Modeling and Control of Bidirectional DCDC Converters for DC Power Systems with
Renewable Energy
BY
Husam Ahmed Ramadan Ahmed
A thesis submitted to
Department of Electrical and Electronic Engineering
In partial fulfillment of the requirements for the degree of
Doctor of Philosophy
in
Electrical Engineering
Graduate School of Information Science and Electrical Engineering
Kyushu University
JAPAN
December, 2014
ACKNOWLEDGMENT
In the name of Allah, most Gracious, most Merciful
All deepest thanks are due to Almighty God, the merciful, and the
compassionate for uncountable gifts given to me.
I would like to express my deepest gratitude and sincere appreciation to my
academic advisor Prof. Masahito Shoyama for his help, precious continuous
guidance, and kind encouragement during carrying out this research.
I am very grateful for the cooperative spirit and the excellent working
atmosphere in the green electronics circuits laboratory.
I would like to express my deep appreciation to my country (Egypt) for
supporting my stay during my graduate studies at Kyushu University.
Importantly, I would like to express my gratitude to my parents, brothers and
sisters for their continuous encouragement and prayers.
Finally, with my deepest love, I would like to thank my lovely wife for her
support and encouragement from my life to my study. Her company made my
life in Fukuoka fruitful and meaningful. I also should thank my son, Ayias, for
the special happiness he brought to us.
Husam Ahmed Ramadan
Fukuoka, Nov. 2014
i
Abstract
ABSTRACT
Bidirectional dc-dc converters (BDC) have recently received a lot of attention due
to the increasing need to systems with the capability of bidirectional energy
transfer between two dc buses. Apart from traditional application in dc motor
drives, new applications of BDC include energy storage in renewable energy
systems, fuel cell energy systems, hybrid electric vehicles (HEV) and
uninterruptible power supplies (UPS).
The fluctuation nature of most renewable energy resources, like wind and solar,
makes them unsuitable for standalone operation as the sole source of power. A
common solution to overcome this problem is to use an energy storage device
besides the renewable energy resource to compensate for these fluctuations and
maintain a smooth and continuous power flow to the load. As the most common
and economical energy storage devices in medium-power range are batteries and
super-capacitors, a DC-DC converter is always required to allow energy exchange
between storage device and the rest of system. Such a converter must have a
bidirectional power flow capability with flexible control in all operating modes.
The modeling and the control of bi-directional DC-DC converters is an important
issue. By using conventional modeling method, two different models are needed.
One model for each power direction (each operation mode). Furthermore, the
control loop also should be changed according to the direction of the power flow.
ii
Abstract
Therefore, analyzing and controlling of a bi-directional DC-DC converter became
very complex. For the sake of solving this problem, unified dynamic models of bidirectional DC-DC converters are proposed in this thesis. Furthermore, the stability
issue for the bi-directional DC-DC converters is investigated in this thesis. The
thesis consists of five chapters, which can be organized as follows:
Firstly, Chapter 1 conveys the detailed introduction of the research background, a
literature review of bidirectional DC-DC converters, their types (isolates and nonisolated), modeling and control. Moreover, it presents the thesis objective and
outlines.
Then, in Chapter 2, a unified model for bi-directional DC-DC converters for both
directions of power flow is presented. The bi-directional DC-DC converter is
analyzed using a seamless dynamic model with an independent voltage source and
an independent current source, which polarity depends on the direction of the
power flow.
A small signal model is derived using a state space averaging
method. Furthermore, the transient response and the frequency characteristics are
discussed. Example circuits for bi-directional DC-DC converter are investigated
analytically, using simulation, and experimentally.
Afterwards, Chapter 3 introduces a new control strategy for bidirectional DC-DC
converter, as well. This strategy aims at controlling a bidirectional DC-DC
converter to behave like a multi-level virtual conductor. As a matter of fact, the
iii
Abstract
voltage difference between the terminals of any conductor is zero volts.
Conversely, the main target of this proposed control strategy is to keep the voltage
difference between the converter terminals constant at a certain value. In other
words, this strategy permits the DC-DC converter to transfer the power between
two nodes at different voltage levels. In this way, the converter performs like a
conductor, but unlike the normal conductor, has a voltage difference between its
terminals. Thus, the authors call it a virtual conductor. This virtual conductor is
considered a base for power routing in dc networks; as it can transfer the electric
power between nodes at different voltage levels. Furthermore, it allows an easy
plug-and-play feature. The proposed bidirectional DC-DC system configuration is
investigated analytically, using PSIM simulator, and experimentally.
Further, in Chapter 4, a new criterion for the stability assessment in a dc power
system is presented. This criterion is the node impedance criterion. The concept,
mathematical, simulation, and experimental analysis of node impedance criterion,
are investigated, as well. The results of the node impedance criterion are compared
with those of the conventional criterion. The comparison shows the validity of the
node impedance as a stability criterion. Moreover, the node impedance criterion is
applied to a dc power system using a MLVC to assess it stability.
Finally, Chapter 5 summarizes the conclusions of this thesis and the future work.
iv
Table Of Contents
TABLE OF CONTENTS
Page
AKNOWLEDGMENT………………………………………………
i
ABSTRACT……………………………………………………………
ii
TABLE OF CONTENTS…………………………………………….
v
CHAPTER 1
INTRODUCTION
1
Background……………………………………...
State-of-the-art Bidirectional DC-DC Converters
1
3
Introduction to Bidirectional DC-DC Converters…..
Non-isolated Bidirectional DC-DC Converters…….
Isolated Bidirectional DC-DC Converters………….
Soft-switching Techniques in Bidirectional DC-DC
Converters…………………………………………..
State-of-the-art Bidirectional DC-DC Converter
Modeling and Control……………………………
Traditional Method without Mode Transition
Consideration……………………………………….
Bidirectional DC-DC Power Stage Modeling and
Control………………………………………………
Thesis objectives and out lines
3
5
7
1.1
1.2
1.2.1
1.2.2
1.2.3
1.2.4
1.3
1.3.1
1.3.2
1.4
CHAPTER 2
2.1
2.2
2.3
2.4
2.5
2.6
CHAPTER 3
3.1
9
10
10
12
13
SEAMLESS DYNAMIC MODEL FOR BIDIRECTIONAL DC-DC CONVERTER
16
Introduction………………..………………………
Circuit Topology …………………………………..
Seamless Averaged Model………………………...
Frequency Characteristics………………………...
Transient Response ……………………………….
Summary …………………………………………..
16
18
19
22
28
32
DC POWER SYSTEMS USING MULTILEVEL VIRTUAL CONDUCTOR BASED A
CONTROLLED BIDIRECTIONAL DC-DC
CONVERTER
33
Introduction………………………………………..
33
v
3.2
3.3
3.4
3.5
3.6
3.7
3.8
CHAPTER 4
Table Of Contents
Using a bi-directional DC-DC converter for
charging and discharging of a battery……………
Dc power system using the proposed bidirectional DC-DC converter (The virtual
conductor)………………………………………….
Implementation of the virtual conductor using a
bi-directional DC-DC converter………………….
Configuration examples and features of the
virtual conductor in dc power system……………
The proposed bi-directional DC-DC circuit
configuration……………………………………….
Transient response
Summary ………………………………………….
34
35
36
37
40
44
53
A New Stability Assessment Criterion for DC
Power Systems with Multi-level Virtual
Conductors
54
4.1
4.2
4.2.1
Introduction………………………………………..
Analysis of Bidirectional DC-DC Converter…….
Small Signal model…………………………………
54
55
55
4.2.2
Small Signal Model considering AC Impedance of
Load/Source Modules………………………………
Node impedance and system stability…………….
Numerical analysis and application example…….
4.3
4.4
4.4.1
Numerical analysis………………………………….
57
59
61
61
4.4.2
4.5
Application example………………………………..
Summary…………………………………………...
62
66
CONCLUSIONS AND FUTURE WORK
67
CHAPTER 5
5.1
5.2
Conclusions………………………………………
67
Future work………………………………………………. 69
References
………………………………………………………
vi
70
Chapter 1: Introduction
CHAPTER 1
INTRODUCTION
1.1 Background
Nowadays, a system uses various types of energy sources has been sought after, and a
hybrid system based on fuel cells and super-capacitors as an environmentally renewable
energy system has been applied in many fields, such as hybrid electric vehicle (HEV),
uninterruptible power supply (UPS) and so on [1]-[6].
The bidirectional DC-DC converter along with energy storage has become a promising
option for many power related systems, including hybrid vehicle [1], fuel cell vehicle
renewable energy system and so forth. It not only reduces the cost and improves efficiency,
but also improves the performance of the system.
Figure (1-1): Configuration of power system in electric vehicle.
1
Chapter 1: Introduction
In the electric vehicle applications, an auxiliary energy storage battery absorbs the
regenerated energy fed back by the electric machine. In addition, a bidirectional DC-DC
converter, shown in Fig. (1-1), is also required to draw power from the auxiliary battery to
boost the high-voltage bus during vehicle starting, accelerate and hill climbing [1].
With its ability to reverse the direction of the current flow, and thereby power, the
bidirectional DC-DC converters are being increasingly used to achieve power transfer
between two dc power sources in either direction.
In renewable energy applications, the multiple-input bidirectional dc-dc converter can be
Figure (1-2): Configuration of EMS
2
Chapter 1: Introduction
used to combine different types of energy sources [2-8]. A configuration of EMS (Energy
Management System) is shown in Fig. (1-2). In this configuration, a battery is connected
between load modules and source modules through bi-directional DC-DC converter.
The fluctuation nature of most renewable-energy sources, like wind and solar, makes them
unsuitable for standalone operation. Thus, bi-directional DC-DC converter and battery are
needed to manage this system. The multi-input bidirectional dc-dc converter is the core
that interconnects power sources and storage elements and manages the power flow [5].
This bidirectional dc-dc converter features galvanic isolation between the load and the fuel
cell, bidirectional power flow, capability to match different voltage levels [9], fast
response to the transient load demand, etc. Recently, clean energy resources such as
photovoltaic arrays and wind turbines have been exploited for developing renewable
electric power generation systems. The bidirectional dc-dc converter is often used to
transfer the solar energy to the capacitive energy source during the sunny time, while to
deliver energy to the load when the dc bus voltage is low [9]. In this thesis, a background
description and review of the state-of-the-art bidirectional dc-dc converters are presented
firstly to define this work and its novelty.
1.2 State-of-the-art Bidirectional DC-DC Converters
1.2.1 Introduction to Bidirectional DC-DC Converters
Most of the existing bidirectional dc-dc converters fall into the generic circuit structure
illustrated in Fig. (1-3), which is characterized by a current fed or voltage fed on one side 3
Chapter 1: Introduction
[10]-[14]. Based on the placement of the auxiliary energy storage, the bidirectional dc-dc
converter can be categorized into buck and boost type. The buck type is to have energy
storage placed on the high voltage side, and the boost type is to have it placed on the low
voltage side.
Figure (1-3): Illustration of bidirectional power flow.
To realize the double sided power flow in bidirectional dc-dc converters, the switch cell
should carry the current on both directions. It is usually implemented with a unidirectional
semiconductor power switch such as power MOSFET (Metal-Oxide-Semiconductor-FieldEffect-Transistor) or IGBT (Insulated Gate Bipolar Transistor) in parallel with a diode,
because the double sided current flow power switch is not available. For the buck and
boost dc-dc type converters, the bidirectional power flow is realized by replacing the
switch and diode with the double sided current switch cell shown in Fig. (1-4) [12].
Numerous topologies for possible implementation as bidirectional dc-dc converters have
4
Chappter 1: Introdduction
bbeen reporrted so farr [15-37]. Basicallyy they are divided innto two tyypes, non--isolated and
a
iisolated coonverters, m
meeting ddifferent appplication requiremeents.
Figuure (1-4): sswitch celll in bidirecctional DC
C-DC convverter.
11.2.2 Non
n-isolated Bidirectional DC-D
DC Convverters
IIn the trannsformer-lless non-issolated poower convversion sysstems, thee boost typpe and buuck
ttype dc-dcc converterr are choseen usually.
T
The high frequencyy transform
mer basedd system is an attrractive onne to obtaain isolatiion
bbetween thhe source and load sides. Buut from thee viewpoiint of impproving thee efficienccy,
ssize, weighht and cosst, the trannsformer-less type iss much more attracttive. Thuss, in the hiigh
ppower or spacecraft
s
power syystem appllications [77, 17, 20, 39-47], w
where weigght or sizee is
5
Chappter 1: Introdduction
tthe main cconcern, thhe transforrmer-less type is moore attracttive in higgh power aapplicationns.
T
The basic non-isolaated bidireectional dcc-dc conveerter topollogy show
wn in Fig. (1-5) is tthe
ccombinatioon of a steep-up stagge togetheer with a step-down
s
n stage connnected inn antiparalllel
[[45]. For tthe motorr drive opperations the
t converrter step-uup stage is used to step up tthe
bbattery vooltage andd control the inveerter input. The veehicle reggenerativee braking is
aaccomplishhed by usiing the coonverter sttep-down stage, whiich gives a path forr the brakiing
ccurrent andd allows thhe recoverry of the vvehicle eneergy in thee battery.
Figurre (1-5): Basic bidireectional DC-DC
D
connverter witth buck annd boost sttructure
F
For the prresent highh power ddensity biidirectionaal dc-dc cconverter, to increasse its pow
wer
ddensity, m
multiphase current innterleavingg technoloogy with m
minimizedd inductannce has beeen
ffound in hhigh powerr applicatiions [38, 442]. It is reeported thhat multiphhase conveerter circuuits
hhave show
wn the advaantage of lless device current stress
s
and better effi
ficiency. A three phaase
bbidirectionnal dc-dc cconverter is shown in Fig. (1-6), wheree the phasse switch is
i controllled
w
with 120-ddegree phaase shift ffrom each other. Thhe ripple on
o the totaal current w
will becom
me
6
Chappter 1: Introdduction
rrelatively ssmall, so a small cappacitance is enough in both loow and higgh sides foor acceptabble
vvoltage rippple.
Figurre (1-6): A high pow
wer densityy non-isolaated interleeaved bidiirectional D
DC-DC
converter
11.2.3 Isolated Bidirrectional DC-DC Converter
C
rs
IIn the bidiirectional dc-dc
d
convverters, isolation is normally provided by a transsformer. T
The
aadded trannsformer im
mplies addditional coost and losses [1]. However,
H
since trannsformer ccan
iisolate the two voltaage sources and provvide the im
mpedance matching between them,
t
it is an
aalternativee in those kinds off applicatioons. As a current source, innductance is normaally
nneeded in bbetween.
7
Chapter 1: Introduction
For the isolated bidirectional dc-dc converters, sub-topology can be a full-bridge, a halfbridge, a push-pull circuit, or their variations [25, 27-30]. One kind of isolated
bidirectional dc-dc converter is based on the half-bridge in the primary side and on the
current fed push-pull in the secondary of a high frequency isolation transformer [48]. The
converter operation is described for both modes; in the presence of dc bus the battery is
being charged, and in the absence of the dc bus the battery supplies power. This converter
is well suited for battery charging and discharging circuits in dc uninterruptible power
supply (UPS). Advantages of this proposed converter topology include galvanic isolation
between the two dc sources using a single transformer, low parts count with the use of
same power components for power flow in either direction. The dual active bridge dc-dc
converter with a voltage-fed bridge on each side of the isolation transformer operates
utilization of the leakage inductance of the transformer as the main energy storing and
transferring element to deliver bidirectional flow power [23],[49-50].
In summary, for the isolated bidirectional dc-dc converter, the operation of the circuit
involves the utilization of the leakage inductance of the transformer as the main energy
storing and transferring element. The half-bridge based topologies have been developed so
far to reduce the device count and increase efficiency [3, 28, 31, 49]. However a voltage
imbalance exists between the two split capacitors, thus an additional control circuit to
eliminate the voltage imbalance problem is required. The full-bridge bidirectional dc-dc
8
Chappter 1: Introdduction
cconverter shown
s
in Fig. (1-7) is considered one oof the bestt choices. However,, this systeem
hhas a compplicated coonfiguratioon, high coost and larrge size.
F
Figure (1-7): A bidiirectional full-bridgge DC-DC
C converteer with a uunified sooft switchiing
sscheme
11.2.4 Softt-switchin
ng Techniq
ques in Biidirection
nal DC-DC
C Converrters
T
The efficieency is onne of the needed
n
perrformancees for manny bidirecttional dc-ddc converrter
aapplicationns. To impprove the eefficiency many advvanced pow
wer conveersion techhniques suuch
aas resonannt and soft--switchingg can be im
mplementeed in the ppower stagge [6, 12-13, 38-39, 42,
444, 52-73]]. A bidireectional dual
d
full-bbridge dc-ddc converrter has beeen developed withh a
uunified soft switchiing schem
me and sofft start caapability sshown in Figure 1..8 [71]. T
The
bbridge on one
o side, ppreferablyy the lowerr voltage sside, is currrent-fed, w
while that on the othher
sside is volttage fed. A simple voltage
v
claamp brancch, which iis compossed of an aactive swittch
9
Chapter 1: Introduction
with its anti-paralleled diode and a capacitive energy storage element in series, is placed
across the current-fed bridge to limit transient voltage across the current-fed bridge and
realize zero-voltage-switching in boost mode operation, while achieving hybrid zerovoltage zero-current switching (ZVZCS) for the voltage-fed bridge in buck mode
operation. In buck mode operation, the voltage-fed bridge is controlled by the well-known
phase shift pulse width modulation (PWM). The clamping branch is activated only briefly
each time after an on duty cycle is executed and the on-time of the clamp switch is just
long enough to reset the transformer leakage current to zero and achieve ZVZCS operation
even under maximum load current.
1.3
State-of-the-art Bidirectional DC-DC Converter Modeling and
Control
1.3.1 Traditional Method without Mode Transition Consideration
Many controller schemes have been discussed for bidirectional dc-dc converter
applications. Most designs follow the unidirectional dc-dc controller methodology [41, 43,
45, 74] because there are different circuits topological changes and associated operating
principles involved in the two power flow directions. Normally, two independent
controllers are needed for battery charging and discharging respectively [45, 92]. No mode
transition discussion has been addressed since the power management is normally not
included in the design. More efforts are needed for smooth mode transition. Otherwise the
transition will cause large current or voltage stress on device.
10
Chappter 1: Introdduction
O
One exampple of deaaling with smooth mode
m
transition is shhown in Fiig. (1-8)[443]. This iss a
rregulated bbus system
m for the spacecraft
s
power system application. Thhe major eeffort in thhis
ssystem is to study tthe trajecttories of tthe system
m operatinng point, w
which aree determinned
aaccording to the staability natuure of thee equilibrium pointss for the ooptimum performan
p
nce
aand stabiliity of the system. T
This type oof study teends to coomplicate the
t designn and reduuce
tthe system
m reliabilityy.
F
Figure (1-88): Block ddiagram of regulatedd bus systeem
F
For exampple, the sttarting operation pooint is froom point A in Fig. (1-9) forr sunlight to
eeclipse traansition. As
A illuminaation leveel decreasees, the sollar array ccurrent deccreases. T
The
sshunt reguulator currrent then ddecreases to regulatte the buss voltage. As soon as the shuunt
ccurrent reaaches zeroo, bus voltaage drops rapidly. T
This is thee dead bannd mode. A
According to
tthe pre-sett value, the bus volttage will bbe regulateed by the bbattery disscharger. B
Between tthe
eequilibrium
m points C and D, thhere is a ddead band,, which is to avoid undesired
u
overlappiing
11
Chappter 1: Introdduction
ooperation. Transiennt behavioor duringg the deaad band m
mode deppends on the circuit
pparameterss includingg bus capaacitor, andd cable indductance. The preseet bus volttage valuee is
nneeded to trigger thhe batteryy dischargger for buus voltagee regulatioon. Plus tthe transieent
bbehavior iss sensitivee to circuitt parameteers. It is noot easy to ppredict.
Figuree (1-9): Graphical annalysis of ssunlight too eclipse trransition
11.3.2 Bidiirectionall DC-DC P
Power Staage Modeeling and Control
C
S
Some reseearchers [331, 51, 72] developeed a switcch frequenncy-dependdable averrage methhod
tto estimatee the systeem perform
mance at ddifferent sw
witching ffrequenciees. This is an extendded
12
Chapter 1: Introduction
state-space averaging model and is developed to predict large- and small-signal
characteristics of the converter in either direction power flow. The model is especially
designed for isolated one.
A digital controller was built after non-linear dynamic model of the converter was derived
using a state space averaging method in [8, 75]. Although it utilized the simplified power
stage model with the traditional modeling approach, it did claim to handle seamless
bidirectional operation. In fact, to design a seamless bidirectional power flow control,
more generalized power stage model is needed.
Based on ref [43], an analog current-injection-control in multiphase was implemented in
[44, 65, 76, 93]. One error amplifier was used for the spacecraft bus voltage regulation
with internal peak current mode control. After careful analysis of the feature of the two
modes (bus voltage regulation mode with charging and discharging mode), a sub-optimal
controller was proposed for the regulation of the two mode operations. It was expected to
reduce the overall system weight. Since the application was focused on the spacecraft
power system, no more average current control for both directions was addressed.
1.4 Thesis objectives and out lines
Thesis objectives can be listed as follows:
 Design and implement a unified dynamic model (seamless model) for the
bidirectional DC-DC converter.
13
Chapter 1: Introduction
 Design and implement a new control strategy for the for the bidirectional DC-DC
converter that begot the multi-level virtual conductor(MLVC), which can be
considered as a paramount component in dc power routing.
 Investigate and test the stability issue for the seamless model and for a dc power
system with multi-level virtual conductors, as well.
The thesis consists of five chapters, which can be organized as follows:
Firstly, Chapter 1 conveys the detailed introduction of the research background, a
literature review of bidirectional DC-DC converters, their types (isolates and non-isolated),
modeling and control. Moreover, it presents the thesis objective and outlines.
Then, in Chapter 2, a seamless dynamic model for bidirectional DC-DC converters is
presented, investigated and implemented; both analytically and experimentally. The
frequency and the transient respond are studied, as well.
Afterwards, Chapter 3 presents a new control strategy for bidirectional DC-DC converters
that can be very useful for dc power routing. This control strategy allows the converter to
behave as a multi-level virtual conductor. For the sake of the validation of this control
strategy, a representative case study is addressed by simulation and experiment.
Further, Chapter 4 introduces a new stability assessment criterion for dc power systems
with interconnected multi-level virtual conductors. This criterion is the node impedance
14
Chapter 1: Introduction
criterion. The concept, mathematical, simulation, and experimental analysis of node
impedance criterion, are investigated, as well.
Finally, Chapter 5 summarizes the conclusions of this thesis and the future work.
15
Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter
CHAPTER 2
SEAMLESS DYNAMIC MODEL FOR BIDIRECTIONAL DC-DC CONVERTER
2.1 Introduction
Bi-directional DC-DC converter has two operating modes as shown in Fig. (2-1), and they
are frequently exchanged. These two modes are: 1- Discharging mode: The power is sent
from the battery to load/source modules when load/source modules need the power. 2Charging mode: The power is sent from the load/source modules to battery when
load/source modules have enough amount of the power.
Power Flow
DC/DC
Load/Source
Modules
Battery
(a) Discharging mode
Power Flow
DC/DC
Load/Source
Modules
Battery
(b) Charging mode.
Figure (2-1): Operating mode of a bi-directional DC-DC Converter.
16
Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter
By using conventional modeling method [94], two different models are needed. One
model for each power direction (each operation mode), as shown in Fig. (2-2).
Furthermore, the control loop also should be changed according to the direction of the
power flow. Therefore, analyzing and controlling of a bi-directional DC-DC converter
became very complex.
1
2
DC/DC
Battery 1'
2'
D
Load
Modules
PWM
VREF
(a) Discharging mode.
2
1
DC/DC
Battery 1'
2'
D
Source
Modules
PWM
VREF
(b) Charging mode.
Figure (2-2): Conventional circuit model of bi-directional DC-DC converter.
For the sake of solving this problem, a seamless dynamic model of a bi-directional DC-DC
converter is proposed in this chapter. This model is derived using a state space averaging
method [95]-[97]. As shown in Fig. (2-3), an independent voltage source represents the
17
Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter
battery, and an independent bi-polar current source represents the load/source modules.
The polarity of the bi-polar current source decides the direction of the power flow. Herein,
only the voltage of the bi-polar current source is sensed and controlled. Hence, the control
loop does not need to be switched according to the direction of the power flow. In other
words, a simple analyzing and controlling of bi-directional DC-DC converter can be
fulfilled via this seamless model.
Z2
1
Bi-polar
Current
I2 Source
DC/DC
Battery 1'
2
2' Load/Source
Modules
D
{ II >< 00 :: Load
Source
2
PWM
VREF
2
Figure (2-3): Proposed seamless circuit model of bi-directional DC-DC converter.
2.2 Circuit Topology
Seamless dynamic models based on two circuit topologies are analyzed and compared,
herein. These two circuit topologies are shown in Fig. (2-4) and Fig. (2-5). Figure (2-4)
presents a buck-based circuit topology, however Fig. (2-5) introduces a boost-based circuit
topology. In Fig. (2-4) and Fig. (2-5), the current source side voltage v2 is considered a
control variable, and duty ratio d of the mean switch SM is considered an input variable.
The current source side voltage v2 is observed and duty ratio d is controlled by the control
18
Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter
circuit. Also, the synchronous switch SS, with a duty ratio d’ (=1- d), has a complementary
state with the main switch SM.
d
iL
SM
(rS)
V1
controller
(rL) L
(rc) C
(rS) SS
vc
v2
I2
Figure (2-4): Circuit topology of buck-based type.
d
iL
controller
SS
(rL) L
(rS)
(rS)
V1
SM
(rc) C
vc
I2
v2
Figure (2-5): Circuit topology of boost-based type.
2.3 Seamless Averaged Model
Considering the state-space vector
[
[
] and the input vector
] , the state space equations at state 1 and state 2 become:
19
Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter
State 1 (SM: ON, SS: OFF)
(2-1)
State 2 (SM : OFF, SS : ON)
(2-2)
Appling the state-space averaging method for Eq. (2-1) and Eq. (2-2), state equations
become:
(2-3)
where:
Next, on the steady state, circuit parameters are:
U
: DC input vector
X
: DC state vector
20
Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter
V2
: DC voltage at current source
D
: DC duty ratio at SM
Next, the converter waveforms are perturbed at this quiescent operating point as follows:
U →U+Δu
X
→X+Δx
V2 →V2+Δv2
D →D+ΔD
where; ΔD is small ac variations in duty ratio and Δu is small ac variations in input
values. The vectors Δx and Δv2 are the resulting small ac variations in the state x and
voltage v2.
The state equations of the small-signal ac model are:
(2-4)
where;
The matrices of
(
)
are illustrated in Table (2-1).
21
Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter
From Eq. (2-4), the transfer function Gdv(s) between ΔD(s) and Δv2(s) can be developed,
as in Eq. (2-5).
(
Table (2-1) Elements of the matrices of
Topology
A
B
𝑟
[
Buck
𝑟
Boost
[
𝑟𝑠
𝐿
1
𝐶
𝑟𝑠
𝐿
′
𝐶
𝑟
1
𝐿]
0
′𝑟
[𝐿
0
′
𝐿
1
[𝐿
0 ]
0
c
𝑟
𝐿 ]
1
𝐶
𝑟
𝐿 ]
1
𝐶
)
ep
e
[𝑟
[ ′𝑟
1]
1]
[0
[0
𝑟]
𝑟]
[𝐿]
0
1
[ ′𝐿
𝑟
1
′𝐶
0
𝑟𝑠
𝐿
]
𝑟
𝑠
′
(2-5)
𝑠
By the same way, the transfer function Gvv(s) between ΔV1(s) and Δv2(s),
and
Giv(s)
between
𝑠
𝑠
𝑠
𝑠
ΔI2(s)
and
Δv2(s)
can
be
developed
as:
{
1
}[ ]
0
(2-6)
{
} [ 0]
1
(2-7)
2.4 Frequency Characteristics
The frequency characteristics of the transfer function Gdv(s) are analyzed according to Eq.
(2-5), and to the circuit parameters that are listed in Table (2-1). The equations of the
transfer function Gdv(s) for both buck-based and boost-based type are presented in Eq. (28), Eq. (2-9) as follows:
22
Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter
𝑠
𝑠
(2-8)
𝑠
𝑠
𝑠
{(
)
(𝐶𝑟
) }
(2-9)
Table (2-2) Circuit Parameters
Value
Symbol
Parameters
Buck
Boost
V1
Voltage at Voltage Source
[V]
50
25
I2
Current at Current Source
[A]
-4~4
-2~2
V2
Voltage at Current Source
[V]
25
50
L
Inductance [μH]
120
C
Capacitance [μF]
100
rL
ESR of L [mΩ]
30
rC
ESR of C [mΩ]
150
rS
On-resistance of switches
[mΩ]
150
f
Switching Frequency [kHz]
100
From Eq. (2-8) and Eq. (2-9), it is noticed that the frequency characteristics of buck-based
type don’t depend on I2.
Nevertheless, the frequency characteristics of boost-based
23
Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter
depend on I2. The frequency characteristics of both buck-based type and boost-based type
are analytically and experimentally investigated based on circuit parameters in Table (2-2).
 For buck-based type, analytical results are shown in Fig. (2-6), and
experimental results are shown in Fig.7. According to Fig. 6 and Fig. (2-7), the
frequency characteristics of Gdv_buck for both current directions are the same,
and they match with Eq. (2-8).
These results mean that frequency
characteristics of Gdv_buck don’t depend on the direction of current I2.
Phase (deg)
Gain (dB)
60
40
20
0
-20
0
-60
-120
-180
-240
10
102
103
Frequency (Hz)
104
Figure (2-6) Frequency characteristics of Gdv (analytical results, buck-based type, for
any I2).
24
Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter
60
0
50
-60
Gain [dB]
30
20
-120
Phase [deg]
40
10
0
10
100
1,000
10,000
-180
100,000
-10
-20
-240
Frequency [Hz]
(a) I2= +4 A
60
0
50
-60
30
20
-120
Phase [deg]
Gain [dB]
40
10
0
10
100
1,000
10,000
-180
100,000
-10
-20
-240
Frequency [Hz]
(b) I2= - 4 A
Figure (2-7) Frequency characteristics of Gdv (experimental results, buck-based
type).
For boost-based type, analytical results are shown in Fig. (2-8), and experimental results
are shown in Fig. (2-9). Considering Fig. (2-8) (a) and (b), it is obvious that the frequency
characteristics of Gdv_boost don’t depend on the direction of the current I2 at low frequency.
However, at high frequency, phase plots depend on the direction of the current I2.
25
The
Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter
stability of the circuit is better when direction of the current I2 is negative. Based on Fig.
(2-8) and Fig. (2-9), the frequency characteristics of Gdv_boost for both current directions
match with Eq. (2-9). In other words, the frequency characteristics of Gdv_boost depend on
the direction of current I2.
Phase (deg) Gain (dB)
60
40
20
0
-20
0
-60
-120
-180
-240
10
102
103
Frequency (Hz)
104
(a) I2= +2 A
Phase (deg) Gain (dB)
60
40
20
0
-20
0
-60
-120
-180
-240
10
1
102
103
Frequency (Hz)
104
(a) I2= - 2 A
Figure (2-8) Frequency characteristics of Gdv (analytical results, boost-based type)
26
Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter
Comparing the results of the buck-based type with those of the boost-based type; it is
found that the buck-based type has an advantage over the boost-based type on designing
the controller; since its frequency characteristics don’t depend on current I2.
60
0
50
-60
30
20
-120
Phase [deg]
Gain [dB]
40
10
0
10
100
1,000
10,000
-180
100,000
-10
-20
-240
Frequency [Hz]
(a) I2= +2 A
60
0
50
-60
30
20
-120
Phase [deg]
Gain [dB]
40
10
0
10
100
1,000
10,000
-180
100,000
-10
-20
-240
Frequency [Hz]
(b) I2= - 2 A
Figure (2-9) Frequency characteristics of Gdv (experimental results, boost-based type)
27
Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter
2.5 Transient Response
To investigate the transient characteristics response of the converter; two prototype 100
watts converters are designed based on the proposed seamless model. One of these
converters is buck-based type, while the other is boost-based type. Each converter is
connected, at one side, to a battery, and at the other side, to a bipolar current source. The
current waveform of the bipolar current source, I2, is intentionally designated to have a
stiff change from positive I2 into negative I2. Accordingly, the voltage at the bipolar
current source side V2 is measured. The voltage of the current source is fed back to control
the duty ratio of the switch SM. The open loop transfer function T(s) becomes:
where;
Kp
: Feedback proportional gain
Gc(s)
: Transfer function of compensator
 For the buck-based type:
A compensator is not needed in buck-based type because its phase doesn’t inverse.
Compensator’s transfer function in buck-based type becomes:
1
Proportional gain is designed as Kp_buck = 0.72 [V-1].
28
Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter
The simulated results are shown in Fig. (2-10), while the experimental results are shown in
Fig. (2-11). It is noticed that the experimental results and the simulated results are
conformed. Also, it is clear that the transient change in V2 (when the I2 change from
positive to negative) is the same transient change in V2 (when the I2 change from negative
to positive). This, in turn, confirms that the buck-based type does not depend on the
direction of I2.
Figure (2-10) Transient response characteristics of buck-based type (simulated result).
29
Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter
i2
5 A/div 0
v2_AC
1 V/div
0
Figure (2-11) Transient response characteristics of buck-based type (experimental result,
time: 1ms/div).
 For the boost-based type:
A compensator is needed in boost-based type because its phase inverses when the
direction of I2 is positive. In this circuit, phase lag compensator is used. Compensator’s
transfer function in boost-based type becomes:
1
1
⁄
⁄
where;
ωp = 4.4 krad/s
ωz = 30 rad/s
Proportional gain is designed as Kp_boost = 0.36 [V-1].
30
Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter
The simulated results are shown in Fig. (2-12), while the experimental results are shown in
Fig. (2-13). It is noticed that the experimental results and the simulated results are the
same. Furthermore, it is clear that the transient change in V2 (when the I2 change from
positive to negative) is higher than the transient change in V2 (when the I2 change from
negative to positive). This, in turn, confirms that the boost-based type depends on the
direction of I2.
Figure (2-12) Transient response characteristics of boost-based type (simulated result)
i2
2 A/div
0
v2_AC
1 V/div
0
Figure (2-13) Transient response characteristics of boost-based type (experimental result,
time: 1ms/div)
31
Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter
2.6 Summary
A unified model for bi-directional DC-DC converters for both directions of power flow is
introduced in this chapter. This unified model is a seamless dynamic model in which the
bidirectional DC-DC converter is connected, at one side, to an independent voltage source
and, at the other side, to independent current source. The direction of the power flow is
designated by the polarity of the independent current source. This seamless dynamic
model is applied to two DC-DC converter circuits (buck-based type and boost-based type).
In case of boost-based type, its frequency characteristics depend on the direction of the
current I2. However, in case of buck-based type, its frequency characteristics don’t depend
on the direction of the current I2. A simulated and experimental prototype for both circuits
(buck-based type and boost-based type) are build up based on this seamless dynamic
model, and their results are compered. Both of the simulated and experimental results
support the seamless dynamic model idea and prove its superiority.
32
Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional
Dc-Dc Converter
CHAPTER 3
DC POWER SYSTEMS USING MULTI-LEVEL
VIRTUAL CONDUCTOR BASED A
CONTROLLED BIDIRECTIONAL DC-DC
CONVERTER
3.1
Introduction
Nowadays, bidirectional DC-DC converters (BDCs) have various applications that include
energy storage in renewable-energy systems, fuel cell systems, hybrid-electric vehicles
(HEVs) and uninterruptible power supplies (UPSs) [20][42][46-47][65][84-85]. The
fluctuation nature of most renewable-energy sources, like wind and solar, makes them
unsuitable for standalone operation. A common solution to overcome this problem is to
use an energy storage device besides the renewable-energy resource to compensate these
fluctuations and maintain a smooth and continuous power flow.
As the most common and economical energy storage devices in a medium-power range
are batteries and super-capacitors, a DC-DC converter is usually required to allow energy
exchange between storage device and the rest of the system. Such converters must have
bidirectional power flow capability with flexible control in all operating modes. Moreover,
33
Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional
Dc-Dc Converter
when integrating various renewable-energy sources with numerous voltage levels into a dc
grid, the main challenge is to have an easy plug and play system with a flexible dc power
routing. This system should be capable of integrating such sources at different voltage
levels. To face this challenge, a proposed strategy based on a bidirectional DC-DC
converter is introduced in this chapter.
In this chapter, a bidirectional DC-DC converter is investigated and controlled. It is
considered that both input and output are independent current sources. The current source
may represent a load, electric double layer capacitors (EDLCs), a battery, or even another
bi-directional converter. Therefore, for such converter, it is required to control both
and
to keep the voltage difference between them at a certain value regardless of any
variation that may be occurred to the currents
3.2
and
.
Using a bi-directional DC-DC converter for charging and
discharging of a battery
Figure (3-1) illustrates an example of a smart house integrates a renewable-energy source
(PV) and a storage battery. The PV is connected to the load via a maximum point power
tracker (MPPT) and a unidirectional DC-DC converter. While, the battery is connected to
the load via bidirectional DC-DC converter; since the power flow between the battery and
the load is required to be bidirectional (charge/discharge). The coupling point Voltage, VN,
is controlled based on VRef-N.
34
Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional
Dc-Dc Converter
V PV I PV
Source
I S-PV
Unidirectional
DC-DC
Converter
PV
D
MPPT
VN
Battery
VB
Bi-dirictional
DC-DC
Converter
D sa =1-D sb
Load
C
IL
VRef-N
Figure (3-1) Using a bi-directional DC-DC converter for charging
and discharging of a battery.
3.3
Dc power system using the proposed bi-directional DC-DC converter
(The virtual conductor)
Regarding the aforementioned example in Fig. (3-1), for the sake of having a flexible dc
power system; it should be easy to integrate different multi-level voltage sources and loads
together. In other words, the coupling point is required to be a multi-level voltages point.
The bidirectional DC-DC converter, with the proposed control strategy, can play the role
of a multi-level voltage coupling point as shown in Fig. (3-2). In this case, the
bidirectional DC-DC converter is called a multi-level virtual conductor.
35
Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional
Dc-Dc Converter
V PV I PV
Source
I S-PV
Unidirectional
DC-DC
converter
PV
WT
MPPT included
D
MPPT
I S-WT
V1
Load
I L1
C1
V2
Bidirectional
DC-DC
converter
Source
I L2
C2
D sa =1-D sb
V 1 VRef-1
V 2 VRef-2
VRef-1
VRef-2
Battery
Bidirectional
DC-DC
converter
VB
D’ sa=1-D’ sb
C
VRef-N
Figure (3-2) The proposed bidirectional DC-DC converter as a multi-level
voltage coupling point.
3.4
Implementation of the virtual conductor using a bi-directional DC-
DC converter
The proposed control strategy for a bidirectional DC-DC is shown in Fig. (3-3).The main
target of this control strategy is to keep the voltage difference between the converter
terminals constant at a certain value. V1 and V2 are adjusted according to VRef-1 and VRef-2
36
Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional
Dc-Dc Converter
respectively. Therefore, the duty ratios
and
of the converter are adjusted to the
desired value when (V1-V2) = (VRef-1-VRef-2). Since VRef-1 and VRef-2 are constant values; then
the difference between V1 and V2 is kept constant at the steady state. For the former
example in Fig. (3-1), there was only one coupling point (VN), but with this proposed
strategy; there are two coupling points V1 and V2.
V1
Source/load
I1
C1
V2
Bidirectional
DC-DC
converter
Source/load
C2
I2
D sa =1-D sb
V 1 VRef-1
V 2 VRef-2
VRef-1
VRef-2
Figure (3-3) Implementation of multi-level virtual conductor using a bidirectional DC-DC converter.
3.5
Configuration examples and features of the virtual conductor in dc
power system
The virtual conductor allows a flexible power transfer through an energy system having
multiple energy sources with different voltage levels, energy storage equipment, and
loads. Factually, it is impossible to use a conductor to connect such an energy system;
however, a virtual conductor, having the voltage conversion function of a bidirectional
DC-DC converter, can be used.
37
Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional
Dc-Dc Converter
The configuration examples of the virtual conductor in dc power system are shown in Fig.
(3-4). The series connection is presented in Fig. (3-4) (a), while the branch connection at a
central node is revealed in Fig. (3-4) (b), and Fig. (3-4) (c) shows a loop connection. A
further complex connection, grid connection, is shown in Fig (3-4) (d). One practical
application of these aforementioned connections can be used in a smart house that
integrates different loads and voltages sources together; as shown in Fig. (3-5). Another
practical application can be used in an electrical vehicles (EV) charger substation; as
shown in Fig. (3-6).The features of a dc power system using virtual conductors can be
VN2
C
/D
DC
Load
PV
System
Battery
Bank
VN3
Battery
Bank
DC
VN3
Load
Load
(a)
PV
System
VN2
VN4
C
/D
DC
/D
C
WT
System
WT
System
/DC
Series connection.
VN5
DC
VN1
C/
D
VN1
DC
PV
System
C
WT
System
D
PV
System
D
C/
D
/DC
Load
C
VN4
Battery
Bank
Load
(b) Regdial conection at central node.
38
Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional
Dc-Dc Converter
PV
System
WT
System
VN1
Load/
source
VN2
DC/DC
V1
V3
Bidirection
al DC-DC
converter
Load/
source
DC
C
/D
/D
C
DC
Battery
Bank
Load/
source
Bidirection
al DC-DC
converter
Bidirection
al DC-DC
converter
I1
Load
V2
Bidirection
al DC-DC
converter
Bidirection
al DC-DC
converter
I3
I2
Bidirection
al DC-DC
converter
Bidirection
al DC-DC
converter
VN3
Load
Load/
source
Battery
Bank
V4
Bidirection
al DC-DC
converter
I4
(c) Loop connection.
Load/
source
V5
I5
(d) Grid connection
Figure (3-4) The configuration examples of the multi-level virtual conductor in dc power
system.
summarized as following:
1- It is possible to have different voltage levels (VN1, VN2 …etc. in Fig. (3-4)).
2- By using the isolated bidirectional DC-DC converter topologies; a galvanic isolation
among nodes can be achieved.
3- The virtual conductor allows an easy plug and play of the equipment that is
connected to the dc power system; hence the dc power system becomes flexible and
reconfigurable.
4- If there is a fault or an accident occurs in one branch or at any node, it is easy to
clear this fault by stopping the operation of the related bidirectional DC-DC
converter.
39
Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional
Dc-Dc Converter
5- Regarding Fig. (3-4) (c), even if there is a fault in one branch, the power will be
transferred via the other branch, and this increases the reliability of the dc power
system.
Figure (3-5) Smart house integrates different voltage sources and loads
Figure (3-6) Electrical vehicles charger substation
3.6
The proposed bi-directional DC-DC circuit configuration
The proposed bi-directional DC-DC circuit configuration is shown in Fig. (3-7). It
employs a DC-DC converter to connect two different Load/supply units. The voltage
difference between the converter sides is controlled by the duty ratio of the main switch (
40
Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional
Dc-Dc Converter
) and of the synchronously switch (
and
, have
components:
internal resistances,
,
). The two bidirectional dc current sources,
and
, consequently.
and . Inductor parasitic resistance
There are three storage
and MOSFET turn-on resistance
are included in the model. The transfer function for this converter has been driven based
on the state space averaging method [95-99]. Considering the state space vector ( )
( )
( )
( ) , and the input vector
; the state space averaged dc
model is shown in (1):
L
vL
V1 Sa
rL V
2
rs
0
I1
ri
ic1
C1
vc1
i c2
iL
Sb
ro
C 2 v c2
rs
I2 0
Figure (3-7) Circuit configuration of the proposed bi-directional DC-DC
converter.
[ ]
[ ]
(3-1)
where;
[
,
[
]
]
By solving (3-1), the following expressions are resulted:
41
Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional
Dc-Dc Converter
(3-2)
(
)
(
(3-3)
)
(
)
(3-4)
The state-space averaged ac model is shown in (3-5).
̂
|̂ |
̂
̂
|̂ |
̂
| | ̂
(3-5)
where,
[
,
[
]
]
By solving (3-5), the following equations (3-6)-(3-8) are obtained:
̂
̂
̂
̂
(3-6)
̂
̂
̂
̂
(
̂
̂
(
)(
(3-7)
)(
)(
)
(
)
(
)
) (
)
Using (3-6)-(3-8), the control-to-voltage difference transfer function
42
(3-8)
( ) can be
Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional
Dc-Dc Converter
̂
obtained as in (3-9), where
( )
̂
̂
̂
[
(
)
̂
(
̂ .
)
]
̂
̂
(
)
(3-9)
For the sake of the model verification, the frequency characteristics for the control-to( ) are analytical and experimentally
voltage difference transfer function
Figure (3-8) The frequency characteristics for
( ) (analytical results)
investigated. Figure (3-8) shows the analytical results, however Fig. (3-9) presents the
43
Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional
Dc-Dc Converter
experimental results. To obtain the frequency characteristics for
( ), the following
parameters are considered:
,
,
,
Figure (3-9)The frequency characteristics for
3.7
,
,
( ) (experimental results)
Transient response
To investigate the transient characteristics response of the virtual conductor; two 100 watt
converters are designed. The transient response investigation for complex systems, such as
the configuration examples in Fig. (3-4), can be extended in the future work. A prototype
dc power system using the virtual conductor is shown in Fig. (3-10). The virtual conductor
44
Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional
Dc-Dc Converter
is connected at its one end to a bi-polar current source (load/ source), and at the other end
to another bi-polar current source and a battery via bidirectional converter. The circuit
parameters are shown in Table (3-1).
These parameters have been used for both
simulation and experimental results. Three cases have been studied:
1- Case (a): when currents of the bipolar current sources I1=+2 A, I2=+4 A.
2- Case (b): when currents of the bipolar current sources I1=-2 A, I2=-4 A.
3- Case (c): when current waveforms of the bipolar current sources (I1, I2) are
intentionally designated to have a stiff change from positive values of (I1, I2) into
negative values of (I1, I2) to investigate the bidirectional power flow through the
virtual conductor. Accordingly, voltages at the bipolar current sources sides (V1, V2)
are measured.
The simulation results for case (a), case (b) and case (c) are shown in Fig. (3-11), Fig. (312) and Fig. (3-13), respectively. However, the experimental results case (a), case (b) and
case (c) are shown in Fig. (3-14), Fig. (3-15) and Fig. (3-16), respectively.
From these results, it is obvious that the voltage deference between V1 and V2 is kept
constant (12 V) regardless of the change in polarities of currents and powers. In other
words the virtual conductor has successfully allowed the power to be transferred in both
directions between two nodes with a voltage difference in between them.
45
Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional
Dc-Dc Converter
The Multi-level virtual conductor
Bidirectional DC-DC converter
Battery
C L Bidirectional
VB
V2
V1
IB
DC-DC
converter
Bi-polar Source/load
Module
C1
CM
I1
D sa =1-D sb
Bidirectional
DC-DC
converter
Bi-polar Source/load
Module
C2
I2
D sa =1-D sb
V 1 VRef-1
VRef-1
V 2 VRef-2
VRef-2
Figure (3-10): The simulation circuit for a multi-level virtual conductor connected to
two bi-polar current sources and a battery
TABLE(3-1) The Circuit Parameters
Symbol
VB
V1
V2
L1
L2
CL
CM
C1
C2
F
Description
Battery voltage
Voltage at node 1
Voltage at node 2
Inductance of the first converter
Inductance of the virtual conductor
Capacitance at the input of the
bidirectional DC-DC converter
Capacitance at the output of the
bidirectional DC-DC converter
Capacitance at the input of the multi-level
virtual conductor
Capacitance at the output of the multilevel virtual conductor
Switching frequency
46
Value
48 V
24 V
12 V
120µH
80 µH
100 µF
200 µF
330 µF
100 µF
100 kHz
Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional
Dc-Dc Converter
Figure (3-11): Simulation results case (a).
47
Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional
Dc-Dc Converter
Figure (3-12): Simulation results case (b).
48
Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional
Dc-Dc Converter
Figure (3-13): Simulation results case (c).
49
Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional
Dc-Dc Converter
Figure (3-14): Experimental results case (a).
50
Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional
Dc-Dc Converter
Figure (3-15): Experimental results case (b).
51
Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional
Dc-Dc Converter
Figure (3-16): Experimental results case (c).
52
Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional
Dc-Dc Converter
3.8
Summary
This chapter proposes a new bidirectional control strategy that leads to a performance of a
virtual conductor. This virtual conductor is considered a base to power routing in dc
networks. It allows an easy plug-and-play feature. This means that any terminal unit
(load/source) can be safely and effectively connected / disconnected at its suitable voltage
level. The basic idea is presented, an average model contains the bidirectional current
sources in both sides is developed, and a representative case study is addressed by
simulation and experiment, as well. Both of simulated and experimental results support the
basic idea and prove its superiority.
53
Chapter 4: A New Stability Assessment Criterion for DC Power Systems with Multi-level Virtual
Conductors
CHAPTER 4
A New Stability Assessment Criterion for DC Power
Systems with Multi-level Virtual Conductors
4.1
Introduction
One of the problems for a DC distribution is the potential stability degradation due to
interactions among converters connected to a common bus [100-102]. Typically, when
tightly regulated, converters behave at their input terminals as constant power loads
(CPLs) within their control loop bandwidth [100-102]. CPLs create the so-called negative
incremental input impedance, which is the cause of the subsystem interaction problem and
origin of the undesired destabilizing effect [101].
The conventional criteria for stability assessment; such as Nyquist criteria and bode
diagram are convenient for a single converter model, but in case of a system contains
many BDCs connected together with loads and sources. For example, the configuration
examples of a multi-level virtual conductor (MLVC) in dc power systems that shown in Fig.
(3-4). For these dc power system configurations with various voltage sources, loads, and
BDCs connected together, it is so difficult to assess the stability by the conventional
method. Therefore, this chapter introduces a new criterion suits such complex dc power
54
Chapter 4: A New Stability Assessment Criterion for DC Power Systems with Multi-level Virtual
Conductors
systems. This criterion is called node impedance criterion. Mathematical analysis,
experimental analysis and the concept of node impedance criterion are presented.
Simulation and experimental results for this criterion are compared with those of the
conventional criterion to show its validity. Ultimately, an experimental setup has been
implemented for a dc power system, and the node impedance criterion is applied to this dc
power system to judge its stability.
Analysis of Bidirectional DC-DC Converter
4.2
Analytical model of bi-directional converter is shown in Fig. (4-1). Seamless model of
bi-directional converter is derived by state-space averaging method [103-104].
4.2.1 Small Signal model
Considering the averaged state-space vector ̅
[
] , and the output variable
[̅
̅
] , the input vector
, small signal model are derived as shown in
(4-1).
(4-1)
where;
|
{
}[ ]
(4-2)
|
{
}[ ]
(4-3)
55
Chapter 4: A New Stability Assessment Criterion for DC Power Systems with Multi-level Virtual
Conductors
|
(4-4)
The block diagram of bi-directional converter including feedback loop is shown in Fig. (42). The voltage of current source
is fed back to the duty ratio
. Loop gain
becomes:
(4-5)
where;
: PWM gain
: Gain of compensator
From (4-1) and (4-5), the equivalent inside impedance of bi-directional DC-DC converter
is obtained as shown in (4-6).
d
1
2
iL
v2
vC
V1
2' I2 >
<0
1'
Figure (4-1). Analytical model of bi-directional DC-DC converter.
56
Chapter 4: A New Stability Assessment Criterion for DC Power Systems with Multi-level Virtual
Conductors
controller
d
1
2
v2
BDC
V1
1'
Z2
>0
I2=IN<
2'
Figure (4-2). The block diagram of seamless model of bi-directional DC-DC
Converter.
controller
1
d
2 I2
C→∞
Battery
v2
BDC
V1
1'
ZL
2'
>0
IN<
Load/source module
Figure (4-3). The seamless model considering AC impedance of load/source
modules.
|
(6)
4.2.2 Small Signal Model considering AC Impedance of Load/Source Modules
In the real system, load/source modules have AC impedance, as shown in Fig. (4-3).
These impedances affect characteristics of the bi-directional DC-DC converter.
Accordingly, the seamless model can be extended to convey the effect of these impedances
57
Chapter 4: A New Stability Assessment Criterion for DC Power Systems with Multi-level Virtual
Conductors
as shown in Fig. (4-4). Considering an AC impedance
of load/source modules, the
transfer function becomes;
(4-7)
In this case, the loop gain,
, of the block diagram, shown in Fig. (4-4), can be
rewritten as follows:
(4-8)
ΔI2
1/ZL(s)
Gvio(s)
ΔV1
Gvvo(s)
+
ΔV2
+
+
Gvdo(s)
ΔD
TL
Controller
PWM
= -Z2(s)
Gc(s)
Figure (4-4). The block diagram of seamless model considering AC impedance of
load/source modules.
Therefore, the characteristic equation can be written as in (4-9).
(4-9)
58
Chapter 4: A New Stability Assessment Criterion for DC Power Systems with Multi-level Virtual
Conductors
Using (4-6) and (4-8) ; the characteristic equation can be written as follows:
(4-10)
4.3
Node impedance and system stability
The node impedance concept can be obviously illustrated using Fig. (4-5). Regarding the
configuration in this figure, when small current
small change in the voltage
is injected into the node; it will cause
. Hence, node impedance
can be calculated as
follows:
(4-11)
From the block diagram of the node impedance
in Fig. (4-6); the following equation
can be expressed.
(4-12)
When,
is an input and
is considered output; therefore the characteristic equation is:
(4-13)
According to Nyquist criterion of stability, when the locus plot of the open loop transfer
function
passes in the right side than the point (-1) in the complex plan, the system is
stable. In other words, it is possible to have information about the system stability from the
59
Chapter 4: A New Stability Assessment Criterion for DC Power Systems with Multi-level Virtual
Conductors
frequency characteristics of
the node impedance
use
. Considering (4-10) and (4-13), the loop gain
and
have the same characteristic equation. Therefore, it is possible to
as a stability criterion. Based on (4-12), the larger is the value of
the system to instability and vice versa.
Z2
I
2 2
C→∞
v2
V2
2'
BDC
ZL
>0
IN <
Load/source
module
ZN
ΔIt
Test signal
Figure (4-5). Measurement method of the node impedance.
ΔIt(s)
-
+
ΔI2
1/ZL(s)
=ZN(s)
ΔV2(s)
-Z2(s)
Figure (4-6). The block diagram of the node impedance.
60
; the closer is
Chapter 4: A New Stability Assessment Criterion for DC Power Systems with Multi-level Virtual
Conductors
4.4
Numerical analysis and application example
4.4.1 Numerical analysis
The circuit to be analyzed is shown in Fig. (4-7). The numerical analysis is done based on
these parameters. It should be noted that, in this analysis, the impedance ZL (s) of the
connected device is:
(4-14)
For stabilization of the circuit the lead-lag compensator is chosen as follows:
(4-15)
where,
K = 0.0656, ωp1= 417 rad/s , ωz1= 64.9 rad/s, ωp2= 3.44 krad/s and ωz2= 37.9
krad/s.
Figure (4-8) shows the frequency characteristics for the loop gain
studied: (a)
A, and at
. Two cases are
A. The gain margin and the phase margin of
case (a) are 11dB, 47.3 deg, respectively, and for case (b) are inf. dB, 105 deg,
respectively. Results of
(a) in
is shown in Fig. (4-9). It is clear that
) is bigger than that for
(case (b) in
). Hence,
for
(case
conveys similar
information for stability like the conventional one. Consequently, it is possible to use
as stability criterion for dc power systems.
61
Chapter 4: A New Stability Assessment Criterion for DC Power Systems with Multi-level Virtual
Conductors
4.4.2 Application example
Node impedance criterion is applied to a dc power system using a multi-level virtual
conductor (MLVC), as shown in Fig. (4-10), at node (V1). The MLVC is connected at its
one end to a bi-polar current source (load/ source), and at the other end to another bi-polar
current source and a battery via bidirectional converter. The circuit parameters are shown
in Table (4-1). The simulation results for this node are shown in Fig. (4-11). Moreover, the
experimental results, for the same node, are shown in Fig. (4-12). Based on these results
together with applying the
criterion; the system is stable at this node.
d
1
iL
SS
(rL) L
2
(rS) (rc)
(rS)
V1
controller
SM
1'
C→∞
C
vc v2
ZL
2'
Figure (4-7). The bi-directional DC-DC converter to be analyzed.
62
IN
Chapter 4: A New Stability Assessment Criterion for DC Power Systems with Multi-level Virtual
Conductors
40
180
180
Gain
Gain
Phase
90
0
0
-20
-40
1
10
100
1000
Frequency [Hz]
20
90
0
0
Gain [dB]
20
Phase [deg]
Gain [dB]
Phase
-90
-20
-180
-40
10000
Phase [deg]
40
-90
-180
1
10
100
1000
Frequency [Hz]
(a) IN= + 2A
10000
(b) IN= - 2A
0.2
0.2
0.1
0.1
Im [Ω]
Im [Ω]
Figure (4-8). The frequency characteristics of the loop gain TL.
0
-0.1
0
-0.1
-0.2
0
0.1
0.2
0.3
0.4
-0.2
0.5
0
Re [Ω]
0.1
0.2
0.3
Re [Ω]
(a) IN= + 2A
(a) IN= -2A
Figure (4-9). ZN is expressed in the complex plane.
63
0.4
0.5
Chapter 4: A New Stability Assessment Criterion for DC Power Systems with Multi-level Virtual
Conductors
The Multi-level virtual conductor
Bi-polar Source/load
Module
Battery
C 1 Bidirectional
VB
V2
V1
IB
DC-DC
converter
C2
C3
I1
D sa =1-D sb
Bidirectional
DC-DC
converter
C4
Bi-polar Source/load
Module
I2
D sa =1-D sb
V 1 VRef-1
V 2 VRef-2
VRef-1
VRef-2
Figure (4-10). The Dc power supply using MLVC.
Table (4-1) The simulation and the experimental circuit parameters
Symbol
Description
Value
VB
Battery voltage
48 V
V1
Voltage at node 1
24 V
V2
Voltage at node 2
12 V
L1
Inductance of the first
converter
120µH
L2
Inductance of the virtual
conductor
80 µH
C1
capacitance
100 µF
C2
capacitance
200 µF
C3
capacitance
330 µF
C4
capacitance
100 µF
F
Switching frequency
100 kHz
64
Chapter 4: A New Stability Assessment Criterion for DC Power Systems with Multi-level Virtual
Conductors
0
100
amp (Zn)
-5
Phase (Zn)
80
-10
60
-15
40
-20
20
-25
0
-30
-20
-35
-40
-40
-60
-45
-80
-50
-100
100
1000
10000
100000
Frequency [Hz]
Figure (4-11). Application of ZN to dc power system to assess its stability
(Analytical).
Figure (4-12). Application of ZN to dc power system to assess its stability (Experimental).
65
Chapter 4: A New Stability Assessment Criterion for DC Power Systems with Multi-level Virtual
Conductors
A stability investigation, based on the node impedance criterion; for complex systems,
such as connection examples in Fig. (3-4), can be extended in the future work.
4.5
Summary
A new criterion for stability assessment in dc power system is presented in this chapter.
This criterion is node impedance criterion. The concept, mathematical, simulation, and
experimental analysis of node impedance criterion, are investigated, as well. The results of
node impedance criterion are compared with those of the conventional criterion. The
comparison shows the validity of node impedance as a stability criterion. Moreover, node
impedance criterion is applied to a dc power system using a MLVC to assess it stability.
66
Chapter 5 Conclusions and Future Work
CHAPTER 5
CONCLUSIONS AND FUTURE WORK
5.1
Conclusions
This work studies the bidirectional DC-DC converter as a paramount component
for dc power routing in dc power systems that integrate various renewable energy
sources, energy storages and loads at different voltage levels. Following are the
most important conclusions that come out from this work:
 A unified model for bi-directional DC-DC converters for both directions of
power flow is introduced in this thesis. This unified model is a seamless
dynamic model in which the bidirectional DC-DC converter is connected, at
one side, to an independent voltage source and, at the other side, to
independent current source. The direction of the power flow is designated by
the polarity of the independent current source. This seamless dynamic model
is applied to two DC-DC converter circuits (buck-based type and boostbased type).
 In case of boost-based type, its frequency characteristics depend on the
direction of the current I2. However, in case of buck-based type, its frequency
characteristics don’t depend on the direction of the current I2. A simulated
67
Chapter 5 Conclusions and Future Work
and experimental prototype for both circuits (buck-based type and boostbased type) are build up based on this seamless dynamic model, and their
results are compered. Both of the simulated and experimental results support
the seamless dynamic model idea and prove its superiority.
 A new bidirectional control strategy lead to a performance of a multi-level
virtual conductor is introduced, as well. This virtual conductor is considered
a base to power routing in dc networks. It allows an easy plug-and-play
feature. This means that any terminal unit (load/source) can be safely and
effectively connected / disconnected at its suitable voltage level. The basic
idea is presented, an average model contains the bidirectional current
sources in both sides is developed, and a representative case study is
addressed by simulation and experiment, as well. Both of simulated and
experimental results support the basic idea and prove its superiority.
 A new criterion for the stability assessment in dc power system is presented.
This criterion is the node impedance criterion. The concept, mathematical,
simulation, and experimental analysis of the node impedance criterion, are
investigated. The results of the node impedance criterion are compared with
those of the conventional criterion. The comparison shows the validity of the
node impedance as a stability criterion. Moreover, the node impedance
criterion is applied to a dc power system using a MLVC to assess it stability.
68
Chapter 5 Conclusions and Future Work
5.2
Future work
 Study and investigate the power management issue and the dc power routing
for a dc micro-grid that uses huge number of multi-level virtual conductors.
 Applying the multi-level virtual conductors to different contemporary
applications such as, smart houses and an electric vehicles charger substation
based renewable energy sources.
 Developing and applying the node impedance criterion of stability to assess
the stability of complex systems that connect many multi-level virtual
conductors together.
69
References
REFERENCES
[1]
J. S. Lai and D. J. Nelson, “Energy management power converters in hybrid
electric and fuel cell vehicles,” in Proc. IEEE Ind. Electron., Taipei,
Taiwan, Volume 95, Issue 4, April 2007, pp. 766 – 777.
[2]
H. Tao, A. Kotsopoulos, J.L. Duarte, and M.A.M. Hendrix, “Multi-input
bidirectional dc-dc converter combining dc-link and magnetic-coupling for
fuel cell systems,” in Proc. IEEE IAS, Hong Kong, China, Volume 3, Oct.
2005, pp. 2021 –2028.
[3]
H. Tao, J. L. Duarte, and M. A. M. Hendrix, “High-power three-port threephase bidirectional dc-dc converter,” in Proc. IEEE IAS, Manchester, UK,
Sept. 2007, pp.2022 – 2029.
[4]
H. J. Chiu, H.-M. Huang, L.-W. Lin, and M.-H. Tseng, “A multiple-input
dc/dc converter for renewable energy systems,” in Proc. IEEE ICIT, Hong
Kong, China, Dec. 2005, pp. 1304 – 1308.
[5]
G.-J. Su, J. P. Cunningham, and L. Tang, “A Reduced-part, triple-voltage
dc-dc converter for electric vehicle power management,” in Proc. IEEE
PESC, Orlando, FL, June 2007, pp. 1989 – 1994.
[6]
T. Mishima, E. Hiraki, T. Tanaka, and M. Nakaoka, “A new soft-switched
bidirectional dc-dc converter topology for automotive high voltage dc Bus
70
References
architectures,” in Conf. Rec. of IEEE VPPC, Windsor, UK, Sept. 2006, pp.
1 – 6.
[7]
H. Matsuo, W. Lin, F. Kurokawa, T. Shigemizu, and N. Watanabe,
“Characteristics of the multiple-input dc-dc converter,” IEEE Trans. Ind.
Electron., Vol.51, No.3, June 2004, pp. 625-630.
[8]
Y. Hu, J. Tatler, and Z. Chen, “A bidirectional dc-dc power electronic
converter for an energy storage device in an autonomous power system,” in
Proc. IEEE IPEMC, Xi’an, China, Volume 1, August 2004, pp. 171 – 176.
[9]
J. L. Duarte, M. Hendrix, and M. G. Simoes, “Three-port bidirectional
converter for hybrid fuel cell systems,” IEEE Trans. Power Electron.,
March 2007, pp. 480-487.
[10] H. Matsuo and F. Kurokawa, “New solar cell power supply system using a
Boost type bidirectional dc-dc converter,” IEEE Trans. Ind. Electron.,
Volume IE-31, Issue1, Feb. 1984, pp. 51 – 55.
[11] H. J. Chiu and L.-W. Lin, “A bidirectional dc-dc converter for fuel cell
electric vehicle driving system,” IEEE Trans. Power Electron., Volume 21,
Issue 4, July 2006, pp. 950 – 958.
[12] G. Chen, D. Xu, and Y.-S. Lee, “A family of soft-switching phase-shift
bidirectional dc-dc converters: synthesis, analysis, and experiment,” in Proc.
71
References
the Power Conversion Conference, Osaka, Japan, Volume 1, 2-5 April 2002,
pp. 122 – 127.
[13] G. Chen, D. Xu, Y. Wang, Y.-S. Lee, “A new family of soft-switching
phase-shift bidirectional dc-dc converters,” in Proc. IEEE PESC,
Vancouver, British Columbia, Canada, Volume 2, June 2001, pp. 859 – 865.
[14] H. Fan, D. Xu, “A family of PWM plus phase-shift bidirectional dc-dc
converters,” in Proc. IEEE PESC, Aachen, Germany, Volume 2, 20-25
June 2004, pp. 1668 –1674.
[15] K. Y. Lee and Y.-S. Lai, “A novel magnetic-less bi-directional dc-dc
converter,” in Proc. IEEE IECON, Busan, Korea, Volume 2, 2-6 Nov. 2004,
pp. 1014 – 1017.
[16] Y. S. Lee and Y.-Y. Chiu, “Zero-current-switching switched-capacitor
bidirectional dc-dc converter,” in Conf. Rec. of IEE Electric Power
Applications, Volume 152, Issue 6, 4 Nov. 2005, pp. 1525 – 1530.
[17] I. D. Kim, S.-H. Paeng, J.-W. Ahn, E.-C. Nho, and J.-S. Ko, “New
bidirectional ZVS PWM Sepic/Zeta dc-dc converter,” in Proc. IEEE ISIE,
Vigo, Spain, June 2007, pp. 555 – 560.
[18] F. Caricchi, F. Crescimbini, F.G. Capponi, and L. Solero, “Study of bidirectional buck-boost converter topologies for application in electrical
72
References
vehicle motor drives”, in Proc. IEEE APEC, Anaheim, CA, Volume 1, 1519 Feb. 1998, pp. 287 – 293.
[19] F. Z. Peng, H. Li, G.-J. Su, and J.S. Lawler, “A new ZVS bidirectional dcdc converter for fuel cell and battery application,” IEEE Trans. Power
Electron.,Volume 19, Issue 1, Jan. 2004, pp. 54 – 65.
[20] P. Jose, N. Mohan, “A Novel Bidirectional DC-DC Converter with ZVS
and interleaving for Dual Voltage Systems in Automobiles,” in Conf. Rec.
of IEEE IAS Annual Meeting, Oct. 2002, pp. 1311–1314.
[21] F. Z. Peng, F. Zhang, and Z. Qian, “A magnetic-less dc-dc converter for
dual voltage automotive systems,” IEEE Trans. Ind. Appl., Volume 39,
Issue 2, March-April 2003, pp. 511 – 518.
[22]
O. Garcia, P. Zumel, A. de Castro, and A. Cobos, “Automotive dc-dc
bidirectional converter made with many interleaved buck stages,” IEEE
Trans. Power Electron.,Volume 21, Issue 3, May 2006, pp. 578 – 586.
[23]
M. Santhi, R. Rajaram, and I.G.C. Raj, “A ZVCS lc-resonant push-pull
power converter circuit for battery-fuel cell hybrid systems,” in Conf. Rec.
of IEEE Conference on Electric and Hybrid Vehicles, Pune, India, Dec.
2006, pp. 1 – 6.
[24] M. Cacciato, F. Caricchi, F. Giuhlii, and E. Santini, “A critical evaluation
and design of bi-directional dc-dc converters for super-capacitors
73
References
interfacing in fuel cell applications,” in Proc. IEEE Industry Applications,
Seattle, Washington, Volume 2, 3-7 Oct. 2004, pp. 1127 – 1133.
[25] K. Yamamoto, E. Hiraki, T. Tanaka, M. Nakaoka, and T. Mishima,
“Bidirectional dc-dc converter with full-bridge/push-pull circuit for
automobile electric power systems,” in Proc. IEEE PESC, Jeju, South
Korea, June 2006, pp. 1 – 5.
[26] C. Qiao and K.M. Smedley, “An isolated full bridge boost converter with
active soft switching,” in Proc. IEEE PESC, Vancouver, British Columbia,
Canada, Volume 2, June, 2001, pp. 896 – 903.
[27] E. Hiraki, K. Yamamoto, T. Tanaka, T. Mishima, and M. Nakaoka, “An
isolated bidirectional dc-dc converter based super-capacitor interface for
automobile electric power systems,” in Conf. Rec. of International Power
Electronics and Motion Control Conference, Shanghai, China, Aug. 2006,
pp. 722 – 727.
[28] F. A. Himmelstoss, “Analysis and comparison of half-bridge bidirectional
dc-dc converters,” in Proc. IEEE PESC, Taipei, Taiwan, 20-25 June 1994,
pp. 922 – 928.
[29] S. Inoue and H. Akagi, “A Bidirectional dc–dc Converter for an energy
storage system with galvanic isolation,” IEEE Trans. Power Electron.,
Volume 22, Issue 6, Nov. 2007, pp. 2299 – 2306.
74
References
[30] R. Li, A. Pottharst, N. Frohleke, and J. Bocker, “Analysis and design of
improved isolated full-bridge bidirectional dc-dc converter,” in Proc. IEEE
PESC, Aachen, Germany, Volume 1, 20-25 June 2004, pp. 521 – 526.
[31] H. Li, D. Liu, F.Z. Peng, and G.-J. Su, “Small signal analysis of a dual half
bridge isolated ZVS bi-directional dc-dc converter for electrical vehicle
applications,” in Proc. IEEE PESC, Recife, Brazil, 16-16 June 2005, pp.
2777 – 2782.
[32] M.
N.
Kheraluwala,
R.W.
Gascoigne,
D.M.
Divan,
and
E.D.
Baumann,“Performance characterization of a high-power dual active bridge
dc-to-dc converter,” IEEE Trans. Ind. Appl., Volume 28, Issue 6, Nov.-Dec.
1992, pp. 1294– 1301.
[33] G. K. Schoneman, “500-W zero-voltage-switched full-bridge two-quadrant
power modulator,” in Proc. IEEE APEC, 7-11 March 1993, pp. 700 – 706.
[34] A. A. Aboulnaga and A. Emadi, “Performance evaluation of the isolated
bidirectional Cuk converter with integrated magnetics,” in Proc. IEEE
PESC, Aachen, Germany, Volume 2, 20-25 June 2004, pp. 1557 – 1562.
[35] Z. Salam, M.Z. Ramli, L.S. Toh, and C.L. Nge, “An isolated bidirectional
inverter using high frequency center-tapped transformer,” in Conf. Rec. of
Second International Conference on Power Electronics, Machines and
75
References
Drives, Volume 2, University of Edinburgh, 31 March-2 April 2004, pp.
644 – 649.
[36] F. Krismer, J. Biela, and J.W. Kolar, “A comparative evaluation of isolated
bidirectional dc/dc converters with wide input and output voltage range,” in
Proc. IEEE IAS, Atlanta, GA, Volume 1, 2-6 Oct. 2005, pp. 599 – 606.
[37] D. Aggeler, J. Biela, S. Inoue, H. Akag, and J. W. Kolar, “Bi-directional
isolated dc-dc converter for next-generation power distribution comparison of converters using Si and SiC devices,” in Proc. IEEE PCC,
Nagoya, Japan, April 2007, pp. 510 – 517.
[38]
J. Zhang, J.-S. Lai, R.-Y. Kim and W. Yu, “High-power density design of a
soft switching high-power bidirectional dc–dc converter,” IEEE Trans.
Power Electron., Volume 22, Issue 4, July 2007, pp. 1145 – 1153.
[39] G. Chen, D. Xu, and Y.-S. Lee “A novel fully zero-voltage-switching
phase-shift bidirectional dc-dc converter,” in Proc. IEEE APEC, Anaheim,
CA, Volume 2, March, 2001, pp. 974 – 979.
[40] H. Xu, X. Wen, E. Qiao, X. Guo, and L. Kong, “High power interleaved
boost converter in fuel cell hybrid electric vehicle,” in Proc. IEEE IEMDC,
San Antonio, TX, May 2005, pp. 1814–1819.
[41] X. Huang, X. Wang, T. Nergaard, J. S. Lai, X. Xu, and L. Zhu, “Parasitic
ringing and design issues of digitally controlled high power interleaved
76
References
boost converters,’’ IEEE Trans. Power Electron., vol. 19, no. 5, Sep. 2004,
pp.1341–1352.
[42] D. P. Urciuoli and C.W. Tipton, “Development of a 90 kW bi-directional
dc–dc converter for power dense applications,” in Proc. IEEE APEC,
Dallas, TX, Mar. 2006, pp. 1375–1378.
[43] S. J. Kim “Modeling and analysis of spacecraft battery charger systems,”
Ph.D. Dissertation, VPI&SU, 1991.
[44] D. M. Sable, “Optimization of space craft battery charger/discharger
systems,” Ph.D. Dissertation, VPI&SU, 1991.
[45] F. Caricchi, F. Crescimbini, G. Noia, and D. Pirolo, “Experimental study of
a bidirectional dc-dc converter for the dc link voltage control and the
regenerative braking in PM motor drives devoted to electrical vehicles ,” in
Proc. IEEE APEC, Orlando, FL, Feb. 1994, pp. 381 – 386.
[46] K. Asano, Y. Inaguma, H. Ohtani, E. Sato, M. Okamua, and S.
Sasaki, ”High performance motor drive technologies for hybrid vehicles,”
in Proc. of PCC, Nogoya, Japan, April 2007, pp. 1584-1589.
[47] S. Aso, M. Kizaki, and Y. Nonobe, “Development of fuel cell hybrid
vehicles in Toyota,” in Proc. of PCC, Nogoya, Japan, April 2007, pp. 16061611.
77
References
[48] M. Jain, P.K. Jain, and M. Daniele, “Analysis of a bi-directional dc-dc
converter topology for low power application,” in Conf. Rec. of IEEE 1997
Canadian Conference on Electrical and Computer Engineering, St. John’s,
NF, Volume 2, 25-28 May 1997, pp. 548 – 551.
[49] R.W. De Doncker, D.M. Divan, and M.H. Kheraluwala, “A three-phase soft
switched high power density dc-to-dc converter for high power
applications,” IEEE Tran. Ind. Appl., Vol. 27, No. 1, Jan. 1991, pp.63-73.
[50] M.H. Kheraluwala, and D.M. Divan, “Design considerations for high power
density DC-DC converters,” in Proc. High Frequency Power Conversion
(HFPC), 1990, pp.324-335.
[51] H. Li, F. Zh. Peng, and J.S. Lawler, “A natural ZVS medium-power
bidirectional dc-dc converter with minimum number of devices,” IEEE
Trans. Ind. Appl. Volume 39, Issue 2, March-April 2003, pp.525 – 535.
[52] X. Yan, A. Seckold, and D. Patterson, “Development of a zero-voltagetransition bidirectional dc-dc converter for a brushless dc machine EV
propulsion system,” in Proc. IEEE PESC, Caims, Queensland, Australia,
Volume 4, 23-27 June, 2002, 1661 – 1666.
[53] D. Xu, C. Zhao, and H. Fan, “A PWM plus phase-shift control bidirectional
dc-dc converter,” IEEE Trans. Power Electron., Volume 19, Issue 3, May
2004, pp. 666 – 675.
78
References
[54] H. Fan and D. Xu, “Synthesis of PWM plus phase-shift bidirectional dc-dc
converters”, TLin-s 4-16 Aug. 2004, pp. 476 – 481.
[55] G. Chen, Y.-S. Lee, D. Xu and Y. Wang, “A novel soft-switching and low
conduction- loss bidirectional dc-dc converter,” in Conf. Rec. of The Third
International Power Electronics and Motion Control Conference, IPEMC,
Beijing, China, Volume 3, 15-18 Aug. 2000, pp. 1166 – 1171.
[56] D. Liu and H Li, “A novel multiple-input ZVS bidirectional dc-dc
converter,” in Proc. IEEE IECON, Raleigh, North Carolina, 6-10 Nov.
2005, pp. 6.
[57] T. Kinjo, T. Senjyu, J. Miyagi, N. U. Sugimoto, and S. T. Takagi, “Bidirectional zero-current-switching approach applied for energy storage
system using electric double layer capacitor,” in Proc. IEEE PESC, Recife,
Brazil, 18-22 June 2006, pp. 1 – 6.
[58] G. Ma, Y. Liu, and W. Qu, “A Novel Soft Switching Bidirectional dc/dc
converter and its output characteristic,” in Conf. Rec. of IEEE Region 10
Conference, TENCON, Hong Kong, China, Nov. 2006, pp.1 – 4.
[59] P. Jose and N. Mohan, “A novel ZVS bidirectional Cuk converter for dual
voltage systems in automobiles,” in Proc. IEEE IECON, Roanoke, VA,
Volume 1, 2-6 Nov. 2003, pp. 117 – 122.
79
References
[60] Z.R. Martinez, and B. Ray, “Bidirectional dc/dc power conversion using
constant frequency multi-resonant topology,” in Proc. IEEE APEC,
Orlando, FL, Feb. 1994, pp. 991 – 997.
[61] B. Ray, “Single-cycle resonant bidirectional dc/dc power conversion,” in
Proc. IEEE APEC, San Diego, CA, March 1993, pp. 44 – 50.
[62] B. Ray and A. Romney-Diaz, “Constant frequency resonant topologies for
bidirectional dc/dc power conversion,” in Proc. IEEE PESC, Seattle, WA,
June 1993, pp. 1031 – 1037.
[63] B. Ray, “Bidirectional dc/dc power conversion using quasi-resonant
topology,” in Proc. IEEE PESC, Toledo, Spain, June-July 1992, pp. 617 –
624.
[64] B. Ray, “Bidirectional dc/dc power conversion using constant-frequency
quasi-resonant topology,” in Proc. IEEE ISCAS, Chicago, Illinois, May
1993, pp. 2347 – 2350.
[65] D.M. Sable, F.C. Lee, and B.H. Cho, “A zero-voltage-switching
bidirectional battery charger/discharger for the NASA EOS satellite,” in
Proc. IEEE APEC, Boston, MA, Feb. 1992, pp. 614 – 621.
[66] K.T. Chau, T.W. Ching, and C.C. Chan, “Bidirectional soft-switching
converter-fed dc motor drives,” in Proc. IEEE PESC, Fukuoka, Japan, May
1998, pp. 416 – 422.
80
References
[67] H.S. H. Chung, W.-L. Cheung, and K.S. Tang, “A ZCS bidirectional fly
back dc/dc converter,” IEEE Trans. Power Electron., Volume 19, Issue 6,
Nov. 2004, pp. 1426 – 1434.
[68] H.L. Chan, K.W.E. Cheng, and D. Sutanto, “ZCS-ZVS bi-directional
phase-shifted dc-dc converter with extended load range,” in Conf. Rec. of
IEE Electric Power Applications, Volume 150, Issue 3, May 2003, pp. 269
– 277.
[69] H.L. Chan, K.W.E. Cheng, and D. Sutanto, “Bidirectional phase-shifted dcdc converter,” Electronics Letters, Volume 35, Issue 7, April 1999, pp. 523
– 524.
[70] E.-S. Kim, K.-Y. Joe, H.-Y. Choi, Y.-H. Kim, and Y.-H. Cho, “An
improved soft switching bi-directional PSPWM FB dc/dc converter,” in
Proc. IEEE IECON, Aachen, Germany, Volume 2, Aug.1998, pp. 740 –
743.
[71] K. Wang, F.C. Lee, and J.-S. Lai, “Operation principles of bi-directional
full-bridge dc/dc converter with unified soft-switching scheme and softstarting capability,” in Proc. IEEE APEC, New Orleans, LA, Volume 1, 610 Feb. 2000, pp. 111 – 118.
81
References
[72] L. Shi, L. Sun, D. Xu, and M. Chen, “Optimal design and control of 5kW
PWM plus phase-shift (PPS) control bidirectional dc-dc converter,” in Proc.
IEEE APEC, Dallas, TX, Feb. 2006, pp.1– 5.
[73] K. Rajashekara, “Power converter and control strategies for fuel cell
vehicles,” in Proc. IEEE IECON, Bologna, Italy, June 2003, vol.3, pp.28652870.
[74] A.M. McLandrich, “Sensorless control of a bidirectional boost converter for
a Fuel cell energy management system,” Master Thesis, Virginia Tech,
2003.
[75] A.D. Swingler and W.G. Dunford, “Development of a bi-directional dc/dc
converter for inverter/charger applications with consideration paid to large
signal operation and quasi-linear digital control,” in Proc. IEEE PESC,
Cairns, Queensland, Australia, Volume 2, June 2002, pp. 961 – 966.
[76] S. Canter and R. J. Lenk, ‘‘Buck-boost dc–dc switching power conversion,’’
U.S. Patent 5359280, Feb.4, 1994.
[77] X. Huang, T. Nergaard., J.-S. Lai, X. Xu, and L. Zhu, “A DSP based
controller for high-power interleaved boost converters,” in Proc. IEEE
APEC, Miami, FL, Feb. 2003, pp. 327–333.
82
References
[78] J. S. Batchvarov, J. L. Duartek, and M. A. M. Hendrix, “Interleaved
converters based on hysteresis current control,” in Proc. IEEE PESC,
Galway Ireland, June 2000, pp. 655–661.
[79] O. Garcia, P. Zumel, A. de Castro, and J. A. Cobo, “Automotive dc-dc
Bidirectional Converter Made with Many Interleaved Buck Stages,” IEEE
Trans. Power Electron., vol. 21, May 2006, pp. 578–586.
[80] Y. Zhang and P. C. Sen, “A New Soft-Switching Technique for Buck,
Boost, and Buck-Boost Converters,” IEEE Trans. Ind. Appl., vol. 39, Nov.
/Dec. 2003, pp. 1775–1781.
[81] C.P. Henze, H.C. Martin, and D.W. Parsley, “Zero-Voltage switching in
high frequency power converters using pulse with modulation,” in Proc.
IEEE APEC, New Orleans, LA , Feb. 1988, pp. 33-40.
[82] J. S. Lai, R. W. Young, and J. W. McKeever, “Efficiency consideration of
dc link soft-switching inverters for motor drive applications,” in Proc. IEEE
PESC, Taipei, Taiwan, June 1994, pp. 1003–1010.
[83] J. S. Lai, J. Zhang, H. Yu, X. Huang, C. Liu, and H. Kouns, “Source and
load adaptive design for a high-power soft-switching inverter,” in Proc. of
IPEC-Niigata, April 2005, Niigata, Japan, pp. 593 -599.
83
References
[84] J. Moreno, M.E. Ortuzar, and J.W. Dixon, “Energy management system for
a hybrid electric vehicle, using ultra-capacitors and neural networks,” IEEE
Trans. IES, vol. 52, April 2006, pp. 614 – 623.
[85] M.E. Ortuzar, J. Moreno, and J.W. Dixon, “Ultracapacitor-based auxiliary
energy system for an electric vehicle: implementation and evaluation,”
IEEE Trans. Ind. Electron., vol. 52, Aug. 2007, pp. 2147 – 2156.
[86] D.M. Sable, “Optimization of spacecraft battery charger/discharger
systems,” Ph. D. Dissertation, Virginia Polytechnic Institute and State
University, 1991.
[87] P. L. Wong, “Performance Improvements of multi-channel interleaving
voltage regulator modules with integrated coupling inductors,” Ph. D.
Dissertation, Virginia Polytechnic Institute and State University, 2001.
[88] Y. Duan and H. Jin, “Digital controller design for switch mode power
converters,” in Proc. IEEE APEC, Dallas, TX, March 1999, pp. 967-973.
[89] Monson H. Hayes, “Digital signal processing”. McGraw-Hill, 1999, pp.304.
[90] R. W. Erickson and D. Maksimovic, “Fundamental of power electronics,”
Kluwer Academic Publishers, 2001.
[91] S. Choudhury, “DSP based digital control design for dc-dc switch mode
power converter,” Texas instruments inc. application note.
84
References
[92] C.G. Yoo, W.-C. Lee, K.-C. Lee, and B.H. Cho, “Transient current
suppression scheme for bidirectional dc-dc converters in 42V automotive
power systems,” in Proc. IEEE APEC, Austin, TX, March 2005, pp. 16001604.
[93] C. G. Yoo, W.-C. Lee, K.C. Lee, and I. Suh, “Current mode PWM
controller for a 42V/14V bidirectional DC/DC converter,” in Proc. IEEE
PESC, Jeju, South Korea, June 2006, pp. 1747-1752.
[94] Danwei Liu, Danwei Liu, “Dynamic Modeling and Control Design for
Bidirectional DC-DC Converter for Fuel Cell Vehicles with Battery as
Energy Storage Element”, IAS 2005, Vol. 3, pp.1632 – 1635, Oct. 2005.
[95] S. Cuk, “Modeling, Analysis, and Design of Switching Converter,” Ph. D.
thesis, California Institute of Technology, November 1976.
[96] R. D. Middlebrook and S. Cuk, “Modeling and Analysis Methods for Dcto-Dc Switching Converters,” Proceedings of the IEEE International
Semiconductor Power Converter Conference1977, pp. 90-111, March 1977.
Reprinted in Advances in Switched-Mode Power Conversion, Vol. 1,
Irvine: Teslaco, 1983.
[97] T. Ninomiya, M. Nakahara, T. Higashi, K. Harada, “A Unified Analysis of
Resonant Converters,” IEEE Transactions on Power Electronics, Vol. 6.
No. 2. April 1991, pp. 260-270.
85
References
[98] S. Yang, K. Goto, Y. Imamura, and M. Shoyama“ Dynamic Characteristics
Model State–space Averaging Method, ” in Proc. of INTELEC, 2012, 19.2,
pp.1-5, Oct. 2012.
[99] R. D. Middlebrook and S. Cuk, "A General Unified Approach to Modelling
Switching-Converter Power Stages," International Journal of Electronics,
Vol. 42, No. 6, pp. 521-550, June 1977.
[100] A. Emadi, A. Khaligh, C. H. Rivetta, and G. A. Williamson, "Constant
power loads and negative impedance instability in automotive systems:
definition, modeling, stability, and control of power electronic converters
and motor drives," IEEE Trans. Vehicular Technology, vol. 55, pp. 11121125, Jul. 2006.
[101] Y. Jang and R. W. Erickson, "Physical origins of input filter oscillations in
current programmed converters," IEEE Trans. Power Electronics, vol. 7, no.
4, pp. 725-733, Jul. 1992.
[102] Emadi, A.; Ehsani, A.; , "Dynamics and control of multi-converter DC
power electronic systems ," Power Electronics Specialists Conference, 2001.
PESC. 2001 IEEE 32nd Annual , vol.1, no., pp.248-253 vol. 1, 2001.
[103] Y. Imamura,
H.
A. Ramadan, Y. Sihun, G.M. Dousoky, M.
Shoyama,"Seamless dynamic model for DC-DC converters applicable to bi-
86
References
directional power transfer," Power Electronics and Applications (EPE),
2013 15th European Conference on , vol., no., pp.1,10, 2-6 Sept. 2013.
[104] Y. Imamura,
H.
Shoyama,"Seamless
A. Ramadan, Y. Sihun, G.M. Dousoky, M.
dynamic
model
for
bi-directional
DC-DC
converter," in Proc. of IEEE 10th International Conference on Power
Electronics and Drive Systems (PEDS), 2013 , pp.1109,1113, 22-25 April
2013.
87