INVESTIGATION ON THE DC-AC UAL ACTIVE BRIDGE ...viii Investigation on the DC-AC Dual Active Bridge...
Transcript of INVESTIGATION ON THE DC-AC UAL ACTIVE BRIDGE ...viii Investigation on the DC-AC Dual Active Bridge...
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;
}