Optimal design of a modular 11kW series parallel resonant converter for a solid state 115-kV long pulse modulator

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1 Otimal design of a modula kw seies aallel esonant convete fo a solid state 5-kV long ulse modulato M. Jaitz and J. Biela Laboatoy fo High Powe Electonic Systems ETH Zuich, Physikstasse 3, CH-8092 Zuich, Switzeland aitz@he.ee.ethz.ch This mateial is osted hee emission of the IEEE. Such emission of the IEEE does not in any way imly IEEE endosement of any of ETH Züich s oducts o sevices. Intenal o esonal use of this mateial is emitted. Howeve, emission to eint/eublish this mateial fo advetising o omotional uoses o fo ceating new collective woks fo esale o edistibution must be obtained fom the IEEE by witing to ubs-emission@ieee.og. By choosing to view this document you agee to all ovisions of the coyight laws otecting it.

2 OPTIMAL DESIGN OF A MODULAR KW SERIES PARALLEL RESONANT CONVERTER FOR A SOLID STATE 5-KV LONG PULSE MODULATOR M. Jaitz and J. Biela Laboatoy fo High Powe Electonic Systems ETH Zuich, Physikstasse 3, CH-8092 Zuich, Switzeland aitz@he.ee.ethz.ch Abstact Moden acceleato diven exeiments like linea collides o sallation souces ae sulied by RF amlifies using klystons. The cathode voltage fo these klystons can be geneated by long ulse modulatos geneating highly accuate voltage ulses in the length of milliseconds. In this ae an otimzation ocedue based on an electical and a themal of a seies aallel esonant convete (SPRC) sulying these klystons is esented. The efficiency of a basic SPRC-module is 95.3% a ulsed owe density of 6.64 kw/l. - V In Basic module Bm 2 Bm 3 Bm n V O V O2 V O3 V On V Om V Om2 V Om3 V Omn I K Klyston V K I. INTRODUCTION The SPRC toology (see Fig.) is a modula design which needs no ulse tansfome. Common designs like Bounce Modulato toologies using ulse tansfomes become huge fo long ulses. The seies aallel esonant convete is a modula toology which avoids this dawback as the tansfome is oeated at high fequencies. The consideed nominal ulse voltage amlitude is 5 kv a ulse owe of 2.88 MW and a ulse length of 2.8 ms. The ulse to ulse eoducibility of 0.02 % and a voltage ile at to of less than 0.05 % ae highly demanding. In ode to meet these highly demanding secifications listed in Tab.I, the modulato is based on inteleaved SPRC modules. A SPRC module [] contains a full bidge connected to a seies aallel cicuit followed by a tansfome a ectifie and a filte caacito. In this ae, an otimal design of a single module accoding to TABLE I PULSE SPECIFICATIONS Pulse voltage V K 5 kv Pulse cuent I K 25 A Pulse owe P K 2.88 MW Pulse eetition ate P RR 20 Hz Pulse width T P 2.8 ms Pulse duty cycle D 0.06 Pulse eoducibility P REP 0.02 % V In A Fig.. B C S L S : n V AB I Ls I C Basic module CP V C SPRC toology and SPRC basic module. C o V O the design consideations in [2] is esented. The basic modules of the SPRC can be connected in seies o in aallel deending on the outut owe and ile secifications and can also be inteleaved. Due to the fact that the ulse shaing is achieved a ectifie and a filte on the seconday side of the tansfome, the ulse duation is elatively indeendent fom the tansfome size. Futhemoe, the SPRC is natually shot cicuit oof and ovides zeo voltage switching (ZVS). Additionally, the seies inductance L S can be integated by the leakage inductance of the tansfome. Due to those advantages, the SPRC toology is investigated in the following. A staight fowad design is difficult due to the high numbe of degees of feedom and geometic aametes of the tansfome. Thus, in this ae an otimization ocedue based on [2] given design constaints is shotly esented in section II. As all s ae aleady commonly intoduced in [2] section III only summaizes the electical SPRC and the themal semiconducto shotly, but ut a detailed emhasis /3/$ IEEE

3 on the themal tansfome as well on the leakage and isolation design ocedues. Finally, section IV esents the otimization esults. II. OPTIMIZATION PROCEDURE Global otimize Global system aamete secifications: Rise time, V-ile, V-level,... Single module design Single module system aamete secifications V In,V o, I o, P o, T max, R th,wdg,max,... Based on the secifications of the ulse in Tab.I, Fig.2 shows the otimal design ocedue of the SPRC. In a fist ste, the otimize vaies the fee aametes in the single module design esect to the chosen design constaints in Tab.II. This single module design ocedue consists of an electical and a themal, and additionally of an insulation and leakage design ocedue. The design of the single module is then veified the constaints of the global secifications and this finally leads to the otimal numbe of single SPRC modules which ae connected in seies and/o in aallel. Electical Comonent values Cuents, voltages, B,... L S, C P, C S, N P, N S,n,... Leakage design ocedue Insulation design ocedue Tansfome otimization Coe loss Winding loss Themal tansfome # of semiconductos otimization Semiconducto loss Themal semiconducto Vaiation of otimization aametes Vaiation of the numbe of modules TABLE II OPTIMIZATION PARAMETERS AND CONSTRAINTS System design of a single module Otimization aametes Tansfome coe Windings Semiconductos l,t,h (see Tab.III) # of tuns # of litz wie stands Constaints Maximum magnetic flux density B max Maximum winding temeatues T, T 2 Maximum temeatues in coe ats T 3, T 4 Maximum change of unction temeatue T J # of switches 80 mt 20 C 20 C 20 C Defined leakage inductance L S (see Tab.III) 5. µh Maximum electical field stength E max 5 kv/mm III. SINGLE MODULE DESIGN MODELS The following section shotly summaizes the electical of the single SPRC-module and the semiconducto themal. Aftewads the design ocedues fo the tansfome insulation, leakage inductance and the themal of the tansfome ae given in detail. A. ELECTRICAL MODEL The electical of the SPRC basic module (see Fig.b) is descibed a fist hamonic analysis [], which also takes the outut caacito and ectifie into account. This consides the tansfome ust as a voltage amlifie tuns atio n and detemines all aametes of the esonant cicuit (C S, C P, L S, n) esectively delives all voltages and cuents. Global secifications fulfilled Otimal design and otimal numbe of modules Fig. 2. Poosed otimization ocedue which leads to an otimal design of a single SPRC-module and an otimal numbe of modules of the oveall system. B. SEMICONDUCTOR THERMAL MODEL In this, the esonant cuent calculated fom the electical is used to detemine the numbe of switches which leads to minimum losses the constaint of a maximum T J. The losses include conduction and switching losses. The conduction losses can be calculated diectly fom data sheet and the switching losses eithe ae included fom measuements o estimated also fom data sheet. T J is used fo lifetime estimations due to [3]. Fo IGBT modules, T J should not exceed 20 C unde the constaint of a maximum unction temeatue of 25 C to each moe than 0 8 ulses. Same limits will be used fo MOSFETs, what esults in an otimal numbe of switches in aallel of 5. The investigated MOSFET is the STY39N65M5 fom ST [4]. The equied heat sink volume can be calculated the Cooling System Pefomance Index (CSPI) as intoduced in [5]. Fig.3 shows the built modulato ototye, each leg 5 switches in aallel. C. TRANSFORMER THERMAL MODEL Based on the oosed tansfome themal in [6], the etuns all citical temeatues (see Fig.4). It contains all tyes of heat tansfe eesented in an equivalent themal esisto and all losses ae led

4 5 MOSFETs in aallel fo each leg h 8 cm Temeatue senso Rth,tan/2 Rth,tan 42 cm Rth,oth/2 Rth,cyc o 29 cm λai λiso λlay Fig. 5. Coss section of a solid wie winding. Fig. 3. Pototye modulato each leg 5 switches in aallel, two legs on one heat sink. by cuent souces. Most of the themal esistos used in Fig.4, as esented in [2], ae well descibed in liteatue [6], but thee exists a lack concening the themal winding esisto Rth,N x. A shot exlanation in the case of solid wie is given below, the full deivation of the themal esistance of solid and litz wie can be found in [7]. Fig.5 shows a tyical solid wie winding containing diffeent heat tansition esistos. Fist, a tangential at which eesents the heat flow along the winding fom laye to laye and second thee ae two diffeent ats in adial diection. The tangential at can be easily calculated by Rth,tan = lw NL λcu o2 πkl () whee NL is the numbe of tuns e laye and lw is the mean length e tun. In adial diection thee exists an othogonal at which is fomed by both halves of the oute layes and an othocyclic at which eesents the heat tansition in the inne winding layes. In othogonal wie aangements the wies in two neighbouing layes ae laying diectly side by side (see Fig.6). The themal esistance then is [7] Rth,oth= 2 (2) 2λAi lw Z V 8λIso /λai 2 α o α Z= β β2 2 3/2 (β 2 ) V = actan β β Ambient! β π 4 β2 Coe Rth,C-Am Rth,N2-Am In othocyclic windings the wies in the neighbouing layes ae laying diectly in the ga of the evious laye (see Fig.7). Rth,cyc can be obtained as [7] Rth,cyc=h i (6) λai o2 4λAi lw MAiMIso o λiso 2 Z π6 cos2 ψ cos ψ cos2 ψ MAi= h i2 dψ (7) 0 cos ψ α( cos2 ψ ) Z π6 sin2 ψ cos ψ cos2 ψ 0.75 MIso= h i2 dψ. (8) 0 cos ψ α( cos2 ψ ) This finally leads to the geneal fom of Rth,N x NL NL (Rth,tan Rth,oth ). NL Rth,N x = (Rth,tan Rth,cyc ) TAm - PN2 Seconday Fig. 4. T4 PC Rth,N Rth,N Rth,N2 Rth,N2 R R th,n-cc th,n2-n 2 T2 2 2 T 2 T3 PN Pimay PCC Themal equivalent cicuit of the tansfome. hz ; β=. (5) α 2o λlay /λai α= o λiso /λai (3) Rth,C actan! β β π 2 (4) β 2β 2 4 and s s y λiso x σ σ φ λai o h ξ 0 -o λlay φ Rth,oth T 2o (9) h T2 Fig. 6. Two othogonal aanged wies ideal assumed themal heat flow lines. Themal heat flow between two wies simulated COMSOL.

5 λ Iso λ Ai ψ R th,cyc 0 2 o Fig. 7. Thee othocyclic aanged wies ideal assumed themal heat flow lines. Themal heat flow between thee wies simulated COMSOL. T 2 T T 3 Contou oints Cunducto d Image chage A7 Φ C A5 Basic box A A6 y Oiginal window X Oiginal Conducto Y x D. INSULATION DESIGN PROCEDURE High electical field stengths can ham the insulation of the tansfome emanently and lead to acs between the windings o the coe. Theefoe, a oe insulations design is unavoidable. Following assumtions ae made fo the insulation design. The bodes of the winding window ae gounded and the sace between the windings and the est of the winding window is comletely filled a homogenous isolation mateial. To calculate the electical field inside the winding window the so called chage simulation method (CSM) (also called mio chage method o image chage method) descibed in [8] is alied and is shotly exlained in the case of one conducto. In Fig.8 the conducto in the oiginal window is eesented by n image chages located inside the conducto on a adius d and belonging contou oints on the adius of the conducto each the same conducto otential Φ C. Φ C is fomed by the sueosition of these image chages in n Φ C = (0) = whee ae the otential coefficients which contain the geometic locations of the images chages. By mioing the oiginal window thee times counteclockwise gives the oiginal box deicted in Fig.8. To build the basic box it would be also ossible to mioing aound the oiginal window but then the automated extension of mioed basic boxes as seen in Fig.8 (c) is much moe comlicated. Alying (0) to all windows in all basic boxes and coesonding image chages leads to a system of linea equations which has to be solved fo the unknown chages [] = [] [Φ C ] () Aftewads is it ossible to calculate the electical field stength E at evey location x and y inside the oiginal window. E = Ex 2 Ey 2 (2) E x = n (A A2... Am) (3) 2πɛ A3 A8 A A4 (c) Fig. 8. Chage simulation method based on mio chages. Conducto eesented by image chages, basic box which contains the oiginal window and thee mioings of it and (c) full set of used mioings. x x xx A= (x x ) 2 (y y ) 2 (xx ) 2 (y y ) 2 (4) xx x x (xx ) 2 (yy ) 2 (x x ) 2 (yy ) 2 x x 2X xx 2X A2= (x x 2X) 2 (y y ) 2 (xx 2X) 2 (y y ) 2 (5) and xx 2X x x 2X (xx 2X) 2 (yy ) 2 (x x 2X) 2 (yy ) 2 E y = n A2 A9 (B B2... Bm) (6) 2πɛ y y y y B= (x x ) 2 (y y ) 2 (xx ) 2 (y y ) 2 (7) yy yy (xx ) 2 (yy ) 2 (x x ) 2 (yy ) 2 y y y y B2= (x x 2X) 2 (y y ) 2 (xx 2X) 2 (y y ) 2 (8) yy yy (xx 2X) 2 (yy ) 2 (x x 2X) 2 (yy ) 2 whee A, B ae the seies of the ositions of the image chages deending on the consideed oint x and y in the oiginal box and A2 Am, B2 Bm ae accoding to the shifted boxes (see Fig.8 (c) doted bown boxes). The vaiables x and y ae the given ositions of the image

6 Pimay 2 Basic box y Oiginal Window X A 0 Y I I 8 6 kv/mm Pimay Sekunday x 4 A7 A5 A6 Seconday 2 A3 A A2 0 Fig. 9. E-field distibution in gounded winding window. A8 A4 A9 chages wheeas X and Y ae the width and the length of the oiginal window. Fo comutational easons m is chosen 9 and the numbe of image chages is 6. This esults in a quite high accuacy. Fig.9 shows the E-field distibution of the final otimized design an aveage field of 5.75 kv/mm and a maximum field of lowe than 5 kv/mm. Deicted design has been also comaed to FEM and gives a deviation of lowe than 8%. E. LEAKAGE DESIGN PROCEDURE Basically, the tansfome is designed to minimum isolation saces which leads to a given leakage inductance that is calculated the cuent mio method. Hee, each conducto is eesented by a single cuent in the oiginal window (see Fig.0 ) which then is mioed in the same way as descibed in the evious section (see Fig.0 and (c)). In contast to the mio chage method whee in a fist ste all unknown chages have to be calculated, the cuent is inheently given. Theefoe H = Hx 2 Hy 2 (9) H y = H x = k k I 2π (A A2... Am ) (20) I 2π (B B2... Bm ). (2) The tems Am, Bm and Am, Bm ae almost the same the diffeence that all factional tems have lussigns. Finally to get the leakage inductance efeed to the imay side L leak,p = 2W m I 2 P W m = l W µ H 2 dxdy (22) 2 whee I P is the total imay cuent and l W the mean winding length. In ode to get the final equested seies (c) Fig. 0. Two conductos eesenting imay and seconday windings by conducto cuents I and I, basic box which contains the oiginal window and thee mioings of it and (c) full set of used mioings inductance L S an auxiliay coe as shown in Fig. delives the missing leakage inductance L leak,aux by adusting the ai ga. L S = L leak,p L leak,aux (23) With this method influences concening the leakage inductance due to manufactuing toleances can be easily balanced. Auxiliay coe Ai ga Pimay Seconday Fig.. Poosed tansfome included leakage inductance fomed by an auxiliay coe. IV. OPTIMIZATION RESULTS Fig.2 and Tab.III summing the esults of a single SPRC module otimization and the final numbe of modules of the oveall system. The main losses ae equally distibuted

7 between tansfome and switches wheeas due to the much moe comlex stuctue of the tansfome which esults in moe comlicated cooling effots, the volume of the tansfome is quite highe than that of the modulato switches (see Fig.2 and ). Comaing the given constaints in Tab.II the esults in Tab.III all values concening temeatues, flux density and electical field stengths fulfilling the limits. Fo the entie system 6 SPRC-modules ae equied. Coe 7.06 W (30.73%) Winding W (9.69%) Seies Caacito (C S ).4388 l (5.09)% Rectifie W (7.67%) Switches 254W (45.63%) Rectifie.6l (5.66%) Tansfome 5.5 l (54.80%) Switches 9.7 l (34.45%) Seies Caacito (C S ) 34.9 W (6.28%) Fig. 2. Comaison of losses and comaison of volume of a single SPRC-module. V. CONCLUSIONS Due to a lage numbe of degees of feedom (e.g. leakage inductance and geometic aametes of the tansfome), an otimal staight fowad design fo the esonant convete system is difficult. Theefoe, in this ae an otimization ocedue is esented, which is based on an electical and a themal of the SPRC convete. Additionally, an insolation design ocedue fo the tansfome and a themal fo the switches is ovided. With this aoach an otimal design fo minimum losses is achieved. The oveall system consists of 2 SPRC modules connected in aallel and 8 of them in seies. Each modulato module has 5 MOSFETs connected in aallel. The efficiency of a single SPRC-module is 95.3% a ulsed owe density of 6.64 kw/l. ACKNOWLEDGEMENT The authos would like to thank the oect atnes CTI and Amegon AG vey much fo thei stong suot of the CTI-eseach oect 335. PFFLR-IW. TABLE III OPTIMIZATION RESULTS OF A SINGLE SPRC-MODULE AND OPTIMAL NUMBER OF MODULES. Resonant Cicuit V Out 5 kv L S 5. µh n 8 I Out 2.5 A C S µf P Out 87.5 kw C P 2.58 nf # of caacitos fo C S Tye 234 MKP B32672L Semiconductos # of aallel switches Tye 5 x 4 STY39N65M5 # of ectifie diodes Tye 56 IXYSDSDI60 Tansfome # of coes Tye 36 U26/9/20 N87 Windings Litz wie Pimay 3 8 x 2000 x 0.05 Seconday x 0.05 Coe dimensions t cm h 8.2 cm l l 25.3 cm Temeatues T 94 C h T C T C T C Flux density t B max 80 mt Electical field stengths E max 3.47 kv/mm E avg 5.75 kv/mm Pefomance of a single module Volume Pulsed owe density Efficiency l 6.64 kw/l 95.3 % Oveall system # of SPRC-modules in aallel and seies 2 x 8 Refeences [] G. Ivensky, A. Kats, and S. Ben-Yaakov, A novel c of caacitive-loaded aallel and seies-aallel esonant DC-DC convetes, in Poc. the IEEE Powe Electonics Secialists Conf. (PESC) Recod, vol. 2, 997, [2] M. Jaitz and J. Biela, Otimal design of a seies aallel esonant convete fo a solid state long ulse modulato. 4th Euo-Asian Pulsed Powe Confeence, 202. [3] A. Volke and M. Honkam, IGBT Modules Technologies, Dive and Alications. Infineon Technologies AG, Munich, 20. [4] STY39N65M5 [5] U. Dofenik, G. Laime, and J. Kola, Theoetical convete owe density limits fo foced convection cooling, in Poc. of the PCIM confeence, [6] I. Villa, Multihysical chaacteization of medium-fequency owe electonic tansfomes, Ph.D. dissetation, Ecole olytechnique fedeal de Lausanne, 200. [7] M. Jaitz and J. Biela, Analytical fo the themal esistance of windings consisting of solid o litz wie. 5th Euoian Confeence on Powe Electonics and Alications, 203. [8] H. Singe, H. Steinbigle, and P. Weiss, A chage simulation method fo the calculation of high voltage fields, no. 5, , 974.