Power Factor Correction Focusing on Magnetic Coupling of Parallel-connected Wires for Inductive Power Transfer System

Transcription

1 Power Fator Corretion Fouing on agneti Couling of Parallel-onneted Wire for Indutive Power Tranfer Sytem Keita Furuawa, Keiue Kuaa, Jun-ihi Itoh Nagaoa Univerity of Tehnology Deartment of Eletrial, Eletroni and Information Nagaoa, Niigata, Jaan Abtrat Thi aer rooe a ower fator orretion method of a non-reonant IPT ytem uing a four-winding tranformer. The rooed tehnique i alied to the IPT ytem with a dual ative bridge onverter to redue ondution lo and winding lo. When two air of the rimary-ide and the eondary-ide wire are onneted in arallel, the low ouling oeffiient between the wire driven by in-hae voltage orret the ower fator from the viewoint of the ower uly due to the imrovement of an equivalent magneti ouling. The effet of the ower fator orretion i aeed by exeriment with two four-winding tranformer, ouling oeffiient of whih i different from eah other. A exerimental reult, it i onfirmed that a maximum effiieny with the lower ouling oeffiient between the arallel onneted wire i imroved by.% in omarion with the ytem, whih ha the high ouling oeffiient. Keyword wirele ower tranfer; multi-winding tranformer; non-reonant indutive ower tranfer; dual ative bridge I. INTRODUCTION In reent year, indutive ower tranfer (IPT) ytem have attrated many reearher a a afety and onvenient battery harger for eletrial vehile (EV) [-6]. The IPT ytem are able to ahieve ower tranmiion without eletrial ontat. An inreae in a tranmiion ditane of tranmiion oil aue a redution of mutual indutane, whih reult in a low ower fator from the view of ower uly beaue the reative urrent inreae [7]. arge reative urrent i one of the fator reduing ytem effiieny. In order to orret the ower fator, the IPT ytem uing reonane henomena have been rooed [-6][8]. Reonant aaitor are onneted in erie or arallel to the tranmiion oil in order to omenate the reatane of the oil by C reonane [-6]. Therefore, the reonant IPT ytem an ahieve unity ower fator at the reonane frequeny beaue reative urrent i aneled. Conidering with atual high-ower aliation, however, oition mialignment of oil or tolerane of reonant omonent degrade the tranmiion effiieny beaue the reonant frequeny doe not math an oeration frequeny [], [6]. In artiular, aaitive load inreae withing lo of a rimary-ide inverter beaue ZVS (zero voltage withing) and ZCS (zero urrent withing) are not ahieved [8]. In order to olve the above-mentioned roblem of the reonant IPT ytem, the non-reonant IPT ytem utilizing a dual ative bridge () onverter ha been rooed [9]. In the ytem, the tranmiion ower i determined by a hae differene between the inverter outut voltage of the rimary ide and the eondary ide. Thi method ahieve the ower fator orretion without reonant aaitor [8]. Beide, ZVS i ahieved at all withing devie deite load ondition [9]-[]. However, high reative urrent till lead to the inreae in a ondution lo of the withing devie and the winding lo of the tranmiion oil due to low magneti ouling []. Thu the non-reonant IPT ytem ha to ahieve the redution of the ondution lo and the winding lo when the ytem i emloyed to lower-magneti ouling aliation. Thi aer rooe a ower-fator-orretion method for non-reonant IPT ytem with a multi-winding tranformer a one of the olution to overome iue of the high ondution lo and winding lo. Two or more wire are onneted to the rimary ore and the eondary ore in arallel. From the equivalent iruit of the ytem, the wea ouling oeffiient between the arallel-onneted wire dereae equivalent leaage indutane. Thu a low- tranformer redue the reative urrent at the ame load. Thi aer i organized a follow; firt, the theoretial exreion of outut ower and the ower fator i derived. Then, the omarative teting reult are howed with a.- W rototye uing two multi-winding tranformer whih have different ouling : the onventional high- tranformer and the rooed low- tranformer. A a reult, ower-fator orretion and redution of inut urrent are ahieved in the rooed tranformer. oreover, the maximum ytem

2 effiieny of the rototye iruit i imroved from 87.% to 9.% with the rooed tranformer. II. CONVENTIONA ETHODS OF IPT SYSTES A. Conventional Reonant Indutive Power Tranfer Sytem Fig. how the equivalent iruit of the reonant IPT ytem fouing on the AC voltage of fundamental frequeny. Reonant aaitor are onneted to inut and outut of the tranmiion oil in erie (S/S tye). The inut urrent Iin and the outut urrent Iout of the ytem are exreed by () and () [8]. r R j C I in V r j r R j C C... () j I out V r j r R j C C... () where V i the inut voltage, i the elf-indutane of the tranmiion oil, r i the equivalent erie reitane, C i the aaitane of the reonant aaitor, R i the load reitane and i the ouling oeffiient between the tranmiion oil. The value C i deigned to anel the reatane of the elfindutane of the tranmiion oil. The reonane angular frequeny i deided by () [8].... () C The oeration frequeny f w of the inverter i generally deigned ame or a little larger than the reonane frequeny / () to redue withing lo with zero-voltage-withing (ZVS) or zero-urrent-withing (ZCS). However, the error of due to oition mialignment of oil or tolerane of the reonant omonent aue the degradation of the ytem effiieny and the outut ower. In artiular, the inverter oerate neither ZCS nor ZVS with a aaitive load. In addition, low ower fator i aued by the inreaed reatane. B. Non-reonant Indutive Power Tranfer Sytem Alied to Dual Ative Bridge Fig. how the non-reonant IPT ytem utilizing the onverter [9]. The ingle-hae full-bridge inverter are emloyed at both the rimary ide and the eondary ide of the tranmiion oil. Fig. how the oeration rinile of the non-reonant IPT ytem. Not only the rimary inverter but alo the eondary inverter uly AC voltage v and v to the tranmiion oil. Note that the inverter outut two-level voltage and the frequeny of the outut voltage i ame. Tranmiion ower P i reented by V in Vout P...(4), f w where V in and V out are the inut and outut DC voltage, i the elf-indutane of the tranmiion oil, and i the lagging hae differene between v and v. The tranmiion ower of the non-reonant IPT ytem i ontrolled by adjuting the lagging hae differene [9]. If i oitive, the ower flow i rimary ide to eondary ide. On the other hand, when i negative, the ower flow i eondary ide to rimary ide. Thu the non-reonant IPT ytem ahieve not only the ontrol of the tranmiion ower, but alo the bi-diretional oeration without additional omenation iruit [9]. I in f w C V r (-) (-) Fig.. Equivalent iruit of a S/S reonant IPT ytem. The elfindutane and the equivalent erie reitane r in eah the rimary ide and eondary ide are ame value for imlify. P (-) V in v i =f w (-) r v i Fig.. Non-reonant IPT ytem alied dual ative bridge. v -V in V out v i i V in -V out /f w Fig.. Voltage and urrent waveform of non-reonant IPT ytem utilized dual ative bridge. The inverter are oerated a two-level inverter. Polaritie of the voltage and diretion of the urrent i defined in Fig.. C V V out I out R

3 in V in P S S I _rm,i Winding P Four-winding tranformer S5 S7 + + v oq in i v v C in i Winding I _rm,i v C out i out P out V out S S4 S6 S8 Primary ide v Winding i i 4 v 4 Winding 4 Seandary ide Fig. 4. Ciruit onfiguration of rooed IPT ytem uing four-winding tranformer. The ore of the four-winding tranformer i hared in eah the rimary ide and the eondary ide. The outut ower P out i defined a lower value of P or P. The total ower fator from the view oint of the inverter i alway lower than, beaue the exitation urrent flow for the mall mutual indutane regardle of [9] []. In artiular, when the ouling oeffiient i ignifiantly low ( =..), the ower fator i greatly dereaed beaue of the large exitation urrent. The inreae in the exitation urrent aue large ondution lo and oer lo. Therefore, it i imortant to ee the ouling oeffiient a high a oible. In the next etion, the rooed ower-fatororretion method with a four-winding tranformer i deribed. III. PROPOSED CIRCUIT CONFIGURATION A. Sytem Configuration Fig. 4 how the ytem onfiguration of the rooed ytem. The differene of the rooed ytem omared with the onventional non-reonant IPT ytem (Fig. ) i that the four-winding tranformer i introdued a the tranmiion oil. Two rimary ide wire are wound onto one hared rimary ore. The ame roedure i arried out at the eondary ide. Through thi winding truture, the winding on eah ide are magnetially ouled with the ouling oeffiient. Conidering the redution of ower lo in the onverter, the multile ingle-hae full-bridge inverter hould be onneted to the eah winding. Beide, eah of the rimaryide inverter and the eondary-ide inverter i driven in hae to avoid ro urrent. However, only one onverter drive the four-winding tranformer in thi exeriment for the imliity. A arallel onnetion of the fullbridge inverter i more effetive to dereae the ondution lo of OSFET beaue the urrent i divided into eah onverter. In next etion, a method of inreaing an equivalent magneti ouling between the rimary ide and the eondary ide i diued. B. Analyi of Four-winding Tranformer Fig. 5 how the equivalent iruit of the four-winding tranformer []. Terminal voltage of winding m (m =,,, 4) ontain not only an indued eletromotive fore from the urrent flowing through the winding m, but alo the um of the indued voltage from the urrent flowing in the other winding. Conequently, the magneti ouling among four winding ha to be onidered. The relationhi between the inut voltage v m and the inut urrent i m of the winding m i exreed by uing a four-order indutane matrix Tran a hown in v i i v v v4 Tran d i i i d i i i i 4 44 d i i i4...(5), where mm i the elf-indutane of the winding m, and mn (m n, n =,,, 4) i the mutual indutane between the winding m and the winding n. The matrix element of mn and nm at a eifi ombination of m and n have the ame value. Beide, the ouling oeffiient mn of two winding i defined by mn mn...(6). mm nn The arameter in Fig. 5 are reented by (7) and (8) []. e e e e 4 e e e e 4 Tran... (7) e e e e4 e4 e4 e4 e44 e e e e 4 4 n e e e e4 n n... (8) n n

4 Next, retrition and relationhi are given by the ymmetry of the iruit. The firt one i that the elf-indutane of all winding mut have the ame value. The eond one i that the ouling oeffiient of, and are defined a hown in Fig. 4. Then the relationhi of the voltage and the urrent i exreed by (9). v i v d i... (9) v i v4 i4 The indutane value in Fig. 5 are reented by ()-() e v v f,, e4...(), i i i e e e e e 4 e e 4 e 4 e e 4 Fig. 5. Equivalent iruit of four-winding tranformer. Thi iruit i extended from the -tye equivalent iruit for two-ort networ. v i Fig. 6. Equivalent iruit of rooed ytem. The four-winding tranformer i hown a the two-winding tranformer. In addition, the two-level full-bridge inverter are hown a the quare-wave voltage oure. Equivalent ouling oeffiient eq =. = Couling oeffiient eq Fig.7. Relationhi of equivalent ouling oeffiient veru ouling oeffiient. Only value i hanged from to. In order to verify the effet of reduing, and are fixed value. i 4 i v v 4 v e f,, e4... (), f,, e 4 e... (), e e e e4.. (), where the funtion f(,, ) i exreed by (4).,, f...(4) When the winding are onneted in arallel in eah the rimary ide and the eondary ide, the relationhi of the voltage and the urrent i hown in (5) and (6) i i v v v v... (5), d i i... (6), where v i the inut voltage of the rimary ide, v i the inut voltage of the eondary ide, i i the equivalent inut urrent of the rimary ide and i i the equivalent inut urrent of the eondary ide. oreover, the equivalent elf-indutane of the rimary ide, the equivalent elf-indutane of the eondary ide and the equivalent mutual indutane are exreed a in (7) and (8)....(7)...(8) Thee equivalent value of, and are ueful to analyze the four-winding tranformer a a two-winding tranformer. Fig. 6 how the equivalent iruit of the rooed ytem. The negative indutane - (- )/ i onneted in erie to the two-winding tranformer, the ouling oeffiient of whih i ( + )/. Therefore, the low i effetive to redue the leaage indutane. The equivalent ouling oeffiient eq of the equivalent iruit i reented by (9). eq... (9) Fig. 7 how the relationhi of eq veru. Both of and are fixed value. The equivalent ouling oeffiient eq i learly imroved with dereaing. The reaon why eq i inreaed with the dereae in uh a (9) and Fig. 7, i redution of and from (7) and (8). Generally, ombined indutane of wounding in arallel i lower than elf-indutane of eah winding beaue. Beide, the ombined indutane i muh lower when the magneti

5 ouling of the winding i maller. Wherea, the value of i deided deite in the ytem. In onequene, eq, whih orreond to ratio of veru the geometri mean of and i imroved. C. Tranmiion Power and Power Fator of Prooed Sytem In thi etion, the tranmiion ower P and the ower fator of the inverter outut are formulated from the equivalent iruit hown in Fig. 6. oreover, the relationhi of the ower fator and the ouling oeffiient i diued in detail. From (4), (7) and (9), P i given by () with ubtituting and eq for and. VinVout P '...() RS value I _rm and I _rm of i and i are hown in () and (). I I _ rm _ rm f w w f i V in V out 4 V invout...() f w w f i V out V in 4 V invout...() When the inut DC voltage V in i a ame a the outut DC voltage V out, the ower fator o q in from the view oint of the outut of the rimary-ide inverter i given by (). oq in V P' I in _ rm 4... () Fig. 8 how theoretial urve of o q in with the ouling < <. Note that and are deigned to be. for IPT ytem. ower (higher eq) mae the ytem higher ower fator o q in over entire load range. Fig. 6 and Fig. 7 alo how that lower redue the equivalent leaage indutane oming from the four-winding tranformer. Thu value hould be mall to imrove o q in. A. Tet Condition Inut ower fator o qin (Diharge) IV. EXPERIENTA RESUTS The rooed imrovement method on the magneti ouling i exerimentally verified. The tet i arried out with the ytem onfiguration hown in Fig. 4. Table I how the tet ondition and arameter of the element. Note that inut and outut voltage i 8 V, and the rated ower i. W. Fig. 9 how the iture of the two four-winding tranformer, whih are ued for the tet. The retangular ore are made of ferrite late (TDK, B6745B4X87). Two four-winding tranformer have the ame ize of ore and the ame ditane between ore for a fair omarion. The arallel-onneted winding on the onventional tranformer are wound loe to eah other in order to inreae value. Wherea, the arallel-onneted winding on the rooed tranformer are earately wound on the outide of oil and loely wound at the enter of the oil in order to redue value without dereaing and. The ouling oeffiient, and are determined by the dioition of the wire. The elf-indutane i adjuted by turn of oil and given by (4) uing maximum ower P max. VinVout...(4) P max Note that P max hould be deigned larger than the rated ower with a margin of %. B. Parameter of Four-winding Tranformer Table II how the meaured and alulated arameter of the four-winding tranformer in Fig. 9. The equivalent value Phae differene degree =., =. = =. =.4 =.6 =.8 = Fig. 8. Theoretial urve of ower fator given by (). Only value i hanged from to. The other ouling oeffiient of and are fixed value in order to verify effet of reduing. Table I. Tet ondition. Parameter Symbol Value Inut DC voltage V in 8 V Outut DC voltage V out 8 V Rated ower P. W Swithing frequeny f w Hz Dead time T dead n Smoothing aaitor C in,c out.7 mf Smoothing indutor in, out mh OSFET S -S 8 IXYS, IXFN8N6P

6 Winding Winding Ga 69 Winding Winding 4 95 Unit: mm (a) Front view of onventional tranformer. (b) To view of onventional tranformer. () Side view of onventional tranformer. Winding Winding Ga 69 Winding 4 Winding 75 5 Unit: mm (d) Front view of rooed tranformer. (e) To view of rooed tranformer. (f) Side view of rooed tranformer. Fig. 9. Two rototye four-winding tranformer. The outline drawing from (a) to () are the onventional tranformer whoe winding of the rimary or eondary ide are loe to eah other. The outline drawing from (d) to (f) are the rooed tranformer whoe winding of the rimary or eondary ide are earated to introdue the rooed method. Table II. eaurement reult of indutane and ouling oeffiient of onventional tranformer and rooed tranformer. The matrix element of Tran are meaured by a CR meter. Aording to (9), the arameter,, and are averaged from the matrix element of Tran. Parameter Conventional Tranformer Prooed Tranformer Primary oil 8 9 Coil turn Seondary oil 8 9 Indutane matrix Tran a 4-winding tranformer [H] [H] Self-indutane eaured value 4.9 H 57.9 H Couling oeffiient eaured value Couling oeffiient eaured value..4 Couling oeffiient eaured value..6 Equivalent rimary elf-indutane eaured value.9 H 44.4 H Calulated value 4. H 4. H Equivalent eondary elf-indutane eaured value 4.5 H 4.4 H Calulated value 4. H 4. H Equivalent mutual indutane eaured value. H 6.4 H Calulated value. H 6. H Equivalent ouling oeffiient eq eaured value.9.77 Calulated value.7.76 aximum error of alulated indutane. %.4 % Error of alulated ouling oeffiient.7 %. %,, and eq how both of alulate value and meaured value by onneting the winding in arallel. The ouling oeffiient of the rooed tranformer i.497 weaer than of the onventional tranformer of.958. Conequently, eq of the rooed tranformer imrove to.77 from.9. In addition, the validity of the formulation i alo onfirmed and all the error of,, and eq i below.4%. Note that and of the rooed tranformer are weaer than the value of the onventional tranformer beaue the ditane of the winding are longer. Equation (9) how that eq i roortional to the um of and. Thu a winding method whih only redue without dereaing and i required to inreae eq. C. Oeration Waveform of Prooed Sytem Fig. how the oeration waveform at rated load and at light load in the ower harging and the diharging oeration. The hae differene i 9 degree at rated load and 5

7 Primary inverter voltage v 5 V/div Primary inverter voltage v 5 V/div Primary inverter urrent i 5 A/div Seondary inverter voltage v 5 V/div Primary inverter urrent i 5 A/div Seondary inverter voltage v 5 V/div 8 /div Outut urrent i out 5 A/div 8 /div Outut urrent i out 5 A/div (a) Rated load (. W) with harging oeration. (b) Rated load (. W) with diharging oeration. Primary inverter voltage v 5 V/div Primary inverter voltage v 5 V/div Primary inverter urrent i 5 A/div Seondary inverter voltage v 5 V/div Primary inverter urrent i 5 A/div Seondary inverter voltage v 5 V/div 8 /div Outut urrent i out 5 A/div 8 /div Outut urrent i out 5 A/div () ight load ( W) with harging oeration. (d) ight load (W) with diharging oeration. Fig.. Oeration waveform of rototye iruit with rooed tranformer. The tranmiion ower and the oeration mode are hanged by the hae differene between the rimary-ide inverter and the eondary-ide inverter outut voltage. (a) = 9 degree. (b) = -9 degree. () = 5 degree. (b) = -5 degree. degree at light load. At light load, the urrent i a triangle wave beaue the reative urrent i dominant. The outut DC urrent i out how that ower tranmitting i ahieved at the rooed tranformer in both of the ower harging and the diharging oeration. D. Charateriti of Inut Current, Power Fator and Effiieny Fig. how harateriti of the rimary urrent I _rm veru outut ower P out. Note that the meaurement value i lotted in the grah, and the theoretial harateriti are drawn by the olid line or the dotted line. Aording to the I _rm value at P out = W, the exitation urrent of the rooed tranformer redue by 5% omared with the onventional value. Fig. how harateriti of the inut ower fator o q in. The x-axi of Fig. (a) i the hae hift angle. The x- axi of Fig. (b) i P out. The meaurement value i lotted in the grah, and the theoretial harateriti are drawn by the olid line or the dotted line. In order to meauring o q in, i and v are deteted diretly. Note that effet of the detetion art are not taen into aount in the alulation roe of theoretial o q in value. RS value of rimary urrent I_rm A (Diharge) Conventional tranformer ( =.958) Prooed tranformer ( =.497) Outut ower P out W Fig.. Charateriti of RS value of rimary-ide inverter AC outut urrent. The theoretial harateriti are hown by urve, wherea the lot are meaurement value. The maximum ower fator of the rooed tranformer i 7% larger than the onventional tranformer. oreover, o q in i imroved the entire load range. Thu a low- tranformer imrove the ytem effiieny owing to the redution of the reative urrent.

8 Fig. how the ytem effiieny veru P out. The ytem effiieny i imroved over the entire P out with the rooed tranformer. The maximum effiieny of the rooed tranformer i 87.% at. W in the harging oeration. The effiieny of the rooed tranformer i imroved over entire load range omared to the onventional tranformer. In artiular, the maximum effiieny of the rooed tranformer i 9. % at 89 W in the diharging oeration, whih i.% higher than that of the onventional tranformer. V. CONCUSION In thi aer, a ower fator orretion method wa rooed for the non-reonant IPT ytem utilizing the dual ative bridge onverter in order to redue ondution lo and winding lo. The looe ouling oeffiient between two air of the rimary-ide and the eondary-ide wire onneted in arallel ontributed to the ower fator orretion from the viewoint of the ower uly. Therefore, the low- four-winding tranformer imroved effiieny beaue of the trong equivalent ouling oeffiient eq between the rimary ide and the eondary ide. From the exeriment, the maximum ower fator of the low- tranformer, value of whih i.497, wa imroved by 7% omared with the high- tranformer beaue of tronger eq by 5%. Beide, the maximum effiieny of the low- tranformer wa imroved by.%. In the future, the rooed method will be introdued to a reonant IPT ytem in order to imrove effiieny. REFERENCES [] Siqi i and Chunting Chri i: Wirele Power Tranfer for Eletri Vehile Aliation, IEEE Tran. PE, Vol., No.. 4-7J. Cler axwell, A Treatie on Eletriity and agnetim, rd ed., vol.. Oxford: Clarendon, 89,.68-7.(5) [] Su Y. Choi, Beom W. Gu, Seog Y. Jeong and Chun T. Rim: Advane in Wirele Power Tranfer Sytem for Roadway-Powered Eletri Vehile, IEEE Tran. PE, Vol., No..8-6 (5)K. Elia, Title of aer if nown, unublihed. [] Fei u, Hua Zhang, Heath Hofmann and Chunting Chri i: An Indutive and Caaitive Combined Wirele Power Tranfer Sytem With C-Comenated Toology, IEEE Tran. PE, Vol.4, No (9) [4] Tutomu izuno, Tauto Ueda, Shintaro Yahi, Ryuhei Ohtomo and Yohihito Goto: "Deendene of Effiieny on Wire Tye and Number of Strand of itz Wire for Wirele Power Tranfer of agneti Reonant Couling", IEEJ Journal of Indutry Aliation, Vol., No.,. 5-4 (4) [5] Hiroi Ihida, Hiroto Furuawa and Tomoai Kyoden: "Develoment of Deign ethodology for 6 Hz Wirele Power Tranmiion Sytem", IEEJ Journal of Indutry Aliation, Vol. 5, No. 6, (6) [6] Daiue Shimode, Tohiai urai and Shunue Fujiwara: "A Study of Struture of Indutive Power Tranfer Coil for Railway Vehile", IEEJ Journal of Indutry Aliation, Vol. 4, No. 5, (5) [7] H. Saamoto, K. Harada, S. Wahimiya, K. Taehara and Y. atuo: "arge Air-Ga Couler for Indutive Charger", IEEE TRANSACTIONS ON AGNETICS, Vol. 5, No. 5, (999) [8] Roman Bohard, Johann Walter Kolar, Jona ühlethaler, Ivia Stevanovi, Bernhard Wunh, and Franio Canale: " odeling and η-α-pareto Otimization of Indutive Power Tranfer Coil for Eletri Vehile", IEEE Tran. PE, Vol., No (5) Inut ower fator o qin Inut ower fator o qin (Diharge) (Diharge) Prooed tranformer ( =.497) Phae hift angle degree (a) Veru hae hift angle. Prooed tranformer ( =.497) Outut ower P out W Conventional tranformer ( =.958) (b) Veru outut ower of the ytem. Conventional tranformer ( =.958) Fig.. Charateriti of ower fator. The theoretial harateriti are hown by urve, wherea the lot are meaurement value. The ower fator o q in i meaured with the ower analyzer (E.E.Cororation, PW6) and Diret Current eaurement Otion (E.E.Cororation, PW9). Effiieny (DC to DC) % (Diharge) Prooed tranformer ( =.497) Outut ower P out W Conventional tranformer ( =.958) Fig.. Effiieny of eah four-winding tranformer. The lot are meaurement value under the ondition of Table I. [9] Keiue Kuaa and Jun-ihi Itoh: Non-reonant Indutive Power Tranfer Sytem baed on the Prinile of Dual Ative Bridge Converter, IEEJ Tran. I.A., Vol. 6, No., (5) [] utanir H. Kheraluwala, Randal W. Gaoigne, Deearaj. Divan, and Eri D. Baumann: Performane Charaterization of a High-Power Dual Ative Bridge d-to-d Converter, IEEE Tran. IA, Vol.8, No (99) [] Keizo Inagai, aaru Higai, Yohiai atui and Kentaro Kurita: Digital rotetion method for ower tranformer baed on an equivalent iruit omoed of invere indutane, IEEE Tran. PD, Vol., No (988)