Comparative Analysis of Single and Three-phase Dual Active Bridge Bidirectional DC-DC Converter Based on the Phase-Shifting Control

Transcription

1 Inernaonal Conference on Energy, ower and Elecrcal Engneerng (EEE 16 Comparave Analy of Sngle and Three-phae Dual Acve Brdge Bdreconal DC-DC Converer Baed on he hae-shfng Conrol Gangu Yan, Yongln * and Q Ja Deparmen of Elecrcal Engneerng, Norhea Danl Unvery, Chuanyng Drc, Jln 131, Chna * Correpondng auhor Abrac In order o analyze and compare he operang characerc of hgh frequency olaed ngle and hree-phae DC-DC converer under he ame radonal conrol mehod. Frly, comparon on ngle-phae dual acve brdge bdreconal DC-DC converer (DAB and hree-phae DAB baed on he radonal phae-hfng conrol were carred ou, operang prncple of ngle and hree-phae DAB under he radonal phae-hfng conrol were nroduced n deal and analy on operaon mode wa provded. Secondly, mahemacal model of he ranmed power and backflow power of ngle and hree-phae DAB were bul. Through analy, howed ha, under ame ranmed power, he hree-phae DAB ha lower backflow power and hgher power ranmon effcency. aly, mulaon model of ngle and hree-phae DAB were bul n EMTDC/SCAD o verfy he operang prncple and ranmed power of ngle and hree-phae DAB and he relave ze of her backflow power. frequency characerc of IBDC. IBDC ha agan raed cholar aenon n recen year wh advancemen n emergng power componen and nanomeer porcelan maeral. Keyword-phae-hfng conrol; ngle-phae DAB; hreephae DAB; ranmon power; backflow power A preen, reearche on IBDC boh a home and abroad are manly concenraed n opologcal rucure, conrol mehod and bac operaon characerc, e al. of nglephae DAB. Operaon mode analy and workng effcency of ngle-phae DAB have been compared n [8] under radonal conrol and dual-hf phae conrol mehod of modal analy and workng effcency, whch concluded ha he dual-hf phae conrol could beer olve he problem of ngle-phae DAB backflow power, mprovng effcency of ngle-phae DAB. Selecon mehod of dual-hf phae angle n he mnmum backflow power under dual-phae hf conrol ha been analyzed on he ba of [8] and an opmal raegy of backflow power ha been alo pu forward n [9]. Turn-off lo of power componen can be reduced baed on reonance and dfferen opmal mehod can be ued for opmzng reonance nework parameer of ngle-phae DAB n [1-11]. A knd of hgh-volage gan bdreconal DC-DC converer appled o DC mcro grd ha been propoed n [1]. A ar-rangle hreephae hgh-frequency DC ranformer rucure ha been adoped n he converer. The nfluence of dfferen wrng mehod for hgh-frequency ranformer n hree-phae DAB on operaonal characerc of hree-phae DAB ha been condered n [13]. A volage ource ype of puh-pull hreephae DC-DC converer ha been propoed n [14, 15]. There are oal 6 power componen n prmary and econdary de of he converer. A magnec core ha been hared by hreephae ranformer, whch ha effecvely mproved he ulzaon rae of he magnec core and largely downzed he I. INTRODUCTION Wh he developmen of mar power grd, power converon yem (CS ha played an ncreangly mporan role n power converon of power grd acce lke drbued power upply and energy orage a well a flexble ranmon [1]. Volage machng and elecrcal blockng among all knd of yem are realzed hrough power frequency olang ranformer n varou exng CS oluon [-3]. However, defec lke large volume and bg noe, e al. ha rerced developmen of CS n mar power grd, whle he hgh-frequency olaed bdreconal DC-DC converer (IBDC feaurng rengh n mall volume, lgh wegh and low co ha been pad more and more aenon [1]. In addon o he above rengh, alo ha eay-orealze of wch, bdreconal energy flow, mall volage and curren re of componen, large power deny, and hgh effcency, e al. The converer ha been wdely appled n occaon lke power elecronc ranformer [4], new energy power generaon [5-7] and uper-capacor energy orage, e al. IBDC wa pu forward n 1991, bu lmed by power componen and magnec maeral a ha me, faled o develop. Wha wore, effcency wa far from reachng acually-appled level due o large crcu lo caued by hgh- 16. The auhor - ublhed by Alan re 36 There are many IBDC opologcal rucure. Accordng o he amoun of ranor, can be dvded no dual-ranor rucure lke wo-ranor fly-back IBDC; hree-ranor rucure lke drec-revere fly-back IBDC; four-ranor rucure lke dual puh-pull IBDC; fve-ranor rucure lke full-brdge fly-back IBDC; x-ranor rucure lke halfbrdge/ full-brdge IBDC and egh-ranor rucure lke dual acve-acve full-brdge IBDC (DAB-IBDC. When volage and curren grade of a wchng ube reman conan, power ranmed capably of IBDC proporonal o he amoun of wch ranor. Therefore, DAB-IBDC poee he large power ranmed capably.

2 ranformer. Bu here no comparon beween ngle-phae DAB and hree-phae DAB conduced and mperfec reearch ha been performed n [1-15]. In ummary, he paper wh dual acve full-brdge IBDC a he reearch objec ha a comparave analy on operang prncple of ngle and hree-phae DAB under he radonal phae-hfng conrol, whch ha alo eablhed mahemacal model of ranmed power and backflow power for ngle and hree-phae DAB, repecvely. Smulaon model of ngle and hree-phae DAB are fnally bul n EMTDC/SCAD o verfy he operang prncple, ranmed power and he relave ze of her backflow power rao. II. OERATING RINCIES OF CONVERTERS A. rncple of he Tradonal hae-shfng Conrol Fgure I a crcu opologcal rucure for ngle and hree-phae DAB. Sngle-phae DAB manly compoed of wo full-brdge converer, wo DC capacor, an auxlary nducon and a hgh-frequency ranformer, a hown n Fgure I(a. Srucure of hree-phae DAB mlar o ha of nglephae DAB a hown n Fgure I(b. And Y-Y wrng form adoped n hree-phae hgh-frequency ranformer. In Fgure I(a, U 1 and U are DC volage of boh de of H 1 and H brdge, repecvely. 1 he um for ere connecon beween leakage nducance and auxlary nducon of he hgh-frequency ranformer. Swchng frequence on boh de of H 1 and H are he ame durng workng proce of ngle-phae DAB. Full-brdge dagonal wche of boh de are conduced n urn a he angle of degree. Full-brdge nver oupu volage u h1 and u h of boh de are he quare wave volage wh duy rao of 5%. Volage ze and flow drecon of boh de of nducance 1 can be conrolled va conrollng phae angle among quare wave. Thu, ze and flow drecon of power can alo be conrolled. ower ranmng from U 1 de o U de aken a an example o carry ou analy n he paper, ha, phae poon of u h1 exceedng u h, operang waveform of ngle-phae DAB can be obaned under radonal hf phae, a hown n Fgure II(a. U1 C 11 C1 S1 S D1 D 1 S3 S4 S 1 D 1 S 3 D 3 S 5 D 5 D 4 D 6 D S 4 S 6 S D3 D4 T n : 1 Q1 Q M1 (a ngle-phae DAB Q3 M Q4 Q 1 Q 4 M3 M4 M 1 M 3 M 5 U 1 U C 1 A B C n : 1 Q 3 Q 5 M 4 M 6 M (b hree-phae DAB FIGURE I. CIRCUIT TOOOGIES OF CONVERTERS Q 6 Q C C 1 C U In Fgure II(a, U 1 and U are DC volage of boh de of H 1 and H brdge, repecvely; u h1 full-brdge nver oupu volage of U 1 de; u h he volage obaned upon full-brdge nver oupu volage of U de convered no U 1 de; n ranformaon rao of he ranformer; T h half of a wchng perod; D he hf phae rao whn half of he wchng perod, D 1; Drvng gnal of wchng ranor S 1 repreened by name S 1 for convenence; kewe, oher wchng ranor are repreened n he ame way. The age ha nducve curren n he oppoe phae poon of he volage of orgnal de, ha, age hown n Fgure II(a. Durng h perod, he ranmed power beng negave flow back o he power ource whch defned a backflow power n [9]. From he Fgure II(a, when he ranmed power conan, backflow power ncreae o compenae for he perod of power; amoun of pove ranmed power alo ncreae, leadng o ncreae n converer power crculaon and curren re. I alo ncreae he lo of power componen and magnec elemen, reducng effcency of he converer. Smlar o ngle-phae DAB operaon mode, hree-phae DAB alo adop he radonal phae-hfng conrol mehod. Conducve angle of each brdge arm degree; Up and down arm of he ame half brdge. Succeve angle of conducon for each phae ha a 1-degree dfference. Sze and flow drecon mpoed on boh end of ere nducance can be conrolled hrough conrollng phae angle among quare wave. Unlke ngle-phae DAB, hree-phae DAB dvded no wo dfferen uaon, ha, <φ<π/3, <D<1/3 and π/3<φ<π/3, 1/3<D</3. Thu, analy conduced by akng A-phae power ranmed from U 1 de o U de a an example, ha, phae poon of u h1a exceedng u ha, operang waveform of hree-phae DAB under radonal hf phae conrol mehod can be obaned durng wo dfferen uaon a hown n Fgure II(b and (c. Dfferng from Fgure II(a, u h1a he A-phae nver oupu volage of U 1 de; u ha he volage obaned upon full-brdge nver oupu volage of U de convered no U 1 de. I can be een from he waveform ha backflow power alo exed n he power ranmon proce due o exence of dplacemen beween u h1a and u ha, a hown n Fgure II(b and n Fgure II(c. B. Operaon Mode Analy of Three-hae Dual Acve Brdge B-Dreconal DC-DC Converer Dealed analy conduced on workng characerc of ngle-phae DAB n [9]. So, hree-phae DAB wll be uded n h chaper. Aumng ha he converer ha been workng n a Table ae, workng mode of he converer can be eparaed no x ae n an half perod under he fr uaon of <φ<π/3, <D<1/3 and he econd uaon of π/3<φ<π/3, 1/3<D</3, accordng o he waveform of operang prncple of hree-phae DAB under he phaehfng conrol whch hown n Fgure II. A phae aken a an example o analyze each workng ae. Specfc analy reul are preened n Table I and Table II: 37

3 S 1 (S 4 DT h T h u h1a DT h /3U 1 T h S (S 3 Q 1 (Q 4 u ha /3nU -1/3U 1 Q (Q 3 A -1/3nU u h1 U 1 -U 1 Backflow ower 1 u h u U 1 +nu U 1 -nu nu -nu (c hree-phae DAB: π/3<φ<π/3, 1/3<D</3 FIGURE II. OERATING WAVEFORMS OF CONVERTERS BASED ON THE TRADITIONA HASE-SHIFTING CONTRO TABE I. THE FIRST KIND OF CIRCUMSTANCE Backflow ower u h1a u ha -U 1 -nu -U 1 +nu (a ngle-phae DAB DT h /3U 1 T h /3nU -1/3U 1 Operaon Mode Inducve Curren U1 ( ( U1 ( 1 ( 1 U1 ( ( U1 ( 3 ( 3 U1 ( 4 ( 4 U1 ( 5 ( 5 TABE II. THE SECOND KIND OF CIRCUMSTANCE Operaon Mode Inducve Curren A Backflow ower -1/3nU (b hree-phae DAB:<φ<π/3, <D<1/ U1 ( ( U1 ( 1 ( 1 U1 ( ( U1 ( 3 ( 3 U1 ( 4 ( 4 U1 ( 5 ( 5 38

4 III. ANAYSIS OF THE OWER CHARACTERISTICS OF CONVERTERS A. Eablhmen Of he Mahemacal Model 1 Mahemacal model of hree-phae dual acve brdge b-dreconal DC-DC converer Accordng o he operaon mode analy on hree-phae DAB by akng A phae a he example n chaper. = gven; And volage regulang rao and wchng frequency are e a k=u 1 /(nu 1 and f =1/(T h, repecvely. Therefore, ymmery of ( = ( 6 obaned. (1 When <φ<π/3, <D<1/3, each momen can be preened a 1 =DT h, =1/3T h, 3 =(1/3+DT h, 4 =/3T h, 5 =(/3+DT h, 6 =T h. Accordng o he Table I, can be obaned: D ( ( k (1 D ( 1 ( k k ( Of whch, f D=1/3, hen: 1 ( D D (9 6f 3 Amax (1 36 f Smlarly, regardng hree-phae ymmerc crcu, hen: 1 B C ( D D (11 6f 3 Then, oal ranmed power : 1 ( D D (1 3 Accordng o he backflow defned n chaper, A-phae backflow power can be obaned: D 1 1 ( ( k (3 1 cra uh1a (d T h 1 ( D k 4 f(1 k (13 D 1 1 ( 3 ( k k (4 In fac, f he nducve curren ha been reduced o pror o, hen backflow power cra =. For he momen, ( gven, namely: Regardng A-phae power, hen: D 1 1 ( 4 ( k (5 D 1 1 ( 5 ( k k (6 D ( 6 ( k (7 3 k 1 D (14 Conderng he correlaon beween he backflow power and he ranmed power, A-phae backflow power rao M cra can be defned a: M cra cra 3(1/ 3D / 9k / 9 4 (1 k( D D 3 (15 Accordng o formula (14, conran condon of formula (13 can be obaned: U U U T [ ( d ( d ( d ] h (8 Equaon (1 - (7 are ubued no he above formula repecvely, A-phae ranmed power can be obaned: 3 k 1 D (16 Smlarly: 39

5 Mcr McrA McrB McrC (17 ( When π/3<φ<π/3 and 1/3<D</3, each momen can be preened a 1 =(D 1/3T h, =1/3T h, 3 =DT h, 4 =/3T h, 5 =(1/3+DT h, 6 =T h. Accordng o Table II, can be obaned: D 1 ( ( k ( D 1 1 ( 1 ( k k (19 9 D 1 1 ( ( k ( Regardng A-phae power, here are: D 1 ( 3 ( k k (1 9 D 1 ( 4 ( k ( 3 9 D 1 ( 5 ( k (3 3 9 D 1 ( 6 ( k ( U U U T [ ( d ( d ( d ] h (5 Equaon (17 - (3 are ubued no he above formula repecvely, A-phae ranmed power can be obaned: Of whch D = 1/, hen: Smlarly: 1 ( D D (6 6f Amax 7 (7 16 f 1 B C ( D D (8 6f Toal ranmed power of hree-phae : 1 ( D D (9 A-phae backflow power can be obaned accordng o backflow power defned n arcle 1.1: 1 cra uh1a (d T h ( D D k Dk D k f ( Dk k 4 f(1 k 9 (3 Conderng ze correlaon beween backflow power and ranmed power, M cra backflow rao of A-phae defned : D D k Dk D k cra M cra 1 D D ( ( Dk k 1 (1 k( D D 9 Smlarly: Mcr McrA McrB McrC (3 Mahemacal model of ngle-phae dual acve brdge B-dreconal DC-DC converer I can be obaned from Fgure II(a ha here are four workng ae for ngle-phae DAB. Analy proce of whch mlar o ha of hree-phae DAB. Tranmed power of ngle-phae DAB under he radonal phae-hfng conrol analy can be obaned: Backflow power : cr D(1 D (33 f [ k (D 1] 16 fk ( 1 (34 33

6 Rao of backflow power : M cr cr [ k(d1] 8( k 1 D(1 D (35 B. Comparave Analy of Tranmed ower and Backflow ower Regardng hree-phae DAB, A-phae alo aken a an example o carry ou comparave analy on regulaon range of ranmed power ha normalzed for convenen analy. Comparng ze of (1 wh ha of (7, can be deermned ha he maxmum ranmed power he andard power N, hen: N 7 (36 16 f Accordng o he (9, (6 and (36, he curve relaonhp of hree-phae DAB andard ranmed power changng along wh phae-hfng rao D hown n Fgure III(a. Smlarly, andard power of ngle-phae DAB : N (37 f Accordng o (33 and (37, he curve relaonhp of nglephae DAB andard ranmed power changng along wh hf phae rao D hown n Fgure III(b <φ<π/3,<d<1/3 π/3<φ <π/3,1/3<d</ D (a hree-phae DAB D (b ngle-phae DAB FIGURE III. ADJUSTMENT CURVES OF TRANSMITTED OWER Regulang curve of hree-phae DAB ranmed power, by Fgure III(a, dvded no wo econ. And ranmed power ncreae along wh ncreae of D before D=.5; I reache he maxmum when D=.5; I decreae along wh ncreae of D when D>.5. Regulang curve of hree-phae DAB ranmed power, by Fgure III(b parabolc. Tranmed power alo reache he maxmum when D =.5. Aumng ha ranmed power of ngle-phae DAB and ha of hree-phae DAB are 6KW, repecvely. hae-hfng rao of cloed-loop conrolled ngle-phae DAB.19, whle ha of hree-phae DAB.3. Varaon curve of backflow power rao M cr along wh volage regulaon rao k, a hown n Fgure IV. Mcr ngle-phae DAB hree-phae DAB k 9 1 FIGURE IV. CURVE OF BACKFOW OWER RATIO VARIED WITH VOTAGE REGUATION RATIO Backflow power rao of boh, by Fgure IV, are ncreang along wh ncreae of volage regulang rao k under he radonal phae hfng conrol; A he ame k value, backflow power rao of hree-phae DAB maller under ame ranmed power, whch ndcae ha power ranmed effcency of hree-phae DAB hgher; A he ame me, dfference of backflow power rao beween ngle-phae DAB and hree-phae DAB ncreae gradually along wh ncreae of k. IV. SIMUATION Sngle and hree-phae DAB mulaon model are bul n EMTDC/SCAD repecvely, o a o verfy workng waveform, ranmon power and backflow power rao relaonhp of ngle-phae DAB and hree-phae DAB. A. Smulaon arameer Smulaon parameer for ngle-phae DAB yem are hown n Table III. Volage ouer-loop conrol adoped n volage conrol raegy of he oupu de; conrol block dagram hown n Fgure V. Smulaon parameer for hreephae DAB yem are hown n Table IV. I volage conrol raegy of he oupu de conen wh ha of nglephae DAB. U ref + + U I Comparaor FIGURE V. CONTRO BOCK DIAGRAM WM 331

7 TABE III. SYSTEM RAMETERS OF SINGE-HASE DAB Value Inpu Volage (V 1 Oupu Volage (V 5 Tranmon ower (W 6 Swchng Frequency (khz 1 Inducance (mh 1.57 Capacor (μf 11 Tranformaon Rao TABE IV. SYSTEM RAMETERS OF THREE-HASE DAB Value Inpu Volage (V 1 Oupu Volage (V 5 Tranmon ower (W 6 Swchng Frequency (khz 1 Inducance (mh.6 Capacor (μf 11 Tranformaon Rao B. Smulaon Reul 1 Operang waveform Volage waveform and he nducve curren waveform of ngle-phae DAB and hree-phae DAB n he prmary and econdary de can be obaned va mulaon, a hown n Fgure VI. Volage waveform and curren waveform on boh end of nducance of ngle-phae DAB are preened n Fgure VI (a-b, of whch, volage waveform n prmary and econdary de belong o quare waveform n hgh-frequency; Volage waveform and curren waveform on boh end of nducance of hree-phae DAB preened n Fgure VI (c-d, of whch, volage waveform n prmary and econdary de belong o hgh-frequency mul-level waveform. The mulaon reul are conen wh he workng waveform of radonal hf phae conrol on ngle-phae DAB and hree-phae DAB a hown n Fgure II prmary volage/v nducance curren /A econdary volage/v /μ (a Waveform of volage and nducve curren of ngle-phae DAB /A /μ (b Waveform of nducve curren of ngle-phae DAB prmary volage/v nducance curren /A econdary volage/v /μ (c Waveform of volage and nducve curren of hree-phae DAB 15 /A /μ (d Waveform of nducve curren of hree-phae DAB FIGURE VI. SIMUATED SWITCHING WAVEFORMS FOR SINGE AND THREE-HASE DAB: 1VDC INUT, 4VDC OUTUT The adjumen curve of ranmed power Regulang curve verfcaon Fgure of ngle-phae DAB and hree-phae DAB ranmed power can be obaned n verfyng mulaon of regulang curve for ranmed power, a hown n Fgure VII. In Fgure VII, ranmed power of ngle-phae DAB and hree-phae DAB reach her maxmum when hf phae rao D =.5 ha conen wh (9, (6 and (33 obaned hrough heorecal analy a well a regulang curve of ranmed power hown n Fgure III. / W D (a ngle-phae DAB 33

8 / W D (b hree-phae DAB FIGURE VII. THE VAIDATION OF THE ADJUSTMENT CURVES OF TRANSMITTED OWER 3 Backflow power rao Inananeou power waveform of ngle-phae DAB and hree-phae DAB can be obaned n he mulaon of verfyng backflow power rao, a hown n Fgure VIII. The par below n he Fgure he backflow power. Smaller backflow power of hree-phae DAB and hgher power ranmed effcency can be obaned by Fgure VIII, whch conen wh he concluon ganed n Fgure IV /μ (a ngle-phae DAB /μ (b hree-phae DAB FIGURE VIII. WAVEFORMS OF INSTANTANEOUS OWER OF CONVERTERS / W / W V. CONCUSION The paper nroduce he operang prncple of nglephae DAB and hree-phae DAB under radonal phaehfng conrol and buld mahemacal model for ranmed power and backflow power hrough gvng ou analy on workng ae of a converer. By comparon of DAB backflow power of ngle-phae DAB and hree-phae power, hree-phae DAB wh a maller backflow power and ranmed effcency hgher han ha of ngle-phae DAB when ranmed power reman conan. Smulaon model of ngle-phae DAB and hree-phae DAB are fnally bul n EMTDC/SCAD repecvely o verfy he workng waveform, regulang curve of ranmed power and backflow power rao relaonhp of ngle-phae DAB and hree-phae DAB. ACKNOWEDGMENT Th work wa uppored by he Naonal Naural Scence Foundaon of Chna ( REFERENCES [1] Qang SONG, Bao ZHAO, Wenhua IU, Yumng ZHAO, Nexgeneraon hgh-frequency-olaon power converon echnology for mar grd, roceedng of he CSEE, vol. 34, pp , 14. [] J. M. Guerrero, J. C. Vaquez, J. Maa, e al. Conrol raegy for flexble mcrogrd baed on parallel lne-neracve US yem, IEEE Tranacon on Indural Elecronc, vol. 56, pp , 9. [3] H. C. Chang, T. T. Ma, Y. H. Cheng, J. M. Chang, W. N. Chang, Degn and mplemenaon of a hybrd regenerave power yem combnng grd-e and unnerrupble power upply funcon, IET Renewable ower Generaon, vol. 4, pp , 9. [4] Mngru ZHANG, Jnhu IU, Xn JIN, Reearch on he FREEDM mcro-grd and relay proecon, ower Syem roecon and Conrol, vol. 39, pp , 11. [5] I, Gang IU, Developmen of b-dreconal DC-DC converer n mulple baery energy orage yem, ower Syem roecon and Conrol, vol. 39, pp. 9-94, 11. [6] Chunhu DU, Chenghu ZHANG, Alan CHEN, Fangde ZHAO, Werong XIAO, Dgal conrol and mplemenaon of phoovolac of-wchng DC-DC converer wh hgh-frequency ep-up ranformer olaon, Tranacon of Chna Elecroechncal Socey, vol. 6, pp , 11. [7] Mngru ZHANG, Chengxn IN, Ruxn XU, Grd-conneced phoovolac power generaon echnology baed on SST, ower Syem roecon and Conrol, vol. 4, pp , 1. [8] Bao ZHAO, Qngguang YU, Wexn SUN, B-dreconal full-brdge DC-DC converer wh dual-phae-hfng conrol and backflow power characerc analy, roceedng of he CSEE, vol. 3, pp. 43-5, 1. [9] Xun ZHANG, Guangzhu WANG, Xujuan SHANG, Tng WANG, An opmzed raegy baed on backflow power of b-dreconal dualacve-brdge DC-DC converer wh dual-phae-hfng conrol, roceedng of he CSEE, vol. 36, pp , 16. [1] n WU, Zhgang IU, Xang HONG, Comparon and analy of power conrol characerc for olaed bdreconal full-brdge DC-DC converer, Tranacon of Chna Elecroechncal Socey, vol. 8, pp , 13. [11] Chunfang WANG, Qnchao XU, Sudy of C reonan converer for varable-frequence mcrowave oven power upply, Tranacon of Chna Elecroechncal Socey, vol. 7, pp , 1. [1] Hong ZHU, Hulong ZHOU, anglang REN, ng GU, Ke JIN, A hree-phae bdreconal DC-DC converer baed on phae hf conrol, Tranacon of Chna Elecroechncal Socey, vol. 3, pp , 15. [13] H. B. Nco, E. Ever, G. E. W. Cornel, A.. Elena, erformance evaluaon of a hree-phae dual acve brdge DC DC converer wh dfferen ranformer wndng confguraon, IEEE Tranacon on ower Elecronc, vol. 31, pp , 16. [14] H. R. E. arco, I. Barb, Three-phae puh-pull DC-DC converer: analy, degn, and expermenaon, IEEE Tranacon on Indural Elecronc, vol. 59, pp , 1. [15] R.. Anderen, I. Barb, A ZVS-WM hree-phae curren-fed puh/pull DC/DC converer, IEEE Tranacon on Indural Elecronc, vol. 6, pp ,