Switching-aid Circuits with Energy Recovery

Transcription

1 BWW haper 9 Swiching id ircui wih Energy Recvery 34 9 Swiching-aid ircui wih Energy Recvery Paive urn- and urn-ff nubber circui fr he IGB ranir, he G and he G hyrir have been cidered in chaper 7. hee nubber circui dify he device I-V wiching rajecry and in ding reduce he device ranien e. Snubber circui aci invve eprary energy red in eiher an inducr r capacir. In reeing hee paive cpen i i uua diipae he red energy in a reir a hea. high frequencie hee e (being prpria frequency) ay bece a iiing facr becaue f he difficuie aciaed wih equipen cing. Inead f diipaing he wiching-aid circui red energy, i ay be viabe recver he energy back in he dc uppy r in he ad, r bh. w caificai f energy recvery circui exi, eiher paive r acive. paive recvery circui invve y paive cpen uch a and whie acive recvery echnique invve exra wiching device, a in a wiched-de pwer uppy, p. reir R newrk and he red inducr energy ½I i diipaed a hea in he reiance f he - R - circui. he pwer i deerined by he wiching frequency and i given by½i f. Fu deign and peraia apec f hi urn- nubber have been cidered in chaper Paive recvery i. Recvery in he dc uppy Figure 9. hw a agneic cuped circui echnique fr paivey recvering he inducive urn- nubber red energy back in he dc uppy V. he inducr i bifiar-wund wih a cach winding. he priary winding i deigned give he required (agneiing) inducance baed cre dieni, prperie, and nuber f urn, = N /. wich urn-ff he curren in he cuped inducr priary i divered he ecdary a ainain cinuu cre fux. he winding are arranged ranfer curren back in he uppy via a dide R which preven revere curren fw. he peraing principe f hi urn- nubber recvery chee are ipe bu a nuber f ipran circui characeriic are exhibied. e he cuped inducr have a priary--ecdary urn rai f :N. urn-ff he cach (ecdary) winding cduc and i vage i hereby caped he uppy rai V. he priary winding herefre ha an induced vage pecified by he urn rai. ha i V = V (V) (9.) p N he wich cecr vage a urn-ff i increaed, abve he uppy vage, by hi cpen, V = ( ) V (V) (9.) c N he urn rai N hud be arge a iniie he wich vage raing in exce f V. N N N n 3 R N (c) f /N R Figure 9.. nvenia inducive urn- nubber principa curren a: (a) urn- and (b) urn-ff. 9. Energy recvery fr inducive urn- nubber circui inge ended Figure 9. hw he cvenia inducive urn- nubber circui fr a inge-ended IGB ranir wiching circui. Equay he wich ay be a G r a G hyrir, fr which an inducive urn- nubber i andary, if wich deraing i be avided. wich urn- he nubber inducance cr he rae f rie f curren a he cecr vage fa zer. he wich urn wihu he refu cdii f iuaneu axiu vage and curren (V, I ) being experienced. urn-ff he inducr curren i divered hrugh he dide and Figure 9.. urn- nubber wih nubber energy recvery via a ecdary cach winding: (a) circui diagra; (b) circui wavefr; and (c) uieve recvery.

2 35 Pwer Eecric haper 9 Swiching id ircui wih Energy Recvery 36 wich urn- he inducr uppr he fu rai vage and, by ranfrer aci, he induced ecdary vage i NV. he revere-bcking vage een by he ecdary bcking dide R i V = N V (V) (9.3) c ( ) hu by decreaing he wich vage requireen wih arge N, he bcking dide revere vage raing i increaed, and vice vera when N i decreaed. ne furher deign cprie invving he urn rai i neceary. he higher he effecive pu-dwn vage, he quicker he red energy i reurned he dc uppy. he ecdary vage during recvery i fixed a V ; hence fr v = di/d he curren wi decreae ineary fr I /N zer in ie f. By equaing he agneicay red priary energy wih he ecdary energy puped back in he dc rai urce V I ½I = V ½ (J) (9.4) p f N he cre ree ie (and he wich iniu ff-ie), ha i he ie fr he agneic cre energy be reurned he uppy, i given by I = N () (9.5) f p hu he wer he urn rai N, he hrer he cre ree ie and he higher he upper wiching frequency ii. nayi aue a hr cecr curren fa ie cpared wih he cre ree ie. Priary eakage inducance reu in a a pri f he cre red energy reaining in he priary circui a urn-ff. hi energy, in he fr f priary curren, can uuay be abrbed and cred by he capaciive urn-ff nubber circui (R- nubber) acr he wich. Figure 9.c hw a recvery arrangeen wih uipe ecdary winding, ike he ink arrangeen f a dide caped uieve inverer (haper 5.3). he refeced vage, ( N / n) V, he wich i ignificany reduced a he nuber f ecdary winding, n, increae. u baancing and reguai f he capacir vage i achieved ince y he we charged (vage) capacir ha energy ranferred i. ii. Recvery in he ad Paive inducive energy recvery in he ad end n ignificany affec ad vage reguai ince he recvered energy i reaed he ad curren agniude. Figure 9.3 hw a paive inducr urn- nubber wih energy recvered in he ad and he hree recvery age. In figure 9.3b, a wich urn-ff, he inducr red energy ½I i reany ranferred he capacir in he pah - -. he wich i aued have a hr urn- ie cpared he rean perid. he capacir vage and erie rean curren are given by i ( ω ) = cω (9.6) V ( ω ) = I Z inω fer ie = ½π he dide bck prevening cinuai f reance and he fina capacir vage i V = I Z = I (9.7) When wich ubequeny urn, he energy red in i reany ranferred he inerediae rage capacir, hrugh he pah - r hwn in figure 9.3c. he energy in i ranferred prvided >, in which cae he dide c acr cduc, caping zer v. he fina vage i V = V I = (9.8) uring he ranfer f energy fr he circui vage and curren wavefr are given by equai (9.) (9.4). he vage given by (9.8) i reained uni ubequen wich urn-ff. he fina age f recvery i hwn in figure 9.3d where he capacir dup i charge a a can rae in he ad a i vage fa ineary zer in a ie, independen f he ad curren V = = (9.9) I during which ie he capacir vage fa accrding = I V ( ω ) = V = I (9.) he ad freewhee dide f hen cduc he fu ad curren I. I c Figure 9.3. Inducive urn- nubber wih nubber energy recvery inerediae capacir: (a) circui diagra; and ucceive (b) urn-ff; (c) urn-; and (d) urn-ff. 9.. cive recvery r I i. Recvery in he dc uppy Figure 9.4 hw an inducive urn- nubber energy recvery chee which uiie a wiched-de pwer uppy (p) baed he b cverer in 5.4, and hwn in figure 9.6a. wich urn-ff he energy red in he nubber inducr i ranferred he arge inerediae rage capacir via he bcking dide, b. he inducr curren fa ineary zer in ie I / V. he p i hen ued b he reaivey w capacir vage in a higher vage uiabe fr feeding energy back in a dc uppy. he capacir charging rae i dependen ad curren agniude. he p can be cred a ainain he capacir vage can, hereby fixing he axiu wich cecr ff-ae vage, r varied wih curren a ainain a can nubber inducr ree ie. ne p and rage capacir can be uiied by a nuber f wiching circui, each wih a bcking/direcing dide a indicaed in figure 9.4. he dide and wich are raed a V V. he p i peraed in a dicinuu inducr curren de in rder reduce wich and dide e and ree. If he ad and inducive urn- nubber are re-arranged be in he cahde circui, hen he cpeenary p in figure 9.6b can be ued recver he nubber energy fr capacir. V b fp > f V p fp V p ff p ee figure 9.6a Figure 9.4. urn- nubber wih acive nubber inducr energy recvery. > (a) (b) (c) (d) c r

3 37 Pwer Eecric haper 9 Swiching id ircui wih Energy Recvery Paive recvery f FF N i. Recvery in he ad Figure 9.6 iurae a paive, e, capaciive urn-ff nubber energy recvery chee which dup he nubber energy, ½V f, in he ad. he wich urn-ff preci i ha wih a cvenia capaciive nubber circui. urn-ff he nubber capacir charge he vage rai V a hwn in figure 9.7a. ubequen wich urn-, he ad curren diver fr he freewheeing dide f he wich. Siuaneuy he nubber capacir reae i charge capacir hrugh he pah hwn in figure 9.7b, When he wich nex urn ff, he nubber capacir charge and he capacir dicharge in he ad. When i dicharged, he freewheeing dide cduc. uring urn-ff and ac effecivey in parae acr he wiching device. cvenien aring pin fr he anayi f he recvery chee i a wich urn- when nubber energy i ranferred fr. Figure 9.5. nvenia capaciive urn-ff nubber hwing curren a IGB ranir: (a) urn-ff and (b) urn-. 9. Energy recvery fr capaciive urn-ff nubber circui inge ended Figure 9.5 hw he cvenia capaciive urn-ff nubber circui ued wih bh he G hyrir and he IGB ranir. urn-ff, cecr curren i divered in he nubber capacir via. he wich urn ff caped he capacir vage which increae quadraicay fr zer. he ubequen wich urn- he energy red in, ½V i diipaed a hea, ainy in he reir R. fu funcia decripi and deign prcedure fr he capaciive urn-ff nubber circui i be fund in chaper high vage and wiching frequencie, wih w wiching device, nubber e ( ½V f ) ay be high be readiy diipaed. n aernaive i recver hi energy (eiher in he ad r back in he dc uppy), uing eiher paive r acive recvery echnique. Figure 9.7. Energy recvery urn-ff nubber hwing he energy recvery age: (a) cvenia nubber aci a urn-ff; (b) inerediae energy ranfer a ubequen wich urn-; and (c) ranferred energy duped in he ad a ubequen wich urn-ff. Figure 9.6. capaciive urn-ff nubber wih paive capacir energy recvery in he ad: (a) wih a capaciive urn-ff nubber and (b) wih an R urn-ff nubber. R (a) (b) wich urn- he acive equivaen circui pri f figure 9.7b are hwn in figure 9.8a. nayi f he - rean circui wih he iniia cdii hwn yied he fwing capacir vage and curren equai. he rean curren i given by where V i( ω) = in ω () (9.) Z n Z = ω = = Z (h) Z = (h) ω n n ω = ω (rad/) ω = (rad/) n n = he nubber capacir vage decreae fr V accrding V = V ( c ω ) (V) n whie he ranfer capacir vage charge fr zer accrding n V = V ( c ω ) (V) n (9.) (9.3)

4 39 Pwer Eecric haper 9 Swiching id ircui wih Energy Recvery 33 wich urn-ff Energy duping fr in he ad and nubber aci ccur in parae and cence when he wich i urned ff. he cecr curren fa zer in ie fi a nuber f eria phae ccur. hee phae, depiced by capacir vage and curren wavefr, are hwn in figure 9.. Figure 9.8. Equivaen circui fr he inerediae energy ranfer phae f nubber energy recvery, ccurring via: (a) he ain wich and (b) hen via he nubber dide. Phae e apacir i charged nv, uni he nubber capacir charge ( n) V, i inacive. nvenia nubber urn-ff aci ccur a dicued in chaper he nubber capacir vage increae accrding I V = ½ (V) (9.5) fi whie reain charged wih a can vage f nv. hi fir phae i cpee a when I V = v = ½ = ( n) V (V) (9.6) fi whence equai (9.) equai (9.4) and he cecr curren ( nv fi ) = () (9.7) I ( ) I = () (9.8) fi equai (9.) equai (9.3) Figure 9.9. ircui wavefr during inerediae energy ranfer phae f nubber energy recvery: (a) ranfer capacir curren; (b) nubber capacir vage; and (c) ranfer capacir vage. Exainai f equai (9.) hw ha if n >, he fina nubber capacir vage a ω = π wi be piive. I i required ha reain n charge, ready fr ubequen wich urn-ff; hu n, ha i. If i greaer han equai (9.) predic wi reain a negaive vage. Wihin he pracica circui f figure 9.6, wi be caped zer v by dide cducing and awing he reaining red energy in be ranferred. he new equivaen circui fr ω = c ( n) i hwn in figure 9.8b. he rean curren, hence ranfer capacir vage are given by i( ω ) = in ( ω φ) () Z (9.4) V = nv c ( ω φ) (V) n where and φ = an n. In ainaining energy baance, fr equai (9.4) when he inducr curren i(ω) =, he fina vage i nv and reain n charge, V =. he vage and curren wavefr fr he rean energy ranfer age are hwn in figure 9.9. Figure 9.. ircui wavefr a wich urn-ff wih urn-ff nubber energy recvery when: (a) he nubber i fuy charged befre he wich curren a urn-ff reache zer and (b) he wich cecr curren ha faen zer befre he nubber capacir ha charged V. Phae w When charge ( ) n V, he capacir begin dicharge in he ad. he equivaen circui i hwn in figure 9.a, where he ad curren i aued can whie he cecr curren fa i aued inear. he fwing Kirchhff cdii u be aified

5 33 Pwer Eecric haper 9 Swiching id ircui wih Energy Recvery 33 fr fi V = V V (V) (9.9) I = i i I ( / ) () (9.) fi Under hee cdii, he nubber capacir vage increae accrding n V = ( I I ) ½ / ( n) V (V) n wih a curren i = { I I ( / )} () n (9.) (9.) r :N p /b N > /b :N he ranfer dup capacir dicharge wih a curren given by i = i / n (9.3) p r (a) (b) Figure 9.. capaciive urn-ff nubber wih paive energy recvery in he uppy: (a) baic capaciive urn-ff nubber and (b) an aernaive cfigurai. wich urn-, he nubber capacir reae wih inducr r hrugh he cuped ranfrer priary p, in he p - p - r -, reurning energy he dc uppy hrugh he cuped ecdary circui. he priary vage i V /N, and prvided hi referred vage i e han a haf V, a he energy i ranferred he dc uppy via he ranfrer. he nubber dide cap he capacir vage zer, and exce energy in r i ranferred he dc uppy, in he p p - r, a he inducr r curren fa ineary zer when pped by he referred dc ink vage via he ranfrer. In figure 9.a, he ecdary winding can be cneced he her erina f. nce he energy ranfer i cpee, he ranfrer cre agneiing curren ree zer in he ae Kirchhff p, bu a a w vage. Ree u be cpee in e cpee perid f wich. Figure 9.. urn-ff nubber equivaen circui during energy recvery in he ad when: (a) begin cduc and (b) afer he wich ha urned ff. Phae hree If he nubber capacir ha n charged he uppy rai vage befre he wich cecr curren ha reached zer, phae hree wi ccur a hwn in figure 9.b. he equivaen circui be anayed i hwn in figure 9.b. he Kirchhff equai decribing hi phae are iiar equai (9.9) and (9.) excep ha in equai (9.) he cpen I (- / ) i zer. he capacir, charging curren i given by n i = I () (9.4) n whie he duping capacir curren i i = i / n () (9.5) he nubber capacir charge ineary, accrding n I V = v (V) (9.6) i n When i charged he rai vage V, i dicharged and he ad freewheeing dide cduc he fu ad curren I. Since he nubber capacir energy i recvered here i n energy penay fr uing a arge nubber capaciance and he arger he capaciance, he wer he wich urn-ff wiching. he energy be recvered in he ad i fixed, ½V and a w ad curren eve he g dicharge ie f ay inhibi prper nubber circui aci. hi i generay n criica ince wiching e are a a w ad curren eve. upu vage reguai i reduced, ince he aun f energy recvered in he ad i independen f he ad curren. ii. Recvery in he dc uppy Figure 9. hw w urn-ff nubber circui where he energy i recvered back in he dc uppy. he ac circui peraia echani are he ae fr bh circui. When he wich i urned ff he nubber capacir charge he dc rai vage V. iii R nubber recvery he IGhyrir i cy ued and characeried wih an R nubber. he figure 9.6b hw hw he nubber dide in figure 9.6a can be repaced by a reir fr an R nubber, prvided dide i ued cap he iniu nubber capacir vage zer. he reir e are ½ V. he nubber capacir red energy afer urn-ff, ½ V, can be recvered a wich urn-, prvided he R ie can i a ea cparabe wih he rean perid an unikey cdii. 9.. cive recvery i. Recvery in he dc uppy cive energy recvery ehd fr he urn-ff nubber are iper han he echnique needed fr acive recvery f urn- nubber circui red energy. hi i becaue he energy be recvered fr he urn-ff nubber i fixed a ½V and i independen f ad curren. In he cae f he urn- nubber, he energy be recvered i ad curren agniude dependen ( α I ) which cpicae acive recvery. cive urn-ff nubber energy recvery uuay invve an inerediae capaciive energy rage age invving a piive r negaive vage rai (wih repec he eier f he principa wich). a Negaive inerediae vage rai wich urn- he nubber capacir red energy i reaed in a arge inerediae rage capacir a hwn in figure 9.3a. Recvery fr a wich urn- ccur hrugh he fwing p: a wich urn- when V > : a (a hwn in figure 9.8a and equai (9.) - (9.3)) hen when V = : a (a hwn in figure 9.8b and equai (9.4)) he wich curren i increaed by he rean curren, which ha a axiu f V / /. I i pibe ue he energy in a a negaive w-vage rai uppy. hi paive recvery echnique uffer fr he prbe ha he recvered energy ½V ay repreen re energy han he wvage uppy require. n independen buck-b p can cver exce energy red in a re uefu vage eve. Prducing he gae drive fr he p wich p preen few difficuie ince he gae-eier ha a w dc ffe and de n experience any dv/d reaive he eier reference vage f he ain wich.

6 333 Pwer Eecric haper 9 Swiching id ircui wih Energy Recvery 334 he baic recvery circui, wih he buck-b p, can fr he bai f an acive urn-ff nubber energy recvery circui when wiche are erie cneced, a cidered in eci 9.4. I ay be niced ha he uk cverer in chaper 7.6 i in fac he nubber energy recvery circui in figure 9.3a, cred in a differen de. c Wheher a piive r negaive inerediae vage i prduced, (ypicay a few en f v, bu uch higher if par f a urn- nubber recvery circui), he energy i uuay p cvered abe gae vage eve f he rder f ±5V. Since a dua rai pariy gae eve uppy i needed, he pariy f he vage (viz., piive r negaive) i incequenia. a R 9.3 Unified urn- and urn-ff nubber circui energy recvery inge ended 9.3. Paive recvery SMPS p p nvenia inducive urn- and capaciive urn-ff nubber circui can bh be incrpraed arund a wiching device a hwn in figure 8. where he red energy i diipaed a hea in he ree reir. Figure 9.4 hw unified urn- and urn-ff nubber circui which aw energy recvery fr bh he nubber capacir and inducr. ff (a) SMPS p ff p i. Recvery in he ad he nubber capacir energy i recvered by he ranfer prce uined in eci 9... Figure 9.4a hw he energy ranfer (recvery) pah a wich urn-ff. he capacir and inducr ranfer heir red energy he ad in parae and iuaneuy, uch ha he inducr vage i caped he capacir vage V. dicharge, he vage acr decreae zer, a which ie he ad freewhee dide f cduc. ny reaining inducr energy i diipaed a unwaned hea in circui reiance. Prper eeci f and ( ½I ½V ) can iniie he energy ha i ahugh a he nubber capacir energy i recvered, negecing dide and ray reiance e. he energy (cred by, and ranferred he urn- nubber inducr ) aciaed wih freewhee dide revere recvery curren, i a recvered. rev p ff c R /b V a p (b) R a :N Figure 9.3. Swiching circui fr recvering urn-ff nubber capacir energy, and fr prviding eiher (a) a negaive vage rai and/r ranferring V, via a buck-b p r (b) a piive vage rai and/r ranferring V, via a b p. b Piive inerediae vage rai piive vage urce, wih repec he ain wich eier, can be prduced wih he recvery circui in figure 9.3b. Pracicay, an exra wich, rev, i needed in rder iniie he ie f curren decay in he p -, afer he wich i urned and he vage he nubber capacir ha reaed zer. paive reir-capacir newrk can be ued ynchrie he urn- (due he ain wich urning ) and urn-ff (due dide becing frward biaed) f he w-vage wiching device rev. Recvery fr a wich urn- ccur hrugh he fwing Kirchhff curren p: a wich urn- when rev i and V > : rev fr a perid ½π hen when rev i ff and V = : - - a fr a perid V /ω V b p cr and ranfer he energy he dc rai hrugh dide p. he baic recvery circui, wih he b p, when cacade cneced, can fr he bai f an acive urn-ff nubber energy recvery circui fr erie cneced wiche, a cidered in 9.4. ii. R nubber recvery he IGhyrir i cy ued and characeried wih an R- nubber (a pped a parae cneced erie capacir-dide urn-ff nubber). he iner in figure 9.3a, fr ue in figure 9.3a and b, hw hw he nubber dide can be repaced by a reir fr an R- nubber, prvided dide c i ued cap he iniu nubber capacir vage zer. he reir e are ½ V. M f he nubber capacir red energy afer urn-ff, ½ V a wich urn-ff, (depending he R - ie can), can be recvered uing eiher f he baic circui in figure 9.3, r he circui in figure 9.6 and 9.4, prvided he R ie can i greaer han he rean perid. (c) (a) (b) Figure 9.4. Swiching circui incrpraing unified urn- and urn-ff nubber, hwing recvery pah f energy (a) in and ; (b) in and hrugh r.; and (c) recvery circui when an R nubber i epyed. wich urn- When he wich i ff, he freewhee dide f cduc he ad curren I, capacir vage V = V and V =. Phae e: P When he wich i urned, he erie inducr perfr he uua urn- nubber funci f cring he wich di/d accrding (auing he wich vage fa ie i reaivey hr) V i = (9.7) ( ) he wich curren rie ineary he ad curren eve I and hen cinue a eve I RR higher a he freewhee dide f recver wih curren in he pah hwn in figure 9.5a. hi dide revere recvery curren I RR i incuded in he anayi ince he aciaed energy ranferred he urn- inducr i ubequeny recvered.

7 335 Pwer Eecric haper 9 Swiching id ircui wih Energy Recvery 336 he peak wich curren I I RR i reached afer he durai P = ( I I ) (9.8) P RR g a he freewhee-dide cduc, he ad i caped near zer v, hu reain charged V. I RR (a) (b) (c) Figure 9.5. Unified urn- and urn-ff nubber a wich urn-, hwing (a) curren buid-up in ; (b) energy rean ranfer fr ; and (c) energy ranfer fr hrugh. Phae w: P he urn-ff nubber capacir charge reae in he pah and hrugh he wich, a hwn in figure 9.5b. he capacir vage and rean curren are given by (n = / ) i ( ω ) = i ( ω ) = inω I c ω (9.9) RR Z ω Z V ( ω ) = V ( c ) I in ω ω RR n (9.3) ω n n ω V ( ω ) = V ( cω ) Z I inω RR (9.3) n ω where V V n Z = ω = = Z (h) Z = (h) n = ω n n ω = ω (rad/) ω = (rad/) n he freewhee dide f vage i V ( ω ) = V V V (9.3) = V ( cω ) I Z inω RR When he freewhee-dide curren reache i peak recvery eve, I RR, i i abe uppr a vage which fr equai (9.3) inuiday increae fr zer. Specificay he freewhee-dide revere bia V i cred uch ha zer vage urn-ff ccur reuing in w recvery pwer e. Sray r inducance deiberaey inrduced in erie wih ( decreae he rean peak curren given by equai (9.9), apprxiaey V / Z) prduce a freewhee-dide recvery ep vage V /( ray ), where he ep i away e han V. he rean perid preaurey end (ince n < ) when he nubber capacir vage reduce zer and i caped zer by cduci f he nubber dide, a hwn in figure 9.5c. uing I RR = ( bain a racabe ui), equaing equai (9.3) zer yied he ie fr perid, P, ha i c ( n ) = (9.33) P ω a which ie i ( ) = ( n ) (9.34) P Z V V and ( ) P V = nv (9.35) Phae hree: P 3 he reaining energy red in i reany ranferred in in he pah - - -, wih iniia cdii given by equai (9.34) and (9.35), accrding V ( ω ) = nv in ( ω φ ) (9.36) and i ( ω ) = n c ( ω φ ) (9.37) Z he rean curren reache zer and energy ranfer i cpee, afer a perid ½π φ P 3 = (9.38) ω If he dide revere recvery energy i reinrduced, baed energy ranfer baance, he fina vage i ( ) ( ) P 3 V = nv Z I (9.39) RR he urn- equai (9.9) (9.37) are eeniay he ae a equai (9.) (9.4) fr he urnff nubber energy recvery circui cidered in eci 9.., excep free-whee dide revere recvery ha nw been incuded. he circui urn- vage and curren wavefr hwn in figure 9.9 are a appicabe. wich urn-ff When he wich i, i cduc he ad curren I and he nubber capacir vage i zer, whie he ranfer capacir vage V ( P 3 ) = n V = (negecing he I RR cpen) i a reu f he previu wich urn-. When he wich i urned ff, he cecr curren decreae ineary fr I ward zer in ie fi. V V R Figure 9.6. Unified urn- and urn-ff nubber a wich urn-ff, hwing (a) curren diveri nubber capacir ; (b) ranfer capacir reeaing energy (c) energy ranfer he ad iuaneuy fr and hrugh R ; and (d) energy ranfer fr in he ad hrugh R. ff Phae : P he ad curren i prgreivey divered he nubber capacir a he cecr curren decreae, giving a capacir (and cecr) vage f I v = V ( ) = ( I i ) d I d ce c fi = = (9.4) fi fi If he cecr curren reache zer befre any her aciaed recvery prcee ccur, hen afer he cecr curren ha reached zer, he cecr and nubber vage rie ineary (being caped in parae), wih curren in he pah hwn in figure 9.6a, accrding V R (a) (b) (c) (d) V R

8 337 Pwer Eecric haper 9 Swiching id ircui wih Energy Recvery 338 I I I v = V = V V (9.4) ( ) ½ prvided ½ fi fi ce he cecr vage reache V a a ie given fr equai (9.4) when V = V V a ff P = ( V V ) ½ (9.4) fi I where i given by equai (9.39) and he perid durai incude he cecr inear fa perid fi. ff Phae : P When he cecr (and nubber) vage V reache V - capacir begin dicharge in he ad prviding he ad curren I. Siuaneuy charge V hrugh, a hwn in figure 9.6b. he reevan circui capacir vage and curren are n i ( ω ) = I cω n n (9.43) V ( ω ) I Z in V V n n ω ω = (9.44) V ( ω ) I Z in V n n ω ω = (9.45) hi phae i cpee when he nubber capacir i charged he uppy vage, V, auing he inducr curren i greaer han zer a ha ie. e he inducr curren be I a he end f he ffperid ff and he capacir vage be V. P ff Phae 3: P 3 he nubber capacir i caped he rai vage. he ranfer capacir and nubber inducr bh reeae energy in parae in he ad hrugh he pah hwn in figure 9.6c. he inducr vage i caped he capacir vage. he nubber inducr curren i V i ( ω ) = I inω ( I I ) c ω (9.46) Z whie he ranfer capacir vage i V ω = V c ω Z I I inω (9.47) ( ) ( ) ne f w cdii fr he cpei f hi phae he ranfer capacir vage reache zer befre he nubber inducr curren reache zer he nubber inducr curren reache zer befre he ranfer capacir vage reache zer he fir cdii repreen he cae where he reaining inducr curren aciaed energy i a i freewhee zer in he w vage pah - - R and he ad. In he ecd cae, he inducr curren given by equai (9.46) reache zer, whie he ranfer capacir cinue dicharge in he ad a hwn in figure 9.6d. he inducr curren i prevened fr revering by dide. nce he inducr curren ha faen zer, he ranfer capacir vage fa ineary zer a i prvide he ad curren I. hi ecd cae repreen he iuai when % f a nubber (inducr and capacir ) and dide revere recvery energy i recvered, ha i ( ) I I ½ V ½ (9.48) RR Snubber ree and recvery i cpee when he nubber inducr curren and ranfer capacir vage are bh zer, he cecr vage ha raped V, and he free-dide cduc he fu ad ff curren I. Fr equai (9.47), hi age i cpee when V ( P 3 ) =, ha i ff 3 an V = P (9.49) ω Z ( I I ) Nw he wich can be urned. ii. R- dua nubber recvery he IGhyrir i cy ued and characeried wih an R nubber and an inducive urn- nubber. Figure 9.4c hw hw he nubber dide in figure 9.4a can be repaced by a reir fr an R nubber, prvided dide cbinai a - i ued cap he iniu nubber capacir vage zer. he reir e are ½ V. he nubber capacir red energy afer urn-ff, ½ V, can be recvered a wich urn-, whie he inducive urn- energy ½ I i recvered a wich urn-ff, prvided he R ie can i greaer han he rean perid. iii. Recvery in he ad and uppy Figure 9.4b hw a dua nubber energy recvery echnique where a pri f he reance energy i ranferred back he dc uppy (a pped he ad) a wich urn-, hrugh a agneicay cuped circui where i i required f he urn rai ha N >. hi reduce he energy ranferred fr he nubber he ad, giving beer ad reguai under igh ad cdii. ad reguai wih igh ad i pr ince he nubber capacir energy i fixed, ½V, independen f he ad, I. In he anayi fw, he recvery cribui f freewhee dide revere recvery energy i negeced. wich urn- he urn- phae i eeniay he ae a he circui cidered in figure 9.4a, excep he ranfrer i een a an pping ef vage urce V /N. Phae e: P he wich curren fa perid i decribed by equai (9.7) and he ie f he fir urn- perid i given by equai (9.8). Phae w: P he equai (9.9) (9.35) are dified accun fr he ranfrer referred vage V /N N i ( ω ) i ( ω ) i ( ω = = ) = in N Z ω (9.5) V ( ω ) = Nn ( N ) cω N ( n (9.5) ) n ( N ) V ( ω ) = c ω (9.5) N n ( ) ( ) he inananeu pwer being reurned he uppy hrugh he ranfrer i given by V V N N V p ( ω ) i ( ω ) = = inω = inω N N N Z N Z (9.53) he ie fr hi perid i given by equai (9.5), when he nubber capacir vage i zer nn = c P ω N (9.54) he energy reurned he uppy i n wran ( ) = = V ½ ince P < V N > N ωz N ( J) (9.55) Phae hree: P 3 Energy cinue be recvered back in he uppy V hrugh he ranfrer when he rean curren ranfer he dide. apacir charge V and i caped V by dide c. he fina vage he ranfer capacir i V ( P 3 ) = nn (9.56) N he a energy ranferred he uppy hrugh he ranfrer i he difference beween he iniia energy in and and he fina energy in. V w ( ) = ½ V ½ I ½ nn ran P P 3 N (9.57) If he urn- inducr curren reache zer befre he hird phae can cence (due N being a), hen he urn-ff nubber de n fuy dicharge, and wi ac a a f cap in he ubequen wich urn-ff cyce. he capacir reain he fwing vage Nn N V = = (9.58) N ( n ) N ( n ) n ( N ) V = V (9.59) N n ( ) wich urn-ff he circui recvery perai a urn-ff i eeniay he ae a when n ranfrer i ued (N ), excep ha he vage a he begin f urn-ff i given by equai (9.59) r equai (9.56), a apprpriae.

9 339 Pwer Eecric haper 9 Swiching id ircui wih Energy Recvery 34 peraing regi f he dua energy recvery circui Bh he paive unified recvery circui anayed can be aeed iuaneuy fr heir peraia bund, ince he bund fr he ranfrere veri in figure 9.4a are bained by eing N infiniey in he apprpriae equai fr he recvery circui in figure 9.4b. Figure 9.7 hw variu peraia bundarie fr he w unified paive energy recvery circui anayed. he variu bundarie are deerined fr he peraing equai fr he circui. he bundarie in figure 9.7a hw he regi f fu nubbering and fr f nubbering where he capacir i n ree zer vage during he rean cyce a urn-. he bundarie are uaried a fw N n < (9.6) N N n < (9.6) N he bundarie in par b and d f figure 9.7 aify equai (9.57), naey he capacir energy i e han he inducr energy. he curren i nraied wih repec nv / Z. Par d hw ha he reaive range fr % recvery, defined a ( I I) / I, i independen f he ranfrer urn rai cive recvery i. Recvery in he dc uppy Bh urn- and urn-ff nubber energy can be recvered in he dc uppy uing a dedicaed buckb p fred by p, p and p, hwn in figure 9.8. Bh nubber (capacir and inducr ) ranfer heir energy he inerediaed rage capacir,, fr which he energy i p ranferred he dc uppy V. he buck-b p a ainain a fixed vage, which faciiae rapid energy ranfer f he urn- nubber inducr energy a wich urn-ff, in ie I / V. he axiu wich ff-ae vage i V V. wich urn-, he urn-ff nubber capacir energy i reaed hrugh he p , a cidered in deai in eci he p i peraed in a dicinuu inducr curren de in rder iniie p wich and dide e and ree. he axiu p wich and dide vage are V V. Figure 9.8b and c hw circui veri wih a reduced cpen cun. Wih he inducr reved, he rean ree curren agniude and perid i nw y cred by he urn- nubber inducr. furher dide can be reved a hwn in figure 9.8c, bu he nuber f erie cpen in he urn- inducr ree pah i increae a i he p inducance aciaed wih he pah. Figure 9.7c hw he nraied (wih repec π n/ω ) ree ie a urn-ff. he ree ie a urn- i he u f perid e and w, bu i dinaed by he ecd urn- perid, naey c = ( n) (9.6) ω p p p ranfrer urn rai N: nraied ree ie n > n > f nubbering fu nubbering / / n N = N= capaciance rai / N= (a) (b) (c) (d) ax ax in in / n nraied curren nraied recvery range capaciance rai / Figure 9.7. Unified, paive nubbering characeriic: (a) peraing regi wih recvery ranfrer; (b) % recvery regi wih differen ranfrer urn rai; (c) nraied circui ree ii; and (d) nraied recvery range independen f ranfrer urn rai a N I % energy recvery < % recvery N infinie Independen f N N= N=4 / n capaciance rai / I Fig 9.4a I I I / n Figure 9.8. Unified, acive urn- and urn-ff nubber energy recvery circui: (a) baic circui and (b) and (c) reduced cpen variai. 9.4 Inverer bridge eg apaciive urn-ff nubber (wihu any urn- nubber circui inducance), bh acive and paive are n nray viabe bridge eg becaue f unwaned capacir dicharging and ubequen uncred charging curren, a cidered in chaper 8.4. be capaciive f urn-ff vage cap (peraia a >V ) can be epyed reduce urn-ff e, a hwn in figure urn- nubber p p ff i. cive recvery - recvery in he dc uppy Figure 9.9 hw inverer bridge eg where bh wiche benefi fr inducr urn- nubber and acive energy recvery circui. he circui a recver he energy aciaed wih freewhee dide revere recvery curren. he urn- energy and dide recvery energie are bh recvered back in he dc uppy, V, via a buck-b p. wich urn-ff, he energy red in i ranferred capacir via dide. Fr given urn- nubber inducance, bh circui give he ae di/d in he wiche. he capacir vage deerine he nubber ree ie. When bh circui reu in he ae wich axiu vage, he ree ie are he ae. Bu he capacir vage in figure 8.9a are haf he fr he circui in figure 9.9b. he ain peraia difference beween he w cfigurai i he perid when he capacir are charged. In figure 9.9a, bh capacir are charged a bh wich urn- and urn-ff. In figure 9.9b, each capacir charge ce per cyce, e capacir i charged a urn-, he her a urn-ff. uping f he urn- inducr reu in virua idenica wavefr a when he inducr are n agneicay cuped. N ne energy aving r gain reu. e cuping i herefre n neceary. (a) (b) (c) p p p p

10 34 Pwer Eecric haper 9 Swiching id ircui wih Energy Recvery 34 /p p p p p p p (a) (b) /p p p p p p p ad give pr reguai a w ad curren eve where he capacir urn-ff energy, which i fixed, ay exceed he ad requireen. Energy recvery invve a cuped agneic circui which can induce high vage ree acr eicducr device. Such cdii can be readiy avided if a pi capacir (uieve) vage rai, fed fr uipe ecdarie, i ued, a hwn in figure 9.c. ua nubber (inducr and capacir) energy recvery ccur a fw. Fr wich S, he urn-ff nubber i fred by S and S, and he urn- nubber cprie S.. he energy red in S i reany ranferred when wich S i wiched, in he pah S S - S - S.. he energy red i reany ranferred he dc uppy V hrugh ranfrer when wich S i urned ff and (afer an underap perid) S i urned (in he pah - r - - S). 3. When S i urned, he urn- nubber inducr S reeae i energy in parae wih capacir (in he pah S - - r - - S - S ). 4. he dide r preven (by caping) he ranfer capacir fr revere charging, by prviding an aernae pah fr he reaining energy in he rean inducr r be reurned V via he cuping ranfrer. 5. he ranfrer agneiing curren i a reurned he dc uppy V, hereby agneicay reeing he cuping ranfrer. I Irr I Irr he nuerica ubcrip and are inerchanged when cidering he recvery prcee aciaed wih wich S. he recvery circui can perae a wiching frequencie far in exce f he appicabe he IGhyrir and he high pwer IGB. he iiing peraia facr end be aciaed wih he variu nubber ree perid which pecify he wich iniu and ff ie. hugh adequae fr IGhyrir requireen, iniu and ff ie are a rerici he IGB. Irr Irr I I V V V V V V V V V V ff ff ff ff V ½V V/p V/p ½ ½ -V -½V (c) (d) Figure 9.. Unified, paive nubber energy recvery circui fr G and G inverer bridge eg. Figure 9.9. cive inducive urn- nubber energy recvery circui: (a) uipe inge-ended circui; (b) cr-cuped high frequency circui; and (c) and (d) repecivey circui wavefr urn- and urn-ff nubber i. Paive recvery - recvery in he dc uppy Figure 9. hw an inverer bridge eg where bh wiche have inducr urn- and capacir urnff nubber and paive energy recvery circui. he circui a recver he energy aciaed wih freewhee dide revere recvery curren. Bh he urn- energy and urn-ff energy are recvered back in he dc uppy, V. hugh hi decreae he energy ranfer efficiency, recvery in he ii. cive recvery - recvery in he dc uppy Figure 9. hw w iiar urn- and urn-ff nubber, acive energy recvery circui, which are paricuary uiabe fr bridge eg cfigurai. In figure 9.a, he urn- nubber eci i iiar in perai ha hwn in figure 9.4 whie he urn-ff nubber eci i iiar in perai ha hwn in figure 9.3a. c buck-b p i ued fr each urn- and urn-ff nubber pair. hi arrangeen i paricuary uefu when he w pwer wiche and aciaed freewhee dide are avaiabe in a inge iaed due package. he acive recvery circui in figure 9.b hw he inducive urn- nubber recaed. he buckb p inpu are cr-cuped, erving he urn- nubber f e wich and he urn-ff nubber f he her wich.

11 343 Pwer Eecric haper 9 Swiching id ircui wih Energy Recvery 344 he ineraci f urn-ff nubber in bh circui can creae high - rean curren a dicued in eci 8.4. In each cae, w buck-b p and inerediae rage capacir can erve nueru bridge eg, a in a hree-phae inverer bridge. hereicay he recvery p dide r can be erie cneced, hereby eiinaing a dide, a hwn in figure 9.c. Bu d aue he w inducr recvery curren are bh ynchried and equa in agniude. Exra dide, i are needed diver any inducr curren agniude ibaance, a hwn in figure 9.c, which negae he dide aving in having erie cneced he recvery dide r. ernaivey, he inge inducr recvery circui in figure 9.d ay be ued prvided he p wiche are n cducing iuaneuy. Synchriai f he p wich i aciaed ain wich avid uch iuaneu perai. he recvery circui in figure 9. par c and d are appicabe bh he bridge eg circui in figure 9. par a and b. he circui in figure 9.a i readiy reduced fr inge-ended perai, a hwn in figure 9.8. p x x r 9.5. Snubber fr he cacaded H-bridge ui-eve inverer Since he cacade uieve inverer (ee figure 5.37) i cpried f idenica H-bridge due, any f he nubber fr bridge eg cidered in eci 9.4 are appicabe. Snubber can be acive r paive, incrpraing y an inducive urn- nubber r a capaciive f urn-ff nubber r bh urn- and urn-ff nubber. When he cacaded H-bridge apprach i ued fr hree-phae Vr cpenai, rea pwer u be reurned he ac ye if he recvered energy i in exce f he inverer e Snubber fr he dide-caped ui-eve inverer Variu nubber have been prped fr he neura pin caped inverer which invve a pi dc rai cped f w erie cneced capacir, a hwn in figure Generay device are ayericay reed r indirecy nubbered. Indirec nubbering apprache hud be avided ince he ain prbe wih high pwer uieve inverer i he decuping f circui inducance. Fr eve higher han hree, y he uer wiche have a fixed dc reference, viz., r V dc, hence recvery circui hee wiche can reurn energy he uer ink capacir. Energy recvery fr nubber he inner wiche i hapered by he caping dide. hu recvery f nubber energy in a hree-eve inverer i viabe ince he w ink capacir are in fac w uer capacir, referenced he dc rai. Recvery u be in he aciaed eve capacir f a given wich, if recvery circui cpen vage raing are be iied ha f he ain wiching eeen. p ee figure Snubber fr he fying-capacir caped ui-eve inverer p p p (d) y x r r x y urn-ff nubber fr he fying capacir caped inverer are prbeaic ince he wich caping principe i baed indirec caping and he eve caping capacir uppr uipe-vage in exce f he individua device peraing vage raing. een in figure 5.36, he fying capacir aciaed wih inner wiche uppr wer vage han he uer capacir. a genera rue, if nubbering i being cidered, hen a erie cneci apprach a in eci 9.6 i viabe, prvided device wiching deay are iniied. he urn-ff deay f he Ghyrir can be reduced e han 4n if high di/d revere gae curren drive i epyed. he key iiai in revering erie cneced device perai i he f apiude duai ffered by ui-eve circui. a cequence, erie cneced device prduce higher upu dv/d vage. he neura pin caped inverer wih erie cneced device i a favured ediu vage cprie. 9.6 Snubber fr erie cneced device p i i p (c) y r ee figure Figure 9.. Unified, acive nubber energy recvery circui: (a) uipe inge-ended circui; (b) cr-cuped high frequency circui; and (c) and (d) cuped p variai. 9.5 Snubber fr ui-eve inverer he ui-eve inverer inrduced in haper 5.3 uiie erie cneced wiching eeen wih each wich peraed in a vage caped de. hree ui-eve inverer cfigurai are cy preened he dide caped ui-eve inverer ee figure 5.34 he fying capacir caped ui-eve inverer ee figure 5.36 and he cacaded H-bridge ui-eve inverer ee figure 5.37 y w baic apprache are adped when pwer-wiching device are erie cneced in rder perae circui a vage in exce f individua device vage raing. Ue a uieve rucure a cidered in haper 5.3, where individua wiche are effecivey f caped r erie cnec device wih fa urn- and urn-ff, iniiing device wiching deay hereby iprving ranien vage haring; piby uing ipe R- nubber he ue f urn- and urn-ff nubber greay increae ye cpexiy and ize bu de ffer a ehd fr reiaby peraing erie cneced device, a duar rucure, and he pibiiy f baining gae drive pwer fr individua erie cneced ce. Fa, nie free, iaed uni/bidirecia igna ranii, wihu any iai r dv/d prbe, virua any vage penia i pibe wih fibre pic. he prduci f iaed gae drive uppy pwer a en, piby hundred f kiv i prbeaic. he uua apprach fr deriving eier eve uppie invve apping energy fr aic vage haring reir, reuing in high reir e, r apping energy fr he R- nubber during wiching ranii. Bh ehd d n prvide fai-afe device perai (in he ff-ae, wih aic dv/d capabiiy) a he iniia appicai f he HV dc ink vage. he ue f inducive and capaciive wiching nubber ffer w advanage, her han enfrcing ranien vage haring f erie cneced device, which ay iigae he aciaed increaed c and cpexiy beer device I-V uiiai and a higher wiching frequency he derivai f ce eve gae pwer uppie fr nubber recvered energy Many f he previuy preened acive nubber energy recvery circui in hi chaper are direcy ranferabe uieve inverer cfigurai, hereby exending he curren and frequency capabiiie f he ain wiching device, paricuary he Ghyrir, and freewhee dide. nce

12 345 Pwer Eecric haper 9 Swiching id ircui wih Energy Recvery 346 nubber are epyed, radiia erie device cneci wih nubber i iper han a uieve apprach, bu de n ffer he uieve upu vage feaure (apiude duai and reduced dv/d) f ui-eve inverer cfigurai. he nubber recvered energy i uuay far in exce f ha ha can be uiied fr gae drive pwer. he pgica naure f erie cneced device precude any fr f reaivey ipe nubber energy recvery (acive r paive) her han recvery back in he dc ink uppy urn-ff nubber circui, acive energy recvery fr erie cneced device i. Recvery in he dc uppy Serie cneci f wiche and dide require aic vage haring (reir) and ranien vage haring circuiry, viz., capaciive urn-ff nubber fr vage haring during urn-ff and inducive urn nubber fr vage haring during urn-. Figure 9. hw erie cneced device, each duar ce eve incrpraing a ain wich and invere parae cneced freewhee dide, pu a urn-ff nubber -, a rean circui -, an inerediae energy rage capacir, and buckb p recvery circuiry p - p - p, a hwn in figure 9.3a and cidered in 9... he recvery p i peraed a ainain a near can vage he inerediae rage capacir. he ce energy recvery wiche p are ynchried, a being urned fr up he wich iniu -ie (iediaey befre he wiche are urned ff), and urned ff when he ain wiche are urned ff. he iing equence fr he cr igna, wich and recvery wich p i hwn in figure 9.b. Ne ha he ranied cr igna i runcaed a he wich urnff edge, by he wich iniu -ie, deay, which i apprxiaey ½π. When p are urned ff, he inducive red energy in each p i reurned he dc ink hrugh each crrepding dide p a hwn in figure 9.a. ny ibaance in he individua inducr curren agniude, invve curren in exce f he iniu f a he inducr curren being divered he ce nubber capacir hrugh p p. he inducr recvery curren differenia are inia cpared he principa curren in he wiche, hence d n unduy affec capaciive urn-ff nubber charging, hence ranien urn-ff vage baancing aci. I a a a >> p p p p p p p p p rai V rai Figure 9.. cive urn-ff nubber energy recvery fr erie G cneced, inverer bridge eg: (a) duar ce circui and (b) iing diagra. igna p p deay (a) (b) he urn- nubber in figure 9. i indirecy caped, wih he red energy reeaed in he erie ring f urn-ff nubber capacir. ink inducance i andary in rder cr recharging f he urn-ff nubber capacir a cidered in eci 8.4. hugh he p wich p and dide p are high vage device, raed a he ce vage eve, bh are n paricuary reed during energy recvery wiching, ince he recvery buck-b p are peraed in a dicinuu inducr curren de. he wich p urn wih zer curren, wihu any dide revere recvery effec, whie dide p uffer inia revere recvery, ince i principa curren reduce zer cred by p, wih recvery di/d curren (r vage) cred (r uppred) by he p inducr p. aic vage-haring reir acr each ce (n hwn in figure 9.) cpenae fr variu aic vage and curren ibaance cdii bh he ain wich and p dide p newrk, paricuar during cverer ar-up and hudwn equencing. Sye ar-up he inerediae ranfer age capacir can be ued prvide a urce f gae eve pwer, via a dedicaed p. ne f w ar-up equence are ued buid-up gae pwer and ce vage befre nra wiching perai can cence. In bh cae, an ac dc inge r hree phae hafcred cverer i ued rap charge he inerediae capacir aciaed wih he we penia ce (ypicay perae a abu 5 V). hi capacir in urn prvide gae pwer, via a dedicae V dc ±5Vdc p, fr he we eve wich. By uing erie bcking/direcing dide, raed a he ce vage raing, e ac dc cverer can uppy he we penia ce f a bridge eg, a hwn in figure 9.3a. Prprieary pre-charging equence are ued charge higher ce eve, depending wheher he dc ink vage i eabihed r n. each i prgreivey charged, i aciaed gae uppy p i ef-acivaed, enabing exerna cr f ha wiching ce. Inverer ar-up can invve he appicai f he dc ink vage befre gae eve pwer ha been eabihed. hi de n preen a prbe fr Ghyrir, bu in he cae f he IGB, a w paive ipedance gae eier circui i needed avid inadveren device urn- due Mier capacir dv/d effec. (a) Sar-up wih an eabihed dc ink vage In he cae f an inverer wih an eabihed dc ink vage, each eve wich, hence ce, uppr haf i nra peraing vage, and each nubber capacir i charged he ce vage eve. he inerediae energy rage capacir are dicharged, excep fr he we penia ce capacir, which ha been rap charged by he ac dc cverer. he recvery p (and ain wich) f he we penia ce i perabe. p f he we penia ce i urned, hen ff and he curren in he aciaed p end vercharge f he we penia ce. hi frce curren increae hrugh he - - cbinai f he higher penia ce a each i frced decreae i charge, herein charging higher-eve capacir. he vage f he we penia ce can be dubed befre he ce reache i nra peraing vage eve. hu fr n erie cneced ce, he peraing ii f he inerediae capacir vage aifie (n-)v < V /n. ha i, any p urcing fr ued prvide gae uppy vage rai fr he ain wich, u be abe funci (cver) dwn a vage eve aified by hi inequaiy equai. When a ce vage reache i peraing vage ii, he aciaed ain wich i urned briefy reany dicharge he nubber capacir. he uppred vage i rediribued ag he her ce, which ypicay, are y uppring haf he nra ce peraing vage. (b) Sar-up wih n pre-exiing dc ink vage In he cae where he dc ink vage ha n been eabihed, a iiar charging prce i ued a fr he cae f a pre-exiing dc ink vage. he dc ink capaciance u be he inverer ide f he iai. he dc ink capacir i iniiay charged hrugh erie dide f he axiu ce vage a capacir f he we penia ce i parae charged fr by i aciaed recvery p. he we penia recvery p i cuaed nueru ie in rder charge he dc ink capaciance which i uuay ignificany arger in capaciance han. nce he ink capacir i charged he axiu awabe ce vage, he ain wich f he we penia ce i urned ree i aciaed nubber vage zer. he ar-up echani ued wih a pre-exiing dc ink vage can hen be ued. nce in each ce i charged ufficieny enabe i gae vage p bece peraia, ynchried ue f he recvery p a each eve aw charging f he dc ink capacir he peraia vage eve (in fac ighy in exce f he recified peak eve). hen he vacuu circui breaker befre he recifier, feeding he erie cneced device circui, can be ced, which reu in zer ine curren in-ruh. nneci f he ad and an inerfacing fier ay be prbeaic wihu dedicaed cacr, a i he infuence f he upu fier he ce charging echani previuy uined. her gae pwer derivai ehd Gae pwer derived fr wiching recvered energy cann be ainained during prged andby perid. Uing drpper reir (a fr aic vage haring) prvide a gae eve pwer

13 347 Pwer Eecric haper 9 Swiching id ircui wih Energy Recvery 348 requireen reu in high diipai e, paricuary during cinuu andby perid (ha i, % diipai duy cyce). hugh reir are ued fr eady-ae erie vage haring, he curren aciaed wih hi echani (, depending f he degree f device aching and peraing eperaure range) i we bew ha needed fr gae pwer ( 5W fr IGhyrir bu uch e fr IGB). Bu hi eve f haring reir curren ( ) ay be ufficien ricke ainain gae eve uppie f ce in he ff-ae during prg andby perid, uing variai f he circui hwn in figure 9.3c. epending he ad and upu fier, i ay be pibe during prg andby perid equence he inverer beween and ae, hereby prducing zer average vage upu beween phae bu acivaing he nubber hence rean recvery circui ha charge each. Prvided ufficien wich vage redundancy i avaiabe, equenia brapping i pibe where each eve i b rapped uppied fr he iediae nex wer eve, a hwn in figure 9.3b. (See figure 7.4). In he cae f a piive vage a hwn in figure 9.3b, each wich, aring fr he we eve i equeniay urned and ff, hereby ranferring gae energy fr he we eve he highe eve. (n expanding repeiive iuaneu -ae equence i ued, prgreivey invving higher penia ce.) hi apprach i viabe in inge-ending erie cneced wich appicai. hugh each brap dide b i raed a he ce eve vage, in he cae f inverer eg, y haf he inverer eg device can be uppied, ince any brap dide bridging he pe cenre ake-ff nde u be raed a he fu dc ink vage (acuay ½n- eve can be charged ince he we eve ce i n brapped). If he brapping vage i referenced wih repec he high penia erina f he ce, hen he uppy vage i brap by ranferring energy fr he highe penia ce dwn he we penia ce. iiar apprach can be ued wih ranfrer iaed p ranferring pwer beween adjacen eve, which need y be raed a he ce eve vage. gain, hi apprach i viabe in inge-ended appicai, bu in he cae f inverer eg, he pe upu ake-ff nde cann be readiy bridged by an p becaue f he high dc ink vage bcking and iai requireen., each p experience dv/d ree when he eve wiche are cuaed. Piby he ipe and reiabe ehd derive gae pwer in erie cneced circui, up a few kv, i ue ac curren ranfrer wih erie cneced inge-urn priarie, where each eve hr-circui he ecdary when n charging. hv ainain he vage near can i aciaed and he higher hi vage he faer he inducr curren i ineary ree zer, in ie ree = I / V. Exce energy i ranfer (recvered) he dc ink by ynchried wiching f p. Miached inducr p curren agniude and durai are divered charge f any ce aeping recver a wer curren agniude, by urning ff a p ju befre a he ain wiche are urned ff, a hwn in figure 9.4b. hi baancing effec i inia (bu de eiinae any p dide frward recvery effec) and any curren ibaance ubequeny end vercharge he upu capaciance f he ain wich f he ce wih recvery curren in exce f he iniu f a he p recvery curren. Se fr f urn-ff nubbering i herefre neceary in rder avid exceive ain wich vage a urn-ff. he vage raing f he variu ce circui eicducr i increaed by he vage. ce aic vage haring reir hep ainain eady-ae vage baance f bh he ain wich and he p dide p. a Sar-up ne ac dc cverer can be ued pre-charge each we eve capacir f each inverer eg, a hwn in figure 9.3a, prvided he pah each inverer eg incrprae a erie bcking/direcing dide, raed a he ce vage eve. he ar-up equence, uing he we eve p charge higher eve and he dc ink he u f a vage, i raighfrward. Synchried perai f a he p can hen graduay fuy charge he dc rai, if i i n aready pre-charged. I p p igna deay b3 b b 3 e 3 5V hv p p 3 b V b e 5V 5V p p p p V (a) (b) (c) Figure 9.3. Gae uppy derivai ehd: (a) ac dc haf-cred cverer fr rap precharging f a we eg eve capacir ; (b) brapping a piive vage uppy; and (c) Zener dide baed urce uing aic vage haring reir r/and R- nubber reir urn- nubber circui acive energy recvery fr erie cneced device i. Recvery in he dc uppy n acive energy recvery, inducive urn- nubber a hwn in figure 9.4 (uuay wih an R- urn-ff nubber), can be adaped and ued a each erie ce eve, herein prviding gae eve pwer pibiiie fr and energy recvery hrugh erie cnec buck-b p recvery circuiry, a hwn in figure 9.4a. he capacir i cfigured be cneced he eier f wich p. Energy red in he urn- nubber inducr i ranferred he inerediae rage capacir via dide a wich urn-ff. he wiching equence i hwn in figure 9.4b. Each recvery p e (a) (b) Figure 9.4. cive urn- nubber energy recvery fr erie G cneced, inverer bridge eg: (a) duar ce circui and (b) iing diagra urn- and urn-ff nubber circui acive energy recvery fr erie cneced device i. Recvery in he dc uppy If a inge inducive urn- nubber i ued in he dc ink a in figure 9.a, i red inducr energy a wich urn-ff i ranferred he capaciive urn-ff nubber f ce uppring ff-ae vage. uring wiching, hi caue vage ringing beween he ce and he ink inducr. hi inducr i raed a he fu dc ink vage and cann be caped by he uua reir-dide parae cneced ree circui a in figure 8.9a. hi i becaue any ree cpen (R-) need high vage raing in exce f he dc ink vage during dide f revere recvery. Fr hi rea, an inducr nubber (piby aurabe) ay be ued a each ce eve, giving a cpee duar ce rucure. cive nubber energy recvery f bh inducive and capaciive energy i pibe, ahugh i ay be cvenien reiivey diipaed he urn- inducive nubber energy, which i ad curren dependan, ½ I.

14 349 Pwer Eecric haper 9 Swiching id ircui wih Energy Recvery 35 ua, unified acive nubber energy recvery can be achieved by uing he recvery circui hwn in figure 9.b, bu wih he p dide erie cneced a hwn in figure 9.5a. Fr a duar ce rucure, a he ce are cfigured a fr he wer wich in figure 9.a. hi wich cfigurai i preferred ince capacir can be readiy pre-charged iniiae he ar-up equence fr charging higher eve, which can be ued derive gae eve pwer fr he aciaed ce. reaivey w vage capacir (if perae a abu 5 % f he ce peraing vage) ay neceiae a g wich iniu ff-ie in rder enure ree f he urn- inducr curren zer. hi i n a prbe fr G ype device which have iniu and ff ie iiai. Higher peraing vage fr neceiae a re cpicaed p derive gae eve pwer fr wich. higher ce peraing vage, he inerediae rage capacir can be dified he circui in figure 9.5b. he w vage upu v can be ued pwer ce ar-up circuiry. he reance inducr (in erie wih he urn- nubber inducance ) i ued cr he agniude and durai f he rean perid f ranferring i charge. he iniu vaue f inducr can be zer if i arge enugh aifacriy cr rean ree circui cdii wihu. furher ipificai can be ade by reving a rean circui dide a hwn in figure 9.5c, which i derived fr he circui in figure 9.8. he iing equence in figure 9.b fr urn-ff nubber i ued. ne funcia deign crain hud be berved. wich urn-, curren buid up in p becaue f he vage, during he aer par f he cyce when reae i charge. hi reaivey a curren agniude ineary increae a agniude dependan he reaive agniude f and p, and he agniude f he vage reained. nce eabihed, a near can, wy decreaing curren fw in a zer vage p, p - p - -, and i recvered during recvery p aci a wich urn-ff. I p p p p p (b) v hv >> p p gae pwer, hence exerna cr i eabihed each ce, judiciu perai f each p and ain wich can faciiae charging f he dc ink capacir and cain a ce vage wihin he raed ce vage. he ar up echani ay neceiae a uiabe dide cneced in erie r ani-parae wih p. (b) Shu dwn fer he dc ink ha been iaed, under zer inverer upu curren cdii, uing a vacuu circui breaker he ac ide, he inerediae capacir f he we penia ce (in each bridge eg) i ainained in a pariay dicharged ae by a reiive ad which i wich cneced he capacir f he we penia ce. he auxiiary ac dc cverer ued iniiay charge i diabed during nra perai and hu-dwn, wih a he ac dc cverer hyrir ff, herefre bcking curren in bh direci. ernaivey, if hi ac dc cverer ha uiabe w quadran peraia de, hen he energy cinuay being ranferred fr her ce, can be recvered in he w vage ac urce. he variu p and ain wiche are peraed a ainain equa vage acr a ce (by equeniay cuaing each ain wich hen ff), graduay decreaing he dc ink vage a energy i cinuay, bu cred, being ranferred and reved fr he we penia ce capacir Genera acive recvery ccep fr erie cneced device In each f he hree nubber circui cidered fr erie cneced device, he c key recvery echani i perfred by a buck-b p, wih cpen raed a he ce vage eve. Figure 9.6 hw w baic underying recvery echnique fr ranferring energy fr hrugh an inducr, in he dc uppy a a higher penia. he key difference beween he w echnique i he pariy rienai f he energy urce and he dc uppy V, wih repec heir c nde. Figure 9.6 par a and b hw b cverer, where energy i drawn fr when energy i being deivered he uppy V, via an inducr. Figure 9.6 par c and b hw buck-b cverer, which d n invve during he perid when energy i being deivered he uppy V, via an inducr. N FF FF p (a) (c) p (a) (b) N Figure 9.5. cive urn- and urn-ff nubber energy recvery: (a) circui fr erie G and IGB inverer bridge eg; (b) high vage repaceen circui fr ; and (c) reduced cpen variai f par a. (a) Sar-up he capacir f he we penia ce (in each bridge eg) i negaivey rap charged by a dedicaed ac dc cverer a hwn in figure 9.3a. hi eabihe ce inernay generaed gae uppy pwer and hence exerna cr f bh wiche f he we penia ce. he recvery p f he we penia ce i peraed in a dicinuu de, which charge up he urn-ff nubber capacir f ha ce. Siuaneuy curren fw in hree her parae pah, ending charge up he dc ink capacir, viz. he erie cneced p - p he erie cneced - f he erie cneced - - f hu prvided he p f he we ce deiver a high curren, each receive charge befre he curren i divered and bui up in inducr p and. he dc ink capacir iuaneuy receive charge. he wich p -ie, hence i curren, i n rericed during he ar-up prcedure. nce Figure 9.6. Underying energy recvery circui when energy in i red a differen penia: (a) and (b) b p recvery and (c) and (d) buck-b p recvery. c requireen i ha an p upu (wheher inducr-dide fr buck-b and inducrdide- fr b) pan a ce, hereby inhereny inercnecing in erie any nuber f ce. Each R (c) (d)

15 35 Pwer Eecric haper 9 Swiching id ircui wih Energy Recvery 35 inerediae rage capacir u herefre be cneced e ce erina. cfine furher he pibiiie, i i unikey ha referenced wih repec he ce cecr wi yied a uefu acive recvery circui. If he capacir i referenced wih repec he wich cecr/ande, underge high dv/d vage wih repec he wich gae. hi cpicae any p uing he red capacir energy fr gae drive purpe. he pariy rienai f and he recvery p cpen are herefre rericed he fur pibiiie hwn in figure 9.7. Serie recvery aue he p inducr cduc an idenica inananeu axiu agniude and ae durai curren. (a) Sar up he genera ce rucure and heir recvery p can inhereny be ued charge her erie cneced ce and he dc ink, and prvide a dc urce (he inerediae rage capacir ) fr which derive ce eve pwer uppie fr he gae eve circuiry. Specific prprieary wiching equence are required a ar-up, depending he ce circui arrangeen, he upu fier and ad, he dc ink and ac recifier inpu arrangeen and iniia cdii. (b) Shu dwn hu dwn, ce he inverer i in andby, he dc ink uppy i iaed (by pening he ac ide vacuu circui breaker) under zer curren cdii, hen he dc ink vage i cycicay dicharged in he ad via he erie cneced ce. Such ink dicharge uing ce wiching equence i prbeaic when each ce vage reache a eve where fa bew a eve ainain perai f he p ued prvide gae eve vage which aw he ce wiche perae; r ce in anher inverer eg ceae perae er. Such iiai are iigaed by enuring he p ha perae acr ha a wide (w iniu bund) inpu vage peraing range. If he ad i iaed a hu dwn, hen he dc ink energy can be equeniay ranferred f he we penia ce in each eg and diipaed in a inge ended reiive duping circui r recvery fr via he ac dc cverer (fuy cred) ued during he ar-up equence, a hwn in figure 9.3a. he equence invve prgreivey, bu equeniay, n uing higher-eve recvery p. Fai-afe ar-up and hu dwn equencing, a n ver-v any ce, uuay require ce peraia crdinai. he fibre pic cunicai ink fr ce eve /ff cr f he ain wich, i herefre bidirecia. eakage r uncuped inducance energy reeae ie-dipaced energy-ranfer cuped-circui, a wih he buck-b cverer r cuped vage a wih puh-pu cenre apped ranfrer circui Bh facr ce in perai wih he w buck-b iaed upu cverer hwn in figure 9.8. When energy i drawn by he cuped circui ecdary, a vage i induced in he priary, increaing he vage experience by he wich in he ff-ae. Energy aciaed wih eakage inducance furher increae he wich vage. If a baic R-- urn-ff nubber i ued, he capacir red energy i increaed fr ½V, if he wich vage were be iied V, in exce f ½ ( / ) V v N, where N i he ranfrer urn rai a defined in figure 9.8. he eakage energy add he vage cpen Paive recvery Figure 9.8a hw a paive urn-ff nubber energy recvery cfigurai fr an iaed buck-b cverer. I i baed he circui in figure 9.3j, where he ranfrer eakage inducance,, i effecivey he urn- nubber inducance. When he wich i urned ff, he nubber capacir charge fr - V a vage v /N, cred by he eakage inducance which caue he capacir charge a higher vage. urn-ff capacir nubbering f he wich i achieved indirecy, hrugh he dc uppy V. wich urn-, he charge reae in he p - r - r, revering he pariy f he charge. hi revere vage i caped V, a he dide cduc and he reaining energy in i ranferred (recvered) he dc uppy V. he wich iniu -ie i ½π r, whi he energy recvered fr r V ccur independen f he ae f he wich. wich urn-ff, afer nubber capacir i fuy charged, an ciai can ccur hrugh r - r - and he ranfrer priary back in he uppy V. hugh a e ciai, i can effec he upu vage reguai, increae upu recifier recvery e, bu can be prevened by uing a erie wich in he r - r pah a hwn in figure 9.8d. hen recvery ccur during wich perid, back in he uppy V, wihu affecing he upu reguai. nce a wich ha been ued, her acive recvery pibiiie ay be re aracive. he ae eakage vage cr and recvery echnique can be ued he puh-pu cverer in figure 9.8c, where w recvery circui are ued. :N r p R v r p :N R v (a) (c) r (b) (d) (a) (b) Figure 9.7. e acive energy recvery fr wih: (a) and (b) a b cverer and (c) and (d) a buck-b cverer. r r r (c) (d) 9.7 Snubber energy recvery fr agneicay-cuped baed wiching circui uped circui can induced circui and in paricuar wich vage ha exceed he uppy vage. hee increaed vage are aciaed wih w facr: Figure 9.8. Recvery f eakage inducance energy: (a) and (c) paive and (b) and (d) acive recvery.

16 353 Pwer Eecric haper 9 Swiching id ircui wih Energy Recvery cive recvery Figure 9.8b hw he circui f an acive urn-ff f nubber energy recvery cfigurai. uped circui eakage inducance energy i ranferred he inerediae rage capacir via a wich urn-ff. he vage i ainained a a vage reaed v /N by he buck-b p fred by r, r and r, which reurn eakage energy he dc uppy V. he circui funci i cap he wich vage raher han perfr a urn-ff nubber aci. he axiu wich vage i near can, where a he vage experience by he wich a urn-ff in figure 9.8a, ahugh variabe, i nubbered, bu dependan f he upu vage v. In bh circui, an R- nubber ay be required acr he wich ince he recvery nubber circui d n decupe ray inducance n aciaed wih he cuped agneic circui. Siiar acive nubber r caping circui can be ued wih puh-pu cverer which uiie a cenreapped ranfrer (r auranfrer), a in figure 9.8d, where, wih a fu-wave recified frward cverer ecdary circui, he vervage i independen f he ranfrer urn rai. he recvery circui wiche preven undeirabe e ciai afer ain wich urn-ff, paricuary when he wich duy cyce i e han 5%. he dide r aw he acive recvery wiche be acivaed wih he ae cr igna iing a he crrepding ain wich, prvided he wich iniu ie i a ea ½π r. In he acive recvery fr, y e c ree inducr r i neceary ranfrer eakage paive recvery ranfrer have eakage inducance. he eakage inducance f a ranfrer driven fr an H- bridge can be uiied a a urn- nubber, prducing urn- zer vage wiching ZVS cdii, which eiinae bh wich urn- e and dide revere recvery curren injeci prbe. cequence f ZVS i purey capaciive nubber (n nubber dide r ree reir) a bece e. he equence f circui diagra in figure 9.9 iurae hw he ranfrer eakage inducance i ued achieve ZVS. 9.8 Genera paive nubber energy recvery ccep fr inge-ended circui Snubber are ued fr re reduci a wich urn- - invving erie inducance wich urn-ff invving hun capaciance freewhee dide recvery - invving erie inducance and he nubber ay incrprae re han e f hee re arreing funci. inge ended wiching circui uuay incrprae a wich, a freewhee dide f and an inducive ad, where he ad ay be cfigured be in he eier/cahde circui f r he cecr/ande circui f. he inpu energy urce, he wich, dide and ad ay be cfigured perfr any f he fwing funci frward cverer buck cverer b cverer r buck-b cverer he differeniai beween he frward cverer and he buck cverer i ha he inducive eeen i par f he acive ad in he cae f he frward cverer. Figure 9.3a hw a wich-dide and inducr circui cbinai, auing a cecr ad circui, which can be cfigured a any ype f cverer viz., frward, buck, b, ec. Equivaen eier ad circui, a we a cecr ading, are hwn in figure 9.3 and 9.3, which preen yeaicay a re cpee range f circui pibiiie, in each cae, wih he ae funcia nubber circui. ff hen 3 when 3 cduc 3 3 Energy recvery in he ad i uuay aciaed wih a parae cneced capacir dicharging (ince an inananeu change in capacir curren ach he ad curren i pibe) whie recvery back in he urce i uuay aciaed wih a parae cneced inducr r agneicay cuped circui reeaing i energy (ince an inananeu change in inducr erina vage equa he uppy vage i pibe). 3 3 x x Bh and ff hen 3 when 3 cduc and 4 when 4 cduc x 3 3 and dc circui hery aw a hee circui cfigurai cbinai be generaied. hi i becaue a nubber i an ac circui perfring a ranien funci - whie he urce and ad end be dc cpen (can vage and can curren urce repecivey). herefre i i pibe inerchange he cneci f he nubber (an ac circui) wih he cneci he dc vage urce, ince ac-wie, a dc urce appear a a hr circui. he nubber funci can be achieved direcy (acr he wich) r indirecy (auing a we decuped uppy). 4 4 ff hen 4 when 4 cduc 4 4 Figure 9.9. H-bridge curren cduci pah: (a) wiche and cducing; (b) wich ff and hen 3 ; (c) wich ff and hen 4 ; and (d) wiche and ff, hen 3 and 4. When any wich ha i cducing curren i urned ff, curren aciaed wih he eakage inducance diver a dide, a hwn in he ff-p in figure 9.9 par b, c, and d. he wich in ani-parae wih ha cducing dide in figure 9.9 can be urned (a zer vage), whie he dide cduc, wihu any wich urn- e, ZVS. he zer v p, figure 9.9 b and c, are aernaed fr w duy cyce. a axiu duy cyce, he negaive vage equence in figure 9.9d i ued, where he eakage inducance curren fa rapidy zer. n inheren cequence f ZVS i ha e capaciive urn-ff nubber (ey capacir, wihu any reiive ree circui) can be epyed acr each bridge wich. If he dc ink i we decuped y e nubber capacir acr eiher wich per eg i needed. x 4 4 (b) (a) (d) (c) n peraia echani be appreciaed i he pgica reaive rienai wihin he principa circui f he urn- nubber inducr r urn-ff nubber capacir. urn-ff nubber - capacir: ircui in figure 9.3c and d hw he urn-ff nubber - cbinai parae he wich (direc nubbering) r aernaivey cneced acr he freewhee dide he dc rai (indirec nubbering). circui wie hee are he ae cneci ince he dc urce can be cidered a a hr circui a high frequency. When - are parae cneced he wich (direc nubbering), he capacir charge a he wich vage rie a urn-ff, whie in he cae f he nubber being acr he freewhee dide (indirec nubbering), he capacir dicharge, and by Kirchhff vage aw, he wich vage i indirecy cred be he difference beween he capacir vage and he urce vage. Pracicay i i preferred pace he - nubber direcy acr he eeen be preced, he wich, ince he urce ay n be we decuped. urn- and dide revere recvery nubber - inducr: ircui in figure 9.3a and b hw he inducr cfigured uch ha he nubber urn- inducr i in erie wih he wich (direc nubbering) r aernaivey in erie wih he freewhee dide (indirec nubbering). Bh arrangeen perfr he ae funci a wich urn-. uing a can curren in he inducr, by Kirchhff curren aw, wheher he urn- inducr cr he rae f rie f curren in he cecr (direc nubbering) r rae f curren fa in he dide (indirec nubbering), he cpeenary eeen ha i curren inverey cred.

17 355 Pwer Eecric haper 9 Swiching id ircui wih Energy Recvery 356 Figure 9.3 hw variai f a nubber fr recvering he energy aciaed wih freewhee dide revere recvery. weve circui have he ae funcia ac peraing echani, ahugh a nuber have been pubihed even paened - a differen. US paen , 997, accrding he hree cai, expiciy cver he b cverer nubber circui in figure 9.3a. In precing he pecific b cverer circui, a he her pgica variai are inadvereny and unwiingy ipiciy precuded. hugh a highy kied exper in he ar, Irving, IEEE PE,, pubihed he nex recvery circui, figure 9.3b, a a new dide recvery nubber fr he b cverer. Paive inducive urn- nubber energy recvery circui variai are hwn in figure 9.3, fr cecr and eier cneced buck, b, frward, and buck b cverer. Six veri exi wih he circuiry in each f he wich eier and cecr circui. Figure 9.33 hw urn-ff and urn-ff pu urn- paive recvery circui variai. he circuiry can be in he eier r cecr (a hwn) circui. inducive freewhee dide revere recvery nubber - paive energy recvery inducive urn- and capaciive urn-ff nubber - paive energy recvery (a) (d) Reading i Behringer,. e a., ranirchaer i Bereich hher eiungen und Frequenzen, EZ, Bd. (979) pp Peer, J. M., he Pwer ranir in i Enviren, h-sf, Sece, 978. Wiia, B. W., e a., Paive nubber energy recvery fr a G hyrir inverer bridge eg, ran. IE EEE, V. 47, N., Feb. () pp. -8. Wiia, B. W., High-vage high-frequency pwer-wiching ranir due wih wiching-aidcircui energy recvery, Prc. EE, Par B, V. 3, N., (984) pp. 7-. Finney, S. J. e a., High-pwer G hyrir chpper appicai wih paive nubber energy recvery, Prc. EE, EP, V. 44, N. 6, (997) pp Generaied wiched-de circui x z V B y Prbe (b) (c) capaciive urn-ff nubber - paive energy recvery 9.. Fr he circui in Figure 9.4a hw ha he upper curren ii fr a energy recvery i given by ½I ½V. 9.. erive capacir vage and curren equai which decribe he perai f he urn-ff nubber energy recvery circui in figure 9.3. ue he rage capacir be an idea vage urce wih pariy a hwn. inducive urn- nubber - paive energy recvery cverer frward /buck pr ranfer funci nde B/ δ xy/xz b / / (- δ) xz/yz buckb -B/ -δ/ (- δ) yx/yz Figure 9.3. Snubber energy recvery circui fr generaied wich-dide-inducive eeen circui.

18 357 Pwer Eecric haper 9 Swiching id ircui wih Energy Recvery 358 (a) (b) b (c) (d) (a) (b) b (c) (d) (e) (f) buck/frward (g) (h) (e) (f) buck/frward (g) (h) (i) (j) buck-b (k) () (i) (j) buck-b (k) () Figure 9.3. Paive energy recvery f freewhee dide recvery energy: (a)-(d) a b cverer; (e)-(h) a buck/frward cverer; and (i)-() a buck-b cverer. Figure 9.3. Paive energy recvery fr inducive urn- nubber: (a)-(d) a b cverer; (e)-(h) a buck/frward cverer; and (i)-() a buck-b cverer.

19 359 Pwer Eecric haper 9 Swiching id ircui wih Energy Recvery 36 bank V V V V V V urn-ff nubber (a) (b) b urn- and ff nubber V V V V V V (c) urn-ff nubber buck/frward (d) urn- and ff nubber V V V V V (e) urn-ff nubber (f) buck/b urn- and ff nubber Figure Paive energy recvery circui fr he capaciive urn-ff nubber and bh urn- and urn-ff nubber circui, fr he differen ype f wiched de cverer. V