Steady State Analysis of the Galvanically Isolated DC/DC Converter with a Commutating LC Filter

Transcription

1 Seady Sae Analysis of he Galvanically solaed DC/DC Converer wih a Commuaing LC Filer Janis Zakis, Dmiri Vinnikov, vars Rankis 2 Tallinn Universiy of Technology 2 Riga Technical Universiy janis.zakis@ieee.org Absrac- This paper presens an analysis of he coninuous curren and he disconinuous curren mode operaion of he ransformer of a sep-up DC/DC converer opology inended for applicaions wih widely changing inpu volages. The proposed opology consiss of a LC nework coupled wih a single-phase inverer on he primary side and a full-bridge recifier on he secondary side of an isolaion ransformer. When he inpu volage is above he nominal value, he converer operaes in he buck mode, bu when he inpu volage level is below he nominal value, he converer operaes in he boos mode.. NTRODUCTON Topologies of laice neworks coupled wih he pulse widh modulaed (PWM) inverer in oday's power elecronic applicaions are numerous [1-6]. These converers have boh volage sep-up (boos) and sep-down (buck) properies. Moreover, hey can buck and boos inpu volage in a single power conversion sage. Reduced number of passive elemens in such laice filers resuls in reduced coss, dimensions and increased power densiy of he whole sysem. The simples filer opology which could be used for volage buck and boos operaion is a convenional LC filer [7, 8]. Bu wihou LC circui modificaion, he boos mode canno be performed since he special operaion sae of he PWM inverer [1-6, 9, 10] does no allow ha. To exclude such a disadvanage an auxiliary swich TA wih aniparallel diode in he filer capacior C circui (Fig. 1) are proposed o be added. This paper presens he mahemaical analysis of a converer conaining an LC filer coupled wih he single-phase inverer wih swiches T], Tb T3, and T4 (Fig. 1). Generally, he onsae ime of one swich pair can be expressed as DTsw, where D is he duy cycle of one swich pair and Tsw is he operaing period of he ransformer. f D<0.5, swich pairs periodically connec he inverer o he primary winding of he ransformer and he converer - ilnil L operaes in he buck mode wih an acive sae of swiches DATo, where DA is he acive sae duy-cycle and To is he operaion period of one swich pair (Fig. 2a). Uj Tj, T2 DATo (a) T3, T4 n :- DATo TA DsTo Tsw Uj 1 r (b) Fig. 2. Operaion principle of he proposed converer: buck mode (a) and boos mode (b). f D>O.5, boh ransisors of one inverer leg are swiched simulaneously, hus periodically shorening he inverer bridge (inervals DsTo in Fig. 2b). This special swiching sae is also known as a shoo-hrough sae [1, 2, 6]. A ha ime he auxiliary swich TA in he capacior circui is urned off and is repeaedly swiched on during DATo. n such a way he boos mode is provided. The secondary winding of he ransformer is conneced o he RC load via a full-bridge recifier (Fig. 1). Capacior Cl in parallel wih he load limis he oupu volage ripple. Ds iw -- 1 UN C1 R Fig. 1. General power circui of he proposed converer /$ EEE 827 let 2012

2 . OPERATON N THE BUCK MODE Uw 0.5nlm R(DA +do). (3) n he buck mode he inpu LC filer is conneced and he duy cycle of he inverer swiches is DA::;l. The basic volage and curren waveforms in he disconinuous curren mode of he primary winding of he ransformer are depiced in Fig. 3. When h T2 are swiched on, he primary winding of he ransformer is being fed wih he supply volage UNU1. Curren i1 of he primary winding of he ransformer is almos linear in he ime inerval DATo and grows from zero up o he ampliude value 1m bu when he swich pair is swiched off, he primary volage of he ransformer changes he polariy o -UN hrough he aniparallel diodes of he inverer bridge and he curren i decreases up o zero in he ime inerval f2. Fig. 3. Basic volage and curren waveforms in he disconinuous curren mode. f he ransformer urns raio is nw/w2, he load curren iw a he oupu of he recifier grows periodically from zero up o nlrn and hen in he inerval f2 decreases up o zero (Fig. 3, where nl ). Changes of he curren i1 of he ransformer primary winding in boh inervals are defined by respecive volages (UN- nuw) and (UN +nuw), as well as by he ransformer leakage inducance LTRL1+n2L2. Using he self-inducance volage equaion we can wrie where (UN - nuw)dato (UN + nuw) 2 ' (1) (UN - nuw)dato 2 -'----- "'--...:..:...""- UN +nuw f i1 change is linear, he load volage is (2) Since he curren i1 ampliude can be found as (U N - nuw)da m L TR"JO {" he load volage can be found as where -(LTRfo +n2rd )+.JB U -U N LD - B (LTRfo +n2 RD ) 2 +4n2 RD LTRfo This equaion can be used unil he momen he coninuous curren i1 of he ransformer sars, i.e. unil (DATo+f2)<To. From (2) a boundary beween coninuous and disconinuous curren mode of he primary winding of he ransformer will occur when Uw(2Drl)UNln. The boundary of disconinuous curren i1 of primary winding of he ransformer in he buck mode can be found from (2) and (3) Dab (0.5 _ LT + (0.5 _ LTRfo fo ) + n R LTRfo ) 2 + n2 R, n2r n he inerval from DAO up o Dab he capacior curren ic in he period To consiss of hree pars: during DATo par ic has linear change from ln up o -(/m-4n); during f2 he linear change of curren is from (/m +ln) up o ln; during (T JDAT J (2) he icln' where ln is he average curren of he DC source uid N RU N The minimal volage value of he capacior UC,min will occur a he end of he swich on (DATo) sae of he swich pair, bu he maximal value will develop approximaely a he beginning of ha inerval. Then 1U U -U. ( rn - N ) 2 DA C Cmax Cmm 2 {" e Jo rn From here he capaciy C necessary in he buck mode can be found ill Uc is given. Basic volage and curren waveforms in he coninuous curren mode (wihin Dab<DA<l ) of he primary winding of he ransformer are depiced in Fig. 4. n his case in he period To he curren i par of ime (f) flows hrough he pair of he swiches of he inverer, bu he res of he ime f2 - hrough he reverse diodes of he ransisor module. Curren i in he inerval f changes from zero up o +-lm' bu in he inerval f2 linearly in ime i ends o zero.. (4) (5) (6) (7) (8) 828

3 i h T' T3, T4 Ul il UN O-----T :, : e i ' -UN. : ' }:D 12 o ic m+11n ' ' i ln ' U i U : 1 UCmin : i : " " '! 7., :! : Fig. 4. Basic volage and curren waveforms in he coninuous curren mode. The average value of he load curren is 1w0.5n1m and he average load volage is Taking ino accoun ha in boh inervals 1 and 2 ransformer primary winding volage polariies are reverse and from he absolue value are equal wih UN, we can wrie where : -" (9) (U1N -nuw )(1'o - 2 ) (UJN +nuw) 2 ' (10) n21 m R n urn, l 0.5To(1 + ). 2U1N (11) Since he curren i1 growh in he inerval 1 is defined by he volage (UlvnUW), hen 1m (U 1N -nuw )l. (12) LTR Using Uw and 1 equaions, he ampliude of he curren i1 can be calculaed as 2UJN r {' 2 {' 2 2 2] 1m -2-2 l-2ltrjo + 4LTRJO +n R.(13) nr Like above, he filer capacior curren ic changes wihin (lm+1n) up o -{1m-lN). The minimal value of he capacior occurs in he swich off momen of he swich pairs, bu he maximal value develops approximaely a he beginning of he inerval 1' Therefore he capacior C volage ripple can be approximaely calculaed as. OPERATON N THE BOOST MODE (14) During he shoo-hrough sae, when he swiches of one inverer leg are swiched on simulaneously (e.g., T1 and T4 in Fig. 1), he periodical shorening of he ransformer inpu is made and a he same ime he filer auxiliary swich TA is swiched off. During he shoo-hrough inerval (DsTo in Fig. 5) he elecromagneic energy is sored in he inducor L, which afer he shoo-hrough sae will be ransferred o he filer capacior C and o he ransformer. ht2; T3, T4 f-1 r ;:;: DsTo U Ul B h 1m ;: r " f"- f"- '\J -( m:j'\j "'J Fig. 5. Basic volage and curren waveforms in he disconinuous curren mode. Also, in his operaion mode he disconinuous and he coninuous curren mode of he primary winding of he ransformer is possible. The disconinuous curren of he primary winding of he ransformer is characerized by he waveforms in Fig. 5. The boosed volage UB seen on he ransformer primary winding afer he shoo-hrough sae [4] can be expressed as U1N U B (15) -D s Such volages occur only in he case of an ideal source wih zero inernal resisance. n Fig. 5 lw is he average value of he load curren: lw 0.51 m (1- D s + 2 1o), D (16) where 2 is he ime in he shoo-hrough inerval when i1 changes from he ampliude value +/-lm up o zero: LTRlm (17) nuw where 1m is he ampliude of he ransformer primary curren i1: 829

4 1 (U B -nuw )(1-Ds ) m LTRfo Ow - average value of he load volage: (18) uwlwr0.5nlmr(1-ds +2 /0) (19) DsTo From (17), aking ino accoun (19) and he fac ha 12 becomes equal o DsTo boundary beween he disconinuous and coninuous curren mode of he primary winding of he ransformer can be defined by shoo-hrough duy-cycle: D - 2L TRfo Sb - (20) R Generally, aking ino accoun (19), 12 for disconinuous curren mode of he primary winding of he ransformer can be expressed as (1 -D ) LTRo s n 2 R /0 Also, from (18) he curren ampliude ij can be expressed as 1m 4UjN 1[4foLTR + n2 R(- DS)2 + + (1-Ds ) n4r2(1-ds)2 + 8n 2 RLTRfo] (21) (22) This expression allows calculaing an average value of he load volage. Assuming ha supply curren is smoohed, he filer capacior C curren changes only wihin To(1-Ds) and peak-o-peak value can be calculaed as (23) _ U2 where 1 N RU N Assuming, ha he curren ic of he capacior C is linear, he volage Uc of capacior is _ ue - U + 0.5Me 0.5Me2 (24) e.min C - C T o where ime 1 in he inerval To(1-Ds) changes from zero up o he lengh of he whole inerval. The ampliude of his volage is a 0.5To(1-Ds): U -U so he full ripple is e,max - e,min + MeTo(1-Ds ) 8C!::..U Me(1-Ds ) e 8Cfo (25) (26) should be aken ino accoun ha he average value of he capacior volage is equal o he boosed volage UB Fig. 6 shows he basic volage and curren waveforms in he coninuous curren mode of he primary winding of he ransformer. Fig. 6. Basic volage and curren waveforms in he coninuous curren mode. The waveform of ransformer primary winding curren (21m) consiss of wo componens: in he inerval DsTo in he inerval (1-Ds)To M 0.51mn2 RDs foltr UN mn2 R(1- Ds ) M 2 foltr Merging, 2mLJj+ LJh and from here 1 U m 2LTRfo - n2 R(Ds - 0.5) The peak-o-peak value of he capacior curren can be expressed as Me 2(1m - )' (27) (28) (29) Curren ripple of he volage source in he boos mode can be calculaed during he shoo-hrough sae: M U /NDS L fol (30) n pracice (30) defmes he parameers necessary for he filer L inducor. A maximal shoo-hrough duy cycle Dsm he full change of he curren mus be on an acceped level k M L m U}NDSm, (31) 1 N. m LfoPN where PN is he nominal load power, /N,m - he larges average value of he source curren. From here L uindsm kfopn (32) 830

5 .. V. SMULATON RESULTS Fig. 7 shows he PSM simulaion resuls of he buck mode of he proposed converer in he disconinuous curren mode of he ransformer curren. subsiued by equivalen resisance Req. was saed ha he inpu volage (UN40 V) should be boosed wo imes (Uour80 V). ln ---+ L Req Fig. 9. Equivalen circui diagram of proposed converer used in experimens. uc, (V) 1\] P1Y1Vf\:'f Time (5) Fig. 7. Basic volage and curren waveforms in he buck mode (disconinuous curren mode of he ransformer). Fig. 8 shows he PSM simulaion resuls of he boos mode of he proposed converer in he coninuous curren mode of he ransformer curren. is seen ha he simulaion resuls are in good agreemen wih he heoreical assumpions discussed earlier. 40 i1, (A) -40 ic, (A) uc, (V) To obain he desired wofold boos he shoo-hrough sae duy cycle Ds of a swich T was se o 0.5. The componen ypes and values used during experimens are summarized in Table. TABLE COMPONENT TYPES AND VALUES USED N EXPERMENTS Componen nducor L CapaciorC Swich T Swich TA Valuefype 110 lh 120 lf SKM50GB123D SKM50GB123D Fig. 10 presens he main operaing waveforms of he discussed converers. These are inpu volage (UN), inpu curren (ln), oupu volage (UOUT), and oupu curren (lout). is obvious ha he proposed converer can sep up he inpu volage wo imes. Tek JL. 0 Trig'd M Pos: 32,28»s CH1 M Coupling!l! BW Limi m 200MHz Vols/Oiv!Em Time (5) Probe SOX Volage Fig. 8. Basic volage and curren waveforms in he boos mode (coninuous curren mode of he ransformer). 3+ nver m J1 50.0V CH2 50.0V M 10,0»s CH3..r 20.8A V. EXPERMENTAL RESULTS CH3 10.0A CH4 10.0A RefC 1,00V 500»s RefD 1,00V 500»s To verify he heory discussed before he experimenal seup wih he raed power of 800 W was developed and esed. Fig. 9 presens he equivalen circui of Fig. 1 which was used in experimens, where inverer (TrT4) is subsiued wih swich T bu he secondary par of converer is Fig. 10. Main operaion waveforms of proposed converer. n he second experimen he volage boos properies were examined. Relaion beween he converer oupu volage UOUT and shoo-hrough duy cycle Ds of he swich T is shown in Fig. 11. can be seen ha a a larger Ds value he experimenal curve becomes lower han he heoreical curve. 831

6 This fac can be explained by he volage drop on he circui elemens. >.. ::J o ::J -experimenal -heoreical 80,-----_ ,1 0,2 0,3 0,4 0,5 Fig. 11. Experimenal and heoreical boos properies of proposed converer. The volage boos properies for proposed converer are he same as i is for classical boos converer. can be explained by he same number of energy sorage elemens c.5 '0 <:: 80 '" :::> 60..i Ds -+-Lf(8) -+-Cf(8) 1,2 1,4 1,6 1,8 2 B Fig. 12. nducance of inducor (L) and capaciance of capaciors (C) of proposed converer dependence on differen boos facors B. Fig. 12 shows he inducance L and capaciance C of commuaing filer as a funcion of he boos facor B for he discussed converers for he assumed inpu curren ripple of 20%. V. CONCLUSONS The discussed DCDC converer wih a commuaing LC filer can operae in boh he buck and he boos mode. n he boos mode he filer capacior C mus be disconneced during he shoo-hrough sae. The expressions obained for he coninuous and he disconinuous curren mode of he isolaion ransformer primary winding in he buck and he boos mode can be used o calculae he parameers of he circui elemens. Changes in he filer capacior volage depend on he difference beween he converer inpu and he source curren. n addiion, in he buck mode he ripple is around he source volage value, bu in he boos mode - around he boosed volage, which is defmed by he boos shor-circui process. The capaciance of he capacior C mus be seleced from he buck mode according o an allowable volage ripple. The inducance of he inducor L mus be seleced from he boos operaion mode a he highes boos (a he highes shoohrough ime). The experimenal resuls show ha proposed converer wih commuaing LC filer has volage boos properies and can be used for volage sepping-up. ACKNOWLEDGMENT This research work was suppored by he Esonian Minisry of Educaion and Research (Projec SFO40016s11), Esonian Science Foundaion (Gran ETF8538) and Esonian Archimedes Foundaion. REFERENCES [1] Fang Zheng Peng; "Z-source inverer," EEE Transacions on ndusry Applicaions, vol. 39, no. 2, pp , Mar/Apr [2] Yuan Li; Anderson, J.; Peng, F.Z.; Dichen Liu, "Quasi-Z-Source nverer for Phoovolaic Power Generaion Sysems," Tweny-Fourh Annual EEE Applied Power Elecronics Conference and Exposiion APEC 2009, pp ,15-19 Feb [3] Ding Li; Feng Gao; Poh Chiang Loh; Miao Zhu; Blaabjerg, F.; "Cascaded impedance neworks for NPC inverer," Conference Proceedings PEC 2010, pp ,27-29 Oc [4] Vinnikov, D., Roaso, 1.; Srzelecki, R, Adamowicz, M., "Two-Sage Quasi-Z-Source Nework Based Sep-Up DCDC Converer", Proc. of EEE nernaional Symposium on ndusrial Elecronics SE'201O, pp , July 4-7, [5] Srzelecki, R; Adamowicz, M.; Srzelecka, N.; Bury, W.; "New ype T Source inverer," Compaibiliy and Power Elecronics CPE '09. pp ,20-22 May, [6] Vinnikov, D.; Roaso, 1.; Zakis, J.; Srzelecki, R "New Sep-Up DC/DC Converer for Fuel Cell Powered Disribued Generaion Sysems: Some Design Guidelines ", Elecrical Review SSN , Vol. 86, Nr 8. pp , [7] Carr, J.A.; Balda, J.C.; "A grid inerface for disribued energy resources wih inegraed energy sorage using a high frequency AC link," EEE Power Elecronics Specialiss Conference PESC 2008., pp , June [8] Kunrong Wang; Lee, F.C.; Lai, J.; "Operaion principles of bidirecional full-bridge DCDC converer wih unified sof-swiching scheme and sof-saring capabiliy," Fifeenh Annual EEE Conference Applied Power Elecronics and Exposiion APEC 2000, vol., pp.l-l8, [9] Roaso, 1.; Vinnikov, D.; Jalakas, T.; Zakis, J.; O, S.; "Experimenal sudy of shoo-hrough conrol mehods for qzs-based DCDC converers," nernaional Symposium on Power Elecronics Elecrical Drives Auomaion and Moion (SPEEDAM), pp , June [10] Zakis, J.; Vinnikov, D.; Roaso, 1.; Jalakas, T. Pracical Design Guidelines of qzs Based Sep-Up DCDC Converer. Scienific proceedings of Riga Technical Universiy. Power and Elecrical Engineering, o be published,