Modelling and Control Design for a High Power Resonant DC-DC Converter

Transcription

1 Mdellg ad Ctl Deg f a Hgh Pwe Reat DC-DC Cvete Chtph Hah #, Membe, IEEE, ad Pete Leh *, Se Membe, IEEE # Cha f Electcal Eegy Sytem, Uvety f Elage Nuembeg, Elage, Gemay chtph.hah@ee.u-elage.de * Depatmet f Electcal ad Cmpute Egeeg, Uvety f Tt Tt, Caada leh@ecf.utt.ca Abtact Th pape vlve the develpmet f a dyamc mdel f a eat dc-dc cvete tplgy ecetly pped at the Uvety f Tt. The mdel make ue f the cevat f eegy pcple. Th dyamc mdel emply a aveagg techque, ce cvete wtchg eglected. A mple tet etwk f valdat f the pped mdel develped. Baed the valdated mdel, a ccept f cled lp ctl f the ytem, cludg the elect f whch vaable ae ptmal t ctl, detemed. Keywd mdellg, ctl deg, dc-dc cvete, tep-up at, aveage mdel ad wtchg fequecy. wa baed athe tplgy pped at the Uvety f Abedee [4]. Th pape addee the pblem f fdg a mathematcal mdel utable f ctl deg. Wth the pped mdel, ytematc ctlle deg ca be caed ut. The eult f mdelg ad ctl deg wll be hw ad dcued f the applcat. Th applcat f the tecect f a pwe uce, lke a ffhe wd fam, wth a hgh pwe dc dtbut gd. Itegat f eewable uce wth hgh pwe eat dc-dc cvete wa dcued [5]. I. INTRODUCTION Recetly, the dee t ue dc bu tecect ha gaed teet. The ea f th teet the ceaed eed t cect dc pwe uce the klwatt ad megawatt pwe age. F example, tegatg ffhe wd fam thugh dc etwk pvdg addtal acce pt t extg HVDC (Hgh-Vltage Dect cuet) le. The advatage f ug a hgh pwe dc-dc cvete tead f a VSC (Vltage Suce Cvete) a LCC (Le Cmmutated Cvete) that thee addtal temedate ac cve tage equed. Thee cvete tplge dectly tecect dc bue f dffeet vltage level. Reewable eegy pduct ha bee pgevely ceag a f late a teatal gal t educe evmetal pllut thugh cab dxde em the geehue gae cme t effect []. T tamt pwe fm ceta type f eewable eegy geeat, uch a ffhe wd fam, t eceay t tafm the electcal eegy t hgh vltage dc. Cuetly th de by ug dc-ac cvete at the wd tube, ac tafme fllwed by ac-dc cve []. The bjectve f hgh pwe dc-dc cve t eplace thee multple cve tage wth a gle, lwe ct cvete, whch eve hghe effcet. I 00 a ew type f eat dc-dc cvete wa pped by Uvety f Tt [3]. Th type f cvete Fgue : Smplfed tuctue f the tep-up cvete Fgue hw the ecetly by Uvety f Tt pped tep-up cvete [3]. The cvete a fequecy ctlled ccut. It ca tep up the put vltage v t the level f the utput vltage v wthut chagg the platy; hece t fuct mla t the clacal bt cvete. Hweve, t t pble t ue mla mdelg techque t the bt cvete due t the fact that the cvete peate a eat mde wth fequecy ctl. The cvete ly peate the DCM mde t w t expeece fced cuet chppg dug cmmutat. It cta a eat duct, L, whch cected t the put bu. I addt, t al ha a tegated eat capactve actve wtchg etwk, C, ad a utput dde valve //$3.00 0IEEE

2 II. CONVERTER MODELLING Aveagg ad mall-gal leazat ae the key tep mdellg cvete [6]. Seveal mdellg techque ae peeted f eat cvete [7], [8]. The fudametal ule whch evey cvete mut bey place ctat the develpmet f a mple cvete mdel. Eegy ad pwe balace ae cluded thee fudametal ule. Iput ad utput eegy, ad pwe, have t be equal f t aumed that the cvete lle. Th mple cvete wtchg le huld be eglected, ubbe ae aumed ad all the cvete elemet ae deal. Hece t pble t deteme the equat f eegy balace f the ecetly pped cvete [3]: γ / ω W W * * TS / TS / V dt + V dt V dt C 0 γ / ω γ / ω V TS / TS / V C dv + V dt V dt C V γ / ω γ / ω TS / VV C dt V V γ / ω * * VV C W W V V 4VV C W W V V * * Whee W ad W ae the put ad utput eegy pe half cycle; W ad W ae the put ad utput eegy pe full cycle. By multplyg the eegy equat by the wtchg fequecy f e yeld the pwe equat f the cvete. P P VV C f V V 4 () () Fgue : Ideal teady tate wavefm f the tep-up cvete Lkg at the wavefm Fgue ad ug Equat (3) e bta the equat f the aveage put cuet. γ / ω TS / I dt + dt C dv + I (4) C C TS T 0 S T γ / ω S V I I 4 fcv + I Accdg t thee equat the cvete equvalet ccut dagam ca be peeted the fllwg way. V Dvdg the utput pwe P VI by the utput vltage V pvde a equat whch peet me kd f aveage utput cuet. V I I V I VV C f V V 4 Ug eegy pwe balace yeld the ft equat f the cvete mdel. F btag athe equat decbg the ccut e ha t lk t athe fudametal ppety the cvete baed up. F th cvete, ce t ly peate DCM, the geeal hape f the cuet wavefm ca be utlzed t cme up wth the ecd equat f the cvete mdel. (3) Fgue 3: Equvalet ccut dagam f the tep-up cvete It apppate et f equat ca be ummazed fm the Equat (3) ad (4). They decbe the ete behavu f the cvete the DCM mde. A. Aumpt F the mdelg cvete thee ae aumpt t whch they ae ubject. F the tep-up cvete mdel tw aumpt ae mptat.

3 3 By ug the ccept f cevat f eegy, ve e ped at eat fequecy, e eglect the vaat the eegy tage wth the cvete. Multplyg the eegy wth the wtchg fequecy yeld the pwe balace. By ug pwe balace thee way t mdel methg lke eegy tage the mdel, but thee eegy ted the capact. Th al the ea f the ft ctat f ug th mdel. If the utput vltage chage t fat, the eegy the capact eed t ceae. The ete cuet wll flw t the capact, ceag the vltage ac the capact; hece thee utput cuet f a ht ped. The ecd fudametal aumpt ued whe cmpag the put ad utput cuet hape. By th pce e culd detect, that the utput cuet jut a pat f the put cuet; hece the ecd mdel equat fud. Whe chg th appach e ha t be awae that all le the cvete ae eglected. B. Ctat ad Lmtat The ue f the ccept f the cevat f eegy pcple, ad aaly f the cuet wavefm t mdel the cvete ha t cequece. The ea f thee cequece ae ce the eegy tage the eat capact ad duct ae t cluded the mdel. The utput vltage t allwed t chage t fat, becaue the eal cvete the vltage ac the eat capact t able t fllw a fat a the utput vltage mght ceae; hece the utput cuet wll deceae t ze f a bef teval. Th t epeeted the mathematcal mdel, ce eegy tage the cvete eglected. The utput cuet wll cvege t the cect teady tate value, but the taet cuet wll t dp t ze. The utput vltage mut alway be hghe tha the put vltage, thewe thee a ple the calculat ad the put cuet a well a the utput cuet wll e ubuded. Th t ly a mdel lmt; t al a cvete lmt. The cvete cat peate a aea whee bth vltage ae equal. Th phycal lmt mapped a mathematcal equat. 4VV C f V V I f V V V V I 4 fcv + I f Thee tw ctat lmt the peatg age f the cvete mdel. Ug t f vey fat cuet ad vltage buld up pcee mght eglect me dyamc behav. III. CONTROL DESIGN Afte develpg a mathematcal mdel f the eat tep up cvete t fllw that e huld vetgate the utablty f the mdel f ctl deg. It caly be vald (5) f a ceta age f peatg cdt. Th age wa qualtatvely dcued the ctat ad lmtat ect. Th ect wll vlve detemat f the lmt f peat mped by ug the develped mathematcal mdel. Al, the bet peatg age f the cvete detemed. Fgue 4 hw the ctl tuctue f the ytem wth the tegated cvete mdel. V ef + - PI Ctlle T N + K T P N f Cvete mdel Fgue 4: Ctl tuctue f the ytem T vetgate the dyamc behav f the cvete, alg wth the bute f the mathematcal mdel, t mptat t che a cvete that ha a matchg put ad utput ccut. F a hgh pwe applcate culd mage cectg eveal wd tube a gd f la pael t the put f the cvete. The utput culd the be cected t a medum hgh vltage dc cable, whch wuld cect the dc-dc cvete t a emte VSC. A a mple cae tudy, a ff-he wd fam wth a 50 kv ubmae cable [9] cect wll be vetgated. Fgue 5 hw a epeetatve mdel f th cae tudy. w w Lle MVDC V C dc-dc Cvete C HVDC V Lle Rle Vl l V VSC ~ C Fgue 5: Applcat f dc-dc Cvete ffhe wd fam Wd fam ad la aay ca each be mdeled by a equvalet cuet uce. The cuet uce wll have vayg ampltude depedg the peet evmetal cdt. The pupe f the mdeled cvete t tep up a vltage de t tamt the electcal eegy ve lg dtace at mmzed le a hgh vltage dc bu. F ffhe wd fam, the methd f tam wuld be thugh a hgh vltage dc ubmae cable, whch typcally at leat 00 km lg. Behd the hgh vltage tam le thee typcally a hgh pwe VSC whch cvet the dc vltage f the cvete t a thee phae ac vltage. The VSC ctl the dc vltage at t put; hece a mplfed mdel f the VSC a vltage uce. The mplfed ytem hw Fgue 6.

4 4 w V C dc-dc Cvete Fgue 6: Cvete mdel de t cect a ffhe wd fam t a VSC The mal value f the cvete elemet egadg t t pevuly meted applcat ae P 60 MW, w 88A, v l 50 kv, C mf, L 9.98 mh, C 800 mf, C 80 mf, f 700 Hz, V 33kV, V 50kV, L le 68mH ad R le.48 Ω, fm [3], [6] ad [9]. The dyamc f th ew ytem ae decbed by the dffeetal equat f Fgue 6 ad the mdel equat f (3) ad (4). C V Lle Rle dv 4C fvv C 4VC f + dt V V dv 4C fvv C l l dt V V dl Lle V Vl R l le dt w w Equat (6) hw the thee tate f the ytem. Thee dffeetal equat ae hghly -lea ad eed t be leazed. Th ca be de thugh ue f the Tayl ee decmpt methd, whee the dffeetal tem wth de geate thae ae eglected. V x V l 4 C ( ) 4 (( ) ) f V Cf V VV 0 C ( ) ( ) V V C V V V 4 C ( ) 4 ( ) f V C f V V ( ) ( ) C + C V V C V V l Rle 0 x L le Lle A C V V 4 ( ) 0 C ( V ) C f 4CV V w C ( ) V V Vl u 0 0 Lle B l Vl (6) (7) The dc-dc cvete pvde vltage egulat f the MVDC etwk, ce lack bu ext the ff-he MVDC etwk. The HVDC le vltage ctlled by the VSC. The VSC mdeled by a vltage uce. Fgue 7 hw the Bde dagam f the cmplete ytem, epeeted equat (7). It eetally a ft de delay except f the peak at appxmately 400ad/ ec. Th peak the eult f addg the tam le t the mdel. Phae (deg) Magtude (db) Phae (deg) Magtude (db) Fequecy (ad/ec) Fgue 7: Bde dagam f the cmplete ytem Fequecy (ad/ec) Fgue 8: Bde plt f the mplfed ytem A mple cvete ctlle ca be deged by ug ly the ft w f the A ad B matce. Thee w yeld a uffcetly accuate tafe fuct f the ytem. Fgue 8 hw that th aumpt vald; the Bde dagam eetally the Bde dagam hw Fgue 7, excludg the peak. The ctlle wll be tued by leazg abut the half ated lad peatg pt wth a wtchg fequecy f 350 Hz. The value eceay f detemg the ctlle wll be malzed t the S.I. ut.

5 5 b b f w a a f V + a 9.7 Equat (8) epeeted by a ft de delay; a uch a ctlle ca be eadly deged, e.g. by the methd f deg wth the help f the fequecy epe chaactetc. w (8) Equat (7) hw the ytem matx A f the ete ytem. The egevalue f A ca be calculated ad pltted wth MATLAB ad the eult ae hw Fgue 0 (blue). Evey egevalue pltted eght tme f wtchg fequece f tatg by 00Hz ad edg by 800 Hz. IV. RESULTS The epe f the ctlled ytem whe the ctlle paamete f equat (9) ae ued hw Fgue 9. F PI 0.003ec + ( ) 0.43 (9) 0.003ec The vltage v f the MVDC etwk egulated at 33 kv. The ctlle ha t hadle fve 300A tep-up chage the wd tube cuet at t.0ec, t 4.0ec, t 3 6.0ec, t 4 7.0ec ad t 5 8.0ec; tatg at w 38A ad edg at w 88 A; whch the ated put cuet f the cvete. Th cea culd epeet the pweg- pce f multple wd tube the ffhe wd fam. The cvete cuet ad vltage have t ema table ad wth ceta bud dug th tug pce de t guaatee accuate peat. Fgue 0: Egevalue f the cled ad pe lp ytem The ytem ha thee egevalue; a pa f cmplex cjugate (whch ae affected by the tam le) ad a eal e (whch affected by the cvete). The egevalue ae detemed equat (0) ad (). e 4 C ( V ) e, f ( V ) C V Rle ± j L L C 84.4± j48.74 le le f (0) () Fgue 9: Cled lp epe wth ptmzed ctlle The ft egevalue, e, eetally the ft ety a f the ytem matx A (th ca be beved thugh a aalytc egevalue calculat) ad hadly deped the wtchg fequecy at whch the cvete peatg at. The dyamc f the cvete deceae at hghe wtchg fequece. T deteme the cled lp egevalue f the ete ytem the PI ctlle alg wth the cvete dffeetal equat ha t be cluded the calculat. Ietg the PI ctlle the A matx f equat (7) yeld a cled lp ytem decpt wth t ytem matx A, c whch peeted equat (). The egevalue f A ae al hw Fgue 0 (ed). c

6 6 A c 0 KP C ( ) 4 ( ) 4 ( ) 4 (( ) ) V C f V C V Cf V VV + K 0 P T ( ) ( ) ( N C V V C V V C ) V V C( V V ) 4CV V 4 C f ( V ) 4CV V 4 C f ( V ) K P T ( ) ( ) ( N C V V C C V V ) V V C( V V ) C R le 0 0 Lle Lle () Fgue 0 hw that the ctlle de t affect the cjugate cmplex egevalue f the ytem. The put vltage ctlled ad theefe de t fluece the egevalue f the utput ytem. Oly the cvete egevalue e wa mved futhe the egatve eal dect mplyg that the ytem wa ped up by the cvete. V. CONCLUSIONS I th pape, a mathematcal mdel utable f ctl deg f a ew famly f dc-dc cvete wa pped. It al cluded the aumpt, ctat, ad lmtat f the mdel. Ug thee, the apppate peatg age f the mdel wa fud, a well a the apppate applcat f the pped cvete. Mathematcal aaly f the pped mdel wa caed ut. Th eulted a et f deg equat allwg accuate detemat f the ctlle paamete. The dyamc f the cvete wee meaued. It wa hw that the mdel equat ft the dyamc f the actual cvete. Mt f the dyamc behav exhbted by the cvete eemble ft de delay behav ad a uch the ctl deg mple. A mple ctlle f the cvete wa detemed. It wa hw that the dyamc f the put ad utput vltage ad cuet match the btaed fm the mathematcal mdel. It wa beved that the ctlle de t affect the egevalue acated wth the tam le. Ay HVDC le dyamc have maj mpact the put ccut f the cvete. Th mple that the ctlle de t eed t tablze the dyamc f the utput le whle ctllg the put vltage. The mathematcal mdel f the tep up dc-dc cvete wa pped, beved ad valdated. REFERENCES [] B. Igelka. Clmate chage mtgat: vevew f the evmetal plcy tumet. Iteatal Jual f Gee Ecmc, vl. (): 0-5, 008. [] S. Hee. Gd Itegat f Wd Eegy Cve Sytem. Jh Wley & S Publhg, Wet Suex, Eglad, 006. [3] A. Haga. A ew Famly f Tafmele Mult-Mdule DC-DC Cvete f Hgh Pwe Applcat. PhD the, Uvety f Tt, 0. [4] D. Jvcc. Step-up DCDC cvete f megawatt ze applcat. IET Pwe Elect 009, vl., I. 6, pp , Nv. 008 [5] D. Jvcc ad B.T. O. Hgh-Pwe, Reat DC/DC Cvete f Itegat f Reewable Suce. IEEE Buchaet Pwe Tech Cfeece, July, 009. [6] R. Eck, D. Makmvc. Fudametal f Pwe Electc. Kluwe Academc Publhe, Bulde, Clad, 004. [7] A. Ple, Taufk, M. Awa. Mdelg ad Smulat f Paalleled See-Lade-Reat Cvete. Secd Aa Iteatal Cfeece Mdellg & Smulat, , 008. [8] B. Baha, M.O. Tkh. Dyamc Mdellg ad Ctl f Reat Swtch Mde Cvete. Ctl Eg. Pacte, vl. 5():533-54, 997. [9] L. Hehld, R. Stubbe. Pwe Cable ad the Applcat. Publhed by Seme Aktegeellchaft, Bel ad Much, 993. Chtph Hah eceved h Dpl.-Ig. degee fm the Uvety f Elage/Nuembeg, Gemay, 0. Cuetly he a Ph.D. tudet at the Uvety f Elage/Nuembeg, Gemay. I 00/0 he dd a eeach pject wth Pf. Pete Leh at the Uvety f Tt. Pete W. Leh eceved the B.Sc. ad M.Sc. degee fm the Uvety f Matba, Wpeg, MB, Caada, 990 ad 99, epectvely, ad the Ph.D. degee fm the Uvety f Tt, Tt, ON, Caada, 999, all electcal egeeg. Fm 99 t 994, he wa wth the Netwk Plag Gup f Seme AG, Elage, Gemay. Cuetly, he Pfe at the Uvety f Tt.