Impedance Networks Matching Mechanism and Design of … · 2016. 3. 8. · matching, output...

Impedance Networks Matching Mechanism and

Design of Impedance Networks Converters

DISSERTATION

zur Erlangung des akademischen Grades

DOKTOR-INGENIEUR

der Fakultät für Mathematik und Informatik

der FernUniversität in Hagen

von

Guidong Zhang

Shantou/China

Hagen, 2015

I

Preface

Thanks to my Ph.D. supervisor, Prof. Bo Zhang, for his recommendation, I made a decision in

June 2011 to pursue a second Ph.D. degree in Germany under the supervision of Prof. Halang

and Prof. Li. Such a small decision would definitely greatly change my future life, just like

the “butterfly effect” in a chaotic system, because the four years’ experience in Germany has

deeply changed my thought and broadened my view of the world.

As I just came to Hagen in October 2011, everything was novel to me: the mentality,

culture, human behaviour, and many details in daily life. I tried my best to adapt to and

integrate into the new life and learn how to rightly think and behave. I went to play soccer

at the TSV Hagen 1860 e.V. on Wednesdays and Saturdays. What impressed me is that all

teammates, aged from 20 to 77 years old, punctually start to play at 6pm and end at 7:30pm in

any weather conditions. I was deeply touched by their passion for soccer and earnest attitude.

Actually, German rigor is reflected in all aspects of life. Also in my research work, Prof. Halang

and Prof. Li helped me revise my scientific articles word by word until they became perfect.

The serious attitude to work and life will benefit me for life.

Although Germans are rigorous, they are warm-hearted. Not only from my supervisors

and colleagues but also from my landlord and other German friends I received much help in all

aspects of my life and work, which greatly eased my life here.

Here I had chances to get to know many famous scientists and students with various cultural

backgrounds from all over the world, as well to attend international conferences, workshops,

and summer schools. For instance, I attended the summer school of complex networks in

Pescara, Italy in 2012, where I met many Ph.D. students from Italy, Russia, Romania, etc. and

professors. We went together for a walk or to drink beer, and had much fun. We have become

friends even after the summer school and the friendship lasts.

With the help of my supervisors, I could gradually get into my research topics. Firstly

I was engaged in the project “suppressing electromagnetic interference in electronic devices

via chaos control”, then in the theme of exploring the emergent behaviour of complex power

grids, and finally I extended my research to the topic of revealing the impedance networks

matching mechanism and designing novel impedance source converters for renewable energy

industrial applications. This topic is of both theoretic and practical significance in the sense

that the impedance networks matching mechanism is for the first time revealed and it lays

II

the foundation for proposing a systematic design methodology of specified impedance source

converters. This work lets me stand in the forefront of the discipline of power electronics.

This thesis has agglomerated painstaking efforts of many persons. It could never be com-

pleted without their help. Here, I would first express my deep gratitude to my supervisor in

China, Prof. Bo Zhang, who encouraged and inspired me to engage in the investigation of

impedance source converters. I am also very grateful to Prof. Halang and Prof. Li for their

patient instructions, so that I could learn how to do research and finish my research work in

Hagen. I owe special thanks to Prof. Li’s wife, Mrs. Mei, and their son, Yifan, for their

meticulous care, which made me feel at home.

Moreover, I would thank Liqiang Yang for helping me do part of the experiments, as well

I thank Profs. Dongyuan Qiu, Guiping Du, Yanfeng Chen, Xuemei Wang, Wenxun Xiao and

Dr. Fan Xie for the fruitful discussions.

Thanks also go to my classmates at the South China University of Technology, Wei Hu,

Xiangfeng Li, Lei Wang, Min Li, Junfeng Han, Hongfei Ma, Xi Chen, Dongdong Wang, and

Jiali Zhou for giving me a lot of good advices on my thesis, and to my colleagues in Hagen,

Mrs. Jutta During, Mrs. Junying Niu, Prof. Yuhong Song, and Mrs. Renate Zielinski for the

kind help.

Sincere thanks are owed to my friends in Hagen and Guangzhou for their help in my life,

Kai Chen, Li Chen, Jianqiu Xu, Jiamin Lu, Lei Xu, Xuqin Liao, Jianhui Liu, and Wei Li.

Furthermore, my greatest gratitude goes to my parents and grandparents for their forever love

and spiritual support, and to my sister and brothers for their contributions to family, without

which I could not focus on my study abroad.

At last but not least, I would mention that this work was partly supported by German

AiF, Alexander von Humboldt Foundation, and the Key Program of National Natural Science

Foundation of China.

Guidong Zhang

September 2015 in Hagen

III

Abstract (in German)

Zunächst wird in dieser Dissertation der Hintergrund der durchgeführten Untersuchungen zusam-

men mit einem kurzen historischen Überblick zur Entwicklung der Leistungselektronik und

dem Stand der Technik von Impedanzquellenwandlern unter Auflistung typischer Beispiele

dargestellt.

Daran schließt sich eine Untersuchung der Eigenschaften von Impedanznetzen und deren

Auswirkungen auf den Aufbau hochwertiger Stromrichter an. Eine qualitative Analyse liefert

die Gründe, warum konventionelle Spannungs- und Stromquellenwandler unter Problemen

wie Überlappungsspitzen, Leerlauf, eingeschränkter Verstärkung von Ausgangsstrom oder -

spannung oder Nichtanwendbarkeit auf induktive und kapazitive Lasten leiden und warum

Impedanzquellenwandler diese Probleme überwinden können. Die Analyse ermöglicht, den für

nichtlineare geschaltete Stromrichter wesentlichen Impedanznetzanpassungsmechanismus, der

sich von Impedanzanpassung in lineareren Schaltkreisen deutlich unterscheidet, eingehend zu

verstehen. Der Mechanismus passt sowohl die Impedanzen der Ein- und Ausgänge als auch die

Phasen der Lasten an.

In Bezug auf den Impedanznetzanpassungsmechanismus wird eine systematische Methodik

zur Entwicklung neuer Impedanzquellenstromrichter dargestellt, die geeignet ist, die tradi-

tionelle, manuell-mühsame Entwurfsmethodik zu ersetzen.

Im Hinblick auf einige spezielle industrielle Anwendungen werden vier neue Impedanzquel-

lenwandler als Beispiele für den Einsatz der vorgeschlagenen Entwurfmethodik entworfen, und

zwar zwei 3-Z-Netz-Gleichspannungsaufwärtswandler nach Spezifikationen der Photovoltaik,

ein für elektrochemische Netzteile geeigneter Z-Quellenhalbbrückenwandler und ein Z-Quellen-

halbbrückenwandler mit dualem Ausgang für Elektrofahrzeuge.

IV

Abstract

This thesis firstly introduces the background of this research with a brief history of the devel-

opment of power electronics, and the state of the art of impedance source converters by listing

typical examples.

Then, the properties of impedance networks and their effects for constructing high-quality

power converters are investigated. A qualitative analysis reveals the reasons why traditional

voltage- and current-source converters suffer from the shoot-through or the open-circuit prob-

lems, from limited output current or voltage gains, and from inapplicability to both inductive

and capacitive loads, and why impedance source converters can overcome these problems. This

analysis lays a foundation to understand well the intrinsic impedance network matching mech-

anism in non-linear switched power converters, which is different from impedance matching

in linear circuits. The impedance network matching mechanism deals with input impedance

matching, output impedance matching and load phase matching.

Further, in terms of the impedance network matching mechanism, a systematic method-

ology for the design of novel power converters to replace traditional tedious, manual designs is

presented.

With regard to some special industrial applications, four novel impedance source convert-

ers are devised as examples to apply this design methodology, namely two 3-Z-network DC-DC

boost converters specified for solar energy systems, a Z-source half-bridge converter for electro-

chemical power supplies, and a dual-output Z-source half-bridge converter for electric vehicle

systems.

CONTENTS V

Contents

Preface I

Abstrakt (In German) III

Abstract (In English) IV

1 Introduction 1

1.1 Power Electronics: A Brief History . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Impedance Networks and Impedance Source Converters 7

2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.1 Voltage Sources and Current Sources . . . . . . . . . . . . . . . . . . . . 7

2.1.2 Impedance Network and Z-Source . . . . . . . . . . . . . . . . . . . . . . 8

2.2 Voltage-Source- and Current-Source-Inverters . . . . . . . . . . . . . . . . . . . 11

2.2.1 Voltage Source Inverters . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.2 Current Source Inverters . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3 Z-Source Inverters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4 State-of-The-Art of Impedance Source Converters . . . . . . . . . . . . . . . . . 20

2.4.1 Quasi-Z-Source Converters . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4.2 Trans-Z-Source Converters . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.4.3 Embedded-Z-Source Converters . . . . . . . . . . . . . . . . . . . . . . . 28

2.4.4 Other Impedance Source Converters . . . . . . . . . . . . . . . . . . . . 28

2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3 Impedance Networks Matching Mechanism 33

3.1 Impedance Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.2 Input Impedance Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.3 Output Impedance Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.4 Load Phase Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

VI CONTENTS

3.5 Matching Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.6 Design Methodology of Power Converters . . . . . . . . . . . . . . . . . . . . . . 44

3.6.1 Topology Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.6.2 Selection of An Impedance Network . . . . . . . . . . . . . . . . . . . . . 46

3.6.3 Input Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.6.4 Output Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.6.5 Analysis of the Operational Status . . . . . . . . . . . . . . . . . . . . . 52

3.6.6 Parameters Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.6.7 Simulations and Experiments . . . . . . . . . . . . . . . . . . . . . . . . 53

3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4 A 3-Z-Network Boost Converter 55

4.1 System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.1.1 Disadvantage of Traditional Boost Converters . . . . . . . . . . . . . . . 56

4.1.2 Selection of Impedance Networks . . . . . . . . . . . . . . . . . . . . . . 57

4.1.3 Calculation of Input and Output Impedances . . . . . . . . . . . . . . . 58

4.2 Operational Modes Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.3 CCM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.3.1 Case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.3.2 Case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.4 DCM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.4.1 Case 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.4.2 Case 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.4.3 Case 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.4.4 Case 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.5 Parameters Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4.5.1 Output Voltage and Voltage Stress of Electrical Components . . . . . . . 71

4.5.2 Parameters of Inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.5.3 Parameters of Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.6 Simulations and Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

5 A Z-Source Half-Bridge Converter 83

5.1 System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.1.1 Disadvantages of A Traditional Half-Bridge Inverter . . . . . . . . . . . . 84

5.1.2 Impedance Matching of Traditional Half-Bridge Inverters . . . . . . . . . 85

5.1.3 Calculation of Input and Output Impedances . . . . . . . . . . . . . . . 86

5.2 Operational Status Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

CONTENTS VII

5.2.1 Case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.2.2 Case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.3 Midpoint Balance of Input Capacitors . . . . . . . . . . . . . . . . . . . . . . . . 94

5.3.1 Midpoint Voltage in Conventional Half-Bridge Converters . . . . . . . . . 94

5.3.2 Midpoint Voltage in Z-Source Half-Bridge Converters . . . . . . . . . . . 95





5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

6 A Dual-Output Z-Source Half-Bridge Converter 105

6.1 System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

6.2 Control Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

6.3 Operational Modes Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

6.4 Deduction of Output Voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113





6.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

7 Conclusions 121

References 123

Appendix: Curriculum Vitae 137

VIII CONTENTS

1 Introduction 1

Chapter 1

Introduction

1.1 Power Electronics: A Brief History

Thunder, lightning and electric fish, which are related to electricity [1], were just natural phe-

nomena in human history, and treated as myths but not energy in human life until the discovery

of electrostatic phenomena by Thales of Miletus (640-540 BC) [2, 3]. Much later in 1752, B.

Franklin discovered electricity [4] and in 1820 H.C. Örsted revealed electromagnetism [5]. Since

then, a series of great discoveries about the principles of electricity and magnetism have been

done by Volta, Coulomb, Gauss, Henry, Faraday, and others, leading to many inventions such

as the batteries (1800), generators (1831), electric motors (1831), telegraphes (1837), and tele-

phones (1876), to list just a few. Until the early 19th century the electrical science has been

established and in the late 19th century the greatest progress has been witnessed in electrical

engineering [6].

In 1882, the first power grid, which was a direct-current (DC) distribution system and

invented by T. Edison, was set up in New York, providing 110 V DC power to supply over

1,000 bulbs in a short distance. Then, the problem was how to transfer energy from power

plants over a long distance to customers at a low loss through transmission lines [7]. It is now

well known that electricity must be transmitted at high voltages and in the form of alternative-

current (AC) because DC voltage cannot be increased or decreased by DC systems at that

time [8]. In 1885, L. Gaulard and J.D. Gibbs developed a device, named a transformer, which

can increase or decrease the electrical voltage of AC systems. Then, G. Westinghouse applied

the transformer in AC distribution systems to make the electricity available to be transported

over long distances efficiently, which promoted the development of electrical engineering [9].

Transformers played a vital rôle in electricity transmission, especially in the energy con-

version between different voltages. However, transformers can only increase or decrease AC

voltage (AC-AC) at the same frequency. Moreover, energy loss of transformers, magnetic ra-

diations, huge volume, and high economic cost of copper became severe problems of applying

2 1 Introduction

transformers [10]. In practical applications, electric energy was expected to convert from one

form to another, for instance, between AC and DC, or just to different voltages or frequencies,

or some combinations of those, which cannot be fully fulfilled by transformers. Hence, novel

techniques were required to solve these problems. With the developments of semiconductor

switches, power electronics appeared and has developed to be a discipline [11].

Power electronics refers to electric power, electronics and control systems. Electric power

deals with the static and rotating power equipments for the generation, transmission and dis-

tribution of electric power; while electronics deals with the study of solid state semiconductor

power devices and circuits together with specified control systems for power conversion to meet

the desired control objectives [12]. Power electronics is one of the main technologies to realize

energy conversion with high efficiency. It is known that about 70% electric energy should be

converted first to the load with power electronics techniques. Nowadays, techniques of power

electronics have become a fundamental and critical technology in the development of energy

conservation, especially for renewable energy [13, 14, 15, 16].

The history of power electronics is linked up with the break-through and evolution of power

semiconductor devices [17]. The first power electronics device developed was the mercury arc

rectifier in 1900. Then, the other power devices like metal tank rectifier, grid controlled vac-

uum tube rectifier, ignitron, phanotron, thyratron and magnetic amplifier, were developed and

used gradually for power control applications until 1950. The second electronics revolution

began in 1958 with the development of the commercial grade thyristor by the General Electric

company (GE). Thus, the new era of power electronics began. Since 1975, more turn-off power

semiconductor elements were developed and implemented during the next 20 years, which had

vastly improved modern electronics. Included here are improved bipolar transistors (with fine

structures, and also shorter switching times), metal-oxide-semiconductor field effects transistors

(MOSFETs), gate turnoff thyristors (GTOs) and insulated gate bipolar transistors (IGBTs).

Thereafter, many different types of power semiconductor devices and power conversion tech-

niques have been introduced. The power electronics revolution has endowed us the ability to

convert, shape and control power [18].

With the development of semiconductor devices, different kinds of control strategies are

also correspondingly developed to realize specified purposes. For example, high-accuracy and

high-frequency control methods based on chips like DSP, FPGA and CPLD were applied to

meet the desired requirements and gain better control of the load; more accurate mathematical

modeling methods of power converters offered better platforms to gain better output features,

reduce the energy loss and increase the efficiency; and improved control algorithms were uti-

lized to improve the efficiency and robustness, reduce the complexity, and gain better output

features.

Power electronics converters fall into four categories, i.e. AC-DC, AC-AC, DC-DC, and

DC-AC converters, and they have been invented and found a wide spectrum of applications in,

1 Introduction 3

for instance, the transportation (electric/hybrid electric vehicles, electric locomotives, electric

trucks), utilities (line transformers, generating systems, grid interface for alternative energy

resources like solar, wind, and fuel cells, and energy storage), industrial/commercial (motor

drive systems, electric machinery and tools, process control, and factory automation), consumer

products (air conditioners/heat pumps, appliances, computers, lighting, telecommunications,

un-interruptible power supplies, and battery chargers), and medical equipments. Moreover,

with the advanced power electronics converters, high-voltage direct current (HVDC) systems

are also available to replace AC transmission systems with unique features. Nowadays, power

electronics has become a scientific discipline [19].

With rapid development of modern industry, more severe problems are faced by power

electronics: how to meet the requirements of the load; how to improve the efficiency and

reliability of power semiconductor devices; how to realize power conversion with smaller volume,

less weight, and lower cost; how to reduce the number of power switches and thus the complexity

and improve the robustness of the whole system; and how to minimize negative influence on

other equipments in the electric power systems and on the electromagnetic environment [20].

In order to solve these problems, some advances were witnessed in the semiconductor

switches in power converters, for example, integrated gate-commutated thyristors (IGCT) were

invented to have lower conduction loss compared to the traditional high capacities switches.

However, due to high switching losses, typical operating frequency is normally set up to 500 Hz.

Accordingly, control strategies were also improved in algorithms with higher accuracy and

speed [21].

To design a new power electronics converter, one can, on the one hand, develop a new

control strategy. On the other hand, one can design a novel power converter topology, so as to

obtain specific outputs, more simple control, higher efficiency, less complexity, lower weight,

minimal cost, and better robustness. In fact, a control strategy is specified to a certain topology,

and the topology determines the control system. Therefore, it is of great significance to coin

new power converter topologies to fulfill various requirements in applications, which will thus

be the main concern of the dissertation.

Due to an input source of a converter being either a voltage source or a current source,

various traditional converters can fall to two categories: voltage source and current source

converters. It is, however, known that voltage source converters suffer from shoot-through

problems, applicability only to capacitive loads, and limited output voltage gains; while current

source converters have open-circuit problems, applicability only to inductive loads, and limited

output current gains [22].

In order to solve these problems, Z-source converters were firstly proposed by Peng in

2002 [23], by coupling an LC impedance network (a two-port network with a combination of

two basic linear energy storage elements, i.e. L and C) with the DC source to form a novel

source, named Z-source, which is a kind of impedance source (an impedance is denoted by

4 1 Introduction

Z) [24, 25]. Impedance source can be regarded as a general source, including the current and

the voltage sources as two extreme cases, i.e. impedance source can be regarded as the current

source when the equivalent impedance is equal to infinity, while as the voltage source when the

equivalent impedance is equal to zero.

Therefore, the topology of impedance source converters has been widely studied and ap-

plied due to its unique features and its design method; for example, a Z-network is applied

to couple with the traditional converters to improve their functions. Inspired from this design

method, more impedance source converters, such as quasi-Z-source converters, trans-Z-source

converters, embedded-Z-source converters, have been coined and widely applied in practice,

e.g. wind energy systems [26, 27, 28], motor drives [29]-[32], vehicle systems [33]-[37], and

solar energy systems [38]-[48]. In fact, the design methodology of Z-source and other extended

impedance source converters is essentially is based on the impedance network matching mech-

anism, which instructs how an impedance network can be matched to the sources to fulfill

certain requirements. However, the essential impedance matching mechanism has not yet been

well understood and revealed, and the design of specific impedance source converters is still an

art, lacking of a systematic design methodology.

In this dissertation, a profound analysis of voltage and current sources converters is to

be conducted in order to well understand why impedance source converters have the unique

features over traditional converters. Furthermore, the impedance network matching mechanism

is to be revealed, which leads to a systematic methodology of designing impedance source

converters for various specific applications.

1.2 Contributions

The contributions of the thesis are listed as follows.

1. Qualitative analysis is for the first time conducted to explain the reasons why traditional

voltage and current sources converters have the problems, like the shoot-through or the

open-circuit, limited output current or voltage gains, and applicability just to inductive

or capacitive loads, and why impedance source converters can overcome these problems.

2. The impedance network matching mechanism, including input impedance matching, out-

put impedance matching and load phase matching, has been revealed. It acts as a criterion

to follow for designing an impedance source converter.

3. Based on the impedance network matching mechanism, a systematic methodology has

been proposed for designing a novel impedance source converter.

1 Introduction 5

4. In terms of the proposed methodology, two novel 3-Z-network DC-DC boost converters

have been coined by cascading three active impedance networks to realize high output

voltage gains. These are specified to the applications in solar energy systems.

5. Similarly, a novel Z-source half-bridge converter has been designed by coupling a Z-

network into a half-bridge converter for input impedance matching, which also balances

the mid-voltage of input capacitors. It is especially applicable to electrochemistry power

supplies.

6. A novel dual-output Z-source half-bridge converter has been devised by parallelizing two

impedance networks for output impedance matching. Here, one forth of switches and

capacitors are reduced, which also decreases the cost but increases the power density in

electric vehicle systems.

1.3 Outline

The rest of the dissertation is constructed as follows.

Chapter 2 introduces first the fundamental concepts of voltage sources, current sources,

Z-source and impedance networks. Then a qualitative analysis is conducted to explain why

traditional voltage and current sources converters have the problems, like the shoot-through

or the open-circuit, limited output current or voltage gains, and applicability just to inductive

or capacitive loads, while impedance source converters can overcome these problems. Finally,

the state-of-the-art of impedance source converters is presented with a detailed list of typical

Z-source converters.

Chapter 3 reveals the impedance network matching mechanism in power converters. Dif-

ferent to impedance matching in linear circuits, the impedance networks matching mechanism

contains input impedance matching, output impedance matching and load phase matching. It

follows with a general and systematic design methodology for designing power converters to be

proposed to replace the traditional tedious, manual design of Z-source converters.

Chapter 4 follows the proposed methodology to design two 3-Z-network boost DC-DC

converters. Therein, impedance networks are cascaded to realize output impedance matching,

which greatly increases the output voltage gain (theoretically reaching 350) and solves the low

output voltage problem in solar energy systems. The system analysis, parameters determina-

tion, simulations and experiments will be given.

Chapter 5 proposes a novel Z-source half-bridge converter, where an impedance network

is subtly embedded into the half-bridge converter to realize input impedance matching, which

also balances the mid-voltage of its input capacitors, and fulfills the rigorous requirements

of electrochemical power supplies. Similarly, the system analysis, parameters determination,

simulations and experiments will be presented.

6 1 Introduction

Chapter 6 devises a dual-output Z-source half-bridge converter with two impedance net-

works being parallelized to realize output impedance matching. Such a design reduces one forth

of switching components and capacitors and fulfills the requirements of dual-output, thus it not

only minimizes the cost but also increases the watt density of electric vehicles. Furthermore,

the system analysis, parameters determination, simulations and experiments are also given.

Chapter 7 draws a conclusion of the whole thesis.


Chapter 2

Impedance Networks and Impedance

Source Converters

Some preliminaries are first introduced, such as voltage sources and current sources, and

impedance network and Z-source, which are fundamental for further exploring the mechanism

of impedance network matching and the methodology of design high-quality impedance source

converters. A qualitative analysis is then conducted to understand the existing problems of

the traditional voltage source and current source converters and the advantages of Z-source

converters. Finally, the state-of-the-art of impedance source converters is presented.

2.1 Preliminaries

2.1.1 Voltage Sources and Current Sources

A power converter processes the flow of energy between two sources, generally between a

generator and a load, as illustrated in Fig. 2.1. An ideal static converter is assumed to transmit

electric energy between the two sources with 100% efficiency. The conversion efficiency is the

main concern in designing a converter. Therefore, in practice, power converter design aims at

improving the efficiency.

There are two types of sources, namely voltage and current sources, any of which could be

a generator or a load.

A real voltage source can be represented as an ideal voltage source in series with a resistance

rVS, with the ideal voltage source having zero resistance, to ensure its output voltage to be

constant. The voltage source is normally equivalent to a capacitor C with infinite capacitance,

i.e. C =∞, so that rC = ZC = −j 1ωC ≈ 0, where ZC denotes the resistance of the capacitor.Similarly, a real current source can be represented as an ideal current source in parallel

with a resistance rCS, with the ideal current source having infinite resistance, so that its output

current is constant, which is normally equivalent to an inductor with infinite inductance, i.e.

8 2 Impedance Networks and Impedance Source Converters

Fig. 2.1: A power converter

L = ∞, which implies also rL = ZL = jωL ≈ ∞, where ZL represents the resistance of theinductor.

Correspondingly, converters can be classified into voltage source converters and current

source converters.

2.1.2 Impedance Network and Z-Source

Impedance

The term, resistance, is associated with DC circuits, which is extended to impedance when

facing both DC and AC circuits. For DC circuits, resistance and impedance are equivalent.

Unlike resistance, which has only magnitude and is represented as a positive real number (ohms

(Ω)), impedance possesses both magnitude and phase and can be represented as a complex

number with the imaginary part denoting the reactance and the real part representing the

resistance.

Impedance is used to measure the opposition that a circuit presents to a current when

a voltage is applied [49], and is defined as the frequency domain ration of the voltage to the

current. For a sinusoidal current or voltage input, the polar form of the complex impedance

relates the amplitude and phase of the voltage and current. In particular,

• the magnitude of the complex impedance is the ratio of the voltage amplitude to thecurrent amplitude, and

• the phase of the complex impedance is the phase shift by which the current lags thevoltage.


Impedance Network and Two-port Network

Like a resistor network, which is a collection of interconnected resistors in series or/and parallel,

an impedance network in the context of power electronics, where exist nonlinear switches, is

a network of impedance components like switches, sources, inductors, and capacitors, inter-

connected in series or/and parallel. An impedance network can be a passive one, if it is just

composed of inductors and/or capacitors, or an active one, if it is constituted of switches and/or

diodes, inductors and/or capacitors.

It is difficult, if not impossible, to analyze an impedance network using (linear) circuit

theory due to the nonlinear switch components in the impedance network. A useful procedure

is to simplify the analysis of the impedance network by reducing the number of components,

which is then normally done by replacing the actual components with notional components

of the same functions. Among some analysis methods, such as Nodal and Mesh analyses, a

two-port network is well suited for analysis of the impedance network.

A two-port network, as shown in Fig. 2.2, is an electrical network or a device with four

terminals, which are arranged into pairs called ports, i.e. each pair of terminals is one port.

As shown in Fig. 2.2, the left port is usually considered as the input port, while the right one

is the output port. Therefore, a two-port network is represented by four external variables,

i.e. voltage U1(s) and current I1(s) at the input port, and voltage U2(s) and current I2(s) at

the output port, so that the two-port network can be treated as a black box modeled by the

relationships between the four variables U1(s), I1(s), U2(s), and I2(s) [50]-[53].

Fig. 2.2: Two-port networks

The transmission equation of a two-port network is given by [54]-[57][U1(s)

I1(s)

]= A(s) ·

[U2(s)

−I2(s)

], (2.1)

where A(s) is the transmission matrix and written as

A(s) =

[A11(s) A12(s)

A21(s) A22(s)

], (2.2)


whose elements are defined as

A11(s) =U1(s)

U2(s)

∣∣∣∣∣I2(s)=0

,

A12(s) =U1(s)

−I2(s)

∣∣∣∣∣U2(s)=0

,

A21(s) =I1(s)

U2

∣∣∣∣∣I2(s)=0

,

A22(s) =I1(s)

−I2(s)

∣∣∣∣∣U2(s)=0

.

(2.3)

Therefore, (2.1) can be rewritten as{U1(s) = A11(s)U2(s) + A12(s)(−I2(s)) ,I1(s) = A21(s)U2(s) + A22(s)(−I2(s)) .

(2.4)

The two-port network model is a mathematical circuit analysis technique to isolate portions

of larger circuits. A two-port network is regarded as a “black box” with its properties specified

by a matrix of numbers, which allows the response of the network to signals applied to the ports

to be calculated easily, without solving all the internal voltages and currents in the network.

Impedance networks can have multiple ports connecting external circuits, but generally

have two ports, and can thus be equivalent to a two-port network. In terms of Thevenin’s

equivalent impedance theorem, the input impedance of a two-port network is the equivalent

impedance of the two-port network with an open input port and an output port connecting

a load; while the output impedance (also named as source impedance or internal impedance)

is the equivalent impedance of the two-port network with a short-circuited input port and an

open output port. Further in terms of Ohm’s law, the input impedance of a two-port network

Zi(s) reads

Zi(s) =U1(s)

I1(s)=A11(s)ZL(s) + A12(s)

A21(s)ZL(s) + A22(s), (2.5)

where ZL(s) is the load impedance of the two-port network’s output port.

Similarly, the output impedance of two-port network Zo(s) writes

Zo(s) =U2(s)

I2(s)=A22(s)ZS(s) + A12(s)

A21(s)ZS(s) + A11(s), (2.6)

where ZS(s) is the source impedance of the two-port network’s input port.

Impedance Source Converters (Z-Source Converters)

An impedance network together with a source constitute an impedance source (also named a

Z-source), with its equivalent impedance Z ∈ [0,+∞). The impedance source is a general


source, including voltage- and current sources as its extreme cases; that is, it becomes a voltage

source for Z = 0; and a current source for Z →∞. It exhibits rich properties for 0 < Z


(a) Voltage source inverters (b) Current source inverters

Fig. 2.3: Voltage source and current source inverters

(a) Voltage source inverters (b) Current source inverters

Fig. 2.4: Equivalent circuits of voltage-source- and current-source-inverters with two-port net-

works


2.2.1 Voltage Source Inverters

Shoot-Through

In terms of (2.3), the transmission matrix of the voltage source inverter in Fig. 2.4(a) readsAV11(s) = 1 ,

AV12(s) = ZVS(s) ,

AV21(s) = 0 ,

AV22(s) = 1 .

(2.7)

Substituting (2.7) into (2.5) results in the input impedance of the voltage source inverter

as

Zi(s) =AV11(s)ZL(s) + AV12(s)

AV21(s)ZL(s) + AV22(s)= ZL(s) + ZVS(s) , (2.8)

while the input current of the voltage source is thus obtained as

IVS(s) =VVS(s)

Zi(s)=

VVS(s)

ZL(s) + ZVS(s). (2.9)

It is obvious that ZL(s) = 0 in case that the switches of the voltage source inverter on a

bridge are turned on simultaneously. Moreover, the source impedance ZVS(s) is normally very

small, i.e. ZVS(s) ≈ 0. Therefore, Zi(s) = ZL(s) + ZVS(s) ≈ 0, which implies IVS(s) → ∞.Thus, the voltage source is shorted and a very large current will break down the switches. This

is the so-called shoot-through problem.

In order to prevent the occurrence of the shoot-through, the dead-time compensation

technique is often used to prevent switches from turning on simultaneously [58].

Limited Output Voltage Gains

In terms of Fig. 2.4(a), substituting ZS(s) = 0 and (2.7) into (2.6) results in its output

impedance as

Zo(s) =AV22(s)ZS(s) + AV12(s)

AV21(s)ZS(s) + AV11(s)= ZVS(s) . (2.10)

Obviously, the voltage of the load can be expressed as

VVL(s) = VVS(s)− IL(s)ZVS(s) . (2.11)

It is straightforward from (2.11) that ZVL(s) ≤ VVS(s) (ZVS(s), IL(s) ≥ 0); namely, theload voltage VVL(s) is lower than or equal the source voltage VVS(s).

In order to fulfill the high output voltage gain requirements in industrial applications like

solar energy applications [59]-[62], DC-DC boost front stage converters can be cascaded to

boost the output voltage, which actually changes its output impedance features to increase its

output voltage gains.


Inapplicability to Capacitive Loads

It is known that the electrical loads can be classified into resistive, capacitive, and inductive

ones. A capacitive load is an AC electrical load in which the current wave reaches its peak

before the voltage, like the flash of the camera; while an inductive load is a load that pulls a

large amount of current when first energised, for example, motors, transformers, and wound

control gear, and a resistive load is a load which consumes electrical energy in a sinusoidal

manner. This means that the current flow is in time with and directly proportional to the

voltage, such as incandescent lighting and electrical heaters.

The impedance ZVS(s) in a two-port network is equivalent to a capacitor with very large

capacitance, which implies that ZVS(s) = −j 1ωC ≈ 0. In term of (2.11), one has VVL(s) =VVS(s). It is remarked if the load impedance ZL(s) is capacitive, a capacitive source offers

energy to a capacitive load, while VVL(s) = VVS(s) at a steady state implies that the voltage

source inverter does not function, and is thus inapplicable to capacitive loads.

It is concluded that, due to the impedance of a two-port network between the voltage

source and the inverter bridges, the voltage source inverter has the problems of the shoot-

through, limited output voltage gains, and inapplicability to capacitive loads, which restrain

its wide applications.

2.2.2 Current Source Inverters

Open-Circuit

In terms of (2.3), the transmission matrix of the current source inverter in Fig. 2.4(b) readsAC11(s) = 1 ,

AC12(s) = 0 ,

AC21(s) = YCS(s) ,

AC22(s) = 1 ,

(2.12)

where YCS(s) is the source admittance of the current source inverter, which is the reciprocal of

its source impedance.

Substituting (2.12) into (2.5) results in the input admittance of the current source inverter

Yi(s) =1

Zi(s)=

AC21(s)1

YL(s)+ AC22(s)

AC11(s)1

YL(s)+ AC12(s)

= YL(s) + YCS(s) , (2.13)

where YL(s) and YCS(s) are the load admittance and source admittance, respectively, as shown


in Fig. 2.4(b), while the input voltage of the current source is thus obtained as

VCS(s) =ICS(s)

YL(s) + YCS(s). (2.14)

where ICS(s) is the current of current source, as shown in Fig. 2.4(b).

An inverter normally includes at least one inverter bridge, while one inverter bridge is

normally composed of one upper switch and one lower switch. At least one of the upper switches

and one of the lower switches in the current source inverter must be kept on; otherwise, an

open-circuit problem occurs and thus YL(s) = 0 in (2.14). Moreover, the source admittance

YCS(s) is normally very small, i.e. YCS(s) ≈ 0. Therefore, Yi(s) = YL(s) + YCS(s) ≈ 0, whichimplies VCS(s)→∞. Thus, the current source is an open-circuit and a very large voltage willbreak down the switches.

In order to prevent the open-circuit problems, the overlapped time technique on upper and

lower switches is normally utilized to ensure at least one of the upper switches and one of the

lower switches being on at any time [58].

Limited Output Current Gains

In terms of (2.6), one can obtain the output admittance of the current source inverter as

Yo(s) =1

Zo(s)=

AC21(s)1

YCS(s)+ AC11(s)

AC22(s)1

YCS(s)+ AC12(s)

= YCS(s) , (2.15)

while the output current is

ICL(s) = ICS(s)− VCS(s)YCS(s) . (2.16)

For VCS(s), YCS ≥ 0, one has ICL ≤ ICS, namely, the load current ICL(s) is lower than orequal to the source current ICS(s).

Inapplicability to Inductive Loads

The admittance YCS(s) in a two-port network is equivalent to an inductor with very large

inductance, which implies that YCS(s) = −j 1ωL ≈ 0. It is remarked if the load admittance YL(s)is inductive, an inductive source offers energy to an inductive load, while ICL(s) = ICS(s) at a

steady state implies that the current source inverter does not work and is thus inapplicable to

inductive loads.

It is concluded that, due to the admittance of the two-port network between the current

source and the inverter bridges, the current source inverter has the problems of open-circuit,

limited output current gains, and inapplicability to inductive loads.


2.3 Z-Source Inverters

Peng [23] has proposed to use an impedance network (named as Z-network) in 2002, as shown

in Fig. 2.6, to couple with a DC source to form a novel source, as shown in the rectangles

in Fig. 2.7, including voltage- and current-type Z-source inverters. Applying this Z-source

technology in other converters results in Z-source DC-DC converters (Fig. 2.5(a)), Z-source

AC-DC rectifiers (Fig. 2.5(b)), and Z-source AC-AC converters (Fig. 2.5(c)).

(a) DC-DC converters

(b) AC-DC rectifiers

(c) AC-AC converters

Fig. 2.5: Other typical Z-source converters

Similarly, voltage-type Z-source inverters are also taken as examples, for simplicity, to ex-

plain the reasons that Z-source converters can overcome the problems of voltage source and cur-

rent source converters. The diagram of a voltage-type Z-source inverter is drawn in Fig. 2.7(a),


whose equivalent two-port network is illustrated in the dashed box in Fig. 2.8.

Assume L1 = L2 = L and C1 = C2 = C, and denote the impedance of diode D by ZZS(s).

Fig. 2.6: A Z-network

(a) Voltage-type (b) Current-type

Fig. 2.7: Z-source inverters

In terms of (2.2), one can obtain the transmission matrix of the Z-network as follows

AZ(s) =

[AZ11(s) AZ12(s)

AZ21(s) AZ22(s)

], (2.17)

where, in terms of (2.3), the elements write

AZ11(s) =1 + s2LC

1− s2LC,

AZ12(s) =2sL

1− s2LC,

AZ21(s) =2sC

1− s2LC,

AZ22(s) =1 + s2LC

1− s2LC.

(2.18)


Fig. 2.8: Equivalent circuit of voltage-type Z-source inverters with two-port network

Substituting ZS(s) = ZZS(s), ZL(s) = ZZL(s) and (2.18) into (2.5) and (2.6) results in the

input and output impedances of the Z-network asZZi(s) =

AZ11(s)ZZL(s) + AZ12(s)

AZ21(s)ZZL(s) + AZ22(s)=

(s2LC + 1)ZZL(s) + 2sL

s2LC + 2sCZZL(s) + 1,

ZZo(s) =AZ22(s)ZZS(s) + AZ12(s)

AZ21(s)ZZS(s) + AZ11(s)=

(s2LC + 1)ZZS(s) + 2sL

s2LC + 2sCZZS(s) + 1,

(2.19)

where ZZS(s) is the source impedance of the input port of the Z-network and ZZL(s) is the load

impedance of the output port of the Z-network, described as

ZZS(s) =

{0, if D is on,

∞, otherwise,(2.20)

and

ZZL(s) =

0, at a shoot-through state,

∞, at an open-circuit state,ZZ(s), at a normal state,

(2.21)

where ZZ(s) is the load impedance of the inverter bridge.

Substituting (2.20) and (2.21) into (2.19) leads to the input and output impedances as

ZZi(s) =

2sL

s2LC + 1, at a shoot-through state,

s2LC + 1

2sC, at an open-circuit state,

(s2LC + 1)ZZ(s) + 2sL

2sCZZ(s) + s2LC + 1, at a normal state,

(2.22)


and

ZZo(s) =

2sL

s2LC + 1, if D is on,

s2LC + 1

2sC, otherwise.

(2.23)

Immunity to the Shoot-Through

The input current of the Z-source inverter is expressed as

IZS(s) =VZS(s)

ZZi(s), (2.24)

where ZZL(s) = 0 if the switches on a bridge are turned on simultaneously. It is obvious that

ZZi(s) 6= 0 holds in all cases in terms of (2.22). Therefore, the Z-source inverter can operate atshoot-through states. Compared to the voltage source inverter, Z-source inverter is immune to

the shoot-through problem, so that the short-circuit phenomenon at the source can be avoided

because the Z-network increases the input impedance.

High Output Voltage Gains

Denote the duty cycle of the diode D as d and assume d ∈ [0, 1]. In terms of (2.23), one canobtain the average output impedance as

ZZo(s) =(1− d)L

2

s4 + s2

(2(1 + d)

(1− d)LC

)+

1

L2C2

s3 + s1

LC

, (2.25)while the output voltage of the Z-source inverter, VZL(s), is expressed as

VZL(s) = VZS(s)− IZL(s)ZZo(s) . (2.26)

It is obvious that ZZo(s) is the function of the duty d in terms of (2.25). Adjusting ZZo(s)

to be negative or positive via d, one can obtain either VZL(s) > VZS(s) or VZL(s) < VZS(s),

which implies that the Z-source inverters can overcome the limited voltage gains of traditional

voltage source inverters.

Applicability both to Capacitive and Inductive Loads

Assume that ZZ(s) is capacitive. Then, in terms of (2.23), one has

ZZ(s) =1

sCL, (2.27)


where CL is the capacitance of the load.

By adjusting the duty d, and the inductance L, capacitance C of the Z-network, the

output impedance of the Z-network can exhibit the inductive feature, implying that the Z-

source inverter is applicable to a capacitive load.

Similarly, assume that ZZ(s) is inductive and one can also prove that the Z-source inverter

is also capable of an inductive load.

It is thus concluded that due to the embedded Z-network, Z-source inverters have unique

advantages over traditional ones, i.e. immunity to the shoot-through, higher output voltage

gains, and applicability both to capacitive and inductive loads, which have a great potential in

renewable energy applications.

2.4 State-of-The-Art of Impedance Source Converters

Based on the typical Z-source converters proposed by Peng, various impedance source converters

have been proposed for different specified applications, such as quasi-Z-source converters, trans-

Z-source converters, embedded-Z-source converters, which are to be reviewed in this section.

2.4.1 Quasi-Z-Source Converters

Inspired by the typical Z-source converters, Anderson and Peng have firstly proposed quasi-

Z-source converters in 2008, which are mainly applied in motor systems, new energy systems,

and micro-grid systems. According to the operational modes in voltage-type or current-type

and continuous or discontinuous current, quasi-Z-source converters can be classified into four

categories, i.e. voltage-fed quasi-Z-source inverters with continuous input current, voltage-fed

quasi-Z-source inverters with discontinuous input current, current-fed quasi-Z-source inverters

with continuous input current, and current-fed quasi-Z-source inverters with discontinuous in-

put current, which are shown in Fig. 2.9 [63]. It is found by Cao and Peng [64] that all of

the impedance networks in Fig. 2.9 can be derived from the one in Fig. 2.6. For instance, a

voltage-fed quasi-Z-source inverter with continuous input current in Fig. 2.9(a) is equivalent to

that in Fig. 2.10, whose switches S1 and S2 are equivalent to the diode D and the inverting

bridge in Fig. 2.9(a), respectively.

It is remarked that the impedance network in Fig. 2.10 is a typical quasi-Z-network, based

on which various quasi-Z-networks can be derived. For example, Cao and Peng have proposed

a family of quasi-Z-source DC-DC converters [64], and Vinikov et.al. have also proposed some

novel quasi-Z-source DC-DC converters for renewable energy systems [65].

Similar to the analysis of the typical Z-source converters, features of quasi-Z-source con-

verters can also be analyzed in terms of the two-port network theory. Here, the voltage-fed

quasi-Z-source inverter is taken as an example and its equivalent circuit with the two-port


(a) Voltage-fed one with continuous current

(b) Voltage-fed one with discontinuous current

(c) Current-fed one with continuous current

(d) Current-fed one with discontinuous current

Fig. 2.9: Quasi-Z-source inverters [63]


Fig. 2.10: Equivalent circuit of the converter in Fig. 2.9 [64]

network is shown as Fig. 2.11. Therein, assume L1 = L2 = L, C1 = C2 = C, and denote the

inverter bridge with the load by ZQL(s).

Fig. 2.11: Equivalent circuit of voltage-fed quasi-Z-source inverters with two-port network

In terms of (2.2), one can obtain the transmission matrix of quasi-Z-network as follows

AQ(s) =

[AQ11(s) AQ12(s)

AQ21(s) AQ22(s)

], (2.28)

where

AQ11(s) = s2LC + 1 ,

AQ12(s) = 2sL ,

AQ21(s) = sC ,

AQ22(s) =2s2LC + 1

1 + s2LC,

if D is on. (2.29)


Substituting ZS(s) = ZQS(s) and ZL(s) = ZQL(s) into (2.5) and (2.6) results in the input

and output impedances of the quasi-Z-network as

ZQi(s) =(s2LC + 1)ZQL(s) + 2sL

sCZQL(s) +2s2LC + 1

s2LC + 1

,

ZQo(s) =2sL

s2LC + 1,

if D is on. (2.30)

As diode D turns off, the elements in the transmission matrix (2.28) write

AQ11(s) = 2 ,

AQ12(s) =1 + s2LC

sC,

AQ21(s) =sC

1 + s2LC,

AQ22(s) = 1 ,

if D is off. (2.31)

Similarly, one can obtain its input and output impedances asZQi(s) =

2(s2LC + 1)sCZQL(s) + (s2LC + 1)2

s2C2ZQL(s) + sC(s2LC + 1),

ZQo(s) =s2LC + 1

sC,

if D is off. (2.32)

Denote the duty cycle of the diode D as d ∈ [0, 1]. The averages of the input and outputimpedances are given by

ZQi(s) = d(s2LC + 1)ZQL(s) + 2sL

sCZQL(s) +2s2LC + 1

s2LC + 1

+ (1− d)2s(s2LC + 1)CZQL(s) + (s

2LC + 1)2

s2C2ZQL(s) + sC(s2LC + 1),

ZQo(s) =2sdL

s2LC + 1+ (1− d)

(s2LC + 1

sC

).

(2.33)

Immunity to Shoot-Through

The input current of the quasi-Z-source inverter is expressed as

IQS(s) =VQS(s)

ZQi(s). (2.34)


In terms of (2.30) and (2.32), it is obvious that ZQi(s) 6= 0 holds in any conditions, i.e. thecurrent will not be infinite according to (2.34), which implies that the quasi-Z-source inverter

is immune to the shoot-through problems.


The output voltage of the quasi-Z-source inverter VQL(s) reads

VQL(s) = VQS(s)− IQL(s)ZQo(s). (2.35)

In terms of (2.33), it is found that ZQo(s) varies with d. In addition, one can obtain

VQL(s) > VQS(s) by adjusting d, which implies that the output voltage of the quasi-Z-source

inverters can be higher than the input voltage.


Assume that the load impedance in (2.33) is capacitive. By adjusting the duty d, and the

inductance L, capacitance C of the quasi-Z-network, the output impedance of the quasi-Z-

network can exhibit the inductive feature, which implies that the energy is exchanged between

the inductive quasi-Z-network and the capacitive load for inversion, i.e. the quasi-Z-source

converter is applicable to a capacitive load.

Similarly, it can be proved that the quasi-Z-source inverter is also applicable to an inductive

load.

It is thus concluded that due to the embedded quasi-Z-network, quasi-Z-source inverters

have unique advantages over traditional ones, i.e. immunity to the shoot-through, higher output

voltage gains, and applicability both to capacitive and inductive loads.

2.4.2 Trans-Z-Source Converters

Compared with traditional voltage source converters, whose voltage gains are normally in scale

of 5 ∼ 6, typical Z-source and quasi-Z-source converters can obtain much larger voltage gainsin scale of 20, which are, however, still not large enough for some special applications. For

example, voltage gains of converters utilized in solar energy systems need to reach the scales of

decades or even hundreds.

In 2010, Qian and Peng et.al have integrated the transformers or coupled inductors into

the Z-networks (shown in Fig. 2.6) and quasi-Z-networks (shown in Fig. 2.10) to construct

trans-Z-networks as shown in the dashed box in Fig. 2.12 [66], and thus various trans-Z-source

converters can be coined.

In terms of different operational modes of input current and coupled inductors, trans-

Z-source converters can be classified into six categories, i.e. voltage-fed trans-quasi-Z-source


(a) Voltage-fed one (b) Current-fed one

(c) Voltage-fed one with coupled inductors (d) Current-fed one with coupled inductors

(e) Voltage-fed trans-quasi-Z-source one (f) Current-fed trans-quasi-Z-source one

Fig. 2.12: Typical trans-Z-source converters [66]

inverters, current-fed trans-quasi-Z-source inverters, voltage-fed trans-quasi-Z-source inverters

with coupled inductors, current-fed trans-quasi-Z-source inverters with two coupled inductors,

voltage-fed trans-quasi-Z-source inverters, and current-fed trans-quasi-Z-source inverters, as

shown in Fig. 2.12. Therein, trans-Z-source converters not only maintain the main features

of traditional Z-source converters, but also exhibit some unique advantages, i.e. increased

voltage gains and reduced voltage stress in the voltage-fed trans-Z-source inverters due to the

transformers or coupled inductors, and the expanded operation quadrant in the current-fed

trans-Z-source inverters. However, transformers and coupled inductors increase volume and

cost.

Similar to the typical Z-source converters, trans-Z-source converters can be also analyzed

using the two-port network theory. Here, the voltage-fed quasi-Z-source inverter is taken as an

example and its equivalent circuit with a two-port network is depicted in Fig. 2.11.


Denote the mutual inductance between the coupled inductors L1 and L2 as M , and the

inverter bridge with the load as ZTL(s), assume L1 = L2 = L, then one has M = n√L1L2 = nL,

where n is the turn ratio between L1 and L2.

Fig. 2.13: Equivalent circuit of trans-Z-source inverters with two-port networks

In terms of (2.2), the transmission matrix of trans-Z-network is given as

AT(s) =

[AT11(s) AT12(s)

AT21(s) AT22(s)

]. (2.36)

When the diode D is on, the elements in (2.36) write

AT11(s) = 1 ,

AT12(s) = sL+(1 + ns2LC)sL

(n+ 1)s2LC + 1,

AT21(s) = 0 ,

AT22(s) = 1 ,

if D is on, (2.37)

then, the input impedance ZTi(s) and the output impedance ZTo(s) are given byZTi(s) = ZTL(s) + sL+

(ns2LC + 1)sL

(n+ 1)s2LC + 1,

ZTo(s) = sL+(ns2LC + 1)sL

(n+ 1)s2LC + 1,

if D is on, (2.38)


where ZTS(s) and ZTL(s) are the equivalent source and load impedances, respectively.

When the diode D is off, the elements in (2.36) read

AT11(s) = 1 ,

AT12(s) = (n+ 1)sL+1

sC,

AT21(s) = 0 ,

AT22(s) = 1 ,

if D is off. (2.39)

Similarly, one can obtain the input impedance ZTi(s) and the output impedance ZTo(s) asZTi(s) = ZQL(s) + (n+ 1)sL+

1

sC,

ZTo(s) = (n+ 1)sL+1

sC,

if D is off. (2.40)

Denote the duty cycle of the diode D as d ∈ [0, 1]. The average of the input and outputimpedance are then obtained as

ZTi(s) = ZTL(s) + d(2 + (2n+ 1)s2LC)sL

1 + (n+ 1)s2LC+ (1− d)

((n+ 1)sL+

1

sC

),

ZTo(s) = d(2 + (2n+ 1)s2LC)sL

1 + (n+ 1)s2LC+ (1− d)

((n+ 1)sL+

1

sC

).

(2.41)

Immunity to the Shoot-Through

The input current of the trans-Z-source inverter is derived as

ITS(s) =VTS(s)

ZTi(s). (2.42)

In terms of (2.41), the input impedance ZTi(s) can prevent the shoot-through occurring

by adjusting the duty d to ensure ZTi(s) 6= 0 at any case, which implies that the trans-Z-sourceinverter is immune to the shoot-through.


The output voltage gain of trans-Z-source inverter VTL(s) reads

VTL(s) = VTS(s)− ITL(s)ZTo(s) . (2.43)


In terms of (2.41), one can obtain VTL(s) > VTS(s) by adjusting ZTo(s) via duty d, which

implies that the output voltage can be higher than the input voltage to realize high voltage

gains. The fact that ZTo(s) is proportional to n in (2.41) ensures that the output voltage gains

of tran-Z-source inverters can be larger than the ones of traditional Z-source converters.


Assume that the load impedance in (2.41) is capacitive. By adjusting the duty d, and the

inductance L, capacitance C of the trans-Z-network, the output impedance of the trans-Z-

network can exhibit the inductive feature, which enables the energy exchange between the

trans-Z-network and the capacitance load. Therefore, the trans-Z-source inverter is applicable

to a capacitive load.

Similarly, it can be proved that the trans-Z-source inverter is also applicable to an inductive

load.

It is thus concluded that trans-Z-source inverters not only possess the features of typical

Z-source inverters, but also obtain higher voltage gains than traditional ones.

2.4.3 Embedded-Z-Source Converters

In order to obtain smaller volume and higher robustness, P.C. Loh et.al proposed embedded-

Z-source converters in 2010 [67]. Instead of using an external LC filter, they proposed an

alternative family of embedded-Z-source inverters, which adopts the concept of embedding the

input DC sources within the LC impedance network, using its existing inductive elements for

current filtering in voltage-type embedded-Z-source inverters, and its capacitive elements for

voltage filtering in current-type embedded-Z-source inverters. The typical topologies can be

classified into two-level type and three-level type, as shown in Fig. 2.14.

Similarly, one can use the two-port network theory to analyze embedded-Z-source inverters.

It is concluded that the embedded-Z-source inverters not only maintain the features of typical

Z-source inverters, but also produce smaller ripples of input voltage and current.

2.4.4 Other Impedance Source Converters

Since the proposal of Z-source converters in 2002, various Z-source converters have been pro-

posed, e.g. Y-source converters (Fig. 2.15) [68], Γ-Z-source converters (Fig. 2.16) [69]-[72],

LCCT-Z-source converters (Fig. 2.17) [73]-[74], and Z-H-source converters (Fig. 2.18) [75], to

list just a few.

Y-source converters shown in Fig. 2.15 are designed based on trans-Z-source converters,

which, however, realize a higher voltage gain by using a smaller duty ratio.


(a) Two-level type

(b) Three-level type

Fig. 2.14: Typical embedded-Z-source converters [67]


Fig. 2.15: Y-source converters [68]

Γ-Z-source converters shown in Fig. 2.16 use fewer components and a coupled transformer

to provide a high voltage gain, and they are essentially derived from the trans-Z-source convert-

ers. Therein, two Γ-shaped inductors (Fig. 2.16(a)) are coupled in trans-Z-source converters to

form Γ-Z-source converters. Moreover, a voltage source is embedded in the Γ-shaped network

in Fig. 2.16(b); therefore, it is also an embedded-Z-source converter.

LCCT-Z-source converters (LCCT stands for the inductor-capacitor-capacitor-transformer)

shown in Fig. 2.17 are extended from trans-Z-source inverters and have unique features, such as

the converter in Fig. 2.17(b), whose two built-in DC blocking capacitors, cascaded with trans-

former windings, can prevent the transformer from saturation, while the one in Fig. 2.17(a),

whose one built-in DC capacitor, cascaded with transformer windings, possesses the features

of both quasi-Z-source and trans-Z-source converters.

Fig. 2.18 depicts a Z-H-source converter, which contains fewer components, but own the

same functions as traditional Z-source converters.

2.5 Summary

Up to now, there have been more than 1100 papers about impedance source converters published

in various professional journals [24, 25], e.g. F.Z. Peng [76], P.C. Loh [77]-[88], Y. Tang [89]-[93],

J.W. Jung [94, 95, 96], A.Y. Varjani [97]-[100], D. Vinnikov [101]-[104], to name just a few. It

shows that designing new impedance source converters has attracted more and more attentions

from scientists and engineers.

Rapidly developing renewable energy industry has posed more stringent and higher re-

quirements on power electronics, especially high quality converters. Unfortunately, until now

designing an impedance source converter is still an art, lacking a systematic designing method-

ology, which can not fulfil the industrial requirements.

Due to the important role of impedance networks, which are coupled with traditional con-


(a) Source placed in series with diode

(b) Source placed in series with inverter bridge

Fig. 2.16: Γ-Z-source converters [69]

verters to construct impedance source converters, the impedance networks matching mechanism

is to be investigated in the next chapter, and a systematic designing methodology can thus be

proposed.


(a) One blocking capacitor type

(b) two blocking capacitors type

Fig. 2.17: LCCT-Z-source converters [73]

Fig. 2.18: Z-H-source converters [75]


Chapter 3

Impedance Networks Matching

Mechanism

This chapter constitutes the key part of the dissertation. The impedance networks matching

mechanism is to be investigated and a systematic design methodology is to be proposed.

3.1 Impedance Matching

In electronics, impedance matching is the practice of designing the input impedance of an

electrical load or the output impedance of its corresponding signal source to maximize the

power transfer or minimize signal reflection from the load [105]. In terms of the maximum

power-transfer theorem, the load impedance should match the source impedance in order to

transfer the maximum amount of power from a source to a load. That is to say, maximum power

is transferred from a source to a load when the load resistance equals the internal resistance of

the source.

For DC, it is well known that maximum power transfer can be achieved if source resistance

is equal to the load resistance; while for radio frequency (RF), impedances should be considered,

and impedance matching aims to make the real part of the impedance equal to the real part of

the load and the real part of reactance equal and opposite in character [50].

The concept of impedance matching deals originally with linear circuits, and is not directly

applicable to power converters, which are essentially nonlinear switched circuits. Nevertheless,

in each operational mode, a power converter works as a linear circuit, which results in the

time-varying characteristics of the impedances matching for impedance networks matching.

Therefore, the concept of the impedance matching can be extended to the impedance network

matching in three aspects: input impedance matching, output impedance matching, and load

phase matching.

34 3 Impedance Networks Matching Mechanism

3.2 Input Impedance Matching

Substituting s = jω into the input impedance of the two-port network in (2.5) results in

Zi(jω) = Re

(A11(jω)ZL(jω) + A12(jω)

A21(jω)ZL(jω) + A22(jω)

)+ jIm

(A11(jω)ZL(jω) + A12(jω)

A21(jω)ZL(jω) + A22(jω)

). (3.1)

The shoot-through state implies that ZL(jω) = 0, so the input impedance in shoot-through

state is derived as

Zi(jω) = Re

(A12(jω)

A22(jω)

)+ jIm

(A12(jω)

A22(jω)

), (3.2)

whereas the input current of the voltage source at the shoot-through states is expressed as

IS(jω) =VS(jω)

Zi(jω)=

VS(jω)

Re

(A12(jω)

A22(jω)

)+ jIm

(A12(jω)

A22(jω)

) . (3.3)

Since inductive components hinder their current change, it is then obvious that the con-

verter can restrain the short-circuit current if its input impedance in (3.2) is inductive.

Im

(A12(jω)

A22(jω)

)> 0. (3.4)

Voltage Source Inverters

Suppose that the inverter bridge of the voltage source inverter is short-circuited. In terms of

(3.2), the input impedance of the voltage source inverter writes

Zi(jω) = Re (ZS(jω)) + jIm (ZS(jω)) , (3.5)

where ZS(jω) is its equivalent source impedance and ZS(jω) is equivalent to a capacitor with

a large capacitance, i.e. Im (ZS(jω)) < 0. Here, in terms of (3.4), the voltage source inverter

does not function for cases of inverter bridges being short-circuited.

Typical Z-Source Inverters

In terms of (2.18) and (3.2), the input impedance in the shoot-through case of the typical

Z-source inverter reads

Zi(jω) = Re

(j2ωL

1− ω2LC

)+ jIm

(j2ωL

1− ω2LC

), (3.6)


where the imaginary part of (3.6) is2ωL

1− ω2LC.

If the switching frequency f of the diode D and the impedance network parameter LC

satisfy the condition

f <1

2π√LC

, (3.7)

then2ωL

1− ω2LC> 0, which means that the input impedance is inductive and satisfies the

condition (3.4). Consequently, the typical Z-source inverter can operate in shoot-through states.

Quasi-Z-Source Inverters

In terms of (3.2), (3.4), (2.29) and (2.31), the imaginary part of the quasi-Z-source inverter’s

input impedance in shoot-through case writes

Im

(AQ12(jω)

AQ22(jω)

)=

2ωL(1− ω2LC)1− 2ω2LC

, if D is on,

2ωC

1− ω2LC, otherwise.

(3.8)



f <1

2π√

2LC, (3.9)

then Im

(AQ12(jω)

AQ22(jω)

)> 0, implying that the input impedance is inductive and satisfies the

condition (3.4). Therefore, the quasi-Z-source converter can operate in shoot-through states.

Trans-Z-Source Inverters

For a trans-Z-source inverter, in terms of (3.2), (3.4), (2.37) and (2.39), when the inverter bridge

is short-circuited, the imaginary part of the input impedance reads

Im

(AT12(jω)

AT22(jω)

)=

ωL(2− (2n+ 1)ω2LC)1− (n+ 1)ω2LC

, if D is on,

−1− (n+ 1)ω2LC

ωC, otherwise.

(3.10)




f >1

2π

√√√√(n+ 12

)LC

, (3.11)

then Im

(AT12(jω)

AT22(jω)

)> 0, which implies that the input impedance is inductive and satisfies

the condition (3.4). Therefore, the trans-Z-source inverter can operate in shoot-through states.

3.3 Output Impedance Matching

Substituting s = jω into the output voltage equation VL(s) = VS(s) − IL(s)Zo(s) results inVL(jω) = VS(jω) − IL(jω)Zo(jω). It is remarked that in order for the output voltage to behigher than the source voltage, the output impedance Zo(jω) should be negative; otherwise,

the output impedance Zo(jω) should be positive.

Substituting s = jω into (2.6) leads to the output impedance of the two-port network as

Zo(jω) = Re

(A22(jω)ZS(jω) + A12(jω)

A21(jω)ZS(jω) + A11(jω)

)+ jIm



), (3.12)

while the corresponding output voltage is

VL(jω) = VS(jω)ZL(jω)

ZL(jω) + Zo(jω). (3.13)

It is obvious that |VL(jω)| > |VS(jω)|, if the voltage gain M satisfies the condition M > 1,namely,

M =|VL(jω)||VS(jω)|

= |ZL(jω)

ZL(jω) + Zo(jω)|

=|ZL(jω)|

|ZL(jω) + Zo(jω)|

=

√[Re(ZL(jω))]2 + [Im(ZL(jω))]2√

[Re(ZL(jω)) + Re(Zo(jω))]2 + [Im(ZL(jω)) + Im(Zo(jω))]2

> 1,

(3.14)


from which one has

[Re(ZL(jω))]2 + [Im(ZL(jω))]

2 > [Re(ZL(jω)) + Re(Zo(jω))]2 + [Im(ZL(jω)) + Im(Zo(jω))]

2 ,

(3.15)

which can be further simplified as

2[Re(ZL(jω))Re(Zo(jω)) + Im(ZL(jω))Im(Zo(jω))] + [Re(Zo(jω))]2 + [Im(Zo(jω))]

2

= 2[Re(ZL(jω))Re(Zo(jω)) + Im(ZL(jω))Im(Zo(jω))] + |Zo(jω)|2

< 0.

(3.16)

Then, if one has

Re(ZL(jω))Re(Zo(jω)) + Im(ZL(jω))Im(Zo(jω)) < −|Zo(jω)|2

2< 0 , (3.17)

(3.14) holds. That is, if Re(ZL(jω))Re(Zo(jω) < 0 or Im(ZL(jω))Im(Zo(jω)) < 0, and their

sum is smaller than 0, then (3.17) holds. Moreover, it is suggested from (3.17) that the real

parts of the load impedance and the output impedance should have opposite signs, or the

imaginary parts of the load impedance and the output impedance should have opposite signs.

This means that the output impedance should have negative impedance features; otherwise,

the output impedance exhibits positive impedance features.


For a voltage source inverter, in terms of (2.10) and (3.12), its output impedance reads

Zo(jω) = ZVS(jω). (3.18)

From ZVS(jω) ≈ 0, it is obvious that (3.17) does not hold, the output impedance exhibitspositive impedance feature, i.e. the output voltage is lower than the source voltage.


In terms of (2.18) and (3.12), the average output impedance of a typical Z-source inverter is

described by

ZZo(jω) = j

(2ωdL

1− ω2LC−

(1− d)(1− ω2LC)2ωC

). (3.19)

Substituting (3.19) into (3.17) results in1 > d >

(1− ω2LC)2

(1 + ω2LC)2,

Im(ZZo(jω)) < −2Im(ZL(jω)) ,

(3.20)


or 0 < d <

(1− ω2LC)2

(1 + ω2LC)2,

Im(ZZo(jω)) > −2Im(ZL(jω)) .

(3.21)

If (3.20) or (3.21) is fulfilled, then (3.17) holds, which implies that the output impedance

exhibits negative impedance feature and the converter realizes boost functions; otherwise, the

output impedance exhibits positive impedance feature and the converter acts buck functions.

When the parameters in a typical Z-source inverter, i.e. the capacitance, inductance, and

frequency, are fixed, one can adjust the average output impedance to match the load impedance

by tuning the duty d to realize either buck or boost function.

Assume L = 1 µH, C = 63 µF and d = 0.5. The bode diagram of the average output

voltage gain is shown in Fig. 3.1, which illustrates the relationships between the duty d and

ω2LC in (3.20) and (3.21) with regard to the switching frequency f .

It is remarked that the magnitude can be positive or negative, implying that a Z-source

inverter can realize both boost and buck functions.

Fig. 3.1: Bode diagram of the output voltage gain of Z-source inverters



In terms of (2.33) and (3.12), one obtains the average output impedance of a quasi-Z-source

inverter as

ZQo(jω) = j

(2ωdL

1− ω2LC− (1− d)

(1− ω2LC)ωC

). (3.22)

Substituting (3.22) into (3.17) leads to1 > d >

(1− ω2LC)2

1 + ω4LC,

Im(ZQo(jω)) < −2Im(ZL(jω)) ,

(3.23)

or 0 < d <

(1− ω2LC)2

1 + ω4LC,


(3.24)

It is straightforward that (3.17) holds, if (3.23) or (3.24) is satisfied, implying that the

output impedance exhibits negative impedance features for boost functions; otherwise, the

output impedance exhibits positive impedance features for buck functions.


From (2.41) and (3.12), one has the average output impedance of a trans-Z-source inverter as

ZTo(jω) = j

(d

(2− (2n+ 1)ω2LC)ωL1− (n+ 1)ω2LC

− (1− d)

(1− (n+ 1)ω2LC

ωC

)). (3.25)

Substituting(3.25) into (3.17) leads to1 > d >

(1− (n+ 1)ω2LC)2

(1− nω2LC)2,

Im(ZQo(jω)) < −2Im(ZL(jω)) ,

(3.26)

or 0 < d <

(1− (n+ 1)ω2LC)2

(1− nω2LC)2,


(3.27)

Similarly, (3.17) holds, if (3.26) or (3.27) is satisfied, implying that the output impedance

exhibits negative impedance features for boost functions; otherwise, the output impedance

illustrates positive impedance features for buck functions.


In summary, the output impedance matching is to adjust the parameters of the impedance

network and the operation conditions in order for the output impedance to be positive or

negative. Thus, the inverter can exhibit either buck or boost functions by adapting the duty d

to change the sign of the output impedance.

3.4 Load Phase Matching

In order to improve the load ability of the converter, so that the inverter is applicable to both

inductive and capacitive loads, the output impedance phase of the inverter should be capacitive

or inductive so as to match the load impedance for reducing the impedance phase angle of the

inverter. Therein, the total impedance phase is the sum of the output impedance phase and

load impedance phase. Moreover, the smaller the total impedance phase is, the larger the power

factor of the inverter is. Therefore, the optimal condition is that its total impedance phase is

0◦.

The impedance phase angle of the converter is given by

ϕ = arctan

(Im (Zo(jω) + ZL(jω))

Re (Zo(jω) + ZL(jω))

). (3.28)

In terms of (3.12),

Im (Zo(jω) + ZL(jω)) = Im


A21(jω)ZS(jω) + A11(jω)+ ZL(jω)

)= 0 (3.29)

implies that its impedance phase angle is 0◦. Moreover, (3.29) also can be further simplified to

Im (ZL(jω)) = −Im (Zo(jω)) = −Im



). (3.30)


For a voltage source inverter, substituting (2.7) into (3.30) results in

Im (ZL(jω)) = −Im (ZS(jω)) . (3.31)

It is obvious that the source impedance of the voltage source inverter is a capacitor with

a very large capacitance, thus, one has Im (ZS(jω)) < 0. Therefore, only when the load

impedance ZL(jω) is inductive, i.e. Im (ZL(jω)) > 0, (3.31) holds, implying that the voltage

source inverter is applicable to a capacitive load.



For a typical Z-source inverter, substituting (2.18) into (3.30) results in

Im (ZL(jω)) = −Im (ZZo(jω)) =(1− d)(1− ω2LC)

2ωC−

2ωdL

1− ω2LC. (3.32)

1 > d >(1− ω2LC)2

(1 + ω2LC)2(3.33)

implies that Im (ZZo(jω)) > 0 and Im (ZL(jω)) < 0, which implies that the inverter is applicable

to a capacitive load; otherwise, one has Im (ZZo(jω)) < 0 and Im (ZL(jω)) > 0, which means

that the converter is applicable to an inductive load. Therefore, the impedance phase of the

typical Z-source inverter can be matched to be 0◦ via duty d for load phase matching.

Assume the impedance network parameters of the typical Z-source inverter as L = 1 µH,

C = 63 µF and d = 0.5. The bode diagram of the output impedance as shown in Fig. 3.2

illustrates the relationships between the duty d and ω2LC with regard to the switching frequency

f . Therein, the phase switches from 90◦ to −90◦, i.e. from inductive to capacitive, whichindicates that the typical Z-source converter is applicable of any kind of load.

Fig. 3.2: Output impedance bode diagram of Z-source inverters



For a quasi-Z-source inverter, substituting (2.29) and (2.31) into (3.30) results in

Im (ZL(jω)) = −Im (ZQo(jω)) =(1− d)(1− ω2LC)

ωC−

2ωdL

1− ω2LC. (3.34)

It is remarked that

1 > d >(1− ω2LC)2

1 + ω4LC, (3.35)

implies Im (ZQo(jω)) > 0 and Im (ZL(jω)) < 0, which means that the inverter is applicable

of a capacitive load; otherwise, one has Im (ZQo(jω)) < 0 and Im (ZL(jω)) > 0, implying

that the inverter is applicable of an inductive load. Therefore, the impedance of the quasi-Z-

source inverter can be matched to be resistive by adapting the duty cycle to realize load phase

matching.


For a trans-Z-source converter, substituting (2.37) and (2.39) into (3.30) results in

Im (ZL(jω)) = −Im (ZTo(jω)) =(1− d)(1− (n+ 1)ω2LC)

ωC−

(2− (2n+ 1)ω2LC)ωdL1− (n+ 1)ω2LC

. (3.36)

It is remarked that

1 > d >(1− (n+ 1)ω2LC)2

(1− nω2LC)2(3.37)

implies Im (ZTo(jω)) > 0 and Im (ZL(jω)) < 0, saying that the inverter is applicable of a

capacitive load; otherwise, one has Im (ZTo(jω)) < 0 and Im (ZL(jω)) > 0, which means that

the converter is applicable of an inductive load. Therefore, the impedance of the trans-Z-

source inverter can be matched to be resistive by adapting the duty cycle to realize load phase

matching.

It is thus concluded that the load phase matching is to adapt the phase of output impedance

for matching its load impedance. In detail, the parameters of the impedance network are

adjusted to make the converter be suitable for any kind of loads and realize the total impedance

phase angle close to 0◦.

3.5 Matching Optimization

The impedance networks matching contains input impedance matching, output impedance

matching and load phase matching. Therein, input impedance matching is to increase the

input impedance in the short-circuit case for making the input impedance inductive and then


to restrain the input current; output impedance matching is to tune the output impedance to

be of positive or negative nature, so as to increase or decrease output voltage by connecting

an impedance network or adjusting the impedance networks parameters; while load phase

matching is to match the output impedance with the load impedance to ensure its impedance

phase angle to be 0◦.

Therefore, to design a reasonable and feasible impedance source converter, input impedance

matching, output impedance matching and load phase matching are overall considered via

parameters design to realize an optimal matching.

From sections 3.2, 3.3 and 3.4, conditions for impedance network matching can be con-

cluded as

Im

(A12(jω)

A22(jω)

)> 0 ,

Re(ZL(jω))Re(Zo(jω)) + Im(ZL(jω))Im(Zo(jω)) < −|Zo(jω)|2

2,

Im (ZL(jω)) = −Im



).

(3.38)

To satisfy the conditions (3.38), it is concerned with the topologies and parameters of the

impedance network, the source impedance, and the load impedance; while the matching process

is to calculate the parameters of the impedance network in terms of (3.38) and other known

parameters.

A typical Z-source inverter is taken as an example to demonstrate the impedance matching

process.

Assume that the load is capacitive, i.e. ZL(jω) = −j 1ωCL . Substituting the transmissionparameters of the typical Z-source inverter (2.18) into (3.38),

Impedance Networks Matching Mechanism and Design of … · 2016. 3. 8. · matching, output...

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