Graph Theory in Power Converters
From Fundamentals to Applications
1st Edition
Will be published approx. on 1. December 2026
Book
Hardback
256 pages
978-1-394-22229-2 (ISBN)
Description
Understand the theory behind an area of rapid engineering innovation
The field of power electronics has been rapidly transformed in recent decades by astonishing advances in power converter network techniques. Innovation in this field, however, has quickly come to outpace standards of mathematical knowledge among engineers, leading to ad hoc research outputs which are sometimes difficult to understand and duplicate. There is an urgent need for research which emphasizes the mathematical foundations of power converter topologies and operations, to equip engineers with the tools they need to continue driving extraordinary technological change.
Graph Theory in Power Converters meets this need with a comprehensive overview of the topological relationships and systematic operations within power converters. Divided into two parts, the first emphasizing mathematical theory and research background and the second emphasizing practical applications, this book promises to fully equip readers with graph theory as a tool for analyzing, modelling and designing power converters.
Graph Theory in Power Converters also provides readers:
Coverage of both mainstream categories of power converters and emerging types, such as multiport converters and new current-source converters
Detailed discussion of topics including matrix-based theory, dual and isomorphic theories, topology transformations, and more
Analysis and implementations driven by the authorial team's own research
Graph Theory in Power Converters is ideal for engineers and researchers working in power electronics, as well as graduate students in power electronics and related fields.
The field of power electronics has been rapidly transformed in recent decades by astonishing advances in power converter network techniques. Innovation in this field, however, has quickly come to outpace standards of mathematical knowledge among engineers, leading to ad hoc research outputs which are sometimes difficult to understand and duplicate. There is an urgent need for research which emphasizes the mathematical foundations of power converter topologies and operations, to equip engineers with the tools they need to continue driving extraordinary technological change.
Graph Theory in Power Converters meets this need with a comprehensive overview of the topological relationships and systematic operations within power converters. Divided into two parts, the first emphasizing mathematical theory and research background and the second emphasizing practical applications, this book promises to fully equip readers with graph theory as a tool for analyzing, modelling and designing power converters.
Graph Theory in Power Converters also provides readers:
Coverage of both mainstream categories of power converters and emerging types, such as multiport converters and new current-source converters
Detailed discussion of topics including matrix-based theory, dual and isomorphic theories, topology transformations, and more
Analysis and implementations driven by the authorial team's own research
Graph Theory in Power Converters is ideal for engineers and researchers working in power electronics, as well as graduate students in power electronics and related fields.
More details
Language
English
Place of publication
United States
Publishing group
John Wiley & Sons Inc
Target group
Professional and scholarly
ISBN-13
978-1-394-22229-2 (9781394222292)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
Yuzhuo Li, PhD, is a Postdoctoral Fellow in the Electric and Intelligent Grid Research Lab, Department of Electrical and Computer Engineering, University of Alberta, Canada. He is also Vice-Chair of the IEEE Northern Canada PELS Chapter.
Yunwei Ryan Li, PhD, is University of Alberta Senior Engineering Research Chair and Chair in the Department of Electrical and Computer Engineering, Alberta, Canada. He also serves as Vice President of the IEEE Power Electronics Society and Editor-in-Chief of IEEE Transactions on Power Electronics (TPEL) Letters, and has published prolifically on power electronics and related subjects.
Yunwei Ryan Li, PhD, is University of Alberta Senior Engineering Research Chair and Chair in the Department of Electrical and Computer Engineering, Alberta, Canada. He also serves as Vice President of the IEEE Power Electronics Society and Editor-in-Chief of IEEE Transactions on Power Electronics (TPEL) Letters, and has published prolifically on power electronics and related subjects.
Content
Contributors xv
Preface xvii
Acronyms xix
1 Introduction 3
1.1 Power Converters in Modern Industry 4
1.2 Why Use Graph Theory in Converter Research 10
1.3 Organization of the Book 18
2 Fundamentals of Power Converters Topologies 23
2.1 The Fundamental Concepts of Power Converter 24
2.2 Classifications of Power Converters 28
2.3 Conclusions 46
3 Introduction of Graph Theory 49
3.1 Development of Graph Theory 50
3.2 Basic Concepts 52
3.3 Advanced Concepts 67
3.4 Conclusions 86
4 Graphical Modeling for Power Converters 89
4.1 A Brief Overview of Graph Theory in Power Electronics 90
4.2 Modeling Basics and Procedures 93
4.3 Converter-level Modeling and Analysis 102
4.4 System-Level Modeling of Power Electronic Networks 133
4.5 Conclusions 145
5 Isomorphic Relationships of Power Converters 147
5.1 Isomorphism in Power Converters 148
5.2 Converter Isomorphisms with Graphical Orientation 161
5.3 Converter Isomorphisms without Graphical Orientation 169
5.4 Conclusions 188
6 Dual Relationships of Power Converters 191
6.1 Basic Dual Methods 192
6.2 Dual Methods for Power Converters 202
6.3 Dual Uniqueness 222
6.4 Conclusions 235
7 Topological Cycling Relationships of Power Converters 237
7.1 The Phenomenon of Topological Cycling 237
7.2 Planar Circuit Topological Cycling 247
7.3 Nonplanar Circuits Topological Cycling 256
7.4 Practical Applications of Topological Cycling 269
7.5 Conclusions 277
8 Systematic Derivation of Multilevel Converters 281
8.1 Introduction 282
8.2 Unified Models and Structures of Multilevel Converters 288
8.3 Synthesis of Voltage-Source and Current-Source Multilevel Converters 307
8.4 Matrix-Type Multilevel Converters 344
8.5 Conclusions 354
9 Topology Development for Multiport Converters 357
9.1 Graphical Modeling for Multiport Converters 358
9.2 Unique Dual Multiport Converters 389
9.3 Multiple Dual Multiport Converters 406
9.4 Conclusions 417
10 PWM Design for Emerging Multilevel Converters 419
10.1 Introduction and Graph-Theoretic Foundations 420
10.2 Carrier-Based PWM Design for ANPC-based Converters 435
10.3 Advanced Topics in Systematic PWM Design 479
10.4 Conclusions 511
11 Derivation of Emerging Current-Source Converter Topologies 515
11.1 Background 516
11.2 Duality-Based Current-Source Converter Derivation 534
11.3 Isomorphism-Based Current-Source Converter Derivation 549
11.4 Flying-Capacitor-Clamped Current-Source Converter 564
11.5 Conclusions 582
12 Power Converter System Operation and Optimization 585
12.1 Fundamentals of Graph Theory for Power Converter Systems 586
12.2 Leveraging Converter Relationships for Power Converter Control 600
12.3 EV Charging Station Optimization in Power-Traffic Coupled Network 617
12.4 Graph Neural Networks and Their Applications 630
12.5 Conclusions 653
Bibliography 654
Index 656
Preface xvii
Acronyms xix
1 Introduction 3
1.1 Power Converters in Modern Industry 4
1.2 Why Use Graph Theory in Converter Research 10
1.3 Organization of the Book 18
2 Fundamentals of Power Converters Topologies 23
2.1 The Fundamental Concepts of Power Converter 24
2.2 Classifications of Power Converters 28
2.3 Conclusions 46
3 Introduction of Graph Theory 49
3.1 Development of Graph Theory 50
3.2 Basic Concepts 52
3.3 Advanced Concepts 67
3.4 Conclusions 86
4 Graphical Modeling for Power Converters 89
4.1 A Brief Overview of Graph Theory in Power Electronics 90
4.2 Modeling Basics and Procedures 93
4.3 Converter-level Modeling and Analysis 102
4.4 System-Level Modeling of Power Electronic Networks 133
4.5 Conclusions 145
5 Isomorphic Relationships of Power Converters 147
5.1 Isomorphism in Power Converters 148
5.2 Converter Isomorphisms with Graphical Orientation 161
5.3 Converter Isomorphisms without Graphical Orientation 169
5.4 Conclusions 188
6 Dual Relationships of Power Converters 191
6.1 Basic Dual Methods 192
6.2 Dual Methods for Power Converters 202
6.3 Dual Uniqueness 222
6.4 Conclusions 235
7 Topological Cycling Relationships of Power Converters 237
7.1 The Phenomenon of Topological Cycling 237
7.2 Planar Circuit Topological Cycling 247
7.3 Nonplanar Circuits Topological Cycling 256
7.4 Practical Applications of Topological Cycling 269
7.5 Conclusions 277
8 Systematic Derivation of Multilevel Converters 281
8.1 Introduction 282
8.2 Unified Models and Structures of Multilevel Converters 288
8.3 Synthesis of Voltage-Source and Current-Source Multilevel Converters 307
8.4 Matrix-Type Multilevel Converters 344
8.5 Conclusions 354
9 Topology Development for Multiport Converters 357
9.1 Graphical Modeling for Multiport Converters 358
9.2 Unique Dual Multiport Converters 389
9.3 Multiple Dual Multiport Converters 406
9.4 Conclusions 417
10 PWM Design for Emerging Multilevel Converters 419
10.1 Introduction and Graph-Theoretic Foundations 420
10.2 Carrier-Based PWM Design for ANPC-based Converters 435
10.3 Advanced Topics in Systematic PWM Design 479
10.4 Conclusions 511
11 Derivation of Emerging Current-Source Converter Topologies 515
11.1 Background 516
11.2 Duality-Based Current-Source Converter Derivation 534
11.3 Isomorphism-Based Current-Source Converter Derivation 549
11.4 Flying-Capacitor-Clamped Current-Source Converter 564
11.5 Conclusions 582
12 Power Converter System Operation and Optimization 585
12.1 Fundamentals of Graph Theory for Power Converter Systems 586
12.2 Leveraging Converter Relationships for Power Converter Control 600
12.3 EV Charging Station Optimization in Power-Traffic Coupled Network 617
12.4 Graph Neural Networks and Their Applications 630
12.5 Conclusions 653
Bibliography 654
Index 656