Comparison Of Single Stage And Two Stage Stage Grid-tie Inverters

Transcription

1 Unvery f Cenral Flrda Elecrnc hee and Deran Maer he Open Acce Cmparn Of Sngle Sage And w Sage Sage Grd-e nverer 007 Keh Manfeld Unvery f Cenral Flrda Fnd mlar wrk a: hp://ar.lbrary.ucf.edu/ed Unvery f Cenral Flrda brare hp://lbrary.ucf.edu Par f he Elecrcal and Elecrnc Cmmn SARS Can Manfeld, Keh, "Cmparn Of Sngle Sage And w Sage Sage Grd-e nverer" 007. Elecrnc hee and Deran hp://ar.lbrary.ucf.edu/ed/355 h Maer he Open Acce brugh yu fr free and pen acce by SARS. ha been acceped fr nclun n Elecrnc hee and Deran by an auhrzed admnrar f SARS. Fr mre nfrman, pleae cnac lee.dn@ucf.edu.

2 COMPARSO OF SGE SAGE AD WO SAGE GRD-E ERERS by KEH ADREW MASFED B.S. Unvery f Cenral Flrda, 005 A he ubmed n paral fulfllmen f he requremen fr he degree f Maer f Scence n Elecrcal Engneerng n he Schl f Elecrcal Engneerng and Cmpuer Scence n he Cllege f Engneerng and Cmpuer Scence a he Unvery f Cenral Flrda Orland, Flrda Summer erm 007

3 007 Keh Manfeld

4 ABSRAC h he cmpare w mehd f degnng grd-e nverer. he fr degn plgy a radnal w age apprach cnng f an laed DC-DC cnverer n he npu fllwed by a hgh wchng frequency SPWM Snudal Pule Wdh Mdulan age prduce he requred lw frequency ne wave upu. he nvel ecnd degn apprach emply a mlar DC-DC npu age capable f beng mdulaed prvde a recfed ne wave upu vlage/curren wavefrm. h age fllwed by a mple lw frequency wched Unfldng Sage recreae he requred ne wave upu. Bh f he abve degn have advanage and dadvanage dependng n perang parameer. he fllwng wrk wll cmpare he Unfldng Oupu Sage and he SPWM Oupu Sage a varu pwer level and pwer dene. npu age plge are mlarly examned n rder deermne he be degn apprach fr each upu age under cnderan.

5 ACKOWEDGMES wuld lke hank my advr Dr. Baareh fr h uppr and gudance. Alng wh Dr. Sr fr h helpful ngh whch aved me mnh f me wrkng n he lab whu eeng daylgh. wuld n be here a h pn f wa n fr hem. Al, wuld lke hank every ne a SURGE lab, ApECOR, and Flrda PEC fr all her unyeldng help, uppr, and gudance a well. wuld have n been able fnh f wa n fr yu all, hank yu very much. v

6 ABE OF COES S OF FGURES...v S OF ABES... x CHAPER : RODUCO... CHAPER : ERER SAGE... 5 nrducn... 5 Cmpnen Selecn... 6 nducance... 6 Capacance... 7 C... 8 C bulk r C n... 0 Frequency... SPWM Drvng Scheme... 4 EHPWM... 8 Mdfed HPWM... 9 Pwer Calculan... 0 Swchng... 0 Cnducn... 4 Drvng... 6 v

7 Overall Effcency... 7 Expermenal Reul CHAPER 3 : PRMARY SAGE nrducn plgy Selecn Secndary Sage plgy Prmary Sage plgy Cnverer Mde f Operan Mde... 4 Mde... 4 Mde Mde Mahemacal Analy Gan Sre Analy Draw Back Smulan CHAPER 4 : SGE SAGE ERER... 5 nrducn... 5 v

8 Bac Sngle Sage... 5 Prped Mdfcan fr B-Drecnal Pwer Flw Parallel Cnverer Synchrnu Recfcan Cycl-Cnverer Apprach Acve Bu Cndner CHAPER 5 : COCUSO APPEDX A: RPPE DFFERECE POS MAAB CODE APPEDX B: HPWM AAYSS MAAB CODE APPEDX C: B-POAR AAYSS MAAB CODE APPEDX D: MAH DERAOS REFERECES v

9 S OF FGURES Fgure Renewable Pwer Prducn Curve... Fgure nverer Syem... 5 Fgure 3 Curren Rpple fr a Cnan... 7 Fgure 4 C v. f fr HPWM... 8 Fgure 5 C v. f fr B-Plar... 9 Fgure 6 lage Rpple fr HPWM and B-Plar Cnan C... 9 Fgure 7 Oupu Pwer... 0 Fgure 8 Pwer v. f HPWM... Fgure 9 Curren Rpple v. f HPWM... 3 Fgure 0 Pwer v. f B-Plar... 3 Fgure Curren Rpple v. f B-Plar... 4 Fgure MOSFE and eg can... 5 Fgure 3 Swchng Scheme B-Plar... 6 Fgure 4 Swchng Scheme HPWM... 6 Fgure 5 Swchng lage... Fgure 6 Curren Flw Pve Half f Sne Wave... 3 Fgure 7 herecal Effcency and Pwer ung HPWM w/ f 50 khz... 8 Fgure 8 Effcency Curve ung HPWM w/ f 50 khz... 9 Fgure 9 Expermenal Reul a Full ad... 3 Fgure 0 Expermenal Reul Purely nducve ad... 3 Fgure Gae Drve lage and g ZS v

10 Fgure B plgy w and w/ Aumpn Fgure 3 Acve Clamp w/ lage Dubler Fgure 4 Mde... 4 Fgure 5 Mde... 4 Fgure 6 Mde Fgure 7 Mde Fgure 8 Curren Wavefrm Fgure 9 Oupu Pwer v. Oupu Curren Fgure 30 Blck Dagram f Sngle Sage Apprach... 5 Fgure 3 Parallel Cnverer Fgure 3 Synchrnu Recfcan Fgure 33 Cycl-Cnverer Fgure 34 Acve Bu Cndner... 6 Fgure 35 Energy Srage ewrk Crcu... 6 x

11 S OF ABES able Swchng Scheme Cmparn... 8 able umber f me Swched... 7 able 3 Cmparn beween Sngle Sage Apprache... 6 able 4 Cmparn beween w Sage and Acve Bu Cndner x

12 CHAPER : RODUCO he law f upply and demand ae ha a he demand fr a prduc ncreae, he upply f ha prduc wll decreae. Snce he uppler can n keep up wh he demand fr he prduc he prce f ha prduc wll ncreae lwer he demand and allw he uppler keep up wh he demand f he cnumer. h lead he re n he prce f he prduc, n h cae energy. Snce m energy cme frm nn-renewable urce uch a fl fuel r nuclear energy, he mre we ue he le upply here wll be furher ncreang he prce. make maer wre, durng he prce f creang h energy, pllun creaed a a by-prduc. h mean he mre energy he wrld requre he mre pllun he wrld creae. here are alernave urce f energy ha d n pllue and are renewable whch mean ha hey can be ued up uch a he fl fuel r nuclear ype f energy. hee renewable energe can help lwer he c f energy and al lw dwn pllun. he way ha he renewable energy can help lwer c by ffeng he demand fr energy. Renewable energy urce culd n here wn replace he nn-renewable ype f energy f prperly zed. Hwever, he renewable energe have a dwn de hem ha m dn prduce energy cnnuuly uch a wh he nn-renewable ype. h due he way ha he renewal prduce he energy uch a: lar nly creang energy durng he dayme and pwer level lwerng dependan n amben cndn, wnd nly creang energy when he wnd beween ceran peed.e. f he wnd lw he generar can prduce energy and hgh he generar wll break, and dal ge pwer relaed he dance he mn frm he earh. Due h nn-cnnuu energy prducn he renewal need energy rage devce uch a baere and uper capacr ha can re he exce energy durng peak

13 pwer prducn and drbue he red up energy durng me f lw pwer prducn. Becaue f h nn-cnnuu energy prducn he renewable energy generar mu be ver zed ha can mee he average pwer need. fnd he mplfed average pwer ha he renewable generar can prduce an aumpn made. h aumpn ha he maxmum pwer ha can be generaed frm he renewable urce cnan a ha maxmum pwer ver he me ha he renewable can generae he pwer a can be een n Fgure. Hwever, ung h mplfcan exce average pwer wll be nrduced and he generar may n be verzed enugh. Pwer prducn Aumed pwer prducn Acual pwer prducn Maxmum pwer n ff me Fgure Renewable Pwer Prducn Curve he amun f pwer ha he renewable pwer generar need be verzed by mee he average pwer need can be calculaed by EQ.. P avg n Ppk d Ppk d d P P pk P avg n n pk n

14 Hwever, f he renewal were n ued replace he nn-renewable urce bu merely ffe he peak pwer prducn a uch a wh drbued generan. hen renewable urce d n need be verzed a f hey were he nly generan urce. Alng wh mre apprpraely zng he renewable urce drbued generan ha he penal lwer c he cnumer, ncreae pwer qualy whch n urn lwer c he uly cmpany, ncreae relably f he grd, enable peak pwer havng, and reduce he need buld r upgrade new ranmn/drbun lne. he renewable urce ha parcularly ueful n drbued generan lar array. h becaue he me ha he uly cmpany ee peak pwer cnumpn durng he day whch when he lar array wuld be prvdng pwer, enablng he ably peak pwer have. h ably f peak pwer havng havng anher pwer generan urce paralleled he grd and nly ar prduce pwer when he pwer beng cnumed re abve a pecfed level. Anher rean ha lar array are preferable her renewable urce fr lwer pwer level lcan and afey. A lar array panel can ealy be nalled n he p f a hue where pace n beng ued waned pace wll n be ued up lke wh her generar. Al unlke wnd generar here are n mvng par here le lkelne f anyne geng hur. he majr draw back lar are ha he panel have lw effcency cnvern bu h can ncreae wh me and he pwer prduced a lw vlage bu culd be acked hgher vlage. he man rean ha he renewable urce are lw be acceped becaue f he hgh nal c he cnumer, unknwn wha addng many mall drbued urce n parallel he pwer grd wll d, and c fr rerucurng he grd fr mprved 3

15 cmmuncan f lad and urce. Hwever, he penal benef fr drbued urce f prperly and carefully cndered can uwegh he c. A aed befre due he hgh nal c and lcan f he urce he preferred renewable urce a lw pwer arund kw lar array whch wha he nverer fr h he baed n. he man purpe f h wrk cmpare Sngle Sage veru he w Sage nverer apprach. CHAPER and CHAPER 3 wll dcu he w Sage apprach whle CHAPER 4 wll fcu n he Sngle Sage and CHAPER 5 wll be a ummery and cnclun f he fndng. 4

16 CHAPER : ERER SAGE nrducn A DC AC nverer yem uually ha w hgh wchng frequency age. he fr age f he nverer yem a DC DC cnverer regulang he npu vlage he ecnd age he bu vlage. Fgure nverer Syem he ecnd age, he nverer Sage, hwn n Fgure, where he cnvern frm DC AC happen. h cnvern happen due he duy ra varyng n a nudal paern fr a waned ne wave upu. Al, alm any her wavefrm can be creaed here where he man lmng facr he frequency f he upued wavefrm. One f he man rean he nverer placed n he ecndary de ha he lan ranfrmer can peraed a hgh frequence, hrnkng he ze and wegh f he ranfrmer gnfcanly. n addn, havng he nverer age n he ecndary de allw fr eaer cnrl, and al enable he yem be mre adapve ver a wder range f requremen. he nverer age yeld mre adapably due naure be b-drecnal, 5

17 whch mean he lad den have be purely reve. Snce he nverer age Bdrecnal by naure an nducve lad can be appled wh mnmum cmpnen ncreae. Cmpnen Selecn nducance he fr ep n creang he nverer age chng he crrec cmpnen. ued fler he upu curren decreae he al harmnc drn HD and a a reul ncreae he pwer facr. he phae dplacemen due he ncreaed nducance value can be ffe hrugh a prperly degned cnrller. S wh a crrecly chen C upu capacr chen d he ame hng a bu fr he vlage and a pwer facr near uny can be acheved. Frm EQ. 4, EQ. 5 ha wll be aed laer he duy ra dfferen fr he HPWM hybrd pule wdh mdulan and B-Plar drvng cheme herefre he curren rpple wll be dfferen fr he w drvng cheme. n addn, he vlage ha beng appled he upu dfferen ung he w cheme. Wh he B-Plar mehd, a pve, negave bu vlage, and zer beng appled whle he HPWM nly ha eher pve and zer r negave and zer beng appled he upu. Snce he B-Plar ha wce he vlage wng f he HPWM, he B-Plar wll requre larger capacance and nducance value have he ame rpple a he HPWM mehd. 6

18 .8.6 B-Plar v. HPWM drvng HPWM B-Plar.4 curren rpple upu vlage Fgure 3 Curren Rpple fr a Cnan Frm Fgure 3 he curren rpple wh a cnan can be berved, baed upn EQ., EQ. 4, and EQ. 5. Fgure 3 hw ha he HPWM ha a much lwer curren rpple han ha f he B- Plar and mply addng mre nducance value mpraccal due he fac ha he ESR equvalen ere reance, he c, he ze, and/r he wegh wll ncreae. D bu f Capacance here are w man capacr ha need be eleced/zed apprpraely fr prper peran f any Swch Mde Pwer Supply SMPS. hee w capacr are C r he upu capacr, whch wll fler he upu vlage, and C bulk r he npu fler ha ued help regulae a cnan DC bu vlage. 7

19 C Whle ued fler he curren, C ued fler he upu vlage r help aenuae he wchng rpple and any her harmnc ha are upermped upn he upu f he nverer. he upermped rpple due he fac ha he nverer ue a frequency much hgher han he fundamenal frequency f he upu. prperly deermne he ze f he upu capacr he upu nducance, he wchng frequency f ha beng aenuaed, he duy cycle D, and he allwable nrmalzed vlage rpple rp all mu be knwn and aken n accun. C D 8 f rp 3 Frm EQ. 3 he mnmum capacance needed fr a pecfc rp can be fund fr varyng wchng frequence mnmze cmpnen ze a well a le acaed wh he ESR f he cmpnen a well a he MOSFE. When he wchng frequency vared, and C need be vared keep a cnan upu curren rpple and vlage rpple. Fgure 4 C v. f fr HPWM 8

20 Fgure 5 C v. f fr B-Plar Fgure 4 and Fgure 5 hw he capacance ncreae fr bh drvng mehd gng frm 0 khz 0 khz whch apprxmaely hree me mre capacance needed keep ha cnan vlage rpple a he lwer wchng frequency han he hgher wchng frequency B-Plar v. HPWM drvng HPWM B-Plar 0.5 vlage rpple upu vlage Fgure 6 lage Rpple fr HPWM and B-Plar Cnan C he pwer l avng, curren rpple, and vlage rpple avng fr he HPWM de n cme a any bvu c. A can be een frm Fgure 6 he vlage rpple fr he HPWM 9

21 drvng cheme lwer han ha f he B-Plar. h due hw he vlage beng appled whch can be een hugh he duy ra gven by EQ. 4 and EQ. 5. D B.5 4 bu D HPWM 5 bu Snce he B-Plar mehd ha bh pve and negave vlage beng appled he upu, h caue a hgher vlage wng. h hgher vlage wng caue he hgher vlage rpple ha need be aenuaed. C bulk r C n Snce he nverer beng degn wll be eed under a cle purely nducve lad, h mean ha he nverer wll receve pwer a well a generang pwer r be b-drecnal wh an average upu pwer f ne klwa. Fgure 7 Oupu Pwer he upu pwer gng be ne quared whch gven by a ne prpery hwn n EQ. 6 hw ha he 60 Hz upu ne wave urned n a 0 Hz rpple upn he npu bu vlage 0

22 due a purely reve lad, f here wa an nducve lad he rpple wuld ncreae and even g negave. n x.5 c x 6 Snce he 0 Hz rpple prpagae back he DC bu vlage here need be a bulk capacr re he npu vlage ha he bu vlage de n drp belw he maxmum upu vlage. deermne he capacance needed EQ. 7 ued keep he mnmum bu vlage abve he maxmum upu vlage due he energy red n he capacr. C bulk P 0 π [ max mn ] 7 n EQ. 7 P he average upu pwer; mn he mnmum accepable DC bu vlage. ban max EQ. 8 ued, where wan he DC bu vlage ha beng appled frm he laed DC--DC cnverer. max wan mn 8 a preferable feaure f he w Sage nverer yem ha he bulk rage capacance placed n he mddle f he w age. Cmpared he bulk capacr needed fr he Sngle Sage apprach, he capacr f a w Sage yem allw a hgher percenage vlage wng, referenced dc value, and hu able accmmdae a larger amun f pwer rpple fr he ame rage deny. Anher advanage ha he alernang cmpnen f he upu pwer capured whn ha age, and n ranmed hrugh he DC-DC cnverer age. n her wrd, he DC-DC cnverer age repnble fr upplyng he averaged pwer, whle he peak pwer re cnfned he effcen, b-drecnal and nnlaed, SPWM nverer age.

23 Frequency Frm he pwer l calculan dne earler can be een ha fr bh mehd he pwer l dependan n he wchng frequency a well a me f he cmpnen. S mnmze he le and cmpnen ze, cmpnen a well a he pwer l calculan need be recalculaed wh varyng wchng frequence. Fgure 8 Pwer v. f HPWM Frm Fgure 8 wh HPWM drvng can be een ha he pwer l decreae and he effcency ncreae a he frequency decreae. h lead u beleve ha he lwer he wchng frequency he hgher he effcency, hwever, h rue bu h n all he nfrman. n addn, a een frm Fgure 4 he yem wll need mre capacr keep he ame vlage rpple bu ha he draw back f ncreaed par ze, c, and bard pace.

24 Fgure 9 Curren Rpple v. f HPWM f he cuner argumen f lwer pwer l n he ESR f he capacr aken han ha ffe by he fac ha very lle curren wll ravel hrugh he capacr a cmpared ha f he nducr. Frm Fgure 9 mu be ncreae by a large facr keep he ame curren rpple. h mean ha he ze and wegh f he nducr wll be exremely large fr maller wchng frequence bu al here wll be an ncreae n he pwer l n he nducr due he ncreae f he ESR frm he ncreaed nducance needed. Fr he B-Plar drvng here al pwer l decreae wh he decreae f wchng frequency a hwn n Fgure 0. Fgure 0 Pwer v. f B-Plar 3

25 Frm Fgure 8 and Fgure 0 can be een ha here le l n he HPWM raher han he B-Plar. Hwever he cmpnen elecn mu be aken n accun and een f he rade f effcency fr cmpnen/ze/pace wrh he prce. S he nex hng ake a lk a he cmpnen pecfcally. Fgure Curren Rpple v. f B-Plar ke he HPWM he B-Plar mu be ncreaed keep he ame upu curren rpple a lwer frequence a cmpared he hgh frequence. S wh he lwer frequence bh HPWM and B-Plar have a mall decreae n pwer l bu h fac ffe by he ncreae n and C. pmze effcency a well a ze, c, and cmpnen elecn a wchng frequency f 50 khz ha been chen. SPWM Drvng Scheme here are everal mehd creae he upued ne wave frm he DC vlage bu. he mehd ha wll be dcued are baed n he H-Brdge nverer plgy wh nudal pule wdh mdulan SPWM echnque. w parcular drvng cheme are cndered; ne mehd, dubbed b-plar, a aed earler, baed n wchng all fur f he MOSFE hu 4

26 applyng pve and negave bu vlage he upu ver he enre ne wave. Wh he B- Plar mehd, he ne wave creaed by varyng he duran he pve bu vlage beng appled. Anyme ha he pve bu vlage n beng appled he negave bu vlage wll be appled he upu, hence he name B-Plar. Fgure MOSFE and eg can Fr he ecnd mehd, he HPWM, whch were nly a pve bu vlage and zer vl wll be appled he upu fr he pve half f he ne wave, and a negave bu vlage and zer vl fr he negave half f he ne wave. he way h acheved by urnng n and ff f he MOSFE f ne leg a he wchng frequency. Whle fr he her leg, he lw de wch kep n and he hgh de wch ff fr he pve half f he ne wave. creae he pve half f a ne wave, leg wll be he wchng leg, whle leg wll have wch D cnanly n, and wch C wll be cnanly ff. hen creae he negave half f he ne wave, leg wll ll be he wchng leg whle wch C wll urn n and D wll urn ff. 5

27 Fgure 3 Swchng Scheme B-Plar Fgure 4 Swchng Scheme HPWM Bh Fgure 3 and Fgure 4 hw he mehd fr wchng nly fr he pve half f he ne wave. creae he negave half f he ne wave wch D and C exchange wchng cheme whle wche A and B wll d he ame fr bh SPWM drvng cheme. he HPWM very mlar ha f he Un-Plar mehd wh he excepn ha half f he wche wll be wchng a wce lne frequency a apped he wchng frequency. Wh he reducn n wchng frequency half he wchng l wll be aved. h wa berved n []; where he HPWM, Un-Plar, and B-Plar wchng le were cmpared. 6

28 Whle n [] he HPWM, B-Plar, and SPWM EM elecr-magnec nerference wa examned and cmpared each her deermne f here are any advere effec n he EM frm he HPWM drvng mehd. Hwever, he ppe rue; he EM wa acually reduced wh he ue f HPWM. he rean ha [] gave fr he reducn f he cnduced EM fr he HPWM due he fac ha n all he wche are wchng a a hgh frequency, whch al he ame rean why he wchng l reduced. A mdfcan hwn n [3] allw ZS be acheved fr all he wche by addng an addnal wch, capacr, and nducr. Whle he added nducance and capacance are mall hey d ncreae he pace needed a well a he drvng and cnrl crcury needed fr he exra wch. Frm [3] here wll be n wchng l acaed wh any f he wche due he ZS, hwever; he cnducn l wll be ncreaed. he ncreae n cnducn l wll be due havng he exra wch drecly n he man pwer flw pah al he renance creae he ZS n all he wche wll ncreae he crculang curren whch n urn wll al ncreae he cnducn l. Whle wchng l a full lad een frm Fgure 7 abu 0 W and he cnducn l 50 W remvng he 0 W f wchng l wuld be benefcal bu he cnducn l f he enre yem wuld apprxmaely duble due he nern f he exra wch, ha why n feable add he exra crcury fr ZS peran a h wchng frequency. Hwever, f he wchng frequency were ncreaed he ZS peran may becme a mre feable pn. w ne her cncern came abu frm HPWM mehd and ha he dfference n he number f me wchng a well a he hea nk ued n dpang he hea n each parcular wch. [4] and [5] purpe and evaluae mdfed wchng cheme fr he HPWM where he 7

29 lw and fa wchng frequency wll be mre evenly drbued amng he MOSFE. n h way he wchng l and number f me wched wll be evenly drbued amng he MOSFE hu ncreang he lfeme f he MOSFE a well a harng he hea evenly amng he MOSFE. Al, wh he le/hea evenly drbued amng he MOSFE here can be ne MOSFE and/r hea nk chen/degned fr all he wche. able hw he advanage and dadvanage f each drvng cheme. able Swchng Scheme Cmparn Swchng Scheme EM Relably Effcency hermal Drbun Swch Selecn Un-Plar Pr Average Pr Average Average B-Plar Pr Average Pr Average Average HPWM Average/Beer Average Beer Pr Hard EHPWM Average Be Average Average Average Mdfed HPWM Average Average Be Pr Hard EHPWM Wh he EHPWM a.k.a. emperaure equalzan HPWM he number f me wchng ccur evenly drbued amng all fur wche may lead a reducn f effcency bu evenly drbue he hea. h reducn due he fac ha f a fa wchng MOSFE wa chen fr he hgh wchng frequency leg and a lw R DS n MOSFE wa chen fr he lw wchng leg a mnmum l culd be acheved. ha why he MOSFE 8

30 elecn fr he HPWM n able led a hard and he effcency he be. Hwever, f h dne he hermal drbun wuld be pr a een n able becaue nly ne de wuld ee he wchng le and nce ha ne de wchng a a hgh frequency he relably f he yem wuld be he ame f n ngnfcanly ncreaed. Al, he EHPWM EM huld be he ame a he HPWM. Hwever, he layu f he EHPWM mre crcal han he layu f HPWM. he rean fr h due he EM urce, he wchng MOSFE, changng w dfferen lcan wh he EHPWM whle he HPWM EM ne urce n a cnan lcan. he generaed EM fr bh EHPWM and HPWM huld be he ame hwever he lcan f he urce vare n he EHPWM whle cnan n he HPWM. h varyng ne urce lcan why he EHPWM need a mre phcaed layu han he HPWM. h why HPWM wa he chen drvng cheme be cmpared ha f he B-Plar mehd nead f he EHPWM beng cmpared he B-Plar. Mdfed HPWM he mdfed HPWM echnque can lghly mprve effcency ver he HPWM echnque by havng w change. he fr mdfcan ha here wll n be a lw wchng leg. nead he lw wche wll be n he hgh de whle he fa wche wll be n he lw de f bh leg. Shwn n Fgure where wche A and C are lw wched whle B and D are fa wched. he ecnd mdfcan nead f a MOSFE beng ued fr he lw wche an GB ued wh a fa revere recvery an-parallel dde. he rean fr h ha he wchng l due he h hrugh caued by he revere recvery f he MOSFE bdy dde wll be reduced. 9

31 h becaue he MOSFE bdy dde nrnc and can be mprved whu adverely affecng he MOSFE elf. Hwever, f an GB replace he MOSFE an anparallel dde can be added. Becaue he added dde n an nrnc dde can be mprved reduce he revere recvery whu any advere effec. h al culd be dne fr he lw wchng MOSFE bu a dde mu be added blck he nrnc bdy dde f he MOSFE. Hwever, when addng h blckng dde he cnducn l wll ncreae and may be even hgher han he pwer ha aved frm addng he dde. Al, he cmpnen cun and c wll ncreae a well a he chance f falure. he mdfed HPWM echnque can ave pwer l h hrugh bu a he prce f cnducn l fr lwer pwer level. h becaue he HPWM cnducn l due MOSFE ver he enre wchng perd excep fr he dead me whch when he bdy dde wll cnduc. Whle he mdfed HPWM l due GB and a dde fr he ff me -D me and an GB and MOSFE fr he n me D me. Al, wh he mdfed HPWM he hgh de drvng becme lghly mre dffcul due he lengh f me ha he wch mu be n. he mehd ha mre ued fr h nmnal pwer level he HPWM echnque. Pwer Calculan Swchng Dead-me nerval are nered n he wchng wavefrm avd hr-crcu cndn durng wchng. he duran f h dead-me degned allw ZS peran f he wche, whenever enabled by plgy peran. Fr he HPWM, wch A and B can 0

32 acheve ZS durng he pve and negave halve f he ne wave, repecvely. Fr B- Plar, bh B and C can acheve ZS fr he pve half f he ne wave and he her w wche can acheve ZS fr he negave half f he ne wave. Operang wche a ZS mnmze her wchng le a well a ncreae relably. he rean ha ZS nly allw he mnmzan f wchng l and n cmpleely rd he yem f wchng le he fac ha he upu curren wll dcharge he bdy capacance, and hen ha ame curren wll ar flw hrugh he bdy dde. Once he curren ar flw hrugh he bdy dde, h wll caue a vlage drp f apprxmaely 0.7. Wh a 0.7 drp acr he MOSFE, he MOSFE nw echncally n a zer vl anymre bu raher 0.7. herefre yu can nly acheve a mnmzed wchng l r mnmzed vlage acr he MOSFE raher han zer vl acr he MOSFE r zer wchng l. Fgure 5 Swchng lage Fgure 5 hw he wchng vlage; he wchng curren lk apprxmaely he ame hwever wh a me hf and he maxmum curren cnanly changng frm wchng perd anher. Pwer l due wchng gven by EQ. 9.

33 P wch n f n ff 9 6 Snce EQ. 9 gve he nananeu pwer and he curren change frm wchng perd wchng perd. EQ. 9 need be mdfed fnd he average pwer l due wchng ver he enre cycle r half f he ne wave perd, whch gven by EQ. 0. he rean ha wchng l nly fund ver he pve half f he ne wave and n he enre ne wave due he fac ha he wchng l repea every half ne wave perd.e. he pwer l n he pve half he ame a he negave half.. P f π wch n n ff ω dω 6π 0 0 P avg n f n 3π R ff ad EQ. 0 can be furher mplfed EQ. where he rm upu vlage, R lad he lad reance, n he bu vlage npu vlage he nverer n yem, f he wchng frequency, and n and ff are he re and fall me befre he MOSFE are cmpleely n r ff. h he wchng pwer l fr each ndvdual wch ha n wchng a ZS. S calculae he wchng l fr he enre yem he ngular wchng pwer l need be mulpled by he number f wche ha are n wchng a ZS ver he half ne wave perd.

34 A C ad B D Fgure 6 Curren Flw Pve Half f Sne Wave Fr he B-Plar mehd, all he wche are ued creae he ne wave. A can be een frm Fgure 6 wche B and C wll have curren flwng hrugh he bdy dde f he MOSFE durng he dead me f he pve half f he ne wave enablng he w MOSFE acheve ZS. S wche A and D wll be hard wched, durng he pve half f he ne wave and fr he negave half wche B and C wll be hard wched. herefre, B-Plar wll alway have w wche ha are beng hard wched he wchng pwer l w me P avg frm EQ.. Fr he HPWM mehd, ne f he lw de wche wll be cnanly n n wchng l wll be acaed wh. Whle ne f he hgh de wche wll be cnanly ff, a a reul n wchng l wll be acaed wh ha ne eher. he HPWM cmpared he B-Plar far ha he ame amun f wche ha d n have wchng l acaed wh hem. Once he dead me curren flw aken n cnderan can be een ha he lw de wch ha wchng a he wchng frequency n wce he lne frequency de ndeed wch a ZS. Whch mean u f he 4 wche fr he HPWM wll n have ZS and u f he 4 wche fr he B-Plar wll n have ZS. h mean ha HPWM n nly ha half he wchng l cmpared he B-Plar bu al he MOSFE f he HPWM wll have he 3

35 ame f n ngnfcanly hgher relably becaue half f he wche wll be wched le fen han n he B-Plar mehd. Cnducn calculae he cnducn l fr bh mehd, he curren pah fr mu be analyzed. Snce, he pve half f he ne wave wchng cheme he ame a he negave half he curren nly need be analyzed fr ha prn. he curren pah fr he B-Plar ha wche A and D n wll flw hrugh hem; h al he pwer delverng me. hen an pmal dead me wll ccur ha ZS ccur acr wche B and C ha wll flw hrugh he bdy dde fr he dead me perd. he rean an pmal dead me chen ha enugh me fr afey can be aken n cnderan whle n much me pen wh he curren flwng hrugh he le effcen bdy dde, befre he MOSFE urned n. Once ha ha happened wche B and C wll urn n and wll flw hrugh hem r he equalzan perd. S, EQ. gve he equan fr he cnducn l n he B-Plar mehd. P cn R H R ω D ω ω RH R ω D ω R RH ω D ω Dd 4d ω Dd he curren wll flw n he HPWM mehd alm n he ame manner a n he B-Plar mehd excep fr he dead me perd. nead f flwng hrugh w MOSFE bdy dde, wll flw hrugh ne lw de MOSFE bdy dde and he her lw de n reance. h enable he degner n be a rc n degnng he pmal dead me and ll acheve he ame f n beer cnducn l dependng n EQ. 5. Al, he Equalzan 4

36 perd f he B-Plar mehd he ame a he free wheelng perd f he HPWM mehd excep ha nead f a hgh and lw de MOSFE beng n, he w lw de MOSFE wll be n. S, EQ. 3 gve he equan fr he cnducn l f he HPWM mehd. P cn R H R ω D ω ω R ω D ω Dd 3 d ω R ω Dd n EQ. and EQ. 3 R H and R are he hgh and lw de R d n reance, D he varyng duy cycle, D d he fxed dead me fr ZS and afey ue, d he vlage drp acr he MOSFE bdy dde, and he varyng upu curren. fnd he average cnducn l he nananeu cnducn l mu be negraed ver half a ne wave perd r frm zer p, and hen he negran ver ha perd mu be dvded by Π a hwn n EQ. 4. he rean fr he negran he ame a fr fndng he average wchng l frm EQ. 0 bu he wchng l culd be ealy mplfed wherea he cnducn l ha many parameer ha are dependan n mega. P avg π P π 0 cn ω dω 4 A can be een frm EQ. and EQ. 3 here a lgh dfference n he cnducn le, whch ccur durng he dead me. he dfference ha B-Plar ha flwng hrugh w bdy dde whle HPWM ha flwng hrugh nly ne bdy dde and ne MOSFE n-ae reance. h dfference allw HPWM have a lwer cnducn l fr h pecfc applcan; hwever he amun f pwer ha reduced by he HPWM mehd neglgble. X R 5 d d 5

37 Each applcan wll have dfference n hw much cnducn l aved r l frm ung he B-Plar r HPWM mehd. Fr eae refer EQ. 5 and f X pve hen B-Plar wll have le cnducn l and f X negave hen HPWM wll have le l acaed wh. Hwever, a aed prevuly, he amun f pwer aved r l neglgble fr m applcan baed purely n cnducn l. n addn, he amun f avng n cnducn n ha gnfcan due he fac ha he B-Plar mehd ha wce he wchng l cmpared ha f he HPWM mehd. Drvng Drvng l arbued bacally urnng n and ff he MOSFE. he way h happen by applyng a charge acr g. apply and ake away h charge ake me pwer herefre a l n effcency. Hwever, he amun f l acaed wh he drvng l very mall bu cnan acr he enre pwer range. h cnan pwer l ngnfcan durng he hgh pwer peran bu durng lw pwer draw, h mall cnan pwer l becme ne f he key facr fr lw effcency. EQ. 6 gve he pwer l ha acaed wh drvng l. P Drvng Ceff f g 6 Frm EQ. 6 he drvng l man cmpnen fr pwer l he wchng frequency becaue he effecve capacance relavely mall. herefre, f here a way brng dwn he wchng frequency he l can be al be reduced. A aed earler fr he B-Plar mehd all fur wche are beng wched a he wchng frequency, bu fr he HPWM mehd, w f he fur wche are beng wched a he wchng frequency and he her w are beng 6

38 wched a wce lne frequency. herefre, he HPWM ha lwer verall wchng frequency. h mean ha he drvng l ha al been lwered fr he HPWM cmpared ha f he B-Plar mehd able umber f me Swched HPWM B-Plar A B C 835 D 835 able hw he amun f me each MOSFE ha been wched ver a ngle lne perd. he verall effecve wchng frequency fr he B-Plar 50 khz whle he HPWM ha an effecve wchng frequency f apprxmaely 5 khz. h lwered effecve wchng frequency reduce he drvng l by half. Al wh he wchng frequency beng lwered fr me f he HPWM MOSFE her lfeme ha been exended hu makng he HPWM mre relable and mre effcen, bu he ncreae n relably ngnfcan. Overall Effcency he verall ecnd age nverer effcency wa meaured; excludng auxlary pwer upple ha were requred pwer up he DSP ha wa ued creae he SPWM and he pwer ued fr drvng he MOSFE. Al nce he cled lp wa n beng eed he enr where n pwered up. Drvng and cnrl pwer le wll all be cndered eparaely when 7

39 cnderng he ver-all yem effcency. Ung he equan abve and her l equan were added acheve a mre accurae mdel emae he yem effcency. he l equan ha wa added wa he reance f he wre ued creae he nducr ESR f he nducr Effcency curve and Pwer l 50 Pwer effcency P eff R ad Pwer R ad Oupu Pwer P wch R ad 0 0 P ESR R ad P cnd R ad Pwer Cmpnen Fgure 7 herecal Effcency and Pwer ung HPWM w/ f 50 khz Frm Fgure 7, he majr area ha pwer l can be een. Such a fr lw pwer level he majr pwer l cmpnen he MOSFE wchng l. Whle n he hgher pwer level he key pwer l due he MOSFE cnducn l. Fgure 7 can be ulzed ncreae peak effcency, che be perang frequency, and flaen u he effcency curve ha a cnan effcency can be acheved acr he hgher pwer level. Hwever, Fgure 7 de n mach he acual effcency curve Fgure 8 exacly. h mmach may be due he nn-deale f he cre l frm he nducr cre alng wh her nn-deale ha are 8

40 unfreeen a h me. he cre l wa n aken n cnderan a h me due he nenve mah alng wh he lmed underandng f he le acaed wh he cre uch a eddy and cre l. Effcency Curve 99% 98% 97% 96% 95% 94% 93% 9% 9% 90% npu Pwer Wa Fgure 8 Effcency Curve ung HPWM w/ f 50 khz he verall effcency wa meaured; a majr prblem ccurred ryng acheve h gal, whch wa achevng accurae readng. he accuracy prblem wa fxed by placng an nducr befre he npu he nverer bacally an npu fler. h nducr enable he npu curren be nudal raher han dcnnuu allwng he npu pwer be calculaed eaer and mre acually. n addn, he npu nducr reduced he harmnc een n he npu curren. A a reul, a mre accurae value f he npu DC curren wa aanable and n lnger needed calculae he value n he cllcpe whch bad due he errr f he cpe. he 9

41 nex gnfcan mdfcan meaurng he pwer came frm he underandng f he cpe ha wa beng ued. Wha wa fund u abu he cpe wa ha all funcn n were calculaed graphcally. ha mean ha f he cpe wa exremely zmed n, u, r par f he pl were ff he creen, hen he vlage and curren readng became naccurae, hu he pwer readng became naccurae. Expermenal Reul A kw prype wa bul fr expermenal eng. he prype wa uccefully eed a abve he raed pwer level a can be een n Fgure 9. he 60 Hz upu ne wave ha near uny pwer facr ha al can be een by Fgure 9. he prype wa al uccefully eed and paed fr B-drecnal capably een by Fgure 0. he B-drecnal e wa a purely nducve lad ha al can be een by he 90-degree phae hf beween he upu curren and vlage wavefrm and repecvely n fgure. 30

42 Fgure 9 Expermenal Reul a Full ad Oupu Curren red Oupu lage yellw npu lage blue npu Curren green Frm Fgure 9 he cmpleed prype expermenal reul can be een. Al, he effcency can be deermned a full lad whch 96.7% effcen. Al, he upu curren and vlage wavefrm are near uny pwer facr due beng n phae and havng bacally nly he fundamenal harmnc n he wavefrm. 3

43 Fgure 0 Expermenal Reul Purely nducve ad Oupu Curren yellw Oupu lage red npu lage blue npu Curren green 3

44 Fgure Gae Drve lage and g ZS g Orange d Pnk Frm Fgure he achevemen f f wchng n ne f he fur wche een. h achevemen een by he vlage acr he dran urce f he MOSFE ge zer befre he wch urned n. h achevemen f f wchng, a aed earler, lwer he wchng l, ncreae effcency, lwer he needed hea be dpaed, and ncreae he relably f he wch and he yem a a whle. 33

45 CHAPER 3: PRMARY SAGE nrducn he prmary age r fr age n he w Sage apprach ake he varyng npu vlage and cnver ha a cnan DC bu vlage, hrugh a ranfrmer fr galvanc lan whch prvde afey and he ably creae an addnal vlage gan. he purpe f h cnan DC bu enable he ecnd age be mre ealy degned and pmzed. f h cnan DC bu wa n creaed he ecnd age degn cmplexy wll ncreae whch culd lwer effcency f he ecnd age a well a ncreae cmpnen cun and c. Hwever, he varyng npu make he prmary age harder degn/pmze, becaue he wr cae cenar mu alway be aken n accun r harde degn parameer mu be afed. he varyng npu ncreae he degn cmplexy becaue he gan needed frm he ranfrmer creae he apprprae upu vlage mu be deermned a he lwer npu vlage ha he DC bu vlage achevable acr he enre npu range. he rean he cncern manly n he ranfrmer due he fac ha he cnverer gan here nly weak he fnal verall gan f he yem. he cnverer gan huld n be mean be he gan f he yem due he ncreaed ree and al he maller he perang range he duy cycle wuld have be. Once h gan frm he ranfrmer fund fr he lwer npu vlage cnan regardle f he npu vlage. S when he hgher npu vlage appled he ranfrmer he upu recfyng dde f he ranfrmer wll have a hgher vlage re han he DC bu vlage. h hgher vlage re ha he dde wll be blckng due he gan f he 34

46 ranfrmer whch mulple he peak npu vlage. S, f he hghe npu vlage wce he lwe npu vlage he vlage re ha he recfyng dde wll have when he hghe npu vlage appled wll be a lea wce ha f he DC bu vlage. Al, any nn-deale uch a leakage nducance f he ranfrmer wll have me advere effec n he whle upu range bu he effec are meme greaer a he lwer npu vlage he degn mu ake ha n accun. Whch uually mean he urn ra mu be ncreaed acheve he dered upu gan. plgy Selecn Secndary Sage plgy A n all degn, plgy elecn a key ue fr ncreaed effcency and relably a well a decreaed c and cmpnen cun. Wh he ecndary age a buck r buck-b plgy needed and becaue f he zer crng ha are requred make he ne wave whch mean ha a b plgy can n be ued. he b-drecn capably and 0 Hz rpple aenuan acheved n he ecndary age hrugh he npu bulk capacance by he energy ha he capacr re. E Cap 7 C Frm EQ. 7 ncreae he amun f energy red.e. ncreae he b-drecnal capably and decreae he 0 Hz rpple by he capacr he capacance r vlage mu be ncreaed. Frm EQ. 7 can be een ha here a lnear dependence n he capacance and a nn-lnear dependence n he vlage. h mean ha he be way ncreae he capably f he capacr re energy and keep cmpnen cun and ze dwn ncreae he bu 35

47 vlage. h n urn mean ha a buck plgy he beer plgy che fr he ecnd age baed purely n he ncreaed energy rage and decreaed 0 Hz rpple. he Buck-B wuld n be a well ued a he Buck plgy becaue he duy cycle fr he Buck-B plgy wuld have be lmed value belw a half, fr he Buck-B plgy have he ame amun f energy rage ha he Buck ha. Wherea he Buck plgy can cnan all he pble duy cycle value, h mean ha he Buck plgy wuld have a wder duy cycle range. h wder duy cycle range help wh he MOSFE curren re by allwng he energy a lnger me wndw flw hrugh. Aumng ha he DC bu vlage he ame n bh Buck and Buck-B acheve he ame 0 Hz rpple aenuan. he curren re wuld have be hgher n he Buck-B han ha f he Buck becaue he energy flwng n bh he ame hwever he Buck-B MOSFE cnducn me wll be hrer han ha f he Buck. E P d E d 8 kng a EQ. 8 he vlage and energy ha beng ranferred n bh buck and buckb he ame he curren re dfference beween he w prprn he amun f me dfference ha he w plge are cnducng. he lnger he ne plgy cnducng han he her he lwer he curren re f ha plgy. Snce he maxmum me ha he buck-b n nly half ha f he buck ha mean he buck wll have a lwer curren re han ha f he buck-b. ha why he Buck plgy chen fr he ecnd age. 36

48 Prmary Sage plgy w fr he prmary age a plgy mu be chen buck, b, r buck-b. Cmparng he vlage ree n he ecndary de f he ranfrmer a b ype plgy derable, h due he fac ha m f he vlage gan ha needed acheved hrugh he cnverer elf raher han he ranfrmer unlke he buck derved plge. When he lw npu vlage appled he npu f he prmary age a gan f apprxmaely even me needed yeld he crrec upu vlage. w f a buck plgy ued he nly way acheve h gan hrugh a ranfrmer wh a lea ha much r hgher number f a urn ra. Hwever, a aed earler when he hgh npu vlage appled ha mean a much hgher upu vlage re wll be appled he recfyng dde due ha cnan vlage gan f he urn ra. w wh a b ype plgy he vlage gan ha requred can be acheved hrugh he crcu elf and a lle hrugh he urn ra lwer he needed duy cycle whch wll enable a lwer vlage re and keep a mre cnan vlage re n he recfyng dde a cmpared he buck derved plgy. S he dde dn have be verraed baed nly n he hghe npu vlage raher he vlage re wuld be mre unfrm acr he dde, hu he dde wll n be verraed m f he me. A buck-b derved plgy can lwer he vlage gan needed frm he ranfrmer cmpared ha f he buck, hwever, dependng n he degn he vlage re n he dde ll culd be larger han ha f he b ype plgy. Al, a aed earler he Buck plgy wll have he wr cae f he vlage re n he dde. 37

49 he nex analy ha dne he prmary de vlage re; here wll be helpful f here are me aumpn made. he aumpn are ha ver a ngle wchng cycle he energy rage devce.e. capacr and nducr are large enugh ha hey can be cndered a urce. h mean ha a capacr can be replaced by a vlage urce n he crcu whle an nducr replaced by a curren urce. he fr plgy ha examned he b. he b plgy ranfrm he npu frm a vlage urce a curren urce when he abve aumpn appled. h change f he npu urce ype affec he vlage re due he nn-deale f he ranfrmer ha he npu feed n al een n Fgure. he affec f he nn-deale f he ranfrmer fr he vlage re wll be analyzed frm he leakage nducance pn f vew. h leakage nducance caue a much hgher vlage re becaue he curren hrugh he leakage nducance mu change quckly due he npu beng a curren urce nw. h hgh change n curren caue a hgh vlage re acr he prmary de MOSFE becaue he vlage een acr an nducr prprnal he rae f change f he curren. B plgy B plgy afer aumpn Fgure B plgy w and w/ Aumpn he buck plgy he ame a he b plgy bu n he her drecn, he npu f a b wuld be he upu f a buck. ha mean ha he prblem f he npu curren 38

50 urce f he b n he prmary de n lnger here. Hwever, ne mgh hnk ha he prblem ha wa n he prmary de f he ranfrmer wll be ranferred he ecndary de. h rue, hwever, f he recfcan f he ecnd de f he ranfrmer wa crrecly chen.e. a full wave recfcan. he ranfrmer curren culd lwly ramp up he upu urce curren whch wuld keep he vlage ree lw. Al, dde are a b mre relen han MOSFE are when cme vlage re and dde can be eleced have a much hgher breakdwn vlage han a MOSFE fr a much cheaper prce. S fr he buck he man vlage re cncern due amplfcan f he hghe npu vlage hrugh he urn ra calculaed fr he lwe npu vlage. ex he buck-b plgy be analyzed. he buck b plgy unlke he buck r he b can have he npu and upu bh be mdeled a vlage urce r curren urce r a cmbnan f he w. h mean he vlage re ha cme frm he nn-deale f he ranfrmer n lnger a much f a cncern when he npu and upu bh are mdeled a vlage urce. Al he buck-b allw he urn ra f he cnverer be pmzed a he cener f he npu vlage range raher han a ne f he end pn whch wha mu be dne wh he buck and b plge. h pmzan a he cener npu vlage range allw fr a mre pmzed cnverer becaue he cnverer wll be peraed n he cener f he npu vlage range m f he me allwng he cnverer be runnng n he m pmzed pn he lnge. Cnverer here are everal buck-b ype cnverer uch a SEPC, Zea, and Cuk name a few. he cnverer beng ued een n Fgure 3 and wll be a cmbnan f an acve clamp 39

51 wh vlage dubler a he recfer. he vlage dubler recfer wll enable anher frm f gan lke he ranfrmer, h gan wll be nly wce he vlage appled, hwever, h gan furher reduce he needed urn ra. herefre, nw he urn ra ha needed wll be apprxmaely hree nead f he even me ha needed fr he buck ype. Al here are a cuple f key feaure f h cnverer, he fr ha he nn-deale f he ranfrmer are ulzed, ener bh fr and hrd quadran f he BH curve f he ranfrmer, he prmary de MOSFE can be wched a ZS, f he ecndary de dde are replaced by MOSFE hey can be wched a ZS and can allw he cnverer be b-drecnal, and laly he cnverer elf pwer lmng. c S Prm D c Mag Sere Sere M n S D c Fgure 3 Acve Clamp w/ lage Dubler Mde f Operan here are w bac mde, hwever he w bac mde repea n ne perd yeld fur man mde f peran fr he acve clamp vlage dubler. he fr w mde wch wll be n and he la w mde he hgh de wch, wch S wll be n. 40

52 Mde Durng h mde wch S ju urned n under ZS cndn and dde D n. he dde D n durng h mde becaue he ere nducr ll ha me energy red n frm he prevu mde and he curren wll cnnue flw n he negave drecn unl he nducr fully dcharged. c S D c Sere n S D c Fgure 4 Mde he curren drecn n he prmary and ecndary are hwn a he hck black arrw n Fgure 4. he pve reference fr he vlage acr he capacr and he curren drecn hrugh he ere nducance al hwn and wll be kep he ame fr all mde belw. n n c c < 9 Durng h mde he amplude f he nducr curren beng decreaed ha he curren wll begn flw n he pve drecn. he duran f h mde nly a fracn f he fully n me f he wch S. h mde wll end when he curren n he nducr dcharge dwn 4

53 zer, knwng ha he me ha h mde la can be calculaed frm EQ. 9 by eng zer. he amun f me ha h mde acually la gven n EQ n c n 0 0 c 0 Mde Durng h mde he wch S ll n hwever he curren n he ere nducance ha changed drecn frm he prevu mde nw he dde D nw cnducng a hwn n Fgure 5. c S D c Sere n S D c Fgure 5 Mde 4

54 n n c c 0 < D h mde end wh wch S urnng ff and hen wch S urnng n. he end f h mde mewha mlar he end f mde fur excep he curren drecn are revered. he end f h mde he peak pve curren ha he ere nducr wll be, gven by EQ.. n c D D Mde 3 h mde begn wh he wch S urnng ff and wch S urnng n wh ZS whle he dde D ll cnducng. c S D c Sere n S D c Fgure 6 Mde 3 43

55 0 D D D c c c c < 3 h mde end when he curren n he ecndary de ge zer much lke mde. c c D D 4 Mde 4 Same a mde h mde ar when he curren wche drecn urnng dde D ff wh ZCS and urnng he dde D n wh ZCS a well. h mde wll end when he wch S urned ff whch wll be he end f he perd and he mde wll ar ver agan. S S c n D c Sere c D Fgure 7 Mde 4 c c c c < 0 5 A aed earler here are w bac mde f peran. h mde mlar ha f mde uch ha he end f h mde yeld a peak ere nducance curren. Hwever, h mde 44

56 dffer frm he mde by nead f he peak beng a pve value a negave value. he peak negave curren can be calculaed frm EQ. 5 and gven by EQ. 6 c c 6 he curren n he ere nducr, ecndary de dde and when he wche are urned n ver he enre wchng perd can be een n Fgure 8. 45

57 S S Sere Prm M D D 0 D Fgure 8 Curren Wavefrm 46

58 Mahemacal Analy Gan he gan f he cnverer can be fund by ung w f he abve fur mde. By cmbnng w f he mde geher ne wh w and hree wh fur yeld EQ. 7 and EQ. 8 eher f whch can be ue calculae he gan. D n c n c 7 D c c c c 8 he nly pn ha he gan f he cnverer can be calculaed whu a recurve lun r nenve mah cmpuan wh a duy cycle f 50 percen. A h pn f a duy cycle f 50 percen allw fr everal mah mplfcan uch a equal, c equal n, and fr c equal c whch al equal half. Frm hee mplfcan and frm he knwledge f ere nducance curren ha 4* a gan equan can be derved fr he cnverer a a duy ra f 50 percen. hrugh he mplfcan and he knwledge f he ere nducance curren he vlage gan can by deermned by EQ

59 n 6 n k P Fgure 9 Oupu Pwer v. Oupu Curren Ung EQ. 9 and enerng parameer fr he urn ra, npu vlage, ere nducance, and wchng frequency 5, n 45, k 0uH, and F 00 khz Fgure 9 wa creaed. Frm Fgure 9 can be een ha he cnverer elf pwer lmng and dependng n he abve led parameer he peak pwer and a leer exen he lcan f he peak can be mdfed. Sre Analy A aed fr he gan equan he analy nly vald fr he duy cycle f 50 percen. h rercn allw equan be fund prvdng valuable ngh n cnverer peran 48

60 and analy nead f ung recurve lun fnd he anwer nly and n he equan. he curren re fr bh he clampng Capacr C and wch S gven by EQ. 30. DC S rm Crm DC DC 30 3 he DC curren ha n he prmary de f he ranfrmer DC equal he pwer ha beng ranferred he upu dvded by he npu vlage. he n he abve and belw equan acually a mplfcan f he lengh f me f mde and 3 whch are equal due he duy cycle mplfcan whch are hwn n EQ. 0 and EQ. 4. he rm curren rang f he upu capacr C and C are bh apprxmaely.3 me ha f he upu curren whle he recfyng dde average curren re ju he upu curren r ne furh he peak curren. Al he curren re f he ere nducance n he ecndary de and herefre he curren re n he ecndary de f he ranfrmer apprxmaely.3 me he upu curren. he la w curren ree are he prmary MOSFE and he ranfrmer prmary de curren re gven by EQ. 3 and EQ. 3 repecvely. DC S rm DC DC prm DC 3 3 Whle he vlage re acr bh MOSFE gven by he npu vlage dvded ne mnu he duy r he ame a a b cnverer. 49

61 Draw Back here are a cuple key draw back ha h plgy ha. he man draw back ha h plgy ha a large DC crculang curren n he prmary de f he ranfrmer. h large crculang curren a funcn f he pwer level and npu vlage gven by EQ. 33. P wer crc 33 n he hgher he pwer level f he cnverer and/r lwer he npu vlage, he hgher he crculang curren wll be n he prmary de. h large crculang ha everal advere effec n he cnverer; ne ha he cnverer ranfrmer ze wll need be ncreaed handle he large crculang curren. Anher ha he cnverer n ued hgh pwer mlar ha f a flyback r ngle ended frward. Al, h crculang curren wll ncreae cnducn le, bu he cnducn l culd be lwer han he wch l ha he crculang decreae. Smulan he acve clamp frward vlage dubler ha been mulaed n bh P-Spce a well a n PECS whch a mulan package ha ued wh Maab Smulnk. Bh mulan fware l agreed wh he mahemacal analy. 50

62 CHAPER 4: SGE SAGE ERER nrducn n rder fr he cnumer acheve maxmum prf frm her lar array, he array mu prduce a much uable pwer a pble. Fr he lar array prduce a much uable pwer a pble w man gal mu be me. he fr gal ha he lar array mu prduce maxmum pwer a all me. Whle he ecnd gal ha he pwer mu be n he requred frm 60 Hz, 0 rm when grd cnneced. Hwever, n rder acheve he ecnd gal and n have an advere effec n he fr, pwer elecrnc wll be ulzed. n rder creae a much pwer fr a lar array a pble MPP maxmum pwer pn rackng wll be ued. Al, ncreang he effcency f he verall nverer yem ha cnverng he npu pwer n he requred upu frm wll furher ncreae he cnumer prf margn. ha a rean fr he ngle age apprach. he ngle age apprach wll be able acheve hgher effcency due he lwer verall een wchng frequency. Hwever, he name behnd he ngle age apprach decevng. h becaue ne wuld beleve frm he name ha here nly ne cnverer, hwever, h n rue. n fac, here he ame number f cnverer n he ngle age a he w age apprach a can be een frm Fgure 30. 5

63 n rm DC Recfed AC Unfldng ad Fgure 30 Blck Dagram f Sngle Sage Apprach he rean behnd he name n due he number f cnverer bu he number f hgh frequency wchng cnverer. Wh he ne age apprach, ne cnverer wchng a he hgh wchng frequency whle he ecnd age nly wchng a wce lne frequency r 0 Hz. he rean fr h becaue he hgh wchng frequency age r he fr age wll ake he cnan DC npu vlage and creae a recfed ne wave upu hrugh lan fr afey. Whle he lne wchng r Unfldng Sage wll hen ake he recfed ne wave and unfld n a ne wave hu he name Unfldng Sage. Whle h apprach de n ave n cmpnen cun wll ncreae effcency due he lwer verall wchng frequency f he yem a aed abve. Frm h ncreae n effcency here wll be lwer le and hu a maller heank requremen. h maller heank requremen yeld a maller cnverer whch n urn yeld a hgh pwer deny, whle reducng he wegh and c f he cnverer. Bac Sngle Sage he blck dagram fr he Bac Sngle Sage cnverer gven n Fgure 30. he Bac Sngle Sage mlar n plgy he w Sage a aed abve. One dfference beween he 5

64 Bac Sngle Sage and he w Sage degn hw bh he laed and nn-laed age are cnrlled. he hgh frequency DC Recfed AC age can have he ame plgy a he w Sage laed DC-DC age, ne dfference he cnrl. Al, he Unfldng Sage can be he ame a he w Sage nverer Sage wh a lgh mdfcan. h mdfcan are frm he zer wchng l n he Unfldng Sage. he rean ha here zer wchng l n he Unfldng Sage becaue h age lw wched and he pn a whch he devce wched aumng a purely reve lad a he zer crng f he upued ne wave. Furhermre, he wchng peed f he Unfldng Sage a wce he lne frequency. h lw wchng peed and zer wchng l allw fr he mdfcan f he ue f GB nead f MOSFE n he Unfldng Sage, wherea fr he nverer Sage n he w Sage apprach MOSFE wuld be he wchng devce f chce. Hwever, n [8] he Unfldng Sage wchng devce wa MOSFE n GB due he pwer level and he paper al hw ha he lan ranfrmer can upu a recfed ne wave whu aurang he cre. he rean ha he Unfldng Sage allwed be lw wched hrugh he cnrl f he DC Recfed AC Sage. he cnrl f he DC Recfed AC ha nead f he bu beng held cnan a me vlage a wh he w Sage apprach he bu vlage wll vary he ame way a a recfed ne wave. Becaue f h varyng vlage n he bu, here can n lnger be a bu capacr nly a fler capacr n he Bac Sngle Sage. he bu capacr n he w Sage mehd ued a energy rage aenuae he 0 Hz. rpple a well a handle b-drecnal pwer flw. Snce here n bu capacr n he Bac Sngle Sage he 0 Hz. rpple nw mu be aenuaed by he lw vlage npu capacr. 53

65 Al, becaue he recfcan n he upu f he Bac Sngle Sage laed age dne by dde and n cnjugan wh he fac ha here n bu capacr h cnverer n lnger capable f b-drecnal pwer flw. Several prblem are frm he fac ha he Bac Sngle Sage de n have he bu capacr. A aed earler he yem n lnger bdrecnal, he 0 Hz. rpple nw mu be aenuaed by he npu capacr whch elf caue me prblem, and he enre yem ha duble pwer peak whch caue he Bac Sngle Sage cnverer be verraed handle he duble pwer peak. he rean fr hee duble pwer peak cme frm EQ. 6. A can be een frm EQ. 6 he prduc f he w amplude wll be halved due h equan. S, n rder ban he needed average upu pwer he cnverer peak pwer mu be wce ha f he average pwer. h mean ha fr he w Sage apprach he nverer Sage mu be verraed handle he peak pwer whle fr he Bac Sngle Sage he enre yem mu be verraed handle h peak pwer. he her prblem wh havng he 0 Hz. rpple n he lw vlage npu ha he capacance ha needed baed ff f wr cae cndn, hwever, nce he capacance n he npu he wr cae cndn n he ame a wh he w Sage mehd. he rean fr he dfference n wr cae cndn ha wh he w Sage mehd he mpedance ha nce gng n he capacr can be held by he laed DC-DC. Whle he mpedance een by he npu capacr n he Bac Sngle Sage frm he lar array panel and can n be held cnan. h varable mpedance ncreae he needed energy rage, whle al he 0 Hz. rpple mu be aenuaed enugh ha de n nerfere wh he MPP algrhm. Snce he capacance n he lw npu vlage wll requre hgher 54

66 capacance ju equal he ame amun f energy rage ha he w Sage mehd ha wh he bu capacance n menn he ncreaed capacance ha needed fr he wr cae cenar. Prped Mdfcan fr B-Drecnal Pwer Flw n rder fr a far cmparn be made beween he Sngle Sage and he w Sage apprache he Sngle Sage mehd mu be able handle b-drecnal pwer flw. n rder acheve h everal apprache can be dne. Sme f he apprache are addng a parallel cnverer, ynchrnu recfcan, and an acve bu cndner each f whch wll be expanded upn furher. he Sngle Sage mehd culd be cmpared he w Sage apprach, whu havng b-drecnal pwer flw and ju cng ha a a dadvanage fr he Sngle Sage mehd. Hwever, he Sngle Sage apprach hen culd n have a and alne mde and mu alway be cnneced he grd r nhng a all. h becme ncnvenen when he uly grd ge dwn. Becaue he me ha pwer needed be delvered frm he nverer n pwer can be delvered due uly grd beng dwn. Parallel Cnverer One mehd f banng b-drecnal pwer flw ung a parallel cnverer. he blck dagram f he Parallel Cnverer apprach gven n Fgure 3.he w parallel prmary npu age a een frm Fgure 3 are bh un-drecnal. 55

67 30-60 n Pwer Flw 0 rm DC Recfed AC Un-fldng ad DC Recfed AC Pwer Flw Fgure 3 Parallel Cnverer Hwever, he drecn ha each age prcee pwer ppn ne anher. h ppn allw fr he b-drecnal pwer flw. Addng h parallel cnverer wa prped n [7]. he Parallel Cnverer mehd bacally a he name ae a cnverer added n parallel he DC Recfed AC age. h parallel cnverer wll hen prce he bdrecnal pwer back he lw vlage npu de where red. Once he lad requre he b-drecnal pwer hen he DC Recfed AC age wll prce ha exra pwer ha wa red n he npu de. he Parallel Cnverer mehd fr he Sngle Sage apprach enable h apprach be capable f achevng b-drecnal pwer flw. A wh he Bac Sngle Sage he Parallel Cnverer ha he ame lw wchng frequency Unfldng Sage and he undrecnal DC Recfed AC age. Hwever, a aed abve wh he addn f he paralleled npu he Paralleled Cnverer enable he ably f b-drecnal pwer flw. 56