Isolated DC-DC Converter for Bidirectional Power Flow Controlling with Soft-Switching Feature and High Step-Up/Down Voltage Conversion

Transcription

1 energies Aricle Isolaed DC-DC Converer for Bidirecional Power Flow Conrolling wih S-Swiching Feaure High Sep-Up/Down Volage Conversion Chih-Lung Shen 1, *, You-Sheng Shen 1 Cheng-Tao Tsai 2 1 Deparmen Elecronic Engineering, Naional Kaohsiung Firs Universiy Science Technology, Kaohsiung 82445, Taiwan; u41593@nkfus.edu.w 2 Deparmen Elecrical Engineering, Naional Chin-Yi Universiy Technology, Taichung 4117, Taiwan; csai@ncu.edu.w * Correspondence: clshen@nkfus.edu.w; Tel.: ; Fax: Academic Edior: Jayana Deb Mondol Received: 29 December 216; Acceped: 27 February 217; Published: 2 March 217 Absrac: In his paper, a novel isolaed bidirecional DC-DC converer is proposed, which is able o accomplish high sep-up/down volage conversion. Therefore, i is suiable for hybrid elecric vehicle, fuel cell vehicle, energy backup sysem, grid-sysem applicaions. The proposed converer incorporaes a coupled inducor o behave forward--flyback energy conversion for high volage raio provide galvanic isolaion. The energy sored in he leakage inducor he coupled inducor can be recycled wihou he use addiional snubber mechanism or clamped circui. No maer in sep-up or sep-down mode, all power swiches can operae wih s swiching. Moreover, here is a inheri feaure ha meal oxide semiconducor field-effec ransisors (MOSFETs) wih smaller on-sae resisance can be adoped because lower volage endurance a primary side. Operaion principle, volage raio derivaion, inducor design are horoughly described in his paper. In addiion, a 1-kW prooype is implemened o validae he feasibiliy correcness he converer. Experimenal resuls indicae ha he peak efficiencies in sep-up sep-down modes can be up o 95.4% 93.6%, respecively. Keywords: bidirecional DC-DC converer; high volage conversion raio; galvanic isolaion; s-swiching feaure 1. Inroducion In order o reduce carbon emission miigae global warming, green energies, such as phoovolaic (PV) panel, fuel cells, wind urbine, arac a grea deal ineres have a high rae growh in insalled capaciy. A complee configuraion disribued generaion sysem (DGS), as shown in 1, no only includes green-energy sources bu also combines an energy sorage sysem for power condiioning o use elecriciy opimally. For grid connecion, a DC-bus volage up o around 4 V is required, which is much higher han a baery volage. Therefore, a bidirecional DC-DC converer (BDC) wih high volage raio o charge/discharge baery is maory in he DGS. Convenional high sep-up converers used in PV panel fuel cells can boos a low volage o a higher level o serve as an inerface beween he disribued generaor he DC bus [1 3]. Neverheless, hey only conrol power flow in unique direcion. Bidirecional power flow conrol is necessary for baery sysem. A soluion is o adop wo high-volage-raio converers. One is high-sep-up converer for baery discharging he oher is high-sep-down converer for charging, bu his approach increases cos significanly. Therefore, BDC is he curren design rend, which is Energies 217, 1, 296; doi:1.339/en

2 Energies 217, 1, Energies 217, 1, which capableis capable governing governing energy inenergy eiher power in eiher flow power direcion flow by direcion a singleby converer. a single converer. BDCs can BDCs be simply can be classified simply classified non-isolaed as non-isolaed ype [4 6] ype isolaed [4 6] ype isolaed [7,8]. ype [7,8]. VB i B Signals DC-Bus Baery Bank Bidirecional DC-DC Converer V Load DC Load v pv i pv High Sep-up DC/DC Converer i Load DC/AC Inverer Uiliy PV Module v pv i pv V B i B V Load i Load Signals AC Load Conroller 1. Configuraion disribued generaion sysem. Increasing swiching frequency power converer can reduce he size magneic Increasing swiching frequency a power converer can reduce he size magneic capaciive elemens hus has he benefi achieving high power densiy. However, he higher capaciive elemens hus has he benefi achieving high power densiy. However, he higher swich frequency is, he lower conversion efficiency will be. In order o eliminae swiching loss, swich frequency is, he lower conversion efficiency will be. In order o eliminae swiching loss, employing resonan uni wih auxiliary swiches for s-swiching achievemen is common employing resonan uni wih auxiliary swiches for s-swiching achievemen is a common approach [9 11]. In lieraure [12], he auhors develop dual-bridge converer o fulfill bidirecional approach [9 11]. In lieraure [12], he auhors develop a dual-bridge converer o fulfill bidirecional power flow conrolling along wih zero volage swiching (ZVS) a main swich, in which even power flow conrolling along wih zero volage swiching (ZVS) a main swich, in which even resonan resonan ank is uilized bu he use addiional auxiliary swich can be avoided. Neverheless, a ank is uilized bu he use addiional auxiliary swich can be avoided. Neverheless, a grea many grea many swiches are needed is volage raio is incapable high sep-up/down applicaions. swiches are needed is volage raio is incapable high sep-up/down applicaions. The open H-bridge converer can funcion as a non-isolaed BDC [13]. Even hough his The open H-bridge converer can funcion as a non-isolaed BDC [13]. Even hough his converer converer can achieve ZVS feaure possesses simple srucure, is volage gain is less han 2 a can achieve ZVS feaure possesses simple srucure, is volage gain is less han 2 a he duy he duy raio.5. For higher volage raio, heavy swich duy cycle is he only soluion o his raio.5. For higher volage raio, heavy swich duy cycle is he only soluion o his problem, problem, bu his approach will degrade converer efficiency. To avoid excessive duy cycle bu his approach will degrade converer efficiency. To avoid excessive duy cycle operaion, swiched operaion, swiched capacior echnology will be an alernaive for high volage-gain conversion [14]. capacior echnology will be an alernaive for high volage-gain conversion [14]. However, curren However, curren spike ha occurs a he swiching ransiens confines is applicaions spike ha occurs a he swiching ransiens confines is applicaions accompanies elecromagneic accompanies elecromagneic inerference (EMI) problem, especially in high power raing. inerference (EMI) problem, especially in high power raing. Incorporaing swiched capacior along Incorporaing swiched capacior along wih coupled inducor ino a power converer is a key o wih coupled inducor ino a power converer is a key o suppressing inrush curren obaining suppressing inrush curren obaining enough volage conversion raio [15 18]. Since he enough volage conversion raio [15 18]. Since he coupled inducor can also feaure elecrical isolaion, coupled inducor can also feaure elecrical isolaion, a BDC including coupled inducor is he major a BDC including coupled inducor is he major developmen. However, he energy dissipaion caused developmen. However, he energy dissipaion caused from leakage inducor will degrade converer from leakage inducor will degrade converer efficiency [19,2]. Tha is, clamped circui or snubber efficiency [19,2]. Tha is, clamped circui or snubber mechanism for leakage energy harvesing is mechanism for leakage energy harvesing is imperaive. Isolaed BDCs based on H-bridge opology imperaive. Isolaed BDCs based on H-bridge opology have been proposed in he lieraure [21,22], have been proposed in he lieraure [21,22], which can achieve ZVS feaure inherenly, avoiding which can achieve ZVS feaure inherenly, avoiding addiional device usage. Neverheless, low addiional device usage. Neverheless, low volage raio more power swiches required become volage raio more power swiches required become heir disadvanages. In [23], anoher heir disadvanages. In [23], anoher isolaed BDC which accomplishes leakage-energy recycling isolaed BDC which accomplishes leakage-energy recycling can obain high volage-raio can obain high volage-raio conversion is presened. Neverheless, some limiaions sill exis, such conversion is presened. Neverheless, some limiaions sill exis, such as ZVS only occurs a as ZVS only occurs a high-volage side duy raio has o be greaer han.5. high-volage side duy raio has o be greaer han.5. In his paper, a novel BDC is proposed, which has he advanages galvanic isolaion, high In his paper, a novel BDC is proposed, which has he advanages galvanic isolaion, high volage conversion raio, s-swiching feaure a all power swiches, high efficiency, being suiable volage conversion raio, s-swiching feaure a all power swiches, high efficiency, being suiable for high power applicaions, low componen coun. 2 shows is configuraion he power for high power applicaions, low componen coun. 2 shows is configuraion he sage. The symbols in he circui are summarized in he followings. V L V H denoe he erminal power sage. The symbols in he circui are summarized in he followings. denoe he volages a low-volage side high-volage side, respecively; L 1 is a choke inducor; S 1, S 2, S 3, S 4, S 5, erminal volages a low-volage side high-volage side, respecively; is a choke inducor;, S 6 are acive swiches, while D D C C express heir relaed ani-parallel body diodes,,,, are acive swiches, while D D C C express heir relaed ani-parallel parasiic capaciors; he magneically-coupled device has winding N 1, magneizing inducor L m1, body diodes parasiic capaciors; he magneically-coupled device has winding, magneizing inducor Lm1, leakage inducor a low-volage side, meanwhile, Lm2,, respecively, a

3 Energies 217, 1, Energies leakage 217, 1, inducor 296 L k1 a low-volage side, meanwhile N 2, L m2, L k2, respecively, a high-volage 3 23 side; C b1 C b2 are low-volage capaciors; C o1 C o2 are high-volage capaciors. The conversion high-volage side; are low-volage capaciors; are high-volage capaciors. efficiency proposed BDC can be improved because he following reasons: The conversion efficiency proposed BDC can be improved because he following reasons: (1) No Nomaer maerin in buck buck or or boos mode, he energy sored sored in in leakage leakage inducors, inducors, L k1 L, can be, can be recycled recycledwihou wihouany anysnubber mechanism or orclamped circui. (2) All acive semiconducor componens can can be be swiched swiched wih wih ZVS ZVS or zero or zero curren curren swiching swiching (ZCS) (ZCS) o eliminae o eliminae swiching swiching losses. losses. (3) Swiches S 1 S 4 endure a low volage sress so ha semiconducor device wih a smaller RRds(on) can be chosen o reduce conducion losses. Low-Volage Side High-Volage Side il = i ids6 ih D vds6 C v ilm2 vlm2 D ids1 vds1 C v i D ilm1 vlm1 D D vds4 C ids4 C vds5 D i Lm2 v i Vref, vds2 Lm1 vds3 Vref, ids2 C ids3 C ids5 i i i Vgs1 Vgs2 Vgs3 Vgs4 Vgs5 Vgs6 Vref, il Vref, ih Conroller Acive filer Schemaic Schemaic he he proposed proposed bidirecional bidirecional converer. converer. Following he inroducion described in Secion in Secion 1, his 1, paper his paper is organized is organized as follows. as The follows. operaion The operaion principle principle he proposed he converer proposed is explained converer in Secion is explained 2. Secion in Secion 3 presens 2. he Secion seady-sae 3 presens analysis. he seady-sae Experimenalanalysis. resuls measured Experimenal from aresuls 1-kW prooype measured are from illusraed a 1-kW prooype discussedare in Secion illusraed 4, while discussed conclusionin issecion summarized 4, while in conclusion Secion 5. is summarized in Secion Operaion Principle he Proposed Converer As shown in 2, he direcion energy flow can be hled by conrolling he acive swiches so ha he converer can operae in eiher sep-up mode or sep-down mode. In sep-up mode, main swiches S, 1,, S 2,, S 3, S 4 are in in swiching paern while S 5 S 6 are in charge recifying. A Ahis his mode, S 1 Soperae 2 operae complemenarily so do so boh do boh swiches swiches S 3. The S 4. volage The volage gain gain o V L o is Vdeermined H is deermined by he by duy he raio duy raio. Wih S 1. respec Wih respec o sep-down o sep-down mode, mode, main swiches main swiches,, S, 2, S 4, S 5, will be S 6 in will swiching be in swiching paern paern he res hemain res swiches main swiches serve as recifier. serve as In recifier. addiion, In addiion,,, S 2, Sare 4, urned S 5 are on urned f on simulaneously f simulaneously complemenary complemenary o. The o duy S 6. raio The duy raio dominaes S 6 dominaes he volage he gain volage o gain in Vsep-down H o V L inmode. sep-down To describe mode. he To operaion describe he he operaion converer, he some converer, assumpions some assumpions are made follows: are made as follows: (1) In 2, capaciances C,,,, C b2, C o1, C o2 are are large enoughso so ha all he volages across hem can be regarded as consan in a swiching cycle. (2) Parasiic capacior body bodydiode diode each eachswich swichare areconsidered, bu bu he he inernal inernal resisance resisance negleced. is negleced. (3) The Theleakage leakageinducance inducance he hecoupled coupledinducor inducoris ismuch muchless lesshan magneizing magneizing inducance. inducance. (4) (4) All All he he magneic magneic componens componens are are designed designed in in coninuous coninuous conducion conducion mode mode (CCM). (CCM). (5) The urns raio secondary o primary he coupled inducor, /, is defined as n. (5) The urns raio secondary o primary he coupled inducor, N 2 /N 1, is defined as n.

4 Energies 217, 1, Sep-Up Mode The converer operaion in sep-up mode is divided ino nine main sages over one swiching cycle, which are discussed sage by sage below. The equivalens he nine sages are depiced in 3, while 4 illusraes he corresponding concepual waveforms. Sage 1 [, 1 ]: In his sage, referring o 3a, all he swiches are in f sae. The energy sored in he parasiic capacior C is drawn ou bu capacior C b1 is charged, as referred o he red dashed line in 3a. Meanwhile, energy L m1 is forwarded o capacior C o2 he oupu V H, where L m1 ss for he oal amoun magneizing inducance seen looking ino he primary (a low-volage side) he coupled inducor. Afer he volage across C drops o zero, he body diode D conducs o coninue he currens flowing hrough L 1 L k1 hus o creae ZVS urn-on condiion for S 3. Sage 2 [ 1, 2 ]: This sage begins a he momen he swiches S 1 S 3 are urned on. The S 3 is urned on wih ZVS. During his ime inerval, S 2, S 4, S 5, S 6 are sill in f-sae. The volage he parasiic capacior C drops. Afer he volage v ds1 is less han inpu volage V L, inducor L 1 will absorb energy from V L he curren i increases, as referred o he blue dashed line in 3b. In sage 2, he energy L k1 is coninuously releasing o C b1. The equivalen circui his sage is illusraed in 3b. When he curren i falls o zero, his mode ends. Sage 3 [ 2, 3 ]: 3c depics he equivalen circui his sage, in which all he swich have he same sauses as in Sage 2. Inducor L 1 coninuously absorbs he energy from V L. Capacior C b1 ransmis energy o L k1, L m1 he secondary (a high-volage side) he coupled inducor, which curren pah is indicaed by he red dashed line in 3c. The currens i i Lm1 increase. In he high-volage side, C o1 is charged via he loop N 2 -D -C o1 -L k2 bu C o2 discharges via he loop L k2 -N 2 -D -V H -C o2. This mode ends when S 3 is urned f. Sage 4 [ 3, 4 ]: This sage begins a ime = 3, he equivalen circui is illusraed in 3d. During his ime inerval, all he swiches are in f sae excep S 1. Inpu V L capacior C b1 charge inducor L 1 capacior C b2, respecively. In addiion, C b1 forwards energy o high-volage side via he coupled inducor o charge C o1. The C releases energy. Tha is, v ds4 decreases. The body diode S 4 will be forward biased afer v ds4 drops o zero, which provides ZVS condiion for S 4. The associaed curren pah is referred o he red dashed line in 3d. The leakage energy in L k2 is recycling o C o1 over he inerval Sage 4. Sage 5 [ 4, 5 ]: When S 4 is urned on, he operaion he converer eners ino Sage 5. As shown in 3e, in his sage swiches S 1 S 4 are closed, whereas S 2, S 3, S 5, S 6 are open. The volage polariy L k1 is reversed he curren i begins decreasing. Capacior C b2 is charged by L k1 C b1 he curren flowing hrough S 4 is decreased, as referred o he red dashed line in 3e. The energy in L k2 is kep on recycling o C o1, which is he same as in Sage 4. A he momen ha i equals zero, his sage ends D is reversely biased. Sage 6 [ 5, 6 ]: During he ime inerval Sage 6, he swiches S 1 S 4 are sill in on sae S 2, S 3, S 5, S 6 in f sae. 3f is he corresponding equivalen, in which C b1 charges L k1, L m1, C b2, as referred o he red dashed line. The currens flowing hrough L k1 L m1 are idenical increase simulaneously. Wih respec o curren i, since he volage across L 1 is V L, he curren i coninues linearly increasing. This sage coninues unil S 1 is urned f. Sage 7 [ 6, 7 ]: 3g depics he equivalen circui Sage 7, in which all swiches are open excep S 4. There are wo loops, V L -L 1 -C b1 -C L k1 -L m1-s 4 -C b2 -C, o draw he energy sored in he parasiic capacior S 2. When he volage across C falls o zero, he body diode S 2 conducs S 2 can achieve ZVS, as referred o he boh dashed lines in red blue in 3g. In he high-volage side he converer, he boh in-series capaciors C o1 C o2 supply power o oupu.

5 Energies 217, 1, Sage 8 [ 7, 8 ]: Afer he ime = 7, swiches S 2 S 4 are in on sae bu S 1, S 3, S 5, S 6 are in f sae. The equivalen circui is illusraed in 3h. As referred o he boh red purple dashed line in 3h, capacior C b1 is charged by V L L 1, while he C b2 absorbs energy from L m1 L k1. All he currens i, i i Lm1 decrease. In addiion, he energy sored in magneizing inducor Energies 217, is 1, forwarded 296 o he secondary he coupled inducor o charge C o2. This sage ends as 5 he 23 curren i falls o zero. Sage 9 [8, 8, 9]: 9 ]: During he heime ime inerval Sage Sage 9, he 9, he swiches S 2 are S 4 sill are sill in on insae on sae,, S 1,, S 3, S 5, in Sf 6 insae. f sae. The equivalen The equivalen circui circui is illusraed is illusraed in in 3i. Capacior 3i. Capacior is C b1 sill is sill charged charged by by V L. Addiionally, L 1. capacior capacior pumps C b2 pumps energy energy o inducor inducor via L k1 swiches via swiches, as Sreferred 4, as referred o he ored hedashed red dashed line line in 3i. 3i. The The energy sored in inhe magneizing inducor is ransferred o he secondary o charge C power he oupu. In his sage, inducor currens ii iilm1 decrease bu i i i i increase. When swiches S 2 S 4 are urned f a = 9, 9, his sage ends. The operaion in sep-up mode over one swiching cycle is compleed. D D C C C D C D C C D D D C D D D D C D C L'm1 C C L'm1 C D D C C C D C D C C D D D C D D D D C D C L'm1 C C L'm1 C (c) (d) D D C C C D C D C C D D D C D D D D C D C L'm1 C C L'm1 C (e) (f) C D D C L'm1 D D C C D C D C C D D C L'm1 D D C C D C D C (g) (h) D C C D C D D D C D C L'm1 C (i) 3. Equivalen circui proposed bidirecional converer in sep-up mode: Sage 1; 3. Equivalen circui proposed bidirecional converer in sep-up mode: Sage 1; Sage 2; Sage 2; (c) Sage 3; (d) Sage 4; (e) Sage 5; (f) Sage 6; (g) Sage 7; (h) Sage 8; (i) Sage 9. (c) Sage 3; (d) Sage 4; (e) Sage 5; (f) Sage 6; (g) Sage 7; (h) Sage 8; (i) Sage 9.

6 Energies 217, 1, Energies 217, 1, v gs1 v gs2 v gs3 v gs4 S 1 S 2 S 3 T s D 1 T s D 2 T s D 3 T s D 4 T s v ds1 i ds1 v ds2 i ds2 v ds3 i ds3 S 4 S 5 v ds4 v ds5 i ds4 i ds5 S 6 i i i Lm1 i i v ds6 i ds6 i Sage 1 Sage 2 Sage 3 Sage 4 Sage 5 Sage 6 Sage 7 Sage 8 Sage Key waveforms he proposed converer in sep-up mode Sep-Down Mode In sep-down mode,, S 2,, S 4, S 5 are conrolled a high swiching paern complemenary o SW6, 6, while SW1 1 SW3 3 serve as recifiers. The converer operaion over one swiching cycle in sep-down mode can be divided ino 12 sages, which are described sage by sage in he following. The relaed equivalens corresponding waveforms are depiced in s 5 6, respecively. Sage 1 [,, 1]: 1 ]: Referringo o 5a, 5a, all all he he swiches are are in in f f sae. sae. Since Since has S 5 has been been urned urned f, he f, volage he volage C increases. C increases. Accordingly, he volage he volage across across L (he m2 inducance (he inducance seen seen looking looking ino he ino he high-volage side side he he coupled inducor), L k2, whichis is equal o vv vds5, v, decreases; meanwhile he energy sored in he parasiic capacior S 6 releases via he loop C---L m2. C -L -L m2. In low In low volage side, side, he he body body diodes S 2 S 4 are are forward biased because he coninuiy ii.. The volage across L 1 equals vv. V L. Sincev v is is larger han, V L he, he curreni i increases negaively, as referred o he red dashed line in 5a. During his sage, C will energize via he coupled inducor he loop --D--D. L 1 -D -C -D This. This mode mode ends ends a he a he momen vds5 v ds5 reaches reaches he he magniude. VTha H. Tha is, is, is S 5 is compleely urned urned f f is blocking is blocking volage volage is clamped is clamped o. o V H. Sage 2 [1, 1, 2]: 2 ]: During his ime inerval, all he swiches sill say in f sae. The equivalen circui his sage is illusraed in 5b. The volage polariy across L L m2 k2 reverses he value vvlm2 + v v is is equal ov. v. Thais, is, magneizing inducor L m2 L m2 leakage inducor L k2 release energy o V H via body dioded, D, as as indicaed by he purple dashed line in 5b. Since volage polariy he coupled inducor has been changed, he body diode D will be reversely

7 Energies 217, 1, volage polariy he coupled inducor has been changed, he body diode D will be reversely biased he parasiic capacior C releases energy o V L. In sage 2, he curren flowing L k1 almos equals ha in L 1. Therefore, swich S 2 is urned f a ZCS. When S 6 is urned on wih ZVS, he operaion he converer eners ino nex sage. Sage 3 [ 2, 3 ]: In his sage, swich S 6 is closed. L m2 L k2 proceed wih energy releasing oward C o1 V H, leakage energy in L k1 is dumped o C b2 a he same ime. Accordingly, all he currens in hem decrease. As referred o he blue dashed line in 5c, he curren L 1 draws ou he sored energy in C hen force he parasiic diode D in forward bias. The L 1 delivers energy o V L is curren decreases linearly. In sage 3, he curren flowing hrough L k2 is greaer han ha in L m2 bu is magniude drops much seeper. This sage coninues unil i drops o zero. 5c shows he equivalen circui his sage. Sage 4 [ 3, 4 ]: This sage begins a ime = 3, he equivalen circui is illusraed in 5d. During his ime inerval, all swiches are sill in urn-f condiion excep S 6. Magneizing inducor L m2 forwards energy o C o1 C b1 via swich S 6 he ideal ransformer, respecively. The curren direcion L k1 changes, which resuls in energy releasing C he charging C. Associaed curren pah is shown as he red dashed line in 5d. The leakage inducor L k1 will confine he charge curren C, resuling in ZCS urn-f a S 4. When he volage v ds4 rises o v, Sage 5 begins. Sage 5 [ 4, 5 ]: The equivalen circui his sage is illusraed in 5e, in which all he swiches are urned f excep S 6. Capacior C o1 sill absorbs energy from L m2 L k2. In addiion, L m2 forwards energy o C b1 by he ideal ransformer via he loop N 1 -L k1 -D -C b1 -D. This curren pah is referred o he red dashed line in 5e. The curren flowing hrough L k2 keeps on decreasing. This sage ends a he ime ha i is zero. Tha is, energy in L k2 is compleely recycled. Sage 6 [ 5, 6 ]: 5f depics he equivalen circui his mode, in which all swiches have he same sauses as in Sage 5. The curren direcion i changes a = 5, L k2 absorbs energy from C o1, as referred o he green dashed line in 5f. The circui operaion in low volage side is idenical o ha in Sage 5. Therefore, he inducor L 1 keeps on energy supplying oward V L is curren decreases linearly. Sage 6 coninues unil swich S 6 is urned f a = 6. Sage 7 [ 6, 7 ]: During he inerval ha S 6 is open, he volage v ds6 increases. Therefore, he volage, v Lm2 + v, drops he parasiic capacior C dumps is sored energy, as referred o he green dashed line in 5g. The circui operaion in low-volage side behaves idenically o Sage 6. When he energy in C is drawn ou compleely v ds6 rises o V H, his sage sops. 5g expresses he operaion he converer in Sage 7. Sage 8 [ 7, 8 ]: In Sage 8, he body diode D is in forward bias, which provides a ZVS condiion for S 5. The green dashed line in 5h shows his curren pah. Leakage energy in inducors L k2 L k1 is recycled o C o2 C b1. In addiion, L 1 proceeds wih energy releasing o V L while L m2 sill forwards energy o low volage side via he ideal ransformer. When swiches S 2, S 4, S 5 are urned on simulaneously, his sage ends. The corresponding equivalen circui is depiced in 5h. Sage 9 [ 8, 9 ]: A = 8, he operaion he converer eners ino Sage 9. 5i is he equivalen. The volage polariy he ideal ransformer reverses because S 2 S 4 are closed. Over he ime inerval Sage 9, L k2 L k1 coninuously dump heir sored energy hus he currens i i reduce. Addiionally, he volage level v is higher han V L, which resuls ha he inducor L 1 absorbs energy from C b1 is curren increases negaively linearly, as referred o he blue dashed line in 5i. This sage lass unil i drops o zero. Sage 1 [ 9, 1 ]: Afer he ime = 9, he curren direcion L k2 changes i increases. Swich saues in Sage 9 are idenical o ha in Sage 1. Tha is, S 2, S 4, S 5 are in on sae, whereas S 1, S 3, S 6 say in f sae. The equivalen circui is shown in 5j, in which he L m2 draws energy from C o2 he volage across L 1 is sill kep a V V L. As he red dashed line in 5j indicaes, leakage inducor L k1 coninues releasing energy i decreases. When i is zero a = 1, his sage ends.

8 Energies 217, 1, Sage 11 [ 1, 11 ]: 5k shows he equivalen circui his sage, in which he sauses all swiches are kep as in Sage 1. During his ime inerval, C b1 coninuously supplies energy o V L L 1 byenergies he loop 217, 1, 296 C b1 -L 1 -V L -S 2, which curren pah is referred o he blue dashed line in k. The curren direcions N 1 N 2 reverse he curren i rises posiively. Meanwhile, capacior C b2 charges The curren direcions C o2 discharges. reverse he curren i rises posiively. Meanwhile, capacior Sage charges 12 [ 11, 12 ]: discharges. From he equivalen circui depiced in 5l, swiches S 2, S 4, S 5 remain Sage 12 [11, 12]: From he equivalen circui depiced in 5l, closed, while S 1, S 3, S 6 are open. In Sage 12, inducors L k2 L swiches,, remain m2 are magneized by C o2 wih closed, while,, are open. In Sage 12, inducors L m2 are magneized by wih he he same circui behavior in Sage 11. Since he magniude i is greaer han i, he curren flowing same circui behavior in Sage 11. Since he magniude i is greaer han i, he curren flowing hrough S 2 becomes reverse, hen S 2 achieves ZCS a urn-f ransiion, as referred o he red hrough becomes reverse, hen achieves ZCS a urn-f ransiion, as referred o he red dashed dashed line line in in 5l. 5l. The The operaion operaion he he converer converer over over one one swiching swiching cycle cycle is compleed is compleed when when he swiches he swiches S 2,, S 4,, S 5 are are urned f simulaneously. D D C C C D C D C C D D C D D D D C D D C C C C D D C C C D C D C C D D C D D D D C D D C C C C (c) (d) D D C C C D C D C C D D C D D D D C D D C C C C (e) (f) D D C C C D C D C C D D C D D D D C D D C C C C (g) (h) D D C C C D C D C C D D C D D D D C D D C C C C (i) (j) D D C C C D C D C C D D C D D D D C D D C C C C (k) (l) 5. Equivalen circui proposed bidirecional converer in sep-down mode. Sage 1; 5. Equivalen circui proposed bidirecional converer in sep-down mode. Sage 1; Sage 2; (c) Sage 3; (d) Sage 4; (e) Sage 5; (f) Sage 6; (g) Sage 7; (h) Sage 8; (i) Sage 9; (j) Sage 1; Sage 2; (c) Sage 3; (d) Sage 4; (e) Sage 5; (f) Sage 6; (g) Sage 7; (h) Sage 8; (i) Sage 9; (j) Sage 1; (k) Sage 11; (l) Sage 12. (k) Sage 11; (l) Sage 12.

9 Energies 217, 1, Energies 217, 1, v gs6 v gs2, v gs4,v gs5 D 6 T s T s D 5 T s S 1 v ds1 i ds1 S 2 v ds2 i ds2 S 3 v ds3 i ds3 S 4 v ds4 i ds4 v ds5 S 5 i ds5 S 6 v ds6 i ds6 i i i i i i i Lm2 Sage 1 Sage 2 Sage 3 Sage 4 Sage 5 Sage 6 Sage 7 Sage 8 Sage Sage 1 Sage Sage Key waveforms he proposed converer in sep-down mode. According According o o he he aforemenioned aforemenioned operaion operaion principle, principle, he he swiching swiching characerisics characerisics all all power power swiches swiches are are summarized in in Table Table 1. The swiching characerisics he proposed converer. Mode Mode Main Circui Main Circui Low-Volage Side High-Volage Side Low-Volage Side High-Volage Side S Sep-up 1 S ZVS ZVS 2 S ZVS 3 S ZVS none 4 S 5 S none 6 Sep-up Sep-down ZVS none ZCS ZVS none ZVSZCS ZVS ZVS none ZVS none Sep-down none ZCS none ZCS ZVS ZVS 3. Seady-Sae Analysis 3. Seady-Sae Analysis In his secion, he seady-sae analysis he BDC includes volage conversion raio, volage sress Inderivaion, his secion, hemagneic seady-sae elemen analysis design. he To BDC simplify includes he analysis, volagehe conversion assumpions raio, made volage in Secion sress derivaion, 2 are considered magneic excep he elemen neglec design. leakage To simplify inducors. he analysis, In addiion, he he assumpions phenomenon made ha in occurs Seciona 2swiching are considered ransien excep is also he ignored. neglec leakage inducors. In addiion, he phenomenon ha occurs a swiching ransien is also ignored.

10 Energies 217, 1, Sep-Up Mode Volage gain he converer in sep-up mode is firs invesigaed. Because he oupu volage V H is he sum V V, he relaionships V o V L V o V L have o be found in advance. The volage V is n imes he magniude V V is n imes he V under he condiion ha leakage inducor is negleced. Accordingly, V V in erms V L should be deermined before he finding for V V. Since S 1 S 2 are swiched complemenarily, he inpu volage V L can be boosed via inducor L 1. As a resul, he volage across C b1 is given by V = V L 1 D 1, (1) where D 1 is he duy raio S 1. Refer o 4 a any ime here are wo swiches in closed sae simulaneously over one swiching cycle. While S 1 S 3 are on, he volage across L m1 is V hus he amoun curren increase can be esimaed by i Lm1,on = V L D 3 T s (2) m1 In Equaion (2), he D 3 denoes he duy raio S 3. Afer S 3 is urned f, swich S 4 will be urned on. Tha is, he boh swiches S 1 S 4 are in on sae. The volage across L m1 becomes V V. If V is greaer han V, he L m1 will proceed wih curren increasing. The incremen can be expressed as i Lm1,o f f = (V V ) L (D 1 D 3 )T s (3) m1 The swich S 2 will be urned on when swich S 1 is urned f. Tha is, S 2 S 4 are in on sae simulaneously he volage across L m1 is V. The curren flowing hrough L m1 decreases, which is given by i Lm1,o f f = V L (1 D 1 )T s (4) m1 In seady sae, he ne curren change on L m1 is equal o zero. From Equaions (2) (4), he following relaionship can be derived V L m1 D 3 T s + (V V ) L m1 Subsiuing Equaion (1) ino Equaion (5) becomes V = (D 1 D 3 )T s V L (1 D 1 )T s = (5) m1 D 1 (1 D 1 )(1 D 3 ) V L (6) The oupu volage V H = V + V, which can be also obained from V H = n(v + V ) (7) Therefore, he conversion raio oupu volage o inpu volage in sep-up mode, M sep-up, can be found by M sep-up = V H = n(1 + D 1 D 3 ) (8) V L (1 D 1 )(1 D 3 ) As referring o he swiching sequence in sep-up mode, during he inerval ha S 2 S 4 are open bu S 1 S 3 are closed, he S 2 S 4 endure he volages V V, respecively. Afer he above swich saus, S 2 S 3 will be open bu S 1 S 4 are closed. The blocking volages a S 2 S 3 are V V, respecively. The swich saus ha S 1 S 3 are f bu S 2 S 4 are on

11 Energies 217, 1, proceeds he converer operaion. The volages across S 1 S 3 in his ime inerval are also V V in urn. In brief, he volage sresses wih respec o S 1, S 2, S 3 S 4 can be deermined as follows: v -sress = v -sress = v -sress = v -sress = V L 1 D 1 (9) D 1 (1 D 1 )(1 D 3 ) V L (1) A high-volage side, he swich S 5 will wihs a volage a leas V H when he inrinsic diode S 6 is forward biased. Similarly, S 6 also endures a reverse volage up o V H during he inerval ha he diode D is on. Tha is, v ds5 = v ds6 = n(1 + D 1 D 3 ) (1 D 1 )(1 D 3 ) V L (11) Wih respec o inducance design, he average curren carried by magneic componen has o be calculaed in advance. For L m1, he applicaion amp-second balance crierion (ASBC) a C b2 can give an assisance o he finding for he average i Lm1. The C b2 charges during he ime inerval [ 5, 6 ], in which S 1 S 4 are in on sae. On he conrary, C b2 discharges during [ 8, 9 ], while S 2 S 4 are closed. The charging curren C b2 is equal o i Lm1 discharging curren will be i Lm1 + ni ds5. Thus, he following relaionship holds: i Lm1 (D 1 D 3 )T s + (i Lm1 n 1 D 1 i H )(1 D 1 )T s = (12) From Equaion (12), he average curren carried by L m1 can be given as I Lm1 = n 1 D 3 I H (13) If he volage across C b1 is close o V, he curren i Lm1 can be regard as consan in Sage 6. This phenomenon can be found in 4. Assume ha L m1 is in BCM. The following relaionship can be found: [(D 1 D 3 )T s + T s ] V L m1 D 3T s 2T s = n 1 D 3 I H (14) Solving for L m1 resuls: L m1,min = D 3(1 D 3 ) 2 R H 2n 2 f s (15) where L m1,min is he minimum inducance L m1 for CCM operaion, R H ss for load resisance a high-volage side, f s is swich frequency. To deermine he minimum inducance L 1, L 1,min, for CCM operaion, average curren i has o be conaced. This average curren can be found by applying ASBC o C b1. Capacior C b1 charges during he ime inerval [ 7, 9 ], in which boh swiches S 2 S 4 are closed. There are wo inervals o discharge he energy in C b1. One is [ 2, 4 ], in which S 1 S 3 are closed, he oher is [ 4, 7 ], in which S 4 S 1 are in on sae. Based on ASBC, he following relaionship holds: ( n D 3 i H i Lm1 )D 3 T s + i Lm1 (D 3 D 1 )T s + i (1 D 1 )T s = (16) Using Equaion (13) subsiuing for i Lm1, he average curren flowing hrough L 1 can be represened as I = n(1 + D 1 D 3 ) (1 D 1 )(1 D 3 ) I H (17)

12 Inducance L' m1 (μh) Inducance (μh) Using Equaion (13) subsiuing for ilm1, he average curren flowing hrough can be represened as 1 3 Energies 217, 1, 296 H 12(17) 23 (1 D1)(1 D3) The curren incremen on, Δi, is esimaed by The curren incremen on L 1, i, is esimaed by Hence, he minimum ii,, I,min, I,min is, is given by by A BCM, II,min = =.. Solving for for Lyields 1 I n(1 D D ) I V L i D T (18) i = V D 1 1T s s L (18) 1 n(1 D D ) V I I DT (1 D )(1 D ) 2L I,min = n(1 + D 1 D3 ) (1 D 1 )(1 D 3 ) I V LL L H D 2L 1 T1 s s (19) 1 1,min = 2 2 D 1(1 D1 ) (1 D3 ) R H L 2n (2) 2 n (1 D D ) ff s in which L,min is he minimum inducance L 1 for CCM. If If RRH H = 64 Ω, Ω, ffs s = 4 khz, n = 3, DD1 1 = D3. D 3. 7a depics he relaionships beween inducance L L m1 duy raio D1 1 while 7b is for inducance 1 versus D1. D s DCM L' m1, min CCM DCM L 1, min CCM Duy Cycle (D 1 = D 3 ) Duy Cycle (D 1 = D 3 ) 7. Magneic componen design for L m1 under he duy raio D1 7. Magneic componen design for L D3. m1 L 1 under he duy raio D 1 = D Sep-Down Sep-Down Mode Mode All All he he assumpions assumpions in in he he above above subsecion subsecion are are also also adoped adoped for for he he seady-sae seady-sae analysis analysis in in sep-down mode. The swiches,, sep-down mode. The swiches S are conrolled simulaneously complemenary o. 2, S 4, S 5 are conrolled simulaneously complemenary o S 6. During he inerval ha is in urned-on sae,, During he inerval ha S are in urned-f sae, he volage 6 is in urned-on sae S 2, S 4, S 5 are in urned-f sae, he volage V will direcly impose on he high-volage side he ransformer. Then, he body diodes Ds1 V will direcly impose on he high-volage side he ransformer. Then, he body diodes D s1 Ds3 forward conduc he volage V will be equal o V/n. The inducor D supplies energy o s3 forward conduc he volage V will be equal o V /n. The inducor L 1 supplies energy o. This sae will las for D6Ts. During he inerval (1 D6)Ts, becomes f bu,, V are on. L. This sae will las for D 6 T s. During he inerval (1 D 6 )T s, S 6 becomes f bu S 2, S 4, S 5 are on. The The volage volage polariy polariy he he coupled coupled inducor inducor a a high-volage high-volage side side reverses reverses is is magniude magniude equals equals V. In addiion, he volage across inducor is V while V V equals V/n. Applying. In addiion, he volage across inducor L 1 is V V L while V equals V /n. Applying vol-second balance crierion (VSBC) o vol-second balance crierion (VSBC) o L yields 1 yields V Equaion (21) can also be expressed as (1 D ) V (21) V 6 L = (1 D 6 )V (21) V L = (1 D 6)V n (22) Similarly, applying VSBC o magneizing inducor L m2, he following relaionships can be found: V = (1 D 6 )V H (23)

13 Volage Gain (/) Volage Gain (/) Similarly, applying VSBC o magneizing inducor L m2, he following relaionships can be found: V Energies 217, 1, H n (1 D ) V (23) V D = 6V H (24) (24) Subsiuing Equaion (23) ino Equaion (22) has he resul: sep-down = = (1 6) 2 (1 D6 ) M down V H n H (25) (25) in which MMsep-down ss for he raio oupu o inpu volage as in sep-down mode. 8a shows he curves MMsep-up versus duy raio DD1, 1, while MMsep-down versus duy raio D6 D 6 is illusraed in 8b n = 4 n = 3 n = 2 n = 1 V L = 48 V V H = 4 V Duy Cycle (D 1 = D 3 ) n = 3 n = 4 n = 2 n = 1 V L = 48 V V H = 4 V Duy Cycle (D 6 ) Volage Volage conversion conversion raio raio he he proposed proposed bidirecional bidirecional converer: converer: sep-up sep-up mode; mode; sep-down sep-down mode. mode. The discussion relaing o he volage sresses he semiconducor devices is followed up. The discussion relaing o he volage sresses he semiconducor devices is followed up. Because he diode D swich conduc complemenarily, from he mesh --, i can be Because he diode D found ha volage sress swich S is idenical 2 conduc complemenarily, from he mesh C o ha equals V. Similarly, b1 -S 1 -S D 2, i can be are in found ha volage sress S complemenary conducion, 1 is idenical o ha S he volage sresses 2 equals V. Similarly, D will be equal S o V. 4 are in A complemenary conducion, he volage sresses S high-volage side, from he ouermos loop, --, he 3 S inpu 4 will be equal o V volage will impose. A high-volage on side, from he ouermos loop, S alernaely. Tha is, have 5 -S o 6 -V s H, he inpu volage V a volage. H will impose on S 5 S 6 alernaely. Tha is, S The 5 S curren 6 have o s a volage V gain he converer is reciprocal H. he volage raio shown in Equaion (25). The curren gain he converer is a reciprocal he volage raio shown in Equaion (25). Therefore, he inpu curren IH is given by Therefore, he inpu curren I H is given by 2 2 (1 D6) (1 D6) IL n I L = (1 D 6) nr 2 V L L IH (26) I H = (1 D 6) 2 n where RL denoes he load resisance a low-volage side. From 5f, he average curren where R L denoes he load resisance a L m2 is equals o i low-volage side. From 5f, he average curren ds3 magneizing inducance L ids6, which can be furher esimaed by m2 is equals o i ds3 i ds6, which can be furher esimaed by nn I Lm2 = (1 D 6)I L nd 6 nr L (26) I H D 6 (27) In addiion, he curren decremen on L m2 over one swiching cycle, i Lm2, can be expressed as i Lm2 = D 6T s V L m2 (28) Using Equaion (23) Equaion (25) o subsiue for V yields i Lm2 = D 6T s nv L (1 D 6 )L m2 (29)

14 Energies 217, 1, The minimum value i Lm2 can be calculaed by I Lm2 i Lm2 2 is compued as I Lm2,min = (1 D 6)V L nr L D 6T s nv L 2(1 D 6 )L m2 (3) A boundary, I Lm2,min =. Then, solving for L m2 can obain he following relaion for deermining he minimum inducance for CCM: L m2,min = n2 D 6 R L 2(1 D 6 ) 2 f s (31) In order o find he minimum value L 1 for coninuous curren operaion, L 1,min, he average curren L 1, I, has o be found. The I is equal o he oupu curren I L, which is given by The change on inducor curren i can be compued from Accordingly, minimum I is Le I,min = solving for L 1 can obains: I = V L R L (32) i = D 6T s V L L 1 (33) I,min = V L R L D 6T s V L 2L 1 (34) L 1,min = D 6R L 2 f s (35) Assume ha R L is Ω, f s is 4 khz, n = 3. 9a depics he relaionship beween D 6 L m2, while L 1 versus D 6 is illusraed in 9b. Energies 217, 1, Inducance L' m2 (mh) CCM L' m2, min DCM Inducance (μh) CCM L 1, min DCM Duy Cycle (D 6 ) Duy Cycle (D 6 ) 9. The relaionship beween he inducance duy raio D6: L m2;. 9. The relaionship beween he inducance duy raio D 6 : L m2; L 1. 1 is he equivalen circui proposed converer considering non-ideal parameers, in which r represens 1 is he he equivalen inducor circui resisance proposed a he low converer volage side considering rds1, rds2, non-ideal rds3, rds4, parameers, rds5, rds6 in are which he on-sae r represens resisance he inducor swiches resisance,,, a, he, low volage, respecively; side r ds1, r rlk1 ds2, r ds3, r rlk2 ds4 are, r ds5 he, primary r ds6 are winding he on-sae resisances resisance he swiches secondary S 1, S one 2, S 3 respecively., S 4, S 5, S By 6, respecively; using VSBC r lk1 ASBC, r he lk2 are non-ideal he primary volage winding conversion resisances raio he M sep-up secondary conversion one efficiency respecively. By ηsep-up in using sep-up VSBC mode ASBC, can be he obained non-ideal as volage conversion raio M sep-up conversion efficiency η sep-up in sep-up mode can be obained as M' Sep-up = -n(-2(1+ D -D ) f L +( -1+ D ) D (-2 r +( -3+2 D ) r )) 1 3 s m 3 3 ds4 3 lk1 ds5 ds6 ((-1+ ) + ( + )-2 ((1+ ) + ( ( ) rlk1))+ ((1+ ) + (-3(-1+ ) 2 2 +(1+ D1 ) r +3( -1+ D1 ) rlk1))) -1+ D1 D ds3 3 ds ds1 1 ds2 1 ds ds1 1 1 ds2 2 2 (-1+ D1 ) D1 (-1+ D3 ) D3 RH RH n D D r D r D r D D r D r D r r D r D D D r D D r 2( -1+ D )(-1+ D ) f L ( s m r - r + +4rlk2 + ) (36)

15 1 is he equivalen circui proposed converer considering non-ideal parameers, in which r represens he inducor resisance a he low volage side rds1, rds2, rds3, rds4, rds5, rds6 are he on-sae resisance swiches,,,,,, respecively; rlk1 rlk2 are he primary winding resisances he secondary one respecively. By using VSBC ASBC, he non-ideal volage conversion raio M sep-up conversion efficiency ηsep-up in sep-up mode can be Energies 217, 1, obained as M Sep-up = -n(-2(1+d1 -D3 )f s Lm +(-1+D3 )D3 (-2rds4 +(-3+2D3 )rlk1 )) n( 2(1+ D M'Sep -up = 1 D3 ) f s Lm +( 1+ D3 ) D3 ( 2rds4 +( 3+2D3 )rlk1 )) rds5 2 rds6 r rds rlk2 1ds5 + D3 3 (3 rds1 + D1 r ) 2D23 2 ( (1+ D1 )rds1 + D1 (rds2 D1 rds2 +r + D1 r +(2 1+ D1 ) rlk1 ))+2D3 ( (1+ D1 ) rds1 + D1 ( 3( 1+ D21 )rds2 +(1+ D12) r +3(- 1+ D1 )+ rlk1 ))) n2 ( ( 1+ D ) D r + D1 + D3 +4rlk2 n 2 ((-1+1D1 ) 21Dds3 D1 ) rlk1 ))+D ((1+D1 ) rds1 +D1 (-3(-1+D1 )rds2 +(1+D1 ) r +3(-1+D1 ) rlk1 ))) -1+D1 D3 +) ) 2( 1+ D12( )( +D 1 rds3 +D3 (rds1 +D1r )-2D3 ((1+D1 )rds1 +D1 (rds2 -D1rds2 +r +D1r +(-1+ 3 ) f s L m ( RH -1+1D + 1+ D1 ) D1 (2 1+ D3 ) D3 R H 1 )(-1+D3 )f s Lm (1+ (-1+D1() 2 D1 (-1+ D3 ) D3 RH RH (36) (1 D1 )(1 D3 ) ηsep-up = M Sep-up 1+ (1 Dn1()(1 DD3 )1 D3 ) (37) Sep-up M'Sep-up D1 efficiency D3 ) In addiion, sep-down volage raio M sep-down η sep-down are esimaed by n(1 sep-down volage raio M sep-down efficiency ηsep-down are esimaed by In addiion, ( 1+ D6 )2 D6 nr L M Sep-down = 3 2 ( 1 D ) 2 D nr 6 +r lk1 6 +LD6 (r ds2 D6 r ds2 +( 2+ D6 )r ds3 + R L +r +( 2+ D6 )r lk1 )) ( 1+ D6 ) ( rds6 + D6 (rds5 +rds6 ))+n (rds1 +rds3 M'Sep-down (38) 3 2 ( 1 D6 ) ( rds 6 D6 (rds 5 rds 6 )) n (rds1 rds 3 rlk1 D6 (rds 2 D6 rds 2 ( 2 D6 )rds 3 RL r ( 2 D6 )rlk1 )) " # n (36) (37) (38) n ηsep-down = M Sep-down (39) (39) Sep-down M'Sep-down (1 D2 ) 2 6 (1 D ) 6 Based Based on Equaions (36) o (39), relaionships volage gain versus duy raios D D3 on Equaions (36) o (39), relaionships volage gain versus duy raios D1 D3 1in in sep-up mode are depiced in 11a,b, respecively; meanwhile, do 11c,d for sep-up mode are depiced in 11a,b, respecively; meanwhile, so doso 11c,d for sep-down operaion shows volage gain in sep-up differen sep-down operaion. showshe henon-ideal non-ideal volage gain in sep-up modemode underunder differen choke resisances. choke resisances. High-Volage Side Low-Volage Side r rds6 rlk1 rds1 Lm1 rds4 rds2 Lm2 rds3 rlk2 rds5 non-idealequivalen equivalen circui hehe converer TheThe non-ideal circui converer. Energies 217, 1, r=13 mω, rds1=rds2=9 mω rds3=rds4=8 mω, rds5=rds6=.12 Ω rlk1= mω, rlk2=1 mω RH=16 Ω 1. ) (D 3 ycle.5 3) 1. le (D Cyc Duy.5 r=13 mω, rds1=rds2=9 mω rds3=rds4=8 mω, rds5=rds6=.12 Ω rlk1= mω, rlk2=1 mω RH=16 Ω Efficiency(ƞ) Volage Gain (/) yc D u Duy Cycle (D1) Duy Cycle (D1) Efficiency(ƞ) r=13 mω 1 Volage Gain (/) rds1=rds2=9 mω.2 rds3=rds4=8 mω rds5=rds6=.12 Ω rlk1= mω, rlk2=1 mω RL=2.34 Ω.15.8 r=13 mω rds1=rds2=9 mω.6 rds3=rds4=8 mω rds5=rds6=.12 Ω rlk1= mω, rlk2=1 mω RL=2.34 Ω Duy Cycle (D6) (c) Duy Cycle (D6) (d) 11. The relaionships volage gain versus duy raio efficiency versus duy raio while 11. The relaionships volage gain versus duy raio efficiency versus duy raio while considering non-ideal effec: M sep-up; ηsep-up; (c) M sep-down; (d) ηsep-down. considering non-ideal effec: M sep-up ; η sep-up ; (c) M sep-down ; (d) η sep-down. MSep-up Ideal 13 mω 16 mω 24 mω 32 mω Ideal

16 Duy Cycle (D 6 ) (c) Duy Cycle (D 6 ) (d) 11. The relaionships volage gain versus duy raio efficiency versus duy raio while considering Energies 217, 1, non-ideal 296 effec: M sep-up; ηsep-up; (c) M sep-down; (d) ηsep-down M Sep-up Ideal 13 mω 16 mω 24 mω 32 mω Ideal Duy cycle (D 1 =D 3 ) 12. The sep-up volage gain under differen choke resisances. 12. The sep-up volage gain under differen choke resisances. Among all power swiches, he main swich S Among all power swiches, he main swich 1 will endure he maximum curren sress no maer will endure he maximum curren sress no in sep-up or sep-down mode. Thereby, he curren sress deerminaion is focused on S maer in sep-up or sep-down mode. Thereby, he curren sress deerminaion 1. This curren is focused on. sress can be esimaed by he sum he valley curren inducor L 1 he peak curren leakage This curren sress can be esimaed by he sum he valley curren inducor he peak inducance L k1. Tha is, curren leakage inducance. Tha is, I ds1,peak = I L(2 D 6 ) V LD 6 (4) D 6 2 f s L 1 I (2 D ) V D L 6 L 6 As for he curren sresses I he oher ds1, peak acive swiches in sep-down mode, he ASBC should be (4) applied o capaciors C o1, C o2, C b2, C b1, whichdyields 6 2 fs As for he curren sresses he oher acive 2 swiches D in sep-down mode, he ASBC should be I ds2,peak = 6 I L V LD 6 (41) applied o capaciors,,,, which yields D 6 2 f s L 1 2 D V D I 6 L 6 ds3,peak = I ds2, peak ds4,peak = 2 I I L(1 D 6 ) (42) L D 6 (41) D6 2 fs I ds5,peak = I ds6,peak = I L(1 D 6 )(2 + D 6 ) nd 6 V L nd 6 2(1 D 6 ) f s L (43) m2 Similarly, in sep-up mode, curren sresses swiches can be expressed as I ds1,peak = ni H [2(1 D 1 + D 1 D 3 ) D 3 2 ] D 3 (1 D 1 )(1 D 3 ) + V LD 3 2 f s L 1 (44) I ds2,peak = ni H 2 D 3 (1 D 1 )(1 D 3 ) + V LD 1 2 f s L 1 (45) I ds3,peak = I ds4,peak = ni H 2 D 3 D 3 (1 D 3 ) + V L D 3 2 f s L m1(1 D 1 ) I ds5,peak = 2I H (1 D 1 ) (46) (47) I ds6,peak = 2I H D 3 (48) 4. Experimenal Resuls To validae he proposed BDC, a 1-kW prooype is buil wih he specificaions componens summarized in Table 2. If a converer operaes in disconinuous conducion mode (DCM), i can easily avoid swiching loss. However, during he inerval high power loading, serious conducion loss will resul in unaccepable efficiency. The proposed converer inrinsically has he ousing feaure

17 Energies 217, 1, s swiching a all power swiches even in CCM. Therefore, we design he converer operaion from DCM ino CCM a 25-W power loading for overall efficiency consideraion. Accordingly, a Toroids A2 MPP core an EE-55 core are adoped o form main inducor coupled inducor, respecively. To make sure he CCM DCM operae, as menioned, he main inducance L 1 should be 46 µh magneizing inducance L m1 is 13 µh wih a urns raio n = 3. Table 2. Specificaions componens used in experimenaions. Symbols Values & Types V L (Low volage) 48 V V H (High volage) 4 V P o (Oupu power) 1 kw f s (Swiching frequency) 4 khz L 1 (Filer inducance) 46.2 µh L m1 (Magneizing inducance) 13 µh L k1 (Leakage inducance) 2.7 µh L k2 (Leakage inducance) µh n (Transformer urns raio) 3 C b1 C b2 (Capaciances) 33 µf C o1 C o2 (Capaciances) 22 µf S 1 S 2 (Swiches) IXFH165T2 S 3 S 4 (Swiches) IXTP16N75T S 5 S 6 (Swiches) IXFH52N5P2 According o he discussion in Secion 3, volage curren sresses all acive swiches can be specified, which fers us a benefi o choose appropriae semiconducor devices for prooype consrucing. Since a lower R ds(on) can achieve a higher conversion efficiency, acive swiches which mee he power raing have conducion resisance as low as possible are considered. A low-volage side, power MOSFETs IXFH165T2 wih on-sae resisance R ds(on) 9 mω is chosen as S 1 S 2, while IXTP16N75T wih 6 mω R ds(on) as S 3 S 4. Wih regard o he acive swiches S 5 S 6 a high-volage side, power MOSFET IXFH52N5P2 is considered, which R ds(on) is.12 Ω. Microconroller ATMEGA328P-PU is in charge he converer conrolling. Addiionally, PV simulaor Chroma 625H-6S, high volage power supply IDRC CDSP-5-1C, elecronic load Chroma 6322 are adoped for erminal source or load. All waveforms are measured by oscilloscope KEYSIGHT DSOX424A. 12 shows he volage curren waveforms measured from swiches S 1 S 6, while D 1 =.44 D 3 =.3. In 13a, he firs race second race are he swich volage curren S 1, respecively, whereas he hird fourh races depic he measuremens S 2. From 13a, i can be found ha S 1 endures a volage around 1 V. This value is consisen wih he esimaion in Equaion (9). The measured i ds1 maches he concepual waveform in 4. In addiion, he waveforms v ds2 i ds2 release ha ZCS urn-f feaure is achieved a S 2. 13b presens he pracical measuremens v ds3, i ds3, v ds4, i ds4, which illusraes ha boh swiches S 3 S 4 can be urned on wih ZVS. While operaed in sep-up mode, S 5 S 6 he converer are in he role recifier. 13c presens he zoomed-in waveforms S 1 S 2, 13d is for S 3 S 4. The blocking volages v ds5 v ds6 are boh equal o 4 V, as shown in 13e, which conforms o he calculaion Equaion (11). 13f confirms a sable oupu CCM operaion in L 1 ; moreover, he measuremens i i are consisen wih he waveforms in 4.

18 illusraes ha boh swiches can be urned on wih ZVS. While operaed in sep-up mode, he converer are in he role recifier. 13c presens he zoomed-in waveforms, 13d is for. The blocking volages vds5 vds6 are boh equal o 4 V, as shown in 13e, which conforms o he calculaion Equaion (11). 13f confirms a sable 217, oupu CCM operaion in ; moreover, he measuremens i i are consisen Energies 1, wih he waveforms in 4. vds1: 1 V/div vds3: 1 V/div ids3: 5 A/div ids1: 5 A/div ZVS urn-on vds4: 1 V/div ZVS urn-on vds2: 1 V/div ids4: 5 A/div ids2: 1 A/div ZVS urn-on ZVS urn-on vds1: 1 V/div ZVS urn-on ids1: 5 A/div vds3: 1 V/div ids3: 5 A/div ZVS urn-on vds4: 1 V/div vds2: 1 V/div ZVS urn-on ids4: 5 A/div ZVS urn-on ids2: 1 A/div Energies 217, 1, 296 (c) vds5: 5 V/div (d) : 5 V/div i: 2 A/div ids5: 1 A/div vds6: 5 V/div i: 5 A/div i: 2 A/div ids6: 1 A/div (e) (f) Experimenal 1 kw: measuremens from Experimenalresuls resulsininsep-up sep-upmode modeoperaion operaionaapop=o = 1 kw: measuremens from S 2; measuremens from ; (c) zoomed-in waveforms measured from ; (d) ; measuremens from ; (c) zoomed-in waveforms measured from ; zoomed-in waveforms ; (e) from from S S 6; (f) waveforms, i, i, (d) zoomed-in waveforms measuremens ; (e) measuremens ; (f) waveforms, 5 i. i, i, i. While operaing in sep-down mode wih D6 =.37, relaed pracical waveforms are shown in While operaing in sep-down mode wih D6 =.37, relaed pracical waveforms are shown in 14. From 14a,b, i can be seen ha boh swiches are jus in charge 14. From 14a,b, i can be seen ha boh swiches are jus in charge recifying recifying whereas can accomplish ZCS urn-f feaure. 14c reveals ha whereas can accomplish ZCS urn-f feaure. 14c reveals ha are urned are urned on wih ZVS heir volage sresses are abou 4 V. The oupu volage a low-volage on wih ZVS heir volage sresses are abou 4 V. The oupu volage a low-volage side he side he currens,, are also given in 14d, in which a consan 48 V oupu currens,, are also given in 14d, in which a consan 48 V oupu CCM CCM operaion in are illusraed. operaion in are illusraed. vds1: 1 V/div vds3: 1 V/div ids1: 1 A/div ids3: 1 A/div vds2: 1 V/div vds4: 5 V/div

19 While operaing in sep-down mode wih D6 =.37, relaed pracical waveforms are shown in 14. From 14a,b, i can be seen ha boh swiches are jus in charge recifying whereas can accomplish ZCS urn-f feaure. 14c reveals ha are urned on wih ZVS heir volage sresses are abou 4 V. The oupu volage a low-volage side he1,currens,, are also given in 14d, in which a consan 48 V oupu Energies 217, CCM operaion in are illusraed. vds1: 1 V/div vds3: 1 V/div ids1: 1 A/div ids3: 1 A/div vds2: 1 V/div vds4: 5 V/div ids2: 1 A/div ZCS urn-f ZCS urn-f ids4: 1 A/div : 5 V/div vds5: 5 V/div ids5: 1 A/div ZVS urn-on i: 1 A/div i: 1 A/div vds6: 5 V/div i: 1 A/div ids6: 2 A/div ZVS urn-on (c) (d) Experimenal resuls in in sep-down sep-down mode mode operaion operaion a a PPo = = 1 kw: measuremens from Experimenal resuls o 1 kw: measuremens from S 2; ; (c) ; (d) he waveforms, i, i, i. ; ; (c) ; (d) he waveforms, i, i, i. Efficiency (%) 15 depics measured efficiency he prooype. The maximum values he pracical 15 depics measured efficiency he prooype. The maximum values he pracical efficiency in sep-up sep-down modes are up o 95.4% 93.6%, respecively, while Po is equal Energies 217, 1, 2 23 efficiency in 296 sep-up sep-down modes are up o 95.4% 93.6%, respecively, while Po is equal o 1 kw. The efficiency values are measured afer 1hr burn-in es he maximum emperaure o 1 kw. The efficiency values are measured afer 1hr burn-in es he maximum emperaure C. allall acive componens he phoo phoo he heprooype, prooype,where where lengh, acive componensisisaround around56 56 C shows shows he isis lengh, widh, heigh are kw/m33..in widh, heigh are17.2, 17.2,14.6, 14.6, cm cmininurn. urn.therefore, Therefore,is ispower power densiy densiy is is kw/m addiion, he converer s weigh is.985 kg.kg. Tha is, is, specific power isis1.15 In addiion, he converer s weigh is.985 Tha specific power 1.15kW/kg. kw/kg Sep-Up Mode Sep-Down Mode Power (W) 15. bidirecionaldc-dc DC-DCconverer. converer. 15.Measured Measuredefficiency efficiency he he proposed proposed bidirecional High-Volage Side Main Circui inches Conroller

20 Ef 9 Sep-Up Mode 89 Sep-Down Mode Power (W) Energies 217, 1, Measured efficiency he proposed bidirecional DC-DC converer. High-Volage Side inches Main Circui Conroller Auxiliary Circui Low-Volage Side 16. The phoo he experimenal seup. Table 33 summarizes he he comparison comparison he proposed he proposed converer converer wih oher wih bidirecional oher bidirecional converers converers in [24 27]. in The [24 27]. proposed The converer proposed has converer he beer has feaures he beer such feaures as galvanic such as isolaion, galvanic s isolaion, swiching s swiching a all swiches, a all no swiches, any diode no any required, diode required, high volage-raio high volage-raio conversion. conversion. For example, For example, in sep-up in sep-up mode mode under he under condiions he condiions ha n = 3ha n duy = 3 cycleduy is.5 cycle (in addiion, is.5 (in Daddiion, D1 = D3 1 = D 3 in he proposed in he proposed converer), converer), he proposed he one proposed can achieve one can a much achieve higher a much volage higher gainvolage up o 12gain while up hose o 12 in while [24 27] hose are in 11, [24 27] 3, 6, are 12, respecively. 11, 3, 6, For 12, clearer respecively. presenaion, For he clearer plospresenaion, o express he he comparison plos o resul express among he comparison he menioned resul converers among are he shown menioned in converers 17. In high are shown conversion in raio17. converers, In high conversion curren-sharing raio converers, pah srucure curren-sharing along wih inerleaved pah srucure conrol along can suppress wih inerleaved curren ripples conrol can hen suppress lowers curren ripples sress conducion hen lowers loss curren [27 3]. sress However, conducion bi-direcional loss [27 3]. power flow However, conrolling bi-direcional or more power flow componens conrolling needed or more are sill power heir componens demeris. needed are sill heir demeris. Table 3. Performance comparisons proposed BDC wih oher bidirecional DC-DC converers proposed in [25 27]. References [24] [25] [26] [27] Proposed References Topology [24] Non-Isolaed [25] Isolaed [26] Isolaed [27] Isolaed Proposed Isolaed Volage conversion Topology raio in [(1 Non-Isolaed + n)/(1 D)] + n Isolaedn Isolaed n/(1 D) Isolaed 2n/(1 D) [n(1 + D1 D3)]/[(1 Isolaed D1)(1 D3)] Volage conversion raio in sep-up mode (V H /V L ) [(1 + n)/(1 D)] + n n n/(1 D) 2n/(1 D) [n(1 + D 1 D 3 )]/[(1 D 1 )(1 D 3 )] Volage conversion raio in sep-down mode (V L /V H ) D/(1 + n + nd) 1/n (1 D)/n (1 D)/2n (1 D 6 ) 2 /n Oupu power 2 W 5 W 1 kw 1.5 kw 1 kw Number MOSFETs Number diodes 2 Number inducors Number coupled inducors Number capaciors Full-load efficiency (Sep-up/sep-down) 93%/9% 92.4%/91.7% 85%/89% 96.5%/95.8% 94.1%/91%

21 Number diodes 2 Number inducors Number coupled inducors Number capaciors Energies Full-load 217, 1, efficiency %/9% 92.4%/91.7% 85%/89% 96.5%/95.8% 94.1%/91% (Sep-up/sep-down) M Sep-up Proposed Proposed [25] [26] [27] [28] M Sep-down Proposed [25] [26] [27] [28] Duy cycle (D 1 ).5.4 Proposed Duy cycle (D 6 ) The The comparison comparison plos plos conversion conversion raio: raio: sep-up sep-up mode; mode; sep-down sep-down mode. mode. 5. Conclusions 5. Conclusions This paper has proposed high efficiency high volage-raio isolaed bidirecional DC-DC This paper has proposed a high efficiency high volage-raio isolaed bidirecional DC-DC converer. coupled inducor is employed for achieving galvanic isolaion, in which he energy converer. A coupled inducor is employed for achieving galvanic isolaion, in which he energy sored sored in leakage inducor can be recycled wihou addiional componens. The main conribuion in leakage inducor can be recycled wihou addiional componens. The main conribuion his his paper is ha volage sress across semiconducor devices can be lowered by adjusing duy raio, paper is ha volage sress across semiconducor devices can be lowered by adjusing duy raio, all all power swiches can complee s swiching feaure in sep-up sep-down modes, higher power swiches can complee s swiching feaure in sep-up sep-down modes, higher volage conversion can inherenly be achieved. Because semiconducor device endures low volage volage conversion can inherenly be achieved. Because semiconducor device endures low volage sress, MOSFETs wih low Rds,on can be employed. Unlike convenional converers whose volage sress, MOSFETs wih low R ds,on can be employed. Unlike convenional converers whose volage gain gain is merely deermined by a fixed duy raio, he proposed converer has he abiliy is merely deermined by a fixed duy raio, he proposed converer has he abiliy compromising he compromising he duy raios swiches a primary side o mee a cerain volage gain o find duy raios swiches a primary side o mee a cerain volage gain o find an available power an available power componen. Operaion principle he circui deailed derivaion volage componen. Operaion principle he circui deailed derivaion volage gain, volage sress, gain, volage sress, curren sress are carried ou. Finally, experimenal resuls measured from a curren sress are carried ou. Finally, experimenal resuls measured from a 1-kW prooype have 1-kW prooype have verified he heoreical analysis feasibiliy. verified he heoreical analysis feasibiliy. Acknowledgmens: The Theauhors auhorswould wouldlike likeo oconvey conveyheir heirappreciaion appreciaionfor forgran gransuppor supporfrom fromhe heminisry Minisry Science Technology (MOST) Taiwan under is is gran gran wih wih Reference Number Number MOST MOST E Auhor Conribuions: Chih-Lung Shen, You-Sheng Shen Shen Cheng-Tao Tsai Tsai conceived conceived designed designed he circui. he circui. You-Sheng You-Sheng Shen Cheng-Tao Cheng-Tao Tsai performed Tsai performed simulaions, simulaions, carried ou carried he prooype, ou he prooype, analyzed daa analyzed wih guidance from Chih-Lung Shen. Chih-Lung Shen revised he manuscrip for submission. daa wih guidance from Chih-Lung Shen. Chih-Lung Shen revised he manuscrip for submission. Conflics Ineres: The auhors declare no conflic ineres. Conflics Ineres: The auhors declare no conflic ineres. References References 1. Shen, C.-L.; Chiu, P.-C.; Lee, Y.-C. Novel Inerleaved Converer wih Exra-High Volage Gain o Process 1. 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23 Energies 217, 1, Li, W.; Li, W.; He, X. Zero-volage ransiion inerleaved high sep up converer wih buil-in ransformer IEEE Trans. Power Elecron. 211, 4, Marinez, W.; Imaoka, J.; Yamamoo, M.; Umeani, K. A Novel High Sep-Down Inerleaved Converer wih Coupled Inducor. In Proceedings he 215 IEEE Inernaional Telecommunicaions Energy Conference (INTELEC), Osaka, Japan, Ocober by he auhors. Licensee MDPI, Basel, Swizerl. This aricle is an open access aricle disribued under he erms condiions he Creaive Commons Aribuion (CC BY) license (hp://creaivecommons.org/licenses/by/4./).