BIDIRECTIONAL DC-DC CONVERTERS FOR HYBRID...

FEDERAL UNIVERSITY OF TECHNOLOGY OF PARANÁ - UTFPR

DEPARTMENT OF ELECTRONIC ENGINEERING

GRADUATE PROGRAM IN ELECTRICAL ENGINEERING

GABRIEL RENAN BRODAY

BIDIRECTIONAL DC-DC CONVERTERS FOR HYBRID ENERGY

STORAGE SYSTEMS IN ELECTRIC VEHICLE APPLICATIONS

MASTER’S THESIS

PONTA GROSSA

2016

GABRIEL RENAN BRODAY

BIDIRECTIONAL DC-DC CONVERTERS FOR HYBRID ENERGY

STORAGE SYSTEMS IN ELECTRIC VEHICLE APPLICATIONS

Master’s Thesis presented as partial requirement for obtaining a Master’s Degree in Electrical Engineering from the Department of Electronic Engineering at Federal University of Technology of Paraná-UTFPR.

Advisor: Prof. Dr. Claudinor Bitencourt Nascimento

Co-Advisor: Prof. Dr. Eloi Agostini Jr.

PONTA GROSSA

2016

Ficha catalográfica elaborada pelo Departamento de Biblioteca da Universidade Tecnológica Federal do Paraná, Campus Ponta Grossa n.05/17

B864 Broday, Gabriel Renan

Bidirectional DC-DC converters for hybrid energy storage systems in electric vehicle applications / Gabriel Renan Broday. -- 2017.

267 f. : il. ; 30 cm.

Orientador: Prof. Dr. Claudinor Bitencourt Nascimento Coorientador: Prof. Dr. Eloi Agostini Junior

Dissertação (Mestrado em Engenharia Elétrica) - Programa de Pós-Graduação em Engenharia Elétrica. Universidade Tecnológica Federal do Paraná. Ponta Grossa, 2017.

1. Veículos elétricos. 2. Energia - Armazenamento. 3. Capacitadores. 4. Baterias elétricas. 5. Conversores de corrente elétrica. I. Nascimento, Claudinor Bitencourt. II. Agostini Junior, Eloi. III. Universidade Tecnológica Federal do Paraná. IV. Título.

CDD 621.3

Universidade Tecnológica Federal do Paraná Campus de Ponta Grossa

Diretoria de Pesquisa e Pós-Graduação PROGRAMA DE PÓS-GRADUAÇÃO EM

ENGENHARIA ELÉTRICA UNIVERSIDADE TECNOLÓGICA FEDERAL DO PARANÁ

PR

FOLHA DE APROVAÇÃO

Título de Dissertação Nº 23/2016

BIDIRECTIONAL DC-DC CONVERTERS FOR HYBRID ENERGY STORAGE SYSTEMS IN ELETRIC VEHICLE APPLICATIONS

por

Gabriel Renan Broday

Esta dissertação foi apresentada às 10 horas do dia 15 de dezembro de 2016 como

requisito parcial para a obtenção do título de MESTRE EM ENGENHARIA ELÉTRICA, com

área de concentração em Controle e Processamento de Energia, Programa de Pós-

Graduação em Engenharia Elétrica. O candidato foi arguido pela Banca Examinadora

composta pelos professores abaixo assinados. Após deliberação, a Banca Examinadora

considerou o trabalho aprovado.

Prof. Dr. Luiz Antonio Correa Lopes (Concordia University)

Prof. Dr. Marcio Mendes Casaro (UTFPR)

Prof. Dr. Claudinor Bitencourt Nascimento (UTFPR)

Orientador

Prof. Dr. Claudinor Bitencourt Nascimento

Coordenador do PPGEE

- A Folha de Aprovação assinada encontra-se arquivada na Secretaria Acadêmica –

To my parents and brothers.

ACKNOWLEDGEMENTS

First, I would like to thank my parents for supporting me in all the way, for

sharing my happiness and my fears, for making me who I am. This work would not be

possible without you!

To my brothers Geovani and Sérgio for making my life more fun.

To my advisor Prof. Dr. Claudinor Bitencourt Nascimento for putting his trust in

me, for believing in me when others did not believe. A person who I hope to take with

me for the rest of my life.

To my co-advisor Prof. Dr. Eloi Agostini Jr. for all his contribution in this work.

Always punctual in his placements, sharing knowledge in an unique way.

To Prof. PhD Luiz A. C. Lopes for all the moments spend in Montreal, for his

technical contribution, experience, good talks and, most important, for his friendship.

Also, I would like to extend this acknowledgment to his wife Mylene and his daughter

Carol, a family that received me so well in Montreal that made me feel at home.

To my friends Marlon Lessing, Remei Haura Jr. and William Kremes for the

technical discussions, friendship and good moments.

To all my friends from the P. D. Ziogas Power Electronics Laboratory at

Concordia University, in special to Arvynd Vias, for the good moments and help when

I was in Montreal.

To the Brazilian and Canadian governments that through their development

agencies could finance this work.

To my better half Lays, for her love and comprehension.

Anyway, to all that somehow helped me in the development of this work.

“Train while they sleep,

Study while they have fun,

Persist while they rest,

And then

Live what they dream”

(Japanese proverb)

RESUMO

BRODAY, G. R. Conversores CC-CC Bidirecionais para Sistemas Híbridos de Armazenamento de Energia em Aplicações de Veículos Elétricos. 2016. 267 p.

Dissertação (Mestrado em Engenharia Elétrica) - Universidade Tecnológica Federal do Paraná. Ponta Grossa, 2016.

Em um momento em que questões ambientais e a segurança energética estão numa posição de destaque, Veículos Elétricos (VEs) estão no centro das atenções. Entretanto, ainda é difícil para eles substituir os tradicionais veículos de combustão interna e a razão principal para isso é o seu sistema de energia. Normalmente, devido a suas características, baterias são usadas como banco de energia para VEs. No entanto, baterias também apresentam algumas limitações para essa aplicação e o problema no sistema de energia é relacionado a essas limitações. Uma das soluções propostas é se colocar baterias e supercapacitores (SC) em paralelo, resultando em um Sistema Híbrido de Armazenamento de Energia (SHAE). Para fazer essa configuração possível e o fluxo de potência controlável em um SHAE, um conversor CC-CC bidirecional interfaceando a bateria e o SC é necessário. Levando isso em consideração, o estudo de topologias CC-CC bidirecionais é apresentado nessa Dissertação de Mestrado. Primeiro, o estudo de um conversor CC-CC bidirecional com indutor dividido, envolvendo sua análise teórica em regime permanente, análise dinâmica e uma metodologia de projeto com resultados de simulação, é apresentado, resultando na construção de um protótipo experimental com as seguintes especificações de projeto: Fonte de tensão 1 de 300 V, fonte de tensão 2 de 96 V, frequência de comutação de 20 kHz e potência nominal de 1000 W. Então, o estudo de uma segunda topologia, um conversor CC-CC Buck-Boost ZVS bidirecional, envolvendo sua análise em regime permanente e uma metodologia de projeto com resultados de simulação, também é apresentado.

Palavras-Chave: Conversores CC-CC Bidirecionais, Baterias, Supercapacitores, Veículos Elétricos, Sistemas Híbridos de Armazenamento de Energia.

ABSTRACT

BRODAY, G. R. Bidirectional DC-DC Converters for Hybrid Energy Storage Systems in Electric Vehicle Applications. 2016. 267 pp. Master’s Thesis (Master’s

Degree in Electrical Engineering) - Federal University of Technology of Paraná. Ponta Grossa, 2016.

In an era where environmental issues and the energetic safety are in an outstanding position, Electric Vehicles (EVs) are in the spotlight. However, it is difficult for them to replace the ICE vehicles and the main reason for that it is their energy system. Normally, due to some of their characteristics, batteries are used as energy bank in Electric Vehicles. Nevertheless, batteries also present some limitations for this application and the energy system problem is related to these limitations. One of the proposed solutions is to place batteries and Supercapacitors (SC) in parallel, resulting in a Hybrid Energy Storage System (HESS). To make this configuration possible and the power flow controllable in the HESS, a bidirectional DC-DC converter interfacing the battery and the SC is necessary. Taking this into account, the study of bidirectional DC-DC topologies is presented in this Master’s Thesis. First, a study of a bidirectional DC-DC converter with tapped inductor, involving its theoretical steady state analysis, dynamic analysis and design methodology with simulation results, is presented, resulting in the design of an experimental prototype with the following design specifications: Voltage source 1 of 300 V, voltage source 2 of 96 V, switching frequency of 20 kHz and rated power of 1000 W. Then, the study of a second topology, a bidirectional ZVS Buck-Boost DC-DC converter, involving the steady state analysis and a design methodology with simulation results, is also presented.

Keywords: Bidirectional DC-DC Converters, Batteries, Supercapacitors, Electric Vehicles, Hybrid Energy Storage Systems.

LIST OF FIGURES

Figure 1.1 – Electric Vehicle by William Morrison......................................................32

Figure 1.2 – Hybrid Vehicle Toyota Prius...................................................................34

Figure 1.3 – Inside view of a PHEV............................................................................35

Figure 1.4 – Electric Vehicle FIAT/Itaipu Binacional Palio Weekend.........................37

Figure 1.5 – First electric accumulator.......................................................................39

Figure 1.6 – Batteries arrangement in EVs................................................................40

Figure 1.7 – Commercial Lead-acid battery...............................................................42

Figure 1.8 – Nickel-metal hydride battery bank for EVs............................................42

Figure 1.9 – Lithium-ion battery module for EVs........................................................43

Figure 1.10 – Commercial Maxwell Supercapacitors.................................................45

Figure 1.11 – Battery/Supercapacitor HESS in EVs applications...............................47

Figure 2.1 – Traditional DC-DC converters: (a) Buck (b) Boost (c) Buck-Boost.........50

Figure 2.2 – Traditional isolated DC-DC converters: (a) Flyback (b) Forward...........51

Figure 2.3 – Traditional bidirectional DC-DC converters: (a) Buck/Boost (b) Boost/Buck (c) Buck-Boost.........................................................................................52

Figure 2.4 – Traditional isolated bidirectional DC-DC converters: (a) Flyback (b) Forward......................................................................................................................52

Figure 2.5 – Integrated bidirectional Buck/Boost/Buck-Boost DC-DC converter........53

Figure 2.6 – Operating stages of the Forward mode: (a) Buck 1 (b) Buck 2 (c) Boost 1 (d) Boost 2 (e) Buck-Boost 1 (f) Buck-Boost 2…………………………………………..54

Figure 2.7 – Operating stages of the Reverse mode: (a) Buck 1 (b) Buck 2 (c) Boost 1 (d) Boost 2 (e) Buck-Boost 1 (f) Buck-Boost 2........................................................54

Figure 2.8 – Bidirectional Boost/Buck DC-DC converter............................................55

Figure 2.9 – Operating stages of the bidirectional Boost/Buck DC-DC converter: (a) Forward Boost 1 (b) Forward Boost 2 (c) Reverse Buck 1 (d) Reverse Buck 2…56

Figure 2.10 – Bidirectional ZVS Boost/Buck DC-DC converter..................................57

Figure 3.1 – Bidirectional DC-DC converter with tapped inductor..............................59

Figure 3.2 – Equivalent circuit of the bidirectional DC-DC converter with tapped inductor.......................................................................................................................60

Figure 3.3 – Forward Buck: Gate signals...................................................................61

Figure 3.4 – Forward Buck: Fist operating stage........................................................62

Figure 3.5 – Forward Buck: Second operating stage.................................................63

Figure 3.6 – Forward Buck: Theoretical voltage waveforms in the switches S1 and S3................................................................................................................................64

Figure 3.7 – Forward Buck: Theoretical voltage waveforms in the tapped inductor……………………………………………………………………………………....65

Figure 3.8 – Forward Buck: Theoretical waveforms in the magnetizing inductance..................................................................................................................65

Figure 3.9 – Forward Buck: Theoretical waveforms of the currents I1 and I2.............65

Figure 3.10 – Forward Buck: Theoretical current waveforms in the switches............66

Figure 3.11 – Forward Buck: Voltage conversion characteristic................................67

Figure 3.12 – Forward Boost: Gate signals................................................................71

Figure 3.13 – Forward Boost: First operating stage...................................................71

Figure 3.14 – Forward Boost: Second operating stage..............................................73

Figure 3.15 – Forward Boost: Theoretical voltage waveforms in the switches S2 and S3................................................................................................................................73

Figure 3.16 – Forward Boost: Theoretical voltage waveforms in the tapped inductor.......................................................................................................................73

Figure 3.17 – Forward Boost: Theoretical waveforms in the magnetizing inductance..................................................................................................................74

Figure 3.18 – Forward Boost: Theoretical waveforms of the currents I1 and I2..........74

Figure 3.19 – Forward Boost: Theoretical current waveforms in the switches……....74

Figure 3.20 – Forward Boost: Voltage conversion characteristic…………………......75

Figure 3.21 – Forward Buck-Boost: Gate signals.......................................................78

Figure 3.22 – Forward Buck-Boost: First operating stage..........................................79

Figure 3.23 – Forward Buck-Boost: Second operating stage.....................................79

Figure 3.24 – Forward Buck-Boost: Theoretical voltage waveforms in the switches S1 and S2.........................................................................................................................80

Figure 3.25 – Forward Buck-Boost: Theoretical voltage waveforms in the tapped inductor.......................................................................................................................80

Figure 3.26 – Forward Buck-Boost: Theoretical waveforms in the magnetizing inductance………………………………………………………………………………...…80

Figure 3.27 – Forward Buck-Boost: Theoretical waveforms of the currents I1 and I2………………………………………………………………………………………………81

Figure 3.28 – Forward Buck-Boost: Theoretical current waveforms in the switches......................................................................................................................81

Figure 3.29 – Forward Buck-Boost: Voltage conversion characteristic……………....82

Figure 3.30 – Reverse Buck: Gate signals.................................................................85

Figure 3.31 – Reverse Buck: First operating stage....................................................85

Figure 3.32 – Reverse Buck: Second operating stage...............................................86

Figure 3.33 – Reverse Buck: Theoretical voltage waveforms in the switches S2 and S3................................................................................................................................86

Figure 3.34 – Reverse Buck: Theoretical voltage waveforms in the tapped inductor.......................................................................................................................86

Figure 3.35 – Reverse Buck: Theoretical waveforms in the magnetizing inductance..................................................................................................................87

Figure 3.36 – Reverse Buck: Theoretical waveforms of the currents I1 and I2...........87

Figure 3.37 – Reverse Buck: Theoretical current waveforms in the switches............87

Figure 3.38 – Reverse Buck: Voltage conversion characteristic................................88

Figure 3.39 – Reverse Boost: Gate signals................................................................91

Figure 3.40 – Reverse Boost: First operating stage...................................................92

Figure 3.41 – Reverse Boost: Second operating stage..............................................92

Figure 3.42 – Reverse Boost: Theoretical voltage waveforms in the switches S1 and S3................................................................................................................................93

Figure 3.43 – Reverse Boost: Theoretical voltage waveforms in the tapped inductor……………………………………………………………………………………....93

Figure 3.44 – Reverse Boost: Theoretical waveforms in the magnetizing inductance..................................................................................................................93

Figure 3.45 – Reverse Boost: Theoretical waveforms of the currents I1 and I2..........94

Figure 3.46 – Reverse Boost: Theoretical current waveforms in the switches...........94

Figure 3.47 – Reverse Boost: Voltage conversion characteristic...............................95

Figure 3.48 – Reverse Buck-Boost: Gate signals.......................................................98

Figure 3.49 – Reverse Buck-Boost: First operating stage..........................................98

Figure 3.50 – Reverse Buck-Boost: Second operating stage....................................99

Figure 3.51 – Reverse Buck-Boost: Theoretical voltage waveforms in the switches S1 and S2……………………………………………………………………………………......99

Figure 3.52 – Reverse Buck-Boost: Theoretical voltage waveforms in the tapped inductor……………………………………………………………………………………..100

Figure 3.53 – Reverse Buck-Boost: Theoretical waveforms in the magnetizing inductance................................................................................................................100

Figure 3.54 – Reverse Buck-Boost: Theoretical waveforms of the current I1 and I2...............................................................................................................................100

Figure 3.55 – Reverse Buck-Boost: Theoretical current waveforms in the switches....................................................................................................................101

Figure 3.56 – Reverse Buck-Boost: Voltage conversion characteristic....................102

Figure 4.1 – Bidirectional ZVS Buck-Boost DC-DC converter..................................106

Figure 4.2 – Equivalent circuit of the bidirectional ZVS Buck-Boost Converter........106

Figure 4.3 – Forward mode: First stage...................................................................108

Figure 4.4 – Forward mode: Second stage..............................................................110

Figure 4.5 – Forward mode: Theoretical voltage waveforms in the switches S1 and S2……………………………………………………………………………………………112

Figure 4.6 – Forward Mode: Theoretical voltage waveforms in the transformer......112

Figure 4.7 – Forward mode: Theoretical waveforms in the magnetizing inductance................................................................................................................113

Figure 4.8 – Forward Mode: Theoretical waveforms in the auxiliary inductance (a) n>1 (b) n<1..........................................................................................................113

Figure 4.9 – Forward mode: Theoretical current waveforms in the voltage source V1

(a) n>1 (b) 0<n<=0.5 (c) 0.5<n<1.............................................................................114

Figure 4.10 – Forward mode: Theoretical current waveforms in the voltage source V2 (a) n>1 (b) 0<n<=0.5 (c) 0.5<n<1............................................................................114

Figure 4.11 – Forward mode: Theoretical current waveforms in the switches (a) n>1 (b) n<1......................................................................................................................114

Figure 4.12 – Reverse mode: Theoretical voltage waveforms in the switches S1 and S2..............................................................................................................................119

Figure 4.13 – Reverse mode: Theoretical voltage waveforms in the transformer....119

Figure 4.14 – Reverse mode: Theoretical waveforms in the magnetizing inductance................................................................................................................119

Figure 4.15 – Reverse mode: Theoretical waveforms in the auxiliary inductance (a) n>1 (b) n<1..........................................................................................................120

Figure 4.16 – Reverse mode: Theoretical current waveforms in the voltage source V1 (a) n>1 (b) 0<n<=0.5 (c) 0.5<n<1.............................................................................120

Figure 4.17 – Reverse mode: Theoretical current waveforms in the voltage source V2 (a) n>1 (b) 0<n<=0.5 (c) 0.5<n<1.............................................................................120

Figure 4.18 – Reverse mode: Theoretical current waveforms in the switches (a) n>1 (b) n<1......................................................................................................................121

Figure 6.1 – Block diagram for the control design....................................................139

Figure 6.2 – Bode diagram of the uncompensated system......................................140

Figure 6.3 – Step response of the compensated system.........................................141

Figure 6.4 – Bode diagram of the compensated system..........................................141

Figure 6.5 – Circuit implemented in PSIM®: Power schematic................................142

Figure 6.6 – Circuit implemented in PSIM®: Control schematic..............................142

Figure 6.7 – Step response: Comparison Converter x Transfer function.................142

Figure 6.8 – Forward Buck: Simulated voltage waveforms in the switches S1 and S3…………………………………………………………………………………………...143

Figure 6.9 – Forward Buck: Simulated voltage waveforms in the tapped inductor.....................................................................................................................144

Figure 6.10 – Forward Buck: Simulated waveforms in the magnetizing inductance LM..............................................................................................................................144

Figure 6.11 – Forward Buck: Simulated current waveform in switch S1...................145



Figure 6.14 – Forward Buck: Simulated waveforms of the currents I1 and I2...........146

Figure 6.15 – Forward Buck: Current control...........................................................146

Figure 6.16 – Forward Buck-Boost: Simulated voltage waveforms in the switches S1 and S2.......................................................................................................................148

Figure 6.17 – Forward Buck-Boost: Simulated voltage waveforms in the tapped inductor.....................................................................................................................148

Figure 6.18 – Forward Buck-Boost: Simulated waveforms in the magnetizing inductance LM……………………………………………………………………………...149

Figure 6.19 – Forward Buck-Boost: Simulated current waveform in switch S1........149

Figure 6.20 – Forward Buck-Boost: Simulated current waveform in switch S2..............................................................................................................................150

Figure 6.21 – Forward Buck-Boost: Simulated current waveform in switch S3........150

Figure 6.22 – Forward Buck-Boost: Simulated waveforms of the currents I1 and I2...............................................................................................................................151

Figure 6.23 – Forward Buck-Boost: Current control.................................................151

Figure 6.24 – Reverse Boost: Simulated voltage waveforms in the switches S1 and S3…………………………………………………………………………………………...153

Figure 6.25 – Reverse Boost: Simulated voltage waveforms in the tapped inductor.....................................................................................................................153

Figure 6.26 – Reverse Boost: Simulated waveforms in the magnetizing inductance LM..............................................................................................................................153

Figure 6.27 – Reverse Boost: Simulated current waveform in switch S1.................154



Figure 6.30 – Reverse Boost: Simulated waveforms of the currents I1 and I2...............................................................................................................................155

Figure 6.31 – Reverse Boost: Current control..........................................................156

Figure 6.32 – Reverse Buck-Boost: Simulated voltage waveforms in the switches S1 and S2………………………………………………………………………………………157

Figure 6.33 – Reverse Buck-Boost: Simulated voltage waveforms in the tapped inductor.....................................................................................................................157

Figure 6.34 – Reverse Buck-Boost: Simulated waveforms in the magnetizing inductance LM...........................................................................................................158

Figure 6.35 – Reverse Buck-Boost: Simulated current waveform in switch S1..............................................................................................................................158



Figure 6.38 – Reverse Buck-Boost: Simulated waveforms of the currents I1 and I2...............................................................................................................................159

Figure 6.39 – Reverse Buck-Boost: Current control.................................................160

Figure 6.40 – Unified controller: Forward Buck to Reverse Boost............................162

Figure 6.41 – Unified controller: Forward Buck-Boost to Reverse Buck-Boost........................................................................................................................162

Figure 7.1 – RMS current in switch S1 for different values of n................................166

Figure 7.2 – RMS current in switch S2 for different values of n................................167

Figure 7.3 – Forward mode: Schematic of simulation..............................................168

Figure 7.4 – Forward mode: Voltage across the RC load........................................169

Figure 7.5 – Forward mode: Simulated Voltage waveform in each turn of the transformer...............................................................................................................170

Figure 7.6 – Forward mode: Simulated waveforms in the magnetizing inductance LM..............................................................................................................................170

Figure 7.7 – Forward mode: Simulated waveforms in the auxiliary inductance LL..............................................................................................................................171

Figure 7.8 – Forward mode: Simulated waveforms in the switch S1........................171

Figure 7.9 – Forward mode: Simulated waveforms in the switch S2........................172

Figure 7.10 – Forward mode: Simulated current waveforms in the voltage sources.....................................................................................................................172

Figure 7.11 – Reverse mode: Schematic of simulation............................................173

Figure 7.12 – Reverse mode: Voltage across the RC load......................................174

Figure 7.13 – Reverse mode: Simulated Voltage waveform in each turn of the transformer...............................................................................................................175

Figure 7.14 – Reverse mode: Simulated waveforms in the magnetizing inductance LM..............................................................................................................................175

Figure 7.15 – Reverse mode: Simulated waveforms in the auxiliary inductance LL..............................................................................................................................176

Figure 7.16 – Reverse mode: Simulated waveforms in the switch S1......................176

Figure 7.17 – Reverse mode: Simulated waveforms in the switch S2......................177

Figure 7.18 – Reverse mode: Simulated current waveforms in the voltage sources.....................................................................................................................177

Figure 8.1 – Clamping circuits: (a) Passive clamping (b) Active clamping...............182

Figure 8.2 – Experimental prototype........................................................................184

Figure 8.3 – Tapped inductor…………………………………………………………….184

Figure 8.4 – Schematic of the experimental setup...................................................186

Figure 8.5 – Forward Buck: Gate signals (10 V/div).................................................186

Figure 8.6 – Forward Buck: Voltage (200 V/div) and current (7 A/div) in the switch S1…………………………………………………………………………………………...187

Figure 8.7 – Forward Buck: Voltage (200 V/div) and current (7 A/div) in the switch S1..............................................................................................................................187

Figure 8.8 – Forward Buck: Turning-on of the switch S1..........................................188

Figure 8.9 – Forward Buck: Turning-off of the switch S1……...................................188



Figure 8.12 – Forward Buck: Turning-on of the switch S3…….................................190

Figure 8.13 – Forward Buck: Turning-off of the switch S3........................................190

Figure 8.14 – Forward Buck: Voltage (100 V/div) and current (7 A/div) in the voltage source 1....................................................................................................................191

Figure 8.15 – Forward Buck: Voltage (30 V/div) and current (7 A/div) in the voltage source 2…................................................................................................................191

Figure 8.16 – Forward Buck: Voltage (100 V/div) and current (10 A/div) in magnetizing inductance............................................................................................192

Figure 8.17 – Forward Buck: Currents (10 A/div) through each switch....................192

Figure 8.18 – Forward Buck: Voltage (100 V/div) and current (7 A/div) in the primary ……..........................................................................................................................193

Figure 8.19 – Forward Buck: Voltage (100 V/div) and current (7 A/div) in the secondary.................................................................................................................193

Figure 8.20 – Forward Buck: Voltage (100 V/div) and current (2 A/div) for the current control of I1...............................................................................................................194

Figure 8.21 – Forward Buck: Current I1 in the voltage source …….........................194

Figure 8.22 – Forward Buck: Efficiency curve..........................................................195

Figure 8.23 – Forward Buck-Boost: Gate signals (10 V/div)....................................196

Figure 8.24 – Forward Buck-Boost: Voltage (300 V/div) and current (10 A/div) in the switch S1……............................................................................................................197

Figure 8.25 – Forward Buck-Boost: Voltage (300 V/div) and current (10 A/div) in the switch S1...................................................................................................................197

Figure 8.26 – Forward Buck-Boost: Turning-on of the switch S1..............................198

Figure 8.27 – Forward Buck-Boost: Turning-off of the switch S1……......................198



Figure 8.30 – Forward Buck-Boost: Turning-on of the switch S2……......................200

Figure 8.31 – Forward Buck-Boost: Turning-off of the switch S2..............................200

Figure 8.32 – Forward Buck-Boost: Voltage (100 V/div) and current (10 A/div) in V1..............................................................................................................................201

Figure 8.33 – Forward Buck-Boost: Voltage (30 V/div) and current (10 A/div) in V2..............................................................................................................................201

Figure 8.34 – Forward Buck-Boost: Voltage (200 V/div) and current (10 A/div) in the magnetizing inductance..................................................................................202

Figure 8.35 – Forward Buck-Boost: Currents (20 A/div) through each switch..........202

Figure 8.36 – Forward Buck-Boost: Voltage (200 V/div) and current (10 A/div) in the primary……..............................................................................................................203

Figure 8.37 – Forward Buck-Boost: Voltage (200 V/div) and current (10 A/div) in the primary......................................................................................................................203

Figure 8.38 – Forward Buck-Boost: Voltage (100 V/div) and current (2 A/div) for the current control of I1...................................................................................................204

Figure 8.39 – Forward Buck-Boost: Efficiency curve……........................................204

Figure 8.40 – Reverse Boost: Gate signals (10 V/div).............................................206

Figure 8.41 – Reverse Boost: Voltage (200 V/div) and current (7 A/div) in the switch S1..............................................................................................................................207

Figure 8.42 – Reverse Boost: Voltage (200 V/div) and current (7 A/div) in the switch S1…….......................................................................................................................207

Figure 8.43 – Reverse Boost: Turning-on of the switch S1.......................................208

Figure 8.44 – Reverse Boost: Turning-off of the switch S1.......................................208

Figure 8.45 – Reverse Boost: Voltage (200 V/div) and current (10 A/div) in the switch S3…..........................................................................................................................209

Figure 8.46 – Reverse Boost: Voltage (200 V/div) and current (10 A/div) in the switch S3..............................................................................................................................209

Figure 8.47 – Reverse Boost: Turning-on of the switch S3.......................................210

Figure 8.48 – Reverse Boost: Turning-off of the switch S3……...............................210

Figure 8.49 – Reverse Boost: Voltage (100 V/div) and current (10 A/div) in the voltage sources V1 and V2..............................................................................211

Figure 8.50 – Reverse Boost: Voltage (100 V/div) and current (10 A/div) in the magnetizing inductance..................................................................................211

Figure 8.51 – Reverse Boost: Voltage (100 V/div) and current (10 A/div) in the primary…..................................................................................................................212

Figure 8.52 – Reverse Boost: Voltage (100 V/div) and current (10 A/div) in the secondary.................................................................................................................212

Figure 8.53 – Reverse Boost: Voltage (100 V/div) and current (5 A/div) for the current control of I1...............................................................................................................213

Figure 8.54 – Reverse Boost: Efficiency curve….....................................................214

Figure 8.55 – Reverse Buck-Boost: Gate signals (10 V/div)....................................215

Figure 8.56 – Reverse Buck-Boost: Voltage (300 V/div) and current (10 A/div) in the switch S1...................................................................................................................216

Figure 8.57 – Reverse Buck-Boost: Voltage (300 V/div) and current (10 A/div) in the switch S1…...............................................................................................................216

Figure 8.58 – Reverse Buck-Boost: Turning-on of the switch S1.............................217

Figure 8.59 – Reverse Buck-Boost: Turning-off of the switch S1.............................217

Figure 8.60 – Reverse Buck-Boost: Voltage (300 V/div) and current (10 A/div) in the switch S2…...............................................................................................................218

Figure 8.61 – Reverse Buck-Boost: Voltage (300 V/div) and current (10 A/div) in the switch S2...................................................................................................................218

Figure 8.62 – Reverse Buck-Boost: Turning-on of the switch S2.............................219

Figure 8.63 – Reverse Buck-Boost: Turning-off of the switch S2…..........................219

Figure 8.64 – Reverse Buck-Boost: Voltage (100 V/div) and current (10 A/div) in V1..............................................................................................................................220

Figure 8.65 – Reverse Buck-Boost: Voltage (30 V/div) and current (10 A/div) in V2..............................................................................................................................220

Figure 8.66 – Reverse Buck-Boost: Voltage (200 V/div) and current (10 A/div) in the magnetizing inductance……...........................................................................221

Figure 8.67 – Reverse Buck-Boost: Currents (20 A/div) through each switch.........221

Figure 8.68 – Reverse Buck-Boost: Voltage (200 V/div) and current (10 A/div) in the primary......................................................................................................................222

Figure 8.69 – Reverse Buck-Boost: Voltage (200 V/div) and current (10 A/div) in the secondary….............................................................................................................222

Figure 8.70 – Reverse Buck-Boost: Voltage (100 V/div) and current (7 A/div) for the current control of I1........................................................................................223

Figure 8.71 – Reverse Buck-Boost: Efficiency curve...............................................223

LIST OF TABLES

Table 1.1 – Characteristics of different types of batteries..........................................40

Table 1.2 – Comparison between batteries...............................................................44

Table 2.1 – Integrated bidirectional Buck/Boost/Buck-Boost DC-DC converter: Switching Logic...........................................................................................................53

Table 2.2 – Bidirectional Boost/Buck DC-DC converter: Switching Logic..................56

Table 6.1 – Battery bank in the traction system of commercial EVs and HEVs.......136

Table 6.2 – Design specifications for the bidirectional DC-DC converter with tapped inductor.....................................................................................................................138

Table 6.3 – Components sizing for the bidirectional DC-DC converter with tapped inductor.....................................................................................................................139

Table 6.4 – Forward Buck: Comparison Theoretical x Simulated............................147

Table 6.5 – Forward Buck-Boost: Comparison Theoretical x Simulated..................152

Table 6.6 – Reverse Boost: Comparison Theoretical x Simulated...........................156

Table 6.7 – Reverse Buck-Boost: Comparison Theoretical x Simulated..................160

Table 7.1 – Design specifications for the bidirectional ZVS Buck-Boost DC-DC converter...................................................................................................................164

Table 7.2 – Components sizing for the bidirectional ZVS Buck-Boost DC-DC converter...................................................................................................................168

Table 7.3 – Forward mode: Comparison Theoretical x Simulated...........................173

Table 7.4 – Reverse mode: Comparison Theoretical x Simulated...........................178

Table 8.1 – Constructive aspects of the tapped inductor.........................................181

Table 8.2 – Components used in the prototype………………………………………..183

Table 8.3 – Forward Buck: Comparison Theoretical x Simulated x Experimental…195

Table 8.4 – Forward Buck-Boost: Comparison Theoretical x Simulated x Experimental……………………………………………………………………………....205

Table 8.5 – Reverse Boost: Comparison Theoretical x Simulated x Experimental..214

Table 8.6 – Reverse Buck-Boost: Comparison Theoretical x Simulated x Experimental……………………………………………………………………………….224

LIST OF ABBREVIATIONS

B.C. before Christ

CARB California Air Resources Board

CrCM Critical Conduction Mode

CCM Continuous Conduction Mode

CNPq-BR Brazilian National Council of Technological and Scientific Development

DC-DC Direct Current to Direct Current

DCM Discontinuous Conduction Mode

DSP Digital Signal Processor

EV Electric Vehicle

Finep Brazilian Financier of Studies and Projects

HESS Hybrid Energy Storage System

HEV Hybrid Electric Vehicle

ICE Internal Combustion Engine

IEA International Energy Agency

IGBT Insulated-Gate Bipolar Transistor

Li-Ion Lithium-Ion

LiOH Lithium Hydroxide

Li3CO3 Lithium Carbonate

LFP Lithium-Iron-Phosphate

MOSFET Metal-Oxide-Field Effect Transistor

Ni-Cd Nickel-Cadmium

Ni-Fe Nickel-Iron

Ni-Metal Nickel-Metal

NCA Nickel-Cobalt-Aluminum

NMC Nickel-Manganese-Cobalt

NiMH Nickel-Metal Hydride

Pb-Acid Lead-Acid

PCB Printed Circuit Board

PHEV Plug-In Hybrid Electric Vehicle

PWM Pulse Width Modulation

RTI Real-Time Interface

SC Supercapacitor

UPS Uninterruptible Power Supply

VRLA Valve-Regulated Lead-Acid

ZCS Zero-Current Switching

ZEV Zero Emission Vehicle

ZVS Zero-Voltage Switching

LIST OF SYMBOLS

∆IM Magnetizing current ripple

∆t Time interval

C1 Decoupling capacitor in parallel with voltage source 1

C2 Decoupling capacitor in parallel with voltage source 2

CC Clamping capacitor

Cf1 Capacitive filter 1

Cf2 Capacitive filter 2

D Duty cycle

D1 Duty cycle from switch 1



DC Clamping diode

fs Switching frequency

IL Inductor current

ILT1 Current in the primary

ILT2 Current in the secondary

IS1 Current through switch 1

IS1_MIN Minimum value of the current through switch 1

IS1_MAX Maximum value of the current through switch 1

Is1_AVG Average current through switch 1

Is1_RMS RMS current through switch 1


IS2_MIN Minimum value of the current through switch 2

IS2_MAX Maximum value of the current through switch 2






I1 Current in the voltage source 1

I1_AVG Average current in the voltage source 1

I2 Current in the voltage source 2

I2_AVG Average current in the voltage source 2

ILL Auxiliary inductance current

IM Magnetizing current

IM1 Instant value 1 of the magnetizing current

IM2 Instant value 2 of the magnetizing current

IM_AVG Average magnetizing current

LL Auxiliary inductance

LM Magnetizing inductance

LT Tapped inductor

n Turn ration

Converter efficiency

NP Turns in the primary of the tapped inductor

NS Turns in the secondary of the tapped inductor

PC Rated power

PV1 Power in the voltage source 1

PV2 Power in the voltage source 2

RC Clamping resistor

RC Parallel resistor/capacitor

S1 Switch 1

S2 Switch 2

S3 Switch 3

S4 Switch 4

to Time interval 0

t1 Time interval 1

t2 Time interval 2

ton Time where the controlled switch is turned-on

toff Time where the controlled switch is turned-off

TS Switching period

V1 Voltage source 1

V2 Voltage source 2

VgS1 Gate signal for switch 1



VS1 Voltage across switch 1

VS1_MAX Maximum voltage across switch 1





VLL Voltage across the auxiliary inductance

VLL_1st Voltage across the auxiliary inductance in the first operating stage

VLL_2nd Voltage across the auxiliary inductance in the second operating stage

VLM Voltage across the magnetizing inductance

VLM_1st Voltage across the magnetizing inductance in the first operating stage

VLM_2nd Voltage across the magnetizing inductance in the second operating stage

VLT1 Voltage across the primary

VLT1_1st Voltage across the primary in the first operating stage

VLT1_2nd Voltage across the primary in the second operating stage

VLT2 Voltage across the secondary

VLT2_1st Voltage across the secondary in the first operating stage

VLT2_2nd Voltage across the secondary in the second operating stage

1d Small signal perturbation in the duty cycle from switch 1



1i Small signal perturbation in the current I1

ˆMi Small signal perturbation in the magnetizing current

SUMMARY

INTRODUCTION........................................................................................................27

THESIS STRUCTURE……........................................................................................28

1 ELECTRIC VEHICLES AND HYBRID ENERGY STORAGE SYSTEMS: AN OVERVIEW…….........................................................................................................30

1.1 CHAPTER INTRODUCTION................................................................................30

1.2 ELECTRIC VEHICLES.........................................................................................30

1.2.1 History and Evolution.........................................................................................32

1.2.2 Current Prospects..............................................................................................35

1.2.3 EVs in Brazil......................................................................................................36

1.3 BATTERIES.........................................................................................................38

1.3.1 Batteries and EVs.............................................................................................40

1.3.2 Lead-Acid Batteries...........................................................................................41

1.3.3 Nickel-Metal Hydride Batteries..........................................................................42

1.3.3 Lithium-Ion Batteries.........................................................................................43

1.4 SUPERCAPACITORS.........................................................................................44

1.5 HYBRID ENERGY STORAGE SYSTEMS..........................................................46

1.5.1 Battery/Supercapacitor Hybrid Energy Storage System………………………...47

1.6 CHAPTER CONCLUSION...................................................................................48

2 BIDIRECTIONAL DC-DC CONVERTERS..............................................................49


2.2 DC-DC CONVERTERS........................................................................................49

2.3 BIDIRECTIONAL DC-DC CONVERTERS...........................................................51

2.3.1 Integrated Bidirectional Buck/Boost/Buck-Boost DC-DC Converter..................52

2.3.2 Bidirectional Boost/Buck DC-DC Converter......................................................55

2.4 CHAPTER CONCLUSION…................................................................................57

3 BIDIRECTIONAL DC-DC CONVERTER WITH TAPPED INDUCTOR: STEADY STATE ANALYSIS...………………………………………………………………………59


3.2 BIDIRECTIONAL DC-DC CONVERTER WITH TAPPED INDUCTOR................59

3.2.1 Forward Buck....................................................................................................61

3.2.2 Forward Boost...................................................................................................71

3.2.3 Forward Buck-Boost..........................................................................................78

3.2.4 Reverse Buck....................................................................................................84

3.2.5 Reverse Boost...................................................................................................91

3.2.6 Reverse Buck-Boost..........................................................................................98

3.3 CHAPTER CONCLUSION.................................................................................104

4 BIDIRECTIONAL ZVS BUCK-BOOST DC-DC CONVERTER: STEADY STATE ANALYSIS…………………………………………………………………………………105

4.1 CHAPTER INTRODUCTION..............................................................................105

4.2 BIDIRECTIONAL ZVS BUCK-BOOST DC-DC CONVERTER...........................105

4.2.1 Forward Mode.................................................................................................108

4.2.2 Reverse Mode.................................................................................................118


5 BIDIRECTIONAL DC-DC BUCK-BOOST DC-DC CONVERTER: DYNAMIC ANALYSIS…..…………………………………………………………………………….125


5.2 SMALL-SIGNAL ANALYSIS...............................................................................125

5.2.1 Forward Buck..................................................................................................127

5.2.2 Forward Boost.................................................................................................128

5.2.3 Forward Buck-Boost........................................................................................129

5.2.4 Reverse Buck..................................................................................................131

5.2.5 Reverse Boost.................................................................................................132

5.2.6 Reverse Buck-Boost........................................................................................133


6 BIDIRECTIONAL DC-DC CONVERTER WITH TAPPED INDUCTOR: DESIGN METHODOLOGY AND SIMULATION RESULTS...................................................136


6.2 DESIGN METHODOLOGY................................................................................136

6.2.1 Sizing of Components.....................................................................................138

6.2.1.1 Magnetizing inductance LM...........................................................................138

6.2.1.2 Capacitors C1 and C2....................................................................................139

6.3 CONTROL DESIGN...........................................................................................139

6.4 SIMULATION RESULTS....................................................................................141

6.4.1 Forward Buck..................................................................................................143


6.4.3 Reverse Boost.................................................................................................152


6.5 UNIFIED CONTROLLER....................................................................................161


7 BIDIRECTIONAL ZVS BUCK-BOOST DC-DC CONVERTER: DESIGN METHODOLOGY AND SIMULATION RESULTS...................................................164


7.2 DESIGN METHODOLOGY…………..................................................................164

7.2.1 Sizing of Components.....................................................................................165

7.2.1.1 Magnetizing inductance LM……………………………………………………...165

7.2.1.2 Auxiliary inductance LL and number of turns ratio n……...............………….165

7.2.1.3 Capacitors Cf1 and Cf2…….……………………………………………………..168

7.3 SIMULATION RESULTS....................................................................................168

7.3.1 Forward Mode.................................................................................................168

7.3.2 Reverse Mode.................................................................................................174


8 BIDIRECTIONAL DC-DC CONVERTER WITH TAPPED INDUCTOR: EXPERIMENTAL RESULTS....................................................................................180


8.2 EXPERIMENTAL PROTOTYPE.........................................................................180

8.2.1 Choice of Components………………………………………………………….…180

8.2.2 Tapped Inductor ……………………………………………………………………181

8.2.3 RCD Clamping……………………………………………………………………...181

8.3 EXPERIMENTAL SETUP……………………………………………………………185

8.4 EXPERIMENTAL RESULTS………………………………………………………...186

8.4.1 Forward Buck……………………………………………………………………….186


8.4.3 Reverse Boost.................................................................................................206



CONCLUSION.........................................................................................................226

REFERENCES.........................................................................................................228

APENDIX A..............................................................................................................234

APENDIX B..............................................................................................................239

APENDIX C..............................................................................................................245

APENDIX D..............................................................................................................250

APENDIX E..............................................................................................................255

APENDIX F..............................................................................................................258

APENDIX G..............................................................................................................261

27

INTRODUCTION

Since the past centuries until nowadays, people have the necessity to move

from a place to other. Looking for food or a place to live as the first civilizations, or

just making the way from home to work every day, people have used different ways

over the history to go wherever they want/need.

In the last century, due their easy access and operation, cars with internal

combustion engine became the most popular transport mean worldwide. However,

with the energy crisis in the world and the environmental issues, some alternatives

are being searched.

Considering that, Electric Vehicles (EVs) are being studied and considered a

key element against this scenario. However, the fundamental problem in EVs, and

what makes difficult for them to replace the traditional vehicles with internal

combustion engines, is their energy system. Because their high energy density,

batteries are widely used as EVs energy bank, but their low power density, low

charge/discharge rates, and the fact of certain loads requires high starting current

(which is not good for battery lifetime) represents some limitations for the system.

To deal with this problem, Hybrid Energy Storage Systems (HESS) are

implemented. Usually, HESS combines different energy sources, and the main

reason to this is to combine benefits and features from different power sources. For

those reasons, batteries and Supercapacitors (SC) are combined as HESS in EVs

where the SC can act like a buffer against large magnitudes and rapid fluctuations in

power, improving the system performance.

There are many advantages over SCs that make them good options for some

power applications, like high power density, high charge/discharge rates and

extended lifetime. But, in EVs, such as the batteries, they cannot fully supply all the

system for two main reasons.

The energy density in SC is low;

The price of a SC bank is high.

In summary, Battery/SC HESS provides, among others, advantages such as:

28

Improvement of the battery lifetime;

Reduction of the stress on battery;

Reduction in the battery size and cost;

Improvement in power management (generation/demand);

SC can recover more energy from the regenerative braking;

Battery supports slow transients and the SC fast transients.

To interface the battery and the SC in a HESS, the use of DC-DC converter has

shown in the literature to be the best way. This converter must be capable to allow

both directions of the power flow and increase or decrease the voltage in each power

flow direction. In other words, this converter needs to be a bidirectional converter,

and act like a Buck or Boost in both directions.

This way, this Master’s Thesis presents the study of 2 bidirectional DC-DC

topologies for HESS. For the first topology, all its theoretical study, involving the

steady state and dynamic analyzes, is presented in details. Also, a design

methodology subsequently verified by digital simulation is proposed and, finally, an

experimental prototype for laboratory implementation is built. Then, for the second

topology, just the theoretical analysis and a design methodology is presented and

verified by a digital simulation.

THESIS STRUCTURE

This present Master´s Thesis is composed, in addition to the appendices, by a

general introduction, eight chapters and a general conclusion, where each chapter

presents its own introduction and conclusion.

First, the purpose of the present section, the general introduction, is to place the

reader in the context of this work, justifying the motivations about the realization of

this research.

In Chapter 1, a brief presentation of the topics that support this work are

presented, focusing in EVs and their elements, covering from their historical

development to their current stage and discussing the role of the power electronics in

this scenario.

29

In Chapter 2, a review of some concepts involving DC-DC converters and their

applications is presented.

In Chapter 3, the theoretical steady state analysis of the first topology presented

in this Master´s Thesis, the bidirectional DC-DC converter with tapped inductor, is

performed and presented in details, providing fundamental knowledge for the

following chapters.

In Chapter 4, the theoretical steady state analysis of the second topology

presented in this Master´s Thesis, the bidirectional ZVS Buck-Boost DC-DC

converter, is performed and presented in details.

In Chapter 5, the dynamic analysis of the bidirectional DC-DC converter with

tapped inductor is performed, leading to all the equations for the control design of the

converter.

In Chapter 6, with the knowledge provided by the theoretical analyses made in

the previous chapters, a design methodology for the bidirectional DC-DC converter

with tapped inductor is proposed, and, to support the design methodology, simulation

results are presented.

In Chapter 7, as well as in Chapter 6, a design methodology and simulation

results for the bidirectional ZVS Buck-Boost DC-DC converter is presented.

Then, the experimental results of the bidirectional DC-DC Converter with tapped

inductor are presented, analyzed and discussed in Chapter 8.

After completing all the stages of this Master´s Thesis, and after the conclusion

of all the chapters, the final conclusions and considerations about this work are

summarized in a general conclusion.

Finally, from Appendix A to Appendix F, documents and files that were

developed in this work, and which are of interest to the reader, are presented.

30

CHAPTER 1

ELECTRIC VEHICLES AND HYBRID ENERGY STORAGE SYSTEMS:

AN OVERVIEW

1.1 CHAPTER INTRODUCTION

In this chapter, the topics that hold the proposal of this work are discussed.

First, a brief presentation of Electric Vehicles (EVs), covering from their historical

development to their actual stage is presented. Then, some important elements of

this technology are presented and discussed.

1.2 ELECTRIC VEHICLES

In an era where the environmental issues and the energetic safety are in an

outstanding position, EVs are increasing their popularity. By definition, an EV is a

vehicle which is pulled by, at least, one electric motor. In other words, it is a vehicle

where the electric motor is directly or indirectly linked to the traction of the vehicle

(CASTRO, B. and FERREIRA, T., 2010).

In EVs, there is no Internal Combustion Engines (ICEs) and the vehicle is fully

powered by electrical energy. This energy can be provided, among others, by fuel

cells and solar panels. However, in most of the cases, it is a battery which makes this

function.

When analyzing this rising appeal for EVs, Emadi (2005) and Baran and Legey

(2010) attribute that especially to the EVs characteristics, and, when punctual those

characteristics, highlight the following points:

Performance Increasing: Electric Motors are more efficient than ICEs. They

show performances in the region of 90% while the ICEs show in a region of

40%;

Better robustness: Electric Motors are reliable, require less maintenance and

work silent and smoothly;

31

Energetic safety: According the International Energy Agency (IEA), from

2007 to 2030, the annual increase of energy demand is 1.5%, whereas the

oil offer, at the same period, is 1%. In accumulated terms, the energy

demand will increase about 40% and the oil offer just 25%. As electricity is a

“home energy” and can be produced independent of the oil, EVs are

independent of the oil volatility and scarcity;

Environmental issues: They are “clean”, with no gas emissions. Even if the

electricity for their recharge is generated by fossil fuels, the regulation in the

generator sources is easier than in EVs costumers.

Nevertheless, EVs also present some limitations, and are those limitations

(normally related to their energy system) that do not allow to them a comprehensive

market conquest. Thus, if the main problem of EVs is related to their energy system

and the same is basically formed by batteries, it is possible to contend that the most

part of the EVs limitations are battery limitations. In summary, those limitations are

based in 4 main topics:

High cost: It is estimated that the battery represents more than 50% of the

EV final cost (CASTRO, B. and FERREIRA, T., 2010);

Battery lifetime: With a lot of charge/discharge cycles, and an inefficient

recharging method, the lifetime of a battery can be reduced significantly.

Even with the care needed, actually, the batteries available do not present an

extended lifetime (BARAN, R. and LEGEY, L., 2010);

Battery recharging: There is no satisfactory infrastructure for this process,

and, depending on the battery type, the recharging process can take a

considerable amount of time (EMADI, A., 2005);

Autonomy: The autonomy of a vehicle is directly related to the energy density

of the energy source. To make a comparison, gasoline presents an energy

density of 12500 Wh/Kg, whereas the Lead-acid (Pb-acid) battery (commonly

used in EVs) presents an energy density of 25 Wh/Kg. That is, to have the

same density, it is needed an implementation of an expressive number of

batteries, making, from the point of view of weight/volume and cost,

impracticable the use of EVs.

32

1.2.1 History and Evolution

In spite of being in focus nowadays, EVs are not as new as they seem. The first

successful EV is dated by 1891 and was created by William Morrison. This vehicle

was equipped with a battery that weighed about 350 kg and could reach 14 km/h.

Figure 1.1 presents this vehicle.

Figure 1.1 Electric Vehicle by William Morrison

Source: May/Jun IEEE Power & Energy Magazine p.66 (2004)

Analyzing the last years of the 19th century and the beginning of the 20th, EVs

were exercising an important role in the American market. To get an idea, in 1899, in

USA, were sold 1,575 EVs, 1,681 steam vehicles and 936 gasoline vehicles (also

called vehicles with Internal Combustion Engines or ICE vehicles) (BARAN, R.,

2010).

In 1900, considering the cities of Boston, Chicago and New York, 800 of a total

of 2.370 vehicles were electric, 1170 were steamers and just 400 were gasoline-

powered (SULZBERGER, C., 2004).

According Sulzberger (2004) and Castro and Ferreira (2010), this scenario can

be explained by some characteristics of the EVs and, most important, by the

disadvantages of the gasoline vehicles at that time. EVs were silent (lower noise

levels and absence of vibrations), clean, simple to operate (lack of transmission) and,

with the best ways in the urban perimeters, the main problem of EVs (their autonomy)

was not a big concern.

33

On the other hand, even the gasoline vehicles presenting some advantages

(they could travel fast, could be equipped with powerful engines and had a great

range due to the easy access to gasoline), they were noisy, smelly and polluting. To

start them, they had to be cranked by hand, process that required a strong arm and

often resulted in injuries to the handler (SULZBERGER, C., 2004).

However, this scenario changed quickly. From 1899 to 1909, gasoline vehicles

sales grew 120 times, whereas the EVs sales just doubled. With that, in 1912 the

fleet of gasoline vehicles was already 30 times bigger than the EVs fleet in New York

(BARAN, R., 2012).

For Baran (2012), the EVs fast decline occurred, mainly, due to the following

factors:

In 1912, with the invention of the electric starting and, consequently, the

abolishing of the manual starting in gasoline vehicles, the starting process on

those vehicles was not a problem anymore;

The discovery of oil reserves dropped the gasoline price;

In 1920, the roads in USA already interconnected a lot of cities, then,

vehicles capable to travel long distances were necessaries;

The production series system, idealized by Henry Ford, allowed the reduction

of the gasoline vehicles price, becoming them very much cheaper than EVs.

With the fast technological development of gasoline vehicles and with the EVs

still stuck to the slow development of batteries, the industry of gasoline vehicles

continued to grow, and EVs were almost forgotten. Their production was reduced

drastically and their use was limited just a few applications, such as trash collecting

and delivery service (BARAN, R., 2012).

Thus, the EVs remained neglected until the 1970s, when, with the oil crises and

the public opinion starting to concern about the environmental and the use of

renewable energies, the major automakers looked back to EVs. However, the

technological development in EVs was still a big impediment, preventing the

developed prototypes to achieve a satisfactory stage and, consequently, the

production lines.

34

Nevertheless, in the early of the 1990s, with the sustainable development

concept even bigger than in the 1970s and with the progress of the batteries

development, the attention came back to EVs. In USA, authorities from California

decided that the automakers from that state should provide EVs to the costumers

and the California Air Resources Board (CARB), government sector responsible for

monitoring the air quality, defined a quota of Zero Emission Vehicles (ZEV) sales of

2% in 1998, increasing to 5% in 2001 and 10% in 2003, with bonus to the

automakers for achieving this goal (BARAN, R., 2012). Even so, some sectors,

specially the major oil companies, were still reluctant to the EVs implementation.

Combining these 2 situations, the Hybrid Electric Vehicles (HEVs) came to the

spotlight. Hybrid vehicles combine, at the same time, an electric motor and an ICE.

This way, the advantages from each technology can be combined, remediating the

previous problems from each one. Then, in 1997, the Toyota launched to the market

the HEV Toyota Prius. In 2000, the Toyota Prius arrived to USA, reaching high sales

rates, confirming the importance of investments and researches in this area.

Figure 1.2 Hybrid Vehicle Toyota Prius

Source: Internet image

Currently, a new approach of HEVs has become more popular, the Plug-In

Hybrid Electric Vehicles (PHEVs). With the capability of recharge the battery from

external energy sources, even from a regular household wall socket (origin of the

term Plug-In), PHEVs combine and optimize the characteristics of EVs and HEVs,

improving the battery and the electric motor capability and decreasing the size of the

ICE (LAFUENTE, C., 2011).

35

Electric

Motor

ICE

Battery

Bank

Gas

Tank

Power

Electronics

Figure 1.3 Inside view of a PHEV

Source: Adapted from Lafuente, C. (2011), p. 6

1.2.2 Current Prospects

Even EVs not being a recent technology, the new generation of costumers sees

them as a novelty. However, they still suffer some distrust from costumers and,

added to questions like lack of infrastructure and technological development, their

insertion in the market is difficult.

Castro and Ferreira (2010) point another factor that has a huge influence in the

EVs insertion in the market: the size and the profile of the vehicles fleet from a

country is directly related to its economical development. That is, when a country

faces low development levels, the vehicular fleet grows slowly and the costumers

keep conservatives. Whereas the personal income of this country rises, the fleet will

grow significantly and the costumers are more open to new possibilities (change the

conventional vehicles for EVs).

Taking these situations into account, to enable the insertion of EVs and

consequently their acceptance and success in the market, government actions are

essential.

According Castro and Ferreira (2010), countries like USA, Canada, China,

Japan and Germany, among others, are investing in five basic incentives to raise the

interest for EVs. They are:

36

Bonus to the buyers: The USA, for example, offers a bonus about US$

7.500,00 in an EV buying, where some regional laws can extend this value.

Other European countries offer similar bonus and, in Japan, this bonus can

reach US$ 10.000,00 (CASTRO, B. and FERREIRA, T., 2010);

Discount on taxes to buyers and manufacturers: It is estimated that until

2020, just in USA, the incentive and help to EVs manufacturers and providers

can reach about US$ 25 billion. (BARAN, R., 2012) Also, some provinces in

Canada offer discounts up to US$ 2.000,00 in taxes for EV buyers and, in the

United Kingdom, EVs have a discount on circulating taxes and are free of

parking fees in London downtown (CASTRO, B. and FERREIRA, T., 2010);

Adoption of restrictions to the conventional vehicles: Many countries are

adopting stricter parameters in the regulation of gases emission and, to

comply these parameters, the development and improvement of the

combustion engine is essential.

Aid to research: In USA, from 2008 to 2013, the government allocated US$

95 million a year for a formation of a human capital specialist in EVs, and, for

researches involving EVs and the development of batteries, this amount

reaches approximately US$ 2.4 billion (BARAN, R., 2012) (CASTRO, B. and

FERREIRA, T., 2010);

Implementation of infrastructure: Some countries with a smaller territorial

size, like Japan and Israel, are investing in the implementation of fast

recharging points all over their territory.

1.2.3 EVs in Brazil

In the global automotive scenario, Brazil has proven to be a leading country.

Being one of the top automakers and relying one of the largest fleets, the vehicular

electrification is a key factor in the next years to guarantee its energetic safety and

the sustainable development.

It is estimated that, in 2030, with the population growth and the economical

development, the Brazilian vehicular fleet will reach the mark of 83.7 million of

vehicles, being the 5th in the world, just behind China, USA, India and Japan. This

37

growth will represent an increase of 127% if compared with the fleet in 2010 (36.9

million of vehicles) (BARAN, R. and LEGEY, L., 2010).

Nevertheless, even with the imminent growth of the fleet, Brazil walks in the

opposite way of the world. There are no governmental politics supporting the

production and sale of EVs and they do not enjoy advantages in terms of taxes and

fees, just in the research field can be seen some public-privates partnerships and

investments for EVs, which is very little if considered the importance that EVs are

gaining over the years.

Among these partnerships, the development of a Hybrid Electric Bus by the

Alberto Luiz Coimbra Institute of Post-Graduate and Engineering Research at the

Federal University of Rio de Janeiro (COPEE-UFRJ) in partnership with companies

such as Petrobras and Eletra, the partnership between the Brazilian Financier of

Studies and Projects (Finep) and Itaipu Binacional for the development of batteries

and storage systems and the partnership between Itaipu Binacional, the automaker

company FIAT and the Swiss company Kraftwerke Oberhasli (KWO) for the

development of a national EV were the most significant in Brazil. It is important to

highlight that, in the later case, the main goal of the project was the vehicular

technological development in order to make it cheaper and more accessible, and not

a serial production (SPERANDIO, M.; SALDANHA, J. and BASSO, C., 2012).

In figure 1.4, the EV developed by Itaipu, FIAT and KWO is presented.

Figure 1.4 Electric Vehicle FIAT/Itaipu Binacional Palio Weekend

Source: Internet Image

38

Also, some public calls from the Brazilian National Council of Technological and

Scientific Development (CNPq-Brazil) for projects related to the development of EVs

technology were relevant in the research field.

Another factor that is directly related to the successful insertion of EVs in the

Brazilian market is the support of the National Bank for Economic and Social

Development (BNDES), the main long-term credit provider in Brazil. Actions such as

a massive marketing for EVs as the technological solution for environmental and

transportation issues, support for technological development and production line

implementation would be a first step in the EVs expansion (CASTRO, B. and

FERREIRA, T., 2010).

Also, the influence of the BNDES in the Flex Fuel Vehicles development can be

used as parameter for EVs, where, with the implementation of the actions mentioned

above in the beginning of their development, they were able to structure themselves

and become the most popular vehicular technology in Brazil.

1.3 BATTERIES

Basically, batteries, also called electric accumulators, are devices that convert

chemical energy in electrical energy through a phenomenon known as electrolysis.

The first record of an electric accumulator is dated by 250 B.C., in Syria, where

a ceramic container with an iron bar surrounded by a copper cylinder could produce

around 1.1 Vdc when full of vinegar (LAFUENTE, C., 2011). Figure 1.5 presents this

device.

However, the landmark of the batteries’ history occurred just in 1800, when

Alessandro Volta, based on the work of Luigi Galvani about animal electricity,

discovered the electrolysis principle and developed the first battery.

In 1859, the French physicist Gastón Plante developed the first Pb-acid

rechargeable battery (LAFUENTE, C., 2011). However, according Sulzberger (2004),

early Pb-acid batteries were heavy, difficult to recharge, very corrosive, and

presented a low power density, around 4 – 6 W/h, requiring approximately between

56 and 80 kg of battery for 0.745 kW/h at the battery terminals. Since then, the Pb-

39

acid batteries have passed for constant changes and improvements, both in

manufacturing or material means, and today they are the most used battery type in

applications requiring energy storage.

Figure 1.5 First electric accumulator

Source: Lafuente, C. (2011), p. 9

Nevertheless, the study and use of other materials in batteries development just

occurred in the early of 1970s, when Nickel-metal (Ni-metal) and Lithium-ion (Li-ion)

batteries were created. According Lafuente (2011), the first Ni-metal batteries were

very unstable in the recharging process, problem that was solved with the addition of

hydride to the battery composition, resulting then in the Nickel-metal hydride (NiMH)

batteries, launched in the market in the early 1990.

Talking about the Li-ion batteries, the first batteries of this type also presented

the same problem of the instability in the recharging process, however this problem

was solved fast with the exchange of lithium metal by lithium ions in the battery

composition and, in 1991, the Sony Corporation started to sell them in Japan

(LAFUENTE, C., 2011).

According Castro and Ferreira (2010), the batteries development intensified in

the end of 90s and early 2000, when, with the fast advance of sectors such as

telecommunications and informatics combined with the spread of mobile devices (cell

phones and laptops), the need for smaller devices with more energy storage made

the researches in the batteries field grow significantly, resulting in considerable

improvements in the battery technology.

40

Table 1.1 presents some characteristics of different types of batteries used

nowadays.

Table 1.1 Characteristics of different types of batteries

Battery Type Battery Voltage per

Cell [V] Temperature Variation [°C]

Charge/Discharge Rates per Module

Lead-acid 2.1 35-70 600

Nickel-cadmium 1.25 30-50 2000

Nickel-metal hydride 1.4 20-60 600

Nickel-zinc 1.6 40-65 250

Nickel-iron 1.25 40-80 800

Sodium-sulfurous 2.08 300-400 350

Zinc-air 1.62 0-45 70

Lithium-iron 1.66 400-450 500

Lithium-polymer 3.5 0-100 300

Source: Lafuente, C. (2011), pp. 13

1.3.1 Batteries and EVs

Due to their high energy density, batteries are widely used as energy bank in

EVs and their main function is the energy storage. Considered the heart of EVs, they

are the main element in this technology, making the success of EVs directly

proportional to the batteries development.

In EVs, batteries are arranged in modules (more than one battery cell) or in

packs (more than one module), as shown in Figure 1.6.

Battery CellBattery

ModuleBattery Pack

Figure 1.6 Batteries arrangement in EVs

Source: Adapted from Castro and Ferreira (2010) in BNDES Setorial 32, pp. 281

41

According Castro and Ferreira (2010) and Baran (2012), there are some factors

that affect the battery choice in EVs. They are:

Power Capacity: Measured in kW, it is related to the energy transfer. The

battery power is a critical factor in EVs, their performance is directly related to

how many kW the battery bank can supply;

Stored Energy: Measured in kWh, it is the parameter that determines the

distance to be performed by an EV (the autonomy of the EV) and the weight

of the battery system;

Safety;

Lifetime: How many charge/discharge cycles and the age of the battery.

Performance: Performance in different operating temperatures, measurement

and thermal management;

Weight and cost.

Currently, there are 3 types of batteries competing for the establishment of a

standard for EVs industry: Pb-acid batteries, NiMH batteries and Li-ion batteries.

1.3.2 Lead-Acid Batteries

The Pb-acid batteries are the most widespread batteries nowadays. Used in

applications like Uninterruptible Power Supplies (UPSs), emergency lighting in

buildings and ICE vehicles for on-board computer and central locking, among others,

those batteries present six cells with 2.1 nominal Volts each, totalizing 12 V in their

terminals and, when maintained properly, can present an extended lifetime

(LAFUENTE, C., 2011). Figure 1.7 presents a commercial Pb-acid battery.

However, they also present some limitations for EVs applications, such as

regular replacement of the electrolyte, mandatory vertical installation and release of

hydrogen in the air. Also, for containing dangerous elements (lead and sulfurous

acid), some environmental regulations about use, disposal and recycling are applied

(CASTRO, B. and FERREIRA, T., 2010).

42

Figure 1.7 Commercial Lead-acid battery


According Lafuente (2011), trying to remedy those problems were created the

Valve-Regulated Lead-acid batteries (VRLA), a Pb-acid battery with better

performance and capability, using a gel as electrolyte and equipped with a valve to

regulate automatically the release of hydrogen.

1.3.3 Nickel-Metal Hydride Batteries

Due to their high energy density, reliability, extended lifetime and allied with the

use of the metallic hydride (which does not contaminate the environment), the NiMH

batteries are, today, the dominant technology in EVs. Figure 1.8 presents a NiMH

battery bank used in EVs.

Figure 1.8 Nickel-metal hydride battery bank for EVs

Source: Internet Image

43

Nevertheless, limitations such as high cost (due to the elevated use of nickel),

weight, heat losses causing a decrement in the efficiency and periodic maintenance

are some factors that do not allow these batteries a more significant market

conquest.

It is important to highlight that, according Baran (2012), there is no expectation

of a growth in the use and technological development of NiMH batteries, while they

have practically reached their maximum point of development.

1.3.4 Lithium-Ion Batteries

Nowadays, due to the potential and success already presented in the electronic

industry, telecommunication applications and mobile devices, the Li-ion batteries are

the biggest bet for the development and future of EVs. Besides, the lithium is not

toxic and is a cheap raw material.

The Li-ion batteries are formed, basically, by an anode (negative electrode)

usually made of graphite and a cathode (positive electrode) usually derived from

Lithium Carbonate (Li3CO3) or Lithium Hydroxide (LiOH). It is estimated that the

cathodes represent 40% of the battery cost. Among the different types of Lithium

batteries, some can be highlighted: the Lithium-Nickel-Cobalt-Aluminum batteries

(NCA); the Lithium-Nickel-Manganese-Cobalt batteries (NMC) and the Lithium-Iron-

Phosphate batteries (LFP) (CASTRO, B. and FERREIRA, T., 2010).

Figure 1.9 presents a Li-ion battery module for EVs.

Figure 1.9 Lithium-ion battery module for EVs

Source: Lafuente, C. (2011), pp. 17

44

Baran (2012) and Lafuente (2011) highlight the following aspects of the Li-ion

batteries when compared with the NiMH batteries:

High power: Between 1.4 and 1.7 times the energy density of a NiMH battery,

resulting in smaller and lighter batteries;

Efficiency: more efficient in charge/discharge, and do not present high

temperature elevation, extending their lifetime;

Elevated discharged current, which is ideal for traction batteries.

Among the disadvantages and aspects that need improvement when compared

with the NiMH batteries, the following aspects are pointed by Baran (2012) and

Lafuente (2011):

Safety: Overload, short-circuits and use in adverse conditions can destroy

the battery;

Cost: the cost per kWh is still high;

Durability: Due to the high cost, it is necessary that the Li-ion batteries last a

long time to make the investment viable for manufacturers and customers

(approximately 7000 charge/discharge cycles for EVs).

In Table 1.2, a brief comparison between these 3 batteries type is presented.

Table 1.2 Comparison between batteries

Battery type Energy [Wh/kg]

Cost Safety Problems

Lead-acid 30-50 X Stable Low Energy

Nickel-metal hydride 60-80 3X Stable No leadership in

cost and performance

Lithium-ion

NCA 100-130

5x Unstable Cost and protection

NMC 100-130

LFP 90-110 Source: Adapted from Castro and Ferreira (2010) in BNDES Setorial 32, pp. 284

1.4 SUPERCAPACITORS

Supercapacitors (SCs) are devices capable of storing energy on surface parallel

plates, presenting characteristics such as high power density, high charge/discharge

45

rates and extended lifetime (Kollimalla, S. et al, 2014). Different from batteries, SCs

do not degrade over the time, even being considerably charged and discharged.

To get an idea, the first batteries presented around 9-13 Wh/kg of energy

density while the current SCs, even with the technological development over the

years, present around 4-8 Wh/kg of energy density. However, the power density is,

depending of the material used in their construction, around 800-1400 W/kg, which is

a lot of times bigger than the power density in batteries (BARAN, R., 2012).

Figure 1.10 Commercial Maxwell Supercapacitors


The development and investment in researches about the use of SCs in EVs

started mainly in the middle of the 90s, trying to find on them an alternative for the

energy system in EVs. Nevertheless, it was concluded that an EV could not be fully

powered by SCs for two main reasons: their energy density, as mentioned before, is

too low and would be very expensive to create a SC bank with the same

performance of a battery bank.

Nowadays, the focus of the researches involving batteries and SC is in the

development of Hybrid Systems, combining these two devices in order to improve

EVs performance and utilization.

For example: some automakers, in order to extend the battery lifetime, project

EVs with batteries bigger than necessary, impacting in the price of EVs. However, if

46

used in conjunction with SCs, the battery bank size can be reduced and, at the same

time, it is allowed better energy storage for the batteries.

1.5 HYBRID ENERGY STORAGE SYSTEMS

According Bocklisch (2015), a Hybrid Energy Storage System (HESS) can be

characterized by a beneficial combination of two or more different energy sources

with supplementary operating characteristics (energy and power density, self-

discharge rate, efficiency, lifetime, etc). On simpler words, a HESS combines

different energy sources in order to create a new system capable to provide the

benefits of each energy source.

In a HESS, one of the energy sources must be characterized by fast response

time, high efficiency and lifetime, being responsible to supply the high power

demand, transients and the fast load fluctuations of the system. On the other hand,

the other energy source will be responsible to supply the high energy demand of the

system, commonly presenting characteristics like low self-discharge rates (Bocklisch,

T., 2015).

According Bocklisch (2015), a HESS presents the following main advantages:

Reduction of total investment costs if compared to a single storage system;

Efficiency increasing of the system;

Increase of energy storage and lifetime.

Currently, HESS are being strongly used in applications like renewable energy

systems, smart grids and EVs, employing different energy sources such as batteries,

SCs and fuel cells, among others.

To make the implementation of a HESS possible, there are different ways to

make the coupling of the storage units. The simplest way is the direct coupling of the

storages, presenting the simplicity and low costs of implementation as the main

advantage of this configuration. However, the possibilities of power flow control

become reduced, resulting in an ineffective utilization of the storage units.

Another energy storage coupling architecture possible is via a bidirectional DC-

DC converter interfacing the storage units. In this case, the bidirectional DC-DC

47

converter will allow the power flow control in the HESS, resulting in an optimization of

the power management in the HESS, protecting the high-energy storage unit against

peak power and fast load fluctuations. The drawback of this solution, according

Bocklisch (2015), is the fluctuation of the DC Bus voltage.

Talking specifically about EVs, the later architecture with a bidirectional DC-DC

converter interfacing a battery bank and a SC is the most common nowadays, being

the focus of different researches for the EVs energy system.

1.5.1 Battery/Supercapacitor Hybrid Energy Storage System

As mentioned before, the Battery/SC HESS with a bidirectional DC-DC

converter interfacing the battery and the SC is the most recent focus of research

involving EVs energy bank. Figure 1.11 presents the schematic of the

implementation of a Battery/SC HESS in EVs.

DC BUS

Icond ISC

IBatteryBidirectional

DC-DC

ConverterVB VSC

Motor

DC-AC

Converter

Traction

System

HESS

Figure 1.11 Battery/Supercapacitor HESS in EVs applications

Source: Self Authorship

In this configuration, the SC can act like a buffer against large magnitudes and

rapid fluctuations in the power, improving the system performance. Among some

characteristics of the Battery/SC HESS, the following can be highlighted:

Improvement of the battery lifetime;

Reduction of the stress on batteries;

Reduction in the battery size/cost;

48

Improvement in power management (generation/demand);

Battery supports slow transients whereas the SC supports the fast;

SC can recover more energy from the regenerative breaking.

Currently, there are different topologies of bidirectional DC-DC converters and

control modes for a HESS implementation, themes that are going to be discussed in

the next chapter.

1.6 CHAPTER CONCLUSION

In this chapter, the topics that hold the proposal of application addressed in this

work, such as EVs and some of their energy system elements, were presented and

discussed.

As shown in chapter 1, EVs are not a recent technology as many people believe

they are and even them presenting considerable advantages when compared to ICE

vehicles, issues such as lack of infrastructure, distrust of costumers and

technological barriers are some of the reasons why EVs do not achieve a significant

market conquest.

In this scenario, government actions and massive support to research have

been shown to be essential for breaking down these barriers and, consequently, to

allow the growth and expansion of EVs.

49

CHAPTER 2

BIDIRECTIONAL DC-DC CONVERTERS


In this chapter, a brief review of DC-DC converters is presented. Considering

the fact that the unidirectional DC-DC converters are a key element in the

development and understanding of bidirectional DC-DC converters, a review

involving the concepts and applications of those converters is carried out.

Then, bidirectional DC-DC converters are presented, discussing their role in the

power electronics scenario nowadays, presenting some concepts and applications

where they are needed. In the end, the two topologies that are references to this

work are discussed.

2.2 DC-DC CONVERTERS

Conceptually, a DC-DC converter can be defined as a system formed by power

devices, such as diodes, Metal-Oxide Field-Effect Transistors (MOSFETs) and

Insulated-Gate Bipolar Transistors (IGBTs) and passive elements, such as capacitors

and inductors (BARBI, I. and MARTINS, D., 2000).

In a DC-DC converter, a DC voltage or current level is applied in the input

terminals and, with a command strategy for the turning-on/off of the power devices,

these levels can be adjusted to desired parameters in the output terminals. In other

words, the function of a DC-DC converter is to convert energy from a DC energy

source to a DC load, where high conversion efficiency is a key factor.

The traditional DC-DC converters are characterized by having a transistor

(operating as a switch), a diode and one or more capacitors and inductors. They also

work with fixed switching frequency and variable duty cycle, presenting voltage step-

down function (Buck) or voltage step-up function (Boost) and, in some cases, both

functions (Buck-Boost).

50

Figure 2.1 presents the traditional DC-DC converters known in the literature.

V2V1 V2

++++

- -

C1 C2

L

S1

D+ +

V1

- -

C1 C2

L

S1

D

+ +

V1 V2

-+

S1

C1 C2L

D

+

+

- +

(a) (b)

(c)

Figure 2.1 Traditional DC-DC converters: (a) Buck (b) Boost (c) Buck-Boost


The operating principle of the topologies presented in Figure 2.1 is based on the

fact that never the transistor and the diode conduct at the same time: when the

transistor is conducting, the diode will be blocked, and when the transistor blocks the

diode starts to conduct.

DC-DC converters may also present three different operation modes, which are

characterized by the inductor current behavior: the Continuous Conduction Mode

(CCM), where the inductor current never reaches zero; the Discontinuous

Conduction Mode (DCM), where the inductor current reaches zero in more than one

instant of time and the Critical Conduction Mode (CrCM), where the current will reach

zero in a single instant of time.

DC-DC converters can also be isolated or non-isolated. The isolated converters

have a transformer on their topology, providing galvanic isolation between the source

and the load. Figure 2.2 presents some of the traditional isolated DC-DC converters.

Furthermore, the switching method is another important factor for DC-DC

converters, where they can operate with hard-switching or soft-switching. Nowadays,

with the increase appeal for high-efficiency systems, the most part of the converters

work with soft-switching.

In the soft-switching, the addition of components to the circuit or the use of

parasitic elements makes the switches of the system achieve a Zero-Voltage

51

Switching (ZVS) or a Zero-Current Switching (ZCS), increasing the efficiency of the

system. Also, with the implementation of the soft-switching, the size, weight and

volume of the system can be reduced, since with soft-switching the switching

frequency can be elevated, reducing the size of the magnetic elements (BELLUR, D.

and KAZIMIERCZUK, M., 2007).

V1

+

V2

+

V1

+

V2

+

C2C1

--

D

(a)

Tr

+ +

-

C2C1++

-

Tr D2

D3

L1

(b)

S1 D1S1

Figure 2.2 Traditional isolated DC-DC converters: (a) Flyback (b) Forward


2.3 BIDIRECTIONAL DC-DC CONVERTERS

Analyzing the topologies presented in Figures 2.1 and 2.2, the energy flows just

in one direction, from the voltage source 1 (V1) to the voltage source 2 (V2), and the

opposite direction is not possible. In this case, the converters are called unidirectional

converters.

Nevertheless, an increasing number of applications requiring a constant

exchange of energy from a source to a load (as motor drives, renewable energy

systems, electric vehicles, hybrid energy systems, among others), and vice versa,

makes impossible the use of unidirectional converters. In those cases, bidirectional

converters are needed, where is the bidirectional converter that will allow the energy

exchange and the power flow control in the system.

Usually, bidirectional DC-DC converters are current controlled by a PWM signal,

where the direction of the current will represent the direction of the power flow.

Because of that, they always work in CCM and there is no DCM or CrCM operation

for bidirectional DC-DC converters (CARDOSO, R., 2007).

According Khan et al (2016), the simplest and easiest way of obtaining

bidirectional DC-DC converters is to replace the diodes of the unidirectional

converters with switches having unidirectional current blocking and bidirectional

52

voltage blocking capability. Figures 2.3 and 2.4 present the bidirectional DC-DC

converters derived from unidirectional topologies.

V2V1 V2

++++

- -

C1 C2

L

S1

(a)

+ +V1

- -

C1 C2

L

S1+ +

(b)

V1 V2

-+S1

C1 C2L+

+

- +

(c)

S2

S2

S2

Figure 2.3 Traditional bidirectional DC-DC converters: (a) Buck/Boost (b) Boost/Buck (c) Buck-Boost


V1

+

V2

+

V1

+

V2

+

C2C1

--

(a)

Tr

+ +

-

C2C1++

-

Tr

S1

L1

(b)

S1

S2

S4

S3

S2

Figure 2.4 Traditional isolated bidirectional DC-DC converters: (a) Flyback (b) Forward


Over the years, more bidirectional DC-DC topologies have been studied, always

aiming to meet the demand of applications, preferably presenting high-efficiency and

different modes of operation. Following, the two topologies that are reference

topologies for the topologies addressed in this thesis are presented.

2.3.1 Integrated Bidirectional Buck/Boost/Buck-Boost DC-DC Converter

In Figure 2.5, an integrated version of the Buck, Boost and Buck-Boost

converters is presented.

53

D1 D2L

V2

+

-

V1

+

-

C1+

C2+

S1 S2

S3 D3 D4 S4

Figure 2.5 Integrated bidirectional Buck/Boost/Buck-Boost DC-DC converter


Introduced by Caracchi et al (1998), this topology is nowadays one of the most

used topologies when a bidirectional DC-DC converter is required, being

implemented in a wide range of applications. The main advantage of this topology is

that it can operate like a Buck, Boost or Buck-Boost for each direction of the power

flow, facilitating its application since the mentioned operations are already widely

known and studied in the literature.

With the current control of the inductor L, the power flow in the converter can be

controlled, making the exchange of energy between V1 and V2 possible. Considering

the direction of the power flow, when the converter is sending energy from V1 to V2 it

will be considered as a Forward converter and, when operating in the opposite way,

as a Reverse converter.

In Table 2.1, the switching logic for each operation mode is presented.

Table 2.1 Integrated bidirectional Buck/Boost/Buck-Boost DC-DC converter: Switching Logic

Operation Mode S1 S2 S3 S4

Forward Buck PWM OFF OFF OFF

Forward Boost ON OFF OFF PWM

Forward Buck-Boost PWM OFF OFF PWM

Reverse Buck OFF PWM OFF OFF

Reverse Boost OFF ON PWM OFF

Reverse Buck-Boost OFF PWM PWM OFF


Considering the switching logic presented in Table 2.1, in Figures 2.6 and 2.7

are presented the operating stages of the integrated bidirectional Buck/Boost/Buck-

Boost converter for each power flow direction.

54

D1 D2L

V2

+

-

V1

+

-

C1+

C2+

S1 S2

S3 D3 D4 S4

(a)

ILI2I1

D1 D2L

V2

+

-

V1

+

-

C1+

C2+

S1 S2

S3 D3 D4 S4

(d)

ILI2I1

D1 D2L

V2

+

-

V1

+

-

C1+

C2+

S1 S2

S3 D3 D4 S4

(c)

ILI1

D1 D2L

V2

+

-

V1

+

-

C1+

C2+

S1 S2

S3 D3 D4 S4

(e)

ILI1

D1 D2L

V2

+

-

V1

+

-

C1+

C2+

S1 S2

S3 D3 D4 S4

(b)

ILI2

D1 D2L

V2

+

-

V1

+

-

C1+

C2+

S1 S2

S3 D3 D4 S4

(f)

ILI2

Figure 2.6 Operating stages of the Forward mode: (a) Buck 1 (b) Buck 2 (c) Boost 1 (d) Boost 2 (e) Buck-Boost 1 (f) Buck-Boost 2


V1

+

D1 D2L

V2

+

--

C1+

C2+

S1 S2

S3 D3 D4 S4

(a)

ILI2I1

D1 D2L

V2

+

--

C1+

C2+

S1 S2

S3 D3 D4 S4

(d)

ILI2I1

D1 D2L

V2

+

-

V1

+

-

C1+

C2+

S1 S2

S3 D3 D4 S4

(c)

ILI2

D1 D2L

V2

+

-

V1

+

-

C1+

C2+

S1 S2

S3 D3 D4 S4

(e)

ILI2

D1 D2L

V2

+

-

V1

+

-

C1+

C2+

S1 S2

S3 D3 D4 S4

(b)

ILI1

D1 D2L

V2

+

-

V1

+

-

C1+

C2+

S1 S2

S3 D3 D4 S4

(f)

ILI1

V1

Figure 2.7 Operating stages of the Reverse mode: (a) Buck 1 (b) Buck 2 (c) Boost 1 (d) Boost 2 (e) Buck-Boost 1 (f) Buck-Boost 2


55

Even the converter presenting the advantages mentioned before, the large

number of switches implemented in its structure (impacting mainly in the converter

efficiency and costs) represents a natural drawback for this topology.

Another issue in the implementation of this converter is the reverse recovery

phenomenon of the antiparallel body-diode of the switches, since they also need to

conduct to ensure the bidirectionality of the converter. It is important to highlight that

this is not only a feature of this topology but also of the most of the bidirectional

converters.

In order to remedy these situations, an increasing number of topologies derived

from the integrated bidirectional Buck/Boost/Buck-Boost converter implementing

active-clamping and different modulation techniques have been tried in the research

field. However, usually these solutions lead to complex converters, losing the main

features of the original converter, such as versatility and simplicity.

2.3.2 Bidirectional Boost/Buck DC-DC converter

Another bidirectional topology that is widely used is the bidirectional Boost/Buck

DC-DC converter. This topology was already presented in Figure 2.2 (b), and it is one

of the traditional converters. In Figure 2.8, this converter is presented again, but in a

different way to facilitate the understanding.

V1

-

+

+C2 V2

-

S1 D1

S2 D2

L

+

+ C1

Figure 2.8 Bidirectional Boost/Buck DC-DC converter


56

Due to its simple arrangement and employing few power elements, this

converter is considered one of the most reliable bidirectional DC-DC converters,

being used in different applications and power levels (MAYER, R. et al, 2015).

In the same way of the converter presented in Figure 2.5, with the current

control of the inductor L, the power flow in the system becomes controllable.

Nevertheless, this converter can only work like a Boost in the Forward mode (V1 to

V2) and like a Buck in the Reverse mode (V2 to V1). In Table 2.2, the switching logic

of the bidirectional Boost/Buck DC-DC converter is presented, where the two

switches S1 and S2 work in a complementary way.

Table 2.2 Bidirectional Boost/Buck DC-DC converter: Switching Logic

Operation Mode S1 S2

Forward Boost PWM OFF

Reverse Buck OFF PWM


In Figure 2.9, the operating stages for each operation mode of the bidirectional

Boost/Buck DC-DC converter are presented.

V1

-

+

+C2 V2

-

S1 D1

S2 D2

L

+

+ C1

(b)

I1IL

I2

V1

-

+

+C2 V2

-

S1 D1

S2 D2

L

+

+ C1

(a)

I1IL

V1

-

+

+C2 V2

-

S1 D1

S2 D2

L

+

+ C1

(d)

I1IL

V1

-

+

+C2 V2

-

S1 D1

S2 D2

L

+

+ C1

(c)

I1IL

I2

Figure 2.9 Operating stages of the bidirectional Boost/Buck DC-DC converter: (a) Forward Boost 1 (b) Forward Boost 2 (c) Reverse Buck 1 (d) Reverse Buck 2


57

Among the advantages of this converter, it can also operate with low ripple

current, which is very good imagining a battery being one of the voltage sources of

the system.

However, the bidirectional Boost/Buck DC-DC converter presents the same

limitations mentioned before related to the antiparallel body diodes and with the

efficiency of the system. Taking this into account, Hyun-Lark Do (2011) proposed a

new version of this converter.

In the converter proposed by Hyun-Lark Do (2011), an additional winding is

added to the main inductor and an auxiliary inductance provides ZVS operation. Also,

with this new configuration, the ripple component of the inductor current is cancelled.

In Figure 2.10, the converter proposed by Hyun-Lark Do (2011) is shown.

S2 D2

S1 D1

V2

-

+

V1

-

+

+

+

Cf2

Cf1

LL

NP NS

Figure 2.10 Bidirectional ZVS Boost/Buck DC-DC converter


All the detailed analyses of the converter presented in Figure 2.10 can be found

in Hyun-Lark Do (2011) and will not be presented in this work.


In a moment where environmental issues and the growing appeal for renewable

systems are in the spotlight, the power electronics and the study of DC-DC

converters have shown to be a key factor, since in the most part of applications of

this field, DC-DC converters are needed to process the energy in the system.

58

Taking this into account, in this chapter, a brief review involving concepts and

applications of DC-DC converters was presented. First, in order to provide a previous

knowledge and consequently a better understanding about bidirectional DC-DC

converters, unidirectional DC-DC converters were addressed and discussed.

Then, bidirectional DC-DC converters were presented. Also, the two topologies

that are reference for the topologies presented in this thesis were presented,

providing fundamental knowledge for the continuation of this work.

59

CHAPTER 3

BIDIRECTIONAL DC-DC CONVERTER WITH TAPPED INDUCTOR:

STEADY STATE ANALYSIS


In this chapter, the first converter presented in this thesis is discussed and

analyzed in details. This topology is an improvement of the topology presented in

Figure 2.5 and was introduced for the first time by Yunmao Ye et al (2013).

This converter can provide three different operating modes in each direction of

the power flow: Buck, Boost or Buck-Boost. Besides, a tapped inductor is proposed

with the goal of remove one of the switches of the original topology and improve the

device utilization adjusting the duty cycle of the converter to a desirable value at a

certain operating point by just using the turn ratio of the tapped inductor.

3.2 BIDIRECTIONAL DC-DC CONVERTER WITH TAPPED INDUCTOR

The bidirectional DC-DC converter with tapped inductor is shown in Figure 3.1.

V1 V2C1 C2

+

-

+

+ +S3

S1 S2

D3

D2D1LT

-

Figure 3.1 Bidirectional DC-DC converter with tapped inductor


The equivalent circuit of the converter considered in the analysis is shown in

Figure 3.2. The tapped inductor LT is modeled as an ideal transformer that has turn

ratio of NP: NS (=n: 1) and a magnetizing inductance LM. It is important to highlight

that, for the steady state analysis, the leakage inductances of the transformer are

disregarded but its effects are considered further in the design of the converter.

60

V1 V2

+ +

S3

S1 S2

D3

D2

+

+

+ + -

+

- -

-

-

- +

LM

VLT1 VLT2

- -

IM

I1 I2D1

: 1nILT1 ILT2

Figure 3.2 Equivalent circuit of the bidirectional DC-DC converter with tapped inductor


For the correct analysis, the equations of the ideal transformer must be

considered. Those equations are given by (3.1) and (3.2).

1

2

LT P

LT S

V Nn

V N (3.1)

1 1 2 2LT LT LT LTV I V I (3.2)

As mentioned before, considering NP / NS= n and replacing (3.2) in (3.1), it is

possible to find the relationship between VLT1 and VLT2.

1 2LT LTV nV (3.3)

Considering that VLM and VLT1 are in parallel and have the same voltage:

1LT LMV V (3.4)

Then, replacing (3.4) in (3.3), VLM can be rewritten as function of VLT2 and n.

2LM

LT

VV

n (3.5)

Finally, replacing (3.3) in (3.2) the relationship between ILT1 and ILT2 is found.

2 1LT LTI nI (3.6)

In the analysis, a switching period TS will be considered.

As the switching period TS is the sum of the time where the controlled switch is

turned-on and turned-off, the switching period TS can be written as the equation (3.7).

61

s on offT t t (3.7)

Considering the duty cycle D of the controlled switch as the relationship

between the time where this switch is turned-on and the switching period TS:

on st DT (3.8)

Then, replacing (3.8) in (3.7), the time where the controlled switch is turned-off

is found and presented by (3.9).

(1 )off St D T (3.9)

3.2.1 Forward Buck

In this operating mode, the switch S1 is controlled and the energy flows from V1

to V2. This mode presents two operating stages.

Figure 3.3 presents the gate signals for the Forward Buck mode.

VgS2

t0 t1 t2

VgS1

t0 t1 t2

TSTS

VgS3

t0 t1 t2

TS

Vg

Figure 3.3 Forward Buck: Gate signals


Stage 1 [t0, t1]: At t0, S1 is turned-on and this stage begins. In this stage, the

current flows through the switch S1 and the diode D2 and the magnetizing current IM

increases linearly from IM1 to IM2. Figure 3.4 shows this stage.

The voltage across the magnetizing inductance LM is defined by the equation

(3.10).

1 2 2 0LM LTV V V V (3.10)

62

+

V1 V2

+

S3

S1 S2

D3

D2

+

+

+ + -

+

- -

-

-

- +

LM

VLT1 VLT2

- -

IM

I1 I2D1

: 1nILT1 ILT2

Figure 3.4 Forward Buck: Fist operating stage


Replacing (3.5) in (3.10), the voltage across the magnetizing inductance VLM

can be found and expressed by (3.11).

1 2

1LM

n V VV

n (3.11)

Replacing (3.11) in (3.4) and (3.5), the voltage in each turn of the tapped

inductor is determined, respectively, by (3.12) and (3.13).

1 2

11

LT

n V VV

n (3.12)

1 2

21

LT

V VV

n (3.13)

Then, the voltage in the switch S3 is determined by the equation (3.14).

3 2 2 0S LTV V V (3.14)

Replacing (3.13) in (3.14), the voltage in the switch S3 is determined and given

by (3.15).

1 2

31

S

V nVV

n (3.15)

Finally, the current I1 and I2 can be expressed, respectively, by equations (3.16)

and (3.17).

1 1LT MI I I (3.16)

63

2 2LTI I (3.17)

For this stage, the relationship between I1 and I2 can be expressed by (3.18).

1 2I I (3.18)

Replacing (3.6) in (3.17) and considering the relationship in (3.18), the current

ILT1 can be rewritten as (3.19).

11LT

II

n (3.19)

Replacing (3.19) in (3.16) and considering the relationship in (3.18), the current

I1 and I2 are determined, respectively, by (3.20) and (3.21).

11

MnII

n (3.20)

21MnI

In

(3.21)

Stage 2 [t1, t2]: At t1, S1 is turned-off and this stage begins. When S1 in turned-

off at t1, the current finds a path through the diodes D3 and D2 and the magnetizing

current IM decreases linearly from IM2 to IM1. Figure 3.5 shows this stage.

V1 V2

+ +

S3

S1 S2

D3

D2

+

+

+ + -

+

- -

-

-

- +

LM

VLT1 VLT2

- -

IM

I1 I2D1

: 1nILT1 ILT2

Figure 3.5 Forward Buck: Second operating stage


For this mode, the voltage VLT2 across the secondary of the tapped inductor is

determined by the equation (3.22).

2 2LTV V (3.22)

64

Replacing (3.22) in (3.3) it is possible to find the voltage VLT1 in the primary of

the tapped inductor. Equation (3.23) expresses that.

1 2LTV nV (3.23)

As mentioned before, VLM and VLT1 are in parallel and have the same voltage,

then:

2LMV nV (3.24)

The voltage across the switch S1 can be expressed by (3.25).

1 1 1 0S LTV V V (3.25)

Replacing (3.23) in (3.25), the voltage in the switch S1 is represented by (3.26).

1 1 2SV V nV (3.26)

In this stage, as the switch S1 is off, there is no current I1:

1 0I (3.27)

Then, replacing (3.27) in (3.16), the current in the primary of tapped inductor is

determined and given by (3.28).

1LT MI I (3.28)

Substituting (3.28) into (3.6) and considering (3.17), the current I2 can be

expressed by (3.29).

2 MI nI (3.29)

Analyzed the two stages, the theoretical waveforms for the Forward Buck mode

can be drawn. Figure 3.6 presents the voltage in the switches.

65

VS3

t0 t1 t2

VS1

t0 t1 t2

V1+nV2V1+nV2

n+1

TS TS

Figure 3.6 Forward Buck: Theoretical voltage waveforms in the switches S1 and S3


Figure 3.7 presents the voltage in the tapped inductor.

VLT2VLT1

n(V1-V2)n+1

(V1-V2)n+1

t0 t1 t2t0 t1 t2

-nV2 -V2

TSTS

Figure 3.7 Forward Buck: Theoretical voltage waveforms in the tapped inductor


Figure 3.8 presents the theoretical waveforms of the voltage VLM and the

magnetizing current IM in the magnetizing inductance LM.

IM

t0 t1 t2

TS

VLM

n(V1-V2)n+1

t0 t1 t2

-nV2

TS

IM2

IM1

Figure 3.8 Forward Buck: Theoretical waveforms in the magnetizing inductance


Then, figure 3.9 shows the waveforms of the current I1 and the current I2.

66

I1

t0 t1 t2

TS

nIM1

n+1

nIM2

n+1

I2

t0 t1 t2

TS

-nIM2

n+1

-nIM1

n+1

-nIM1

-nIM2

Figure 3.9 Forward Buck: Theoretical waveforms of the currents I1 and I2


Finally, as the current in each switch depends on the currents I1 and I2, the

waveforms of that can be drawn and represented by figure 3.10

IS1

t0 t1 t2

TS

nIM1

n+1

nIM2

n+1

IS2

t0 t1 t2

TS

-nIM2

n+1

-nIM1

n+1

-nIM1

-nIM2

IS3

t0 t1 t2

TS

-nIM1

-nIM2

Figure 3.10 Forward Buck: Theoretical current waveforms in the switches


Determined all those parameters and making the Volt-second balance in the

magnetizing inductance LM, it is possible to find the voltage conversion characteristic

in the Forward Buck mode. Equation (3.30) presents that.

_ _LM ton on Controlled Switch LM toff off Controlled Switch LM AVGV t V t V (3.30)

Replacing (3.8), (3.9), (3.11) and (3.24) in (3.30), and considering <VLM>AVG=0,

the voltage conversion characteristic for the Forward Buck mode is found and

presented by (3.32).

1 2

1 2 11 01

S S

n V VDT nV D T

n (3.31)

2 1

1 11

V D

V n nD (3.32)

67

Figure 3.11 presents the voltage conversion characteristic for different values of

n in the Forward Buck mode.

Figure 3.11 Forward Buck: Voltage conversion characteristic


To find the instantaneous values of the magnetizing current IM2 and IM1, first the

average values of the currents I1 and I2 must be calculated. That can be done

calculating the area of the waveforms of I1 and I2. Equations (3.33) and (3.34)

present that.

2 11_ 1

1

1 2M M

AVG S

S

I InI DT

T n (3.33)

2 1 2 12 _ 1 1

11

2 1 2M M M M

AVG S S

S

I I I InI DT n D T

T n (3.34)

Making the correct mathematical manipulations, equation (3.33) and (3.34) can

be rewritten as (3.35) and (3.36), respectively.

2 11_ 1

1 2M M

AVG

I InI D

n (3.35)

2 2

2 1 12 _

2 1M M

AVG

I I n D n nI

n (3.36)

68

Considering equation (3.37) and analyzing the magnetizing inductance in the

first stage, it is possible to find the first relationship between IM1 and IM2. This

relationship is presented by (3.38).

MLM M

IV L

t (3.37)

1 2 1

2 11

M M

S M

n V V DI I

f L n (3.38)

Considering the ideal converter, the power processed PC by the converter must

be the same in the voltage source V1 and V2. This can be expressed by the equation

(3.39).

1 2C V VP P P (3.39)

Then, the power PV1 in the source V1 can be represented by (3.40).

1 1 1_V AVGP VI (3.40)

Replacing (3.35) and (3.39) in (3.40), and making the correct mathematical

manipulations, the second relationship between IM1 and IM2 can be found. This

relation is presented by (3.41).

2 1

1 1

2 1C

M M

P nI I

V D n (3.41)

Now, summing equations (3.38) and (3.41) the value of the magnetizing current

IM2 is found and given by equation (3.42).

2 2 2

1 1 1 2

2

1 1

2 1

2 1

C S M

M

S M

P f L n V D n V VI

V D f L n n (3.42)

Then, replacing (3.42) in (3.41), IM1 can be found and determined by (3.43).

2 2 2

1 1 1 2

1

1 1

2 1

2 1

C S M

M

S M

P f L n V D n V VI

V D f L n n (3.43)

69

Specified the values of IM1 and IM2, the RMS value of the current in the

semiconductors can be calculated. Equation (3.44) represents the RMS current for

the switch S1.

2

1_ 1

0

1( )

ST

S RMS S

S

I I t dtT

(3.44)

Considering the function of IS1(t) given by (3.45).

2 11 1

1 1

1

, 0( ) 1 1

0,

M MM S

S S

S S

I In nt I t DT

I t n D T n

DT t T

(3.45)

Then, replacing (3.45) in (3.44), equation (3.44) can be rewritten as (3.46).

1

1

2

22 11_ 1

10

10

1 1

S S

S

D T T

M MS RMS M

S S D T

I In nI t I dt dt

T n DT n (3.46)

Replacing (3.42) and (3.43) in (3.46) and solving the equation, IS1_RMS is found

and given by (3.47).

24 2 4

1 1 1 2

1_ 2 42 2 211

1 1

32 1 12 1S RMS

M s M C S

D V n V VI

DV L f n L P f n (3.47)

The same procedure can be applied to switches S2 and S3. Equation (3.48)

expresses the RMS current for the switch S2.

2

2 _ 2

0

1( )

ST

S RMS S

S

I I t dtT

(3.48)


2 11 1

1

2

2 1 1 1 2 1

1 1

, 01 1

( )

,1 1

M MM S

S

S

M M M M S S

S

I In nt I t DT

n DT nI t

n nI I t D I I DT t T

D T D

(3.49)

70


1

1

2

2 11

10

2

2 _ 2 1

1

1 1 2

1

1 1

1

1

1

S

S

S

D T

M MM

S

S RMS M MTS S

D T

M M

I In nt I dt

n DT n

nI I I tT D T

dtn

D I ID

(3.50)

Substituting (3.42) and (3.43) into (3.50), and solving the equation, IS2_RMS is

found and given by (3.51).

2 22 4 4

1 1 1 2 1

62 2 2 6 5 4 3 2

1

2 _ 2

1 1

3 1 2

36 1 6 14 16 9 2

6 1

M C S

S RMS

M S

V D n V V n D n n

L P f n D n n n n n nI

V D L f n (3.51)

Finally, equation (3.52) expresses the RMS current in the switch S3

2

3 _ 3

0

1( )

ST

S RMS S

S

I I t dtT

(3.52)


1

3

2 1 1 1 2 1

1 1

0, 0

( ),

1 1

S

S

M M M M S S

S

t DT

I t n nI I t D I I DT t T

D T D

(3.53)

This way, replacing (3.53) in (3.52), equation (3.52) can be rewritten as (3.54).

1

1

2

2 12

1

3 _

0

1 1 2

1

110

1

S S

S

M MD T TS

S RMS

S D T

M M

nI I t

D TI dt dt

T nD I I

D

(3.54)

71

Then, replacing (3.42) and (3.43) in (3.54), and solving the equation, IS3_RMS is


24 2 4

1 1 1 21

3 _ 42 2 21 1

11

2 1 3 12 1S RMS

M sM C S

D V n V VDI

DV L f n L P f n (3.55)

3.2.2 Forward Boost

In this operating mode the switch S3 is controlled whereas the switch S1 is

always turned-on. The energy flows from V1 to V2 and this mode presents two

operating stages.

Figure 3.12 presents the gate signals for the Forward Boost mode.

VgS2

t0 t1 t2

VgS1

t0 t1 t2

TSTS

VgS3

t0 t1 t2

TS

VgVg

Figure 3.12 Forward Boost: Gate signals


Stage 1 [t0, t1]: At t0, S1 is already on and S3 is turned-on. In this moment this

stage begins. In this stage, the current flows through the switch S1 and the switch S3

and the magnetizing current IM increases linearly from IM1 to IM2. Figure 3.13 shows

this stage.

V1 V2

+ +

S3

S1 S2

D3

D2

+

+

+ + -

+

- -

-

-

- +

LM

VLT1 VLT2

- -

IM

I1 I2D1

: 1nILT1 ILT2

Figure 3.13 Forward Boost: First operating stage


72

For this mode, the voltage across the magnetizing inductance LM is defined by

the equation (3.56).

1LMV V (3.56)

Replacing (3.56) in (3.4) and (3.5), the voltage in each turn of the tapped

inductor can be determined.

1 1LTV V (3.57)

12LT

VV

n (3.58)

Then, the voltage in the switch S2 is determined by (3.59).

2 2 2 0S LTV V V (3.59)

Replacing (3.58) in (3.59), the voltage in the switch S2 is given by (3.60).

1 22S

V nVV

n (3.60)

In this stage, as the switch S2 is turned-off, there is no current I2. This can be


2 0I (3.61)

Replacing (3.61) in (3.17), the current in the secondary of the tapped inductor is

found.

2 0LTI (3.62)

Then, replacing (3.62) in (3.6), the current in the primary of the tapped inductor

is determined and expressed by (3.63).

1 0LTI (3.63)

Finally, replacing (3.63) in (3.16), the current I1 is found and given by (3.64).

1 MI I (3.64)

73

Stage 2 [t1, t2]: At t1, S1 remains on and S3 is turned-off. At this moment this

stage begins. When S3 in turned-off at t1, the current continues to flow through the

switch S1 and finds a path through the diode D2. The magnetizing current IM

decreases linearly from IM2 to IM1. Figure 3.14 shows this stage.

V1 V2

+ +

S3

S1 S2

D3

D2

+

+

+ + -

+

- -

-

-

- +

LM

VLT1 VLT2

- -

IM

I1 I2D1

: 1nILT1 ILT2

Figure 3.14 Forward Boost: Second operating stage


The equivalent circuit of the second stage in the Forward Boost is the same that

the first stage in the Forward Buck. This way, the mathematical analyses are the

same and will not be presented again.

Figure 3.15 presents the voltage in the switches and the figure 3.16 presents

the voltage in the primary and secondary of the tapped inductor for the Forward

Boost mode.

VS3

t0 t1 t2

V1+nV2

n+1

VS2

t0 t1 t2

V1+nV2

n

TSTS

Figure 3.15 Forward Boost: Theoretical voltage waveforms in the switches S2 and S3


VLT2VLT1

n(V1-V2)n+1

(V1-V2)n+1

t0 t1 t2

V1 nV1

t0 t1 t2

TSTS

Figure 3.16 Forward Boost: Theoretical voltage waveforms in the tapped inductor


74

Figure 3.17 presents the theoretical waveforms of the voltage VLM and the

magnetizing current IM in the magnetizing inductance LM.

t0 t1 t2

TS

IM

t0 t1 t2

TS

VLM

IM2

IM1

n(V1-V2)n+1

V1

Figure 3.17 Forward Boost: Theoretical waveforms in the magnetizing inductance


Figure 3.18 shows the waveforms of the currents I1 and I2.

I1

t0 t1 t2

TS

nIM1

n+1

nIM2

n+1

I2

t0 t1 t2

TS

-nIM2

n+1

-nIM1

n+1

IM2

IM1

Figure 3.18 Forward Boost: Theoretical waveforms of the currents I1 and I2


Figure 3.19 presents the current in the switches for the Forward Boost mode.

IS1

t0 t1 t2

TS

nIM1

n+1

nIM2

n+1

IS2

t0 t1 t2

TS

-nIM2

n+1

-nIM1

n+1

IM2

IM1

IS3

t0 t1 t2

TS

IM2

IM1

Figure 3.19 Forward Boost: Theoretical current waveforms in the switches


75

Determined all those parameters and making the Volt-second balance in the

magnetizing inductance LM, it is possible to find the voltage conversion characteristic

for the Forward Boost mode.

Then, replacing (3.8), (3.9), (3.11) and (3.56) in (3.30) and considering

<VLM>AVG= 0, the voltage conversion characteristic is found and presented by (3.66).

1 2

1 3 31 01

S S

n V VV D T D T

n (3.65)

32

1 31

n DV

V n D (3.66)

Figure 3.20 presents the voltage conversion characteristic for different values of

n in the Forward Boost mode.

Figure 3.20 Forward Boost: Voltage conversion characteristic


To find the instantaneous values of the magnetizing current IM1 and IM2, the

same procedure described in the Forward Buck will be applied. First, the average

values of the currents I1 and I2 are defined, respectively, by (3.67) and (3.68).

32 11_

2 1M M

AVG

n DI II

n (3.67)

76

2 12 _ 31

2 1M M

AVG

I I nI D

n (3.68)

Then, analyzing the magnetizing inductance LM, the first relationship between

IM1 and IM2 is found and represented by (3.69).

1 32 1M M

S M

V DI I

f L (3.69)

Making the power balance in the voltage source V1, the second relationship

between IM1 and IM2 is found and presented by (3.70).

2 1

1 3

2 1C

M M

P nI I

V n D (3.70)

Summing equations (3.69) and (3.70), the instantaneous value of the

magnetizing current IM2 can be defined by (3.71).

2

1 3 3

2

1 3

2 1

2

C S M

M

S M

P f L n V D n DI

V f L n D (3.71)

Then, replacing (3.71) in (3.70), the instantaneous value of the magnetizing

current IM1 can be represented by (3.72).

2

1 3 3

1

1 3

2 1

2

C S M

M

S M

P f L n V D n DI

V f L n D (3.72)

Defined the values of IM1 and IM2, the RMS current in the semiconductors can be

calculated.


2 11 3

3

1

2 1 32 13

3 3

, 0

( )

,1 1 1 1

M MM S

S

S

M MM MS S

S

I It I t D T

D TI t

I I DI In nt D T t T

n D T n D

(3.73)

Replacing (3.73) in (3.44), equation (3.44) can be rewritten as (3.74).

77

3

3

2

2 11

30

1_ 2

2 1 32 1

3 3

1

1 1 1 1

S

S

S

D T

M MM

S

S RMST

SM MM M

SD T

I It I dt

D TI

TI I DI In n

t dtn D T n D

(3.74)

Replacing (3.71) and (3.72) in (3.74), and solving the equation, IS1_RMS is found

and given by (3.75).

4 2 3 2 2 3 4 3 2 2

1 3 3 3 3 3

2 2 2 3 4 2 3 2

3 3 3 3

1_

1 3

3 2 5 4 2

36 2 5 2 4

6 1

M C S

S RMS

M S

V D D n D n D n n D D n Dn

L P f D n n D n n D n n DI

V L f D n n (3.75)

Now, considering the function of IS2(t) given by (3.76):

3

2 2 1 32 13

3 3

0, 0

( ),

1 1 1 1

S

S M MM MS S

S

t D T

I t I I DI In nt D T t T

n D T n D

(3.76)


3

3

2

2 12

3

2 _

0 2 1 3

3

1 110

1 1

S S

S

M M

D T TS

S RMS

S D T M M

I Int

n D TI dt dt

T I I Dn

n D

(3.77)



22 4

3 1 3

2 _ 3 22 2 21 3

3 16 1 12 1

S RMS

M sM C S

D V n DnI D

V L f n n D L P f n (3.78)

Finally, considering the function of IS3(t) given by (3.79):

78

2 11 3

3 3

3

, 0( )

0,

M MM S

S S

S S

I It I t D T

I t D T

D T t T

(3.79)


3

3

2

22 13 _ 1

30

10

S S

S

D T T

M MS RMS M

S S D T

I II t I dt dt

T D T (3.80)

This way, substituting (3.71) and (3.72) into (3.80) and solving the equation,

IS3_RMS is found and given by (3.81).

23 4

3 1 3

3 _ 22 2 21 3

3

13

6 12 1S RMS

M sM C S

D V n DI

V L f n D D L P f n (3.81)

3.2.3 Forward Buck-Boost



operating stages.

Figure 3.21 presents the gate signals for the forward Buck-Boost mode.

TSTS TS

Vg

VgS2

t0 t1 t2

VgS1

t0 t1 t2

VgS3

t0 t1 t2

Vg

Figure 3.21 Forward Buck-Boost: Gate signals




and the magnetizing current IM increases linearly from IM1 to IM2. Figure 3.22 shows

this stage.

79

V1 V2

+ +

S3

S1 S2

D3

D2

+

+

+ + -

+

- -

-

-

- +

LM

VLT1 VLT2

- -

IM

I1 I2D1

: 1nILT1 ILT2

Figure 3.22 Forward Buck-Boost: First operating stage


The equivalent circuit of the first stage in the Forward Buck-Boost is the same

that the first stage in the Forward Boost. Then, the mathematical analyses are the

same and will not be presented again.

Stage 2 [t1, t2]: At t1, S3 remains on and S1 is turned off. At this moment, this

stage begins. The current continues to flow through the switch S3 and finds a path

through the diode D2. For this stage, the magnetizing current decreases linearly from

IM2 to IM1. Figure 3.23 shows this stage.

V1 V2

+ +

S3

S1 S2

D3

D2

+

+

+ + -

+

- -

-

-

- +

LM

VLT1 VLT2

- -

IM

I1 I2D1

: 1nILT1 ILT2

Figure 3.23 Forward Buck-Boost: Second operating stage


The equivalent circuit of the second stage in the Forward Buck-Boost is the

same that the second stage in the Forward Buck. Then, the mathematical analyses

are the same and will not be presented again.

Figure 3.24 presents the voltage in the switches and the figure 3.25 presents

the voltage in the primary and secondary of the tapped inductor for the Forward

Buck-Boost mode.

80

VS1

t0 t1 t2

V1+nV2

TS

VS2

t0 t1 t2

V1+nV2

n

TS

Figure 3.24 Forward Buck-Boost: Theoretical voltage waveforms in the switches S1 and S2


VLT2VLT1

V1

t0 t1 t2t0 t1 t2

V1

TSTS

-nV2 -V2

n

Figure 3.25 Forward Buck-Boost: Theoretical voltage waveforms in the tapped inductor


Figure 3.26 shows the theoretical waveforms of the voltage VLM in the

magnetizing inductance LM and the magnetizing current IM.

t0 t1 t2

TS

IM

t0 t1 t2

TS

VLM

IM2

IM1V1

-nV2

Figure 3.26 Forward Buck-Boost: Theoretical waveforms in the magnetizing inductance


In Figure 3.27, the waveforms of the current I1 and the current I2 are presented.

81

I1

t0 t1 t2

TS

I2

t0 t1 t2

TS

-nIM2

-nIM1

IM2

IM1

Figure 3.27 Forward Buck-Boost: Theoretical waveforms of the currents I1 and I2


Finally, the currents in the switches are determined by Figure 3.28.

IS1

t0 t1 t2

TS

IS2

t0 t1 t2

TS

-nIM2

-nIM1

IM2

IM1

IS3

t0 t1 t2

TS

-nIM1

-nIM2

IM2

IM1

Figure 3.28 Forward Buck-Boost: Theoretical current waveforms in the switches


With the Volt-second balance in the magnetizing inductance LM, it is possible to

find the voltage conversion characteristic in the Forward Buck-Boost mode.

Replacing (3.8), (3.9), (3.24) and (3.56) in (3.30) and considering <VLM>AVG =0,

the voltage conversion characteristic for the Forward Buck-Boost is found and

presented by (3.83).

1 1 2 11 0S SV DT nV D T (3.82)

2 1

1 11

V D

V n D (3.83)

Figure 3.29 presents the voltage conversion characteristic for the forward Buck-

Boost mode.

82

Figure 3.29 Forward Buck-Boost: Voltage conversion characteristic


Following, the average values of the current I1 and I2 are expressed,

respectively, by (3.84) and (3.85).

2 1 1

1_2

M M

AVG

I I DI (3.84)

2 12 _ 11

2 1M M

AVG

I I nI D

n (3.85)

Then, analyzing the magnetizing inductance in the first stage, it is possible to

find the first relationship between IM1 and IM2. This relationship is expressed by (3.86).

1 12 1M M

S M

V DI I

f L (3.86)



2 1

1 1

2 CM M

PI I

V D (3.87)

Summing (3.86) and (3.87), the instantaneous value of the magnetizing current

IM2 is found and expressed by (3.88).

83

2 2

1 12

1 1

2

2C S M

M

S M

P f L V DI

V D f L (3.88)

Replacing (3.88) in (3.87), the instantaneous value of the magnetizing current

IM1 is determined by (3.89).

2 2

1 11

1 1

2

2C S M

M

S M

P f L V DI

V D f L (3.89)


calculated.

Considering the function of IS1(t) given by (3.90):

2 11 1

1 1

1

, 0( )

0,

M MM S

S S

S S

I It I t DT

I t DT

DT t T

(3.90)


1

1

2

22 11_ 1

10

10

S S

S

D T T

M MS RMS M

S S D T

I II t I dt dt

T DT (3.91)


found and determined by (3.92).

4 4 2 2 2

1 11_

1 1

1213

6M C S

S RMS

M s

D V L P fI

V L f D (3.92)

Then, considering the function of IS2(t) given by (3.93).

1

2 2 1 12 11

1 1

0, 0

( ),

1 1

S

S M MM MS S

S

t DT

I t I I DI In t n DT t T

D T D

(3.93)


84

1

1

2

2 2 1 12 12 _

1 10

10

1 1

S S

S

D T T

M MM MS RMS

S SD T

I I DI II dt n t n dt

T D T D (3.94)



4 4 2 2 212 _ 1 1

1 1

112

2 3S RMS M C S

M s

DnI D V L P f

V D L f (3.95)`


2 11 1

1

3

2 1 12 11

1 1

, 0

( )

,1 1

M MM S

S

S

M MM MS S

S

I It I t DT

DTI t

I I DI In t n DT t T

D T D

(3.96)

Replacing (3.96) in (3.52), equation (3.52) can be rewritten as(3.97).

1

1

2

2 11

10

3 _ 2

2 1 12 1

1 1

1

1 1

S

S

S

D T

M MM

S

S RMST

SM MM M

SD T

I It I dt

DTI

T I I DI In t n dt

D T D

(3.97)



2 2 4 4 2 2 2

3 _ 1 1 1 1

1 1

13 12

6S RMS M C S

M s

I n D D n D V L P fV D L f

(3.98)

3.2.4 Reverse Buck

In this operating mode the switch S2 is controlled. Then, the energy flows from

V2 to V1 and this mode presents two operating stages.

Figure 3.30 presents the gate signals for the Reverse Buck mode.

85

VgS2

t0 t1 t2

VgS1

t0 t1 t2

TSTS

VgS3

t0 t1 t2

TS

Vg

Figure 3.30 Reverse Buck: Gate signals


Stage 1 [t0, t1]: At t0, S2 is turned-on and this stage begins. In this stage, the

current flows through the switch S2 and the diode D1 and the magnetizing current IM

decreases linearly from –IM1 to –IM2. Figure 3.31 shows this stage.

V1 V2

+ +

S3

S1 S2

D3

D2

+

+

+ + -

+

- -

-

-

- +

LM

VLT1 VLT2

- -

IM

I1 I2D1

: 1nILT1 ILT2

Figure 3.31 Reverse Buck: First operating stage


For the mathematical analyses, it is indifferent if the current is flowing through

the switch or through its respective antiparallel body-diode, the equivalent circuit is

the same. This way, the equivalent circuit of the first stage in the Forward Buck mode

is the same that in the first stage of the Reverse Buck mode, therefore the

mathematical analyses will not be presented again.

Stage 2 [t1, t2]: At t1, S2 is turned-off and this stage begins. When S2 in turned-

off at t1, the current finds a path through the diodes D3 and D1 and the magnetizing

current IM increases linearly from –IM2 to - IM1. Figure 3.32 shows this stage.

The equivalent circuit of the second stage in the Reverse Buck mode is the

same that in the first stage of the Forward Boost mode, therefore the mathematical

analyses will not be presented again.

86

V1 V2

+ +

S3

S1 S2

D3

D2

+

+

+ + -

+

- -

-

-

- +

LM

VLT1 VLT2

- -

IM

I1 I2D1

: 1nILT1 ILT2

Figure 3.32 Reverse Buck: Second operating stage


Figure 3.33 presents the voltage in the switches and Figure 3.34 presents the

voltage in the primary and secondary of the tapped inductor for the Reverse Buck

mode.

VS3

t0 t1 t2

V1+nV2

n+1

VS2

t0 t1 t2

V1+nV2

n

TSTS

Figure 3.33 Reverse Buck: Theoretical voltage waveforms in the switches S2 and S3


VLT2VLT1

n(V1-V2)n+1

(V1-V2)n+1

t0 t1 t2t0 t1 t2

V1 nV1

TSTS

Figure 3.34 Reverse Buck: Theoretical voltage waveforms in the tapped inductor



magnetizing inductance LM and the magnetizing current IM for the Reverse Buck

mode.

87

VLM

n(V1-V2)n+1

t0 t1 t2

V1

TS

IM

t0 t1 t2

-IM2

-IM1

TS

Figure 3.35 Reverse Buck: Theoretical waveforms in the magnetizing inductance


In Figure 3.36 are represented the waveforms of the current I1 and the current I2

for the Reverse Buck mode.

I1

t0 t1 t2

TS

-nIM2

n+1

-nIM1

n+1

-IM1

-IM2

I2

t0 t1 t2

TS

nIM1

n+1

nIM2

n+1

Figure 3.36 Reverse Buck: Theoretical waveforms of the currents I1 and I2


The currents in the switches for the Reverse Buck mode are determined by the

Figure 3.37.

TS

IS2

t0 t1 t2

nIM1

n+1

nIM2

n+1

TS

IS1

t0 t1 t2

-nIM2

n+1

-nIM1

n+1

-IM1

-IM2

IS3

TS

t0 t1 t2

-IM1

-IM2

Figure 3.37 Reverse Buck: Theoretical current waveforms in the switches


88

Making the Volt-second balance in the magnetizing inductance LM, it is possible

to find the voltage conversion characteristic in the Reverse Buck mode.

Replacing (3.8), (3.9), (3.11) and (3.56) in (3.30) and considering <VLM>AVG=0,

the voltage conversion characteristic is found and presented by (3.100).

1 2

2 1 21 01

S S

n V VD T V D T

n (3.99)

1 2

2 21

V nD

V n D (3.100)

Figure 3.38 presents the voltage conversion characteristic for the Reverse Buck

mode.

Figure 3.38 Reverse Buck: Voltage conversion characteristic


To find the instantaneous values of the magnetizing current IM1 and IM2, the

same procedure described in the Forward mode will be applied. First, the average

values of the currents I1 and I2 are defined, respectively, by (3.101) and (3.102).

2 2 11_

1

1 2M M

AVG

D n I II

n (3.101)

2 12 _ 2

1 2M M

AVG

I InI D

n (3.102)

89

Analyzing the magnetizing inductance in the first stage, it is possible to find the

first relationship between IM1 and IM2. This relationship is expressed by (3.103).

2 1 2

1 21

M M

S M

D n V VI I

f L n (3.103)

To guarantee the correct power balance in the converter, for the Reverse mode

the power PV1 in the voltage source V1 will be considered negative. This can be


1V CP P (3.104)

This way, making the power balance in the voltage source V1, the second

relationship between IM1 and IM2 is found and presented by (3.105).

1 2

1 2

2 1

1

C

M M

P nI I

V n D (3.105)

Summing (3.103) and (3.105), the instantaneous value of the magnetizing

current IM1 is found and expressed by (3.106).

2

1 2 1 2 2

1

1 2

2 1 1

2 1 1

C S M

M

S M

P n f L nV D V V n DI

V f L n D n (3.106)


current IM2 is determined by (3.107).

2

1 2 1 2 2

2

1 2

2 1 1

2 1 1

C S M

M

S M

P n f L nV D V V n DI

V f L n D n (3.107)


calculated.


2 11 2

2

1

1 2 22 12

2 2

, 01 1

( )

,1 1

M MM S

S

S

M MM MS S

S

I I n nt I t D T

D T n nI t

I D II It D T t T

D T D

(3.108)

90


2

2

2

2 11

20

1_ 2

1 2 22 1

2 2

1 11

1 1

S

S

S

D T

M MM

S

S RMST

SM MM M

SD T

I I n nt I dt

D T n nI

T I D II It dt

D T D

(3.109)


found and expressed by (3.110).

2

2 2

2 2 2 2 2 3 2 2

1 2 1 2 2 2 2

3 4 3 2 2 3

2 2 2

5 4 362 2 2

2 2

2

2

1_ 2

1

1 4 3 6 10

3 3 4 11 8

4 5 2

2 9 1636 1

14 6 1

1

6 1

M C S

S RMS

S M

n D n D n

V V V n D D n D n D n

D n D n D n D n

n n nL P f n D

n n

D nI

V f L n (3.110)

For the switch S2 the function of IS2(t) given by (3.111) must be considered.

2 11 2

2 2

2

, 0( ) 1 1

0,

M MM S

S S

S S

I I n nt I t D T

I t D T n n

D T t T

(3.111)


2

2

2

22 12 _ 1

20

10

1 1

S S

S

D T T

M MS RMS M

S S D T

I I n nI t I dt dt

T D T n n (3.112)

Then, substituting (3.106) and (3.107) into (3.112) and solving the equation,

IS2_RMS is found and expressed by (3.113).

22 2 2

2 1 1 2

2 42 2 22 _ 2

1 2

2

12 132 11

S RMSM C S

M s

n D V V V

DnI L P f n

V L f nD n

(3.113)

91


2

3 1 2 22 12

2 2

0, 0

( ),

1 1

S

S M MM MS S

S

t D T

I t I D II It D T t T

D T D

(3.114)

And replacing (3.114) in (3.52), equation (3.52) can be rewritten as (3.115).

2

2

2

2 1 2 22 13 _

2 20

10

1 1

S S

S

D T T

M MM MS RMS

S SD T

I D II II dt t dt

T D T D (3.115)

Then, replacing (3.106) and (3.107) in (3.115), and solving the equation, IS3_RMS

is found and expressed by (3.116).

22 2 2

2 1 1 2

2 42 2 23 _

12

2

1112 12 1 3

1

S RMSM C S

M s

n D V V V

DI L P f nV L f n

D n

(3.116)

3.2.5 Reverse Boost



operating stages.

Figure 3.39 presents de gate signals for the reverse boost mode.

VgS2

t0 t1 t2

VgS1

t0 t1 t2

TSTS

VgS3

t0 t1 t2

TS

VgVg

Figure 3.39 Reverse Boost: Gate signals


92



and the magnetizing current IM decreases linearly from –IM1 to –IM2. Figure 3.40

shows this stage.

V1 V2

+ +

S3

S1 S2

D3

D2

+

+

+ + -

+

- -

-

-

- +

LM

VLT1 VLT2

- -

IM

I1 I2D1

: 1nILT1 ILT2

Figure 3.40 Reverse Boost: First operating stage


The equivalent circuit of the first stage in the Reverse Boost mode is the same

that in the second stage of the Forward Buck mode. Then, the mathematical


Stage 2 [t1, t2]: At t1, S2 remains on and S3 is turned-off. At this moment this

stage begins. When S3 in turned-off at t1, the current continues to flow through the

switch S2 and finds a path through the diode D1. In this stage, the magnetizing

current IM increases linearly from –IM2 to –IM1. Figure 3.41 shows this stage.

V1 V2

+ +

S3

S1 S2

D3

D2

+

+

+ + -

+

- -

-

-

- +

LM

VLT1 VLT2

- -

IM

I1 I2D1

: 1nILT1 ILT2

Figure 3.41 Reverse Boost: Second operating stage


The equivalent circuit of the second stage in the Reverse Boost mode is the

same that in the first stage of the Forward Buck mode. Then, the mathematical


93

Figure 3.42 presents the voltage in the switches and Figure 3.43 presents the

voltage in the primary and secondary of the tapped inductor for the Reverse Boost

mode.

VS1

t0 t1 t2

VS3

t0 t1 t2

TS TS

V1+nV2

n+1V1+nV2

Figure 3.42 Reverse Boost: Theoretical voltage waveforms in the switches S1 and S3


VLT2VLT1

t0 t1 t2t0 t1 t2

TSTS

(V1-V2)n+1

-nV2 -V2

n(V1-V2)n+1

Figure 3.43 Reverse Boost: Theoretical voltage waveforms in the tapped inductor



magnetizing inductance LM and the magnetizing current IM for the Reverse Boost

mode.

VLM

t0 t1 t2

TS

IM

t0 t1 t2

-IM2

-IM1

TS

-nV2

n(V1-V2)n+1

Figure 3.44 Reverse Boost: Theoretical waveforms in the magnetizing inductance


94

In Figure 3.45 the waveforms of the current I1 and the current I2 for the Reverse

Boost mode are represented.

I1

t0 t1 t2

TS

-nIM2

n+1

-nIM1

n+1

I2

t0 t1 t2

TS

nIM1

nIM2

nIM1

n+1

nIM2

n+1

Figure 3.45 Reverse Boost: Theoretical waveforms of the currents I1 and I2


The currents in the switches for the Reverse Boost mode are determined by

Figure 3.46.

IS1

t0 t1 t2

TS

-nIM2

n+1

-nIM1

n+1

IS2

t0 t1 t2

TS

nIM1

nIM2

nIM1

n+1

nIM2

n+1

TS

t0 t1 t2

IS3

nIM1

nIM2

Figure 3.46 Reverse Boost: Theoretical current waveforms in the switches



to find the voltage conversion characteristic in the Reverse Boost mode.

This way, replacing (3.8), (3.9), (3.11) and (3.24) in (3.30) and considering

<VLM>AVG=0, the voltage conversion characteristic for the Reverse Boost Mode is

found and presented by (3.118).

1 2

2 3 31 01

S S

n V VnV D T D T

n (3.117)

31

2 3

1

1

nDV

V D (3.118)

95

Figure 3.47 presents the voltage conversion characteristic for the reverse Boost

mode.

Figure 3.47 Reverse Boost: Voltage conversion characteristic


Following, the average values of the current I1 and I2 are defined, respectively,

by (3.119) and (3.120).

2 11_ 31

1 2M M

AVG

I InI D

n (3.119)

2

3 2 12 _

1 2M M

AVG

D n n I II

n (3.120)

Then, analyzing the magnetizing inductance in the first stage is possible to find

the first relationship between IM1 and IM2. This relationship is expressed by (3.121).

2 31 2M M

S M

nV DI I

f L (3.121)



2 1

1 3

2 1

1

C

M M

P nI I

nV D (3.122)

96

Summing (3.121) and (3.122), the instantaneous value of the magnetizing

current IM1 is found and expressed by (3.123).

2

1 2 3 3

1

1 3

2 1 1

2 1

C S M

M

S M

P n f L n VV D DI

V f L D n (3.123)


current IM2 is determined by(3.107)

2

1 2 3 3

2

1 3

2 1 1

2 1

C S M

M

S M

P n f L n VV D DI

V f L D n (3.124)


calculated.


3

1 3 1 22 13

3 3

0, 0

( ),

1 1 1 1

S

S M MM MS S

S

t D T

I t D I II I n nt D T t T

D T n D n

(3.125)


3

3

2

2 1

2 3

1_

0 3 1 2

3

1 110

1 1

S S

S

M M

D T TS

S RMS

S D T M M

I I nt

D T nI dt dt

T D I I n

D n

(3.126)

Then, substituting (3.123) and (3.124) into (3.126), and solving the equation,


24 2 2 2

3 1 2 3

1_ 22 2 21 3

11 3

6 1 1 12 1S RMS

M sM C S

n D V V DI

V L f n D L P f n (3.127)

For the switch S2, function of IS2(t) given by (3.128) must be considered.

97

2 1

1 3

3

2

3 1 22 13

3 3

, 0

( )

,1 1 1 1

M M

M S

S

S

M MM MS S

S

n I It nI t D T

D TI t

D I II I n nt D T t T

D T n D n

(3.128)

Now, replacing (3.128) in (3.48), equation (3.48) can be rewritten as (3.129).

3

3

2

2 1

1

30

2 _ 2

3 1 22 1

3 3

1

1 1 1 1

S

S

S

D T

M M

M

S

S RMST

SM MM M

SD T

n I It nI dt

D TI

TD I II I n n

t dtD T n D n

(3.129)

This way, substituting (3.123) and (3.124) into (3.129), and solving the equation,


22 2 2 4 2

3 1 2 3 3 3

22 2 2 3 2

3

2

3

2 _

1

3 1 1 2

36 1 4 5 2

1

6 1

M C S

S RMS

M S

D V V n D D n D n

L P f n D n n n n

DI

V L f n (3.130)


2 1

1 3

3 3

3

, 0( )

0,

M M

M S

S S

S S

n I It nI t D T

I t D T

D T t T

(3.131)


3

3

2

22 1

3 _ 1

30

10

S S

S

D T T

M M

S RMS M

S S D T

n I II t nI dt dt

T D T (3.132)

Then, replacing (3.123) and (3.124) in (3.132), and solving the equation, IS3_RMS

is found and expressed by (3.133).

98

24 2 2 2

3 1 2 33

3 _ 2 22 2 21 3

131

6 1 12 1S RMS

M sM C S

n D V V DD

IV L f D L P f n

(3.133)

3.2.6 Reverse Buck-Boost

In this operating mode, the switch S2 is controlled whereas the switch S3 is


operating stages.

Figure 3.48 presents the gate signal for the Reverse Buck-Boost mode.

TSTS TS

Vg

VgS2

t0 t1 t2

VgS1

t0 t1 t2

VgS3

t0 t1 t2

Vg

Figure 3.48 Reverse Buck-Boost: Gate signals




and the magnetizing current IM decreases linearly from –IM1 to –IM2. Figure 3.49

shows this stage.

V1 V2

+ +

S3

S1 S2

D3

D2

+

+

+ + -

+

- -

-

-

- +

LM

VLT1 VLT2

- -

IM

I1 I2D1

: 1nILT1 ILT2

Figure 3.49 Reverse Buck-Boost: First operating stage


99

The equivalent circuit of the first stage in the Reverse Buck-Boost mode is the

same that in the second stage of the Forward Buck mode. Then, the mathematical


Stage 2 [t1, t2]: At t1, S3 remains on and S2 is turned-off. At this moment, this

stage begins. The current continues to flow through the switch S3 and finds a path

through the diode D1. The magnetizing current increases linearly from –IM2 to –IM1.

Figure 3.50 shows this stage.

V1 V2

+ +

S3

S1 S2

D3

D2

+

+

+ + -

+

- -

-

-

- +

LM

VLT1 VLT2

- -

IM

I1 I2D1

: 1nILT1 ILT2

Figure 3.50 Reverse Buck-Boost: Second operating stage


The equivalent circuit of the second stage in the Reverse Buck-Boost mode is

the same that in the first stage of the Forward Boost mode. Then, the mathematical


Figure 3.51 presents the voltage in the switches and figure 3.52 presents the

voltage in the primary and secondary of the tapped inductor for the Reverse Buck-

Boost mode.

VS2

t0 t1 t2

V1+nV2

n

VS1

t0 t1 t2

V1+nV2

TSTS

Figure 3.51 Reverse Buck-Boost: Theoretical voltage waveforms in the switches S1 and S2


100

VLT2VLT1

t0 t1 t2t0 t1 t2

V1 nV1

TSTS

-nV2 V2

Figure 3.52 Reverse Buck-Boost: Theoretical voltage waveforms in the tapped inductor



magnetizing inductance LM and the magnetizing current IM for the Reverse Buck-

Boost mode.

VLM

t0 t1 t2

TS

IM

t0 t1 t2

-IM2

-IM1

TS

-nV2

V1

Figure 3.53 Reverse Buck-Boost: Theoretical waveforms in the magnetizing inductance


In Figure 3.54 are represented the waveforms of the current I1 and the current I2

for the Reverse Buck-Boost mode.

I1

t0 t1 t2

TS

-IM2

-IM1

I2

t0 t1 t2

TS

nIM1

nIM2

Figure 3.54 Reverse Buck-Boost: Theoretical waveforms of the current I1 and I2


101

Finally, the currents in the switches for the Reverse Buck-Boost mode are

determined by the figure 3.55.

IS3

t0 t1 t2

TS

IS1

t0 t1 t2

TS

-IM2

-IM1

IS2

t0 t1 t2

TS

nIM1

nIM2

nIM1

nIM2

-IM2

-IM1

Figure 3.55 Reverse Buck-Boost: Theoretical current waveforms in the switches



to find the voltage conversion characteristic in the Reverse Buck-Boost mode.

This way, replacing (3.8), (3.9), (3.24) and (3.56) in (3.30) and considering

<VLM>AVG=0, the voltage conversion characteristic is found and presented by (3.135).

2 2 1 21 0S SnV D T V D T (3.134)

1 2

2 21

V nD

V D (3.135)

Figure 3.56 presents the voltage conversion characteristic for the Reverse

Buck-Boost mode.

Then, the average values of the currents I1 and I2 are defined, respectively, by

(3.136) and (3.137).

2 11_ 21

2M M

AVG

I II D (3.136)

2 12 _ 2

2M M

AVG

I II nD (3.137)

102

Figure 3.56 Reverse Buck-Boost: Voltage conversion characteristic


Analyzing the magnetizing inductance in the first stage, it is possible to find the

first relationship between IM1 and IM2. This relationship is given by (3.138).

2 21 2M M

S M

nV DI I

f L (3.138)



2 1

1 2

2

1C

M M

PI I

V D (3.139)

This way, summing (3.138) and (3.139), the instantaneous value of the

magnetizing current IM1 is found and expressed by (3.140).

1 2 2 2

1

1 2

2 1

2 1

C S M

M

S M

P f L nVV D DI

V f L D (3.140)


current IM2 is determined by (3.141).

1 2 2 2

2

1 2

2 1

2 1

C S M

M

S M

P f L nVV D DI

V f L D (3.141)

103


calculated.


2

1 1 2 22 12

2 2

0, 0

( ),

1 1

S

S M MM MS S

S

t D T

I t I D II It D T t T

D T D

(3.142)


2

2

2

2 1 2 22 11_

2 20

10

1 1

S S

S

D T T

M MM MS RMS

S SD T

I D II II dt t dt

T D T D (3.143)


IS1_RMS is found and given by (3.144).

22 2 2 2

2 1 2 2

1_2 2 2

1 2

11 3

6 1 12S RMS

M s M C S

n D V V DI

V L f D L P f (3.144)

For the switch S2 the function of IS2(t) given by (3.145) must be considered.

2 11 2

2 2

2

, 0( )

0,

M MM S

S S

S S

I In t nI t D T

I t D T

D T t T

(3.145)


2

2

2

22 12 _ 1

20

10

S S

S

D T T

M MS RMS M

S S D T

I II n t nI dt dt

T D T (3.146)



2 2 22 2 2 22

2 _ 2 1 2 2

1 2

12

2 3 1

M C SS RMS

M s

L P fDnI n D V V

V L f D (3.147)

104


2 11 2

2

3

1 2 22 12

2 2

, 0

( )

,1 1

M MM S

S

S

M MM MS S

S

I In t nI t D T

D TI t

I D II It D T t T

D T D

(3.148)


2

2

2

2 2 1

2 12

3 _ 2

0 1 2 21

2

11

1

S S

S

M M

D T TM MS

S RMS S

S D T M MM

I ItI I

D Tn tI dt dtD T

T I D InI

D

(3.149)

Then, replacing (3.140) and (3.141) in (3.149) and solving the equation, IS3_RMS

is found and determined by (3.150).

2 2 2 2 3 2 2 2 3 2 2

2 1 2 2 2 2 2 2 2

2 2 2 2

2 2

2

2

3 _

1

3 2 3 3 1

36 1

1

6

M C S

S RMS

M S

D V V n D n D n D D n D D

L P f D n D

DI

V L f (3.150)


In this chapter, all the theoretical steady state analysis of the bidirectional DC-

DC converter with tapped inductor was presented.

Thinking in an experimental converter implementation, the analysis made in the

present chapter is essential, since with the knowledge provided all the parameters of

the converter become known and, consequently, a design methodology can be

proposed.

105

CHAPTER 4

BIDIRECTIONAL ZVS BUCK-BOOST DC-DC CONVERTER:

STEADY STATE ANALYSIS


In this chapter, the second topology presented in this thesis is analyzed in

details. As well as the topology presented in chapter 3, this converter is also a

modification of a well-know topology, topology that was presented in Figure 2.10

As mentioned before, the converter presented in Figure 2.10 can just work with

one operation mode for each power flow direction, Buck or Boost, making this

converter unfeasible for applications where one of the voltage sources can present a

wide variation on its value, becoming higher or lower than the other voltage source.

For situations like the one described, in this chapter, a Buck-Boost operation for

both power flow directions is proposed. This operation is allowed just with the

reallocation of the voltage source V2 from the original topology.

Working with the Buck-Boost operation, the converter retains the characteristics

of the original converter. Nevertheless, the proposed converter becomes

conceptually different from the original: in the original converter the voltage sources

are in parallel, whereas in the Buck-Boost operation the voltage sources are in

series.

With this conceptual change, the Buck-Boost converter becomes inappropriate

for applications where the voltage sources are working independent, as, for example,

when they are supplying independent DC buses. However, for applications where the

voltage sources work in conjunction, as a Battery/SC HESS where the SC acts just

like a buffer for the battery, this converter can be used without any restriction.

4.2 BIDIRECTIONAL ZVS BUCK-BOOST DC-DC CONVERTER

Figure 4.1 presents the converter discussed in this chapter.

106

S2 D2

S1 D1

V2

-

+

V1

-

+

+

+

Cf2

Cf1

LL

NP NS

Figure 4.1 Bidirectional ZVS Buck-Boost DC-DC converter


The equivalent circuit of the converter considered in the analyses is shown in

Figure 4.2. The transformer is modeled like an ideal transformer that has turn ratio of

NP: NS (=n: 1) and a magnetizing inductance LM. Another approach of this converter

is that the auxiliary inductance LL, inductance that will allow the ZVS operation, can

be the leakage inductance of the transformer.

V2

V1

S2 D2

S1 D1

-

+

-

+

+

+

Cf2

Cf1

1 n

+ -LM

IM

ILT1

+ -LT1 - +LT2 + -LL

+

-

+

-

ILT2

ILL

IS1

IS2

ICf1

ICf2

I1

I2

Figure 4.2 Equivalent circuit of the bidirectional ZVS Buck-Boost Converter


For the correct analyses, some considerations must be determined.

107

As the average voltage across an inductor in steady state is equal to zero,

the voltage VCf1 and VCf2 in the capacitors Cf1 and Cf2 will be, respectively,

according to Kirchhoff Voltage Law (KVL), the values of V1 and V2

1 1CfV V (4.1)

2 2CfV V (4.2)

As the average current through a capacitor in steady state is equal to zero

and the inductance LL is connected in a point with two capacitors, the current

ILL is divided equally between Cf1 and Cf2 and has average value equal to

zero.

1 22LL

Cf Cf

II I (4.3)

_ 0LL AVGI (4.4)

The equations of the ideal transformer

1

2

LT P

LT S

V N

V N (4.5)

1 1 2 2LT LT LT LTV I V I (4.6)

Considering NP=1 and NS=n, equations (4.5) and (4.6) can be rewritten,

respectively, as (4.7) and (4.8).

2 1LT LTV nV (4.7)

1 2LT LTI nI (4.8)

As the magnetizing inductance LM is in parallel with the primary of the

transformer, they have the same voltage. Then:

1LT LMV V (4.9)

2LT LMV nV (4.10)

108

4.2.1 Forward Mode

In the forward mode, the energy flows from V1 to V2. The proposed converter

presents 6 stages within one switching period TS for each power flow direction, being

4 operating stages and 2 commutation stages. In the static analysis, as the

commutation stages are very fast they are disregarded for not presenting a

considerable influence in the converter operation. On the other hand, the 4 operating

stages are condensed in just 2 due to the fact that the equivalent circuit when the

current is flowing through the switch or through its antiparallel body diode is the

same, making the mathematical analyses equal for both cases.

Stage 1 [t0, t1]: In this stage, the switch S2 is always turned-off, then, the current

IS2 is equal to zero. The time of this stage is determined by the duty cycle D1 from the

switch S1. The current IS1 flows through the switch S1 or the diode D1. Considering

the direction of the current determined in the equivalent circuit, when the current is

flowing through the diode D1, IS1 is negative. This double direction of the current IS1

will allow the ZVS operation in the converter. Figure 4.3 shows this stage.

V2

V1

S2 D2

S1 D1

-

+

-

+

+

+

Cf2

Cf1

1 n

+ -LM

IM

ILT1

+ -LT1 - +LT2 + -LL

+

-

+

-

ILT2

ILL

IS1

IS2

ICf1

ICf2

I1

I2

Figure 4.3 Forward mode: First stage


The voltage VLM across the magnetizing inductance LM is determined by

equation (4.11).

1LMV V (4.11)

109

Replacing (4.11) in (4.9) and (4.10), the voltage in each turn of the transformer

is found and determined by (4.12) and (4.13).

1 1LTV V (4.12)

2 1LTV nV (4.13)

The voltage VLL across the auxiliary inductance LL can be determined by (4.14).

1 1 2 1 0LT LT LL CfV V V V V (4.14)

Substituting (4.1), (4.12) and (4.13) into (4.14), VLL is found and given by (4.15).

1 1LLV V n (4.15)

Then, the voltage VS2 in the switch S2 is determined by (4.16).

2 1 2 0S LTV V V (4.16)

Replacing (4.12) in (4.16), VS2 is represented by (4.17).

2 1 2SV V V (4.17)

Analyzing the currents in the equivalent circuit, some relationships can be

found. As the secondary of the transformer LT2 and the inductance LL are in series,

they have the same current, then:

2LT LLI I (4.18)

Replacing (4.18) in (4.8), the current ILT1 in the primary of the transformer is


1LT LLI nI (4.19)

The current I2 in the voltage source V2 can be expressed by (4.20).

2 2CfI I (4.20)

Substituting (4.3) into (4.20), I2 can be expressed as function of ILL.

110

22LLI

I (4.21)

The current I1 in the voltage source V1 can be written as the equation (4.22).

1 2 1LT MI I I I (4.22)

Replacing (4.19) and (4.21) in (4.22), equation (4.22) can be rewritten as (4.23).

1

2 1

2M LL

nI I I (4.23)

Finally, the current IS1 in the switch S1 can be determined by (4.24).

1 1 1S CfI I I (4.24)

Replacing (4.3) and (4.23) in (4.24), IS1 is found and expressed by (4.25).

1 1S M LLI I I n (4.25)

Stage 2 [t1, t2]: In this stage, the switch S1 will be always turned-off, then, the

current IS1 is equal to zero. The duration of this stage is determined by the

complementary time of the stage 1. As it happens in the current IS1, the current IS2

must have the same double direction to guarantee the ZVS operation. Figure 4.4

shows this stage.

V2

V1

S2 D2

S1 D1

-

+

-

+

+

+

Cf2

Cf1

1 n

+ -LM

IM

ILT1

+ -LT1 - +LT2 + -LL

+

-

+

-

ILT2

ILL

IS1

IS2

ICf1

ICf2

I1

I2

Figure 4.4 Forward mode: Second stage


The voltage VLM across the magnetizing inductance LM is determined by (4.26).

111

2LMV V (4.26)

Replacing (4.26) in (4.9) and (4.10), the voltage in each turn of the transformer

is found and determined by equations (4.27) and (4.28).

1 2LTV V (4.27)

2 2LTV nV (4.28)

The voltage VLL across the auxiliary inductance LL can be determined by (4.29).

2 2 0LT LL CfV V V (4.29)

Substituting (4.2) and (4.28) into (4.29), VLL is found and given by (4.30).

2 1LLV V n (4.30)

The voltage VS1 in the switch S1 is determined by equation (4.31).

1 1 1 0LT SV V V (4.31)

Replacing (4.27) in (4.31), VS1 is represented by (4.32).

1 1 2SV V V (4.32)

The current I1 in the voltage source V1 can be expressed by (4.33).

1 1CfI I (4.33)

Substituting (4.3) into (4.33), I1 can be rewritten as (4.34).

12LLI

I (4.34)

The current I2 in the voltage source V2 can be determined by equation (4.35).

2 1 1M LTI I I I (4.35)

Replacing (4.19) and (4.34) in (4.35), I2 is found and presented by (4.36).

112

2

2 1

2M LL

nI I I (4.36)

Finally, the current IS2 in the switch S2 is determined by (4.37).

2 2 2S CfI I I (4.37)

Replacing (4.3) and (4.36) in (4.37), IS2 can be rewritten as (4.38).

2 1S M LLI I I n (4.38)

Analyzed the two stages, the theoretical waveforms for the Forward mode can

be drawn. Figure 4.5 presents the voltage waveforms for the switches and Figure 4.6

the voltage waveforms in each turn of the transformer.

VS2

t0 t1 t2

TS

V1+V2

VS1

t0 t1 t2

TS

V1+V2

Figure 4.5 Forward mode: Theoretical voltage waveforms in the switches S1 and S2


VLT2VLT1

t0 t1 t2t0 t1 t2

V1

TSTS

-V2

nV1

-nV2

Figure 4.6 Forward Mode: Theoretical voltage waveforms in the transformer


The waveforms of the magnetizing inductance LM are presented in Figure 4.7.

113

t0 t1 t2

TS

IM

t0 t1 t2

TS

VLM

IM2

IM1V1

-V2

Figure 4.7 Forward mode: Theoretical waveforms in the magnetizing inductance


The expected waveforms of the auxiliary inductance LL are presented in Figure

4.8. It is important to note that the behavior of the waveforms will be directly related

with the value of n. When n is bigger than 1, in the first stage the voltage across this

inductance will be positive, consequently, the current ILL will increase linearly in this

stage, and decrease in the second stage.

The opposite happens when n is smaller than 1. In this case, the voltage across

this inductance will be negative in the first stage, consequently the current will

decrease linearly, and increase in the second stage.

t0 t1 t2

TS

ILL

t0 t1 t2

TS

VLL

ILL

-ILL

(n-1)V1

(1-n)V2

(a)

t0 t1 t2

TS

ILL

t0 t1 t2

TS

VLL

ILL

-ILL

(n-1)V1

(1-n)V2

(b)

Figure 4.8 Forward Mode: Theoretical waveforms in the auxiliary inductance (a) n>1 (b) n<1


Determined the currents IM and ILL, the currents in the voltage sources and in

the switches can be drawn. Figure 4.9 and 4.10 present, respectively, the currents I1

and I2 in the voltage sources V1 and V2 for different values of n.

114

I1

t0 t1 t2

TS

(a)

ILL

2

-ILL

2

IM1-ILL( )2n-1

2

IM2+ILL( )2n-1

2

I1

t0 t1 t2

TS

(b)

ILL

2

-ILL

2

IM1+ILL( )2n-1

2

IM2-ILL( )2n-1

2

I1

t0 t1 t2

TS

(c)

ILL

2

-ILL

2

IM2-ILL( )2n-1

2

IM1+ILL( )2n-1

2

Figure 4.9 Forward mode: Theoretical current waveforms in the voltage source V1

(a) n>1 (b) 0<n<=0.5 (c) 0.5<n<1


I2

t0 t1 t2

TS

(a)

ILL

2

-ILL

2

I2

t0 t1 t2

TS

(b)

ILL

2

-ILL

2

I2

t0 t1 t2

TS

(c)

ILL

2

-ILL

2

-IM2-ILL( )2n-1

2

-IM1+ILL( )2n-1

2-IM1-ILL( )

2n-12

-IM2+ILL( )2n-1

2-IM1-ILL( )

2n-12

-IM2+ILL( )2n-1

2

Figure 4.10 Forward mode: Theoretical current waveforms in the voltage source V2 (a) n>1 (b) 0<n<=0.5 (c) 0.5<n<1


Finally, Figure 4.11 presents the current waveforms in the switches for different

values of n.

IM2+ILL(n-1)

IS2

t0 t1

TS

IS1

t0 t1 t2

TS (a)

t2

IM1-ILL(n-1)

-IM1+ILL(n-1)

-IM2-ILL(n-1)

IS2

t0 t1

TS

IS1

t0 t1 t2

TS (b)

t2

IM2-ILL(n-1)

IM1+ILL(n-1) -IM2+ILL(n-1)

-IM1-ILL(n-1)

Figure 4.11 Forward mode: Theoretical current waveforms in the switches (a) n>1 (b) n<1


Determined all the waveforms of the Forward Mode, some important

relationships can be found.

115

First, making the Volt-second balance in the magnetizing inductance LM, it is

possible to find the voltage conversion characteristic for the Forward mode. Equation

(4.40) presents the result.

1 1 2 11 0S SV DT V D T (4.39)

2 1

1 11

V D

V D (4.40)

To find the instantaneous values IM1 and IM2 of the magnetizing current IM, some

steps must be followed. First, the average value of the current I1 can be determined

calculating the area of the current waveform in the voltage source V1.

1_ 1 2 1

1 1 2 1 2 1

2 2 2AVG M LL M LL S

S

n nI I I I I DT

T (4.41)

1 1 2

1_2

M M

AVG

D I II (4.42)

Then, considering the ideal converter, the power processed PC by the converter

must be the same in the voltage source V1 and V2. This can be expressed by the

equation (4.43).

1 2C V VP P P (4.43)

The power PV1 in the voltage source V1 can be determined by (4.44).

1 1 1_V AVGP VI (4.44)

This way, replacing (4.42) and (4.43) in (4.44), the first relationship between IM1

and IM2 is found and given by (4.45).

2 1

1 1

2 CM M

PI I

V D (4.45)

Now, analyzing the magnetizing inductance LM in the stage 1, it is possible to

determine the second relationship between IM1 and IM2.

116

1 12 1M M

S M

V DI I

f L (4.46)

Summing equations (4.45) and (4.46), the value of IM2 is found and expressed

by (4.47).

2 2

1 12

1 1

2

2C S M

M

S M

P f L V DI

V D f L (4.47)

Replacing (4.47) in (4.45), the value of IM1 can be found and determined by

(4.48).

2 2

1 11

1 1

2

2C S M

M

S M

P f L V DI

V D f L (4.48)

The same procedure can be applied to the auxiliary inductance LL. Using

equation (4.49) and analyzing this inductance in the stage 1 of the Forward mode,

the instantaneous value of ILL is determined.

LLLL L

IV L

t (4.49)

1 11

LL

s L

V n DI

f L (4.50)

As the value of n can determine a positive or negative voltage in this stage, for

the calculations will be considered the module of the result. And, considering that ∆ILL

must be equal to 2ILL to respect the condition determined by (4.4), ILL is found and

determined by (4.52).

1 11

2 LL

s L

V n DI

f L (4.51)

1 11

2LL

s L

V n DI

f L (4.52)

To guarantee the ZVS operation, the relationship presented by (4.53) must be

respected.

117

1 1 0M LLI I n (4.53)

Replacing (4.48) and (4.52) in (4.53), equation (4.54) is found.

2 21 11 1

1 1

121 0

2 2C S M

S M s L

V n DP f L V Dn

V D f L f L (4.54)

Making the correct mathematical manipulations in (4.54), the value of the

auxiliary inductance that guarantee the ZVS operation is found and determined by

(4.56).

22 2 2 2

1 1 1 12 1 0C S M L L MP f L L V D L V D L n (4.55)

22 2

1 1

2 2

1 1

1

2

M

L

C S M

V D L nL

P f L V D (4.56)

Finally, the RMS value of the currents IS1 and IS2 can be determined.

2

1_ 1

0

1( )

ST

S RMS S

S

I I t dtT

(4.57)

2

2 _ 2

0

1( )

ST

S RMS S

S

I I t dtT

(4.58)

Where the values of IS1 and IS2 can be determined, respectively, by (4.59) and

(4.60).

2 1

1 1

1 1

1

2 11 , 0

( )

0,

M M LL

M LL S

S S

S S

I I I nt I I n t DT

I t DT

DT t T

(4.59)

1

2 1

2

1

2 1

1 1

1

0, 0

2 1( )

1

2 11 ,

1

S

M M LL

S

S

M M LL

M LL S S

t DT

I I I nI t t

D T

I I I nI I n DT t T

D

(4.60)

118

Replacing (4.59) in (4.57) and (4.60) in (4.58), equations (4.57) and (4.58) can

be rewritten, respectively, as (4.61) and (4.62).

1

2

2 1

1_ 1

10

2 111

SD T

M M LL

S RMS M LL

S S

I I I nI t I I n dt

T DT (4.61)

1

2

2 1

1

2 _

2 1

1

1

2 1

11

2 11

1

S

S

M M LL

TS

S RMS

S D T M M LL

M LL

I I I nt

D TI dt

T I I I nI I n

D

(4.62)`

Finally, the RMS values of IS1 and IS2 are determined, respectively, by (4.63)

and (4.64).

4 24 4 2 2

1 1

2 2 2 2

1_

1

1 2 13

1 12

6

M L M L

M L C S

S RMS

S M L

D V L n L L L n

D L L P fI

f L L V (4.63)

4 24 4 2 2

1 1

12 2 2 2

2 _

1 1

1 2 13 1

12

6

M L M L

M L C S

S RMS

S M L

D V L n L L L nD

L L P fI

f L L V D (4.64)

4.2.2 Reverse Mode

In the Reverse mode, the energy flows from V2 to V1 and the controlled switch is

the switch S2. Exactly as the Forward mode, the Reverse mode presents six stages,

being 2 commutation stages and 4 operating stages condensed in just two for the

same reason presented before.

This mode will present inverted stages if compared with the forward mode, that

is, the first stage of the Forward mode will be the second stage in the Reverse mode,

and the second stage of the Forward mode will be the first stage in the Reverse

mode.

119

For this reason, the analyses for this mode are the same of the Forward mode

and will not be presented again.

Figure 4.12 presents the voltage waveforms in the switches and Figure 4.13

presents the voltage in each turn of the transformer for the Reverse mode.

VS2

t0 t1 t2

VS1

t0 t1 t2

TSTS

V1+V2 V1+V2

Figure 4.12 Reverse mode: Theoretical voltage waveforms in the switches S1 and S2


VLT2VLT1

t0 t1 t2t0 t1 t2

V1

TSTS

-V2

nV1

-nV2

Figure 4.13 Reverse mode: Theoretical voltage waveforms in the transformer


Figure 4.14 presents the waveforms in the magnetizing inductance LM.

VLM

t0 t1 t2

TS

IM

t0 t1 t2

-IM2

-IM1

TS

-V2

V1

Figure 4.14 Reverse mode: Theoretical waveforms in the magnetizing inductance


120

Figure 4.15 presents the waveforms in the auxiliary inductance LL.

t0 t1 t2

TS

ILL

t0 t1 t2

TS

VLL

ILL

-ILL

(1-n)V2

(n-1)V1

(a)

t0 t1 t2

TS

ILL

t0 t1 t2

TS

VLL

ILL

-ILL

(1-n)V2

(n-1)V1

(b)

Figure 4.15 Reverse mode: Theoretical waveforms in the auxiliary inductance (a) n>1 (b) n<1


Figures 4.16 and 4.17 present, respectively, the waveforms of the current I1 and

I2.

I1

t0 t1 t2

TS

(a)

ILL

2

-ILL

2

I1

t0 t1 t2

TS

(b)

ILL

2

-ILL

2

I1

t0 t1 t2

TS

(c)

ILL

2

-ILL

2

-IM2-ILL( )2n-1

2

-IM1+ILL( )2n-1

2-IM1-ILL( )

2n-12

-IM2+ILL( )2n-1

2-IM1-ILL( )

2n-12

-IM2+ILL( )2n-1

2

Figure 4.16 Reverse mode: Theoretical current waveforms in the voltage source V1 (a) n>1 (b) 0<n<=0.5 (c) 0.5<n<1


I2

t0 t1 t2

TS

(a)

ILL

2

-ILL

2

I2

t0 t1 t2

TS

(b)

ILL

2

-ILL

2

I2

t0 t1 t2

TS

(c)

ILL

2

-ILL

2

IM2+ILL( )2n-1

2

IM1-ILL( )2n-1

2

IM2-ILL( )2n-1

2IM1+ILL( )

2n-12

IM2-ILL( )2n-1

2IM1+ILL( )

2n-12

Figure 4.17 Reverse mode: Theoretical current waveforms in the voltage source V2 (a) n>1 (b) 0<n<=0.5 (c) 0.5<n<1


Finally, the current in the switches S1 and S2 are presented by Figure 4.18.

121

IM2+ILL(n-1)

IS1

t0 t1

TS

IS2

t0 t1 t2

TS(a)

t2

IM1-ILL(n-1)

-IM1+ILL(n-1)

-IM2-ILL(n-1)

IS1

t0 t1

TS

IS2

t0 t1 t2

TS(b)

t2

IM2-ILL(n-1)

IM1+ILL(n-1)-IM2+ILL(n-1)

-IM1-ILL(n-1)

Figure 4.18 Reverse mode: Theoretical current waveforms in the switches (a) n>1 (b) n<1


Making the Volt-second balance in the magnetizing inductance LM, the voltage

conversion characteristic for the Reverse mode is determined by (4.66).

2 2 1 21 0S SV D T V D T (4.65)

1 2

2 21

V D

V D (4.66)

The same procedure used in the Forward mode to find the instantaneous

values of IM1 and IM2 is followed in the reverse mode. First, the average value of the

current I1 is determined by (4.67).

2 1 2

1_

1

2

M M

AVG

D I II (4.67)

To guarantee the correct power balance in the converter, for the Reverse mode

the power PV1 in the voltage source V1 will be considered negative. This can be


1V CP P (4.68)

Then, making the power balance in the voltage source V1:

1 1 1_V AVGP VI (4.69)

And replacing (4.67) and (4.68) in (4.69), the first relationship between IM1 and

IM2 is found and determined by (4.70).

122

2 1

1 2

2

1C

M M

PI I

V D (4.70)

Analyzing the magnetizing inductance LM in the first stage, the second

relationship between IM1 and IM2 is found and expressed by (4.71).

2 22 1M M

S M

V DI I

f L (4.71)

Summing (4.70) and (4.71), the value of IM1 is found and given by (4.72).

1 2 2 2

1

1 2

2 1

2 1

C S M

M

S M

P f L VV D DI

V D f L (4.72)

Then, substituting (4.72) into (4.70), the value of IM2 is found and presented:

1 2 2 2

2

1 2

2 1

2 1

C S M

M

S M

P f L VV D DI

V D f L (4.73)

Analyzing the auxiliary inductance LL and considering the same conditions from

the Forward mode, ILL is defined by (4.74).

2 21

2LL

s L

V n DI

f L (4.74)

To guarantee the ZVS operation, the relationship presented by (4.75) must be

respected.

1 1 0M LLI I n (4.75)

Then, replacing (4.72) and (4.74) in (4.75), the maximum value of the auxiliary

inductance LL that allow the ZVS operation is found and expressed by (4.76).

2

2 1 2 2

2 1 2 2

1 1

2 1

M

L

C S M

V V D L D nL

P f L V V D D (4.76)

Finally, the RMS value of the currents IS1 and IS2 can be calculated.

Equations (4.77) and (4.78) present, respectively, the values of IS1 and IS2.

123

2

2 1

1

1

2 1

1 2

1

0, 0

2 1( )

1

2 11 ,

1

S

M M LL

S

S

M M LL

M LL S S

t D T

I I I nI t t

D T

I I I nI I n D T t T

D

(4.77)

2 1

1 2

2 1

2

2 11 , 0

( )

0,

M M LL

M LL S

S S

S S

I I I nt I I n t D T

I t DT

D T t T

(4.78)

Replacing (4.77) in (4.57) and (4.78) in (4.58), equations (4.57) and (4.58) can

be rewritten, respectively, as (4.79) and (4.80).

2

2

2 1

1

1_

2 1

1

1

2 1

11

2 11

1

S

S

M M LL

TS

S RMS

S D T M M LL

M LL

I I I nt

D TI dt

T I I I nI I n

D

(4.79)

2

2

2 1

2 _ 1

10

2 111

SD T

M M LL

S RMS M LL

S S

I I I nI t I I n dt

T DT (4.80)

Then, solving equations (4.79) and (4.80), the RMS value of the currents IS1 and

IS2 are determined, respectively, by (4.81) and (4.82).

4 24 2 2 2 2

2 1 2

2 2 2 22

1_

1

1 2 13

1 12

6

M L M L

M L C S

S RMS

S M L

D V V L n L L L n

D L L P fI

f L L V

(4.81)

4 24 2 2 2 2

2 1 2

22 2 2 2

2 _

1 2

(1 ) 1 2 13

12

6

M L M L

M L C S

S RMS

S M L

D V V L n L L L nD

L L P fI

f L L V D

(4.82)

124


In the present chapter, all the theoretical steady state analysis of the

bidirectional ZVS Buck-Boost DC-DC converter was presented.

As well as in chapter 3, the knowledge provided by this chapter is essential for

an experimental implementation, since all the converter parameters become known

and, consequently, a design methodology can be proposed.

125

CHAPTER 5


DYNAMIC ANALYSIS


As mentioned earlier in this thesis, in bidirectional DC-DC converters is the

current control that will allow the power flow exchange in the system. However, to

make it possible, a relationship between the current to be controlled and the duty

cycle of the controlled switch must be found.

In order to find this relationship, in this chapter, the dynamic analysis of the

bidirectional DC-DC converter with tapped inductor is presented. Using the instant

average value concept and the small signal approach, the transfer function of each

operation mode of the converter is determined.

5.2 SMALL-SIGNAL ANALYSIS

Considering a Battery/SC HESS in EVs applications, the battery current must

respect some constraints and it is function of the control to guarantee that. Taking

into account the equivalent circuit of the bidirectional DC-DC converter with tapped

inductor presented by Figure 3.2 and imagining a battery as the voltage source 1(V1),

a relationship between the current I1 and the controlled switch for each operation

mode must be found. Nevertheless, before starting the equation method for the

converter, the instant average value concept must be introduced.

According Erickson and Maksimovic (2001), the instant average value concept

can be understood as the average value of a magnitude in a switching period TS.

In this concept, the starting hypothesis is that the time constants of a converter

are much higher than the switching period TS. This way, it is possible to realize the

average of the converter waveforms in a short period of time if compared with the

converter time constant, without significant influence in the system response

(ERICKSON, R. and MAKSIMOVIC, D., 2001).

126

In summary, the resulting average model represents the low frequency behavior

of the converter, disregarding the high frequency harmonics produced by

commutations. The equations that represent the average values of the magnetizing

voltage VLM and the current I1 through the voltage source V1 are given, respectively,

by equations (5.1) and (5.2).

_ _SLM T LM ton on Controlled Switch LM toff off Controlled SwitchV V t V t (5.1)

1 1 _ 1 _ST ton on Controlled Switch toff off Controlled SwitchI I t I t (5.2)

Another important factor for the correct dynamic model of the converter is the

small-signal approach.

Many systems are non-linear, making difficult the use of known control

techniques in their control. However, applying the small signal analysis, linear models

are found by the linearization around an operating point. In this technique, a small

perturbation is applied in the input signal and this perturbation will cause a

perturbation in the output signal, which is already considered linearized (ERICKSON,

R. and MAKSIMOVIC, D., 2001).

In the small signal analysis, a signal can be written as its average value plus a

small perturbation, where the average value is so much bigger than the perturbation.

From equation (5.3) to (5.7), the signals involved for the control of the converter are

rewritten in the small signal form. Assuming that in this work the goal of the control is

the current control of the system and as the voltage across the voltage sources will

not present a significant variation and will not be controlled, for the analyses will not

be considered perturbations on the two voltage sources.

( )M M MI t I i t

(5.3)

1 1 1I t I i t

(5.4)

1 1 1( )D t D d t

(5.5)

2 2 2( )D t D d t

(5.6)

127

3 3 3( )D t D d t

(5.7)

Following, the analyses for each operation mode of the converter are

presented.

5.2.1 Forward Buck

Considering the analyses made in chapter 3, the values of the magnetizing

voltage VLM for each operation stage are already known. This way, for the Forward

Buck, equation (5.1) can be rewritten as (5.8).

1 21 2 1

(V V )1

1

M

M

d I t nL D t nV D t

dt n

(5.8)

Replacing equations (5.3) and (5.5) in (5.8), equation (5.9) is found.

1 21 1 2 1 1

( )(V V )

( ) 1 ( )1

M M

M

d I i tn

L D d t nV D d tdt n

(5.9)

Then, separating the first order terms of (5.9) and applying the Laplace

Transform, the transfer function of the magnetizing current by the controlled duty

cycle of the Forward Buck is found and presented by (5.10).

2 1

1

( )

1( )

M

M

n nV Vi s

n L sd s

(5.10)

The same method is used to find the transfer function of the current I1 through

the voltage source V1 by the duty cycle. First, with the analyses made in chapter 3,

equation (5.2) can be rewritten as (5.11) for the Forward Buck.

1 11

MnI tI t D t

n

(5.11)


1 1 1 1( ) ( )1

M M

nI i t I i t D d t

n

(5.12)

128

Separating the first order terms and applying the Laplace Transform in (5.12),

(5.13) is found.

1 11

( ) ( )( )

1M MnI d s nD i s

i sn

(5.13)

For the Forward Buck, the value of the magnetizing current can be determined

by (5.14).

1 1

1C

M

P nI

nDV

(5.14)

Finally, replacing (5.10) and (5.14) in (5.13), the transfer function of the current

I1 by the duty cycle is found and presented by (5.15).

2 2 2

1 1 2 11

2

1 11

1( )

1( )

C M

M

P n L s n D V nV Vi s

DV n L sd s

(5.15)

5.2.2 Forward Boost

For the Forward Boost, equation (5.1) can be rewritten as (5.16).

1 21 3 3

(V V )1

1

M

M

d I t nL V D t D t

dt n

(5.16)


1 21 3 3 3 3

( )(V V )

( ) 1 ( )1

M M

M

d I i tn

L V D d t D d tdt n

(5.17)

Then, separating the first order terms of (5.17) and applying the Laplace

Transform, the transfer function of the magnetizing current by the controlled duty

cycle of the Forward Boost is found and presented by (5.18).

2 1

3

( )

1( )

M

M

i s nV V

n L sd s

(5.18)

129

Doing the same for the current I1 through the voltage source V1, equation (5.2)

can be rewritten as (5.19) for the Forward Boost.

1 3 311

M

M

nI tI t I t D t D t

n

(5.19)


1 1 3 3 3 3( ) ( ) ( ) 1 ( )1

M M M M

nI i t I i t D d t I i t D d t

n

(5.20)

Then, separating the first order terms and applying the Laplace Transform in

(5.20), (5.21) can be determined.

3 3

1

( ) ( )( )

1

M MI d s n D i si s

n

(5.21)

For the Forward Boost, the value of the magnetizing current can be determined

by (5.22).

1 3

1C

M

P nI

V n D

(5.22)


I1 by the controlled duty cycle for the Forward Boost is given and presented by (5.23).

2 2

1 3 2 11

2

1 33

1( )

1( )

C M

M

P n L s V n D nV Vi s

V n D n L sd s

(5.23)


For the Forward Buck-Boost, equation (5.1) can be rewritten as (5.24).

1 1 2 11M

M

d I tL V D t nV D t

dt (5.24)

Then, replacing equations (5.3) and (5.5) in (5.24), equation (5.25) is found.

130

1 1 1 2 1 1

( )

( ) 1 ( )M M

M

d I i t

L V D d t nV D d tdt

(5.25)

Separating the first order terms of (5.25) and applying the Laplace Transform,

the transfer function of the magnetizing current by the duty cycle of the Forward

Buck-Boost is found and presented by (5.26).

2 1

1

( )

( )

M

M

i s nV V

L sd s

(5.26)


can be rewritten as (5.27) for the Forward Buck-Boost.

1 1MI t I t D t (5.27)


1 1 1 1( ) ( )M MI i t I i t D d t

(5.28)



1 1 1( ) ( ) ( )M Mi s I d s D i s

(5.29)

For the Forward Buck-Boost, the value of the magnetizing current can be


1 1

CM

PI

V D (5.30)


I1 by the duty cycle for the Forward Buck-Boost is found and presented by (5.31).

2

1 1 2 11

1 11

( )

( )

C M

M

P L s D V nV Vi s

DV L sd s

(5.31)

131

5.2.4 Reverse Buck

For the Reverse Buck, equation (5.1) can be rewritten as (5.32).

1 22 1 2

(V V )1

1

M

M

d I t nL D t V D t

dt n

(5.32)


1 22 2 1 2 2

( )(V V )

( ) 1 ( )1

M M

M

d I i tn

L D d t V D d tdt n

(5.33)


the transfer function of the magnetizing current by the duty cycle of the Reverse Buck

is found and presented by (5.34).

2 1

2

( )

1( )

M

M

nV Vi s

n L sd s

(5.34)


can be rewritten as (5.35) for the Reverse Buck.

1 2 211

M

M

nI tI t D t I t D t

n

(5.35)

Then, replacing equations (5.4) and (5.6) in (5.35), equation (5.36) is found.

1 1 2 2 2 2( ) ( ) ( ) 1 ( )1

M M M M

nI i t I i t D d t I i t D d t

n

(5.36)

Separating the first order terms and applying the Laplace Transform in (5.36),

(5.37) can be determined.

2 2

1

( ) 1 ( )( )

1

M MI d s n D i si s

n

(5.37)

For the Reverse Buck, the value of the magnetizing current can be determined

by (5.38).

132

1 2

1

1

C

M

P nI

V n D

(5.38)

This way, replacing (5.34) and (5.38) in (5.37), the transfer function of the

current I1 by the duty cycle for the Reverse Buck is found and presented by (5.39).

2 2

1 2 2 11

2

1 22

1 1( )

1 1( )

C M

M

P n L s V n D nV Vi s

V n D n L sd s

(5.39)

5.2.5 Reverse Boost

For the Reverse Boost, equation (5.1) can be rewritten as (5.40).

1 22 3 3

(V V )1

1

M

M

d I t nL nV D t D t

dt n

(5.40)


1 22 3 3 3 3

( )(V V )

( ) 1 ( )1

M M

M

d I i tn

L nV D d t D d tdt n

(5.41)


the transfer function of the magnetizing current by the duty cycle of the Reverse

Boost is found and presented by (5.42).

2 1

3

( )

1( )

M

M

n nV Vi s

n L sd s

(5.42)


can be rewritten as (5.43) for the Reverse Boost.

1 311

MnI tI t D t

n

(5.43)


133

1 1 3 3( ) 1 ( )1

M M

nI i t I i t D d t

n

(5.44)



3 3

1

( ) 1 ( )( )

1

M MnI d s n D i si s

n

(5.45)

For the Reverse Boost, the value of the magnetizing current can be determined

by (5.46).

1 3

1

1

C

M

P nI

nV D

(5.46)

Then, replacing (5.42) and (5.46) in (5.45), the transfer function of the current I1

by the duty cycle for the Reverse Boost is found and presented by (5.47).

2 22

3 1 2 11

2

3 13

1 1( )

1 1( )

C M

M

P n L s n D V nV Vi s

D V n L sd s

(5.47)


For the Reverse Buck-Boost, equation (5.1) can be rewritten as (5.48).

2 2 1 21M

M

d I tL nV D t V D t

dt (5.48)


2 2 2 1 2 2

( )

( ) 1 ( )M M

M

d I i t

L nV D d t V D d tdt

(5.49)


the transfer function of the magnetizing current by the duty cycle of the Reverse

Buck-Boost is found and presented by (5.50).

134

2 1

2

( )

( )

M

M

nV Vi s

L sd s

(5.50)


can be rewritten as (5.51) for the Reverse Buck-Boost.

1 21MI t I t D t (5.51)


1 1 2 2( ) 1 ( )M MI i t I i t D d t

(5.52)



1 2 2( ) ( ) 1 ( )M Mi s I d s D i s

(5.53)

For the Reverse Buck-Boost, the value of the magnetizing current can be


1 21

CM

PI

V D

(5.54)


I1 by the duty cycle for the Reverse Buck-Boost is found and presented by (5.55).

2

2 1 2 11

2 12

1( )

1( )

C M

M

P L s D V nV Vi s

D V L sd s

(5.55)


As it is well-known in the literature, different kinds of systems are required to

respect certain operating parameters, and it is function of the control to guarantee

that. However, to make it possible, a relationship, in the form of an equation, between

the parameter to be controlled and the controlled device must be found.

135

Then, in this chapter, all the dynamic analysis of the bidirectional DC-DC

converter with tapped inductor was presented. The dynamic analysis of the system is

a key factor in the system implementation, since it is the dynamic model which will

make possible to find the equations for the control design.

With the equations performed in this chapter, it is possible to design the control

of the converter, since the equations performed are a relationship between the

current to be controlled and the duty cycle from the controlled switches.

136

CHAPTER 6


DESIGN METHODOLOGY AND SIMULATION RESULTS


In order to prove the veracity of the analyses made in chapter 3, in this chapter

a design methodology for the bidirectional DC-DC converter with tapped inductor is

proposed. Then, using the power electronics simulation software PSIM®, the

theoretical results are validated with a digital simulation.

6.2 DESIGN METHODOLOGY

To start a design methodology, the design specifications must be determined.

These specifications are determined to fit the needs of a given application, in the

case of this thesis a Battery/SC HESS for EVs.

As determined in chapter 5 the voltage source V1 corresponds to the battery

bank voltage. In order to determine the value of V1, it is necessary to know the

battery voltage levels in some commercial vehicles, as presented in Table 6.1

Table 6.1 Battery bank in the traction system of commercial EVs and HEVs

Vehicle/Year Battery Type Battery Voltage

HEV Toyota Prius 3rd

generation NiMH 201.6 V

HEV Toyota Camry 2012 NiMH 244.8 V

HEV Ford Fusion 2012 NiMH 275 V

EV Honda Fit 2013 Li-ion 331 V

EV Nissan Leaf 2012 Li-ion 360 V

EV BMW i3 2013 Li-ion 360 V


Analyzing the values presented in Table 6.1, it was chosen a value of 300 V for

the voltage source V1.

137

As this research is a partnership between UTFPR-PG and Concordia

University, to determine the value of the voltage source V2 (SC side) was considered

the availability of SCs in the P. D. Ziogas Power Electronics Laboratory at Concordia

University. Considering the availability of two 48 V SCs at Concordia University and

thinking in a future implementation using those SCs, it was decided to use the value

of 96 V for the voltage source V2.

The rated power PC of the converter was determined in 1000 W due to some

limitations of implementation, such as availability of components for the experimental

setup in the UTFPR-PG Research Center.

About the switching frequency of the converter, the first idea of this project was

the implementation of the converter using the Real-Time Interface (RTI) DSPACE®

for its control, and then the switching frequency fs was determined in 20 kHz

(maximum switching frequency to a good performance of the DSPACE®). Later, it

was decided to change the DSPACE® for a Digital Signal Processor (DSP), but the

switching frequency was maintained the same.

To determine the value of the turn ratio n of the converter, it was considered the

value of the duty cycle to the maximum efficiency of the converter. As it is well-known

that Buck-Boost converters present the maximum efficiency when operating with a

duty cycle of 0.5, rewriting equation (3.32) and applying this concept, it is possible to

find the turn ratio n for the maximum efficiency of the converter.

1 1 2

2 1

300 0.5 961.125

1 96 1 0.5

V D Vn

V D

(6.1)

However, it was decided to sacrifice a bit the efficiency of the converter and

reduce the turn ratio n to 1, mainly to facilitate the building of the tapped inductor,

since with a turn ratio of 1 the turns of the inductor can be made together.

Finally, due to the availability of cores and wires in the UTFPR Research Center

for the building of the tapped inductor, it was determined a magnetizing current ripple

of 35%.

In Table 6.2 the design specifications determined in this section are

summarized.

138

Table 6.2 Design specifications for the bidirectional DC-DC converter with tapped inductor

Specification Symbol Value

Voltage Source 1 V1 300 V


Rated Power PC 1000 W

Switching Frequency fs 20 kHz

Turn ratio n 1

Magnetizing Current Ripple

∆IM 35%


6.2.1 Sizing of Components

Considering the values determined in Table 6.2, the bidirectional DC-DC

converter with tapped inductor can operate with 4 of the 6 operating modes: Buck

and Buck-Boost in the Forward mode; Boost and Buck-Boost in the Reverse mode.

Nevertheless, it would be unfeasible to make a sizing of components for each mode

since it would remove one of the main features of this converter, its versatility.

Taking this into account, to the sizing of components it was decided to use the

Forward Buck mode. In equation (6.2), the duty cycle of switch S1 for this mode that

fits the design specifications is determined.

2

1

1 2

1 96 1 10.4848

300 1 96

V nD

V nV

(6.2)

6.2.1.1 Magnetizing inductance LM

With the design specifications determined in Table 6.1 and the value found by

(6.2), the value of the magnetizing inductance LM for the correct working of the

converter can be determined. For this, the value of the average magnetizing current

must be calculated first, as given by (6.3):

_

1 1

1 1000 1 113.75A

1 300 0.4848

C

M AVG

P nI

nDV

(6.3)

139

Then, based on equation (3.37), the value of the magnetizing inductance LM is

determined.

1 2 1

_

1 300 96 0.4848513.711 H

20k 13.75 35% 1 11M

S M AVG M

n V V DL

f I I n

(6.4)

6.2.1.2 Capacitors C1 and C2

After a brief review in the literature and in other works employing bidirectional

DC-DC converters in HESS, it was decided to use the value of 40 µF for the

capacitances C1 and C2 in parallel with the voltage sources. Following, in Table 6.3

the values determined in this section are summarized.

Table 6.3 Components sizing for the bidirectional DC-DC converter with tapped inductor


Magnetizing Inductance LM 513.711 µH

Decoupling Capacitors C1 , C2 40 µF


6.3 CONTROL DESIGN

Aiming to design a controller with no error in steady state, it was determined the

use of a PI controller since a PID controller, mainly because of the derivative gain,

would present more sensibility to noises in the input signal in a experimental

implementation (OGATA, K., 2003). In Figure 6.1, the block diagram considered for

the control design is presented.

Current Sensor

+-CPI(s)

G(s)

i1_Refi1(s)/d1(s)

i1

PI Controller

1st Order Filter

1 + RCs

1

Figure 6.1 Block diagram for the control design


140

Replacing the values determined by Tables 6.1 and 6.2 in (5.15), the transfer

function of the converter working as the Forward Buck is found and given by (6.5).

41

1

2.055 2.7927 10

0.2989

i s s

d s s

(6.5)

In Figure 6.2, the Bode Diagram of the transfer function presented in (6.5) is

shown.

102

103

104

105

106

-90

-60

-30

0P.M.: inf

Freq: NaN

Frequency (rad/s)

Ph

ase

(d

eg)

15

20

25

30

35

40

45

50

55

G.M.: inf

Freq: NaN

Stable loop

Bode Diagram

Ma

gn

itu

de

(d

B)

Figure 6.2 Bode diagram of the uncompensated system


Using the SISOTOOL function of the software MatLab®, the controller is

designed. The main goal of the control design is to find a controller with a fast settling

time (less than 5 ms) and little overshoot (around 10%) when applied a step in the

input signal. Besides, for the control design the influence of the current sensor can be

disregarded since it will just represent a gain in the system, and this gain can be

compensated later in the DSP programming. For the 1st Order Filter, a resistor of 10

kΩ and a capacitor of 2.2 nF were considered.

In equation (6.6), the transfer function of the PI controller is presented.

0.05 70

PI

sC s

s

(6.6)

Then, in Figure 6.3, the step response of the compensated system is presented.

Analyzing the Figure 6.3, it was possible to conclude that the controller was designed

in a satisfactory way, where the settling was 2.35 ms and the overshoot 12.1%.

141

Time (ms)

Am

plit

ud

e (

A)

0 0.5 1 1.5 2 2.5 3 3.5

1

1.33

1.67

2

2.33

2.67

3

3.33

3.66

4

Figure 6.3 Step response of the compensated system


-20

0

20

40

60

80

100

120

Ma

gn

itu

de

(d

B)

101

102

103

104

105

106

-180

-135

-90

-45

0

Ph

ase

(d

eg

)

Bode Diagram

Frequency (rad/s)

Figure 6.4 Bode diagram of the compensated system


6.4 SIMULATION RESULTS

Before starting the simulation of each mode, it is important first to check if the

control is working, and if the equation (6.5) used for the control design was correctly

developed. First, the circuits implemented in PSIM® for the simulation are presented

in Figures 6.5 and 6.6, where all the elements used are ideal elements.

142

V2

Figure 6.5 Circuit implemented in PSIM®: Power schematic


Figure 6.6 Circuit implemented in PSIM®: Control schematic


Applying a step in the current reference for both the converter and the transfer

function determined by (6.5), it is possible to see in Figure 6.7 the step response of

each one. Moreover, knowing that the current I1 is a pulsed current, for its better view

a first order filter is used in the simulations.

1

1.5

2

2.5

3

3.5

4

4.5I1_CONVERTER_FILTER

I1_TF_BUCK_BOOST

I1_CONVERTER_FILTER I1_TF_BUCK_BOOST

Figure 6.7 Step response: Comparison Converter x Transfer function


143

Analyzing the Figure 6.7, it is possible to see that both the converter and the

transfer function presented the same response for a positive current step of 50%, fact

that shows that equation (6.5) was correct. Another point to be highlighted from

Figure 6.7 is the high similarity with Figure 6.3, showing the accuracy of the control

design.

6.4.1 Forward Buck

Following, the simulation results for the Forward Buck are presented. First, the

voltage across the switches is presented in Figure 6.8, where the switch S1 presented

a maximum value of 396 V whereas the switch S3 presented a value of 198 V as

maximum voltage.

0

100

200

300

400

VS1

0

-50

50

100

150

200

VS3

Figure 6.8 Forward Buck: Simulated voltage waveforms in the switches S1 and S3


In Figure 6.9, the voltage in each turn of the tapped inductor is presented. As

expected, because of the unitary turn ratio, both turns presented the same voltage in

each operating stage: 102 V in the first and -96 V in the second.

Already in Figure 6.10, the simulated voltage waveforms in the magnetizing

inductance LM are presented. The magnetizing voltage presented a value of 102 V in

the first operating stage and -96 V in the second. The magnetizing current presented

an average value of 13.743 A, with 16.148 A as maximum value and 11.334 A as

minimum.

144

0

-50

-100

50

100

150

VLT1

0

-50

-100

50

100

150

VLT2

Figure 6.9 Forward Buck: Simulated voltage waveforms in the tapped inductor


0

-50

-100

50

100

150

VLM

11

12

13

14

15

16

17

IM

Figure 6.10 Forward Buck: Simulated waveforms in the magnetizing inductance LM


From Figure 6.11 to Figure 6.13, the simulated current waveform for each

switch of the converter is presented.

In Figure 6.11 the current through switch S1 presented a RMS value of 4.783 A.

About the current through the switch S2, the simulated RMS value was 11.052 A

whereas the switch S3 presented a RMS value of 9.962 A in the simulation.

145

0

2

4

6

8

10

IS1

Figure 6.11 Forward Buck: Simulated current waveform in switch S1


-18

-16

-14

-12

-10

-8

-6

-4

-2

IS2



0

-5

-10

-15

-20

IS3



146

Next, in Figure 6.14, the current waveforms in the voltage sources are shown.

The current I1 presented a simulated average value of 3.327 A and for the current I2

this value was -10.415 A.

0

2

4

6

8

10

I1

-18

-16

-14

-12

-10

-8

-6

-4

-2

I2

Figure 6.14 Forward Buck: Simulated waveforms of the currents I1 and I2


To see the current control on the converter, Figure 6.15 is presented. Applying

steps in the current reference from 50% to 100% of the rated power (from 1.665 A to

3.333 A), and vice versa, it is possible to see the action of the control taking the

current from one value to another.

0.1 0.2 0.3 0.4 0.5 0.6 0.7Time (s)

0

1

2

3

4

5I1_CONVERTER_FILTER

I1_CONVERTER_FILTER

I1_REF

I1_REF

Figure 6.15 Forward Buck: Current control


147

Following, a comparison between the theoretical and the simulated values for

the Forward Buck is presented in Table 6.4. This comparison is important to check if

both theoretical analyses and simulation were performed correctly and, in some

cases, to help to find and solve a possible problem.

Table 6.4 Forward Buck: Comparison Theoretical x Simulated

Symbol Theoretical Simulated Error (%)

VS1_MAX 396 V 396 V -

VS3_MAX 198 V 198 V -

VLT1_1st 102 V 102 V -

VLT1_2nd -96 V -96 V -

VLT2_1st 102 V 102 V -

VLT2_2nd -96 V -96 V -

VLM_1st 102 V 102 V -

VLM_2nd -96 V -96 V -

IM1 11.343 A 11.334 A -0.079

IM2 16.157 A 16.148 A -0.055

IM_AVG 13.75 A 13.743 A -0.050

I1_AVG 3.333 A 3.327 A -0.180

I2_AVG -10.417 A -10.415 A +0.019

IS1_RMS 4.812 A 4.783 A -0.602

IS2_RMS 11.024 A 11.052 A +0.253

IS3_RMS 9.919 A 9.962A +0.443



Just as for the Forward Buck, the simulation results for the Forward Buck-Boost

mode are presented next.

In Figure 6.16, the maximum voltage across the switches is presented, where

both switches presented the maximum value of 396 V.

148

0

100

200

300

400

VS1

0

-100

100

200

300

400

VS2

Figure 6.16 Forward Buck-Boost: Simulated voltage waveforms in the switches S1 and S2


In Figure 6.17, the voltage in each turn of the tapped inductor is presented. Both

turns presented the value of 300 V in the first operating stage and -96 V in the

second.

0

-100

100

200

300

VLT1

0

-100

100

200

300

VLT2

Figure 6.17 Forward Buck-Boost: Simulated voltage waveforms in the tapped inductor


The magnetizing inductance waveforms for the Forward Buck-Boost are

presented in Figure 6.18. The magnetizing voltage presented a value of 300 V in the

first operating stage and -96 V in the second whereas the magnetizing current

presented an average value of 13.75 A, with 17.247 A as maximum value and 10.193

A as minimum.

149

0

-100

100

200

300

VLM

10

12

14

16

18

ILM

Figure 6.18 Forward Buck-Boost: Simulated waveforms in the magnetizing inductance LM


The current through the switch S1 is shown by Figure 6.19, where the simulated

RMS value of this current was 6.818 A.

0

5

10

15

20

IS1

Figure 6.19 Forward Buck-Boost: Simulated current waveform in switch S1


The currents through the switches S2 and S3 are presented, respectively, by

Figures 6.20 and 6.21. The simulated RMS values of the currents were 12.100 A for

switch S2 and 13.898 A for switch S3.

150

0

-5

-10

-15

-20

IS2



0

-10

-20

10

20

IS3



In Figure 6.22, the simulated current waveforms through the voltage sources

are presented.

The current I1 presented an average value of 3.305 A and the current I2 an

average value of -10.432 A.

151

0

5

10

15

20

I1

0

-5

-10

-15

-20

5

I2

Figure 6.22 Forward Buck-Boost: Simulated waveforms of the currents I1 and I2


Then, in Figure 6.23 it is possible to see the action of the control for the Forward

Buck-Boost mode. As can be seen in Figure 6.23, even the control being designed

for a different operation mode, the control worked well, with no overshoot and

responding fast to a reference change.

0.1 0.2 0.3 0.4 0.5 0.6 0.7Time (s)

0

1

2

3

4

5I1_CONVERTER_FILTER I1_REF

I1_REF

I1_CONVERTER_FILTER

Figure 6.23 Forward Buck-Boost: Current control


Finally, the comparison between the theoretical values and the simulated values

for the Forward Buck-Boost is presented in Table 6.5.

152

Table 6.5 Forward Buck-Boost: Comparison Theoretical x Simulated


VS1_MAX 396 V 396 V -

VS2_MAX 396 V 396 V -

VLT1_1st 300 V 300 V -

VLT1_2nd -96 V -96 V -

VLT2_1st 300 V 300 V -

VLT2_2nd -96 V -96 V -

VLM_1st 300 V 300 V -

VLM_2nd -96 V -96 V -

IM1 10.211 A 10.193 A -0.176

IM2 17.289 A 17.247 A -0.242

IM_AVG 13.75 A 13.738 A -0.087

I1_AVG 3.333 A 3.305 A -0.840

I2_AVG -10.417 A -10.432 A -0.143

IS1_RMS 6.844 A 6.818 A -0.379

IS2_RMS 12.099 A 12.100 A +0.008

IS3_RMS 13.901 A 13.898 A -0.021


6.4.3 Reverse Boost

Following, the simulation results for the Reverse Boost are presented. First, the

voltage across the switches is presented in Figure 6.24, where the switch S1

presented a maximum value of 396 V and the switch S3 a value of 198 V.

In Figure 6.25, the voltage in each turn of the tapped inductor is shown. Both

turns presented the same voltage in each operating stage: -96 V in the first and 102

V in the second.

Already in Figure 6.26, the simulated voltage waveforms in the magnetizing

inductance LM are presented. The magnetizing voltage presented a value of -96 V in

the first operating stage and 102 V in the second. The magnetizing current presented

average value of -13.748 A, with -11.340 A as maximum and -16.150 A as minimum.

153

0

-100

100

200

300

400

VS1

0

50

100

150

200

VS3

Figure 6.24 Reverse Boost: Simulated voltage waveforms in the switches S1 and S3


0

-50

-100

50

100

150

VLT1

0

-50

-100

50

100

150

VLT2

Figure 6.25 Reverse Boost: Simulated voltage waveforms in the tapped inductor


0

-50

-100

50

100

150

VLM

-17

-16

-15

-14

-13

-12

-11

-10

ILM

Figure 6.26 Reverse Boost: Simulated waveforms in the magnetizing inductance LM


154

The simulated current waveforms for the switches S1 and S2 are presented,

respectively, by Figures 6.27 and 6.28.

0

-2

-4

-6

-8

-10

IS1

Figure 6.27 Reverse Boost: Simulated current waveform in switch S1


4

6

8

10

12

14

16

18

IS2



The switch S1 presented a simulated RMS value of 4.803 A whereas in the

switch S2 the RMS current in the simulation was 11.032 A.

In Figure 6.29, the current in switch S3 is shown. This current presented a

simulated RMS value of 9.932 A.

155

0

5

10

15

20

IS3



Next, in Figure 6.30, the current waveforms in the voltage sources are shown.

The current I1 presented a simulated average value of -3.328 A and for the current I2

this value was 10.420 A.

0

-2

-4

-6

-8

-10

2

I1

4

6

8

10

12

14

16

18

I2

Figure 6.30 Reverse Boost: Simulated waveforms of the currents I1 and I2


Then, in Figure 6.31 the current control for the Reverse Boost is presented.

Now, as the converter is working in the Reverse mode, negative values are set in the

current reference, but in the same way as the Forward mode, from 50% to 100% of

the rated power (-1.665 A to -3.333A). Again, the control showed a good working,

only presenting an overshoot a way higher than in the Forward mode, but nothing to

concern in the converter operation.

156

0.1 0.2 0.3 0.4 0.5 0.6 0.7Time (s)

0

-1

-2

-3

-4

-5

I1_CONVERTER_FILTER I1_REF

I1_CONVERTER_FILTER

I1_REF

Figure 6.31 Reverse Boost: Current control


Then, the comparison between the theoretical values and the simulated values

for the Reverse Boost is presented in Table 6.6.

Table 6.6 Reverse Boost: Comparison Theoretical x Simulated


VS1_MAX 396 V 396 V -

VS3_MAX 198 V 198 V -

VLT1_1st -96 V -96 V -

VLT1_2nd 102 V 102 V -

VLT2_1st -96 V -96 V -

VLT2_2nd 102 V 102 V -

VLM_1st -96 V -96 V -

VLM_2nd 102 V 102 V -

IM1 -11.343 A -11.340 A +0.026

IM2 -16.157 A -16.152 A +0.030

IM_AVG -13.75 A -13.748 A +0.014

I1_AVG -3.333 A -3.328 A +0.150

I2_AVG 10.417 A 10.420 A +0.028

IS1_RMS 4.812 A 4.803 A -0.187

IS2_RMS 11.024 A 11.032 A +0.072

IS3_RMS 9.919 A 9.932 A +0.131


157


Following, the simulation results for the last operation mode, the Reverse Buck-

Boost mode, are going to be presented. First, the voltage across the switches S1 and

S2 are presented by Figure 6.32.

The simulated maximum voltage for the switch S1 was 396 V as soon as for the

switch S2.

0

-100

100

200

300

400

VS1

0

100

200

300

400

VS2

Figure 6.32 Reverse Buck-Boost: Simulated voltage waveforms in the switches S1 and S2


In Figure 6.33, the voltage in each turn of the tapped inductor is shown. Both

turns presented the same voltage in each operating stage: -96 V in the first and 300

V in the second

0

-100

100

200

300

400

VLT1

0

-100

100

200

300

400

VLT2

Figure 6.33 Reverse Buck-Boost: Simulated voltage waveforms in the tapped inductor


158

The waveforms of the Reverse Buck-Boost are presented in Figure 6.34. The

magnetizing voltage presented a value of -96 V in the first operating stage and 300 V

in the second. About the magnetizing current, this current presented an average

value of -13.75 A, with -10.207 A as maximum value and -17.261 A as minimum.

0

-100

100

200

300

400

VLM

-18

-16

-14

-12

-10

-8

ILM

Figure 6.34 Reverse Buck-Boost: Simulated waveforms in the magnetizing inductance LM


The current in switch S1 for the Reverse Buck-Boost mode is shown in Figure

6.35 where the simulated RMS value was 6.864 A.

0

-5

-10

-15

-20

IS1

Figure 6.35 Reverse Buck-Boost: Simulated current waveform in switch S1


The currents through the switches S2 and S3 are presented, respectively, by

Figures 6.36 and 6.37. The simulated RMS values of the currents were 12.084 A for

switch S2 and 13.897 A for switch S3. In Figure 6.38 the current I1 presented a

simulated average value of -3.353 A and for the current I2 this value was 10.397 A.

159

0

5

10

15

20

IS2



0

-10

-20

10

20

IS3



0

-5

-10

-15

-20

5

I1

0

5

10

15

20

I2

Figure 6.38 Reverse Buck-Boost: Simulated waveforms of the currents I1 and I2


160

Then, in Figure 6.39 the action of the control for the Reverse Buck-Boost is

presented.

0.1 0.2 0.3 0.4 0.5 0.6 0.7Time (s)

0

-1

-2

-3

-4

-5

-6


I1_REF

I1_CONVERTER_FILTER

Figure 6.39 Reverse Buck-Boost: Current control


As can be seen in Figure 6.39, as well as for all the previous modes presented,

the control worked well, presenting fast response to a current reference change.

Nevertheless, even the converter presenting a higher overshoot if compared with the

other modes, in the experimental implementation it is reduced, mainly because the

simulation is done with ideal elements and in the practical implementation the

intrinsic resistances of the components lead the system to a more damped response.

Finally, the comparison between the theoretical values and the simulated values

for the Reverse Buck-Boost is presented in Table 6.7.

Table 6.7 Reverse Buck-Boost: Comparison Theoretical x Simulated (to be continued)


VS1_MAX 396 V 396 V -

VS2_MAX 396 V 396 V -

VLT1_1st -96 V -96 V -

VLT1_2nd 300 V 300 V -

VLT2_1st -96 V -96 V -

VLT2_2nd 300 V 300 V -

VLM_1st -96 V -96 V -

VLM_2nd 300 V 300 V -

161

Table 6.7 Reverse Buck-Boost: Comparison Theoretical x Simulated (conclusion)


IM1 -10.211 A -10.207 A +0.039

IM2 -17.289 A -17.261 A +0.161

IM_AVG -13.75 A -13.746 A +0.029

I1_AVG -3.333 A -3.353 A -0.600

I2_AVG 10.417 A 10.397 A -0.191

IS1_RMS 6.844 A 6.864 A +0.292

IS2_RMS 12.099 A 12.084 A -0.123

IS3_RMS 13.901 A 13.897 A -0.028


6.5 UNIFIED CONTROLLER

Analyzing the equations (5.15) and (5.47), respectively the equations related to

the current control of the current I1 for the Forward Buck and the Reverse Boost, it is

possible to see that both equations are equal, just with the equation (5.47) presenting

a negative value. This happens because the mentioned operation modes present the

same operating stages (but reverted between them) and because in the equivalent

circuit of the converter was determined that for the Forward operation the current I1

would be positive and, consequently, the current I1 for the Reverse mode would be

negative. The same can be seen between the equations from the Forward Buck-

Boost and the Reverse Buck-Boost, respectively (5.31) and (5.55).

Then, taking this into account, there is no need to implement one control for

each operation, and a unified controller may be used. In this concept, the same

controller will work for both operations, where a positive reference will represent the

converter working in the Forward mode, and a negative reference in the Reverse

mode.

Following, to check if the unified controller is working, steps from a positive

value to a negative value are given in the current reference. The current steps are

given from 3.333 A to -3.333 A, which represents the current in the rated power for

162

each operation mode, Forward and Reverse. The results are shown by Figures 6.40

and 6.41.

0.1 0.2 0.3 0.4 0.5 0.6 0.7Time (s)

0

-2

-4

-6

2

4

6


I1_REF

I1_CONVERTER_FILTER

Figure 6.40 Unified controller: Forward Buck to Reverse Boost


0.1 0.2 0.3 0.4 0.5 0.6 0.7Time (s)

0

-5

5


I1_REF

I1_CONVERTER_FILTER

Figure 6.41 Unified controller: Forward Buck-Boost to Reverse Buck-Boost


Based on Figures 6.40 and 6.41, it is possible to see that the unified controller

worked well, with no problems in the operation change.

163


In this chapter, the design methodology of the bidirectional DC-DC converter

with tapped inductor was presented. Also, in order to validate the theoretical analysis

from chapter 3, a digital simulation using the power electronics simulation software

PSIM® was performed.

Analyzing the simulation results presented in chapter 6 and the values provided

by Tables 6.4, 6.5, 6.6 and 6.7, it was possible to conclude that both theoretical

steady state analysis and simulations were performed correctly, since all the

theoretical and simulated values presented a high proximity, where the maximum

error found was 0.8%, a value considered insignificant for engineering projects.

Talking specifically about the working modes, the Forward Buck-Boost/Reverse

Buck-Boost presented higher RMS currents values if compared to the Forward

Buck/Reverse Boost, fact that is going to impact in the converter efficiency in these

modes.

About the control of the converter, it was possible to see that the designed

controller meet the design specifications, working well for all the simulated modes,

just presenting a higher overshoot in the Forward and Reverse Buck-Boost.

However, this is not an issue to concern, since in an experimental implementation the

converter will present a more damped response due to the parasitic elements of the

experimental setup.

164

CHAPTER 7

BIDIRECTIONAL ZVS BUCK-BOOST DC-DC CONVERTER:

DESIGN METHODOLOGY AND SIMULATION RESULTS


In order to prove the veracity of the analyses made in chapter 4, in this chapter

a design methodology for the bidirectional ZVS Buck-Boost DC-DC converter is

proposed. Then, using the power electronics simulation software PSIM®, the

theoretical results are validated with a digital simulation.

7.2 DESIGN METHODOLOGY

In Table 7.1, the specifications for the design of the proposed converter are

presented.

Table 7.1 Design specifications for the bidirectional ZVS Buck-Boost DC-DC converter




Rated Power PC 1000 W

Switching Frequency fs 100 kHz


∆IM 40%


Considering that both converters presented in this work are a solution for the

same application, the values of the voltage sources V1 and V2 and the rated power

PC are the same that were used in chapter 6.

Nevertheless, for being a soft-switching converter, the switching frequency fs for

the bidirectional ZVS Buck-Boost DC-DC converter is raised to 100 kHz. Also,

thinking in an experimental implementation and mainly because of the availability of

cores and wires in the UTFPR-PG Research Center, the value of the magnetizing

current ripple is readjusted to 40%.

165

7.2.1 Sizing of Components

With the values determined in Table 7.1, it is possible to calculate the values of

the elements that fit the project needs. However, first the duty cycle values from each

switch must be known.

Based on equation (4.40), the value of the duty cycle D1 is given by (7.1)

21

1 2

960.2424

396

VD

V V

(7.1)

As the switches S1 and S2 work complementarily, the duty cycle D2 can be


2 11 1 0.2424 0.7576D D (7.2)

7.2.1.1 Magnetizing inductance LM

With the design specifications determined in Table 7.1 and the values provided

by (7.1) and (7.2), the value of the magnetizing inductance LM for the correct working

of the converter can be determined. For this, the value of the average magnetizing

current must be calculated first.

_

1 1

100013.75 A

300 0.2424C

M AVG

PI

V D

(7.3)

Then, based on equation (4.46), the value of the magnetizing inductance LM can

be calculated by (7.4).

1 1

_

300 0.2424132.231 H

13.75 40% 100M

M AVG M S

V DL

kI I f

(7.4)

7.2.1.2 Auxiliary inductance LL and number of turns ratio n

As mentioned in chapter 4, the ZVS operation is directly related to the correct

choice of the inductance LL.

166

To determine the value of this inductance, there are two possible approaches:

Setting a randomly value for the turn ratio n and with equation (4.56) find the

maximum value for the inductance LL that allows the ZVS operation;

Setting a randomly value for the inductance LL and with the manipulation of

equation (4.56) find a maximum value for the turn ratio n that allows the ZVS

operation.

In this work, the second one was chosen and a value of 6 µH was determined

for the auxiliary inductance LL.

6LL H (7.5)

Determined the value of the inductance LL, the next step is to determine the

value of the number of turns ratio n. Nevertheless, it is important first to observe the

influence of this parameter on the switches currents.

Figures 7.1 and 7.2 present, respectively, the behavior of the currents IS1_RMS

and IS2_RMS in function of n.

0 0.5 1 1.5 2 2.5 35

9.5

14

18.5

23

27.5

32

36.5

41

45.5

50

IS1RMS n( )

n

Figure 7.1 RMS current in switch S1 for different values of n


167

0 0.5 1 1.5 2 2.5 30

5

10

15

20

25

30

35

40

45

50

IS2RMS n( )

n

Figure 7.2 RMS current in switch S2 for different values of n


As can be seen in Figures 7.1 and 7.2, the range of values that present the

lowest values of RMS current is from 0.5 to 1.5. Any value outside this range will

represent a significant increase of the RMS currents and, consequently, the losses in

the converter are going to be increased.

Considering that and manipulating the equation (4.56), it is possible to find the

maximum value of n that guarantee the ZVS operation in the converter. It can be

expressed by (7.6).

2 2

1 1

max 2 2

1 1

21

L C S M

M

L P f L V Dn

V D L

(7.6)

Replacing the values determined earlier in (7.6), the maximum value of n for the

ZVS operation is found:

max 0.611n (7.7)

Then, re-analyzing the graphs presented by Figures 7.1 and 7.2, it was

concluded that the value of 0.54 for the turn ration would be the better choice in

terms of operation.

0.54n (7.8)

168

7.2.1.3 Capacitors Cf1 and Cf2

For the capacitors Cf1 and Cf2 were determined the values of 100 µF.

In Table 7.2, the values determined by section 7.2 are summarized.

Table 7.2 Components sizing for the bidirectional ZVS Buck-Boost DC-DC converter


Magnetizing Inductance LM 132.231 µH

Auxiliary Inductance LL 6 µH

Turn Ratio n 0.54

Capacitive Filters Cf1 , Cf2 100 µF


7.3 SIMULATION RESULTS

Determined the design specifications and with the sizing of components, the

simulation can be performed. All the results presented are obtained simulating the

converter with ideal elements.

7.3.1 Forward Mode

In Figure 7.1, the circuit implemented on PSIM® for the simulation of the

Forward mode is presented.

Figure 7.3 Forward mode: Schematic of simulation


169

As the simulation is performed in open loop, it is impossible to simulate the

converter with two voltage sources. Taking this into account, for the Forward mode

the voltage source V2 is replaced by a parallel RC load in order to emulate a voltage

source behavior in this side of energy, where the value of the resistance is

determined by equation (7.9) whereas for the capacitance is set a value of 100 µF.

2 2

2 969.216

1000C

VR

P (7.9)

In Figure 7.4, the voltage across the RC load is presented. The voltage

presented the expected value of 96 V, making the simulation possible.

60

80

100

120

V2

Figure 7.4 Forward mode: Voltage across the RC load


In Figure 7.5, the voltage in each turn of the transformer is presented. The

voltage VLT1 in the primary presented a value of 300 V in the first operating stage and

-96.057 V in the second stage whereas the voltage VLT2 on the secondary presented

the values of 162 V and -51.871 V.

170

0

-100

100

200

300

VLT1

0

-50

-100

50

100

150

200

VLT2

Figure 7.5 Forward mode: Simulated Voltage waveform in each turn of the transformer


The magnetizing inductance waveforms are presented in Figure 7.6. The

magnetizing voltage presented values of 300 V and -96.057 V for each operating

stage. The magnetizing current presented average value of 13.75 A, with 11 A as

minimum and 16.482 A as maximum value.

0

-100

100

200

300

VLM

11

12

13

14

15

16

17

ILM

Figure 7.6 Forward mode: Simulated waveforms in the magnetizing inductance LM


The simulated waveforms of the auxiliary inductance LL are presented in Figure

7.7. The voltage across this inductance presented values of -138.226 V in the first

operating stage and 44.033 V in the second. The current in this inductance presented

a value of 27.916 A.

171

0

-50

-100

-150

50

VLL

0

-10

-20

-30

10

20

30

ILL

Figure 7.7 Forward mode: Simulated waveforms in the auxiliary inductance LL


In Figure 7.8 the simulated waveforms for the switch S1 are presented, where

this switch presented a value of 396.057 V as maximum voltage. About its currents,

the simulations presented values of 3.330 A and 8.085 A for its average and RMS

current. Also, the current IS1 presented a maximum value of 29.021 A and a minimum

value of -1.826 A, ensuring the soft-switching as highlighted in Figure 7.8.

0

-100

100

200

300

400

VS1

0

-5

5

10

15

20

25

30

IS1

ZVS

Figure 7.8 Forward mode: Simulated waveforms in the switch S1


For the switch S2, the simulated waveforms are presented in Figure 7.9. This

switch presented a simulated value of 396.054 V for its maximum voltage. Its current

presented a maximum value of 1.841 A and a minimum value of -29.232 A whereas

the average and RMS values were, respectively, -10.380 A and 14.286 A.

172

ZVS

0

-100

100

200

300

400

VS2

0

-5

-10

-15

-20

-25

-30

5

IS2

Figure 7.9 Forward mode: Simulated waveforms in the switch S2


Finally, the currents in the voltage sources are presented in Figure 7.10.

0

-5

-10

-15

5

10

15

I1

0

-5

-10

-15

5

10

I2

Figure 7.10 Forward mode: Simulated current waveforms in the voltage sources


The current I1 presented a simulated average value of 3.336 A whereas the

current I2 presented an average value of -10.417 A.

After the simulations of the Forward mode, in Table 7.3 a comparison between

the theoretical and the simulated values is presented.

173

Table 7.3 Forward mode: Comparison Theoretical x Simulated


V2 96 V 96 V -

VLT1_1st 300 V 300 V -

VLT1_2nd -96 V -96.057 V -0.059

VLT2_1st 162 V 162 V -

VLT2_2nd -51.85 V -51.871 V -0.059

VLM_1st 300 V 300 V -

VLM_2nd -96 V -96.057 V -0.059

IM1 11 A 11 A -

IM2 16.5 A 16.482 A -0.109

IM_AVG 13.75 A 13.75 A -

VLL_1st -138 V -138.226 V -0.163

VLL_2st 44.16 V 44.033 V -0.288

ILL 27.879 A 27.916 A +0.132

VS1_MAX 396 V 396.057 V +0.014

IS1_MIN -1.824 A -1.826 A -0.109

IS1_MAX 29.324 A 29.021 A -1.033

IS1_AVG 3.333 A 3.330 A -0.090

IS1_RMS 8.089 A 8.085 A -0.049

VS2_MAX 396 V 396.054 V +0.013

IS2_MIN -29.324 A -29.232 A +0.313

IS2_MAX 1.824 A 1.841 A +0.932

IS2_AVG -10.417 A -10.380 A +0.355

IS2_RMS 14.3 A 14.286 A -0.097

I1_AVG 3.333 A 3.336 A +0.090

I2_AVG -10.417 A -10.417 A -


174

7.3.2 Reverse Mode

In Figure 7.11, the circuit implemented on PSIM® for the simulation of the

Reverse mode is presented.

Figure 7.11 Reverse mode: Schematic of simulation


In the same way as the Forward mode, one of the voltage sources must be

replaced by a parallel RC load to make the simulation possible. In the Reverse mode,

the voltage source 1 is replaced by a 90 Ω resistance and the same 100 µF

capacitance.

In Figure 7.12, the voltage across the RC load is presented. The voltage

presented the expected value of 300 V, making the simulation possible.

280

290

300

310

320

V1

Figure 7.12 Reverse mode: Voltage across the RC load


175

The voltage in each turn of the transformer for the Reverse mode is presented

in Figure 7.13. The voltage VLT1 in the primary presented a value of -96 V in the first

operating stage and 300.123 V in the second stage whereas the voltage VLT2 on the

secondary presented the values of -51.839 V and 162.066 V.

0

-100

100

200

300

400

VLT1

0

-50

-100

50

100

150

200

VLT2

Figure 7.13 Reverse mode: Simulated Voltage waveform in each turn of the transformer


In Figure 7.14, the simulated waveforms in the magnetizing inductance LM for

the Reverse mode are presented.

0

-100

100

200

300

400

VLM

-17

-16

-15

-14

-13

-12

-11

-10

ILM

Figure 7.14 Reverse mode: Simulated waveforms in the magnetizing inductance LM


The magnetizing voltage presented values of -96 V and 300.120 V for each

operating stage. The magnetizing current presented average value of -13.758 A, with

-11.051 A as maximum and -16.496 A as minimum value.

176

The simulated waveforms of the auxiliary inductance LL are presented in Figure

7.15. The voltage across this inductance presented values of 43.962 V in the first

operating stage and -138.168 V in the second. The current in this inductance

presented a value of 27.832 A.

0

-50

-100

-150

50

VLL

0

-10

-20

-30

10

20

30

ILL

Figure 7.15 Reverse mode: Simulated waveforms in the auxiliary inductance LL


The simulated waveforms for the switch S1 are presented in Figure 7.16. This

switch presented maximum voltage of 396.175 V. The current IS1 in the Reverse

mode presented average value of -3.326 A and RMS value of 8.098 A, with a

minimum current of -29.071 A and a maximum current of 1.832 A.

0

-100

100

200

300

400

VS1

0

-5

-10

-15

-20

-25

-30

5

IS1

ZVS

Figure 7.16 Reverse mode: Simulated waveforms in the switch S1


177

For the switch S2 the simulated waveforms are presented in Figure 7.17. This

switch presented simulated maximum voltage of 396.123 V. Its current presented a

maximum value of 29.272 A and a minimum value of -1.830 A whereas the average

and RMS values were, respectively, 10.410 A and 14.308 A.

ZVS

0

-100

100

200

300

400

VS2

0

-5

5

10

15

20

25

30

IS2

Figure 7.17 Reverse mode: Simulated waveforms in the switch S2


Finally, the currents in the voltage sources are presented in Figure 7.18. The

current I1 presented a simulated average value of -3.344 A whereas the current I2

presented an average value of 10.438 A.

0

-5

-10

-15

5

10

I1

0

-5

-10

5

10

15

20

I2

Figure 7.18 Reverse mode: Simulated current waveforms in the voltage sources


178

Similar to the Forward mode, a comparison between the theoretical and the

simulated values is presented in Table 7.4 for the Reverse mode.

Table 7.4 Reverse mode: Comparison Theoretical x Simulated


V1 300 V 300 V -

VLT1_1st -96 V -96 V -

VLT1_2nd 300 V 300.123 V +0.041

VLT2_1st -51.85 V -51.839 V +0.021

VLT2_2nd 162 V 162.066 V +0.040

VLM_1st -96 V -96 V -

VLM_2nd 300 V 300.120 V +0.040

IM1 -11 A -11.051 A -0.463

IM2 -16.5 A -16.496 A +0.024

IM_AVG -13.75 A -13.758 A -0.058

VLL_1st 44.16 V 43.962 V -0.448

VLL_2st -138 V -138.168 V -0.121

ILL 27.879 A 27.832 A -0.168

VS1_MAX 396 V 396.175 V +0.044

IS1_MIN -29.324 A -29.071 A +0.862

IS1_MAX 1.824 A 1.832 A -0.438

IS1_AVG -3.333 A -3.326 A +0.210

IS1_RMS 8.089 A 8.098 A +0.111

VS2_MAX 396 V 396.123 V +0.031

IS2_MIN -1.824 A -1.830 A -0.328

IS2_MAX 29.324 A 29.272 A -0.177

IS2_AVG 10.417 A 10.410 A -0.067

IS2_RMS 14.3 A 14.308 A +0.055

I1_AVG -3.333 A -3.344 A -0.330

I2_AVG 10.417 A 10.438 A +0.201


179


In this chapter, the design methodology of the bidirectional ZVS Buck-Boost

DC-DC converter was presented. Also, in order to validate the theoretical analysis

from chapter 4, a digital simulation using the power electronics simulation software

PSIM® was performed.

Analyzing the simulation results presented in chapter 7 and the values provided

by Tables 7.3 and 7.4, it was possible to conclude that both theoretical steady state

analysis and simulations were performed correctly, since all the theoretical and

simulated values presented a high proximity, where the maximum error found was

1.033%, a value considered insignificant for engineering projects.

Also, with the ZVS operation the problem related to the reverse recovery

phenomenon of the antiparallel-body diodes from switches is solved and the

converter efficiency is increased, which is essential when thinking in an experimental

implementation.

180

CHAPTER 8


EXPERIMENTAL RESULTS


In this chapter, after all the knowledge provided by the previous chapters, the

experimental prototype of the bidirectional DC-DC converter with tapped inductor is

built. Then, experimental results for the 4 simulated modes in chapter 6 are

presented and discussed.

8.2 EXPERIMENTAL PROTOTYPE

With the values determined and verified by chapter 6, the choice of components

and the design of the tapped inductor may be done. Nevertheless, it is important to

highlight that as the converter can operate in different operating modes, the

requirements considered for the choice of components must attend the worst

scenario of the operations.

8.2.1 Choice of Components

For the choice of the switches to be used, the requirements considered were

their maximum voltage and the maximum current reached in steady state by any

point of the converter. As determined in chapter 6, the maximum voltage across the

switches is 396 V and the maximum current reached in the converter is 17.261 A.

Then, in a first moment, it was decided the use of the MOSFET SPW47N60C3 (650

V / 47 A).

However, after the first experimental tests, due to the high overvoltage in the

switches caused by the influence of the leakage inductance of the tapper inductor, it

was concluded to be unfeasible the use of the mentioned MOSFETs. Then, for

181

presenting a higher maximum voltage and a better antiparallel body-diode, the IGBT

IRGP20B120UD-EP (1200 V/ 40 A) was implemented in the experimental prototype.

Also, three 10 kΩ/ 0.25 W resistors were used as gate resistor for the switches,

and for their driving system 2 drivers from the company Supplier were selected: one

double isolated driver (Supplier DRO100D25A) and one simple isolated driver

(Supplier DRO100S25A).

About the decoupling capacitors C1 and C2, because of the reliability and

extended lifetime of polypropylene capacitors, two 40 µF/450 V polypropylene

capacitors were used.

For the current sensor, the sensor LEM LA 25-NP was selected, mainly

because of its reliability, accuracy and good linearity, factors that facilitate an

experimental implementation.

8.2.2 Tapped Inductor Design

In Table 8.1, the constructive aspects of the tapped inductor are presented. All

the design methodology of the tapped inductor may be seen in the Appendix D.

Table 8.1 Constructive aspects of the Tapped inductor

Component Specification

Tapped inductor

Magnetizing Inductance: LM = 513.711 µH Turns in the primary: 29

Turns in the secondary: 29 Wire in the primary: 23 x 25 AWG

Wire in the secondary: 10 x 25 AWG Core: EE-76 Thornton IP12R


8.2.3 RCD Clamping

One of the recurring issues in power converters implementing tapped inductors

and transformers is the influence of the leakage inductance in the system. When in

series with switches, these inductances can cause even the destruction of the power

elements.

182

This happens because the leakage inductance accumulates energy during the

time period where the switch in turned-on, and when this switch is turned-off the

current on this inductance is abruptly interrupted and the energy is consequently

suddenly discharged, resulting in an overvoltage to the switches.

In order to remedy that, clamping circuits are commonly implemented. The idea

behind clamping circuits is to provide an alternative path for the leakage inductance

energy when the switch is turned-off, preventing the overvoltage effect and the

destruction of the power switches. In Figure 8.1, the two classical clamping circuits

are presented.

Dc

Cc CcRc

Sc

(a) (b)

Figure 8.1 Clamping circuits: (a) Passive clamping (b) Active clamping


In this work, it was determined the use of the passive clamping circuit for each

switch, mainly because the implementation of an active clamping would lead to a

very complex circuit and the addition of 3 more switches would counter one of the

main appeals of the converter, the use of the tapped inductor for reducing switches

from the original topology.

In the passive clamping, the energy from the leakage inductance is transferred

to the clamping capacitor Cc by the clamping diode Dc, and it is completely dissipated

in the clamping resistor Rc.

Then, assuming the specifications determined earlier in this chapter, the

components of the clamping circuit may be determined. As all the switches

implemented are the same and are under very close conditions, the same elements

were used in all 3 switches.

183

First, the clamping diode must attend the same voltage parameter than the

switch selected. As the switch chosen presents a maximum voltage of 1200 V, for

presenting a close value of maximum voltage, it was chosen the diode MUR 1100

(1000 V/ 1 A) for the clamping circuit.

The clamping capacitors were selected to support the maximum voltage of the

clamping circuit with a very small ripple. For this, due to the availability of

components in the UTFPR-PG Research Center and after some initial tests using

arbitrary capacitances, it was determined the use of two 470 nF/ 400 V polyester

capacitors in series as the best choice in terms of operation.

Finally, it is function of the clamping resistor to limit the clamping voltage and

reduce the dissipated power by the clamping circuit. Then, to determine the value of

this resistor, tests were performed to find the resistance which would combine the

best relationship between converter performance and clamping voltage. After that,

the use of two 56 kΩ / 3 W resistance in series for each switch proved to be the best

solution for the converter operation.

Then, all the components determined in this section and implemented in the

prototype are summarized in Table 8.2.

Table 8.2 Components used in the prototype

Component Specification

Switches S1, S2 and S3 3 x IRGP20B120UD-EP (1200 V/ 40 A)

Decoupling capacitors C1 and C2 2 x Polypropylene 40 µF / 450 V

Clamping capacitors 6 x 470 nF / 400 V

(3 x 235 nF / 800 V)

Clamping diodes 3 x MUR 1100 (1000 V/ 1 A)

Clamping resistors 6 x 56 kΩ / 3W

(3 x 112 kΩ / 6W )

Current sensor LEM LA 25-NP

Gate resistors 3 x 10 kΩ / 0.25 W

Drivers 1 x Supplier DRO100D25A 1 x Supplier DRO100S25A


Following, the experimental prototype is presented in Figure 8.2 whereas the

tapped inductor is shown by Figure 8.3.

184

16.75 cm16 c

m

Figure 8.2 Experimental prototype


7.5 cm7.

5 cm

Figure 8.3 Tapped inductor


185

8.3 EXPERIMENTAL SETUP

Due to the lack of a battery bank and SCs or any bidirectional DC power source

in the UTFPR-PG Research Center, the experimental tests were performed with the

converter working unidirectionally, that is, with a DC power source supplying a RC

load.

When the converter is tested operating in the Forward mode, the DC power

source is placed as the voltage source V1 and the RC load is placed as the voltage

source V2. Already for the Reverse mode, the opposite is done, the DC power source

is placed as the voltage source V2 and the RC load is placed as the voltage source

V1.

Following, all the elements used in the experimental setup implemented in

laboratory are described:

The Bidirectional DC-DC converter with tapped inductor;

1 DSP Texas Instruments TMS320F28335 Experimenter Kit : Used for the

control of the converter;

1 Voltage gain circuit: Implemented to adapt the gate signals for the switches

from the DSP level (3.3 V) to the Drivers level (15 V) (Schematic and PCB

layout available in the Appendix E);

1 Signal treatment circuit: Implemented to adapt the power measurements to

DSP level signals (Schematic and PCB layout available in the Appendix F);

1 Supplier DC Power Source: to supply the converter as one of the voltage

sources;

1 parallel RC load: Used to emulate the remaining voltage source, where the

value of the resistance is adjusted according the desired power and the

capacitance is a capacitor bank of 2.82 mF / 400 V.

1 Digital Phosphor Oscilloscope Tektronix DPO7254C: Used to obtain all the

waveforms from the experimental prototype;

1 Power Analyzer Yokogawa WT500: Used to obtain all the efficiency results

from the experimental prototype;

This way, a schematic of the experimental setup implemented in laboratory is

presented in Figure 8.4.

186

DSPDC-DC

CONVERTER

OPEN LOOP

CLOSED LOOP

SIGNAL

TREATMENT

15V

PWM SIGNAL

3.3V

PWM SIGNAL

VOLTAGE

GAIN

V1

V2

I1

Figure 8.4 Schematic of the experimental setup


8.4 EXPERIMENTAL RESULTS

In this section, all the closed loop experimental results of the bidirectional DC-

DC converter with tapped inductor are going to be presented.

8.4.1 Forward Buck

First, the gate signals for the Forward Buck are presented in Figure 8.5.

t = 20 µs/div

VgS2

VgS3

VgS1

Figure 8.5 Forward Buck: Gate signals (10 V/div)


187

As can be seen in Figure 8.5, switches S1 and S3 are receiving complementary

PWM signals with amplitude of 15 V whereas the switch S2 is receiving a continuous

15 V signal. This configuration of signals is important to guarantee, when the

converter is operating bidirectionally, the possibility of the direct change from the

Forward to the Reverse mode (and vice versa) just changing the current reference.

Then, in Figures 8.6 and 8.7, the voltage and the current in switch S1 are

presented, where the maximum voltage reached in this switch was 543.2 V and the

RMS value of the current was 4.862 A. However, after the initial voltage spike, it is

possible to see that the voltage across this switch stabilizes in approximately 400 V.

t = 20 µs/div

VS1

IS1

Figure 8.6 Forward Buck: Voltage (200 V/div) and current (7 A/div) in the switch S1


t = 20 µs/div

VS1

IS1



188

Other important aspects to be considered from Figures 8.6 and 8.7 are the

already mentioned influence of the leakage inductance in the switches, resulting in

the overvoltage in the switch, and the reverse recovery phenomenon of the

antiparallel-body diodes of the switches, resulting in the current spikes seen in the

mentioned Figures.

Using a zoom tool in Figure 8.7, the turning-on and turning-off of the switch S1

may be seen, respectively, in Figures 8.8 and 8.9. With a view of the turning-on/off of

the switch, some important details of the switching, as the clamping action and the

tail current from the IGBT use, can be perceived.

t = 20 µs/div

VS1

IS1

Figure 8.8 Forward Buck: Turning-on of the switch S1


t = 20 µs/div

VS1

IS1

Clamping action

IGBT Tail Current

Figure 8.9 Forward Buck: Turning-off of the switch S1


189

Now, the current and the voltage in switch S3 are presented by Figures 8.10 and

8.11, where the maximum voltage in this switch reached the value of 242.4 V and the

RMS current was 9.093 A. Again, even being more moderated than in switch S1, the

influence of the leakage inductance can be seen in the switch S3 as well as the

reverse recovery phenomenon of the antiparallel-body diode. Similar to switch S1, it

is possible to see that after the initial voltage spike the voltage across S3 stabilizes,

but now around 200 V.

t = 20 µs/div

IS3

VS3



t = 20 µs/div

VS3

IS3



190

Then, in the same way as for the switch S1, the turning-on and the turning-off of

the switch S3 can be seen with a zoom in Figure 8.11 and are presented,

respectively, by Figures 8.12 and 8.13.

t = 20 µs/div

VS3

IS3

Figure 8.12 Forward Buck: Turning-on of the switch S3


t = 20 µs/div

VS3

IS3

Figure 8.13 Forward Buck: Turning-off of the switch S3


In Figures 8.14 and 8.15, the voltage and current waveforms in the voltage

sources are presented. In the voltage source 1, the average current was 3.344 A

whereas in the voltage source 2 this value was -9.635 A. About the voltage in each

voltage source, both presented the expected values, 300 V in V1 and 96 V in V2.

191

t = 20 µs/div

V1

I1

Figure 8.14 Forward Buck: Voltage (100 V/div) and current (7 A/div) in the voltage source 1


t = 20 µs/div

V2

I2

Figure 8.15 Forward Buck: Voltage (30 V/div) and current (7 A/div) in the voltage source 2


In Figure 8.16, the experimental waveforms of the magnetizing inductance are

presented. In the first operating stage, the magnetizing voltage reached a maximum

value of 168.8 V and a value of -219.2 V in the second operating stage. Again, after

the voltage spikes, the voltage stabilizes in approximately 100 V in the first operating

stage and -100 V in the second. About the magnetizing current, the average value of

this current was 12.73 A, and, disregarding the current spikes, the instantaneous

values measured were 10.72 A and 14.77 A.

192

t = 20 µs/div

VLM

IM

Figure 8.16 Forward Buck: Voltage (100 V/div) and current (10 A/div) in magnetizing inductance


The currents through the switches are shown in Figure 8.17. As mentioned

earlier, the RMS currents through the switches S1 and S3 were, respectively, 4.862 A

and 9.093 A whereas the RMS value of the current through switch S2 was 10.088 A.

t = 20 µs/div

IS1

IS2

IS3

Figure 8.17 Forward Buck: Currents (10 A/div) through each switch


Already in Figures 8.18 and 8.19, the waveforms in the primary and the

secondary of the tapped inductor are presented. As expected, both presented the

same aspects, just with the primary presenting higher spikes in the voltage

waveform, but this can be explained due to the fact that this turn is in the “switch S1

side”, where the leakage inductance influence is higher.

193

t = 20 µs/div

VLT1

ILT1

Figure 8.18 Forward Buck: Voltage (100 V/div) and current (7 A/div) in the primary


t = 20 µs/div

VLT2

ILT2

Figure 8.19 Forward Buck: Voltage (100 V/div) and current (7 A/div) in the secondary


Then, the current control action of the system is presented in Figure 8.20. As

well as in the simulations made in chapter 6, the control was tested with a step from

50% to 100% of the rated power (1.667 A – 3.335 A) in the current reference. As can

be seen in 8.20, the control worked well, where the current provided by the DC power

source changed properly with the reference steps, with no variations in the voltage

V1. Another important aspect to be seen in Figure 8.21 is that, even without the use

of a filter in the input, just using the decoupling capacitor C1 and the inductance of the

wires used in the experimental setup, that is, just with the experimental setup

194

arrangement, the DC power source does not see a pulsed current, but a “filtered

current”. To a better understanding of this aspect, Figure 8.21 is presented.

t = 500 ms/div

V1

I1

1.667 A

3.335 A

IREF

Figure 8.20 Forward Buck: Voltage (100 V/div) and current (2 A/div) for the current control of I1


Filtered I1

t = 500 ms/div

Pulsed I1

Figure 8.21 Forward Buck: Current I1 in the voltage souce


Finally, the efficiency curve of the converter is shown in Figure 8.22. The

efficiency tests of the converter were performed always maintaining the energy

conversion from 300 V to 96 V, but varying the operation power in ten different points

(from 100 W to 1000 W). As may be seen in Figure 8.22, the converter reached its

maximum efficiency when operating with 50% of the rated power (500 W), presenting

an efficiency of 93.424%.

195

50 150 250 350 450 550 650 750 850 950 1050

90.25

90.75

91.25

91.75

92.25

92.75

93.25

93.75

Power (W)

Effic

ien

cy (

%)

Figure 8.22 Forward Buck: Efficiency curve


With the experimental results of the Forward Buck presented, a comparison

with the theoretical and simulated values is proposed in Table 8.3.

Table 8.3 Forward Buck: Comparison Theoretical x Simulated x Experimental

Symbol Theoretical Simulated Experimental

Stabilized Value Peak Value

VS1_MAX 396 V 396 V 400 V 543.2 V

VS3_MAX 198 V 198 V 200 V 242.4 V

VLT1_1st 102 V 102 V 100 V 170.8 V

VLT1_2nd -96 V -96 V -100 V -221.6 V

VLT2_1st 102 V 102 V 100 V 156.8 V

VLT2_2nd -96 V -96 V -100 V -135.6 V

VLM_1st 102 V 102 V 100 V 168.8 V

VLM_2nd -96 V -96 V -100 V -219.2 V

IM1 11.343 A 11.334 A 10.72 A

IM2 16.157 A 16.148 A 14.77 A

IM_AVG 13.75 A 13.743 A 12.73 A

I1_AVG 3.333 A 3.327 A 3.344 A

I2_AVG -10.417 A -10.415 A -9.635 A

IS1_RMS 4.812 A 4.783 A 4.862 A

IS2_RMS 11.024 A 11.052 A 10.088 A

IS3_RMS 9.919 A 9.962 A 9.093 A


196

From the experimental results presented for the Forward Buck and the values

presented in Table 8.3, it is possible to conclude that both the analyses and

simulations made in the previous chapters are correct, since the values obtained in

the experimental results are very close to the theoretical/simulated values.

Nevertheless, some significant differences can be seen in the currents of the

converter, which was an expected fact, since the converter was analyzed and

simulated with ideal elements, and in an experimental implementation the losses in

the converter components interfere directly in those aspects.

Also, the influence of the leakage inductance showed to be a difficult aspect to

deal. But again, for being a recurring issue in converters with transformers and

tapped inductors, it was an expected fact and could be solved by employing a

clamping circuit for each switch. Also, it is worth to mention the influence of the

reverse recovery phenomenon of the antiparallel-body switch of the diodes, resulting

in current spikes in the converter.

Finally, even without the use of high technological components, the converter

showed a very good efficiency (between 90% and 93.75%), which is essential for

applications like the one addressed in this work.


The gate signals for the Forward Buck-Boost are presented in Figure 8.23.

VgS1

t = 20 µs/div

VgS2

VgS3

Figure 8.23 Forward Buck-Boost: Gate signals (10 V/div)


197

As shown in Figure 8.23, switches S1 and S2 are receiving the PWM 15 V

complementary signals and the switch S3 is receiving the 15 V continuous signal.

Again, as well as for the Forward Buck mode, this signal configuration is important to

allow the possibility of change from the Forward operation to the Reverse operation.

Now, in Figures 8.24 and 8.25, the voltage and the current in switch S1 are

presented. The voltage in the switch S1 presented a stabilized value of approximately

400 V and, due to the leakage inductance influence, a voltage spike in its turning-off

reaching the value of 586.8 V. About the RMS current in this switch, the experimental

value was 6.903 A.

t = 20 µs/div

VS1

IS1

Figure 8.24 Forward Buck-Boost: Voltage (300 V/div) and current (10 A/div) in the switch S1


t = 20 µs/div

VS1 IS1



198

Again, the influence of the leakage inductance and the reverse recovery

phenomenon of the antiparallel-body diode from the switch can be seen, and this

time, even more if compared with the Forward Buck operation.

Then, using the zoom function of the oscilloscope in Figure 8.25, the turning-on

and the turning-off of the switch S1 are presented, respectively, by Figures 8.26 and

8.27.

t = 20 µs/div

VS1

IS1

Figure 8.26 Forward Buck-Boost: Turning-on of the switch S1


IGBT Tail Current

t = 20 µs/div

VS1IS1

Clamping action

Figure 8.27 Forward Buck-Boost: Turning-off of the switch S1


199

After the experimental waveforms of the switch S1 being presented, in Figures

8.28 and 8.29 the experimental results from switch S2 for the Forward Buck-Boost are

presented, where the maximum voltage reached in this switch was 507.6 V and the

RMS value of the current was 10.994 A. However, after the initial voltage spike, it is

possible to see that the voltage across this switch stabilizes in approximately 400 V.

t = 20 µs/div

VS2

IS2



t = 20 µs/div

VS2

IS2



200

In the same way as the switch S1, using the zoom function of the oscilloscope in

Figure 8.29, the turning-on of the switch S2 is presented by Figure 8.30 whereas the

turning-off is shown in Figure 8.31.

t = 20 µs/div

VS2

IS2

Figure 8.30 Forward Buck-Boost: Turning-on of the switch S2


t = 20 µs/div

VS2

IS2

Clamping action

IGBT Tail Current

Figure 8.31 Forward Buck-Boost: Turning-off of the switch S2



sources are presented. In the voltage source 1, the average current was 3.362 A

whereas in the voltage source 2 this value was -9.249 A. About the voltage in each

voltage source, both presented the expected values, 300 V in V1 and 96 V in V2.

201

V1

I1

t = 20 µs/div

Figure 8.32 Forward Buck-Boost: Voltage (100 V/div) and current (10 A/div) in V1


t = 20 µs/div

V2

I2

Figure 8.33 Forward Buck-Boost: Voltage (30 V/div) and current (10 A/div) in V2


The experimental waveforms of the magnetizing inductance are presented in

Figure 8.34. In the first operating stage, the magnetizing voltage presented a

stabilized value around 300 V and -100 V in the second. However, considering the

voltage spikes in the magnetizing voltage, the maximum value reached was 365.6 V

and the minimum was -300 V. About the magnetizing current, the average value of

this current was 12.51 A, and, disregarding the current spikes, the instantaneous

values measured were 9.889 A and 16.147 A.

202

t = 20 µs/div

VLM

IM

Figure 8.34 Forward Buck-Boost: Voltage (200 V/div) and current (10 A/div) in the magnetizing inductance


Then, in Figure 8.35 the currents through the switches are shown. The switches

S1, S2 and S3 presented, respectively, the RMS values of 6.903 A, 10.994 A and

12.324 A.

t = 20 µs/div

IS1

IS2

IS3

Figure 8.35 Forward Buck-Boost: Currents (20 A/div) through each switch


In Figures 8.36 and 8.37, the waveforms in each turn of the tapped inductor are

presented. Again, due to the turn ratio n=1, the waveforms presented the same

aspects, presenting a stabilized value of 300 V in the first operating stage and -100 V

in the second. About the voltage spikes, the maximum value reached was 420 V and

the minimum -300.8 V.

203

t = 20 µs/div

VLT1

ILT1

Figure 8.36 Forward Buck-Boost: Voltage (200 V/div) and current (10 A/div) in the primary


t = 20 µs/div

VLT2

ILT2

Figure 8.37 Forward Buck-Boost: Voltage (200 V/div) and current (10 A/div) in the primary


The experimental results of the control for the Forward Buck-Boost are

presented by Figure 8.38. The control tests were performed with the same

methodology of the Forward Buck, applying steps in the current I1 reference and

checking its behavior after that. Again, the control showed to be working well and, as

well as the Forward Buck, the experimental setup arrangement worked as a filter for

the current seen by the DC power source. Nevertheless, it is important to highlight

that as this feature of the experimental setup was already presented in Figure 8.21, it

will not be presented again for the next operating modes.

204

t = 500 ms/div

V1

I1

IREF

1.667 A

3.335 A

Figure 8.38 Forward Buck-Boost: Voltage (100 V/div) and current (2 A/div) for the current control of I1


The efficiency curve of the converter is shown in Figure 8.39. The efficiency

tests of the converter were performed in the same way as for the Forward Buck,

always maintaining the energy conversion from 300 V to 96 V and varying the

operation power in ten different points (from 100 W to 1000 W). As presented in the

following Figure, the converter reached its maximum efficiency when operating with

60% of the rated power (600 W), presenting an efficiency of 87.898%.

50 150 250 350 450 550 650 750 850 950 1050

82

83

84

85

86

87

88

89

Power (W)

Effic

ien

cy (

%)

Figure 8.39 Forward Buck-Boost: Efficiency curve


Finally, the same comparison proposed in Table 8.3 is presented in Table 8.4,

but this time for the Forward Buck-Boost.

205

Table 8.4 Forward Buck-Boost: Comparison Theoretical x Simulated x Experimental



VS1_MAX 396 V 396 V 400 V 586.8 V

VS3_MAX 396 V 396 V 400 V 507.6 V

VLT1_1st 300 V 300 V 300 V 364 V

VLT1_2nd -96 V -96 V -100 V -300.8 V

VLT2_1st 300 V 300 V 300 V 420 V

VLT2_2nd -96 V -96 V -100 V -163.2 V

VLM_1st 300 V 300 V 300 V 365.6 V

VLM_2nd -96 V -96 V -100 V -300 V

IM1 10.211 A 10.193 A 9.889 A

IM2 17.289 A 17.247 A 16.147 A

IM_AVG 13.75 A 13.738 A 12.51 A

I1_AVG 3.333 A 3.305 A 3.362 A

I2_AVG -10.417 A -10.432 A -9.249 A

IS1_RMS 6.844 A 6.818 A 6.903 A

IS2_RMS 12.099 A 12.100 A 10.994 A

IS3_RMS 13.901 A 13.898 A 12.324 A


From the analysis of the experimental results of the Forward Buck-Boost, the

same conclusions from the Forward Buck can be seen in the Forward Buck-Boost.

The experimental results presented very close values when compared with the

theoretical/simulated values and issues such as the overvoltage across the switches

caused by the leakage inductance influence and the reverse recovery phenomenon

of the antiparallel-body diode continued to show a considerable influence in the

converter operation.

However, different from the Forward Buck, the Forward Buck-Boost did not

present good efficiency results, where the efficiency range presented by the Forward

Buck-Boost (81% - 88%) makes unfeasible the use of this operation for the

application addressed in this thesis. Taking this into account, improvements in the

converter such as the use of better components or an optimization in the converter

layout must be considered.

206

8.4.3 Reverse Boost

The experimental results for the Reverse mode are presented following. First,

the gate signals for the Reverse Boost are shown in Figure 8.40.

t = 20 µs/div

VgS1

VgS3

VgS2

Figure 8.40 Reverse Boost: Gate signals (10 V/div)


As may be seen in Figure 8.40, the gate signals for the Reverse Boost are the

same than for Forward Buck, where the switches S1 and S3 are receiving the 15 V

PWM complementary signals and switch S2 is receiving a 15 V continuous signal. As

mentioned earlier and proven by Figure 8.40, this gate signal configuration

guarantees both the Forward and the Reverse operation.

Next, in Figures 8.41 and 8.42, the experimental waveforms of the voltage and

current in the switch S1 are presented. As expected, again the voltage across the

switch S1 presented an initial voltage spike, reaching a maximum value of 519.2 V.

After that, the voltage stabilizes in approximately 400 V, which is very close to the

expected theoretical value of 396 V.

About the current in this switch, for being the Reverse mode, the current is

negative, presenting a RMS value of 4.796 A. As shown in Figures 8.41 and 8.42,

also in the Reverse Mode the reverse recovery phenomenon of the antiparallel-body

diode of the switches presents a significant influence in the switch’s current, resulting

in the current spikes seen in these Figures.

207

t = 20 µs/div

VS1

IS1

Figure 8.41 Reverse Boost: Voltage (200 V/div) and current (7 A/div) in the switch S1


t = 20 µs/div

VS1

IS1



Then, using the zoom tool of the digital oscilloscope in Figure 8.42, the turning-

on and the turning-off of the switch S1 are presented, respectively, by Figures 8.43

and 8.44, where some aspects of the switching such as the clamping action limiting

the voltage spike in the switch and the IGBT tail current can be seen.

208

t = 20 µs/div

VS1

IS1

Figure 8.43 Reverse Boost: Turning-on of the switch S1


t = 20 µs/div

IS1

VS1

Clamping Action

IGBT Tail Current

Figure 8.44 Reverse Boost: Turning-off of the switch S1


Now, the current and the voltage in switch S3 are presented by Figures 8.45

and 8.46, where the voltage in this switch presented a stabilized value of

approximately 200 V, with a peak value of 221.6 V.

About the current in this switch, the experimental RMS value measured was

10.933 A.

209

t = 20 µs/div

VS3

IS3



t = 20 µs/div

VS3

IS3



In the same way as the switch S1, using the zoom function of the digital

oscilloscope in Figure 8.46, the turning-on of the switch S3 is presented by Figure

8.47 whereas the turning-off is shown in Figure 8.48.

210

t = 20 µs/div

VS3

IS3

Figure 8.47 Reverse Boost: Turning-on of the switch S3


t = 20 µs/div

VS3

IS3

IGBT Tail Current

Figure 8.48 Reverse Boost: Turning-off of the switch S3


Following, the current and the voltage waveforms in the voltage sources V1 and

V2 are presented in Figure 8.49.

The voltage source V1 presented the expected value of 300 V and an average

current of -3.323 A whereas the voltage source V2 presented an average current of

12.211 A and 96 V.

211

t = 20 µs/div

V1

V2

I1

I2

Figure 8.49 Reverse Boost: Voltage (100 V/div) and current (10 A/div) in the voltage sources V1 and V2


In Figure 8.50, the experimental waveforms of the magnetizing inductance for

the Reverse Boost are presented. In the first operating stage, the magnetizing

voltage reached a value of -226.4 V and a value of 208.4 V in the second operating

stage. Again, after the initial voltage spikes, the voltage stabilizes in approximately -

100 V in the first operating stage and 100 V in the second. About the magnetizing

current, the average value of this current was -14.352 A, and, disregarding the

current spikes, the instantaneous values measured were -17.872 A and -11.936 A.

t = 20 µs/div

IM

VLM

Figure 8.50 Reverse Boost: Voltage (100 V/div) and current (10 A/div) in the magnetizing inductance


212

Already in Figures 8.51 and 8.52, the waveforms in the primary and the

secondary of the tapped inductor for the Reverse Boost are presented. As expected,

both presented the same aspects, just with the primary presenting higher spikes in

the voltage waveform, due to the fact that S1 is switching in this mode and S2 is

always turned-on.

ILT1

VLT1

t = 20 µs/div

Figure 8.51 Reverse Boost: Voltage (100 V/div) and current (10 A/div) in the primary


t = 20 µs/div

VLT2

ILT2

Figure 8.52 Reverse Boost: Voltage (100 V/div) and current (10 A/div) in the primary


Following, to check the current control of the converter operating as the

Reverse Boost, Figure 8.53 is presented.

213

In the Reverse mode, with the placement of the RC load as the voltage source

V1, the current control of the converter is tested in a different way than for the

Forward mode. Now, instead of applying current steps in the current reference, the

current reference is set in -3.335 A and load steps from 50% to 100% of the rated

power, and vice versa, are given in the converter.

As can be seen in Figure 8.53, when the load step happens, the current I1

follows the reference and maintains the value of -3.335 A, only with a small

oscillation at the point where the load step occurred, showing the good work and

accuracy of the control. However, the voltage source V1 changes its value, since

different resistances with the same current will lead to different voltage values.

t = 500 ms/div

IREF

I1

V1

Load Step

-3.335 A

Figure 8.53 Reverse Boost: Voltage (100 V/div) and current (5 A/div) for the current control of I1


Then, the efficiency curve of the Reverse Boost is shown in Figure 8.54. As well

as for the Forward Mode, the efficiency tests were performed measuring the

efficiency of the converter in ten different operation points, in a range from 100 W to

1000 W, maintaining the energy conversion from 300 V to 96 V in all cases. As

shown in Figure 8.54, the converter reached its maximum efficiency when operating

with 40% of the rated power (400 W), presenting an efficiency of 91.599% and when

operating in the rated power, the efficiency measured was 88.958%.

214

50 150 250 350 450 550 650 750 850 950 1050

88.5

89

89.5

90

90.5

91

91.5

92

Power (W)

Effic

ien

cy (

%)

Figure 8.54 Reverse Boost: Efficiency curve


Finally, the comparison between the theoretical/simulated values and the

experimental results for the Reverse Boost is presented in Table 8.5.

Table 8.5 Reverse Boost: Comparison Theoretical x Simulated x Experimental



VS1_MAX 396 V 396 V 400 V 519.2 V

VS3_MAX 198 V 198 V 200 V 221.6 V

VLT1_1st -96 V -96 V -100 V -227.6 V

VLT1_2nd 102 V 102 V 100 V 230.6 V

VLT2_1st -96 V -96 V -100 V -106 V

VLT2_2nd 102 V 102 V 100 V 126.4 V

VLM_1st -96 V -96 V -100 V -226.4 V

VLM_2nd 102 V 102 V 100 V 228.4 V

IM1 -11.343 A -11.340 A -11.936 A

IM2 -16.157 A -16.152 A -17.872 A

IM_AVG -13.75 A -13.748 A -14.354 A

I1_AVG -3.333 A -3.328 A -3.323 A

I2_AVG 10.417 A 10.420 A 12.211 A

IS1_RMS 4.812 A 4.803 A 4.796 A

IS2_RMS 11.024 A 11.032 A 12.86 A

IS3_RMS 9.919 A 9.932 A 10.933 A


215

From the analysis of the experimental results of the Reverse Boost, it is

possible to see that the converter presented satisfactory results, where the

experimental results presented very close values when compared with the

theoretical/simulated values. As well as for the Forward Mode, the leakage

inductance and the reverse recovery phenomenon of the antiparallel-body diode of

the switches continued to show significant influence in the converter operation for the

Reverse mode.

About the converter efficiency, even presenting a lower efficiency if compared

with the Forward Buck, the converter showed a very good efficiency (between 88.9%

and 92 %), showing that the complementary operations Forward Buck/Reverse Boost

are a good option for an experimental implementation.


Following, the experimental results of the last operating mode are presented.

First, the gate signals for the Reverse Buck-Boost are shown in Figure 8.55.

t = 20 µs/div

VgS1

VgS3

VgS2

Figure 8.55 Reverse Buck-Boost: Gate signals (10 V/div)


In the same way as for the Forward Buck and the Reverse Boost, the Forward

Buck-Boost and the Reverse Buck-Boost present the same gate signals

configuration, where the operation of the converter is defined just setting a positive

(Forward mode) or a negative (Reverse mode) current reference.

216

In Figures 8.56 and 8.57, the voltage and the current in switch S1 for the

Reverse Buck-Boost are presented. The voltage in the switch S1 presented a

stabilized value of approximately 400 V and, due to the leakage inductance influence,

a voltage spike in its turning-off reaching the value of 457.2 V. About the RMS

current in this switch, the experimental value measured was 7.018 A.

t = 20 µs/div

VS1

IS1

Figure 8.56 Reverse Buck-Boost: Voltage (300 V/div) and current (10 A/div) in the switch S1


t = 20 µs/div

VS1

IS1



217

Then, using the zoom function of the oscilloscope in Figure 8.57, the turning-on

and the turning-off of the switch S1 are presented, respectively, by Figures 8.58 and

8.59.

t = 20 µs/div

VS1

IS1

Figure 8.58 Reverse Buck-Boost: Turning-on of the switch S1


t = 20 µs/div

VS1

IS1

Clamping Action

IGBT Tail Current

Figure 8.59 Reverse Buck-Boost: Turning-off of the switch S1


After the experimental waveforms of the switch S1 being presented, in Figures

8.60 and 8.61 the experimental results from switch S2 for the Reverse Buck-Boost

are presented where the maximum voltage reached in this switch was 592.8 V and

the RMS value of the current was 14.163 A. However, after the initial voltage spike, it

218

is possible to see that the voltage across this switch stabilizes in approximately 400

V.

t = 20 µs/div

VS2

IS2



t = 20 µs/div

VS2

IS2



Similar to switch S1, using the zoom function of the digital oscilloscope in Figure

8.61, the turning-on of the switch S2 is presented by Figure 8.62 whereas the turning-

off of the switch S2, presenting the clamping action and the IGBT tail current is shown

in Figure 8.63.

219

t = 20 µs/div

VS2 IS2

Figure 8.62 Reverse Buck-Boost: Turning-on of the switch S2


IGBT Tail Current

t = 20 µs/div

VS2

IS2

Clamping Action

Figure 8.63 Reverse Buck-Boost: Turning-off of the switch S2



sources are presented.

In the voltage source V1, the average current was -3.363 A whereas in the

voltage source V2 this value was 12.712 A. About the voltage in each voltage source,

both presented the expected values, 300 V in V1 and 96 V in V2.

220

V1

I1

t = 20 µs/div

Figure 8.64 Reverse Buck-Boost: Voltage (100 V/div) and current (10 A/div) in V1


t = 20 µs/div

V2

I2

Figure 8.65 Reverse Buck-Boost: Voltage (30 V/div) and current (10 A/div) in V2


The experimental waveforms of the magnetizing inductance for the Reverse

Buck-Boost are presented in Figure 8.66. In the first operating stage, after an initial

voltage spike reaching the value of -189.6 V, the magnetizing voltage presented a

stabilized value around -100 V. Already in the second operating stage, the stabilized

value of the magnetizing voltage was approximately 300 V with a peak value of 391.2

V. About the magnetizing current, the average value of this current was -15.59 A,

221

and, disregarding the current spikes, the instantaneous values measured were -

12.793 A and -18.227 A.

t = 20 µs/div

VLM

IM

Figure 8.66 Reverse Buck-Boost: Voltage (200 V/div) and current (10 A/div) in the magnetizing inductance


In Figure 8.67 the currents through the switches are shown. The switches S1, S2

and S3 presented, respectively, the RMS values of 7.018 A, 14.163 A and 15.195 A.

t = 20 µs/div

IS3

IS1

IS2

Figure 8.67 Reverse Buck-Boost: Currents (20 A/div) through each switch


222

In Figures 8.68 and 8.69, the waveforms in each turn of the tapped inductor are

presented. Again, due to the turn ratio n=1, the waveforms presented the same

aspects, presenting a stabilized value of -100 V in the first operating stage and 300 V

in the second. About the voltage spikes, the maximum value reached was 500 V and

the minimum -191.2 V.

t = 20 µs/div

ILT1

VLT1

Figure 8.68 Reverse Buck-Boost: Voltage (200 V/div) and current (10 A/div) in the primary


t = 20 µs/div

VLT1

ILT1

Figure 8.69 Reverse Buck-Boost: Voltage (200 V/div) and current (10 A/div) in the secondary


Then, the current control of the current I1 for the Reverse Buck-Boost is shown

in Figure 8.70. As well as for the Reverse Boost, in the Reverse Buck-Boost the

223

control tests are performed with a fixed current reference (-3.335 A) and load steps

are given in the V1 side.

-3.335 A

t = 500 ms/div

IREF

I1

Load Step

V1

Figure 8.70 Reverse Buck-Boost: Voltage (100 V/div) and current (7 A/div) for the current control of I1


As may be seen in Figure 8.70, the control worked well, maintaining the

current I1 at the desired value for different values of resistances.

Then, the efficiency curve of the Reverse Buck-Boost is presented in Figure

8.71. In this operating mode, the converter presented 86.282% as its maximum

efficiency when operating at 40% of the rated power (400 W).

50 150 250 350 450 550 650 750 850 950 1050

81

82

83

84

85

86

87

88

Power (W)

Eff

icie

ncy

(%

)

Figure 8.71 Reverse Buck-Boost: Efficiency curve


224

Finally, in Table 8.6 the experimental results of the Reverse Buck-Boost are

summarized and a comparison with the theoretical/simulated values for this mode is

presented.

Table 8.6 Reverse Buck-Boost: Comparison Theoretical x Simulated x Experimental



VS1_MAX 396 V 396 V 400 V 457.2 V

VS2_MAX 396 V 396 V 400 V 592.8 V

VLT1_1st -96 V -96 V -100 V -191.2 V

VLT1_2nd 300 V 300 V 300 V 392.6 V

VLT2_1st -96 V -96 V -100 V -113.6 V

VLT2_2nd 300 V 300 V 300 V 500 V

VLM_1st -96 V -96 V -100 V -189.6 V

VLM_2nd 300 V 300 V 300 V 391.2 V

IM1 -10.211 A -10.207 A -12.793 A

IM2 -17.289 A -17.261 A -18.227 A

IM_AVG -13.75 A -13.746 A -15.59 A

I1_AVG -3.333 A -3.353 A -3.363 A

I2_AVG 10.417 A 10.397 A 12.712 A

IS1_RMS 6.844 A 6.864 A 7.018 A

IS2_RMS 12.099 A 12.084 A 14.163 A

IS3_RMS 13.901 A 13.897 A 15.195 A


From the analysis of the experimental results of the Reverse Buck-Boost, the

same conclusions from the Forward Buck-Boost can be seen. The experimental

results presented very close values when compared with the theoretical/simulated

values and issues such as the overvoltage across the switches caused by the

leakage inductance influence and the reverse recovery phenomenon of the

antiparallel-body diode continued to show a considerable influence in the converter

operation.

Also, as well as the Forward Buck-Boost, the Reverse Buck-Boost did not

present good efficiency results, where the efficiency range presented (81% - 86%)

225

makes unfeasible the use of this operation for the application addressed in this

thesis.


In this chapter, all the experimental results for the bidirectional DC-DC converter

with tapped inductor were presented and discussed. Analyzing the results presented

by the waveforms and the values presented from Tables 8.3 to 8.6, it is possible to

conclude that the experimental implementation was satisfactory, where the

experimental waveforms presented format with high similarity when compared with

the expected theoretical/simulated waveforms. Also, the experimental values were

very close do the theoretical/simulated values, where just the currents in the

converter presented some significant differences, which was an expected fact, since

the converter was analyzed and simulated with ideal elements, and in an

experimental implementation the losses in the converter components interfere

directly in those aspects.

About the operations, the Forward Buck/Reverse Boost presented good

efficiency results, supporting the use of this topology/operation in a commercial

application. On the other hand, the Forward Buck-Boost/Reverse Buck-Boost did not

present good efficiency results, and improvements such as the use of better

components or an optimization in the converter layout must be considered for this

mode. However, it was already expected that the Buck-Boost operation would

present less efficiency than the Forward Buck/Reverse Boost since the Buck-Boost

operations presented higher values in their RMS currents through the switches.

Other important aspects to be highlighted are the considerable influence of the

leakage inductance and the reverse recovery phenomenon of the antiparallel-body

diodes of the switches, aspects that are very difficult to deal in an experimental

implementation.

Nevertheless, for the leakage inductance effect the use of a RCD clamping

circuit showed to be a good solution whereas for the problem related to the reverse

recovery phenomenon of the antiparallel-body diode of the switches, a possible

solution is the use of better/faster power components.

226

CONCLUSION

In this Master’s Thesis, the study of two bidirectional topologies for HESS in

EVs applications was presented. In the first two chapters, after a careful bibliographic

review, the topics that hold the proposal of this work, such as EVs, HESS and

bidirectional DC-DC converters were discussed, giving the fundamental background

for the development of this research.

Then, in the chapters that followed, the first topology studied in this Master ’s

Thesis, the bidirectional DC-DC converter with tapped inductor, was analyzed in

details, leading to the construction of an experimental prototype for laboratory

implementation. The study of the converter included, among others, the theoretical

steady state and dynamic analyzes, the proposal of a design methodology

subsequently verified by a digital simulation performed in the power electronics

simulation software PSIM®, and, as mentioned earlier, the construction of an

experimental prototype.

About the experimental results of the first topology, the results were considered

satisfactory, since the values and the format of the waveforms were very close to the

expected theoretical values/waveforms. However, for 2 of the 4 implemented

operations, the Forward and the Reverse Buck-Boost, the efficiency results were not

good, demanding future improvements in the converter.

Already for the second topology, the bidirectional ZVS Buck-Boost DC-DC

converter, its study was restricted only to the theoretical steady state analysis and

the proposal of a design methodology subsequently verified by a digital simulation.

This can be explained due to the fact that, as this topology is a new proposal of this

present thesis, the authors are aiming for a feedback if this topology is worth of

further investigation, since in the authors vision, considering the problem related to

the efficiency results of the Buck-Boost operation in the first topology, this converter

could be a suitable alternative when Buck-Boost operations are needed.

Finally, as possible alternatives of future works derived from this thesis, the

following are suggested:

227

Study of different bidirectional DC-DC topologies and switching techniques

applied in HESS and EVs;

Improvement in the efficiency of the bidirectional DC-DC converter with

tapped inductor for the Forward and the Reverse Buck-Boost operation;

Implementation of the bidirectional DC-DC converter with tapped inductor

using a battery and a SC as voltage sources;

Dynamic analysis and control design for the bidirectional ZVS Buck-Boost

DC-DC converter;

Construction of the bidirectional ZVS Buck-Boost DC-DC converter;

Implementation of the bidirectional ZVS Buck-Boost DC-DC converter using

a battery and a SC as voltage sources.

228

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234

APPENDIX A – BIDIRECTIONAL DC-DC CONVERTER WITH TAPPED

INDUCTOR: BUCK/BOOST CALCULATIONS

235

Bidirectional DC-DC Converter with Tapped Inductor:

Buck/Boost Calculations

Voltage Source V1

Voltage Source V2

Turn ratio

Switching frequency

Rated power

Magnetizing Inductance

Duty Cycle - Switch S1


Resistive Load

Forward Buck

Resistive Load

Reverse Boost

For the Forward Buck/Reverse Boost, the switch S2 is always turned-on.

Forward Buck

V1 300 V( )

V2 96 V( )

n 1

fs 20000 Hz( )

PC 1000 W( )

Lm 513.711 106

H( )

D1 V21 n

V1 V2 n

D1 0.4848

D3 1 D1

D3 0.5152

RForward

V22

PC

RForward 9.216 ( )

RReverse

V12

PC

RReverse 90 ( )

VS1_max_Forward V1 n V2

VS1_max_Forward 396 V( )

VS3_max_Forward

V1 V2 1 n

V2

236

Voltage in the primary

(1st opt stg)


(2nd opt stg)

Voltage in the secondary

(1st opt stg)


(2nd opt stg)

Magnetizing Current

Inst. value 2

Magnetizing Current

Inst. value 1

Magnetizing Current

Average

S1 - RMS current


VLT1_1st_Forward

n V1 V2

1 n

VLT1_1st_Forward 102 V( )

VLT1_2nd_Forward n V2

VLT1_2nd_Forward 96 V( )

VLT2_1st_Forward

V1 V2 1 n


VLT2_2nd_Forward V2


IM2_F

2 PC n 1( )2

fs Lm V1 V1 V2 D12

n2

2 V1 D1 n n 1( ) fs Lm

IM2_F 16.157 A( )

IM1_F

2 PC n 1( )2

fs Lm V1 V1 V2 D12

n2

2 V1 D1 n n 1( ) fs Lm

IM1_F 11.343 A( )

IM_F

IM2_F IM1_F

2

IM_F 13.75 A( )

IS1_RMS_F1

2 V1 Lm fs n 1( )2

D14

V12

n4

V1 V2 2 12 Lm2

PC2

fs2

n 1( )4

3 D1

IS1_RMS_F 4.812 A( )

237

S3 - RMS current

V1 Average current

V2 Average current

Reverse Boost


(1st opt stg)


(2nd opt stg)


(1st opt stg)


(2nd opt stg)

IS3_RMS_F1

2 V1 D1 Lm fs n 1( )

1 D1 D1

4V1

2 n

4 V1 V2

2 12 Lm

2 PC

2 fs

2 n 1( )

4

3

IS3_RMS_F 9.919 A( )

I1_Forward

PC

V1

I1_Forward 3.333 A( )

I2_Forward

PC

V2


VS1_max_Reverse V1 n V2

VS1_max_Reverse 396 V( )

VS3_max_Reverse

V1 V2 1 n

V2


VLT1_1st_Reverse n V2

VLT1_1st_Reverse 96 V( )

VLT1_2nd_Reverse

n V1 V2

1 n

VLT1_2nd_Reverse 102 V( )

VLT2_1st_Reverse V2


VLT2_2nd_Reverse

V1 V2 1 n

238

Magnetizing Current

Inst. value 2

Magnetizing Current

Inst. value 1

Magnetizing Current

Average

S1 - RMS current

S2 - RMS current

S3 - RMS current

V1 Average current

V2 Average current


IM2_R

2 PC n 1( ) fs Lm V1 V2 D3 1 D3 n2

2 V1 n 1 D3 fs Lm

IM2_R 16.157 A( )

IM1_R

2 PC n 1( ) fs Lm V1 V2 D3 1 D3 n2

2 V1 n 1 D3 fs Lm

IM1_R 11.343 A( )

IM_R

IM2_F IM1_F

2

IM_R 13.75 A( )

IS1_RMS_R1

6 V1 Lm fs n 1( )

3 D32

V12

V22

n4

D3 1 2

12 Lm2

PC2

fs2

n 1( )2

1 D3

IS1_RMS_R 4.812 A( )

IS2_RMS_R1

6 V1 Lm fs n 1( )

3 D32

V12

V22

n4

D3 1 2 1 D3 n2

2 D3 n

12 Lm

2 PC

2 fs

2 n 1( )

2D3 n n

34 n

2 5 n 2

D3 1 2

IS2_RMS_R 11.025 A( )

IS3_RMS_R1

6 V1 Lm fs

3D3

1 D3 2

D32

V22

V12

n4

D3 1 2

12 Lm2

PC2

fs2

n 1( )2

IS3_RMS_R 9.919 A( )

I1_Reverse

PC

V1

I1_Reverse 3.333 A( )

I2_Reverse

PC

V2


239

APPENDIX B - BIDIRECTIONAL DC-DC CONVERTER WITH TAPPED

INDUCTOR: BUCK-BOOST CALCULATIONS

240

Bidirectional DC-DC Converter with Tapped Inductor:

Buck-Boost Calculations

Voltage Source V1

Voltage Source V2

Turn ratio

Switching frequency

Rated power




Resistive Load

Forward Buck-Boost

Resistive Load

Reverse Buck-Boost

For the Forward Buck-Boost/Reverse Buck-Boost, the switch S3 is always

turned-on. Forward Buck-Boost

V1 300 V( )

V2 96 V( )

n 1

fs 20000 Hz( )

PC 1000 W( )

Lm 513.711 106

H( )

D1 V2n

V1 V2 n

D1 0.2424

D2 1 D1

D2 0.7576

RForward

V22

PC

RForward 9.216 ( )

RReverse

V12

PC

RReverse 90 ( )

VS1_max_Forward V1 n V2


VS3_max_Forward

V1 n V2 n

241


(1st opt stg)


(2nd opt stg)


(1st opt stg)


(2nd opt stg)

Magnetizing Current

Inst. value 2

Magnetizing Current

Inst. value 1

Magnetizing Current

Average

S1 - RMS current


VLT1_1st_Forward V1


VLT1_2nd_Forward n V2


VLT2_1st_Forward

V1 n


VLT2_2nd_Forward V2


IM2_F

2 PC fs Lm V12

D12

2 V1 D1 fs Lm

IM2_F 17.289 A( )

IM1_F

2 PC fs Lm V12

D12

2 V1 D1 fs Lm

IM1_F 10.211 A( )

IM_F

IM2_F IM1_F

2

IM_F 13.75 A( )

IS1_RMS_F1

6 V1 Lm fs

3D14

V14

36 Lm2

PC2

fs2

D1

IS1_RMS_F 6.844 A( )

242

S2 - RMS current

S3 - RMS current

V1 Average current

V2 Average current

Reverse Buck-Boost


(1st opt stg)


(2nd opt stg)


(1st opt stg)

IS2_RMS_Fn

2 V1 D1 Lm fs

1 D1 D1

4V1

4 12 Lm

2 PC

2 fs

2

3

IS2_RMS_F 12.099 A( )

IS3_RMS_F1

6 V1 D1 Lm fs

3 n2

D1 D1 n2

D1

4V1

4 12 Lm

2 PC

2 fs

2

IS3_RMS_F 13.901 A( )

I1_Forward

PC

V1


I2_Forward

PC

V2


VS1_max_Reverse V1 n V2


VS3_max_Reverse

V1 n V2 n


VLT1_1st_Reverse n V2


VLT1_2nd_Reverse V1


VLT2_1st_Reverse V2

243


(2nd opt stg)

Magnetizing Current

Inst. value 2

Magnetizing Current

Inst. value 1

Magnetizing Current

Average

S1 - RMS current

S2 - RMS current

S3 - RMS current


VLT2_2nd_Reverse

V1 n


IM2_R

2 PC fs Lm n V1 V2 D2 1 D2 2 V1 1 D2 fs Lm

IM2_R 17.289 A( )

IM1_R

2 PC fs Lm n V1 V2 D2 1 D2 2 V1 1 D2 fs Lm

IM1_R 10.211 A( )

IM_R

IM2_F IM1_F

2

IM_R 13.75 A( )

IS1_RMS_R1

6 V1 Lm fs

3 D22

V12

V22

n2

D2 1 2

12 Lm2

PC2

fs2

1 D2

IS1_RMS_R 6.844 A( )

IS2_RMS_Rn

2 V1 Lm fs

D2 D22

V12

V22

n2

12 Lm2

PC2

fs

2

D2 1 2

3

IS2_RMS_R 12.099 A( )

IS3_RMS_R1

6 V1 Lm fs

3

D2 1 2

D22

V12

V22

n2

D23

n2

2D22

n2

1 D23

D2 n2

3D22

3D2

12 Lm

2 PC

2 fs

2 D2 n

2 D2 1

IS3_RMS_R 13.901 A( )

I1_Reverse

PC

V1

244

V1 Average current

V2 Average current


I2_Reverse

PC

V2


245

APPENDIX C – BIDIRECTIONAL ZVS BUCK-BOOST DC-DC

CONVERTER: CALCULATIONS

246

Bidirectional ZVS Buck-Boost DC-DC Converter: Calculations

Voltage Source V1

Voltage Source V2

Duty cycle - Switch S1

Rated Power

Switching frequency

Magnetizing Current - Average



Magnetizing Current - Inst. value 2

Magnetizing Current - Inst. value 1

Choosing an arbitrary value for the auxiliary inductance, it is possible to find the

maximum n (turn ratio of the ideal transformer) that will allow the converter to work

with ZVS. Auxiliary Inductance

Maximum n for the ZVS operation

V1 300V

V2 96V

D1V2

V1 V2

D1 0.242

Pc 1000W

fs 100kHz

IMavgPc

V1 D1

IMavg 13.75A

IM 40%

LmV1 D1

fs IM IMavg

Lm 132.231 H

IM22 Pc fs Lm V1

2D1

2

2 V1 D1 Lm fs

IM2 16.5A

IM12 Pc fs Lm V1

2D1

2

2 V1 D1 Lm fs

IM1 11A

Ld 6H

nmaxLd 2 Pc fs Lm V1

2D1

2

V12

D12

Lm

1

nmax 0.574

247

Then, an n is defined:

Turn ration

Auxiliary inductance current

S1 - Minimum current

S1 - Maximum current

S2 - Minimum current

S2 - Maximum current

S1 - Average current

S2 - Average current

S1 - RMS current

S2 - RMS current

n 0.54

ILdV1 n 1( ) D1

2 fs Ld

ILd 27.879 A

IS1min IM1 ILd n 1( )

IS1min 1.824 A

IS1max IM2 ILd n 1( )

IS1max 29.324A

IS2min IM2 ILd n 1( )

IS2min 29.324 A

IS2max IM1 ILd n 1( )

IS2max 1.824A

IS1avgPc

V1

IS1avg 3.333A

IS2avgPc 1 D1( )

V1 D1

IS2avg 10.417 A

IS1rms

3

D1

D14

V14

Lm2

n 1( )4

Ld2

2Lm Ld n 1( )2

12 Lm2

Pc2

fs2

Ld2

6 fs Lm Ld V1

IS1rms 8.089A

IS2rms3 1 D1( )[ ] D1

4V1

4 Lm

2n 1( )

4 Ld

2 2Lm Ld n 1( )

2 12 Lm

2 Pc

2 fs

2 Ld

2

6 fs Lm Ld V1 D1

IS2rms 14.3A

248

n1 0 0.1 10

IS1 n1

3

D1

D14

V14

Lm2

n1 1 4

Ld2

2Lm Ld n1 1 2

12 Lm

2 Pc

2 fs

2 Ld

2

6 fs Lm Ld V1

0 1 2 3 4 50

10

20

30

40

IS1 RMS in function of n

IS1 n1

n1

IS2 n1 3 1 D1( )[ ] D1

4V1

4 Lm

2n1 1

4 Ld

2 2Lm Ld n1 1

2

12 Lm

2 Pc

2 fs

2 Ld

2

6 fs Lm Ld V1 D1

0 1 2 3 4 510

20

30

40

IS2 RMS in function of n

IS2 n1

n1

249

Ld n1 V1

2D1

2 Lm n1 1

2 10

6

2 Pc fs Lm V12

D12

0 1 2 3 4 50

10

20

30

40

50

Maximum value of the Auxiliary Inductance ( H) in function of n

Ld n1

n1

Ld n1 33.058

26.777

21.157

16.198

11.901

8.264

5.289

2.975

1.322

0.331

0

0.331

1.322

2.975

5.289

8.264

11.901

16.198

21.157

...

H

IS1 n1 19.24

16.217

13.611

11.442

9.727

8.469

7.639

7.161

6.928

6.837

6.815

6.837

6.928

7.161

7.639

8.469

9.727

11.442

13.611

...

A

IS2 n1 34.013

28.669

24.061

20.226

17.195

14.972

13.504

12.658

12.247

12.086

12.047

12.086

12.247

12.658

13.504

14.972

17.195

20.226

24.061

...

A

250

APPENDIX D – TAPPED INDUCTOR DESIGN

251

Tapped Inductor Design

1. Design Specifications:


Magnetizing Current - Maximum value

Current 1 (RMS)

Current 2 (RMS)


Np/Ns

Maximum Induction Flow

Current density (RMS)

Core area - Utilization Factor

Switching Frequency

2. Choice of Core:

Selected Core: EE-76 Thornton IP12R

3. Number of turns - Calculation:

4. Air Gap - Calculation:

Lm1 513.711H

ILmpico 16.158A

I1ef 11.025A

I2ef 4.811A

I Lm1 4.813A

a 1

Bmax 0.15T

Jef 300A

cm2

kw 0.7

f 20 kHz

AeAw

Lm1 ILmpico I1ef

I2ef

a

Bmax Jef kw AeAw 41.729 cm

4

Ae 19.35cm2

Aw 6.45cm2

N1 ceilLm1 ILmpico

Bmax Ae

N1 29

N2 ceilN1

a

N2 29

Bmax

Lm1 ILmpico

N1 Ae Bmax 0.148 T

o 4 107

H

m

252

5. Conductor gauge - Calculation:

Wire Diameter:

The selected wire is the 25AWG.

6. Losses - Calculation:

6.1 Wire Losses:

lent referro

N12

o Ae 102 m

cm

Lm1

lent referro 3.981 mm

7.5 s

0.5 cm

f 0.053 cm

Dfio 2 Dfio 0.106 cm

Sfio 0.001624 cm2

Sfioiso 0.002078 cm2

Scobre1

I1ef

Jef

Scobre1 0.037 cm2

ncond1 ceilScobre1

Sfio

ncond1 23

Scobre2

I2ef

Jef

Scobre2 0.016 cm2

ncond2 ceilScobre2

Sfio

ncond2 10

fio 0.001419

cm

lespira 21.8cm

lfio1 N1 lespira lfio1 6.322m

Rcobre1

fio lespira N1

ncond1

Rcobre1 39.004 103

lfio2 N2 lespira lfio2 6.322m

Rcobre2

fio lespira N2

ncond2

Rcobre2 89.709 103

253

6.2 Magnetic Losses:

6.3 Total Losses:

6.4 Core - Thermal Resistance:

Pcobre Rcobre1 I1ef2

Rcobre2 I2ef2

Pcobre 6.817 W

Vnucleo 421.35cm3

k 1.052W

m3

1.5 2.44

BLm1 I Lm1

N1 Ae

1

T B 0.044

Pnucleo kf

Hz

1

2B

Vnucleo Pnucleo 0.114 W

ki

k

2 ( ) 1

2

0

2

cos ( )

d

ki 0.063W

m3

Pv

f

Hz

ki B( )

0

Hz

2f

tB2f

Hz

d

0

Hz

2f

tB2f

Hz

d

Pv 0.246kW

m3

Pnucleo Pv Vnucleo Pnucleo 0.104 W

Ptotais Pcobre Pnucleo Pto tais 6.921 W

Rtnucleo 23K

W

Ae Aw

cm4

0.37

Rtnucleo 3.856K

W

254

6.5 Temperature Increasing:

7. Possibility of Execution:

T Pcobre Pnucleo Rtnucleo T 26.686K

Aw_min

N1 Sfioiso ncond1 N2 Sfioiso ncond2

kw

Aw_min 2.841 cm

2

ExecAw_min

Aw

Exec 0.44

255

APPENDIX E – VOLTAGE GAIN CIRCUIT

256

VOLTAGE GAIN CIRCUIT

1k 1k 1k

330

330

330

6k8

6k8

6k8

GND

GND

GND

DSP

PWM 1

DSP

PWM 2

DSP

PWM 3

1 2

3 4

5 6

SN7407

SN7407

SN7407

+15 V

PWM 1

PWM 2

PWM 3

1

2

3

4

5

6

7

14

13

12

11

10

9

8

+5 V

GND

SN

74

07

1

2

3

4

MOLEX 1

1

2

3

MOLEX 2

1

2

3

MOLEX 3

1

2

3

MOLEX 4

GND

GND

GND

DSP PWM 1

DSP PWM 2

DSP PWM 3

+15 V

-15 V

+5 V

-5 V

PWM 1

PWM 2

PWM 3

Figure E.1 Voltage gain circuit: Schematic


4.2 cm

4.5

cm

Figure E.2 Voltage gain circuit: PCB Layout


257

4.2

cm4.5

cm

Figure E.3 Voltage gain circuit


258

APPENDIX F – SIGNAL TREATMENT CIRCUIT

259

SIGNAL TREATMENT CIRCUIT

1

2

3

4

5

6

7

14

13

12

11

10

9

8

-15 V

GND

LF

34

7N

1

2

3

4

MOLEX 1

1

2

3

MOLEX 2

1

2

3

MOLEX 3

GND

GND

DSP AN 1

DSP AN 2

DSP AN 3

+15 V

-15 V

V1

V2

IMEAS

+15 V

1

2

3

4

8

7

6

5TL

77

26 +3 VGND4

11

41

1

41

1

41

1

1

7

814

2

3

6

5

9

10

13

12

+15 V

-15 V

+15 V

-15 V

+15 V

-15 V

+15 V

-15 V+15 V

560

560

560

56k

15k

560k

4.7k

100k

100k

100

100k

100k

5k

10

µF

/25

V

10k

GND

GND GND

GND

GND

GND GND

V1

V2

IMEAS

LF347N

LF347N

LF347NLF347N

DSP AN 1

DSP AN 2

DSP AN 3

+3 V GND

TL7726

8 1

2

+3 V GND

TL7726

8 1

3

+3 V GND

TL7726

8 1

4

22

0 µ

F/3

5 V

+

+22

0

LM317

+3 V

100 nF

+15 V

2k

GND

GNDVIN VOUT

ADJ

220 µF

35 V

220 µF

35 V

+

+

100 nF

100 nF

+15 V

-15 V

GND

2.2

nF

2.2

nF

2.2

nF

Decoupling capacitors:

Placed close to the IC LF347N

Figure F.1 Signal treatment circuit: Schematic


4.5

cm

9 cm

Figure F.2 Signal treatment circuit: PCB Layout


260

9 cm

4.5

cm

Figure F.3 Signal treatment circuit


261

APPENDIX G – DSP PROGRAMMING

262

DSP PROGRAMMING

#include "DSP28x_Project.h" #define MODE_BUCK_BOOST 0x0 #define MODE_BOOST 0x1 #define MODE_BUCK 0x2 #define DUTY_LIM_INF 0.375 #define DUTY_LIM_SUP 0.8 #define Ireflow 1.65 #define Irefhigh 3.3 #define KI 10 #define Kpi1 0.04 #define Kpi2 0.03992 #define Kfilt1 0.5335 #define Kfilt2 0.4665 #if (CPU_FRQ_150MHZ) #define ADC_MODCLK 0x3 #endif #if (CPU_FRQ_100MHZ) #define ADC_MODCLK 0x2 #endif void Config_PWM(void); void Set_Duty(void); void Config_IO(void); void Config_AD(void); void Set_Mode(void); interrupt void adc_isr(void); Uint32 n; Uint16 buffer, count; double voltage_an0, voltage_an1, voltage_an2, voltage_zero, duty, i1, iref, err, y_old, x_old, i1_old, i1_filt; int period, dead_time, mode, dir; int main(void) count = 0; int i; n = 0; dir = 0; iref = 1.2; err = 0; y_old = 0; x_old = 0; //mode = MODE_BUCK_BOOST; //mode = MODE_BOOST; mode = MODE_BUCK;

263

InitSysCtrl(); EALLOW; SysCtrlRegs.HISPCP.all = ADC_MODCLK; EDIS; DINT; InitPieCtrl(); IER = 0x0000; IFR = 0x0000; InitPieVectTable(); period = 7500; dead_time = 200; duty = 0.535; Config_IO(); Config_AD(); buffer = 0; voltage_zero = 0; for(i = 0; i < 10; i++) AdcRegs.ADCTRL2.bit.SOC_SEQ1 = 1; DELAY_US(10000); buffer = (AdcRegs.ADCRESULT0>>4); voltage_zero = voltage_zero + (3*(double)buffer)/(40950); AdcRegs.ADCTRL1.bit.CONT_RUN = 0; Config_PWM(); Set_Mode(); Set_Duty(); for(;;); void Config_PWM(void) EALLOW; SysCtrlRegs.PCLKCR0.bit.TBCLKSYNC = 0; EDIS; EPwm1Regs.TBCTL.bit.PRDLD = TB_IMMEDIATE; EPwm1Regs.TBPRD = period/2; EPwm1Regs.CMPA.half.CMPA = 0; EPwm1Regs.CMPA.half.CMPAHR = (1 << 8); EPwm1Regs.CMPB = 0; EPwm1Regs.TBPHS.all = 0; EPwm1Regs.TBCTR = 0; EPwm1Regs.TBCTL.bit.CTRMODE = TB_COUNT_UPDOWN; EPwm1Regs.TBCTL.bit.PHSEN = TB_ENABLE; EPwm1Regs.TBCTL.bit.SYNCOSEL = TB_SYNC_IN; EPwm1Regs.TBCTL.bit.HSPCLKDIV = TB_DIV1; EPwm1Regs.TBCTL.bit.CLKDIV = TB_DIV1;

264

EPwm1Regs.CMPCTL.bit.LOADAMODE = CC_CTR_ZERO; EPwm1Regs.CMPCTL.bit.LOADBMODE = CC_CTR_ZERO; EPwm1Regs.CMPCTL.bit.SHDWAMODE = CC_SHADOW; EPwm1Regs.CMPCTL.bit.SHDWBMODE = CC_SHADOW; EPwm1Regs.AQCTLA.bit.CAD = AQ_SET; EPwm1Regs.AQCTLA.bit.CAU = AQ_CLEAR; EPwm1Regs.AQCTLB.bit.CBU = AQ_SET; EPwm1Regs.AQCTLB.bit.CBD = AQ_CLEAR; EPwm1Regs.ETSEL.bit.SOCAEN = 1; EPwm1Regs.ETSEL.bit.SOCASEL = ET_CTR_ZERO; EPwm1Regs.ETPS.bit.SOCAPRD = ET_1ST; EALLOW; EPwm1Regs.HRCNFG.all = 0x0; EPwm1Regs.HRCNFG.bit.EDGMODE = HR_REP; EPwm1Regs.HRCNFG.bit.CTLMODE = HR_CMP; EPwm1Regs.HRCNFG.bit.HRLOAD = HR_CTR_ZERO; EDIS; EPwm2Regs.TBCTL.bit.PRDLD = TB_IMMEDIATE; EPwm2Regs.TBPRD = period/2; EPwm2Regs.CMPA.half.CMPA = 0; EPwm2Regs.CMPA.half.CMPAHR = (1 << 8); EPwm2Regs.CMPB = 0; EPwm2Regs.TBPHS.all = 0; EPwm2Regs.TBCTR = 0; EPwm2Regs.TBCTL.bit.CTRMODE = TB_COUNT_UPDOWN; EPwm2Regs.TBCTL.bit.PHSEN = TB_ENABLE; EPwm2Regs.TBCTL.bit.SYNCOSEL = TB_SYNC_IN; EPwm2Regs.TBCTL.bit.HSPCLKDIV = TB_DIV1; EPwm2Regs.TBCTL.bit.CLKDIV = TB_DIV1; EPwm2Regs.CMPCTL.bit.LOADAMODE = CC_CTR_ZERO; EPwm2Regs.CMPCTL.bit.LOADBMODE = CC_CTR_ZERO; EPwm2Regs.CMPCTL.bit.SHDWAMODE = CC_SHADOW; EPwm2Regs.CMPCTL.bit.SHDWBMODE = CC_SHADOW; EPwm2Regs.AQCTLA.bit.CAD = AQ_SET; EPwm2Regs.AQCTLA.bit.CAU = AQ_CLEAR; EPwm2Regs.AQCTLB.bit.CBU = AQ_SET; EPwm2Regs.AQCTLB.bit.CBD = AQ_CLEAR; EALLOW; EPwm2Regs.HRCNFG.all = 0x0; EPwm2Regs.HRCNFG.bit.EDGMODE = HR_REP; EPwm2Regs.HRCNFG.bit.CTLMODE = HR_CMP; EPwm2Regs.HRCNFG.bit.HRLOAD = HR_CTR_ZERO; EDIS; InitEPwm1Gpio(); InitEPwm2Gpio(); EALLOW; SysCtrlRegs.PCLKCR0.bit.TBCLKSYNC = 1; EDIS;

265

void Set_Duty(void) if(duty) if(mode == MODE_BUCK_BOOST) EPwm1Regs.CMPA.half.CMPA = (duty*period/2) - (dead_time/2); EPwm1Regs.CMPB = 0; EPwm2Regs.CMPA.half.CMPA = (duty*period/2) + (dead_time/2); else if(mode == MODE_BOOST) EPwm1Regs.CMPA.half.CMPA = 0; EPwm1Regs.CMPB = (duty*period/2) - (dead_time/2); EPwm2Regs.CMPA.half.CMPA = (duty*period/2) + (dead_time/2); else if(mode == MODE_BUCK) EPwm1Regs.CMPA.half.CMPA = (duty*period/2) - (dead_time/2); EPwm1Regs.CMPB = (duty*period/2) + (dead_time/2); EPwm2Regs.CMPA.half.CMPA = 0; void Config_IO(void) EALLOW; GpioCtrlRegs.GPAMUX1.bit.GPIO15 = 0; GpioCtrlRegs.GPAPUD.bit.GPIO15 = 0; GpioCtrlRegs.GPADIR.bit.GPIO15 = 1; EDIS; void Config_AD(void) EALLOW; PieVectTable.ADCINT = &adc_isr; EDIS; InitAdc(); PieCtrlRegs.PIEIER1.bit.INTx6 = 1; IER |= M_INT1; EINT; ERTM; AdcRegs.ADCMAXCONV.all = 0x0002; AdcRegs.ADCCHSELSEQ1.bit.CONV00 = 0x0; AdcRegs.ADCCHSELSEQ1.bit.CONV01 = 0x1; AdcRegs.ADCCHSELSEQ1.bit.CONV02 = 0x2; AdcRegs.ADCTRL2.bit.EPWM_SOCA_SEQ1 = 1; AdcRegs.ADCTRL2.bit.INT_ENA_SEQ1 = 1; interrupt void adc_isr(void) count++;

266

GpioDataRegs.GPADAT.bit.GPIO15 = 1; buffer = AdcRegs.ADCRESULT0>>4; voltage_an0 = (3*(double)buffer)/(4095); //buffer = AdcRegs.ADCRESULT1>>4; //voltage_an1 = (3*(double)buffer)/(4095); //buffer = AdcRegs.ADCRESULT2>>4; //voltage_an2 = (3*(double)buffer)/(4095); i1 = KI*(voltage_an0 - voltage_zero); i1_filt = Kfilt1*i1 + Kfilt2*i1_old; i1_old = i1; err = iref - i1_filt; duty = y_old + Kpi1*err - Kpi2*x_old; if(duty < DUTY_LIM_INF) duty = DUTY_LIM_INF; else if(duty > DUTY_LIM_SUP) duty = DUTY_LIM_SUP; Set_Duty(); y_old = duty; x_old = err; if(n > 40000 && dir == 0) iref = Irefhigh; n = 0; dir = 1; if(n > 40000 && dir == 1) iref = Ireflow; n = 0; dir = 0; n++; AdcRegs.ADCTRL2.bit.RST_SEQ1 = 1; AdcRegs.ADCST.bit.INT_SEQ1_CLR = 1; PieCtrlRegs.PIEACK.all = PIEACK_GROUP1; GpioDataRegs.GPADAT.bit.GPIO15 = 0; return; void Set_Mode(void) if(mode == MODE_BUCK_BOOST)

267

EPwm1Regs.AQCTLA.bit.CAU = AQ_CLEAR; EPwm1Regs.AQCTLA.bit.CAD = AQ_SET; EPwm1Regs.AQCTLB.bit.CBU = AQ_SET; EPwm1Regs.AQCTLB.bit.CBD = AQ_SET; EPwm2Regs.AQCTLA.bit.CAU = AQ_SET; EPwm2Regs.AQCTLA.bit.CAD = AQ_CLEAR; else if(mode == MODE_BOOST) EPwm1Regs.AQCTLA.bit.CAU = AQ_SET; EPwm1Regs.AQCTLA.bit.CAD = AQ_SET; EPwm1Regs.AQCTLB.bit.CBU = AQ_CLEAR; EPwm1Regs.AQCTLB.bit.CBD = AQ_SET; EPwm2Regs.AQCTLA.bit.CAU = AQ_SET; EPwm2Regs.AQCTLA.bit.CAD = AQ_CLEAR; else if(mode == MODE_BUCK) EPwm1Regs.AQCTLA.bit.CAU = AQ_CLEAR; EPwm1Regs.AQCTLA.bit.CAD = AQ_SET; EPwm1Regs.AQCTLB.bit.CBU = AQ_SET; EPwm1Regs.AQCTLB.bit.CBD = AQ_CLEAR; EPwm2Regs.AQCTLA.bit.CAU = AQ_SET; EPwm2Regs.AQCTLA.bit.CAD = AQ_SET;

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