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1 Three-port bi-directional converter for electric vehicles: focs on high-freqency coaxial transformer Waltrich, G.; Darte, J.L.; Hendrix, M.A.M.; Palides, J.J.H. Pblished in: Proceedings of the 5th EVER Conference, 5-8 March 00, Monaco Pblished: 0/0/00 Docment Version Pblisher s PDF, also known as Version of Record (incldes final page, isse and volme nmbers) Please check the docment version of this pblication: A sbmitted manscript is the athor's version of the article pon sbmission and before peer-review. There can be important differences between the sbmitted version and the official pblished version of record. People interested in the research are advised to contact the athor for the final version of the pblication, or visit the DOI to the pblisher's website. The final athor version and the galley proof are versions of the pblication after peer review. The final pblished version featres the final layot of the paper inclding the volme, isse and page nmbers. Link to pblication General rights Copyright and moral rights for the pblications made accessible in the pblic portal are retained by the athors and/or other copyright owners and it is a condition of accessing pblications that sers recognise and abide by the legal reqirements associated with these rights. Users may download and print one copy of any pblication from the pblic portal for the prpose of private stdy or research. Yo may not frther distribte the material or se it for any profit-making activity or commercial gain Yo may freely distribte the URL identifying the pblication in the pblic portal? Take down policy If yo believe that this docment breaches copyright please contact s providing details, and we will remove access to the work immediately and investigate yor claim. Download date: 0. Sep. 08

2 MARCH 5-8 Three-Port Bi-directional Converter for Electric Vehicles: Focs on High-Freqency Coaxial Transformer Gierri Waltrich, Jorge L. Darte, Marcel A.M. Hendrix and Johannes J.H. Palides Electromechanics and Power Electronics grop Department of Electrical Engineering Eindhoven University of Technology, Eindhoven, The Netherlands Copyright 00 MCD & MITI Abstract: A bi-directional mlti-port converter can accommodate varios energy storages and sorces. Therefore, a mltiport converter will be a good candidate for application as a ftre niversal converter for (hybrid) electrical vehicles or local distribtion systems. The main design challenge of the mltiport converter analyzed in this paper is the design of its three-phase symmetrical transformer. In this converter symmetry of the leakage indctances is essential to ensre balanced three-phase crrents (transferred power). These crrents are interconnected by three-phase bridges which are linked together by a three-phase, three-port, transformer. To realize the eqality of the leakage indctances a specific transformer design is necessary. Since conventionally wond three-phase transformer core shapes sitable for high-freqency are expensive and difficlt to bild, a coaxial wond transformer will be designed in this paper. Keywords: Coaxial wond transformer, high-power three-port three-phase triple-active-bridge, bidirectional dc-dc converter, finite element analysis.. Introdction In (hybrid) electric vehicle applications, energy storage elements [], e.g., battery, spercapacitor and flywheel, enable the captre and release of energy dring startp and braking. A bi-directional mlti-port converter can accommodate these energy storages and sorces, and combine their advantages. The mlti-port strctre enables the bidirectional interconnection of the sorces and storages to allow energy flow between the varios ports, classifying as a good candidate for application as ftre niversal converter for (hybrid) electrical vehicles or local distribtion systems. In the past decades, traditional power converter topologies have been evolving in varios directions, e.g., from single-phase to mltiphase interleaving, and from two-level to mltilevel. Nowadays, most dc-dc power converters still deal with single-inpt and single-otpt. Recently, attention has been paid to extend the topologies to mltiport converters. According to [], two categories of integrated isolated mltiport converter are known. One type of converter involves a transformer in which there is a separate winding for each port, as shown in fig. a. Therefore, all ports are flly electrically isolated. The other type has a redced part cont, with some windings absent, as illstrated in fig. b, where the system allows the corresponding ports to share a common grond. However, in most applications the voltage magnitdes at each port are sbstantially different. For example, in renewable energy generation systems, safe, extra low voltage batteries or spercapacitors are preferable since these lead to fewer storage nits connected in series and fewer voltage balancing circits. Adjstment of the voltage levels via the transformer trns ratio is beneficial in avoiding the device handling both high voltage and high crrent simltaneosly.

3 Figre : Mltiport converters with: a) separate winding for each port and b) windings sharing the same port. A high-power three-port three-phase tripleactive-bridge (TAB) bidirectional dc-dc converter with three separate windings has been proposed by [3], as shown in fig.. The main design challenge of the proposed high-power three-phase three-port converter is the three-phase transformer, where symmetry of the leakage indctances is essential to ensre balanced three-phase crrents (transferred power). These crrents are handled by threephase bridges, which are linked together by the three-phase three-port transformer. The leakage indctances in the transformer in fig. are represented by external indctors, L n A..C. To realize the eqality of the leakage indctances, a specific transformer design is necessary, as described in the next sections. a) b). Coaxially Wond Transformer Transformers that can provide natral leakage symmetry are either conventionally [4] or coaxially [5] wond, as shown in fig. 3. Since conventionally wond high-freqency threephase transformer core shapes are expensive and difficlt to bild, a coaxially wond transformer is proposed in this paper. Coaxial winding techniqes are commonly sed in radio-freqency transformers, offering a feasible soltion to confine the leakage flx within the inter-winding space. This prevents the core from being satrated locally [5]. As a reslt, the core and copper losses are lower, and local heating is avoided. Frthermore, from a mechanical point of view, this techniqe reslts in redced forces within the transformer and a robst constrction. In [5], it has been demonstrated that coaxial windings can lead to low loss and low leakage indctance power transformers in high-freqency soft-switched dc-dc and resonant converters. Some of the important loss aspects sch as the inflence of skin effect on winding resistance, the variation of core loss cased by non-niform core flx density, and the choice of the dimensions and aspect ratios for maximm efficiency were examined in [6]. Coaxial winding techniqes therefore provide a viable method for the constrction of the converter transformer in fig.. Figre : High-power three-port three-phase triple-active-bridge (TAB) bidirectional dc-dc converter.

4 Figre 4: Coaxial cable view with magnetic field profile, considering direct crrent circlating in the primary winding and this same crrent retrning from the secondary winding. Figre 3: Two different techniqes to bild mltiport transformers: a) conventionally and b) coaxially wond transformer. As demonstrated by [3], a mlti-port threephase transformer can be thoght of as three separate phases for analysis prposes. Ths, the stdy of only one single-phase transformer is enogh in the following. A Two windings coaxially wond transformer To start with, the calclation of leakage indctances is considered only for two windings: the primary winding as an oter tbe and an inner tbe as the secondary, as shown in fig. 4. To make the calclations easier, the secondary is considered as a solid tbe. The methodology presented in [7] was sed to calclate the leakage indctance in the coaxial transformer. In fig. 4, a view of the coaxial cable with the magnetic field profile is shown. To determine the total leakage indctance in fig. 4 the calclation of the magnetic field in zones to 4 is necessary. Becase the cable is coaxial, in zone 4 the magnetic field is zero. By means of the magnetic field vales it is possible to calclate the total energy in fig. 4 sing W BHdvol Lleak i. () vol After some mathematical maniplations the total leakage indctance per meter is fond to be 4 N R R R R 3R 3 L Leak o 3 3 ln ln 4 R R R 4R3 R 3 R () where μ o is the permeability of free space, which is eqal to 4π x 0-7 A/m, and N is the nmber of trns (made eqal to in fig. 4). Eqation () was developed considering direct crrent circlating in the primary winding and this same crrent retrning from the secondary winding. A D nmerical model of the coaxial transformer in fig. 4 was developed with Maxwell software, to calclate the energy in the for zones of the transformer. When a crrent with the same vale in the oter tbe and inner tbe is imposed with opposite direction, the energy will be concentrated in the zones to 3, as shown in fig. 5. The nmerical calclations confirm that the reslt fond in () is correct. If high-freqency crrent is sed, skin effects shold be considered. The magnetic field profile will change, bt it can be estimated as illstrated by the dotted line in fig. 4. Ths, to calclate the leakage indctance at high freqency, radii R and R3 mst be recalclated by sbtracting the skin depth as defined by, (3) o c

5 where the terms ω, σ and μ c are, respectively, the anglar freqency, which is eqal to πf, the condctor s condctivity, in Siemens/meter, and the relative permeability of copper. leakage indctances observed from each side, as discssed in the next section. 3. Indctance Matrix Now we have a method to calclate leakage and magnetizing indctances of a mlti-port coaxial transformer, the related indctance matrix can be defined. Figre 5: D model, developed with Maxwell software, assming the crrent in the oter and inner tbes to have the same vale and opposite directions. The magnetizing indctance o fe N R 4 Lmag ln, (4) R3 where, μ fe is the relative permeability of the ferrite, can be calclated considering crrent only in the primary (oter tbe) or secondary (inner tbe) winding. Therefore, all energy will be concentrated in the toroidal core, as demonstrated in fig. 6, and only a small amont of energy will concentrated in zones to 3. However, to keep (4) simple, only the core was considered. Using the same procedre, as before, the magnetizing indctance observed from the secondary side was calclated, leading to the same reslt. Once the magnetizing and leakage indctances are known, it is possible to determine the by indctance matrix of this transformer. A 3D model (fig. 7) was also made to evalate the fringing flx from the external cables. In the next sections an experimental set p will be bild and the fringing flx will be compared with this model. B Three windings coaxial wond transformer The procedre explained in sbsection A was repeated here, however, sing three windings instead of two. A 3 by 3 indctance matrix can be calclated. However, to obtain this matrix it is necessary to find six parameters, i.e., the magnetizing and Figre 6: D model, developed at Maxwell software, considering crrent only in the oter tbe or inner tbe. Based on Faraday s Law, the voltage across the terminal of a winding composed of several trns, considering the magnetic flx eqal in all trns, is defined as d j. (5) dt Figre 7: 3D model from Maxwell software. j Assming it is composed of several windings, the voltage across a terminal winding i is described by N i d i ji, ji,... j dt, (6) where i is the nmber of the windings and j is the nmber of trns. Ths, Ф ji denotes the flx throgh the trn j of the winding nmber i. The

6 secondary index is referring to the different crrents throgh winding,,3, The flx Ф ji is cased by the crrent i throgh the winding j, and is proportional to this crrent. Ths, it is possible to write a matrix, normalizing the flx to the crrent, as primary side, leaving the secondary open, shortcircit the secondary or primary side and measre the leakage from both sides and measre the magnetizing from secondary side with the primary open. Using these three steps is possible to define the components in fig. 8. N N j, j,... j i j i i N N j, j, d... i j i j i dt, (7) where the terms in the diagonal are known as measrable indctances and will be designed as L ij. The others terms are mtal indctances and will be addressed as M ij. Ths, the matrix can now be represented by L M... i d M L... i dt. (8) It is sefl to define copling coefficients as M ij kij. (9) L L ii jj Figre 8: Circit diagram of π-model for a winding transformer. B Indctance matrix for a three-windings transformer For a three-winding transformer the indctance matrix is defined as L M M i. (3) 3 d M L M 3 i dt 3 M3 M3 L 3 i 3 The circit diagram for the π-model sing threewinding is shown in fig. 9. A Indctance matrix for two-windings transformer Using the indctance matrix (8) it is possible to determine the terms of a π-model transformer with i windings. The indctance matrix L M d i M L dt i (0) represents the π-eqivalent circit diagram shown in fig. 8. In this figre we assme M =M =M. The primary and secondary leakage indctance eqations are defined in accordance with L L NM () lp M Lls L () N respectively, based on fig. 8. Becase the model has 4 parameters and (0) only 3, this model is nderdetermined. Some designers se this fact set the primary and secondary leakage indctance eqal. To measre the 3 parameters in () and () for a real transformer, three steps are carried ot: measre the magnetizing indctance in the Figre 9: Circit diagram of the π-model for a 3 winding transformer. Becase the indctance matrix and circit diagram both have 6 parameters, this system is therefore niqely determined. The 6 parameters from fig. 9 are fond to be MM3 MM3 LL L M M3 M3 MM3 M3 LL L N. (4) M3 M3 M3M3 M3 LL3 L3 N3 M M

7 To calclate these 6 parameters in a real transformer, 6 steps mst be carried ot: measre 3 reflected magnetizing indctances on each side, considering the other windings open, then short-circit two windings and measre the remaining two leakage indctances for all windings. For transformers with more than 3 windings a π-model is overdetermined. The indctance matrix can, of corse, always be calclated sing (8). 4. Experimental Reslts To check the theoretical and simlation reslts a simple one trn and two windings coaxial transformer prototype was constrcted. Two prototypes were made: one sing a tbe 8.6 cm long (fig. 0a) and another sing two tbes, each with a length of 4.3 cm (fig. 0b). Both prototypes sed toroidal ferrite cores, with a relative permeability (μ fe ) of 700. Reslts obtained from experimental measrements sing an impedance analyzer are smmarized in Table. A 3D Maxwell model was only developed for two tbes becase most of leakage indctance is concentrated inside of the core, when one tbe prototype is sed. Ths, the fringing flx of the prototype from fig. 0a was neglected. Theoretical, simlation and experimental reslts were obtained at 0 khz. Theory and simlation considered the skin effect. Table : Experimental reslts for two-winding coaxial transformer prototypes. Theoretical ( tbe) Theoretical ( tbes) disregarding external cables 3D Maxell software ( tbes) 3D Maxell software ( tbes) Experimental ( tbe) Experimental ( tbes) Leakage indctance (nh) Magnetizing indctance (μh) (internal leakage) 3. (external leakage) = Table shows the theoretical, simlation and experimental indctance matrix of the configration described in fig. 0a. Becase a prototype of a coaxial transformer sing three windings was not yet bild, Table only shows theoretical and simlation reslts. Since the theoretical and simlation vales were very close to each other, only one 3 by 3 matrix is shown. Figre 0: Prototype coaxial transformers sing: a) one tbe and b) two tbes. a) b) Table Matrix indctances for two and threewinding transformers. Two-winding transformers Theoretical (μh) Simlation (μh) Experimental (μh) Three-winding transformers Theoretical (μh/m) Simlation (μh/m) Conclsions Theoretical and simlation reslts were obtained for a single phase coaxial transformer which will be sed on each phase of a mltiport converter proposed by [3]. Experimental reslts are given for one trn and two windings. The measred magnetizing and leakage indctances compare qite well with the theoretical and simlated vales.

8 Once the dimensions of the coaxial transformer and some of its desired characteristics, e.g., nmber of trns and relative permeability of ferrite, are defined the leakage and magnetizing indctance can be accrately calclated. Acknowledgement The athors grateflly acknowledge the financial spport provided by the Erams Mnds Programme and Eindhoven University of Technology. References [] F. Brke, Batteries and ltracapacitors for electric, hybrid, and fel cell vehicles, Proc. IEEE, vol. 95, no. 4, pp , Apr [] Chanhong Zhao, Rond, S.D., Kolar, J.W.; An Isolated Three-Port Bidirectional - Converter With Decopled Power Flow Management Power Electronics, IEEE Transactions on, vol. 3, Isse 5, Sept. 008, pp [3] H. Tao, J. L. Darte, and M. A. M. Hendrix, High-power three-port threephase bidirectional - converter, in Proc. IEEE Indstry Application Society Conference and Annal Meeting (IAS 07), New Orleans, USA, Sep. 007, pp [4] R. W. DeDoncker, D. M. Divan, and M. H. Kheralwala, A three-phase soft-switched high-power-density / converter for high power applications, IEEE Trans. Ind. Appl., vol. 7, no., pp , Jan./Feb. 99. [5] M. H. Kheralwala, D. W. Novotny, and D. M. Divan, Coaxially wond transformers for high-power high-freqency applications, IEEE Trans. Power Electron., vol. 7, no., pp. 54 6, Jan. 99. [6] M. S. Rals, D. W. Novotny, and D. M. Divan, Design considerations for highfreqency coaxial winding power transformers, IEEE Trans. Ind. Appl., vol. 9, no., pp , Mar./Apr [7] W. H. Hayt, Engineering Electromagnetics, Fifth Edition, Mcgraw- Hill Editions, 989, pages