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Electronic Theses, Treatises and Dissertations
The Graduate School
2012
Interleaved Multi-Phase Isolated
Bidirectional DC-DC Converter and Its
Extension
Zhan Wang
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THE FLORIDA STATE UNIVERSITY
COLLEGE OF ENGINEERING
INTERLEAVED MULTI-PHASE ISOLATED BIDIRECTIONAL DC-DC
CONVERTER AND ITS EXTENSION
By
ZHAN WANG
A Dissertation submitted to the
Department of Electrical and Computer Engineering
in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
Degree Awarded:
Summer Semester, 2012
Zhan Wang defended this dissertation on March 16, 2012.
The members of the supervisory committee were:
Hui Li
Professor Directing Dissertation
Anke Meyer-Baese
University Representative
Simon Y. Foo
Committee Member
Jim P. Zheng
Committee Member
Petru Andrei
Committee Member
The Graduate School has verified and approved the above-named committee members, and
certifies that the dissertation has been approved in accordance with university requirements.
ii
To my parents: Guoliang Wang and Changhua Deng
iii
ACKNOWLEDGEMENTS
First of all I want to thank my advisor, Dr. Hui Li, for giving me the opportunity to do my
Ph. D program in Center for Advance Power Systems (CAPS) at FSU, providing me valuable
ideas, suggestions on the field of power electronics. I also learned the rigorous attitude towards
research and effective research skills from her, which will be useful for my future study and life.
I am grateful to my committee: Dr. Simon Y. Foo, Dr. Jim P. Zheng, Dr. Petru Andrei
and Dr. Anke Meyer-Baese for giving me their valuable advices and broadening my horizon on
the research.
I would also thank CAPS to provide me so convenient research environment, and thank
the staff, scientists and technicians in CAPS for their support during my Ph.D study. Many
thanks to our director, Dr. Steinar Dale, and Mr. Steve McClellan, Mr. Michael Coleman, Ms.
Nancy Rainey, Ms. Joann Jirak, Mr. John Hauer, Mr. Steve Ranner, Mr. Ted Williams, Ms.
Bianca Trociewitz, and Mr. Michael Sloan.
I would thank my group colleagues, Dr. Liming Liu, Xiaohu Liu, Yan Zhou, Passinam
Tatcho, Dr. Lei Wang, Dr. Haifeng Fan, Lei Wang and other students at CAPS, for their valuable
suggestion, comments, discussions and support.
Finally, I wish to express my sincere gratitude to my family for their love, support and
understanding during hard times.
iv
TABLE OF CONTENTS
List of Tables ................................................................................................................................ vii
List of Figures .............................................................................................................................. viii
Abstract ......................................................................................................................................... xii
1 INTRODUCTION ....................................................................................................................... 1
1.1 Research Background ........................................................................................................... 1
1.1.1 Electricity Vehicle Infrastructure with Energy Storage .............................................. 1
1.1.2 DC Distribution System with Renewable Energy Source ........................................... 2
1.2 Objective and Outline of the Research ................................................................................. 4
2 STATE-OF-THE-ART TECHNOLOGY .................................................................................... 6
2.1 Bidirectional DC-DC Converters.......................................................................................... 6
2.1.1 Buck-boost Half Bridge DC-DC Converters............................................................... 6
2.1.2 Dual Active Bridge DC-DC Converters ...................................................................... 7
2.1.3 Current-fed full-bridge bidirectional DC-DC Converter............................................. 8
2.1.4 Current-fed Boost Dual-half-bridge (DHB) Bidirectional Converter ....................... 10
2.2 Multiphase Interleaved DC-DC Converter ......................................................................... 10
2.3 Multi-port DC-DC Converters ............................................................................................ 11
2.4 The Proposed Three-phase DAB Bidirectional DC-DC Converter .................................... 13
3 THREE-PHASE TWO-PORT DUAL-ACTIVE-BRIDGE (DAB) DC-DC CONVERTER .... 14
3.1 Introduction ......................................................................................................................... 14
3.2 The Proposed Topology and Comparison .......................................................................... 16
3.2.1 Topology Description ................................................................................................ 16
3.2.2 Operating Mode Analysis .......................................................................................... 18
3.2.2.1 50% Fixed duty cycle .................................................................................... 18
3.2.2.2 Varied duty cycle........................................................................................... 23
3.3 Analysis of ZVS Conditions ............................................................................................... 28
3.3.1 ZVS Conditions for Voltage Source DAB3 Converter ............................................. 28
3.3.2 ZVS Conditions for Current-fed DAB3 Converter ................................................... 29
3.4 Analysis of Unbalance Issue ............................................................................................... 33
3.4.1 Analysis of Current Unbalance ................................................................................. 33
3.4.2 Current Sharing Control ............................................................................................ 37
v
3.5 Converter Design Guideline ............................................................................................... 43
3.5.1 Transformer Design ................................................................................................... 43
3.5.2 DC Inductor Design................................................................................................... 45
3.5.3 Power Loss Analysis ................................................................................................. 46
3.6 Control Strategies for Current-fed Topology...................................................................... 51
3.6.1 Small Signal Modeling .............................................................................................. 51
3.6.2 Control system design ............................................................................................... 55
3.7 Experimental Results .......................................................................................................... 56
3.8 Summary ............................................................................................................................. 62
4 INTEGRATED THREE-PORT THREE-PHASE DAB DC-DC CONVERTER ..................... 64
4.1 Introduction ......................................................................................................................... 64
4.2 Converter Description ......................................................................................................... 67
4.3 ZVS Conditions Analysis ................................................................................................... 71
4.3.1 Pseudo two-port ZVS Analysis ................................................................................. 72
4.3.2 ZVS conditions in three-port mode ........................................................................... 74
4.3.3 ZVS Conditions in General ....................................................................................... 76
4.4 Control System Design ....................................................................................................... 78
4.5 Experimental Results .......................................................................................................... 85
4.6 Summary ............................................................................................................................. 90
5 CONCLUSION AND FUTURE WORK .................................................................................. 91
5.1 Conclusions ......................................................................................................................... 91
5.2 Future work ......................................................................................................................... 92
REFERENCES ............................................................................................................................. 93
BIOGRAPHICAL SKETCH ...................................................................................................... 104
vi
LIST OF TABLES
3.1 ΔI/Iavg resulting from unbalanced leakage inductance ...........................................................37
3.2 The relationship between regulation of φ and ΔI/Iavg ............................................................39
3.3 Leakage inductance of each phase (refer to LVS) .................................................................44
3.4 Specifications and parameters of converter..............................................................................56
4.1 Operation modes in terms of different power flow ...............................................................70
4.2 ZVS Conditions in Different Operation ................................................................................78
4.3 Three-port Converter Parameters ..........................................................................................80
4.4 Parameters of PV panel Sunpower 215 (25◦C, 1000W/m2) ..................................................85
vii
LIST OF FIGURES
1.1 Fuel Cell Electric Vehicle Power Train with Energy Storage .................................................2
1.2 PV residential complex in DC distribution system .................................................................3
2.1 Single phase buck-boost converter ..........................................................................................6
2.2 Three-phase buck-boost converter ..........................................................................................7
2.3 Full bridge dual-active-bridge (DAB) bidirectional converter ................................................8
2.4 Dual-half-bridge (DHB) bidirectional converter .....................................................................8
2.5 Current-fed full bridge bidirectional converter .......................................................................9
2.6 Current-fed boost dual-half-bridge bidirectional converter ....................................................9
2.7 Three-phase dual-active-bridge bidirectional dc-dc converter ..............................................11
2.8 Three-phase six-leg dc-dc converter .....................................................................................11
2.9 Tri-mode half-bridge converter .............................................................................................12
2.10 Three-port bidirectional dc-dc converter ...............................................................................12
3.1 Proposed three-phase current-fed dual-active-bridge bidirectional DC-DC converter .........16
3.2 Voltage and current waveforms in transformer and DC input inductor: (a) φ ≤ π/3; (b) π/3 <
φ < 2π/3; .........................................................................................................................................17
3.3 Comparison of Power and power factor for DAB3 and 3DHB converters ...........................21
3.4 Comparison of power and power factor for DAB3 and 3DHB converters ...........................22
3.5 Six operating areas with different (D, φ) and corresponding transformer current waveforms
...............................................................................................................................................24
3.6 Power flow versus duty cycle D and phase shift angle φ ......................................................24
3.7 Power flow of DAB3 and 3DHB converter with different (D, φ) .........................................25
3.8 PF of DAB3 and 3DHB converter with different (D, φ) .....................................................26
3.9 Comparison of PF of DAB3 and 3DHB converter with different (D, φ) ..............................27
viii
3.10 RMS current curves on LVS MOSFETs ...............................................................................28
3.11 ZVS boundaries and power curves at different D: (a) D = 1/3, 2/3; (b) D = ½ ....................30
3.12 The middle points of one leg on LVS and HVS ....................................................................31
3.13 DC inductor current in one switching period ........................................................................31
3.14 ZVS boundaries under different m ........................................................................................32
3.15 Transformation between Y-model to Δ-model ......................................................................33
3.16 Four Transformer connection types DC-DC converter: (a) Y-Y DAB3; (b) 3DHB; (c) Δ-Δ
DAB3 with integrated Ls; (d) Δ-Δ DAB3 with external Ls ............................................................35
3.17 Phasor diagram of phase voltage and current ........................................................................36
3.18 Flow chart of ratio presetting current sharing control ...........................................................40
3.19 Phase current and transformer current waveforms without unbalance controller: (a) Splitcap type; (b) Y-Y type; (c) Δ- Δ type ............................................................................................41
3.20 Phase current and transformer current waveforms with unbalance controller: (a) Split-cap
type; (b) Y-Y type; (c) Δ- Δ type ...................................................................................................42
3.21 The sectional view of transformer .........................................................................................43
3.22 Input current ripple versus duty cycle ...................................................................................45
3.23 Total winding copper loss ratio versus ξ and number of layers M ........................................49
3.24 Ploss distribution in different output power in different D .....................................................50
3.25 Total Ploss curves in different D .............................................................................................50
3.26 Equivalent circuit of average model ......................................................................................51
3.27 Equivalent small signal circuit model ...................................................................................52
3.28 Bode plots of control to output ..............................................................................................54
3.29 Bode plots of voltage loop gain with compensator ...............................................................55
3.30 Photo of 6kW experimental prototype ..................................................................................57
3.31 System control system including current sharing controller .................................................57
ix
3.32 Three-phase inductor current and total input current: (a) Idc at D = 1/3, (b) Idc at D = 1/2, (c)
Idc at D = 2/3...................................................................................................................................59
3.33 Transformer current on secondary side with different D: (a) D = 1/3; (b) D = 1/2; (c) D =
2/3 ...............................................................................................................................................60
3.34 ZVS waveforms for Sa1 and Sa2 at Po=1200W in (a) Vin=24V; (b) Vin=36V; (c)Vin=48V ....61
3.35 Voltage and current waveforms when Vin varies between 24V and 48V ..............................62
3.36 Measured efficiency of proposed converter at Vin = 24V, 36V and 48V...............................62
4.1 A DC distribution system with basic cell for PV applications: Energy sources, Energy
storage and Load ............................................................................................................................66
4.2 Three-port integrated bi-directional dc-dc converter ............................................................68
4.3 Six operation areas with different duty cycle and phase-shift angle, and shadowed part is
the practical operating area ............................................................................................................69
4.4 Operation modes in different power flow. (A) P1>0, P2<0, P3<0; (B) P1>0, P2>0, P3<0; (C)
P1>0, P2<0, P3>0; (D) P1=0, P2<0, P3>0; (E) P1=0, P2>0, P3<0; ...................................................69
4.5 Battery’s voltage in charge/discharge performance ..............................................................73
4.6 ZVS boundaries in pseudo “two-port” mode ........................................................................74
4.7 The key current waveforms in different operation modes .....................................................76
4.8 The equivalent circuit of three-port dc-dc converter .............................................................79
4.9 Control system diagram .........................................................................................................79
4.10 Current open loop gain of DAB3 stage built in the laboratory .............................................81
4.11 Average model of three-port dc-dc converter .......................................................................82
4.12 Simulation results comparison: 1, Circuit model; 2, Equivalent circuit model; 3, Average
model..............................................................................................................................................82
4.13 One day simulation results using average model ..................................................................84
4.14 Discharge performance of one battery module .....................................................................86
4.15 Charge performance of one battery module ..........................................................................86
x
4.16 Experimental set up ...............................................................................................................87
4.17 V-I characteristics curve for five PV panels in parallel ........................................................87
4.18 One day scale down experimental results .............................................................................88
4.19 ZVS waveforms of Sa2 in different operating modes: (a) mode B; (b) mode C; (c) mode E ....
...............................................................................................................................................89
xi
ABSTRACT
Recently, along with the development of renewable energy technology and threat of
energy shortage, hybrid electric vehicles (HEV) and DC microgrid system are increasingly
attracting attentions in industry and academia. By combining internal combustion engine (ICE)
and high-performance energy storage such as battery, fuel-cell and ultracapacitors, HEVs can
achieve twice the fuel economy of conventional vehicles. DC microgrid is an appropriate system
to interconnect dc energy sources and to supply high quality power. To enable the usage of dc
energy storage, developing power converters as the power electronics interface of dc energy
sources becomes imminent.
Currently, the voltage type bidirectional converter is dominating topology in dc-dc
applications, which is not suitable for renewable energy source with wide voltage range.
Although some current type converters have been proposed, most of them are dealing with
unidirectional or low power system. For a high power energy storage system, high voltage
conversion ratios, high input currents and wide input voltage range are the major barriers to
achieving high-efficiency power conversions. This thesis proposes a novel three-phase currentfed dual-active-bridge (DAB) dc-dc converter with transformer isolation to overcome these
obstacles. The major features of the proposed converter are the following: (1) Increase converter
power rating by paralleling phases; (2) Reduce the size of input dc inductors and dc link
capacitor with interleaved control; (3) Achieve Zero-Voltage Switching (ZVS) over a wide load
range and wide input voltage rage without auxiliary circuitry; High conversion efficiency above
94% is verified with wide input voltage range. The detailed operation analysis and experimental
results to prove the proposed converter are given in chapter 3.
For integrating primary sources and energy storage, this thesis also proposes an
integrated three-port bidirectional dc-dc converter based on three-phase current-fed DAB
converter. Comparing to the individual dc-dc converters, the major advantages of the proposed
integrated three-port converter include: (1) Higher power density due to multiport and
multiphase interleaved structure; (2) Easier implementation of centralized control; (3) Decoupled
power management control due to natural decoupled control variables; (4) Zero voltage
switching in different operation mode.
Comparing to two-port dc-dc converter, there are much more operation modes for
integrated three-port dc-dc converter. Based on the integrated three-port converter, a
xii
photovoltaic (PV) system with battery backup is discussed. PV panel with wide voltage variation
is connected to the current-fed port and battery as an energy storage with small voltage variation
is connected to the dc link. By controlling the phase shift angle, the power exchange can be
controlled between low voltage side (LVS) and high voltage side (HVS). By controlling the duty
cycle, the PV can realize maximum power point tracking control (MPPT). The battery as an
energy buffer is charging or discharging to wipe off the gap between generated power and
required power. For the grid-connected mode, it is also helpful to manage the SOC of battery.
The detailed analysis, simulation and experimental verification are provided in chapter 4.
Finally, the last chapter concludes the previous work and gives the scope of the future
work.
xiii
CHAPTER ONE
1 INTRODUCTION
1.1 Research Background
1.1.1 Electricity Vehicle Infrastructure with Energy Storage
Global warming is becoming the most complicated and important issue facing the human
being in this century. The surface temperature of the earth has increased by about 1 ºF over the
past 100 years [1]. The global warming is mainly caused by the greenhouse gases emission. The
greenhouse effect also results in climate change. In United States, the main source of greenhouse
gases emissions is fossil fuel combustion, which provides around 85% of national energy supply
[2]. According to DOE 2009 report [3], transportation will deplete around 70% of total oil usage.
Abundant exhaust gases emission will also result in a series of environment issues. Under this
background, advanced pure electric vehicles and hybrid vehicles are developed in many vehicle
companies and research institutes. Mass-produced hybrid electric vehicles have been introduced
worldwide such as Toyota Prius, Nissan Leaf and Chevrolet Volt, etc. High performance
batteries as main power source together with Internal Combustion Engine (ICE) together are
installed in hybrid cars, thus the efficiency being remarkably improved. The bidirectional dc-dc
converters as the key components in future electric cars are paid attention in the field of power
electronics. Many topologies and system structures are addressed to improve the efficiency and
system performance. To integrate 14V and 42V dc source on the vehicle, a three-port isolated
bidirectional dc-dc converter was proposed [4]. In order to improve the dynamic characteristic,
battery with high energy density and supercapacitor with high power density were used and
interfaced using a three-port dc-dc converter at the same time [5, 6]. The fuel cell and battery
hybrid vehicle is also a promising solution for the future vehicle because of it zero emission and
fast dynamic performance. The battery is connected to the dc-link through a bidirectional dc-dc
converter so it is easy to control the power flow of system and improve the life cycle of battery.
Fig. 1 gives a Fuel Cell electric vehicle drive train. The main power is provided by fuel cell
through unidirectional DC-DC converter. The battery and ultracapacitor are interfaced to DC bus
as auxiliary energy source to improve dynamic performance and absorb the braking regenerated
energy. Normally, the battery in vehicle also provides power to some accessory device such as
1
CD player, air-conditioner and power steering system. For safety concern, the voltage of battery
and ultracapacitor are lower than human safe voltage, so the isolated transformers between low
voltage energy storage and high voltage dc bus are needed. So the dc-dc converter to interface
battery and ultracapacitors should have such characteristics: 1, Bidirectional power flow
capability; 2, high power density so as to reduce the converter size; 3, high efficiency under wide
input voltage range.
DC Bus
300~500V
Fuel Cell
DC/DC
Converter
Traction
Inverter
Battery
Traction
Motor
Bidirectional
DC/DC
Converter
Ultra
capacitor
Bidirectional
DC/DC
Converter
Fig. 1.1 Fuel Cell Electric Vehicle Power Train with Energy Storage
1.1.2 DC Distribution System with Renewable Energy Source
With the application of renewable energy in residential utility system, DC microgrid [7 9] as a new utility grid for local power generation has been developed. The conventional
electrical system in place today sees our electrical devices powered by AC mains. But as
renewable technologies such as solar photovoltaics and wind power become more prevalent at a
household level, DC microgrids could be a cheaper and more efficient alternative. Renewable
2
energy source such as fuel cells and many small scale sustainable energy sources generate low
voltage DC power. The small DC power sources send power to AC utility grid, thus requiring
costly and inefficient DC/AC inverters, and even the power may ultimately be utilized by a DC
device such as personal computer, TV and LED lighting, etc. A possible solution is to install a
DC microgrid linking DC power supplies to DC devices. The renewable energy sources generate
power and send to a DC bus to interface the DC load and energy storage system. There is no
DC/AC/DC conversion between DC load and DC power supplies, thus reducing the power loss
and simplifying the system.
Utility
Grid
AC
DC
AC/DC
DC
Bus
...
DC/DC
DC/DC
DC/DC
DC/DC
DC
Load
ESS
PV
DC
Load
ESS
PV
...
DC/DC
DC/DC
DC
Load
ESS
PV
Fig. 1.2 PV residential complex in DC distribution system
Fig. 2 shows a PV residential DC microgrid system with energy storage. The power
generated by PV panel supports local DC load, and the ESS as an energy buffer balances the
power between PV and load. The common DC bus is connected to an AC utility grid through
inverter, so that utility grid can provide power to the residential and in some conditions the
excessive power from PV can send to the AC grid. DC-DC converters are applied in microgrid
3
system to interface the DG and ESS. So the converter should meet the following requirement: 1,
Bidirectional function to charge and discharge ESS; 2, Maximum power point tracking function
so as to utilize the power from DG as much as possible; 3, Multiport topology to interface with
multiple DG (PV and DC wind turbine) and ESS (Battery and Ultracapacitor) to reduce the count
of DC-DC converter.
1.2 Objective and Outline of the Research
Based on the applications discussed above, the first main objective is to develop a
bidirectional isolated dc-dc converter. A three-phase bidirectional current-fed dc-dc converter is
proposed as the interface converter between low voltage ESS and high voltage load.
Three phase dual active bridge is first proposed by [10] for high power high power
density applications. With the advantages of bidirectional, natural soft-switching and interleaving
features, DAB converters are widely studied and applied in power electronics and power system
fields. Several types of bidirectional DC-DC converters were derived from DAB converter to
satisfy specific requirement [11 - 13]. In [11], a current-fed full-bridge bidirectional dc-dc
converter was proposed to reduce the switching loss and increase voltage transfer ratio. In [13], a
current-fed dual half bridge was addressed for the minimum device counts and total device rating
(TDR) approach. The converter can also operate in phase shift angle plus duty cycle control
mode so as to handle with varied input voltage. Using this topology, [14] and [15] developed
different three-port dc-dc converter for vehicle applications.
Combined with three-phase DAB converter with current-fed DHB converter, a threephase current-fed DAB converter is proposed for high power and high power density application.
In this project, we try to realize the following targets.

Realization of high efficiency under wide voltage range. The devices can be soft-
switched if the dc link voltages on both sides are matched, and the switching loss and reactive
power loss will be low in this operating condition.

Detailed operation mode and ZVS conditions analysis on current-fed DAB3 converter. In
order to keep the dc link voltage constant, phase shift + duty cycle control is applied and the
operating modes will be more complex than phase shift control method. The operating modes
should be clarified for hardware and controller design.
4

Based on the principle analysis, 6kW dc-dc converter will be developed and hardware
design and optimization guideline are also studied.
The second main objective is to develop a PV grid interactive system using current-fed
DAB3 as a three-port bidirectional dc-dc converter to interface with PV panels, energy storage
and DC bus. In this three-port PV grid interactive system, the following topics will be reached.

Analysis on power flow control and power management. Using a three-port DAB3
converter, the power flow can be controlled bidirectional by phase shift angle tuning. The PV
panel can realize maximum power point tracking (MPPT) control by controlling duty cycle. The
charging or discharging ESS is depending on the power difference between that generated by PV
and that consumed by load and grid.
Optimization of energy source sizing for PV residential system. How to design ESS and
PV size is also a crucial object in the application. Based on the specific household renewable
energy system, we try to design and optimize the ESS and PV volume for better economics and
efficiency.
5
CHAPTER TWO
2 STATE-OF-THE-ART TECHNOLOGY
2.1 Bidirectional DC-DC Converters
2.1.1 Buck-boost Half Bridge DC-DC Converters
Fig. 2.1 gives a simple buck-boost bidirectional converter. This simple topology is widely
applied because it can meet the requirement to interface with different energy storage [1 - 4]. It
can realize bidirectional power flow and high efficiency because of small counts of components.
The topology can extend to multiphase interleaved structure for high power application and
smaller passive components. Fig. 2.2 shows a three-phase bidirectional buck-boost converter [5].
The size of inductors and capacitor are significantly reduced comparing with single phase
topology, but the current ripple is also reduced.
i2
Sa1
i1
Ldc
C1
VL
Sa2
Fig. 2.1 Single phase buck-boost converter
6
VH
i2
Sa1
ia
ib
ic
Sc1
Sb1
Ldc1
Ldc2
Ldc3
C1
VH
VL
Sa2
Sc2
Sb2
Fig. 2.2 Three-phase buck-boost converter
2.1.2 Dual Active Bridge DC-DC Converters
Buck-boost bidirectional converter can interface with the different energy sources if their
voltage ratings are close. In some cases, the converters with large turns ration isolated
transformers are used for the reason that the voltage ratings have a tremendous difference
between different energy source and electrical isolation is necessary for safety concern.
So far, there are many galvanically isolated high power bidirectional dc-dc converter
topologies, and the dual active bridge (DAB) dc-dc converter [6] are most frequently reported
and studied in [7 - 10] because of its merits such as bidirectional power flow, buck-boost
operation and zero voltage switching operation without additional components.
The DAB converter was first proposed in [6], and Fig. 2.3 shows the full bridge topology.
The converter utilizes the leakage inductance of the isolated transformer as the main energy
storage element and the direction and magnitude of power flow is controlled by phase shift angle
between the voltage exerted on the LVS and HVS of transformer. Fig. 2.4 shows a dual-halfbridge dc-dc converter [11] which is suitable to high voltage, low current fields due to the lower
transformer core loss. Moreover DHB has only half of the number of switching devices as DAB
so that it is a good selection for cascaded modules structure.
7
LVS
i1
Sa1
Sb1
a
Sr1
isa
1 : N
ir
VL
Ss1
c
b
C1
Sa2
i2
HVS
Sb2
Sr2
C2
is
VH
d
Ss2
Figure 2.3 Full bridge dual-active-bridge (DAB) bidirectional converter
i1
LVS
Sa1
HVS
C1
iLs
C3
Ls
i2
Sr1
1 : N
ir
VL
VH
C2
C4
Sr2
Sa2
Figure 2.4 Dual-half-bridge (DHB) bidirectional converter
2.1.3 Current-fed full-bridge bidirectional DC-DC Converter
A current-fed full-bridge bidirectional dc-dc converter [12 - 13] shown in Fig. 2.5 was
proposed to reduce switching loss and increase the voltage transfer ratio. The converter can
operate in boost-mode and buck-mode. A simple clamp circuit consisted of an active switch and
a capacitor is used on the current-fed side to achieve soft-switching operation in both modes. In
buck mode, the converter can achieve hybrid zero-voltage and zero-current switching (ZVZCS)
8
for voltage-fed side switches and the switches on current-fed side operate in synchronous
rectified mode to reduce the conduction loss. In boost mode, the converter achieves ZVS for
current-fed side switches and the switches on voltage-fed side operated in synchronous rectified
mode. High efficiency under wide voltage range can be obtained in this topology. Since the
modulation methods for buck mode and boost mode are different, the control strategy will be
complex.
LVS
Lin
Sa1
Sb1
a
Sa
Sr1
isa
Ls 1 : N
is
b
C1
Sa2
Sb2
Ss1
c
ir
VL
i2
HVS
C2
VH
d
Ss2
Sr2
Figure 2.5 Current-fed full bridge bidirectional converter
LVS
Sa1
iLs
HVS
C1
Ls
C3
i2
Sr1
1 : N
ir
i1 Ldc
VH
VL
C2
C4
Sr2
Sa2
Figure 2.6 Current-fed boost dual-half-bridge bidirectional converter
9
2.1.4 Current-fed Boost Dual-half-bridge (DHB) Bidirectional Converter
Fig. 2.6 shows a current-fed boost DHB converter [14]. Combined the boost converter
with dual-half-bridge, a current-fed boost dual-half-bridge (DHB) converter is proposed in some
literatures. Similar to the DAB converter, the power flow is also controlled by phase shift angle
between the transformer voltage on LVS side and HVS side. The current-fed side voltage can be
boosted by duty cycle control and make the voltage on both sides to be matched so as to
implement soft-switching operation.
2.2 Multiphase Interleaved DC-DC Converter
For high-power-density high-power applications, multiphase interleaved soft-switching
dc-dc converters are promising topologies because of smaller passive components and
conduction loss. Fig. 2.7 shows a three-phase DAB bidirectional dc-dc converter [6, 15] in which
the power flow is controlled by phase shift angle. In some literatures, the topology operated in
different duty cycle is discussed. The high efficiency and high power density is verified in the
experiment.
For the unidirectional application, Fig. 2.8 provides another three-phase interleaved
topology. The power rating is increased by paralleling phases, and output voltage is doubled by
transformer Δ-Y connection, thus lowering the transformer turns ratio. Moreover, the circuit
operates in ZVZCS over a wide load range without auxiliary circuitry. But the disadvantage is
doubled count of switching devices.
10
i1
LVS
Sa1
Sc1
Sb1
a
VL
C1
c
St1
r
Ls2
Ls3 n
C2
s
m
VH
t
Sc2
Sb2
Sa2
Ss1
Sr1
Ls1
b
i2
HVS
1 : N
Ss2
Sr2
St2
Figure 2.7 Three-phase dual-active-bridge bidirectional dc-dc converter
i1
LVS
Sa1
Sb1
Sc1
Sr1
Ss1
St1
1 : N
Vin
C2
Vo
C1
Sa2
Sb2
Sc2
Sr2
St2
Ss2
Figure 2.8 Three-phase six-leg dc-dc converter
2.3 Multi-port DC-DC Converters
For the alternative renewable energy applications, there is growing concern about multiport dc-dc converter because of its attractive features such as lower switching devices, universal
controller and flexible power flow control strategy. Fig. 2.9 gives a three-port converter topology
[17 - 18]. The proposed converter is formed by a half-bridge topology with a free-wheeling
branch. The two input ports are connected to the dc link and middle point of capacitors. The gate
signals of three switches are turned on in sequence and the power flow on two ports can be
11
controlled independently. The converter can achieved soft-switching on all of the switches over
wide input voltage. But since the input current is discontinuous, it is more suitable for low power
applications. On the other hand, the power flow on transformer is unidirectional so that the
energy sources on primary side cannot be charged by the HVS source.
S2
C2
D1
Lf
Vin
S3
D2
C1
Vbi
S1
Vo
Cf
1:n:n
Figure 2.9 Tri-mode half-bridge converter
i2
LVS
Sa1
iLs
HVS
C1
Ls
C3
i3
Sr1
1 : N
ir
i1 Ldc
VH
V1
V2
Sa2
Sb
C2
C4
Sr2
2
Figure 2.10 Three-port bidirectional dc-dc converter
12
Based on current-fed boost dual-half converter, a three-port topology is proposed in [19 20] to interface 14V and 42V battery for vehicle applications. In Fig. 2.10 shows that another
port is connected to the LVS dc link. The power flow between the LVS and HVS is controlled by
phase shift angle, and the power distribution of two ports on LVS is controlled by duty cycle.
Every port is bidirectional, so that the battery can be charged and discharged using this
converter.
2.4 The Proposed Three-phase DAB Bidirectional DC-DC Converter
In this thesis, a three-phase DAB bidirectional dc-dc converter is proposed for high
power applications [21]. The topology integrates a three-phase boost converter with a threephase galvanically isolated bidirectional dc-dc converter. Keeping dc bus voltage constant allows
high efficient energy conversion over a wide input voltage and maintains ZVS conditions in the
whole operation range. By using compact small inductance dc inductors the ZVS conditions can
be improved in low power range and the switching losses of the lower switches are reduced. At
the same time the input current ripple can be alleviated by three-phase interleaved structure.
The three phase current-fed DAB converter can also be utilized in multiport application.
A three port integrated bidirectional dc-dc converter is proposed for PV system with battery
backup. The three-phase interleaved topology is suitable for higher power application, and all
three ports are capable of bidirectional power flow so battery can be charged from PV and the
grid as well.
13
CHAPTER THREE
3 THREE-PHASE TWO-PORT DUAL-ACTIVE-BRIDGE (DAB)
DC-DC CONVERTER
3.1 Introduction
With the requirements of lower greenhouse gases, sustainable development of economics,
and threat of exhaust of conventional energy source, etc, the application of renewable energy
sources becomes more and more popular in every field of our life. Generally, the energy of
renewable source is converted to the electricity power, however the utilization of renewable
source is constrained by its wide varied terminal voltage range and intermittent characteristics.
The new energy source or energy storage elements, such as PV have intermittent nature and
varied terminal voltage to realize the max power point tracking (MPPT). The phase-shift
controlled dc-dc converters have been reported in many literatures [1 - 6] as a good candidate to
interface with such sources.
Most of researches in the literatures focus on the voltage source DAB converters [7-18].
In the voltage source DAB converters, the DC-link voltage cannot be regulated by phase shift
control. Therefore, the converter will fail to satisfy the soft switching conditions when the ratio
of input to output voltage is not close to the transformer turns ratio [7]. Furthermore, the
mismatch between the primary side and secondary side DC-link voltages will result in large
RMS and peak current in both transformer and switches even in no load condition [8], thus high
efficiency is hard to achieve over wide input or output voltage ranges [18].
In order to improve performance in wide operating range, many optimized modulation
methods are proposed for voltage source DAB converters to maintain soft switching conditions
and reduce reactive power loss. In [19], phase shift plus duty cycle control is used to maintain
ZVS conditions, but the maximum phase shift is constrained and the power flow is therefore
limited. A novel dual-phase-shift control is proposed in [20] to eliminate reactive power and
increase system efficiency when input and output voltages do not match. In this case, the
converter control becomes complicated due to the output power being related to two phase shift
variables, and the circulating current still exists in this mode even though the reactive power is
eliminated totally. A hybrid modulation method is applied to extend power range for
14
ultracapacitor application in [21], in which a proposed triangular modulation and common phase
shift modulation are applied together to increase the power transfer range with wide input
voltage.
Current-fed topology provides another solution to improve performance for the wide
operating range. In [22], an isolated boost full-bridge DC-DC converter is addressed to fulfill the
requirements of wide voltage range, bidirectional power flow and high-efficiency. Another
current-fed dual-half-bridge (DHB) converter is proposed for fuel cell application [23], in which
the DC-link voltage of low voltage side can be controlled by adjusting the duty cycle. In these
two current-fed converters, auxiliary clamp circuit or comparable large DC inductors are
required to avoid voltage spikes and high input current ripples.
Although current-fed topologies have advantages to improve performance for the wide
operating range compared to the voltage-fed counterparts, a large dc inductor is usually required
to lower the input current ripple. In addition, the dc inductor current will affect and complicate
the soft switching condition analysis. In this chapter, a three-phase current-fed dual-active-bridge
(DAB) DC-DC converter with isolated Y-Y connected transformers is proposed to solve the
above issues. The major features of the proposed converter are as following: (1) Increased
converter power rating by paralleling phases; (2) Reduced size of input DC inductors and DClink capacitor with interleaving structure; (3) Maintained soft switching conditions and high
efficiency over a wide load range and wide input voltage range without auxiliary circuitry; and
(4) Easy-implemented power flow management because of decoupled duty cycle and phase shift
control.
In this chapter, the voltage-fed topology will be discussed firstly, and the operating
modes are presented in detail. The current-fed topology is similar to the voltage-fed type, but it
can handle with various input voltage. Since the duty cycle is a control variable to make the dclink voltage constant, the operating modes are more complex than those of voltage-fed type.
15
LVS
ii
Sa1
ia
C1
O
Ldc1
ib
Ldc2
ic
Ldc3
Sb1
a
Sc1
Sr1
isa
Ls1
b isb
ir
Ls2
c
Ls3
n
io
HVS
1 : N
m
Ss1
St1
Vo
O' C2 R
L
r
s
is
t
it
isc
Vin
Sa2
Sb2
Sr2
Sc2
Ss2
St2
Figure 3.1 Proposed three-phase current-fed dual-active-bridge bidirectional DC-DC converter
3.2 The Proposed Topology and Comparison
3.2.1 Topology Description
The topology of proposed converter is shown in Fig. 3.1, which consists of three DC
inductors and a three-phase DAB bidirectional DC-DC converter. A low voltage energy storage
element such as battery or ultracapacitor can be connected in the current-fed port and the high
voltage side can be connected to the high voltage DC bus to provide power to inverter for
specific applications. The converter can be operated in boost mode when the power flows from
low voltage side (LVS) to high voltage side (HVS) or in buck mode when the energy source
absorbs power from HVS. In the boost mode, the boost function is achieved by DC inductors and
three half bridges on LVS, to keep DC bus voltage constant so as to allow high efficiency
conversion for wide varied input voltage source. Comparatively, in buck mode, three small DC
inductors Ldc1 – Ldc3 are used as filters to smooth the charging current. In order to achieve soft
switching and reduce the turn-off switching loss, small snubber capacitors are paralleled with the
MOSFETs on LVS and HVS. Three single-phase high frequency transformers are connected in
Y-Y type to reduce circulating current and alleviate current unbalance issue. The leakage
inductance is implemented in each transformer as an energy transfer element.
Benefitting from interleaving structure, the three-phase current-fed DAB converter has
much smaller passive components comparing with the single-phase DHB converter. Similar to
16
van
ωt
vrm
φ
idc_a
0
π/3
ia
HVS
LVS
Dr1 on
Dr2 Sr2
on on
Da1 on
t1 t2 t3
Sa1
Sr1
gated gated
on
on
π
2π/3
5π/3
4π/3
Dr2 on
Sr1
on
t5 t6
Sa2 on
Da2
t7 t8
on
Sa2
Sc1
Sr2
St1
Sb1 Ss1
Sb2 Ss2
gated gated gated gated gated gated gated gated
on
on
on
on
on
on
on
on
Dr1 on
Sr2
on
Da1 on
Sa1 on
Sa1 on
t4
Sc2
St2
gated gated
on
on
ωt
2π
t9
Sa1 Sr1
gated gated
on
on
Sc2
gated
on
(a)
van
ωt
φ
vrm
idc_a
0
π/3
ia
HVS
LVS
Dr2 on
Sr2 on
Da1 on
t1
t2
π
2π/3
Dr1 on
Sa1 on
t3 t4
5π/3
Sr1 on
t5 t6
Da2
on
ωt
4π/3
2π
Dr2 on
Sr2 on
Sa2 on
t7
t8
Da1 on
t9
Ss1 Sc1 Sr2 Sb2 St1 Sa1 Ss2 Sc2 Sr1
Sa1 Ss2 Sc2 Sr1 Sb1 St2 Sa2
gated gated gatedgatedgated gated gated gated gatedgated gated gated gated gated gatedgated
on on on on
on
on
on on on
on
on
on
on on
on on
(b)
Figure 3.2 Voltage and current waveforms in transformer and DC input inductor:
(a) φ ≤ π/3; (b) π/3 < φ < 2π/3;
17
the three-phase DAB converter, the gate signals for upper and bottom switches on each
phase are complementary, with the phase angle 2π/3 between phase legs on one side. The power
flow is bidirectional by controlling the phase shift angle between the active switches on LVS and
HVS. Unlike the fixed duty cycle control in voltage source DAB converter, the duty cycle is
controllable to keep the DC-link voltage constant on LVS in wide input voltage range or to keep
the DC-link voltages on both sides to be matched. Due to the two control variables, duty cycle D
and phase shift angle φ, the operation will be more complicated than voltage source three-phase
DAB (DAB3) converter. Detailed analysis will be given in the following.
3.2.2 Operating Mode Analysis
3.2.2.1 50% Fixed duty cycle
Considering that the duty cycle is 50% fixed, the operation principle is similar to the
three-phase voltage source DAB converter. The power equation can be derived by the integration
of the instantaneous power p(t) over one switching period,
Po 
3
2

2
0
v an ( t )ia (t )dt
(3.1)
Where the van(ωt) is the voltage on the primary side of transformer and ia(ωt) is the primary side
transformer current. Fig. 3.2 shows the voltage and current waveforms on transformer in
different cases. Taking phase a in case a as an example, ignore the capacitor resonance during
the dead time zone which is discussed in [23], and the interval t1 to t9 of Fig. 2 (a) can illustrate
the stages of operation during one switching period. The situation of switches on LVS is
determined by the sum of dc inductor current idc_a and transformer current ia, and stage of
switches on HVS is just depended on the transformer current. The brief description of each stage
is given as follows.
Stage 1 t1-t2: At t1, Sa1 is gated on. ia is increasing but negative, so Dr2 is conducting. idc_a
is decreasing but higher than ia, thus Da1 is conducting in accordance of Kirchoff’s Current Law
(KCL).
Stage 2 t2-t3: At t2, ia increases to be positive and Sr2 begins to conduct. But it is lower
than idc_a, so Da1 continues conducting.
Stage 3 t3-t4: At t3, Sr1 is gated on. ia is positive and Dr1 is conducting. idc_a continues
decreasing but ia is still lower than idc_a, therefore Da1 is conducting.
18
Stage 4 t4-t5: At t4, idc_a decreases and is lower than ia, so Sa1 begins to conduct.
Stage 5 t5-t6: At t5, Sa2 is gated on. Since ia is higher than idc_a, Dr2 conducts first until t6
when idc_a surpasses ia.
Stage 6 t6-t7: At t6, Sa2 begins to conduct. ia is positive, so Dr1 continues conducting.
Stage 7 t7-t8: At t7, ia decreases to be negative and Sr1 begins to conduct.
Stage 8 t8-t9: At t8, Sr2 is gated on. ia is negative, so Dr2 is conducting. At t9, one
switching period is completed and the converter operation will repeat.
The stage of operation of case b can also be derived in the same way. The exact value of
van(ωt) can be expressed as,
V d
 3 ,0   t   / 3

 2V
v an ( t )   d ,  / 3   t  2 / 3
 3
V d
,2 / 3   t  

 3
(3.2)
There is a phase delay φ between van and vrm,
v rm (t )  v an (t   )
(3.3)
The voltage on the leakage inductance is the difference between van and vrm. For each
time interval, van and vrm are constants, so the current on leakage inductance can be calculated as,
ia (t )  ia (t 0 ) 
Van  Vrm
(t  t 0 )
Ls
(3.4)
Where ia(ωt0) is the initial current of corresponding time interval. ia(ωt) can be expressed by
ia(0) using iterative method. As D was given 1/2, the current waveform is symmetrical in one
switching period, i.e. ia(0) = - ia(π). Solve for ia(0),
  2Vd (1  d ) / 2  d 
, 0  /3

3L s

i a (0)  
  2Vd 3d (   / 2)    ,  / 3    2 / 3

9L s
(3.5)
Where d = Vo/N·Vd, and N is the transformer turns ratio.
According to (3.3) – (3.5), the current in each time interval can be obtained and the
power equation can be calculated as,
19
Po _ DAB 3
 dVd2 (4  3  )
,   /3

6 Ls

 2
2
 dVd (18   18     /  )
,  / 3    2 / 3

18 Ls

(3.6)
In order to minimize the peak current and RMS current, the voltages on LVS and HVS should be
matched, i.e. d = 1. The base power is defined as, 1p.u. = Vd2/ωLs, and the power equation could
be rewritten as,
 (4  3 )
,   / 3

6
Po _ DAB 3 ( p.u.)  
2
2
  18  18   ,  / 3    2 / 3

18
(3.7)
If the neutral points of transformer n and m are connected to the corresponding middle points (o
and o΄) of DC-link capacitors, the converter turns to be three interleaving single-phase DHB
(3DHB) converter [24] and the power equation will be,
Po _ 3 DHB ( p.u.) 
3 (   )
,0 
4
(3.8)
Fig. 3.3 shows the power curves of DAB3 and 3DHB converters. Under the same
conditions, 3DHB converter has higher output power than DAB3 before 60° phase shift angle.
The maximum output power of two converters are both at π/2,
Po _ max
7
 36   0.611 p.u. , DAB 3

 3   0.589 p.u. ,3DHB
16
(3.9)
On the other hand, the transformer size and reactive power loss are determined by
apparent power rating, which can be calculated by:
S  3Van _ rms  I a _ rms ,
(3.10)
Where the RMS value of current for different converter is,
I a _ rms
 V  2  
 d

 3 Ls


 V  2(4  3 )
  d

 6 Ls

 Vd  (3  2 )
  Ls
6
,0     / 3
DAB3
,  / 3    2 / 3
(3.11)
3DHB
20
Define the ratio of Po/S as power factor (PF) of the transformer, and PF on these 2 converters
can be derived as:
 (4  3 )

, 0 

3
 2 2 (2   )

3(18   2  18 2 )
2


 
,
PF  
2
2
3
3

3
3
 2 6 (9   81    54 )
 3(   )


 3 (3  2 )
1
(3.12)
,3DHB
0.66
0.9
0.6
0.8
0.48
0.7
0.36
0.6
0.24
0.5
0.4
0
0.12
DAB3
3DHB
20
40
60
φ/º
P/p.u.
Po
PF
Power Factor
, DAB3
80
100
0
120
Figure 3.3 Comparison of Power and power factor for DAB3 and 3DHB converters
21
1
DAB3
3DHB
0.9
0.9
Power Factor
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0
0.1
0.1
0.2
0.2
0.3
0.4
0.3
0.4
P/p.u.
0.5
0.5
0.6
0.6
Figure 3.4 Comparison of power and power factor for DAB3 and 3DHB converters
The power factor curves are also plotted in Fig. 3.3. As shown, the PF of 3DHB
decreases faster than DAB3 with the phase shift angle increasing. Furthermore, the curves of PF
versus output power are also plotted in Fig. 3.4. It shows that the power factor of DAB3
converter is always higher when generating the same real power, therefore less reactive power
loss and higher efficiency is expected in DAB3 converter.
22
3.2.2.2 Varied duty cycle
Another feature of current-fed DAB3 converter comes from its ability to interface with
voltage varied energy source. With the changes of the input voltage, duty cycle D is controlled to
keep the DC-link voltage constant. For different duty cycle D and phase shift angle φ, the
operating range can be divided into six areas, which are shown in Fig. 3.5. The corresponding
current waveforms in different operating areas are also given in Fig. 3.5, and according to
different current waveforms and voltage, the corresponding power equations can be derived. The
calculation process of power flow is similar to the fixed duty cycle, which is described in (3.13):
Po _ DAB 3
I
 K  (4 D   ) / 2 ,

2
2
 K  4 (3D  1) sgn( )  3 (9   4  12 D )  / 36 , II

III
 K  (4  3 ) / 6 ,

  
1 2

2
IV
 K   18( D  2 )    sgn( )  18 (    )  / 9 ,





 K  4 2 (2  3D) 2 sgn( )  3 (9   16  12 D )  / 36 , V



 K   (4(1  D)   )  / 2 ,
VI

 
(3.13)
Where K = Vd2/ωLs. The 3D power flow is plotted in Fig. 3.6, and the global maximum power is
still located at (1/2, π/2).
In the practical use, duty cycle D is limited in [1/3, 2/3] considering the efficiency of
converter and the variation range of input voltage, so that the DC-link voltage of LVS can keep
constant with 100% variation of input voltage, i.e. Vin ∈ [Vd/3, 2Vd/3], which includes area II, III,
IV and V. Therefore we focus on this operating range in this study. The power of current-fed
3DHB converter can be derived similarly,
3 (4 D  4 D 2   )
Po _ 3 DHB ( p.u.) 
,   2 / 3,1 / 3  D  2 / 3
4
23
(3.14)
φ
2π/3
isa
φ
isa
IV
Area I
2π
I
φ
V
II
VI
III
isa
φ
Area II
1/3
2π
1/2
D
Area IV
2π
φ
isa
2/3
Area V
2π
φ
isa
isa
-2π/3
φ
Area III
Area VI
2π
2π
Figure 3.5 Six operating areas with different (D, φ) and corresponding transformer current
waveforms
0.6
0.6
0.4
0.4
DAB3
Po/p.u.
0.2
0.2
00
-0.2
-0.2
-0.4
-0.4
-0.6
-0.6
120
90
120
φ/º
60
60
30
30
0 00
0.2
0.2
0.6
0.6
0.4
0.4
0.8
0.8
D
Figure 3.6 Power flow versus duty cycle D and phase shift angle φ
24
11
0.6
0.2
Po/p.u.
0.15
0.45
0.1
0.3
0.05
0.15
DAB3
3DHB
00
120
120
90
90
φ/º
60
60
30
30
0
0
0.35
0.35
0.4
0.4
0.45
0.45
0.5
0.5
0.55
0.55
0.6
0.6
0.65
0.65
D
Figure 3.7 Power flow of DAB3 and 3DHB converter with different (D, φ)
In Fig. 3.7, the power flow curves of DAB3 and 3DHB in 3D plot were drawn. The grey
and black areas are the power of 3DHB and DAB3 converter, respectively. As shown, the power
of 3DHB is higher than that of DAB3 converter with φ < 60˚, which has the same conclusion as
the case of 50% fixed duty cycle.
The reactive power on transformer and PF values of two converters can be calculated
piecewise. Fig. 3.8 shows the PF curves versus phase shift angle φ in different D. The PF
achieves the highest value at D = 1/2 which will decrease when D is moving away from 1/2.
Furthermore, the PF in DAB3 is always higher than 3DHB until D comes to 1/3 or 2/3, where
they are squared.
25
1
0.8
DAB3
3DHB
D=0.5
D=0.4,0.6
D=1/3,2/3
0.7
D=0.4,0
.6
0.9
Power Factor
D=0.5
0.6
D=1/
3,2/3
0.5
0.4
0.3
0.3
0
20
40
40
60
60
φ/º
80
80
100
120
120
Figure 3.8 PF of DAB3 and 3DHB converter with different (D, φ)
Fig. 3.9 also gives a comparison of PF between DAB3 and 3DHB -- the ratio of PFDAB3
to PF3DHB is always higher than 1. The analysis above indicates clearly that the reactive power
loss increases with the increasing of phase shift angle, and the reactive power loss in D = 1/2 is
the smallest value so that the power efficiency is the highest. Practically, the magnetic flux swing
and RMS current rating in transformer should be considered separately. For example, the power
density can be higher at D = 1/3 [25], as the maximum flux swing is smaller than D =1/2, which
means smaller core or winding turns are needed. Thus, in application level, different D is chosen
in voltage type converter based on different criteria.
26
1.12
1.12
1.1
1.1
PFDAB3/PF3DHB
PFDAB3/PF3DHB
1.08
1.08
1.06
1.06
1.04
1.04
1.02
1.02
11
120
120
90
90
60
60
φ/º
30
30
00
0.35
0.35
0.4
0.4
0.45
0.45
0.5
0.5
0.55
0.55
0.6
0.6
0.65
0.65
D
Figure 3.9 Comparison of PF of DAB3 and 3DHB converter with different (D, φ)
When the input voltage changes, current-fed DAB3 (CF-DAB3) converter has smaller
RMS current on the MOSFETs compared with the voltage type DAB3 converter. Define the base
input voltage Vin_DAB3(1p.u.) = Vo/N, Vin_CF-DAB3(1p.u.) = Vo/2N, and RMS current on MOSFETs
can be calculated and plotted in Fig. 3.10. As shown, when Vin = 1p.u., voltage source DAB3
converter has smaller RMS current value compared with CF-DAB3. But when Vin changes, the
RMS current on current-fed type will be lower than voltage type since it is able to maintain
“d=1” by controlling the duty cycle D. In summary, CF-DAB3 converter is a suitable topology
for renewable energy source applications.
27
CF-DAB3
DAB3
0.5
Vin=2/3p.u.
Irms2/p.u.
0.4
0.3
Vin=1p.u.
0.2
0.1
0
Vin=4/3p.u.
0
10
20
30
40
50
60
φ/º
Figure 3.10 RMS current curves on LVS MOSFETs
3.3 Analysis of ZVS Conditions
In section 3.2, we showed that the reactive power in DAB3 is lower than in 3DHB
converter, which also indicates the difficulty in maintaining soft switching conditions compared
to DHB converter, as DAB3 converter has less reactive current. However, the ZVS condition is
more critical in the current-fed type due to the effect of DC inductor current. This section will
focus on the analysis of the ZVS conditions for DAB3 under different duty cycle and also find
the relationship between the soft switching conditions and DC inductor.
3.3.1 ZVS Conditions for Voltage Source DAB3 Converter
In [8], the ZVS conditions are detailed analyzed at D =1/2. However, the ZVS conditions
will also vary when D changes. The ZVS conditions of voltage type DAB3 converter turn to be,
28
iLs (0)  0,
i (2 D )  0,
 Ls

iLs ( )  0,

iLs (2 D   )  0,
for LVS upper switches
for LVS lowerer switches
for HVS upper switches
(3.15)
for HVS lower switches
According to the calculation in Section 3.2, the current values can be obtained, as well as ZVS
conditions in different operating area. The ZVS conditions of each switch in operation area III
can be further simplified to,

d


d

d


d

2
,
2  3
2  3
,

2
2
,

2  3
2  3
,

2

for LVS upper switches
for HVS upper switches
, Area III
(3.16)
for LVS lower switches
for HVS lower switches
Similarly, ZVS conditions in other operation areas can also be described by d and φ. Fig.
3.11 plots the ZVS boundaries when D varies from 1/3 to 2/3. As shown, the ZVS boundaries
will vary with various duty cycles, but ZVS is very well maintained on all switches when the
DC-link voltages on LVS and HVS match each other. Therefore, d = 1 is the key point to keep
ZVS conditions and lower switching loss.
3.3.2 ZVS Conditions for Current-fed DAB3 Converter
For the current-fed topology, the ZVS conditions are complicated than voltage source
type, since the DC input current changes the current waveforms on the switches of LVS.
However, the transformer current is not affected by DC input current, thus the ZVS conditions
on HVS switches are the same as voltage source DAB3 converter. ZVS conditions in boost mode
and buck mode are symmetrical [23], so only boost mode is considered in this study.
Fig. 3.12 shows the circuits of one leg on LVS and HVS, as well as the denotation of
current in each branch. Write the ZVS conditions on LVS as,
ils (0)  idc (0)  0,

idc (2 D )  ils (2 D )  0,
for LVS upper switches
for LVS lower switches
29
(3.17)
D=1/3(2/3)
0.25
0.2
P/p.u.
Spu(Spl)
ZVS boundary
Hard-switching
Soft-switching
pl: primary lower switch
pu: primary upper switch
sl: secondary lower switch
su: secondary upper switch
Spl(Spu)
d=1.5
d=1
0.15
d=0.75
Ssl(Ssu)
0.1
0.05
0
Ssu(Ssl)
0
0.2
0.4
φ/rad
0.6
0.8
1
(a)
D=1/2
Spl
Spu
0.25
d=1.5
Po/p.u.
0.2
d=1
0.15
d=0.75
0.1
Ssu
Ssl
0.05
0
0
0.2
0.4
φ/rad
0.6
0.8
1
(b)
Figure 3.11 ZVS boundaries and power curves at different D: (a) D = 1/3, 2/3; (b) D = 1/2
30
LVS
HVS
Spu
idc
Ldc
C1
Vd
Sr1
ipu
is
Ls
ir
r
a
isl
ipl
Vin
isu
O'
C2
RL
Vo
Sr2
Spl
Figure 3.12 The middle points of one leg on LVS and HVS
2Dπ
2π
idc
ΔI
Idc_avg
ωt
0
φ
Figure 3.13 DC inductor current in one switching period
The DC input current is related to the input power and DC inductor, which is shown in
Fig. 3.13. Three operating areas (D  [1/3，2/3]，φ  [0，π/3]) are under consideration here. By
calculation, if d = 1, the ZVS conditions are always satisfied when d = 1, except in area III. The
ZVS conditions in Area III are described in (3.18),
31
P
 1 Vd
(1  D)Vin
 0,
 2  2d  3d   o _ III 

 Ldc
3Vin
 9  Ls

 Po _ III  1 Vd  2  2d  3d   (1  D)Vin  0,

 Ldc
 3Vin 9  Ls
for LVS upper switches
, Area III
(3.18)
for LVS lower switches
In (3.18), the upper switches on LVS can be soft switched, but the ZVS condition on lower
switches is related to the DC inductor. Define m = Ldc/Ls, and the in-equation in (3.18) can be
simplified to:
 (4  3 ) D(1  D) 

 0
18 D
m
3
(3.19)
Fig. 3.14 plots the ZVS region under different m, and it is clear that the soft switching region will
increase when m decreases. Small DC inductor will result in large input current ripple, but the
current ripples on each phase can be cancelled each other using interleaving strategy so the total
current ripple can be alleviated significantly [26].
2
Hard switching region
1.5
Soft switching region
Soft switching region
m=Ldc/Ls
1
ZVS boundaries
φ/rad
0.5
15
50
0
m=∞
100
100
15 50
-0.5
-1
-1.5
Soft switching region
-2
0
0.1
0.2
0.3
0.4
0.5
D
0.6
0.7
Figure 3.14 ZVS boundaries under different m
32
0.8
0.9
1
3.4 Analysis of Unbalance Issue
Comparing to the single phase converters, multiphase converters have many advantages,
but phase current unbalance is an important issue that should be solved. It is necessary to find the
reason of unbalance current and solution to alleviate the impact.
3.4.1 Analysis of Current Unbalance
According to the power equation, since the phase current is inversely proportional to the
leakage inductance, the unbalanced leakage inductance will lead to unbalanced phase current. In
[27], the relationship between phase current unbalance ratio (ΔIφ%) and leakage inductance
unbalance ratio (ΔLs%) was analyzed. Different transformer connection type has different impact
on phase current. There are several sub types in DAB3 converter according to different
transformer connection. Y-Y connection and Δ-Δ connection model can be transferred each
other, which are shown in Fig. 3.15, so they have the same operation modes. Due to the features
of phase shift method, the voltage waveforms on both sides of the transformer should have the
same shape to avoid high reactive current, thus Δ-Y (or Y-Δ) connection type is not
recommended. Fig. 3.16 shows the different transformer connection type of DAB3 and 3DHB
converters. In Fig. 3.16, two different Δ-Δ types are distinguished by the position of leakage
inductance. For Δ-Δ type DAB3 converter, the unbalanced leakage inductance will result in
unbalanced transformer current, as well as unbalanced phase current.
a
a
ia
ia
iab
Ls
L sca
ab
Lsa
Lsb
Lsc
ica
ib
b
ib
ic
b
c
ibc
Lsbc
Figure 3.15 Transformation between Y-model to Δ-model
33
ic
c
Take Fig. 3.16 (c) as an example, and define Kxy(xy=ab,bc,ca) as the coefficient to describe how
far away the leakage inductance of each transformer is from the normal value Lφ0, then,
Lxy  K xy L 0  (1  K xy ) L 0 , xy  ab, bc or ca
(3.20)
Where ΔKab+ ΔKbc+ ΔKca=0.
The fundamental model [8, 28] is applied in this study, and the current and voltage
phasors are shown in Fig. 3.17. The phase voltage on HVS lags corresponding phase voltage on
LVS φ0. The transformer current iab is calculated as,



V0

Vab
Vab
(1  K ab ) 


I ab 
2
jLab
jL 0 K ab L 0
(3.21)
Where |ΔV0|=Vdφ0sin(Dπ)/π. So the amplitude of iab is,

V0
(1  K ab )  (1  K ab ) I 0
I ab 
L 0
(3.22)
The phase current ia can be obtained by,



I a  I ab  I ca 


V0
Vab
Vca


jL 0 K ab jL 0 K ca L 0
2
2

K ab
 K ca
 K ab K ca

(Vab  )
K ab K ca
3
(3.23)
By simplifying (3.23), we can get,

Ia  I0
K bc
1
)I 0
 (1 
1  (K ab  K ca ) / 2
2
34
(3.24)
Lsa
a
a
r
Lsa
r
Lsb
b
m
s
n
t
Lsc
c
t
L
L sb
sc
s
c
b
(a)
(b)
c
Lsc
c
t
L sb
t
Ls
ca
c
a
r
s
s
r
b
Lsab
a
(c)
Lsa
Lsb
b
(d)
Figure 3.16 Four Transformer connection types DC-DC converter
(a) Y-Y DAB3; (b) 3DHB; (c) Δ-Δ DAB3 with integrated Ls; (d) Δ-Δ DAB3 with external Ls;
35
Vbc
V fst
I bc
V fbc
b
a
V fab
I ab
c
Vab

V frs
V ftr
I ca
Vca
V fca
Figure 3.17 Phasor diagram of phase voltage and current
From (3.22) and (3.24), it can be seen that the transformer current unbalance ratio is the
same as that of leakage inductance, i.e. Δiab ~ -ΔKab, and the phase current unbalance ratio is just
half of it, i.e. Δia ~ ΔKbc/2. Using the same method, the relationship of current unbalance ratio
and leakage inductance for other types of converters can be found and listed in Table 3.1.
In table 3.1, “A” and “D” have the same performance that ΔI/I0 is halved comparing with
ΔI/I0, so they have inherent current sharing capability. The ΔI/I0 in topology “B” is equal to ΔK
of its own phase. In “C” the ΔI/I0 of phase current and that of transformer current are not
consistence, which also implies that phase current and transformer current cannot be controlled
to balance at the same time. In part B, the current sharing control analysis will be given in detail.
36
Table 3.1 ΔI/Iavg resulting from unbalanced leakage inductance
Index
Connection type
A
Y-Y connection
Phase current
Transformer current
ΔIa/I0 = -ΔKa/2
ΔIb/I0= -ΔKb/2
ΔIc/I0= -ΔKc/2
B
ΔIa/I0 = -ΔKa
3DHB
ΔIb/I0= -ΔKb
ΔIc/I0= -ΔKc
C
D
Δ-Δ connection with
ΔIa/I0= ΔKbc/2
ΔIab/Iφ0= -ΔKab
integrated Ls
ΔIb/I0= ΔKca/2
ΔIbc/Iφ0= -ΔKbc
ΔIc/I0= ΔKab/2
ΔIca/Iφ0= -ΔKca
Δ-Δ connection with
ΔIa/I0= -ΔKb/2
ΔIab/Iφ0= -ΔKc/2
external Ls
ΔIb/I0= -ΔKc/2
ΔIbc/Iφ0= -ΔKa/2
ΔIc/I0= -ΔKa/2
ΔIca/Iφ0= -ΔKb/2
*: the subscript of K depends on the position of the Ls
3.4.2 Current Sharing Control
Though topology “A” and “D” have inherent current sharing capability, the phase current
are still asymmetrical when leakage inductances are not equivalent. The current sharing
controller should be developed to make the current balance. We still use topology “C” as the
objective, but transfer Δ-model to Y-model for simplicity. Define phase shift angles on each
phase,
 a   a 0

b   b 0
   
c 0
 c
(3.25)
Where σx(x=a,b or c)=1+Δσx is the coefficient to describe how far away the phase shift angle of each
phase is from the normal value φ0 and Δσa+ Δσb+ Δσc=0.
The phase current ia can be expressed as,
37




V0 (1   a )


Van
(1   a )
Ia 

(Van  )  I 0
(Van  )
jLsa L0 (1  K a )
2
(1  K a )
2
(3.26)
In order to let |Ia| equal to the average value |I0|,
1   a
1
1  K a
(3.27)
 x  K x , x  a, b or c
(3.28)
So we have,
Consider the transformer current Iab in Δ-model.
 c

(1 
)



V 0 (1   ab )


Vab
2
(Vab  )  I 0
(Vab  )
I ab 

jLsab  3L0 (1  K c )
(1  K c )
2
2
(3.29)
To make the transformer current iab balance, the regulation of phase shift angle is,
 c
)
2 1
(1  K c )
(1 
(3.30)
So for three-phase system, the regulation of phase shift angle is,
 x  2K x ,
x  a, b or c
(3.31)
The equations (3.28) and (3.31) cannot be satisfied at the same time, so for topology “C” there is
no current sharing controller which can make the phase current and transformer current to be
balanced. Using the same method, the regulation of phase shift angle in other topology can be
calculated and listed in Table 3.2. In Table 3.2, only topology “C” cannot realized current
sharing control, so Δ-Δ type should be avoided if using integrated leakage inductance as the main
power transfer element.
Based on the relationship between phase shift angle and unbalanced current ratio, the
ratio of each phase shift angle σx can be set and applied to phase shift controller. Fig. 3.18 shows
the flow chart of ratio presetting current sharing control, where Ni is the times of tuning (1 ~ ∞).
Using this method, the ratio of phase shift angle can be tuned faster than a PI controller.
38
Table 3.2 The relationship between regulation of φ and ΔI/Iavg
Index
Connection type
A
Y-Y connection
ΔIa/I0 = Δσa/2; ΔIb/I0= Δσb/2; ΔIc/I0= Δσc/2
B
3DHB
ΔIa/I0 = Δσa; ΔIb/I0= Δσb; ΔIc/I0= Δσc
C
Δ-Δ connection with integrated Ls
D
Phase current
Transformer current
ΔIa/I0= Δσa/2
ΔIab/Iφ0= Δσc
ΔIb/I0= Δσb/2
ΔIbc/Iφ0= Δσa
ΔIc/I0= Δσc/2
ΔIca/Iφ0= Δσb
Δ-Δ connection with
ΔIa/I0= Δσa/2
ΔIab/Iφ0= Δσc/2
external Ls
ΔIb/I0= Δσb/2
ΔIbc/Iφ0= Δσa/2
ΔIc/I0= Δσc/2
ΔIca/Iφ0= Δσb/2
The simulation in Psim is to verify the analysis. In the simulation, the leakage
inductances were selected as: Lsa = 520nH, Lsb =444nH, Lsc =370nH, which demonstrated 17%
inductance unbalance. Fig. 3.19 and Fig. 3.20 show the simulation results for split capacitor and
Y-Y type converters when output power is 4kW and input voltage is 24V. For split capacitor
type converter, without current sharing control, the phase shift angle is 0.043π and the phase
current are Isa = 34.9A, Isb = 40.9A and Isc = 49.1A, respectively, which are shown in Fig. 3.19
(a) and have 16% unbalance ratio. With current sharing control, the phase shift angles are
different and the phase current are balanced with the value 41.6A. With current sharing control,
square of RMS current value decreases from 5302 A2 to 5217 A2, so it will help to decrease the
conducting loss and improve the efficiency. For Y-Y type converter, without current sharing
control, as shown in Fig. 3.20(a), the phase shift angle is 0.043π and Isa = 37.7A, Isb = 41.2A and
Isc = 44.2A, which have only 8.7% difference. With current sharing control, the phase current is
balanced and Isa = Isb = Isc = 41.0A. The square of RMS current value decreases from 5115 A2 to
5018 A2. Comparing Y-Y type with split capacitor type, former has smaller RMS current and
higher efficiency.
39
Start
Calculate Iaverage
Calculate ΔIa%, ΔIb%, ΔIc%
Ir
Is
It
Update Ir, Is, It
σa=σa(1-2ΔIa%),
σb=σb(1-2ΔIb%),
σc=σc(1-2ΔIc%),
Save σa, σb, σc
φa=σaφ0,
φb=σbφ0,
φc=σcφ0,
N
n=Ni?
Y
End
Figure 3.18 Flow chart of ratio presetting current sharing control
40
ir / A
 /103 
80
60
40
20
0
-20
-40
-60
I sc=49.1A
I sb=40.9A
Isa =34.9A
43.75
43.70
43.65
43.60
43.55
43.50
43.45
φ=0.0436π
0
12
6
18
24
30
t/µs
(a)
ir / A
80
60
40
20
0
-20
-40
Isc=44.2A
Isb=41.24A
Isa=37.68A
 /103 
43.56
43.55
φ=0.0436π
43.54
0
5
10
15
20
25
30
t/µs
(b)
40
ir / A
20
Isc=27.8A
Isa=19.8A
Isb=23.2A
Ic=44.6A
Ia=39.8A
Ib=38.2A
0
-20
-40
ir / A
80
60
40
20
0
-20
-40
t/µs
(c)
Figure 3.19 Phase current and transformer current waveforms without unbalance controller:
(a) Split-cap type; (b) Y-Y type; (c) Δ- Δ type
41
ir / A
 /103 
80
60
40
20
0
-20
-40
55
50
Isb=41.6A
φa=0.052π
45
φb=0.045π
40
35
Isa=41.6A
Isc=41.6A
0
5
φc=0.037π
10
15
20
25
t/µs
 /103 
ir / A
(a)
80
60
40
20
0
-20
-40
55
50
φa=0.0514π
45
φc=0.0369π
φb=0.0444π
40
35
Isa=41.0A
Isc=40.9A
Isb=41.0A
0
5
10
15
20
25
30
t/µs
(b)
il / A
ir / A
40
20
Isc=25.6A
0
Isb=23.7A
Isa=21.7A
-20
-40
80
60
40
20
0
-20
-40
0
Ic=40.9A
5
Ib=40.9A
Ia=40.9A
10
15
20
25
30
t/µs
(c)
Figure 3.20 Phase current and transformer current waveforms with unbalance controller:
(a) Split-cap type; (b) Y-Y type; (c) Δ- Δ type
42
3.5 Converter Design Guideline
3.5.1 Transformer Design
A 6kW converter is designed with varied low input voltage (24V - 48V) and rated high
output voltage 288V. The DC-link voltage on LVS Vd = Vin/D is keeping constant, therefore the
transformer turns ratio is determined by N = Vo/Vd = DVo/Vin = 4. The leakage inductance is
integrated into the transformer. Comparing to traditional transformers, PCB planar transformers
provide better consistency and flexibility. Each transformer consists of 2 E64-3C92 planar cores
with separate primary and secondary PCBs. The primary and secondary windings have 4 turns
and 16 turns respectively. Each turn on LVS and HVS is made up of two paralleled 4 oz copper
windings, therefore satisfying the requirement of current density and helping to reduce AC
resistance. Though the interleaving transformer windings structure can reduce the AC resistance
significantly, it is very hard to provide enough leakage inductance as energy transfer element
thus additional leakage inductance is needed. By using two separate PCB windings as primary
and secondary winding, the desired leakage inductance can be controlled by adjusting the
distance between the two PCBs. The single-phase transformer prototype is shown in Fig. 3.21.
The primary and secondary PCBs are separated by a thickness hΔ and the leakage inductance for
the non-interleaved structure is given in (3.32) [29]:
Ls  0 N 2
lw  h1  h2

 h 

bw  3

(3.32)
Where μ0 is the permeability of air (H/m), N is turns ratio, lw is the mean length of traces (m),
and bw is the width of primary trace (m). h1 and h2 are the thickness of primary and secondary
side, and hΔ is the distance between them. Table 3.3 gives the designed and measured leakage
inductance of each transformer.
43
Insulation Layer
h2
Secondary Side
PCB
hΔ
h1
Primary Side
PCB
Primary Side Copper Layer
Secondary Side Copper Layer
Insulation Layer
Figure 3.21 The sectional view of transformer
Table 3.3 Leakage inductance of each phase (refer to LVS)
Leakage inductance
Designed Ls
510nH
Measured Lsa
511.8nH
Measured Lsb
517.5nH
Measured Lsc
505nH
44
3.5.2 DC Inductor Design
The main goals of DC inductor design are to maintain the ZVS and achieve small size.
The DC inductance should meet the in-equation (3.21), i.e. Ldc < 11Ls. In the experiment, the
DC inductor is designed as Ldc = 12Ls = 6μH, so the phase current ripple Idc is as large as 2Idc at
rated power, and at the same time ZVS can be guaranteed in a majority of operation area. For
three-phase interleaving structure, the total input current ripple is given as,
I tot _ ripple 
3Vd ( D  1/ 3)( D  2 / 3)
f s Ldc
(3.33)
20
18
16
Itot_ripple/A
14
12
10
8
6
4
2
0
0.35
0.4
0.45
0.5
0.55
0.6
D
Figure 3.22 Input current ripple versus duty cycle
45
0.65
Fig. 3.22 shows the total input current ripple will reach zero at D = 1/3 and 2/3 but
maximum value is 20A at D = 1/2.
3.5.3 Power Loss Analysis
The power loss of converter is the key factor for components selection and design. For
DC-DC converters, the losses are mainly caused by switching loss and conduction loss. For the
switching loss, the converter is operating in ZVS situation, so there is no turn-on loss, only turnoff loss is considered, which can be approximately calculated by [30],
Psw _ off 
2 2
I off
t f fs
(3.34)
24C
Where Ioff is the turn off current, tf is the falling time of MOSFET, and C is the snubber
capacitance. Larger snubber capacitance will get smaller turn-off loss, but it will cause turn-on
loss especially at light load since there is not enough current to release the energy stored in the
snubber capacitors and the ZVS condition will be unsatisfied. So choosing proper snubber
capacitor is important. In the experiment, 0.2µF and 0.03 µF capacitors are selected as snubber
capacitors on LVS and HVS MOSFETs, respectively.
The conduction losses include the losses in DC inductor windings, MOSFETs and
transformer windings. The current ripple IΔ on DC inductor is not related to the output power,
which can be written as,
I 
Vd D(1  D)
Ldc f s
(3.35)
And the AC flux density of inductor can be calculated by,
BAC 
Ldc  I 
Ac N L
(3.36)
Where Ac is the sectional area of magnetic core, and NL is the turns number. BAC always exists
even at no load thus AC core loss dominating the major power loss at the light load. When there
is power drawn from the energy source, the RMS current value on each inductor is derived by,
I Ldc _ rms
1

2

2
0
2

Po
1 
 I   dx
i ( )d 
 I x 

0
3Vin 2 
 
2
Ldc
1
1
46
(3.37)
Where Po is the output power and η is the efficiency. In order to find the transformer conduction
loss, the transformer RMS current value can also be calculated as,
I Ls _ rms
 Vd

1 2 2
 3 Ls




(
)
i
t
d
t

Ls
2 0
 Vd
 6 L
s

2  

,
2(4  3 )

D  1/ 2
(3.38)
, D  1/ 3, 2 / 3
From equations (3.36) to (3.38), the DC inductor core loss can be obtained by the
following empirical formula,
PLdc _ core  VeCm f x B y AC
(3.39)
where Ve is effective core volume of transformer, Cm, x, and y are coefficient related to core
material. The DC inductor conduction loss is,
PLdc _ con  I 2 Ldc _ rms RLdc
(3.40)
The transformer core loss has the same form as equation (3.39), and the conduction loss can be
written by
PTx _ con  I 2 Ls _ rms  Rdc  Rac 
(3.41)
The total conduction loss of MOSFETs on HVS can be calculated as,
PHVS _ con  6( I 2 Ls _ rms Rds _ on / 2)  3I 2 Ls _ rms Rds _ on
(3.42)
Where Rds_on is the turn on resistance of MOSFET.
The conduction loss on one MOSFET of LVS is different from that of HVS since the dc
inductor current will affect the current waveform in MOSFET. What’s more, the current flowing
through the upper switches and lower switches are asymmetrical, the RMS values of current in
different D can be calculated as follow,
47
I upper _ rms
 Vd
972 2 2  16524 3  19683 4  4 4
, D  1/ 3


L
324
s

 Vd

2(320 2 2  864 3  576 4  3 4 )
, D  1/ 2
144 Ls
 Vd
2(1944 2 2  34020 3  19683 4  16 4 ) , D  2 / 3

 648 Ls
I lower _ rms
(3.43)
 Vd
17253 2 2  35235 3  19683 4  648 3  14 4
, D  1/ 3

162

L
s

 Vd
6(1472 2 2  1760 3  576 4   4 )
, D  1/ 2

144

L
s

 Vd
144828 2 2  246888 3  98415 4  2592 3  98415 4 , D  2 / 3

 648 Ls
(3.44)
So the conduction loss of MOSFET on LVS can be expressed as,
PLVS _ con  3( I 2upper _ rms  I 2lower _ rms ) Rds _ on
(3.45)
For the transformer design, using 2 paralleled 4oz PCB windings to replace 8oz PCB
winding, the AC resistance of transformer winding Rac is reduced from 2.9Rdc to 0.79 Rdc [31].
Define the ratio of total copper loss to DC copper loss FR= Ptot_loss/Pdc_loss, and the ratio of the
conductor thickness h to the skin depth δ, i.e. ξ=h/δ. Fig. 3.23 shows FR versus ξ in different
number of layers. It is clear that the total copper loss is reduced from 3.914Pdc_loss to
1.789Pdc_loss. In Fig. 3.23, when the number of copper layers M increases to 12, the total copper
loss just decreases by 0.43Pdc_loss, but more counts of copper layers will increase the cost.
48
M=12
2
10
FR 
M=8
M=4
Ptot _ loss 101
Pdc _ loss
X: 0.875
Y: 3.914
X: 0.295
Y: 1.362
0
10 -1
10
X: 0.44
Y: 1.789
0
10

1
10
h

Figure 3.23 Total winding copper loss ratio versus ξ and number of layers M
Fig. 3.24 gives the power loss distribution in different power rating at different duty
cycle. It can be seen that the DC inductors’ loss always exists because of the ripple current and it
is dominant at the light load, and the conduction loss and switching loss will be dominant at the
heavy load. Fig. 3.25 shows the total power loss curve in different duty cycle. Lower power loss
in D = 1/2 can be obtained due to the smaller transformer and switches’ current, which is also
consistent with the analysis in section II.
49
600
600
Tx Cor
D=1/3
Switch
D=1/2
Conduction Lo
D=2/3
Ldc Loss
Capacitor Loss
Capac
Tx Core
Loss
Tx Core
Loss
Switching Loss
Switching Loss
Conduction Loss
Conduction Loss
Ldc Loss
Ldc Loss
Capacitor
Loss
500
500
Ploss/W
400
400
300
300
200
200
100
100
00
0
1000
2000
Po/W
4000
6000
Figure 3.24 Ploss distribution in different output power in different D
600
500
D=1/3
D=1/2
Ploss/W
400
D=2/3
300
200
100
0
0
1000
2000
3000
4000
5000
Po/W
Figure 3.25 Total Ploss curves in different D
50
6000
3.6 Control Strategies for Current-fed Topology
3.6.1 Small Signal Modeling
In order to investigate the steady and dynamic performance of the converter, the average
model of the converter is developed to analyze its steady state and dynamic performance.
Because of the symmetric property of three-phase dc-dc converter, the multiphase converter can
be treated as a single phase converter and the operation principles of boost mode and buck mode
are similar. The state variables are the dc inductor current iLdc, the primary side dc-link voltage
vd, and the output voltage vo. The state equation is given as,
 di Ldc
 Ldc dt  vin  Dvd

 dvd
 DiLdc  io1
Cd
dt

vo
 dvo
Co dt   R  io1
L

(3.46)
Since the power of each phase is:
Vd2 (4  3 )
Po 
, when d  1.
18Ls
(3.47)
the average value of io1 referred to the primary side is,
io1 
Po Vd  (4  3  )

Vd
18 Ls
(3.48)
The equivalent circuit of average model is presented in Fig. 3.26.
Ldc
gvo
D:1
+
vin
Cd
-
+
vd
-
gvd
Co
g=φ(4π-3|φ|)/18πωLs
Figure 3.26 Equivalent circuit of average model
51
+
vo
-
RL
To obtain a linear small signal model, add perturbation around the operating point, and
the small signal equation can be calculated after remove DC part and higher order nonlinear
terms. In terms of (3.46), the small signal model could be developed as follows:

diˆ Ldc
 vˆ in  Dvˆ d  V d Dˆ
 L dc
dt


 (4  3  )
Vo (4  6  )
dvˆ d
ˆ
vˆ d 
 DiˆLdc  I Ldc Dˆ 
C d
18 Ls
18 Ls
dt

 dvˆ o
 (4  3  )
V d (4  6  )
vˆ
ˆ
vˆ d 
 o 
C o
18 Ls
dt
RL
18 Ls

(3.49)
Based on (3.49), the equivalent small circuit model is developed in Fig. 3.27.
Ldc
+
^vin
^
VdD
+ -
D:1
^
ILdcD m1φ^
Cd
^
g1vo
^
g2vd m2φ^
+
^vd
-
-
^
vo
Co
+
RL
-
Figure 3.27 Equivalent small signal circuit model
In Fig. 3.27, g1=g2=(4π-3|φ|)φ/18πωLs, m1=(4π-6|φ|)Vo’/18πωLs, and m2=(4π6|φ|)Vd/18πωLs. Vo’ is the dc-link voltage on HVS referred to the LVS, and RL is an equivalent
load resistance of the output port, RL = Vo’2/Po.= .18 πωLs /(4π-3|φ|)φ. The equation (3.44) can
be written as space state equations in (3.50):
dXˆ
 A  Xˆ  B Uˆ , Yˆ  C  Xˆ
dt
(3.50)
Where,

 0
iˆLdc 

 D
 
ˆ
X   vˆd  , A  
Cd
 vˆo 

 
 0

D
Ldc
Vo (4  3  )


C d 18L s
 (4  3  )
C o 18L s
52




0


1 


Co  RL 
0
vˆin 
ˆ
U   Dˆ  ,
 ̂ 
 1

 Ldc

B 0

 0



Vd
Ldc
I Ldc
Cd
0



Vo (4  6  ) 

Cd 18 Ls 

Vd (4  6  ) 
Cd 18 Ls 
0
The output Yˆ can be obtained as:
vo (s)  C1 (sI  A)1 BU (s) , C1  [0 0 1]
(3.51)
According to (3.51), the control-to-output transfer function can be derived as:
Gv ( s)  mR L
In (3.52), the term
s / 0 2  2s / 0  1

s
1 
 1 / C o RL

s2
1  2
 D / C d Ldc

s
 2 2
 D /g L R
dc L

(3.52)
s
is very small, so it can be ignored, and the transfer function
D / g 2 Ldc RL
2
becomes:
Gv ( s)  mR L
s / 0 2  2s / 0  1

s
1 
 1 / C o RL

s2
1  2
 D / C d Ldc




(3.53)
There are a pair of conjugated right half plane zeros, so the stability criterion is Фm = -2×180°
+180°+∠Gvφ(j2πfc) > 0, where fc is the crossover frequency. The parameters of the system are
listed below:
Vin = 24~48V, D = 1/3~2/3, φ = 8π/180, Vd = Vo’ = 72V, fs = 40kHz, Ldc = 7.5uH, Ls = 510nH,
Cd = 5600μF, Co = 3120uF, RL = Vd φ (4 π-3 φ)/(18 π ω Ls).
In transfer function Gvφ(s), The zeros and poles are located at: z1,2 = 0.0128 ± j1625.5,
and the poles are located at: p1,2 = -0.01253 ± j1627.5, and p3=-19.02. Because the two poles and
two zero are very close and far away from origin and the main pole is p3, the magnitude curve of
transfer function is just like an integral but the phase angle has –(360+90)° delay at ω=∞. The
open loop bode plot of control to output transfer function Gvφ(s) is shown in Fig. 3.28. The
crossover frequency is fc = 5.94 kHz, and Фm = -270.4° < 0.
53
Gvφ(s) Bode Diagram
Magnitude (dB)
150
D=1/3
D=1/2
D=2/3
100
50
0
-50
360
Phase (deg)
270
180
90
0
-90
-1
10
0
10
1
2
10
10
3
10
4
10
Frequency (Hz)
Figure 3.28 Bode plots of control to output
Considering the change of input voltage Vin, the duty cycle is regulated to maintain the
LVS dc-link voltage Vd constant. The transfer function of duty cycle to dc-link voltage can be
developed by:
vd (s)  C2 (sI  A) 1 BU (s) , C2  [0 1 0]
(3.54)
The transfer function Gvd_d(s) is:

s 

LdcVd g / D 3  1 s1 
1
/
C
R
o L 

Gvd _ d ( s) 


s 
s2

1  2
1 
 1 / Co RL  D / Cd Ldc 


54
(3.55)
3.6.2 Control system design
In order to keep the output voltage constant, an output voltage controller is designed to
make the system stable. The compensator Gvc(s) consists of a PI and a lag compensator, which is,
5(1  0.00083 s)(1  0.0073s)
s(1  0.003s)
Gvc ( s) 
(3.56)
After the compensation, Фm becomes 45.2°, but the bandwidth decreases to 110Hz.This is
because that the crossover frequency of the open-loop gain is severely restricted by the right
half-place zeros. If higher closed-loop performance is necessary, the multiloop control scheme
can be considered.
Gvφ(s)Gc(s)
Magnitude (dB)
100
Bode Diagram
D=1/3
D=1/2
D=2/3
50
0
fc=110Hz
-50
-100
270
Φm=45.2º
Phase (deg)
180
90
0
-90
-180
0
10
1
10
2
10
3
10
Frequency (Hz)
Figure 3.29 Bode plots of voltage loop gain with compensator
55
4
10
3.7 Experimental Results
A 6kW experimental prototype is built in the lab, and the specification and parameters of
converter are listed in Table IV. The input voltage varies from 24V to 48V, and output voltage is
288V. Fig. 3.30 shows a photo of 6-kW prototype with a liquid-cooled heat sink. The size of this
converter is 13.7″ by 7.8″. The DC inductors and transformers are implemented with PCBs and 6
E64-3C92 planar cores. Fig. 3.31 is the control diagram including current sharing controller. The
duty cycle D is just controlled to keep LVS DC-link voltage constant, and phase shift angle is
used to control the output voltage. The duty cycle D and phase shift angle is used to control the
output voltage.
Table 3.4 Specifications and parameters of converter
Input voltage Vin (V)
24~48
Output voltage Vo (V)
288
Rated power Po (W)
6000
Switching frequency fs (kHz)
40
LVS MOSFETs
SK 260MB10
LVS Snubber
0.2 µF
HVS MOSFETs
ST W45NM50FD
HVS Snubber
30 nF
LVS Capacitor
5600µF + 10 µF*25 (MLCC)
HVS Capacitor
390 µF + 10 µF*5 (Film)
HF Transformer
E64-3C92*6
DC Inductor
E64-3C92*6
56
GND
+Vin
Low Voltage
Side
High Voltage
Side
DC inductor
Transformer
Figure 3.30 Photo of 6kW experimental prototype
+
+
-
-
PI
PI
÷
×
Tper1
φa
φb
Fig. 3.18
φc
φ0
+
Sa1
D
Tper2 φbS
s1 φb
D
+
Sb1
Tper3
Sc1
D0
φa Sr1 φa
D
φc St1 φc
Sa1 ia,b,c Vo
Sa1
Sb1
Sb2
Sc1 3-phase
Sc2
Sr1 DC-DC
Sr2 converter
Ss1
Ss2
St1
St2 Vd Vin
D
PWM generator
Figure 3.31 System control system including current sharing controller
57
Fig. 3.32 shows the transformer current with different duty cycle. The current become 2
level waveforms in D = 1/3, 2/3, which are the same as 3DHB converter. Fig. 3.33 shows the DC
inductor current and total input current with D = 1/3, 1/2 and 2/3, respectively. The large DC
inductor current ripple of each phase is benefit for device ZVS operation and lower inductor
volume size but a total small current ripple can be achieved by interleaving three-phase current.
It can be seen that when D = 1/3 and 2/3, the input current ripple is minimum, and when D = 1/2,
the current ripple reaches maximum value. As shown in Fig. 3.34, the ZVS is always guaranteed
in the switches of LVS in the light load under varied input voltage. Fig. 3.35 shows that when the
input voltage changes from 24V to 48V, duty cycle is changed with the input voltage Vin and
satisfies D = Vd/Vin. The measured efficiency from 450W to 4.5kW with different input voltage is
shown in Fig. 3.32. The efficiencies in different input voltage keep stable, and the highest
efficiency is 96.4% at Vin = 36V and Po = 2.3kW.
58
Idc_total(20A/div)
Idc_a Idc_b Idc_c (10A/div)
(a)
Idc_a Idc_b Idc_c (10A/div)
Idc_total(20A/div)
(b)
Idc_a Idc_b Idc_c (10A/div)
Idc_total(20A/div)
(c)
Figure 3.32 Three-phase inductor current and total input current:
(a) Idc at D = 1/3, (b) Idc at D = 1/2, (c) Idc at D = 2/3
59
Isa, 3.8A/div
Isb, 3.8A/div
Isc, 3.8A/div
(a)
Isa, 3.8A/div
Isb, 3.8A/div
Isc, 3.8A/div
(b)
Isa, 3.8A/div
Isb, 3.8A/div
Isc, 3.8A/div
(c)
Figure 3.33 Transformer current on secondary side with different D
(a) D = 1/3; (b) D = 1/2; (c) D = 2/3
60
Vds_a1
20V/div
Vgs_a1
10V/div
Vds_a2
20V/div
Vgs_a2
10V/div
Vds_a2
20V/div
Vgs_a2
10V/div
(a)
Vds_a1
20V/div
Vgs_a1
10V/div
(b)
Vds_a1
20V/div
Vgs_a1
10V/div
Vds_a2
20V/div
Vgs_a2
10V/div
(c)
Figure 3.34 ZVS waveforms for Sa1 and Sa2 at Po=1200W in (a) Vin=24V; (b) Vin=36V;
61
(c)Vin=48V
288V
Vo 50V/div
72V
48V
Vd 20V/div
24V
Vin 10V/div
7.65A
Io 5A/div
η/%
Figure 3.35 Voltage and current waveforms when Vin varies between 24V and 48V
Po/W
Figure 3.36 Measured efficiency of proposed converter at Vin = 24V, 36V and 48V
3.8 Summary
This chapter proposes a three-phase current-fed bidirectional isolated DC-DC converter
to achieve high efficiency over a wide input voltage range. By using proposed technology, the
reactive power loss is always maintained to be low and ZVS conditions can be maintained when
62
input voltage changes, so high efficiency can be guaranteed over a wide operation range.
Another feature of the proposed topology is to allow the small passive components while the
current and voltage ripples can still keep small due to three- phase interleaving structure. The
maximum input current ripple is no more than 20% of total input current. With respected to the
leakage inductance unbalance ratio, the proposed topology with Y-Y connected transformers
decreases the current unbalance ratio by half. Although Δ-Δ type topology achieves the similar
performance, the phase current and transformer current cannot be regulated to balance at the
same time. In addition, PCB planar transformers are applied to achieve the lower profile and
better consistency compared with conventional transformers. Finally, both the power loss
calculation and the experimental results based on a 6-kW optimal designed prototype validate the
effectiveness of the proposed topology.
63
CHAPTER FOUR
INTEGRATED THREE-PORT THREE-PHASE DAB DC-DC
CONVERTER
4.1 Introduction
DC distribution energy systems (DES) have the advantages to interact with renewable
energy source due to the simplicity and efficiency [1]. DES include but are not limited to
photovoltaic (PV), fuel cells, which generate DC voltage, and wind turbine, microturbine and
internal combustion engines (ICE), which generate AC voltage. All of these DE resources have
to be interfaced with a DC bus and feed power to the load or the utility grid, therefore dc-dc or
ac-dc power electronics converters are essential units [2-7]. Moreover, many energy storage
systems, for example batteries, super capacitors and flywheels, are considered to be installed in
DES to provide dispatchability of their distributed resources which are renewable energy
sources, like solar and wind power without dispachability by their own. Proper sizing selection
of the renewable energy source can meet the energy requirement, and the energy storage system
can balance the difference between the renewable energy source and the load requirement. It also
helps intensive penetration of renewable energy production such as PV into the grid by
proposing peak shaving service at the lowest cost [1, 8-10]. The similar power electronics
converters are necessary to interface energy storage elements to the grid or load. A common DC
distribution bus shared by these converters is an effective solution, since the total number of
converters is lower compared with the ac solution, even if it is necessary to have an ac-dc
interface converter with the utility grid [7].
Dc-dc converters have got a fair amount of use in DES. Compared to the individual twoport dc-dc converter, integrated multi-port dc-dc converter is a popular topic for its less
components, higher system efficiency and easier centralized control. This paper is focused on
DC distribution system for PV applications, which is shown is Fig. 4.1. In DC distribution
system, a basic cell of DES consists of an energy source (PV panels), and an energy storage
element such as batteries. The PV panels and batteries are widely of utilization due to the
decrease of the costs. Multi-port dc-dc converter as an attractive solution is suitable to integrate
the PV and energy storage element with the advantages of high efficiency, high power density
64
and cost-effective, which has been addressed in various literatures. In [11-12], a three-port
converter is proposed to interface with PV and batteries. However, the presented converter is not
able to charge the battery from common dc bus side due to the unidirectional power flow
between primary side and secondary side. Moreover, the power control of PV and battery is
coupled so that a decoupled controller should be designed. Another popular topology is the
three-port transformer coupled dual-active-bridge (DAB) converter for renewable energy system
application which is addressed in [13-17]. Since it is magnetic coupled, all of three-port are
galvanic isolated and the bidirectional power flow. In this topology, since only one multiwinding transformer is applied to interface with three half or full bridges, there exists circulating
current in the three-port dc-dc converter. How to minimize the circulation power loss is another
issue for this type of topology [16, 18]. An interleaved triple-voltage dc-dc converter is discussed
in [19], which consists of two half-bridges and a high-frequency transformer to provide voltage
level matching and galvanic isolation. The interleaved structure is to reduce the capacitor
requirement and current ripple. A low cost, soft-switched bidirectional dc-dc converter for
connecting the three voltage nets is discussed in [20]. Based on this topology, an interleaved
reduced-component-count three voltage bus dc-dc converter is proposed for fuel cell electric
vehicle applications to reduce the capacitor requirements and current ripple [21]. The dc inductor
is removed, but it is not easy to realize the power flow management between two low voltage
ports. Since the voltage is fixed in these applications [19-21], the duty cycle is set to around 1/3
and varied duty cycle control is not analyzed, the power flow between two low voltages ports is
not mentioned neither. Therefore, it can be expected that when the duty cycle control is applied,
the power flow management will be flexible. On the other hand, the soft-switching conditions
and controller will be affected, which are necessary to be investigated.
65
Utility
Grid
AC
AC/DC
DC
DC Distribution Bus
DC
Load
DC/DC
DC/DC
PV Panel
Energy Storage
System
DC/DC
DC
Load
PV Panel
DC/DC
Energy Storage
System
Figure 4.1 A DC distribution system with basic cell for PV applications:
Energy sources, Energy storage element and Load
In this chapter, a three-port bidirectional dc-dc converter for PV system applied on DC
distribution is proposed. The PV panels are connected to the current source port to meet the
maximum power point tracking (MPPT) and voltage variation requirement. The battery pack is
connected to the low voltage side (LVS) dc-link due to the relative constant voltage. The DC
distributed bus is connected to the high voltage side (HVS) port to realize galvanic isolation by
high frequency transformer. Compared to the single-phase dual-half-bridge (DHB) and DAB
converters, the three-phase interleaved structure reduces passive components size, current and
voltage ripples. ZVS can be guaranteed in different operation mode even PV voltage varies in a
wide voltage range and battery voltage change in small voltage range due to different state of
charge (SOC) and charge/discharge status. In addition, the three-port power flow control is
natural decoupled in a wide operation range, so it can be treated as a conventional two stage dcdc converter which consists of a boost converter and a three-phase DAB converter. Therefore the
66
controller can be easily designed separately that the boost circuit part is for MPPT and voltage
step up functions and isolated DAB circuit is for interface with battery and dc distribution bus.
4.2 Converter Description
Fig. 4.2 shows the proposed integrated three-port dc-dc converter topology. A threephase DAB converter is applied to realize the bidirectional power flow function and the Y-Y
connected high frequency transformers can provide galvanic isolation and voltage-level
matching between low voltage energy sources and high voltage dc bus [22]. The leakage
inductance of transformer Ls1~Ls3 is as energy storage elements to transfer the power between
two sides and the power flow is mainly controlled by a phase-shift angle φ. The middle points of
three legs in LVS are connected to one energy source port through three dc inductors Ldc1~Ldc3,
and duty cycle D is another control variable to adjust the power distribution between the two
ports of LVS. In the application of PV system on dc distribution bus, the converter is applied to
interface with PV panels, battery unit (BU) and dc bus or load. BU as an energy storage element
is connected to the LVS dc-link. The voltage of battery changes slowly with different SOC, so
the primary side dc-link voltage can keep constant. The PV panels as energy sources are
connected to the current source port. The output voltage and current of PV change in a large
range due to different solar irradiation and ambient temperature. Three-phase dc inductors and
primary side switches are used to boost the PV voltage and MPPT can be realized by the duty
cycle control. With the help of dc inductors, ZVS is guaranteed in all operation modes even
though the battery’s voltage changes with different SOC. Compared to the single-phase
topology, three-phase interleaved topology can reduce the current and voltage ripples so as to
reduce the inductor and capacitor’s size.
67
Three-port integrated DC-DC converter
i2
Primary dc link
1:n
Secondary dc link
=
i3
P2
Port II
(BU)
i1
V2
C2
P1
Port I
(PV)
Sr1
Sa1
Sb1 Sc1
Ldc1
a
Ldc2
b
Ls2
Ldc3
Ls3
C1 V1
Sa2
c
Sb2
Ls1
St1
V3
r
s
t
Sr2
Sc2
Ss1
Ss2
C3
P3
Port III
(DC Bus/
Load)
St2
Figure 4.2 Three-port integrated bi-directional dc-dc converter
The modulation strategy of the three-port is similar to that of two-port DAB3 converter,
so the operation principle can be referred to that in [22]. It can be seen that the converter can be
divided into six operation area and the power flow between two sides will change according to
different combination of duty cycle and phase-shift angle, which is shown in Fig. 4.3. In practice,
in order to operate converter to achieve high efficiency, the duty cycle is limited between 1/3 and
2/3, and the phase-shift angle should be smaller than π/3 for low reactive power loss. For
example, when the converter is mainly operating in Area III, the power equation is given as [22]:
(4.1)
Where V3’ is the HV bus voltage referred to the LV side, and V3’= V3/n. The phase-shift angle φ
can be calculated as:
(4.2)
68
φ
IV
II
V
I
VI
III
D
2/3
1/2
1/3
VI
I
V
II
IV
Figure 4.3 Six operation areas with different duty cycle and phase-shift angle, and shadowed part
is the practical operating area
Three-port Converter
P3
P2
P1
P3
P2
P1
(A)
P3
P2
P1
(B)
P3
P2
P1
(C)
P3
P2
P1
(D)
(E)
Figure 4.4 Operation modes in different power flow. (A) P1>0, P2<0, P3<0; (B) P1>0, P2>0,
P3<0; (C) P1>0, P2<0, P3>0; (D) P1=0, P2<0, P3>0; (E) P1=0, P2>0, P3<0;
The operation modes of three-port converter can be distinguished by the power flow
combination, which are listed in Table I. Since the PV panels cannot sink power, there are five
operation modes. Fig.4.4. shows the operation modes in different power flow, P1, P2 and P3
represent the power from the corresponding three ports, and the positive power means that the
power is generated from the port. Due to the power conservation law, the power satisfies
69
(4.3)
Table 4.1 Operation modes in terms of different power flow
Mode A
Doesn’t exist
Mode B
Mode D
Mode C
Mode E
Doesn’t exist
Doesn’t exist
In mode A, when the solar irradiation is high, PV can provide power to the DC bus and
charge the battery at the same time. According to different power management strategy, the
objective of power control can be the battery’s charging current Ibat or the scheduled DC bus
current Ibus.
(4.4)
In this mode, the BU functions as an energy storage element to store the excess energy. The
bolded part is the control objective.
In mode B, when the solar power is not high enough, PV with BU together will provide
power to meet the scheduled DC bus load requirement, and the bus current Ibus is the control
objective,
(4.5)
In this mode, the BU functions as an energy source to support the DC bus load.
In mode C, when SOC of battery is low, PV and DC bus will provide power to charge the
battery.
70
(4.6)
Since the constant charging current is preferred, the DC bus power is used to make it constant
and mitigate the disturbance resulted from the PV power.
In mode D, when there is no solar power in the evening or cloudy days, the power from
DC bus can charge the battery.
(4.7)
This mode is used to save the grid energy into the energy storage system when the utility price is
low at night or there is excessive power generated from other energy source. The optimized
power management strategy is out of scope here, so the mode sequence optimization will not
discuss in this paper.
In mode E, when there is no PV power, battery can discharge to meet the requirement of
DC bus load.
(4.8)
This mode mainly happens in the stand-alone mode and there is no other energy source available
to support the load. The BU functions as a back-up energy source to provide uninterruptable
power.
There are other operations modes in which solar power is only to charge the battery or
solar power is only to support the DC bus load, but they are not common and can be avoided
with proper power management strategy.
4.3 ZVS Conditions Analysis
The soft-switching condition of three-port topology is different from that of two-port case
[22], because the power generated or sunk from energy storage element will have influence on
the switches’ current on primary side. Hence the ZVS analysis is necessary and described in the
following section.
The natural soft-switching is the characteristic of DAB3 when the dc-link voltages on
both sides are matched. For three-port dc-dc converter in PV application on dc distribution
71
system, the ZVS conditions should be calculated in different operation mode. The ZVS
conditions will be also affected by the voltage variation due to the battery’s voltage changes with
the SOC.
4.3.1 Pseudo “two-port” ZVS Analysis
When PV does not provide power, it becomes two-port converter soft switching analysis.
However, this two-port soft switching is different from that of two-port in [23], because in [23]
the power in primary side is generated from current source port and in this paper the power is
provided from battery which is connected to the primary side dc-link. It is also different from
that of DAB3 converter in [22] because there is existing dc inductor current in primary side
which will change the current waveform in switches, thus affecting the ZVS conditions.
Therefore, it is defined as pseudo “two-port” ZVS condition in this paper.
In the DC distribution system, the voltage variation of battery due to the state of charge
(SOC) should also be considered. When the primary side dc-link voltage changes according to
the SOC of battery, the d=V3’/V2 will change around 1, which is shown in Fig. 4.5. During
discharging, the battery’s voltage will decrease and d is higher than “1”. During charging, the
battery’s voltage will increase and d is lower than “1”. However, with the help of dc inductor
current ripples, the ZVS can be guaranteed when d is changing (0.9~1.1). Define m=iLdc/iLs, the
dc inductor current ripple of each phase can be calculated as,
(4.9)
The ZVS conditions of the switches for one phase should satisfy the inequation (4.10):
(4.10)
According to (4.10), the constraint conditions of ZVS related to d can be derived. Because in
different operation areas, the transformer current is different, the ZVS conditions should be
calculated separately. In practice, the converter is mainly operating in the area of
∈
, and the expressions of power and current can be calculated in corresponding
operating Area II, III and V. The detailed calculation for Area III is shown here. For instance, in
the range of d should satisfy (4.11) to meet the ZVS conditions,
72
(4.11)
The worst case happens when φ is 0,
(4.12)
In DAB3 converter, only “d = 1” can meet the requirement at the point φ = 0. Compared to
DAB3 converter, the ZVS range is enlarged in the primary side. In practice, the battery’s voltage
will vary with different SOC and charge/discharge status. Fig. 4.5 shows the battery’s voltage
curves during charging and discharging, and d varies around “1” by selecting proper rated value
of V2 and V3. Based on (4.11), the ZVS boundaries are plotted in Fig. 4.6. In Fig. 4.6, the
converter is operating in the shadowed area. d is changed between the values in the worst case
due to the variation of battery’s voltage, i.e. d is 0.9 in charging mode and 1.1 in discharging
mode. It can be seen that the operation curves are always located between the upper and lower
ZVS boundaries so that soft-switching can be guaranteed in the whole operating range.
VB
d=V3'/V2
Discharge Curve (V)
d
VB
Charge Curve (V)
d<1
VB_up
VB0
VB_low
VB_up
0.9
d=1
VB_low
1.1
d>1
60%
80%
Discharge
Performance
(0.2C)
100%
80%
Charge
Performance
(0.2C)
Figure 4.5 Battery’s voltage in charge/discharge performance
73
60%
2.1
2.1
ZVS boundary with dc current ripple
ZVS boundary for DAB3
1.9
1.9
d=V2'/V1
1.7
1.7
1.5
1.5
ZVS upper boundary
1.3
1.3
d=1.1
1.1
1.1
Mode E, battery discharging (d>1)
0.9
0.9
Mode D, battery charging (d<1)
d=0.9
0.7
0.7
0.5
0.5
ZVS lower boundary
-1
-1
-0.8
-0.8
-0.6
-0.6
-0.4
-0.4
-0.2
-0.2
0
0
φ/rad
0.2
0.2
0.4
0.4
0.6
0.6
0.8
0.8
1
1
Figure 4.6 ZVS boundaries in pseudo “two-port” mode
4.3.2 ZVS conditions in three-port mode
In three-port mode, the soft-switching is not only related to dc inductor current but also
related to the PV power. Define the PV power
, and then the average PV current of
each phase is,
(4.13)
According to different power flow direction, the inequations should be satisfied in all the
three cases:
(4.14)
74
According to (4.14), the ZVS conditions of each switch in Area III can be calculated as,
(4.15)
So the general ZVS condition is:
(4.16)
In the worst case when φ is 0:
(4.17)
In (4.17), it can be seen that if the Ppv is large enough to make d<1, there will always be hardswitched when φ is 0. The solution of d exists only when
(4.18)
Based on (4.18), ZVS can be guaranteed by selecting proper m. According to (4.16), the
ZVS boundaries are plotted in Fig. 4.7. In Fig. 4.7, the d is set to the worst case value due to the
variation of battery’s voltage and n is 0.1 which is half of the rated power. The operation curves
are located between the upper and lower ZVS boundaries except Mode A when phase-shift angle
is small and d is less than 1, but the ZVS range is still improved compared to that of DAB3
converter.
75
2.2
2.2
ZVS boundary with dc current ripple
2.02
ZVS boundary with dc current ripple and n=0.05
1.8
1.8
1.6
d=V2'/V1
1.6
ZVS upper boundary
1.4
1.4
1.2
1.2
d=1.1
Mode B, battery discharging (d>1)
1
Mode C, battery charging (d<1)
1.0
d=0.9
0.8
Mode A, battery charging (d<1)
d=0.9
Hard switching
0.8
ZVS lower boundary
0.6
0.6
-1
-1
-0.8
-0.8
-0.6
-0.6
-0.4
-0.4
-0.2
-0.2
0
φ/rad
0.2
0.4
0.6
0.8
0.8
11
Figure 4.7 The key current waveforms in different operation modes
4.3.3 ZVS Conditions in General Case
In general case, the ZVS conditions of each switch is rewritten here,
(4.19)
Where the dc inductor current
changes with time,
(4.20)
76
and transformer current
will change with different operation area. Since in steady state the
average transformer current is zero and voltage-second balance should be satisfied, the
transformer current
at the time tSa1_on can be calculated,
(4.21)
The transfer current at other time can be calculated in the same way. When
and
is negative,
are exchanged. The dc inductor current ripple is
(4.22)
Where
.
The average dc inductor current can be calculated by
(4.23)
Since the rated power of the converter is at
,
(4.24)
In order to maintain the high efficiency and lower reactive power,
selected as
, the rated power
should be not high. If
is
is,
(4.25)
The PV power should be less than
, i.e. n<0.2.
Substitute (4.20)-(4.23) into (4.19), the ZVS conditions in different case can be calculated and
summarized in Table 4.2.
According to Table 4.2, it can be seen that the ZVS range changes with
help enlarge ZVS range but
reduces it. If
and
.
can
, the converter can operate with ZVS at
, which can be derived,
(4.26)
77
Table 4.2 ZVS Conditions in Different Operation Area
Operation
ZVS Conditions
ZVS Condition at
Area
II
III
V
Where
4.4 Control System Design
Since the power between the primary side and secondary side in Area III (1/3<D<2/3,
φ<2π(D-1/3), φ<2π(2/3-D)) is:
(4. 27)
Different from the single phase DHB converter [24] and DAB converter [15], it is just related to
the phase-shift angle φ but has no relation to D. The three-port converter can be treated as a
three-phase boost converter with duty cycle control connected to a three-phase DAB converter
with phase-shift angle control which is shown in Fig. 4.8. It becomes a conventional two stage
DC-DC converter, and the controller includes boost controller and DAB controller with fixed
duty cycle. Fig. 4.9 illustrates the controller for two converters.
78
Three-phase Boost Converter
i12
DAB3 Converter
i23 iin_DAB3 Primary dc link
1:n
Secondary dc link io_DAB3
i3
Sw
i1
Port I
(PV)
Su1 Sv1
1
Ldc1
u
Ldc2
v
Ldc3
w
Su2
Sv2
i2
Sa1
V2
C2
Port II
(BU)
Sw
Sa2
Sb1
a
Sr1 Ss1
Sc1
Ls1
b
Sb2
r
Ls2
c
St1
V3
s
C3
t
Ls3
Sr2
Sc2
Ss2
Port III
(DC Bus)
St2
2
Figure 4.8 The equivalent circuit of three-port dc-dc converter
H1(s)
i1
PV
model v1
Sin
Tin
MPPT
Controller
(P&O)
i3a*
p pv +
ibu
vb
u
SOC
Controller
ibu*
vbu*
pbat
*
÷
v3
+
Mode
sw
i pv
D
Ci(s)
-
i3
Gid_boost(s)
φ
i3
Giφ _DAB(s)
H2(s)
i3b*
Figure 4.9 Control system diagram
For three-phase DAB converter, since there are 12 sub-periods in one switching cycle, it
is much more complicated to derive the full-order small-signal model than that of full-bridge
DAB converter [25-26]. According to the power equation (4.27), the average state equation can
be written as:
(4.28)
79
Where
,
, and Re is the equivalent
DC load resistance.
The small signal model can be derived by expanding the average model into Taylor series
around the operating point, and then neglecting the higher order nonlinear terms, which is
described as follows:
(4.29)
Where
,
,
The output current to control transfer function can be derived
(4.30)
A converter with proposed topology was built in the laboratory. In order to design the
controller for this converter, the parameters are listed in the Table 4.3. The duty cycle D is
controlled by the MPPT controller, and the phase-shift angle control is implemented by the
compensator
, which is expressed as:
Table 4.3 Three-port Converter Parameters
DC bus voltage V3
270V
Battery voltage V2
67.5V
PV voltage V1
32~42V
Rated power P3
2kW
Switching frequency f
40kHz
Transformer turns ratio
1:4
Leakage inductor Ls
1µH
DC inductor Ldc
7.5µH
Input capacitor C2
5600µF
DC-link capacitor C3
780 µF
80
(4.31)
Where
.
After compensation, the cross frequency of current open loop is 1.69kHz and the phase-
margin is
, which is shown is Fig. 4.10.
The average model of the three-port dc-dc converter is developed for verification of
operation mode simulation. Based on the equivalent circuit, the converter can be divided into two
stages: boost stage and DAB3 stage. According to (4.19), the average model can be derived,
which is shown in Fig. 4.11.
Bode Diagram
Magnitude (dB)
100
50
0
-50
Phase (deg)
-100
0
-45
-90
-135
-180
101
102
103
104
Frequency (rad/sec)
105
Figure 4.10 Current open loop gain of DAB3 stage built in the laboratory
81
106
C1
Ldc I1 DV2 DI1 C2
PV
Model
V2
+
-
gV3'
gV2
C3' Io' V3'
+
-
+
DAB3 Converter
Boost Converter
g=φ(4π-3|φ|)/6πωLs
Figure 4.11 Average model of three-port dc-dc converter
IoA
i
iIoB
O2
Dutyavg
1
D
D2Duty1 D3
φ1
phiavg*180/3.14
2
3
Ioavg
O1
iO3
22
20
20
18
18
16
16
14
14
12
12
10
10
8
8
Io(A)
22
Duty
Duty
4
0.64
2
0.62
.6
0.6
8
0.58
6
0.56
4
0.54
phiA*180/3.14
φ
φ
φ(◦)
0.1
phiB*180/3.14
1,3
60
50
50
40
40
30
30
20
20
10
10
60
0.15
2
0.2
0.25
0.3
0.35
Time(s)
Figure 4.12 Simulation results comparison: 1, Circuit model; 2, Equivalent circuit model; 3,
Average model
The comparison of three-port converter, the equivalent circuit and the average model are
simulated and displayed in Fig. 4.12, in which the load power changes from 4150W to 6150W at
0.2s and changes back to 4150W at 0.25s, and the PV voltage changes from 32V to 42V with a
finite slope. In the equivalent circuit, the duty cycle D of DAB3 stage is fixed 0.5.
82
The simulation results show that the three models are almost consistent with each other.
The difference happens at when the output current is high and input voltage is relatively large.
Since in this condition, the converter is operating in Area V which has different power equation
[23], i.e.:
(4.32)
Under this condition, the controlled phase-shift angle is not consistent with each other.
Considering that difference of power equation in Area III and V is no more than 10%, the
average model derived from Area III can still be applied approximately in the whole operation
range.
Fig. 4.13 shows the one day scaled down simulation results of proposal controller based
on the average model.
In Fig. 4.13, from 0s to 6s, there is no solar power, and the DC distribution bus provides
power to charge the battery, so the converter is operating in Mode D.
At 6s, solar irradiation starts to increase from 200W/m2 to 1000W/m2. From 6s to 7s, the
PV with DC distribution bus together generates power to charge the battery, and the converter is
operating in Mode C.
At 7s, there is a peak power requirement on DC distribution bus side, and PV and battery
provide power to the DC bus load. The converter operates in Mode B when the PV power is
lower than the DC bus load requirement, and operates in Mode A when the PV power is higher
than DC bus load.
At 18s, there is another peak power requirement from DC bus side, and the battery
provides main power due to the low solar irradiation level. After 19s, the solar power is zero, and
the DC bus load is supported by the battery, so the converter is operating in Mode E.
From Fig. 4.13, it can be seen that when the irradiation changes, only duty cycle is
controlled to realize the MPPT. Phase-shift angle only changes when there is power flow
response between the two sides such as variation of battery’s charging current or DC load
current.
83
D
Sin(W/m2)
Mode
1500
1500
C
B
Night
A
B
E
Day time
Night
1000
1000
1000W/m2
500
500
00
0
6
12
18
(a) 24
18
(b) 24
PPV(W)
4000
4000
2150W
2000
2000
00
0W
0
ibat(A)
50
50
6
12
10A
10A
00
-20A
-61A
-50
-50
-100
100
0
6
12
18
i3(A)
20
20
5A
-2.5A
00
-10
-10
15A
10A
10
10
0
6
12
18
φ/rad
0.2
0.2
0.148rad
0.047rad
-0.023rad
00
0
6
12
D
0.6
18
(e) 24
18
18
24
24
(f)
0.55
0.47
0.5
0.5
0.4
0.4
(d) 24
0.096rad
0.1
0.1
-0.1
-0.1
(c) 24
00
66
12
12
t(s)
Figure 4.13 One day simulation results using average model
84
4.5 Experimental Results
A 3kW three-port DC-DC converter is developed for experimental verification. The
parameters of the system are the same as those in the simulation, which are listed in Table 4.2. In
the experiment, the PV panels are emulated by a 4kW, 50V, 80A PV emulator, and the
parameters of PV panels are listed in Table 4.3, which is referred to the Sunpower 215 PV panel.
Five U27-12RT 12.8V lithium iron magnesium phosphate (LFMP) battery modules in parallel
are used as an energy storage element. Fig. 4.14 and Fig. 4.15 show the discharge and charge
performance of the battery, respectively [27]. It can be seen that the voltage range is [12.9V,
13.4V] during discharging with 0.2C and [13.6V, 14.6V] during charging status. So the rated
primary side DC link voltage can be set to 13.5V*5 = 67.5V, and the range of d is [0.956, 0.99]
in discharging mode and [1.01, 1.08] in charging mode, which is satisfy the ZVS conditions
mentioned in section 4.4.
Table 4.4 Parameters of PV panel Sunpower 215 (25◦C, 1000W/m2)
Max. Power Voltage (Vpm)
39.8 V
Max. Power Current (Ipm)
5.40 A
Open Circuit Voltage (Voc)
48.3 V
Short Circuit Current (Isc)
5.80 A
Module Efficiency
17.3%
Peak Power (Pmax)
215 W
Power Coefficient
-0.38%/K
Voltage Coefficient
-136.8mV/K
Current Coefficient
3.5mA/K
85
x
13.4V
x
12.9V
Figure 4.14 Discharge performance of one battery module
x
14.6V
13.6V
x
Fig. 4.15 Charge performance of one battery module
The experiment set up is shown in Fig. 4.16. The PV parameters are set in PPPE software and
interface with PV emulator via USB communication. Fig. 4.17 shows the V-I characteristics and
that the maximum power point (MPP) can be tracked when MPPT method is applied in the threeport DC-DC converter.
86
PC Interface
(PPPE)
Battery Packs
13.5x5=67.5V
Comm Cable
DC
Load
PV Panel
4kW Magna PV Emulator
3-port DC-DC Converter
Figure 4.16 Experimental set up
Maximum Power Point
28.0
800W/m2
24.0
20.0
Ipv/A
16.0
12.0
8.0
4.0
0.0
0.0
10.0
20.0
30.0
40.0
50.0
Vpv/A
Figure 4.17 V-I characteristics curve for five PV panels in parallel
Fig. 4.18 gives a time scale down one day performance of the three-port converter. In the
morning the solar irradiation begins to increase, so the PV current increases and the battery’s
current decreases. There is one load peak period during the morning, and battery with PV
87
together will provide power to the load, where the converter is running in Mode B. When the PV
power is higher than load power, the excess power is charging battery, where the converter is in
Mode C. In the afternoon, the irradiation begins to decrease from 1000W/m2 to 150W/m2, it can
be seen that the PV current is decreasing with the same trend and the MPPT is always satisfied.
In the evening, the PV current is 0, and the DC load is supported by battery, where the converter
operates in Mode E.
Fig. 4.19 shows the Vds and Vgs voltage waveforms on Sa2 in three different Modes, since
the lower switches on LVS are hardest to achieve ZVS conditions. It can be seen that, before Vgs
increases, the Vds has decreased and the anti-parallel diode is conducting, so the Sa2 is zero
voltage turn-on.
vo (50V/div)
vpv (10V/div)
vbat (10V/div)
ipv (5A/div)
ibat (5A/div)
io (2A/div)
Evening
Mode B
Morning
Afternoon
Mode C
Mode B
Evening
Mode E
Figure 4.18 One day scale down experimental results
88
(a)
(b)
(c)
Figure 4.19 ZVS waveforms of Sa2 in different operating modes:
(a) mode B; (b) mode C; (c) mode E
89
4.6 Summary
In this chapter, a three-port PV system with energy storage for DC distribution system
using three-phase interleaved bidirectional dc-dc converter was proposed. The high frequency
transformers provide voltage boost capability and galvanic isolation. PV and battery interfacing
with different type of ports can realize MPPT and soft switching under wide variation of PV
voltage. The soft switching can be guaranteed in most of operation mode even the battery’s
voltage changes due to the different charge/discharge status. The two control variables, duty
cycle and phase shift angle, can be controlled independently to realize MPPT and power flow
between energy sources and load. The benefit of bidirectional power flow is helpful to manage
the SOC of battery in grid connected mode. Simulation and experimental results verified the
principles.
90
CHAPTER V
CONLUSION AND FUTURE WORK
5.1 Conclusions
In the presented work, an interleaved three-phase current-fed bidirectional DC-DC
converter for hybrid electric vehicle application is investigated. Based on the literature survey of
several low voltage high current bidirectional DC-DC converters, current-fed bidirectional dc-dc
converters are selected as candidates for hybrid.
The three-phase interleaved structure is helpful to reduce the current and voltage ripple or
reduce the capacitor and inductor sizing. The maximum input current ripple is no more than 20%
of total input current even when the phase current ripple is as high as the rated current value. In
this work, it is first proved that three-phase DAB converter has lower reactive power than singlephase DHB converter or full-bridge DAB converter. It also reveals in this work that Y-Y
transformer connection type converter can provide inherent current sharing capability compare to
other type of transformer connection.
The phase shift angle and duty cycle control are employed in the converter to realize the
power flow control and soft-switching in wide voltage range, which is suitable for renewable
energy sources or super capacitors. The operation principle of three-phase bidirectional dc-dc
converter is thoroughly analyzed in this thesis, and the soft-switching condition is also derived in
different operation mode. The analysis is necessary for hardware design and optimization.
In addition, by using phase shift and duty cycle control, the reactive power loss is always
maintained to be low and ZVS conditions can be satisfied when input voltage changes, so high
efficiency can be guaranteed over a wide operation range.
A three-port PV system with energy storage for DC distribution system using three-phase
interleaved bidirectional dc-dc converter was proposed in this work. The high frequency
transformers provide voltage boost capability and galvanic isolation. PV and battery interfacing
with different type of ports can realize MPPT and flexible power management. The soft
switching can be guaranteed in most of operation mode even the battery’s voltage changes due to
the different charge/discharge status. Based on the power control analysis, it is clear that the
natural decoupled power flow management is one of the features of three-phase topology. So the
91
two control variables duty cycle and phase shift angle, can be controlled independently to realize
MPPT and power flow between energy sources and load, respectively.
5.2 Future work
Future research on the current-fed multiphase DAB DC–DC converter can be related to
the DAB converter modeling, the DAB converter hardware optimization, new modulation
strategy and new topology derived from multiphase DAB converter for new applications.

The converter model presented in this work is just accurate in one operation area. When
the operation area changes, new converter model should be calculated. One solution is
that the harmonics model is used to replace this piecewise model, so that only one model
can be applied in all operation areas.

The hardware design can also be optimized further: the three-phase coupled inductor and
one three-phase high frequency transformer can replace the single phase inductors and
transformers to reduce power loss and improve power density.

There are several control variables in current-fed DC-DC converter, which can provide
flexible control strategy to implement some specific functions, such as minimum RSM
current operation mode, zero reactive power mode or double frequency cancellation for
PV or fuel cell applications. New modulation with duty cycle and phase shift angle
combination is also useful to improve the system performance.

New multiphase topology derived from multiphase DC-DC converter for high voltage,
high power application. It is attractive for industry and academia to utilize Solid State
Transformer (SST) to replace the conventional transformer for the features of
instantaneous voltage regulation, fault isolation, power factor correction, etc. As the key
component, DAB converter is a very good candidate for the bidirectional DC-DC
converter. Multilevel multiphase DC-DC converter can be used in SST system. Due to
the multilevel structure, conventional high voltage semiconductor such as IGBT, IGCT
can be applied in 12kV distribution system. In addition, even less reactive power loss will
be evaluated in the multiphase, multilevel DAB converters.
92
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103
BIOGRAPHICAL SKETCH
Zhan Wang was born in Hubei, China. He received his B.S. and M.S. degree in Electrical
Engineering from Huazhong University of Science and Technology in 2002 and 2005,
respectively. He is currently a Ph.D candidate in the ECE department at FAMU-FSU College of
Engineering and also a Graduate Research Assistant with the Center for Advanced Power
Systems (CAPS) at Florida State University (FSU). His research interests include energy storage
elements, dc-dc converter, and renewable energy system.
He has 9 publications listed below since 2007.
[1] Zhan Wang; Hui Li, "A Soft Switching Three-phase Current-fed Bidirectional DC-DC
Converter With High Efficiency Over a Wide Input Voltage Range," Power Electronics,
IEEE Transactions on, vol.27, no.2, pp.669-684, Feb. 2012
[2] Lei Wang; Zhan Wang; Hui Li, "Asymmetrical Duty Cycle Control and Decoupled Power
Flow Design of a Three-port Bidirectional DC-DC Converter for Fuel Cell Vehicle
Application," Power Electronics, IEEE Transactions on , vol.27, no.2, pp.891-904, Feb.
2012
[3] Zhan Wang; Hui Li, " An Integrated Three-port Bidirectional DC-DC Converter for
PVApplication on DC Distribution System," Power Electronics, IEEE Transactions on ,
Submitted.
[4] Thomas Butschen; Zhan Wang; Murat Kaymak and Rik W. De Doncker, "Compact High
Temperature Package with Smart Size-Optimized Gate Drive Unit for assembly of the DualICT," Accepted by IEEE Energy Conversion Congress and Expo (ECCE), 2012, Raleigh,
NC, USA
[5] Zhan Wang; Hui Li, "Integrated MPPT and bidirectional battery charger for PV application
using one multiphase interleaved three-port dc-dc converter," Applied Power Electronics
Conference and Exposition (APEC), 2011 Twenty-Sixth Annual IEEE , pp.295-300, 6-11
March 2011
[6] Zhan Wang; Hui Li, "Three-phase bidirectional DC-DC converter with enhanced current
sharing capability," Energy Conversion Congress and Exposition (ECCE), 2010 IEEE ,
pp.1116-1122, 12-16 Sept. 2010
104
[7] Zhan Wang; Hui Li, "Unified modulation for three-phase current-fed bidirectional dc-dc
converter under varied input voltage," Applied Power Electronics Conference and
Exposition (APEC), 2010 Twenty-Fifth Annual IEEE , pp.807-812, 21-25 Feb. 2010
[8] Zhan Wang; Hui Li, "Optimized operating mode of current-fed dual half bridges dc-dc
converters for energy storage applications," Energy Conversion Congress and Exposition,
2009. ECCE 2009. IEEE , pp.731-737, 20-24 Sept. 2009
[9] Lei Wang; Zhan Wang; Hui Li, "Optimized energy storage system design for a fuel cell
vehicle using a novel phase shift and duty cycle control," Energy Conversion Congress and
Exposition, 2009. ECCE 2009. IEEE , pp.1432-1438, 20-24 Sept. 2009
105