THE EFFECTS OF COUPED INDUCTORS IN PARAE INTEREAVED BUCK CONVERTERS Paul Seria, David Fi ad Geoff Walker pseria@itee.uq.edu.au School of Iformatio Techology ad Electrical Egieerig Uiversity of Queeslad Abstract Iterleaved switchig ad coupled iductors are prove methods for reducig DC-DC coverter output ripple. This paper furthers discussios of these techiques to arragemets of may buck coverters coected i parallel. The differet possible arragemets of the DC-DC coverters are discussed ad criteria for fair comparisos betwee them are chose. The effects of iterleaved switchig o ripple values are preseted ad subsequet effects of couplig the iductors is the ivestigated. A geeralised solutio for curret ripple i coupled iductor coverters is preseted. Simulatios are used to verify the solutio ad characterise the coverter ad output ripple for all cofiguratios. 1 INTRODUCTION Iterleaved switchig ad coupled iductors are two commo methods used to improve the output waveform quality i multiple coverter architectures [2-4]. A coupled iductor system ca be viewed as a extesio of iterleaved coverters. The aim of this ivestigatio was to characterise the improvemets, if ay, gaied from couplig the iductors of iterleaved coverters. This is doe through aalysis ad simulatio of multiple buck coverters arraged i parallel. The characterisatio is geeric ad ca be applied to ay umber () of parallel coected coverters. Some example applicatios where this implemetatio is relevat are voltage regulator modules (VR), battery or fuel cell baks ad solar cell arrays. Parallel coectio offers low ripple curret output ad/or improved trasiet respose [4]. Baks of DC sources such as batteries or solar cells already have maagemet electroics o a per cell basis ad these electroics ca be further used for output ripple improvemet. 2 HARDWARE ARRANGEENT The arragemet of the buck coverters uder cosideratio is show i Figure 1. Each coverter has itetioally bee left as a stadaloe uit to exclude variatios caused by architectural differeces. For aalysis purposes, the values of iterest are iductor ripple curret ad output ripple curret. V i i 1 3 IPROVEENT TECHNIQUES 3.1 Iterleaved Switchig Iterleaved switchig is used i all comparisos. The output ripple is miimised whe the tur-o istats of each coverter are spaced equally over oe switchig period. Figure 2 shows the characteristic reductio caused by iterleaved switchig. It ca be observed that the peak output ripple reduces by 1/ for iterleaved coverters ad that the miimum output ripple duty ratio is at multiples of 1/, givig the theoretical case of complete cacellatio. 1 v C v C1 C C 1 Figure 1. Coectio of buck coverters i parallel. i tot
It is easiest to express the relatioship betwee coupled iductors i coverters i the form of (1). v 1 1 = v 1 O di1 1 dt di dt (1) Directly Coupled Idirectly Coupled V 1 V 2 V 1 V 2 Figure 2. Percetage decrease i output curret ripple at varyig duty ratios for N parallel coverters. For the case of three parallel iterleaved coverters, a duty ratio of 0.25 will produce the waveforms show i Figure 3. The output curret ripple (the ubroke lie) is the sum of these three phase shifted ripple currets ad is oe third of their peak-peak magitude. Note also that the output curret ripple frequecy is 3 times the switchig frequecy. I the geeral case, the output ripple frequecy will be times the switchig frequecy. Figure 3. Coverter ripple currets ad their iterleaved output (D = 0.25) 3.2 Coupled iductors Iductors ca be coupled the two ways show i Figure 4. Direct couplig sees all iductors woud with the same polarity about the core ad is better suited to a arbitrary umber of iductors. Idirect couplig is better suited to pairs of iductors because of flux cacellatio advatages. A thorough magetic aalysis of coupled iductors has bee preseted i [5]. Figure 4. Coupled iductor arragemets. The iductace of each idividual widig is ad ij is the mutual iductace betwee i ad j. For are equal this paper we assume all iductaces ( ) i.e. [ = =... = ] 1 2, ad all iductors are coupled 12 = 13 =... =. equally i.e. [ ] The resultig simultaeous equatios ca be difficult to solve, however they offer some iitial isight ito the effects of couplig iductors. A couplig coefficiet α = is defied to represet the degree to which the magetizig iductace is divided betwee leakage ad mutual iductace [1]. Figure 5a shows that for a coupled iductor system, the curret ripple i each coverter will icrease with closer couplig. The curret waveforms of Figure 3 have bee further modified by couplig the iductors ad the resultig wave shapes are show i Figure 5b. 4 SIUATION All simulatios of the multiple buck coverters were implemeted usig the atlab software package. The primary cosideratio whe developig a simulatio methodology was to esure that obtaied beefits were a result of iterleavig ad/or couplig oly. I keepig with this methodology, wheever the umber of buck coverters beig cosidered was chaged, the eergy storage compoets were also chaged so that the overall volume was costat. This strategy is also based o practical examples such as mobile or limited volume situatios where size ad weight are critical such as a laptop power supply or electric vehicle battery pack.
arragemet is show i Figure 6. The leakage iductace flux paths of each iductor are the circular broke lies passig through the cetral air gap. The heavier lies aroud the perimeter represet the mutual iductace flux path. Figure 5. Percetage icrease i iductor ripple for varyig couplig coefficiet ad coverter ripple currets ( α = 1 3) for coupled iductors. 4.1 Costat Volume Direct Couplig Calculatios for maitaiig a costat total volume i direct couplig are relatively simple. As the umber of coverters () i parallel icreases, the average curret I i each iductor reduces to I. Usig equatio (2)[1], the cross sectioal area A will become A, reducig the volume of that core. Overall there are coverters i parallel, hece the total volume will be uchaged whe compared with the base case of a sigle coverter. The iductace value i each coverter is also the same as that of the base case. NI = BAR (2) 4.2 Costat Volume Idirect Couplig Because of the physical iductor arragemet i idirect couplig, its use is mostly applicable for pairs of iductors. Subsequetly, ad for the purposes of this paper, oly two iductors will be cosidered i a idirect arragemet. This alleviates the problem experieced i direct couplig of chagig core sizes due to varyig umbers of coverters. Aalyses for higher umbers of iductors have bee doe i [5]. Idirect couplig does however have its ow characteristic that determies resizig of the core. A example of a possible widig ad core structure As ca be see, the mutual iductace fluxes from the two iductors cacel each other out. As the iductors become more closely coupled, the total flux is distributed further i favour of the mutual Figure 6. Flux paths of a iductace path. idirectly coupled iductor. This reduces the RS flux i the core ad the ripple curret becomes the primary cosideratio whe sizig. I the cotext of maitaiig a costat core volume, the iductor parameters are modified to achieve the required couplig coefficiet without chagig the amout of core material. This is a recursive process ad becomes difficult to implemet because multiple variables are chagig simultaeously. A simplified strategy was devised i this paper to overcome this problem. Whe varyig the couplig coefficiet, the leakage iductaces were kept costat ad the mutual iductace was modified to suit the couplig coefficiet. The chage i core volume that resulted was the used to put ay observed ripple advatages ito cotext. 5 RESUTS Other tha the topological variatios metioed i previous sectios, all variables of the coverter are held costat for these aalyses. 5.1 Parallel Direct Couplig The first aspect of direct couplig ivestigated was the effect o the iductor ripple curret. From Figure 5a it is already expected that the curret ripple see by the coverter will icrease with couplig. As a further measure, the iductor ripple curret ( i ) is compared with the average coverter curret ( i ) for varyig duty ratios. For the case show i Figure 7, the ripple curret becomes a icreasigly large percetage of the average curret. For a couplig coefficiet (α ) of 0.5, i reaches 100% of i with oly four
coverters i parallel. This rapid icrease is the compoudig effect of a icreased ripple due to the couplig ad a decreased average coverter curret. As a further clarificatio, the graph shows that the peak-to-peak coverter curret depicted i Figure 5b will be about 30% greater tha the peak to peak curret i Figure 3. The ext compariso was of the output curret ripple effects, show i Figure 8, for varyig duty ratio ad varyig couplig coefficiet. Comparig Figure 8a with that of Figure 2, where the couplig is abset, it is obvious that the output curret is reduced as a result of the coupled iductors. The geeral shape of this reductio is show i Figure 8b. Hece, the compromise of icreasig the iductor ripple is to achieve a reductio i the output ripple. The couplig coefficiet must also be carefully selected so that the iductor ripple does ot become too large as the umber of coverters i parallel icreases, although this is largely depedet o the iitial curret ratig of the coverter. 5.1.1 Parallel Idirect Couplig coupled, the maximum coverter ripple is about 25% of the average coverter curret. As the couplig icreases (the couplig coefficiet becomig more egative) this maximum percetage ripple decreases. However, the decrease i ripple is a result of a icrease i core volume ad iductace. Figure 9b shows the rate of icrease i the iductor core volume with the rate of decrease i maximum ripple curret for chagig couplig coefficiets. As ca be observed, a 10% icrease i core volume results i a 35% decrease i coverter ripple. The large differece i rates of chage idicates that eve if the core value did ot icrease, the maximum percetage ripple curret would still decrease, although ot to the degree show i Figure 9a. It should also be oted that the output ripple will icrease by the same proportio uder those coditios. The curve of the graph i Figure 9b also suggests that the most beefit is gaied i applicatios where the ripple is already low, as the maximum rate of decrease occurs at lower couplig coefficiets. The method described i Sectio 4.2 for compariso of idirectly coupled coverters was carried out usig two coverters. The output ripple was kept costat for all cases, so that the oly two parameters ivolved i the compariso were the percetage ratio of coverter ripple to average curret ad the percetage icrease i iductor volume required to achieve a specific couplig coefficiet. The results of this ca be see i Figure 9a. Whe the iductors are ot Figure 7. Iductor curret ripple compared with average iductor curret for varyig duty. Figure 8. The effects of duty ratio ad couplig o the output curret ripple.
Idirect couplig is better suited for pairs of iductors. Sizig of iductor cores is a little more flexible due to flux cacellatio i the mutual iductace path ad ca be used to reduce the coverter curret ripple as the couplig coefficiet is icreased. The output ripple ca icrease as a result of chagig the core parameters. Both couplig techiques require specific applicatios for their advatages to be exploited. Applicatios where output ripple miimisatio ad cotrol is prioritised would be beefited most by a directly coupled cofiguratio, whilst idirect couplig would best suit a situatio where either the ripple i the coverter or the size of iductor cores eeds to be reduced without affectig the output ripple curret. 7 REFERENCES 1. R.W. Erickso,D. aksimovic, Fudametals of Power Electroics. 2d ed. 2001, Norwell: Kluwer Academic Publishers. 6 CONCUSION Figure 9. Coverter ripple variatio with chagig couplig coefficiet ad iductor volume for two idirectly coupled coverters. The purpose of the described aalyses was to ivestigate the effects of iterleaved switchig ad the further improvemets from coupled iductor techiques for may parallel coected buck coverters. Simulatios were used to show the ripple curret waveforms i the coverter ad at the output of the coverters. The simulatios also showed the behaviour of maximum ripple values for varyig duty cycles ad couplig coefficiets. Direct couplig of the coverters is well suited for a arbitrary umber of coverters i parallel. Icreasig the couplig coefficiet results i a reductio of output curret ripple. The compromise is a icrease i the relative coverter curret ripple, which ca lead to icreased losses i the iductor core. 2. B. iwa, D.. Otte,.F. Schlecht, High Efficiecy Power Factor Correctio Usig Iterleavig Techiques. Seveth Aual Applied Power Electroics Coferece ad Expositio - CofereceProceedigs, 1992. 92(3): p. 557-568. 3. S. Seii,P.J. Wolfs, The Coupled Iductor Filter: Aalysis ad Desig for AC Systems. IEEE Trasactios o Idustrial Electroics, 1998. 45(4): p. 574-578. 4. P.-. Wog, P. Xu, B. Yag,F.C. ee, Performace Improvemets of Iterleavig VRs with Couplig Iductors. IEEE Trasactios o Power Electroics, 2001. 16(4): p. 499-507. 5. P. Zumel, O. Garcia, J.A. Cobos,J. Uceda. agetic Itegratio for Iterleaved Coverters. i IEEE Aual Power Electroics Coferece ad Expositio (APEC). 2003.