Experimental Validation of a Series Parallel Resonant Converter Model for a Solid State 115-kV Long Pulse Modulator

Transcription

1 Experimental Validation of a Series Parallel Resonant Converter Model for a Solid State 115-kV Long Pulse Modulator M. Jaritz, S. Blume, D. Leuenberger and J. Biela Power Electronic Systems Laboratory, ETH Zürich Physikstrasse 3, 8092 Zürich, Switzerland This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of ETH Zürich s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permission@ieee.org. By choosing to view this document you agree to all provisions of the copyright laws protecting it.

2 3392 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 43, NO. 10, OCTOBER 2015 Experimental Validation of a Series Parallel Resonant Converter Model for a Solid State 115-kV Long Pulse Modulator Michael Jaritz, Student Member, IEEE, Sebastian Blume, David Leuenberger, Student Member, IEEE, and Juergen Biela, Member, IEEE Abstract Medium and high beta cavities used in linear colliders or spallation sources are supplied by klystrons or inductive output tubes amplifiers. The cathode voltage for these amplifiers can be generated by long-pulse modulators generating highly accurate high voltage pulses in the length of milliseconds. With existing modulator topologies, all the demanding requirements like fast pulse rise time, high accuracy, and low voltage ripple hardly can be satisfied at the same time. Common designs like bouncer modulator topologies using pulse transformers become huge for long pulses. The series parallel resonant converter (SPRC) avoids this drawback as the transformer is operated at high frequencies. In this paper, the comprehensive multidomain model of an SPRC including an electrical model of the inverter, a magnetic model, and an isolation design procedure of the transformer is verified with a prototype of a single module operated under full-load conditions. In addition, a comparison between the predicted parasitics like leakage inductance and stray capacitance of the transformer and the measured values are given. An evaluation of the isolation of the transformer, which is especially crucial for a series connection of the modules, is also performed. In addition, different possibilities to realize the desired series inductance are discussed. Index Terms High-voltage techniques, magnetic fields, optimization, parasitic capacitance, resonant inverters, transformers. TABLE I PULSE SPECIFICATIONS I. INTRODUCTION BASED on the optimization procedure presented in [1], a single SPRC module has been designed. A single SPRC module [2] contains a full bridge connected to a series-parallel resonant circuit followed by a transformer, a rectifier, and a filter capacitor (Fig. 1). Two single SPRC modules are connected in parallel at the output and in series at the input forming a stack. Eight of these stacks have to be connected in series at the output to obtain the required pulse voltage (see specifications in Table I) and are connected in parallel at the input (Fig. 1). In this paper, the comprehensive multidomain model of a single Manuscript received November 28, 2014; accepted December 23, Date of publication February 11, 2015; date of current version October 7, This work was supported by the Project Partners Commission for technology and innovation (CTI) and Ampegon AG through the CTI-Research Project under Grant PFFLR-IW. The authors are with the Department of Electrical Engineering, ETH Zurich, Zurich 8092, Switzerland ( jaritz@hpe.ee.ethz.ch; blume@hpe.ee.ethz.ch; leuenberger@hpe.ee.ethz.ch; jbiela@ethz.ch). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TPS Fig. 1. Full system with two single SPRC modules connected in series at the input and in parallel at the output forming a stack. Eight of these stacks are connected in series at the output to obtain the required pulse voltage. SPRC module including an electrical model of the inverter, a magnetic model, and an isolation design procedure of the transformer is verified with a prototype of a single module operated under full-load conditions. Section II shortly discusses the results of a single SPRC module with its optimized parameters including the resonant tank, the transformer, and the outputrectifier. Different possibilities to realize the desired series inductance (integrated or separately) are presented in Section III. In Section IV, a comparison between the analytical approach that is used in the optimization procedure and the Finite element method (FEM) calculations of the leakage IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

3 JARITZ et al.: EXPERIMENTAL VALIDATION OF A SERIES PARALLEL RESONANT CONVERTER MODEL 3393 TABLE II OPTIMIZATION RESULTS OF A SINGLE SPRC MODULE AND OPTIMAL NUMBER OF MODULES Fig. 2. Proposed optimization procedure that leads to an optimal design of a single SPRC-module and an optimal number of modules of the overall system. inductance and the stray capacitance is given and compared with measurements. Section V presents the E-field conform isolation design of the transformer. All built components are discussed in Section VI and finally, Section VII presents the pulse measurements of the prototype. II. OPTIMIZATION RESULTS Because of the high number of degrees of freedom during the design process, e.g., geometric parameters of the transformer or the design of the resonant tank, the optimization procedure presented in [1] has been developed for optimally designing the modulator (Fig. 2). Table II summarizes the optimization results of the resonant tank and the transformer. To achieve a proper insulation design, the isolation distance is determined according to an E-max design by varying the distance between primary and secondary windings in a first step. Afterward, in a postinsulation design check, an E-field conform design is carried out. Before starting modeling the optimization, a model for the series inductance either included in the transformer or formed by an separately inductor has to be chosen. It turned out that due to the high-resonant current I Ls, the best way to realize the series inductance L S is an air toroid plus the leakage inductance of the transformer. A comparison of the evaluated structures between volume and losses is given in the next section. Fig. 3. Different possibilities to realize the series inductance. (a) Integrated in the transformer as leakage inductance either as U- or E-core. (b) Using a stray core wounded by the secondary winding, inductance adaptations can be made by varying the air gap of the stray core. (c) Transformer is designed with respect to minimum insulation distances and the desired series inductance is formed by the transformers leakage inductance plus a nonsaturable air toroid. III. ALTERNATIVE WAYS TO REALIZE THE SERIES INDUCTANCE The series inductance in the optimization procedure is modeled as an air toroid. Alternative ways to realize the series inductance and a comparison of them by volume and losses are shown next. The following discussion is based on the results in Table II and all transformers are designed to the same isolation distances and turn ratios. A possible way to realize the series inductance L S is to integrate it completely with the transformer leakage inductance [Fig. 3(a)]. By adapting x and y in the case of the U-core transformer or only

4 3394 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 43, NO. 10, OCTOBER 2015 TABLE III COMPARISON BETWEEN VOLUME AND LOSSES y in the case of the E-core transformer, the leakage inductance can be modified. This leads to a high boxed volume. Another possibility is to use an additional stray core wound by the primary or the secondary winding [3] [Fig. 3(b)]. The inductance is set by varying the air gap of the stray core. If it is possible to use all turns of the secondary winding, the isolation distance x min has a minimum. Otherwise, if not all turns of the secondary could be used to keep the air gap as short as possible, two times of the insulation distances have to be added to x min and it increases the volume. In addition, using a stray core leads to higher losses due to the high resonant current I Ls. The third option to realize the series inductance L S is an air toroid [Fig. 3(c)]. The transformer is designed with respect to minimum insulation distances and the air toroid causes no core losses. Thus, using a transformer and an air toroid, it is the best compromise between volume and losses to realize the series inductance. In Table III, a comparison of the discussed possibilities between volume and losses is listed. As the output characteristic of the SPRC is directly influenced by the parasitics of the transformer, it is necessary to accurately know the leakage and the stray capacitance of the transformer. An evaluation of the transformer parasitics calculations compared with measurements is given in the next section. Fig. 4. Integration areas and paths for 3-D, 2-D FEM, and 2-D numerical parasitics calculations of the transformer. (a) Top view. (b) Front view. (c) Side view. TABLE IV COMPARISON BETWEEN 3-D FEM, MIRROR METHOD, AND THE MEASURED LEAKAGE INDUCTANCE IV. TRANSFORMER PARASITICS VALIDATION A. Leakage Inductance As presented in [1], the calculation of the leakage inductance is based on the mirror current method. To increase the accuracy of this method different mirror planes are used inside and outside the core. Inside the core window, mirroring on all four core walls is applied [Fig. 4(b)] and for the region outside, the core mirroring just to the left wall is used [Fig. 4(c)]. Therefore, (15) and (16) in [1] can be simplified in the left mirroring case to H x = I ( j x x j 2π (x x j ) 2 + (y y j ) 2 ) x + x j + (x + x j ) 2 + (y y j ) 2 (1) H y = I ( j y y j 2π (x x j ) 2 + (y y j ) 2 ) y y j + (x + x j ) 2 + (y y j ) 2 (2) and using (17) from [1] leads to the desired leakage inductance, where l W is the integration length inside the core l W,in and outside the core l W,out [Fig. 4(a)]. Finally, with this method, it is possible to calculate the magnetic energy W m inside the transformer window [Fig. 4(b)], in the air box outside the transformers front [Fig. 4(a)], but it is not possible to consider the energy above and under the transformer core. It is assumed that there is a negligible amount of energy inside the core due to the high permeability of the core material. Table IV compares the error between FEM and the mirror current method related to the measured leakage inductance by varying the parameter n 1. If the areas in the core above and below the transformer are also considered in the FEM evaluation, the leakage inductance results in 1.59 μh and leads to an error of 0.94% related to the measured value. B. Stray Capacitance As presented in [1], the calculation of the electrical field is based on the mirror charge method, with mirroring inside the core at all four walls. Another possibility to calculate the electrical field inside and outside the transformer is to use additional core image charges [4], [5]. Their contour points are placed at the edges of the core window, as shown

5 JARITZ et al.: EXPERIMENTAL VALIDATION OF A SERIES PARALLEL RESONANT CONVERTER MODEL 3395 Fig. 5. Arrangement of the image charges and their contour points inside the transformer at the (a) core window and (b) outer edges of the transformer core. TABLE V COMPARISON BETWEEN 2-D FEM, CICM, AND THE MEASURED STRAY CAPACITANCE IN AIR in Fig. 5(a), and at the outer edges of the core, as shown in Fig. 5(b). They provide the ground potential and form the geometry. With this method, the areas above and below the transformer can be considered. In addition, arbitrary core geometries as well as winding arrangements can be included into optimization procedures minimizing the stray capacitance. The calculations are performed in free space, therefore, (8) and (11) in [1] can be simplified to E x = Q ( ) j x x j 2πɛ (x x j ) 2 + (y y j ) 2 (3) E y = Q ( ) j y y j 2πɛ (x x j ) 2 + (y y j ) 2. (4) Using the same integration lengths as for the leakage inductance, the stray capacitance related to the secondary side of the transformer then is determined by C stray = 2W e V 2 VoutPulsed with W e = l W ɛ r ɛ 0 2 (E 2 x + E2 y )dxdy where ɛ r is the permittivity of the dielectric. A comparison is given between the 2-D FEM, the core image charge method (CICM), and the measurements in Table V. No values are given for 3-D FEM because little deviations of the turns arrangement or the radii of the winding edges in the 3-D model lead to high deviations in the electrical field, respectively, in the capacitance. V. INSULATION DESIGN PROCEDURE The following section describes an insulation postdesign check that is performed after the transformer optimization (5) Fig. 6. (a) Potential lines with evaluated critical paths and (b) design curve and averaged cumulated electrical field strengths of the investigated paths Pa and Pb. Fig. 7. (a) Built transformer prototype. (b) Top view of the transformer without any mountings between primary and secondary inside the transformer. procedure in Fig. 2. It is not possible to integrate a full analytical model of the transformer in all details, e.g., bobbins

6 3396 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 43, NO. 10, OCTOBER 2015 and winding fastenings (Fig. 6) in the procedure. A basic insulation design is included in the optimization procedure by calculating the maximum electrical field and varying the distances between primary and secondary [1]. Partial discharges as well as sliding discharges can harm the insulation of the transformer permanently and lead to arcs between the windings or the core. In addition, the electrical strength of long oil gaps is decreasing due to the volume and the area effect [6]. Therefore, for long life times, a proper insulation design is necessary, and a detailed analysis of the electrical field distribution along creepage paths and long oil paths inside the transformer was carried out with the help of the Weidmann design curve method [7]. This design method is based on oil design curves that are derived from homogenous electrical breakdown tests [8]. These are then compared with the averaged cumulated electrical field strength E avg,cum along certain paths. Fig. 6(a) shows in an evaluated oil gap P b and a creepage path P a. For a valid design E avg,cum, both paths have to be below the design curve in Fig. 6(b). The design curves of the used transformer oil MIDEL7131 [9] are derived from [10] and [11]. With this method, insulations designs with homogenous as well as inhomogeneous field distributions can be investigated. Finally, applying this method leads to an electrical field conform design, which means that the potential lines just have a tangential component along insulation fastenings [Fig. 6(a)]. Hence, the insulator is stressed in normal direction by the electrical field and has its maximum electrical strength. Fig. 7(a) shows the built transformer prototype without any mountings between primary and secondary bobbins inside the transformer to avoid creepage paths between them, as shown in Fig. 7(b). The bobbins are fixed outside the transformer, leading to a longer creepage distance between the windings. The next section summarizes the built components of a single SPRC module. Fig. 8. Prototype modulator each leg with five switches in parallel, with two legs on one heat sink. Photo: Ampegon AG. Fig. 9. (a) Simplified diagram of the series capacitance. 896 NP0 capacitances and corresponding balancing resistors are distributed on four Printed circuit boards to provide optimal current sharing. (b) Built series capacitance C S. VI. COMPONENTS OF A SINGLE SPRC MODULE The following discussed components are related to the single SPRC module shown in Fig. 1 and are the results of the optimization procedure. Fig. 10. Prototype of the HF-air toroid coil L S formed by 22 turns. A. HF-MOSFET Modulator The modulator in Fig. 8 is operated at 100 khz and consists of 20 MOSFET switches, each leg with five switches in parallel, with two legs on one heat sink. For high lifetime, the calculated junction temperature swing T J of a single MOSFET is kept below 12 K at nominal pulse duty cycle [1]. B. Resonant Tank: Series Capacitance and Series Inductance Due to the high resonant current, the series capacitor C S is designed with respect to a balanced current sharing, and thus four double layered circuit boards are used (Fig. 9). NP0 dielectric ceramic capacitors are utilized for C S,which are stable in a wide range of temperatures and frequencies Fig. 11. (a) Simplified diagram of the rectifier including the parallel capacitance and the output filter. (b) Built rectifier with parallel capacitance C P and the output filter. and also do not suffer from dc voltage derating. The series inductance in Fig. 10 is built as an air toroid coil to avoid

7 JARITZ et al.: EXPERIMENTAL VALIDATION OF A SERIES PARALLEL RESONANT CONVERTER MODEL 3397 VIII. CONCLUSION In this paper, a comprehensive multidomain model of the SPRC is verified with a prototype of a single module by measurements. The simulated data show good accordance with the measured one. In addition, a comparison between the predicted parasitics like leakage inductance and stray capacitance of the transformer and the measured ones is given. The error between calculated and measured parasitics is low. An evaluation of the isolation of the transformer is also carried out. Additionally, different possibilities to realize the desired series inductance are discussed and compared by volume and losses. Fig. 12. Measured pulse V Out,meas (t) (50 MHz low pass filtered), simulated pulse V Out,sim (t), and averaged pulse V Out,avg (t). saturation and to minimize the losses due to the high current. Its winding consists of litz wire with 2000 mm 0.05 mm strands, eight wires in parallel and 22 turns. C. HV-HF-Transformer The high voltage (HV) high frequency (HF) transformer is shown in Fig. 7(a) and (b). To keep the losses low, ferrite as core material and litz wire for the windings are used due to the high operating frequency. Thin copper plates are used to transfer the heat out of the transformer to ambient. D. Rectifier, Parallel Capacitance, and Output Filter The rectifier is built of 156 diodes, 39 in series in each leg. Each layer of one circuit board is used for one diode leg and has to isolate the full output voltage of a single SPRC module. The parallel capacitance C P is built with 624 NP0 ceramic capacitors that are also used to symmetrize the voltage over each rectifier diode [Fig. 11(a)]. In addition, balancing resistors are also used to symmetrize the voltage over each diode and the output filter C 0 is realized as a series parallel connection of NP0 capacitors. REFERENCES [1] M. Jaritz and J. Biela, Optimal design of a modular series parallel resonant converter for a solid state 2.88 MW/115-kV long pulse modulator, IEEE Trans. Plasma Sci., vol. 42, no. 10, pp , Oct [2] G. Ivensky, A. Kats, and S. Ben-Yaakov, An RC load model of parallel and series-parallel resonant DC DC converters with capacitive output filter, IEEE Trans. Power Electron., vol. 14, no. 3, pp , May [3] A. Kats, G. Ivensky, and S. Ben-Yaakov, Application of integrated magnetics in resonant converters, in Proc. Conf. 12th Annu. Appl. Power Electron. Conf. Expo. (APEC), vol. 2. Feb. 1997, pp [4] N. H. Malik, A review of the charge simulation method and its applications, IEEE Trans. Elect. Insul., vol. 24, no. 1, pp. 3 20, Feb [5] H. Singer, H. Steinbigler, and P. Weiss, A charge simulation method for the calculation of high voltage fields, IEEE Trans. Power App. Syst., vol. PAS-93, no. 5, pp , Sep [6] A. Küchler, Hochspannungstechnik: Grundlagen Technologie Anwendungen (VDI-Buch). New York, NY, USA: Springer-Verlag, [7] F. Derler, H. J. Kirch, C. Krause, and E. Schneider, Development of a design method for insulating structures exposed to electric stress in long oil gaps and along oil/transformerboard interfaces, in Proc. 7th Int. Symp. High Voltage Eng. (ISH), 1991, pp [8] H. P. Moser, V. Dahinden, and H. Friedrich, Transformerboard: Die Verwendung von Transformerboard in Grossleistungstransformatoren. Basel, Switzerland: Birkhäuser, [9] MIDEL7131. [Online]. Available: accessed Sep. 6, [10] Q. Liu, Electrical performance of ester liquids under impulse voltage for application in power transformers, Ph.D. dissertation, Dept. Elect. Electron. Eng., Univ. Manchester, Manchester, U.K., [11] S. Blume, M. Jaritz, and J. Biela, Design and optimization procedure for high voltage pulse power transformers, in Proc. EAPPC, Michael Jaritz (S 13) was born in Graz, Austria, in He received the Dipl.-Ing. degree in electrical engineering from the Technical University of Graz, Graz, in His diploma thesis dealt with dc voltage link inverters in a power range of 500kW. He is currently pursuing the Ph.D. degree with the High Power Electronics Laboratory with a focus on series-parallel resonant converters, which are used in long pulse modulators generating highly accurate voltage pulses. VII. MEASUREMENTS In the following, the measurement results are presented. The green curve V Out,meas (t) in Fig. 12 shows the measured output voltage pulse V O1 of a single SPRC module. The simulated blue curve V Out,sim (t) shows good accordance with the measured one and the red curve V Out,avg (t) is the mean average of V Out,meas (t), used to determine the rise and the fall time. Rise and fall times are well below the given limits in Table I. Just a 300-μs pulseisshowninfig.12toshow the pulse rise and fall time in one picture. Sebastian Blume was born in Frankfurt am Main, Germany, in He received the degree in electrical engineering from the Karlsruhe Institute of Technology, Karlsruhe, Germany, with specialization on renewable energies focusing on power electronics. In his thesis, he investigated a new approach determining the harmonic emissions of Photo voltaics (PV) inverters at the Fraunhofer-Institut für Solare Energiesysteme, Freiburg im Breisgau, Germany, where he received the Dipl.-Ing. degree in He is currently pursuing the Ph.D. degree with the Laboratory for High Power Electronic Systems. He is involved in the development of Ultra High Precision Klystron Modulators for Compact Linear Colliders.

8 3398 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 43, NO. 10, OCTOBER 2015 David Leuenberger (S 14) received the M.Sc. degree in electrical engineering from the Swiss Federal Institute of Technology (ETH) Zurich, with a focus on power electronics and electrical drives. He is currently pursuing the Ph.D. degree with the Laboratory for High Power Electronic Systems, with a focus on inverters for grid connection of PV systems. He was an Engineer in Propulsion Control for Railway Application. Juergen Biela (S 04 M 06) received the Diploma (Hons.) degree from Friedrich-Alexander- Universitaet, Erlangen, Germany, and the Ph.D. degree from the Swiss Federal Institute of Technology (ETH Zurich), Switzerland, in 1999 and 2006, respectively. He dealt, in particular, with resonant dc-link inverters with the University of Strathclyde, Glasgow, U.K., and the active control of seriesconnected Integrated gate commutated thyristors with the Technical University of Munich, Munich, Germany, during his studies. In 2000, he joined the Research Department of Siemens Automation and Drives, Erlangen, where he was involved in inverters with very high switching frequencies, Silicon carbide components, and EMC. In 2002, he joined the Power Electronic Systems Laboratory (PES), ETH Zurich, for the Ph.D. degree with a focus on optimized electromagnetically integrated resonant converters. From 2006 to 2007, he was a Post-Doctoral Fellow at PES and a Guest Researcher with the Tokyo Institute of Technology, Tokyo, Japan. From 2007 to 2010, he was a Senior Research Associate at PES. Since 2010, he has been an Associate Professor of High-Power Electronic Systems at ETH Zurich. His current research interests include the design, modeling, and optimization of PFC, dc dc and multilevel converters with emphasis on passive components, and the design of pulsed-power systems and power electronic systems for future energy distribution.