Minimization of the transformer inter-winding parasitic capacitance for modular stacking power supply applications

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1 Downloaded from orb.du.dk on: Jan, 08 Mnmzaon of he ransformer ner-wndng parasc capacance for modular sackng power supply applcaons Nguyen-Duy, Khem; Ouyang, Zwe; Kno, Arnold; Andersen, Mchael A. E. ublshed n: roceedng of The 6h European conference on ower Elecroncs and Applcaons Lnk o arcle, DOI: 0.09/EE ublcaon dae: 04 Documen Verson eer revewed verson Lnk back o DTU Orb Caon (AA): Nguyen-Duy, K., Ouyang, Z., Kno, A., & Andersen, M. A. E. (04). Mnmzaon of he ransformer nerwndng parasc capacance for modular sackng power supply applcaons. In roceedng of The 6h European conference on ower Elecroncs and Applcaons [690843] IEEE. (04 6h European Conference on ower Elecroncs and Applcaons, Epe-ecce Europe 04). DOI: 0.09/EE General rghs Copyrgh and moral rghs for he publcaons made accessble n he publc poral are reaned by he auhors and/or oher copyrgh owners and s a condon of accessng publcaons ha users recognse and abde by he legal requremens assocaed wh hese rghs. Users may download and prn one copy of any publcaon from he publc poral for he purpose of prvae sudy or research. You may no furher dsrbue he maeral or use for any prof-makng acvy or commercal gan You may freely dsrbue he URL denfyng he publcaon n he publc poral If you beleve ha hs documen breaches copyrgh please conac us provdng deals, and we wll remove access o he work mmedaely and nvesgae your clam.

2 Mnmzaon of he ransformer ner-wndng parasc capacance for modular sackng power supply applcaons Khem Nguyen-Duy, Zwe Ouyang, Arnold Kno, and Mchael A.E. Andersen TECHNICAL UNIVERSITY OF DENMARK Deparmen of Elecrcal Engneerng Oerseds lads, buldng 349, ground floor, 800 Kongens Lyngby, Denmark Tel.: 45 / Fax: 45 / E-Mal: knduy@elekro.du.dk, zo@elekro.du.dk, akn@elekro.du.dk, ma@elekro.du.dk URL: hp:// Acknowledgemens Ths work s suppored by he Techncal Unversy of Denmark and he Hgh Tech Foundaon of Denmark. Keywords «arasc capacance», «curren ransformers», «dc-dc power converers», «elecromagnec devces» Absrac In an solaed power supply, he ner-wndng parasc capacance plays a val role n he mgaon of common mode nose currens creaed by fas volage ransen responses. The lower he ransformer ner-wndng capacance, he more mmune he power supply s o fas volage ransen responses. Ths requremen s even more crcal for modular sackng applcaons n whch mulple power supples are sacked. Ths paper addresses he ssue by presenng a dealed analyss and desgn of an unconvenonal solaed power supply ha uses a rng core ransformer wh a very low ner-wndng parasc capacance of 0 pf. Consderng s oupu power of 300 W, hs approach yelds abou pf/w ner-wndng capacance over oupu power, approxmaely hry mes lower han exsng approaches n he leraure. Ths makes he converer a suable soluon for modular sackng of fas volage swchng applcaons. Mahemacal dervaon of he ner-wndng capacance and expermens are carred ou o prove he valdy of he approach. Inroducon In solaed power supply applcaons, he ransformer parasc capacance can have a sgnfcan effec o he converer operaon [-]. Some of he adverse effecs are dsoron of he curren waveform on he excaon sde or a decrease n he overall converer effcency. Subjeced o hghvolage sresses, he ner-wndng capacance causes leakage currens and, consequenly, EMI problems [3-6]. However, mos publcaons abou he ransformer desgn concern he reducon n leakage nducances and hgh-frequency wndng losses, whle wndng capacances have rarely been consdered effecvely. Lmng he ner-wndng capacance s crcal for sackng of power supples because large ner-wndng capacance creaes a sgnfcan amoun of common mode nose a hgh frequency [6-7]. Exsng ransformers n a. kw converer desgn are repored o have.5 nf ner-wndng capacance [8]. An E-core ransformer used n fly-back converer wh a power rang of 30 W s repored n [9] o have 34 pf of ner-wndng capacance. One of he prmary applcaons of hs work s supplyng energy for ulra-fas rackng converers. Fg. shows a confguraon n whch mulple modules of he proposed power supply provde energy o mulple modules of he ulra-fas rackng converer. The ulra-fas rackng converers are ypcal of

3 V S 0 V S Z 0 400V DC V S 0 Fg.. A ypcal modular sackng applcaon of power supples. rado frequency power amplfers used n communcaon sysem based saons [0]. Due o he hgh dv/d a he oupu of he rackng converers, here wll be a large amoun of conducve common mode curren draw from her oupu. Ths curren s lnearly proporonal o he npu-oupu capacance of he power supply: dv com = Co. () d Take, for example, a confguraon wh hree sacked power supply-rackng converers. The rackng converer oupus are conneced n seres o ncrease he volage. The rae of change a he oupu volage s 000 V/µs. Suppose we have a change from 0 o 000 V n one mcro second. The frs converer oupu experences a change of 333 V/µs. The second converer oupu experences a change of 666 V/µs. The hrd one experences a change of 000 V/µs. The couplng curren hrough he crcu npu-o-oupu parasc capacance s as follows. For he frs converer: dv 333V = common Co 0 pf 3.33 ma. d = us = () For he second converer: dv 666V = common Co 0 pf 6.66 ma. d = us = (3) For he hrd converer: dv 000V = common3 Co 0 pf 0 ma. d = us = (4) These currens are drawn from he rackng converers oupu. Therefore, hey dsor he oupu curren waveforms of he rackng converers, and he performance of he rackng s mpared. The adverse effecs become worse when he number of sacked power supples ncreases. Therefore, n order o rapdly change he rackng converer oupu volage, he crcu npu o oupu parasc capacance mus be mnmzed, especally n modular sackng power converer applcaons. Noe also ha havng mnmal crcu npu-o-oupu parasc capacance provdes an advanage no only for fas changng volage applcaons bu also for oher slower dynamc converers n erms of conduced nose mmuny. Ths paper sudes he converer opology n Fg., whch was frs presened n []. The prmary goal s o aan a low ransformer ner-wndng parasc capacance; specfcally, 0 pf n a 300 W oupu power desgn. Mahemacal dervaon of he ransformer ner-wndng capacance and crcu operaon wll be presened.

4 V S D S 3 D3 S D S4 () L D 4 v L V n : n () S V S D S D S IS D S3 () S 5 D S4 D S5 V o D 5 Load C Fg.. Topology of he examned converer. Crcu operaon Suppose ha a he npu, a power facor correcon converer ha convers a sngle phase 0 V ac no 400 V dc s used as he upsream converer. The magnude of npu volage s herefore 400 V dc. The oupu volage s 60 V dc. The oupu curren s desgned o be 5 A dc maxmum. The maxmum oupu power ha s avalable n he oupu ermnals s 300 W. Hgher oupu volage or hgher oupu curren can be acheved by sackng mulple converers n seres or parallel. The desgn of a ransformer ha possesses very low ner-wndng capacance normally nvolves loose couplng of he ransformer wndngs. Ths resuls n he ransformer havng a relavely hgh leakage nducance. Ths hgh leakage nducance mus be ulzed wh a proper selecon of a suable opology. Examples of suable opologes are resonan converers [-] and he dual acve brdge converer [3-4]. The proposed opology n Fg.. s, o some exen, smlar o a sngle acve brdge [5-6]. However, here are dfferences n he secondary sde confguraon and large dfferences n he conrol approach compared o hose exsng opologes. A sngle acve brdge converer does no have he shun swch as n he proposed converer. All of he conrol of he oupu volage and oupu curren n a sngle acve brdge converer are performed on he prmary sde. On he conrary, wh he ulzaon of he shun swch S 5 as n he proposed opology, s possble o conrol he oupu volage ndependenly on he secondary sde; he advanage s he elmnaon of any necessary conrol feedback from one sde o he oher. Exsng conrol approaches n solaed power supples usually nvolve feedback from one sde o he oher across he solaon boundary [-6]. These approaches, however, nroduce addonal parasc capacance from he feedback elemens, such as hgh frequency ransformers and opo-couplers, whch ncrease he oal crcu npu-o-oupu capacance and degrade he mmuny agans fas sep volages. For ha reason, n hs paper, a conrol approach whou solaed feedback s adoped o acheve mnmum crcu npu-o-oupu parasc capacance and maxmum mmuny o fas sep volage responses. The block dagram of he proposed crcu layou s shown n Fg. 3. There are wo conrol loops whose block dagrams are shown n Fg. 4. The secondary sde conroller regulaes he oupu volage o be consan a 60 V. The oupu volage s sensed by a volage dvder and compared o a hyseress reference o swch on and off he shun swch S 5. When he swch S 5 s on, shunng he secondary sde, he converer operaes n s shun mode (see Fg.5a,c), and he oupu volage decreases. Vce versa, when S 5 s off, he converer operaes n s power mode, whch s shown n Fg. 5b,c; he oupu volage ncreases. In he prmary sde conrol, he prmary sde curren L s sensed. I s recfed and flered o produce a recfed-dc value. Ths value s hen compared o a recfed-dc reference and processed by an analog proporonal-negraor (I) conroller. The oupu of he I conroller s fed o a volage-conrolled oscllaor (VCO) ha wll auomacally adjus he swchng frequency o keep he recfed prmary dc curren o be consan a A dc. The duy cycle of he prmary swches s regulaed a 50 %. Wh a urns rao of 5:, he recfed dc curren a he secondary sde s conrolled a 5 A dc.

5 Fg. 3. Block dagram of he crcu layou. () L abs LF L dc I L ref k k d p Vo ref Vo () S 5 ε ε ( V ) S 5 (a) (b) Fg. 4. Conrol block dagram: a) average curren mode conrol n he prmary sde b) hyseress conrol n he secondary sde. v () AB V v () AB WM S, 4 WM S,3 WM S, 4 WM S,3 V V A B L () () IS () V o C v () L V D D 4 S S 4 D D 3 V S S 3 V v () L V V D D 4 V V S S 4 D D 3 V S S 3 T V V T (a) () L () L V V I S () I S () V A B () L () IS () Vo C VS () VS () V o V o B() B() B max (b) B mn (c) (d) Fg. 5. Operaon modes a) shun mode, b) power mode. Analycal waveforms when converer operaes n c) shun mode, and d) power mode.

6 Calculaon of he ransformer ner-wndng capacance The general srucure of he ransformer under es s llusraed n Fg. 6a, and he ransformer prooype phoo s n Fg. 6b. In s wndng confguraon, he wndng wh fewer urns wll be placed n he geomercal cener of he core. I forms a recangular frame symmercally around he core. The remanng wndng, wh more urns s wounded ghly around he core. Ths s respecvely he case of he secondary wndng and prmary wndng n Fg. 6b. B A r B 3 l A r C C r r o A 3 4 (a) (b) (c) Fg. 6. Transformer srucure: a) concepual srucure b) he ransformer under es. c) wndng geomery convenon B I should be noed ha, n general, ferre does no cause a sgnfcan change n he parasc capacance. Bu ferre wh hgh conducvy maeral and very hgh operaon frequency may cause a change on he parasc capacance. In hs work, maeral N87 [7] s used for he ferre core and s no consdered o have hgh conducvy. Therefore, s effec on he parasc capacance can be gnored. The ner-wndng capacance can be calculaed by usng he sored elecrc energy mehod, n whch volage dsrbuon plays a val role. Frs, he ner-wndng capacance caused by he neracon beween segmen A of he secondary wndng hrough he core cener o he parallel segmens and of he prmary wndng (see Fg. 6c) wll be calculaed. Segmens and are he wndng pars around he permeers of he nner rng and ouer rng, respecvely. Table I provdes dmensonal nformaon of he core and wndng wh respec o he noaons n Fg. 6c. The secondary has urns sranded ogeher, so each urn can be approxmaely reaed as locaed n he cener of he magnec core, as shown n Fg. 7. The sac capacance beween he nner prmary urns and he secondary urns can be expressed as [4, 6]: ε0s ε0dπl C = =, (5) r r where ε o s he permvy of free ar space, d s he dameer of each urns (he same sze of wre s seleced for boh prmary and secondary urns), l and r are he overlapped lengh and he dsance beween he nner prmary urns and he secondary urns, respecvely. Wh respec o he ouer prmary urns, he sac capacance can be expressed wh a dfferen dsance r o, ε0s ε0dπl Co = =. (6) ro ro Assumng ha he volage poenal dsrbuon along he prmary urns vares lnearly, V[] = V. (=0,,,3,... n-) (7) n

7 (a) (b) (c) Fg. 7. -D cross-seconal op vew: effec of parasc capacance from he secondary wndng of a) segmen A o he nner prmary wndng, b) segmen A he ouer prmary wndng, c) segmen C o he ouer prmary wndng Then he oal sored elecrc energy beween all secondary urns and he nner prmary urns s: n s np Vp Vs j E = C ( ) j= 0 = 0 np ns Vp ns np (np ) Vs np ns (ns ) = C [ Vp Vs np ns]. (8) 4 3 ( n ) 3 ( n ) p Wh he same analycal approach, he oal sored elecrc energy beween all secondary urns and he ouer prmary urns can be acheved: Vp ns np (np ) Vs np ns (ns ) Eo = Co [ Vp Vs np ns]. (9) 4 3 ( n ) 3 ( n ) p The capacance caused by he sde segmens B, B o he prmary wndng s: ε0dπlb CB =. (0) rb Segmens B and B face he mddle pars of he prmary wndng. I s approprae o assume ha here are fve urns from he prmary wndng, whch le n segmen 3 or 4 of Fg. 6c, facng segmen B and B respecvely. They are urn number (n )/, (n )/ o (n )/. For example, n a specfc desgn wh 55 prmary urns, or n = 55, hey wll correspond o urn number 5 o 9. The sored elecrc energy caused by B and B s: ns ( n )/ Vp Vs j EB = CB. () j= 0 = ( n )/ n p n s Nex, he conrbuon of segmen C of he secondary wndng o he ouer rng of he prmary wndng s compued. Referrng o Fg. 7c, s helpful o express he dsance from pon C o he urns lyng n he ouer rng of he prmary mahemacally. In rangle CDB, dsance CB s relaed o oher sdes of he rangle by: CB = CD BD CDBDcos( Φ) = ( r r ) r ( r r ) r cos( π π n ). () 0 o 0 0 Therefore, dsance from C o he h urn of he ouer-prmary wndng s (see Fg. 7c) π rcou, = ro ( ro r ) ro ( ro r ) cos( π ). ( = 0,,,3,..., n ) (3) n s s

8 The capacance from segmen C of he secondary wndng o he urn number h of he ouer prmary wndng s: εodπlc εodπlc CCou, = =. ( = 0,,,3,..., n ) (4) rcou, π ro ( ro r) ro( ro r) cos( π ) n The oal sored energy caused by segmen C of secondary wndng o he ouer sde of prmary wndng s hen: E Cou V V j = ( ) ns n p s CCou, j= 0 = 0 np ns ε dπl V V j ns n o c p s = ( ). (5) j= 0 = 0 π np ns ro ( ro r) ro( ro r) cos( π ) n Smlarly, he sored energy caused by segmen C of secondary wndng o he nner sde of prmary wndng s: E Cn V V j = ns n p s CCn, ( ), (6) j= 0 = 0 np ns where εodπlc CCn, =. ( = 0,,,3,..., n ) (7) π ( ) ( ) r ro r r ro r cos( π ) n The oal sored elecrc energy s hen Eoal = E Eo EB ECn ECou = Ceq ( Vp Vs ). (8) The calculaed ner-wndng capacance based on he parameers on Table I s 0 pf. Table II shows he calculaed energy and capacance. I s observed ha segmen A domnaes he sored energy, and he conrbuons of segmens B and B are neglgble. The desgn gudelne s ha ncreasng he core geomery and ncreasng dsance from segmen C o he core wll effecvely reduce he ner-wndng capacance. Table I: arameers of he magnec core and wndng geomeres ε F/m d mm l 6 mm r.5 mm r o 8 mm n p 55 n s V p 300 V V s 60 V r B mm l B 6.5 mm 6 mm l c

9 Table II: Calculaed energy and ner-wndng capacance arameers E E o E B E Cn ECou Eoal Value.3e-7 J 8.4e-8 J.e-9 3.8e-8 J 3.e-8 J.9e-7 J J E 45.9% 9.3% 0.4% 3.%.3% 00% / oal C eq 9.97e- F Absolue Impedance (Ohm) (a) Fg. 8. Iner-wndng mpedance measuremen: a) magnude, b) phase. hase (deg) (b) Transformer C n (F) 0 - Leakage Inducance (H) Fg. 9. Inerpreed parasc capacance Fg. 0. The leakage nducance Impedance (Ohm) hase (degree) (a) (b) Fg.. Crcu npu-o-oupu mpedance measuremen Lef: magnude, Rgh: phase.

10 Expermenal resuls The measuremen of he ransformer s carred ou by he Aglen 494A recson Impedance Analyzer, whch has a precson of ±3 % as clamed by he manufacurer. The measured mpedance and phase beween he prmary and secondary wndngs, wh each wndng ermnal shored, are shown n Fg. 8. The measured ner-wndng capacance s shown n Fg. 9. I s shown ha he measured capacance s around 0 pf from 3 khz up o 0 MHz. The calculaon and he measuremens, are herefore, mached reasonably well wh each oher. The resulng leakage nducance s 70 µh, whch s shown n Fg. 0. In he end, he overall desgn goal s fulflled, whch s o have a very low ner-wndng capacance of 0 pf. Fg. shows he mpedance magnude and phase of he crcu. These were found by measurng he mpedance beween he npu and he oupu ermnals of he converer wh he npu and oupu shored o her own reurn grounds. The measured crcu npu-o-oupu parasc capacance s deduced from hese measuremens and s shown n Fg.. Is value s 0 pf, he same as wh he ner-wndng capacance of he ransformer. As a resul, can be sad ha he proposed crcu layou, conrol, and ransformer desgn has mnmzed he oal crcu npu-o-oupu capacance, makng a powerful soluon for modular sackng applcaons. Fnally, Fgs. 3 and 4 show he expermenal operaon from power mode o shun mode and from shun mode o power mode. I can be seen ha expermens mach very well o he analyss presened n he crcu operaon secon. The feasbly of he converer s herefore valdaed. 0-0 Capacance (F) Fg.. Crcu npu-o-oupu parasc capacance Fg. 3. Transen response from power mode o shun mode: oupu volage (0V/dv), nducor curren (A/dv), me scale: 0us/dv). Fg. 4. Transen response from shun mode o power mode: oupu volage (0V/dv), nducor curren (A/dv), me scale: 0us/dv).

11 Concluson The resulng ransformer has a parasc capacance of 0 pf, whch s exremely low compared o oher exsng solaed power converers of smlar power rang. The mahemacal dervaon yelds accepably accurae resuls ha agree well wh measuremen. The resuls also provde gudelnes abou how he ransformer geomery should be consdered when he ner-wndng capacance s of concern. Fnally, he overall resul acheved wh he prooype provdes very hgh mmuny o he common mode nose curren caused by fas volage ransens, and herefore makes he converer suable for modular sackng applcaons. References [] M. A. E. Andersen.: MOS gae drver crcu wh exremely hgh galvanc solaon, EE 995. Sevlla, Span, vol., p [] S. Wang,. Kong and F. C. Lee.: Common mode nose reducon for boos converers usng general balance echnque, IEEE Trans. ower Elecron., vol., no. 4, pp.40-46, Jul. 007 [3] J. Bela and J. W. Kolar.: Usng ransformer parascs for resonan converers A revew of he calculaon of he sray capacance of ransformers, IEEE Trans. Ind. Appl., vol. 44, no., pp. 3 33, Jan./Feb [4] L. Dalessandro, F. S. Cavalcane, and J. W. Kolar.: Self-capacance of hgh-volage ransformers, IEEE Trans. ower Elecron., vol., no. 5, pp , Sep [5] H.-Y. Lu, J.-G. Zhu, and S. Y. R. Hu.: Expermenal deermnaon of sray capacances n hgh frequency ransformers, IEEE Trans. ower Elecron., vol. 8, no. 5, pp. 05, Sep [6] Z. Ouyang, O. C. Thomsen and M. A. E. Andersen.: Opmal desgn and radeoff analyss of planar ransformer n hgh power dc dc converers, IEEE Trans. Ind. Elecron., vol.59, no.7, pp , July 0. [7] T. Duerbaum and G. Sauerlaender.: Energy based capacance model for magnec devces, n roc. IEEE Appl. ower Elecron. Conf. Expo., pp.09-5, 0. [8] D. Garabandc, D. W.G. Dunford, M. Edmunds.: Zero-volage-zero-curren swchng n hgh-oupu-volage full brdge WM converers usng he nerwndng capacance, IEEE Trans. ower Elecron., vol.4, no., pp.343,349, Mar 999. [9] K. engju and F.C. Lee.: Transformer srucure and s effecs on common mode EMI nose n solaed power converers, Appled ower Elecroncs Conference and Exposon (AEC), 00 Tweny-Ffh Annual IEEE, pp.44,49, -5 Feb. 00. [0]M. Hoyerby and M. A.E. Andersen.: Ulrafas rackng power supply wh fourh-order oupu fler and fxed-frequency hyserec conrol, IEEE Trans. ower Elecron., vol. 3, no. 5, pp , Sep []C. In-Ho, K. Young-Do and M. Gun-Woo.: A half-brdge LLC resonan converer adopng boos WM conrol scheme for hold-up sae operaon, IEEE Trans. ower Elecron., vol. 9, no., pp , Feb. 04. []H. Manl, J. Bocker and N. Frohleke.: Frequency / duy cycle curren-mode fuzzy conrol for LCC resonan converer," 0-4h European Conference on ower Elecroncs and Applcaons (EE), Aug Sep. 0. [3]D. Cosne, D. Maksmovc, D.; R. Zane.: Desgn and conrol for hgh effcency n hgh sep-down dual acve brdge converers operang a hgh swchng frequency, IEEE Trans. ower Elecron., vol.8, no. 8, pp , Aug. 03. [4]G. Gud, A. Kawamura, Y. Sasak and T. Imakubo.: Dual acve brdge modulaon wh complee zero volage swchng akng resonan ransons no accoun, 0-4h European Conference on ower Elecroncs and Applcaons (EE), Aug Sep. 0. [5]A. Garca-Bedaga, A. Rujas, I. Vllar,. Barrade and A. Rufer, A.: New paramerc model of medumfrequency sngle-acve-brdge converers, 03-5h European Conference on ower Elecroncs and Applcaons (EE), -6 Sep. 03 [6]. Kwoo and C. Zhe.: Analyss and desgn of a parallel-conneced sngle acve brdge DC-DC converer for hgh-power wnd farm applcaons, 03-5h European Conference on ower Elecroncs and Applcaons (EE), -6 Sep. 03 [7]ECOS.: SIFERRIT maeral N87, Sep. 006, avalable:hp://