A NEW FAMILY OF TRANSFORMERLESS MODULAR DC-DC CONVERTERS FOR HIGH POWER APPLICATIONS

Transcription

1 A NEW FAMIY OF TRANSFORMERESS MODUAR D-D ONVERTERS FOR HIGH POWER APPIATIONS by Abdelahman Haga A thess submtted n cnfmty wth the equements f the degee f Dct f Phlsphy Gaduate Depatment f Electcal and mpute Engneeng Unesty f Tnt pyght by Abdelahman Haga 011

2 A New Famly f Tansfmeless Mdula D-D netes f Hgh Pwe Applcatns Abstact Abdelahman Haga Dct f Phlsphy Depatment f Electcal and mpute Engneeng Unesty f Tnt 011 Ths thess pesents a new famly f cnetes f hgh pwe ntecnnectn f dc buses wth dffeent ltage leels. Ppsed cnetes achee hgh ltage dc-dc cnesn wthut an ntemedate ac cnesn stage. Ths functn s mplemented wthut sees cnnectn f acte swtches, the use f slatn tansfmes. The salent featues f ppsed cnetes ae () desgn and cnstuctn smplcty, () lw swtchng lsses thugh sft tun-n and sft tun-ff, () sngle stage dc-dc cnesn wthut hgh-cuent chppng, () mdula stuctue, () equal ltage shang amng the cnete mdules. Thee cnete ccuts ae nestgated. The fst pefms undectnal pwe tansfe fm a dc bus wth hghe ltage t a dc bus wth lwe ltage. The secnd pefms undectnal pwe tansfe fm a dc bus wth lwe ltage t a dc bus wth hghe ltage. Bth cnetes ae sutable f ntecnnectng sngle ple dc buses wth same platy, duble ple dc buses. A thd cnete s als pesented whch pefms the functn f ethe the fst the secnd cnete wth platy eesal. The thd cnete s sutable f ntecnnectng sngle ple dc buses wth dffeent plates, duble ple dc buses. By hybd

3 ntegatn f the ppsed thee cnetes, the thess als nestgates the tplges f bdectnal pwe tansfe between tw dc buses. Ppsed cnetes peate nly n dscntnuus cnductn mde and exhbt sft swtchng peatn f the acte and passe swtches. A cmmn featue between the ppsed cnetes s the self cuent tun-ff f the acte swtches at ze ltage. Ths allws the use f thysts as acte swtches alleatng the eese ecey lsses. F each cnete tplgy, the stuctue s pesented, ts peatn pncple s explaned and a cmplete set f desgn equatns ae deed. mpasns ae pefmed n hgh-pwe and hgh-ltage desgn examples. The mets and lmtatns f each cnete ae cncluded. Pactcal cnsdeatns egadng cmpnents selectn, lss analyss, flte desgn and the nn-dealtes f the ccuts ae studed. Expemental mplementatn f scaled-dwn labaty pttypes s pesented t pde a pf f cncept and aldate the peatn pncple f the ppsed cnete tplges.

4 Acknwledgments Fst f all I wuld lke t expess my gattude and appecatn t my thess ads, Pf. Pete W. ehn. Hs cntnuus adce, gudance, feedback and encuagement ae much behnd the ealzatn f ths wk. I als we a lt t my cmmttee membes, whse adce and feedback wee a aluable cntbutn t my thess. I wuld lke t thank M. Jack Gldsten, the labaty manage, f hs help and naluable adce dung the expemental phase f ths pject. Fnally, I d lke t thank M. Mke Ranjam f hs assstance n the labaty.

5 Table f ntents Acknwledgments... Table f ntents... st f Tables... x st f Fgues... x st f Appendces... x Nmenclatue... x hapte 1 Intductn Statement f the Pblem Thess Objectes Backgund lasscal PWM netes D-D netes wth Tansfmes upled Inducts Mult-mdule sees-paallel dc-dc cnetes Tansfmeless swtched capact dc-dc cnetes Vltage Multple-based Hybd D-D netes Sft-swtched Tanfmeless D-D netes Thess Outlne... 1 hapte Stuctue and Opeatn Pncple....1 Intductn.... Stuctue f the acte swtchng netwk The Mdula Step-dwn nete The Mdula Step-up nete The Mdula Inetng nete... 39

6 .6 Mdula Bdectnal netes Summay hapte 3 nete Mdelng and Desgn Intductn Assumptns Resnant capacts desgn Step-dwn cnete Step-up cnete Inetng cnete mments uent and ltage n esnant elements The cnductn angle Resnant nduct szng Semcnducts cuent atngs Semcnducts ltage atngs Summay... 7 hapte 4 Pactcal Aspects Intductn Fault ppagatn Input temnal faults Output temnal faults Semcnducts pwe lsses Thyst lsses Dde lsses Flteng capacts Black-stat dung step-up peatn... 89

7 4.6 The ESR effect n the maxmum step-up at Effect f the stay nductance Thysts tun-ff tme Desgn steps Desgn tade-ffs Summay hapte 5 Desgn Examples and Expemental Pttypng Intductn netes desgn Swtch selectn Resnant capactance nete cells Dde selectn Induct szng Desgn esults Gaphcal mpasns Expemental pttypng hapte 6 nclusns and Futue Wk nclusns Thess ntbutns Suggested Futue Wk Refeences Appendx A Appendx B Appendx Appendx D

8 Appendx E Appendx F

9 st f Tables Table 3-1 Summay f basc desgn paametes deed n chapte Table 5-1 mpasn between the atngs f lght tggeed thysts Table 5- mpasn between the atngs f fast ecey ddes Table 5-3 Desgn paametes f the cnetes f the fst desgn example Table 5-4 Desgn paametes f the cnetes f the secnd desgn example Table 5-5 Desgn paametes f the cnetes f the thd desgn example Table 5-6 Desgn paametes f the cnetes f the futh desgn example Table 5-7 mpasn between desgn paametes f the ppsed cnete f the fu desgn examples Table 5-8 ss analyss f the ppsed cnetes f the fu desgn examples Table 5-9 mpasn between netng and nn-netng step-up cnetes Table 5-10 mpasn between netng and nn-netng step-up cnetes... 1 Table 5-11 Desgn paametes f the expemental cnetes Table 5-1 Semcnduct paametes f the cnductn lsses calculatns Table 5-13 ss analyss f the cnetes Table F- 6- Smulatn paametes x

10 st f Fgues Fgue 1-1 Altenates f the cnnectn f tw dc buses wth dffeent ltage leels... Fgue 1- Basc classfcatn f dc-dc cnetes... 4 Fgue 1-3 lasscal dc-dc cnetes. (a) Bst cnete, (b) buck cnete... 6 Fgue 1-4 (a) uk cnete, (b) Mddlebk s cnete [6]... 7 Fgue 1-5 Quadatc dc-dc cnete [8]... 7 Fgue 1-6 D-D cnete tplgy wth cupled nducts []... 9 Fgue 1-7 An acte clamp flyback cnete [3]... 9 Fgue 1-8 Vltage fed full Bdge dc-dc cnete [3] Fgue 1-9 uent fed full bdge dc-dc cnete [1] Fgue 1-10 Mult-mdule cnetes. (a) Input-Sees Output-Sees, (b) Input-Sees Output- Paallel, (c) Input-Paallel Output-Sees, (d) Input-Paallel Output-Paallel Fgue 1-11 Example f an ISOP cnete [8] Fgue 1-1 Swtched capact multleel dc-dc cnete ppsed n [30] Fgue 1-13 Mdula multleel capact clamped cnete ppsed n [31] Fgue 1-14 Resnant swtched capact dc-dc cnetes [33] Fgue 1-15 ckft-waltn ltage multple Fgue 1-16 A dc-dc multleel bst cnete [1] Fgue 1-17 Bdectnal hgh pwe dc-dc cnete f [10] Fgue 1-18 Hgh-pwe step dwn dc-dc cnete f [13]... 0 Fgue 1-19 Hgh pwe step-dwn dc-dc cnete f [37]... 0 x

11 Fgue -1 Stuctue f the mdula acte swtchng netwk... 4 Fgue - Dffeent swtchng schemes f the acte swtchng netwk... 5 Fgue -3 Stuctue f the mdula step-dwn cnete... 8 Fgue -4 Step-dwn cnete dung nteals a, b, c f the fst swtchng half-cycle... 9 Fgue -5 Step-dwn cnete dung nteals d, e, f f the secnd swtchng half-cycle Fgue -6 Ideal steady-state waefms f the mdula step-dwn cnete Fgue -7 Stuctue f the mdula step-up cnete Fgue -8 Step-up cnete dung nteals a, b, c f the fst swtchng half-cycle Fgue -9 Step-up cnete dung nteals d, e, f f the secnd swtchng half-cycle Fgue -10 Ideal steady-state waefms f the mdula step-up cnete Fgue -11 apact ltage buld-up pcess dung the step-up cnete black-stat Fgue -1 Induct and utput cuents f the step-up cnete dung the black-stat pcess Fgue -13 Stuctue f the mdula netng cnete Fgue -14 apact ltage buld-up f the netng cnete n step-up mde Fgue -15 Inetng cnete dung nteals a, b, c f the fst swtchng half-cycle... 4 Fgue -16 Inetng cnete dung nteals d, e, f f the secnd swtchng half-cycle Fgue -17 Ideal steady-state waefms f the netng cnete dung step-dwn Fgue -18 Ideal steady-state waefms f the netng cnete dung step-up Fgue -19 Stuctue f the mdula bdectnal cnete Fgue -0 Stuctue f the sngle-nduct mdula bdectnal cnete x

12 Fgue -1 Stuctue f the netng mdula bdectnal cnete Fgue - Stuctue f the sngle-nduct netng mdula bdectnal cnete Fgue 3-1 Smplfed stuctue f (a) step-dwn, (b) step-up and (c) netng cnetes Fgue 3- Basc waefms f step-dwn peatn dung cntnuus cnductn Fgue 3-3 Basc waefms f step-up peatn dung cntnuus cnductn Fgue 3-4 Equalent ccut f the cnetes when the acte swtches ae cnductng Fgue 3-5 The ltage gan s. the cnductn angle f the step-dwn cnete Fgue 3-6 The ltage gan s. the cnductn angle f the step-up cnete Fgue 3-7 The ltage gan s. the cnductn angle f the netng cnete Fgue 3-8 Vltage and cuent waefms f the swtches and ddes dung step-dwn peatn Fgue 3-9 Vltage and cuent waefms f the swtches and ddes dung step-dwn peatn Fgue 4-1 Ze mpedance nput fault cndtn f the (a) step dwn, (b) step up and (c) netng cnetes Fgue 4- Vltage and cuent waefms f the netng cnete dung a ze mpedance nput fault cndtn dung the step up mde Fgue 4-3 Ze mpedance utput fault cndtn f the (a) step dwn, (b) step up and (c) netng cnetes Fgue 4-4 Vltage and cuent waefms f the step-dwn cnete dung a ze mpedance utput fault cndtn at ts temnal... 8 Fgue 4-5 Vltage and cuent waefms f the netng cnete dung a ze mpedance utput fault cndtn at ts temnal x

13 Fgue 4-6 nea mdel t estmate the eese ecey lsses Fgue 4-7 The nfluence f the cmmutatng nductance n the cuent and ltage waefms dung step-dwn peatn... 9 Fgue 4-8 The nfluence f the cmmutatng nductance n the cuent and ltage waefms f the swtches and ddes dung step-dwn peatn Fgue 4-9 The nfluence f the cmmutatng nductance n the cuent and ltage waefms dung step-dwn peatn Fgue 4-10 The nfluence f the cmmutatng nductance n the cuent and ltage waefms f the swtches and ddes dung step-dwn peatn Fgue 4-11 Smplfed desgn flw-chat Fgue 5-1 mpasn between the esnant nductance alues (unts ae n m.h pe ple) Fgue 5- mpasn between the esnant capactance alues (unts ae n µ.f pe ple) Fgue 5-3 mpasn between the semcnduct lsses Fgue 5-4 Pctue shwng tw acte swtchng cells Fgue 5-5 Pctue shwng the ddes and measuement unts Fgue 5-6 Pctue shwng the tansfme f the hgh ltage sde Fgue 5-7 Schematcs f the expemental (a) Step-dwn and (b) step-up cnetes Fgue 5-8 Step-dwn cnete expemental waefms. The fgue shws the nduct cuent n h1, the dde cuent n h4, the ltage f the capact f the fst cell n h and the ltage f the capact f the secnd cell n h Fgue 5-9 Step-dwn cnete expemental waefms. The fgue shws the nduct cuent n h1, the capacts cuent n h4, the swtch ltage s1 n h and the swtch ltage s n h x

14 Fgue 5-10 Step-dwn cnete expemental waefms. The fgue shws the nduct cuent n h1, the dde cuent n h4, the dde ltage n h and the ltage f the acte swtchng netwk * c n h Fgue 5-11 Step-up cnete expemental waefms. The fgue shws the nduct cuent n h4, the dde cuent n h1, the ltage f the capact f the fst cell n h3 and the ltage f the capact f the secnd cell n h Fgue 5-1 Step-up cnete expemental waefms. The fgue shws the nduct cuent n h4, the capacts cuent n h1, the swtch ltage s1 n h3 and the swtch ltage s n h Fgue 5-13 Step-up cnete expemental waefms. The fgue shws the nduct cuent n h4, the dde cuent n h1, the dde ltage n h and the ltage f the acte swtchng netwk * c n h Fgue 5-14 The effcency f the expemental pttypes x

15 st f Appendces Appendx A Vltage gan f passe lads Appendx B Deatn f the maxmum step-up at Appendx The stay nductance Appendx D Bdectnal sngle-nduct cnete desgn Appendx E Fnal desgn paametes Appendx F Pwe cntlle desgn x

16 Nmenclatue Acnyms A M W D DM ESR EMI HVD IGBT IGT IPOP IPOS ISOP ISOS PF PWM RMS RB-IGBT VS ZS ZVS Altenatng uent ntnuus nductn Mde ckft Waltn Dect uent Dscntnuus nductn Mde Equalent Sees Resstance Electmagnetc Intefeence Hgh Vltage Dect uent Insulated Gate Bpla Tansst Insulated Gate mmutated Thyst Input Paallel Output Paallel Input Paallel Output Sees Input Sees Output Paallel Input Sees Output Sees ne mmutated nete w Pass Flte Pulse Wdth Mdulatn Rt-Mean-Squae Reese Blckng IGBT Vltage Suced nete Ze uent Swtchng Ze Vltage Swtchng x

17 Symbls c apactance pe cnete cell (F) n Equalent esnant capactance f the cnete (F) / Equalent esnant capactance pe ple (F) f Flte capactance (F) Equalent esnant nductance f the cnete (H) / Equalent esnant capactance pe ple (H) f c Flte nductance (H) Stay nductance n the cmmutatn ccut (H) / Natual ( esnant) fequency f the cnete (ad/s) f s f s abs max Ts TBS t t ff Swtchng fequency f the acte swtches (Hz) Abslute maxmum swtchng fequency (Hz) Swtchng ped f the acte swtches (s) Black-stat tme f the step-up cnete (s) Dscntnuus tme nteal f the nduct s cuent (s) Thyst ff-tme duatn whle eese based (s) t f tq N c ff Thyst ff-tme duatn whle fwad based (s) cut cmmutated tun-ff tme f thysts (s) Numbe f cnete cells nductn angle at whch cmmutatn stats (ad) Vltage f the equalent esnant capactance (V) c n c Vltage f the capact f ne cnete cell (V) Intal esnant capact ltage befe swtchng (V) x

18 * c s Vltage f the acte swtchng netwk (V) Reese blckng ltage f the acte swtch (V) s f Fwad blckng ltage f the acte swtch (V), Peak ltage f the equalent esnant capact (V) c p c pk c pk D ff s VT ff VTO VFRM T f max D n max a RMS pk Peak ltage f the equalent esnant capact dung fault (V) Vltage f the nput sde f the cnete (V) Vltage f the utput sde f the cnete (V) Tun-ff ltage f the dde (V) Tun-ff ltage f the swtch (V) On-state ltage dp n a thyst/ dde (V) Theshld ltage f a thyst/dde (V) Maxmum fwad ecey ltage f the dde (V) Maxmum n-state ltage dp n a thyst (V) Maxmum n-state ltage dp n a dde (V) Aeage cuent (A) Rt-mean-squae cuent (A) Resnant nduct cuent (A) Peak esnant nduct cuent (A), Resnant capact cuent (A) c n c D s I IT Dde cuent (A) Acte swtch cuent (A) Input cuent (A) Output cuent (A) ntnuus cnductn cuent (A) Thyst n-state cuent (A) x

19 fault P P pk f Fault cuent (A) Peak cuent f the esnant nduct dung fault (A) Input pwe (W) Output pwe (W) P Pnd Tun ON ad pwe (W) nductn pwe lss (W) P Swtchng pwe lss dung tun-n (W) P Swtchng pwe lss dung tun-ff (W) Tun OFF W Swtchng enegy lss dung tun-n (J) Tun ON W Swtchng enegy lss dung tun-ff (J) Tun OFF W On-state enegy lss (J) ON State W Off-state enegy lss (J) OFF d D dt d S dt d s dt E Q I RM State ff n ff Dde cuent ate f change at tun-ff (A/s) Swtch cuent ate f change dung tun-n (A/s) Rate f change f the fwad bas ltage f a thyst whle n the ff-state (V/s) Reese ecey enegy lss (J) Reese ecey chage () Maxmum eese ecey cuent (A) xx

20 1 hapte 1 Intductn Statement f the Pblem Whle hgh pwe Hgh Vltage Dect uent (HVD) tansmssn s nw cnsdeed a wellestablshed technlgy, ts applcatn s stll dependent n utlzng ethe ne mmutated netes () Vltage Suced netes (VS). These cnetes cnnect dc buses wth ac buses and handle pwe f hundeds f megawatts at ltages f hundeds f kllts. Recently, the subject f dc bus ntecnnectns has stated t gan nceased nteest. Ths nteest s den by the dese t () nteface pwe suces that geneate dc n a megawatt pwe ange [1], [], () ntegate wndfams thugh ffshe dc netwks [3], () buld dc dstbutn netwks and dc mcgds [4]-[6], () buld dc back-up enegy systems [7], () buld medum-ltage ndustal des, hgh-speed tan pwe systems and undesea bseates [8],[9] and () pde addtnal access pnts t the exstng HVD lnes [10]. Tw pssble altenates enable the ntecnnectn f dc buses and ae shwn n Fg.1-1. The fst s by usng VS systems whle the secnd by dect dc-dc cnesn. In cntast t VS and systems, the use f dc-dc cnetes wll dectly ntecnnects dc buses f dffeent ltage leels wthut use f ntemedate ac cnesn stage. w-ltage and lw-pwe dc-dc cnetes hae lng been studed and mplemented. Hgh ltage lw-pwe dc-dc cnetes ae less ppula but ae used n sme applcatns, such as medcal X-ay magng, ad fequency geneatn, taellng-wae tubes, lases and hgh ntensty dschage lamps [11], [1]. Hgh-ltage and hgh-pwe dc-dc cnetes ae nt aalable as maket pducts yet, but ae subject t eseach effts [10],[13]-[15],[37]. lasscal dc-dc cnete tplges hae lmtatns peentng the use f hgh-pwe and hgh-ltage applcatns. Snce pwe semcnducts hae lmted ltage atngs, the hghltage ealzatn f classcal tplges wuld eque sees cnnectn f acte swtches (IGBTs n ths case). Ths eques acte gate cntl t ensue equal ltage shang between all

21 deces at swtchng nstances [16],[17]. Implementng acte gate cntl technques esults n sgnfcant ncease n swtchng lsses (up t 36% as n [18] ). Addtnally, classcal PWM ccuts (e.g. buck and bst tplges) eque exteme duty cycles at hghe cnesn ats. An exteme duty cycle mpas effcency and may cause malfunctns due t the ey sht cnductn tme f pwe semcnduct deces [19]. Othe classcal tplges use ntemedate slatn tansfmes, such as the fly-back cnete. If the applcatn des nt eque slatn, the use f a tansfme wuld nly ncease the cst, the lume, and the lsses especally f hgh pwe applcatns, as detaled n [19]-[1]. Specfcally, the lage numbe f tuns at wth the need f hgh ltage slatn nceases the leakage nductance and paastc capactance f the wndngs. Ths causes undesable ltage and cuent spkes t swtches leadng t nceased lsses and educed elablty [11]. Ppsed tansfmeless sftswtched tplges f hgh ltage and hgh pwe applcatns n [10], [13]-[15] hae seeal lmtatns f unequal ltage stesses n semcnducts as n [13], estctns t bpla dc netwk ntecnnectns as n [10], [14], [15] wth ptental sht-thugh pblems dung fault cndtns. Mee, these tplges eque the use f hgh ltage esnant capact banks, and lng sees stngs f hgh ltage acte swtches. Fgue 1-1 Altenates f the cnnectn f tw dc buses wth dffeent ltage leels 1. Thess Objectes Ths thess addesses the pblem f dc-dc cnetes sutable f hgh-pwe and hghltage applcatns. A new famly f cnete tplges s ppsed and studed f these

22 3 applcatns. Ppsed cnetes emply ZS and ZVS f the swtches, hang mdula stuctue and equal ltage dstbutn amng the cnete mdules.. The man bjectes f ths thess ae: 1. T ppse a new famly f cnete tplges f hgh ltage and hgh pwe dc applcatns, specfcally kllt and megawatt scale. Fu tplges ae pesented:. Mdula step-dwn cnete. Ths cnete pefms undectnal pwe tansfe fm a dc bus wth hghe ltage t a dc bus wth lwe ltage wthut the need f a tansfme sees cnnectn f acte swtches. It peates n bth unpla and bpla buses and has mdula stuctue wth sft swtchng beha f pwe semcnduct deces.. Mdula step-up cnete. Ths cnete pefms undectnal pwe tansfe fm a dc bus wth lwe ltage t a dc bus wth hghe ltage wth the same featues mentned n.. Mdula platy-eesal cnete. Ths cnete pefms undectnal pwe tansfe between tw dc buses wth dffeent platy and ltage leels. It can peate n ethe step-dwn step-up mdes, mantanng the same featues mentned n.. Mdula bdectnal cnetes. These tplges use hybd cnnectns f the cnetes mentned n, and t pefm bdectnal pwe tansfe between dc buses.. T deelp a cmplete set f mathematcal desgn equatns f the ppsed cnetes t allw selectn f the cmpnents based n the desed ltage and pwe atng. 3. T suppt the theetcal pedctns and demnstate mplementatn feasblty. The tplges hae been nestgated thugh desgn examples f dffeent ltage and pwe leels, and thugh expemental setup f scaled-dwn labaty pttypes.

23 4 1.3 Backgund Ths sectn eews exstng dc-dc cnete tplges and dentfes the lmtatns f hghltage and hgh-pwe applcatns. D-D cnetes hae lng been studed f lw-pwe (klwatt ange) lw-ltage ange (hundeds f lts), but extendng the peatn t the megawatt pwe ange at kllt ltage leels mples sme estctns. In ths sectn, these estctns ae utlned f knwn tplges. Aalable dc-dc cnetes n lteatue can be classfed nt maj famles shwn n Fg The fllwng subsectns pde me detals n each f these cnete famles. D D netes lasscal PWM cnete.3. netes wth tansfmes cuple nducts Mult-mdule sees paallel cnetes Tansfmeless swtchedcapact cnetes Vltage multple-based hybd cnetes Tansfmeless sft-swtched cnetes Fgue 1- Basc classfcatn f dc-dc cnetes lasscal PWM netes The mst ppula and wdely used dc-dc cnetes ae the buck, bst, buck-bst cnetes. The undelyng cncept f these ccuts depends n chppng the nput dc ltage wth a specfc duty cycle t geneate a desed utput ltage leel. The swtchng fequency s usually mantaned at cnstant alue and the pulse wdth (n state duatn) s mdulated. Fg. 1- shws the buck and bst cnete ccuts. These ccuts ae smple n cnstuctn but suffe fm

24 5 lmtatns peentng the use n hgh-pwe and hgh-ltage applcatns. These lmtatns can be summazed as fllws: F hgh dc ltage cnesn at, these cnetes peate wth an exteme alue f duty cycle. Ths peatng mde esults n nceasng the lsses asscated wth the ccut cmpnents degadng the effcency [7]. The exteme duty cycle may een cause malfunctn f the semcnduct swtches due t the ey sht cnductn tme [19]. T ealze hgh ltage swtches, sees cnnectn f acte swtches (IGBTs n ths case) s needed. Ths eques acte gate cntl t ensue equal ltage shang between deces at swtchng nstances [16],[17]. Implementng acte gate cntl technques esults n sgnfcant ncease n swtchng lsses (up t 36% as n [18] ). In case f fault cndtns, cuent chppng cnetes ethe allw utput faults t ppagate t the nput suce, eque the acte swtch t nteupt the fault cuent. Bth scenas ae unacceptable f many hgh pwe and hgh ltage applcatns. Seeal ccuts wee ppsed n lteatue t ecme the abe mentned lmtatns. uk and Mddlebk ppsed tansfmeless dc-dc cnetes wth lage cnesn ats [6], shwn n Fg uk als ppsed a famly f quadatc dc-dc cnetes n [8]. These cnetes can achee hgh cnesn ats at hgh effcences wth lwe swtchng stesses as cmpaed t classcal buck-bst and buck-bst cnetes. F hgh ltage and hgh pwe applcatns, these cnetes wuld eque hgh ltage ales f sees acte swtches, hgh ltage capacts and hae n mdula stuctue.

25 6 D S (a) S D (b) Fgue 1-3 lasscal dc-dc cnetes. (a) Bst cnete, (b) buck cnete

26 7 S D (a) 1 S S D (b) Fgue 1-4 (a) uk cnete, (b) Mddlebk s cnete [6] S D 1 D 3 D Fgue 1-5 Quadatc dc-dc cnete [8]

27 D-D netes wth Tansfmes upled Inducts mpaed wth classcal buck, bst and buck-bst ccuts, tansfme-based cnetes can achee hghe cnesn ats wth lwe lsses [5]. The same featue apples t cnetes wth cupled nducts [7]. The tuns at f the tansfme the cupled nducts help ealze hghe steppng ats [4]. Fg 1-6 shws a hgh step-up cnete wth cupled nduct []. Fg. 1-7 shws an acte clamp flyback cnete [3]. The man lmtatn f these cnetes s the pblems elated t the tansfme. The lage tuns at and hgh ltage slatn equements nceases the leakage nductance and paastc capactance f the wndng. At swtchng nstants, the tansfme paastcs wll esult n hghltage spkes acss the swtches [7]. Vltage and cuent spkes lead t nceased lsses and educed elablty, and may damage ccut cmpnents [11], [1]. Ths pblem can nly be addessed by cnnectng snubbe ccuts t the swtches by utlzng the tansfme paastcs as esnant tank and peatng these cnetes as esnant sft-swtched cnetes. A cmpaate theetcal study f thee dc-dc tplges can be fund n [3]. It shws that the ltage-fed full-bdge cnete (shwn n Fg.1-8), can be attacte fm the enegy effcency pnt f ew. The lmtatn s that ths tplgy ncpates an slatn tansfme and eques snubbe capacts t achee sft swtchng. In ths cnete, thee s n sutable alue f the snubbe capacts f the whle peatn ange [3]. Ths tplgy als needs an utput nduct whch ceates hgh ltage spkes n the ddes f the utput bdge [3]. Fnally, the ce lsses n the tansfme can be sgnfcant hgh at educed pwe peatn.

28 9 1 D S D 1 D 1 Fgue 1-6 D-D cnete tplgy wth cupled nducts []. 1 N 1 N D S a S 1 Fgue 1-7 An acte clamp flyback cnete [3]

29 10 f S 1 S 3 N1:N s D D 1 S S 4 D D 3 4 Fgue 1-8 Vltage fed full Bdge dc-dc cnete [3]. Unlke the ltage-fed cnetes, cuent-fed esnant cnetes (shwn n Fg.1-9) need n utput nduct snubbe ccuts n the swtches [1]. Ze-uent Swtchng (ZS) can be acheed f the swtches by utlzng the tansfme paastcs as a esnant tank. Ths allws eductns n ltage and cuent spkes n the pwe deces, as well as deceasng the swtchng lsses. As a esult, these cnetes ae me attacte f hgh ltage dc-dc cnesn. A maj lmtatn f ths cnete s the senstty t the paametes f the esnant tank n de t mantan ZS. As the tansfme paastcs ae used t achee ZS, these cnetes eque elately hgh fequency peatn (45-150KHz) [1].

30 11 n S 1 S 3 Tansfme D D 1 c S S 4 D 3 D 4 Fgue 1-9 uent fed full bdge dc-dc cnete [1]. F hgh-pwe and hgh-ltage applcatns n whch slatn s nt equed, the pesence f the tansfme wll sgnfcantly add t the sze, weght and cst f the cnete. The cnete desgn pblem becmes me cmplcated n de t addess the desgn ssues f the hgh-ltage mddle-fequency tansfme wth pe-specfed paastcs. These ssues nclude the alues f the leakage nductance and paastc capactance f the wndng, as well as the hgh ltage nsulatn and magnetc ce mateal [0]. Tansfme satuatn can hae hamful cnsequences, lke nceasng cnductn and swtchng lsses f semcnducts. Pmay swtch falue caused by lage peak cuents dung satuatn s the mst hamful theat [0]. These pblems make tansfme based cnetes less elable and unattacte f hgh-pwe and hgh-ltage applcatns.

31 Mult-mdule sees-paallel dc-dc cnetes Mult-mdule dc-dc cnetes cnsst f dentcal standadzed pwe mdules cnnected n sees paallel at the nput and utput sdes [5]-[9]. The adantages f mult-mdule sees/paallel cnetes ae: Sht desgn pcess and lwe pductn cst because f standadzed mdules. Enhanced system elablty because f edundancy. Ease f themal desgn, because the ttal pwe s dded between the mdules. Scalablty and ease f expansn. Mult-mdule dc-dc cnetes can be classfed nt fu achtectues. () nput-sees utput sees (ISOS) shwn n Fg a, () nput-sees utput-paallel (ISOP) shwn n Fg b, () nput-paallel utput-sees (IPOS) shwn n Fg c, () nput-paallel utput-paallel shwn n Fg d. Each mdule has an slated dc-dc sub-cnete. An example f ISOP cnete s shwn n Fg Sees mdules ae cnnected t the hgh ltage sde f the bus, whle paallel mdules ae cnnected t the hgh-cuent sde f the bus. Thus, a step-dwn dc-dc cnete wll utlze the ISOP achtectue, whle a step-up dc-dc cnete wll utlze the IPOS achtectue. These cnetes ae nt estcted t dc-dc peatn. F example, n [5] the ISOP achtectue s used as a dc/ac cnete. T date, nne f these cnetes hae been ppsed f hgh-ltage and hgh-pwe dc-dc applcatns. The IPOP achtectue has been wdely used n dstbuted pwe systems, pwe fact cectn cnetes, and unnteuptable pwe supples whle the ISOP achtectue s used n hgh-speed tan pwe systems [5], [7]. The man demet f these cnetes s the use f an slatn tansfme n each cnete mdule.

32 m m - - m m (a) (b) m m - m m (c) (d) Fgue 1-10 Mult-mdule cnetes. (a) Input-Sees Output-Sees, (b) Input-Sees Output-Paallel, (c) Input-Paallel Output-Sees, (d) Input-Paallel Output-Paallel

33 14 S 11 S 13 D 11 f 1 D 1 S 1 S 14 S 1 S 3 D 1 f D S S 4 Fgue 1-11 Example f an ISOP cnete [8] F hgh pwe applcatn, whee slatn s nt equed, the cst and weght f the submdule slatn tansfmes s nt justfed. Addtnally, f hgh ltage applcatns, the slatn tansfmes need t be nsulated up t the alue f the hgh ltage al. Pdng such nsulatn leel eques a specal stuctue and wll be cstly. Takng nt cnsdeatns the demets mentned eale, t s cncluded that the mult-mdule cnete tplges may nt be pactcal f megawatt and kllt sze applcatns.

34 Tansfmeless swtched capact dc-dc cnetes The quest f tansfmeless dc-dc cnetes peatng at hgh cnesn ats led t the deelpment f swtched-capact and swtched-nduct cnetes [19]. In cntast t swtched-nduct ccuts, swtched capact cnetes ad usng magnetc elements. Ths allws pducng cmpact and lght-weght ccuts peatng at hghe tempeatues. Fg. 1-1 shws a swtched-capact multleel dc-dc cnete ppsed n [30]. Ths tplgy s ppsed f lw ltage lght pwe applcatns and can achee hgh effcency. In [31], the lmtatns f ths tplgy f hgh pwe applcatns ae summazed as fllws: 1) nnmdula stuctue; ) elately cmplcated swtchng scheme; 3) dffculty n hgh fequency peatn and equement f cmplcated capact ltage balancng scheme; 4) excesse ltage dp acss the swtches; 5) lack f bdectnal pwe management and; 6) n fault bypass capablty. T ecme these lmtatns, a multleel mdula capact-clamped cnete s ppsed n [31] and shwn n Fg S 3 p S p S 1 p 1 S 1n 1 S n S 3n Fgue 1-1 Swtched capact multleel dc-dc cnete ppsed n [30].

35 16 S 1 S S 5 S S 3 S 6 S 9 S 4 S 7 S 10 Fgue 1-13 Mdula multleel capact clamped cnete ppsed n [31] The adantages f ths tplgy ae: 1) hgh fequency peatn capablty; ) lw nput/utput cuent pple; 3) lw ON-state ltage dp, and bdectnal pwe flw management. F hgh ltage applcatns, hwee, ths tplgy has a maj lmtatn. T ensue equal ltage stess acss the swtches, capacts n dffeent mdules hae t wthstand unequal ltage stess. A cmmn dsadantage f swtched-capact cnetes s the hgh cuent spkes esultng fm capacts swtchng. Such cuent spkes ae nly lmted by the equalent sees esstance between capacts. F hgh pwe applcatns, ths mpses seee stesses n the swtches. T sle ths pblem, esnant swtched-capact cnetes ae ppsed n [3], [33] and s shwn n Fg Ths tplgy ncludes a esnant nduct n the ccut allwng ZS f all swtches. The techncal feasblty f ths tplgy has been ctczed n [34] as t suffes fm p egulatn aganst lad and nput ltage aatn. [35], [36] als ppse the tplges f swtched capact cnetes but they shae the same lmtatns f peus tplges and ae nt sutable f hgh-pwe and hgh ltage applcatns. S 1 n S p S n S 3 p S 3n S 4 p S 4n S 1 p 4 Fgue 1-14 Resnant swtched capact dc-dc cnetes [33]

36 Vltage Multple-based Hybd D-D netes The ckft-waltn (W) ccut (shwn n Fg.1-15) was fst ntduced n 193. Ths ccut peates as a ltage multple fed by a pulsatng lw ltage waefm t geneate a hgh ltage dc n ts utput temnal. Its man applcatn s t geneate hgh ltage dc equed f nsulatn testng geneats and patcle acceleats. As the multplcatn at nceases, the W ccut suffes fm p lad egulatn esultng n a lage ltage dp at ts utput temnal. F ths easn, the W ccut needs anthe cnete t pde utput ltage egulatn. In [11] an slated hybd dc-dc cnete cmpsed f sees-esnant and a W ccut s ppsed f medcal-use hgh-ltage X-ay pwe geneat. In [1] a tansfmeless multleel bst cnete (shwn n Fg.1-16) s ntduced by hybd cnnectn f W and a classcal bst cnete. The late tagets factnal klwatt enewable pwe applcatns. Bth cnetes n [1] and [11] can pde ey lage dc ltage step-up at at hgh effcency. Hwee, these ccuts can nt be used f hgh pwe applcatns. They shae the same hgh cuent-spke pblem esultng fm chagng/dschagng capacts cnnected n paallel. Ths was the same lmtatn f the swtched-capact cnete dscussed eale. The ccut shwn n Fg.1-16 als eles n a hgh-cuent bst cnete at the nput stage. Ths bst ccut s necessay t pde a pulsatng nput ltage waefm f the W ccut, and pde utput ltage egulatn thugh PWM. The pesence f ths bst ccut s als unattacte f hgh pwe applcatns. Fnally, ltage multple hybd dc-dc cnetes can nt achee dc ltage step-dwn peatn. Fgue 1-15 ckft-waltn ltage multple

37 18 D 1 1 D D D 4 D 5 S 5 Fgue 1-16 A dc-dc multleel bst cnete [1] Sft-swtched Tanfmeless D-D netes The quest f hgh pwe dc-dc cnetes led t deelpng sft-swtched tansfmeless tplges usng thysts as acte swtches [10],[13]-[15],[37]. The sft-swtchng beha elmnates the pblems asscated wth had cuent chppng. Adng the use f tansfmes esults n lght weght and less expense ccuts. The use f hgh ltage thysts nstead f IGBTs educes the cnductn lsses cnsdeably. In [10], a bdectnal cnete s ppsed and s shwn n Fg The ccut eles n usng bdectnal hgh-ltage thyst ales, hgh ltage esnant capacts and nducts t achee dc-dc cnesn wthut an ntemedate tansfme. The cnete can nt ntecnnect unpla buses shang cmmn gund and s nly estcted f bpla buses. The step-dwn ccut can nt be mdeled n clsed fm mathematcal fmulas, makng the desgn had. The ccut has sht-thugh mdes leadng t pssble fault ppagatn amng

38 19 ntecnnected buses [15]. Fnally, the nn-mdula stuctue and the use f hgh-ltage esnant capact banks mply expense mplementatn and lage ftpnt. In [13] a hgh pwe step-dwn dc-dc cnete has been ppsed and s shwn n Fg The ccut als ads the use f tansfmes hgh-cuent chppng. It can cnnect bth unpla and bpla buses and uses thysts as acte swtches. The man lmtatn, hwee, s the unequal ltage stesses n the thysts. Ths pblem s aded wth the cnete tplgy f [37] shwn n Fg Ths ccut uses lssless capacte snubbes t ensue equal ltage dstbutn n sees-cnnected thysts. The man lmtatn, hwee, s that the utput ltage s flatng elate t the nput ltage. Ths makes the ccut unattacte f many applcatns. Bth cnetes ppsed n [15] and [37] (Fg and Fg.1-19) ae nly estcted t dc ltage step-dwn peatn mde. f1 / 1 / s s 7 s 8 / f / / f1 s 3 s 4 s 5 s 6 f / f1 s s 8 s 7 f / f1/ / 1 s 4 s 3 s 6 s 5 / f / / Fgue 1-17 Bdectnal hgh pwe dc-dc cnete f [10]

39 0 s s 3 s 4 s 5 1 D 1 D D 3 D 4 n D 5 D6 D7 D8 Fgue 1-18 Hgh-pwe step dwn dc-dc cnete f [13] c c s D 1 D / c s 3 c D 3 D 4 / c s 4 Fgue 1-19 Hgh pwe step-dwn dc-dc cnete f [37]

40 1 1.4 Thess Outlne The next chaptes f the thess ae ganzed as fllws: hapte pesents the stuctue and peatn pncple f the ppsed cnetes. Ths ncludes a mdula step-dwn cnete f undectnal pwe tansfe between dc buses, a mdula step-up cnete f undectnal pwe tansfe between dc buses, a mdula netng step-up, step-dwn cnete f undectnal pwe tansfe between dc buses, and fnally bdectnal pwe tansfe cnetes. hapte 3 deelps a mathematcal mdel f the ppsed cnetes and establshes the basc desgn equatns. hapte 4 pnts t sme pactcal cnsdeatns egadng the mplementatn f the ppsed cnetes. It tackles the flte desgn, lss analyss, fault analyss and pactcal ealzatn ssues. hapte 5 pesents a pf f cncept f ppsed cnetes thugh desgn examples n seeal pwe and ltage leels, and thugh expemental pttypes. hapte 6 cncludes the thess, hghlghts the cntbutn and ppses futue wk.

41 hapte Stuctue and Opeatn Pncple.1 Intductn In ths chapte, the stuctue f each cnete ccut s dscussed. Ths s fllwed by pesentatn f the peatng pncples at steady-state. Fu cnete ccuts ae tackled n ths thess. They all shae the same mets, they (1) depend n mdula acte swtchng netwk, () emply sft-swtchng and ad hgh-cuent chppng, (3) can be used f ntecnnectng bth unpla and bpla dc buses, (4) d nt cntan hgh-ltage capacts, tansfmes cupled nducts, (5) ffe a systematc desgn pcedue based n clsed-fm mathematcal expessns. The ppsed cnetes theefe ad the lmtatns f exstng ccuts dscussed n the peus chapte, and ae attacte f a wde ange f hgh-pwe and hghltage applcatns. The stuctue f the acte swtchng netwk f each cnete cntans sees dentcal pwe mdules peatng synchnusly. The maj adantages f ths stuctue ae: ) shtened desgn pcess, ) lweed manufactung, pductn and assembly csts thugh use f standadzed dentcal mdules, and ) enhanced system elablty thugh edundancy. Sft-swtchng s emplyed f all swtches. In cntast t had-swtched cnetes, the ppsed ccuts ad fced chppng f hgh cuents. All acte swtches hae self cuent tun-ff at ze ltage. Ths mples; ) lwe swtchng lsses, ) educed pblems esultng fm elect-magnetc ntefeence (EMI), ) n need f acte ltage shang between semcnducts, ) the ablty t use thysts as the man acte swtches. The stuctue f the ppsed cnetes always allws unpla and bpla mplementatns wthut usng slatn tansfmes, specal gundng nsulatn technques. The absence f hgh-ltage acte swtchng ales allws cmpact mplementatn usng ff-the-shelf semcnduct deces. The ppsed tplges ad usng dect sees/paallel ntecnnectn f acte swtches and theefe d nt eque acte-ltage shang technques between semcnducts.

42 3. Stuctue f the acte swtchng netwk The Ppsed cnetes ely n a ccut cmpsed f a sngle esnant nduct tgethe wth capacts embedded wthn an acte swtchng netwk. Detals f the stuctue f each cnete ccut wll be pesented late n ths chapte. Ths sectn pesents the stuctue f the acte swtchng netwk shaed by all ppsed cnetes. Ths ccut s shwn n Fg. -1. The acte swtchng netwk cnssts f dentcal mdules cnnected n sees. Each mdule cntans a lw-ltage ac (nn-plazed) capact and fu dentcal acte swtches wth a eese blckng chaactestc. The fwad and eese blckng ltages f each swtch equal t the peak ltage f the lw-ltage capacts. Snce capacts always hae equal ltages, equal blckng ltages amng swtches s guaanteed. All mdules peate synchnusly by sequental swtchng f S 1 and S. As a esult, the acte swtchng netwk s seen as a sngle hgh ltage tatng capact fm ts temnals as shwn n Fg.-1. By swtchng-n S 1 ( S ), all lw-ltage capacts becme cnnected n sees thugh the swtches S 1 ( S ). Tun-n f the swtches always ccus at ze cuent as the ppsed cnetes peate nly n the dscntnuus cnductn mde (DM). DM peatn allws nly thee swtchng pssbltes shwn n Fg.-. A esnant nduct (nt shwn) wll play an mptant le dung swtchng. Ths le mples natual cuent cmmutatn fm the acte swtchng netwk at ze ltage. Ths esults n self tun-ff f all acte swtches S 1 and S. Theefe, thysts can be used t ealze the acte swtches S 1 and S. Othe semcnduct deces can als be used such as, the IGT cnentnal IGBTs wth sees ddes RB- IGBTs whch all hae eese blckng chaactestcs. Snce the acte swtches S 1 and S ae sngle quadant swtches, they allw cuent cnductn nly n ne dectn ndcated by the aw (see Fg. -1, Fg. -). Ths stuctue peents any sht ccut scena t happen acss capacts temnals, egadless f the swtchng state. Snce nly dscntnuus cnductn mde s allwed, the swtchng scenas (a) and (c) ae fllwed by a ze-cuent ( nn-cnductn) ped shwn n (b). Ths means that the swtchng states fllw the (a), (b), (c), (b), (a) sequence. At the tun-ff nstants, mng fm (a) t (b) fm (c) t (b), the cuent cmmutates fm the acte swtchng netwk t an extenal ccut natually wthut fced tun-ff f the swtches. Ths featue wll be explaned f each cnete n me detals.

43 4 c s c c 1 c 1 s * c c * c ell N.1 s c n c n s ell N.n Fgue -1 Stuctue f the mdula acte swtchng netwk

44 5 s s c 1 c 1 c 1 c c 1 c s s s s c n c n c n c c n c s s (a) (b) (c) Fgue - Dffeent swtchng schemes f the acte swtchng netwk

45 6.3 The Mdula Step-dwn nete. The ppsed step dwn cnete has the genec stuctue shwn n Fg. -3. Geneally, the cnete s fed fm a bpla nput dc bus ( +, - ) and supples a bpla utput dc bus ( +, - ) wth lwe ltage than the nput bus. The nput s cnnected t acte swtchng buses actng as tatng hgh ltage esnant capacts ( +, - ), as explaned eale. The stuctue shwn n Fg.-3 allws bpla unpla pwe tansfe fm the nput buses. In cntast t Pulse Wdth Mdulated cnetes, the ppsed ccut s a fequency cntlled cnete. Its functn s smla t the classcal buck cnete whch can step dwn the nput ltage t the alue f the utput ltage wthut changng the platy. But unlke the classcal PWM cntlled buck cnete, the ppsed ccut desn t expeence fced cuent chppng. uent cmmutatn fm the acte swtchng netwk t the ddes ccus at ze ltage. Als the ccut peates nly n the dscntnuus cnductn mde (DM) mplyng ze cuent tun-n f the acte swtches and ze cuent tun-ff f the ddes. As a esult, all semcnduct deces peate at sft-swtchng mde educng the swtchng lsses damatcally. F each ple, the cnete cntans a esnant nduct ( + - ), an ntegated esnant capacte acte swtchng netwk ( + - ) and a dde ale. Detals f the peatng pncple ae shwn n Fg. -4, Fg. -5 and Fg.-6. F each swtchng cycle, the ccut peates n sx nteals shwn n Fg.-4, Fg.-5 wth the asscated waefms shwn n Fg. -6. These nteals can be explaned as fllws: a) By fng S 1 a snusdal nput cuent flws fm t 0 t t, n the sees esnant ccut. s defned as the cnductn ped f S 1. Dung ths nteal, the capacts ae chaged and the ltages swng fm c pk t c pk whle the ddes eman eesed based. c pk s the steady-state peak ltage f the capacts. Ths nteal ends when the summatn f the capact ltages n the mdules eaches the alue f the nput bus ltage. At ths nstant, the fwad ltage n S 1 becmes ze and cuent cmmutates t the ddes. Ths nteal s shwn n Fg.-4 (a).

46 7 b) At t, the summatn f the capact ltages equals t the nput bus ltage and as a esult, the eese ltage acss the ddes becmes ze. At ths mment, the ddes tun n at ZVS, clampng the net capact ltage t c pk. The cuent cmmutates t the ddes and the nduct sted enegy s dschaged lnealy nt the utput ccut. Dung ths nteal, n cuent s dawn fm the nput bus whle the utput bus ecees cuent suppled fm the esnant nduct. Ths nteal s shwn n Fg.-4 (b). c) Once the nduct s fully dschaged nt the utput bus, ddes tun-ff at ze cuent blckng a ltage f. Afte the nduct dschage, bth nput and utput cuents equal t ze. Ths s the last nteal n the fst swtchng half cycle. Ths nteal s shwn n Fg. -4 (c). d) The secnd swtchng half-cycle stats by fng S. Because the nduct was fully dschaged n the peus half-cycle, S tun-n ccus wth ZS at the begnnng f ths nteal, whch s shwn n Fg.-5 (d). Anthe snusdal cuent pulse flws thugh the esnant ccut f a tme ped. Dung ths ped, the net capact ltage swngs negately fm c pk t c pk whle the ddes eman eese based. Ths nteal ends when the summatn f the capact ltages n the mdules eaches the alue f the nput bus ltage. At ths nstant, the cuent cmmutates t the ddes. e) At t T /, the summatn f the capact ltages equals t the bus nput s ltage and as a esult, the eese ltage acss the ddes becmes ze. At ths mment, ddes tun n at ZVS, clampng the net capact ltage t c pk. The cuent cmmutates t the ddes and the nduct sted enegy s dschaged lnealy nt the utput ccut. Dung ths nteal, n cuent s dawn fm the nput bus whle the utput bus ecees cuent suppled fm the esnant nduct. Ths nteal s shwn n Fg. - 5 (e). f) As the nduct s fully dschaged n the utput bus, ddes tun-ff at ze cuent blckng a ltage f. Afte the nduct dschage, bth nput and utput cuents equal

47 8 t ze. Ths s the last nteal n the secnd swtchng half cycle. Ths nteal s shwn n Fg. -5 (f). D D Fgue -3 Stuctue f the mdula step-dwn cnete In cntast t had cmmutatn n the classcal PWM buck cnete, cuent cmmutatn n ths tplgy ccus at ze ltage. Ths esults n self tun-ff f the acte swtches S 1, S at ze ltage and sft tun-n f the ddes at ze ltage. Because the ccut nly peates n DM, the acte swtches (S 1 and S ) tun-n at ze cuent and the ddes tun-ff at ze cuent as well.

48 9 s + - c n s D (a) s D - + c n s s - + c n s (b) D s D + - c n s s - + c n s (c) D s D s + - c n Fgue -4 Step-dwn cnete dung nteals a, b, c f the fst swtchng half-cycle

49 30 s - + c n s D (d) s D + - c n s s + - c n s (e) D s D - + c n s s + - c n s D (f) s D - s + c n Fgue -5 Step-dwn cnete dung nteals d, e, f f the secnd swtchng half-cycle

50 Dde cuent uents n capacts Induct and utput cuent Mdule capact ltage 31 c pk 0 c n c pk pk pk and swtches S1, S 0 pk n S1 n S D pk D (a) (b) (c) (d) (e) (f) 0 T s Ts Fgue -6 Ideal steady-state waefms f the mdula step-dwn cnete t

51 3.4 The Mdula Step-up nete. The ppsed step dwn cnete als utlzes the swtchng netwk f Fg.-1. Its genec stuctue s shwn n Fg. -7. Smla t the step-dwn cnete dscussed eale, the step-up cnete s fed fm a bpla nput dc bus ( +, - ) and supples a bpla utput dc bus ( +, - ) wth hghe ltage than the nput bus. The acte swtchng netwk acts as a tatng hgh ltage esnant capact ( +, - ) as explaned eale. Bth unpla and bpla pwe tansfe s pssble between nput and utput dc buses. The cnete s als a fequency cntlled ccut. Its functn s smla t the classcal bst cnete whch can step up the nput ltage t the alue f the utput ltage wthut changng the platy. But unlke the classcal PWM cntlled bst cnete, the ppsed ccut desn t expeence fced cuent chppng dung cmmutatn and peates nly n the DM mde. The cnete shwn n Fg.-7 cntans a esnant nduct ( + - ) n each ple whch s dectly cnnected t the nput dc bus. In addtn, t als has an ntegated esnant capacte acte swtchng netwk ( + - ) and an utput dde ale f each ple. The peatng pncple, at steady-state, can be explaned wth the help f Fg. -8, Fg. -9 and Fg.-10. Smla t the step-dwn cnete, ths ccut peates n sx nteals dung each swtchng cycle and can be explaned as fllws: a) The fst nteal s shwn n Fg.-8 (a). By fng S 1 a snusdal cuent pulse s dawn fm t 0 t t,n the sees esnant ccut. The capacts ae chaged smultaneusly and the ltages swng pstely fm c pk t c pk whle the ddes ae eesed based. Ths nteal ends when the summatn f the capact ltages n the mdules eaches the alue f the utput bus ltage. At ths nstant, the fwad ltage n S 1 becmes ze and cuent cmmutates t the ddes. b) At t, the summatn f the capact ltages equals t the utput bus ltage and as a esult, the eese ltage acss the ddes becmes ze. At ths mment, ddes tun n at ZVS, clampng the net capact ltage t c pk. The cuent cmmutates t the ddes and the nduct sted enegy s dschaged lnealy nt the utput ccut. Ths nteal s shwn n Fg. -8 (b).

52 33 c) When the nduct s fully dschaged, ddes tun-ff at ze cuent blckng ltage f ( - ). Dung ths nteal bth nput and utput cuents equal t ze. Ths s the last nteal n the fst swtchng half cycle whch s shwn n Fg. -8 (c). d) The secnd swtchng half cycle s smla t the fst half-cycle and stats by fng S. Because the nduct has fully dschaged nt the peus half-cycle, S tun-n ccus at ZS at the begnnng f ths nteal whch s shwn n Fg.-9 (d). In ths nteal, anthe snusdal cuent pulse s dawn n the esnant ccut f a tme ped. Dung ths ped, net capact ltage swngs negately fm c pk t c pk whle the ddes ae eese based. Ths nteal als ends when the summatn f the capact ltages n the mdules eaches the alue f the utput bus ltage. At ths nstant cuent cmmutates t the ddes. D D Fgue -7 Stuctue f the mdula step-up cnete

53 34 e) At t T /, the summatn f the capact ltages equals t the utput bus S ltage and as a esult, the eese ltage acss the ddes becmes ze. At ths mment, ddes tun n at ZVS clampng the capacts ltages t c pk. The cuent cmmutates t the ddes and the nduct sted enegy s dschaged lnealy nt the utput ccut. Ths nteal s shwn n Fg. -9 (e). f) When the nduct s fully dschaged nt the utput bus, ddes tun-ff at ze cuent blckng ( - ). Dung ths nteal bth nput and utput cuents equal t ze. Ths s the last nteal n the secnd swtchng half cycle whch s shwn n Fg. -9 (f). In cntast t had cmmutatn n the classcal PWM bst cnete, cuent cmmutatn ccus at ze ltage. Ths esults n natual tun-ff f the acte swtches S 1, S at ze ltage and tun-n f the ddes at ze ltage. Because the ccut nly peates n DM, the acte swtches (S 1 and S ) tun-n at ze cuent and the ddes tun-ff at ze cuent as well. The step-up cnete wll stat njectng pwe nt the utput ccut, and peate n steadystate afte capacts ae chaged. When the cnete stats whle all capacts ae dschaged, capacts ltage buld-up pcess ccus. Ths pcess wll be efeed t as the black-stat mde. Dung ths mde, n cuent s njected nt the utput ccut. The pwe wthdawn fm the nput bus s tansfeed t the capacts t chage them. Ths mde can be explaned wth Fg. -8, Fg. -9, Fg. -11 and Fg. -1. Fg. -11 shws the temnal ltage f the acte swtchng netwk ( * c ) dung the blackstat mde. The waefm labeled c s the net tatng capact ltage shwn n Fg. -1 whch s cmpsed f the sees cnnectn f the actual mdula capacts. Dung ths mde, the cnete peates nly n nteals (a), (c), (d), (f), (a), shwn n Fg. -8 and Fg. -9. Afte each half-cycle the temnal ltage f the acte swtchng netwk nceases by. Ths wll be dscussed n detals n hapte 3 f ths thess. When * c eaches the utput ltage leel ( ), each capact s then chaged t the ltage leel c pk shwn n Fg. -10 and the cnete peates n steady-state as dscussed eale.

54 35 D s (a) - + c n s D D s (b) + - c n s D D s (c) + - c n s D Fgue -8 Step-up cnete dung nteals a, b, c f the fst swtchng half-cycle

55 36 D (d) + - s c n s D D s (e) - + c n s D D s (f) - + c n s D Fgue -9 Step-up cnete dung nteals d, e, f f the secnd swtchng half-cycle

56 37 Induct and utput cuent Mdule capact ltage c pk 0 c pk pk c n pk Dde cuent uents n capacts and swtches S1, S D pk 0 D pk pk D pk n D S1 n S t (a) (b) (c) (d) (e) (f) 0 T T s s Fgue -10 Ideal steady-state waefms f the mdula step-up cnete

57 38 c * c Fgue -11 apact ltage buld-up pcess dung the step-up cnete black-stat pk Fgue -1 Induct and utput cuents f the step-up cnete dung the black-stat pcess

58 39.5 The Mdula Inetng nete The ppsed swtchng netwk f Fg.-1 can als be utlzed t make a platy netng cnete, smla n functn t the classcal buck-bst PWM cnete. The genec stuctue f ths ccut s shwn n Fg Smla t the step-dwn and step-up cnetes dscussed eale, the netng cnete s fed fm a bpla nput dc bus ( +, - ) and supples a bpla utput dc bus ( +, - ) wth hghe lwe ltage than the nput bus but wth eesed platy. In case f unpla ealzatn, the nput and utput buses wll hae dffeent platy and ltage leels. In case f bpla ealzatn, the cnete wll shae the same functn f ethe the step-dwn step-up ccuts dscussed eale. Smla t peus ccuts dscussed eale, the platy netng cnete s als a fequency cntlled ccut pefmng pwe tansfe between tw dc buses wth dffeent ltages and plates wthut cuent chppng. It enjys the same sft cuent cmmutatn featue and peates nly n the DM mde. F bpla ealzatn, the ccut needs tw acte swtchng buses (ne f each ple), but can utlze nly ne esnant nduct. Hwee, the cnete shwn n Fg.-13 cntans tw nducts t allw sngle ple pwe tansfe, f needed. The steady-state peatng pncple can be explaned wth the help f Fg. -14, Fg espndng waefms dung step-dwn mde and step-up mde ae shwn n Fg. -17, Fg.-18 espectely. Ths ccut als peates n sx nteals dung each swtchng cycle as fllws: a) By fng S 1 a snusdal cuent pulse s dawn fm t 0 t t, n the sees esnant ccut. The capacts ae chaged and the ltages swng pstely fm t whle the ddes ae eesed based. Ths nteal ends when the summatn c pk c pk f the capact ltages n the mdules each the alue f ( + ). At ths nstant, the fwad ltage n S 1 becmes ze and cuent cmmutates t the ddes. Ths nteal s shwn n Fg.-15 (a). b) At t, the summatn f the capact ltages equals ( + ) and as a esult, the eese ltage acss the ddes becmes ze. At ths mment, ddes tun n at ZVS clampng the net capact ltage t c pk. The cuent cmmutates t the ddes and the

59 40 nduct sted enegy s dschaged lnealy nt the utput ccut. Dung ths nteal, n cuent s dawn fm the nput bus whle the utput bus ecees cuent suppled fm the esnant nduct. Ths nteal s shwn n Fg.-15 (b). c) When the nduct s fully dschaged nt the utput bus, ddes tun-ff at ze cuent blckng. Dung ths nteal bth nput and utput cuents equal t ze. Ths s the last nteal n the fst swtchng half cycle whch s shwn n Fg. -15 (c). d) The secnd swtchng half cycle stats by fng S. Because the nduct has fully dschaged dung the peus half-cycle, S has tuned n at ZS at the begnnng f ths nteal whch s shwn n Fg.-16 (d). In ths nteal, anthe snusdal cuent pulse s dawn n the sees esnant ccut f a tme ped and the net capact ltage swngs negately fm t c pk c pk whle the ddes eman eese based. Ths nteal ends when the summatn f the capact ltages n the mdules eaches ( + ). At ths nstant, the cuent cmmutates t the ddes. D D Fgue -13 Stuctue f the mdula netng cnete

60 41 e) At t T /, the summatn f the capact ltages equals ( + ) and as a s esult, the eese ltage acss the ddes becmes ze. At ths mment, ddes tun n at ZVS clampng the capacts ltages t - c pk. The cuent cmmutates t the ddes and the nduct sted enegy s dschaged lnealy n the utput ccut. Dung ths nteal, n cuent s dawn fm the nput bus whle the utput bus ecees cuent suppled fm the esnant nduct. Ths nteal s shwn n Fg. -16 (e). f) As the nduct s fully dschaged n the utput bus, ddes tun-ff at ze cuent. Dung ths nteal bth nput and utput cuents equal t ze. Ths s the last nteal n the secnd swtchng half cycle whch s shwn n Fg. -16 (f). In cntast t had cmmutatn n the classcal PWM buck-bst cnete, cuent cmmutatn ccus at ze ltage. Ths esults n self tun-ff f the acte swtches S 1, S at ze ltage and sft tun-n f the ddes at ze ltage. Because the ccut nly peates n DM, the acte swtches (S 1 and S ) tun-n at ze cuent and the ddes tun-ff at ze cuent as well. In the step-up mde, the cnete wll stat njectng pwe nt the utput ccut, and peate n steady-state afte capacts ae chaged. Ths als smla t the step-up cnete dscussed eale. When the cnete stats whle all capacts ae dschaged, capacts ltage buld-up pcess ccus as shwn n Fg -14. c * c Fgue -14 apact ltage buld-up f the netng cnete n step-up mde

61 4 s + - c n s D (a) s - + c n D s s - + c n s D (b) s + - c n D s s - + c n s D (c) D s s + - c n Fgue -15 Inetng cnete dung nteals a, b, c f the fst swtchng half-cycle

62 43 s - + c n s D (d) s + - c n D s c n s s + - D (e) s - + c n s D s + - c n s D (f) s - D s + c n Fgue -16 Inetng cnete dung nteals d, e, f f the secnd swtchng half-cycle

63 Dde cuent uents n capacts Induct and utput cuent Mdule capact ltage 44 c pk 0 c n c pk pk pk and swtches S1, S 0 pk n S1 n S D pk D (a) (b) (c) (d) (e) (f) 0 T s Ts t Fgue -17 Ideal steady-state waefms f the netng cnete dung step-dwn

64 45 Induct and utput cuent Mdule capact ltage c pk c pk pk c n pk Dde cuent uents n capacts and swtches S1, S D pk 0 D pk pk D pk n D S1 n S t (a) (b) (c) (d) (e) (f) 0 T s T s Fgue -18 Ideal steady-state waefms f the netng cnete dung step-up

65 46.6 Mdula Bdectnal netes A bdectnal dc-dc cnete, als efeed t as a dc tansfme allws bdectnal pwe tansfe between tw dc buses wth dffeent ltage leels. Ths featue can be btaned by a hybd cnnectn f a step-up and a step-dwn cnete. Fg. -19 shws the stuctue f ths cnete. In ths fgue t s assumed that ( +, - ) s the dc bus wth lwe ltage than the ( +, - ). The cnete cntans tw bpla sepaate sub-cnetes, namely: a mdula step-up cnete and a mdula step-dwn cnete. The step-up subcnete cnssts f the esnant nducts ( up+, up- ), the acte swtchng netwks ( up+, up- ) and the dde ales (D up+,d up- ). The step-dwn subcnete cnssts f the esnant nducts ( dwn+, dwn- ), the acte swtchng netwks ( dwn+, dwn- ) and the dde ales (D dwn+,d dwn- ). Each cnete can peate ndependently accdng t the peatng pncples descbed eale n ths chapte. dwn dwn up D up D dwn V up HV D dwn V up up D up HV dwn dwn Fgue -19 Stuctue f the mdula bdectnal cnete

66 47 The stuctue f Fg. -19 uses tw sepaate nducts; ne f the step-up functn and ne f the step-dwn functn. Altenately, t s als pssble t use ne nduct f bth functns n each ple. In ths case, the stuctue f Fg.-19 can be smplfed as shwn n Fg.-0. In ths stuctue, nly ne cnete peates at a gen tme accdng t the peatng pncple descbed eale n ths chapte. Ths cnete beas esemblance t the -quadanct chppe ccut. dwn D up up / dwn V up D dwn HV V up D dwn HV up / dwn dwn D up Fgue -0 Stuctue f the sngle-nduct mdula bdectnal cnete

67 48 Bdectnal cnetes can als be made fm hybd cnnectn f tw mdula netng cnetes. Fg. -1 shws the stuctue f tw mdula netng cnetes cnnected n antpaallel cnnectn wth sepaate nducts t make a bdectnal netng cnete. Bth step-up and step-dwn peatns peate ndependently f the cnete f Fg.-1. It s als pssble t assemble the same cnete wth a sngle nduct f bth step-up and step-dwn peatns and f bth ples. Ths s shwn n Fg.-. In ths case nly ne cnete peates at a gen tme. D dwn dwn D up up V HV dwn up V up HV D up D dwn dwn Fgue -1 Stuctue f the netng mdula bdectnal cnete

68 49 dwn D dwn D up V up HV V up HV D up D dwn dwn Fgue - Stuctue f the sngle-nduct netng mdula bdectnal cnete

69 50.7 Summay In ths chapte, the basc stuctue and peatng pncple f the ppsed cnetes wee pesented. Resemblance between the classcal dc-dc cnetes (buck, bst, buck-bst) and the ppsed ccuts can be bseed. But, unlke classcal ccuts, the ppsed cnetes d nt eque fced cuent chppng. Instead, all ccuts enjy natual cuent cmmutatn at ze ltage. The ppsed cnetes utlze mdula acte swtchng netwks cmpsed f lw-ltage sngle-quadant swtches and lw-ltage capacts. Hgh ltage capact banks ae nt needed n the ppsed tplges. All capacts ae enclsed nsde the mdules and eque n specal sht ccut ptectn. The ppsed cnetes ae scalable and allw edundant mdules t be added. These stuctual featues esult n sutablty f a wde ange f hgh-pwe applcatns at hgh elablty and lw cst. It s cncluded that despte the dffeent functns f the aus ppsed cnetes, the peatng pncples shw geat smlaty. Ths can be bseed when cmpang the sx cnductn nteals f the cnetes f sectn.3,.4 and.5. F the netng cnete, we cnclude that t s step-up and step-dwn waefms ae smla t the nn-netng step-up and step-dwn ccuts. A basc dffeence, hwee, s the peak ltage swng f the capacts and hence, the numbe f equed mdules. The bseed esemblance n the peatng pncples f the cnetes allws unfed mathematcal analyss, desgn pcedue, and cntl t be cnducted n the subsequent chaptes.

70 51 hapte 3 nete Mdelng and Desgn Intductn Afte pesentng the peatng pncples f the cnetes ppsed n the peus chapte, ths chapte studes these cnetes analytcally. Ths s dne by pefmng steady-state mathematcal mdelng. The bjecte s t dee a set f clsed fm mathematcal expessns descbng the beha f each cnete ccut. These expessns ae pmaly useful t desgn the cnetes and select the cmpnents. Befe statng the desgn pcess, dentfyng the functn f the cnete (step-up, stepdwn, etc.), and the desed pwe atng s essental. Ths s fllwed by detemnng the peatng ltage steppng at. Gen the cnete s pwe, and ts temnal ltages, the desgn pcess wll esult n: 1. Detemnng the alue f the esnant capacts n the acte swtchng netwk.. Detemne the alue f the esnant nduct t guaantee DM peatn. 3. hsng ppe atngs f the pwe semcnduct deces. T tackle the abe mentned pnts, ths chapte stats by studyng the enegy tansfeed thugh each cnete fllwng each swtchng pulse. Then, the ltage and cuent elatns n the esnant elements ae studed analytcally. Fnally, the cuent and ltage equements f the pwe semcnduct deces ae studed. Secnday desgn cnsdeatns wll be dscussed n the next chaptes. These cnsdeatns nclude semcnducts pwe lsses, desgn f the flteng capacts and the effects f the ccut nn-dealtes.

71 5 3. Assumptns T mdel the ppsed cnetes, deal cmpnents wll be assumed. Ths cndtn wll be elaxed n the next chapte, takng nt cnsdeatn the nn-dealtes asscated wth each cmpnent nddually. Unless thewse stated, the dscussn n ths chapte assumes the fllwng: 1. All semcnduct deces hae ze cnductn lsses (.e. n ltage dp dung the n-state nteals).. All semcnduct deces hae deal swtchng beha wth ze tun-n and tun-ff swtchng lsses. 3. Stay nductances and capactances asscated wth bus-bas ae neglgble. 4. Resnant capacts ae dentcal and lssless. 5. Resnant nducts ae dentcal and lssless. 6. Input and utput dc buses hae cnstant ltage wth neglgble dynamcs. In the peus chapte, the stuctues ppsed f all cnete ccuts assume duble platy mult-cell ealzatn as a geneal case. It was shwn that each cnete can als cnnect sngle platy buses wthut specal nsulatn technques mantanng a cmmn gund etun f bth nput and utput dc buses. Thughut ths chapte, sngle platy sngle cell ealzatn f all cnete ccuts wll be assumed. Wthut lss f genealty, ths assumptn helps educe the numbe f aables n the deed equatns. The sngle platy tplges ae shwn n Fg Analytcally, ths use f sngle platy mples the fllwng elatns t the tplges pesented n the peus chapte: (3.1) (3.) (3.3)

72 53 (3.4) N n c n (3.5) whee N s the numbe f sees ntecnnected cnete cells. s c (a) * c s D D (b) c s * c s s c D (c) * c s Fgue 3-1 Smplfed stuctue f (a) step-dwn, (b) step-up and (c) netng cnetes

73 Resnant capacts desgn The fundamental elatns descbng the beha f the ppsed cnete ae the enegy and pwe elatns. Ths sectn dees these elatns f the step-up, step-dwn and netng cnetes. Snce the bdectnal cnete epesents a hybd cnnectn between step-dwn and step-up cnetes, the same elatns apply t t Step-dwn cnete In Sectn.3, the stuctue and peatng pncple f the step-dwn cnete wee pesented wth the help f the deal steady-state waefms f Fg.-6. Fm Fg. -4 and Fg.-5, we nte that each swtchng cycle extacts tw cuent pulses fm the nput bus, the enegy asscated wth each cuent pulse s: Ts / * w dt (3.6) 0 Ths nput cuent pulse passes thugh bth the nput and utput suces and flws nt the sees esnant ccut. Ths descbes nteals (a) and (d) shwn n Fg. -4 t Fg. -6. Thus equatn (3.6) can be e-wtten as: Ts / * w dt (3.7) 0 c Ths cuent pulse chages ( dschages) the esnant capacts causng ltage swng between c = c pk and c = - c pk, whee c pk =. Thus equatn (3.7) yelds: w * d c (3.8) And the nput enegy asscated wth the whle swtchng cycle becmes: w Ts 0 dt 4 (3.9) The aeage nput pwe can then be descbed by the elatn (3.10) as:

74 55 P w 4 f s (3.10) Ts whee f s s the swtchng fequency f the swtches S 1 and S. Fnally, the desgn equatn f the esnant capact s: P (3.11) 4 f s 3.3. Step-up cnete The stuctue and peatng pncple f the step-up cnete wee pesented n Sectn.4. The deal steady-state waefms wee shwn n Fg.-10. Fg.-8 and Fg.-9 shw that each swtchng cycle wthdaws tw cuent pulses fm the nput suce. The enegy asscated wth each cuent pulse s expessed as: w * Ts / 0 dt / 0 dt Ts / / dt (3.1) In cntast t step-dwn cnete, the nput suce supples cuent n tw stages, the fst s befe the cnductn angle whle the secnd s afte t. The fst stage f the nput cuent pulse passes fm the nput bus supplyng the sees esnant ccut dung the nteal 0 t /. Ths nteal s shwn n Fg. -8 (a). The secnd stage f the nput cuent pulse flws fm the nput bus thugh the esnant nduct supplyng the utput bus dung the nteal t T / whch s shwn n Fg. -8 (b). Thus equatn (3.1) can be e-wtten as: / s w * / 0 c dt Ts / / dt (3.13) Whee c s the esnant capact cuent and s the utput cuent.

75 56 Smla t the step-dwn cnete, the fst stage f the nput cuent pulse chages/ dschages the esnant capacts causng ts ltage t swng between c = c pk and c = - c pk, whee c pk = n ths case. Thus equatn (3.13) yelds: / 0 / / * Ts Ts c dt dt d w (3.14) The enegy cntaned n the utput enegy pulse s expessed n (3.15). / 0 * Ts dt w (3.15) Assumng a lssless cnete, * w can be equated t * w leadng t: w * (3.16) Thus the utput enegy pe full cycle s: w 4 (3.17) and the aeage nput pwe expessn wuld be s f P 4 (3.18) Fnally, the capact desgn equatn f the step-up cnete s: s f P 4 (3.19)

76 Inetng cnete The netng cnete was dscussed n Sectn.5, and ts peatng pncple was explaned wth the help f Fg.-15, Fg.-16. Smla t the step-up and step-dwn cnetes, each swtchng cycle wthdaws tw cuent pulses fm the nput bus. The enegy asscated wth each cuent pulse s gen by the expessns f (3.6) and (3.7). Ths nput cuent pulse passes fm the nput bus and flws nt the sees esnant ccut. Ths stuatn descbes nteals (a) and (d) shwn n Fg. -15 and Fg Ths cuent pulse chages the esnant capacts causng ltage swng between c = c pk and c = - c pk, whee c pk = +. Thus, the nput enegy asscated wth each half-cycle s: ) ( ) ( / 0 * c Ts d dt w (3.0) And the nput enegy asscated wth the full swtchng cycle becmes: Ts dt w 0 4 (3.1) whle the aeage nput pwe wuld be: s s f T w P 4 (3.) and the capact desgn equatn f the netng cnete wuld be: s f P 4 (3.3)

77 mments The analyss pesented n sectns deelped mathematcal expessns f the enegy and pwe f each cnete ccut. Fm these expessns, the pmay desgn equatns f the esnant capacts wee pesented. In cntast t classcal ccuts, the ppsed cnetes shw dffeent behau as fllws: F a gen cnete tansfeng pwe between nput and utput dc suces, expessns (3.10), (3.18) and (3.) shw that the nput pwe s cntlled nly thugh the swtchng fequency f s.the elatn between the steady state pwe and the swtchng fequency s lnea. The pwe and enegy elatns d nt cntan the esnant nductance. Theefe, f a gen swtchng fequency the alue f the esnant nduct desn t nfluence the pwe suppled by the cnete, pded that DM peatn s mantaned. Sectn 3.6 wll tackle the nduct szng n detal. The alue f the esnant capact s detemned based n the equed pwe and ltage atng f a cnete, at a specfed maxmum swtchng fequency. The peak ltage f the esnant capacts s: f the step dwn cnetes, f the step-up cnete and + f the netng cnete. In mdula ealzatn, ths ltage s shaed equally between all capacts n the acte netwk cells. All acte swtches f each cell wll hae a fwad and eese blckng ltage. T chse the cuent atngs f the semcnduct deces, and the alue f the esnant nduct, cuent and ltage elatns f each cnete ccut wll be deed n the next sectn.

78 uent waefm f the esnant nduct Vltage waefm f the esnant capact uent and ltage n esnant elements T undestand the beha f the ppsed cnetes and hw t detemne the alue f the esnant nduct and the semcnduct atngs, t s essental t dee the mathematcal elatns genng ltages and cuents n the esnant elements. The nduct shuld guaantee DM peatn up t the maxmum pwe atng f the cnete. F these cnetes, DM peatn s a specal case f M peatn. F ths easn, M peatn wll be assumed n ths sectn f the sake f deng the equed mathematcal elatns n geneal fms. Fg. 3- shws the basc cntnuus cnductn waefms f step-dwn peatn whle Fg 3-3 shws the same waefms f step-up peatn. c pk c 0 c pk c pk I 0 T s / t Fgue 3- Basc waefms f step-dwn peatn dung cntnuus cnductn

79 uent waefm f the esnant nduct Vltage waefm f the esnant capact 60 c pk c 0 c pk pk I 0 T s / t Fgue 3-3 Basc waefms f step-up peatn dung cntnuus cnductn F all cnetes ppsed peatng n the nteal 0 t, the esnant elements ae cnnected n sees tgethe wth an extenal ltage suce ex as shwn n Fg Ths extenal suce s ( ) f the step dwn cnete, ( ) f the step-up and netng cnetes. Ths emans f a duatn t. The geneal slutn t ths secnd de ccut s: ex c t I cs t sn t, t 0 d dt / t t (3.4) c ex, 0 (3.5) whee c s the ntal ltage f the capact and I s the ntal cuent f the nduct.

80 61 ex I + - c 0 t Fgue 3-4 Equalent ccut f the cnetes when the acte swtches ae cnductng F each f the ppsed cnetes, (3.4), (3.5) yeld the fllwng: F the step-dwn cnete: t t t I t 0 sn / cs (3.6) t t t I t c 0 cs sn / (3.7) F the step-up cnete : t t t I t 0 sn / cs (3.8) t t t I t c 0 cs sn / (3.9) F the netng cnete : t t t I t 0 sn / cs (3.30) t t t I t c 0 cs sn / (3.31)

81 6 whee t 0 epesents nteals (a) n Fg. -3, Fg. -8, Fg Smla elatns hld f the nteals (d). The nduct dschage equatns apply afte the swng equatns fm / T s t whch epesents nteals (b) n Fg. -3, Fg.-8, Fg Smla elatns apples f nteal s s T t T /. The nduct dschage equatns ae as fllws: F the step-dwn cnete: / sn / cs s T t t I t (3.3) c t / T s t (3.33) F the step-up cnete: / sn / cs s T t t I t (3.34) c t / T s t (3.35) F the netng cnete: / sn / cs s T t t I t (3.36) c t / T s t (3.37)

82 The cnductn angle In de t desgn the esnant nducts, the cnductn angle needs t be calculated. Ths can be dne by equatng (3.7) and (3.33) f the step-dwn cnete, (3.9) and (3.35) f the stepup cnete, (3.31) and (3.37) f the netng cnete. At DM (I =0), ths yelds the fllwng: F the step-dwn cnete: c (3.38) F the step-up cnete: 1 cs (3.39) F the netng cnete: c (3.40) Fm the abe elatns, we nte that all ppsed cnetes peate at F the netng cnete, the step-dwn peatn ccu at , whle the stepup peatn ccu at The cnductn angle s an ntenal un-cntlled aable dependng nly n the nput and utput ltages. Fg. 3-5, Fg. 3-6, Fg. 3-7 shw the aatn f the cnductn angle wth the ltage gan ( / ) f the step-dwn, step-up and netng cnetes espectely.

83 nductn angle (deg.) nductn angle (deg.) nductn angle (deg.) 64 Vltage gan ( / ) Fgue 3-5 The ltage gan s. the cnductn angle f the step-dwn cnete Vltage gan ( / ) Fgue 3-6 The ltage gan s. the cnductn angle f the step-up cnete Vltage gan ( / ) Fgue 3-7 The ltage gan s. the cnductn angle f the netng cnete

84 Resnant nduct szng The alue f the esnant nduct s chsen t mantan dscntnuus peatn f ated pwe at maxmum swtchng fequency. Equatns (3.3), (3.34) and (3.36) ae used by applyng the fllwng cndtns: 0 I 0 at T s t Ths mples peatng at the bunday between DM and M. It yelds the fllwng: F the step-dwn cnete: 0 1 sn / s f (3.41) F the step-up cnete: 0 1 sn / s f (3.4) F the netng cnete: 0 1 sn / s f (3.43) By substtutng the alue f the cnductn angle fm (3.38)-(3.40), equatns (3.41)-(3.43) ae sled t ge the alue f the nduct that guaantees peatn at the bunday between DM and M at maxmum swtchng fequency.

85 Semcnducts cuent atngs The nduct cuent elatns f (3.6), (3.8) and (3.30) can be used t detemne the peak cuent n the acte swtches S 1, S and ts maxmum ate f change at the tun-n nstant. By substtutng f the cnductn angle alue fm (3.38), (3.39) and (3.40), the ddes peak cuents can als be detemned. Fnally, the dde cuent ate f change at ts tun-ff nstant can be detemned fm (3.33), (3.35) and (3.37). All these elatns, dung dscntnuus cnductn mde, can be summazed as fllws: F the step-dwn cnete: S pk (3.44) / ds dt nmax (3.45) D pk sn (3.46) / F the step-up cnete: d dt D ff max (3.47) S pk (3.48) / ds dt nmax (3.49) D pk sn (3.50) / d dt D ff max (3.51)

86 67 F the netng cnete: S pk (3.5) / ds dt nmax (3.53) D pk sn (3.54) / d dt D ff max (3.55) The aeage cuent n the acte swtches and ddes f all cnetes can be expessed as: f 1cs (3.56) S a S pk s D a d dt D pk f s D ff max (3.57) The elatns (3.44) t (3.57) allw the selectn f ppe semcnduct cuent atngs and the calculatn f swtchng lsses asscated wth them. The ltage atng f the acte swtches (S 1, S ) wll be dscussed n the next sectn. Fnally, t shuld be nted that the swtchng lsses asscated wth tunng-n and tunng-ff the acte swtches (S 1, S ) ae neglgble as the tun-n ccus at ZS, due t DM peatn, and the tun-ff ccus at zeltage. The stay nductance wll lmt the ate f change f the tun-n cuent f the ddes and the tun-ff cuent f the acte swtches (S 1, S ). Ths wll be dscussed n the next chapte n geate detal.

87 Semcnducts ltage atngs Ths sectn cmplements the peus sectn, by studyng the cuent and ltage waefms f the pwe semcnduct deces. Ths s useful n de t quantfy the lsses and specfy the sutable deces accdngly. Fg. 3-8 shws the ltage and cuent waefms f the swtches and ddes, f the step-dwn cnete and f the netng cnete peatng n the stepdwn mde. Fg. 3-9 shws the same waefms f the step-up cnete and f the netng cnete peatng n the step-up mde. By examnng the cuent and ltage waefms f the deces, we nte that each acte swtch stats cnductng at ze cuent fllwng a snusdal cue peakng at pk. Sectn 3.7 ges the alue f the maxmum cuent ate f change and ts peak. Then the swtch cuent natually dps t ze and the cuent cmmutates t the dde abuptly. The swtch ltage and the dde ltage at the cmmutatn nstant equal t ze. We efe t ths as ze ltage cmmutatn. Afte cmmutatn, the dde cuent deceases lnealy wth a ate f change gen n sectn 3.7 f each cnete. The dde tuns ff at ze cuent blckng a ltage D ff. Fm the fgues we nte that the swtches ae equed t hae a peak fwad blckng ltage s f wth a ate f se n the ff-state d s /dt ff and peak eese blckng ltage s, whle the dde wuld be equed t hae t tun ff at D ff and wthstand a peak blckng ltage f D pk. Quantfyng these alues s mptant t select ppe deces. Wth efeence t Fg. 3-8 and Fg. 3-9, and the capact ltage equatns f sectn 3.4, the semcnduct ltage atngs can be expessed as fllws: F the step-dwn cnete: s f (3.58) s c pk d dt s ff max (3.59) N (3.60) Dff (3.61) D pk

88 69 F the step-up cnete: s f (3.6) s c pk d dt s ff max (3.63) N Dff (3.64) (3.65) D pk F the netng cnete: s f (3.66) s c pk d dt s ff max (3.67) N (3.68) Dff (3.69) D pk

89 Vltage waefm f the dde Vltage waefms f the swtches uent waefms f the swtches and ddes 70 pk S1 D S c pk t ff t f ff S ff 0 0 S S1 c pk 0 D ff D D pk S ON D ON t 0 S 1 D ON ON 0 T s / T s t Fgue 3-8 Vltage and cuent waefms f the swtches and ddes dung step-dwn peatn

90 Vltage waefm f the dde Vltage waefms f the swtches uent waefms f the swtches and ddes 71 pk S1 D S c pk t ff t f ff S ff 0 0 S S1 c pk 0 D ff D D pk S D t t 0 S 1 D ON ON ON ON 0 T s / T s Fgue 3-9 Vltage and cuent waefms f the swtches and ddes dung step-dwn peatn

91 7 3.9 Summay In ths chapte, the ppsed cnetes hae been analytcally studed and the basc desgn equatns hae been deed. A fundamental featue f the ppsed cnetes s the lnea elatnshp between the pwe and the swtchng fequency. The alue f the esnant capact s specfed by dentfyng the pwe, ltage and fequency atngs f each cnete. The cnetes peate nly n DM and the nly cntl aable s the swtchng fequency. The cnductn angle s an uncntlled ntenal aable dependng n the temnal ltages f the cnete. Ths s a maj dffeence between the ppsed cnetes and the classcal buck, bst and buck-bst tplges. The cnductn angle s fund t ay nnlnealy wth the ltage steppng at. The alue f the esnant nduct s chsen t guaantee dscntnuus peatn at maxmum pwe and fequency atngs f the cnetes. The semcnduct cuent and ltage atngs hae been dentfed analytcally. Table 3-1 shws a summay f the basc desgn paametes dscussed n ths chapte.

92 73 Paamete Step-dwn cnete Step-up cnete Inetng cnete 4 s f P s f P 4 s f P 4 c 1 cs c 0 1 sn / s f 0 1 sn / s f 0 1 sn / s f a S 1cs s pk S f pk S / / / nmax S dt d pk c s f s max ff s dt d N N N a D max / ff D s D pk D a dt d f D pk sn / sn / sn / max ff D dt d D pk Table 3-1 Summay f basc desgn paametes deed n chapte 3

93 74 hapte 4 Pactcal Aspects Intductn Hang pesented the stuctue and pefmed basc mathematcal analyss f the ppsed cnetes n the peus chaptes, ths chapte dscusses pactcal cnsdeatns egadng mplementng the ppsed cnetes t ntecnnect dc buses. The dscussn pesented n the peus chaptes was theetcal cntanng numeus deal assumptns. Ths chapte bdges the gap between theetcal dscussns and the pactcal mplementatns pesented n chapte 5. Ths chapte stats by studyng the mpact f ntecnnectng dc buses wth the ppsed cnetes n netwk fault ppagatn. In ths cntext, t s mptant t undestand whethe a fault at ne cnete temnal wll be suppled fm the the temnal, thugh the cnete, and whethe ths fault culd esult n sht-thugh mdes f the acte swtchng netwks. The swtchng and cnductn lsses f the semcnduct deces ae als studed n ths chapte, nt nly f the beneft f estmatng the semcnduct lsses f the cnetes, but als t facltate engneeng f the themal ccut. Snce the nput and utput pwe f the ppsed tplges ae pulsed, flteng capacts ae added t the cnetes temnals. Sectn 4.4 pesents the desgn equatns f the flteng capacts. In sectn 4.5, the black-stat mde dung the step-up peatn s studed n de t dee an expessn f the mnmum black-stat tme. Sectn 4.6 studes the effect f the equalent sees esstance (ESR) n lmtng the step-up ltage at. Sectn 4.7 studes the effect f the stay nductance n the peatn f the ppsed cnetes. In sectn 4.8, the mnmum thyst tun-f tme s studed as t lmts the maxmum swtchng fequency. The chapte cncludes by pesentng systematc desgn steps f the ppsed cnetes and the desgn tade-ffs, takng nt cnsdeatn the dscussed pactcal aspects.

94 75 4. Fault ppagatn Ths sectn studes the effect f ntecnnectng dc buses, usng the ppsed cnetes, n the fault ppagatn amng these buses. It s mptant t undestand whethe a fault at ne dc bus wll be fed fm the the dc bus, thugh the cnete, and whethe ths fault culd esult n sht-thugh mdes n the acte swtchng netwks. The wst-case scena f hang a zempedance fault at the temnals f the cnete wll be cnsdeed. Fg. 4-1 shws a edaw f the smplfed tplges f Fg.3-1, hang a sht ccut at the nput temnals ( = 0). Fg. 4-3 shw the same tplges hang a sht ccut at the utput temnals ( = 0) Input temnal faults Snce the step-dwn, step-up and netng cnetes nly allw undectnal pwe flw, fm the nput suce t the utput suce (as shwn n Fg. 3-1), a fault n the nput sde wll nt be fed fm the utput sde. Fg.4-1 shws the cnetes dung the fst swtchng nteal whle S 1 s clsed. Snce S 1 allws cuent t flw nly n the dectn ndcated by the aw, the nput sde fault cuent wll be blcked by S 1 n case f the step-dwn cnete (Fg. 4-1 a). F the step-up cnete (Fg. 4-1 b), the fault cuent wll be blcked by the utput dde ale D. The same apples t the netng cnete (Fg. 4-1 c), whee the fault cuent s als blcked by the dde. Ths scena s ald f the fault ccus dung any f the the swtchng nteals. Fm the abe dscussn, we cnclude that the fault cuent at the nput temnals f the cnetes wll nt be fed fm the utput bus. Ths cnclusn emans ald n case f symmetcal asymmetcal faults f bpla cnetes. It shuld be nted, hwee, that n case f the netng cnete (Fg. 4-1 c), the nput fault cuent wll be fed fm the sted enegy f the esnant ccut. Ths s demnstated n Fg.4-. If the fng sgnals ae nt stpped, each swtchng nstant wll allw the faulted temnals t be suppled by dscntnuus cuent pulses hang half-snusd waefms descbed by:

95 76 (4.1) / c t sn t whee c s the ntal capact ltage at the begnnng f each swtchng nstant whch equals (- ) f the fst pulse and (- ) at steady-state. Equatn (4.1) shws that ths cuent wll hae lwe peak cuent than nmnal cuent gen by (3.53), as shwn n Fg.4-. Ths cuent can smply be suppessed by stppng the fng sgnals. 4.. Output temnal faults Step dwn cnete In case f faults at the utput sde, the beha f the cnetes aes. Fg.4-3 (a) shws a fault at the utput temnals f a step-dwn cnete whle S 1 s clsed. Ths fault cuent s suppled fm the nput bus thugh the esnant ccut. If the fault ccus befe S 1 clses, upn clsng the swtch the ntal fault cuent pulse equals t the nduct cuent and s descbed by: (4.) / t sn t Equatn (4.) nly descbes the fst pulse f the fault cuent and shws that t wll hae slghtly hghe peak cuent than nmnal cuent gen by (3.45); as descbed n Fg.4.4. It s mptant t nte that ths cuent wll cmmutate fm S 1 t D when the capact ltage s chaged t the alue f the nput ltage. The capact ltage wll eman chaged t afte the cuent cmmutatn, theefe the cuent f the swtch S 1 wll natually dp t ze. As a esult, n sht-thugh ccus t S 1 afte the fault nstant. Ths s well demnstated n Fg.4-4. The fault cuent wll eman cculatng n the utput ccut thugh the dde but wll nt be fed fm the nput bus.

96 77 s + - (a) s fault D D (b) s fault - + s s + - D (c) fault s Fgue 4-1 Ze mpedance nput fault cndtn f the (a) step dwn, (b) step up and (c) netng cnetes

97 Swtches cuent waefms Induct cuent waefm apact ltage waefm 78 c pk c pk f c 0 c pk f c pk pk pk f 1 pk f pk pk f 1 pk f s s1 Pe-fault Dung Fault t Fault nstant Fgue 4- Vltage and cuent waefms f the netng cnete dung a ze mpedance nput fault cndtn dung the step up mde

98 79 s + - (a) s D fault D (b) - + s fault s s + - D (c) s fault Fgue 4-3 Ze mpedance utput fault cndtn f the (a) step dwn, (b) step up and (c) netng cnetes

99 80 Upn detectng the fault, gatng sgnals shuld be suppessed. Othewse, the fault cuent wll ncease afte each swtchng sgnal as shwn n Fg.4-4. In ths case, equatn (4.) des nt apply as the cnete peates n the M. At M, the nduct cuent afte each swtchng nstant wll be descbed by (4.3). (4.3) / t I cs t sn t whee I s the ntal cuent f the nduct befe swtchng. Een dung M, afte each swtchng nstant, the swtch cuent wll always tun-ff natually as the cuent cmmutates t the dde wth n sht thugh mde. If the fault ccued afte cmmutatn whle the nduct (and the dde) s cnductng, the cnete entes M afte the fst swtchng nstant. In ths case, the fault cuent fllws equatn (4.3) whee I s the ntal cuent f the nduct befe swtchng. The swtch cuent wll als tun-ff natually as the cuent cmmutates t the dde wth n sht thugh mde. Fm ths dscussn we cnclude that a fault at the utput temnals f the step-dwn cnetes can be peented fm ppagatn t the nput bus by suppessng the gatng sgnals, and wll nt esult n sht-thugh mdes n the swtches Step-up cnete In case f a fault at the utput temnal f the step-up cnete shwn n Fg. 4-3 (b), we nte that ths fault wll be fed dectly fm the nput bus thugh the dde ale. Unlke the case wth the step-dwn cnete whee the fault cuent pass thugh the esnant ccut, the fault cuent f the step-up cnete nly passes thugh the nduct. Ths means that the cuent wll cntnue nceasng lnealy chagng-up the nduct uncntllably. Ths shws that a fault at the utput temnal f a step-up cnete wll ppagate t the nput bus een f the gatng sgnals ae stpped. An exceptn t ths wuld happen f a hgh mpedance fault ccus esultng n a fault ltage, at the utput temnals, hghe than the nput ltage f the cnete. In ths case stppng the gatng sgnals wll stp supplyng the fault cuent.

100 Inetng cnete In case f the netng cnete shwn n Fg. 4- (c) hang a fault at ts utput temnal whle S 1 s clsed, we nte that the fault cuent s suppled fm the esnant nduct, but has n dect cnnectn t the nput bus. Intally upn clsng S 1 afte the fault nstant, the nduct cuent s descbed by: (4.4) / c t sn t whee c s the ntal capact ltage at the begnnng f the swtchng nstant whch equals t (- - ) f the fst pulse and (- ) at steady-state. Equatn (4.4) shws that ths ntal cuent wll hae the same peak alue as the nmnal cuent gen by (3.53). It s mptant t nte that ths cuent wll cmmutate fm S 1 t D at the nstant t when the capact ltage s chaged t the alue f the nput ltage. The capact ltage wll eman chaged t afte the cuent cmmutatn. Theefe the cuent f the swtch S 1 wll natually dp t ze. Smla t the step-dwn cnete, n sht-thugh ccus t S 1 afte the fault nstant. Ths s well demnstated n Fg.4-5. The fault cuent wll eman cculatng n the utput ccut thugh the dde but wll nt be fed fm the nput bus. Upn detectng the fault, gatng sgnals shuld be suppessed t peent nceasng the fault cuent by anthe cuent pulse. If gatng sgnals dd nt stp, the fault cuent wuld ncease afte each swtchng sgnal as shwn n Fg.4-5. In ths case, equatn (4.4) des nt apply as the cnete peates n the M. At M, the nduct cuent afte each swtchng nstant wll be descbed by (4.3) smla t the step-dwn cnete. Een dung M, afte each swtchng nstant, the swtch cuent wll always tun-ff natually as the cuent cmmutates t the dde. If the fault ccued whle the nduct (and the dde) s cnductng, the cnete entes M afte the fst swtchng nstant. In ths case, the fault cuent fllws equatn (4.3) whee I s the ntal cuent f the nduct befe swtchng. The swtch cuent wll als tun-ff natually as the capact ltage s chaged t the alue f the nput ltage and n sht thugh ccus t the swtches. Fm ths dscussn we cnclude that a fault at the utput temnals f the step-dwn cnetes can be peented fm ppagatn t the nput bus by suppessng the gatng sgnals, and wll nt esult n sht-thugh mdes n the swtches.

101 Swtches cuent waefms Induct cuent waefm apact ltage waefm 8 c pk c 0 c pk pk f pk f 1 pk pk f pk f 1 pk s Pe-fault Dung Fault t Fault nstant Fgue 4-4 Vltage and cuent waefms f the step-dwn cnete dung a ze mpedance utput fault cndtn at ts temnal

102 Swtches cuent waefms Induct cuent waefm apact ltage waefm 83 c pk c 0 c pk pk f 1 pk pk f 1 pk s s1 Pe-fault Dung Fault t Fault nstant Fgue 4-5 Vltage and cuent waefms f the netng cnete dung a ze mpedance utput fault cndtn at ts temnal

103 Semcnducts pwe lsses The effcency f ppsed cnetes can be estmated by calculatng the lsses f aus cmpnents. In ths sectn, we fcus n the lsses asscated wth acte and passe swtches. These lsses ay dependng n the type f the swtch, but ae geneally cmpsed f cnductn and swtchng lsses. An estmate t these lsses can be btaned by examnng the ltage and cuent waefms f the deal swtches dscussed n the peus chapte, and the lss nfmatn btaned fm the manufactues datasheets and applcatn ntes [38]-[41]. In ths chapte, thysts wll be used as acte swtches Thyst lsses An estmate f the thyst lsses can be btaned usng the nfmatn gen n the dece s datasheet, these lsses cnsst f the fllwng [38]-[40]: 1. On-state lsses, dung thyst cnductn.. Off-state lsses, due-t the leakage cuent whle the dece s ff. 3. Tun-n lsses. 4. Tun-ff lsses. The n-state lsses depend n the ltage dp acss the thyst (V T ) and the cuent thugh t (I T ) when the dece s n. F EUPE T1503N, the n-state ltage s between.8 3 V. It can be estmated appxmately fm the fllwng lnea elatn [40]: V T V 0 I (4.5) T T T whee the slpe esstance ( T ) and the theshld ltage (V TO ) ae gen n the datasheet. Altenately, a me pecse functn t calculate the n-state ltage s [40]: V T T IT D IT A B I ln 1 (4.6) whee the paametes A,B,,D ae gen n the data-sheet. The n-state lsses (W ON-State ) pe swtch pe cycle can then be expessed as:

104 85 W ON State / 0 V T s dt (4.7) whee s s the thyst cuent (I T n the datasheet), and s = V T when the dece s n. The ff-state lsses depend n the ff-state fwad and eese leakage cuents ( l ) whch equal t 600 ma f EUPE T1503N at ated ff-state fwad and eese ltages ( ated ) and maxmum tempeatue. The ff-state lsses (W OFF-State ) can be calculated by cnsdeng a lnea elatn between the leakage cuent ( l ) and the ff-state fwad and eese ltages and can be expessed as: W OFF State t ff t 0 f ff l s ated dt (4.8) The tun-n lsses (W Tun-ON ) n a thyst ae geneated afte tggeng. When the thyst s tggeed, the ande t cathde ltage stats t dp dynamcally tll t eaches the statc nstate ltage V T. Dung ths ntal cnductn tme, the thyst ltage wll be hghe than the statc ltage, geneatng exta lsses. Sme manufactues gne these lsses fm the datasheets [40]. Othes [39] pde cues f tun-n enegy pe cycle, f dffeent ates f se f the n-state cuents. In ths thess, lght tggeed thysts (TT) ae assumed and the manufactue gnes the tun-n lsses fm the datasheets [40]. The tun-ff lsses (W Tun-OFF ) n a thyst ase fm the eese ecey phenmenn. Smla t all mnty cae deces, when a thyst tuns ff, a eese-ecey cuent s geneated. Its ampltude depends pmaly n the ate f cuent decease. Theefe, thyst cuent becmes mmentaly negate eachng a peak alue f I RM befe etunng t ze dung the ecey phase. A smple dagam f ths phenmenn s shwn n Fg.4-6. Fm ths fgue, the eese ecey enegy lss (W Tun-OFF ) pe cycle s expessed as: W t dt I t RM Tun OFF s s S ff (4.9) 0

105 86 Fm the manufactue s datasheet, the peak eese ecey cuent I RM and the eese ecey chage Q ae btaned. Usng these data, wth the smple mdel f Fg.4-8, t 1 and t can be calculated fm the fllwng elatns: d I RM t 1 (4.10) dt Q I RM t 1 t (4.11) S t t 1 0 S 0 d/dt T Q I RM S ff Fgue 4-6 nea mdel t estmate the eese ecey lsses Snce thysts tun ff at ze ltage (.e. S ff = 0), the eese ecey lsses ae deally ze. Dung the eese ecey a thyst acts as a cuent suce. Pactcally, an R snubbe ccut may be cnnected paallel t hgh ltage thysts t dsspate the eese ecey chage and ad ngng n the ccut [4]. In ths case, the lsses asscated wth the snubbe ccut wuld be taken nt cnsdeatn.

106 Dde lsses Smla t the thyst, a dde wll hae the fu types f lsses mentned abe. The n-state lsses can be calculated fm (4.7) afte calculatng the dde n-state ltage usng ethe (4.5) (4.6). The ff-state lsses can be calculated fm (4.8) knwng the eese leakage cuent and the eese ltage f the dde. The tun-ff lsses due t eese ecey can be estmated fm (4.9) usng the same technque f the thyst. The tun-n lsses (W Tun-ON ) pe cycle can be estmated fm the fllwng elatn [4]: W Tun 1 dd ON VFRM t f (4.1) 6 dt whee V FRM s the peak fwad ecey ltage at the tun-n cuent ate f change, and t f s the tme cnstant f V FRM. When tuned n wth a hgh cuent ate f change, the ntal fwad ltage f the dde expeences an esht. Ths esht gnates fm the fact that cnductty f the dde s educed, because the numbe f fee chage caes aalable s much lwe than n the steady-state. The dece needs tme t buld up the equed electn and hle cncentatn, wthn the bulk f the slcn [4]. In the dde data sheet, V FRM s gen as a cue aganst the cuent gadent pe wafe unt aea.

107 Flteng capacts In the peus dscussns, deal nput and utput ltage suces wee cnnected t the nput and utput temnals f the ppsed cnetes. In pactce, nput and utput flteng capacts wll eplace these ltage suces. The desgn f these capacts depends n a pe-specfed alues f the ampltude f the nput and utput ltage pples Δ, Δ. afte each swtchng nstant. Fm (3.8), (3.17) and (3.1), szng the flteng capacts can be dne as fllws: F the step-dwn cnete: f nput (4.13) f ut (4.14) F the step-up cnete: f nput (4.15) f ut (4.16) F the netng cnete: f f nput (4.17) ut (4.18)

108 Black-stat dung step-up peatn Upn statng the step-up cnete the netng cnete (n the step-up mde) whle the esnant capacts ae dschaged, a ltage buld-up pcess takes place. Dung ths pcess, pwe s wthdawn fm the nput bus t chage the capacts but n cuent s njected n the utput bus. Ths pcess was explaned n the peus chapte wth the help f Fg.-11, Fg. -1 and Fg In ths sectn, we ae nteested t study the stat-up dynamcs n de t btan a elatn f the black-stat tme. Fm (3.4) and (3.5), the DM nduct cuent and capact ltage dung the stat-up pcess can be descbed as fllws: c t sn t t 0 / (4.19) c t. cs t c 0 t (4.0) Whee c s the esnant capact s ntal ltage at the nstant f swtchng. The peak alue f the nduct cuent ccus at t / 4 whch yelds: T c c pk sn T / 4 (4.1) / / and the peak capact ltage ccus at t / whch yelds T c pk c T / c cs (4.) The expessn n (4.) means that each swtchng nstant (.e.half-swtchng cycle) esults n chagng the capact and amplfyng ts ltage by. Snce the cnete s ltage buld-up pcess ends when the capact s ltage equals f the step-up cnete and f the netng cnete, the black-stat tme can be expessed by (3.6) and (3.63) espectely: T T T s BS (4.3) 4 f s T s BS (4.4) 4 f s

109 The ESR effect n the maxmum step-up at The analyss dne n the peus sectn assumed lss-fee cnete. As a esult, n bunday n the maxmum ltage steppng at has been dentfed. In pactce, the esnant ccut expeences a degee f dampng. Ths dampng s caused by the esstances f the cmpnents n the esnance path. Ths ncludes the equalent sees esstance (ESR) f the esnant nduct and capacts as well as the cllecte esstance f the swtches. Takng ths dampng nt cnsdeatn wll allw us t dee an expessn f the maxmum ltage steppng at at DM. nsdeng a lumped esstance n the esnant ccut, the nduct cuent and capact ltage elatns wll be gen by: t e I t d t c d 1 sn (4.5) t e t t t d d c d c 1 tan cs (4.6) whee c s the ntal capact ltage at the begnnng f the swtchng nstant. Dung the stuatn f a maxmum steppng at, tatng the esnant capact desn t yeld any ltage step-up. Mathematcally ths s expessed by the fllwng cndtn max, T t at c c (4.7) Substtutng (4.7), (4.5) nt (4.6) and neglectng / T yelds: D D d d max (4.8) Whee D s a negate quantty equal t: d d T d d T c T e T D, 4 1, 4 1, tan cs 1 At ths cndtn, n cuent eaches the utput ccut and all the nput pwe s dsspated nt the lumped esstance.

110 Effect f the stay nductance As pat f the ccut nn-dealtes, a stay nductance c n the cmmutatn ccut wll nfluence the peatn f the cnetes. The stay nductance c exsts due t the bus-bas nductance, the nductance f the swtches, capact and ddes. The effect f ths nductance appeas dung cmmutatn. In the deal cnetes, the cmmutatn eent s an nstant n whch the cuent f the esnant nduct cmmutates abuptly t the utput ccut. Any nductance n sees wth the dde, wth the acte swtchng netwk wll ppse ths abupt cmmutatn by elngatng t. The esult appeaed as a sft swtchng f the dde tun-n and the swtches tun-ff, as the cuent wll hae fnte slpe dung cmmutatn. Fg. 4-7 and Fg. 4-8 shw hw the cmmutatn nductance nfluences the waefms dung step dwn peatn, whle Fg. 4-9 and Fg shw ts nfluence n the step-up peatn. The waefms ae geneated f an exaggeated alue f the stay nductance t ease demnstatng ts effect. By examnng the abe fgues, the fllwng cmments can be made abut the nfluence f the stay nductance n cmmutatn: The stay nductance c elngates the cmmutatn ped and educes the acte swtch tun ff tme. By elngatng the cmmutatn ped, esnant capacts ae echaged. The cnete s pwe nceases f a gen swtchng fequency. As the peak capact ltage nceases, the peak nduct cuent nceases. The swtches shuld blck a hghe peak capact ltage and wthstand hghe peak nduct cuent. The peak blckng ltage f the dde nceases, and ts peak cuent nceases as well. The dde and swtches wll hae lwe cuent ate f change dung cmmutatn. The tun-ff ltage f the swtches has a nn-ze alue The tun-ff ltage f the dde s unaffected.

111 uents f the swtches and ddes Resnant nduct cuent Resnant capact ltage 9 * c pk c pk c pk 0 c pk c wthut c c wth c c c * pk * pk pk wthut c pk wth c * pk pk wthut c wth c mmutatn ped wth c 0 mmutatn nstant wthut c t Fgue 4-7 The nfluence f the cmmutatng nductance n the cuent and ltage waefms dung step-dwn peatn

112 Vltage waefm f the dde Vltage waefms f the swtches uents f the swtches and ddes 93 * pk pk pk wthut c wth c S wthut c 0 S wth c D pk 0 D wthut c D wth c D ff D pk * D pk D pk mmutatn ped wth c t 0 mmutatn nstant wthut c Fgue 4-8 The nfluence f the cmmutatng nductance n the cuent and ltage waefms f the swtches and ddes dung step-dwn peatn

113 uents f the swtches and ddes Resnant nduct cuent Resnant capact ltage 94 * c pk c pk c pk 0 c wthut c c wth c c pk * c pk * pk pk pk wthut c wth c * pk pk wthut c pk wth c t mmutatn ped wth c 0 mmutatn nstant wthut c Fgue 4-9 The nfluence f the cmmutatng nductance n the cuent and ltage waefms dung step-dwn peatn

114 Vltage waefm f the dde Vltage waefms f the swtches uents f the swtches and ddes 95 * pk pk pk wthut c wth c S wthut c S wth c 0 D pk 0 D wthut c D ff D wth c D pk * D pk D pk t 0 mmutatn ped wth c mmutatn nstant wthut c Fgue 4-10 The nfluence f the cmmutatng nductance n the cuent and ltage waefms f the swtches and ddes dung step-dwn peatn

115 96 We cnclude that the nfluence f the stay nductance wuld hae sme adantages by nceasng the cnete s pwe densty and lweng the cuent deates. Ths cmes wth the cst f hghe blckng ltage f the semcnducts and hghe lsses. Quantfyng these nfluences ae dne thugh smulatn mdels, as btanng clsed mathematcal elatns can be qute cmplex. F example, wth the effect f the stay nductance, the dde cuent f the step-up cnete appeas as: D ( ( c c c ) / c ) / sn sn cs t / sn t c t c c c c c / (4.9) whee c s the capact ntal ltage, s the capact ltage at and c 1/ c. c

116 Thysts tun-ff tme In case f usng thysts as acte swtches, upn cmmutatn a fnte tme delay must elapse befe the dece can agan be pstely based mantanng ts ff-state. Ths mnmum delay s called the ccut cmmutated tun ff tme (t q ). Dung the desgn stage, the thyst tun ff tme at maxmum pwe shuld be hghe than t q. Ths wll put a cnstant n the maxmum swtchng fequency f the cnete. Fm Fg. 3-7, Fg. 3-8 ths mples that t ff t q. Fm equatns (3.7), (3.9), (3.31) ths ssue can be cnsdeed by ensung the fllwng cndtns ae met: F the step-dwn cnete: s q T t 1 cs (4.30) F the step-up cnete: s q T t cs 1 (4.31) F the netng cnete: s q T t cs 1 (4.3)

117 98 The cndtns (4.30), (4.31) and (4.3) mply an abslute maxmum swtchng fequency f each cnete as fllws: F the step-dwn cnete: q abs s t f 1 1 max cs cs 1 (4.33) F the step-up cnete: q abs s t f cs cs max (4.34) F the netng cnete: q abs s t f cs cs max (4.35) The desgne shuld ensue that the chsen swtchng fequency be lwe than the maxmum alues gen n the abe elatns. If swtches the than thysts ae used, such as symmetcal IGTs, RB-IGBTs then the abe fequency cnstants ae nt necessay. The cnete s fequency wll nly be lmted by the ctcal electcal lmts f the ltage and cuent gadents f the deces, the themal lmts f the ccut, and the swtchng lsses.

118 Desgn steps The desgn pcess usually ncludes seeal tade-ffs between the cmpnent cst, sze, lsses and aalablty. A smplfed desgn flw-chat s shwn n Fg Geneally, the fllwng desgn steps can be fllwed t desgn any f the ppsed cnetes: 1. Detemne the maxmum pwe and temnal ltages f the cnete.. hse an acte swtch and the utput dde. The acte swtch shuld at least wthstand half the aeage cuent f the lw-ltage sde. The dde shuld wthstand the aeage cuent f the hgh-ltage sde. If the cnete pwe s t hgh, cnsde ddng ths pwe amng paalleled nteleaed cnetes, paalleled cmpnents. 3. Detemne the sze f the capact fm (3.11) (3.0) (3.4). T d ths, chse a alue f the maxmum swtchng fequency belw (f s = 1/t q ). 4. Detemne the sze f the nduct fm (3.4) (3.43) (3.44). T d ths, calculate the alue f the cnductn angle fm (3.39) (3.40) (3.41). 5. Adjust the alue f the nduct and/ the swtchng fequency t satsfy the cndtns (4.30) (4.31) (4.3). Repeatng steps 3 and/ 4 mght be equed. 6. alculate the ctcal cuent and ltage paametes f the semcnducts fm sectns 3.7 and 4.4; als detemne the numbe f cnete cells and sees ddes. Fnally, estmate the cnete lsses fm sectn Estmate the alue f the stay nductance and smulate ts effects n the ccut f t s hghe than % f the esnant nductance. 8. alculate the alue f the capact f each cnete cell fm (3.5).

119 100 P,, P Inteleaed? *, S a Da Select Deces f s t q * lsses End Fgue 4-11 Smplfed desgn flw-chat

120 Desgn tade-ffs In ths sectn we befly dscuss the desgn tade-ffs asscated wth sme desgn bjectes. we cnete sze/weght: ths can be dne by peatng the cnete at the hghest pssble fequency. Ths hwee wll mply usng fast tun-ff thysts swtches the than thysts. In bth cases ths mples hghe n-state lsses and hghe cuent and ltage ate f change. we n-state cuent: Ths can be acheed ethe by paalleled nteleaed cnetes, by paalleled thysts. In ethe case, ths esults n hghe numbe f cmpnents and hghe sze/ weght f the cnete. we peak cuents: The peak cuents can be educed by nceasng the sze f the esnant nduct, effectely by educng the maxmum swtchng fequency. Ths esults n hghe sze and weght f nduct and als hghe alue f the esnant capacts. we cuent deates: Ths can be educed by nceasng the sze f the esnant nduct and addng a cmmutatng nduct. The tade-ffs f bth slutns has been dscussed n the peus pnt and sectn (4.7) espectely. Usng lw n-state ltage dp thysts: Ths leads t lwe n-state lsses but usually hae als hghe swtchng lsses and tun-ff tmes. Usng paallel swtches ddes: Ths wll natually esult n hghe numbe f cmpnents t educe the n-state cuent. Ths wll esult n hghe ff-state lsses but wn t change the nstate lsses cnsdeably.

121 Summay In ths chapte numeus pactcal cnsdeatns hae been studed t cmplement the dscussn n the pecus chaptes. The study f the ze-mpedance faults at the utput temnals f the cnete shw that n sht-thugh mdes can ccu t the acte swtches dung the fault. Wth the exceptn f the step-up cnete, faults at the utput temnals f the step-dwn cnete and the netng cnetes can be peented fm ppagatng t the nput temnal f the cnete by suppessng the gatng sgnals. Expessns f the cnductn and swtchng lsses f the semcnducts hae been deed n ths chapte. Ths wll be used n the next chapte t quantfy the semcnduct lsses f each f the ppsed tplges. The desgn equatns f the dc flteng capacts hae been deed. Expessns f the black-stat tme f the step-up cnete and the netng cnete (n the step-up mde) hae been deed. Studyng the beha f the step-up cnete and the netng cnete (n the step-up mde) takng nt cnsdeatn the ESR, eealed an expessn f the maxmum theetcal ltage step-up at. The stay nductance f the ccut was als studed n ths chapte. It was fund that ths nductance wll lmt the ate f change f the dde cuent and the acte swtches cuent dung cmmutatn. It wll cntbute t chagng the esnant capact and wuld esult n hghe blckng ltages n the pwe semcnducts. In case f usng thysts as acte swtches, t was fund the mnmum tun-ff tme wuld lmt the maxmum swtchng fequency f the ppsed cnetes. Expessns f the abslute maxmum swtchng fequency wee pesented. The chapte cncludes wth a set f systematc desgn steps f the ppsed cnetes and hghlghts the maj desgn tade-ffs.

122 103 hapte 5 Desgn Examples and Expemental Pttypng Intductn In de t pe the cncept f the ppsed cnetes f hgh ltage and hgh pwe dc-dc cnesn, ths chapte pesents desgn examples and expemental pttypng. Whle the expemental pttype s lmted n ltage and pwe atngs, the desgn examples ae dne f the tageted pwe and ltage ange f the ppsed cnetes. Fu desgn examples ae pesented f the fllwng atngs: 1. 6 MW cnetes cnnectng ±1.5, ±7.5 k dc buses.. 30 MW cnetes cnnectng ±7.5, ±33 k dc buses MW cnetes cnnectng ±33, ±150 k dc buses MW cnetes cnnectng ±7.5, ±150 k dc buses. F each desgn example, full desgn and analyss wll be dne f the step dwn, step up and netng cnetes and the esults wll be cmpaed. Appendx D extends the dscussn t bdectnal sngle nduct cnetes. These desgns yeld cmpnents szng, detemnatn f ctcal paametes and lss analyss n the semcnduct deces. The man bjecte f these examples s t undestand the lmtatns f the ppsed cnetes f hgh ltage and hgh pwe atngs, and t cmpae the lsses and the equed numbe f pwe semcnducts deces f each cnete tplgy. Dung the desgn, a safety fact f (at least) 00% s cnsdeed f the semcnducts ltage atngs. ght tggeed thysts (TT) ae used as acte swtches. Ths ensues synchnzed fng between the thysts, elmnatng the need f cmplex desgn f the gate fng ccuts. The ddes wll be f the fast ecey class. Table 5.1 and Table 5. shw seeal cuently aalable thysts and ddes. The ddes lsted n Table 5. ae pmaly desgned as feewheel ddes f hgh ltage GTOs and IGTs. They ae ptmzed f lw swtchng lsses and can wthstand hgh swtchng tansents [41].

123 104 Paamete S f pk S pk S a S RMS ds dt n max ds dt ff max T max tq Unt V A A A/ µs V/ µs V µs T553N T1503N T563N T4003N Table 5-1 mpasn between the atngs f lght tggeed thysts Paamete D pk D a D RMS D n max E max Unt V A A V J 5SDF 07F SDF 13H SDF 10H SDF 05F SDF 10H SDF 10H SDF 10H SDF SDF 04F SDF 08H Table 5- mpasn between the atngs f fast ecey ddes

124 netes desgn 5..1 Swtch selectn A lwe cnete weght/space wuld esult f the swtchng fequency s maxmzed. Fm Table 5-1, we nte that the T553N swtch has the hghest mnmum tun-ff tme (t q ) and wuld esult n a lwe swtchng fequency and hghe cnete weght/space. Theefe, T553N wll nt be selected. The T4003N swtch has the lwest tun-ff tme (t q ), but has much lwe ltage and ey hgh cuent atngs. If the T4003N s selected, ths wll esult n a lage numbe f cnete cells and lwe cuent utlzatn f the swtch. Theefe, T4003N wll nt be selected as well. The T1503N and T563N swtches hae md-ange cuent atng, hgh ltage atng and elately lw tun-ff tme (t q ). Theefe these swtches ae me sutable t chse fm t desgn the ppsed cnetes. In the desgn, an ntal swtchng fequency f 700Hz wll be used t desgn all the ppsed cnetes. Ths swtchng fequency s selected t be belw 1/t q t ensue a mnmum tun-ff tme f the swtches well abe t q, as detemned fm (4.39)-(4.41). Table 5-3 t Table 5-6 shw the fundamental paametes f the ppsed cnetes f all f the desgn examples. By examnng the alue f the maxmum aeage swtch cuent at 700Hz ( S a max ), we nte that t can be as lw as 00A f the step dwn cnete and as hgh a000a f the netng step-up cnete. The T1503N swtch s ated f an aeage cuent f 1770A whle T563N swtch s ated f 50A. If used, the T563N wll esult n hghe cst, lwe cuent utlzatn but lwe cnductn lsses. The T1503N swtch wll be ntally selected t mnmze the cnete cst. 5.. Resnant capactance The esnant capactance s detemned fm (3.11) (3.0) (3.4). The maxmum swtchng fequency was ntally chsen n the peus step as 700Hz f all the cnetes. Tables 5-3 t 5-6 ge the alue f the esnant capactance pe ple ( ) f each cnete.,

125 nete cells The numbe f cnete cells f each cnete s chsen such that a mnmum safety fact f 00% f the thyst peak ltage s guaanteed. Ths means that the desgned peak ltage f any pwe deces des nt exceed half the peak ltage n the datasheet. Based n ths, the alue f the capactance f each cell c s detemned. Desgn esults ae gen n Table 5-7. n 5..4 Dde selectn Fm Tables 5-3 t 5-6, we nte that the aeage dde cuent f step-dwn cnetes s always hghe than 1400A, wheeas t s lwe than 500A f the step up cnetes. By examnng Table 5-, we chse the dde 5SDF 13H4501 f all cnetes as t has lw tunn ltage and lw enegy ecey at elately hgh aeage cuent f 1100A. F the step-up cnetes, dde ales f sees unts cmpsng ne stng wll be used. F the step-dwn cnetes and dde ales f thee paallel stngs wll be used f the step-dwn cnetes. The stay nductance f the ccut wll be assumed t lmt the ate f change f the dde tun-n cuent t 1000 A/ µs. Ths lw stay nductance wll ntduce sgnfcant fwad ecey tun-n lsses n the dde ales but wll ensue neglgble eese ecey tun-ff lsses n the thysts. Fm the dde s datasheet, the peak fwad ecey ltage V FRM wll be 85 V/ dde. The numbe f sees dde unts n each stng wll be chsen such that a mnmum safety fact f 00% f peak ltage atng s guaanteed. Table 5-7 shws the numbe f sees ddes f each desgn example.

126 Induct szng The nducts ae szed t allw a mnmum f 100 µs dscntnuus cuent nteal at the maxmum peatng fequency f 700Hz. Ths s dne by ntducng a desgn paamete δ = 100 µs n the nduct desgn elatns f (3.41)-(3.43) t yeld (5.1)-(5.3): F the step-dwn cnete: / sn 1 f 0 s (5.1) F the step-up cnete: / sn 1 f 0 s (5.) F the netng cnetes: / sn 1 f 0 s (5.3) 5..6 Desgn esults Table 5-7 ges the fllwng detals f each cnete: () the numbe f acte swtchng cells pe ple, () the numbe f ddes n each dde ale pe ple (n d ), () the alue f the capactance n each cell (c n ) and ts peak ltage cn, whch s the peak ltage f each thyst unt. The semcnduct lsses f each cnete hae been analytcally calculated and ae shwn n Table 5-8. The lss analyss ncludes: () the ttal cnductn lsses n the thysts and ddes (W nd ) whch ncludes the n-state lsses W On-State lsses W On-State fm (4.31) and the ff-state fm (4.3). () the tun n lsses f the ddes (W Tun-ON ), () the tun-ff lsses f the ddes (W Tun-OFF ), and () the pecentage f the ttal semcnduct lsses. The swtchng lsses f the thysts ae neglected, as they tun n at ze cuent and tun ff at ze ltage.

127 108 nete Paamete a A 6 MW cnetes cnnectng ±1.5, ±7.5 KV dc buses Step-dwn Step-up In. Step-up In. Step-dwn a A , F ad , mh a A RMS max RMS A A S max a A S max pk S KA ds n max A/ s dt ds ff max ( V / s) dt D RMS max a A A D max pk D KA dd ff max A/ s dt f (Hz) s absmax Table 5-3 Desgn paametes f the cnetes f the fst desgn example

128 109 nete Paamete a A 30 MW cnetes cnnectng ±7.5, ±33 KV dc buses Step-dwn Step-up In. Step-up In. Step-dwn a A , F ad , mh a A RMS max RMS A A S max a A S max pk S KA ds n max A/ s dt ds ff max ( V / s) dt D RMS max a A A D max pk D KA dd ff max A/ s dt f (Hz) s absmax Table 5-4 Desgn paametes f the cnetes f the secnd desgn example

129 110 nete Paamete a A 10 MW cnetes cnnectng ±33, ±150 KV dc buses Step-dwn Step-up In. Step-up In. Step-dwn a A , F ad , mh a A RMS max RMS A A S max a A S max pk S KA ds n max A/ s dt ds ff max ( V / s) dt D RMS max a A A D max pk D KA dd ff max A/ s dt f (Hz) s absmax Table 5-5 Desgn paametes f the cnetes f the thd desgn example

130 111 nete Paamete a A 30 MW cnetes cnnectng ±7.5, ±150 KV dc buses Step-dwn Step-up In. Step-up In. Step-dwn a A , F ad , mh a A RMS max RMS A A S max a A S max pk S KA ds n max A/ s dt ds ff max ( V / s) dt D RMS max a A A D max pk D KA dd ff max A/ s dt f (Hz) s absmax Table 5-6 Desgn paametes f the cnetes f the futh desgn example

131 11 nete Paamete 6 MW cnetes cnnectng ±1.5, ±7.5 KV dc buses Step-dwn Step-up In. Step-up In. Step-dwn N. ells / ple 3 3 N. sees ddes c n F n c k nete Paamete 30 MW cnetes cnnectng ±7.5, ±33 KV dc buses N. ells / ple N. sees ddes c n F n c k nete Paamete 10 MW cnetes cnnectng ±33, ±150 KV dc buses N. ells / ple N. sees dde c n F n c k nete Paamete 30 MW cnetes cnnectng ±7.5, ±150 KV dc buses N. ells / ple N. sees ddes c n F n c k Table 5-7 mpasn between desgn paametes f the ppsed cnete f the fu desgn examples

132 113 nete lss 6 MW cnetes cnnectng ±1.5, ±7.5 KV dc buses Paamete Step-dwn Step-up In. Step-up In. Step-dwn P cnd KW PTun ON KW PTun OFF KW % sse.3 % 1.5 %.3 % % nete 30 MW cnetes cnnectng ±7.5, ±33 KV dc buses Paamete P cnd KW PTun ON KW PTun OFF KW % sse.1 % 1. % 1.9 % 1.8 % nete 10 MW cnetes cnnectng ±33, ±150 KV dc buses Paamete P cnd KW PTun ON KW PTun OFF KW % sse.1 % 1. % % 1.8 % nete 30 MW cnetes cnnectng ±7.5, ±150 KV dc buses Paamete P cnd KW PTun ON KW PTun OFF KW % sses 4.63 % 5.6 % 6.33 % 5.1 % Table 5-8 ss analyss f the ppsed cnetes f the fu desgn examples

133 114 Fm the desgn esults pesented n the last sectn, the fllwng cmments can be made: Semcnduct sses: Step up cnetes (netng nn-netng) hae hghe cnductn lsses n the acte swtches than step dwn cnetes. Ths s because the acte swtches n step-up cnetes cay hghe aeage cuent and theefe cntbute hghe than the ddes t the semcnduct pwe lsses. T enhance the effcency f the step-up cnetes, thysts wth lwe cnductn lsses can be used (e.g. T563N nstead f T1503N). Ths s mptant especally f the step-up cnetes wkng at hgh ltage steppng ats. The ddes f the step dwn cnetes (netng nn-netng) hae hghe aeage cuent than the acte swtches. As a esult the ddes cntbute hghe than the acte swtches t the semcnduct pwe lsses. T enhance the effcency f the step-dwn cnetes, ddes wth lwe cnductn lsses can be used, addtnal paallel ales f sees ddes can be added. Ths s mptant especally f the step-dwn cnetes wkng at hgh ltage steppng ats. The netng cnetes (step up and step dwn) hae hghe semcnduct lsses than nn-netng cnetes. Ths s bseed f bth cnductn and swtchng lsses. Ths s because they eque hghe numbe f semcnduct cmpnents t wthstand hghe peak ltages. F the same pwe atng and maxmum swtchng fequency, cnetes wth hghe steppng ats suffe fm hghe lsses. Ths s als because they eque hghe numbe f semcnduct cmpnents. The swtchng lsses f all cnetes ae geneally much smalle than the cnductn lsses, f ths ange f swtchng fequences. The swtchng lsses ae manly n the dde ales due t the fwad and eese ecey lsses.

134 115 Swtchng fequency: The chce f a maxmum fequency f 700 Hz was a bt cnseate f the step-dwn cnetes (bth netng and nn-netng). As can be bseed fm the esults, these cnetes can theetcally peate at fequences abe 800 Hz, f the selected cmpnents, wthut latng the mnmum tun-ff tme f thysts. Appendx E shws the fnal desgn paametes f the step-dwn cnetes peatng at hghe swtchng fequency. The chce f a maxmum fequency f 700 Hz f the nn-netng step-up cnetes f the fst thee desgn examples (wth lw ltage steppng at) was als cnseate as these cnetes can theetcally peate at fequences abe 800 Hz f the selected cmpnents. Anthe und f desgn wth hghe fequency than 700Hz has been caed ut and gen n Appendx E. F the nn-netng step-up cnete f the 4 th desgn example (wth hgh ltage steppng at), the swtchng fequency shuld be lweed than 700 Hz n de t guaantee adequate mnmum tun-ff tme f the thysts. Ths cnete has been edesgned and s shwn n Appendx E. F the netng step-up cnetes (at mdeate and hgh ltage steppng ats), a lwe swtchng fequency than 700 Hz f all the desgn examples s needed n de t guaantee adequate mnmum tun-ff tme f the thysts. These cnetes ae edesgned and ae shwn n Appendx E. Sze f esnant capacts and nducts: F the same pwe atng, temnal ltages and maxmum swtchng fequency, step-up cnetes eque lage alues f the esnant nducts and capacts than step-dwn cnetes. The passe enegy stage elements f the step-up cnetes help pump the cuent fm the lw-ltage sde t the hgh ltage sde. The alues f the esnant cmpnents f the netng step-up cnete ae hghe than thse f the nn-netng cnete. The ppste s ald f the step-dwn cnetes whee the esnant cmpnents hae hghe alues n the nn-netng cnete.

135 116 Inducts and capacts cuent atng: The aeage cuent f the esnant nducts ae the same f bth step-up and stepdwn cnete f smla pwe atngs. Ths means that f the cppe lsses f the nducts ae cnsdeed n the lsses, step-dwn cnetes wll hae lwe lsses as they eque much lwe nductance alue than step-up cnetes. Ths pnt s als ald f the netng step-up and step-dwn cnetes. Snce the nducts hae hgh peak cuents and ltages. A ce nducts ae pefeed n de t ad satuatng the ce mateal. The RMS and peak cuent atngs f the capacts ae equal t slghtly less than the RMS and peak nput cuent f the cnetes. Semcnducts cuent atngs: Step dwn cnetes hae lwe aeage cuent n the acte swtches than step-up cnetes. Ths s because the acte swtches eque cnductng f shte tme n the step dwn cnetes. Step dwn cnetes hae hghe aeage cuent n the ddes than step-up cnetes. Paallel dde cnnectns mght be necessay f hgh pwe step-dwn cnetes. Step dwn cnetes hae hghe cuent and ltage ate f change n the acte swtches. The ppste can be bseed f the ddes, whee the cuent ate f change s lwe n the step dwn cnete. The at between peak and aeage cuents n the swtches and ddes f all the cnetes s hgh. Ths means that all semcnducts hae lw cuent utlzatn as a cnsequence f DM peatn whch s essental t ad excesse swtchng lsses. The acte swtches eman ff f half swtchng ped. Ths causes the aeage cuent t be half the nput cuent (f the step-dwn and netng cnetes) and less than half the nput cuent f the step-up cnete. Ths als educes cuent utlzatn f the swtches.

136 117 netes lmtatns: The desgned cnetes hae a ange f semcnduct lsses between 1- % f ltage steppng ats aund 5. They hae a ange f semcnduct lsses aund 4-6 % f ltage steppng at f 0. Theefe, the hghe the ltage steppng atn, the me semcnduct lsses exst n the cnetes. When thysts ae used as acte swtches, the maxmum swtchng fequency s lmted by the mnmum tun-ff tme f the thysts. Inetng step-up cnetes ae me senste than the cnetes t ths lmtatn. Step dwn cnetes wth hgh steppng at suffe, at tun-n nstant, fm hgh cuent ate f change n the acte swtches, whch can exceed the datasheet s ctcal alues as n the futh desgn example. Ths s addessed by nceasng the alue f the esnant nduct and unnng the cnete at lwe swtchng fequency despte the fact that n latn t the mnmum tun-ff tme f the thysts ccued. Ths can be bseed fm the fnal desgn alues f the futh desgn example n Appendx E. As pe table 5.3 the swtches cay an RMS cuent that s up t 0 tmes hghe than the aeage cuent. Ths s an bus cst f usng a esnant as ppsed t a had swtched tplgy. Ths s an bus tadeff between educng the swtchng lsses thugh sftswtchng, and nceasng the cnductn lsses. Ths als mpses lmtatns n the desgn f the esnant nducts and the selectn f the esnant capacts.

137 Gaphcal mpasns Results f the analytcal study ae summazed n tables 5.3 thugh 5.8. Data s ey had t extact fm tabulated data n the peus sectn. F ths pupse, cmpaate summay s ffeed n ths sectn. The data was taken f the fnal desgn paametes f Appendx E. Fgue 5-1 mpasn between the esnant nductance alues (unts ae n m.h pe ple)

138 Fgue 5- mpasn between the esnant capactance alues (unts ae n µ.f pe ple) 119

139 Fgue 5-3 mpasn between the semcnduct lsses 10

140 11 tea Step-up Inetng step-up a a,, a Smla Smla Hghe by 0% f lw steppng we by 0% f lw steppng at and 5% f hgh steppng at at and 5% f hgh steppng at Vey clse Hghe by 0% f lw steppng we by 0% f lw steppng at and 5% f hgh steppng at at and 5% f hgh steppng at a a a RMS we than RMS RMS S a max a a a lwe hghe S pk ds dt ds dt n max ff max D a max Hgh and exceeds lmts f hgh steppng ats lw smla dd dt lwe hghe D pk ff max f s absmax lwe Hghe than 700 Hz f lw steppng at. we than 700 Hz f hgh steppng at hghe we than 700 Hz sses lwe hghe Table 5-9 mpasn between netng and nn-netng step-up cnetes

141 1 tea Step-dwn Inetng step-dwn a a Smla Smla, we by 5% f lw steppng at Hghe by 5% f lw steppng at Vey clse f hgh ltage steppng ats we by 3% f lw steppng at Hghe by 3% f lw steppng at Vey clse f hgh ltage steppng ats, Vey clse a RMS a a a RMS RMS Smla S a max lwe hghe S pk ds dt ds dt n max ff max D a max lw lw a a a lwe hghe D pk dd dt ff max lwe hghe f hghe than 800 Hz hghe than 800 Hz s absmax sses lwe hghe Table 5-10 mpasn between netng and nn-netng step-up cnetes

142 Expemental pttypng In ths sectn, expemental pttypes f the step-up and step-dwn cnetes ae bult f a 5KW scaled dwn system unnng n temnal ltages f 115V, 60V. Unpla mdula tplges ae mplemented usng tw acte swtchng cells. Fg. 5-1 shws the swtchng cells. Each cell uses SKM00GBD13D mdules t mplement the acte swtches. Each swtch cnssts f an IGBT n sees wth a dde. The sees dde s needed t ge the swtch eese blckng chaacteestcs. The 115V dc sde (lw ltage temnal) s a dc geneat. The 60V temnal (hgh ltage temnal) s mplemented by ectfyng an ac ltage usng the ectfe shwn n Fg.5-1. A esste lad bank s emplyed n the 60V bus t ensue the bus can ethe suce snk pwe as equed. The ac ltage s egulated wth the adjustable tansfme shwn n Fg The cnete ddes ae mplemented wth tw sees unts f S4110. Fg. 5- shws a pctue f the ddes and the measuement deces cnnected t the cnete mdules. The nput and utput pwe s calculated by multplyng the aeage ltage and the aeage cuent. The aeage ltage s measued wth a dc ltmete. The aeage cuent s measued by a mll-ltmete measung the ltage dp f a small sees esstance a shunt. Fg. 5-4 shws schematcs f the cnetes. Table 5-11 shws the desgn paametes f the mplemented cnetes. A tz-we fete-ce aable nduct wth lw ce lsses s used n the expemental pttypes. The bjecte f the expemental pttype s t efy the fllwng: Vltage s beng shaed equally between the tw swtchng cells f bth step-dwn and step-up peatns. Theetcal waefms f the cnetes ae aldated expementally. ss estmatn f the cnetes s aldated.

143 14 Acte swtchng cell ntl and measuements Rectfe ccut Fgue 5-4 Pctue shwng tw acte swtchng cells

144 15 Dde uent Measuement Vltage Measuement Fgue 5-5 Pctue shwng the ddes and measuement unts cut beake Adjustable Tansfme Statng essts Fgue 5-6 Pctue shwng the tansfme f the hgh ltage sde

145 16 s s 5 F 5 F 500 H s s 60 V SKM00GBD13D x S V 500 H x S4110 s 0 F s 115 V 60 V ell 1 SKM00GBD13D 0 F s s ell Fgue 5-7 Schematcs f the expemental (a) Step-dwn and (b) step-up cnetes

146 17 nete Paamete a A 5 KW cnetes cnnectng +115, +60 V dc buses Step-dwn Step-up 8 44 a A F.5 10 ad mh a A RMS max RMS A A 3 56 S max a A S max 4 18 pk A S ds n max A/ s dt ds ff max ( V / s) dt D RMS max a A A D max pk A D dd ff max A/ s dt f s (Hz) Table 5-11 Desgn paametes f the expemental cnetes

147 18 In cntast t n ce nducts, ths nduct has lw ce lsses (5 W 0.5% at full lad) f the paametes shwn n Table In cntast t a-ce nducts, ths nduct uses less amunt f cppe t ge the same dc esstance. The nduct has a dc esstance f 15 mω and uses tz we t mnmze the skn and pxmty effects. The nduct s dc esstance cntbutes t 0.6 % f the cnete s lsses at full lad. The capacts used ae SRN45R whch has flm-pape delectc. Each capact unt has a capactance f 10 µf and ated f 100A RMS, 6.5 KVA. Seeal capact unts ae cnnected nt banks t ge the equed capactance. These capacts hae e-ated alues n de t yeld lw lsses. Fg. 5-5 t Fg. 5-7 shw the expemental waefms btaned f the step-dwn cnete. Fg. 5-8 t Fg shw the waefms f the step-up cnetes. Table 5-1 shw the semcnducts paametes and Table 5-13 pesents the lss analyss f bth cnetes. D 1 Fgue 5-8 Step-dwn cnete expemental waefms. The fgue shws the nduct cuent n h1, the dde cuent n h4, the ltage f the capact f the fst cell n h and the ltage f the capact f the secnd cell n h3.

148 19 A gd matchng s bseed between the expemental waefms and theetcal nes (pesented n hapte ). We als nte a small nfluence f the stay-nductance n the waefms as expected fm sectn 4.7 n chapte 4. By nspectng the cell capacts ltage f Fg. 5-5 (f the step-dwn cnete) and Fg. 5-8 (f the step-up cnete), we nte that the ttal ltage s dded amng the tw swtchng cells equally. Ths means that the ltage stess s shaed equally between the swtches f the cnetes. Ths can als be efed by bseng the ltage waefms f the swtches shwn n Fg.5-6 (f the step dwn cnete) and Fg.5-9 (f the step-up cnete). The peak alues f the ltages and cuents ae slghtly hghe than thse stated n Table 5-11 due t the stay nductance as expected. Ths can als be bseed by nspectng the lmted ate f change n the dde cuent at swtch-n nstants, the lmted ate f change f the swtches cuents at tun-ff nstants (Fg.5-6, Fg.5-9), and the ltage acss the acte swtchng netwks (Fg. 5-7, Fg. 5-10) at these nstants. S1 S Fgue 5-9 Step-dwn cnete expemental waefms. The fgue shws the nduct cuent n h1, the capacts cuent n h4, the swtch ltage s1 n h and the swtch ltage s n h3

149 130 The hgh-fequency scllatns appeang n the ltage f the swtches (Fg. 5-6, Fg. 5-9) and dde ltage waefms (Fg. 5-7, Fg. 5-10), ae due t ngng between the utput capactance f the ddes, and the stay nductance dung the dde eese ecey. As the ddes hae nn-ze tun-ff ltage, the eese ecey chage causes these scllatns. They ae me bus n the step-up cnete as the ddes blck hghe ltage at tun-ff nstants. These scllatns hwee, ae almst neglgble n the cuent waefms f the ddes due t the slw ate f change f the dde cuent at tun-ff nstants. These scllatns can pactcally be damped wth tuned dde snubbe ccuts, f equed. Ths phenmenn s educed by usng fast ecey ddes. It s als nted that these scllatns d nt appea at the tun-ff nstants f the swtches (despte hang hghe cuent ate f change at tun-ff nstants). Ths s because the acte swtches expeence ze ltage swtchng at tun-ff. Wth ths bseatn we cnclude that snubbe ccuts n the swtches ae nt necessay. D D * Fgue 5-10 Step-dwn cnete expemental waefms. The fgue shws the nduct cuent n h1, the dde cuent n h4, the dde ltage n h and the ltage f the acte swtchng netwk c * n h3.

150 131 D 1 Fgue 5-11 Step-up cnete expemental waefms. The fgue shws the nduct cuent n h4, the dde cuent n h1, the ltage f the capact f the fst cell n h3 and the ltage f the capact f the secnd cell n h. Semcnduct dece V TO (V) T (mω) IGBT IGBT s sees dde Equalent pe acte swtch nete s dde ale Table 5-1 Semcnduct paametes f the cnductn lsses calculatns

151 13 S 1 S Fgue 5-1 Step-up cnete expemental waefms. The fgue shws the nduct cuent n h4, the capacts cuent n h1, the swtch ltage s1 n h3 and the swtch ltage s n h nete s lss paamete Step-dwn Step-up p cnd (acte swtch) (W) p cnd (dde) (W) p (cppe lsses) (W) Ttal % Effcency (calculated) 96. % 89.7 % Effcency (expemental) 95.5 % 88.7 % Table 5-13 ss analyss f the cnetes

152 133 D D * Fgue 5-13 Step-up cnete expemental waefms. The fgue shws the nduct cuent n h4, the dde cuent n h1, the dde ltage n h and the ltage f the acte swtchng netwk c * n h3.