Multiphase transformer-coupled converter: two different strategies for energy conversion

Transcription

1 Muliphase ransformercoupled converer: wo differen sraegies for energy conversion M.C.Gonzalez, P.Alou, O.Garcia, J.A.Oliver, J.A.Cobos Cenro de Elecrónica Indusrial Universidad Poliecnica de Madrid Madrid, España Absrac The operaion of a muliphase opology, ideally, wihou energy sorage presens he advanage of achieving very high efficiency over a wide load range as well as a fas dynamic response. However, ideal noenergy sorage operaion also implies a limiaion in he regulaion capabiliy of he opology, he oupu volage can only ake discree values. These feaures (high efficiency and discree regulaion capabiliy) of he proposed energy conversion sraegy enable he opology as a candidae for DCDC ransformer applicaions. The advanages, drawbacks and he operaing principle of his concep, implemened wih a closed chain magneic srucure have been already presened. In his work, he minimum energy sorage operaion, is applied o wo differen magneic srucures. These magneic srucures are called closed chain and pyramidal ; he main advanage of he pyramidal coupling srucure is o improve he size of he converer wihou increasing he operaing frequency. Boh magneic srucures are analyzed, compared and experimenally implemened. I. INTRODUCTION A muliphase ransformercoupled opology wih (ideally) no energy sorage, has proved o achieve a reducion in he oupu impedance of he converer which allows an improvemen in he dynamic response ([1], [2]). In his opology, he coupling among he phases is done by ransformers insead of coupled inducors ([3], [4]) in order o minimize he energy sorage of he converer; an appropriae conrol sraegy ha allows he converer o operae (ideally) wihou oupu filer is required. One of he implicaions of operaing a converer wih minimum energy sorage, is ha he operaing frequency and he dynamic response of he converer are decoupled. This is he main advanage of his concep, providing very fas dynamic response as well as very high efficiency over a wide load range. However, minimum energy sorage operaion also implies ha he duy cycle can no be variaed in a coninuous way. This is he main drawback of his concep, he duy cycle can only ake discree seps. The high efficiency makes his opology a good candidae for a preregulaor in wosage power archiecures. In his kind of applicaions, he firs sage can be a DC/DC ransformer and he final regulaion is provided by a poin of load converer. Twosage power archiecures can achieve beer efficiency and size in comparison wih a single sage power archiecure if boh sages are adequaely designed. Examples of wosage power archiecures can be found in [5] and [6]. As said above, in he proposed opology he ransfer of he energy and he operaing frequency are decoupled; fas dynamics are achieved while keeping very high efficiency ([1]). The decoupling beween energy ransfer and swiching frequency provides a degree of freedom in he design since he operaing frequency can be seleced o opimize he efficiency wihou affecing he dynamics of he converer. However, he radeoff beween size and efficiency is no changed by he minimum energy sorage operaion: if he ransformers have a larger size, a higher efficiency can be achieved. As usual, he size of he ransformers can be reduced by increasing he swiching frequency of he converer, always a he cos of degrading efficiency. Examples of differen coupling sraegies, based on discree ransformers are presened in [7]. One of he magneic srucures presened in [7] is he closed chain magneic srucure; previously, his magneic srucure has been used o implemen he minimum energy sorage concep which is validaed in [1] and [2]. In his paper, a magneic srucure ha could enable an improvemen in he size of he converer is proposed for he implemenaion of he minimum energy sorage converer. This coupling sraegy has been called pyramidal magneic srucure and is based on an arrangemen of discree ransformers. Wih his coupling sraegy, he size of he converer can be reduced wihou increasing he swiching frequency; hus i could be possible o reduce he size wihou degrading he efficiency and he dynamic response. An analysis of his magneic srucure operaed under he no energy sorage condiion is presened in secion III and he concep is validaed by means of an experimenal prooype which is presened in secion IV and compared wih he closed chain implemenaion. The efficiencies and dynamic responses obained wih boh conversion sraegies ( closed chain and pyramidal magneic srucures) are compared in secion IV. II. MINIMUM ENERGY STORAGE: CONCEPT REVIEW In order o achieve minimum energy sorage, he coupling beween he phases of he converer is done by means of ransformers since ideally, ransformers do no sore energy. Besides, wih he aim of operaing ideally wihou oupu filer, a specific conrol sraegy is required. In figure 1a), a n phases opology is shown. The conrol sraegy is also /11/$ IEEE 141

2 = =...= in= io/n...i n=io MAG i O V C i O V O v C V O a) v n i n a) v n k={,1,2,...,n} T V O n k v C = V O T b) Fig. 1. n phases converer. a) General magneic srucure. b) proposed conrol sraegy:... v n mus be consan for every insan of ime Fig b) Example of ransformercoupled opology wih wo phases illusraed in figure 1b). The conrol sraegy mus saisfy he following condiions: The sum of he volages a he inpu of he magneic srucure ( v i ) mus be consan for every insan of ime along a swiching cycle. In figure 1,... v n = consan The mean value of he volage in each phase ( v i ) mus be equal among all phases, in order o avoid ransformer sauraion. Besides, his value ( v i ) is equal o he oupu volage of he converer (V OUT ) since he mean value of he volage across each ransformer of he magneic srucure is zero. In figure 1, = =... = v n = V OUT If hese condiions are accomplished for every insan of ime, he oupu volage will be also consan for every insan of ime wihou he need of an oupu filer. The duy cycles where his conrol sraegy is achieved are called operaing nodes. And are given by: d = k 1 (1) n where n is he number of he phases and k is an ineger, ranging from o n. Also, i is necessary ha he shifing of he conrol signals is given by 36 n. Regardless he coupling magneic srucure, he oupu of he converer is given by he following equaion: V OUT = v i = d (2) and for duy cycles where he sum of he inpu volages o he magneic srucure is consan ( v i = consan), v C = is also consan, and no oupu inducor ( F IT ER ) is necessary. The number of available oupu volage values is relaed o he number of phases; hence, increasing he number of phases in he converer means increasing he available oupu volage values. The curren sharing is guaraneed by he operaion of he opology; he ampereurns balance makes i possible ha he mean value of all phase currens is he same: ī OUT = ī 1 = ī 2 =... = i n (3) n and he value of he oupu curren is given by: i OUT =... i n (4) Toal ripple cancellaion is assumed. A wophase converer is shown in figure 2. For a wophase converer, here is only one operaing node a 5% duy cycle; so only one oupu volage value is available. For every insan of ime, oupu volage of he ransformer (v C ) is given by: v C = (5) 2 and = = v C ; wih he applied conrol sraegy i is assessed ha =, hence V OUT = (6) 2 If he magneizing curren is negleced, he ampereurns balance asses ha = and i OUT =. III. MINIMUM ENERGY STORAGE: CANDIDATE MAGNETIC STRUCTURES Differen arrangemens of ransformers are available in he lieraure in order o couple he phases of a muliphase converer ([8], [7]). Among hese arrangemens, closed chain and pyramidal magneic srucures are repored. All hese ransformer arrangemens are used in combinaion wih an oupu filer. 1411

3 v IN i 3 v 3 i 4 v T1A T1 v T1B v T3A T3 v T2A T2 v T2B v T4B T4 v C i O C OUT vo TA1 TA2 TB1 TJ1 v 4 v T3B v T4A TA Fig. 3. Closed Chain magneic srucure (previous) TB i v1 v2 v3 v Fig. 4. v1 v2 v3 v4 TA1 i3 TA2 vta1 TB1 vta2 va vb vtb1 a) b) c) Pyramidal magneic srucure for fourphase opology In his paper, boh he closed chain magneic srucure (figure 3) and he pyramidal magneic srucure are compared when used for implemening he minimum energy sorage converer. Ideally, boh magneic srucures are operaed wihou oupu filer. For boh magneic srucures, he paricular form of equaions 1, 2, 3 and 4 for a fourphase opology are valid. However he way in which he energy is processed inside he magneic srucure does change from one coupling srucure o anoher. Regarding energy processing, he main characerisic of he closed chain magneic srucure (shown in figure 3) is ha he curren hrough all he ransformers is equal. On he oher hand, i can be said ha he pyramidal magneic srucure shown in figure 4b is composed by differen levels. I can be said ha, in figure 4 he firs level comprises ransformers T A1 and T A2 while he second level is composed by ransformer T B1. Neglecing magneizing curren, he currens hrough T A1 and T A2 are equal, bu differen from he curren handled by ransformer T B1. The curren hrough T B1 is wice he curren hrough each of he ransformers in he firs level (T A1,T A2 ). The main difference beween boh coupling sraegies is he number and he design of he ransformers. For example, a four phase converer implemened wih he pyramidal magneic srucure (figure 4b) can be implemened wih hree ransformers; for he implemenaion of a four phase converer wih he closed chain magneic srucure, four ransformers are required. The pyramidal magneic srucure can be exended o any powerofwo number of phases; a generalizaion of he pyramidal magneic srucure, is shown in figure 5. In order o compare boh magneic srucures for he implemenaion of a ransformercoupled converer wih minimum i OUT V OUT va V OUT vb Fig. 5. TA i Generalizaion of pyramidal magneic srucure energy sorage, an analysis of he seady sae operaion of each magneic srucure is presened. Boh analyses are done in he ime domain and under he following assumpions: eakage inducances of he ransformer are negligible ( KEQ = ). The magneizing inducance ( MAG ) is he same for all he ransformers in he converer. The converer operaes only in he duy cycles given by equaion 1; for a fourphase converer (n = 4), hree duy cycles are available: 25%, 5%, 75%. The objecive of he analysis is o obain he relaionship beween he magneizing inducance of he ransformers and he swiching frequency of he converer, wih his informaion, a losses analysis can be done for each magneic srucure. A. Analysis of closed chain magneic srucure An analysis of he magneic srucure shown in figure 3, operaed wih he proposed conrol sraegy is presened. The objecive of he analysis is o deduce he magniude of he phase curren ripples, in order o calculae he losses of he magneic srucure. As said before, in his magneic srucure, he average currens seen by all he ransformers are equal among hem, so i is necessary o deduce only one equaion for each phase. Two paricular assumpions are done in order o analyze he closed chain magneic srucure: The relaion beween he volages of he windings in each ransformer is defined by he following equaions: v T 1A = v T 1B (7) v T 2A = v T 2B (8) v T 3A = v T 3B (9) v T 4A = v T 4B (1) The nodes a which he converer is operaed, coincide wih he duy cycles where oal ripple cancellaion is 1412

4 achieved, and i can be assumed ha I OUT is consan, hence: d d d d di3 d d d = (11) Wih hese assumpions, he volage across he ransformers can be deduced: v T 1A() = v v v C (12) i 3 i 4 Di3= 21mA D= 21mA D= 21mA v T 2A() = v v v C (13) D= 21mA v T 3A() = v v v C (14) v T 4A() = v v v C (15) Where,, v 3 and v 4 sand for he inpu volages o he ransformers (figure 3), and he values of v i are only or. Phase ripple due o he magneizing inducance and he swiching frequency of he converer can be expressed as follows: I MAGphase1 = 1/4 (v T1A v T3A 2 v T4A ) I MAGphase2 = 1/4 (3 v T1A v T3A v T4A ) I MAGphase3 = 1/4 (v T1A 3 v T3A 2 v T4A ) (16) (17) (18) I MAGphase4 = 1/4 (v T1A v T3A 2 v T4A ) (19) where v T 1A, v T 2A, v T 3A and v T 2A represen he volages of he ransformers in he magneic srucure (figure 3). These ripples are shown in figure 6 for 25% duy cycle. Wih hese equaions, he relaion among he magneizing inducance ( MAG ), he phase ripple and he swiching frequency is esablished, and differen designs can be evaluaed. B. Analysis of pyramidal magneic srucure Three paricular assumpions are done in order o analyze he pyramidal magneic srucure: The relaion beween he volages of he windings in each ransformer is defined by he following equaions: v T A1 = v T A1p (2) v T A2 = v T A2p (21) v T B1 = v T B1p (22) The currens of he second level of he pyramidal srucure (i A, i B ) are obained by summing he currens in he firs level: d d d d = d (23) d i3 =1 mh, f =5kHz MAG Fig. 6. Magneizing ripple of phase currens,, i 3 and i 4 in cenral chain magneic srucure SW di3 d d d = d d (24) The nodes a which he converer is operaed, coincide wih he duy cycles where oal ripple cancellaion is achieved, and i can be assumed ha I OUT is consan, hence: d d d = (25) d For his magneic srucure, wo se of expressions (one for each level) mus be obained in order o find he ripple in boh levels of he pyramid. The firs level comprises he ransformers T A1 and T A2. The currens of he firs level are,, i 3 and i 4 (figure 4b); he second level is formed by ransformer T B1 and he currens in his level are i A and i B. The volages of he ransformers (v T A1, v T A2 and v T B1 ) for he pyramidal magneic srucure can be easily deermined aking ino accoun he equaion ha describes he behavior of he basic cell (fig. 2, eq. 5) and equaions 2 hrough 22. Volages hrough he ransformers are given by: v TA1 = 1/2 ( ) (26) v TA2 = 1/2 (v 3 v 4 ) (27) v TB1 = 1/2 ( ) V OUT (28) The ripple of he currens,, i 3 and i 4 (firs level) of he pyramidal magneic srucure is a funcion of he magneizing inducances in boh levels, he volages of he ransformers, he swiching frequency of he converer and he duy cycle. The curren ripples of he firs level are given by: 1413

5 I MAG = 1/4 (2 MAG B v TA1 MAGA v TB1 ) (29) MAGA MAGB D= 21mA I MAG = 1/4 (2 MAG B v TA1 MAGA v TB1 ) D= 21mA i A = D= 1mA MAGA MAGB (3) I MAGi3 = 1/4 ( 2 MAG B v TA2 MAGA v TB1 ) MAGA MAGB (31) i 3 i 4 D= 21mA Di3= 21mA i B i OUT = i3 D= 1mA i OUT = I MAG = 1/4 (2 MAG B v TA2 MAGA v TB1 ) MAGA MAGB (32) a) b) i3 v T A1, v T A2 and v T B1 are he volages across he ransformers T A1, T A2 and T B1 respecively. MAGA and MAGB represen he magneizing inducances of ransformers in he firs and second level of he pyramid, respecively. Since he magniudes of he ripple across he ransformers in he firs level (T A1 and T A2) are equal, he design of he ransformers of his level can be idenical.. Ripple magniudes in he second level of his magneic srucure, are given by he following equaions: I = 1/2 vt B1 MAGB (33) I = 1/2 vt B1 MAGB (34) v T B1 represens he volage across he ransformer T B1. The mean value of he curren across he ransformer of level wo is iout 2 while for he ransformers in level one he mean value of he curren is iout 4. Due o his facor, he design of he ransformers of level one (T A1 and T A2) can be differen from he design of he ransformer in level wo. I is also imporan o poin ou, ha in he firs level, he value of he ripple is relaed o he magneizing inducance of boh levels and his has o be aken ino accoun in order o realize a good design. The ripple currens for his magneic srucure are represened in figure 7 for a duy cycle of 25%. C. Comparison of boh srucures osses have been evaluaed for boh magneic srucures. Using equaions (16)(19) he losses of he closed chain magneic srucure are calculaed wih he losses model presened in [1]. Also, using his model, he losses are calculaed for he pyramidal magneic srucure, using he equaions (29)(34) repored in IV. In order o compare boh magneic srucures, he losses are evaluaed using he following specificaions: Inpu volage 12V, duy cycle 5%, MAG = 7µH, f SW = 8kHz. The same MOSFETs and drivers are used in order o calculae he losses in boh prooypes for a fair comparison, daa from IRF7831 MOSFETs and IR2181 drivers has been considered in he losses model. = =1 mh, f =5kHz Fig. 7. Currens of boh levels of he pyramidal magneic srucure. a)ripple due o he magneizing inducances on he firs level. b)ripple due o he magneizing inducances on he second level. Efficiency (%) MAGA MAGB SW 8 khz Pyramidal Calculaion 8 KHz Closed Chain Calculaion Fig. 8. Power losses calculaion for wo converers, wih he closed chain and pyramidal magneic srucure for 5% duy cycle The resuling calculaions are shown in he graph in figure 8. I can be seen ha boh magneic srucures, resul in almos he same losses. IV. EXPERIMENTA VAIDATION A. Implemenaion of boh magneic srucures In order o validae he proposed magneic srucure, boh magneic srucure configuraions have been esed under he same specificaions and wih he same ransformers. This specificaions are: 12V inpu volage, 6V oupu volage, 3A maximum oupu curren, swiching frequency 8kHz, ransformers are implemened in a RM63F3 core wih an MAG = 7µH. The raio of all he ransformers is 1:1. In figure 9, he efficiencies of boh magneic srucure for differen loads and a swiching frequency of 8kHz are presened when operaing a5% duy cycles, he achievable power is he same for boh magneic srucures. In figure 1, he efficiencies of boh magneic srucures, operaing wih 1414

6 Efficiency ficiency (%) khz Pyramidal 8 khz Closed Chain Efficiency ficiency (%) khz Pyramidal 8 khz Closed Chain Fig. 9. For 25% duy cycle and V OUT = 3V, comparison of he efficiency of closed chain and pyramidal magneic srucures Fig. 1. For 5% duy cycle and V OUT = 6V, comparison of he efficiency of closed chain and pyramidal magneic srucures. 5% duy cycle are shown, i can be seen ha he efficiency of boh seups is very similar. Efficiency from 6W o 15W is higher han 95%. The measuremens in figure 1 can be compared wih he calculaions done in previous secion. I can be seen ha, he losses are prediced wih accepable accuracy, however, in he real prooypes he differences beween he efficiencies of boh converers are higher. Dynamic response of he opology wih he pyramidal magneic srucure is shown in figure 11. This response is achieved a 3V of oupu volage and i can be seen ha, under a 1A (4A/µs) load sep, he oupu volage drop is less han 5%. Oupu capacior is formed by 6 ceramic capaciors of 22µF a he oupu of he converer; inpu capacior of he converer for his load sep is formed by a 47µF OSCON capacior plus four MC Capaciors of 22µF. Wih he same oupu capaciances and specificaions, a 1A load sep (4A/µs) is applied o he closed chain prooype. The response of he converer is shown in figure 12. I can be seen ha boh responses are very similar. I is imporan o poin ou, ha he main difference beween boh magneic srucures is he number of ransformers. While he closed chain srucure is composed by four ransformers, he pyramidal magneic srucure is composed by hree. This represens a reducion of 25% in he size of he magneic srucure. B. Design example for efficiency opimizaion The wophase converer, shown in figure 2a, can be considered o be he basic cell of boh magneic srucures (pyramidal and closed chain). This basic cell has been used for he design and implemenaion of a wophase converer wih very high efficiency in a very wide load range. The specificaions of his design are: inpu volage 12V, oupu volage 6V, operaing frequency 6kHz, oupu curren 6A. Since i is a wophase converer, he duy cycle is fixed o 5%. The seleced MOSFETs are PSMN1R225Y, for boh he conrol and synchronous recifier swich, and he driver is IR2181. The magneic srucure is build wih a 25.3/14.8/1 N27 EPCOS oroid. The aforemenioned losses model (repored in [1]) is used in order o design a converer where he equivalen series resisance is minimized. The seleced MOSFETs and he design of he magneic srucure have been adressed wih his model in order o reduce he conducion resisance which is he main cause of he losses a high loads. A picure of he converer is shown in figure 13. Efficiency measuremens of he converer are shown in figure 14. I can be seen ha he efficiency is almos % from 9W, o 36W (15A o 6A). V. CONCUSION In his paper, he minimum energy sorage conversion sraegy based on a pyramidal magneic srucure is presened, analyzed and compared wih a previous magneic srucure. The main feaure of his concep is ha, wih he use of ransformers as a coupling elemen and an adequae conrol sraegy, he converer is operaed wih minimum energy sorage. Main advanage of minimum energy sorage operaion is ha he dynamic response of he converer and he swiching frequency are decoupled. Hence, wih his opology i is possible o obain very high efficiency along wih a fas dynamic response. The main advanage of he pyramidal magneic srucure compared wih he closed chain, is ha a reducion in he size of he converer can be achieved wihou increasing he operaing frequency. Also, in he pyramidal magneic srucure he placemen of he ransformers is symmeric which improves a reducion in he associaed parasiics (series resisance associaed o PCB racks, inducance associaed o connexions, ec). In he experimenal prooypes presened in Secion IV, a reducion of around 25% in he size of he magneic srucure is achieved when using he pyramidal magneic srucure. The efficiency of he prooype is very 1415

7 Fig. 11. Fig. 12. x1 DV OUT DI OUT=1A =12mV Dynamic response obained wih pyramidal magneic srucure DV OUT DI OUT=1A =16mV Dynamic response obained wih closed chain magneic srucure high in a wide load range: from 6W o 15W efficiency is higher han 95% (for 5% duy cycle and 6 V of oupu volage). Compared wih he previous magneic srucure, efficiency and dynamic response are very similar. In order o obain he same dynamic response wih an equivalen buck converer, around 1 khz bandwidh would be needed. A converer wih his bandwidh would need around 5 khz of swiching frequency. In conras, he proposed converer operaes in open loop and wih 4 khz of swiching frequency, his conribues o reduce he swiching losses. REFERENCES [1] M. Gonzalez, P. Alou, O. Garcia, J. Oliver, J. Cobos, and H. Visairo, Dcdc ransformer muliphase converer wih ransformer coupling for wosage archiecure, in Applied Power Elecronics Conference and Exposiion (APEC), 21 TwenyFifh Annual IEEE, , pp [2] M. Gonzalez,. aguna, P. Alou, O. Garcia, J. Cobos, and H. Visairo, New conrol sraegy for energy conversion based on coupled magneic srucures, in Power Elecronics Specialiss Conference, 28. PESC 28. IEEE, , pp [3] P.. Wong, P. Xu, P. Yang, and F. ee, Performance improvemens of inerleaving vrms wih coupling inducors, Power Elecronics, IEEE Transacions on, vol. 16, no. 4, pp , Jul 21. [4] J. i, C. Sullivan, and A. Schulz, Coupledinducor design opimizaion for fasresponse lowvolage dcdc converers, in Applied Power Elecronics Conference and Exposiion, 22. APEC 22. Seveneenh Annual IEEE, vol. 2, 22, pp vol.2. [5] J. Sun, M. Xu, Y. Ying, and F. ee, High power densiy, high efficiency sysem wosage power archiecure for lapop compuers, in Power Elecronics Specialiss Conference, 26. PESC 6. 37h IEEE, 12 26, pp [6] Y. Ren, M. Xu, K. Yao, Y. Meng, and F. ee, Twosage approach for 12v vr, Power Elecronics, IEEE Transacions on, vol. 19, no. 6, pp , nov. 24. [7] P. Zumel, O. Garcia, J. Cobos, and J. Uceda, Tigh magneic coupling in muliphase inerleaved converers based on simple ransformers, in Applied Power Elecronics Conference and Exposiion, 25. APEC 25. Twenieh Annual IEEE, vol. 1, 61 25, pp Vol. 1. [8] R. M. P. Anaoli V. edenev, Gennady G. Gurov, Muliple power converer sysem using combining ransformers, Paen , 2. Fig. 13. Picure of a wophase prooype wih 25.3/14.8/1 N27 EPCOS oroid and designed for high efficiency in a wide load range. Efficiency ficiency (%) W, h=.7% 6W, h=8% 9W, h= % 6 khz Wh= % Fig. 14. Efficiency measuremens for 5% duy cycle and V OUT = 6V for he wophase prooype 1416