Opimized Modulaion of a Four-Por Isolaed DC DC Converer Formed by Inegraion of Three Dual Acive Bridge Converer Sages J. Böhler, F. Krismer, T. Sen and J. W. Kolar Power Elecronic Sysems Laboraory, ETH Zurich, Swizerland boehler@lem.ee.ehz.ch Absrac Muli-por converers have gained more and more ineres in research during recen years, due o he increasing field of possible applicaions, e.g., DC micro grids, energy disribuion in elecric vehicles and more elecric aircraf, and power supplies for cascaded muli-cell converers. This paper presens an opimized modulaion sraegy for a bidirecional muli-por DC DC converer, which consiss of he Inegraion of Three (3) convenional Dual-Acive Bridge (I3DAB) converers ino a srucure ha combines he primary-side full bridges ino a common hree-phase wo-level inverer. The resuling srucure feaures one inpu por and hree isolaed oupu pors. By uilizing so far unused degrees of freedom for he conrol of he power converer, i is shown ha a reducion of he power dissipaion can be achieved by adaping he primary-side duy cycles o he oupu power levels. According o he oucome of a comparaive evaluaion of convenional and opimized modulaion sraegies for an example sysem wih inpu and oupu por volages of and 3 1 V, respecively, and wih a oal nominal power of 3 4 kw, reducions of he conducion losses of up o 23 % and reduced addiional hardware effors o achieve ZVS operaion (wih regard o reduced ransformers magneizing inducances) wihin wide power ranges are achievable and are also expeced for deviaing por volages. Thus, in combinaion wih he presened opimized modulaion sraegy, he I3DAB converer is found o be well suied o muli-por applicaions ha require bidirecional conversion capabiliies, galvanic isolaion, and are subjec o unequal load condiions wih subsanially differen power levels provided by he oupu pors. I. INTRODUCTION Bidirecional and isolaed muli-por converers are beneficial wih respec o efficiency, par coun, and sysem complexiy in applicaions where isolaed power conversion beween muliple sources and loads is required. Prominen examples are DC micro grids, which gain more and more ineres due o he inegraion of renewable energy sources ino he disribuion grid, since energy needs o be exchanged beween differen pars of equipmen (energy sources, disribued energy sorage componens, and loads) [1]. Furher applicaions include power sysems insalled in elecric vehicles (charging infrasrucure or energy exchange beween differen DC-buses) [2,3], he inerconnecions of several DC sysems required in More Elecric Aircraf [4], and muli-cell cascaded H-bridge srucures where he inverer sage of each converer cell requires is individual isolaed DC power supply [5]. Thus, bidirecional muli-por converer opologies are an acive research opic since many years, which is confirmed by a large number of relaed scienific conribuions [6] [8]. U T p,a+ T p,b+ T p,c+ T p,a T p,b T p,c i a i b i c i p,a i p,b i p,c u p,a u p,b u p,c L A L B L C T s,1+ u s,a T s,1 u s,b u s,c T s,2+ T s,2 Fig. 1. Converer opology formed by Inegraion of Three (3) Dual Acive Bridge (I3DAB) converer sages. The considered work invesigaes a power converer sysem wih four pors, where one main (primary-side) por provides power o hree isolaed secondary-side pors. A respecive convenional realizaion employs muliple wo-por converers, e.g. Dual Acive Bridge (DAB) converers, ha share a common inpu DC por. This soluion feaures an independen conrol of he differen converers a he cos of a high number of power semiconducors. A reducion of he required power swiches can be achieved by replacing he converers full bridges by half bridges, which, however, reduces he degrees of freedom for conrol. Alernaively, muli-por DAB converers realize highly inegraed soluions [4,9], respecive invesigaions, however, reveal a comparably high complexiy wih regard o converer conrol and opimizaion. Furhermore, in he considered applicaion, he primary-side full bridge of a muli-por DAB converer is subjec o he oal power delivered o all oupu pors. A disribuion of he oal power o more han wo half bridges is achieved by he Inegraion of Three (3) Dual Acive Bridge (I3DAB) converers and leads o he converer opology proposed in [1] and depiced in Fig. 1: i uses a hree-phase wo-level inverer on he primary side, e.g., realized wih a convenional six-pack power module and feaures a reducion of he number of power semiconducors, compared o hree parallel operaed DAB converers. Besides U A U B U C
he invesigaions of he I3DAB converer presened in [5,1], a variaion of his concep has been recenly used o realize a resonan power converer [11]. However, all documened invesigaions relaed o he I3DAB converer are confined o he operaion wih equal power levels and volages a he oupu pors. Furhermore, only simplified modulaion sraegies have been analyzed, which do no uilize all degrees of freedom available for converer opimizaion. This paper exends he previously documened resuls, invesigaes load scenarios wih unequal power levels a he oupu pors, and presens he developmen of an opimized modulaion sraegy, which akes previously unused degrees of freedom for converer conrol ino consideraion in order o achieve minimum conducion losses. The srucure is organized as follows. Secion II inroduces he operaing principle of he I3DAB converer and specifies he modulaion parameers available for converer conrol. Secion III presens an opimizaion procedure based on a fundamenal frequency analysis of he converer waveforms, which minimizes oal conducion losses of he sysem. Finally, in Secion IV, he resuls obained from he opimizaion are analyzed and verified by means of numerical circui simulaion and Secion V concludes his paper. II. SYSTEM DESCRIPTION The invesigaed I3DAB converer, depiced in Fig. 1, uses hree High Frequency (HF) ransformers, a hree-phase wolevel inverer on he primary side, and hree full bridges on he secondary sides o power he isolaed oupu pors of he hree converer phases A, B, and C. The primary-side winding of each HF ransformer is conneced o he swiching nodes of wo adjacen phases of he hree-phase inverer, which is illusraed in Fig. 2 for phase A, and, hus, he sysem of Fig. 1 has srong similariies o he parallel connecion of hree DAB converers, since he ransformers sray inducances are uilized for power ransfer. For his reason, he basic operaing principles of he DAB and he I3DAB converers are he same: he primary-side and secondary-side power converers apply alernaing volage waveforms o HF ransformer and sray inducance of he corresponding phase, e.g. u p,a ()/n A u s,a () o L A in case of phase A, in order o generae he ransformer currens and provide he required oupu power. Fig. 3 depics examples of hese volage and curren waveforms and defines he hree conrol variables ha are available for phase A, i.e., he duy cycles of u p,a and u s,a and he phase shif beween u p,a and u s,a, 1, 1, and 2 ϕ A 2. (1) Corresponding definiions apply o he duy cycles and phase shifs of phases B and C, however, due o he inegraion of he hree DAB converers primary-side full bridges ino a single hree-phase wo-level inverer, applies. + D p,b + 2, (2) Deailed analysis reveals ha he selecion of +D p,b + < 2 is feasible and exends he parameer space for opimizaion, however, furher improvemens are only achievable for operaion wih low power levels a wo or hree oupu pors and a he cos of increased complexiy due o addiional boundary condiions. For hese reason, he presened analysis is confined o + D p,b + = 2. (3) Thus, compared o he operaion of hree parallel DAB converers, he oal degrees of freedom for he conrol of he hree oupu power levels reduces from nine o eigh (wo primaryside duy cycles, hree secondary-side duy cycles, and hree phase shifs). Furhermore, i is no possible o simulaneously operae all phases wih primary-side duy cycles greaer han 2/3, because > 2/3 D p,b > 2/3 > 2/3 violaes (3). Fig. 3 presens he principal waveforms obained wih he convenional modulaion sraegy described in [5], which operaes he primary-side inverer wih consan duy cycles of D p,{a,b,c} = 2/3 and, hus, uilizes only six degrees of freedom, i.e., D {A,B,C} and ϕ {A,B,C}. Consequenly, a recangular volage as shown in Fig. 3 wih an acive pulse duraion of 2/3 of he swiching period is applied o he primary side of each ransformer. Based on he findings relaed o minimizaion of apparen power and subsequen simplificaions, he convenional modulaion sraegy suggess he secondary-side full bridges o be operaed wih duy cycles of D {A,B,C} = 2 3 + (2 2) ϕ {A,B,C} ϕ{a,b,c} 2. (4) The respecive phase shifs, ϕ {A,B,C}, are seleced in order o provide he required oupu power levels. Based on hese consideraions and he specificaions lised in Tab. I, he ransformers urns raios, n {A,B,C}, and sray inducances, L {A,B,C}, can be deermined. The DAB converer achieves mos efficien converer operaion if he urns raio is equal o he raio of inpu o oupu dc volages [12] and, hus, n A = n B = n C = 1 V = 7 (5) resuls. According o Tab. I, he sysem provides a maximum power of 6.7 kw a all hree oupu pors and, for his reason, all hree sray inducances mus no exceed L {A,B,C},max = U U {A,B,C} 9f s n {A,B,C} P {A,B,C},max = 3.3 µh. (6) Based on his resul and he consideraions of an accepable increase of he reacive power in he HF converer pars a nominal power (4 kw) and pracicable sensiiviies of he converer s oupu dc volages wih respec o changing conrol parameers a low power, L {A,B,C} = 8 %L {A,B,C},max = 2.7 µh (7) has been seleced. Margins of 2 % wih respec o L max cover evenually arising addiional needs due o losses and shor-ime ransien oupu currens.
U T p,a+ T p,b+ T s,1+ Ts,2+ L A i p,a u p,a u s,a U A u p,a =.9 T p,a T p,b T s,1 T s,2 - Fig. 2. Phase A of he I3DAB converer. This figure reveals he known opology of a convenional DAB converer. - 1 V -1 V u p,a u s,a i {A,B,C} 1 A -1 A T s / 2 T s / 2 / (2 f s ) i A T s / 6 T s / 3 T s / 2 2 T s / 3 5 T s / 6 T s Fig. 3. Volage and curren waveforms for phase A of he I3DAB converer. Since he operaing principles of boh converer srucures is he same, he depiced waveforms show large similariies o he volages and currens occuring in a sandard DAB converer. III. TABLE I. i B SPECIFICATIONS OF THE INVESTIGATED I3DAB CONVERTER. Nominal dc volage a inpu por U Nominal dc volages a all oupu pors, U A, U B, U C Raed power a all oupu pors, P A,, P B,, P C, Maximum shor-ime power, P A,max, P B,max, P C,max Swiching frequency, f s i C 1 V 4 kw 6.7 kw 5 khz OPTIMIZATION FOR MINIMUM CONDUCTION LOSSES This Secion describes an opimized modulaion sraegy, which does no confine D p,{a,b,c} o 2/3, as shown in Fig. 4, and, in addiion, uses opimized values for D s,{a,b,c}. The proposed modulaion sraegy faciliaes considerable loss reducions in case of subsanially differen power levels a he oupu pors. A. Developed Modulaion Sraegy The presened derivaions are based on he Fundamenal Frequency Analysis (FFA), o achieve simplified expressions for he oupu power levels, P {A,B,C}, and he rms values of he primary-side referred ransformer currens, I {A,B,C}, and sill achieve reasonable accuracies [13]. By way of example, Up,A(1) 2 + n2 A U s,a(1) 2 2U p,a(1)n A U s,a(1) cos(ϕ A ) I A(1) = 2f s n 2 A L, A (8) u p,b - u p,c - D p,b =.7 =.4 T s / 6 T s / 3 T s / 2 2 T s / 3 5 T s / 6 T s Fig. 4. General volage waveforms on he primary side for =.9, D p,b =.7, and =.4. The dashed lines illusrae he swiching insans of he primary-side half bridges. P A(1) = U p,a(1)u s,a(1) sin(ϕ A ), (9) 2f s n A L A 2 2 ( ) U p,a(1) = U sin 2 [, 1], and (1) 2 2 ( ) U s,a(1) = U A sin 2 [, 1] (11) are obained for phase A, for he fundamenal frequency componens of i A (), he power, u p,a (), and u s,a (), cf. Fig. 1, and similar expressions resul for phases B and C; he index (1) denoes he fundamenal frequency componen, I A(1), U p,a(1), and U s,a(1) are rms values. The conducion losses are calculaed wih he rms ransformer currens I {A,B,C}(1) and he equivalen loss resisors, R {A,B,C}, ha are considered in series o he ransformers primary-side erminals. These resisors ake he conribuions of he on-sae channel resisances of he primary-side and secondary-side MOSFETs, R DS,on,p and R DS,on,s,{A,B,C}, 1 and he primary-side referred effecive coil resisances of he HF ransformers, R Cu,{A,B,C}, ino accoun. A wo-sep derivaion, illusraed in Fig. 5, yields he conribuions of R DS,on,p o he equivalen loss resisances, R {A,B,C} : in a firs sep, same conducion losses resul if he swiches on-sae resisances are moved from he verical branches of he primary-side half bridges o he connecing wires beween he oupus of he half bridges and he HF neworks ( 1 in Fig. 5). In a second sep, an analyical invesigaion using wye-dela ransformaion reveals ha he conducion losses remain same for an equivalen resisance of 3R DS,on,p being conneced in series o each HF ransformer ( 2 in Fig. 5). Wih regard o he secondary-side full bridges, always wo swiches conduc he respecive ransformer curren and, hus, he conribuion o R {A,B,C} is 2n 2 {A,B,C} R DS,on,s,{A,B,C}. Based 1 This analysis considers six idenical MOSFETs for he primary-side hreephase wo-level inverer and four idenical MOSFETs for each secondary-side full bridge.
Power Limi 182 Power Limi 1 U 1 R DS,on R DS,on R DS,on 2 3R DS,on u i A p,a u p,b i B u i C p,c u L,A L A L B L C R s,a u s,a Fig. 5. Illusraion of he ransformaion of he channel on-sae resisances of he primary-side MOSFETs, R DS,on, ino equivalen resisances, R eq,p = 3R DS,on, conneced in series o he primary-side ransformer windings. R s,a R s,c u s,b u s,c IA(1) 2 / A 2 (a) 8 6 4 2 P A(1) = 1 kw, =.4 P A(1) = 3 kw, =.6.2.4.8 1.2.4.6.8 1,op,min D D,op s,a s,a,min (b) on hese consideraions, R {A,B,C} = 3R DS,on,p + R Cu,{A,B,C} + 2n 2 {A,B,C} R DS,on,s,{A,B,C} (12) and he fundamenal frequency componen of he conducion losses, resul. P c(1) = R A I 2 A(1) + R B I 2 B(1) + R C I 2 C(1), (13) Expression (13) is he basis for he derivaion of a modulaion sraegy ha minimizes he conducion losses and enables he calculaion of opimal duy cycles, D p,{a,b,c},op and D s,{a,b,c},op. In a firs sep, he secondary-side duy cycles are opimized, since he secondary-side full bridges can be operaed independen of each oher. In his regard, Fig. 6 illusraes he conduced calculaion and plos he characerisic of IA(1) 2 agains for < 1 for wo differen primary-side duy cycles and power levels, i.e, P A(1) = 1 kw, =.4 in Fig. 6(a) and P A(1) = 3 kw, =.6 in Fig. 6(b). Wih respec o he depiced minima of IA(1) 2, Figs. 6(a) and (b) reveal opimal duy cycles of,op =.42 and,op =.71, respecively. The corresponding calculaion, hus, needs o evaluae d [ ] Ik(1) 2 d [ sin ( )] =, k {A, B, C}, (14) D s,k 2 which yields ( ) sin 2 D s,k,op = 16U ( 4 sin4 2 D p,k) + 6 fs 2 n 4 k L2 k P k(1) 2 4U n k U k sin ( 2 D ). (15) p,k The calculaion of opimal primary-side duy cycles involves all converer phases, due o he couplings of he primary-side duy cycles according o (3). For his reason, he complee expression (13) needs o be aken ino accoun. However, due o same raings of he hree oupu pors, cf. Tab. I, equal equivalen resisances are considered, R A = R B = R C, (16) which simplifies he cos funcion for he opimizaion o f cos = I 2 A(1) + I 2 B(1) + I 2 C(1). (17) Fig. 6. Squares of he rms values of he primary-side ransformer curren of phase A for inpu and oupu por dc volages according o Tab. I, n A = 7, L A = 2.7 µh, varying values of, and differen power levels and primaryside duy cycles: (a) P A(1) = 1 kw, =.4, and (b) P A(1) = 3 kw, =.6. The required oupu power canno be provided for <,min. Minima in IA(1) 2 resul for: (a) =.42 and (b) =.71. Dp,B Dp,B,op (a) 1.6.4.2 324 256 + D p,b + = 2 196 169 324 256.2.4.6 1,op.2.4.6.8 1 (b) 196 144 121 9 77 + D p,b + = 2 7 67 64,op Fig. 7. Resuls deermined for f cos, cf. (17), for inpu and oupu volages according o Tab. I, n {A,B,C} = 7, L {A,B,C} = 2.7 µh, differen primary-side duy cycles, and D p,b ( = 2 D p,b ), opimal duy cycle values for he secondary-side full bridges, and differen oupu power levels: (a) P A(1) = P B(1) = P C(1) = 4 kw, (b) P B(1) = 2 kw, P C(1) = 1 kw. Opimal primary-side duy cycles of = D p,b = =.67 and =.86, D p,b =.69, =.45 resul for he wo load scenarios, respecively. Operaion in he hached region is no possible because his would imply > 1 according o (3). Fig. 7 illusraes he resuls compued for f cos for 1, D p,b 1, opimized secondary-side duy cycles, and for wo differen load scenarios: a symmerical load case wih P A(1) = P B(1) = P C(1) = 4 kw in Fig. 7(a) and an asymmerical load scenario in Fig. 7(b) wih P B(1) = 2 kw, P C(1) = 1 kw. The hached area in Fig. 7 denoes combinaions of unallowed values for and D p,b, which would violae (3). Due o he operaion wih differen power levels a he oupu pors, he opimal primary-side duy cycles ha minimize he cos funcion in Fig. 7(b) are,op =.86, D p,b,op =.69 and,op =.45, i.e., differen o 2/3 whereas opimal operaion in he symmerical case is achieved for,op = D p,b,op =,op = 2/3. The mahemaical descripion of he opimizaion illusraed in Fig. 7 is df cos d [ sin ( )] = 2 df cos d [ sin ( D p,b 2 Dp,B,op )] =. (18) However, no closed-form analyical soluion has been found
for (18). Hence, a numerical solver is used o deermine he opimal duy cycle values. Wih known duy cycles and oupu power levels, he corresponding phase shifs, ϕ {A,B,C},op, are deermined according o (9), which, for phase k, k {A, B, C}, is ϕ k,op = arcsin [ B. Discussion and ZVS 3 f s n k L k P k(1) 4U U k sin ( 2 D ( p,k,op) sin 2 D ) s,k,op ]. (19) This Secion evaluaes he opimized modulaion sraegy for he I3DAB converer specified and designed in Secion II and for 24 characerisic operaing poins ha resul from he combinaions of he seleced oupu power levels lised below. P A(1) = 4. kw P B(1) = [., 2., 4. ] 1 kw P C(1) = [.,.1,.25,.5, 1., 2., 3., 4. ] 1 kw (2) To begin wih, Fig. 8 depics he conrol variables, D p,{a,b,c}, D s,{a,b,c}, and ϕ {A,B,C}, for he convenional modulaion sraegy presened in [1], which uses D p,{a,b,c} = 2/3 for all operaing poins and confines he ranges for D s,{a,b,c} o values beween 2/3 and 1, according o (4). Wih D p,{a,b,c} = 2/3, he convenional modulaion sraegy faciliaes decoupled conrol of oupu power and por volage of each phase, however, excludes a grea range of poenial opions for improved converer operaion. Fig. 9 presens he conrol variables deermined wih he developed opimized modulaion sraegy and reveals he expeced change of he primary-side duy cycles for changing oupu power levels. The major findings drawn from Fig. 9 are summarized below. An increase of he oupu power of a cerain converer phase leads o an increase of he corresponding primary-side duy cycle, e.g., for increasing P C(1) in Fig. 9, and, due o (3), a decrease of one or boh of he remaining primary-side duy cycles. The primary-side duy cycles are disribued according o he corresponding power levels, i.e., he greaes primary-side duy cycle resuls for he converer phase wih he highes oupu power and he smalles duy cycle for he phase wih he lowes oupu power. In comparison o he convenional modulaion sraegy, he linear relaionship beween D s,{a,b,c} and ϕ s,{a,b,c} does no apply anymore and he full range of D s,{a,b,c} 1 is uilized. The opimized modulaion sraegy achieves a reducion of he value of he cos funcion by up o 23 %, which is deailed in he course of he verificaion presened in Secion IV. However, boh, he convenional and he opimized modulaion sraegies are found o lose ZVS a he primary side a operaing poins wih subsanially differen power levels of he hree converer pors, e.g., one half bridge of he hreephase inverer loses ZVS for P A(1) = 3 kw, P B(1) = 3 kw, and P C(1) = 1 kw. Reduced magneizing inducances of he (a) (b).9.6.3.9.6.3.9.6 Phase A P B(1) = P B(1) = 2 kw.3 P B(1) = 4 kw (c) 1 2 3 4 Phase B D p,b, D s,b D p,b D s,b D p,b D s,b Phase C 4 3 2 1 4 3 2 1 4 3 2 1 1 2 3 4 1 2 3 4 Fig. 8. Conrol parameers calculaed wih he convenional modulaion scheme proposed in [1] for < P C(1) < 4 kw, and differen power a he oupu por of phase B: (a) P B(1) =, (b) P B(1) = 2 kw, (c) P B(1) = 4 kw. All primary-side duy cycles are fixed o D p,{a,b,c} = 2/3. The values of D s,{a,b,c} and ϕ {A,B,C} are deermined by he according power flow, where a linear relaionship beween D s,{a,b,c} and ϕ {A,B,C} according o (4) is considered. HF ransformers can be uilized o gain ZVS again and he value of he required magneizing inducance is used as a Figure of Meri for evaluaing he modulaion sraegies wih regard o heir suiabiliies for operaion wih ZVS, i.e., a larger allowable magneizing inducance denoes a modulaion sraegy ha is more suiable wih respec o ZVS. The calculaion of maximum allowable magneizing inducances for 512 differen operaing poins, creaed from all combinaions of P {A,B,C}(1) = [.,.1,.25,.5, 1., 2., 3., 4. ] 1 kw, reurns maximum magneizing inducances of L mag,conv < 1.47 mh and L mag,op < 4.59 mh (21) for he hree HF ransformers and he convenional and opimized modulaion sraegies, respecively. 2 According o his resul, he opimized modulaion sraegy is far more robus wih respec o ZVS operaion han he convenional modulaion. On a final noe, i is worh o menion ha boh invesigaed modulaion sraegies feaure complee four-por operaion, i.e., bidirecional operaion of he hree converer phases 2 L mag,conv and L mag,op are deermined based on he assumpion ha zero insananeous curren enables ZVS. However, a pracical implemenaion of ZVS requires increased currens a he swiching insans. Thus, he magneizing inducances need o be reduced, accordingly.
(a) (b).9.6.3.9.6.3.9.6 Phase A P B(1) = P B(1) = 2 kw Dp,A.3 P B(1) = 4 kw (c) 1 2 3 4 Phase B D p,b, D s,b D s,b D p,b D s,b D p,b Phase C 4 3 2 1 4 3 2 1 4 3 2 1 1 2 3 4 1 2 3 4 Fig. 9. Conrol parameers for minimum oal rms ransformer curren, < P C(1) < 4 kw, and differen power a he oupu por of phase B: (a) P B(1) =, (b) P B(1) = 2 kw, (c) P B(1) = 4 kw. The primaryside duy cycles are disribued according o he corresponding power levels where increasing power levels correspond wih increasing duy cycles of he according phase. and converer operaion wih differen oupu por volages, which is only limied by he maximum oupu power levels, he requiremen of posiive por volages, and he addiional limiaions imposed by he converer hardware (e.g. hermal limiaions). IV. VERIFICATION AND RESULTS The resuls obained from he opimizaion described in Secion III are verified by means of numerical circui simulaion. For his purpose, wo characerisic load scenarios wih differen oupu power levels are chosen: Scenario I: P B(1) = P C(1) = ; Scenario II: P B(1) = 2 kw, P C(1) =.1 kw. Fig. 1 and Fig. 11 depic he simulaed waveforms corresponding o he wo load scenarios, respecively, and for convenional and opimized modulaion sraegies. Comparing he primary-side volage waveforms for boh modulaion sraegies i is clearly visible ha for he opimized modulaion sraegy he acive duy cycles applied o he primary sides of he ransformers deviae beween he phases. In he firs load scenario, depiced in Fig. 1, he primary-side duy cycle of he only por delivering oupu power (phase A) is se o he maximum value of 1. Due o he larger volage ime area applied o he ransformer, he corresponding phase curren ampliude can be reduced when compared o he convenional modulaion. By reason of (3), he remaining phases are operaed wih a primary-side duy cycle of D p,b = =.5. Power flow for all phases is conrolled via heir corresponding secondaryside duy cycles and he phase shifs beween primary and secondary sides, which are chosen according o (15) and (19). In he second load scenario, depiced in Fig. 11, he rms currens of phases A and B are reduced by maximizing he primary-side duy cycles of he corresponding phase volages, which is similar o he resuls obained for scenario I, cf. Fig. 1. As a consequence, his leads o a reducion of, resuling in a small acive on-ime of phase C as he according oupu power approaches zero. The opimized primary-side duy cycles, hus, allow for low losses in phase C and, a he same ime, feaure 1 and D p,b 1, which enables a reducion of he rms currens in he remaining phases. The opimized modulaion sraegy reduces he values of he cos funcion, f cos, defined wih (17), from 56 A 2 and 7 A 2 o 4 A 2 and 49 A 2 for load scenarios I and II, respecively. Fig. 12 presens he values of f cos for boh modulaion sraegies and for he 24 operaing poins defined wih (2), cf. Secion III-B. The value of f cos is proporional o he oal conducion losses of he converer sysem and is, hus, a suiable measure for comparison. From he presened graphs i becomes eviden ha calculaed and simulaed values of fundamenal frequency componens exacly mach. Compared o he convenional modulaion scheme, he opimized modulaion sraegy achieves reducions of he oal conducion losses of up o 23 % (e.g., a P B(1) = 4 kw, and P C(1) = ). As expeced, he opimized conrol of he primary-side volages is especially favorable for cases where large deviaions beween he hree oupu power levels occur. The resuls of Fig. 12, however, only ake he fundamenal frequency componens ino consideraion and neglec higher order harmonics in he waveforms. The addiional conribuions of higher order harmonics increase he power levels and he rms currens in all converer componens. In order o compensae he deviaions and precisely mee he desired oupu power levels, he values of P A(1), P B(1), and P C(1), which denoe he inpu parameers for he compuaion of duy cycles and phase angles, are slighly reduced. Fig. 13 presens he corresponding resuls, which include all frequency componens in rms currens and power levels. The obained resuls confirm he effeciveness of he opimized modulaion scheme also when aking higher order harmonic componens ino accoun, wih he conducion losses being reduced by up o 3 % (e.g., a P A = 4 kw, P B = 4 kw, and P C = ). A direc comparison of Figs. 12 and 13 reveals only minor differences beween he resuls obained wih FFA and he deailed resuls ha include all harmonic componens, which jusifies he presened opimizaion procedure. V. CONCLUSION This paper presens an opimized modulaion sraegy for he I3DAB converer opology, which minimizes he conducion losses generaed by he power converer sysem. Based on fundamenal frequency analysis, he operaing behavior of
up,k us,k ik 1 kv 5 V -5 V -1 kv 1 kv 5 V -5 V -1 kv 12 A 6 A -6 A Phase A, P A(1) = 4 kw Phase B, P B(1) = Phase C, P C(1) = Op. -12 A 1 µs 2 µs 3 µs 4 µs 5 µs 6 µs Op. 1 µs 2 µs 3 µs 4 µs 5 µs 6 µs Time Op. 1 µs 2 µs 3 µs 4 µs 5 µs 6 µs Fig. 1. Simulaed volage and curren waveforms for P B(1) =, and P C(1) =. Only one por (phase A) delivers oupu power, herefore, he according primary-side duy cycle is se o he maximum value in order o minimize he rms curren. Due o addiional harmonic componens which are negleced in he FFA, higher oupu powers han expeced resul, leading o oal oupu power levels of P A = 4.4 kw and P B = P C =. The values of he cos funcion, cf. (17), are 56 A 2 and 4 A 2 for convenional and opimized modulaion sraegies, respecively. 1 kv 5 V Phase A, P A(1) = 4 kw Op. Phase B, P B(1) = 2 kw Op. Phase C, P C(1) =.1 kw Op. up,k -5 V -1 kv 1 kv 5 V us,k -5 V -1 kv 12 A 6 A ik -6 A -12 A 1 µs 2 µs 3 µs 4 µs 5 µs 6 µs 1 µs 2 µs 3 µs 4 µs 5 µs 6 µs Time 1 µs 2 µs 3 µs 4 µs 5 µs 6 µs Fig. 11. Simulaed volage and curren waveforms for P B(1) = 2 kw and P C(1) =.1 kw. Due o addiional harmonic componens, increased oupu power levels of P A = 4.4 kw, P B = 2.2 kw, and P C =.3 kw resul. Similar o he resuls of Fig. 1, increased primary-side duy cycles are used for he phases ha are subjec o high loads (phases B and C). The values of he cos funcion, cf. (17), are 7 A 2 and 49 A 2 for convenional and opimized modulaion sraegies, respecively. he converer is described and available degrees of freedom for converer opimizaion are idenified. The invesigaed modulaion sraegy adaps he primary-side duy cycles in accordance o he oupu power levels, o achieve reduced rms currens in he power semiconducors and he windings of he HF ransformers. Compared o he convenional modulaion sraegy, i is found ha reducions of he oal conducion losses are especially feasible if he oupu power levels provided by he differen oupu pors are subjec o large differences. Furhermore, invesigaions wih respec o ZVS reveal ha
Toal RMS Curren / A 2 18 12 6 P B(1) = 1 2 3 4 Convenional (calc.) Opimized (calc.) P B(1) = 2 kw 1 2 3 4 Convenional (sim.) Opimized (sim.) P B(1) = 4 kw 1 2 3 4 Fig. 12. Comparison of he calculaed and simulaed rms ransformer currens for boh modulaion sraegies. Only he fundamenal frequency componens of curren and power are considered. The simulaed resuls precisely mach he calculaed values obained from he opimizaion. Based on hese resuls, reducions of he conducion losses by up o 23 % are esimaed (e.g., a P B(1) = 4 kw, and P C(1) = ). Toal RMS Curren / A 2 18 12 Convenional (calc.) Opimized (calc.) Convenional (sim.) Opimized (sim.) 6 P A = 4 kw, P A = 4 kw, P A = 4 kw, P B = P B = 2 kw P B = 4 kw 1 2 3 4 1 2 3 4 1 2 3 4 P C / kw P C / kw P C / kw Fig. 13. Simulaion resuls for he convenional and he opimized modulaion scheme wih all specral componens being aken ino accoun. The simulaion resuls prove ha he prediced reducion in conducion losses is sill achieved when higher order harmonic componens are considered, hereby jusifying he presened FFA-based opimizaion. The opimized modulaion sraegy reduces conducion losses by up o 3 % (e.g., a P A = 4 kw, P B = 4 kw, and P C = ). he I3DAB converer may lose ZVS in case of unequal load condiions for boh, convenional and opimized modulaion sraegies. However, ZVS can be regained by reducing he magneizing inducance of he HF ransformers. An exemplary I3DAB converer sysem serves for he purpose of evaluaion. I provides inpu and oupu por dc volages of and 1 V, respecively, and power levels of up o 4 kw a each oupu por, i.e., a oal power of 12 kw. Depending on he considered operaing poin, he opimized modulaion sraegy is found o enable reducions of he oal conducion losses of up o 23 %, which is successfully verified by means of numerical circui simulaions. Wih regard o ZVS, calculaed resuls for 512 differen operaing poins render he opimized modulaion scheme more advanageous wih respec o ZVS robusness, due o a significanly higher allowable value of he magneizing inducance (4.59 mh insead of 1.47 mh). Follow-up invesigaions, in addiion, reveal ha he opimized modulaion sraegy achieves reduced losses also in case of deviaing por volages. Currenly, he realizaion of he hardware prooype is ongoing, which, in a nex sep, will serve for experimenal verificaion. According o he obained findings, he I3DAB converer feaures a high level of inegraion combined wih he capabiliy o opimize he uilizaion of is power componens wih respec o he disribuions of he oupu power levels. Thus, i is highly suiable for muli-por applicaions, which require bidirecional conversion capabiliy, galvanic isolaion, and are subjec o unequal load condiions. REFERENCES [1] Z. Wang, Inerleaved muli-phase isolaed bidirecional DC-DC converer and is exension, Ph.D. disseraion, Florida Sae Universiy, March 212. [2] M. Jafari, Z. Malekjamshidi, G. Pla, J. G. Zhu, and D. G. Dorrell, A muli-por converer based renewable energy sysem for residenial consumers of smar grid, in Proc. 41s Annual IEEE Indusrial Elecronics Sociey Conf. (IECON), Yokohama, Japan, 9 12 Nov. 215, pp. 5168 5173. [3] G. Walrich, J. L. Duare, and M. A. M. Hendrix, Mulipor converers for fas chargers of elecrical vehicles - focus on high-frequency coaxial ransformers, in Proc. IEEE Energy Conversion Congr. and Expo. (ECCE Asia), Sapporo, Japan, 21 24 June 21, pp. 3151 3157. [4] G. Buicchi, L. F. Cosa, D. Baraer, M. Liserre, and E. Dominguez, A quadruple acive bridge converer for he sorage inegraion on he more elecric aircraf, IEEE Trans. Power Elecron., vol. 33, no. 8, pp. 8174 8186, Sep. 218. [5] H. Wrede, Beiräge zur Erhhung von Versorgungssicherhei und Spannungsqualiä in der Überragung und Vereilung elekrischer Energie durch leisungselekronische Beriebsmiel (in German), Ph.D. disseraion, Ruhr Universiy Bochum, Jan. 24. [6] B. J. D. Vermuls, J. L. Duare, E. A. Lomonova, and K. G. E. Wijnands, Scalable muli-por acive-bridge converers: Modelling and opimised conrol, IET Power Elecronics, vol. 1, no. 1, pp. 8 91, Jan. 217. [7] F. Jauch and J. Biela, An innovaive bidirecional isolaed muli-por converer wih muli-phase AC pors and DC pors, in Proc. 15h European Conf. on Power Elecronics and Applicaions (EPE), Lille, France, 2 6 Sep. 213, pp. 1 7. [8] J. Schäfer, D. Boris, and J. W. Kolar, Muli-por muli-cell DC/DC converer opology for elecric vehicle s power disribuion neworks, in Proc. 18h IEEE Workshop on Conrol and Modeling for Power Elecronics (COMPEL), Sanford, CA, USA, 9 12 July 217, pp. 1 9. [9] L. Cosa, G. Buicchi, and M. Liserre, Opimum design of a mulipleacive-bridge dc-dc converer for smar ransformer, IEEE Trans. Power Elecron., pp. 1 11, Jan. 218, early access. [1] H. Wrede, V. Saud, and A. Seimel, A sof-swiched dual acive bridge 3dc-o-1dc converer employed in a high-volage elecronic power ransformer, in Proc. 1h European Conf. on Power Elecronics and Applicaions (EPE), Toulouse, France, 2 4 Sep. 23, pp. 1 8. [11] B. Li, Q. Li, and F. Lee, A WBG based hree phase 12.5 kw 5 khz CLLC resonan converer wih inegraed PCB winding ransformer, in Proc. IEEE Applied Power Elecronics Conf. and Expo. (APEC), San Anonio, TX, USA, 4 8 March 218, pp. 469 475. [12] F. Krismer and J. Kolar, Efficiency-opimized high-curren dual acive bridge converer for auomoive applicaions, IEEE Trans. Ind. Elecron., vol. 59, no. 7, pp. 2745 276, July 212. [13] B. Zhao, Q. Song, W. Liu, G. Liu, and Y. Zhao, Universal highfrequency-link characerizaion and pracical fundamenal-opimal sraegy for dual-acive-bridge dc-dc converer under pwm plus phase-shif conrol, IEEE Trans. Power Elecron., vol. 3, no. 12, pp. 6488 6494, Dec. 215.