Interleaved DC/DC Converter with Coupled Inductor Theory and Application

Transcription

1 American Journal of Engineering Research (AJER) e-issn: p-issn : Volume-7, Issue-5, pp Research Paper Open Access Inerleaved DC/DC Converer wih Coupled Inducor Theory and Applicaion Miriam Jarabicova 1,Michal Prazenica 1,Slavomir Kascak 1 1(Deparmen of Mecharonics and Elecronics, Universiy of Zilina, Slovak Republic) Corresponding auhor: Miriam Jarabicova1 ABSTRACT: This paper deals wih he analysis of buck inerleaved DC-DC converer wih a coupled inducor on he same magneic core. The advanage of he coupled inducor over he non-coupled case is invesigaed. The curren ripple equaions as an oupu curren for he buck operaion mode and he ripple curren in individual phase of he inerleaved converer using coupled inducor are explained analyically and suppored by simulaion and experimenal resuls. The novely of he paper is an invesigaion of curren ripples of inerleaved buck converer operaed over 50 % of duy raio and uilizaion of he converer in he applicaion of elecric drive vehicle. KEYWORDS: Coupled inducor, inerleaved converer,bidirecional converer Dae of Submission: Dae of accepance: d D i C1 i C2 i 1, i 2, i 3, i 4 i ou, i m I 1, I 2 I 1pp, I 2pp I ou K m lk PFC,, S 1, S 2 T S V CE(SAT) V ou V in V 1, V 2 V lk1, V lk2 V m VRM I. NOMENCATURE Time inerval for calculaion of curren ripple Duy cycle Oupu curren of noncoupled converer Oupu curren of coupled converer Inducor 1, 2, 3, 4 curren Oupu curren Magneizing curren Inducor 1, 2 curren ripple Inducor 1, 2 curren ripple in analyzed inerval Oupu curren ripple Coupling coefficien Inducance Magneizing inducance eakage inducance Power facor correcor Power swiches Swiching period Transisor collecor-emier volage Oupu volage Inpu volage Inpu volage eakage inducance Magneizing volage Volage regulaor module II. INTRODUCTI Nowadays, he inerleaved opologies are widely used due o heir advanageous properies such as w w w. a j e r. o r g Page 80

2 lowered curren ripple and volume reducion [1]- [3]. For he higher power applicaions, here are more possibiliies how o perform higher power densiy regarding he efficiency of he converer. The firs choice is o uilize of he paralleling of he power swiches, shown in Fig. 1a. This converer includes only one inducor and parallel conneced wo half-bridge legs. This is done for reasons of obaining higher curren raings, hermal improvemens, and someimes for redundancy. If losses are no equally shared, he hermal differences beween he devices will lead o oher problems and he possible failure of he ransisors. Therefore, he hermal coefficien of he collecor-emier volage V CE(SAT) is an imporan parameer when paralleling IGBTs. I mus be a posiive o allow curren sharing. On he oher hand, he higher posiive hermal coefficien brings he higher conducive losses because a high emperaure he V CE(SAT) is increased. The second opion how o share he curren is o use he inerleaved bidirecional opology, Fig. 1b [5]. The same problem as in he previous opology wih curren sharing is eliminaed because he curren is divided ino wo parallel buck converers. The advanageous of his connecion is in improved power densiy, he inerleaved effec reduces he oal inpu and oupu curren ripple, so his means he smaller inpu and oupu filers (bulk capacior), beer disribuion of power wih lower curren sress for semiconducor devices [3]. In he high curren applicaion, here are used he inerleaved opologies even wih he coupled inducors. The advanageous of he coupled inducor is in lowered curren ripple direc on he inducors no only in he oupu or inpu curren of he converers. The inerleaved buck converer wih coupled inducance is used in VRM applicaion where volage abou 1V and curren of hundreds of amps are applied. On he oher side, uilizaion of coupled inducor in higher volage applicaion does no have any limiaion as is seen in PFC applicaion [6]- [10]. Therefore, he advanageous feaures of he coupled inducor will be analyzed for he converer, which serves for recovery energy a he ime of regeneraive braking of he racion moor [11]. The analysis includes invesigaion of curren ripple on he oupu of he converer and change of he inducor curren ripple in case of he coupled inducor in comparison wih he non-coupled case. V in DC BUS DC BUS V ou S1 S 2 V ou S 1 S 2 a) b) Fig. 1 a) Buck DC/DC converer for higher power applicaion, b) Inerleaved buck DC/DC converer for baery/ulracapacior applicaion III. CURRENT RIPPE REDUCTI EFFECT OF COUPED INDUCTOR The inenion of he curren ripple reducion in case of baery applicaion is o prolong he baery lifeime because is sensiive o high dynamic curren sress. Therefore, he buck inerleaved opology wih reduced oupu curren ripple is proposed o solve his issue. The oupus of he converers shown in Fig. 1a, bare conneced o he baery/ulracapacior pack and inpu o he DC BUS of he hree-phase inverer. This secion is divided ino wo pars. Firsly, an impac of he non-coupled inducor on buck opology is invesigaed. Then, in some following subheads, he advanage of coupled inducor is analyzed wih emphasis o he reduced inducor curren ripple. In he wo-phase inerleaved converer, he four differen operaing modes occur as shown in Fig. 2. The firs inerval begins when he swich and S 2 are closed, he second inerval when S 1 and S 2 are on. In he hird inerval, and S 1 are urn on. I means ha he curve of he curren i 2 in he second phase is same as he curren i 1 in he firs inerval, bu phase-shifed by 180. Therefore, he ripple of currens in he hird inerval is same as in firs one (exchange of curren i 2 wih i 1 and vice versa). From he Fig. 2 is seen ha ripples I 1 and I 2 are he same. Bu, he oupu curren ripple is dependen on I 1 and I 2pp, no I 2. Then, an appropriae equaion for inducor curren ripples in a firs inerval can be obained, (1) and (2). w w w. a j e r. o r g Page 81

3 i 1 ΔI 1 i 2 ΔI 2pp ΔI 2 i ou ΔI ou I II III IV D.T S ½.T S TS Fig. 2 Curren ripples of inerleaved non-coupled buck converer I1 1 D (1) I2 pp D (2) Then, by summing (1) and (2) he equaion for oupu curren ripple reducion is Iou I1 I2pp 1 2D. (3) Using he same procedure, i can be achieved he oupu curren ripple calculaion for all inervals. On he oher hand, in case of seady sae i is no necessary, because he curren ripple in all inervals is he same. A. Dual Inerleaved Coupled Buck Converer A simplified schemaic for a coupled buck converer is depiced in Fig. 3. Two-phase coupled buck converer is divided ino four inervals same as in non-coupled case, Fig. 4, Fig. 5. V 1 V lk1 V m i ou V in S 1 i 1 i 2 i 1 V ou V 2 S 2 V lk2 V m i m Fig. 3A schemaic of dual buck converer using coupled inducor According Kirchhoff s law he following equaion for wo-phase coupled buck converer in firs inerval can be wrien (4) - (8): w w w. a j e r. o r g Page 82

4 iou i1 i 2 (4) im i1 i 2 (5) Vlk 1 Vou Vm (6) Vlk 2 Vm Vou (7) m Vm 2m (8) Using he mahemaical apparaus, he following equaions refer o he firs inerval of operaion are given, (9) (11): m I1 1 D 2m (9) m I 2_ I D 2m (10) Iou I1 I 2_ I 1 2D (11) These equaions also apply for he hird inerval wih he difference ha I 1 is I 2 and vice versa. Using Kirchhoff s laws, he equaions for he second inerval are as follows, (12) - (14). Vlk 1 Vou Vm (12) Vlk 2 Vm Vou (13) Vm 0 (14) Using he same procedure as in inerval I and III we can obain curren ripples in inerval II and IV. The given equaions are as follows: I 1_ II I 2_ II 05. D (15) Iou I 1_ II I 2_ II 1 2D (16) For he second and fourh inerval of operaion, he ripple is same for boh phase currens. If we wan o deermine he oal inducor curren ripple we mus sum he ripple currens in inerval II, III and IV or calculae he ripple in inerval I. For he ripple curren in he second phase we can apply he same approach wih he difference ha we mus calculae he ripple in III inerval. On he oher hand, he oupu curren ripple is he sum of inducor curren ripples corresponding o each ime inerval. i 1 ΔI 1_I =ΔI 1 ΔI 1_II i 2 ΔI 2_I ΔI 2_II ΔI 2 ΔI ou i ou I II III IV D.T S ½.T S T S Fig. 4 Curren ripples of inerleaved coupled buck converer for D < 0.5 w w w. a j e r. o r g Page 83

5 The operaion of buck inerleaved converer wih duy raio over 0.5 is shown in a Fig. 5. From his figure is seen ha upper swiches of he converer can be swiched on a once (inerval I and III). I means ha in his inerval he magneizing volage V m equals zero. Analyically, i is saed in some following equaions (17) (23). Vlk 1 Vou Vm (17) Vlk 2 Vm Vou (18) Vm 0 (19) d D 05. (20) I 1_ I 1 D D 0. 5 TS (21) I 2_ I 1 D D 0. 5 TS (22) Iou I 1_ I I 2_ I 2 2D D 0. 5 TS (23) Similarly, for he II and IV inerval he following equaion apply (24) (30). Vlk 1 Vou Vm (24) Vlk 2 Vm Vou (25) m Vm 2m (26) d 1 D (27) m I 1_ II 1 D 2m (28) m I 2_ II D 2m (29) Iou I 1_ II I 2_ II 1 2D 1 D TS (30) ΔI 1 ΔI 1_II i 1 ΔI 1_I i 2 ΔI 2_II =ΔI 2 ΔI 2_I i ou ΔI ou I II III IV d.t S ½.T S D.T S T S Fig. 5 Curren ripples of inerleaved coupled buck converer for D > 0.5 w w w. a j e r. o r g Page 84

6 From (3), (11) and (16) is eviden ha oupu curren ripple is he same (excep he negaive sign in (16)) under he condiion ha leakage inducance lk is equaled o non-coupled inducance. If we fi ino he equaions (24) and (30) he value of duy raio we find ha he ripple is same as in he equaion (3), (11) and (16). The condiion of D < 0.5 for equaion (24) and D > 0.5 for equaion (30) mus be fulfilled. The coupling coefficien k is he mos imporan parameer which affecs inducor curren ripple. m k m (31) Using he high value of he coupling coefficien (near 1) hen he leakage inducance is small and i leads o increasing of he oupu curren ripple I ou, bu he ripple of he phase curren I 1 or I 2 is minimized. Using he smaller value, hen he magneizing inducance is smaller and he ripple of he phase curren is higher bu he ripple of he oupu curren is smaller and hen he bulky oupu filer is reduced. Therefore, here is a rade-off beween choosing coupling coefficien. IV. SIMUATI RESUTS As menioned in secion II, he inducor curren ripple is srongly dependen on he coupling coefficien k of he coupled inducor. In order o have he maximum inducor curren ripple reducion, he coupled inducor should have high k and also have enough leakage inducance o reduce oupu curren ripple for he buck converer respecively. The swiching frequency of he one leg of he inerleaved converer was se o 20 khz, due o use of he inverer. Therefore, because of he inerleaving effec, he oupu swiching frequency is doubled, which is shown in Fig. 6, Fig.7 and Fig. 8. The self-inducance of he non-coupled inducor was se a 672 μh. In order o saisfy he condiion of he ripple curren equaliy, he leakage inducance was also se o 672 μh. Then, he coupling coefficien was se o value of 0.55 and i follows ha he magneizing inducance is 834 μh. The addiional parameers of he converer are given in a Table 1. The simulaion resuls are done for duy raio 28% (minimum oupu volage), 50% (almos zero curren oupu ripple) and 58% (maximum oupu volage). TABE I. SETUP CDITIS PARAMETER COUPED INDUCTOR N-COUPED INDUCTOR Swiching frequency 20 khz 20 khz eakage inducance 672μH - Magneizing Inducance 834 μh - Self-inducance μh Duy cycle Inpu volage V in 560 V 560 V Oupu volage V V The ime waveforms of ripple curren for he minimum and maximum value of duy cycle are depiced in Fig. 6 and Fig. 7. From he simulaion resuls in Fig. 7 and Fig. 8 is eviden ha he inducor curren ripple of he converer wih a coupled inducor (i5, i8) is smaller han he non-coupled case (i2, i3). In Fig. 9 are given ime waveforms of ripple currens for non-coupled (i5, i8) coupled inducor (i2, i3) wih he difference ha he ripple of oupu curren ( ic1 and ic2) equals almos zero. The advanage is no in zero value of oupu curren because same opion occurs in inerleaved connecion wih a non-coupled inducor, bu he fac here is reduced inducor curren ripple. 9.6A 8.0A 6.4A 4.8A 3.2A 1.6A 0.0A 12.0A I(2) I(C1)+I(R1) I(5) I(C2)+I(R2) 9.3A 6.5A 39.90ms 39.92ms 39.94ms 39.96ms 39.98ms 40.00ms Fig. 6 Inducor curren ripples wih D = 28% for coupled (i5) and non-coupled inducor (i2)- up, oupu curren ripples for coupled (I C2 +I R2 ) and non-coupled inducor(ic1+ir1)-down w w w. a j e r. o r g Page 85

7 12A I(2) I(3) I(5) I(8) 7A 1A 1.5A 0.9A 0.3A -0.3A -0.9A I(C1) -1.5A 39.90ms 39.92ms 39.94ms 39.96ms 39.98ms 40.00ms Fig. 7 Inducor curren ripples wih D = 58% for coupled (i5) and non-coupled inducor (i2)- up, oupu curren ripples for coupled (I C2 +I R2 ) and non-coupled inducor(ic1+ir1)-down I(C2) 11A I(2) I(3) I(5) I(8) 6A 0A 12mA I(C1) I(C2) -1mA -14mA 39.90ms 39.92ms 39.94ms 39.96ms 39.98ms 40.00ms Fig. 8 Inducor curren ripples wih D = 50% for coupled (i5) and non-coupled inducor (i2)- up, oupu curren ripples for coupled (I C2 +I R2 ) and non-coupled inducor(ic1+ir1)-down The comparison of he raio beween oupu and inducor curren is depiced in Fig. 9. I is obvious, ha he raio is increased when he coupling effec is uilized. This means ha he inducor curren ripple is smaller in a whole range of duy cycle, insead of D = 0.5. Then, he ripples are equal. To saisfy he same ripple of he oupu curren for he coupled and non-coupled case, he condiion of he same leakage inducance mus agree. Fig. 9 The raio of oupu curren ripple and inducor curren ripple for non- and coupled case V. EXPERIMENTA VERIFICATI In coupled inducor design, here should be a problem how o mainain he required leakage inducance. The easies way how o manage his issue, i is used he addiional non-coupled inducor. The powder core is ideal for his inducor, which is capable o carry high dc curren. Then he magneizing inducance will wound as a coupled inducor and only he ac componen of he curren will flow hrough i because he dc curren is canceled wih he negaive coupling of he inducors. I means, ha he inducors are wound agains each oher and he magneic flux of boh inducors is canceled. Therefore, he soluion wih he ferrie core should be w w w. a j e r. o r g Page 86

8 uilized. The proposed coupled inducor in his paper does no use an addiional inducor. The coils consis of wo EE cores, where each winding is wound on he ouer leg of he core. This ensures a sufficienly large value of leakage inducor and magneizing inducance is adjused wih a change of an air gap in he cener leg or he ouer legs.the final values of he leakage and magneizing inducance are given in Table 1. Subsequenly, he experimenal measuremens of he converer wih a coupled inducor were performed. Fig. 10 The ime waveforms of inducor curren ripple (urquoise and blue one), oupu curren (viole) and inpu volage (green) for D <0.5 The oscilloscope waveform wih he duy lower han 50% (minimum operaing duy raio 28%) is shown in Fig. 11 and for duy higher han 50% (maximum operaing duy raio 58%) in a Fig. 11. Fig. 11 The ime waveforms of inducor curren ripple (urquoise and blue one), oupu curren (viole) and inpu volage (green) for D >0.5 From he Fig. 10 and Fig. 11 is visible ha he ripple of he oupu curren is markedly reduced which allows o use smaller oupu capacior value and exend he lifeime of he ulracapacior/baery pack conneced o he oupu of he converer. VI. CCUSI In order o reduce inducor curren ripple as well as oupu curren ripple respecively, he wo inducors should be coupled o he same core. I is preferable o use coupled inducor opology in baery/ulracapacior applicaion due o less sress of hese energy sources and lower conducion losses of he semiconducor swiches because of he lower effecive value of he inducor curren ripple. To mainain he required ripples on he inducor and on he oupu respecively, he coupling coefficien mus agree. For he oupu curren, he leakage inducance is very imporan and i mus be equal o he non-coupled inducance o mainain crierion. Then, for he high value of coupling coefficien, he muual inducance increases and leakage inducance decreases and vice versa. The soluion is o find an appropriae compromise beween he oupu and inducor ripple value. In he fuure work, he hree and four phase converer wih a coupled inducor will be invesigaed. ACKNOWEDGEMENTS This paper is suppored by he following projecs: APVV w w w. a j e r. o r g Page 87

9 REFERENCES [1]. S.J. Kim, H.. Do, Inerleaved Flyback Converer wih a ossless Snubber, Inernaional Review of Elecrical Engineering(IREE), vol. 9 n. 5, 2014, pp [2]. T. Azib, M. Bendali, Ch. arouci, K. E. Hemsas, Faul Toleran Conrol of Inerleaved Buck Converer for Auomoive Applicaion, Inernaional Review of Elecrical Engineering (IREE), vol. 10 n. 3, 2015, pp [3]. J.P.ee, H. Cha, D. Shin, K.J. ee, Analysis and Design of Coupled Inducors fortwo-phase Inerleaved DC-DC Converers, Journal of Power Elecronics, Vol. 13, No. 3,2013, pp [4]. J. Perdulak, D. Kovac, I. Kovacova, M. Ocilka, A. Gladyr, D. Mamchur, I. Zachepa, T. ce, J. Molnár, Effecive uilizaion of phoovolaic energy using muliphase boos converer in compare wih single phase boos converer, CS Communicaions Scienific leers of universiy of Zilina, Vol. 15, No.3, 2013, ISSN [5]. T. Beres, M. Olejar, J. Dudrik, Bi-direcional DC/DC converer for hybrid baery, Power Elecronics and Moion Conrol Conference (EPE/PEMC), 2010, pp.t9-78,t9-81. [6]. J. Gallagher, Coupled Inducors Improve Muliphase Buck Efficiency, Power Elecronics Technology, pp , January [7]. K. Kroics, U. Sirmelis, V. Brazis Design of coupled inducor for inerleaved boos converer, Przeglad Elekroechniczny,Vol. 90, Nr. 12,2014. [8]. Y.W. Yang, Single-Sage Boos-Buck Converer wih Sof/Swiching Operaion and Ripple/ Free Oupu Curren, Inernaional Review of Elecrical Engineering (IREE), vol. 11 n. 4, 2016, pp [9]. P. Spanik, M. Frivaldsky, P. Drgona, J. Kucha, Properies of SiC Power Diodes and heir Performance Invesigaion in CCM PFC Boos Converer, 17h Inernaional Conference on Elecrical Drives and Power Elecronics EDPE 2013, 2013, Dubrovnik, Croaia, pp , ISBN , ISSN [10]. J. Dudrik, P. Spanik, N. D. Trip, Zero-Volage and Zero-Curren Swiching Full-Bridge; DC Converer Wih Auxiliary Transformer, Power Elecronics, IEEE Transacions, Vol. 21, issue 5, ISSN ,p , 06sepember [11]. M. Frivaldsky, B. Hanko, M.Prazenica, J. Morgos, High Gain Boos Inerleaved Converers wih Coupled Inducors and wih Demagneizing Circuis, Energies, 11(1), 2018, 130. Miriam Jarabicova1" Inerleaved DC/DC Converer Wih Coupled Inducor Theory And Applicaion American Journal of Engineering Research (AJER), vol. 7, no. 5, 2018, pp w w w. a j e r. o r g Page 88