Application of Optimization Techniques to the Design of a Boost Power Factor Correction Converter

Applcaton of Optmzaton Technques to the Desgn of a Boost Power Factor Correcton Converter by Sergo Busquets-Monge Thess submtted to the Faculty of the Vrgna Polytechnc Insttute and State Unversty n partal fulfllment of the requrements of the degree of MASTER OF SCIENCE n Electrcal Engneerng Dr. Dushan Boroyevch, Charman Dr. Fred C. Lee Dr. Douglas K. Lndner July 2, 2001 Blacksburg, Vrgna Keywords: power electroncs, desgn optmzaton, contnuous optmzaton, dscrete optmzaton, genetc algorthm, power factor correcton, boost, EMI, EMC

Applcaton of Optmzaton Technques to the Desgn of a Boost Power Factor Correcton Converter by Sergo Busquets-Monge Dushan Boroyevch, Charman Electrcal Engneerng (ABSTRACT) Ths thess analyzes the procedural approach and benefts of applyng optmzaton technques to the desgn of a boost power factor correcton (PFC) converter wth an nput electromagnetc nterference (EMI) flter at the component level. The analyss s performed based on the partcular mnmum cost desgn study of a 1.15 kw unt satsfyng a set of specfcatons. A tradtonal desgn methodology s ntally analyzed and employed to obtan a frst desgn. A contnuous desgn optmzaton s then formulated and solved to gan nsght nto the converter desgn tradeoffs and partculartes. Fnally, a dscrete optmzaton approach usng a genetc algorthm s defned to develop a completely automated user-frendly software desgn tool able to provde n a short perod of tme globally optmum desgns of the system for dfferent sets of specfcatons. The software desgn tool s then employed to optmze the system desgn, and the savngs wth respect to the tradtonal desgn methodology are hghlghted. The optmzaton problem formulaton n both the contnuous and dscrete cases s presented n detal. The system desgn varables, objectve functon (system component cost) and constrants are dentfed. The objectve functon s expressed as a functon of the desgn varables. A computatonally effcent and expermentally valdated model of the system, ncludng second-order effects, allows the constrant values (also as a functon of the desgn varables) to be obtaned.

Acknowledgments Ths thess s the result of a jont effort of a number of colleagues and frends. Frst of all, I would lke to specally thank my advsor Dr. Dushan Boroyevch, a brllant engneer and excellent human beng, who lghted my way through the course of my graduate work and lfe at CPES for the past two years. Hs enthusasm, broad knowledge and sharp thnkng ganed my most sncere admraton. Hs carng and understandng touched me deeply. I would also lke to acknowledge and thank Dr. Douglas K. Lndner and Dr. Zafer Gurdal, from whose teachng, dscussons and contrbutons I ganed sgnfcant nsght nto the feld of desgn optmzaton. I am grateful to my professor Dr. Fred C. Lee for hs teachng and gudance throughout these two years at CPES. I feel ndebted for the opportunty to be a member of a center whose excellence would not be possble wthout hs tremendous efforts and brght leadershp. My sncere thanks to my frends Dr. Scott Ragon and Grant Soremekun, whose expertse n desgn optmzaton, hard work and patence made possble the applcaton of optmzaton technques. It has been a pleasure to work wth them and I greatly enjoyed our frendshp. I would also lke to express my grattude to my frend Dr. Chrstophe Creber, who not only provded the EMI modelng and expertse, but also guded all the other modelng work and created a healthy work envronment. I would lke to thank Dr. Henry Zhang, Ja We and Janwen Shao for ther contrbutons to the project gudance, boost nductor and layout desgn, and prototype testng. My specal thanks also to my frends Dr. Jose Burdo, Peter Barbosa and Francsco Canales for ther nvaluable help and teachng. Many thanks to my frend Erk Hertz, wth whom I most closely worked and who dd an excellent and huge job n buldng the prototypes and performng the expermental analyss. Many of hs nce deas were ncorporated n ths work. I thank hm for hs contrbutons and for makng the work so enjoyable.

I would also lke to thank Mr. Mchel Arpllere, Mr. Herve Boutller and Mr. Alan Tardy for ther gudance, encouragement and contrbutons to the development of a practcal desgn optmzaton tool, n especal for the tremendous effort to gather all the requred cost nformaton. Fnally, I would lke to extend my grattude to all other students and staff at CPES, for the nce envronment, help and frendshp they always provded. Ths work was supported by Schneder Electrc S.A. and made use of the ERC Shared Facltes supported by the Natonal Scence Foundaton under Award Number EEC-9731677. v

Table of Contents 1. Introducton... 1 1.1. Motvaton and Objectve... 1 1.2. Revew of Prevous Research... 2 1.3. Power Factor Correcton Unt Specfcatons... 4 1.4. Thess Outlne and Major Results... 6 2. Intal Converter Desgn... 7 2.1. Sngle-Phase Boost Power Factor Correcton Converter: Prncple of Operaton... 7 2.2. Power Stage Component Desgn... 9 2.2.1. General Desgn Process and Consderatons... 9 2.2.2. Desgn of the Boost PFC stage... 11 2.2.3. Desgn of the EMI Flter... 16 2.2.4. Magnetc Component Desgn... 24 2.2.5. Desgn Results... 26 2.3. Controller Desgn... 29 2.4. Functonalty... 29 3. Converter Desgn Optmzaton... 30 3.1. Introducton... 30 3.2. Contnuous Optmzaton... 30 3.2.1. Desgn Varables... 31 3.2.2. Objectve Functon: Cost of the System... 32 3.2.3. Constrants... 33 3.2.4. Desgn Analyss Models and Assumptons... 36 3.2.5. Optmzaton Results... 43 v

3.2.6. Dscusson... 46 3.3. Dscrete Optmzaton... 50 3.3.1. Desgn Varables... 50 3.3.2. Objectve Functon: Cost of the System... 51 3.3.3. Constrants... 52 3.3.4. Optmzaton Algorthm: DARWIN... 56 3.3.5. Software Tool: OPES... 60 3.3.6. Results... 64 3.3.7. Concluson... 71 4. Concluson and Future of Optmzaton n Power Electroncs... 72 4.1. Usefulness of Optmzaton n the Desgn of Power Electroncs Systems... 74 4.2. Possble Future Work... 76 4.2.1. Subsystem Desgn... 76 4.2.2. System Desgn... 77 References..78 Appendx A. Optmzaton Desgn Analyss Functon Computatons...82 Appendx B. Expermental Verfcaton of the Desgn Analyss Functon Predctons...148 Appendx C. Converter Desgn Condtons and Component Database... 169 Appendx D. Optmzaton Software.172 Vta... 173 v

Lst of Illustratons Fgure 1.1. Schematc of the PFC front-end converter.... 4 Fgure 2.1. Sngle-phase boost PFC converter [5].... 7 Fgure 2.2. Man steady-state waveforms.... 8 Fgure 2.3. Desgn process dagram... 9 Fgure 2.4. Output voltage range based upon 2.2% tolerance n the average output voltage and a 0 µf output boost capactor.... 12 Fgure 2.5. Current through L B and swtch S duty rato... 12 Fgure 2.6. Equvalent conducton model for the MOSFET swtch.... 14 Fgure 2.7. Equvalent conducton model for the IGBT swtch, fast dode and rectfer dode... 15 Fgure 2.8. BS EN 55011 regulaton lmts... 16 Fgure 2.9. System schematc, ncludng LISN, EMI flter and sngle-phase boost PFC stage... 18 Fgure 2.10. Tme doman evoluton of an equvalent voltage source substtutng the commutaton cell.... 19 Fgure 2.11. Equvalent mpedance dagram of the whole system shown n Fgure 2.9... 20 Fgure 2.12. Dfferental and common mode dsturbance levels n the voltage across resstor ZN.... 22 Fgure 2.13. Total LISN EMI levels on resstor ZN.... 22 Fgure 2.14. Dfferental and common mode dsturbance levels n the voltage across resstor ZN.... 23 Fgure 2.15. Total LISN EMI levels on resstor ZN.... 23 Fgure 2.16. Desgn procedure of ron powder core boost nductors... 25 Fgure 3.1. Boost nductor desgn varables... 32 v

Fgure 3.2. Core temperature as a functon of the hours of operaton for Mcrometals T184-26 core. The lfe of the core s assumed to termnate after a certan temperature rse has been acheved... 38 Fgure 3.3. Thermocouple placement for the measurement of the devce s heat snk temperature.... 39 Fgure 3.4. System topology ncludng parastcs. Those crcled are the parastcs to whch the EMI levels are hghly senstve.... 40 Fgure 3.5. Measurement of swtch dran / collector-to-ground parastc capactance.... 41 Fgure 3.6. Measurement of the choke parastc dfferental mode nductance.... 42 Fgure 3.7. Measurement of the parastcs RLb and CLb n the boost nductor.... 42 Fgure 3.8. Requred attenuaton of the mnmum-order harmonc EMI nose level as a functon of the swtchng frequency.... 48 Fgure 3.9. Requred attenuaton of the mnmum-order harmonc EMI nose level as a functon of the swtchng frequency (close-up vew of low swtchng frequences).... 48 Fgure 3.10. Qualtatve descrpton of the varaton of the optmum desgn components cost and total components cost as a functon of the swtchng frequency... 49 Fgure 3.11. Genetc algorthm procedure.... 58 Fgure 3.12. Specfcatons and condtons.... 61 Fgure 3.13. Inductor core database.... 61 Fgure 3.14. Man wndow.... 62 Fgure 3.15. Desgn report nformaton... 63 Fgure 3.16. Sngle Desgn Analyss Mode... 63 Fgure 3.17. Total EMI nose, dfferental and common mode nose and L B current n the case Vn=230 Vrms for (a) Optmum B and (b) Optmum C.... 68 Fgure 3.18. Qualtatve descrpton of the varaton of the optmum desgn components cost as a functon of the swtchng frequency.... 69 v

Fgure 3.19. Prototype correspondng to Optmum B... 70 Fgure 4.1. Cost evoluton of the dfferent desgns... 72 Fgure A.1. EMI flter and boost PFC stage schematc... 84 Fgure A.2. Voltage waveform across C B.... 84 Fgure A.3. Smplfed representaton of the MOSFET and gate drver... 94 Fgure A.4. Turn-on of S (MOSFET).... 95 Fgure A.5. Turn-off of S (MOSFET)... 95 Fgure A.6. Equvalent crcut dagram durng t=t1 t2 (turn-on) (bold) and t=t8 t9 (turn-off) (talcs)... 96 Fgure A.7. Equvalent crcut dagram durng t=t2 t3, t=t3 t4 (turn-on) (bold) and t=t6 t7, t=t7 t8 (turn-off) (talcs).... 96 Fgure A.8. Reverse-recovery phenomena model... 99 Fgure A.9. Boost nductor desgn varables n the contnuous approach... 104 Fgure A.10. Turn-on transent topology.... 112 Fgure A.11. Turn-on transent of the current through the boost nductor... 112 Fgure A.12. Tme doman evoluton of the commutaton cell equvalent voltage source... 119 Fgure A.13. Equvalent mpedance dagram of the whole system (LISN + EMI flter + boost PFC stage).... 122 Fgure A.14. Cost of the boost nductor wre and manufacturng and ts approxmaton by a frstorder polynomal functon of the wre volume... 130 Fgure A.15. Heat snk cost as a functon of the nverse of the thermal resstance and polynomal approxmaton... 131 Fgure A.16. Boost nductor cost as a functon of the volume of the core and polynomal approxmaton... 133 Fgure A.17. Dfferental mode capactor cost as a functon of the capactance and polynomal approxmaton... 135 x

Fgure A.18. Common mode capactor cost as a functon of the capactance and polynomal approxmaton... 136 Fgure B.1. Measured total EMI nose.... 153 Fgure B.2. Predcted total EMI nose n the conservatve case... 154 Fgure B.3. Predcted total EMI nose n the average case.... 155 Fgure B.4. Predcted total EMI nose n the non-conservatve case.... 155 Fgure B.5. Measured dfferental mode nose... 156 Fgure B.6. Measured common mode nose... 156 Fgure B.7. Predcted dfferental and common mode nose n the conservatve case... 157 Fgure B.8. Predcted dfferental and common mode nose n the average case.... 157 Fgure B.9. Predcted dfferental and common mode nose n the non-conservatve case.... 158 Fgure B.10. Measured total EMI nose.... 160 Fgure B.11. Predcted total EMI nose n the conservatve case... 161 Fgure B.12. Predcted total EMI nose n the average case.... 162 Fgure B.13. Predcted total EMI nose n the non-conservatve case.... 162 Fgure B.14. Measured dfferental mode nose... 163 Fgure B.15. Measured common mode nose... 163 Fgure B.16. Predcted dfferental and common mode nose n the conservatve case... 164 Fgure B.17. Predcted dfferental and common mode nose n the average case.... 164 Fgure B.18. Predcted dfferental and common mode nose n the non-conservatve case.... 165 Fgure B.19. Measures (total nose).... 167 Fgure B.20. Measures (dfferental mode nose)... 168 Fgure B.21. Measures (common mode nose).... 168 Fgure D.1. Desgn analyss and desgn optmzaton software (Software.zp, 8,990KB)... 172 x

Lst of Tables Table 1.1. General specfcatons.... 5 Table 1.2. Standards to satsfy.... 5 Table 2.1. Specfcatons.... 21 Table 2.2. Total component cost for the dfferent desgns, expressed as the addton of the cost of the cores, capactors, devces and heat snk.... 27 Table 3.1. Contnuous optmzaton desgn varables.... 31 Table 3.2. Desgn varable values and cost for the manual and optmum desgns... 45 Table 3.3. Constrant Statuses for the Manual and Optmum Desgns.... 46 Table 3.4. Dscrete optmzaton desgn varables.... 50 Table 3.5. Swtchng frequency and average boost nductance for optmum desgns A, B and C.... 65 Table 3.6. EMI flter, boost PFC, and total cost for optmum desgns A, B and C.... 66 Table 3.7. Boost PFC components cost for optmum desgns A, B and C.... 66 Table 3.8. Dfferent constrant values of the optmum desgns A, B and C.... 67 Table 3.9. Practcal selecton of swtchng frequences for optmum desgns A, B and C.... 70 Table A.1. Programmng constants... 83 Table A.2. General condtons / specfcatons.... 83 Table A.3. Boost capactor (C B ): 68µF, 450 V.... 85 Table A.4. Boost nductor wre.... 85 Table A.5. Boost nductor mscellaneous... 85 Table A.6. Devces voltage ratngs... 86 Table A.7. Devces current ratngs.... 86 Table A.8. Swtch... 86 x

Table A.9. Drver.... 87 Table A.10. Heat snk... 87 Table A.11. Prnted crcut board (PCB)... 88 Table A.12. Standard... 88 Table A.13. Voltage ratngs.... 88 Table A.14. LISN components... 88 Table A.15. Parastc elements of the propagaton paths.... 89 Table A.16. Other EMI constants... 90 Table A.17. Swtch parameters.... 92 Table A.18. Brdge dode parameters... 97 Table A.19. Fast dode parameters... 98 Table A.20. Boost nductor core parameters... 100 Table A.21. Codfcaton of the dfferent core types... 101 Table A.22. Boost nductor wre parameters... 101 Table A.23. Boost nductor number of turns... 102 Table A.24. Common mode choke parameters... 102 Table A.25. Dfferental mode capactor Cx parameters.... 102 Table A.26. Common mode capactor Cy parameters.... 103 Table A.27. Contnuous optmzaton desgn varables.... 104 Table A.28. Breakdown of the cost of several boost nductors... 129 Table A.29. Thermal resstance heat snk-to-ambent and cost for several heat snks.... 131 Table A.30. Volume and cost of several boost nductor cores... 132 Table A.31. Common mode nductance and cost of several common mode chokes... 134 Table A.32. Capactance and cost of several dfferental mode capactors... 134 x

Table A.33. Capactance and cost of several common mode capactors.... 136 Table A.34. Proposed new defnton of the boost nductor core parameters.... 145 Table B.1. Devaton wth respect to the nomnal value of dfferent parameters and magntudes.... 148 Table B.2. Condtons... 149 Table B.3. Measures and predctons.... 149 Table B.4. Condtons: Modfed L B s T225-26 wth 75 turns... 150 Table B.5. Measures and predctons.... 150 Table B.6. Condtons: Modfed swtchng frequency Fs = 55 khz... 151 Table B.7. Measures and predctons.... 151 Table B.8. Condtons... 152 Table B.9. Measures and predctons.... 152 Table B.10. Condtons... 153 Table B.11. Condtons... 159 Table B.12. Measures and predctons.... 159 Table B.13. Condtons: Common mode choke s SDI 142-22 (Lcm=3.3mH).... 160 Table B.14. Condtons... 166 Table B.15. Measures... 166 Table B.16. Condtons... 167 Table C.1. Number of components of each type n the database.... 171 x

CHAPTER 1. INTRODUCTION 1.1. Motvaton and Objectve The desgn of power electroncs systems nvolves a large number of desgn varables and the applcaton of knowledge from several dfferent engneerng felds (electrcal, magnetc, thermal and mechancal). In order to smplfy the desgn problem, tradtonal desgn procedures fx a subset of the desgn varables and ntroduce assumptons (smplfcatons) based on the desgner s understandng of the problem. These smplfcatons allow an ntal desgn to be obtaned n a reasonable amount of tme, but further teratons through hardware prototype testng are usually requred. The ablty and expertse of the desgner usually leads to good, but not optmum, desgns. Mathematcal optmzaton technques offer an organzed and methodcal way of approachng the desgn problem. They allow the desgner to use more desgn varables and fewer smplfcatons. Ths, n turn, reduces the number of teratons durng the hardware-testng phase. The ncreasng speed of computer hardware and the development of faster computatonal models allow optmum desgns to be obtaned n a relatvely short tme. Furthermore, the applcaton of the optmzaton technques can provde a better understandng of the tradeoffs nvolved n the desgn, and may even hghlght some that were ntally gnored. Several optmzaton algorthms can be appled to solve a desgn problem. Among them, the tradtonal gradent-based algorthms have been wdely appled to solve contnuous desgn varable problems. Other stochastc approaches such as genetc algorthms have been also successfully appled to solve both contnuous and/or dscrete desgn varable problems. The two types of algorthms present dfferent advantages. The am of the present work s to study and hghlght the benefts of applyng these optmzaton technques to the desgn of a low-cost boost power factor correcton (PFC) frontend converter wth nput electromagnetc (EMI) flter, the ultmate goal beng to develop a practcal and user-frendly software tool able to automatcally obtan wthn a short desgn tme the mnmum-cost desgns for dfferent sets of specfcatons and condtons. 1

Hopefully, ths work wll contrbute to the enhancement of the desgn methodology n the feld of power electroncs, leadng to automatc and faster desgn methods that are able to provde mproved desgn solutons. 1.2. Revew of Prevous Research Even though there s not a broad range of lterature on the topc of optmzaton n power electroncs, a few efforts have been made n the past. Some dscuss the partculartes and advantages of applyng optmzaton technques n the desgn of power electroncs systems, and present a contnuous varable optmzaton approach appled to the desgn of the power stage of buck, boost, buck-boost and half-brdge DC-DC converters [1,2,3]. Passve components, swtchng frequency and teffcency are consdered to be contnuous desgn varables (several desgn varables related to the core and wndngs are consdered to defne the nductors). The objectve functon to mnmze s the weght of the converter. Constrants are defned accordng to the desgn specfcatons and physcal lmtatons. An optmzaton algorthm known as the ALAG (Augmented Lagrangan) penalty functon s selected to solve the problem. Several optmum desgn solutons are obtaned by settng the swtchng frequency at dfferent values and the results are then analyzed. The swtchng frequency s fxed n order to allevate convergence dffcultes that mght otherwse cause a substantal ncrease n the requred computaton tme. Another paper ntroduces several mprovements nto the prevous optmzaton approach n order to obtan a practcal nonlnear optmzaton tool [4]. The methodology s demonstrated n the case of the half-brdge converter desgn. The paper dscusses how the number of desgn varables can be reduced n order to smplfy the desgn problem. Also, decouplng the desgn problem nto two or more sub-desgn optmzaton problems s suggested whenever the nterrelaton of the sub-desgn problems s weak. In order to facltate the use of the software developed, the equatons that model the desgn problem are separated from the optmzaton algorthm codfcaton, so that a user-frendly revew of the problem formulaton s allowed. Last, snce the desgn varables are consdered contnuous, but real components are only avalable wth dscrete values of ther defnng parameters, a methodology s proposed to obtan realstc desgn results. Ths methodology conssts of runnng the optmzaton, fxng the desgn varables of one of the components to ther closest real values, and then rerunnng the optmzaton. The process s 2

repeated untl all the desgn varables contan values correspondng to avalable components. In a later paper [5], ths tool [4] s used n the desgn of a boost PFC converter. In all prevous artcles, the desgn varables refer only to those components that can be easly consdered to be defned by contnuous real values, such as capactors, resstors, cores and wres. Others, such as the devces, are consdered to be fxed. Ths s a result of the fact that the nature of the desgn problem s essentally dscrete; therefore, the use of contnuous optmzaton technques has ts lmtatons. The defnton of the effcency as a desgn varable s qute questonable from a conceptual pont of vew. The authors ntroduced ths desgn varable to avod havng to defne an teratve computatonal method to estmate ts value, snce there s no explct equaton for calculatng the effcency of the system as a functon of the desgn varables. Instead, they decded to use the optmzaton algorthm tself as the teratve method for obtanng the effcency value, by defnng a desgn varable as the effcency and then establshng a constrant so that the calculated value of the effcency matches the assumed value n the desgn varable. As mentoned, the desgn of a boost PFC converter s consdered n prevous research [5]. But a varable hysteress control strategy s consdered for the swtch, as opposed to the fxed frequency strategy consdered n the present work. Addtonally, snce no nput flter and no EMI requrements are consdered n the desgn problem, the optmzaton runs, whch consder the rpple allowed n the boost nductor current as a desgn varable, presented a dscontnuous current mode soluton as the optmum, snce for ths case the boost nductor sze and weght are mnmzed. Ths forced the authors to set the rpple n the boost nductor to an estmated good value, leavng as desgn varables only those referrng to the boost nductor confguraton. A more approprate desgn optmzaton problem formulaton should therefore nclude the nput EMI flter and the EMI requrements. On the other hand, the authors decded to set the desgn varable effcency to 95% n the optmzaton runs, whch n the opnon of the author of the present text consttutes an unnecessary restrcton on the desgn problem formulaton. More recent efforts toward the applcaton of optmzaton technques to the desgn of power converters can be found [6,7]. One proposes the use of genetc algorthms to optmze the desgn of the power converter [6]. The desgn problem s decoupled nto the desgn of the power stage and the desgn of the controller, and these are optmzed separately. The only desgn 3

varables consdered are the passve components that defne both subsystems: the resstors, capactors and nductors. Each of these components s defned by a real number specfyng the correspondng resstance, capactance and nductance. The objectve functon or ftness value assgned to each desgn ncludes electrcal performance nformaton manly. Another paper presents a software tool developed to ad n the desgn of power electroncs systems [7]. An expert system and knowledge base helps n the selecton of power and control topologes and components. Contnuous varable optmzaton technques are appled n the desgn of magnetc components. The electrcal models contaned n the software tool appear to be farly complete and detaled. 1.3. Power Factor Correcton Unt Specfcatons The goal s to fnd the lowest-cost desgn of a boost PFC front-end converter wth nput EMI flter (Fgure 1.1) that meets a set of specfcatons. The load contans an addtonal EMI flter, an nrush current crcutry and an electrolytc capactor C Load. The general specfcatons are presented n Table 1.1, and Table 1.2 summarzes the standards wth whch t must comply. EMI Flter Boost PFC L B D F + P out Load Inrush Crcut CM Choke D R v n C X C Y C X S C B V out EMI Flter C Load C Y - Fgure 1.1. Schematc of the PFC front-end converter. 4

Table 1.1. General specfcatons. Magntude Value Vn (Vrms) 180 264 180 240 (Complyng wth IEC 1000-3-2 [8]) F_lne (Hz) 47.5 63 P out (W) 1150 Llne (µh) 750 C Load (µf) 624 1060 Maxmum Vout (V) 375 Vout_nrush (voltage above whch the nrush resstor n load s shorted) (V) 200 Storage: -25 80 Ambent temperature ( C) Nomnal Operaton: -10 50 * Operaton wth Current Deratng: -10 60 Maxmum unt physcal dmensons (mm) 130 x 105 x 40 Unts per year 20000 * Intally, the maxmum temperature consdered was 40 C. Table 1.2. Standards to satsfy. Type Standard Level EN 55011 Conducted: Class B (Publc sector) Emsson IEC 61800-3 (1) Radated: Class B (Publc sector) 61000-4-2 (Level 3) 61000-4-3 (Level 3) EMC 61000-4-4 (Level 4) Immunty * IEC 61800-3 61000-4-5 (Level 3) IEC 6100-4-X 61000-4-6 (Level 3) 61000-4-11 (Level 3) 61000-4-12 (Level 3) Input harmonc current IEC 61000-3-2 [8] Class A * These specfcatons wll not be consdered n the desgn process. They wll be expermentally verfed afterwards. 5

Other specal specfcatons are: The load can change from 100% to 0% n t 1ms, and from 0% to 100% n t 1ms (to be consdered n the control desgn). The PFC stage should be able to operate wth an nput voltage V n = 100 Vrms and P out =555 W. (Ths specfcaton wll not be consdered n the desgn process. It wll be expermentally verfed afterwards.) In a hot state (after one or two hours of operaton) the PFC stage must be able to provde P out =1750 W for 15 seconds wthout any PFC and electromagnetc compatblty (EMC) requrement. (Ths specfcaton wll not be consdered n the desgn process. It wll be expermentally verfed afterwards.) 1.4. Thess Outlne and Major Results The thess s organzed n the followng manner. In Chapter 2, a set of manual desgns s generated followng a tradtonal desgn methodology. In Chapter 3, optmzaton technques are appled to the desgn problem. Formulatons and solutons are presented for both a contnuous varable optmzaton that s ntended to provde nsght nto the converter behavor and desgn tradeoffs, and later, for a dscrete varable optmzaton. A user-frendly software tool, based on the dscrete optmzaton formulaton, s presented. Ths software tool allows the novce desgner to quckly and automatcally obtan the mnmum-cost desgns for dfferent sets of specfcatons and condtons. The best desgn obtaned usng ths tool s compared to the ntal ones, and the mprovements are hghlghted. Fnally, n Chapter 4, the thess s concluded and a bref dscusson on the future of the applcaton of optmzaton technques n the desgn of power electroncs systems s presented. 6

CHAPTER 2. INITIAL CONVERTER DESIGN 2.1. Sngle-Phase Boost Power Factor Correcton Converter: Prncple of Operaton Many applcatons requre an ac-to-dc converson from the lne voltage. In ts most smple form, ths converson s performed by means of a brdge rectfer and a bulk capactor. The bulk capactor flters the rectfed voltage and provdes certan energy storage n case of a lne falure. But the resultant lne current pulsates, causng a low power factor due to ts harmoncs and ts dsplacement wth respect to the lne voltage. In many countres, ths low qualty n the power usage s not acceptable above certan mnmum power levels, and the correspondng standards requre mproved techncal solutons. One of the topologes most commonly used to deal wth ths problem s the so-called sngle-phase boost PFC (see Fgure 2.1). s(t) Fgure 2.1. Sngle-phase boost PFC converter [5]. 7

In ths confguraton the actve swtch s controlled so that the average (n a swtchng perod) nput current s shaped as a snusod n phase wth the nput voltage, therefore substantally mprovng the power factor. Addtonally, the dc output voltage s regulated wthn a bandwdth of less than the lne frequency. All ths s acheved by sensng the nductor current, comparng t to a sensed rectfed nput voltage (scaled accordng to the low-frequency error n the output voltage), and usng the resultant sgnal to generate the control for the swtch [9]. The scheme s smple and relable, and t s wdely used n ndustry. The man steady-state waveforms of the system are depcted n Fgure 2.2. It s mportant to note that the average output voltage (V CB_dc ) must be greater than the peak nput voltage (v n ) for the system to operate normally (provdng PFC n the nput). Ths output voltage presents a rpple of frequency twce the lne frequency due to the nstantaneous power mbalance between the nput and the output. The harmoncs n the nput current due to the swtchng are fltered by means of an EMI flter n order to meet the lmt set by the correspondng standard. d(t) 1 t d ( t) = s( t) dt t Ts Ts: Swtchng perod v CB (t) v n (t) LB (t) v CB (t) t V CB_dc v n (t) LB (t) t Fgure 2.2. Man steady-state waveforms. 8

2.2. Power Stage Component Desgn 2.2.1. General Desgn Process and Consderatons The general desgn process followed to obtan the ntal desgns s summarzed n Fgure 2.3. Specfcatons + Choce of Fs + Choce of I LB(max) + Assumpton of T J (max) n the swtch S + Assumpton of d/dt swtchng + Assumpton of leakage nductance n common mode choke Cost V CB_dc, C B, I CB (rms) L B I LB (rms) I LB (peak) Inrush transent analyss C Y I CY_rms V S (peak) I S (rms)/ I S (av) V DF (peak) I DF (av) I DF_FSM V DR (peak) I DR (av) I DR_FSM L CM I choke_rms C X I CX_rms Selecton S Selecton D F Selecton D R Magnetcs desgn Losses n devces Magnetcs desgn Heat snk desgn Fgure 2.3. Desgn process dagram. 9

The desgn of the system s performed based on the worst case dentfed n each nstance. The desgn process begns wth the selecton of swtchng frequency Fs and the maxmum current rpple through the boost nductor L B, I LB(max). The juncton temperature of the swtch S, T J (max), the value of the d/dt of the current through S and D F n the swtchng transtons, and the leakage nductance n the common mode choke, CM Choke, must be assumed. In the next step, the average output voltage and output boost capactance are selected accordng to the specfcatons. Ths selecton s dscussed n Secton 2.2.2.1. Once these two values are determned, the rest of the components n the converter can be desgned. The boost nductor nductance and current ratngs can be determned. These calculatons are gven n Secton 2.2.2.2. In Secton 2.2.2.3, the selecton of the devces s dscussed. An ntal study of the nrush transents and the possble desgn solutons to handle them s requred n order to determne some of the devce ratngs. Once the devces are selected, the desgn of the heat snk can be performed from the estmaton of ther losses. In Secton 2.2.3, the methodology for the desgn of the EMI flter s presented. Fnally, the detaled desgn of the magnetc components (boost nductor and common mode choke) s dscussed n Secton 2.2.4. In the desgn of the system, several tradeoffs are dentfed. The optmum swtchng frequency and boost nductor current rpple are not clear due to the exstence of these tradeoffs. Therefore, n the frst stage, t was decded that some desgns for several pars of values of the swtchng frequency/boost nductor current rpple should be explored n order to nvestgate the aforementoned tradeoffs and to dentfy the swtchng frequency / boost nductor current rpple range n whch the cheapest desgn could be found. In Secton 2.2.5, a descrpton of the desgns obtaned for the varous pars of swtchng frequency / boost nductor current rpple values s presented. The am of ths chapter s to descrbe n general the desgn process followed and to present the results obtaned. A more detaled descrpton of the desgn process and the equatons used can be found n a prevous report [10]. 10

2.2.2. Desgn of the Boost PFC stage The boost PFC stage s desgned n terms of the worst case: mnmum nput voltage and maxmum load. 2.2.2.1. Boost Output Capactor and Average Output Voltage Due to the weak nteracton between the desgn of the boost capactor and those of the remanng components, the man goal here was to select the average output voltage and boost capactance n order to mnmze the cost of ths capactor whle meetng the specfcatons. In the specfcatons, the maxmum nstantaneous output voltage s 375 V. The mnmum average output voltage can be determned from the maxmum nput voltage for whch the PFC standard must be satsfed, as 240 Vrms*sqrt(2) = 340 V. The tolerance n the value of the average output voltage due to the tolerances n the control IC and the output voltage dvder network has been estmated to be 2.2%. To estmate the sze of the boost capactor requred, t s mportant to remember that an nternal capactor exsts n the load, whch has a mnmum capactance of 624 µf. From the analyss, t turned out that there s no boost capactance requred n ths stuaton. The hghest possble nomnal average output voltage s selected to maxmze the range of voltages for whch PFC can be acheved. Ths nomnal average output voltage s 359 V. The maxmum nput voltage for whch PFC can be acheved gven ths nomnal average output voltage s 248 Vrms. The soluton selected s depcted n Fgure 2.4. Even though no need for a boost capactor was dentfed, t was decded that a 68 µf boost capactor should be chosen to avod possble nteractons between the boost power stage and the EMI flter contaned n the nput of the load. Ths capactor also provdes some addtonal margn n the desgn. 2.2.2.2. Inductance and Current Ratngs of the Boost Inductor The determnaton of the boost nductor nductance can be obtaned from the choce of the maxmum boost nductor current rpple and swtchng frequency. The saturaton of the core s neglected, and therefore a sngle value of nductance s consdered for the entre half lne cycle. 11

In ths stuaton, the maxmum current rpple occurs when the duty cycle s 0.5, as shown n Fgure 2.5. Voltage (V) 375 367 359 v CB_dc maxmum v CB_dc nomnal 351 v CB_dc mnmum v CB v CB_dc 340 t (s) Fgure 2.4. Output voltage range based upon 2.2% tolerance n the average output voltage and a 0 µf output boost capactor. LB (t)(a) LB (t) nmax(t) Inmax_pk dimax Lrpple (t) = LB (t) - nmax(t) d (t) 1 t Dmaxrpple = 0.5 t Fgure 2.5. Current through L B and swtch S duty rato. 12

Once the nductance has been determned, the rpple on each swtchng cycle s computed, and usng ths nformaton, the peak and rms values of the boost nductor current are calculated. 2.2.2.3. Devce Selecton and Heat Snk Desgn 2.2.2.3.1. Inrush Transents Inrush transents resultng from start-up and fast dsconnect from / reconnect to the mans must be consdered for converter layout and devce selecton. These transents cause both an nrush current through the dodes and boost capactor, and an overshoot n the voltage across the boost capactor and swtch. A SABER model was developed to study these nrush transents [11]. The worst-case scenaro for both nrush current and voltage overshoot was dentfed. In the case of nrush current, the worst case occurs durng fast dsconnect from / reconnect to the mans. The worst case for voltage overshoot occurs durng start-up. From the results of these smulatons, the recommended ratngs to allow the dfferent components to wthstand these transents wthout any addtonal crcutry are as follows. Boost Capactor: Rectfer Brdge: Fast Dode: Swtch: V max = 400V I max = 20Arms I FSM = 150A I FSM = 150A V BR = 500V (MOSFET) V BR = 600V (IGBT) Snce these ratngs are reasonable, t was consdered to be more cost-effectve to deal wth the nrush transents by ncreasng the component ratngs nstead of ntroducng addtonal crcutry, whch adds sgnfcant cost to the converter and whch may also decrease the overall relablty. 13

2.2.2.3.2. Devce Selecton From the boost nductor current waveform obtaned n Secton 2.2.2.2 wthout takng nto account the effect of saturaton of the core, the steady-state operaton current ratngs of the swtch (IGBT: average current; MOSFET: rms current), fast dode (average current) and rectfer dodes (average current) can be obtaned. Now that the current and voltage ratngs have been obtaned, the cheapest devces meetng these ratngs can be selected from a database of components. 2.2.2.3.3. Heat Snk Desgn The losses of the devces are computed, takng nto account both conducton and swtchng losses. The detaled models can be found n Appendx A or n a prevous report [10]. In the case of a swtch MOSFET, a statc model consstng of a resstor that s dependent on the juncton temperature of the devce s consdered for the estmaton of the conducton losses (see Fgure 2.6). A dynamc model, together wth the parastc capactance values, other specfc parameters of the devce (such as the threshold voltage, etc.), and the values of the voltage, on-resstance and off-resstance of the gate drver that are n agreement wth the swtchng assumed d/dt, are used to estmate the swtchng losses that occur due to overlap of the sem-deal (wthout consderng voltage and current overshoots) current and voltage waveforms. The losses due to the parastc nductance n seres wth the swtch, whch causes over-voltages durng turn-off of the devce, are also estmated. Fnally, the losses due to the dsspaton of the energy stored n the Coss (dran-to-source capactance) durng turn-on are also calculated. S (MOSFET) R on Fgure 2.6. Equvalent conducton model for the MOSFET swtch. 14

In the case of the swtch IGBT, a statc model consstng of a resstor n seres wth a voltage source (see Fgure 2.7) s consdered for the estmaton of the conducton losses. To estmate the swtchng losses, the expermental parameters Eon and Eoff provded n the data sheet for a gven swtch current and voltage are used. These parameters specfy the energy lost durng the swtchng transtons. The parameters are scaled lnearly accordng to the voltage and current for whch the energy lost n the transtons should be estmated. Ths approach, based on expermental parameter nformaton, was chosen due to the lack of a smple dynamc model able to accurately estmate these losses. S (IGBT) D R, D F Ron V F Fgure 2.7. Equvalent conducton model for the IGBT swtch, fast dode and rectfer dode. In the case of the fast dode, a statc model consstng of a resstor n seres wth a voltage source (see Fgure 2.7) s consdered for the estmaton of the conducton losses. The swtchng losses due to overlap of the sem-deal current and voltage waveforms are neglected, snce n a boost confguraton of the pulsewdth modulaton (PWM) swtch, these losses take place manly n the swtch. Estmaton of the reverse-recovery losses nvolves use of the expermental parameter Qrr n the data sheet approxmated as a functon of the forward current and provded for a gven swtchng d/dt. Ths parameter specfes the extra charge requred to turn off the dode that results n addtonal losses. These losses do not exclusvely take place n the fast dode. Part of the losses are dsspated n the swtch. Ths has been taken nto consderaton n the models and usually a 50/50 share of the losses has been assumed. In the case of the rectfer dode, a statc model consstng of a resstor n seres wth a voltage source (see Fgure 2.7) s consdered for the estmaton of the conducton losses. 15

From ths devce loss nformaton, the heat snk can be desgned. A sngle heat snk for all the devces was assumed n these ntal desgns, and the mnmum heat snk sze to avod heat snk temperatures above 80 C (maxmum temperature allowed n an external heat snk) was selected. It was assumed that for a heat snk temperature of 80 C none of the devces would have a juncton temperature beyond ts correspondng maxmum. 2.2.3. Desgn of the EMI Flter Ths secton presents the methodology appled to the desgn of the EMI flter n order to guarantee complance wth the correspondng standards. 2.2.3.1. EMI Standards BS EN 55011 [12] and CISPR 16-2 [13] are the standards relevant to the conducted EMI nose lmts n the nput of the converter. The former descrbes the lmts and test condtons under whch the converter must comply wth regulatons. The quas-peak lmt spectrum n the voltage across the LISN resstors for Class A, Group 1 and Class B, Group 1 of the apparatuses s presented n Fgure 2.8. (dbµv) 80 Class A Class B 70 60 50 1.E+05 100k 1.E+06 1M F(Hz) 1.E+07 10M 1.E+08 100M Fgure 2.8. BS EN 55011 regulaton lmts. For commercal sale, an nput EMI flter must be added to the boost PFC stage n order to lmt conducted emssons. The topology selected s shown n Fgure 1.1. The common mode choke s defned by the common mode nductance (Lcm) and the parastc (leakage) dfferental mode nductance (Ldm). Cy and Cx are the common and dfferental mode capactances, 16

respectvely. Lcm and Cy confgure the common mode flter, and Ldm and Cx the dfferental mode flter. The modelng approach and desgn process appled to obtan the desgn of the EMI flter n these frst manual desgns s presented next. 2.2.3.2. System Modelng Approach for EMI Analyss The desgn procedure s based on a frequency doman model descrbed n other work [14, 15]. It s based on both a complete representaton of possble propagaton paths for dfferental and common mode dsturbances and a frequency doman representaton of conducted EMI sources present n the converter (exstng n both types of propagaton paths). The propagaton path model takes nto account CISPR 16-2 test condtons (ground plane, LISN, etc ) and a hgh-frequency model representaton of the converter, ncludng parastcs. By accountng for the effects of the test condtons n the flter desgn, the teratons n the desgn process are mnmzed. The fundamentals of the modelng approach appled to estmate the EMI levels are presented next. The dagram n Fgure 2.9 represents all the components of the system and the parastcs consdered. The crcut components are shown n black, whle the crcut parastcs are shown n red. The commutaton cell can be represented by an equvalent voltage source wth the tme doman voltage waveform shown n Fgure 2.10 for only two swtchng perods. In fact, the duty rato of the swtch vares for each swtchng perod. As a result, the perod of the voltage waveform Vds(t) s equal to half of the lne perod. But snce the rectfer brdge changes the polarty of the voltage each half lne perod, ths voltage, Vds(t), propagates to the system located before the brdge rectfer wth a perod equal to the lne perod. Ths voltage source can be approprately characterzed n the frequency doman by means of the Laplace transformaton, followed by applcaton of the approprate converson to the Fourer representaton. In essence, by means of these steps, the prevous voltage waveform s represented by an addton of snusods, each at a multple of the fundamental frequency (n ths case, the lne frequency). For each of these frequences, and assumng that the system s symmetrc between the mans and the rectfer brdge (wth respect to ground), t s possble to derve from Fgure 2.9 the dagram shown n Fgure 2.11. 17

The commutaton cell n Fgure 2.11 has been represented as a snusodal voltage source (Vpert) correspondng to the harmonc of the relevant frequency. The dfferent mpedances (Z#) correspond to the system components and parastc mpedances at ths frequency. Lres LN lh Llha Ldm A C1 CN Cfy + Vn lm ZN Cfx Lcm Cfx ZN - C1 CN Cfy LN ld Lldb Ldm B Llmg g RLb E CLb Lblkg D CONMUTATION CELL K A DR Lb DF CAg CEg CDg Swtch Cb CKg B CBg S F LFS CFg CSg g Fgure 2.9. System schematc, ncludng LISN, EMI flter and sngle-phase boost PFC stage. 18

Vds(t) Rngng (not ncluded) Vbus_DC 0 Ts 2*Ts d_vec *Ts d_vec (+1) *Ts t(s) Fgure 2.10. Tme doman evoluton of an equvalent voltage source substtutng the commutaton cell. Hence, by usng standard electrcal network analyss methods, t s now possble to compute, for each desred frequency, the perturbaton voltage levels n the LISN resstors (ZN). In ths project, the quas-peak standard lmts defned for the voltage levels n the LISN resstors have been consdered. A maxmum voltage level s specfed at each frequency. However, ths maxmum not only refers to the voltage harmonc at ths specfc frequency, but to a bandwdth of frequences (9 khz) around the relevant frequency. In fact, the operaton of the measurement devce whle obtanng the quas-peak level at one specfc frequency (f * ) can be compared to obtanng the square root of the quadratc sum of all the harmoncs wthn f * - bandwdth/2 and f * + bandwdth/2. Computng all harmoncs to be able to precsely emulate the behavor of the measurement devce would be too labor-ntensve n terms of the computatons nvolved. Only the sgnfcant levels (those at the frst multples of the swtchng frequency) are estmated. These estmatons are obtaned by computng the square root of the quadratc sum of several harmoncs around some multples of the swtchng frequency. To speed up the analyss, not all harmoncs n the bandwdth are normally computed. The level obtaned s consequently corrected by addng a certan amount of db. Ths amount depends upon the number of harmoncs consdered. Ths estmaton s then compared to the maxmum quas-peak level defned by the standard for the consdered frequency. In the partcular topology studed here, the dfferental and common mode EMI levels can be easly dentfed, snce the odd harmoncs correspond to dfferental mode nose and the even harmoncs to common mode nose. Therefore, the dfferental mode nose level at each multple 19

of the swtchng frequency can be evaluated by calculatng the square root of the quadratc sum of the odd harmoncs around ths frequency. The same approach s taken for the common mode nose level, except that the even harmoncs are used n the calculatons. The square root of the quadratc sum of the dfferental and common mode levels s equal to the total nose. The decomposton of the total nose nto dfferental and common mode nose provdes valuable nformaton for estmatng the ndvdual performances of the dfferental and common mode parts of the flter, and wll therefore be an ad n the desgn. Z1 Z4 Z8 Z13 Z17 D Vn + - I 1 Z2 I 2 Z6 I 4 Z9 Z11 I 12 Z23 I 6 Z15 Z24 G I 13 Z22 I 8 I 10 Z19 Z20 + - Vpert Z3 I 3 Z7 I 5 Z10 Z12 I 7 Z16 I 9 Z21 I 11 S Z5 Z14 Z18 Fgure 2.11. Equvalent mpedance dagram of the whole system shown n Fgure 2.9. 2.2.3.3. Desgn Process The followng desgn process can be performed usng any of the avalable software tools ( Canalyze.m and Danalyze.m functons mplemented n MATLAB and the fnal OPES-PFC Boost Rectfer tool), whch are descrbed n Chapter 3 and n Appendx A, and whch can be found n Appendx D. Frst of all, t s mportant to hghlght that the value of Ldm s dependent on the value of Lcm, snce the former s a parastc of the common mode choke. The Ldm has been assumed to be 3% of Lcm whenever expermental measurements of the leakage nductance were not avalable. The desgn process can be outlned as follows: 20

1. Fx Cy to 10 nf (ths s the maxmum allowed value n order to lmt the leakage current n the common mode capactors). Assume some ntal value for the common mode choke nductance (Lcm) and Cx. 2. The Lcm should be ncreased (f the common mode nose s above the standard) or decreased (f below the standard) untl the common mode nose level reaches the lmt mnus 3 db (equvalent to checkng that the constrant related to common mode nose s equal to zero). 3. The Cx should be ncreased (f the dfferental mode nose s above the standard) or decreased (f below the standard) untl the dfferental mode nose level reaches the lmt mnus 3 db (equvalent to checkng that the constrant related to dfferental mode nose s equal to zero). 2.2.3.3.1. Desgn Example In ths example, the specfcatons n Table 2.1 are consdered. Certan components have been selected for the devces, and a certan desgn for the boost nductor. Table 2.1. Specfcatons. Magntude P out V out V n Fs Lne nductance Value 1000 W 353 V 230 Vrms 40 khz 200 µh 1. Intal guess: Cy = 10 nf; Lcm = 400 µh; Cx = 0.9 µf. The results obtaned are depcted n Fgures 2.12 and 2.13. These results clearly show that ths frst guess s not so bad (t was chosen n order to shorten the teraton process presented here). However, both the common and dfferental mode levels are hgher than the standard lmts mnus 3 db. The total level therefore surpasses the standard lmt. 21

CMC and DMC dsturbance levels n the voltage across one of the LISN leg resstors: 140 Dfferental mode harmoncs (quadratc sum) Common mode harmoncs (quadratc sum) 120 Standard 100 Magntude (dbuv) 80 60 40 20 0 10 4 10 5 10 6 10 7 Frequency (Hz) Fgure 2.12. Dfferental and common mode dsturbance levels n the voltage across resstor ZN. 140 120 Dsturbance levels n the voltage across one of the LISN leg resstors: All computed harmoncs Quadratc sum Standard 100 Magntude (dbuv) 80 60 40 20 0 10 4 10 5 10 6 10 7 Frequency (Hz) Fgure 2.13. Total LISN EMI levels on resstor ZN. 2. Increase Lcm to 600 µh. The results obtaned are presented n Fgures 2.14 and 2.15. It can be observed that both the common and dfferental mode levels are now at around the standard lmt mnus 3 db. Fgure 2.15 shows that the total EMI nose level meets the standard. Snce the dfferental mode level s already at around the standard lmt mnus 3 db, there s no need to proceed to step 3 n the desgn process, whch would nvolve varyng the Cx to adjust the dfferental mode level. 22

CMC and DMC dsturbance levels n the voltage across one of the LISN leg resstors: 150 Dfferental mode harmoncs (quadratc sum) Common mode harmoncs (quadratc sum) Standard Magntude (dbuv) 100 50 0 10 4 10 5 10 6 10 7 Frequency (Hz) Fgure 2.14. Dfferental and common mode dsturbance levels n the voltage across resstor ZN. 160 140 Dsturbance levels n the voltage across one of the LISN leg resstors: All computed harmoncs Quadratc sum Standard 120 Magntude (dbuv) 100 80 60 40 20 0-20 10 4 10 5 10 6 10 7 Frequency (Hz) Fgure 2.15. Total LISN EMI levels on resstor ZN. 2.2.3.4. Accuracy and Effectveness of the System Model and Desgn Methodology Appled It s dffcult to accurately measure or estmate the system parastcs consdered n the system model. Ths essentally mples the model s lack of accuracy n predctng the hghfrequency (n the order of MHz) EMI levels. Due to the lack of accuracy n the parastc estmaton, t has been decded not to nclude the rngng n the model of the voltage across the commutaton cell (see Fgure 2.10). Ths rngng also affects the levels at hgh frequency, and s dependent on parastc values. Therefore, the model does not provde an accurate estmaton of the EMI levels at hgh frequences. However, t s observed that, n general, the crtcal harmoncs (those closer to the standard lmts) that drve the desgn of the EMI flter are those centered at the frst multples of the swtchng frequency above the ntal frequency for whch the standards are defned (150 khz). Consequently, a model that correctly predcts the levels at 23

these frequences s, n most cases, suffcently accurate. The modelng approach presented here has the capablty of good accuracy at low frequences. Of course, ths accuracy s stll dependent on the accuracy of the estmaton of the parastcs (gudelnes n the estmaton of the man parastcs are presented n Sectons 3.2.4.1.2 and 4.2.3 n a prevous report [10]). Ths s especally crtcal n the case of the parastc swtch capactance dran-to-ground (or collector-toground) wth respect to the common mode EMI nose level. Specal accuracy n the estmaton of ths parastc should be pursued. If ths s not possble, the desgn obtaned by means of the desgn process presented wll probably requre some practcal adjustments to tghtly meet the standard levels. The desgn process presented does not consder the possblty of system nstablty / hgh oscllatons n the nterconnecton of the EMI flter and the boost PFC stage. Ths could occur whenever the magntude of the output mpedance of the flter s hgher than the nput mpedance of the boost PFC stage. Should ths nstablty / hgh oscllaton occur, a hgher value of some of the EMI flter components should be chosen n order to decrease the magntude of the output mpedance and to solve the nstablty / hgh oscllaton problem. Further studes of ths ssue led to the concluson that n PFC operaton, nstablty s mprobable (snce the operatng pont s constantly varyng), but that there could be sgnfcant oscllatons that would mply the necessty for hgh current ratngs n the flter components. 2.2.4. Magnetc Component Desgn 1 2.2.4.1. Boost Inductor Desgn Once the nductance and current ratngs for the boost nductor are known, the next step s to select a core, a wre gauge and the number of turns n order to obtan a fnal desgn. A bref study (both analytcal and expermental [10]) hghlghted ron powder torods as the most costeffectve choce for the core materal and shape. The desgn process followed has been extracted from the correspondng catalog [16]. Ths process s descrbed n the followng subsecton. 2.2.4.1.1. Desgn Procedure of Iron Powder Core Boost Inductors 1. Select core materal permeablty. 24

2. Compute the product of 0.5LI 2 where: L = requred nductance (µh) and I = peak value of the lne frequency component of the current (A). sze. 3. Locate the 0.5LI 2 value on the catalog s energy storage table. Fnd the approprate core 4. Read the nomnal nductance ratng, A L, of ths core sze from the core data sheet. 5. From the permeablty vs. energy storage curves, obtan the percentage of ntal permeablty, pu, at the energy storage. 6. Calculate the number of turns that yelds the requred nductance by means of the expresson: L n = 1000. A pu L 7. Choose the approprate wre sze usng a wre table. Ths desgn procedure can be summarzed as shown n the block dagram of Fgure 2.16. Gven L(uH), I pk (A) Select permeablty. Energy storage 1 2 K = LI. 1 2 pk Energy storage table Select core sze. Core data sheet A L of the core Get pu value. n = Permeablty vs. energy storage curves 1000 L A pu L I pk I rms = 2 I A W > J rms m Select a wre. I pk : Peak value of nductor current (A) I rms : Rms value of nductor current (A) A W : Wre cross-secton area (cm 2 ) J m : Maxmum current densty (A/cm 2 ) n : Number of turns A L : Nomnal nductance ratng (mh/1000 turns 2 ) pu : Per unt value of ntal permeablty Fgure 2.16. Desgn procedure of ron powder core boost nductors. 1 Work performed by Ja We 25

It s the understandng of the author that the prevous desgn procedure leads to desgns that wll guarantee at least the specfed nductance value over the range of operatng currents, allowng a small percentage of saturaton. In a PFC applcaton, for whch a precse nductance value s not requred, ths may lead to sub-optmal desgns. Allowng a hgher level of saturaton to occur, even f ths saturaton s sgnfcant at hgh current levels, may generate less expensve overall system desgns. Ths desgn mprovement s usually acheved through expermental teratons. 2.2.4.2. Common Mode Choke Desgn The desgn of the common mode choke s smlar to that of a normal transformer wth a turns rato of 1:1. Ferrte torod was selected as the most approprate core materal and shape for ts mplementaton. 2.2.5. Desgn Results Several values of the swtchng frequency and the maxmum current rpple through the boost nductor have been consdered n order to explore whch s the optmum value range for these desgn varables. In the followng, nne desgns are presented. They all make the followng assumptons: T J(max) of S = 100 C (ths value s an estmaton of the juncton temperature of the swtch for a gven external sngle heat snk desgn, such that ts temperature s the maxmum admssble (80 C)). d/dt = 100 A/µs These nne desgns dffer only n the choce of swtchng frequency (Fs) and the maxmum current rpple across the nductor ( I LB(max) ). Addtonally, the desgns for Fs=100 khz and Fs = 70 khz consder the use of a MOSFET for the mplementaton of the swtch S, whle the desgns for Fs = 40 khz and Fs = 30kHz consder the use of an IGBT. Ths s due to the fact that the IGBT presents lower conducton losses and hgher swtchng losses than the MOSFET. Therefore, the former s more sutable for low swtchng frequences, and the second for hgh swtchng frequences. 26

Table 2.2. Total component cost for the dfferent desgns, expressed as the addton of the cost of the cores, capactors, devces and heat snk. Fs (khz) 100 70 I LB _max (%Inmax_pk) 45 30 15 30 Cost (%) * 90.7 93.2 100 84.1 Fs (khz) 40 30 I LB _max (%Inmax_pk) 45 30 15 45 30 Cost (%) * 70.5 71.83 80.5 68.4 * Ths s the percentage wth respect to the cost of the desgn at Fs = 100 khz and I LB _max = 15 %. Sgnfcant current osclatons n the EMI flter components were detected n these two desgns. The cost of the dfferent heat snks n monetary unts (m.u.) has been approxmated by the expresson: Cost_Heat Snk=K HS / Rth_ HS (m.u.), where K HS (m.u.*( C/W)) was a constant, the determnaton of whch was based on the cost of a typcal heat snk. Table 2.2 shows that the cheapest desgns are obtaned for a low swtchng frequency and a hgh boost nductor current rpple. However, desgns wth a sgnfcantly low swtchng frequency mght present oscllatons. The desgn at Fs = 40 khz and I LB _max = 45 % (of Inmax_pk) was fnally selected for mplementaton. 2.2.5.1. Comments on the Results From the results obtaned for the nne desgns nvestgated, the followng observatons can be made. For a gven current rpple through the boost nductor L B, as the swtchng frequency decreases, the sze of the boost nductance L B ncreases. However, the dfferental part of the EMI flter (L DM, C X ) and the comon mode choke (L CM ) decrease, and there s a decrease n losses 70 27

(lower cost of the heat snk) due to the reduced number of commutatons n a lne perod, whch suggests a possble tradeoff. For a gven swtchng frequency, as the desred current rpple through the boost nductor L B ncreases, the sze of the boost nductor s consderably reduced. Also, losses due to dode reverse recovery are reduced because current through the dode s lower durng turn-on of the swtch. However, the sze of the dfferental part of the EMI flter ncreases, especally f the swtchng frequency s hgh, due to the fact that the EMI requrements are strct at hgh frequences (f the swtchng frequency s low there s no sgnfcant ncrease n the sze of the dfferental part of the EMI flter). On the other hand, as the current rpple ncreases, the copper losses n the boost nductor also ncrease, leadng to hgher boost nductor temperatures. The boost nductor s desgned based on a targeted value of the boost nductance. However, desgns allowng more varaton of the boost nductance value over half the lne cycle (allowng more saturaton to occur) mght be less expensve overall. In general, the conducton losses n an IGBT are lower than n a MOSFET, but the IGBT s swtchng losses are hgher for the same swtchng frequency. MOSFETs are then more sutable for hgh swtchng frequences, and IGBTs are more sutable for low ones. However, at ntermedate swtchng frequences, there s not a clear best choce; n ths case the selecton depends on the characterstcs of the partcular devces, ther cost, and the cost of the heat snk per unt of power loss. On the other hand, the cheapest devces meetng the current and voltage ratngs are not necessarly the optmum choce. The optmum value of the swtchng frequency and boost nductor current rpple depends on the relatve cost of the dfferent elements ntegratng the converter, especally the boost nductor, the EMI flter components and the heat snk. The concluson from the nformaton presented up to ths pont s that the best choce seems to keep the swtchng frequency as low as possble wthout producng sgnfcant oscllatons. The optmum value of the boost nductor current rpple s not as easy to predct, and should be obtaned consderng the possble tradeoffs and the relatve cost of the dfferent components. Ths optmum value, however, seems to be relatvely large. 28

2.3. Controller Desgn The constant-frequency average-current-mode control for contnuous-current-mode operaton was chosen as the control strategy for the swtch [17]. It was desgned based upon nformaton provded n the SGS-Thompson applcaton note for the L4981A PFC control IC [11]. No feed-forward network was mplemented to compensate for varatons n the nput lne voltage. 2.4. Functonalty The functonalty of the converter was evaluated through smulatons and experments [11]. SABER swtchng and average models were developed to perform the smulatons. The operaton of the crcut under normal condtons was verfed. Addtonally, the converter operaton was explored under other specal condtons, accordng to the specfcatons. Frst, the operaton of the system at nput voltages n the range of 248-260 Vrms at dfferent output loads was nvestgated. At these nput voltages, the output voltage s less than the nput lne voltage durng part of the lne cycle. Durng these ntervals, the converter operates as a rectfer, and the average output voltage reaches a hgher level (the output voltage does not, however, reach the 375 V maxmum). The rectfer behavor s caused by the fact that the voltage loop s saturated at ts most negatve value and consequently the swtchng stops. The converter resumes normal boost PFC operaton durng the entre lne cycle once the nput lne voltage s reduced below the correspondng hgh lne range (below 248 Vrms n the worst case). Second and last, the correct operaton of the system was also expermentally verfed at the worst case North Amercan lne voltage range (100 Vrms) for a maxmum power of 555 W, accordng to the correspondng specfcatons gven n Secton 1.3. 29

CHAPTER 3. CONVERTER DESIGN OPTIMIZATION 3.1. Introducton The desgn results at the component level presented n Chapter 2 hghlght the exstence of several tradeoffs and possble room for mprovement n the desgn of the power stage. To obtan the lowest-cost desgn that meets the specfcatons, the relatve cost of all components n the desgn process must be taken nto account together wth these tradeoffs and consderatons. Mathematcal optmzaton technques offer an organzed and methodcal way to reach ths goal. Intally, contnuous optmzaton algorthms were appled to the desgn problem. Some of the desgn varables (such as the devces) were held constant and others (such as capactances) were allowed to vary contnuously. The objectve of ths effort was to acqure a better understandng of the tradeoffs nvolved n the desgn and to explore potental tradeoffs not prevously dentfed [18]. After applyng the contnuous algorthms to the desgn problem, a genetc based dscrete optmzaton algorthm (DARWIN) was appled to the desgn of the power stage. The dscrete optmzaton algorthm s partcularly approprate for obtanng the globally optmum desgn. Ths algorthm operates drectly on all the dscrete varables, and there s no need to fx them or convert them to contnuous varables. Software featurng a graphcal user nterface was developed to run the optmzaton code (OPES), and optmum desgns were obtaned for three sets of specfcatons. The results obtaned are n accordance wth the understandng of the problem acqured n the prevous stage [19]. 3.2. Contnuous Optmzaton In the contnuous optmzaton approach for the component desgn of the system the output capactor C B and the average value of the output voltage (v o ) are fxed. Ths capactor s fxed because the nteracton of ts desgn wth the desgn of the rest of components s weak, and n case ths component were ntroduced as a desgn varable and ts nteracton wth the rest of the system were to be modeled, then a complex and computatonally expensve transent should 30

be ncluded n the analyss of each desgn n order to determne the mnmum surge current that the devces need to wthstand. For the mplementaton of the common mode choke, t was decded to choose among commercally avalable desgns,.e., avalable dscrete components. The core shape (torodal) and materal of the boost nductor L B represented n Fgure 3.1 are fxed. For the vablty of the applcaton of a contnuous varable optmzaton approach, all devces (rectfer dodes D R, fast dode D F, and controlled swtch S) are also fxed. The cheapest devces meetng the requrements of the system under study are chosen. In partcular, for the controlled swtch S, an IGBT wth an external ant-parallel dode was selected. However, other analyses consderng a MOSFET have been performed. It s possble to select ether a sngle heat snk or separated heat snks for all devces. In the optmzaton runs presented n ths secton, a sngle heat snk was selected. The layout s also assumed fxed, and the correspondng parastcs are estmated for a more accurate predcton of the EMI levels. 3.2.1. Desgn Varables The desgn varables n the contnuous optmzaton approach are presented n Table 3.1. Table 3.1. Contnuous optmzaton desgn varables. EMI flter Boost nductor (See Fgure 3.1) Cx (F) Cy (F) Lcm (H) nturn Aw (cm 2 ) OD (cm) ID (cm) Ht (cm) Dfferental mode capactance Common mode capactance Common mode choke nductance Number of turns Area of the wre copper Outsde dameter of the core Insde dameter of the core Heght of the core 31

Fs (Hz) Rth_hs_amb ( C/W) Swtchng frequency Thermal resstance of the sngle / swtch * heat snk to the ambent * A sngle heat snk or separated heat snks for all devces can be consdered. In the frst case, the desgn varable corresponds to the thermal resstance of the sngle heat snk. In the second case, t corresponds to the thermal resstance of the swtch heat snk. Ht ID OD Aw nturn Fgure 3.1. Boost nductor desgn varables. 3.2.2. Objectve Functon: Cost of the System In an optmzaton problem, the desgn varable values that maxmze or mnmze a gven objectve functon must be determned. In the case under dscusson, ths objectve functon s the cost of the system expressed as a functon of the desgn varables (3.1). The goal s to obtan the set of desgn varable values that mnmze ths functon. Sys_Cost = 2*Cost_Cx + 2*Cost_Cy + Cost_Choke + Cost_L B _core + Cost_L B _fxwrng + Cost_L B _varwrng + Cost_HS + Cost_S + Cost_D F + 4*Cost_D R + Cost_C B, (3.1) where talcs denotes varable costs. Gven a set of components and ther costs (see Appendx A), the cost of the dfferent components expressed n m.u. as a functon of the dfferent desgn varables has been approxmated n the followng manner. 1. Cost of the dfferental mode capactor: Cost_Cx=K1Cx+K2Cx*Cx 2, 32

where K1Cx, K2Cx = constants. 2. Cost of the common mode capactor: Cost_Cy=K1Cy+K2Cy*Cy, where K1Cy, K2Cy = constants. 3. Cost of the common mode choke: Cost_Choke = K1Lcm+K2Lcm*Lcm, where K1Lcm, K2Lcm = constants. 4. Cost of the boost nductor core: Cost_L B _core = K1L Bc +K2L Bc *Vc+K3L Bc *Vc 2, where K1L Bc, K2L Bc, K3L Bc = constants, and Vc s the volume of the core expressed n cm 3. 5. Fxed manufacturng cost of the boost nductor: Cost_L B _fxwrng = constant. 6. Cost of the boost nductor wre and varable manufacturng cost: Cost_L B _varwrng = Cost_wpv*Aw*MLT*nturn, where Cost_wpv = constant (m.u./cm 3 ), and MLT s the mean length per turn of the core, expressed n cm. 7. Cost of the heat snk/s: Cost_HS=K1HS+K2HS*(1/Rth_hs_amb), where K1HS, K2HS = constants. 3.2.3. Constrants The goal of the optmzaton procedure s to fnd the desgn varable values that mnmze the objectve functon whle satsfyng all constrants. These constrants have been specfed as follows. Geometrcal constrants: 33

cm. 1. The nternal dameter of the core must be smaller than the external dameter mnus 0.5 2. The wre should ft n the avalable wndow area of the core, accordng to the maxmum fllng factor (Ku). The area occuped by the wre s assumed to be the area of a square wth sde length equal to the dameter of the wre. Temperature constrants: 3. The temperature of the boost nductor core should be lower than ts maxmum (determned as explaned n Secton 3.2.4). 4. The juncton temperature of the swtch should be lower than ts maxmum, as specfed n the component data sheet (25 C were subtracted from ths maxmum to be more conservatve). 5. The juncton temperature of the fast dode should be lower than ts maxmum, as specfed n the component data sheet (25 C were subtracted from ths maxmum to be more conservatve). 6. The juncton temperature of the rectfer dode (or rectfer brdge) should be lower than ts maxmum, as specfed n the component data sheet (25 C were subtracted from ths maxmum to be more conservatve). 7. The temperature of the heat snk should be lower than ts maxmum. The maxmum temperature of the heat snk s 80 C n the case of an external heat snk, and 100 C n the case of an nternal heat snk. EMI constrants: 8. The dfferental mode dsturbance level for the group of harmoncs around the frst multple of the swtchng frequency above the mnmum frequency at whch the EMC standard lmts are defned (150 khz) should be lower than the standard level defned for ts frequency mnus 3 db. 9. The common mode dsturbance level for the group of harmoncs around the frst multple of the swtchng frequency above the mnmum frequency at whch the EMC standard lmts are defned should be lower than the standard level defned for ts frequency mnus 3 db. 34

Specal constrants: 10. The maxmum peak-to-peak current rpple n the boost nductor cannot be hgher than 150 % of the peak average (n a swtchng perod) boost nductor current. Ths constrant s set to lmt the amount of tme the converter operates n dscontnuous current mode. The models used n the analyss are only vald for contnuous current mode operaton. If the computatons were modfed to be able to account also for the dscontnuous current mode case, ths constrant could be removed. However, n all runs performed ths constrant was never actve, whch suggests that the contnuous current mode operaton s optmal for the problem analyzed. 11. The peak value of the flux densty n the boost nductor core cannot exceed the maxmum value defned for ts materal. Ths constrant can be removed f the saturaton of the core s modeled n the analyss. In ths case, ths constrant wll never be actve. However, even though n the case under dscusson the approprate equatons to model the saturaton of the core are ntroduced, ths constrant was retaned n case new materals were consdered for whch the saturaton models have not been not nserted n the analyss code. 12. The current densty n the boost nductor wre cannot exceed the maxmum current densty outlned for copper. Ths constrant s also not needed when the copper losses n the boost nductor wre are computed and ther effect on the boost nductor core temperature rse are consdered. Agan, ths s the case under dscusson, but the constrant was kept n the event that these models are removed. Boundares for the desgn varables: 13. The mnmum value of ID, OD, Ht, Lcm, Cx, and Cy s zero. 14. The mnmum value of the number of turns s one. 15. The mnmum bare area of the wre copper s 0.0202*10-3 cm 2 (correspondng to an AWG 44). 16. The mnmum thermal resstance of the heat snk s 0.1 (value correspondng to a good water coolng system). 35

17. The lower boundary for the swtchng frequency s 20 khz (audble range lmt) and the upper boundary s 150 khz (ntal frequency for whch the EMI standard lmts are defned). 18. The capactance of the common mode capactor Cy should not exceed 10 nf due to the maxmum leakage current allowed n the AC lne for safety reasons. All the constrants should be expressed n a normalzed form (see equatons n Appendx A, Secton A.2.5). 3.2.4. Desgn Analyss Models and Assumptons For computng the values of the varous constrants as a functon of the desgn varables, several models and assumptons have been appled. Here, the goal s to obtan a computatonally effcent method of calculatng the system responses, accurate enough to nclude all the mportant tradeoffs and fast enough to be able to perform a broad search of the desgn space n a reasonable perod of tme (optmzaton algorthms typcally requre that a large number of constrant evaluatons be performed for dfferent sets of desgn varable values). Steady-state algebrac models for the worst-case operaton were consdered. The mnmum nput voltage and maxmum average output voltage represent the worst case. The component tolerances are also taken nto account n the degree desred so that anywhere from the most pessmstc to the most optmstc predctons can be obtaned. The models used for the estmaton of the losses n the devces and the model to estmate the EMI levels have already been descrbed and dscussed n Sectons 2.2.2.3.3, 2.2.3.2 and 2.2.3.4. The estmaton of the temperature of the dfferent devces and heat snk/s s performed through a smple statc thermal lumped parameter model, n whch the lost power flows through the correspondng thermal resstance and causes a temperature rse. The models referrng to the boost nductor are modfed compared to the models dscussed n Chapter 2. More detaled models are now taken nto account. Second-order effects, such as the saturaton of the boost nductor core as a functon of the DC magnetzng force, AC flux densty, boost nductor core temperature and swtchng frequency, have been ncluded. Ths allows more degrees of freedom to optmze the desgn of the boost nductor. On the other hand, the skn and proxmty effects have also been ncluded. Losses n the wre and core are calculated 36

n order to predct the core temperature. Ths temperature s predcted by means of the followng [20]: o o P _ corelb( mw ) + P _ copperlb( mw ) TLB _ core( C) = Tamb( C) + TLbcoef ( 2 ), (3.2) Asurf cm where Tamb s the ambent temperature; Tlbcoef s the correcton coeffcent for the estmaton of the boost nductor core temperature; P_coreLb s the power lost n the boost nductor core; P_copperLb s the power lost n the boost nductor wre; and Asurf s the surface area of the boost nductor. Ths computaton s especally mportant, snce n Chapter 2 the core temperature was dentfed as a crtcal constrant. It s assumed that the temperature n all parts of the boost nductor s equal to the calculated temperature of the core. The coeffcent Tlbcoef allows adjustments to be made n the predctons of dfferent thermal scenaros (prototype exposed, prototype enclosed, use of a fan to cool down the boost nductor, etc ) and correctons to be made for the defcences of the models n predctng the boost nductor losses. Ths coeffcent could have also been appled to modfy the effectve surface area of the boost nductor (n the equaton, t could have drectly multpled Asurf). Several core materals are modeled: ron powder, hgh flux, molypermalloy, and kool Mµ. In the case of ron powder, the maxmum core temperature has a lmt based on relablty consderatons (.e., the thermal agng problem). Software provded by Mcrometals [21] was used to obtan predctons of the lfetme of a core as a functon of the ntal core temperature and other factors such as the swtchng frequency (see Fgure 3.2). The maxmum ntal core temperature for whch a lfetme of at least 20,000 hours was acheved was nvestgated. Ths was performed for each partcular Mcrometals ron powder core, by selectng a wndng, a low swtchng frequency (worst case), and typcal values for the other operatng condtons, then varyng the current flowng through the nductor untl the 37 0.833

lfetme predcted was 20,000 hours (ncreasng the current ncreases the losses and therefore reduces the lfetme). Once ths was obtaned, from the plot of the core temperature as a functon of the hours of operaton (see example n Fgure 3.2), the core temperature for zero hours of operaton was estmated and regstered as the maxmum ntal core temperature to guarantee a lfetme longer than 20,000 hours. The maxmum temperature of the wre (to avod damagng ts coatng) and the maxmum temperature of the PCB were also consdered. The mnmum of these three values was set as the maxmum core temperature n constrant number 3. Fgure 3.2. Core temperature as a functon of the hours of operaton for Mcrometals T184-26 core. The lfe of the core s assumed to termnate after a certan temperature rse has been acheved. All these models and assumptons, and the process followed to obtan the constrant values, are descrbed n detal n Appendx A. 3.2.4.1. Calbraton of the Models 3.2.4.1.1. Boost Inductor Core Temperature Predcton The core temperature rse s dependent on the prototype thermal condtons. On the other hand, the predcted losses may not match the real ones, snce the expermental data n whch these predctons are based was obtaned for a dfferent operatng condton (snusodal voltage appled to the core wthout any DC bas). The coeffcent Tlbcoef allows the predctons of these 38

dfferent thermal condtons and loss predcton errors to be adjusted. The value of ths coeffcent can be adjusted expermentally by means of the followng two-step process. 1) Tamb determnaton: Run an experment wth a prototype. Measure the devce s heat snk temperatures by usng (for example) the thermocouples, as shown n Fgure 3.3. Then, adjust the Tamb value n the model equatons so that the model predctons for the devce s heat snk temperatures match the measured values. The value of Tamb obtaned wll then represent the ambent temperature n the prototype envronment to be used n Equaton (3.2). Fgure 3.3. Thermocouple placement for the measurement of the devce s heat snk temperature. 2) Adjust then Tlbcoef n Equaton (3.2) so that the predcton usng ths equaton matches the measured core temperature. Ths temperature can be measured by placng a thermocouple nsde the wndng near the core. The value of Tlbcoef has been estmated to be 1.0 for a prototype wth a fan coolng the boost nductor and 1.3 for a prototype wthout a fan coolng the boost nductor, as shown n Appendx B. 3.2.4.1.2. EMI Levels Predcton To accurately ascertan the EMI levels, several parastcs need to be carefully measured or estmated. The most mportant parastcs are shown n Fgure 3.4 and are descrbed as follows. 39

RLb CLb E Lblkg D K Lres LN lh Llha Ldm A DR Lb DF + Vn - C1 C1 lm CN ZN ZN CN Cx Lcm Cy Cy Cx CAg B CBg CEg CDg Swtch S Cb CKg LN ld Lldb Ldm B F LFS Llmg CFg CSg g g Fgure 3.4. System topology ncludng parastcs. Those crcled are the parastcs to whch the EMI levels are hghly senstve. From the common mode nose pont of vew: 1. The swtch dran / collector-to-ground parastc capactance: Two capactances n parallel contrbute to the total swtch dran / collector-to-ground parastc capactance. These capactances are shown n Fgure 3.5 (C HM and C CG ). They can be measured by means of a network analyzer selectng a seres RLC confguraton. The results for both capactances are added to gve the fnal estmaton of the total swtch dran / collector-to-ground parastc capactance. The common mode nose levels are sgnfcantly senstve to the value of ths parastc. Therefore, an accurate estmaton of ts value s mportant. In one of the prototypes tested n Appendx B, the total collectorto-ground parastc capactance was 9 pf. In a second prototype t was 21.5 pf. From the dfferental mode nose pont of vew: 2. The choke parastc dfferental mode nductance: Fgure 3.6 shows the setup requred to measure the dfferental mode nductance of the common mode choke wth a network analyzer. In the contnuous optmzaton approach, the value of ths parastc has been assumed to be 0.2 % of the common mode nductance (Lcm), based on the dfferental mode nductance value measured for dfferent common mode chokes. 3. The boost nductor parastcs: 40

The parastcs consdered n the boost nductor are those shown n Fgure 3.4. The leakage nductance Lblkg s estmated by means of Equaton (3.3), whch s extracted from the manufacturer s catalog [22]: TolLblkg = 1.065 Ac Lblkg 1 292 nturn 8 (H), 100 lm 10 (3.3) where TolLblkg s the tolerance n the value of the leakage nductance; Nturn s the number of turns; Ac s the cross-sectonal area of the core (cm 2 ); and Lm s the mean magnetc path length (cm). The other two parastcs (RLb and CLb) are measured wth the network analyzer, usng the connecton confguraton shown n Fgure 3.7. Network analyzer C HM Swtch heat snk Metallc enclosure Collector / Dran PCB Network analyzer Ground connecton C CG Ground plane Fgure 3.5. Measurement of swtch dran / collector-to-ground parastc capactance. 41

Network analyzer Parastc capactance s not consdered Fgure 3.6. Measurement of the choke parastc dfferental mode nductance. Network analyzer Fgure 3.7. Measurement of the parastcs RLb and CLb n the boost nductor. On the other hand, the EMI model used to estmate the EMI nose levels consders only a sngle value of the boost nductance over half the lne cycle. Snce saturaton can occur, the boost nductance value vares over half the lne cycle. Whch value of the boost nductance should be consdered n the models to estmate the EMI nose? The value of L B n the range L B_mn L B L B_max that better approxmates a calbratng measurement wll be selected. From the experence of the authors, the average value over the lne cycle seems to be a good choce. 42

3.2.4.2. Expermental Valdaton Once calbrated, the models were expermentally valdated for dfferent operatng condtons. The detals of the dfferent experments performed and the comparson between predcted and expermental results can be found n Appendx B. 3.2.5. Optmzaton Results In the contnuous optmzaton approach to the power stage desgn (sngle-phase boost PFC and EMI flter) one MATLAB functon was developed: the Canalyze(x), avalable n Appendx D. Ths functon performs the cost and electrcal analyss of the system. The functon receves as nputs a vector x (the so-called desgn varables) and gves as outputs the value of the cost functon (the cost of the system n m.u.) and the values of the constrants defned for the problem. A summary of the specfcatons and addtonal performance nformaton for a gven set of desgn varables can be obtaned by settng an nternal varable n the program ( aff ) to one. The optmzaton results reported here correspond to optmzaton runs performed wth a prevous verson of the MATLAB functon Canalyze(x). In that verson, the effect of the ac flux on the saturaton of the core was not ncluded. Therefore, the analyss program predcted a hgher current rpple than would be expected. On the other hand, the skn and proxmty effects were not ncluded n the estmaton of the losses n the boost nductor wre. Ths, together wth the fact that the coeffcent to estmate the temperature rse of the boost nductor core was too low for the condtons n whch the converter operates, and that the ambent temperature was set to be 40 C, mples that the temperature of the core predcted by the software was probably too optmstc. Fnally, the fll factor was set to 0.3 and the maxmum rms current through the boost nductor wre to 600 A/cm 2 (both values are too conservatve). Snce both correspondng constrants (wound area and maxmum wre current densty) were actve (see Table 3.3), these conservatve values affected the result obtaned for the optmum. However, even though the results obtaned may not correspond to the real optmum desred, the conclusons reached are stll vald snce the verson of the analyss functon captured the essental behavor and tradeoffs of the system. In these optmzaton runs, the fxed desgn varables were as follows. 43

1. Swtch: IGBT + Ant-parallel dode 2. Brdge rectfer 3. Fast dode 4. Boost nductor core materal: ron powder wth a specfc permeablty 5. Boost capactor: 100 µf, 450 V Addtonally, a sngle heat snk for all devces was consdered. The functon Canalyze(x) was lnked to a commercal optmzaton software code called VsualDOC (VMA Engneerng) [23]. Both the Sequental Quadratc Programmng [24] and Modfed Method of Feasble Drectons [24] algorthms were utlzed n obtanng the present results. Constrant dervatves were computed usng fnte dfferences. The optmzaton algorthms used for the present work belong to a class of optmzaton algorthms termed gradent-based methods. In order to begn the optmzaton process, these algorthms are typcally provded wth an ntal desgn. Once an ntal desgn s specfed, gradents of the objectve functon and constrants are computed wth respect to the desgn varables n order to compute a search drecton n the desgn space. Next, the desgn space s searched along the computed drecton so as to mnmze the objectve functon whle satsfyng all the constrants. Gradents are then recomputed at the new desgn pont, and the process contnues untl no further mprovements are possble. If the desgn space contans several local mnma, there s a possblty that a gradent-based optmzer may be trapped by a local mnmum, and the answer wll depend on the selecton of the ntal desgn pont. In order to ncrease the probablty of fndng the pont wth the smallest objectve functon value (the global mnmum), t s customary to execute the optmzaton algorthm from several dfferent ntal desgns. In the present work, t was found that there were local mnma n the desgn space, although n all cases studed, even the local mnma were less expensve than the manual desgn. The results reported here correspond to the best desgn found durng the course of the study and t s lkely to be the globally optmum desgn. In Table 3.2, the value of the desgn varables for a manual desgn and the desgn obtaned by means of the optmzaton are presented. The cost of both desgns s also specfed. The manual desgn was obtaned by ntally fxng the value of the swtchng frequency to 40 44

khz and choosng a commercal core, whch seemed to be approprate accordng to the results of the ntal desgns presented n Chapter 2 (these values correspond to one of the best desgns reported). All the other desgn varables were adjusted manually wth the ad of the developed MATLAB functon, by assumng some ntal value, checkng the status of the constrants, and makng the correctons needed n order to meet all constrants whle mnmzng the cost as much as possble (to desgn the EMI flter, the process detaled n Secton 2.2.3.3 was appled). Table 3.3 shows the statuses of the constrants for both the manual and optmzed desgns. A constrant s classfed as actve when the boundary specfed on the desgn response s reached, nactve f the boundary specfed s not reached and volated f the response value goes beyond the boundary. Table 3.2. Desgn varable values and cost for the manual and optmum desgns. Desgn varable Manual desgn Optmum desgn Cx (µf) 2.8 2.23 Cy (nf) 5 7.58 Lcm (mh) 1.50 0.97 nturn 122 88 Aw (cm 2 ) 11.20*10-3 11.41*10-3 OD (cm) 4.45 4.62 ID (cm) 2.72 2.33 Ht (cm) 1.65 1.62 Fs (khz) 40 29.78 Rth_hs_amb (C/W) 2.20 2.38 Cost (%) * 100 90.7 * Ths s the percentage wth respect to the manual desgn cost. 45

Table 3.3. Constrant statuses for the manual and optmum desgns. Constrant ref. Manual desgn * Optmum desgn * 1. ID-OD I I 2. W A A A 3. T_core_Lb I A 4. Tjsw I I 5. Tjfd I I 6. Tjrd I I 7. Ths A A 8. DM A A 9. CM A I 10. dil I I 11. Bpk I I 12. L_rms A A 13-18. Bounds I I * A denotes actve constrant; I denotes nactve constrant. 3.2.6. Dscusson In the optmzaton runs performed, several tradeoffs and system behavor characterstcs were dentfed. They are dscussed next. For a gven Fs, there s a tradeoff among the desgn varables Lcm, Cx and boost nductor desgn varables, snce all of them contrbute to a reducton n the dfferental mode nose. The Cy also slghtly affects the dfferental mode level. The relatve cost-effectveness of these components determnes the optmum set of values that meet the constrant specfed for the dfferental mode nose. Note that a varaton n the desgn of the boost nductor would vary the optmum heat snk sze due to the varaton n the peak-to-peak current waveform that would n turn cause varatons n the swtchng losses. Therefore, for the estmaton of the costeffectveness of the boost nductor, the cost of the heat snk should be ncluded. Smlarly, for a gven Fs, there s also a tradeoff between Lcm and Cy, snce both desgn varables contrbute to the reducton of the common mode nose. 46

The selecton of the optmum value of the swtchng frequency s not obvous. If the value of the swtchng frequency (Fs) s fxed, and the optmum desgn s obtaned for a gven set of dfferent Fs values, the qualtatve cost behavor sketched n Fgure 3.10 could be observed for the EMI flter, heat snk and boost nductor. The heat snk cost ncreases wth an ncrease n the swtchng frequency, due to ncreased swtchng losses. The boost nductor cost ncreases as Fs decreases, due to an ncrease n the peak-to-peak current generatng an ncrease n the copper loss and because of an ncrease n the core loss, both of whch lead to an ncrease n the core temperature. Consequently, the nductance and / or nductor surface must ncrease to meet the constrant n the core temperature. The cost of the EMI flter depends essentally on the ampltude of the mnmum-order harmonc (group of harmoncs centered at multples of the swtchng frequency) of Vpert (Fgure 2.11, Secton 2.2.3.2) that enters nto the frequency range wthn whch the standard lmts are defned (150 khz - 30 MHz). Fgures 3.8 and 3.9 show the requred attenuaton for ths harmonc as a functon of the swtchng frequency, when all other desgn varables reman constant. Typcally, ths mnmum-order harmonc wthn the EMI range s placed between 150 khz and 500 khz, the range n whch the standard lmt has a slope of approxmately 20 db/dec. As Fs s ncreased, ths harmonc moves towards a hgher frequency at whch the standard lmt s lower. But snce the attenuaton of the EMI flter requred s hgher than 20 db/dec, the resultng cost of the needed EMI flter s lower. The dscontnutes n the EMI flter cost are due to the fact that, as Fs ncreases, new lower-order harmoncs (wth ncreasng ampltudes) enter nto the frequency range wthn whch the standard lmts are defned. For nstance, at Fs = 150 khz / 7 = 21.43 khz, the seventh harmonc needs to be lmted to the standard level for 150 khz. Smlarly, for the sxth harmonc at Fs = 25 khz, for the ffth harmonc at Fs = 30 khz, and so on. The mnmum of the addton of the cost of the EMI flter, the heat snk, and the boost nductor as a functon of the Fs determnes the optmum value of ths desgn varable. One of the most valuable results of ths optmzaton s the dentfcaton of ths mnmum. 47

35 Frequency sweep of the requred nose attenuaton 30 Requred attenuaton (dbuv) 25 20 15 10 5 0 20 40 60 80 100 120 140 160 Frequency (khz) Fgure 3.8. Requred attenuaton of the mnmum-order harmonc EMI nose level as a functon of the swtchng frequency. 14 Frequency sweep of the requred nose attenuaton 12 Requred attenuaton (dbuv) 10 8 6 4 2 0 20 22 24 26 28 30 32 34 36 38 Frequency (khz) Fgure 3.9. Requred attenuaton of the mnmum-order harmonc EMI nose level as a functon of the swtchng frequency (close-up vew of low swtchng frequences). 48

Cost Total Cost EMI Flter Heat Snk Boost Inductor 21.43 {7} 25 30 {6} {5} 37.5 {4} 50 {3} 75 {2} Fs {mnmum harmonc group order wth respect to Fs located nsde the EMI standard frequency range} Fgure 3.10. Qualtatve descrpton of the varaton of the optmum desgn components cost and total components cost as a functon of the swtchng frequency. * * The sketch does not ntend to reflect the relatve cost of the three components. In all optmzaton runs performed, the value of the swtchng frequency for the optmum desgn was located mmedately below one of the swtchng frequences at whch a new harmonc entered nto the range of frequences defned by the standard; or, n other words, rght before one of the corners of the cost curve for the EMI flter n Fgure 3.10 (21 khz, 24 khz, 29 khz, 37 khz ). In the prevous stage (Chapter 2), several manual desgns were obtaned for several values of the swtchng frequency. For nstance, 30 khz and 40 khz were selected randomly. Fgure 3.10 shows that ths choce was sub-optmal, snce both frequences correspond to the peak regon of the total cost. By means of the contnuous optmzaton, an mproved understandng of the system cost pattern as a functon of the swtchng frequency was ganed, whch led to a reducton n the overall cost of the system. 49

3.3. Dscrete Optmzaton In the dscrete optmzaton approach for the component desgn of the system, and as opposed to the contnuous approach, all desgn varables are treated as dscrete. Ths allows all the components n the power stage to be ncluded as desgn varables. The only component that s fxed s the boost capactor, for the reason already dscussed n Secton 3.2. The average value of the output voltage (v o ) s also fxed. For the mplementaton of the common mode choke, t was decded to choose among commercally avalable desgns. The core shape of the boost nductor L B s fxed to smplfy the desgn problem. The torodal core shape has been selected, snce t appears to be the most cost-effectve for ths applcaton. However, dfferent core shapes could be consdered by ncorporatng an addtonal desgn varable (core gap) and mnor modfcatons nto the graphcal user nterface and desgn analyss (see Secton A.3.1 n Appendx A). The layout s also assumed fxed, and the correspondng parastcs are estmated for a more accurate predcton of the EMI levels. 3.3.1. Desgn Varables The desgn varables n the dscrete optmzaton approach are presented n Table 3.4. Table 3.4. Dscrete optmzaton desgn varables. Dfferental mode capactor Cx EMI flter Common mode capactor Cy Common mode choke Core Boost nductor Wre Number of turns 50

Controlled swtch Devces Swtchng frequency (Fs) Brdge dode Fast dode Thermal resstance of the sngle / swtch * heat snk to the ambent (Rth_hs_amb) * A sngle heat snk or separated heat snks for all devces can be consdered. In the frst case, the desgn varable corresponds to the thermal resstance of the sngle heat snk. In the second case, t corresponds to the thermal resstance of the swtch heat snk. Each desgn varable (controlled swtch, brdge dode, etc except for the heat snk thermal resstance, swtchng frequency and number of turns for the boost nductor) s defned by a set of parameters, whch are specfed n Appendx A. A database s then bult by specfyng the values of the parameters for each of the consdered components. The boost nductor s number of turns, the swtchng frequency, and the thermal resstance of the heat snk to the ambent are treated as dscretzed contnuous varables that can have a value wthn a predefned range. 3.3.2. Objectve Functon: Cost of the System In ths case, each component contans a parameter that specfes ts cost. Therefore, the total cost of the system can be computed as the smple addton of these ndvdual costs: Sys_Cost = 2*Cost_Cx + 2*Cost_Cy + Cost_Choke + Cost_L B _core + Cost_L B _fxwrng + Cost_ L B _varwrng + Cost_HS + Cost_S + Cost_D F + 4*Cost_D R + Cost_C B, (3.4) where talcs denotes varable costs. The only exceptons are for the estmaton of the cost of the boost nductor wrng (whch depends on the volume of wre used) and the estmaton of the cost of the heat snk (treated as a dscretzed contnuous varable). These costs expressed n m.u. are estmated as follows. Fxed manufacturng cost of the boost nductor: Cost_ L B _fxwrng = constant. 51

Cost of the boost nductor wre and varable manufacturng cost: Cost_ L B _varwrng = Cost_wpv*Aw*MLT*nturn, where Cost_wpv = constant (m.u./cm 3 ), and MLT s the mean length per turn of the core, expressed n cm. Cost of the heat snk/s: The cost of the heat snk has been approxmated by means of a polynomal functon based on the cost nformaton avalable (see Appendx A), as follows: Cost_HS = K1HS + K2HS*(1/Rth_hs_amb), where K1HS, K2HS = constants. 3.3.3. Constrants The goal of the optmzaton procedure s to fnd the desgn varable values that mnmze the objectve functon whle satsfyng all constrants. These constrants are specfed as follows. Geometrcal constrants: 1. The wre should ft n the avalable wndow area of the core, accordng to the maxmum fllng factor (Ku). The area occuped by the wre s consdered to be the area of a square wth sde length equal to the dameter of the wre. Temperature constrants: 2. The temperature of the boost nductor core should be lower than ts maxmum. 3. The juncton temperature of the swtch should be lower than ts maxmum. 4. The juncton temperature of the fast dode should be lower than ts maxmum. 5. The juncton temperature of the rectfer dode (or rectfer brdge) should be lower than ts maxmum. 6. The temperature of the heat snk should be lower than ts maxmum. Voltage ratng constrants: 52

7. The breakdown voltage of the MOSFET should exceed the mnmum requred breakdown voltage. 8. The breakdown voltage of the IGBT should exceed the mnmum requred breakdown voltage. 9. The breakdown voltage of the fast dode should exceed the mnmum requred breakdown voltage. 10. The breakdown voltage of the rectfer dode should exceed the mnmum requred breakdown voltage. 11. The ac voltage of the dfferental mode capactor Cx should exceed the mnmum requred AC voltage. 12. The ac voltage of the common mode capactor Cy should exceed the mnmum requred AC voltage. Current ratng constrants: 13. The rms current n the MOSFET cannot exceed the maxmum allowed rms current. Ths constrant s not needed f the correspondng maxmum juncton temperature constrant s consdered (constrant 3). However, t was retaned n order to montor the current level compared to the maxmum current level specfed n the data sheet. 14. The average current n the IGBT cannot exceed the maxmum allowed average current. Ths constrant s not needed f the correspondng maxmum juncton temperature constrant s consdered (constrant 3). However, t was kept n order to montor the current level compared to the maxmum current level specfed n the data sheet. 15. The average current n the fast dode cannot exceed the maxmum allowed average current. Ths constrant s not needed f the correspondng maxmum juncton temperature constrant s consdered (constrant 4). However, t was retaned n order to montor the current level compared to the maxmum current level specfed n the data sheet. 16. The average current n the rectfer dode cannot exceed the maxmum allowed average current. Ths constrant s not needed f the correspondng maxmum juncton 53

temperature constrant s consdered (constrant 5). However, t was kept n order to montor the current level compared to the maxmum current level specfed n the data sheet. 17. The maxmum surge current that the fast dode s able to wthstand should exceed the maxmum surge current determned for the system. 18. The maxmum surge current that the rectfer dode s able to wthstand should exceed the maxmum surge current determned for the system. 19. The rms current n the common mode choke cannot exceed the maxmum allowed rms current. Due to the lack of thermal models to estmate the common mode choke temperature, ths constrant s set n order to ndrectly take nto account the lmt on ths temperature. 20. The rms current n the common and dfferental mode capactors cannot exceed the maxmum allowed rms current. Due to the lack of thermal models to estmate the capactors s temperature, ths constrant s set n order to ndrectly take nto account the lmt on these temperatures. EMI constrants: 21. The dfferental mode dsturbance level for each of the consdered group of harmoncs around a multple of the swtchng frequency above the mnmum frequency at whch the EMC standard lmts are defned should be lower than the standard level defned for ts frequency mnus 3 db. 22. The common mode dsturbance level for each of the consdered group of harmoncs around a multple of the swtchng frequency above the mnmum frequency at whch the standard lmts are defned should be lower than the standard level defned for ts frequency mnus 3 db. Specal constrants: 23. The maxmum peak-to-peak current rpple n the boost nductor cannot be hgher than 150% of the peak average (n a swtchng perod) nput current. Ths constrant s set n order to lmt the amount of tme the converter operates n dscontnuous current mode. The models used n the analyss are only vald for contnuous current mode operaton. If the computatons were modfed to be able to account also for the dscontnuous current mode case, ths constrant could 54

be removed. However, n all runs performed ths constrant was never actve, whch suggests that the contnuous current mode operaton s optmal for the problem analyzed. 24. The peak value of the flux densty n the boost nductor core cannot exceed the maxmum value defned for ts materal. Ths constrant can be removed f the saturaton of the core s modeled n the analyss. In ths case, ths constrant wll never be actve. However, even though ths work has ntroduced the approprate equatons to model the saturaton of the core, the constrant was kept n case new materals were consdered for whch the saturaton models has not been nserted n the analyss code. 25. The current densty n the boost nductor wre cannot exceed the maxmum current densty for the copper. Ths constrant s also not needed when the copper losses n the boost nductor wre are computed and ther effects on the boost nductor core temperature rse are consdered. Agan, ths constrant was kept n the event that these proposed models are removed, but s unnecessary for the case under dscusson. Boundares for the contnuous desgn varables: 26. The mnmum value of the number of turns s one. 27. The mnmum thermal resstance of the heat snk s 0.1 (value correspondng to a good water coolng system). 27. The lower boundary for the swtchng frequency s 20 khz (audble range lmt), and the upper boundary s 150 khz. These constrants should all be expressed n a normalzed form (see equatons n Appendx A, Secton A.2.5). Note that constrants 7-12, 17 and 18 are smply boundares for some of the desgn varable parameters. Therefore, they can ntally be computed for all components n the database n order to dscard those not meetng the requrements. To compute the value of all other constrants as a functon of the desgn varables, several models and assumptons have been appled. These models and assumptons and the process 55

followed to obtan the constrant values are dscussed n Secton 3.2.4, and can also be found n detal n Appendx A. 3.3.4. Optmzaton Algorthm: DARWIN 3.3.4.1. Introducton DARWIN s an advanced genetc algorthm (GA) optmzaton code developed by ADOPTECH, Inc. that has been talored specfcally for engneerng system desgn. GAs are one of the few optmzaton algorthms that work drectly wth dscrete desgn varables. GAs are also excellent all-purpose dscrete optmzaton algorthms because they can handle non-lnear and nosy search spaces by usng objectve functon nformaton only. Compared to tradtonal gradent-based optmzers, genetc optmzers are more lkely to fnd the overall best (globally optmal) desgn. In addton to fndng the overall best desgn, GAs are also capable of fndng many near-optmal desgns as well, provdng the user wth many optons when selectng a fnal desgn confguraton. 3.3.4.2. Genetc Algorthm Theory Genetc algorthms use technques derved from bology and rely on the applcaton of Darwn s prncple of survval of the fttest. When a populaton of bologcal ndvduals s allowed to evolve over generatons, ndvdual characterstcs that are useful for survval tend to be passed on to future generatons, because ndvduals carryng them get more chances to breed. In bologcal populatons, these characterstcs are stored n genetc strngs. The mechancs of natural genetcs are based on operatons that result n a structured yet randomzed exchange of genetc nformaton between the genetc strngs of reproducng parents. These operatons consst of reproducton, crossover, and occasonal mutaton of the genetc strngs. Genetc algorthms, developed by Holland [25], mmc the mechancs of natural genetcs for artfcal systems based on operatons that are the counterpart of ther natural ones. Although these operatons may appear as a completely random search of the desgn space, genetc algorthms have been expermentally proven to be robust searchng algorthms (see Goldberg [26]). 56

3.3.4.2.1. GA Codng Applyng a genetc algorthm to a search problem frst requres the representaton of the possble combnatons of the varables n terms of nteger or real valued strngs, whch are the counterparts of genetc strngs found n nature. Typcally, genes are coded usng a bnary alphabet showng whether a gene s actve (represented by a 1) or nactve (represented by a 0). However, for the PFC boost rectfer EMI flter desgn problem, each gene n the genetc strng s used to model a sngle electrcal component, and thus s gven ts own alphabet of nteger values. Ths s because the number of possble choces for each component wll lkely be dfferent. For example, f the frst gene n the genetc strng s used to represent the specfc fast dode used n the system and there are 15 dfferent fast dodes n the database, then the alphabet for the frst gene wll contan 15 nteger values rangng from 1 to 15. The second gene may be used to represent the brdge dode for whch there are eght dfferent types. Therefore, the alphabet for the second gene would contan eght nteger values rangng from 1 to 8. The contnuous varables requred by the PFC boost rectfer EMI flter desgn problem are modeled drectly n a separate real-value genetc strng and do not requre encodng. 3.3.4.2.2. GA procedure The GA procedure starts by selectng an ntal populaton of randomly chosen strngs, each of whch represents a desgn. For the PFC boost rectfer EMI flter desgn problem, each desgn conssts of a strng of ntegers representng all of the electrcal components as well as a strng of real values representng the swtchng frequency, number of wre turns n the nductor core, and the thermal resstance of the heat snk. The sze of the populaton remans constant throughout the genetc optmzaton, although the members of the populaton evolve over tme. In order to form successve generatons, parents are chosen from the current populaton based on ther performance (desgns wth the best performance are gven the hghest probablty of beng selected as parents). After parents have been selected, genetc operators (see Secton 3.3.4.2.3) are appled to create chldren. Dependng on the selecton procedure that s used to determne the next populaton of desgns, selected chld desgns wll replace ther parents n the next generaton (see Secton 3.3.4.2.4). One generaton after another s created untl some convergence crteron s met. DARWIN s currently confgured to run for whatever fxed number of generatons s set by the user. A schematc of the GA procedure s gven n Fgure 3.11. 57

3.3.4.2.3. Genetc Operators Each genetc operator s mplemented wth ts own specfc probablty P. To determne whether an operator wll be mplemented, a unformly dstrbuted random number s selected and compared aganst the operator s probablty. If the random number s smaller than P, the operator s appled to the genetc strng. Start Intal populaton Performance evaluaton Crossover Mutaton Y Apply crossover? N Y Apply mutaton? N Rank desgns Parent selecton Performance evaluaton Rank chld desgns Select next generaton of desgns. End Y Has GA converged N? Fgure 3.11. Genetc algorthm procedure. 3.3.4.2.3.1. Crossover Chld desgns are created by combnng a porton of each parent s genetc strng n an operaton called crossover. DARWIN utlzes the unform crossover procedure, whch s mplemented by drawng a unformly dstrbuted random number for each gene n the genetc strng. If the random number s less than 0.5, then the frst gene n parent 1 s gven to chld 1 and 58

the frst gene n parent 2 s gven to chld 2. If the random number s greater than or equal to 0.5, then chld 1 receves a gene from parent 2 and chld 2 receves a gene from parent 1. Ths process s repeated untl two new chld desgns are created. DARWIN also utlzes a separate crossover operator that has been specally desgned to work wth contnuous varables. In general, all crossover operators are typcally appled wth a hgh probablty (0.8 P c 1.0) because they are the GA s prmary means of traversng the desgn space. However, f crossover s not appled, then the parent strngs are cloned nto the chld strngs. Chld strngs are also forced to be dstnct from each other. If a dstnct chld cannot be found after a prescrbed number of teratons, then one of the parents s cloned nto the chld populaton. The crossover process s repeated as many tmes as necessary to create a new populaton of desgns. 3.3.4.2.3.2. Mutaton Mutaton performs the valuable task of preventng premature loss of mportant genetc nformaton by occasonally ntroducng random alteratons n the strng. Mutaton s also needed n case all of the possble values for each gene are not represented n the ntal populaton. Mutaton s almost always appled wth a low probablty (0.01 P m 0.1), and s mplemented by changng, at random, a sngle value n the strng to any other permssble value. As wth crossover, DARWIN also has an addtonal mutaton operator that has been specally desgned to work wth contnuous varables. 3.3.4.2.4. Selecton The GA s selecton scheme s the mechansm that determnes whch desgns from the parent populaton and newly created chld populaton wll be chosen to make up the next generaton of desgns. DARWIN utlzes eltst selecton, where the chld populaton and parent populaton are ranked separately. The best converter from the parent populaton and the worst converter from the chld populaton are dentfed. To create the new populaton, the best desgn from the parent populaton replaces the worst desgn from the chld populaton. The eltst method provdes an exploratve genetc search, snce each successve populaton s provded wth a large number of new desgns. 59

3.3.5. Software Tool: OPES In the dscrete optmzaton approach for the component desgn of the system one MATLAB functon was developed: Danalyze, descrbed n Appendx D. As n the contnuous case, ths functon performs the cost and electrcal analyss of the system. It receves as nputs the values of the desgn varables, and provdes as outputs the cost of the system n m.u. and the value of the varous constrants consdered. Addtonal performance nformaton for these gven values of the desgn varables can be obtaned by settng an nternal varable n the program ( aff ) to one. Ths functon was then translated nto FORTRAN ( pfcbr_analyss.f90 ) and ted to a GA (DARWIN) n order to perform the optmzaton. The optmzaton process s controlled by means of a graphcal user nterface (developed by ADOPTECH, Inc., n JAVA), whch not only allows the executon and montorng of the optmzaton process, but also provdes a userfrendly envronment for the management of the condtons / specfcatons and component database consdered n the optmzaton, and provdes detaled electrcal performance nformaton for any desgn desred. A demo verson of the prevous software, termed OPES (Optmzaton of Power Electroncs Systems), s ncluded n Appendx D. The man features of the software tool are descrbed n the followng sectons. 3.3.5.1. Defntons of Specfcatons and Condtons Fgure 3.12 shows the wndows avalable for defnng the specfcatons and condtons for whch we desre to obtan the optmum desgn. These condtons are classfed nto three categores: general, boost PFC stage and EMI flter. They contan a wde varety of parameters that can be specfed, such as the output power level, nput and output voltages, and the values of the dfferent layout parastcs accordng to the layout selected. The user can also select the EMI standard to be consdered, whether a sngle heat snk for all devces or separated heat snks should be used, and how conservatve the desgn analyss results should be. 3.3.5.2. Component Databases The software tool also allows the user to manage the component databases that wll be used n the optmzaton process (see example n Fgure 3.13). Component databases for the EMI flter capactors, common mode choke, swtch (IGBT and MOSFET), fast dodes, brdge dodes, cores and wres have been created. The user can update and organze these databases as requred. 60

The optmzaton process only consders those components selected by the user. Ths provdes flexblty, and allows the user to perform a varety of desgn studes. The user can also set the upper and lower bounds for each contnuous desgn varable. Fgure 3.12. Specfcatons and condtons. Fgure 3.13. Inductor core database. 3.3.5.3. Control and Montorng of the Optmzaton Process Once the condtons and component databases have been loaded, the optmzaton process to fnd the combnaton of components and contnuous varables that yelds the cheapest desgn wthout volatng any of the constrants can be controlled and montored from the man wndow 61

shown n Fgure 3.14. The optmzaton process populaton sze and the number of generatons must frst be selected. A specfed number of the best desgns found by the optmzer can be dsplayed at any tme durng the optmzaton process. The percentage of optmzaton process completed s also dsplayed. Fgure 3.14. Man wndow. 3.3.5.4. Desgn Reports After the optmzaton process s completed, a report can be generated that detals each of the best desgns found. Ths desgn report ncludes a detaled cost breakdown of the desgn, statuses of the dfferent constrants, electrcal performance nformaton (general and specfc for each component), and a set of plots contanng nformaton on the EMI levels, boost nductor current, boost capactor voltage and duty-rato waveforms. Fgure 3.15 shows some of the wndows contanng ths nformaton. 62

Fgure 3.15. Desgn report nformaton. 3.3.5.5. Sngle Desgn Analyss Addtonally, the software allows the desgner to examne the response of any specfed desgn by selectng the Sngle Desgn Analyss Mode (Fgure 3.16). Ths mode s especally useful for tunng some of the parameters contaned n the operatng condtons wndow, as the predcted performance can be compared to the expermental results obtaned from a prototype. It can also be used for educatonal purposes, allowng exploraton of changes n the system cost and performance as a functon of certan desgn parameters. Fgure 3.16. Sngle Desgn Analyss Mode. 63

3.3.5.6. Onlne Help Onlne help to operate the software s avalable from the menu bar, and local help buttons exst n the partcular wndows. 3.3.6. Results It was decded to nvestgate (usng OPES) the optmum desgn for the followng cases: A) Optmum A mn Vn = 180 Vrms (except for EMI levels, checked at 230 Vrms). B) Optmum B mn Vn = 195 Vrms (except for EMI levels, checked at 230 Vrms). C) Optmum C mn Vn = 230 Vrms All three optmums have been obtaned assumng separated heat snks. The brdge rectfer has been consdered to be attached to the box, and t has been assumed that the box has a thermal resstance low enough to avod over temperatures n t and n the brdge rectfer. Therefore, the desgn costs presented nclude only the cost of the swtch and fast dode heat snks. Appendx C contans detaled nformaton on the condtons / specfcatons and the sze of the component database n the software used to obtan these optmums. A two-step process has been followed to obtan the optmums, as follows. 1. Frst, a search of the optmum set of dscrete desgn varables (all except for the swtchng frequency, the number of turns, and the thermal resstance) has been performed. For ths, t s necessary to run the optmzaton several tmes and to check that almost all optmzatons lead to the same set of optmum dscrete components. On the other hand, n any optmzaton run, t s nterestng to apply the smallest possble value of the desgn populaton sze and number of teratons parameters n order to reduce the tme requred to complete the optmzaton process. In the runs presented here, and for the database sze consdered, a desgn 64

populaton sze of 100 and a number of teratons of 500 have proven to be farly low values, guaranteeng convergence of the dscrete desgn varables. 2. Second, by fxng the set of optmum dscrete desgn varables found prevously (ths s done by smply unselectng all the other possble components n the database), a search of the optmum values of the contnuous varables (swtchng frequency, number of turns and thermal resstance) s performed. Agan, t s necessary to run the optmzaton several tmes and to check that almost all optmzatons lead to approxmately the same values of the contnuous desgn varables. In the runs presented here, and for the contnuous desgn varable value ranges consdered, a desgn populaton sze of 25 and a number of teratons of 500 have proven to be farly low values, guaranteeng convergence of the contnuous desgn varables. In Table 3.5, the swtchng frequency and average boost nductance of the optmum desgns A, B and C are presented. In Table 3.6, the costs of the EMI flter, boost PFC and total cost n the condtons A, B and C are presented. The costs are expressed as a percentage of the cost estmated by the software for the selected desgn at Fs = 40 khz n the ntal desgn stage (Chapter 2) followng tradtonal desgn procedures. Ths desgn meets the specfcatons n the condtons of the optmums B and C, but at a mn Vn = 180 Vrms (condtons of optmum A), the temperature of the boost nductor core s too hgh. It can be seen that as the mnmum nput voltage ncreases, the total cost of the optmum desgn decreases. In these three optmums, the EMI flter s the same. Only the boost PFC desgn dffers. In Table 3.7, the costs of the dfferent components ntegratng the boost PFC stage are presented. The selecton of the devces and boost output capactor s the same for the three optmum desgns. In optmum B, the same core as n optmum A s consdered, but a reducton n the cost of the wrng (due to a choce of a smaller wre gage and number of turns) s expermented. The cost of the heat snks, especally the swtch heat snk, s also reduced compared to optmum A. In optmum C, a cheaper core s selected compared to optmum B. Addtonal savngs are obtaned n the heat snk, especally n the swtch heat snk. 65

Table 3.5. Swtchng frequency and average boost nductance for optmum desgns A, B and C. Optmum desgn A B C Swtchng frequency (khz) 21 24 24 Average boost nductance * (mh) 1.54 1.41 1.33 * At Vn = 230 Vrms Table 3.6. EMI flter, boost PFC, and total cost for optmum desgns A, B and C. Optmum desgn A B C EMI flter cost (%) * 13.3 13.3 13.3 Boost PFC cost (%) * 77.5 75.3 70 Total cost (%) * 90.8 88.6 83.3 * Percentage wth respect to the cost of the chosen desgn at Fs = 40 khz n Chapter 2. Table 3.7. Boost PFC components cost for optmum desgns A, B and C. Optmum desgn A B C Devces + C B cost (%) * 35.6 35.6 35.6 Core cost (%) * 10.0 10.0 5.8 Wrng cost (%) * 32.7 30.6 30.5 Heat snks cost (%) * 7.0 6.7 5.2 * Percentage wth respect to the cost of the chosen desgn at Fs = 40 khz n Chapter 2. In Table 3.8, the value of dfferent constrants s specfed for the three optmum desgns. Ths value represents the per unt value of the dstance between the response varable of the system and the correspondng lmt. For example, n the case of the constrant related to the maxmum temperature of the heat snk, the constrant value s defned as: Cstr _ T HS T HS max HS =, (3.5) T T HS max where T HS s the heat snk temperature, and T HSmax s the maxmum temperature of the heat snk. 66

Table 3.8. Dfferent constrant values of the optmum desgns A, B and C. Optmum desgn A B C 1. Cstr_W A (p.u.) -0.2749-0.4423-0.2580 2. Cstr_T_core_L B (p.u.) -0.0014-0.0024-0.0055 Constrants * 6. Cstr_T HS (p.u.) -0.0023-0.0096-0.0050 21. Cstr_DM (p.u.) -0.0270 0.0030-0.0237 22. Cstr_CM (p.u.) -0.1294-0.1123-0.1392 * Bold denotes actve constrants. A negatve value of the constrant ndcates that the lmt has not been trespassed (nactve constrant), a zero value ndcates that the lmt has been reached (actve constrant), and a postve value ndcates that the lmt has been trespassed (volated constrant). In all three desgns, the constrant related to the maxmum temperature n the boost nductor core (2. Cstr_T_core_L B ), the maxmum temperature n the swtch heat snk (6. Cstr_T HS ), and the lmt n the dfferental mode nose (21. Cstr_DM) are the actve constrants. All other constrants are nactve. In partcular, the constrant related to the maxmum amount of wre turns that can ft n the avalable wndow area (1. Cstr_W A ) s not actve wth a wde margn. Ths s because f the smaller (and cheaper, n ths case) cores are used, ether the number of wre turns needed to mantan the core temperature below the lmt does not ft n the avalable wndow area or the amount of wre requred s so large that the overall cost of the boost nductor s slghtly hgher. Another nactve constrant s that related to the lmt n the common mode nose (22.Cstr_ CM). Ths constrant s not actve because the smaller common mode capactor n the database s selected and there s a common mode choke n the database wth a common mode nductance hgher than requred but cheaper than the common mode chokes wth lower common mode nductance. It s nterestng to note that the value of constrant Cstr_DM s lower n optmum C than n optmum B, n spte of both desgns havng the same swtchng frequency and EMI flter, and the average boost nductance n optmum C beng lower than n optmum B. Intutvely, t mght seem that the result should be the opposte. However, the dfferental mode nose level s more 67

crtcal n optmum desgn B due to some resonance between the boost nductor and the EMI flter capactors, whch s not as pronounced n optmum C, as can be seen n Fgure 3.17. (a) (b) Fgure 3.17. Total EMI nose, dfferental and common mode nose and L B current n the case Vn=230 Vrms for (a) Optmum B and (b) Optmum C. 68

The swtchng frequency of the optmum desgns obtaned, as seen n the contnuous optmzaton approach, has a magntude mmedately below the frequences at whch the EMI flter encounters a jump n cost (see Fgure 3.18). Ths result boosts the confdence n the results obtaned by the OPES optmzaton tool. Cost EMI Flter Heat Snk Boost Inductor 21.43 {7} 25 {6} 30 {5} 37.5 {4} 50 {3} 75 {2} Fs (khz) {mnmum harmonc group order wth respect to Fs located nsde the EMI standard frequency range} Fgure 3.18. Qualtatve descrpton of the varaton of the optmum desgn components cost as a functon of the swtchng frequency. * * The sketch does not ntend to reflect the relatve cost of the three components. However, n a practcal mplementaton, the swtchng frequency tolerance should be consdered. Otherwse, due to ths tolerance, the prototype could work at a frequency hgher than the closest corner frequency, and consequently, the EMI standard lmts would not be met. Therefore, n a practcal mplementaton of Optmums A, B and C, the swtchng frequences should be selected accordng to Table 3.9. In Chapter 2, a concern wth respect to possble sgnfcant oscllatons n the EMI flter component currents at low swtchng frequences was rased. However, the currents through the EMI flter components for all three desgns presented have been nvestgated by means of the analyss functon developed, and no sgnfcant oscllatons n these currents were detected. 69

Optmum B was selected and mplemented. Fgure 3.19 shows the prototype. Expermental tests were performed and the desgn proved to meet both thermal and EMI requrements (see Appendx B). Table 3.9. Practcal selecton of swtchng frequences for optmum desgns A, B and C. Optmum Swtchng frequency A 21.43 khz- TolFs * B 25 khz - TolFs * C 25kHz TolFs * * TolFs s the swtchng frequency tolerance, expressed n khz. Fgure 3.19. Prototype correspondng to Optmum B. 70

3.3.7. Concluson The dscrete optmzaton approach developed and appled has proved to be a valuable tool for desgn. In a short desgn tme, t led to a cost reducton n the order of 10 to 15 % wth respect to the best desgns obtaned followng the tradtonal methodology presented n Chapter 2, n whch the swtchng frequency and boost nductor swtchng rpple were fxed based on the desgner s ntutve understandng of the problem. OPES, the software tool developed, can also be used to rapdly estmate the mnmum cost of the system under dfferent desgn specfcatons and condtons, to quanttatvely study the senstvty of the cost to certan specfcatons or operatng condtons n order to nvestgate possble ways of reducng the system cost, etc. Due to the short tme requred to obtan ths nformaton, the tool s therefore especally useful for ntal project evaluatons (vablty, etc.). Fnally, the possblty of explorng the whole desgn space through the Sngle Desgn Analyss Mode n the software allows the desgner to gan a better understandng of the system behavor, crtcal constrants, etc., conferrng the tool an added educatonal value. 71

CHAPTER 4. CONCLUSION AND FUTURE OF OPTIMIZATION IN POWER ELECTRONICS In Fgure 4.1, the evoluton of the cost of the dfferent desgns obtaned s presented. Intally, Schneder Electrc, S.A, provded a frst desgn. In ths desgn, a swtchng frequency of 100 khz was selected. By means of the tradtonal desgn methodology descrbed n Chapter 2, a new prototype was developed at 40 khz that provded sgnfcant savngs as compared to the prevous desgn. From the understandng ganed after applyng the contnuous optmzaton to the desgn of the system, t was understood that by smply choosng a swtchng frequency of 35 khz nstead of 40 khz, the sze and cost of the EMI flter could have been reduced wthout varyng any other components. Fnally, by means of the dscrete optmzaton software tool, an optmal desgn at 24 khz was dentfed, wth addtonal savngs. Cost 100 khz Cost - 45 50 % Cost - 58 % 40 khz New layout No nrush New C B Cost - 8 13 % Intal desgns s 40 khz 24 khz 35 khz Contnuous optmzaton Dscrete optmzaton Tme Fgure 4.1. Cost evoluton of the dfferent desgns. A fnal estmated cost reducton of approxmately 58% was acheved n the optmum desgn, as compared to that of ts predecessor. Around 45-50% of ths reducton can be attrbuted to the followng: 72

Elmnaton of the nrush current crcutry by selectng brdge dodes and fast dodes wth enough surge current ratng to wthstand the possble transents. Reducton of the requred output boost capactance n the optmum desgn by prudent selecton of the boost output voltage and by utlzng the dc-lnk capactor n the load. Selecton of ron powder as the core materal nstead of kool Mµ, and custom desgn of the boost nductor nstead of buyng a standard one from a manufacturer. Selecton of separated heat snks, whch decreases the common mode nose levels, and therefore allows a smaller common mode choke to be selected. The ntal desgn operates at a hgh swtchng frequency (100 khz), thus requrng a more expensve heat snk and EMI flter as a result of the ncreased swtchng losses and EMI nose level. Of the 58% mprovement, the remanng 10% (approxmately) can be attrbuted to the automated optmzaton desgn performed. The software tool developed (OPES) for the desgn optmzaton of the boost PFC stage and nput EMI flter could be nvaluable n the desgn of future prototypes, provdng n a short tme low-cost desgns for any desred specfcatons for whch the topology consdered s approprate, or helpng to determne the value of certan specfcatons / condtons that mnmze the desgn cost. 73

4.1. Usefulness of Optmzaton n the Desgn of Power Electroncs Systems The use of optmzaton technques n the component desgn of power electroncs systems offers the followng attractve advantages: Complete automated component desgn tools can be developed that allow mproved solutons wth respect to tradtonal desgn procedures, snce more complexty can be consdered n the desgn process, n a reduced desgn tme, once the optmzaton problem has been specfed and the approprate tools to solve t developed. Quck assessment of optmum solutons for dfferent sets of specfcatons, evaluaton of the desgn objectve functon senstvty wth the varaton of certan specfcatons and parameters, etc. The applcaton of optmzaton technques n the desgn has also an added educatonal value, snce the optmzaton tool wll hghlght the crtcal aspects n each desgn scenaro, allowng the user to focus hs or her attenton on these aspects and gan a better understandng of the system desgn peculartes. In the work presented n ths thess, specal nsght was ganed, for nstance, n how to approach the desgn of the boost nductor and EMI flter, based on the results obtaned through the optmzaton process. In a tradtonal desgn approach, each desgner often follows hs or her own partcular desgn methodology whch, on the other hand, s not rgorously specfed anywhere. In contrary, the use of optmzaton technques pushes the desgn team to work jontly to clearly and rgorously specfy the desgn problem and methodology for ts soluton, whch also allows future revsons to mprove the desgn formulaton. It provdes a wrtten and clear record of the desgn approach. On the other hand, there are stll several challenges to mprovng the practcalty of optmzaton technques: 74

Effcent models of the system cost, performance, etc., have to be developed, fast and accurate enough for an optmzaton process requrng hundreds of desgn evaluatons. The component data sheets do not always contan all the requred nformaton, and there are often sgnfcant dfferences among the data provded by each manufacturer. Some standardzaton would help the applcaton of optmzaton technques n the desgn process. The formulaton of the optmzaton problem and the development of the tools to solve t requre some tme. The tme requred, however, decreases substantally once several desgn problems have been solved, snce the component parameter defnton, the component database, certan common models, etc., are already avalable. A real desgn process s complex, nvolvng several consderatons, some of whch are hard to dentfy and express quanttatvely. However, the author beleves that once dentfed, they can normally be expressed n some acceptable mathematcal form n order to be ncorporated nto the desgn problem formulaton. Based on prevous comments, t can be concluded that the applcaton of optmzaton technques s especally recommended n those stuatons n whch a bg yeld of the desgned unt s desred, several desgns wll be needed for dfferent sets of specfcatons, or n any other case for whch any small mprovement n the desgn could be mportant. In other stuatons t may be more effcent (from the desgn tme and cost pont of vew) to ask an expert desgner to perform the desgn, snce a farly good desgn could be obtaned faster ths way. 75

4.2. Possble Future Work In the followng, some suggestons for future work n the desgn of power electroncs systems are presented, at both the subsystem and system desgn levels. 4.2.1. Subsystem Desgn 4.2.1.1. Component Desgn The optmzaton work presented n ths thess belongs to ths category. Some mprovements and extensons n the models are stll possble. For nstance, the possblty of selectng dfferent core shapes could be ncluded n the software. Ths and other modfcatons are dscussed n Appendx A, Secton A.2.3. The selecton of the components for a gven control scheme could also be ncorporated nto the optmzaton formulaton. 4.2.1.2. Layout Desgn The desgn varables specfyng the layout geometry could also be ncluded n the optmzaton formulaton. Ths would allow mprovements to be made n both the EMI and thermal models of the system (due to the strong dependence of the EMI and thermal behavor on such desgn varables), and exploraton of the dfferent tradeoffs nvolved n the layout desgn. 4.2.1.3. Power Stage Topologes and Control Schemes The desgn optmzaton could be performed for dfferent desgn topologes and control schemes n order to nvestgate whch of them s optmal. 4.2.1.4. Other Applcatons The desgn methodology presented here could also be appled to applcatons other than the desgn of a front-end converter provdng power factor correcton. For nstance, the desgn of popular topologes such as the two-swtch forward converter or the zero voltage swtchng (ZVS) full-brdge converter could be nvestgated. Several objectve functons to mnmze or maxmze could be consdered, dependng on the applcaton: sze, weght, cost, performance, etc., or even mult-objectve functons contanng a combnaton of any of these factors. 76

4.2.1.5. Integrated Desgn Currently, several research efforts am to develop more ntegrated desgns of power electroncs converters, n whch an ntegrated passve component soluton and semconductors are packaged nto the same unt, rather than desgnng the system usng dscrete components. The use of optmzaton technques n the desgn of such unts could provde substantal benefts. 4.2.2. System Desgn Optmzaton technques can also be appled to the desgn of the system nto whch the converters are ntegrated as a whole, whle smultaneously consderng ts dfferent subsystems. Due to subsystem nteractons, the desgn optmzaton of large power electroncs systems as a whole wll potentally mprove the results obtaned by optmzng ndvdual parts of the system separately. The ncreased complexty of the desgn problem (large number of desgn varables and complex non-lnear constrants, essentally), whch causes tradtonal optmzaton approaches to be mpractcal or neffectve, could be handled by means of optmzaton methodologes such as the Global/Local [27] [28]. The methodology s based on a decomposton of the optmzaton problem nto several herarchcal levels. 77

References [1] S. Balachandran and F.C. Lee, Algorthms for Power Converter Desgn Optmzaton, IEEE Transactons on Aerospace and Electroncs Systems, vol. AES-17, No. 3, pp. 422-432, May 1981. [2] S. Rahman and F.C. Lee, Nonlnear Program Based Optmzaton of Boost and Buck-Boost Converter Desgns, Proceedngs of the IEEE PESC, June 29-July 3, 1981, pp. 180-191. [3] C.J. Wu, F.C. Lee, S. Balachandran and H.L. Gon, Desgn Optmzaton for a Half-Brdge DC-DC Converter, IEEE Transactons on Aerospace and Electronc Systems, vol. AES-18, No. 4, pp. 497-508, July 1982. [4] R.B. Rdley and F.C. Lee, Practcal Nonlnear Desgn Optmzaton Tool for Power Converter Components, Proceedngs of the IEEE PESC, June 1987, pp. 314-323. [5] C. Zhou, R.B. Rdley and F.C. Lee, Desgn and Analyss of an Actve Unty Power Factor Correcton Crcut, Proceedngs of the VPEC Semnar, Sept. 1989, pp. 98-107. [6] J. Zhang, H. Chung, W.L. Lo, S.Y.R. Hu and A. Wu, Decoupled Optmzaton Technque for Desgn of Swtchng Regulators Usng Genetc Algorthms, Proceedngs of the IEEE ISCAS, vol. 3, May 2000, pp. 495-498. [7] N. Froehleke, H. Mundnger, H. Njende, P. Wallmeer and H. Puder, CAE-Tool for Optmzng Development of Swtched Mode Power Supples, Proceedngs of the IEEE APEC, vol. 2, March 2001, pp. 752-758. [8] BS EN 61000-3-2:1995, Electromagnetc compatblty (EMC). Part 3. Lmts. Secton 2. Lmts for harmonc current emssons (equpment nput current 16A per phase), IEC 1000-3- 2: 1995. [9] Robert W. Erckson, Fundamentals of Power Electroncs, Kluwer Academc Publshers, Boston/Dordrecht/London, 1999, Chapters 17-18 and Secton 12.4, pp. 474-490. [10] S. Busquets-Monge, E. M. Hertz, S. Ragon, G. Soremekun, J.C. Creber, P. We, H. Zhang, D. Boroyevch, Z. Gürdal and D. K. Lndner, Desgn Optmzaton of a Boost Power Factor Correcton Crcut, Fnal Project Report, CPES, March 2001. 78

[11] E. Hertz, Thermal and EMI Modelng and Analyss of a Boost PFC Crcut Desgned Usng a Genetc-Based Optmzaton, M.Sc. thess, Vrgna Polytechnc Insttute and State Unversty, Vrgna, July 2001. [12] BS EN 55011:1998, Lmts and methods of measurement of rado dsturbance characterstcs of ndustral, scentfc and medcal (ISM) rado-frequency equpment, CISPR 11:1997 [13] CISPR 16-2, Specfcaton for rado dsturbance and mmunty measurng apparatus and methods, 1996. [14] F.R. Walsh, et al., Analyss and Influence of Modelsaton Scheme on the Szng of the Input Flter n a PWM Rectfer, EPE'97, pp. 929-933. [15] J.C. Creber, Contrbuton à l'étude des Perturbatons Condutes dans les Redresseurs Commandés, Ph.D. dssertaton, INPG, May 1999. [16] Mcrometals, Mcrometals Iron Powder Cores. Power Converson & Lne Flter Applcatons, ISSUE H, June 1995. [17] L. H. Dxon, Average Current-Mode Control of Swtchng Power Supples, Untrode Power Supply Desgn Semnar Handbook, 1990. [18] S. Busquets-Monge, C. Creber, S. Ragon, E. Hertz, J. We, J. Zhang, D. Boroyevch, Z. Gürdal, D. K. Lndner and M. Arpllere, Optmzaton Technques Appled to the Desgn of a Boost Power Factor Correcton Converter, Proceedngs of the IEEE PESC, June 2001, pp. 920-925. [19] S. Busquets-Monge, G. Soremekun, E. Hertz, C. Creber, S. Ragon, J. Zhang, D. Boroyevch, Z. Gürdal, D. K. Lndner and M. Arpllere, Desgn of a Boost Power Factor Correcton Converter Usng Genetc Algorthms, Proceedngs of the CPES Semnar, Aprl 2001, pp. 99-104. [20] Mcrometals Inc., Mcrometals Iron Powder Cores. Power Converson & Lne Flter Applcatons, ISSUE I, February 1998, pp. 26, 28 and 63. 79

[21] Mcrometals Inc., Mcrometals Iron Powder Cores. Desgn of Inductors for Power Converson and Lne Flter Applcatons Usng Mcrometals Iron Powder Cores (software), Anahem, CA, USA, June 2000. [22] Magnetcs, Hgh Flux Powder Cores, Catalog HCF-1.1, 2000. [23] G.N. Vanderplaats, Numercal Optmzaton Technques for Engneerng Desgn: Wth Applcatons, Vanderplaats R&D Inc., Colorado Sprngs, CO, USA, 1988. [24] R.T. Haftka, and Z. Gürdal, Elements of Structural Optmzaton, Thrd Revsed and Expanded Edton, Kluwer Academc Publshers, Dordrecht, 1992, pp. 182-186. [25] J.H. Holland, Adaptaton of Natural and Artfcal Systems. Unversty of Mchgan Press, Ann Arbor, MI, USA, 1975. [26] Goldberg, D.E., Genetc Algorthms n Search, Optmzaton, and Machne Learnng. Addson-Wesley Publshng Co., Inc., 1989. [27] S.A. Ragon, Z. Gürdal, R.T. Haftka and T.J. Tzong, "Global/Local Structural Wng Desgn Usng Response Surface Technques," AIAA Paper 97-1051, Proceedngs of the 38th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamcs and Materals Conference, Kssmmee, FL, USA, Aprl 7-10, 1997, pp. 1204-1214. [28] B. Lu, R.T. Haftka and M.A. Akgün, "Two Level Composte Wng Structural Optmzaton Usng Response Surfaces," Structural Optmzaton, 2000, 20:87-96. [29] Ronald H. Randall, Alan Laprade and Barry Wood, Characterzng IGBT Losses for Swtched Mode Operaton, IPEC-Tokyo, 2000, pp. 767-772. [30] Magnetcs, Hgh Flux Powder Cores, Catal. HCF-1.1, 2000, pp. 4-16, 4-17; 4-5 to 4-9. [31] Magnetcs, Kool Mu Powder Cores, Catalog KMC 2.1, 2001, pp. 4-12. [32] Magnetcs, Curve Ft Formulae, Kool Mµ, Magnetcs web page, www.mag-nc.com, 2000. [33] Magnetcs, Molypermalloy Powder Cores, Catalog MPC-1.0, 2000, pp. 4-20, 4-22; 4-6 to 4-12. 80

[34] J.C. Creber, J. Roudet and J.L. Schanen, "EMI Analyss of Sngle-Phase Boost Rectfer n the Frequency Doman," Revue Internatonale de Géne Électrque (RIGE). [35] J.C. Creber, J. Roudet and J.L. Schanen, "Problems Usng LISN n EMI Charactersaton of Power Electronc Converters, Proceedngs of the IEEE PESC, 1999. [36] W. Zhang, M. T. Zhang, F. C. Lee, et al., Conducted EMI Analyss of a Boost PFC Crcut, n Conf. Record of IEEE APEC, 1997, pp. 223-229. [37] N. Mohan, T. M. Underland and W. P. Robbns, Power Electroncs Converters, Applcatons, and Desgn, Second Edton, John Wley and Sons, Inc., 1995, pp. 635-636. 81

Appendx A. Optmzaton Desgn Analyss Functon Computatons A.1. Introducton In ths appendx, the computatons performed by the desgn analyss functon are descrbed for both the dscrete and contnuous optmzaton approaches. In the contnuous optmzaton approach of the whole system (sngle-phase boost PFC and EMI flter) one MATLAB functon has been developed: Canalyze.m. In the dscrete optmzaton approach, the correspondng MATLAB functon s called Danalyze.m. Ths MATLAB functon was then translated nto Fortran ( pfcbr_analyss.f90 ) to be able to te t to the genetc algorthm n charge of performng the optmzaton. Snce the graphcal user nterface developed was bult n the dscrete optmzaton envronment and the functon pfcbr_analyss.f90 can be modfed by the user, the desgn analyss functon computatons for the dscrete optmzaton wll be the frst descrbed. The am s to provde a frendly descrpton of the computatons performed n ths functon. The functon computatons for the contnuous case are smlar to those n the dscrete approach. The dfferences, f any, are hghlghted at the end of each secton. These functons receve as nputs the so-called desgn varables and gve as outputs the value of the cost functon (cost of the system n m.u.) and the values of the physcal constrants defned for the problem, for the gven values of the desgn varables. Addtonal performance nformaton for these gven values of the desgn varables can be obtaned by settng an nternal varable n the programs, aff, to one. In all functons, the layout and the boost capactor are assumed to be fxed, concentrated parameters are consdered n the models, no need for an nrush current crcutry has been assumed, and ether a sngle or separated heat snks can be consdered. A.2. Functon Computatons In ths secton, a detaled descrpton of the process and equatons used for the computaton of the cost functon and constrants for a gven value of the desgn varables s presented. The recommended values for the optmzaton runs n the case of the desgn 82

consdered n ths project for the dfferent condtons, specfcatons and constants are also dsplayed. They may be used as a reference n further runs. A.2.1. Condtons, Specfcatons and Constants Table A.1. Programmng constants. Name Descrpton Value aff The value stored n ths constant determnes whether the addtonal nformaton wth regard to the performance of the desgn s presented or not. A value of 1 makes ths nformaton avalable. Any other value prevents the presentaton of the extra nformaton. 1 Tol_eff * Tolerance n the effcency 0.0001 Tol_Tjsw * Tolerance n the juncton temperature of the swtch 0.01 Tol_TcoreLb * Tolerance n boost nductor core temperature 0.01 * Snce there s no explct equaton for obtanng the value of the effcency, the juncton temperature of the swtch and the boost nductor core temperature, some values are assumed and then are recomputed, based on the crcut equatons. If the assumed and calculated values do not match, the set s assumed and the process s repeated teratvely untl a match s attaned. A.2.1.1. Condtons / Specfcatons A.2.1.1.1. General Table A.2. General condtons / specfcatons. Name Descrpton Value Vnmn_rms Mnmum nput voltage (Fgure A.1-1) 180 V Vnnom_rms Nomnal nput voltage (Fgure A.1-1) 230 V flne Nomnal lne frequency 50 Hz Po Output power (Fgure A.1-4) 1150 W 83

Vbus_DC Dc value of the voltage across the output boost capactor C B (see Fgure A.2) 368 V Tamb Ambent temperature 40 C Conservatve Degree of conservatve analyss to perform: -1(Nonconservatve) Conservatve 1(Most conservatve) -1 Boost PFC L B D F EMI Flter CHOKE D R v n C X C Y C X S C B Load C Y 1 2 3 4 Fgure A.1. EMI flter and boost PFC stage schematc. V CB (t) Vbus_DC Tlne/2 t Fgure A.2. Voltage waveform across C B. 84

A.2.1.1.2. Sngle-Phase Boost PFC Table A.3. Boost capactor (C B ): 68µF, 450 V. Name Descrpton Value Cb Capactance n PFC stage (68 µf)+ Capactance (worst case) n load (624 µf) 692E-6 F Cost_Cb Cost of the boost capactor *** m.u. Table A.4. Boost nductor wre. Name Descrpton Value Jm Maxmum current densty of the copper 1000 A/cm 2 Row100 Resstvty of the copper at 100 C 2.208E-6 Ω.cm Kcu Temperature coeffcent for the copper resstvty 0.0039 Ω.cm/ C Ku Maxmum fllng factor consderng that the cross-secton of the wre s a square of sde Dw (dameter of the wre) 0.4 Cost_Lbfxwrng * Fxed wrng cost for the boost nductor *** m.u. * See Secton A.2.4 for a method to estmate ths cost f t s not drectly avalable. Table A.5. Boost nductor mscellaneous. Name Descrpton Value TolLblkg Boost nductor leakage nductance tolerance 50 % TLbcoef Boost nductor temperature coeffcent 1.2 85

Table A.6. Devces voltage ratngs. Name Descrpton Value VpkMmn Mnmum breakdown voltage of the MOSFET 500 V VpkIGmn Mnmum breakdown voltage of the IGBT 600 V Vpkfdmn Mnmum breakdown voltage of the fast dode 600 V Vpkrdmn Mnmum breakdown voltage of the rectfer dode 800 V Table A.7. Devces current ratngs. Name Descrpton Value IFSMmn Mnmum requred surge current that the rectfer dodes and the fast dode need to wthstand 150 A Table A.8. Swtch. Name Descrpton Value Ls Inductance n seres wth MOSFETs 10e-9 H TrseIGBT TfallIGBT Perswqrr Rse tme of the voltage across the swtch (IGBT) (obtaned from other work [29], Fgure A.3) Fall tme of the voltage across the swtch (IGBT) (assumed to be equal to the rse tme) Percentage of the reverse-recovery losses dsspated n the swtch 50e-9 s 50e-9 s 50 % 86

Table A.9. Drver. Name Descrpton Value VGG Drver source voltage 15 V Rgon Drver resstance n the turn-on 33 Ω Rgoff Drver resstance n the turn-off 10 Ω Table A.10. Heat snk. Name Descrpton Value SngHS HSfd HSrd Boolean varable ndcatng whether a sngle heat snk or separated heat snks are used (1: Sngle heat snk, 0: Separated heat snks) Boolean varable ndcatng whether the fast dode s attached to a commercal heat snk or not (1: It s attached, 0: It s not attached) Boolean varable ndcatng whether the rectfer dodes are attached to a commercal heat snk or not (1: They are attached, 0: They are not attached) 0 1 0 TmaxHS Maxmum temperature of the heat snk/s 100 C K1HS * K2HS * Frst coeffcent of the approxmaton of the heat snk cost as a functon of the nverse thermal resstance Second coeffcent of the approxmaton of the heat snk cost as a functon of the nverse thermal resstance * See cost approxmaton equaton n Secton A.2.4. *** m.u. *** m.u.*(w/c) 87

Table A.11. Prnted crcut board (PCB). Name Descrpton Value TmaxPCB Maxmum temperature allowed n the PCB 125 C DT_pcb_Lbcore Estmated temperature dfference between the boost nductor core and the PCB (T_coreLb-T_PCB) 5 C A.2.1.1.3. EMI Flter Table A.12. Standard. Name Descrpton Value Class_type Integer code number ndcatng the EMI standard to meet (0: Class B, Group 1; 1: Class A, Group 1) 0 Table A.13. Voltage ratngs. Name Descrpton Value VacCxmn VacCymn Mnmum ac breakdown voltage of the dfferental mode capactor Cx. Mnmum ac breakdown voltage of the common mode capactor Cy. 275 V 250 V Table A.14. LISN components. Name Descrpton Value LN LISN nductance 50e-6 H CN LISN capactance n seres wth ZN 100e-9 F 88

C1 LISN capactance n the mans sde of the LISN 10e-6 F ZN LISN resstance 50 Ω Table A.15. Parastc elements of the propagaton paths. Name Descrpton Value Lres Lne mpedance nductance 150e-6 H Llmg Cable or trace parastc nductance 500e-9 H Llha Cable or trace parastc nductance 250e-9 H Lldb Cable or trace parastc nductance 250e-9 H Lfs Cable or trace parastc nductance 30e-9 H Csg Parastc capactance from node S to ground 1e-12 F Cdg Parastc capactance from node D to ground. Common mode nose very senstve to the value of ths parastc 21.5e-12 F Ckg Parastc capactance from node K to ground 1e-12 F Ceg Parastc capactance from node E to ground 1e-12 F Cfg Parastc capactance from node F to ground 1e-12 F Cag Parastc capactance from node A to ground 1e-12 F Cbg Parastc capactance from node B to ground 1e-12 F CLb Boost nductor parastc capactance 25e-12 F RLb Boost nductor parastc resstance 25.8e3 Ω 89

Table A.16. Other EMI constants. Name Descrpton Value std nharmgr nd ncr Matrx contanng the quas-peak lmts of the voltage across ZN n the LISN (frst column: frequency; second column: voltage lmt n LISN resstor (dbµv)) Ts s the number of the harmoncs groups multples of the swtchng frequency to be consdered above the mnmum frequency for whch the standard specfes a lmt. As nharmgr ncreases the computaton tme ncreases. Ths s the number of harmoncs multples of the lne frequency to be consdered on each sde of each multple of the swtchng frequency. As nd ncreases, the accuracy of the results mproves but the computaton tme ncreases. Ths s the ncrement n EMI levels, and represents a correcton n the estmaton of the EMI levels needed because not all harmoncs are computed, just the nd that are more sgnfcant on each sde of each multple of the swtchng frequency. Ths value must be set accordng to the lne frequency, the bandwdth of the measurement, and the value of nd: for flne=50 Hz, a bandwdth of 9 khz, and nd=3 set ncr=3 db; for flne=50 Hz, a bandwdth of 9 khz, and nd=10 set ncr=2 db; and for flne=50 Hz, a bandwdth of 9 khz, and nd=90 set ncr=0 db. (see program) 1 3 3 db 90

A.2.1.1.4. Contnuous Optmzaton Condtons / Specfcatons See dscusson n Secton A.2.2.12. 91

A.2.2. Desgn Varables In the dscrete optmzaton, most of the desgn varables (such as the devces) requre more than one parameter to be descrbed. Therefore, a vector correspondng to the value of the dfferent parameters needed to defne each desgn varable wll be used. All these vectors wll consttute the nput of the functon n charge of performng the desgn analyss. In the followng, each of the parameters consdered to defne each of the desgn varables wll be presented. Note: whenever one of the parameters depends on the juncton temperature of a devce, the worst value for a juncton temperature equal or greater than 100 C s selected. A.2.2.1. Swtch Table A.17. Swtch parameters. Parameter name Descrpton Unts Swtch_type (MI) Boolean parameter that determnes the swtch type: (0) IGBT, (1) MOSFET ----- Cost_swtch (MI) Cost of the swtch (If the swtch s an IGBT and does not have an nternal ant-parallel dode, ths cost should nclude the cost of the ant-parallel dode.) m.u. Vpksw (MI) Breakdown voltage of the swtch V Iswrmsmax (M) Maxmum rms current of the swtch A Iswavmax (I) Maxmum average current of the swtch A VFsw (I) Ths s the constant conducton voltage drop, obtaned as the voltage V CE correspondng to a current I CE =0 A, n the lnear approxmaton of the curve I CE -V CE presented n the data sheet. V 92

Ronsw1 (MI) MOSFET: Frst coeffcent of the lnear approxmaton of the swtch on-resstance as a functon of the juncton temperature. (Ronsw=Ronsw1+Ronsw2*Tjsw); obtaned from the correspondng plot n the data sheet. Ω Ronsw2 (M) G (M) IGBT: Conducton resstance; obtaned from the curve I CE - V CE n data sheet. It corresponds to the slope of the lnear approxmaton of the curve n the normal operatng range of currents (I CE ): 1 to 10 A n ths project. Second coeffcent of the lnear approxmaton of the swtch onresstance as a functon of the juncton temperature. (Ronsw=Ronsw1+Ronsw2*Tjsw). Obtaned from the correspondng plot n the data sheet. di D /dv GS. Obtaned from the curve I D -V GS n the data sheet, makng a lnear approxmaton n the applcaton range of dran currents (I D ): 0A to 10 A n ths project. Ω/ C A/V Crssh (M) Value of Crss for a hgh value of V DG F Crssl (M) Value of Crss for a low value of V DG F Cssh (M) Value of Css for a hgh value of V DG F Cssl (M) Value of Css for a low value of V DG F Coss (M) Value of Coss at V DS = 80 % of V DSS F Vp (M) VT (M) VCE_E (I) Ths s the value of the voltage V GS at whch the curve V GS - Q G presents a plateau for the average boost nductor current obtaned from the curve I D -V GS n the data sheet. Ths s the typcal threshold voltage of V GS, obtaned from the electrcal characterstcs n the data sheet. Ths s the collector-emtter voltage at whch Eon and Eoff are provded. V V V 93

IC_E (I) Ths s the collector current at whch Eon and Eoff are provded. A Eon (I) Ths s the energy lost n the turn-on (at VCE_E and IC_E). J Eoff (I) Ths s the energy lost n the turn-off (at VCE_E and IC_E) (ncludng the tal losses). J RSth_j_c (MI) Thermal resstance juncton-to-case C/W RSth_c_s (MI) Thermal resstance case-to-heat snk C/W Tmaxsw (MI) Maxmum operatng juncton temperature C (MI) For both MOSFET and IGBT. (M) For MOSFET only. (I) For IGBT only. Note: If the swtch s a MOSFET, the parameters for only the IGBT can have any value (for nstance, zero). Vce-versa n the case of the IGBT. I D Cdg D Rgon G Cds V GG Rgoff Cgs S Ls Fgure A.3. Smplfed representaton of the MOSFET and gate drver. 94

v GS (t) V GG V P VT D (t) OVERLAP I -V t v DS (t) t V P t1 t2 t12 t23 t3 t34 t4 t Fgure A.4. Turn-on of S (MOSFET). v GS (t) V GG V P VT D (t) OVERLAP I -V t v DS (t) t V P t 6 t 7 t 8 t 9 t67 t78 t89 t Fgure A.5. Turn-off of S (MOSFET). 95

+ Rgon + Req Rgoff + Req G V GG 0 Css_h S Fgure A.6. Equvalent crcut dagram durng t=t1 t2 (turn-on) (bold) and t=t8 t9 (turn-off) (talcs). Rgon Rgoff G (V GG -V P )/Rgon (-V P )/Rgoff Crss_h ( t23, t78) Crss_l ( t34, t67) D Fgure A.7. Equvalent crcut dagram durng t=t2 t3, t=t3 t4 (turn-on) (bold) and t=t6 t7, t=t7 t8 (turn-off) (talcs). 96

A.2.2.2. Brdge Dode Table A.18. Brdge dode parameters. Parameter name Descrpton Unts Cost_rectdode Cost of one rectfer dode m.u. Vpkrd Breakdown voltage of the dode V Irdavmax Maxmum average current of the dode A IFSMrd VFrd Ronrd RRDth_j_c RRDth_c_s Maxmum surge current of the dode (at the lne frequency) Ths s the constant conducton voltage drop, obtaned as the voltage V F correspondng to a current I F =0 A, n the lnear approxmaton of the curve I F -V F presented n the data sheet. Ths s the conducton resstance, obtaned from the curve I F -V F n the data sheet. It corresponds to the slope of the lnear approxmaton of the curve n the normal operatng range of currents (I F ). Ths s the thermal resstance juncton-to-case to be appled to the average (n a lne perod) power lost n one rectfer dode. Ths s the thermal resstance case-to-heat snk to be appled to the average (n a lne perod) power lost n one rectfer dode. In a package of two/four rectfer dodes t corresponds to two/four tmes the Rth_c_s of the package. A V Ω C/W C/W Tmaxrd Maxmum operatng juncton temperature C 97

A.2.2.3. Fast Dode Table A.19. Fast dode parameters. Parameter name Descrpton Unts Cost_fastdode Cost of the fast dode m.u. Vpkfd Breakdown voltage of the dode V Ifdavmax Maxmum average current of the dode A IFSMfd Maxmum surge current of the dode (at flne) A VFfd Ronfd Qrr1 * Qrr2 * Ths s the constant conducton voltage drop, obtaned as the voltage V F correspondng to a current I F =0 A, n the lnear approxmaton of the curve I F -V F presented n the data sheet. Ths s the conducton resstance, obtaned from the curve I F -V F n the data sheet. It corresponds to the slope of the lnear approxmaton of the curve n the normal operatng range of currents (I F ): 1 to 10 A n ths project Ths s the frst coeffcent of the lnear approxmaton of the dode reverse-recovery charge as a functon of the forward current, assumng a certan d F /dt (Qrr=Qrr1+Qrr2*f). Ths s the second coeffcent of the lnear approxmaton of the dode reverse-recovery charge as a functon of the forward current, assumng a certan d F /dt (Qrr=Qrr1+Qrr2*f). V Ω C C/A RFDth_j_c Thermal resstance juncton-to-case C/W 98

RFDth_c_s Thermal resstance case-to-heat snk C/W Tmaxfd Maxmum operatng juncton temperature C * Whenever Qrr s not drectly avalable n the data sheet and t rr (total reverse-recovery tme) and I RM (maxmum reverse-recovery current) or t A (ntal perod of tme of the reverse-recovery process) are avalable nstead, the followng formula to calculate Qrr1 and Qrr2 s used: 1 1 d = F, 2 2 dt F Qrr trr I RM = trr t A = Qrr1 + Qrr2 * where t rr : total reverse-recovery tme, I RM : maxmum reverse-recovery current, and t A : ntal reverse-recovery tme (untl I RM s reached). Ether t rr or t A s expressed as a lnear functon of the forward current, whchever presents a major dependence on ths last one. If t rr s expressed as a lnear functon of the forward current, t A wll be consdered to be constant, and vce-versa. Ths constant s obtaned for a forward current I F equal to the average nput current ( 6A n ths project). DF V DF (= Vbus_DC) t A t rr I RM V S (= Vbus_DC) Qrr Fgure A.8. Reverse-recovery phenomena model. 99

A.2.2.4. Boost Inductor Core Table A.20. Boost nductor core parameters. Parameter name Descrpton Unts Cost_Lbcore Cost of the boost nductor core m.u. Cd1 Cd2 AL Integer value to codfy the manufacturer / core materal (see Table A.21) Integer value to codfy the types of core wthn a materal defned n cd1, typcally the dfferent permeabltes possble (see Table A.21) Inductance ratng of the core (nh for one turn mh for 1000 turns) ------- ------- nh/(turn^2) mh/(1000_turn^2) TolAL Tolerance of the value of AL % OD Outsde dameter of the core cm ID Insde dameter of the core cm Ht Heght of the core cm lm Mean magnetc path cm Ac Cross-sectonal area of the core cm 2 Vc Volume of the core cm 3 MLT Mean length per turn. (n the case of Mcrometals catalog, ths value can be obtaned from pages 60-61) cm T_coreLbmax Maxmum temperature of the core C 100

Table A.21. Codfcaton of the dfferent core types. Cd1: Manufacturer / Materal 1: Mcrometals Iron Powder 1: Mx 2 2: Mx 8 3: Mx 18 4: Mx 26 5: Mx 28 2: Magnetcs Hgh Flux 1: µ = 14 2: µ = 26 3: µ = 60 3: Magnetcs Kool Mµ 1: µ = 26 2: µ = 60 3: µ = 75 4: Magnetcs Molypermalloy 1: µ = 14 2: µ = 26 3: µ = 60 4: µ = 125 5: µ = 147 Cd2: Core type 6: Mx 33 7: Mx 38 8: Mx 40 9: Mx 45 10: Mx 52 4: µ = 125 5: µ = 147 6: µ =160 4: µ = 90 5: µ = 125 6: µ = 160 7: µ = 173 8: µ =200 9: µ = 300 10: µ = 550 A.2.2.5. Boost Inductor Wre Table A.22. Boost nductor wre parameters. Parameter name Cost_Lbwre * Descrpton Cost per unt of length of the wre (ncludes varable manufacturng cost) Unts m.u./ cm Aw Bare area of the wre cm 2 Dw External dameter of the wre cm Tmaxwre Maxmum temperature of the wre C * See Secton A.2.4 for a method to estmate ths cost f t s not drectly avalable. 101

A.2.2.6. Boost Inductor Number of Turns Table A.23. Boost nductor number of turns. Parameter name Descrpton Unts nturn Number of turns of the boost nductor ---------- A.2.2.7. Common Mode Choke Table A.24. Common mode choke parameters. Parameter Name Descrpton Unts Cost_choke Cost of the common mode choke m.u. Lcm Common mode nductance H TolLcm Tolerance n the value of Lcm (%) Ldm Leakage nductance (dfferental mode nductance) H ICHrms_max Maxmum rms current A A.2.2.8. Dfferental Mode Capactor Cx Table A.25. Dfferental mode capactor Cx parameters. Parameter name Descrpton Unts Cost_Cx Cost of the dfferental mode capactor m.u. Cfx Capactance of the dfferental mode capactor F 102

TolCx Tolerance n the value of Cfx (%) ICxrms_max Maxmum rms current A VacCx Maxmum ac voltage V A.2.2.9. Common Mode Capactor Cy Table A.26. Common mode capactor Cy parameters. Parameter name Descrpton Unts Cost_Cy Cost of the common mode capactor m.u. Cfy Capactance of the common mode capactor F TolCy Tolerance n the value of Cfy (%) ICyrms_max Maxmum rms current A VacCy Maxmum AC voltage V A.2.2.10. Thermal Resstance Heat Snk-to-Ambent: Rth_hs_amb ( C/W) If a sngle heat snk s selected, Rth_hs_amb refers to the thermal resstance of ths heat snk. If separate heat snks are selected, Rth_hs_amb refers to the thermal resstance of the swtch heat snk. A.2.2.11. Swtchng Frequency: fs (Hz) A.2.2.12. Contnuous Optmzaton Desgn Varables In the contnuous optmzaton approach all the devces and the boost nductor core shape (torodal) and materal are fxed due to the contnuous nature of the approach to obtan the optmum. Therefore, the prevously explaned parameters of the correspondng desgn varables become constants. Other dscrete desgn varables, such as the EMI flter capactors and the 103

common mode choke, become contnuous and are represented by the correspondng capactance or nductance. The desgn varables are summarzed n Table A.27. Table A.27. Contnuous optmzaton desgn varables. Name Descrpton Unts Cfx Capactance of the dfferental mode capactor Cx F EMI flter Cfy Capactance of the common mode capactor Cy F Lcm Magnetzng nductance of the common mode choke H nturn Boost nductor number of turns -- Boost nductor L B Aw Copper area of the boost nductor wre cm 2 OD External dameter of the boost nductor core cm ID Internal dameter of the boost nductor core cm Ht Heght of the boost nductor core cm fs Swtchng frequency Hz Rth_hs_amb Thermal resstance heat snk to ambent C/W Ht ID OD Aw nturn Fgure A.9. Boost nductor desgn varables n the contnuous approach. 104

A.2.3. Calculatons The equatons and assumptons consdered for the analyss of a desgn defned by a determned choce of the desgn varables are presented n the followng. A.2.3.1. Boost PFC - Assumptons: a) The swtchng frequency >> lne frequency. b) The nput voltage magntude n Fgure A.1-1 s the same as both the magntude of the voltage n Fgure A.1-2 and the magntude of the rectfed voltage n Fgure A.1-3. c) The effect of the dc bas pont of the flux densty n each swtchng perod on the core losses s neglected, accordng to the manufacturer s catalog [20, p. 28]. d) A d/dt =200 A/µs s assumed for the computaton of the reverse-recovery losses of the fast dode. - Equatons: Number of swtchng perods n one half of a lne cycle: num = floor 2 fs flne. Lne and swtchng angular speeds and perods: wlne = 2 π flne, 1 Tlne =, flne ws = 2 π 1 Ts =. fs fs, and 105

Vector contanng the values of the output voltage n Fgure A.1-4 n the mddle of each swtchng perod for one half of a lne cycle: = 1.. num, t = ( 0.5) Ts, and vout = Vbus _ DC 2 Po sn(2 wlne t). wlne Cb Equvalent resstance n seres wth the gate resstance of the MOSFET due to the equvalent seres nductance of the MOSFET: Ls G Re q =. Cssh Inductance ratng consderng the tolerance: tolal = -9 H AL mn AL 1 10 2. 100 nturn Leakage nductance n the boost nductor (formula extracted from the Magnetcs catalogs): TolLblkg 1 292 nturn 100 Ac lm 10 = 1.065 8 Lblkg ( ) Wndow area of the boost nductor core: 2 ID 2 Wa = π (cm ). 4 H. 106

Surface area of the boost nductor, takng nto account the wre (the number of external and nternal layers of wre are estmated): nturn Dw Exlay =, π OD nturn Dw Inlay =, and π OD Asurf = π + + DC resstance of the boost nductor wndng: 2 ( OD + 2 Dw Exlay) ( ID 2 Dw Inlay) 2 ( Ht + 2 Dw Exlay) ( OD + 2 Dw Exlay) ( Ht + 2 Dw Inlay) ( ID 2 Dw Inlay) + +. 2 o Resstvty of the copper, assumng the core s at ts maxmum allowed temperature: [ T _ corelbmax, T max wre, T max PCB dt _ pcb _ ] row = row100 ( 1+ Kcu mn + Lbcore ). o DC resstance value of the wndng: Rcopper = row nturn MLT / Aw. Parameters needed for the estmaton of the skn and proxmty effects [9]: o Skn depth at 100 C and at Fs: deltafs 7.5 = ( ) fs cm. o Average number of layers: nturn Dw em =. lm o Average number of turns per layer: lm nturnlay =. Dw 107

o Bare dameter of the wre (copper only): Aw Dwb = 2. π o Conductor spacng factor or wndng porosty: π nturnlay η = wpor = Dwb. 4 lm o Effectve rato of the conductor thckness to the skn depth: π Dwb ϕ = ph = wpor. 4 deltafs o DC resstance of a layer: 3 nturnlay RcopperDC = row MLT. 2 wpor lm o Auxlary functons of ϕ to estmate the hgh-frequency losses n the wndngs: snh G1 = cosh snh G2 = ( 2 ϕ ) + sn( 2 ϕ ), and ( 2 ϕ ) cos( 2 ϕ ) ( ϕ ) cos( ϕ ) + cosh( ϕ ) sn( ϕ ) cosh( 2 ϕ ) cos( 2 ϕ ). Peak voltage n Fgure A.1-2: Vn _ pk = Vn _ rms 2. Vector contanng the values of the nput voltage n Fgure A.1-2 n the mddle of each swtchng perod for one half of a lne cycle: vn _ vec = Vn _ pk sn( wlne t ). By assumng a certan value of the effcency (eff) from 2 to 4 n Fgure A.1, the juncton temperature of the swtch (Tjsw) n the case of the MOSFET, and the temperature of the boost nductor core (T_coreLb): 108

Input power n Fgure A.1-2: Po Pn =. eff Vector contanng the values of the average (n the swtchng cycle) current n Fgure A.1-2 n the mddle of each swtchng cycle for one half of a lne cycle: On-resstance of the swtch: In _ pk = n _ vec Ronsw = Ronsw Pn 2, and Vn _ rms = In _ pk sn( wlne t 1 ( IGBT ) Ronsw = Ronsw1 + Ronsw2 Tjsw )., and ( MOSFET ). Vector contanng the duty ratos of the swtch for each swtchng perod: vout + VFfd + n _ vec Rcopper vn _ vec d _ vec =. vout + VFfd VFsw n _ vec Ronsw Vector contanng the value of the dc magnetzng force n the boost nductor core for each swtchng cycle: H _ Lb nturn = 0.4 π n _ vec (oersteds). lm Vector contanng the value of the ac flux n the boost nductor core for each swtchng cycle: Bacpk vn _ vec d _ vec Ts 10 = 2 Ac nturn 8 ( Gauss ). Saturaton: The saturaton as a functon of the dc magnetzng force, ac flux, boost nductor core temperature and swtchng frequency s estmated by usng the curve-ft formulae provded by each manufacturer for each core materal. The dfferent coeffcents n the formulae needed for the estmaton of the saturaton are contaned n a matrx called ft. Ths matrx s ntally stored n memory, and ts sze and contents dffer accordng to the core manufacturer 109

/ materal consdered. Snce the curve-ft formulae are only vald for a lmted range of values of the dc magnetzng force, ac flux, boost nductor core temperature and swtchng frequency, and whenever n the process of optmzaton values of these magntudes may go beyond these lmts, some correctons are ntroduced to these equatons to avod unrealstc predctons or crashes of the program. For nstance, f the percentage of saturaton as a functon of the dc magnetzng force s evaluated at a value of the dc magnetzng force hgher than the maxmum value for whch the curve-ft equaton s vald, a complex number may be obtaned by evaluatng the square root of a negatve number, and the program wll crash snce the user wll try to store ths value n a real varable. The program would not crash f a real number were obtaned, but t would stll be a wrong predcton, snce the value of the dc magnetzng force surpassed the maxmum for whch the equaton was vald. o Vector sat contanng the per unt saturaton coeffcent of the boost nductor core for each swtchng cycle: Tol_LBsatdc satdc = 1-100 Tol_LBsatac satac = 1-100 Tol_LBsatac satac = 1-100 1 sat = satdc satac (p.u.). 4 10 Mcrometals ron powder [20]: asdc + csdc H _ Lb + esdc H _ Lb 2 1+ bsdc H _ Lb + dsdc H _ Lb asac + csac Bacpk + esac Bacpk 2 1+ bsac Bacpk + dsac Bacpk 2 2 (%), (%) { Mx. = 2,8,18,26,40}, 2 ( asac + bsac Bacpk + csac Bacpk + dsac Bacpk ) (%) { Mx. = 28,33,38,45,52}, and Tol_LBsatdc satdc = 1-100 Tol_LBsatac satac = 1-100 Tol_LBsatT satt = 1-100 sat = satdc satac satt. Magnetcs hgh flux [30]: 2 1+ asdc µ r H _ Lb + bsdc µ r H _ Lb 2 1+ csdc µ H _ Lb + dsdc µ H _ Lb r 2 3 4 ( asac + bsac Bacpk + csac Bacpk + dsac Bacpk + esac Bacpk ) 2 ( ast + bst T _ corelb + cst T _ corelb ) r 2 2 (p.u.), (p.u.), and (p.u.), 110

Tol_LBsatdc satdc = 1-100 Tol_LBsatac satac = 1-100 Tol_LBsatT satt = 1-100 satt sat = satdc satac 100 Magnetcs kool Mµ [31,32]: 2 1+ asdc µ r H _ Lb + bsdc µ r H _ Lb 2 1+ csdc µ H _ Lb + dsdc µ H _ Lb 2 3 4 ( 1+ asac + bsac Bacpk + csac Bacpk + dsac Bacpk + esac Bacpk ) 2 3 ( 100 + ast + bst TcoreLb + cst TcoreLb + dst TcoreLb + est TcoreLb) (p.u.). r r 2 2 (p.u.), (p.u.), 4 (%.), and Tol_LBsatdc satdc = 1-100 Tol_LBsatac satac = 1-100 Magnetcs molypermalloy [33]: 2 1+ asdc µ r H _ Lb + bsdc µ r H _ Lb 2 1+ csdc µ H _ Lb + dsdc µ H _ Lb 2 3 ( asac + bsac Bacpk + csac Bacpk + dsac Bacpk ) 2 fs fs asfs + bsfs 3 + csfs 3 Tol_LBsatFs 10 10 satfs = 1-2 100 fs fs 1 dsfs esfs + 3 + 3 10 10 Tol_LBsatT satt = 1 ( 1+ ast ( T_coreLb 25) ) (p.u.), and 100 sat = satdc satac satfs satt (p.u.). r r 2 2 2 (p.u.), (p.u.), (p.u.), Vector contanng the value of the boost nductance n each swtchng cycle, consderng the saturaton effect: 2 Lboost = AL mn nturn sat. Vector contanng the value of the peak-to-peak rpple of the boost nductor current for each swtchng cycle. It s obtaned by solvng the dfferental equaton on the boost nductor current durng turn-on of the swtch n each swtchng cycle (see Fgures A.10 and A.11): 111

Lrpple where = vn _ vec VFsw 1 exp d _ vec Ronsw Rcopper + o : Intal nstantaneous current n the swtchng cycle and Ronsw + Rcopper o Ts ln1 o, Lboost Lblkg onmax + vn _ vec VFsw on max : Maxmum possble current durng turn - on =. Ronsw + Rcopper Lboost Lblkg Rcopper Vn_vec + (t) Ronsw Vonsw Fgure A.10. Turn-on transent topology. (t) onmax o d_vec Ts t vn _ vec Vonsw = d( t) dt ( Lboost + Lblkg ) + ( Rcopper + Ronsw) ( t) Fgure A.11. Turn-on transent of the current through the boost nductor. 112

Vector contanng the maxmum value of the boost nductor current n each swtchng perod: Lrpple L max = n _ vec +. 2 Vector contanng the mnmum value of the boost nductor current n each swtchng perod (f any of the components of ths vector s negatve, t s set to zero): L mn Lrpple = n _ vec. 2 Computaton of rms and average currents: o Rms value of the boost nductor current: L _ rms = In _ rms _ sq In _ rms _ sq + ILrpple _ rms _ sq, =, and Ts ILrpple _ rms _ sq = 0.5 Tlne 2 In _ pk 2 Lrpple 2 3 2. o Average current through the rectfer dode: In _ pk Ird _ av =. π o Rms current of the rectfer dode: 1 Ird _ rms = Lrms. 2 o Average current through the swtch: Ts Isw _ av = ( d _ vec n _ vec ). 0.5 Tlne o Rms current of the swtch: 2 Ts 2 1 Lrpple Isw _ rms = d _ vec + n _ vec. 0.5 Tlne 3 2 113

o Average current through the fast dode: Ts Ifd _ av = ( ( 1 d _ vec ) n _ vec ). 0.5 Tlne o Rms current of the fast dode: 2 Ts ( ) 2 1 Lrpple Ifd _ rms = 1 d _ vec + n _ vec. 0.5 Tlne 3 2 Computaton of losses: - Average conducton power loss n one rectfer dode: P _ rd 2 = VFrd Ird _ av + Ronrd Ird _ rms. - Average conducton power loss n the fast dode: P _ fd _ con 2 = VFfd Ifd _ av + Ronfd Ifd _ rms. - Average power loss due to the reverse recovery of the fast dode durng the turn-off of the fast dode: 2 P _ qrr = ( vout ( Qrr1 + Qrr2 L mn )). Tlne - Total average power loss n the fast dode: Perswqrr P _ fd _ tot = P _ fd _ con + P _ qrr 1. 100 - MOSFET:. Average conducton power loss: P _ sw _ con 2 = Ronsw Isw _ rms.. Swtchng loss (refer to Fgures A.3 - A.7): ( log( VGG VT ) log( VGG Vp) ) vart12 = Cssh ( Rgon + Re q), VGG Vp Ig1 =, Rgon 114

115 Crssh Ig Vp vout t = 1 23 var, Crrsl Ig L Ronsw Vp t = 1 mn 34 var, Rgoff Vp Ig = 2, Crssl Ig L Ronsw Vp t = 2 max 67 var, Crssh Ig Vp vout t = 2 78 var, ( ) ) log( ) log( ) Re ( 89 var VT Vp q Rgoff Cssh t + =, ( ) ( ), mn 2 34 var 2 23 var 23 var 2 12 var mn 2 + + + = L Ronsw Vp t Vp vout t t Vp vout t L Tlne on mos P ( ) ( ), max 2 67 var 2 78 var 78 var 2 89 var max 2 + + + = L Ronsw Vp t Vp vout t t Vp vout t L Tlne off mos P ( ) = vout Coss Tlne Coss mos P 2 0.5 2 1, and Coss mos P off mos P on mos P swtch sw P + + =.

- IGBT:. Average conducton power loss: P _ sw _ con 2 = VFsw Isw _ av + Ronsw Isw _ rms.. Swtchng loss: 2 L mn vout P _ gbt _ on = Eon, Tlne IC _ E VCE _ E P _ gbt _ off 2 = Tlne Eoff L max IC _ E vout, and VCE _ E P _ sw _ swt = P _ gbt _ on + P _ gbt _ off. - Total average power loss n the swtch: Perswqrr P _ sw _ tot = P _ sw _ con + P _ sw _ swtch + P _ qrr. 100 - Boost nductor core losses:. Vector contanng the power densty of losses n the boost nductor core for each swtchng cycle: Mcrometals ron powder [20]: Pden Tol _ LBcoreloss 1 + 100 al Bacpk 2 2 mw ( dl fs Bacpk ). _ corelb = + 3 3 fs bl + Bacpk 2.3 cl + Bacpk 1.65 cm Magnetcs Hgh Flux [30]: Pden _ corelb bl cl = 3 Tol _ LBcoreloss Bacpk 1 + al 100 1000 fs 1000 mw. cm Magnetcs Kool Mu [31]: Pden _ corelb al bl = 3 Tol _ LBcoreloss Bacpk 1 + 100 1000 fs 1000 mw. cm 116

Magnetcs Mollypermalloy [33]: Pden _ corelb bl cl = 3 Tol _ LBcoreloss Bacpk 1 + al 100 1000 fs 1000 mw. cm. Average (n half a lne cycle) power loss n the boost nductor core: 3 1 P _ corelb = 10 Vc Pden _ corelb Ts (W). 0.5 Tlne - Boost nductor copper losses:. Hgh-frequency power lost: 2 ( em 1) ( G1 2 2) (W). 2 P _ copperlbhf = Lrpple _ rms _ sq em RcoperDC ph G1 + G 3. Low frequency power lost: P _ copperlblf = Rcopper In _ rms _ sq (W).. Total average power lost: P _ copperlb = P _ copperlblf + P _ copperlbhf (W). - Summary of losses: P _ con = 4 P _ rd + P _ fd _ con + P _ sw _ con, P _ swtchng = P _ qrr + P _ sw _ swt, P _ all _ dev = P _ con + P _ swtchng, and P _ all = P _ all _ dev + P _ corelb + P _ copperlb. - Calculated effcency from 2 to 4 n Fgure A.1: eff P _ all = 1. Po + P _ all Temperatures: - Temperature of the heat snk (the heat snk to whch the swtch s attached): Ths = Power _ dsspated Rth _ hs _ amb + Tamb, where Power_dsspated refers to the power flowng through the heat snk n each case. 117

- Calculated juncton temperature of the swtch: ( RSth _ j _ c + RSth _ c s) Ths Tjsw = P _ sw _ tot _ +. - Juncton temperature of the rectfer dode: ( RRDth _ j _ c + RRDth _ c _ s) Ths _ rd Tjrd = P _ rd +. - Juncton temperature of the fast dode: ( RRDth _ j _ c + RRDth _ c _ s) Ths _ fd Tjfd = P _ fd _ tot +. - Calculated temperature of the boost nductor core [20]: T _ corelb = Tamb + TLbcoef ( P _ corelb + P _ copperlb) Asurf 10 3 0.833 (C). Maxmum value of the peak-to-peak rpple n the boost nductor current: ( ) dil max = max Lrpple. Maxmum nstantaneous value of the boost nductor current: L _ pk = max ( L max ). Peak value of the boost nductor core DC magnetzng force: Hdc _ pk max [ H _ Lb ] (oersteds) =. Peak value of the boost nductor core flux densty: Bdc 1 = Brem, Bdc = Bdc Bpk = max 1 + Lboost n _ vec + 1 n _ vec 4 nturn Ac 10 4 [ Bdc + Bacpk 10 ] (T). (T), and where Brem s the resdual flux densty n the core (value of the flux densty n the crossng of the B-H curve wth the axs H=0). 118

A.2.3.2. EMI Flter - Assumptons: a) Accordng to the methodology used to estmate the EMI levels, only one value of the boost nductance needs to be consdered. Therefore, the dfferent values of nductance obtaned can not be used due to the effect of saturaton of the core. The value of the boost nductance wll be assumed to be the average value of the nductance along the lne cycle consderng the saturaton. b) A waveform wth constant slopes for the rsng and fallng edges has been consdered for the perturbaton source (see Fgure A.12). The rngng has not been ncluded. Vds(t) Vbus_DC 0 Ts 2*Ts d_vec *Ts d_vec (+1) *Ts t(s) Fgure A.12. Tme doman evoluton of the commutaton cell equvalent voltage source. c) The system confguraton between mans and the brdge rectfer s assumed to be symmetrcal wth respect to ground. 119

General computaton of parameters: Vector contanng the rse tme of the voltage across the MOSFET durng turn-off n each swtchng perod: Trse = var t78. Vector contanng the fall tme of the voltage across the MOSFET durng turn-on n each swtchng perod: Tfall = var t23. Value of boost nductance to be consdered: Lboost Lb = Lbav =. num Spectral doman defnton: Order wth respect to the swtchng frequency of the frst and last group of harmoncs (at multples of the swtchng frequency) to be consdered above the ntal frequency for whch the standard s defned: std1,1 ord1stlmhgr = celng, and fs ordmaxlmhgr = ord1stlmhgr + nharmgr + 1. Order wth respect to the swtchng frequency of the frst group of harmoncs (at multples of the swtchng frequency) to be analyzed: For the optmzaton process: ndexharm = ord1stlmhgr and For desgn performance report: ndexharm = 1. Harmonc number wth respect to the lne frequency correspondng to the swtchng frequency: fs Fs hn = floor. flne 120

Frequency of the last group of harmoncs to be consdered: F max = fs ordmaxlmhgr. Number of harmoncs (multple of the lne frequency) n each group of harmoncs (at multples of the swtchng frequency) to be consdered for the estmaton of the EMI levels of each group: lar = 2 nd. Vector contanng the harmonc number (wth respect to the lne frequency) of the harmoncs to be analyzed: Spec = [ a Fs ( a + 1) Fs ( a + 2) Fs b Fs hn hn hn hn nd + 1, nd + 1, nd + 1, nd + 1,,,,, b Fs a Fs ( a + 1) Fs ( a + 2) Fs hn 1, hn 1, hn hn b Fs 1, 1, hn, a Fs hn, ( a + 1) Fs ( a + 2) Fs b Fs hn a Fs hn + 1,, hn hn,, + 1,, ( a + 1) Fs ( a + 2) Fs b Fs hn hn a Fs + 1, hn + 1, + nd, hn + nd,,, ],, ( a + 1) Fs hn ( a + 2) Fs + nd, hn + nd,,, where a = ndexharm and b = ordmaxlmhgr. Ths vector contans the harmonc number of those harmoncs multple of the swtchng frequency to be consdered untl Fmax, plus several harmoncs around all of them. Number of harmoncs contaned n Spec: nharm = length(spec). Vector contanng the Laplace operator for each harmonc n Spec: p n = wlne Spec j n=1,.., nharm. n 121

Computaton of the dsturbance voltage source (Vpert n Fgure A.13) harmoncs Z1 Z4 Z8 Z13 Z17 D Vn + - I 1 Z2 I 2 Z6 I 4 Z9 Z11 I 12 Z23 I 6 Z15 Z24 G I 13 Z22 I 8 I 10 Z19 Z20 + - Vpert Z3 I 3 Z7 I 5 Z10 Z12 I 7 Z16 I 9 Z21 I 11 S Z5 Z14 Z18 Fgure A.13. Equvalent mpedance dagram of the whole system (LISN + EMI flter + boost PFC stage). Vector contanng the nharm harmoncs specfed n Spec: C5 n Vbus _ DC = 2 flne 1 e p n voutk + Trse p k 2 n Tlne pn 2 + num k = 1 voutk Tfallk p ( ( k 1) + d _ vec ) ( ( ( 1) + _ ) + ) k Ts pn k d veck Ts Trsek pn ( e e ). Vector contanng the ampltude of the prevous harmoncs: 2 n Mod = 2 * C5. n n ( k 1) Ts pn ( ( k 1) Ts+ Tfallk ) pn ( e + e ) + 122

Computaton of the mpedance model of the system Impedances n Fgure A.13: Z1 = Lres p( n), 1 Z2 = Z3 =, C1 p( n) Z4 = Z5 = LN p( n), 1 Z6 = Z7 = ZN +, CN p( n) Z8 = Llha p( n), Z9 = Llmg p( n), Z10 = Lldb p( n), Z11 = Z12 = 10 Z13 = Z14 = Ldm p( n), Z15 = Z16 = 7 1 ( Ceg + Cag + Cfy) 1 ( Cfg + Cbg + Cfy),, p( n), p( n) 1 Z17 = 1 CLb p( n) + + Lb p( n) Z18 = Lfs p( n), 1 Z19 =, Cdg p( n) 1 Z 20 =, Csg p( n) 1 Z 21 =, Ckg p( n) 1 Z 22 = Z 23 = Cfx p( n) Z 24 = Lcm p( n)., and, 1 + Lblkg p( n) RLb Defnng the loop currents ndcated n red n Fgure A.13 allows for the dervaton the mpedance matrx (A) related to these loop currents, such that: H H V = [ A] I, I 1 H I 2 I : Vector _ of _ loop _ currents =, and I13 V1 = Vn 0 H 0 V : Vector _ of _ loop _ voltage _ sources =. V 10 = Vpert 0 0 123

Dagonal elements of the mpedance matrx (A), descrptve of the system n Fgure A.13: ZC1 = Z1 + Z2 + Z3, ZC2 = Z2 + Z4 + Z6, ZC3 = Z3 + Z5 + Z7, ZC4 = Z6 + Z8 + Z9 + Z11, ZC5 = Z7 + Z9 + Z10 + Z12, ZC6 = Z11 + Z13 + Z15 + Z24, ZC7 = Z12 + Z14 + Z16 + Z24, ZC8 = Z15 + Z17 + Z19, ZC9 = Z16 + Z18 + Z20, ZC10 = Z19 + Z20, ZC11 = Z20 + Z21, ZC12 = Z11 + Z12 + Z23, and ZC13 = Z15 + Z16 + Z22. Impedance matrx A: A n =[ZC1 -Z2 Z3 0 0 0 0 0 0 0 0 0 0; -Z2 ZC2 0 -Z6 0 0 0 0 0 0 0 0 0; Z3 0 ZC3 0 -Z7 0 0 0 0 0 0 0 0; 0 -Z6 0 ZC4 Z9 -Z11 0 0 0 0 0 -Z11 0; 0 0 -Z7 Z9 ZC5 0 -Z12 0 0 0 0 Z12 0; 0 0 0 -Z11 0 ZC6 Z24 -Z15 0 0 0 Z11 -Z15; 0 0 0 0 -Z12 Z24 ZC7 0 -Z16 0 0 -Z12 Z16; 0 0 0 0 0 -Z15 0 ZC8 0 -Z19 0 0 Z15; 0 0 0 0 0 0 -Z16 0 ZC9 Z20 Z20 0 -Z16; 0 0 0 0 0 0 0 -Z19 Z20 ZC10 Z20 0 0; 0 0 0 0 0 0 0 0 Z20 Z20 ZC11 0 0; 0 0 0 -Z11 Z12 Z11 -Z12 0 0 0 0 ZC12 0; 0 0 0 0 0 -Z15 Z16 Z15 -Z16 0 0 0 ZC13] 124

Computaton of EMI flter capactor currents and EMI levels Vector contanng the voltage sources n the model of Fgure A.13 for the harmonc n of frequency hgher than the lne frequency: V = 0 h 10, and h V = C5. 10 n Matrx contanng all the loop currents n Fgure A.13 for the harmoncs of order n: R n = A 1, n Vh. Varables contanng the rms current of the EMI flter capactors Cx and Cy (only computed when a desgn report s requred): Capactors Cx: Capactors Cy: ICfx 1 _ rms, ICfx2 _ rms and ICfy 1 _ rms, ICfy2 _ rms. LISN leg current harmonc of order n: Ihf Tlne p ( ) n 2 = R2, n R4, n R5, n R3, n e. Vector contanng the magntude of the voltage harmoncs generated n LISN leg resstance (ZN): MIhf n = Ihf ZN. Vector contanng the square root of the quadratc sum of the odd harmoncs of Mhf n around each multple of the swtchng frequency, correspondng to dfferental mode dsturbance (harmonc group numbers from ndexharm to ordmaxlmhgr), addng ncr dbµv: HDQuad m (dbµv). Vector contanng the square root of the quadratc sum of the even harmoncs of Mhf n around each multple of the swtchng frequency, correspondng to common mode 125

dsturbance (harmonc group numbers from ndexharm to ordmaxlmhgr), addng ncr dbµv: HCQuad m (dbµv). Vector contanng the square root of the quadratc sum of all harmoncs of Mhf n around each multple of the swtchng frequency, correspondng to the total nose (harmonc group numbers from 1 to ordmaxlmhgr). Strctly, these total nose levels are the ones that should be smaller than the maxmum levels specfed by the standard. Ths vector s only computed when a desgn report s requred. HQuad m (dbµv). Vector contanng the requred level n the LISN resstor voltage specfed by the standard at each multple of the swtchng frequency (from ord1stlmhgr fs to ordmaxlmhgr fs): Re q _ Level q (dbµv). Vector contanng the requred attenuaton n the LISN resstor voltage correspondng to dfferental mode nose n order for the harmonc group numbers from ord1stlmhgr to ordmaxlmhgr to meet the standard (the dfferental nose level must be less than the standard level expressed n V dvded by 126 2 or, what s equvalent, the standard level expressed n dbµ mnus 3 db). The requred attenuaton s expressed n a per unt value: HDQuad m Re q _ DM _ attq = 1 (p.u.). Re q _ Level 3 Vector contanng the requred attenuaton n the LISN resstor voltage correspondng to common mode nose n order for the harmonc group numbers from ord1stlmhgr to ordmaxlmhgr to meet the standard (the common nose level must be less than the standard level expressed n V dvded by q 2 or, what s equvalent, the standard level expressed n dbµ mnus 3 db). The requred attenuaton s expressed n a per unt value: HCQuad m Re q _ CM _ attq = 1 (p.u.). Re q _ Level 3 q

A.2.3.3. Contnuous optmzaton calculatons In the contnuous optmzaton approach, the calculatons are essentally analogous to the dscrete approach, wth the followng addtons: Core mean magnetc path length: OD ID lm = π (cm). 2 Core cross-secton area: OD ID Ac = Ht (cm). 2 Core volume: Mean length per turn: 2 2 π 3 ( OD ID ) (cm ) Vc = Ht. 4 MLT ( OD ) (cm) = 2 Ht + ID. Wndow area: 2 ID 2 Wa = π (cm ). 4 Inductance ratng of the core: Wre dameter: 2 Ac AL = 10 uo ur lm 7 ( uo = 4 π 10 ). 4 Aw Dw = (cm). π H turn 2 127

Parastc (resultng from leakage) dfferental mode nductance of the common mode choke. Assumed to be 0.2% of the common mode nductance: Ldm = 0.002 Lcm (cm). 128

A.2.4. Cost Functon The cost functon to be mnmzed by the optmzer refers to the total cost of the desgn expressed n m.u. It s the frst component of the response vector that the functon provdes as an output. It s as follows: resp(1) = Cost_HS+Cost_Lbcore+Cost_Lbfxwrng+Cost_Lbvarwrng+Cost_choke+ +2*Cost_Cx+2*Cost_Cy+Cost_Cb+Cost_swtch+Cost_fastdode+4*Cost_rectdode. Boost nductor wre and manufacturng cost: Cost _ Lbwre _ and _ manuf = Cost _ Lbfxwrng + Cost _ Lb var wrng Cost _ Lb var wrng = Cost _ Lbwre nturn MLT. If anyone of the coeffcents Cost_Lbfxwrng or Cost_Lbwre s not drectly avalable, the followng procedure can be used to obtan an estmaton of ts value. a) Select a set of boost nductors for whch the total cost and the cost of the core s known. Calculate the wre and manufacturng cost by subtractng the cost of the core to the total cost. Addtonally, calculate the volume of wre used n each boost nductor. In Table A.28, an example s shown. Table A.28. Breakdown of the cost of several boost nductors. Boost nductor Total cost (m.u.) Cost core (m.u.) Cost_Lbwre_and_manuf =Total Cost-Cost Core (m.u.) Wre volume =Aw.nturn.MLT (cm 3 ) 1 49.6 10.528 39.072 4.713 2 52.8 10.528 42.272 4.713 3 33.6 4.704 28.896 7.326 4 62.4 10.528 51.872 11.781 5 52.48 10.528 41.952 8.659 6 53.76 10.528 43.232 12.242 7 57.28 10.528 46.752 15.526 129

b) Approxmate the wre and manufacturng cost by a frst order polynomal functon of the wre volume. For nstance, n the prevous example: Cost _ Lbwre _ and _ manuf K1 = 35.2 m. u., and m. u. K2 = 0. 736. 3 cm = K1 + K2 Volume _ wre 3 ( cm ) (m.u.), 60 50 Cost_Lbwre_and_manuf (m.u.) 40 30 20 10 Cost_Lbwre_and_manuf Approxmaton 0 0 5 10 15 20 25 Wre volume (cm3) Fgure A.14. Cost of the boost nductor wre and manufacturng and ts approxmaton by a frstorder polynomal functon of the wre volume. c) Fnally, the coeffcents sought can be estmated to be: Cost of the heat snk: Cost _ Lbfxwrng = K1 (m.u.), and Cost _ Lb var wrng = K2 Aw cm 2 m.u. ( ). The cost of the heat snk has been approxmated by means of a polynomal functon based on the cost nformaton avalable. The cost of the heat snk has been assumed to be a functon of ts cm 130

thermal resstance to the ambent. In Table A.29, the cost nformaton of several heat snks specfyng ther thermal resstance s presented. Table A.29. Thermal resstance heat snk-to-ambent and cost for several heat snks. Heat snk Rth_HS Cost (m.u.) 7.8 4.64 5.3 4.96 3.7 5.28 Heat snk Rth_HS Cost (m.u.) 2.3 17.6 1.4 25.92 0.7 57.6 In Fgure A.15, ths cost nformaton s plotted as a functon of the thermal resstance heat snk to ambent (dots). 70 60 Data Polynomal 50 Cost_HS (m.u.) 40 30 20 10 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1/Rth_hs_amb (W/C) Fgure A.15. Heat snk cost as a functon of the nverse of the thermal resstance and polynomal approxmaton. 131

The functon that approxmates ths data s also plotted n Fgure A.15 (contnuous lne). The expresson for ths functon s: Cost_HS=K1HS+K2HS*(1/Rth_hs_amb), K1HS = 0 (m.u.), and K2HS = 40.64 (m.u.*c/w). A.2.4.1. Addtonal Cost Estmatons for Contnuous Optmzaton In the contnuous optmzaton approach, the cost of the boost nductor core, the cost of the common mode choke, and the cost of the two EMI flter capactors must be estmated as a functon of the correspondng desgn varables. Ths cost approxmaton has been performed by means of polynomal functons based on the cost nformaton avalable, as shown next. Cost of the boost nductor core: The cost of the boost nductor core has been assumed to be a functon of the volume of the core. In Table A.30, the cost nformaton of several ron powder cores specfyng ther volume s presented. Table A.30. Volume and cost of several boost nductor cores. L B core Vc (cm 3 ) Cost (m.u.) 2.16 1.536 4.28 2.304 3.55 2.112 5.78 2.88 6.84 3.456 6.41 3.264 6.16 3.072 8.31 4.032 10.7 4.992 L B core Vc (cm 3 ) Cost (m.u.) 15 6.528 21 9.024 16.4 7.296 33.2 13.824 20.7 8.832 52.3 21.696 57.4 24 33.4 14.016 86.4 36.096 132

In Fgure A.16, ths cost nformaton s plotted as a functon of the volume of the core (dots). 40 35 30 Data Polynomal Cost (m.u.) 25 20 15 10 5 0 0 20 40 60 80 100 Vc(cm^3) Fgure A.16. Boost nductor cost as a functon of the volume of the core and polynomal approxmaton. The functon that approxmates ths data s also plotted (contnuous lne). The expresson for ths functon s: Cost_Lbcore = K1Lbc+K2Lbc*Vc+K3Lbc*Vc 2, K1Lbc = 0.7008, K2Lbc = 0.3904, and K3Lbc = 0.000216. Cost of the common mode choke: The cost of the common mode choke has been assumed to be a functon of the common mode nductance (Lcm) of the component (for a gven value of the rated rms current). In Table A.31, the cost nformaton avalable at the tme the approxmaton was performed s presented (only cores of 7.5 maxmum rms current have been consdered). 133

Table A.31. Common mode nductance and cost of several common mode chokes. Common mode choke Lcm (H) Cost (m.u.) 1.50E-03 20.8 3.30E-03 31.2 Snce at that tme there were only two data ponts avalable, the cost of the common mode choke was approxmated by a straght lne passng through them: Cost_Lcm = K1Lcm+K2Lcm*Lcm, K1Lcm = 12.13, and K2Lcm = 5777.78. Cost of the capactor Cx: The cost of the capactor Cx has been assumed to be a functon of ts capactance. In Table A.32, the cost nformaton of several capactors specfyng ther capactance s presented. Table A.32. Capactance and cost of several dfferental mode capactors. Capactor Cx Cfx (F) Cost (m.u.) 2.20E-07 1.856 3.30E-07 2.176 4.70E-07 2.496 1.00E-06 3.52 2.20E-06 9.28 134

In Fgure A.17, ths cost nformaton s plotted as a functon of the capactance (dots). 3.5 3 Data Sngle Polynomal 2.5 Cost (m.u.) 2 1.5 1 0.5 0 0.00E+00 5.00E-07 1.00E-06 1.50E-06 2.00E-06 2.50E-06 Cx (F) Fgure A.17. Dfferental mode capactor cost as a functon of the capactance and polynomal approxmaton. The functon that approxmates ths data s also plotted (contnuous lne). The expresson for ths functon s: Cost_Cx=K1Cx+K2Cx*Cfx 2, K1Cx = 1.9904, and K2Cx = 1.51e+12. Cost of the capactor Cy: The cost of the capactor Cy has been assumed to be a functon of ts capactance. In Table A.33, the cost nformaton of several capactors specfyng ther capactance s presented. 135

Table A.33. Capactance and cost of several common mode capactors. Capactor Cy Cfy (F) Cost (m.u.) 4.70E-09 1.248 1.00E-08 1.472 4.70E-08 2.528 1.00E-07 3.584 3.30E-07 7.968 In Fgure A.18, ths cost nformaton s plotted as a functon of the capactance (dots). 9 8 7 Data Sngle Polynomal 6 Cost (m.u.) 5 4 3 2 1 0 0.00E+00 5.00E-08 1.00E-07 1.50E-07 2.00E-07 2.50E-07 3.00E-07 3.50E-07 Cy(F) Fgure A.18. Common mode capactor cost as a functon of the capactance and polynomal approxmaton. 136

The functon that approxmates ths data s also plotted (contnuous lne). The expresson for ths functon s: Cost_Cy = K1Cy+K2Cy*Cfy, K1Cy = 1.3696, and K2Cy = 2024e4. 137

A.2.5. Constrants All the values of the constrants consttute the rest of the components of the response vector of the functon (the value of the cost functon s the frst component of ths vector). These constrants are normalzed and expressed n such a way that f the correspondng component of the response vector obtaned s negatve then the constrant s not volated. If t s postve, the constrant s volated. The constrants consdered are the followng (notce that ther poston n the response vector (resp) s also specfed). The maxmum peak-to-peak current rpple n the boost nductor cannot be hgher than 150% of the peak average (n a swtchng perod) nput current. Ths constrant s set to lmt the amount of tme the converter s operatng n dscontnuous current mode: dil max resp 2 = 1. 1.5 In _ pk Temperature constrants: o The juncton temperature of the swtch should be lower than ts maxmum: Tjsw resp = 1 3 T max sw. o The temperature of the heat snk should be lower than ts maxmum: Ths resp = 1 4 T max HS. o The temperature of the boost nductor core should be lower than ts maxmum: resp = mn T _ corelb ( T _ corelbmax, T max wre, T max PCB + dt _ pcb _ Lbcore) 5 1. o The juncton temperature of the fast dode should be lower than ts maxmum: Tjfd resp 6 = 1. T max fd 138

o The juncton temperature of the rectfer dode (or rectfer brdge) should be lower than ts maxmum: Tjrd resp = 1 7 T max rd. Voltage ratng constrants: o The breakdown voltage of the MOSFET should exceed the mnmum requred breakdown voltage: resp 8 Vpksw = 1. VpkM mn o The breakdown voltage of the IGBT should exceed the mnmum requred breakdown voltage: resp 8 Vpksw = 1. VpkIG mn o The breakdown voltage of the fast dode should exceed the mnmum requred breakdown voltage: resp 9 Vpkfd = 1. Vpkfd mn o The breakdown voltage of the rectfer dode should exceed the mnmum requred breakdown voltage: resp 10 Vpkrd = 1. Vpkrd mn o The maxmum AC (rms) voltage of the dfferental mode capactor Cx should exceed the mnmum requred AC (rms) voltage: resp 11 VacCx = 1. VacCx mn o The maxmum AC (rms) voltage of the common mode capactor Cy should exceed the mnmum requred AC (rms) voltage: 139

resp 12 VacCy = 1. VacCy mn Current ratng constrants: o The rms current n the MOSFET cannot exceed the maxmum allowed rms current: Isw _ rms resp 13 = 1. Iswrms max o The average current n the IGBT cannot exceed the maxmum allowed average current: Isw _ av resp 13 = 1. Iswav max o The average current n the fast dode cannot exceed the maxmum allowed average current: Ifd _ av resp 14 = 1. Ifdav max o The average current n the rectfer dode cannot exceed the maxmum allowed average current: Ird _ av resp 15 = 1. Irdav max o The maxmum surge current that the fast dode s able to wthstand should exceed the maxmum surge current determned for the system: resp 16 IFSMfd = 1. IFSM mn o The maxmum surge current that the rectfer dode s able to wthstand should exceed the maxmum surge current determned for the system: resp 17 IFSMrd = 1. IFSM mn 140

o The rms current through the common mode choke cannot exceed the maxmum allowed rms current: L _ rms resp 18= 1. ICHrms _ max The peak value of the flux densty n the boost nductor core cannot exceed the maxmum value defned for ts materal. Bpk resp = 1 19 B max( cd 2). The current densty n the boost nductor wre cannot exceed the maxmum current densty defned for the copper: L _ rms Aw resp 20 = 1. Jm The wre should ft n the avalable wndow area of the core, accordng to the fllng factor (Ku) consdered. The cross-secton of the wre s consdered to be a square of sde the dameter of the wre (conservatve assumpton): 2 nturn Dw resp 21 = 1. Ku Wa The dfferental mode dsturbance level for each of the nharmgr group of harmoncs around a multple of the swtchng frequency consdered above the mnmum frequency where the standard lmts are defned should be lower than the standard level defned for ts frequency dvded by the square root of two: resp 22 = max m HDQuad q = 1. ( Re _ DM _ att ) m m ( Re q _ Level 3) q The common mode dsturbance level for each of the nharmgr group of harmoncs around a multple of the swtchng frequency consdered above the mnmum frequency where 141

the standard lmts are defned should be lower than the standard level defned for ts frequency dvded by the square root of two: resp HCQuad m max m ( Re q _ CM _ att m ) = 1. 23 = ( Re q _ Level 3) If the prevous two constrants are satsfed, then the total EMI nose level wll be smaller than the standard lmts. Constrants resp 8 to resp 12, resp 16 and resp 17 are essentally boundares for the desgn varable parameters that can be checked ntally wthout requrng an analyss of the desgn. Therefore, n the OPES software all components are checked n the begnnng and those not meetng these constrants are dscarded. - Specal boundares on the desgn varables: o Swtchng frequency boundares: 20kHz fs 150kHz. o Number of turns boundary: nturn 1. o Heat snk thermal resstance boundary: Rth _ hs _ amb > 0. A.2.5.1. Contnuous Optmzaton Constrants In the contnuous optmzaton approach, the constrants are essentally the same as n the dscrete, except for the followng. There s no need to check n the analyss the constrants related to resp 8 to resp 12, resp 16 and resp 17. By choosng the approprate fxed devces, these constrants wll be met. 142

Addtonal constrant: The nternal dameter of the core must be at least 0.5 cm smaller than the external dameter: ( OD ID) resp = 1. 0.5 Boundares on the desgn varables: ID, OD, Ht, Lcm, Cfx, Cfy 0, nturn 1, Aw 0.0202 10 Rth_hs_amb 01,. 20 khz fs 150 khz, and Cfy 10 8 F. 3 cm 2, 143

A.2.6. User Gude to Run the MATLAB Analyss Program Before usng the program, the fles Danalyze.m, Boost_analyss.m, Zmodel.m and Ddesgndata.m must be placed n the default folder used by MATLAB or the user should go to Fle>Set Path and specfy the folder where these fles have been placed. Once ths s done, the fle Ddesgndata.m must be edted to ntroduce the desgn varable parameter values. Each desgn varable s defned as a vector of parameters. In Secton A.2.2, these desgn varables are presented, and ther parameters are specfed n the same order as they must be ntroduced n the vectors of the fle Ddesgndata.m. An example of nput vectors contanng the values of the dfferent parameters that defne the desgn varables can be found n ths fle. Once ths nformaton s edted, the fle must be saved and run from the MATLAB envronment by typng: Ddesgndata. (In ths fle not only are the desgn varable parameters ntroduced, but also the functon Danalyze s called, so that the analyss of the desgn s performed.) A desgn report ncludng several plots wll appear f the nternal constant aff of the functon Danalyze s set to 1. For a descrpton of the nformaton presented n the report, please refer to the OPES software User Manual. If aff s set to a value dfferent from 1, only the vector resp contanng the responses of the analyss wll be echoed n the screen. Ths vector contans n ts frst component the estmated cost of the desgn n m.u. and, n all the others, the value of the constrants (refer to Sectons A.2.4 and A.2.5 for more nformaton). A negatve value of the constrants means that the lmt specfed by the constrant has not been reached. A postve value means that t has been surpassed. To modfy any of the constants or equatons prevously descrbed n the appendx, edt the fle Danalyze.m. A.2.6.1. Contnuous Optmzaton In the contnuous optmzaton approach, the gudelnes for edtng the desgn varable nformaton and runnng the MATLAB analyss program are analogous to those prevously presented. In ths case, however, the correspondng fles are: Canalyze.m, Boost_analyss.m, Zmodel.m, and Cdesgndata.m. To run the desgn analyss, we must now type: Cdesgndata. 144

A.3. Possble Model Improvements and Extensons In ths secton, some possble modfcatons to the component parameter defnton n order to extend the capabltes of the software desgn tool developed wll be dscussed. A.3.1. Boost Inductor Core In the OPES software desgn tool, only torodal cores can be consdered. The torodal shape was assumed to be the most cost-effectve soluton. However, f there was an nterest n consderng other core shapes, some modfcatons should be ntroduced. Frst of all and n general, a new contnuous desgn varable should be ntroduced,.e., the gap of the core, because some of the core shapes present ths geometrcal parameter as a desgn varable. The core parameters should also be modfed, so that they are approprate for the dfferent core shape optons. In Table A.34, a defnton of these parameters s proposed. Table A.34. Proposed new defnton of the boost nductor core parameters. Parameter name Descrpton Unts Cost_Lbcore Cost of the boost nductor core m.u. Cd1 Integer value to codfy the core shape ------- Cd2 * Cd3 AL Integer value to codfy the manufacturer-core materal Integer value to codfy the types of core wthn a materal defned n cd1, typcally the dfferent permeabltes possble Inductance ratng of the core (nh for one turn mh for 1000 turns) ------- ------- nh/(turn^2) mh/(1000_turn^2) TolAL Tolerance of the value of AL % 145

Dm1 Dm2 Parameter 1 to specfy a characterstc dmenson of the core shape geometry Parameter 2 to specfy a characterstc dmenson of the core shape geometry cm cm Dm10 Parameter 10 to specfy a characterstc dmenson of the core shape geometry cm lm Mean magnetc path cm Ac Cross-sectonal area of the core cm 2 Vc Volume of the core cm 3 MLT Mean length per turn (In the case of the Mcrometals catalog, ths value can be obtaned from pages 60-61.) cm T_coreLbmax Maxmum temperature of the core C * Snce shapes that can be gapped can be ncluded, ferrte wll now become a possble choce for the materal. Wth ths parameter defnton, the user should be able to nclude as many core shapes and materals as desred by smply modfyng the Fortran desgn analyss code. No modfcaton to the graphcal user nterface would be requred. A.3.2. Capactors and Common Mode Choke Among the desgn parameters for the capactors and common mode choke, the equvalent seres resstance (ESR) should be specfed, so that the power lost n the component can be computed by smply multplyng ths resstance by the rms current through the component. Ths power lost would then modfy the estmaton of the overall nput power requred for a gven output power. If a thermal resstance for the component were provded, t could also be ncluded as a parameter so that the temperature rse n the component could be estmated by smply multplyng ths thermal resstance to the power lost n the component. Then, by addng the 146

ambent temperature, the temperature of the component could be predcted and a new constrant added that specfed the lmt on ths temperature. Ths constrant would naturally replace the constrant specfyng the maxmum component rms current, snce ths constrant was set to ndrectly specfy the maxmum temperature of the component. In ths case, the component parameter specfyng the maxmum rms current for a gven ambent temperature should be replaced by the maxmum temperature of the component. 147

Appendx B. Expermental Verfcaton of the Desgn Analyss Functon Predctons Ths appendx presents the tunng and predcton valdaton of the models by means of expermental testng for two dfferent prototypes. The frst expermental test for each prototype s used to tune the core temperature predcton by adjustng the value of the parameter TLbcoef. Also, the swtch collector-to-ground parastc capactance (C DG ) s measured to adjust the common mode nose predctons n the software. The common mode nose level s sgnfcantly senstve to the value of ths parastc. Three dfferent predcton values are presented for the dfferent magntudes nvestgated: non-conservatve, average and conservatve. Based on the tolerances provded by the manufacturer, these dfferent predcton values have been obtaned consderng the followng devatons wth respect to the nomnal values, and are shown n Table B.1. Table B.1. Devaton wth respect to the nomnal value of dfferent parameters and magntudes. Devaton Predcton (% wth respect to nomnal value) Non-conservatve Average Conservatve AL +10 0-10 Percent permeablty vs. +10 0-10 dc magnetzng force Percent permeablty vs. +10 0-10 ac magnetzng force Core loss vs. peak ac flux -15 0 +15 densty Capactance Cx +10 0-10 Capactance Cy +20 0-20 Common mode choke nductance Lcm +30 0-30 148

B.1. Prototype 1 B.1.1. TEST 1: Model Tunng Test Table B.2. Condtons. Parameter Value Tamb_ext Tamb_prot * Vn flne Po Vo * Ths s the assumed value. 23 o C 28 o C 180 Vrms 50 Hz 1155 W 368 V Table B.3. Measures and predctons. Magntude Measured Predcted Non-conservatve Average Conservatve Pn (W) * 1217 1224 1203 1205 1208 In_rms (A) * 6.83 6.70 6.74 6.79 L_pk (A) * 11.16 10.68 11.12 11.80 dilmax (A) 4.35 2.49 3.34 4.67 Lb_mn (µh) 636 863 647 471 T_coreLb ( o C) 165 147 160 172 Ths_sw ( o C) 78 77.3 78.0 79.2 Ths_fd ( o C) 45 46.4 46.4 46.4 Ths_rd ( o C) 135 134.9 135.2 135.8 C DG (pf) 9 --------- --------- --------- * The predctons do not nclude the power dsspated n both the PFC stage EMI flter, measured 8.9W, and load nternal EMI flter and electrolytc capactors, measured 3 6W, globally estmated to be between 11.9 and 14.9W. Wthout rngng ampltude, measured 0.6 A; Settng TL B coef = 1.3. 149

B.1.2. TEST 2: Modfcaton of the Boost Inductor Number of Turns Table B.4. Condtons: Modfed L B s T225-26 wth 75 turns. Parameter Value Tamb_ext ( o C) 23 Tamb_prot * 28 o C Vn (V) 180 Flne (Hz) 50 Po (W) 1154 Vo (V) 368.5 * Ths s the assumed value. Table B.5. Measures and predctons. Predcted Magntude Measured Non-conservatve Average Conservatve Pn (W) * 1234 1210 1215 1219 In_rms (A) * 6.87 6.76 6.82 6.9 Lb_pk (A) 12.76 11.08 11.66 12.55 dilbmax (A) 5.83 3.20 4.30 6.01 Lb_mn (µh) 444.06 675 505 367 T_coreLb ( o C) 199 192 213 233 Ths _sw ( o C) 76 78.2 79.3 80.9 Ths _fd ( o C) 49 46.5 46.5 46.6 Ths _rd ( o C) 131 135.7 136.4 137.3 * The predctons do not nclude the power dsspated n the PFC stage EMI flter, load nternal EMI flter and electrolytc capactors. 150

B.1.3. TEST 3: Modfcaton of the Swtchng Frequency Table B.6. Condtons: Modfed swtchng frequency Fs = 55 khz. Parameter Value Tamb_ext ( o C) 23 Tamb_prot * 34 o C Vn (V) 180 Flne (Hz) 50 Po (W) 1156 Vo (V) 368.7 * Ths s the assumed value. Table B.7. Measures and predctons. Predcted Magntude Measured Non-conservatve Average Conservatve Pn (W) * 1230 1204 1206 1209 In_rms (A) * 6.85 6.70 6.72 6.76 Lb_pk (A) 11.48 10.35 10.68 11.17 dilbmax (A) 3.08 1.81 2.43 3.40 Lb_mn (µh) 615 754 565 412 T_coreLb ( o C) 131 133 142 151 Ths _sw ( o C) 100 100.1 100.9 102.2 Ths _fd ( o C) 55 54.8 54.8 54.8 Ths _rd ( o C) 131 141.0 141.2 141.6 * The predctons do not nclude the power dsspated n the PFC stage EMI flter, load nternal EMI flter and electrolytc capactors. 151

B.1.4. TEST 4: Varaton n the Output Power Table B.8. Condtons. Parameter Value Tamb ( o C) 22 Tamb_prot * 30 o C Vn (V) 180 Flne (Hz) 50 Po (W) 740 Vo (V) 367 * Ths s the assumed value. Table B.9. Measures and predctons. Predcted Magntude Measured Non-conservatve Average Conservatve Pn (W) * 782 774 776 779 In_rms (A) * 4.36 4.32 4.35 4.40 Lb_pk (A) 7.6 6.97 7.29 7.78 dilbmax (A) 3.2 1.80 2.42 3.36 Lb_mn (µh) 795 1204 902 656 T_coreLb ( o C) 140 131 144 156 Ths _sw ( o C) 59 61.6 62.2 63.1 Ths _fd ( o C) 43 41.8 41.8 41.8 Ths _rd ( o C) 98 94.1 94.4 94.8 * The predctons do not nclude the power dsspated n the PFC stage EMI flter, load nternal EMI flter and electrolytc capactors. 152

B.1.5. TEST 5: Valdaton of EMI Levels Predcton Table B.10. Condtons. Parameter Value Tamb Tamb_prot * Vn flne Po Vo 27 o C 35 o C 230 Vrms 50 Hz 1150 W 368 V * Ths s the assumed value. B.1.5.1. Measures and predctons for EMI Levels I) Total nose: I.1) Measured 65 Total Nose: Desgn #1: Vn=230, Vo=368, Io=3.125 60 55 Ampltude (dbuv) 50 45 40 35 10 6 10 7 Frequency (Hz) Fgure B.1. Measured total EMI nose. 153

I.2) Predcted (consderng L B = L B_mn ): - Frst lmted group of harmoncs: Group of harmoncs order = 5 Frequency (khz) = 175.05 Standard level (dbuv) = 64.7173 I.2.1) Conservatve: - Frst lmted group of harmoncs: Total nose (dbuv) = 58.4948 140 120 Dsturbance levels n the voltage across one of the LISN leg resstors: All computed harmoncs Quadratc sum Standard Magntude (dbuv) 100 80 60 40 20 10 4 10 5 10 6 10 7 Frequency (Hz) Fgure B.2. Predcted total EMI nose n the conservatve case. I.2.2) Average: - Frst lmted group of harmoncs: Total nose (dbuv) = 53.5524 154

120 110 100 Dsturbance levels n the voltage across one of the LISN leg resstors: All computed harmoncs Quadratc sum Standard 90 Magntude (dbuv) 80 70 60 50 40 30 I.2.3) Non-conservatve: 20 10 4 10 5 10 6 10 7 Frequency (Hz) Fgure B.3. Predcted total EMI nose n the average case. - Frst lmted group of harmoncs: Total nose (dbuv) = 49.265 120 110 100 Dsturbance levels n the voltage across one of the LISN leg resstors: All computed harmoncs Quadratc sum Standard 90 Magntude (dbuv) 80 70 60 50 40 30 20 10 4 10 5 10 6 10 7 Frequency (Hz) Fgure B.4. Predcted total EMI nose n the non-conservatve case. 155

II) Dfferental and common mode nose: II.1) Measured 65 DM Nose: Desgn #1: Vn=230, Vo=368, Io=3.125 60 55 Ampltude (dbuv) 50 45 40 35 30 10 6 10 7 Frequency (Hz) Fgure B.5. Measured dfferental mode nose. 65 CM Nose: Desgn #1: Vn=230, Vo=368, Io=3.125 60 55 Ampltude (dbuv) 50 45 40 35 30 25 10 6 10 7 Frequency (Hz) Fgure B.6. Measured common mode nose. II.2) Predcted (consderng L B =L B_mn ): II.2.1) Conservatve: - Frst lmted group of harmoncs: Dfferental mode nose (dbuv) = 57.7082. Common mode nose (dbuv) = 50.687. 156

CMC and DMC dsturbance levels n the voltage across one of the LISN leg resstors: 130 120 110 Dfferental mode harmoncs (quadratc sum) Common mode harmoncs (quadratc sum) Standard Magntude (dbuv) 100 90 80 70 60 50 10 4 10 5 10 6 10 7 Frequency (Hz) Fgure B.7. Predcted dfferental and common mode nose n the conservatve case. II.2.2) Average: - Frst lmted group of harmoncs: Dfferental mode nose (dbuv) = 52.8139. Common mode nose (dbuv) = 45.4939. CMC and DMC dsturbance levels n the voltage across one of the LISN leg resstors: 120 110 100 Dfferental mode harmoncs (quadratc sum) Common mode harmoncs (quadratc sum) Standard Magntude (dbuv) 90 80 70 60 50 40 10 4 10 5 10 6 10 7 Frequency (Hz) Fgure B.8. Predcted dfferental and common mode nose n the average case. 157

II.2.3) Non-conservatve: - Frst lmted group of harmoncs: Dfferental mode nose (dbuv) = 48.457. Common mode nose (dbuv) = 41.5638. CMC and DMC dsturbance levels n the voltage across one of the LISN leg resstors: 120 110 100 Dfferental mode harmoncs (quadratc sum) Common mode harmoncs (quadratc sum) Standard Magntude (dbuv) 90 80 70 60 50 40 10 4 10 5 10 6 10 7 Frequency (Hz) Fgure B.9. Predcted dfferental and common mode nose n the non-conservatve case. 158

B.2. Prototype 2 B.2.1. TEST 1: Model Tunng Test Table B.11. Condtons. Parameter Value Tamb_ext Tamb_prot * Vn Flne Po Vo * Ths s the assumed value. 23 o C 50 o C 230 Vrms 50 Hz 1151 W 355.7 V Table B.12. Measures and predctons. Magntude Measured Predcted Non-conservatve Average Conservatve Pn (W) * 1193 1179 1179 1180 In_rms (A) * 5.22 5.13 5.13 5.14 Lb_pk (A) 8.88 7.49 7.58 7.72 dilbmax (A) 0.95 0.88 1.18 1.64 Lb_mn (µh) 935 1274 957 697 Ptot_Lb (W) 10.8 7.05 7.6 8.1 T_coreLb ( o C) 81 91.4 93.9 96.5 Ths_sw ( o C) 86 85.4 85.6 86.0 Ths_fd ( o C) 65 68.0 68.0 68.0 Ths_rd ( o C) 114 120.5 120.6 120.7 C DG (pf) 21.5 -------- -------- -------- * The predctons do not nclude the power dsspated n the PFC stage EMI flter, load nternal EMI flter and electrolytc capactors. Wthout rngng ampltude. Settng TL B coef = 1.00. Ths coeffcent has not been reduced below 1.00 to better approxmate the measured temperature of the core, because the sensor could not have been placed n the hottest spot of the core. 159

B.2.2. TEST 2: Valdaton of EMI Levels Predcton Table B.13. Condtons: Common mode choke s SDI 142-22 (Lcm=3.3mH). Parameter Value Tamb_ext Tamb_prot * Vn flne Po Vo * Ths s the assumed value. 27 o C 50 o C 230 Vrms 50 Hz 1147.9 W 356.5 V B.2.2.1. Measures and predctons for EMI Levels I) Total nose: I.1) Measured 65 Total Nose: SE Prototype, Full Load, Vn=230 60 55 dbuv 50 45 40 10 6 10 7 frequency Fgure B.10. Measured total EMI nose. 160

I.2) Predcted (consderng L B = L B_mn ): - Frst lmted group of harmoncs: Group of harmoncs order = 4 Frequency (khz) = 172.05 Standard level (dbuv) = 64.8609 I.2.1) Conservatve: - Frst lmted group of harmoncs: Total nose (dbuv) = 59.53 140 120 Dsturbance levels n the voltage across one of the LISN leg resstors: All computed harmoncs Quadratc sum Standard Magntude (dbuv) 100 80 60 40 20 10 4 10 5 10 6 10 7 Frequency (Hz) Fgure B.11. Predcted total EMI nose n the conservatve case. I.2.2) Average: - Frst lmted group of harmoncs: Total nose (dbuv) = 54.8772 161

140 120 Dsturbance levels n the voltage across one of the LISN leg resstors: All computed harmoncs Quadratc sum Standard Magntude (dbuv) 100 80 60 40 20 10 4 10 5 10 6 10 7 Frequency (Hz) Fgure B.12. Predcted total EMI nose n the average case. I.2.3) Non-conservatve: - Frst lmted group of harmoncs: Total nose (dbuv) = 50.9041 140 120 Dsturbance levels n the voltage across one of the LISN leg resstors: All computed harmoncs Quadratc sum Standard Magntude (dbuv) 100 80 60 40 20 10 4 10 5 10 6 10 7 Frequency (Hz) Fgure B.13. Predcted total EMI nose n the non-conservatve case. 162

II) Dfferental and common mode nose: II.1) Measured 65 DM Nose: SE Prototype, Full Load, Vn=230 60 55 dbuv 50 45 10 6 10 7 frequency Fgure B.14. Measured dfferental mode nose. 65 CM Nose: SE Prototype, Full Load, Vn=230 60 55 50 dbuv 45 40 35 30 10 6 10 7 frequency Fgure B.15. Measured common mode nose. II.2) Predcted (consderng L B = L B_mn ): II.2.1) Conservatve: - Frst lmted group of harmoncs: 163

Dfferental mode nose (dbuv) = 58.13 Common mode nose (dbuv) = 53.91 CMC and DMC dsturbance levels n the voltage across one of the LISN leg resstors: 130 120 110 Dfferental mode harmoncs (quadratc sum) Common mode harmoncs (quadratc sum) Standard Magntude (dbuv) 100 90 80 70 60 50 10 4 10 5 10 6 10 7 Frequency (Hz) Fgure B.16. Predcted dfferental and common mode nose n the conservatve case. II.2.2) Average: - Frst lmted group of harmoncs: Dfferental mode nose (dbuv) = 53.6348. Common mode nose (dbuv) = 48.8358. CMC and DMC dsturbance levels n the voltage across one of the LISN leg resstors: 130 120 110 Dfferental mode harmoncs (quadratc sum) Common mode harmoncs (quadratc sum) Standard Magntude (dbuv) 100 90 80 70 60 50 40 10 4 10 5 10 6 10 7 Frequency (Hz) Fgure B.17. Predcted dfferental and common mode nose n the average case. 164

II.2.3) Non-conservatve: - Frst lmted group of harmoncs: Dfferental mode nose (dbuv) = 49.6343. Common mode nose (dbuv) = 44.9442. CMC and DMC dsturbance levels n the voltage across one of the LISN leg resstors: 130 120 110 Dfferental mode harmoncs (quadratc sum) Common mode harmoncs (quadratc sum) Standard Magntude (dbuv) 100 90 80 70 60 50 40 10 4 10 5 10 6 10 7 Frequency (Hz) Fgure B.18. Predcted dfferental and common mode nose n the non-conservatve case. 165

B.3. Fnal Optmum Desgn B.3.1. TEST 1: Thermal Measurements Table B.14. Condtons. Parameter Tamb_ext Vn flne Po Value 24 o C 195 Vrms 50 Hz 1052 W Vo 354.6V Table B.15. Measures. Magntude Measured Pn (W) 1102 Effcency 95.5% In_rms (A) 5.67 Lb_pk (A) 9.26 dilbmax (A) 2.67 Lb_mn (µh) 1067 T_coreLb ( o C) 104 Ths_sw ( o C) 75 Ths_fd ( o C) 62 Ths_rd ( o C) 134 166

B.3.2. TEST 2: Measurement of EMI Nose Levels Table B.16. Condtons. Parameter Tamb_ext Vn flne Po Vo Value 27 o C 230 Vrms 50 Hz 1140 W 356 V 70 65 60 LISN Resstor Voltage Level (dbuv) 55 50 45 40 35 30 25 20 1.00E+05 1.00E+06 1.00E+07 1.00E+08 Frequency (Hz) Total Nose Avg Standard Fgure B.19. Measures (total nose). 167

70 65 60 LISN Resstor Voltage Level (dbuv) 55 50 45 40 35 30 25 20 1.00E+05 1.00E+06 1.00E+07 1.00E+08 Frequency (Hz) DM Nose Avg Standard Fgure B.20. Measures (dfferental mode nose). 70 65 60 LISN Resstor Voltage Level (dbuv) 55 50 45 40 35 30 25 20 1.00E+05 1.00E+06 1.00E+07 1.00E+08 Frequency (Hz) CM Nose Avg Standard Fgure B.21. Measures (common mode nose). 168

Appendx C. Converter Desgn Condtons and Component Database In the followng, the converter desgn condtons / specfcatons used to obtan the optmum desgns presented n Secton 3.3.6 (Dscrete Optmzaton) and the number of components contaned n the component database are detaled. The unts of the dfferent magntudes can be found n the onlne help area of the software. C.1. Converter Desgn Condtons/Specfcatons C.1.1. General vnmn_rms = 180/195/230 vnnom_rms = 230 flne = 50 po = 1150 vbus_dc = 368 tamb = 50 conservatve = 1 C.1.2. Boost PFC snghs = 0 hsfd = 1 hsrd = 0 tmaxhs = 100 k1hs = *** k2hs = *** jm = 1000 kcu = 0.0039 row100 = 2.208E-6 ku = 0.5 tlbcoef = 1.2 cost_lbfxmanuf = *** tollblk = 50 tmaxpcb = 125 dtpcblbcore = 5 cb = 6.92E-4 cost_cb = *** 169

vpkmmn = 500 vpkigmn = 600 vpkfdmn = 600 vpkrdmn = 800 fsmmn = 150 ls = 1.0E-8 perswqrr = 50 trsegbt = 5.0E-8 tfallgbt = 5.0E-8 vgg = 15 rgon = 33 rgoff = 10 C.1.3. EMI Flter Class_type = Class B, Group 1 vaccxmn = 275 vaccymn = 250 llha = 2.5E-7 lldb = 2.5E-7 lsf = 3E-8 ld = 1.0E-7 llmg = 5E-7 lres = 1.5E-4 csg = 1E-12 cdg = 2E-11 ckg = 1E-12 ceg = 1E-12 cfg = 1E-12 cag = 1E-12 cbg = 1E-12 clb = 1E-12 rlb = 1000000 ln = 5E-5 cn = 1E-7 c1 = 1E-5 zn = 50 harm_number = 1 nd = 3 ncr = 3 170

C.2. Component Database Table C.1. Number of components of each type n the database. Component type Swtch MOSFET IGBT Brdge dode Fast dode Boost nductor Core Wre Common mode capactor Dfferental mode capactor Common mode choke Number of components n the database 6 21 11 15 28 5 5 5 11 171

Appendx D. Optmzaton Software Fgure D.1 allows access to a compressed fle contanng a demo verson of the desgn software tool developed as well as the contnuous and dscrete MATLAB desgn analyss functons. The herarchcal organzaton of the fles ncluded s specfed. Fgure D.1. Desgn analyss and desgn optmzaton software (Software.zp, 8,990KB). To nstall the demo verson of the software just double clck on the fle opes_demo_v1.2.exe. 172