Novel High Voltage Conversion Ratio Rainstick DC/DC Converters

Transcription

1 3 IEEE Proceedings of he IEEE Energy Conversion Congress and Exposiion (ECCE USA 3), Denver, Colorado, USA, Sepember 5-9, 3 Novel High Volage Conversion Raio Rainsick / Converers M. Kasper, D. Boris, J. W. Kolar This maerial is published in order o provide access o research resuls of he Power Elecronic Sysems Laboraory / D-ITET / ETH Zurich. Inernal or personal use of his maerial is permied. However, permission o reprin/republish his maerial for adverising or promoional purposes or for creaing new collecive works for resale or redisribuion mus be obained from he copyrigh holder. By choosing o view his documen, you agree o all provisions of he copyrigh laws proecing i.

2 Novel High Volage Conversion Raio Rainsick / Converers Mahias Kasper, Dominik Boris and Johann W. Kolar Power Elecronic Sysems Laboraory ETH Zurich, Physiksrasse 3 Zurich, 89, Swizerland kasper@lem.ee.ehz.ch Absrac Volage conversions wih high sep-down raios are required in many medium volage applicaions for supplying auxiliary elecronics. In his paper a new opology for high conversion raios wih low volage sresses of componens, modular srucure and simple conrol is presened. The operaion principles are described ogeher wih analyical descripions of he average value of he inducor currens and RMS values of he swiches. In addiion, he influence of he efficiency of he individual modules on he oal converer efficiency is provided. Possible modificaions of he Rainsick converer wih benefis for differen applicaions are shown. Furhermore, he measuremen resuls of a prooype wih an inpu volage range of up o.4kv and 3W oupu power are shown. I. INTRODUCTION Sae-of-he-ar power elecronic sysems comprise no only power elecronic componens bu also auxiliary elecronics such as digial signal processors, measuremen elecronics required for he conrol of he whole sysem and gae drives o name jus a few. These pars of he sysem usually require a low supply volage (e.g. 3.3V for a DSP) and heir combined power consumpion ofen lies in he low doubledigi Was range. Generally, i is preferable o generae his auxiliary supply volage from he inpu volage of he power elecronic sysem o avoid furher connecions o an exernal supply. However, in high power sysems e.g. racion converers, he inpu volage is in he medium volage range and/or up o some ens of kvs and hus a volage conversion wih a high sep-down raio is needed. A high sep-down raio can be reached in several differen ways. The mos sraigh forward opion is o use buck converers which are cascaded in order o avoid oo small duy cycles. Anoher opion would be o use a flyback or forward converer. The aforemenioned possibiliies, however, share a common drawback: he employed swiches have o be raed for he full inpu volage of he sysem. Due o ha, hose swiches will mainly be IGBT swiches, if available for he volage raing, or a series connecion of such. This will lead o an increased size of he passive componens, since hey operae a a lower swiching frequency han MOSFETs. Furhermore, as he auxiliary supply draws only a small curren, he conducion losses will be increased if IGBTs have o be used insead of MOSFETs. The Inpu Series Oupu Parallel (ISOP) converer (Fig. ) is anoher ype of converer ha has been presened in lieraure /3/$3. 3 IEEE 789 Fig. : Converer conceps for high sep-down raios presened in lieraure: ISOP (Inpu Series Oupu Parallel) converer and swiched capacior converer (resonan version). [],[] o faciliae he volage conversion wih a high sepdown raio. Here, he inpu erminals of several isolaed - converers are conneced in series in order o divide he inpu volage by he number of converers and o limi he volage sress of he employed swiches of each converer. The converer oupu erminals are conneced in parallel o each oher. Addiionally, conrol mehods have been published o accomplish an equal sharing of he inpu volage as in [3]. One disadvanage is ha he employemen of ransformers is necessary and he isolaion beween he primary and secondary side needs o wihsand volages as high as he oal inpu volage. Anoher concep o obain a high sep-down conversion raio is

3 Fig. : Mulilevel converer conceps: diode-clamped opology and flying capacior opology. by using swiched capacior converers (Fig. ) [4],[5]. The circuis consis of a capaciive volage divider where he load is aached o one or more capaciors. A volage balancing circui is aached in order o sill ensure an equal volage disribuion among he capaciors despie he asymmeric load connecion. Such balancing circuis are known from baery managemen sysems [6],[7]. Capaciors of he balancing circui are alernaely conneced in parallel o adjacen capaciors of he volage divider. As a modificaion, he opology can also be implemened as a resonan circui where addiional inducors are conneced in series o each capacior of he balancing circui [8]. A main drawback is ha he swiches of he balancing circui have o be conrolled synchronously for proper operaion of he sysem. Accordingly, a cenral conrol sage and a disribuion of he gae drive signals wih high isolaion volage has o be provided. The mulilevel converer concep has also been proposed for high sep down volage conversion [9],[]. The mos basic srucure does no comprise inducive componens and hus feaures a high power densiy. Common ypes of mulilevel converers are he diode-clamped opology (Fig. ) and he flying capacior opology (Fig. ). The former caegory exhibis high volage sresses on he diodes and hence requires a large number of series conneced diodes which leads o increased conducion losses. The laer caegory exhibis high volage sresses on he capaciors, hus requiring many capaciors o be conneced in a series connecion. Since he oal capaciance of series conneced capaciors is smaller han ha of a single capacior, muliple capacior cascades need o be paralleled. Furhermore, only he flying capacior opology can acively balance he inpu volages of he - converers equally by means of redundan swiching saes []. The diode-clamped opology, however, requires an addiional balancing circui []. The problem of high conversion raios, alhough wih reversed power flow direcion, can also be found in phoovolaic (PV) archiecures. A -bus volage which is much larger han he individual PV panel volages has o be supplied for feeding power ino he grid. Among he suiable converer conceps for ha applicaion, he parallel conneced parialpower converer (P-PPC) [3] equalizes he PV panel volages of in series conneced PV panels. Thus i ensures he operaion of all panels in or close o heir Maximum Power Poin [4], [5], [6], [7], [8]. These P-PPC opologies, many of hem known from baery charge equalizaion circuis [6],[7], can also be applied o verically sacked volage domains such as proposed for muli-core microprocessor power supplies [9], []. They allow regulaing he operaing volage of each C S I L L I L B I L B S 3 I L L C S I L,avg C 3 S4 S5 L 3 S L N- C N S (N-) S +Tp Fig. 3: New Rainsick (RSTC) converer opology: circui diagram showing capaciive volage divider (C...C N) and balancing modules highlighed (B,B ) and characerisic curren waveform and gae signals of one balancing module. 79

4 P = 4 P = P 3 = 3 Fig. 4: Seady sae analysis of RSTC converer: curren disribuion in converer and differen represenaion of he converer wih muliple buck-boos converers for an easier undersanding of power flows. The power is no a once direcly ransferred from he source o he load bu hrough a cascade of differen converer sages, comparable o he pebbles falling down in a rainsick. in series conneced load from a fixed -bus. Thus, as he loads are no longer conneced in parallel, he load curren is decreased, which leads o a higher sysem efficiency. This paper inroduces a new ype of high sep-down converers, based on he P-PPC concep. Due o is operaing principle, his new converer is denominaed as Rainsick (RSTC) converer. The converer feaures low volage sresses of he employed componens and a simple conrol scheme. Firs, he fundamenal principle of operaion is explained in Sec. II. Subsequenly, an analysis of he average curren values in he inducors and RMS curren values in he swiches along wih he conversion efficiency is presened in Sec. III. In addiion, he opology and he working principle of an on-board auxiliary power supply are deailed in Sec. IV. Furhermore, differen alernaive converer realizaions of he Rainsick converer principle are described in Sec. V. The opimizaion and realizaion of a RSTC prooype are shown in Sec. VI and he measuremen resuls are depiced in Sec. VII. II. OPERATING PRINCIPLE In his secion he srucure of he RSTC converer and he fundamenal operaing principle are described. The converer, as depiced in Fig. 3, has a modular srucure which is based on a capaciive volage divider (C...C N ) wih buck-boos - converers as balancing modules (e.g. B ). These balancing modules are conneced around wo adjacen capaciors. This means, ha a RSTC converer consising of N capaciors conains (N ) balancing modules i.e. ((N )) swiches and(n ) inducive componens in oal. A load can be aached o one or more capaciors of he volage divider. The converer oupu volage a he load is a fixed divider of he inpu volage, deermined by he number N of capaciors. For he sake of simpliciy, he load is depiced as a single resisor whereas in realiy i would usually consis of an addiional - converer in order o provide a variable volage conversion of he RSTC oupu volage o he volage level of he load. The swiches of each buck-boos converer can be conrolled 79 by a simple PWM signal wih a fixed duy cycle of (slighly less han) 5% and a 8 phase shif a a fixed swiching frequency. There is no communicaion or synchronizaion needed beween he differen balancing modules which allows hem o operae independenly from each oher. The waveform of he gae signals and he resuling inducor curren and is average value are shown for one balancing module in Fig. 3. The sysem can operae wih zero volage swiching (ZVS) as he direcion of he inducor curren reverses during each half period. Thus, in combinaion wih he parasiic drain-source capaciances of he MOSFETs, ZVS can be provided. The converer can operae in ZVS over he whole range of inpu volages by linearly increasing he swiching frequency wih increasing inpu volage, which yields a consan peak-o-peak curren ripple I L of he inducor curren I L. In his paper, he main focus is on he sep-down operaion bu he converer srucure is bidirecional and hus equally well suied for sep-up operaion, oo. For ha kind of operaion he source would be conneced o one or more capaciors and he load would be aached across he whole sack of capaciors. III. ANALYTICAL DESCRIPTION In case of no load operaion, he inducor currens yield no value. However, if a load is conneced o he sysem, he currens in he inducors exhibi a value wih superimposed swiching ripple as shown in Fig. 3. The average curren value in he inducors (I L,avg ) can be calculaed for a given load curren. The highes average curren is obained when he load is conneced across only one capacior and a he same ime one erminal of he load is eiher conneced o he highes or lowes poenial of he sysem, i.e. he capacior is conneced around he firs or las capacior in he sack of capaciors. Then, for a sysem wih N capaciors, he average curren values in he inducors o N are given by I L,avg i = i N, i {,,...,N } () where each of hose values appears only in one inducor. So, in a converer wih e.g. N = 5 capaciors, he average curren

5 I L, I CC Energy ransfer o C aux C I L L S C Auxiliary Supply V CC V CC,h V CC,h D aux S I CC S aux C V aux CC Saux Fig. 5: Srucure and analysis of on-board auxiliary power supply uni: balancing module wih auxiliary power supply uni comprising swich S aux, diode D aux and capacior C aux; characerisic waveforms of inducor curren I L, charging curren I CC of auxiliary capacior C aux, auxiliary volage V CC and gae signal of auxiliary swich S aux. values in he inducors are 5, 4 5, 6 5 and 8 5 of he load curren. The larges value occurs in he inducor closes o he load. For N he maximum average curren value approaches. The main sources of losses in he RSTC converer are winding and core losses in he inducors and conducion losses of he swiches. The RMS values of he currens in he swiches of a balancing module depend on he average value I L,avg and he peak-o-peak ampliude I L of he inducor curren ripple in ha module, by I sw,rms = IL,avg + 6 I L. () For calculaions of he sysem efficiency, he power flow in he converer has o be analyzed. In general, he converer srucure can be visualized as a sack of muliple buck-boos converers, as shown in Fig. 4, which faciliaes he power flow analysis. Similar o he pebbles in a rainsick, he power is no a once ransferred from he source o he load bu hrough a cascade of buck-boos sages. As seen in Fig. 4, he larges amoun of power is ransferred in he lowes converer of he chain, i.e. he converer closes o he load. I is ineresing o noe ha none of he balancing converers have o ransfer he full amoun of load power. Thus, his converer concep can be classified as parial-power converer []. For he calculaion of he RSTC converer efficiency, i is assumed ha each of he balancing modules has a cerain conversion efficiency which is a funcion of he module oupu power P i, i.e. η i (P i ). Then he oal converer efficiency can be calculaed as ( ) + N N η j (P j ) i= j=i η sys,n =. (3) N For he above menioned example of a RSTC converer wih 4 capaciors and 3 balancing modules, his equaion yields η sys,4 = /4 ( + η 3 (P 3 ) + η 3 (P 3 ) η (P ) + η 3 (P 3 ) η (P ) η (P )). However, he conversion efficiency is usually of minor ineres, since he main idea of he RSTC concep is a high volage conversion raio for low power (e.g. auxiliary) 79 elecronics. Since he power consumpion of he auxiliary elecronics in a power elecronic sysem is usually very small compared o he raed power of such a sysem, he impac of he efficiency of he auxiliary power supply on he overall sysem efficiency is very small. Neverheless, he RSTC converer efficiency can sill be opimized, if he hardware of each buckboos balancing modules is opimized for heir power level. The oupu power of he individual balancing modules can be found as { ( ) PLoad N η P i = sys,n, i = N P i+ η. (4) PLoad i+(p i+) N η sys,n, i {,,...,N } The values of η sys and P i can be calculaed in an ieraive process as hey are dependen on each oher. This is due o he fac, ha he losses of one balancing module influence he power, ha has o be delivered by he balancing modules before ha module (in direcion of power flow). IV. ON-BOARD AUXILIARY POWER SUPPLY In order o supply he gae drives and he conrol elecronics on each module wih power, an on-board power supply wih a low componen coun and simple conrollabiliy is preferable. Thus, each module can operae wihou an exernal power supply or exernal gae signals. The proposed power supply consiss of capacior C aux, diode D aux and swich S aux which are inegraed in he exising balancing module, as depiced in Fig. 5. Wih he swich S aux being urned on, he balancing module operaes as usual. If he volage V CC drops below he lower hreshold V CC,h, however, he swich S aux is urned off, as shown a ime in Fig. 5. A ime, when he swich S conducs he inducor curren I L, capacior C aux is charged via he diode D aux. This charging inerval ends when curren I L changes is direcion, i.e. a 3, which is necessary for ZVS operaion of he swiches S and S. Then, he inernal body diode of S aux (or an exernal diode placed in parallel o ha swich) conducs he curren I L. The charging coninues a ime 4 when swich S is urned on again. The swich S aux is urned on when he volage V CC of capacior C aux reaches he

6 4 Fig. 6: Possible modificaions of he Rainsick converer concep: load connecion o a capacior in he middle of he capacior sack, yielding lower average curren values in he inducors and connecion of source o only a fracion of he sacked capaciors. upper hreshold V CC,h. The minimum energy ransfer o C aux during a swiching period of S and S can be calculaed for he case of an inducor curren wihou an average value (i.e. I L,avg = ), as wih increasing load curren he energy ransfer is increased (cf. Fig. 5). Under he simplificaion of a narrow band of volage hresholds (i.e. V CC V CC,h V CC,h ), he ransferred energy equals W aux = TP V CC () I CC ()d TP = V CC I CC ()d = V CC 6 I L. (5) f sw Hence, he minimum average power ha can be delivered by he auxiliary supply is independen of he swiching frequency, as i is given by P aux = W aux f sw = V CC I 6. (6) The proposed power supply uni can also be used in oher converer opologies. A drawback of his auxiliary supply uni is, ha he volage, which is applied across inducor L, is alered by he value of V CC each ime he auxiliary swich S aux is urned on or off. V. ALTERNATIVE DESIGNS The concep of he Rainsick converer can be realized in differen ways. In his secion a number of possible modificaions of he basic circui from Fig. 3 are described and examples of heir applicaion are given. A. Load connecion The load can also be conneced o capaciors in he middle of he volage divider, as shown for example in Fig. 6. This offers he advanage o limi he maximum average curren value ha appears in any inducor o { ILoad, if N is even I ind,avg max = N N I (7) Load, if N is odd R L R L RL (c) (d) Fig. 7: Possible modificaions of he RSTC converer concep wih reduced componen coun by use of coupled inducors: (a, b) resonan version wih differen load connecion and (c, d) isolaed oupu sage. 793 RL

7 Hence, inducor losses and conducion losses decrease and he overall sysem efficiency increases when he load is conneced o capaciors closer o he middle of he volage divider. Moreover, in sysems where he load of he RSTC converer is already isolaed, he maximum required volage srengh of his isolaion can be reduced as no he full bus volage has o be isolaed. W 4 3 P oal f sw 5 khz a,max B. Source connecion The RSTC converer operaion principle does also apply when he source is only conneced o some of hen capaciors. An example wih corresponding power flows is given in Fig. 6. In conras o he original idea of he RSTC converer, hose balancing modules ha are no conneced o he source need o carry he full load power and any losses. C. Coupled inducors and isolaion The componen coun can be reduced by he use of coupled inducors i.e. ransformers wih volage raio :, insead of inducors as depiced in Fig. 7. The basic circui of he RSTC converer can be modified in such way, ha for an even number (N) of capaciors only (N/ ) ransformers and (N) swiches are needed. Wih resonan capaciors in series wih he ransformers he sysem can sill be operaed in ZVS. This can be done by adjusing he swiching frequency o he resonance frequency of he resonance capaciors and he leakage inducance of he ransformer. A disadvanage resuling from he coupling is, ha he conrol of all swiches has o be synchronized. VI. PROTOTYPE OPTIMIZATION AND REALIZATION A prooype of he RSTC converer comprising five balancing modules, each wih is own on-board power supply uni (cf. Sec. IV), has been assembled and is shown in Fig. 8. As five balancing modules are used, he converer oupu volage is equal o one sixh of he inpu volage. The prooype is designed for a maximum inpu volage of,max =.4kV Modules...5 P winding P core λ L / mvs Fig. 9: Calculaed inducor losses in dependence of applied volsecond (λ L) for an EFD5 N87 core and capacior volages of V c = 3V. The oal inducor losses P oal consis of core losses P core and winding losses P winding. and a raed oupu power of P ou = 3W (a inpu volages beween =.6kV...4kV). Thus, each balancing capacior has o be raed for a volage of a leas 4V and he employed swiches have o wihsand volages of up o V DS,max = 8V. The swiching frequency of each balancing module is adjused by a volage conrolled oscillaor (VCO) ha senses he volage accross boh balancing capaciors. Hence, he swiching frequency is linearly increased wih increasing converer inpu volage, yielding a consan volsecond λ L = V C /(f sw ) which is applied across he main inducor during all swiching periods. As a cerain peak-opeak inducor curren ripple I L is required by he auxiliary supply, he inducance of he main inducor L equals L = λ L. (8) I L The power consumpion of he conrol elecronics was esimaed o be less han 4 mw. Wih a lower volage hreshold level of he auxiliary supply of V CC,h = 8V a minimum required peak-o-peak curren ripple in he inducor of I L =.8A can be calculaed. In order o selec a suiable value of λ L, an inducor opimizaion has been performed. Here, he inducor design wih he lowes losses for a given value of λ L is compued. For his opimizaion all available EPCOS N87 cores wih eiher ETD or EFD core shape and a selecion of Rupali liz wires have been considered. The resuls for an EFD5 core are demonsraed in Fig. 9 for a 5 [mm] Tab. I: Lis of main componens of RSTC prooype. (Noe: All quaniies are given per balancing module.) [mm] Mainboard 7 [mm] Fig. 8: Rainsick converer prooype wih five balancing modules for an inpu volage of up o,max =.4kV and P ou = 3W. 794 Componen x MOSFETs x Gae driver x Inducor x VCO x Capaciors Specificaions STD3NKZ / ST [R DS,on = 5.4Ω, V DS = V, I D =.5A] Half-bridge gae driver IR4 / In. Recifier EFD5/3/7, N87 ferrie / EPCOS [L mh, 6 urns, liz wire (6x7µm), l airgap =.5mm] MCB446B / ON Semionducor X7R ceramic capaciors [C =.5µF (7x5nF), V raed = 5V]

8 η / % η / % V C = V 5 5 V C = 3V V C = 4V 5 3 P ou / W =. kv =.8 kv 5 5 = kv =. kv 5 3 P ou / W Fig. : Efficiency measuremen resuls of he RSTC converer ploed over he oupu power: single balancing module a wo differen levels of capacior volages V C and full sysem comprising five balancing modules a differen levels of inpu volage. The doed lines denoe calculaed sysem efficiency values. Remark: The measuremen for =.kv and P ou = 3W could no be performed as he prooype can only supply he raed oupu power a inpu volages beween =.6kV...4kV. capacior volage of V C = 3V. Even hough he lowes inducor losses can be achieved a a vol-second value of λ L =.4mVs, values below.8mvs already yield swiching frequencies above f sw = 5kHz which proved o be unpracical in combinaion wih he seleced gae drive due o high gae drive losses. Thus, a value of λ L =.8mVs was seleced for he prooype. Furhermore, he employed componens of RSTC prooype are lised in Tab. I. VII. MEASUREMENT RESULTS The converer efficiency measuremens resuls of a single balancing module a differen levels of capacior volages are presened in Fig. in dependence of he oupu power. The resuls show, ha for higher capacior volages and hus higher swiching frequencies he efficiency decreases. This is due o he fac, ha any increase of he swiching frequency resuls in higher inducor losses since he core losses as well as he winding losses are frequency dependen. Furhermore, he power consumpion of he gae-drive is also linearly increasing wih he swiching frequency. One way o increase he efficiency of he sysem would be o design he sysem wih a larger value for λ L and wih a larger core size. Thereby, he swiching frequency of he balancing modules could be decreased wihou increasing he magneic flux densiy, boh being conribuors o core losses. This, however, would decrease he power densiy of he sysem and hus has o be considered as a rade-off. Based on he efficiency measuremens of an individual module, he sysem efficiency has been calculaed based on (3) and (4) for differen levels of inpu volages. The calculaed efficiency values are compared o he measured sysem efficiency in Fig.. I can be seen ha he calculaion resuls correspond well wih he measuremen resuls wih a maximum error of around 7% a raed power. The measured waveforms of he inducor curren I L and he inducor volageu L of he balancing module closes o he load are shown in Fig. for he operaion a an inpu volage of =.8kV and an oupu power of P load = W. The small curren spikes of he inducor curren during he reversal of he inducor volage is caused by inra-winding capaciances of he inducor. % V C V C V C3 Curren / A. -. I L - Volage / V U L Time / µs Fig. : Measured waveforms of he inducor curren I L and inducor volage U L of he balancing module closes o he load. The measuremens were performed during he operaion wih an inpu volage of =.8kV and an oupu power of P load = W V C4 V C V C / kv Fig. : Disribuion of he inpu volage among he six capaciors of he RSTC converer prooype in percen of nominal value (i.e. /6). The capaciors are numbered wih C being he uppermos and C 6 he lowes capacior of he sack. The load is conneced in parallel o capacior C 6.

9 The volage disribuion of he inpu volage among he six capaciors of he RSTC prooype is shown for no-load operaion in Fig.. I is visible, ha he inpu volage is no equally divided among he capaciors. Insead, he volage of he uppermos capacior is up o around 7% higher han he expeced value whereas he volage of he lowes capacior is around 6% lower han wha is expeced if perfec equalizaion was assumed. This can parly be explained by he fac, ha he auxiliary power supply uni is conneced in series o he lower capacior of a balancing module. Thus, each ime he auxiliary swich S aux (cf. Fig. 5) is urned off, he volage of he upper capacior (C ) is equalized wih he volage of he series connecion of he lower capacior (C ) and he auxiliary capacior (C aux ). If a load is conneced o he RSTC converer, his unequal volage disribuion ends o become slighly worse, as he superimposed load curren causes volage drops across he MOSFETs and he inducor in each balancing module which influence he volage equalizaion. A soluion would be o include a conroller in each individual balancing module ha adaps he duy-cycles of he swiches o values slighly differen from 5%. This can be implemened e.g. as a feedback loop wih he volage difference of he capaciors as inpu variable for a PI conroller. VIII. CONCLUSION A novel modular converer srucure, named he Rainsick converer, has been presened. The converer allows for bidirecional power flow wih a fixed volage conversion raio, which, due o is modular srucure, can be easily adaped for high conversion raios. Based on he curren and power flow analysis, his converer srucure can be classified as parial power converer as none of he employed modules needs o ransfer he full amoun load power. Furhermore, i is shown, ha he basic concep can be modified wih coupled inducors in order o isolae he converer oupu, if required. In addiion o he converer srucure, a self-conrolled on-board power supply uni wih a low par coun has been presened. The proposed RSTC converer concep has been opimized for inpu volages up o =.4kV and an oupu power up o = 3W. The measuremen resuls show ha he converer can be operaed over a wide range of inpu volages beginning from = V. In fuure work, a prooype of he modified RSTC converer wih isolaed oupu is going o be opimized and experimenally verified. REFERENCES [] R. Giri, V. Choudhary, R. Ayyanar, and N. Mohan, Common-Duy- Raio Conrol of Inpu-Series Conneced Modular - Converers wih Acive Inpu Volage and Load-Curren Sharing, IEEE Trans. Ind. Appl., vol. 4, no. 4, pp., 6. [] W. Chen, K. Zhuang, and X. Ruan, A Inpu-Series- and Oupu-Parallel- Conneced Inverer Sysem for High-Inpu-Volage Applicaions, IEEE Trans. Power Elecron., vol. 4, no. 9, pp. 7 37, 9. [3] J.-W. Kim, J.-S. Yon, and B. H. Cho, Modeling, Conrol, and Design of Inpu-Series-Oupu-Parallel-Conneced Converer for High-Speed- Train Power Sysem, IEEE Trans. Ind. Elecron., vol. 48, no. 3, pp ,. [4] M. D. Seeman and S. R. 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