INVESTIGATION ON THE DC-AC DUAL

ACTIVE BRIDGE CONVERTER AND ITS

PHOTOVOLTAIC APPLICATIONS

Jiatu Hong

Submitted in fulfilment of the requirements for the degree of

Master of Engineering (Research)

Electrical Engineering and Computer Science

Science and Engineering Faculty

Queensland University of Technology

2018

Investigation on the DC-AC Dual Active Bridge Converter and its Photovoltaic Applications i

Keywords

DC-AC, dual active bridge, MPPT, photovoltaics, power decoupling, series

resonant converter.

Investigation on the DC-AC Dual Active Bridge Converter and its Photovoltaic Applications iii

Abstract

The dual active bridge (DAB) converter is widely used in industrial

applications where high power density, isolation and bidirectional power transfer are

required. This thesis investigates on the DC-AC DAB series resonant single-stage (1-

S) converter. In single-phase DC-AC systems, double-line-frequency power ripple

appears at the DC side inherently. Normally a large electrolytic capacitor can be used

to reduce the power ripple at the DC side. But there are several problems with this

method: (1) First, the using of the large electrolytic capacitor can decrease the power

density of the converter significantly. (2) Second, the diffusion of the electrolyte

results in low reliability of the converter. (3) Third, even the using of the large

electrolytic capacitor cannot completely eliminate the power ripple. Based on these

reasons, an alternative power decoupling method is proposed to completely eliminate

the double-line-frequency power ripple at the DC side without the commonly used

large electrolytic capacitor. Specifically, a LC power decoupling circuit with the

specific control strategy is proposed to completely eliminate the ripple power.

Based on the proposed power decoupling method for the DC-AC DAB

converter, an example of its application in photovoltaic systems is presented. Due to

the presence of the inherent double-line-frequency power ripple at the AC side, the

operation of the maximum power point tracking (MPPT) can be significantly

affected in single-phase DC-AC photovoltaic applications. To reduce the ripple

power and enhance the MPPT performance, a large capacitor at the DC side is

normally used. However, as discussed before, it can decrease the power density of

the converter and cannot completely eliminate the ripple power. To mitigate the

effect of power ripple and achieve a high accuracy of MPPT, the performance of the

proposed single-phase DC-AC DAB converter for photovoltaic applications is

presented and analyzed. It is free of the commonly used large capacitor at DC power

stages with the proposed control strategy. As a result, high accuracy of MPPT of the

converter can be obtained.

Investigation on the DC-AC Dual Active Bridge Converter and its Photovoltaic Applications v

Table of Contents

Keywords .................................................................................................................................. i

Abstract ................................................................................................................................... iii

Table of Contents ......................................................................................................................v

List of Figures ........................................................................................................................ vii

List of Tables ............................................................................................................................x

List of Abbreviations .............................................................................................................. xi

Acknowledgements .................................................................................................................xv

Introduction ...................................................................................... 1 Chapter 1:

1.1 Background .....................................................................................................................1

1.2 Purpose ...........................................................................................................................3

1.3 Motivation ......................................................................................................................3

1.4 Methodology ...................................................................................................................3

1.5 Thesis Outline .................................................................................................................3

Literature Review ............................................................................. 5 Chapter 2:

2.1 DC-DC DAB Converter .................................................................................................5

2.2 DC-AC DAB Converter .................................................................................................9

2.3 Summary .......................................................................................................................10

Basic Analysis ................................................................................. 13 Chapter 3:

3.1 Basic Analysis of the DAB Converter ..........................................................................13

3.2 Analysis with Proportional-Resonant (PR) Control .....................................................18

3.3 Summary .......................................................................................................................27

Simulations ...................................................................................... 29 Chapter 4:

4.1 Simulation Results ........................................................................................................29

4.2 Summary .......................................................................................................................37

Experiments .................................................................................... 39 Chapter 5:

5.1 Hardware ......................................................................................................................39

5.2 Experimental Settings ...................................................................................................45

5.3 Experimental Results ....................................................................................................45

5.4 Summary .......................................................................................................................52

The Proposed Converter for Photovoltaic Applications ............. 53 Chapter 6:

6.1 Basic Analysis ..............................................................................................................53

6.2 Simulation results .........................................................................................................56

6.3 Summary .......................................................................................................................63

vi Investigation on the DC-AC Dual Active Bridge Converter and its Photovoltaic Applications

Conclusions and Recommendations.............................................. 65 Chapter 7:

7.1 Conclusions .................................................................................................................. 65

7.2 Recommendations ........................................................................................................ 66

Bibliography ............................................................................................................. 67

Appendices ................................................................................................................ 71

Appendix A Bilinear transformation of PR controller transfer function ................................ 71

Investigation on the DC-AC Dual Active Bridge Converter and its Photovoltaic Applications vii

List of Figures

Figure 3.1 The proposed DC-AC DAB converter.................................................... 14

Figure 3.2 Triple phase shift modulation scheme for the DAB converter. .............. 14

Figure 3.3 Frequency-domain model of the converter. ............................................ 15

Figure 3.4 The transmission power characterization of the SPS control. ................ 17

Figure 3.5 The modulation scheme of the phase angle φ2. ...................................... 17

Figure 3.6 A three-dimensional plot of the transmission power

characterization. ........................................................................................... 18

Figure 3.7 The double-line-frequency power transmission nature at the AC

side. .............................................................................................................. 19

Figure 3.8 The bode diagram of the ideal PR controller .......................................... 21

Figure 3.9 The bode diagram of the non-ideal PR controller................................... 21

Figure 3.10 Proposed duty cycle modulation scheme. ............................................. 22

Figure 3.11 Three-dimensional plot of the transmission power

characterization with duty cycle modulation (dmax=0.05). ........................... 24

Figure 3.12 Three-dimensional plot of the transmission power

characterization with duty cycle modulation (dmax=0.35). ........................... 24

Figure 3.13 The control diagram for the proposed DC-AC DAB converter

with PR control. ........................................................................................... 25

Figure 3.14 Designed control system for the purpose of Iavg control. ...................... 25

Figure 3.15 The bode diagram of the open-loop transfer function for Iavg

control. ......................................................................................................... 26

Figure 4.1 The AC side voltage vg without PR control. ........................................... 29

Figure 4.2 The AC side current ig without PR control. ............................................ 30

Figure 4.3 The DC side current iDC without PR control. .......................................... 30

Figure 4.4 The AC side current ig with PR control (φ1=π/2, θ=π/2). ....................... 30

Figure 4.5 The DC side current iDC with PR control (φ1=π/2, θ=π/2). ..................... 31

Figure 4.6 The power decoupling capacitor Cs voltage us and current is with

PR control. ................................................................................................... 31

Figure 4.7 The voltages vAB, vCD, and the transformer primary side current ir

(φ1=π/2, θ=π/2). ............................................................................................ 32

Figure 4.8 The envelope of the transformer secondary voltage vCD (φ1=π/2,

θ=π/2). .......................................................................................................... 32

Figure 4.9 (a) The AC side current ig, (b) The DC side current iDC with PR

control (φ1=2π/3, θ=π/2). ............................................................................. 33

viii Investigation on the DC-AC Dual Active Bridge Converter and its Photovoltaic Applications

Figure 4.10 The voltages vAB, vCD, and the transformer primary side current ir

(φ1=2π/3, θ=π/2). .......................................................................................... 33

Figure 4.11 (a) The AC side current ig, (b) The DC side current iDC with PR

control (φ1=π/2, θ=π/4). ............................................................................... 34

Figure 4.12 The voltages vAB, vCD, and the transformer primary side current ir

(φ1=π/2, θ=π/4). ............................................................................................ 34

Figure 4.13 (a) The AC side current ig, (b) The DC side current iDC with PR

control (φ1=π/2, θ=-π/2). .............................................................................. 35

Figure 4.14 The voltages vAB, vCD, and the transformer primary side current ir

(φ1=π/2, θ=-π/2). .......................................................................................... 35

Figure 4.15 (a) The AC side current ig, (b) The DC side current iDC (Iavg*=0.5

A). ................................................................................................................ 36

Figure 4.16 φ1 with the proposed control strategy (Iavg*=0.5 A). ............................. 36

Figure 4.17 (a) The AC side current ig, (b) DC side current iDC and (c) The

controlled phase angle φ1with PR control (Iavg*=1 A). ................................ 37

Figure 5.1 Communications between ARM and FPGA. .......................................... 40

Figure 5.2 The programming process for the FPGA. ............................................... 40

Figure 5.3 The diagram of the PLL. ......................................................................... 42

Figure 5.4 The programming process for the ARM. ................................................ 44

Figure 5.5 The experimental settings ....................................................................... 45

Figure 5.6 The AC side voltage vg and current ig without PR control. .................... 46

Figure 5.7 The DC side current iDC without PR control. .......................................... 46

Figure 5.8 The AC side voltage vg and current ig with PR control (φ1=π/2,

θ=π/2). .......................................................................................................... 46

Figure 5.9 The DC side current iDC with PR control (φ1=π/2, θ=π/2). ..................... 47

Figure 5.10 The power decoupling capacitor Cs voltage us and current is with

PR control (φ1=π/2, θ=π/2). .......................................................................... 47

Figure 5.11 The experimental result of the transformer secondary voltage vCD

(φ1=π/2, θ=π/2). ............................................................................................ 48

Figure 5.12 The AC side voltage vg and current ig with PR control (φ1=2π/3,

θ=π/2). .......................................................................................................... 48

Figure 5.13 The DC side current iDC with PR control (φ1=2π/3, θ=π/2). ................. 48

Figure 5.14 The experimental results of the transformer primary voltage vAB

and current ir (φ1=2π/3, θ=π/2) ..................................................................... 49

Figure 5.15 The AC side voltage vg and current ig with PR control (φ1=π/2,

θ=π/4). .......................................................................................................... 49

Figure 5.16 The DC side current iDC with PR control (φ1=π/2, θ=π/4). ................... 50

Figure 5.17 (a) The AC side voltage vg, current ig, (b) The DC side current iDC

with PR control (Iavg*=0.5 A). ...................................................................... 51

Investigation on the DC-AC Dual Active Bridge Converter and its Photovoltaic Applications ix

Figure 5.18 (a) The AC side voltage vg, current ig, (b) The DC side current iDC

with PR control (Iavg*=1 A). ......................................................................... 51

Figure 6.1 The proposed converter for photovoltaic applications. .......................... 53

Figure 6.2 The operation feature of the PV model. .................................................. 54

Figure 6.3 MPPT algorithm. .................................................................................... 55

Figure 6.4 Overall control diagram of the converter for photovoltaic

applications .................................................................................................. 55

Figure 6.5 (a) DC side voltage vDC and (b) DC side current iDC without the

proposed control strategy (CDC=1500 µF). .................................................. 56

Figure 6.6 The zoom-in figures of (a) DC side voltage vDC, (b) DC side

current iDC and (c) DC side power pDC (CDC=1500 µF). ............................. 57

Figure 6.7 The grid current (a) zoom-out, (b) zoom-in (CDC=1500 µF). ................. 58

Figure 6.8 (a) DC side voltage vDC and (b) DC side current iDC without the

proposed control strategy (CDC=3000 µF). .................................................. 59

Figure 6.9 The PV side power with CDC=3000 µF. ................................................. 59

Figure 6.10 The grid current with CDC=3000 µF. .................................................... 60

Figure 6.11 (a) DC side voltage vDC and (b) DC side current iDC with the

proposed control strategy (CDC=200 µF). .................................................... 60

Figure 6.12 The zoom-in figures of (a) The DC side voltage vDC, (b) current

iDC and (c) power pDC with the proposed control strategy (CDC=200

µF). ............................................................................................................... 61

Figure 6.13 The grid current (a) zoom-out, (b) zoom-in with the proposed

control strategy............................................................................................. 61

Figure 6.14 (a) The DC voltage reference value VDC*, (b) The error value VE

and (c) The phase-shift angle φ1. ................................................................. 62

Figure 6.15 The decoupling capacitor Cs voltage us and current is. ......................... 63

x Investigation on the DC-AC Dual Active Bridge Converter and its Photovoltaic Applications

List of Tables

Table 4.1 The main parameters of the MATLAB Simulink model. ......................... 29

Table 5.1 Basic resources of the Cyclone Ⅳ EP4CE6 FPGA. ................................. 39

Table 5.2 The main parameters of the converter for experiments. ........................... 45

Table 6.1 Main parameters of the proposed DC-AC DAB converter. ..................... 56

Investigation on the DC-AC Dual Active Bridge Converter and its Photovoltaic Applications xi

List of Abbreviations

DAB dual active bridge

HF high frequency

HFL high-frequency link

PHEV plug-in hybrid electric vehicle

UPS uninterruptible power supply

V2G vehicle-to-grid

ZVS zero voltage switching

ZCS zero current switching

PWM pulse-width modulation

SPS single-phase-shift

EPS extended-phase-shift

DPS dual-phase-shift

TPS triple-phase-shift

DBSRC dual active bridge series resonant converter

1-S single-stage

2-S dual-stage

PI proportional-integral

PR proportional-resonant

PV photovoltaic

LPF low-pass filter

SR synchronous rectifier

PLL phase lock loop

MPPT maximum power point tracking

THD total harmonic distortion

xii Investigation on the DC-AC Dual Active Bridge Converter and its Photovoltaic Applications

MCU microcontroller unit

FPGA Field Programmable Gate Array

RISC Reduced Instruction-Set Computing

ARM Advanced RISC Machine

FPU floating point unit

ADC Analog-to-Digital Converter

DAC Digital-to-Analog Converter

DMA Direct Memory Access

GPIO General-purpose I/O

NVIC Nested vectored interrupt controller

FSMC Flexible static memory controller

MSPS Million Samples per Second

Investigation on the DC-AC Dual Active Bridge Converter and its Photovoltaic Applications xiii

Statement of Original Authorship

The work contained in this thesis has not been previously submitted to meet

requirements for an award at this or any other higher education institution. To the

best of my knowledge and belief, the thesis contains no material previously

published or written by another person except where due reference is made.

Signature:

Date: _________________________

QUT Verified Signature

Investigation on the DC-AC Dual Active Bridge Converter and its Photovoltaic Applications xv

Acknowledgements

Time flies and it comes to the end of this relatively short one-year research

master course, which began in June of last year. I want to thank Professor Mahinda

Vilathgamuwa, who is introduced by Professor Choi San Shing, for his technical

advice, weekly meetings, his kindness and patient proofreading for the paper and the

thesis. I also want to thank Lecturer Negareh Ghasemi, as she is always kind and

ready to help others. I also want to thank Dr. Negareh for the proofreading for the

paper and the thesis.

I also want to thank Associate Professor Jiang You from Harbin engineering

university, who is a visiting fellow of Professor Mahinda Vilathgamuwa. Dr. Jiang is

kind too and experienced on power electronics research and practical issues. He is

always ready to help others, and our meeting in this beautiful country is a precious

experience for me.

Last but not least, I want to thank my office friends and housemate friends,

countless great time with all of you on talking, cooking, playing and travelling. And

thanks also go to my parents, you are always positive and supportive for me,

although thousands of miles away in my homeland.

Introduction 1

Introduction Chapter 1:

This chapter outlines the background, purpose, motivation and methodology of

the research course. Finally, section 1.5 gives an outline of the remaining chapters of

this thesis.

1.1 BACKGROUND

Present day industrial applications such as battery chargers for plug-in hybrid

electric vehicles (PHEVs) [1], interfaces for renewable energy sources like

photovoltaic power systems [2], uninterruptible power supplies (UPS) [3] and

vehicle-to-grid (V2G) applications [4, 5] require isolated single-phase DC-AC bi-

directional power transfer, and the dual active bridge (DAB) converter can be

considered as a suitable topology [6-8]. Proposed in the early 1990s, the DAB DC-

DC converter attracts great research interests, mainly for its high-power-density,

isolated and bidirectional characteristics.

Massive research work has been conducted on the DAB in terms of the basic

mathematical model analysis, converter topology, control strategy, soft-switching

operation, hardware design and industrial applications [9]. Similar to the

classification way for traditional DC-DC converters, isolated bidirectional DC-DC

converters can be classified based on the number of the switches, ranging from two

switches to eight switches [9]. Among these topologies with different number of

switches, the eight-switch DAB converter has the biggest power transmission

capacity, as the transferred power of the isolated bidirectional DC–DC converter is

proportional to the number of switches with specific rated voltage and current values

of switches. For example, the transmission power of the four-switch DC-DC

converter is double that of the two-switch DC-DC converter and half that of the

eight-switch DC-DC converter. A typical DC-DC DAB converter is composed of

two full bridges, two DC sources, two DC capacitors, an auxiliary inductor, and a

high-frequency (HF) transformer. The HF transformer realizes galvanic isolation and

voltage matching between the two DC sources.

The DC-DC DAB converter is the basis of the DC-AC DAB converter. A

common dual-stage (2-S) topology for the DC-AC DAB converter consists of a

2 Introduction

galvanically isolated DC-DC DAB converter, followed by a DC-AC single-phase

voltage source inverter [10]. As the AC side power fluctuates at twice line frequency,

while the power through the DC-DC DAB converter is almost constant, a large DC

link electrolytic capacitor is normally used to stabilize the DC link voltage and

balance the power mismatch between the voltage source inverter and the DAB

converter. However, the electrolytic capacitor is well-known for its low reliability

caused by the diffusion of the inside electrolyte [11].

A single-phase single-stage DC-AC DAB converter with unity power factor

control is introduced in [7]. As the diode-bridge rectifier is used, the introduced

converter can only achieve unidirectional power transfer and thus works as a DC

power supply. Since the input of the DC-DC DAB converter is variable in the single-

stage case, soft-switching operation for a full power range cannot be achieved [12].

With the synchronous rectifier (SR), a bidirectional single-phase single-stage DC-AC

DAB converter with the extended ZVS operation range is introduced in [13].

Compared with the commonly used dual-stage topology, the single-stage topology

benefits the converter performance in terms of higher efficiency, power density,

reliability and lower costs, due to the effective omission of a complete power

conversion stage ( intermediate DC link of the dual-stage topology consisting of a

large low-frequency electrolytic capacitor) [14].

In addition to the common topologies of the DC-AC DAB converter mentioned

above, some new topologies like a matrix converter based resonant DAB DC-AC

converter have been proposed. They have a simpler power conversion process

though increase the complexity of the modulation since bidirectional switches are

used [4, 15].

In this thesis, a DAB series resonant single-stage converter is proposed with

both active power decoupling and DC current control. For active power decoupling,

the objective is to eliminate the inherent double-line-frequency power ripple at the

DC side. For DC current control, the objective is to control the power and current

transferred into the AC side.

Introduction 3

1.2 PURPOSE

The purpose of this research project is to investigate on the characteristics of

the single-stage DC-AC DAB series resonant converter, including the basic

modulation scheme, transmission power characterization, control strategies, power

decoupling technique and its applications in photovoltaic systems. Simulations and

experiments of the proposed converter will be conducted to verify the theoretical

analysis.

1.3 MOTIVATION

In high-power, isolated and bidirectional industrial applications, the DAB

converters are widely used and many research works have been conducted. In the

single-phase DC-AC systems, high power ripple appears at the DC side due to the

double-line frequency characteristics of the transmission power at the AC side. In

specific situations such as photovoltaic applications, more stable transmission power

is required to achieve high accuracy of MPPT. If a large electrolytic capacitor simply

used at DC side, the power density and the reliability of the converter can decrease

significantly and it is not able to completely eliminate the ripple power at the DC

side. Therefore specific power decoupling techniques should be adopted to solve this

contradiction and eliminate the ripple power at the DC side.

1.4 METHODOLOGY

Theoretical analysis will be firstly presented for the proposed DC-AC DAB

converter based on basic circuit theory and then the specific control strategy for the

realization of the purpose will be presented. After that, the converter simulations

under different operating conditions will be conducted by the software MATLAB.

To verify the simulation results, experimental tests will be conducted, where the

ARM and FPGA are used as core control chips and the programming is conducted

with the Altera Quartus II and Keil uVision softwares.

1.5 THESIS OUTLINE

Chapter 2 presents a detailed literature review of the DAB converter in terms

of the overall introduction, control strategies, transmission power characterization,

soft-switching operation and topologies. Chapter 3 gives the basic analysis of the

proposed converter without or with the proposed control strategy. The developed

4 Introduction

simulation model and the simulation results are presented in Chapter 4. The

experimental procedure and results are discussed in Chapter 5. Chapter 6 introduces

the photovoltaic applications of the proposed converter. The performances of the

converter either with or without the proposed control strategy are discussed. Chapter

7 makes a conclusion of the previous content and points out several further research

directions.

Literature Review 5

Literature Review Chapter 2:

This chapter gives an overview for the DAB converter, mainly for both the

DC-DC DAB converter and DC-AC DAB converter. The DC-DC DAB converter is

the focus of the relevant DAB research so far. The first section presents several

research aspects about the DC-DC DAB converter, including: the overall

introduction, the control strategy, the transmission power characterization, the soft-

switching operation and the topology. The second section discusses about the DC-

AC DAB converters.

2.1 DC-DC DAB CONVERTER

An overall introduction of the operation, design, and control of the isolated

bidirectional DC-DC dual active bridge (DAB) converter is presented in [16] and

[17]. The inductor current and output power are analysed in detail under heavy load

conditions, light load conditions and boundary conditions [16]. It is noted that only

the phase-shift between the two full bridges is considered and only the leakage

inductance is involved in the high-frequency link in this case. In addition, some

special issues in the DC-DC converter design such as the dead-band effect and safe

operation area (SOA) are further discussed. Waveform distortion and spikes resulting

from the dead-band effect are detected both from experimental and simulation results,

which may cause electro-magnetic interference in the system. Based on the steady-

state analysis, [17] has obtained a small-signal model for the isolated bidirectional

DC-DC DAB converter and also given some guidelines for design such as the soft-

switching operation range for the converter.

2.1.1 Control Strategy

For typical DC-DC dual active bridge converter, phase-shift control, single-

side PWM plus phase-shift control and dual-side PWM plus phase-shift control have

all been demonstrated. [9] has given a detailed overview for the control strategy of

the isolated bidirectional DC-DC DAB converter. Four general control strategies are

classified based on the degree of freedom including SPS control, EPS control, DPS

control and TPS control [9].

6 Literature Review

The SPS (single-phase-shift) control only focuses on the control of the phase-

shift angle between the two active bridges, and two pairs of diagonal switches of

each bridge turn on and turn off alternately to generate two phase-shifted two-level

square waves. By controlling the phase-shift angle between two bridges, the voltage

across the inductor of the high-frequency link (HFL) can be adjusted accordingly,

based on which the direction and the magnitude of the power can be easily controlled.

EPS (extended-phase-shift) control adds one degree of freedom based on the SPS

control. Two pairs of diagonal switches of one active bridge are inner phase-shifted

to generate one phase-shifted three-level square wave, and the other bridge operates

in the same way of the SPS control. This added inner phase-shift angle can help to

expand the ZVS range of the converter. In the similar way, DPS (dual-phase-shift)

control adds another degree of freedom based on the EPS control. Switch pairs of

both active bridges are inner phase-shifted to generate two phase-shifted three-level

square waves. It is noted that since the modulation strategies for both bridges are

more similar compared with the EPS control, the dynamic performance of the DPS

control may be better such as in the case when the power transmission direction

suddenly changes [9]. TPS (triple-phase-shift) control is similar with the DPS control

but the inner phase-shift may be unequal. The biggest problem of this control method

is the difficulty of the implementation.

2.1.2 Transmission Power Characterization

The transmission power characterization of the DC-DC DAB converter under

the SPS control is presented in [18]. The per-unit value of the transmission power is

given by

*

o 4 (1 )P kD D (2.1)

where *

oP , k and = /D represent the per-unit value of the transmission power,

the coefficient related to the system parameters and the phase-shift angle ratio of the

two bridges respectively. According to (2.1), it is clear that the sign of D determines

the power direction. The transmission power of the converter increases with the

increase of D ( 0.5)D , and decreases with the increase of D ( 0.5)D

symmetrically.

The transmission power characterization of the DC-DC DAB converter under

the EPS control is presented in [19]. Compared with the SPS control, it is noted that

Literature Review 7

the transmission power regulating range becomes wider and thus is more flexible in

the cases that wider power range is required.

2.1.3 Soft-switching operation

Soft-switching operation is a major consideration for the design of the dual

active bridge converter as it has direct correlation with the efficiency of the converter

[20]. Under certain conditions the switching loss during one switching cycle can be

considered as constant, so the whole switching loss of the converter is proportional to

the switching frequency. As the switching frequency increases, the whole switching

loss also increases dramatically, thus the efficiency of the converter decreases though

the high switching frequency can benefit the power density of the converter.

When the SPS control is adopted, zero-voltage-switching (ZVS) lost at light

load (except in the case that the primary/secondary voltage ratio matches the

transformer primary/secondary turns ratio) [18]. In addition, high circulating power

appears if the voltages of the primary side and the secondary side don’t match. For a

specific value of the transmission power, the forward power will increase with the

increase of the circulating power, which can cause high current stress and low

efficiency of the converter [19].

For this reason, the performances of the other two control strategies are also

investigated. Frist, the EPS control is investigated to realize ZVS over the whole load

range while greatly reduce the root-mean-square (RMS) current under the proposed

optimized control strategy [18]. A comprehensive analysis has been conducted on the

EPS control with a conclusion of four benefits of this control strategy [19]: (a)

Expansion of the regulating range of the converter transmission power, (b) Lower

circulating power and thus higher converter efficiency, (c) Lower current stress and

thus flexible and economical device selection scheme, (d) Easy implementation.

To further reduce the circulation loss at light load, the characteristics of the

DAB converter in the TPS control is analysed [18]. By adjusting the three controlled

phase angles in the specific optimized range, the RMS current is minimum and the

DAB converter achieves critical ZVS at light load. However, the efficiency of this

TPS control is lower than that of the EPS control due to the critical ZVS at light load.

8 Literature Review

2.1.4 Topology

The improvement of HFL resonant tank is considered as a possible solution to

expand the soft-switching range of the DAB converter and massive research has been

conducted in this aspect.

Several literatures have discussed about the dual active bridge series resonant

DC-DC converter (DBSRC) which is used in this thesis [21-30]. [22] and [29] gives

the basic approximate equivalent circuit model of the DBSRC. The non-resonant

DAB and the DBSRC in resonant mode are compared in [23]. Since the resonant

DBSRC adds a capacitor in the HFL, a unified mathematical model describing both

converters is presented by considering the non-resonant DAB as a boundary

condition of the resonant DBSRC with infinite capacitance in the HFL.

[24] has presented detailed analysis for the DBSRC. Two simplified AC

equivalent circuit analysis methods are presented for approximation considerations

with only fundamental components of the circuit waveforms are used. Two different

load conditions, either the voltage-source type of load or the resistive load, are

discussed. ZVS turn-on for primary side switches and ZCS turn-off for secondary

side switches can be realized for all load and input/output voltage conditions.

Performance of the proposed DBSRC and the traditional DAB converter are

compared. For the traditional DAB converter, performance of the converter is mainly

dependent on the leakage inductance in the HFL, whereas the leakage inductance is

used as a part of the resonant tank in the HFL for the DBSRC. ZVS of primary side

switches of the converter is hard to be achieved when wide input/output voltage

ranges are required for the traditional DAB converter. In addition, by adding the

capacitor in the HFL, the DBSRC has low possibility of transformer saturation. The

major shortcoming of the DBSRC is the size of the resonant tank (capacitor in the

HFL), which decrease the power density of the converter. [27] proposes an improved

analytical method for the DBSRC. Compared with the existing approximate

analytical method, it considers the harmonic components of the voltage and the

transformer internal resistance.

Besides, a CLLC-type asymmetric resonant DC-DC DAB converter [31] and a

CLLC-type symmetric resonant DC-DC DAB converter [32] have been proposed. [9]

has presented a comprehensive comparison for these two different soft-switching

solutions. Compared with the traditional DAB converter and the DBSRC, the CLLC-

Literature Review 9

type resonant DAB converters adopt frequency modulation which increases the

control complexity and the CLLC resonant tank requires more components which

results in lower power density and reliability and higher cost. In addition, the power

transfer direction of CLLC-type DAB converters is determined by the position of the

operating stage of the switches, while the conventional DAB converter and the

DBSRC are controlled by three phase-shift angles, therefore the bidirectional power

transfer transition speed of the conventional DAB converter and the DBSRC is

supposed to be faster. On the other hand, from the perspective of soft-switching

operation, the CLLC-type resonant DAB converters have wider soft-switching

operation ranges compared with the conventional DAB converter and the DBSRC.

Therefore, they are more suitable for applications with wide input/output voltage and

power ranges in order to achieve high converter efficiency. Compared with the

CLLC-type symmetric resonant DAB converter, the CLLC-type asymmetric resonant

DAB converter shows different operation characteristics in forward and backward

bidirectional power transfer conditions as the structure of the resonant networks are

asymmetric.

2.2 DC-AC DAB CONVERTER

A common dual-stage DC-AC DAB converter consists of a galvanically

isolated DC-DC DAB converter, followed by a DC-AC single phase voltage source

inverter [10]. As the AC side power fluctuates at double line frequency, while the

power through the DC-DC DAB converter is almost constant, a large DC link

electrolytic capacitor is normally used to stabilize the DC link voltage and balance

the power mismatch between the voltage source inverter and the DAB converter.

In addition to the common topology of DC-AC DAB converter mentioned

above, some new topologies like a matrix converter based resonant DAB DC-AC

converter have been proposed. They have a simpler power conversion process

though more complex modulation is required since bidirectional switches are

adopted [4]. The proposed converter in [4] consists of a matrix converter linked to

the electric vehicle (EV) side full-bridge with a HF transformer and a tuned LCL

resonant network. The tuned LCL resonant network improves the efficiency of the

converter and contributes to the operation of the matrix converter and the full-bridge

at near unity power factor with varied input/output conditions. From the idealized

10 Literature Review

phasor analysis for the dual active bridges, the value of the transmission power of the

converter depends on the three phase-shift angle parameters of the converter.

Compared with the commonly used dual-stage (2-S) DC-AC DAB converters,

the 1-S DC-AC DAB converter has the potential to benefit the system performance

in terms of efficiency, power density, reliability and costs, due to the effective

omission of a complete DC power stage [14]. An isolated 1-S DC-AC converter with

bidirectional power flow is introduced in [33, 34] using a cycloconverter on the

primary side and a voltage source converter on the secondary side of the HF

transformer. [35] investigates the feasibility and suitability of a 1-S DAB DC-AC

converter for the realization of bidirectional energy conversions. There are

limitations about the soft-switching modulation schemes for DAB converters with

large input/output voltage ranges and large power ranges. [35] proposes a novel

‘current-dependent charge-based’ (CDCB) ZVS verification approach to address the

limitations of the current-based (CB) and energy-based (EB) ZVS analysis. Three

approaches are presented including a numerical approach, an analytical approach,

and a semi-analytical approach, all based on the proposed CDCB ZVS verification

method to assure that the soft-switching operation with quasi zero switching losses

can be realized within the derived ZVS soft-switching regions.

2.3 SUMMARY

This chapter gives an overview for the DAB converter including the DC-DC

DAB converter and DC-AC DAB converter. The overall introduction about the

operation, design, and control of the DC-DC DAB converter is first presented. Four

basic control strategies, including the SPS, EPS, DPS and TPS control are introduced

in detail and the basic features of these control strategies are reviewed. The

transmission power characterization is then discussed. The soft-switching operation

of the SPS, EPS and TPS are discussed in detail. Different HFL resonant tank

topologies including DBSRC, the CLLC-type asymmetric resonant DAB converter

and the CLLC-type symmetric resonant DAB converter are discussed in terms of the

power transfer transition performance, soft-switching range and power density.

The second section reviews the single-stage and dual-stage DC-AC DAB

converters. The single-stage DC-AC converter is with a pseudo intermediate DC link

Literature Review 11

which can benefit the converter with the higher power density. In addition, the soft-

switching issues for the single-stage DC-AC DAB converter are also discussed.

Basic Analysis 13

Basic Analysis Chapter 3:

Chapter 3 gives the mathematical analysis for the proposed converter without

or with the proposed modulation scheme. Transmission power characterizations of

both conditions are analyzed in detail. Based on the mathematical analysis, the

control structure is presented to realize the objective of the power decoupling.

3.1 BASIC ANALYSIS OF THE DAB CONVERTER

Three analysis approaches are normally used for analyzing resonant converters

in the steady state as follows [36]:

1. Approximate analysis with the AC-circuit theory: For this approach, only

the fundamental components of the circuit voltages and currents

waveforms are used. This method is not able to analyze the circuit

voltage and current waveforms precisely and should only be used for

approximation considerations.

2. State-space or differential equations approach: This approach is more

accurate than the approximate analysis, but it is very difficult to be used.

An example of the state-space analysis of the series resonant DAB

converter is presented in [37].

3. Fourier-series method or frequency domain approach: For this approach,

the significant harmonics of the circuit waveforms are all taken into

account, and the basic AC-circuit theory is used to analyze the resonant

converter. Therefore, this method is relatively easy to be utilized and more

accurate than the approximate analysis. Based on these reasons, the

Fourier-series method is adopted for the mathematical analysis of the

converter in this chapter.

The proposed DC-AC DAB converter is shown in Figure 3.1.

14 Basic Analysis

vg

Sp1

Sp2

Sp3

Sp4

Ss1 Ss3

Ss2 Ss4

Sr1

Sr2

Sr3

Sr4

Lr CrLf

CfCDC1

CDC

vDC vDC1

Primary Secondary

Ls

Cs

riDCig

HF Transformer

vAB vCD

A

B

C

D

O

1:N. .

Figure 3.1 The proposed DC-AC DAB converter.

This is a single-stage DC-AC converter with a pseudo intermediate DC link

between the synchronous rectifier and the DAB converter, which is free of the large

electrolytic capacitor at the DC link required for the dual-stage DC-AC converter.

The AC voltage vg is folded into the voltage vDC1 with a frequency twice that of the

AC voltage, which is given by

DC1 g g sin gv v V t (3.1)

where Vg is the magnitude of vg and ωg is the angular frequency of vg.

The DAB converters are normally controlled by a triple phase shift (TPS)

modulation scheme which is shown in Figure 3.2. Every half bridge is operating with

50% duty cycle with one switch on and the other off at any time. Two legs in the

primary side are phase shifted by the phase angle φ1 and two legs in the secondary

side are phase shifted by the phase angle φ2. The phase shift angle θ between the

voltages vAB and vCD is the third element of this TPS modulation scheme, which

determines the direction of the power transfer.

vsp2

vsp4

vAB

vCD

φ1

θ

vDC

vDC1

vDC

vDC

φ2

Figure 3.2 Triple phase shift modulation scheme for the DAB converter.

Basic Analysis 15

The voltage across the switch Sp2 vAO and the voltage across the switch Sp4 vBO

are given by

DC DCAO s

1

2 1sin cos

2 2 2n

v v nv n t

n

(3.2)

DC DCBO s 1

1

2 1sin cos

2 2 2n

v v nv n t

n

(3.3)

where s is the switching frequency. From (3.2) and (3.3), vAB is given by

DC 1 1AB AO BO s

1,3...

4 1sin cos

2 2n

v nv v v n t

n

(3.4)

Also, vCD is given similarly by

DC1 2 1CD s

1,3...

4 1sin cos

2 2n

v nv n t

n

(3.5)

This converter can be represented by using the frequency-domain model shown in

Figure 3.3.

vCD' Lr Cr

ir

vAB

Figure 3.3 Frequency-domain model of the converter.

The nth

harmonic component of ir is given by

s r CDnrn ABn2 2

s r r1

jn C UI U

n L C N

(3.6)

where and represent the nth

harmonic phasors of vAB and vCD, N is the

transformer turns ratio. and are given by

DC 1 1 1ABn

4sin cos sin

2 2 2

v n n nU j

n

(3.7)

DC1 2 1 1CDn

4sin cos sin

2 2 2

v nU n j n

n

(3.8)

The nth

harmonic average power component Pan is given by

* s ran ABn rn ABn CDn ABn CDn2 2

s r r

Re sin1

n CP U I U U

n L C N

(3.9)

16 Basic Analysis

where UABn and UCDn represent the magnitudes of the nth

harmonic phasors and

respectively. ABn and CDn represent the arguments of the nth

harmonic phasors

and respectively.

The transmission power of the converter is given by

DC DC1 s r 1 2a 2 2 2

1,3... s r r

8 1sin sin sin

2 2 1n

v v C n nP n

N n n L C

(3.10)

By substituting relevant parameters of the converter, the denominator of (3.10),

namely 2 2

s r r 1n n L C , increases rapidly with higher harmonics. Its value is 1.27,

58.18, 278.26 and 770.26 for fundamental, third, fifth and seventh harmonics

respectively. Thus it is reasonable to analyze only the fundamental transmission

power of the converter. Considering only the fundamental power component, the

transmission power of the converter is given by

DC DC1 1 2a1 2

1

8sin sin sin

2 2

v vP

X N

(3.11)

where the the reactance X1 of the resonant tank at the fundamental frequency is given

by

1 s r

s r

1X L

C

(3.12)

From (3.11) it is evident that the phase shift angle θ between the voltages vAB

and vCD determines the direction of the power transfer. When vAB leads vCD by the

phase shift angle θ, the power transfers from the DC side to the AC side. When vAB

lags vCD, then the power transfers from the AC side to the DC side. The bidirectional

power transfer feature of the DAB converters is thus realized through the control of

the phase shift angle θ.

According to (3.11), if the SPS control is adopted, then the transmission power

characterization is shown in Figure 3.4, where the y-axis label p is defined as

a1 N/p P P , and the x-axis label d is defined as /d . NP is given by

DC DC1N 2

1

8v vP

X N (3.13)

From Figure 3.4, the transmission power characteristics curve of the converter

is symmetrical and achieves highest forward power when d=0.5 or θ=π/2, and

highest backward power when d=-0.5 or θ=-π/2.

Basic Analysis 17

Figure 3.4 The transmission power characterization of the SPS control.

According to (3.11), if 1 and are fixed, then 2 should be regulated as follows:

2 g2 t in order to achieve unity power factor at the AC side, which is shown in

Figure 3.5. Tg represents the AC voltage period. This modulation method for φ2

ensures the balance between the transmission power of the DAB converter and the

AC side power, which realizes a pseudo DC link between the DAB converter and the

synchronous rectifier free of the large electrolytic capacitor used in a dual-stage

converter. Assuming θ=π/2, a three-dimensional plot of the transmission power

characterization is shown in Figure 3.6. It is clear that the transmission power of the

DAB converter fluctuates at 100 Hz frequency and the transmission power increases

with bigger phase angle φ1. In this condition, p is defined as '

a1 N/p P P . '

NP is given

by

DC g'

N 2

1

8v VP

X N (3.14)

OO

2π 2π

g

2

TgT g3

2

Tg2T g5

2

T tt

2

Figure 3.5 The modulation scheme of the phase angle φ2.

18 Basic Analysis

Figure 3.6 A three-dimensional plot of the transmission power characterization.

The average power transferred to the grid is given by

1g DC

2

1

4 sin sin2

g

V v

PX N

(3.15)

Then the magnitude of ig is given by

1DC

g

g 2

g 1

8 sin sin2 2

vP

IV X N

(3.16)

3.2 ANALYSIS WITH PROPORTIONAL-RESONANT (PR) CONTROL

3.2.1 PR Control

The double-line-frequency power transmission nature at the AC side of single-

phase power converters is shown in Figure 3.7.

Basic Analysis 19

Figure 3.7 The double-line-frequency power transmission nature at the AC side.

To eliminate the double-line-frequency ripple power at the DC side in single-

phase power converters, different power decoupling techniques are introduced and

classified [38]. If only conventional electrolytic capacitor is used, the required value

for the capacitor is given in [38] as

g g

DC

g DC DC8

V IC

f V V

(3.17)

where DCV is the magnitude of the DC voltage ripple. From (3.17), in order to

further reduce the ripple power, a larger DC side capacitor is always required if the

DC voltage keeps constant.

An active power decoupling method is introduced for CLLC-type resonant DC-

AC DAB converter operating in open loop [39]. The basic concept of the active

power decoupling technique is to balance the AC and DC side instantaneous power

through intermediate energy buffers so that the ripple power at DC side can be

reduced. For example, we can design appropriate LC circuits connected in parallel

with the existing switches of either full bridge to form a DC ripple power reduction

circuit. By actively controlling the voltage of the specific switches, or the duty cycle

of the specific leg of two bridges, the ripple power appearing at the DC side can be

steered into such LC circuits and thus DC ripple power reduction can be realized.

The relation between the power decoupling capacitor Cs and the duty cycle

deviation d is given in [39] as

g g

s 2

g DC max2

V IC

V d (3.18)

20 Basic Analysis

where maxd is the maximum deviation magnitude of the modulated duty cycle D.

The proposed active power decoupling method is able to completely eliminate

the double-line-frequency ripple power at the DC side by using proper control

methods. Among those control methods, proportional resonant (PR) control can be

adopted.

According to the internal model principle, if a sinusoidal mathematical model

is included, the controller can realize zero steady-state error following a sinusoidal

reference input signal at the specific frequency [40]. The non-ideal PR controller

transfer function is given in [41] as

i cPR P 2 2

c 0

2( )

2

K sG s K

s s

(3.19)

where the PK , iK , c and 0 represent the proportional term, the resonant term

gain, the cut-off frequency and the resonant frequency respectively. Compared with

the ideal PR controller which is given by (3.20), the gain at 0 is finite. In addition,

the bandwidth can be widened by setting c appropriately. The bode diagrams of the

ideal and non-ideal PR controller are shown in Figure 3.8 and Figure 3.9 respectively,

with PK =1, iK =10, c =5, 10, 20 rad/s and 0 =200π rad/s. As shown in Figure 3.9,

the bandwidth can be widened with a higher value of c and vice versa. A wider

bandwidth is helpful when the frequency variation effect occurs.

iPR P 2 2

0

2( )

K sG s K

s

(3.20)

Basic Analysis 21

Figure 3.8 The bode diagram of the ideal PR controller

5 rad/sc 10 rad/sc

20 rad/sc

Figure 3.9 The bode diagram of the non-ideal PR controller

3.2.2 Converter Analysis with Duty Cycle Modulation

The converter with the duty cycle modulation on leg A shown in Figure 3.1 is

controlled by a modified triple phase shift modulation scheme which is shown in

Figure 3.10. The duty cycle of the leg A can be regulated, while the duty cycles of

other legs are fixed at 50%.

22 Basic Analysis

vsp2

vsp4

vAB

vCD

φ1

θ

vDC

vDC1

vDC

vDC

φ2

2πD(1-D)2π

Figure 3.10 Proposed duty cycle modulation scheme.

The voltage across the switch Sp2 vAO and the voltage across the switch Sp4 vBO

with the duty cycle modulation are given by

DCAO DC s

1

2 1sin cos

n

vv Dv nD n t D

n

(3.21)

DC DCBO s 1

1

2 1sin cos

2 2 2n

v v nv n t

n

(3.22)

From (3.21) and (3.22), uAB is given by

s

DCAB AO BO DC

1 s 1

sin cos21 1

2 sin cos2 2

n

nD n t Dv

v v v D v nn n t

(3.23)

Also, vCD is given similarly by

DC1 2 1CD s

1,3...

4 1sin cos

2 2n

v nv n t

n

(3.24)

The nth

harmonic component of ir is given by

s r CDnrn ABn2 2

s r r1

jn C UI U

n L C N

(3.25)

and are given by

DC

1 1

sin cos sin2

sin cos sin2 2 2

ABn

nD nD j nDv

U nn n j n

(3.26)

DC1 2 1 14

sin cos sin2 2 2

CDn

v nU n j n

n

(3.27)

Basic Analysis 23

The nth

harmonic average power component Pan is given by

* s san sn ABn CDn ABn CDn2 2

s s s

Re sin1

ABn

n CP U I U U

n L C N

(3.28)

The transmission power of the converter is given by

1

DC DC1 s r 2

2 2 21,3... s r r 1

sin sin24 1

sin2 1

sin sin2 2

a

n

nD n Dv v C n

PN n n L C n

n

(3.29)

Considering only the fundamental power component, the transmission power of the

converter is given by

1

DC DC1 21 2

1 1

sin sin24

sin2

sin2

a

D Dv v

PX N

(3.30)

If D is regulated near 1/2, then the equation (3.30) can be simplified as the equation

(3.11). According to (3.30), assuming θ=π/2, two three-dimensional plots of the

transmission power characterization with max =0.05d and max =0.35d (as mentioned

before, maxd is the maximum deviation magnitude of the duty cycle D) are shown in

Figure 3.11 and Figure 3.12 respectively. It is clear that the transmission power of

the DAB converter is near the ideal 100 Hz sinusoidal waveform with dmax=0.05, and

is greatly distorted with higher dmax=0.35 compared with Figure 3.6. The distorted

transmission power with dmax=0.35 can cause distortion in the AC side current.

Therefore, it is reasonable to use the simplified equation (3.11) if a small dmax value

can be obtained.

24 Basic Analysis

Figure 3.11 Three-dimensional plot of the transmission power characterization with duty cycle

modulation (dmax=0.05).

Figure 3.12 Three-dimensional plot of the transmission power characterization with duty cycle

modulation (dmax=0.35).

Basic Analysis 25

3.2.3 Control Strategy

The control diagram is shown in Figure 3.13. Iavg and iripple represent the DC

component and the AC component of the iDC respectively. Iavg* and i

* represent

reference values for Iavg and iripple respectively. The phase shift angle φ2 is as follows:

2 g2 t (shown in Figure 3.5) and the phase shift angle θ is fixed as π/2. φ1 is used

to control Iavg through a proportional-integral (PI) controller (error value IE as input,

φ1 as output), thus the power delivered from the DC side can be regulated based on

the value of Iavg*. Additionally, iripple is controlled by the PR controller (-iripple as input,

D as output).

ModulatorMain

CircuitFilter

iDC

Iavg

iripple

Iavg*

i*=0

φ1

D

-+

+

-

iripple

Iavg

IE

Figure 3.13 The control diagram for the proposed DC-AC DAB converter with PR control.

The control system designed to control Iavg is shown in Figure 3.14. GLPF

represents the transfer function of the low-pass filter (LPF). GPI represents the PI

controller. Gc represents the transfer function from φ1 to iDC. Iavg* is set as 0.5 A in the

following analysis.

GPI Gc

GLPF

+

-

Iavg*

1 DCi

Figure 3.14 Designed control system for the purpose of Iavg control.

According to (3.15), assuming that the PR controller is working appropriately

and the DC side power ripple is almost eliminated, then iDC can be given by

1g

DC 2

1

4 sin sin2

V

iX N

(3.31)

26 Basic Analysis

Gc is given by

Dc

gC 1

2

1 1

ˆ 2 sin( ) cos

ˆ 2

Vis

X NG

(3.32)

GLPF is given by

2

n

2F 2

n

LP

n

=2

Gs s

(3.33)

where the damping coefficient =0.7, natural angular frequency n 20 rad/s.

GPI is given as

PI

505

sG (3.34)

the parameters of the PI controller are chosen mainly based on the appropriate

dynamic performance of the PI controller in the simulations, and the system stability

requirement analysed below.

The open-loop transfer function of the system is given by

Lo PI c PFG G GG (3.35)

In the steady state, 1 is calculated as 1.03 rad/s according to (3.31) assuming

that iDC is ideally controlled as Iavg*. Then the bode diagram of the open-loop transfer

function is shown in Figure 3.15. As shown in the figure, the phase margin is enough

to meet the stability requirement of the system.

Figure 3.15 The bode diagram of the open-loop transfer function for Iavg control.

Basic Analysis 27

3.3 SUMMARY

The mathematical analysis for the proposed DC-AC DAB converter either

without or with the duty cycle modulation is discussed by means of the Fourier-series

method. Transmission power characterizations are derived for both conditions. And

the results of the converter with the duty cycle modulation match the results without

the duty cycle modulation if the modulation range of the duty cycle D is small

enough. The control strategy is presented with the adoption of the PR control, which

is able to completely eliminate the power ripple at the DC side (the performance will

be presented in the following chapters). In addition, the degree of freedom phase

shift angle φ1 is used as a control variable for controlling the transmission power of

the converter. By simply adding the PI control, the transmission power or the DC

side current can be regulated.

Simulations 29

Simulations Chapter 4:

This chapter presents the results of the simulations for the proposed DC-AC

DAB converter. The parameter settings are firstly given and then the performances of

the converter under different conditions: either with or without the proposed control

strategy, either with higher or lower phase angle values in simulations are presented

and analyzed.

4.1 SIMULATION RESULTS

The simulation results of the proposed DC-AC DAB converter are shown in

this section. The main parameters of the MATLAB Simulink model are given in

Table 4.1. Cs is set at a relatively large value in order to obtain a small modulation

range for the duty cycle D as explained in 3.2.2. Ls is also set at a relatively large

value to filter the high-frequency current in the proposed LC circuit. The two values

can be regulated manually in the simulations to obtain an appropriate system

performance for the proposed converter.

Table 4.1 The main parameters of the MATLAB Simulink model.

Parameter vg fg VDC Cs Ls

Value 18 V(Vg) 50 Hz 30 V 1910 µF 1560 µH

Parameter Cr Lr N fs

Value 1.4 µF 102.5 µH 1:1 20 kHz

4.1.1 Simulation Results Without the Proposed Control Strategy

With φ1=π/2, θ=π/2, the AC side voltage vg and current ig, DC side current iDC

without the PR control are shown in Figure 4.1, Figure 4.2 and Figure 4.3

respectively.

Figure 4.1 The AC side voltage vg without PR control.

30 Simulations

Figure 4.2 The AC side current ig without PR control.

Figure 4.3 The DC side current iDC without PR control.

From Figure 4.3, there is a 100 Hz ripple current, or a 100 Hz ripple power at

the DC side because of the 100 Hz power transmission nature at the AC side. It is

noted that the unity power factor is achieved at the AC side due to the applied

modulation scheme for the phase angle φ2.

4.1.2 Simulation Results with the Proposed Control Strategy (Constant φ1)

According to (3.19), the parameters of the PR controller for the simulations are

as follows: P =0.3K , i =3K , c =5 rad/s and

0 200 rad/s.

With φ1=π/2, θ=π/2, the AC side current ig, DC side current iDC, the power

decoupling capacitor Cs voltage us and current is with the PR control are shown in

Figure 4.4, Figure 4.5 and Figure 4.6 respectively.

Figure 4.4 The AC side current ig with PR control (φ1=π/2, θ=π/2).

Simulations 31

Figure 4.5 The DC side current iDC with PR control (φ1=π/2, θ=π/2).

Figure 4.6 The power decoupling capacitor Cs voltage us and current is with PR control.

From Figure 4.5, the 100 Hz ripple power at the DC side is almost eliminated,

thus a relatively stable DC side current is obtained, which is important in the case

that the DC source is a photovoltaic cell panel (the case will be shown in chapter 6).

From Figure 4.6, as the duty cycle of leg A is modulated, the power decoupling

capacitor Cs voltage us fluctuates at 100 Hz frequency and balances the 100 Hz ripple

power at the DC side. Also, the fluctuation range of us is relatively small, thus the

modulation range of the duty cycle is small, which will not cause a distortion in the

transmission power and the AC side current ig [39].

The voltages vAB, vCD, and the transformer primary side current ir are shown in

Figure 4.7. As φ1 is set as π/2, the width of the positive part and the negative part of

vAB is π/2, and vAB leads vCD by θ=π/2. The envelope of the transformer secondary

voltage vCD under this condition is shown in Figure 4.8. According to vCD1 given in

(3.1), the magnitude of vCD has a 100 Hz envelope.

32 Simulations

vAB

ir

vCD

Figure 4.7 The voltages vAB, vCD, and the transformer primary side current ir (φ1=π/2, θ=π/2).

Figure 4.8 The envelope of the transformer secondary voltage vCD (φ1=π/2, θ=π/2).

With φ1=2π/3, θ=π/2, the AC side current ig and DC side current iDC with PR

control are shown in Figure 4.9. According to (3.11), the magnitudes of ig and iDC are

theoretically 1.22 times that of values in Figure 4.4 and Figure 4.5, which can be

verified in Figure 4.9. The voltages vAB, vCD, and the transformer primary side

current ir under this condition are shown in Figure 4.10. As φ1 is set as 2π/3, the

width of the positive part and the negative part of vAB is 2π/3, and vAB leads vCD by

θ=π/2.

With φ1=π/2, θ=π/4, the AC side current ig and DC side current iDC with PR

control are shown in Figure 4.11. According to (3.11), the magnitudes of ig and iDC

are theoretically 2

2 times that of values in Figure 4.4 and Figure 4.5, which can be

verified in Figure 4.11. The voltages vAB, vCD, and the transformer primary side

current ir under this condition are shown in Figure 4.12. The width of the positive

part and the negative part of vAB is π/2, and vAB leads vCD by θ=π/4.

With φ1=π/2, θ=-π/2, the AC side current ig and DC side current iDC with PR

control are shown in Figure 4.13. According to (3.11), the transmission power under

this situation reverses and is delivered from the AC side to DC side, which can be

verified in Figure 4.13. Therefore, it proves that the phase shift angle θ determines

Simulations 33

the direction of the power transfer of the converter. The voltages vAB, vCD, and the

transformer primary side current ir under this condition are shown in Figure 4.14.

The width of the positive part and the negative part of vAB is π/2 and since θ=-π/2,

vCD leads vAB by θ=π/2 under this condition.

(a)

(b)

Figure 4.9 (a) The AC side current ig, (b) The DC side current iDC with PR control (φ1=2π/3, θ=π/2).

vAB

ir

vCD

Figure 4.10 The voltages vAB, vCD, and the transformer primary side current ir (φ1=2π/3, θ=π/2).

34 Simulations

(a)

(b)

Figure 4.11 (a) The AC side current ig, (b) The DC side current iDC with PR control (φ1=π/2, θ=π/4).

vAB

ir

vCD

Figure 4.12 The voltages vAB, vCD, and the transformer primary side current ir (φ1=π/2, θ=π/4).

Simulations 35

(a)

(b)

Figure 4.13 (a) The AC side current ig, (b) The DC side current iDC with PR control (φ1=π/2, θ=-π/2).

vAB

ir

vCD

Figure 4.14 The voltages vAB, vCD, and the transformer primary side current ir (φ1=π/2, θ=-π/2).

4.1.3 Simulation Results With the Proposed Control Strategy (Controlled φ1)

As discussed in Section 3.2.3, with the proposed control strategy (controlled φ1)

shown in Figure 3.13, the AC side current ig and DC side current iDC with PR control

and Iavg*=0.5 A are shown in Figure 4.15. From Figure 4.15 (b) iDC is controlled as

Iavg*=0.5 A, which means the transmission power of the converter can be regulated

accordingly..

36 Simulations

(b)

(a)

Figure 4.15 (a) The AC side current ig, (b) The DC side current iDC (Iavg*=0.5 A).

The controlled phase angle φ1 is shown in Figure 4.16. As shown in this figure,

φ1 is near 1 rad/s in the simulations, which verifies the theoretical value (1.03 rad/s)

obtained according to Section 3.2.3. By regulating φ1, the DC side current iDC and the

power of the converter can be controlled at the desired value.

Figure 4.16 φ1 with the proposed control strategy (Iavg*=0.5 A).

The AC side current ig, DC side current iDC and the controlled phase angle φ1

with PR control and Iavg*=1 A are shown in Figure 4.17. From Figure 4.17 (b), iDC is

controlled around 1 A as Iavg*=1 A. As shown in Figure 4.17 (c), φ1 in this condition

is controlled at a higher value compared with Figure 4.16. Theoretically, φ1 in this

condition can be estimated as follows: 1 2arcsin 2sin(1/ 2) 2.56 , which is near

the value shown in Figure 4.17 (c).

Simulations 37

(c)

(a)

(b)

Figure 4.17 (a) The AC side current ig, (b) DC side current iDC and (c) The controlled phase angle

φ1with PR control (Iavg*=1 A).

4.2 SUMMARY

The simulation results for the proposed DC-AC DAB converter are presented.

The simulation results under seven conditions: (A) φ1=π/2, θ=π/2, without PR control,

(B) φ1=π/2, θ=π/2, with PR control, (C) φ1=2π/3, θ=π/2, with PR control, (D) φ1=π/2,

θ=π/4 with PR control, (E) φ1=π/2, θ=-π/2 with PR control, (F) Controlled φ1 with

Iavg*=0.5 A, (G) Controlled φ1 with Iavg

*=1 A are presented and analysed.

Experiments 39

Experiments Chapter 5:

5.1 HARDWARE

This section gives an introduction of the hardware settings for the experiments.

The advanced ARM-based 32-bit MCU (Microcontroller Unit) and FPGA (Field

Programmable Gate Array) are two key components for the processing of the drive

signals. Basic resources and general programming procedures of ARM and FPGA

are introduced.

5.1.1 FPGA

1) Basic Resources

A Cyclone Ⅳ EP4CE6 FPGA device is used, which is known for low power,

high functionality and low cost. Basic resources of the Cyclone Ⅳ EP4CE6 FPGA

are shown in Table 5.1 [42].

Table 5.1 Basic resources of the Cyclone Ⅳ EP4CE6 FPGA.

Resources

Logic

elements

Embedded

memory

(Kbits)

Embedded

18 × 18

multipliers

General-

purpose

PLLs

Global

Clock

Networks

User I/O

Banks

Maximum

user I/O

EP4CE6 6272 270 15 2 10 8 179

2) Programming

The programming of FPGA is conducted by the software Altera Quartus II.

The diagram for communications between ARM and FPGA is shown in Figure 5.1.

In addition to three phase angle control variables, Ref1~ Ref4 represent the reference

values for comparing with the four sawtooth waveforms (based on which eight drive

signals of the DAB are generated), and the SR signal represents the control signal for

the synchronous rectifier (based on which the four drive signals of the

synchronous rectifier are generated).

40 Experiments

FPGA ARM

φ1 φ2 θ

Ref1~Ref4

SR

Figure 5.1 Communications between ARM and FPGA.

The programming process for the FPGA is shown in Figure 5.2. The clock of

the FPGA is chosen as 200 MHz. To achieve a 20kHz switching frequency, the

counter is set as

. Based on the φ1, φ2, and θ from ARM, four phase-

shifted sawtooth signals are obtained. Four reference values Ref1~ Ref4 from ARM

compare with the four sawtooth waveforms and eight drive signals for the DAB are

obtained. By regulating the value of the Ref1, the proposed duty cycle modulation is

realized for the relevant leg. At the same time with the control signal SR four drive

signals for synchronous rectifier are obtained. The total twelve drive signals get a

dead-time delay before output, which is set as 1 µs.

Reference

Sawtooth

φ1 φ2 θ Four Phase-

shifted

Sawtooths

Ref1~Ref4 Eight Drive

Signals for

DAB

Four Drive

Signals for

Rectifier

SR

Dead-time

Delay

Output

Figure 5.2 The programming process for the FPGA.

5.1.2 ARM

1) Basic Resources

The ARM-based 32-bit MCU STM32F407IGT6 is used, which is based on the

high-performance ARM Cortex-M4 32-bit RISC core with an operating frequency of

up to 168 MHz. The Cortex-M4F core features a floating point unit (FPU) single

precision which supports ARM single precision instructions and data types. Basic

features of ARM are as follow [43]:

Experiments 41

Memories: 1 Mbyte Flash memory; 192+4 Kbytes of SRAM including 64 Kbyte

of CCM (core coupled memory) data RAM; FSMC supporting Compact Flash,

SRAM, PSRAM, NOR and NAND memories.

Clock, reset and supply management: 1.8 V to 3.6 V supply; 4 to 26 MHz crystal

oscillator; Internal 16 MHz factory-trimmed RC (1% accuracy); 32 kHz

oscillator for RTC with calibration; Internal 32 kHz RC with calibration.

Three 12-bit, 2.4 MSPS ADCs: 24 channels and 7.2 MSPS in triple interleaved

mode.

Two 12-bit DACs.

General-purpose DMA: 16-stream DMA controller with FIFOs and burst

support.

17 Timers: twelve 16-bit and two 32-bit timers with an operating frequency of

up to 168 MHz.

140 I/O ports with interrupt capability.

2) Programming

The programming of ARM is conducted by the software Keil uVision. Detailed

tips are given below as:

Peripherals configuration includes the configuration of the ADC, DAC, DMA,

GPIO, Timer, NVIC, FSMC, etc. The initialization process includes the reset of

some system monitoring values.

The ADC sampling process includes the collecting of several measuring values

including voltages and currents, the data transferring through DMA and

generating the DMA interrupt signal.

The Voltage/Current protection process ensures the system values, including the

grid side voltage and current, DC side voltage and current and so on, are in safe

conditions. If any overvoltage or overcurrent cases are detected, the output of the

drive signals will be locked.

The phase lock loop (PLL) is used to get the phase angle of the grid voltage [44-

46]. In 1 -SRF-PLL, normally αu is the input signal, and βu is the generated

42 Experiments

orthogonal signal. The diagram of the 1 -SRF-PLL is shown in Figure 5.3. uα

and uβ are defined as

g g

2 2

β q

α

d

= = sin

+ sin( )2

gu U

u

u

u u

(5.1)

where gu is the grid voltage,

gU is the magnitude of the grid voltage and g is the

grid voltage phase angle. In the steady state condition, the generated orthogonal

signal βu is given as

β g gsin( )

2u U

(5.2)

Applying the dq-reference frame transformation, the following result can be

given as

d g

g

q β g

α cos( )sin cos=

sin( )cos sin

u

u

uU

u

(5.3)

From (5.3), the phase angle is locked at grid voltage phase angle g when

the following conditions are satisfied:

g

d g

q

=

=

=0

u U

u

(5.4)

It means if the output is locked as the grid voltage phase angle g , the value

of du is equal to the magnitude of the grid voltage gU and

qu is equal to zero. Thus

the objective of the PLL diagram in Figure 5.3 is to regulate qu to zero through a PI

controller, then the can be locked as the grid voltage phase angle.

PI

Controller

uq*=0 +

-

αβ

dquα

uβ

Lowpass

Filter

ω0 +

-1/s

sin(φ-π/2)

φ

ud

uq Ug

´

2 2

d q+u u

Figure 5.3 The diagram of the PLL.

Experiments 43

Check the condition for opening synchronous rectifier: This process is used to

ensure that the synchronous rectifier is opened at the end of the grid voltage

period, thus security for the synchronous rectifier switches is guaranteed.

PR control: This process realizes the quasi proportional resonant digital control.

The resonant part of the PR controller can be discretized by the bilinear method

(shown in Appendix A) as

-2

0 20 2-1 -2

0 1 2

-( )= , ( )

( ) + +

b b zY zb b

X z a a z a z (5.5)

Thus Y( )z is given by

-2

-20 20 2-1 -2

0 1 2

-( ) = ( ) ( )( - )

+ +

b b zY z X z W z b b z

a a z a z (5.6)

where ( )W z is given by

0-1 -2

0 1 2

( )( ) = , ( 1)

+ +

X zW z a

a a z a z (5.7)

Thus the recursive relation of the quasi resonant controller is given by

k 0 k 1 k-1 2 k-2

k 0 k k-2

=

= ( )

W a X a W a W

Y b W W

(5.8)

Phase angles calculation: Through this process, the relevant phase-shift angles

for sawtooth signals of FPGA are calculated.

The programming process for the ARM is shown in Figure 5.4.

44 Experiments

StartStart

Peripherals

Configuration

and

Initialization

Peripherals

Configuration

and

Initialization

ADC SamplingADC Sampling

Timer Update

Interrupt

Timer Update

Interrupt

Current/Voltage

Protection

Current/Voltage

Protection

Phase Lock

Loop

Phase Lock

Loop

Check the

Condition for

Opening

Synchronous

Rectifier

Check the

Condition for

Opening

Synchronous

Rectifier

PR Control PR Control

Phase Angle

Calculation

Phase Angle

Calculation

Open

Synchronous

Rectifier and

DAB

Open

Synchronous

Rectifier and

DAB

EndEnd

Figure 5.4 The programming process for the ARM.

Experiments 45

5.2 EXPERIMENTAL SETTINGS

The experimental settings are shown in Figure 5.5. The control board is

responsible for signals sampling including the DC side voltage, DC side current, AC

side voltage, AC side current and power decoupling LC circuit current. ARM is

mainly used for the control purpose and it transmits relevant information including

phase angles φ1, φ2, θ, reference values and the control signal for the

synchronous rectifier to FPGA. FPGA is mainly used for the purpose of 12 switch

drive signals processing.

DC Source

AC Source

Dual Active

Bridges

HF Transformer

RectifierControl Board

Figure 5.5 The experimental settings

The experimental results of the proposed DC-AC DAB converter are shown in

the following section. The main parameters of the converter are given in Table 5.2.

These parameters are the same as the simulation parameters shown in Table 4.1.

Table 5.2 The main parameters of the converter for experiments.

Parameter vg fg VDC Cs Ls

Value 18 V(Vg) 50 Hz 30 V 1910 µF 1560 µH

Parameter Cr Lr N fs Cf

Value 1.4 µF 102.5 µH 1:1 20 kHz 55 µF

5.3 EXPERIMENTAL RESULTS

5.3.1 Experimental Results without the Proposed Control Strategy

With φ1=π/2, θ=π/2, experimental results of the AC side voltage vg and current

ig, DC side current iDC without PR control are shown in Figure 5.6 and Figure 5.7

respectively.

46 Experiments

vg (20V/div)

ig (2A/div)

10ms/div

Figure 5.6 The AC side voltage vg and current ig without PR control.

10ms/diviDC (1A/div)

Figure 5.7 The DC side current iDC without PR control.

Similar with the simulation results shown in Figure 4.3, there appears a 100 Hz

ripple current, or a 100 Hz ripple power at the DC side because of the 100 Hz power

transmission nature at the AC side.

5.3.2 Experimental Results with the Proposed Control Strategy (Constant φ1)

With φ1=π/2, θ=π/2, experimental results of the AC side voltage vg and current

ig, DC side current iDC and the power decoupling capacitor Cs voltage us and current

is with PR control are shown in Figure 5.8, Figure 5.9 and Figure 5.10 respectively.

vg (20V/div)

ig (2A/div)

10ms/div

Figure 5.8 The AC side voltage vg and current ig with PR control (φ1=π/2, θ=π/2).

Experiments 47

10ms/diviDC (1A/div)

Figure 5.9 The DC side current iDC with PR control (φ1=π/2, θ=π/2).

us (5V/div)

is (2A/div)

10ms/div

Figure 5.10 The power decoupling capacitor Cs voltage us and current is with PR control (φ1=π/2,

θ=π/2).

Comparing Figure 5.8 with Figure 4.4, and Figure 5.9 with Figure 4.5, it is

obvious that the experimental results verify the simulation results. The experimental

result of iDC is about 0.91 A, which is near the simulation result of iDC. The 100 Hz

ripple power at the DC side is almost eliminated compared with Figure 5.7, thus a

more stable DC side current is obtained. Compared with Figure 4.6, the average

value of us in Figure 5.10 is a bit lower than the expected value due to the voltage

drop at the DC side in the experimental test. With the duty cycle modulation, the

power decoupling capacitor Cs voltage us fluctuates at 100 Hz frequency and thus

eliminate the 100 Hz ripple power at the DC side.

From Figure 5.8, the AC side current contains harmonics resulting from the

harmonics of the AC voltage. The elimination of the harmonics of the AC current

and the enhancement of the power quality is regarded as the next research step which

will be pointed out in the Recommendations part of the thesis.

The experimental result of the transformer secondary voltage vCD in this

condition is shown in Figure 5.11.

48 Experiments

vCD (10V/div) 2ms/div

Figure 5.11 The experimental result of the transformer secondary voltage vCD (φ1=π/2, θ=π/2).

According to vDC1 given in (3.1), vCD shows a 100 Hz envelope with a

magnitude of 18 V (Vg).

With φ1=2π/3, θ=π/2 and PR control, experimental results of the AC side

voltage vg, current ig and DC side current iDC are shown in Figure 5.12 and Figure

5.13 respectively. Under this condition, the experimental result of iDC is about 1.17 A,

which is 1.28 times that of the value shown in Figure 5.9 (near the theoretical value

1.22 given in Section 4.1.2).

vg (20V/div)

ig (2A/div)

10ms/div

Figure 5.12 The AC side voltage vg and current ig with PR control (φ1=2π/3, θ=π/2).

10ms/diviDC (1A/div)

Figure 5.13 The DC side current iDC with PR control (φ1=2π/3, θ=π/2).

The experimental results of the transformer primary voltage vAB and current ir

with φ1=2π/3, θ=π/2 are shown in Figure 5.14. Compared with Figure 3.10, the time

spans of the positive part and the negative part of vAB is almost the same, which

Experiments 49

means the modulation range of the duty cycle D is relatively small. This can also be

verified in Figure 5.10, where the fluctuation range of us is small. Therefore the

transmission power and the AC side current ig distortion effect can be ignored [39].

HFL current ir is near sinusoidal resulting from the series resonant part Lr and Cr.

vAB (20V/div)

ir (10A/div)

20µs/div

Figure 5.14 The experimental results of the transformer primary voltage vAB and current ir (φ1=2π/3,

θ=π/2)

With φ1=π/2, θ=π/4 and PR control, the experimental results of the AC side

voltage vg, current ig and DC side current iDC are shown in Figure 5.15 and Figure

5.16 respectively. In this condition, the experimental result of iDC is about 0.61 A,

which is 0.67 times that of the value shown in Figure 5.9 (near the theoretical value

20.71

2 given in the Section 4.1.2).

vg (20V/div)

ig (2A/div)

10ms/div

Figure 5.15 The AC side voltage vg and current ig with PR control (φ1=π/2, θ=π/4).

50 Experiments

10ms/diviDC (0.5A/div)

Figure 5.16 The DC side current iDC with PR control (φ1=π/2, θ=π/4).

5.3.3 Experimental Results with the Proposed Control Strategy (Controlled φ1)

With the proposed control strategy (controlled φ1) shown in Figure 3.13, the

experimental results of the AC side voltage vg, current ig and DC side current iDC

with PR control and Iavg*=0.5 A are shown in Figure 5.17. In this condition, φ1 is

controlled as 0.84 rad/s compared with the simulation result of 1 rad/s shown in

Figure 4.16. It is noted that iDC is controlled near Iavg*=0.5 A. And relatively high AC

current harmonics appear under this condition. So further power quality enhancement

method is required.

The experimental results of the AC side voltage vg, current ig and DC side

current iDC with PR control and Iavg*=1 A are shown in Figure 5.18. In this condition,

φ1 is controlled as 1.62 rad/s compared with the simulation result of 2.2 rad/s shown

in Figure 4.17. It is noted that iDC is controlled as Iavg*=1 A.

Experiments 51

（a）

(b)

vg (20V/div)

ig (1A/div)

10ms/div

10ms/diviDC (0.5A/div)

Figure 5.17 (a) The AC side voltage vg, current ig, (b) The DC side current iDC with PR control

(Iavg*=0.5 A).

(a)

(b)

vg (20V/div)

ig (2A/div)

10ms/div

10ms/diviDC (1A/div)

Figure 5.18 (a) The AC side voltage vg, current ig, (b) The DC side current iDC with PR control

(Iavg*=1 A).

52 Experiments

5.4 SUMMARY

This chapter gives a general introduction of the hardware settings, mainly for

the two key components ARM and FPGA of the control board. Basic resources and

programming procedures of ARM and FPGA are presented. FPGA works as a

generator of twelve drive signals for the main circuit, eight for the DAB and four for

the synchronous rectifier. ARM is mainly for the purpose of control and it delivers φ1,

φ2, θ, reference values and the control signal for the synchronous rectifier to FPGA.

The experiments results for the proposed DC-AC DAB converter are presented.

Among the simulation conditions discussed in chapter 4, namely (A) φ1=π/2, θ=π/2,

without PR control, (B) φ1=π/2, θ=π/2, with PR control, (C) φ1=2π/3, θ=π/2, with PR

control, (D) φ1=π/2, θ=π/4 with PR control, (E) φ1=π/2, θ=-π/2 with PR control, (F)

Controlled φ1 with Iavg*=0.5 A, (G) Controlled φ1 with Iavg

*=1 A, the experimental

results are presented and analyzed to verify the theoretical analysis and the

simulation results under conditions (A)~(D), (F)~(G). The experiments results

successfully verify the theoretical analysis and the simulation results.

The Proposed Converter for Photovoltaic Applications 53

The Proposed Converter for Chapter 6:

Photovoltaic Applications

Due to the presence of inherent double-line-frequency power ripple, the

operation of maximum power point tracking (MPPT) can be significantly affected.

To reduce the ripple power, a large capacitor at the DC side is normally used.

However, it will decrease the power density of the converter and cannot completely

eliminate the ripple power. By using the proposed DC-AC DAB converter, the ripple

power can be completely eliminated and thus high accuracy of MPPT can be

achieved.

6.1 BASIC ANALYSIS

The proposed converter for photovoltaic applications is shown in Figure 6.1.

Transmission power characterization of the converter with three phase shift angles

and the duty cycle D is similar with Section 3.2.2.

vg

Sp1

Sp2

Sp3

Sp4

Ss1 Ss3

Ss2 Ss4

Sr1

Sr2

Sr3

Sr4

Lr CrLf

CfCDC1

CDC

vDC vDC1

Primary Secondary

Ls

Cs

iDCig

HF Transformer

vAB vCD

PV

is. .

Figure 6.1 The proposed converter for photovoltaic applications.

In the simulation, the operation feature of the PV model is shown in Figure 6.2.

The red line represents the operation feature when the sun irradiance is 1 kW/m2, and

the blue one represents the operation feature when the sun irradiance is 0.5 kW/m2,

both at 25 °C. Point A represents the maximum power point in the former sun

irradiance condition, and point B represents the maximum power point in the latter

sun irradiance condition.

54 The Proposed Converter for Photovoltaic Applications

A

B

Figure 6.2 The operation feature of the PV model.

Phase shift angle φ2 is as follows: 2 g2 t , which is shown in Figure 3.5.

And the phase shift angle θ is fixed as π/2. φ1 is used to control the DC side voltage

through a PI controller (VE as input, φ1 as output). The target reference value of the

DC side voltage is obtained by the proposed MPPT algorithm, which is shown in

Figure 6.3. The output power of the PV panel is given by

PV =P V I (6.1)

where the V and I represent the output voltage and output current respectively.

Then the following equation can be given as

PV

d V IdP dII V

dV dV dV

(6.2)

PV

,

PV

,

PV

,

0

0

0

dPdI I

dV V dV

dPdI I

dV V dV

dPdI I

dV V dV

(6.3)

According to Figure 6.2 and (6.3), by comparing the values of dI

dV and

I

V , V

will be regulated accordingly to achieve the maximum power point tracking.

The Proposed Converter for Photovoltaic Applications 55

Start

Get V(k) I(k)

d(V)=V(k)-V(k-1)

d(I)=I(k)-I(k-1)

d(V)=0?

dI=0?dI/dV=-I/V?

dI/dV>-I/V? dI>0?

Vref=Vref-∆V Vref=Vref+∆V Vref=Vref+∆V Vref=Vref-∆V

Return

No Yes

No

No

No

No

YesYes

YesYes

V(k-1)=V(k)

I(k-1)=I(k)

Figure 6.3 MPPT algorithm.

Additionally, the ripple power elimination is realized by the PR controller (-

vripple as input, D as output). The overall control diagram is shown in Figure 6.4. The

average component Vavg and ripple component vripple of the DC side voltage vDC are

returned as feedback signals for the control system.

ModulatorMain

CircuitFilter

vDC

Vavg

VDC*

vripple*=0

φ1

D

-+

+

- vripple

vripple

MPPT

algorithm

Vavg

vDC iDC

Figure 6.4 Overall control diagram of the converter for photovoltaic applications

56 The Proposed Converter for Photovoltaic Applications

6.2 SIMULATION RESULTS

The main parameters of the proposed DC-AC converter are given in Table 6.1.

In the simulation, the sun irradiance drops from 1 kW/m2

to 0.5 kW/m2 at 1 s, and

rises back to 1 kW/m2 at 2.5 s.

Table 6.1 Main parameters of the proposed DC-AC DAB converter.

Parameter vg fg fs Cs Ls

Value 150 V(Vg) 50 Hz 20 kHz 2500 µF 1000 µH

Parameter Cf Lf Cr Lr N

Value 50 µF 0.3 mH 2 µF 44 µH 1:4

6.2.1 Simulation Results with CDC=1500 µF

The DC side voltage vDC and current iDC with CDC=1500 µF at the DC side, but

without the proposed ripple reduction control strategy are shown in Figure 6.5. The

system fluctuates near the maximum power point due to the presence of the ripple

power thus the accuracy of MPPT is relatively low.

(a)

(b)

Figure 6.5 (a) DC side voltage vDC and (b) DC side current iDC without the proposed control strategy

(CDC=1500 µF).

The zoom-in figures of the DC side voltage vDC, current iDC and power pDC

with CDC=1500 µF are shown in Figure 6.6. From Figure 6.6, it is clear that the

power at PV side is distorted, which can cause distortion in the grid current.

The Proposed Converter for Photovoltaic Applications 57

(a)

(b)

(c)

Figure 6.6 The zoom-in figures of (a) DC side voltage vDC, (b) DC side current iDC and (c) DC side

power pDC (CDC=1500 µF).

The grid current is shown in Figure 6.7 and the THD of the grid current is

7.69%. It is clear that the grid current is distorted resulting from the ripple power at

PV side. Therefore, normally a larger capacitor at the DC side is required to reduce

the ripple power and decrease the THD of the grid current, which will be presented

in Section 6.2.2 with CDC=3000 µF at the DC side.

58 The Proposed Converter for Photovoltaic Applications

(a)

(b)

Figure 6.7 The grid current (a) zoom-out, (b) zoom-in (CDC=1500 µF).

6.2.2 Simulation Results with CDC=3000 µF

To address the issues presented in Section 6.2.1, a larger DC side capacitor can

normally be used. With CDC=3000 µF, the system simulations are conducted in this

section. The DC side voltage vDC and current iDC with a larger capacitor CDC=3000

µF at the DC side, but without the proposed ripple reduction control strategy are

shown in Figure 6.8. Compared with Figure 6.5, it is clear that the fluctuation ranges

of vDC and iDC get smaller. But according to (3.17), in order to further reduce the

ripple power, an even larger DC side capacitor is required if the DC voltage keeps

constant, which can decrease the power density of the converter further.

The Proposed Converter for Photovoltaic Applications 59

(a)

(b)

Figure 6.8 (a) DC side voltage vDC and (b) DC side current iDC without the proposed control strategy

(CDC=3000 µF).

The PV side power with CDC=3000 µF is shown in Figure 6.9. Compared with

Figure 6.6 (c), the ripple power at PV side gets smaller. However, the ripple power

still cannot be eliminated and an even larger DC side capacitor is required if no

alternative method is adopted.

Figure 6.9 The PV side power with CDC=3000 µF.

The grid current with CDC=3000 µF is shown in Figure 6.10. Compared with

Figure 6.7 (b), the THD of the grid current is 5.78%. Thus the distortion effect in the

grid current gets better but still cannot be eliminated.

60 The Proposed Converter for Photovoltaic Applications

Figure 6.10 The grid current with CDC=3000 µF.

6.2.3 Simulation Results with the Proposed Control Strategy

The DC side voltage vDC and current iDC with CDC=200 µF at the DC side, and

with the proposed ripple reduction control strategy are shown in Figure 6.11.

Compared with Figure 6.5 and Figure 6.8, vDC and iDC get more stable at the

maximum power point.

(b)

(a)

Figure 6.11 (a) DC side voltage vDC and (b) DC side current iDC with the proposed control strategy

(CDC=200 µF).

The zoom-in figures of the DC side voltage vDC, current iDC and power pDC

with CDC=200 µF at the DC side, and with the proposed ripple reduction control

strategy are shown in Figure 6.12. It is clear that the ripple power at PV side is

almost eliminated and thus high accuracy of MPPT is obtained. The grid current in

this case is shown in Figure 6.13. Compared with Figure 6.7 (b) and Figure 6.10, the

THD of the grid current is 1.48%. Thus the grid current distortion effect is addressed

with the proposed control strategy.

The Proposed Converter for Photovoltaic Applications 61

(a)

(b)

(c)

Figure 6.12 The zoom-in figures of (a) The DC side voltage vDC, (b) current iDC and (c) power pDC

with the proposed control strategy (CDC=200 µF).

(a)

(b)

Figure 6.13 The grid current (a) zoom-out, (b) zoom-in with the proposed control strategy.

62 The Proposed Converter for Photovoltaic Applications

The DC voltage reference value VDC* (calculated by MPPT algorithm), error

value VE, and the phase-shift angle φ1 is shown in Figure 6.14. According to Figure

6.14 (b), the maximum power point tracking is realized near 1 s, 2 s and 3.5 s in three

periods of different sun irradiance conditions. With the regulation of φ1, the DC

voltage can be controlled as the desired value VDC* (which is obtained by the MPPT

algorithm) through the PI controller (VE as input).

(a)

(b)

(c)

Figure 6.14 (a) The DC voltage reference value VDC*, (b) The error value VE and (c) The phase-shift

angle φ1.

The decoupling capacitor Cs voltage vs and current is are shown in Figure 6.15.

From Figure 6.15, the 100 Hz ripple power is steered into the decoupling LC circuit,

and the voltage (or the energy storage) of the decoupling capacitor Cs fluctuates at

100 Hz.

The Proposed Converter for Photovoltaic Applications 63

Figure 6.15 The decoupling capacitor Cs voltage us and current is.

6.3 SUMMARY

This chapter presents a single-phase DC-AC DAB series resonant single-stage

converter to realize active power decoupling and MPPT operation for photovoltaic

applications. Simulations have been conducted under three conditions: (A)

CDC=1500 µF, (B) CDC=3000 µF and (C) CDC=200 µF with the proposed control

strategy. A larger DC capacitor CDC is able to improve the MPPT operation but still

cannot eliminate the ripple power. In addition, a larger DC capacitor can decrease the

power density of the converter. By using the proposed control strategy, the ripple

power can be completely eliminated with a relatively small capacitor at the DC side

and thus high accuracy of MPPT can be achieved.

Conclusions and Recommendations 65

Conclusions and Chapter 7:

Recommendations

7.1 CONCLUSIONS

The basic characteristics of the single-stage DC-AC DAB converter is analysed

in detail based on the mathematical analysis, simulations and experiments. Three

degrees of freedom, namely three phase shift angles of the dual active bridges φ1, φ2

and θ and their respective impact on the converter transmission power magnitude and

direction are introduced, where all of these three phase angles can influence the

transmission power magnitude, and the phase shift angle θ also determines the

direction of the power transfer. According to the basic analysis, the single-stage DC-

AC DAB converter with a pseudo intermediate DC link is proposed compared with

the common dual-stage DC-AC DAB converter by the specific modulation scheme

for the phase shift angle φ2. The single-stage DC-AC DAB converter is free of the

commonly required large electrolytic capacitor at the DC link between the

synchronous rectifier and the DAB converter. In addition, the using of the degree of

freedom φ1 as a control variable for the transmission power of the converter is

discussed and verified. In the case that the DC side is a constant DC power source,

by controlling φ1 the transmission power or the DC side current can be regulated. In

the case that the DC side is a photovoltaic cell array, by controlling φ1 the DC side

voltage can be regulated accordingly, which is verified in the simulations.

In terms of the power decoupling, a LC circuit is proposed to realize power

decoupling for the DC-AC DAB series resonant single-stage converter with the

specific control strategy. By controlling the duty cycle D, the proposed LC circuit is

able to completely eliminate the double-line-frequency ripple power with PR control,

which is verified in the simulation and experimental results. The performance of the

proposed converter for photovoltaic applications is verified based on the simulations.

From the simulation results, a larger electrolytic capacitor is able to decrease the

power ripple, whereas it cannot completely eliminate the ripple power and decrease

the power density and the reliability of the converter. Resulting from the complete

elimination of the power ripple, high accuracy of MPPT can be achieved.

66 Conclusions and Recommendations

7.2 RECOMMENDATIONS

Several recommendations for the future research based on the DC-AC DAB

converter are as follows.

1) As shown in the experiments results, the AC side current contains

harmonics resulting from the harmonics of the AC voltage. Specific

control strategy may need to be proposed to eliminate the harmonics of the

AC current and thus enhance the power quality.

2) The performance of the proposed DC-AC DAB converters in parallel can

be investigated. The cooperative control methods for the parallel DC-AC

DAB converters such as the current-sharing control remain massive

research works to investigate.

3) One of the features of the DC-AC DAB converter is the bidirectional

power transfer. Therefore the dynamic characteristics of the DC-AC DAB

converter at the transition of the reversing of the power transfer direction

can be a research subject for the future research on the DC-AC DAB

converter.

4) To further decrease the power loss and enhance the efficiency of the

converter, the soft-switching operation range of the proposed DC-AC

DAB series resonant single-stage converter can be investigated. The effect

of the proposed series resonant tank in the HFL on the soft-switching

operation ranges of the switches of the dual active bridges can be studied

in the future research.

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Appendices 71

Appendices

Appendix A

Bilinear transformation of PR controller transfer function

The bilinear transformation of the resonant part of the PR controller transfer

function shown in (3.19) is as follows in (1), where 1 , T and z represent the pre-

warped frequency, the sampling period and the forward shift operator. Substituting (1)

into (3.19), the z-domain discrete transfer function is obtained, based on which the

difference equation used for programming can be obtained.

1T

1

1 1

tan( / 2) 1 1

z zs K

T z z

(1)

-2

0 2

-1 -2

0 1 2

0 2 i T c

2 2

0 T T c 0

2 2

1 0 T

2 2

2 T 0 T c

-( )=

( ) + +

2

2

2 2

2

b b zY z

X z a a z a z

b b K K

a K K

a K

a K K

(2)

The code for the PR controller is shown below:

float ResonantCtrl(float CurErr) //PR for ripple power reduction

{

float TempRst;

RMemW[0] =PrC2[0]*CurErr-PrC2[1]*RMemW [1]-PrC2[2]*RMemW[2] ; //resonant part

TempRst = PrC1*(RMemW[0]-RMemW[2]);

if (TempRst > RESMAX)

{

RMemW[0]=RMemW[0]*RESMAX/TempRst;

RMemW[1]=RMemW[1]*RESMAX/TempRst;

RMemW[2]=RMemW[2]*RESMAX/TempRst;

TempRst=RESMAX;

72 Appendices

}

else if(TempRst < -RESMAX)

{

RMemW[0]=-RMemW[0]*RESMAX/TempRst;

RMemW[1]=-RMemW[1]*RESMAX/TempRst;

RMemW[2]=-RMemW[2]*RESMAX/TempRst;

TempRst=-RESMAX;

}

RMemW[2]=RMemW[1];

RMemW[1]=RMemW[0];

TempRst=TempRst+PrC0*CurErr; //proportional part

if (TempRst>750) //amplitude limiting

{

TempRst=750;

}

if (TempRst<-750)

{

TempRst=-750;

}

return TempRst;

}