Novel Three-Phase Three-Por UP Employing a ingle High-Frequency Isolaion Transformer Chuanhong Zhao and Johann W. Kolar ETH Zurich, Power Elecronic ysems Laboraory ETH Zenrum / ETL H, Physiksr., CH-89 Zurich / WITZERLND Tel.: +-- 8 Fax.: +-- Email: kolar@lem.ee.ehz.ch bsrac hree-phase PWM recifier and a hree-phase PWM inverer are coupled via wo four-quadran full-bridge converer cells and a high-frequency isolaion ransformer. By employing a hird ransformer winding and furher full-bridge cell baery energy sorage is incorporaed ino he power ransfer beween recifier and inverer resuling in a Three-Por UP concep. The phase shif conrol of he power flow beween he pors is analyzed for square-wave operaion of he full-bridge cells. Furhermore, he uilizaion of he degrees of freedom of he sysem conrol, i.e. he exension o duy cycle conrol for opimizing he sysem behavior is discussed and conrol laws ensuring minimum overall sysem losses are derived. Finally, a conrol-oriened converer model is proposed and he decoupled conrol of he power flow of he pors is reaed briefly. ll heoreical consideraions are verified by simulaions using PIM. I. INTRODUCTION Highly reliable hree-phase on-line uninerruped power supply sysems (UP are formed by back-o-back connecion, i.e. DC side coupling of a mains-side volage source recifier and a load-side volage source inverer []. There, he baery energy sorage is direcly conneced o he DC link or coupled via a DC/DC converer in order o allow a conrol of he charging or discharging curren and a compensaion of baery volage changes. Furhermore, for safey reasons and volage level adapion in general a 5/Hz isolaion ransformer is employed on he inpu or oupu side which, however, consiues a significan drawback concerning volume/weigh, coss and efficiency. In his paper a novel UP concep wih high frequency isolaion of a hree-phase PWM recifier sage (sysem/por, a hree-phase PWM inverer sage (sysem/por and a baery energy sorage (sysem/por is proposed, [] (cf. Fig.. There, por, por and por are coupled via hree four-quadran full-bridge converer cells operaing in phase-shif mode and a single hree-winding ransformer. ccordingly, he sysem will be denoed as Three-Por UP in he following. For realizing he hree-phase recifier and inverer funcion of he sysem (+++ power ransisors wih ani-parallel diodes have o be employed. Therefore, he realizaion effor is lower han, e.g. for a hree-phase high-frequency link C/C marix converer comprising ransisors and diodes []. s furher advanage one has o poin ou he coninuous shape of he inpu and oupu currens and he decoupling of he mains and he load concerning power and volage flucuaions in case sufficien DC link capaciance C and C is provided for he recifier and/or he inverer. lernaively, C and C could be realized as foil capaciors ensuring only a consan DC link volage level for swiching ransiens. The sysem shown in Fig. in general allows a bidirecional energy conversion beween wo hree-phase volage sysems and a DC volage source and herefore is of poenial ineres also in connecion wih fuure disribued generaor of elecric energy. There, he mains could, e.g. be formed by a wind urbine or a variable frequency generaor powered by a micro urbine where he baery sorage could compensae power flucuaions of he regeneraive energy sources. lso, furher oher sorage elemens like flywheels or ME or a fuel cell or phoovolaic generaor could be incorporaed in parallel by individual full-bridge converer cells and relaed ransformer windings. n ineresing applicaion area of such X-por UP-ype converer sysem would e.g. be fuure inelligen nodes of he energy disribuion sysem which also could be exended o a power qualiy conrol cenre [5] feauring symmerizaion of unbalanced loads and acive filering of mains volage or load curren harmonics. The conrol of he power flow in he hree-por sysem is in he simples case by proper phase shif of he individual full-bridge cells operaing in square-wave mode. In ecion II he sysem conrol characerisics are deermined based on he equivalen circui of a hree-winding ransformer [] and he dependency of he power ransfer beween wo full-bridge cells on he phase displacemen of he conrol signals. There, in a firs sep a urns raio of N :N :N :: is assumed and he PWM recifier, he PWM inverer and he volage-ype energy sorage are replaced by equal a b c :N B C U u U :N U u Fig.: Proposed hree-phase hree-por high-frequency link converer (Three-Por UP, []. The high frequency coupling of muliple four-quadran full-bridge converer cells via a single ransformer has been shown in principle in [] (cf. Fig.8 in [], however, no procedure for conrolling he sysem has been given here.
:N L i L i L i L u i L u L u i i i L +L T L m :N L i u L u L i u L i u u u u L u u L u T Fig.: (a Equivalen circui of a hree-winding ransformer; (b Y-equivalen circui of he proposed converer used for analyzing he dependency of he power ransfer beween he pors on he conrol signal phase displacemens; (c -equivalen circui of he hree-por sysem; (d equivalen circui for sudying he power flow beween wo pors when he hird por is opened. volage sources U U U ; subsequenly he consideraions are generalized o differen DC volages. I is shown ha a zero ne power flow can be achieved for one por while power is ransferred beween he wo oher pors. The inroducion of duy cycle conrol for minimizing he overall sysem conducion and swiching losses is discussed in ecion III. The converer conrol using a decoupling nework is reaed briefly in ecion IV. Finally, in ecion V he heoreical consideraions are verified by simulaions using PIM. II. CONTROLLBILITY OF THE POWER FLOW IN THE THREE-PORT CONVERTER. Equivalen Circui of a Three-Winding Transformer The equivalen circui of a hree-winding ransformer given in [], is shown in Fig.(a where L m is he effecive magneizing inducance and T and T are wo ideal ransformers wih urn raios :N and :N. The ransformer leakage inducances which are deermining he power ransfer in connecion wih he phase displacemen of he individual full-bridge converer cell conrol signals are represened by L, L, and L. The parameers of he equivalen circui can be derived from he measured values of he self inducances Z, Z, Z and he muual inducances M, M, and M of he ransformer windings M N M L Z Lm M N M L Z N Lm B. Direcion of he Converer Power Flow MM Lm M L Z NLm For limiing o he essenials we represen he oupu volages of he full-bridge cells by square wave volage sources wih a duy cycle of.5. Furhermore, we assume N and N o be equal o and neglec he ransformer magneizing curren and/or magneizing inducance. The resuling equivalen circui of he proposed sysem is shown in Fig.(b. The phase shif of conrol signals of wo full-bridge cells and/or of he square wave volage sources and u is denoed as φ in he following; accordingly, φ denoes he phase displacemen of and u. There, φ and/or φ are defined as posiive when is leading u and/or is leading u. The conrol range of φ and φ is from -/ o /. The hree-por converer can be simplified o a wo-por converer if he hird por is open. Based on [] we hen have for he power flow beween wo full-bridge phase-shif conrolled converer cells (cf. ( Fig.(d φ( φ VV Ts P ( ( L + L where V and V are he DC volages of he converers generaing and u and T s denoes he swiching cycle. ccording o ( he amoun and direcion of he power flow is deermined by he phase shif φ. This is also immediaely clear from a phasor diagram of he fundamenals of he volages and currens which is depiced in Fig.. The fundamenal power ransferred from por and/or o por and/or u is u α φ i i (a φ > (b φ < Fig.: The phasor diagram of he fundamenals of he volages and currens when he hird por is open U P UI cos( α U cos( α ( ω( L + L where Û /V, Û /V, Û is he absolue value of u, ω/t and α denoes he phase displacemen of and he curren i which is oriened perpendicular o. For φ > (cf. Fig.(a, and/or in case is leading u, α is smaller han /. Therefore, we have P >, he power flow is physically oriened from por and/or o por and/or u and reverses for φ < since α hen is larger han / (cf. Fig.(b. The Y-equivalen circui depiced in Fig.(b can be ransformed ino a D-equivalen circui [7] shown in Fig.(c which allows o deermine he resuling power flow of he hree-por sysem by superposiion of he power ransfer of hree wo-por sysems,u,,u, and u,u. E.g., for φ >, φ > and φ > φ (cf. Fig. (a he power flow is from o u, o u and u o u as φ > φ. Therefore, is acing as a source and u is consuming power. Dependen on he relaion of φ and φ and of V, V and V, Por and/or u can be sinking or sourcing power or remain a zero power. α φ u φ > φ > φ < φ < φ < φ > φ > φ > φ φ > φ < φ φ < φ > φ φ < φ < φ φ > φ < φ φ < φ > φ Fig.: Equivalen circui for sudying he power flow beween hree pors. The direcion of power flow is only deermined by φ, φ, no by V, V and V.
5% 5% u φ 5% u φ 5% u 5% φ u 5% φ u u u L u L i i u L i u L i u L i Fig.5: Key waveforms for achieving zero ne power flow o por assuming equal levels of he full-bridge converer cell DC volages, i.e.v V V. In summary, a power ransfer is possible in any direcion beween any pors simulaneously and he direcion is only deermined by φ, and φ (cf. Fig.. C. Conrol Leaving One Por a Zero verage Power n imporan funcion of an UP sysem is o direcly supply power from he mains o he load wihou charging or discharging he baery energy sorage. For he hree-por UP his canno be realized a low baery volage even if all power ransisors of he baery por full-bridge cell are remaining in he off-sae as he ani-parallel free-wheeling diodes would be forced ino conducion by high oupu volages of he mains or load por full-bridge cells. Therefore, φ and φ have o be seleced properly in order o achieve P and a given value of P P P (since he sum of he power of hree volage sources has o be zero, P +P +P, if losses are negleced. s he currens in he leakage inducances are direcly he currens of he volage sources of he Y-equivalen circui, he following consideraions are referring o Fig.(b. Here, again φ >, φ > and φ > φ is assumed. The key waveforms resuling in P are shown in Fig.5 for V V V and for he general case of differen u L i Fig.: Key waveforms for P and/or P P P for differing levels of he full-bridge converer cell DC volages V, V, V. DC volage levels V, V, V in Fig.. ccording o he law of superposiion, u conained, u, u is u ul L + ull + ull LL + LL + LL ( For he power flow of he pors we hen have φ( φ VV L + φ( φ VV L P T s ( LL + LL + LL φ( φ VV L + ( φ φ( φ φ VV L P T s ( LL + LL + LL φ( φ VV L + ( φ φ( φ + φ VV L P T s ( LL + LL + LL From (5 now he relaion of P and φ and of φ and φ can be derived under he side condiion of P and P P P. s shown in Fig.7 and Fig.8 for V 5V, V V, V V, P P 5kW, P, L L L µh, and f s khz, here are wo soluions for φ and φ. s a higher phase shif φ and φ resul in a higher peak value of he curren in he corresponding leakage inducance and/or in higher conducion and swiching losses he lower phase shif values φ and φ which have o be seleced for he sysem conrol. (5 Phase shif (rad 5,φ 5,φ Phase shif (rad 8 8 φ,φ φ,φ 8 Inpu power from square wave volage source (W Fig.7: Phase shif φ for achieving P P 5kW and P. Operaing parameers: V 5V, V V, V V, L L L µh, and f s khz. Phase shif φ (rad Fig.8: Dependency of phase shif φ on φ for achieving zero ne power flow o por, i.e. P (cf. Fig.7. Operaing parameers: as for Fig.7.
III. MINIMIZTION OF THE OVERLL YTEM LOE. Inroducion of Duy Cycle Conrol In order o gain degrees of freedom for minimizing he overall sysem losses, duy cycle variaion of he full-bridge converer cell oupu volages, u and u could be inroduced in addiion o phase shif conrol as shown in Fig.9. There, he conrol range of δ, δ and δ is from o /. α cosα j ω O i α φ φ u φ δ ω i i φ δ u δ Fig.9: Definiion of phase displacemen and duy cycle of he converer cell oupu volages, u and u. B. Zero Circulaing Power The power ransferred from o u, from u o u and from u o will be denoed as P, P and P in he following. iming for minimizing losses a circulaion of power inside he sysem which would no conribue o he power flow of he pors has o be prevened, i.e. P +P +P ( has o be ensured. Considering P P +P and P P +P, we have for P, P, and P in dependency on P, P wih ( P P P P P P (7 P P + P For he sake of simpliciy he furher consideraions are resriced o fundamenals of he volages and currens. Furhermore, L L L, φ >, φ > and φ >φ is assumed. The corresponding phasor diagram is shown in Fig. where defines he orienaion of he real axis u U + j (8 We hen have for P U P cos( UI α U cos( α (9 Considering he phase displacemen φ of and u (cf. Fig.9 and/or of and u, u can be expressed as (cf. Fig. u cos( φ sin( φ j ( ccordingly, formed by and u is u u u ( cos( φ + sin( φ j Inroducing he phase displacemen α of and i, which is leading i by / can be alernaively formulaed as u cos( α + sin( α j ( sin( α + cos( α j Combining ( and ( resuls in ω U cos( α sin( ( φ Considering (, he power flow P (cf. (9 now can be represened as U P cos U α U sin( φ ( Taking finally ino accoun ha he area OB of he riangle OB in Fig. is OB UU sin( φ (5 he power ransferred beween wo pors in general is proporional o he area of he riangle defined by he phasors of he volages of he pors and is inversely proporional o he equivalen impedance and/or inducance connecing he pors (cf. Fig.c, P sin( φ ccordingly, P and P can expressed as P OC P OB OBC ( (7 where OC denoes he area of he riangle OC and OBC denoes he area of he riangle OBC. Considering P +P +P, and L L L as assumed above, (7 yields in combinaion wih ( P sin( φ ( j + P + P P P implifying (8, resuls in φ u B u ( C Fig.: Phasor diagram of he fundamenals of he sysem volages and currens. P OB OB OBC OBC OB OBC + OC OC OC (8 (9 ccordingly, for prevening circulaing power flow, he head of u shown as poin C in Fig. has o be locaed on he line B and/or and have o be aligned wha resuls in an alignmen of i, i, and i i +i wha considerably simplifies he closed-form sysem
descripion. C. Range of φ and φ ubsiuing ω /Τ s, Û / V cos(δ, and Û / V cos(δ in (, P can be represened as P U sin( φ ( V cos( δ V cos( δ sin( φ L nalogously, we have for P and P P V cos( δ V cos( δsin( φ L ( P V cos( δ V cos( δsin( φ φ L Referring o ( and ( he duy cycles δ, δ, and δ now can be expressed as PPL (an( φ an( φ a cos( if ( φ > ( φ V PTs an( φ an( φ δ PPL (an( φ an( φ a cos( oherwise V PTs an( φ an( φ PL ( δ a cos( VV cos( δsin( φ PL δ a cos( VV cos( δsin( φ For conrolling he sysem 5 degrees of freedom, i.e. he phase displacemens φ, φ, and he duy cycles δ, δ and δ are available. Defining he power flow of wo pors, e.g. P and P and ensuring zero circulaing power wo degrees of freedom are remaining, i.e. he converer characerisics can be expressed in dependency of φ and φ. Taking ino accoun he resricion of he argumen of an inverse cosine funcion o [, ], ( resuls in a limiaion of he operaing range of he converer and/or in a limiaion of he admissible range of φ and φ. E.g., here follows considering δ (φ, φ, PPL(an( φ an( φ ( V PT s an( φ an( φ (rad Phaseshifφ 5 reaδ reaδ rea Phaseshifφ (rad 5 reaδ Fig.: Operaing rea, i.e. admissible range of phase shif φ and phase shif φ resuling form (. ssumed operaing parameers: P kw, P kw, P kw, V 5V, V V, V V, L L L µh, and f s khz. The corresponding range of φ,φ is denoed as reaδ in he following (cf. Fig.. In analogy, reaδ and reaδ are resuling from δ (φ, φ and δ (φ, φ. Considering all resricions, he sysem operaion finally has o be resriced o he rea defined by he inersecion of reaδ, reaδ and reaδ. D. Minimizaion of Overall ysem Losses For realizing he full-bridge converer cells in IGBT echnology for a raed power in he range of 5 kw, he sysem swiching and conducion losses could be derived based on []. There, we have for he urn-on and urn-off energy loss of a power ransisor and he urn-off energy loss of a power diode woff ( u, i K off + K off + K off u + K off + K off 5 won ( u, i K on + K on + K on u + K on + K on5 wdoff ( u, i K Doff + K Doff u i + K Doff u + K Doff u i + K Doff 5 ( where he indices, D denoe wheher he ransisor or he diode is considered, and u and i are he volage and he curren being swiched. The coefficiens K i are deermined by measuremens and specified in []. For he conducion losses of he valves we have again according o [] p / D U F, / D i + r / D irms (5 where ī denoes he average value and i rms is he rms value of he ransisor or he diode curren. The overall sysem losses resuling for, e.g. P kw, P kw, P kw, V 5V, V V, V V, L L L µh, and f s khz are shown in Fig.. There, operaing poin resuls in minimum overall power semiconducor losses. This is clearly verified by operaing poin B which is characerized by significanly higher curren ampliudes and higher volage and curren phase displacemens and/or significanly higher losses (cf. Fig.. Fig. also jusifies he approximaion of he acual curren waveforms wih he fundamenals (cf. (b and (d. ccordingly, he calculaion of φ and φ based on ( allows an accurae pre-conrol he sysem power flow (cf. Fig.. Phase shif φ (rad.7..5..... 8 5 58 8 7 7...5..7.8.9 Phase shif φ (rad Fig.: Overall sysem losses in dependency of φ and φ. ssumed operaing parameers: P kw, P kw, P kw, V 5V, V V, V V, L L L µh, and f s khz. B (W
- - - - i i i u u - - - - - - - - i, u u i, i, - - - - - - - - (a - - - - (b - - (c - - (d Fig.: cual ime behavior of, u, u and i, i, i (cf. (a and (c and of he fundamenal approximaion of i,, i,, i, of i, i, i (cf. (b and (d for operaion poin (cf. (a and (b and operaion in poin B (cf. (c and (d in Fig.; ssumed operaing parameers: P kw, P kw, P kw, V 5V, V V, V V, L L L µh, and f s khz. One has o noe, ha operaing poin in general is characerized by low swiching losses. IV. CONTROL TRTEGIE s menioned in ecion.c, wo degrees of freedom, i.e. φ and φ are available for he sysem conrol. ccordingly, he sysem could In analogy, linearizing P a operaing poin yields P P + P P P P + P be considered as a wo inpu (φ and φ and wo oupu (P and P K sin( φ K sin( φ φ conrol sysem. + K cos( φ + φ φ (8 The power P of por is he sum of P (cf. ( and P (cf. ( + K cos( φ φ K cos( φ + φ φ P P + P P + P P + G φ + G φ ( K sin( φ + K sin( φ φ where G K cos( φ + φ G K cos( φ K cos( φ + φ where K V cos( δ V cos( δ L P K sin( φ K sin( φ φ K V cos( δ V cos( δ wih L K V cos( δ cos( V δ. ssuming ha sysem operaion is close o poin is ensured by L proper pre-conrol (cf. Fig., where φ and φ is, and δ, δ, δ could be deermined based on ( he conroller only has o In summary, we have for he small signal model of he sysem slighly adjus φ and φ in a given operaing region. Therefore, for P G G φ φ deriving a conrol-oriened sysem model, ( can be linearized a G (9 P G G φ φ he desired operaing poin resuling in The ineracion of he conrol loops (9 can now be eliminaed P P + P K sin( φ + K sin( φ φ φ + K cos( φ φ K cos( φ + φ φ (7 P * φ ' φ H + K cos( φ + φ φ P + G φ + G φ φ P where G K cos( φ K cos( φ + φ wih - - - - - G K cos( φ + φ P K sin( φ + K sin( φ φ K V cos( δ cos( V δ L K V cos( δ cos( V δ L i i i u u - - - - - P * - - - - - u u i, φ ' i, H H H i, φ φ φ - - - - - Three-por UP δ δ δ Fig.: ysem power conrol employing a decoupling nework. P * and P * are he power reference signals. ysem operaion close o he opimum operaing poin is ensured by pre-conrol signals φ, φ, and δ, δ, δ. P
using a decoupling nework H (cf. e.g., []. The resuling conrol srucure is depiced in Fig.. Based on P φ' GH ( P φ' he decoupling marix can be found as H H H G G H G G H G G GG G G G G G V. IMULTION REULT ( The above heoreical consideraions have been verified by digial simulaions using PIM based on he circui schemaic shown in Fig.5 assuming he following operaing parameers and componen values: V 5V, V V, V V, L L L µh, f s khz, C C C µf. U I I i C L :N L C u L u L u i U VI. CONCLUION novel Three-Por UP formed by linking a hree-phase PWM recifier, a hree-phase PWM inverer and a baery energy sorage via a single hree-winding isolaion ransformer and corresponding full-bridge converer cells is proposed. ccording o he heoreical analysis and simulaion resuls he converer sysem shows he following feaures: The bidirecional power flow beween he pors can conrolled by he phase-shif of he individual full-bridge cells; uilizaion of duy cycle conrol allows o operae he sysem wih minimum power semiconducor losses For employing a decoupling nework, he power of he pors can be conrolled independenly, where operaion of he sysem in he opimum region is ensured by proper pre-conrol derived from analyzing he sysem behavior wih resricion o he fundamenals of he volages and currens. In a nex sep a DP-conrolled 5kW laboraory model of he sysem shown in Fig. will be realized for verifying he proposed conrol concep. Furhermore, he opimizaion of he sysem behavior will be exended o a proper selecion of V and V for a given operaing poin. I :N REFERENCE U The simulaed sysem conrol behavior is shown in Fig.. he power reference signals are P * kw and P * kw (a negaive power value indicaes ha power is absorbed by he corresponding por and/or converer cell, in he case a hand power is delivered from por o pors and. The power reference signal P * is sepped o kw a.s and P * is sepped o a.7s. The conrol shows excellen dynamics and only a weak cross-coupling of he conrol loops is remaining. deailed descripion of he dynamic modeling of he sysem and he exension of he basic conrol srucure o conrolling V and he baery charging curren I will be discussed in a fuure paper. P and P (W i -5 - - - - u C L u L Fig.5: Circui schemaic employed for he circui simulaion.....8 Time (s Fig.: imulaion of he sysem conrol behavior for V 5V, V V, V V, L L L µh, and f s khz. he power reference signals P * and P * are kw and kw..s P * is sepped o kw, and P * is sepped o a.7s. P P [] N. Blacha, The Perspecives of UP and Fuel Cells on he Base of a New Flexible Modular UP Technology, in Proc. Power Qualiy of PCIM conf., pp -7. [] J.W. Kolar, and C. Zhao, Vorrichung zur hochfrequen-poenialgerennen bidirekionalen Kopplung von Dreiphasensysemen und Gleichspannungsquellen (in German, wiss Paen pplicaion, filed: pril. [] G. Chen, D. Xu, Y. Wang, and Y. Lee, New Family of of-wiching Phase-hif Bidirecional DC-DC Converer, in Proc. IEEE Power Elecronics pecialiss Conference (PEC conf., vol., pp 859-85. [] J.C. Han, and N.E. Prasad, Three-Phase C/C High-Frequency Link Marix Converer for VCF pplicaions, in Proc. IEEE Power Elecronics pecialiss Conference (PEC conf., vol., pp 97-97. [5] Y. Hayashi, T. Ise, and K. Tsuji, Power Converer ysem for Flexible, Reliable and Inelligen Elecrical energey Delivery ysem, in Proc. h European Conference on Power Elecronics and pplicaions (EPE conf., CD-ROM, IBN: 9-7585-7-7. [].G. Ganz, simple, exac equivalen circui for he hree-winding ransformer, IRE Trans. Componen pars, vol. 9, issue, pp -, December, 9. [7] MIT aff, Magneic Circuis and Transformers, John Wiley and ons, Inc., New York, 9. [8] N. chibli,. Rufer, ingle- and Three- Phase Mulilevel Converers for Tracion ysems 5Hz / / Hz, in Proc 7 h European Conference on Power Elecronics and pplicaions (EPE 997 conf., pp -5. [9] W. Holger,. Volker, and. ndreas, of-wiched Dual cive Bridge DC-o-DC Converer employed in a High-Volage Elecronic Power Transformer, in Proc. h European Conference on Power Elecronics and pplicaions (EPE conf., CD-ROM, IBN: 9-7585-7-7. [] F. chafmeiser,. Herold, J.W. Kolar, Evaluaion of V-i-IGBTs and V-ic-JFETs for pplicaion in Three-Phase Very parse Marix C-C Converer ysems, in Proc. IEEE pplied Power Elecronics Conference and Exposiion (PEC conf., vol., pp. -55. [] W.L. Luyben, Disillaion Decoupling, Journal IChE, vol. -, pp. 98-, 97