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Modeling of Parasitic Elements in High Voltage Multiplier Modules

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Modeling of Parasitic Elements in High Voltage Multiplier Modules Modeling of parasitic elements in high voltage multiplier modules Jianing Wang 王 佳 宁 Electrical Power Processing (EPP) Group Electrical Sustainable Energy Department Delft University of Technology Modeling of parasitic elements in high voltage multiplier modules Proefschrift ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magnificus prof. ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties, in het openbaar te verdedigen op maandag 30 juni 2014 om 15.00 uur door Jianing Wang Master of Engineering, Power Electronics and Renewable Energy Center Xi’an Jiaotong University, China geboren te Anhui, China Dit proefschrift is goedgekeurd door de promotor: Prof. Dr. J.A. Ferreira Copromotor Ir. S.W.H. de Haan Copromotor Dr. Ir. M.D. Verweij Samenstelling promotiecommissie: Rector Magnificus voorzitter, Technische Universiteit Delft Prof. Dr. J.A. Ferreira Technische Universiteit Delft, promotor Ir. S.W.H. de Haan Technische Universiteit Delft, copromotor Dr. Ir. M.D. Verweij Technische Universiteit Delft, copromotor Prof. Dr. J.A. La Poutre Technische Universiteit Delft Prof. Dr. Ir. F.B.J. Leferink Universiteit Twente Prof. Dr. J.J. Smit Technische Universiteit Delft Prof. Dr. A. Yaravoy Technische Universiteit Delft Prof. Ir. L. Van der Sluis Technische Universiteit Delft, reservelid Copyright © 2014 by Jianing Wang All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without the prior permission of the author. ISBN: 978-94-6186-322-5 Acknowledgement Life is short. Life is to experience the necessary experiences. I sincerely appreciate anyone who makes a mark in the travel of my life. The research presented in this thesis was carried out at Delft University of Technology in the Netherlands, in the research group of Electrical Power Processing (EPP), cooperated with Philips Solid State Lighting. Here, I would like to express my deep appreciation for the people who directly contributes to the thesis. First of all, I would like to thank you, my promoter Professor Jan A. Ferreira. You always have positive attitude to my research and give me confidence when I am dispirited. Thank you very much. I would like to thank you, my daily supervisors, Associated Professor Sjoerd W.H. de Haan and Martin D. Verweij. Prof. de Haan, you taught me the importance of the writing and presentation of the research work, which I ignored before. Martin, you helped me greatly with your abundant knowledge on the EM fields and your friendship on my personal problems. Thank you both very much. I would like to thank you also, Dr. Peter Luerkens from Philips. You always gave me detailed and valuable comments on my research all the way along, without which I can hardly finish my work on time. Thank you very much. Furthermore, I would like to thank you, Frans Pansier from NXP. Your door is always open to me and your rich knowledge is always helpful to solve my strange questions. Thank you very much. I would like to thank you, Aniel Shri for the dutch translation of the summary and propositions of this thesis. In the end, I would like to thank you, my colleagues, Rob Schoevaars, Kasper Zwetsloot, Harrie Olsthoorn and Bart Roodenburg for the helps on the experiments and computers. I would like to thank you, Marcelo, Ilija, Yeh and Prasanth for the frequent discussions, which push my work forward step-by-step. Thank you very much. Last but not least, maybe more importantly, I would like to express all my appreciation to all the colleagues, secretaries, friends, families and people I met. You touched my heart, let me fell what life is and gave me joy and courage to go further and further. Thank you all very much. Especially, I would like to thank you, Prof. Xu Yang, my supervisor in master study, who took me into the world of power electronics and introduced EPP group. Without you, I can not join EPP group for the Ph.D study. Thank you very much. I would like to express my acknowledgement to the European Commission and the Dutch Ministry of Economic Affairs for supporting this project under envelope of the ENIAC project SmartPM with the Grant Agreement no. 120008 Abbreviations and Symbols 3D Three dimensional A, B ··· Node number A, B ··· AC Alternating current AC+ Upper AC side of multiplier AC- Lower AC side of multiplier a, b, m, p Parameters aCstru Ratio of the new added structural capacitance Cdt to the original structural capacitance Cdg C Capacitance CT Computed tomography C-V Capacitance voltage curve C.W. Cockcroft Walton C0 Per-unit-length capacitance of transmission line C1, C2 ··· Capacitor number 1, number 2 ··· CDcht Total equivalent parasitic capacitance of diode chains CTS Stray capacitance of transformer windings Cdd Structural capacitance between diodes in multiplier module Cdg Structural capacitance between diode and ground in multiplier module Cdpp Structural capacitance between diode and push-pull capacitors in multiplier module Ceac Equivalent capacitance of the rectifier in LCC by fundamental frequency analysis Cem Equivalent parasitic capacitance of multiplier Cj Junction capacitance of diode Cj0 Initial junction capacitance of diode with zero-bias Co Output capacitor in rectifier or multiplier Co1, Co2 ··· Output capacitor number 1, number 2 ··· Cp Parallel resonant capacitance Cpa Parasitic capacitance, in general Cpp Push-pull capacitors in multiplier Cppg Structural capacitance between push-pull capacitor and ground in multiplier module Cppgt Total structural capacitance between push-pull capacitor and ground in multiplier module Cs Series resonant capacitance Cstru Structural capacitances between the diode and other components in multiplier module, including the capacitances Cdg, Cdpp, Cppg, Cppgt D Diode DC Direct current Dch Diode chain d Distance D1, D2 ··· Diode number 1, number 2 ··· Dch1, Dch2 ··· Diode chain number 1, number 2 ··· E Vector indicating magnitude and direction of electric field E Magnitude of electric field EM Electromagnetic EMI Electromagnetic interference E0, E1 ··· Zero-order electric field, first-order electric field ··· th Ek k -order electric field Ent Electric field on the surface of the diode in the multiplier module without shielding trace Et Electric field on the surface of the diode in the multiplier module with shielding trace F Function FE Finite element f Frequency F Fourier transform GaN Gallium nitride GND Ground H Vector indicating magnitude and direction of magnetic field H Magnitude of magnetic field HV High voltage H0, H1 ··· Zero-order magnetic field, first-order magnetic field ··· th Hk k -order magnetic field I Time invariant current IGBT Insulated gate bipolar transistor i Unit vector ix, iy, iz Unit vector at x direction, y direction and z direction respectively i Time-varying current iCp Current through parallel resonant capacitance iCo1, iCo2 ··· Current through capacitor Co1, Co2 ··· iD1, iD2 ··· Current through diode D1, D2 ··· iLs Current through series resonant inductance iTLin Input current of transmission line io Output current irect Input current of multiplier irect(1) Fundamental element of input current of multiplier irect+ Input current of multiplier at AC+ side irect- Input current of multiplier at AC- side is Source current is 0,1 Source current correct up to and including the first-order quantity th is 0..k Source current correct up to and including the k -order quantity j Imaginary unit K Surface current density k Number Kr Surface current density as reference L Inductor LCC/SPRC Series parallel resonant converter LME Lumped multi element LV Low voltage l Length or physical dimensions, in general L0 Per-unit-length inductance of transmission line Lpa Parasitic inductance, in general Lpae Effective parasitic inductance Ls Series resonant inductance MOSFET Metal-oxide-semiconductor field effect transistor N Turn ratio of transformer nd Diode number per chain nst Number of stages in multiplier PCB Printed circuit board PRC Parallel resonant converter PWM Pulse width modulation Q Charge RL Load Rdp Damping resistor Reac Equivalent resistance of the rectifier in LCC by fundamental frequency analysis rCstru Reduction factor of the structural capacitance Cdg by adding the trace rE Reduction factor of the electric field rv Ratio of the voltage vdt to vdg S Spatial surface vector S Spatial surface scalar Si Silicon SiC Silicon carbide T Thickness t Time t1 Time instant 1 tVch1, tVch2 Time when voltages across diode chain are Vch1, Vch2 tpulse Width of a pulse tr Rise time of a pulse U0 Initial voltage V Time invariant voltage VBR Breakdown voltage of diode Vch1, Vch2 Voltages across diode chain Vk Voltage at node k Vo Output voltage Vpk Peak input voltage of multiplier v Time varying voltage vC1, vC2 ··· Voltage across capacitor C1, C2 ··· vCo1 Voltage across Co1 vDch1, vDch2 ··· Voltage across the diode chain Dch1, Dch2 ··· in the multiplier vTLin Input voltage of transmission line vac+ Unipolar input voltage of multiplier at AC+ side vac- Unipolar input voltage of multiplier at AC- side vcc1+, vcc2+ ··· Voltage on node cc1+, cc2+ ··· vcp Voltage across the parallel resonant capacitor vdd Voltage across the capacitance Cdd vdg Voltage across the capacitance Cdg vdt Voltage across the capacitance Cdt vin Input voltage vrect Input voltage of multiplier vrect(1) Fundamental element of input voltage of multiplier vs Source voltage
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