5) φ (fo o π) d ( /) c) chcec of he elve vle of he op volge d d) hodogph of he pce veco of op volge ) The eech w ced o he fe of GEO pojec de he efeece e GEO/ 877/5. REEREE [] Mlowć J. Hk e. Effec of lod dyc o powe ye dpg EEE T. Powe y. (995). 8 [] M o J. Tgoz R. Eope powe ly vey epo eodo Eegy gve ovee 8 [] Djokc Z. Dee J. Vle G. Mlovc J. oc k. evy of peol cope o volge g d ho epo EEE T. Powe Del. (5) o [4] lce. M G. D lv Y. Volge g ly d olo fo dl pl wh eedded dco PRZEGĄD EETROTEHZY -97 R. 9 R /5 7
6 oo Poc. EEE dy pplco ofeece 4 4 (4) [5] D -Goez J. E je P Woo.. Effec of volge g o djle-peed dve: ccl evlo o ppoch o pove pefoce EEE T. d. ppl. 5 (999) o [6] Jg D. hoe G. ep-p/dow c volge eglo g foe wh p chge d PWM c choppe EEE T. d. Eleco. 45 (998) o [7] po Rodígez J.. opez J. V ggl Oly.. edez. M Gc R. V.. Gcí. M Dl-Tp hoppg lze Wh cyclc of wchg EEE T. d. Eleco. 57 () o [8] edyc z k Z. PWM volge fog cc vey of Zelo Go Pe ( Polh) [9] edyczk Z. zeleck R. eyek G. glephe PWM / ecodco foe opologe d pplco Poc. PE () 48 5 [] Moeo-Hedez O.. Eje P.. pplco of oo - ovee o opee fo Volge g Elecc Powe Do ye Poc PE Glwy () [] edyczk Z. zeleck R. ozń k. ool d eg of Dyc Volge Reoe (DVR) ed volge level EEE T. Powe Eleco. 9 (4) 86 8 [] eolz E.. Eje. P Mo.. Moeo- Hedez O.. g ly d Deg of ovel Volge g opeo fo cl od Eleccl Powe Do ye EEE T. d. ppl. 9 () 4 5 [] h o. Y. Modelg d ly of e odoe ed o Thee-Phe PWM k - ovee Poc. dl Elecoc ocey ofeece EO 4 oe (4) [4] edyczk Z. ą ckowk. Jkowk M. e p k. gle-phe el Volge oolle ed o pol PWM Mx-Recce hoppe Poc. Powe Elecoc d pplco Eope ofeece EPE 5 Dede (5) [5] ele J. G. ew M. ele H. ljeg. ool d Teg of Dyc Volge Reoe (DVR) Med Volge evel EEE T. Powe Eleco. 9 (4) 86 8 [6] jyg P. gh. hd. l-hddd. R Theoy Reved o ool elf-ppoed Dyc Volge Reoe (DVR) fo lced d ole od EEE T. d. ppl. 49 () o.5 4 [7] Gc-Ve P. M. Mcll-Dvd. Rez J. M. Pe-eece Veco-wchg Mx ovee Modle fo Volge Reglo EEE T. d. Eleco. 6 () o [8] ozo J. M. Rez J. M. oe R. E. ovel Dyc Volge Reoe ed o Mx ovee Poc. Mode Elecc Powe ye MEP Woclw Pold () 7 [9] hpo. Rez ef. Dyc Volge Reoe ed o Mx ovee wh zzy oolle dvce Eleccl d Elecoc Egeeg () o. 4 5 [] Ezoj H.. hekholel T M. eed M. M. lo of Dyc Volge Reoe g Hyee Volge ool Eope Jol of cefc Reech 7 (9) 5 66 [] Vlhgw M.. Pee.. D R. ho. Pefoce povee of he Dyc Volge Reoe Wh loed-oop od Volge d e-mode ool EEE T. Powe Eleco. 7 () o [] eloz E.. Eje P.. Mo.. Pel. ex Geeo Do Tfoe: o dde Powe Qly fo cl od Poc. Powe Elecoc pecl ofeece PE cplco Mexco () 66 7 [] e d yc z k Z. ew k J. l y M. gle-phe Hyd Tfoe g Mx-Recce choppe wh Ćk Topology Poc. Powe Elecoc d pplco Eope ofeece EPE 7 Dek log (7) [4] edyc z k Z. ew k J. Modelg d ly of Thee-Phe Hyd Tfoe g Mx ovee Poc. oply Powe Elecoc PE 7 Gdńk Pold (7) 6 [5] ewk J. edyczk Z. Modellg d ly of Thee-Phe Hyd Tfoe g Mx-Recce hoppe Pzegląd Elekoechczy (9) o. 5 [6] ewk J. edyczk Z. ly M. kewk M. zczek P. pleeo of Thee-Phe Hyd Tfoe g Mx hoppe Poc. Powe Elecoc d pplco Eope ofeece EPE 9 celo p (9) [7] ew k J. edyc z k Z. Modelg d ly of Thee-Phe Qde Phe hfe wh Hyd Tfoe Pzegląd Elekoechczy (8) o [8] ew k J. Pccl pplco of ee cve opeo. Powe Theoe fo poved Powe Qly ed. G. eyek M. Pko pge odo [9] ew k J. Modelg d ly of Thee-Phe Hyd Tfoe g ck-oo MR Poc. oply d Powe Elecoc PE Tll Eo () 7 [] ew k J. ly d dy of popee of he hyd foe Ph.D. deo vey of Zelo Gó Pe Zelo Gó ( Polh). [] ewk J. edyczk Z. eyek G. Volge g/well opeo ed o Thee-Phe Hyd Tfoe wh ck-oo Mx-Recce hoppe EEE T. d. Eleco. 6 (4) o [] zcześk P. ew k J. Volge Reglo/ odoe ed o Hyd Tfoe wh Mx ovee Poc. dl Elecoc ocey ofeece EO 4 Dll (4) 9 97 [] e d yc z k Z. T d G. ly M. pleeo of he e oce Mx ovee pce Veco Modlo Poc. Powe Elecoc d Moo ool ofeece EPE-PEM Ohd () T-97 T- [4] V e M. d le. The Geelzed Tfoe: ew -Decol odl Wvefo eecy ovee wh ooly djle p Powe co Poc. EEE Powe Elecoc pecl ofeece PE 8 (98) 4-5 [5] Wheele P. W. Rodgez J. le J.. Epgh. Weej. Mx covee: Techology Revew EEE T. d. Eleco. 49 () o [6]. yo R. G of wo od o fee plco y OWEG () ho: d h. ż. Zgew edyczk pof. Z vey of Zelo Gó e of Eleccl Egeeg l Podgó Zelo Gó E-l: Z.edyczk@ee.z.zgo.pl d ż. Pweł zcześk vey of Zelo Gó e of Eleccl Egeeg l Podgó Zelo Gó E-l: P.zczek@ee.z.zgo.pl d ż. Jcek ewk vey of Zelo Gó e of Eleccl Egeeg l Podgó Zelo Gó E-l: J.ewk@ee.z.zgo.pl; 8 PRZEGĄD EETROTEHZY -97 R. 9 R /5
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