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Digital GeometricSequence Control Technique
for Bidirectional Dual Active Bridge DCDC
Converters Used in Future Electric Vehicles
by
Iman Askarian Abyaneh
A thesis submitted to the
Faculty of Electrical and Computer Engineering
in conformity with the requirements for
the degree of Master of Applied Science
Queen’s University
Kingston, Ontario, Canada
September 2016
Copyright c© Iman Askarian Abyaneh, 2016
Abstract
Bidirectional DCDC converters are widely used in different applications such as
energy storage systems, Electric Vehicles (EVs), Interruptible Power Supplies (UPS),
etc. In particular, future EVs require bidirectional power flow in order to integrate
energy storage units into smart grids. These bidirectional power converters provide
Grid to Vehicle (V2G)/ Vehicle to Grid (G2V) power flow capability for future EVs.
Generally, there are two control loops used for bidirectional DCDC converters:
The inner current loop and The outer loop. The control of Dual Active Bridge (DAB)
converters used in EVs are proved to be challenging due to the wide range of oper
ating conditions and nonlinear behaviour of the converter. In this thesis, the precise
mathematical model of the converter is derived and nonlinear control schemes are
proposed for the control system of bidirectional DCDC converters based on the de
rived model. The proposed inner current control technique is developed based on a
novel GeometricSequence Control (GSC) approach. The proposed control technique
offers significantly improved performance as compared to one for conventional control
approaches. The proposed technique utilizes a simple control algorithm which saves
on the computational resources. Therefore, it has higher reliability, which is essen
tial in this application. Although, the proposed control technique is based on the
mathematical model of the converter, its robustness against parameter uncertainties
i
is proven.
Three different control modes for charging the traction batteries in EVs are in
vestigated in this thesis: the voltage mode control, the current mode control, and
the power mode control. The outer loop control is determined by each of the three
control modes. The structure of the outer control loop provides the current reference
for the inner current loop.
Comprehensive computer simulations have been conducted in order to evaluate
the performance of the proposed control methods. In addition, the proposed control
have been verified on a 3.3 kW experimental prototype. Simulation and experimental
results show the superior performance of the proposed control techniques over the
conventional ones.
ii
Acknowledgements
I would like to thank my supervisor, Professor Alireza Bakhshai, for his ongoing
support and supervision. He has offered encouragement and guidance throughout my
research. Without his belief in my abilities, this work would not have been possible.
I would like to thank Dr. Majid Pahlevaninezhad for his mentorship, support, and
friendship throughout this project. His guidance had a large impact in completing
this research.
I am very grateful to have had such an amazing group of lab colleagues, friends.
Thank you all for your friendship and support in making this possible.
Thank you to Debra Fraser and the rest of the ECE department staff for always
having an open door and being there whenever I needed a little help.
Last but not least, I would like to thank my parents, Shahnaz Jafarian Abyaneh
and Hossein Askarian Abyaneh, and my brother Ehsan Askarian for all of their love
and support throughout this endeavour.
iii
Contents
Abstract i
Acknowledgements iii
Contents iv
Glossary vi
List of Figures viii
List of Tables xiii
Chapter 1: Introduction 11.1 Thesis contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 Thesis organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Chapter 2: Literature Review 72.1 Overview of Bidirectional DAB DCDC Converters . . . . . . . . . . 72.2 Control of DAB Converters . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Control Parameters of DAB Converters . . . . . . . . . . . . . 92.2.2 Closed Loop Control schemes . . . . . . . . . . . . . . . . . . 10
2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Chapter 3: Bidirectional Dual Active Bridge (DAB) DCDC Converters 23
3.1 Lossless DAB Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2 Different Modulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2.1 Phase Shift Modulation . . . . . . . . . . . . . . . . . . . . . 273.2.2 Alternative Modulation Methods . . . . . . . . . . . . . . . . 303.2.3 Optimized Modulation . . . . . . . . . . . . . . . . . . . . . . 36
3.3 SteadyState Model of the converter . . . . . . . . . . . . . . . . . . . 423.4 Loss Analysis of the DAB Converter . . . . . . . . . . . . . . . . . . 46
iv
3.4.1 Power Loss in Switch Converters . . . . . . . . . . . . . . . . 463.4.2 Transformer, Inductor . . . . . . . . . . . . . . . . . . . . . . 503.4.3 Total Losses  Predicted Efficiency . . . . . . . . . . . . . . . 53
3.5 Linear Control for DAB converters . . . . . . . . . . . . . . . . . . . 533.5.1 Closed Loop PI Control . . . . . . . . . . . . . . . . . . . . . 543.5.2 Digitalization of the PI control . . . . . . . . . . . . . . . . . 55
3.6 Simulation and Experimental Results . . . . . . . . . . . . . . . . . . 563.7 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Chapter 4: Controller Design 724.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.2 Modulation Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.3 Digital Current Control in DAB Converters Based on Novel Geometric
Sequence Control (GSC) Approach . . . . . . . . . . . . . . . . . . . 754.3.1 Oscillation Problem . . . . . . . . . . . . . . . . . . . . . . . . 764.3.2 GeometricSequence Current Control Approach . . . . . . . . 76
4.4 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 874.5 Robustness and Reliability . . . . . . . . . . . . . . . . . . . . . . . . 884.6 Outer Control Loop Design . . . . . . . . . . . . . . . . . . . . . . . 904.7 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 914.8 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Chapter 5: Conclusions and Future Work 995.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Bibliography 102
v
Glossary
ADC Analog to Digital Conversion.
CCM Continuous Current Mode.
CUL Counter Upper Limit.
DAB Dual Active Bridge.
DAC Digital to Analog Conversion.
DCM Discontinuous Current Mode.
DG Distributed Generator.
DSP Digital Signal Processing.
EV Electric Vehicle.
FPGA Field Programmable Gate Arrays.
G2V Grid to Vehicle.
GSC GeometricSequence Control.
vi
HF High Frequency.
PEV Purely Electric Vehicle.
PHEV Plugin Hybrid Electric Vehicle.
PSM PhaseShift Modulation.
SCM Sensorless Current Mode.
SSOC Self Sustained Oscillating Control.
UPS Interruptible Power Supplies.
V2G Vehicle to Grid.
ZVS Zero Voltage Switching.
vii
List of Figures
1.1 Nonfossil energy sources for the utility grid . . . . . . . . . . . . . . 2
1.2 Typical Electricity load variation of the utility grid during 24 hours . 3
1.3 ACDC Converter used in G2V/V2G applications . . . . . . . . . . . 4
2.1 Dual Active Bridge (DAB) converter . . . . . . . . . . . . . . . . . . 8
2.2 Negative feedback for Dual Active Bridge (DAB) converters . . . . . 11
2.3 Digitally controlled converter under an outer voltage and an inner cur
rent loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 Closed loop control based with Predictive duty cylce modulation . . . 15
2.5 Investigated cascade control structure consisting of an outer voltage
loop and inner current loop . . . . . . . . . . . . . . . . . . . . . . . 16
2.6 control structure for the synchronous buck converter . . . . . . . . . . 17
2.7 Battery charging profile for Electric Vehicles (EV) . . . . . . . . . . . 18
2.8 A control structure for DAB DCDC converter for aerospace application 19
2.9 Controller to operate converter with optimal efficiency . . . . . . . . 20
2.10 Self Sustained Oscillating Control Modulation structure . . . . . . . . 21
2.11 SSOCPCM control system . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1 Dual active bridge converter . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 Lossless model of Dual Active Bridge (DAB) converter . . . . . . . . 25
viii
3.3 4 control parameters (ϕ, ϕA, ϕB, TS) to control single stage dual active
bridge converters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4 Phase shift modulation waveforms . . . . . . . . . . . . . . . . . . . . 29
3.5 Voltage and current waveforms for power transfer from port A to port
B for triangular current mode modulator when VA > kVB . . . . . . 31
3.6 Voltage and current waveforms for power transfer from port B to port
A for triangular current mode modulator when VA > kVB . . . . . . 32
3.7 Voltage and current waveforms for power transfer from port A to port
B for triangular current mode modulator when VA < kVB . . . . . . 34
3.8 Voltage and current waveforms for power transfer from port B to port
A for triangular current mode modulator when VA < kVB . . . . . . 35
3.9 Voltage and current waveforms for power transfer from port A to port
B for trapezoidal current mode modulator when VA > kVB . . . . . . 36
3.10 Voltage and current waveforms for power transfer from port B to port
A for trapezoidal current mode modulator when VA > kVB . . . . . . 37
3.11 The 12 basic voltage sequences generated with DAB converter . . . . 39
3.12 Waveform of Dual Active Bridge Converter operating in Continuous
Current Mode (CCM) with Zero Voltage Switching (ZVS) . . . . . . 42
3.13 Area of the Current Waveform of DAB operating in CCM . . . . . . 45
3.14 3D ZVS region space for Va=400 Vb=350 . . . . . . . . . . . . . . . 51
3.15 2DZVS region space for Va= 400 V, Vb= 350 V . . . . . . . . . . . 52
3.16 PI controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.17 Conversion of Continuous PI controller to Discrete PI controller . . . 55
3.18 operation for Va=400 Vb=350 ϕAB = 0.116 . . . . . . . . . . . . . . 57
ix
3.19 (A) depicts operation for Va=400 Vb=350 ϕAB = 0.058 and (B) depicts
depicts operation for Va=400 Vb=350 ϕAB = 0.029 . . . . . . . . . . 58
3.20 (A) depicts operation for Va=400 Vb=350 ϕAB = 0.116 and (B) depicts
depicts operation for Va=400 Vb=350 ϕAB = 0.063 . . . . . . . . . . 59
3.21 operation for Va=400 Vb=250 ϕAB = 0.3, IBat = 12.1A With ZVS . . 60
3.22 operation for Va=400 Vb=250 ϕAB = 0.2, IBat = 10A without ZVS . 61
3.23 operation for Va=400 Vb=250 ϕAB = 0.2, ϕA = 0.31, and ϕB = 0.5
with IBat = 10A with ZVS . . . . . . . . . . . . . . . . . . . . . . . . 62
3.24 Steady state operation of the DAB converter with the operating con
ditions: VA = 360, VB = 400, iBat = 6A . . . . . . . . . . . . . . . . 63
3.25 Steady state operation of the DAB converter with the operating con
ditions: VA = 360, VB = 400, iBat = 8A . . . . . . . . . . . . . . . . 64
3.26 Transient response of the DAB converter VA = 360, VB = 400 I=8 A
to I=4 A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.27 Transient response of the DAB converter VA = 360, VB = 400 I=8 A
to I=6 A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.28 Transient response of the DAB converter VA = 400, VB = 250 I=14 A
to I=12 A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.29 instability in some operating conditions for PI controller . . . . . . . 66
3.30 transient response when VB = 400V , I = 6A VA = 360V to VA = 400V 66
3.31 steady state operation at VA = 100V , VB = 90V without ZVS . . . . 68
3.32 steady state operation at VA = 100V , VB = 120V without ZVS . . . . 69
3.33 steady state operation at VA = 100V , VB = 120V , I = 2.2A with
achieved ZVS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
x
3.34 steady state operation at VB = 100V , VA = 90V with achieved ZVS . 71
3.35 transient response at VB = 100V , VA = 120V with achieved ZVS . . . 71
4.1 Sawtooth counter created based on the digital counter for PSM . . . 74
4.2 switching instants created based on their respective sawtooth counter 75
4.3 Oscillation in CCM mode in response to perturbation . . . . . . . . . 77
4.4 Oscillation in CCM mode in response to poor control scheme . . . . . 77
4.5 Effect of Change in ϕAB on the current waveform . . . . . . . . . . . 78
4.6 Transient and steadystate waveforms in one halfcycle . . . . . . . . 81
4.7 Overall procedure of the applied control method . . . . . . . . . . . . 84
4.8 Inner control block diagram . . . . . . . . . . . . . . . . . . . . . . . 85
4.9 Overall procedure of the waveform when a = 1 . . . . . . . . . . . . . 87
4.10 Outer loop control in order to set the current reference for the inner
current loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.11 GSC control approach for 50% step change in current for Va=360 V
and Vb=400V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.12 GSC control approach for 50% step change in current for Va=360 V
and Vb=400V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.13 GSC control approach for 25% step change in current for Va=360 V
and Vb=400V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.14 GSC control approach for 50% step change in current for Va=400 V
and Vb=250V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.15 GSC control approach for 50% step change in current for Va=400 V
and Vb=250V with ∆LS% = 20% . . . . . . . . . . . . . . . . . . . . 94
xi
4.16 GSC control approach for 50% step change in current for Va=360 V
and Vb=400V with ∆LS% = −20% . . . . . . . . . . . . . . . . . . . 95
4.17 GSC control approach for change in primary voltage: Va=360 V to
Va=400 V and fixed Vb=400V . . . . . . . . . . . . . . . . . . . . . 95
4.18 3kW bidirectional AC/DC converter prototype . . . . . . . . . . . . . 97
4.19 transient response at VB = 100V , VA = 90V with achieved ZVS . . . 97
4.20 transient response at VB = 100V , VA = 120V with achieved ZVS . . . 98
xii
List of Tables
2.1 PERIODDOUBLING OSCILLATIONS OCCUR FOR THE INDI
CATED RANGE OF DUTY RATIOS; * DENOTES NO OSCILLA
TION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.1 The criteria required to enable each modulation . . . . . . . . . . . . 40
3.2 The Power levels of DAB with respect to the each modulation for the
applied DC voltages, duty cycles and the phaseshift . . . . . . . . . 40
3.3 Phaseshift required to achieve a certain power level . . . . . . . . . 41
3.4 The RMS current IL with respect to the considered voltage sequences 41
3.5 DAB waveform details for VA = 360 VDC and VB = 400 VDC with
different power levels . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.6 DAB converter Specifications . . . . . . . . . . . . . . . . . . . . . . 67
3.7 DAB system parameters . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.1 Elimination of the error current by a geometric progression procedure
with a common ratio of 12
. . . . . . . . . . . . . . . . . . . . . . . . 84
4.2 DAB converter Specifications . . . . . . . . . . . . . . . . . . . . . . 96
4.3 DAB system parameters . . . . . . . . . . . . . . . . . . . . . . . . . 96
xiii
1
Chapter 1
Introduction
Human activities, since the industrial revolution, have constantly changed the natural
composition of Earth’s atmosphere. The revolution had an enormous impact on the
concentration of greenhouse gases in the atmosphere. This has resulted in global
warming and an increase in air pollution, which continues on its trend with even a
steeper slope everyday. There is indisputable evidence that the conversion of forests
to agricultural land, the emission of industrial chemicals, and the consumption of
fossil fuels are the major contributing factors to air pollution [1].
According to [1], the Earth’s surface temperature has risen by about 1F in the
past century, with accelerated warming occurring in the past three decades. Accord
ing to statistical reviews of the atmospheric and climatic records, there is abundant
evidence that global warming over the past 50 years is directly attributable to human
activities [2].
In order to mitigate air pollution and the CO2caused global climate change,
mankind has to increase the efficiency of their uses, and shift to non fossil energy
sources as depicted in Figure 1.1.
One of the greatest achievements of modern technology was the development of
2
PVPanel Sun
BatteryPack
+ ‐
WindEnergyConversionSystem PhotovoltaicInverter
EVPowerConditioningSystems
Wind
WindTurbines
ElectricVehicle
EnergyStorage
Grid
`
Figure 1.1: Nonfossil energy sources for the utility grid
internal combustion engine vehicle, especially automobiles. The mass usage of auto
mobiles has caused carbon dioxide to aggregate in the atmosphere which significantly
accounts for the catastrophic problem of global warming [3]. Recent research and
development suggest a replacement of high efficiency, clean and safe transportation
such as Electric Vehicles, Hybrid Electric vehicles, and fuel cell vehicles over conven
tional vehicles which use combustion engines [3]. Hybrid Electric Vehicles utilize an
optimized internal combustion engine with electric machines to improve the efficiency.
For CO2 free emissions, electric vehicles powered by battery packs and fuel cell are
used [4, 5].
In order to have a conventional way to charge the traction batteries of electric vehi
cles, it is desirable to have the option of charging the batteries from inside our homes
with the utility grid the socalled Grid to Vehicle (G2V). It is also beneficial to
have a bidirectional power flow between the grid and the EV batteries. This allows
the Electric Vehicle (EV) to act as a local Distributed Generator (DG) and help the
3
Ele
ctri
city
load
Time12:00AM 12:00PM 12:00AM
G2V
V2G
Valley filling
Peak Shaving
Figure 1.2: Typical Electricity load variation of the utility grid during 24 hours
power grid [6–9].
Uncontrolled recharging of Purely Electric Vehicle (PEV) could cause significant
impacts on power systems [6,9,9–13]. Basically, the electricity load in the grid load is
desirable to have a flat line shape. However, as depicted in Figure 1.2 the electricity
load base lines typically demonstrate a valley and a rising electricity load during
specific times of the day. The valley happens during midnight and the peak is around
19:00 to 22:00 [14]. Moreover, there is a high correlation between the electricity load
and the cost of electricity generation [15]. Therefore, a valleyfilling pattern is ideal
for utilizing the idle capacity of power generators and minimizing recharging cost [10].
Recent trends in the automotive industry toward EVs has create the need for
highly compact, lightweight, and efficient power converters to exchange electrical
power between the power grid and EVs [16].
Figure 1.3 depicts the schematic structure of a bidirectional ACDC converter used
for the purpose of power transfer between the grid and the EV. The ACDC con
verter used in this thesis is comprised of a fullbridge ACDC converter followed by
a bidirectional DCDC converter. In the G2V application, the grid applies 240 RMS
1.1. THESIS CONTRIBUTIONS 4
Ls K:1
CB
IB
SA3SA1
SA2 SA4
SB3SB1
SB2 SB4
CA
+

VB
+

VATractionBattery
SFB3SFB1
SFB2 SFB4
PowerGrid
ACDC Converter DCDC Converter
CFB
Lg
Figure 1.3: ACDC Converter used in G2V/V2G applications
voltage to the input of the ACDC converter. The inductor Lg makes the ACDC
converter act as a boost converter meaning the output DC voltage (VA) has to be
above 350 V DC. In order to have a low RMS current at the high frequency network
(transformer winding) of the DCDC converter, it is desirable to have a flexible DC
bus (Side A) voltage ranging from 350 VDC to 450 VDC. The traction battery volt
ages in the Electric Vehicles (EVs) are typically between 250 V DC to 430 V DC.
Therefore, In order to have a converter applicable for charging all the traction electric
vehicles, a DCDC converter is introduced which converts the DC bus voltage of side
A to a range of 230 VDC and 450 VDC at side B.
1.1 Thesis contributions
The main contribution of this thesis are summarized as follows:
1. Design and development of bidirectional DCDC converter with V2G/G2V ca
pability
2. Development of the precise discretetime domain model for steadystate opera
tion and during transients.
1.2. THESIS ORGANIZATION 5
3. digital current programmed control technique for Dual Active Bridge (DAB)
converters based on a novel GeometricSequence Control (GSC) approach.
4. Development of a variable structure outer loop for three different modes of
operations during charging process of the traction batteries.
5. Stability Analysis of the closed loop control schemes.
1.2 Thesis organization
The following describes the contents of the chapters:
chapter 2, Literature Review
In this chapter a brief description of the degree’s of freedom to control DAB converters
are explained. Moreover, some of the literature control structures for DCDC convert
ers are explored. The benefits and drawbacks of the conventional control structures
are also discussed.
chapter 3, Bidirectional DAB DCDC converter
Steady state, soft switching, and loss analysis of the system is evaluated. Also, a PI
control is designed and used to control the power flow between the two DC Buses.
chapter 4, Proposed control
To solve the drawbacks of conventional linear controllers, a digital current control
based on the proposed geometricsequence control approach is proposed. The perfor
mance, stability, and robustness of the control is explored in this chapter. Moreover,
1.2. THESIS ORGANIZATION 6
the modulation scheme specifically made for the proposed control method is presented
to create the switching instants of the semiconductors. Simulation and experimen
tal results are provided to verify the behaviour of the proposed geometricsequence
control approach.
chapter 6, Conclusion
A conclusion of the thesis along with future work in the field.
7
Chapter 2
Literature Review
Bidirectional DCDC converters with galvanic isolation are used in Plugin Hybrid
Electric Vehicles (PHEVs), Purely Electric Vehicles (PEVs) and energy storage sys
tems for the purpose of charging batteries from the grid and releasing the battery
charge back to the grid. Dual Active Bridge (DAB) converters are one of the most
prominent bidirectional DCDC converters [17, 18, 18–22]. The DAB topology offers
the low number of passive components, the evenly shared currents in the switches,
and its soft switching properties which make it a good candidate for bidirectional
DCDC converters [23–25]. In this chapter, a literature review of DAB converters
and their control schemes are explained.
2.1 Overview of Bidirectional DAB DCDC Converters
Figure 2.1 depicts a typical fullbridge DAB converter that is widely used in Vehicle
to Grid (V2G)/ Grid to Vehicle (G2V) applications. DAB converters consist of two
active bridges (A and B), two filters (CA and CB) and a high frequency transformer
.
2.1. OVERVIEW OF BIDIRECTIONAL DAB DCDC CONVERTERS8
Ls K:1
CB
IB
SA3SA1
SA2 SA4
SB3SB1
SB2 SB4
CA
+

VB
+

VA
Bridge A Bridge B
TractionBattery
Figure 2.1: Dual Active Bridge (DAB) converter
• CA and CB absorb the high frequency current ripple produced by the two active
bridges. This results in smooth terminal DC voltages and currents with low
ripple at the ports A and B.
• The DCAC inverter converts the DC voltage on the input bus to a quasi square
wave high frequency voltage. This voltage is then applied to the high frequency
transformer. The ACDC bridge converts the high frequency AC voltage to the
DC voltage at the output bus. Bidirectional power transfer can be achieved by
interchanging the role of the bridge A and the bridge B.
• The high frequency transformer allows large voltage and current transfer ratio
as well as providing galvanic isolation [26]. The transformer and the filter com
ponents become smaller when the switching frequency is high. The transformer
leakage inductance (Ls) is used to control the power flow in DAB convert
ers [26, 27].
A typical DAB converter has 4 degrees of freedom in terms of control to adjust
the power transfer:
• The phaseshift, ϕ, between vACA(t) and vACB
(t) within −π < ϕ < π,
2.2. CONTROL OF DAB CONVERTERS 9
• The duty cycle, DA, of vACA(t) within 0 < DA < 1/2 or equivalently the phase
shift between the leading and lagging leg of bridge A,
• The duty cycle, DB, of vACB(t) within 0 < DB < 1/2 or equivalently the phase
shift between the leading and lagging leg of bridge B,
• The switching frequency fs
2.2 Control of DAB Converters
2.2.1 Control Parameters of DAB Converters
The most common and conventional way to control the power transfer between the
two DC ports A and B in a DAB converter is to utilize the phaseshift between the
two active bridges, ϕ, as the only control parameter out of the 4 control parameters
mentioned above. This method is called the PhaseShift Modulation (PSM) scheme
for DAB converters [28]. The advantage of PSM scheme is its simplicity and easy
control since it only has one degree of freedom in terms of control. Additionally,
due to the symmetric circuit topology on the primary and the secondary sides of the
transformer, fast and smooth bidirectional power flow for G2V and V2G applications
can be achieved by simply using positive or negative phaseshifts. However, the main
disadvantage of the conventional PSM is the poor efficiency at light loads. This is due
to high RMS currents in the high frequency and the high switching losses transformer
when DAB is operated in wide voltage ranges operations and the hard switching of
the semiconductors specially at light loads.
In order to overcome the aforementioned issues for DAB converters with PSM
scheme, complex control structures and alternative modulation methods have been
2.2. CONTROL OF DAB CONVERTERS 10
proposed in literature (cf. Section 3.2) [29,30].
The proposed modulation schemes take advantage of the multiple degrees of free
dom offered by DAB converters in order to optimize the performance.
The modulation schemes investigated in [31] extend the zero voltage switching of
the DAB converter and reduce the transformer RMS current. Detailed investigation
of the behaviour of the control parameter in [31] with either D1 ≤ 0.5 and D2 = 0.5
or D1 = 0.5 and D2 ≤ 0.5 is given in [23, 32]. Therefore, these modulations are
faced with a one dimensional (1D) optimization problem to improve the converter
efficiency since either D1 or D2 changes [23].
[32–34] represent a 2dimensional (D1 and D2 change simultaneously) optimiza
tion approach in which highly efficient operation of the DAB converter is reported.
However, compared to the 1d problem, the 2d problem is considerably more complex
to solve. More on modulations are investigated in Section 3.2.
In addition to an optimized modulation scheme, a robust control structure is of
great importance for an optimal performance of DAB converters. Here, we are going
to introduce some of the control structures presented in literature.
2.2.2 Closed Loop Control schemes
Figure 2.2 depicts a simple negative feedback structure for controlling a DAB con
verter. The output load of a DAB converter depends on the input and output volt
ages, the high frequency inductance (transformer leakage inductance), transformer
ratio and the 4 control parameters. The objective in DCDC power converters is
to maintain a constant output voltage/ current, in spite of the disturbances in the
2.2. CONTROL OF DAB CONVERTERS 11
Switching Dual Active Bridge(DAB) DCDC Converter
v(t)=f(vg ,iload ,d)vg(t)
iload(t)
φDA
DB
freq
Disturbances
Control inputs
SensorGain
compansator Modulator+vc
e(t)vref /iref
v(t)/i(t)
+
Figure 2.2: Negative feedback for Dual Active Bridge (DAB) converters
system. Therefore, in order to obtain a given constant output voltage under all con
ditions, a negative feedback has to be built in the system to automatically adjust the
control parameters as necessary.
The negative feedback controls of the DAB converter can typically be categorized
into single measurement controllers (voltage controller/ current controller) or a cas
caded control consisting of an inner current control loop and an outer voltage control
loop which provides a current reference for the inner loop.
The current programmed control can be controlled analogy or digitally.
• Analogue current programmed control for DAB converters can be used in wide
applications and power factor correction application [35–42] . Analog current
programmed control is categorized into peak or valley current control. Since the
inductor current is controlled tightly, the converter dynamics becomes simpler
2.2. CONTROL OF DAB CONVERTERS 12
and consequently resulting in simple and robust widebandwidth control in DC
DC converter. Moreover, the peak current control provides an overcurrent
switch protection.
• Digital control offers advantages as such lower sensitivity to parameter vari
ations, programmability and possibilities to improve performance using more
advanced control structures [43]. However, as compared to analog control, dig
ital control suffers from a smaller control loop bandwidth due to the presence
of time delays the digital control structure and the computation.
There are two ways to observe the current feedback of the system; One way is to
observe the input or output DC current. This way includes the capacitor dynamics
and that might result in a slow inner current loop. Another way is to detect the high
frequency current. Sampling the high frequency current can make the inner current
control loop in cascade control very fast compared to the outer voltage loop. Two
very common control methods based on these current observations are the average
current control [44–47] and the peak current control [48–51].
• In average current control the outer voltage loop gives the desired Iref and the
inner current loop produces the phase shift to match the average current equal
to Iref . The advantage of average controller is its simplicity.
• In Peak Current Mode, the outer voltage loop outputs the desired peak current
of the high frequency network. This current reference is then compared with
the high frequency current. The output of this comparison is then given to the
modulation scheme to produce the switching instants
2.2. CONTROL OF DAB CONVERTERS 13
Power Stage
p A/D DPWMFrequency
Divider
+Voltage Loop
Regulator
+
+
Current LoopRegulator
Vref
vout[n]
fso
d(t)
fs
ig(t)
vg(t)vout(t)
vg[n] ig[n]
ei[n]
d(n)
ev[n]
Multiplier
+
A/D
Figure 2.3: Digitally controlled converter under an outer voltage and an inner currentloop
In the following we are mainly reviewing some of digital control structures in lit
eratures:
Sampling delays (e.g. Analog to Digital Conversion (ADC) or Digital to Analog Con
version (DAC)) and digital calculation processes of the microcontrollers (e.g. Digital
Signal Processing (DSP) and/or Field Programmable Gate Arrays (FPGA)) can com
promise control performance, especially in highfrequency applications. One way to
improve the digital control performance is to use predictive technique by calculating
the duty cycle for the next switching cycle based on the sensed or observed state and
input/output information in each switching cycle, such that the error related to the
controlled variable is minimized in the next cycle or in the next several cycles. pre
dictive and deadbeat digital current programmed control are investigated in [52–55]
. In [52] a predictive digital control for valley, peak or average current is discussed
2.2. CONTROL OF DAB CONVERTERS 14
Table 2.1: PERIODDOUBLING OSCILLATIONS OCCUR FOR THE INDICATED RANGE OF DUTY RATIOS; * DENOTES NO OSCILLATION
Modulation Valley Peak Average
Trailing * D > 0.5 D > 0.5
Leading D < 0.5 * D < 0.5
Trailing Triangle * D > 0.5 *
Leading Triangle D < 0.5 * *
in [52] for three basic converters: buck, boost, buckboost. It is shown in [52] that
the current controller in predictive valley control under trailing edge modulation, is
inherently stable for all operating points where in predictive average current control
and predictive peak current control oscillations occur under the operating conditions
when the duty cycle is greater than 0.5. This is exactly the same as in analogue
currentprogrammed control, where usually a slopecompensation ramp signal to the
sensed current signal is used to suppress the instability. [52] summarizes the corre
lation between different modulation methods and the controlled variables of interest
can be organized as shown in Table 2.1
In [56–59] predictive current mode control is used in bidirectional isolated DCDC
converter. [58] presents predictive phase shift current mode coontrol and predictive
duty cycle mode (Figure 2.4) of control for single phase high frequency transformer
isolated DAB DCDC converter. The predictive control algorithm increases the band
width of the current loop of the converter which enables tracing of the current refer
ence within one switching cycle.
[59] proposes a valleypeak current control for the dual active bridge (DAB)
converter to improve dynamic responses. With this control approach, the reference
current, can be achieved in one switching cycle. The valleypeak current control
2.2. CONTROL OF DAB CONVERTERS 15
+ PI
Predictiveequation
1Predictiveequation
Vref
Vout
Iref
Id2ref
Id1ref
ITs/2
d2
I0
d1
Figure 2.4: Closed loop control based with Predictive duty cylce modulation
strategy offers a fast overcurrent switch protection, and meanwhile eliminates the
possible saturation of the highfrequency transformer.
In [60,61] an accurate smallsignal model for a galvanic isolated, bidirectional DCDC
converter and the implementation of a corresponding digital controller are detailed.
Figure 2.5 depicts a cascaded digital control loop block diagram which is used in
[60, 61]. The voltage controller GC,V and the current controller GC,I is implemented
based on the precise small signal model derived in the papers.
[62] proposes a new digital control solution for bidirectional DCDC converters
for energy storage (figure 2.6). the charging algorithm of the battery is divided into
two states; the first state, when the battery is discharged the converter must supply a
constant current. This current is maintained constant until the voltage on one storage
cell reaches a certain limit (e.g. 4.2 V for Liion cell), after that in the second state
the voltage is kept constant and the current decreases. At the end of the charging
2.2. CONTROL OF DAB CONVERTERS 16
+ +Voltage
ControllerGC,V
CurrentController
GC,I
ModulatorGMod,PS or
GMod,TT
DelayDSP,
GTd,DSP
PowerElec.GPE
HFilter
HAvg
nVdc(z) V2(z)
DAB Control Plant GDAB
TMI 2,M
ode(
z)
V2(z) I2,Ref(z)
Avg(If2)
nVf1(z)
Vf2(z)
If2(z) 
+ +
DelayMeas
GTd,meas
Figure 2.5: Investigated cascade control structure consisting of an outer voltage loopand inner current loop
process a minimum current is supplied to the battery to compensate the self discharge
phenomenon. The charging characteristic which the converter follows to ensure higher
life expectancy for battery is depicted in Figure 2.7. One important issue of this
implementation that must be considered for this digital control topology is the windup
effect. In the direct transfer mode, in the first charging cycle when the current
is constant, the voltage PID controller is saturated to its maximum output value.
During this time the integral element increases. If the calculations are implemented in
a fixed point format this element can reach high values. When reaching the predefined
threshold the voltage PID controller must come out of saturation to keep the battery
voltage constant. This is impossible because of the high value of the integral element.
In the reverse mode, the converter must supply to the DC bus the amount of power
that is demanded by the energy management master control system.
[63] presents a controller for bidirectional control of a DAB DCDC converter
2.2. CONTROL OF DAB CONVERTERS 17
PWMCin
S1
S2
Cin
+
+
L
+Controller+
+PID
PID PID
DC BUS
Vin
Vin_max
Vout
Vbat_max
Iref
+
+
Battery
Figure 2.6: control structure for the synchronous buck converter
which uses the current at the high frequency network of the DAB as a control pa
rameter to meet the dynamic power and regeneration demand of advanced aircraft
electric loads using ultracapacitors. (figure 2.8)
[30] analyses the performance of a high current DAB DCDC converter when oper
ated over a wide operating range. [30] shows that the high currents on the battery side
cause significant design issue in order to obtain a high efficiency. The conventional
phase shift modulation can have high conduction and switching losses. Therefore,
a combined triangular and traapezoidal modulation method is used to reduce losses
over the wide operating range. The control modulation was implemented on a fuel
cell vehicle application where a bidirectional DAB converter is used as an interface
between a 12 V battery and a high voltage DC bus; the result was 2% improvement
2.2. CONTROL OF DAB CONVERTERS 18
4
5
3
2
1
02 2.51.510.50 3.5 43
Charge Time/h
Cha
rge
Vol
tage
/h
100
125
75
50
25
0
Cha
rge
Cap
acity
%
1600
2000
1200
800
400
0
Cha
rge
Cur
rent
/mA
Charge Voltage
Charge Capacity
Charge Current
Figure 2.7: Battery charging profile for Electric Vehicles (EV)
in efficiency compared to phase shift modulation.
[64–66] proposes a multivariable control system for an efficient Zero Voltage
Switching (ZVS) fullbridge DCDC converter used in a (Plugin Hybrid Electric Ve
hicle (PHEV)). This converter processes the power between the high voltage traction
battery and low voltage (12V) battery. Generally, Phaseshift between the two legs of
the fullbridge converter is the main control parameter to regulate the output power.
However, the zero voltage switching cannot be guaranteed by merely controlling the
phaseshift particularly for light load conditions. Efficient operation of the converter
is crucial in order to maintain the energy of traction battery for a longer time and for
increasing driving distance. Therefore, In order to extend the soft switching operation
of the converter for light loads, asymmetrical passive auxiliary circuits are used to
2.2. CONTROL OF DAB CONVERTERS 19
FBC1 FBC2
ioiL Ls
VsVp
iin
+
VDC
Referencesignals
Calculationof IL values
A B
Modulator
Io
Average outputcurrent demand
Polarity
Figure 2.8: A control structure for DAB DCDC converter for aerospace application
provide reactive current. However, the auxiliary circuits increase extra current bur
den on the power MOSFETs, leading to lower efficiency. To obtain the optimal power
transfer, the duty cycle of bridge legs (as another control parameter) is also controlled
to minimize the conduction losses of the converter. Basically, the multivariable con
troller adjusts the phase shift angle to mainly serve as the output regulation control
parameter while duty cycle control of bridge legs are varied to keep converter in the
soft switching region in such a way that the circulating currents are kept at their
minimum level which helps in reduction of conduction losses.
In [64] a modified DAB topology with a modulation technique is proposed for bidi
rectional DCDC conversion that improves the soft switching range of the converter
and reduces the large current ripples at low voltage side (figure 2.9). Phase shift
and duty cycles of active bridges on two sides, (DA, DB, ϕ), are used to control the
converter in order to extend the soft switching range against wide range of operating
2.2. CONTROL OF DAB CONVERTERS 20
Voltage andcurrent
controllers
Multiplier
D1Lookuptable for(VA,VB)
D2Lookuptable for(VA,VB)
?Lookuptable for(VA,VB)
Measure
DCDCConverter
Bus voltagesare
(VA,VB)
VA
VB
IA1
IA2
IB
VA
IA1,d PA,d
d1
d2
?
Figure 2.9: Controller to operate converter with optimal efficiency
voltages on both ports while reducing the circulating current to obtain an optimal
efficiency for DAB converter. The converter operation is analysed and the soft switch
ing conditions are extracted.
[67] presents Peak Current Mode Self Sustained Oscillating Control (PCMSSOC)
technique for DAB DCDC converter. The proposed control improves the performance
of the bidirectional DAB DCDC converter over wide operating conditions. Basically,
the proposed PCMSSOC technique adaptively regulates the frequency and the peak
current of the high frequency network for a triangular modulation to achieve an op
timal performance (figure 2.10).
2.2. CONTROL OF DAB CONVERTERS 21
Bridge ADC/AC
Ls K:1
SSOCModulator
ipfsw fsw
Bridge BAC/DC
Figure 2.10: Self Sustained Oscillating Control Modulation structure
In [68] a control approach for a currentdriven fullbridge DCDC converter, which
significantly improves the converter efficiency over a very wide range of operating con
ditions is presented. The proposed control approach is based on the Self Sustained
Oscillating Control (SSOC) scheme, which adaptively changes the phase shift and
the switching frequency of the converter for different operating points. In this control
technique, the switching instants of the power mosfets are determined by the primary
current feedback and the timing signal produced based on the zero crossing instants
of the transformer primary current. Therefore, for different operating conditions the
control systems automatically tunes the the control variable in order to achieve an
improved converter performance as depicted in Figure 2.11.
2.3. SUMMARY 22
Ls K:1
CB
IB
S3S1
S2 S4
D3D1
D2 D4
CA
+

VB
+

VA
ADC
ADC
+Charging
ProfilePIDAC+
ABS
+ DeadtimeGenerator
DeadtimeGenerator
Q
Q
ZCD
Q
Q
ξ
+
VBAT
iref [n]
iBAT [n]
ic [n]ic
ip
CLK+

++
S1 S2S3 S4
ip
ip
CLK
Figure 2.11: SSOCPCM control system
2.3 Summary
Overall, the dynamical equations of DAB converter has nonlinear characteristics.
Therefore, a linear control can be utilized by linearisation of the dynamical equation
at a particular point small signal model of the system. This method is selected
when the converter is operating at a particular point in which the DC voltage and
DC current remain constant. However, linear control of the DAB converter over wide
range of operating conditions will show poor performance performance since it lacks
the required control flexibility to regulate the output of the DAB converter. To solve
this issue, in this thesis, a digital current control based on the mathematical model
of the system is proposed which offers improved transient response, higher reliability,
and robustness against parameter uncertainties.
23
Chapter 3
Bidirectional Dual Active Bridge (DAB) DCDC
Converters
3.1 Lossless DAB Model
The DAB converter introduced in the previous chapter is redrawn in Figure 3.1. The
two DC voltages in the input and output DC ports are converted to quasi square wave
forms (VACAand VACB
) and applied to the high frequency transformer. Therefore,
with assuming ideal conversion no losses, ideal transformer transformer magnetiz
ing and parasitic capacitance are neglected, and assuming constant supply voltage
VA and VB, the fullbridge circuits can be replaced by the respective squarewave
voltages(Figure 3.2).
For lossless converter with no switching losses or conduction losses, the quasi
3.1. LOSSLESS DAB MODEL 24
square waveform of vACA(t) can obtain the following three different voltage levels,
vACA(t) =
+VA for state I : TA1, TA4 on, TA2, TA3 off
0 for state II : TA1, TA3 on, TA2, TA4 off
0 for state III : TA2, TA4 on, TA1, TA3 off
−VA for state IV : TA2, TA3 on, TA1, TA4 off
(3.1)
By replacing every A in (3.1) with B, the different voltage levels of vACB(t) is similarly
determined. To avoid the high frequency transformer from saturating, it is crucial
that in steady state the average values of vACA(t) and vACB
(t) evaluated over one
switching cycle becomes zero. The resulting voltage across the inductor vL(t) is:
Ls K:1
CB
IB
SA3SA1
SA2 SA4
SB3SB1
SB2 SB4
CA
+

VB
+

VA
Bridge A Bridge B
TractionBattery
Figure 3.1: Dual active bridge converter
VL(t) = vACA(t)− kvACB
(t) (3.2)
The High Frequency (HF) inductor current at time t1, with respect to an initial
current of iL(t0) is derived as follows:
iL(t1) = iL(t0)− 1
L
∫ t1
t0
vL(t)dt ∀ t0 < t1 (3.3)
3.1. LOSSLESS DAB MODEL 25
k .VACB
LsiL=iACA
+

iACB / k+
VACA
Figure 3.2: Lossless model of Dual Active Bridge (DAB) converter
The produced/ received instantaneous power is calculated by PA(t) = vACA(t).iL(t)
and PB(t) = kvACB(t).iL(t). Since the Dual Active Bridge (DAB) is lossless, PA(t) =
PB(t). To simplify the calculations in (3.3), ti and ti+1 are selected such that vACAand
vACBremain constant during that respective time intervals.
The average power over on switching cycle, Ts = 1/fs, is computed as
PA =1
Ts
∫ t0+Ts
t0
PA(t)dt (3.4)
for side A and
PB =1
Ts
∫ t0+Ts
t0
PB(t)dt (3.5)
for side B. Thus, one switching period, t0 < t < t0 + Ts, is split up into m time
intervals (numbered with the index counter i) with constant voltages vACA(t) and
vACB(t) to further simplify the average power calculation,
3.1. LOSSLESS DAB MODEL 26
vp
vS
t
t
TS
φ TS /2 φ TS /2
φA TS
φB TS
Figure 3.3: 4 control parameters (ϕ, ϕA, ϕB, TS) to control single stage dual activebridge converters
time interval I: t0 < t < t1
time interval II: t1 < t < t2
.
. (3.6)
.
final time interval : tm−1 < t < tm = t0 + Ts
According to (3.4) and (3.5), PA is determined by vACA(t) and iL(t) and similarly, PB
is determined by kvACB(t) and iL(t) .
3.2. DIFFERENT MODULATIONS 27
Figure 3.3 depicts 4 control parameters that adjust power flow in DAB converters:
• The phaseshift, ϕ, between vACA(t) and vACB
(t) with −π < ϕ < π,
• The duty cycle, DA, of vACA(t) with 0 < DA < 1/2 / also the phaseshift
between the leading and lagging leg of bridge A (ϕA),
• The duty cycle, DB, of vACB(t) with 0 < DB < 1/2 / also called the phaseshift
between the leading and lagging leg of bridge B (ϕB),
• The switching frequency fs
3.2 Different Modulations
3.2.1 Phase Shift Modulation
Phase Shift Modulation (PSM) is the most common modulation principle. This
modulation only uses one of the 4 control parameters which is the phase shift, ϕ,
between the two full bridge converters to adjust the transferred power. It operates
the DAB converter with a fixed switching frequency and keeps the duty cycles at its
maximum (DA = DB = 1/2). Therefore, out of the three voltage levels for vACA(t)
and vACB(t) based on (3.1), the zero voltage level is eliminated and the resulted
voltage is square wave voltage with only positive and negative values (Figure 3.4).
At steadystate operation, the phaseshift time Tϕ and the DC supply voltage VA and
VB remain constant during one cycle. This property results in vACA(t), vACB
(t), and
3.2. DIFFERENT MODULATIONS 28
iL(t) with the following characteristic [69]:
vACA(t+
Ts2
) = −vACA(t)
vACB(t+
Ts2
) = −vACB(t) (3.7)
iL(t+Ts2
) = −iL(t)
Therefore, the power flow can be recalculated and derived by evaluating one halfcycle
as follows:
PA =1
Ts
∫ Ts
0
PA(t)dt =2
Ts
∫ Ts2
0
vACA(t)iL(t)dt =
2VATs
∫ Ts2
0
iL(t)dt (3.8)
with t0 = 0.
To determine iL(t) in the time interval 0 < t < Ts/2, t needs to be broken into
time intervals I and II (Figure 3.4). In each of these intervals voltage across the
inductor remains constant. For a positive phase shift, 0 < ϕ < π, the instantaneous
inductor current can be written as:
time interval I: iL(t) = il,0 +1
L(VA + kVB)t ∀ 0 < t < t1
time interval II: iL(t) = il(t1) +1
L(VA + kVB)t ∀ 0 < t < t2
(3.9)
With consideration of PA = PB and (3.8), and by extending the results to the full
phaseshift range (−π < ϕ < π) the transferred power is
P = PA = PB =kVAVBϕ(π − ϕ)
2π2fsL∀ − π < ϕ < π (3.10)
where P > 0 (positive ϕ) denotes a power transfer from side A to side B and P < 0
3.2. DIFFERENT MODULATIONS 29
t
I III IV
TS
t1
VACA
K VACB
iL
½TS
Figure 3.4: Phase shift modulation waveforms
(negative ϕ) denotes a power transfer from side B to side A. Maximum power transfer
occurs for ϕ = ±π/2 with the solution
PPS,max =kVAVB8fsL
(3.11)
The resulting expression for the phaseshift needed to obtain a given power transfer
is derived by rearranging (3.10):
ϕ =π
2
(1−
√1− 8fsLP 
kVAVB
)sgn(p) ∀ P  < PPS,max (3.12)
The wide usage of phaseshift modulation is because of its simplicity to adjust the
transferred power. Drawbacks of DAB converters operated under phaseshift modu
lation are high switching losses at some operating conditions and large RMS currents
in the HF transformer for most operating conditions when operated in wide voltage
3.2. DIFFERENT MODULATIONS 30
ranges. Effective transformer utilization is obtained only when VA is close to VB.
3.2.2 Alternative Modulation Methods
In this section, some alternative modulations are investigated, which use not only the
phase shift between vACA(t) and vACB
(t), but also change the duty cycles of vACA(t)
and vACB(t) to overcome the phaseshift modulation problems. The alternative mod
ulation schemes bring the following advantages as compared to the phaseshift modu
lation: Minimum RMS HF inductor current (IL) that results in low conduction losses;
soft switching over a wide range of operating conditions.
For simplicity, a more intuitive method is typically used to determine DA and DB,
where DA and DB are selected in order to achieve a triangular or trapezoidal shape
of the transformer current which results in low switching losses and low conduction
losses. With the triangular and trapezoidal current mode modulation schemes, con
siderable efficiency improvements are reported [30,69].
Triangular Current Mode modulation
This modulation scheme provides zero current switching for some switches and reduces
the transformer RMS current to achieve low conduction losses. The typical voltage
and current waveforms for the triangular current mode modulation are depicted in
Figure 3.5 and Figure 3.6. From Figure 3.5 it can be seen that at t=0 the inductor
current, iL, is zero. Therefore, zero current switching is achieved at t = t0. According
to this Figure 3.5, the inductor current during time interval 0 < t < t1 increases as:
iL(t) = 0 +VA − kVB
Lt ∀ 0 < t < t1 (3.13)
3.2. DIFFERENT MODULATIONS 31
t
I II
TS
t1
VACA
K VACB
iL½TS
III
t2
Figure 3.5: Voltage and current waveforms for power transfer from port A to port Bfor triangular current mode modulator when VA > kVB
At t = t1, the ZVS condition for side A fullbridge is fulfilled, and during t1 < t <
t2, VACA(t) changes its value to zero while the voltage at side B remains constant
(VACB= VB). Therefore, the inductor current changes according to:
iL(t) = iL(t1)− kV2
L(t− t1) ∀ t1 < t < t2 (3.14)
At t = t2 the inductor current is zero and voltage at side B changes to vACB= 0.
Consequently, the inductor current remains zero during t2 < t < Ts/2
iL(t) = 0 ∀ t2 < t <Ts2
(3.15)
The transferred power in the triangular modulation is calculated according to
P =kVBTsLs
(VAT1(2T2 − T1)− kVBT 2
2
)∀ VA > kVB (3.16)
3.2. DIFFERENT MODULATIONS 32
t
III
TS
t1
VACA
K VACB
iL
½TS
III
t2
Figure 3.6: Voltage and current waveforms for power transfer from port B to port Afor triangular current mode modulator when VA > kVB
Moreover, T2 depends on T1 in order to achieve iL(t2) = 0
T2 = T1VA − kVBkVB
(3.17)
ϕ = 2πfs
(T1 + T2
2− T1
2
)= πfsT2 (3.18)
where ϕ is the phaseshift. From equations 3.16, 3.17 and 3.18, the transferred power
can be recalculated as
P =ϕ2VA(kVB)2
π2fsL(VA − kVB)∀ VA > kVB and 0 < ϕ < ϕ∆,max (3.19)
where ϕ is the only control parameter.
3.2. DIFFERENT MODULATIONS 33
To achieve a given power level, ϕ, T1, and T2 are calculated as:
ϕ = π
√fsLP
VA − kVBVA(kVB)2
∀ VA > kVB and 0 < ϕ < ϕ∆,a,mx (3.20)
T1 =ϕ
πfs
kVBVA − kVB
(3.21)
T2 =ϕ
πfs(3.22)
The maximum power transfer in triangular current mode modulations is restricted
by the maximum phaseshift angle (ϕ∆,a,max). This is because increasing the power
transfer (P ) results in the reduction of T3 = TS/2−T1−T2. Consequently, the upper
power limit for this triangular current mode modulation is achieved for T3 = 0 and is
equal to
P∆,a,max =k2V 2
B(VA − kVB)
4fsLVA(3.23)
The respective maximum phase shift angle is
ϕ∆,a,max = ϕ(P∆,a,max) =π
2
(1− kVB
VA
)(3.24)
The general power flow for different voltage conditions can be written as:
P =
ϕ2V 2
A(kVB)
π2fSL(kVB − VA)∀ VA < kVB ∩ 0 < ϕ < ϕ∆,b,max
−ϕ2V 2A(kVB)
π2fSL(kVB − VA)∀ VA < kVB ∩ −ϕ∆,b,max < ϕ < 0
(3.25)
Similar to the power transfer in the positive direction, maximum power transfer for
the combined triangular current mode modulation schemes (Figure 3.5, 3.6, 3.7 and
3.2. DIFFERENT MODULATIONS 34
tTS
t1
VACA
K VACB
iL½TS
t2
Figure 3.7: Voltage and current waveforms for power transfer from port A to port Bfor triangular current mode modulator when VA < kVB
3.8) is achieved when T3 = 0, which results in t2 = TS/2 and is equal to
P∆,max =
k2V 2B(VA − kVB)
4fSLVAfor VA > kVB
0 for VA = kVB
V 2A(kVB − VA)
4fSLkVBfor VA > kVB
(3.26)
with a maximum phase shift angle of:
ϕ∆,b,max = ϕ(P∆,b,max) =π
2
(1− VA
kVB
)(3.27)
3.2. DIFFERENT MODULATIONS 35
tTS
t1
VACA
K VACB
iL
t2 ½TS
Figure 3.8: Voltage and current waveforms for power transfer from port B to port Afor triangular current mode modulator when VA < kVB
Trapezoidal Current Mode Modulation
A disadvantage of using triangular current mode modulation schemes is that there
exists an upper limit to the power transfer (P  < P,max). This is particularly un
desirable when VA ≈ kVB where P∆,max is very close to zero and thus there is no
power transfer at these operating conditions. The operation of DAB for P  > P∆,max
can be achieved by using a trapezoidal current mode modulation. One of the main
disadvantages of this modulation is that it does not maintain zero current switching
at side B.
Typical waveforms of trapezoidal current mode modulation is depicted in Figure
3.9 and Figure 3.10. Three different intervals can be recognized for the trapezoidal
current mode modulation. In the first interval (during time 0 < t < t1), vACA(t) =
VA and vACB(t) = 0 and the absolute value of the HF transformer current, iL(t),
increases; starting its trajectory from zero. In the second interval (during time t1 <
t < t2)vACA(t) remains constant and vACB
(t) changes to vACB(t) = kVB. In the third
3.2. DIFFERENT MODULATIONS 36
t
T1
TS
t1
VACA
K VACB
iL
t2 ½TS
T2 T3
Figure 3.9: Voltage and current waveforms for power transfer from port A to port Bfor trapezoidal current mode modulator when VA > kVB
time interval (during t2 < t < Ts/2) vACA(t) changes to vACA
(t) = 0 and vACB(t)
remains constant at vACB(t) = kVB . The respective power levels are calculated as
follows:
P = sgn(ϕ)kVAVB
(2kVAVB(π2 − 2ϕ2)−
(V 2A + (kVB)2
)(π − 2ϕ2
))4π2fsL(VA + VB)2
(3.28)
∀ ϕ∆,max < ϕ < ϕtrapezoidal,max
3.2.3 Optimized Modulation
The trapezoidal and triangular current mode modulations mentioned above have been
selected intuitively due to the low switching losses and the low RMS current, which
results in lower conduction losses. In order to obtain the lowest conduction losses,
3.2. DIFFERENT MODULATIONS 37
t
T1
TS
t1
VACA
K VACB iL
t2
T2T3
½TS
Figure 3.10: Voltage and current waveforms for power transfer from port B to portA for trapezoidal current mode modulator when VA > kVB
switching losses, and/or magnetizing losses, a more systematic approach is needed
in order to find the modulation scheme that leads to the lowest total losses. In this
section, the discussion focuses merely on the minimization of RMS current (IL).
As depicted in Figure 3.11, DAB converters can be operated with 12 different
basic voltage sequences which form 12 different modulation schemes. These voltage
sequences are distinguished with respect to the different sequences of rising and falling
edges of vACAand vACB
depicted in Figure 3.11. However, to find the modulation
scheme with the lowest IL, only the 6 sequences 1, 9, 2, 11, 12, and 8 are considered.
This is because in the remaining 6 options, an increase in IL does not necessarily
result in a higher DAB power transfer level.
Table 3.1 shows the criteria needed to implement each of the selected 6 voltage
sequences. Power levels , phaseshifts required to obtain specific power levels, and
the inductor RMS current (IL) for different voltage sequences are given in Table 3.2,
3.2. DIFFERENT MODULATIONS 38
t
VACA
k VACB
iL
TS
t
VACA
k VACB
iL
TS
t
VACA
k VACB
iL
TS
t
VACA
k VACB
iL
TS
t
VACA
k VACB
iL`
`
TS
VACA
k VACB
TS
iL
tt
k VACB
TS
iL
t
VACA
k VACB
iL
VACA
TS
Sequence 5 Sequence 6
Sequence 7 Sequence 8
Sequence 1 Sequence 2
Sequence 3 Sequence 4
3.2. DIFFERENT MODULATIONS 39
t
VACA
k VACB
iL
t
k VACB
iL
VACA
TS
t
VACA
k VACB
iL
TSt
VACA
k VACB
iL
Sequence 9 Sequence 10
Sequence 11 Sequence 12
Figure 3.11: The 12 basic voltage sequences generated with DAB converter
Table 3.3, and Table 3.4, respectively.
To achieve the minimal IL for P  < P∆,max, triangular current mode modulation
is suggested [69] . For P  > P∆,max, however, a modulation scheme different to
the trapezoidal current mode modulation is obtained: According to [30], optimal
modulation schemes for high power levels are voltage sequence 11 for P > P∆,max and
12 for P < −P∆,max.
The respective values of the optimal duty cycles depend on the ratio VA/(kVB).
1. Phase shift modulation
VA = kVB
VA > kVB ∩ P  > Pa,max
VA < kVB ∩ P  > Pb,max
3.2. DIFFERENT MODULATIONS 40
Table 3.1: The criteria required to enable each modulation
Mode Criteria
1 D1 −D2 <ϕπ< −D1 +D2
9 −D1 +D2 <ϕπ< D1 −D2
2 D1 −D2 < ϕπ< min
(D1 +D2, 1− (D1 +D2)
)8 D1 −D2 < −ϕ
π< min
(D1 +D2, 1− (D1 +D2)
)10 1− (D1 −D2) < ϕ
π< D1 +D2
12 1− (D1 −D2) < −ϕπ< D1 +D2
Table 3.2: The Power levels of DAB with respect to the each modulation for theapplied DC voltages, duty cycles and the phaseshift
Mode DAB power level
All P = P1 = P2 = kVAVBfSL
eP
1 eP = DAϕπ
9 eP = DBϕπ
2 eP = −14
(ϕ2
π2 − 2ϕπ
+ (DA +DB) + (DA −DB)2
)
8 eP = 14
(ϕ2
π2 + 2ϕπ
+ (DA +DB) + (DA −DB)2
)
10 eP = −12
(ϕ2
π2 − ϕπ
+[
12−DA(1−DA)−DB(1−DB)
])
12 eP = 12
(ϕ2
π2 + ϕπ
+[
12−DA(1−DA)−DB(1−DB)
])
2. Optimal transition mode (D1,opt is calculated and D2,opt = 0.5) for
VA > kVB ∩ P∆,max < P  < Pa,max
3. optimal transition mode (D2,opt is calculated and D1,opt = 0.5) for
VA < kVB ∩ P∆,max < P  < Pb,max
3.2. DIFFERENT MODULATIONS 41
Table 3.3: Phaseshift required to achieve a certain power level
Mode ϕ
1 ϕ = πLfSPkDAVAVB
9 ϕ = πLfSPkDBVAVB
2, 8 ϕ = πsgn(P ).
(DA +DB − 2
√DADB − LP fS
kVAVB
)
10, 12 ϕ = πsgn(P ).
(12−√DA(1−DA) +DB(1−DB)− 1
4− 2fSLP 
kVAVB
)
Table 3.4: The RMS current IL with respect to the considered voltage sequences
Mode Inductor RMS current IL
ALL IL = 12fSL
√D2AV
2A
(1− 4
3D1
)+D2
Bk2V 2
B
(1− 4
3DB
)+ kVAVB
3eRMS
1 eRMS = 6DA
(ϕ2
π2 +[DB(DB − 1) +
D2A
3
])
9 eRMS = 6DB
(ϕ2
π2 +[DA(DA − 1) +
D2B
3
])2 eRMS = D3
A + 3D2A
(DB − ϕ
π
)+ 3DA
[ϕ2
π2 −DB
(2− 2ϕ
π−DB
)]+(DB − ϕ
π
)3
8 eRMS = D3A + 3D2
A
(DB + ϕ
π
)+ 3DA
[ϕ2
π2 −DB
(2 + 2ϕ
π+DB
)]+(DB + ϕ
π
)3
10 eRMS =
(1− 2ϕ
π
)(1− ϕ
π+ ϕ2
π2 − 3[DA(1−DA) +DB(1−DB)
])
12 eRMS =
(1 + 2ϕ
π
)(1 + ϕ
π+ ϕ2
π2 − 3[DA(1−DA) +DB(1−DB)
])
where Pa,max and Pb,max are
Pa,max : DA,opt(Pa,max) = 0.5 ∩ P∆,max < Pa,max < PPS,max
Pb,max : DB,opt(Pb,max) = 0.5 ∩ P∆,max < Pb,max < PPS,max
3.3. STEADYSTATE MODEL OF THE CONVERTER 42
tTS
t1
VA
K VB
iLs
t2 ½TSt3
TIITI TIII TIV
i0
i1
i2i3
Figure 3.12: Waveform of Dual Active Bridge Converter operating in Continuous Current Mode (CCM) with Zero Voltage Switching (ZVS)
3.3 SteadyState Model of the converter
Figure 3.12 depicts the voltage and current waveforms of sequence 11 in Figure 3.12.
For simplicity, let
iL(t0) = iL(0) = −i0
iL(t1) = i1
iL(t2) = i2
iL(t3) = i3
(3.29)
By considering the halfcycle symmetry of the current waveform in DAB converters
(3.7)
iL(1
2Ts) = iL(0) => (3.30)
iL(1
2Ts)− iL(t0) = 2iL(0) (3.31)
3.3. STEADYSTATE MODEL OF THE CONVERTER 43
is derived. From Figure 3.12, i0 is calculated in terms of the two DC voltages and
the time interval between each switching.
i1 =1
Lω(VA + kVB)TI + i0 (3.32)
i2 =1
Lω(VA)TII + i1 (3.33)
i3 =1
Lω(VA − kVB)TIII + i2 (3.34)
i(1/2Ts) =1
Lω(−kVB)TIV + i3 (3.35)
by adding the two sides of (3.32), (3.33), (3.34), and (3.35), the following equation is
derived:
iL(1/2Ts)− iL(t0) =1
Lω
[VA(TI + TII + TIII)− kVB(TIII + TIV − TI)
]=>
i0 =1
2Lω
[VA(TI + TII + TIII)− kVB(TIII + TIV − TI)
](3.36)
Similarly i1, i2, i3 can be calculated as follows:
i1 =−1
2Lω
[VA(TII + TIII − TI)− kVB(TIII + TIV + TI)
](3.37)
i2 =−1
2Lω
[VA(−TI − TII + TIII)− kVB(TIII + TIV + TI)
](3.38)
i3 =−1
2Lω
[VA(−TI − TII − TIII)− kVB(−TIII + TIV + TI)
](3.39)
As discussed before in the literature review dual active bridge converters are controlled
by 4 control parameters; the phase shift (ϕ) between the two bridges, the duty cycle,
DA, of side A, the duty cycle, DB, of side B, and the switching frequency (fS).
Therefore, it is desired to calculate the edge currents (i0, i1, i2, and i3) as a function
3.3. STEADYSTATE MODEL OF THE CONVERTER 44
of the DC voltages, transformer ratio, and the 4 control parameters instead of the 4
different time intervals (TI , TII , TIII , and TIV ) depicted in Figure 3.12.
To do this first the relation between the control parameters and the time intervals
are presented as follows:
TI + TII + TIII = 2πDA
TI + TIII + TIV = 2πDB
1
2(2TI + TII + TIV ) = πϕ
TI + TII + TIIITIV = π
(3.40)
using (3.40) , the time intervals are calculated as follows:
TI = (DA +DB + ϕ− 1)π (3.41)
TII = (1− 2DB)π (3.42)
TIII = (DA +DB − ϕ)π (3.43)
TIV = (1− 2DA)π (3.44)
Replacing (3.36), (3.37), (3.38), and (3.39) with (3.41), (3.42), (3.43) and (3.44)
results in:
i0 =π
Lω
(DAVA + (DA + ϕ− 1)kVB
)(3.45)
i1 =π
Lω
((DB + ϕ− 1)VA + (DB)kVB
)(3.46)
i2 =π
Lω
((ϕ−DB)VA + (DB)kVB
)(3.47)
i3 =π
Lω
(DAVA + (ϕ−DA)kVB
)(3.48)
3.3. STEADYSTATE MODEL OF THE CONVERTER 45
tTS
t1
VA
iLs
t2 ½TSt3
TIITI TIII TIV
i0
i2i3
i1
i2i3
A3A2A1
Figure 3.13: Area of the Current Waveform of DAB operating in CCM
From Figure 3.13 the area of the current in each interval is calculated as:
A1 =(i1 − i0)t1
2
A2 =(i1 − i0)t1
2
A3 =(i1 − i0)t1
2
(3.49)
and ∫ t3
0
iL(t)dt = A1 + A2 + A3 (3.50)
By replacing (3.45), (3.46), (3.47), (3.48), (3.49), and (3.50) into (3.8) the power
flow for sequence 11 is derived as:
P =πVAkVBLω
(1
4−(
(DA −1
2)2 + (DB −
1
2)2 + (ϕ− 1
2)2))
(3.51)
3.4. LOSS ANALYSIS OF THE DAB CONVERTER 46
and the average output current is calculated by PVB
. Therefore,
I∗ =πVAk
Lω
(1
4−(
(DA −1
2)2 + (DB −
1
2)2 + (ϕ− 1
2)2))
(3.52)
3.4 Loss Analysis of the DAB Converter
In this thesis, the lossless electric DAB model (Figure 3.2) is used to evaluate the loss
analysis of the DAB converter and to determine the converter stress values mentioned
below.
• RMS currents related to the semiconductor switches, the transformer windings,
and the inductor windings (which result in conduction losses) ;
• Instantaneous currents during switching (which result in switching losses);
• peak inductor currents (which result in inductor core loss);
• voltagetime areas applied to the transformer core (which result in transformer
core loss).
The calculation of the power dissipated in DAB converters considers the windings,
semiconductors, inductor and transformer, and the surrounding parasitic components
(e.g. PCB stray inductances). The parasitic components are neglected in the simple
loss model evaluated in this section.
3.4.1 Power Loss in Switch Converters
the total dissipated power in switch converters consist of conduction losses and switch
ing losses.
3.4. LOSS ANALYSIS OF THE DAB CONVERTER 47
Conduction losses of each switch is determined based on their respective RMS
current. Due to the halfcycle symmetry of the current and voltage waveforms in
DAB converters and that every switch conducts a total of half a switching cycle in
each period (TS), the semiconductor RMS current of side A (ISA) and side B (ISB)
are derived as follows
ISA =IL√
2(3.53)
ISB =kIL√
2(3.54)
Where IL is the RMS value of iL(t). Therefore, switches in side A and side B generate
the total conduction losses of
PSA,cond = 4RSAI2SA (3.55)
PSB,cond = 4RSBI2SB (3.56)
In this application, Litz wire is used in the high frequency network, which helps reduce
the skin effect by a noticeable amount. Therefore, the influence of high frequency skin
and proximity effect are neglected.
The DC switch resistance of the MOSFETs are obtained from the data sheet values:
RSA = RSB = 0.11Ω VGS = 10V, ID = 12.7A, Tj = 150C (3.57)
Calculation of the switching losses is obtained from Ploss,sw =∫v(t)i(t) over the
switching interval. Therefore, if the switching transition occurs when the voltage is
leaning towards 0 (Zero Voltage Switching)/ the current is almost 0 (Zero current
3.4. LOSS ANALYSIS OF THE DAB CONVERTER 48
switching), the power dissipated as switching losses can be neglected.
Soft Switching Conditions for DAB Converters
In power converters, Soft switching of a semiconductor device happens when the
switching process occurs with considerably low power dissipation. This phenomena
can occur in two ways: either the voltage across the semiconductor is kept at zero
(Zero Voltage Switching (ZVS)) or the current passed through the switch remains
near zero (Zero Current Switching (ZCS)) while the switching takes place.
In DAB converters, turnon zero voltage switching of MOSFETs is achieved when
the body diode is on and the voltage across the switch is almost zero (body diode
voltage). Turn off ZVS occurs when the current of the MOSFET just before turn off
passes through the switch rather than the body diode. This way when the switch
is turned off the transformer stray inductance won’t allow sudden changes in the
current. Subsequently, the current will have no choice but to alter its way through
the inherent capacitor across the transistor. The capacitor slows down the trend
of the rising voltage across the MOSFET, making it stay at almost zero while the
switching takes place. It is evident that the use of snubber capacitors can help keep
the voltage at zero for a longer duration; Thus, improving the ZVS at turn off when
needed.
For the specific case of DAB converters, the ZVS can be determined from the cur
rent and voltage waveforms of the HF network of the conveter rather than analyzing
each bridge at every switching instant. When two switches are arranged as a leg on
a dc bus (e.g. SA1 and SA2 or SA3 and SA4 in Figure 2.1), the ZVS condition for
both switches on each leg is met when the net current leaving the leg pole (centre
3.4. LOSS ANALYSIS OF THE DAB CONVERTER 49
of the leg) lags the voltage of the pole.. A short amount of time should be set aside
between the turnoff and turnon time of the two switches on single leg; This time
interval is called the dead time and its duration plays a major role in achieving a
better ZVS for turnon of the MOSFETs. Basically, the dead time allows the current
to have enough time to discharge the snubber capacitor with the DC bus voltage and
charge the other snubber capacitor from 0 to the DC bus voltage. Dead times should
not be too short to allow complete charge/discharge of snubber capacitors nor should
they be too long to let the current alter its direction, which results in reversing the
charge/discharge process of the capacitor. These charge and discharges are basically
a resonant between snubber capacitors and the stray inductance of the high frequency
transformer. With the assumption of a given dead time (td) and a constant current
during the dead time, the minimum current required to achieve ZVS in each leg is
calculated from
IminZV S = 2CossVBustd
(3.58)
Operating under ZVS results in very low switching losses, since SA1 is turned off with
vDS,T1 ≈ 0 (zero voltage turnoff), and with the assumption of sufficient Tdeadtime, SA2
is turned on with vDS,T2 = −vD ≈ 0 (zero voltage turnon; typically, the losses due
to the forward voltage drop vD of the body diode can be neglected during the short
time the diode conducts). Therefore, this switching operation is termed Zero Voltage
Switching (ZVS) or soft switching.
3.4. LOSS ANALYSIS OF THE DAB CONVERTER 50
Optimal Transition Mode for High Power
As explained previously the optimal transition mode of the converter uses sequence
11 in Figure 3.11 for power transfer higher than P∆,max. In this modulation, the
current leaving the centre pole of each leg lags the corresponding voltage of the node.
Therefore, the condition for a turnoff and turnon ZVS is satisfied. However, to
achieve the rising and falling sequence of the voltages VACAand VACB
for the desired
modulation depicted in Figure 3.12, the discrimination characteristics explored in
Table 3.1 must be satisfied. Figure 3.14 depicts the 3D control space (DA, DB, and
ϕAB) where the conditions for ZVS is satisfied for Va = 400V and Vb = 350V . This
plane depicts the combination of all the three phaseshifts at each point required to
achieve ZVS for certain switching frequency (here, fS = 300kHz) and DC voltage
levels. Therefore, this plane is called the 3D ZVS region.
Figure 3.15 depicts the 2D ZVS plane for the same DC voltage levels. However,
in this figure, the DA −DB plane for different values of ϕAB is depicted. The planes
in Figure 3.15 show the ZVS regions of the converter at certain operating conditions
(DC voltages) and switching frequency; Hence, they are termed the soft switching
zones. In order to achieve a high efficiency converter operating at high frequencies,
it is essential to follow these ZVS regions.
3.4.2 Transformer, Inductor
The power dissipated in the high frequency transformer can be categorized into:
conduction losses and core losses. The transformer copper losses are obtained from
Ptr,cond = (RtrA + k2RtrB)I2L (3.59)
3.4. LOSS ANALYSIS OF THE DAB CONVERTER 51
Figure 3.14: 3D ZVS region space for Va=400 Vb=350
Where RtrB and RtrB are the respective resistance of the side A and B windings.
The transformer core losses are derived from Steinmetz equation,
Ptr,core ≈ Vtr,corekfαSB
βtr,peak (3.60)
3.4. LOSS ANALYSIS OF THE DAB CONVERTER 52
Figure 3.15: 2DZVS region space for Va= 400 V, Vb= 350 V
with the Steinmetz parameters k, α, and β, the total core volume Vtr,core, and the
peak magnetic flux density Btr,peak,
Btr,peak =max[Φtr(t)−min[Φtr(t]
2
1
Atr,core∀ 0 < t ≤ TS (3.61)
3.5. LINEAR CONTROL FOR DAB CONVERTERS 53
and
Φtr(t) =
∫ t
0
vM(tint)
NA
dtint + Φ(0) (3.62)
(NA is the number of turns of side A winding, Atr,core is the core cross sectional area,
and vM is the voltage applied to the magnetizing inductance.)
3.4.3 Total Losses  Predicted Efficiency
The auxiliary power losses is not calculated in this thesis. Therefore, the total losses
Pt are calculated with
Pt = PSA,cond + PSA,sw + Ptr,cond + Ptr,core + PSB,cond + PSB,sw (3.63)
The most simple loss model evaluates all required characteristics (e.g. RMS current
values) at a given input power, Pin, in order to include the impact of the losses on
these quantities. The efficiency η = Pout/Pin is then calculated.
3.5 Linear Control for DAB converters
In this section, a closedloop PI control loop is introduced for the DAB converter. The
control loop consist of a modulator, lookup table, linear compensator, and a feedback
which are explained in more detail in this section. Moreover, the digitalization of the
control will be explained.
3.5. LINEAR CONTROL FOR DAB CONVERTERS 54
Ls k:1
CB
IB
SA3SA1
SA2 SA4
SB3SB1
SB2 SB4
CA
+

VB
+

VA
Bridge A Bridge B
TractionBattery
+
ADC
k1
LUT
LUT
LUT
φA
φB
φAB
Modulator
SA1 , SA2 , SA3 , SA4
SB1 , SB2 , SB3 , SB4
iref
+
k2
+
∫
Figure 3.16: PI controller
3.5.1 Closed Loop PI Control
As depicted in Figure 3.16, the closed loop PI control used in this section is con
structed with a modulator, lookup table, linear compensator, and a current feedback.
The modulator of the DAB converter creates the switching instants for both of the
bridges A and B based on a set of inputs: ϕA, ϕB, ϕAB, and the frequency. Therefore,
in order to control the DAB converter, the 4 control parameters ϕA, ϕB, ϕAB, and the
frequency need to be given to the modulator. As explained previously, it is desirable
to have ZVS for all the switching. Thus, in order to achieve ZVS a lookup table is
constructed that for every given power, outputs the 4 control parameter in such way
that the discrimination characteristics explored in Table 3.1 is satisfied.
An average current mode control which is the current at the DC ports is used
to regulate the current at the output of the DAB converter. As depicted in Figure
3.16 the current at the output is given back to the controller as a feedback and the
3.5. LINEAR CONTROL FOR DAB CONVERTERS 55
k1 +
++
k2 ∫z
k11 + +
+ ++
k22 1/Z 1/Z
PI
sT
sTk1
1
1
211
1
2
z
zTkk S
A. B. C.
222
2111
kk
kkk
Figure 3.17: Conversion of Continuous PI controller to Discrete PI controller
error of the current is passed through a PI controller that creates a reference power
for the lookup table.
3.5.2 Digitalization of the PI control
Digital control is based on discrete control rather than continuous control. In digital
control the feedback to the control system is converted from analog to digital values
via Analog to Digital Conversion (ADC) with a specific sampling rate. The sampling
rate of the ADC used in this section is 400 kHz.
As for the compensator, a conversion has to be made from continuous transfer function
to discrete transfer function s domain to z domain. Figure 3.17 (A) depicts a PI
controller with the transfer function k 1+sTsT
. By converting the stransfer function to
zdomain transfer function via Tustin’s method, k1 + k2TS2
1+z−1
1−z−1 is achieved (Figure
3.17 B). To simplify the digital coding into the microcontroller (in this project FPGA
is used), a conversion is made from the block diagram illustrated in Figure 3.17 (B)
3.6. SIMULATION AND EXPERIMENTAL RESULTS 56
to the block diagram in Figure 3.17 (C) K11 and K22 is calculated as follows:
Y (z)
X(z)= k1 + k2
TS2
1 + z−1
1− z−1−→
Y (z)(
1− z−1)
= k1
(1− z−1
)X(z) + k2
TS2
(1 + z−1
)X(z) −→
Y (z) =
(k1 + k2
TS2︸ ︷︷ ︸
k11
)X(z)−
(k1 − k2
TS2︸ ︷︷ ︸
k22
)X(z − 1) + Y (z − 1) −→
k11 = k1 + k2TS2
& k22 = k1 − k2TS2
(3.64)
The above equation shows that k11+k22 represents the integral coefficient and k11−k22
corresponds to the gain of the controller.
3.6 Simulation and Experimental Results
In this section, Simulation results are provided to demonstrate phaseshift modula
tion with ϕA = 0.5 and ϕB = 0.5, or with either ϕA or ϕB set to 0.5 and the other
variable. Moreover, the transient behaviour of the linear control system is examined
for the step load change at the output of the converter and for step voltage change
at the input of the converter. It will be shown that the linear controller is unstable
at some points.
Figure 3.18 shows the the steady state operating points for different cases with dif
ferent voltage and power levels.
Table 3.5 shows different cases of phase shift control for VA = 360 VDC and VB = 400
VDC. The estimate current (I∗) and the estimate power (P ∗) in the table is calculated
via (3.52) and (3.51), respectively.
Figure 3.18 depicts the waveforms of the switching instant for Cases 3 and 6
3.6. SIMULATION AND EXPERIMENTAL RESULTS 57
0.000102 0.000104 0.000106 0.000108 0.00011Time (s)
0
200
400
200
400
Vp Vs 10*ip
Vp
Vs
10*ip
Figure 3.18: operation for Va=400 Vb=350 ϕAB = 0.116
in Table 3.5. Figure 3.18 (A) depicts case 6, where P = 2137W and ZVS is fully
achieved. Figure 3.18 (B) depicts case 3, where P = 1195W and ZVS is critically
achieved. The minimum Required transformer current (ip) in order to achieve ZVS
is derived by replacing Coss = 160pF , VBus = 360V , and td = 41ns into (3.58). With
the assumption of a constant current while switching (I1ZV S = I2
ZV S), the minimum
current is calculated as IminZV S = 2.76A. However, the assumption of the constant
current is while switching does not hold in this case. Figure 3.18 A and B both
demonstrate that the magnitude of ip decreases during the deadtime. Therefore, in
order to achieve ZVS the charge of the mosfet output capacitor∫ td ip(t)d(t) has to
be above 0.1152µ A.sec. The charge current in case 6 is much higher than 0.1152µ
A.sec and consequently it can be seen in Figure 3.18 (A) that turn on for SA2 occurs
much after transformer primary voltage (Vp) has altered its value form −VA to VB.
3.6. SIMULATION AND EXPERIMENTAL RESULTS 58
Table 3.5: DAB waveform details for VA = 360 VDC and VB = 400 VDC with different power levels
Case 1 2 3 4 5 6 7 8 9
ϕA 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.44
ϕB 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.44 0.5
ϕAB 0.029 0.058 0.063 0.069 0.087 0.116 0.232 0.232 0.232
IB 1.17 A 2.66 A 3 A 3.28 A 4.1 A 5.33 A 9.18 A 9 A 8.96 A
IestB 1.45 A 2.80 A 3.07 A 3.33 A 4.09 A 5.28 A 9.17 A 9 A 9 A
P 470 W 1066 W 1195 W 1317 W 1647 W 2137 W 3691 W 3634 W 3600 W
P est 580 W 1126 W 1231 W 1335 W 1638 W 2114 W 3671 W 3601 W 3602 W
I1ZV S 1.32 A 3.22 A 3.54 A 3.97 A 5.16 A 6.9 A 13.66 A 13.67 A 6.95 A
I2ZV S 0.45 A 1.12 A 1.29 A 3.29 A 4.1 A 3.9 A 10.3 A 10.39 A 3.23 A
ZVS 7 7 Critical3 3 3 3 3 3 3
0
200
400
600
200
400
100*ip
Vs
Vp
0.0001062 0.00010622 0.00010624 0.00010626 0.00010628
Time (s)
0
0.5
1SA2SA1
td
I1
ZVS
I2
ZVS
(A)
0
200
400
600
800
200
400
100*ip
Vs
Vp
0.00010628 0.0001063 0.00010632 0.00010634 0.00010636
Time (s)
0
0.5
1 SA2SA1
I1ZVS
I2
ZVS
td
(B)
Figure 3.19: (A) depicts operation for Va=400 Vb=350 ϕAB = 0.058 and (B) depictsdepicts operation for Va=400 Vb=350 ϕAB = 0.029
The Charge current in Figure 3.18 (B) is exactly 0.1152µ A.sec. Therefore, critical
ZVS is achieved. Turn on of SA2 occurs exactly when transformer primary voltage
(Vp) reaches +VA.
Figure 3.20 A and B show the case where ZVS is not fully achieved because the output
capacitors across the mosfet did not have enough time to discharge and charge. In this
case the charge of the output capacitance is less than 0.1152µ A.sec. It can be seen
that in both cases switch SA2 turns on before Vp reaches +VA. Next, we are going
3.6. SIMULATION AND EXPERIMENTAL RESULTS 59
0
200
400
600
200
400
Vs
100*ipVp
0.00010628 0.0001063 0.00010632 0.00010634 0.00010636
Time (s)
0
0.4
0.8 SA2SA1
0
200
400
600
200
400
Vs
100*ip
Vp
0.0001063 0.00010635 0.0001064 0.00010645 0.0001065
Time (s)
0
0.2
0.4
0.6
0.8
1
SA2SA1
I1ZVS
I2
ZVSI1
ZVS
I2ZVS
(A) (B)
Figure 3.20: (A) depicts operation for Va=400 Vb=350 ϕAB = 0.116 and (B) depictsdepicts operation for Va=400 Vb=350 ϕAB = 0.063
to investigate the case where either ϕA or ϕB is variable. In the previous chapters
we explained that it is desirable to have ϕA and ϕB as close to 0.5 as possible. This
results in less circulating current which means higher efficiency. Therefore, as long as
the desired power level is achieved with conventional phase shift control, there is no
need to modify ϕA or ϕB.
Let us consider different voltage levels for the DAB converter. Figure 3.21 depicts the
steady state operation of the DAB converter with VA = 400 VDC, VB = 250 VDC.
In this figure, conventional phaseshift ϕA = ϕB = 0.5 is used to transfer the power
for high load (IBat = 12A). It can be seen that the operation takes place with full
achieved ZVS for all the switching instants. However, Figure 3.22 depicts another case
for the same voltage levels, where the conventional phaseshift modulation is used for
lower power transfer (IBat = 10A). Here, it can be depicted that the switching in
bridge B do not achieve ZVS while Vs changes its state from VB to + VB. This is
because the inductor current at this switching state is still negative the circle area in
Figure 3.22 and this prevents ZVS from happening while switching takes place. To
go around this, some modifications can be done to achieve ZVS for the same power
level. Figure 3.23 shows the case where ϕB remains at 0.5, however ϕA is set to 0.3.
3.6. SIMULATION AND EXPERIMENTAL RESULTS 60
0.000118 0.00012 0.000122 0.000124 0.000126
Time (s)
0
200
400
200
400
10*ip
Vp
Vs
Figure 3.21: operation for Va=400 Vb=250 ϕAB = 0.3, IBat = 12.1A With ZVS
This modification, enables ZVS operation for the DAB converter for lower battery
current (IBAT = 10A) lower power levels. As explained previously, the ϕ values are
achieved from the ZVS regions for different power level.
Figure 3.26, 3.27, and 3.28 depict different transient responses of the converter.
The gain and the time constant k and T in Figure 3.17 (A), respectively is tuned
at k = 6 and T = 0.000028. Using Tustin’s method k1 and k2 in Figure 3.17 (B) is
calculated to be:
k1 = 6 (3.65)
k2 = 600000 (3.66)
3.6. SIMULATION AND EXPERIMENTAL RESULTS 61
0.000118 0.00012 0.000122 0.000124 0.000126
Time (s)
0
200
400
200
400
10*ip
Vp
Vs
Figure 3.22: operation for Va=400 Vb=250 ϕAB = 0.2, IBat = 10A without ZVS
The sampling frequency of the ADC used in this application is 400 kHz (TS =
400kHz). By substituting (3.65), (3.66) and TS = 400kHz in (3.64), coefficients
of Figure 3.17 (C) are calculated as follows:
k11 = 6.75 (3.67)
k22 = 5.25 (3.68)
One of the major problems of using a PI controller in DAB converters is that due to
the nonlinearity of the systemdynamics, it is not always stable over a wide voltage
range and load range. Figure 3.29 depicts a case of instability in the system.
3.6. SIMULATION AND EXPERIMENTAL RESULTS 62
0.000118 0.00012 0.000122 0.000124 0.000126
Time (s)
0
200
400
200
400
10*ip
Vp
Vs
Figure 3.23: operation for Va=400 Vb=250 ϕAB = 0.2, ϕA = 0.31, and ϕB = 0.5with IBat = 10A with ZVS
3.6. SIMULATION AND EXPERIMENTAL RESULTS 63
0.00025 0.000252 0.000254 0.000256 0.000258 0.00026Time (s)
0
200
400
600
200
400
10*ip Vp Vs
Figure 3.24: Steady state operation of the DAB converter with the operating conditions: VA = 360, VB = 400, iBat = 6A
3.6. SIMULATION AND EXPERIMENTAL RESULTS 64
0.000258 0.00026 0.000262 0.000264 0.000266 0.000268 0.00027Time (s)
0
200
400
200
400
10*ip Vp Vs
Figure 3.25: Steady state operation of the DAB converter with the operating conditions: VA = 360, VB = 400, iBat = 8A
4
5
6
7
8 I(BAT)
0.0002 0.0003 0.0004 0.0005
Time (s)
0
200
400
600
200
400
600
Figure 3.26: Transient response of the DAB converter VA = 360, VB = 400 I=8 A toI=4 A
3.6. SIMULATION AND EXPERIMENTAL RESULTS 65
6
6.5
7
7.5
8I(BAT)
0.0002 0.0003 0.0004 0.0005
Time (s)
0
200
400
600
200
400
600
Figure 3.27: Transient response of the DAB converter VA = 360, VB = 400 I=8 A toI=6 A
11.5
12
12.5
13
13.5
14
I(BAT)
0.0003 0.0004 0.0005
Time (s)
0
200
400
600
200
400
600
Figure 3.28: Transient response of the DAB converter VA = 400, VB = 250 I=14 Ato I=12 A
3.6. SIMULATION AND EXPERIMENTAL RESULTS 66
0
5
10
5e005 0.0001 0.00015 0.0002 0.00025 0.0003
Time (s)
0
500
500
Figure 3.29: instability in some operating conditions for PI controller
360
370
380
390
400
V_A
6
6.2
6.4
I_BAT
0.0002 0.0003 0.0004Time (s)
0
200
400
200
400
Figure 3.30: transient response when VB = 400V , I = 6A VA = 360V to VA = 400V
3.7. EXPERIMENTAL RESULTS 67
3.7 Experimental Results
A 3kW prototype is implemented to verify the performance of the proposed converter.
The proposed high voltage DC/DC converter is a part of the 3KW AC/DC converter.
The converter specifications are shown in Table 3.6. Table 3.7 shows the passive
components used to implement the DAB converter.
Figures 3.31 and 3.32 depict the steady state operation where the discrimination
Table 3.6: DAB converter Specifications
Symbol Parameter Value
Po Output Power 0  3.3 kW
VA Input Voltage 350  450 VDC
VB Traction Battery 250  430 VDC
fsw Frequency 200  350 kHz
Iin(max) Maximum input current 10 A
Table 3.7: DAB system parameters
Symbol Parameter Value
Ls Leakage Inductance 9 uH
k Transformer Turn’s Ratio 0.9:1
CA Filter Capacitance 2*80 uF
CB Filter Capacitance 2*80 uF
S Mosfets IPB65R110CFD
of the ZVS region is not taken into account. It can be seen in the figures that this
results in hard switching for some switches causing voltage spikes and ringing on the
transistors. Switching without ZVS will cause dissipation in the semiconductors and
at high voltage levels, the spikes can burn out the switches. Figures 3.33 and 3.33,
3.7. EXPERIMENTAL RESULTS 68
ip
Vp Vs
ZVS not achieved
Figure 3.31: steady state operation at VA = 100V , VB = 90V without ZVS
however, depict the steady state operation of the DAB converter with the necessary
calculation required to achieve ZVS. It can be seen that to maintain ZVS, ϕA and ϕB
is modified.
Transient response for some operating conditions of the converter is depicted in
Figure 3.35.
3.7. EXPERIMENTAL RESULTS 69
ip
Vp
Vs
ZVS not achieved
Figure 3.32: steady state operation at VA = 100V , VB = 120V without ZVS
3.7. EXPERIMENTAL RESULTS 70
ipVp
VsIBAT
Figure 3.33: steady state operation at VA = 100V , VB = 120V , I = 2.2A withachieved ZVS
3.7. EXPERIMENTAL RESULTS 71
ip
Vp Vs
Figure 3.34: steady state operation at VB = 100V , VA = 90V with achieved ZVS
Figure 3.35: transient response at VB = 100V , VA = 120V with achieved ZVS
72
Chapter 4
Controller Design
4.1 Introduction
The employed controller, in this thesis, is similar to that of a traditional 2loop
controller, where the inner current loop shows a very fast dynamic response and
the outer loop control (Voltage loop, Current loop, and Power loop) has very slow
dynamics due to the large capacitances on the DC buses A and B.
The inner current loop is a digital current control designed based on a novel
GeometricSequence Control (GSC) approach for Dual Active Bridge (DAB) convert
ers. The control variable in the GSC approach is calculated such that the error reduces
with a geometricprogression trend. Although the GSC control is derived based on the
mathematical model of the converter, it is very robust against parameter variations
and system uncertainties.
In this chapter, first the modulation scheme is described. After that, the proposed
GSC approach is explained for digital current control and Robustness of the control
will be investigated. The outer voltage loop that creates the current reference for the
fast inner current loop is also explained. Simulation and Experimental results are
4.2. MODULATION SCHEME 73
provided to verify the validity behaviour of the proposed control structure.
4.2 Modulation Scheme
The modulation scheme used for the proposed control in this thesis is based on Phase
shift Control. Phaseshift modulation creates switching instants of the DAB
converter based on 4 input parameters: ϕA, ϕB, ϕAB and the switching frequency as
described in Chapter 3. The method used in this thesis constitutes of digital counter,
sawtooth counters, and construction of the switching instants based on the sawtooth
counters.
First a digital counter is created based on the switching frequency of the converter.
The digital counter counts to the highest value (Counter Upper Limit (CUL)) before
it resets. The CUL is defined to be:
CUL =fClkfSW
(4.1)
where fClk is the clock frequency of the microcontroller and fSW is the switching
frequency.
After creating the counter, 4 sawtooth counters with the same CUL as the counter are
created (Figure 4.2). The starting point of the sawtooth counters are created based
on the remaining 3 input parameters of the modulation: ϕA, ϕB, ϕAB. However, in
order to have a simpler modulation design ϕP,AB replaced ϕAB.
ϕP,AB =1
2
(ϕA − ϕB
)+ ϕAB (4.2)
Figure 4.2 demonstrates how the switching instants of the converter is created based
4.2. MODULATION SCHEME 74
k VB
VA
φA
φB
φP_AB
Counter
t
t
t
t
t
t
B_Sawtooth_I
B_Sawtooth_II
A_Sawtooth_I
A_Sawtooth_II
Figure 4.1: Sawtooth counter created based on the digital counter for PSM
4.3. DIGITAL CURRENT CONTROL IN DAB CONVERTERSBASED ON NOVEL GEOMETRICSEQUENCE CONTROL (GSC)APPROACH 75
t
t
SA1
SA2
t
A_Sawtooth_I
(A)
t
t
SA3
SA4
t
A_Sawtooth_II
(B)
t
t
SB1
SB2
t
B_Sawtooth_I
(C)
t
t
SB3
SB4
t
B_Sawtooth_II
(D)
Figure 4.2: switching instants created based on their respective sawtooth counter
on each sawtooth counter. It can been seen that each of the sawtooth counter are
responsible for creating two of the semiconductor switches which correspond to the
switches of each individual leg. The rising and falling edges of the switching takes
place when the sawtooth counters reach half switching cycle (TS/2) or when the
sawtooth is reset to zero.
4.3 Digital Current Control in DAB Converters Based on Novel Geometric
Sequence Control (GSC) Approach
In this thesis, a digital current control technique is used to determine the control
parameter of the next switching cycle based on a sensed or observed state and in
put/output information. A Novel GSC approach is proposed to design a discrete
4.3. DIGITAL CURRENT CONTROL IN DAB CONVERTERSBASED ON NOVEL GEOMETRICSEQUENCE CONTROL (GSC)APPROACH 76
control law for current programmed control technique. Basically, the proposed con
trol scheme acts in such way that the magnitude of the feedback error is reduced by
a geometricsequence trend in each cycle.
4.3.1 Oscillation Problem
Figure 4.3 depicts open loop control of the DAB converter when there is current
perturbation. The current error, ∆i(n), is defined as the current difference between
the desired steady state current and the actual instantaneous current at that spe
cific halfcycle (i(n)). Therefore, perturbation of the current can be denoted as ∆i
at the beginning of any halfcycle. In can be seen from Figure 4.3 that if −∆i oc
curs, provided that the phaseshift remains constant during the whole switching cycle
(openloop), the error oscillates between +∆i and −∆i in the each half switching cy
cle. This creates an oscillatory behaviour in the system. Typically, in basic converters
such as buck, boost, etc the control is designed such that the current error, ∆i, is
compensated in one iteration. However, as depicted in Figure 4.4, compensation of
the error in one halfcycle results in oscillation of the current waveform.
To avoid these oscillations, the progression of the current waveform in response to
a change in the phaseshift is investigated. Through that, a digital control approach
is proposed to improve the state space current waveforms and remove/ attenuate
oscillations.
4.3.2 GeometricSequence Current Control Approach
As explained in the previous section, poor control performance is achieved by simply
changing the phase shift for one half switching cycle. Therefore, to move from one
4.3. DIGITAL CURRENT CONTROL IN DAB CONVERTERSBASED ON NOVEL GEOMETRICSEQUENCE CONTROL (GSC)APPROACH 77
i(n1) Δ i
+i(n)m1
m2
m3
m4
+Δ i
Δ i
+i(n+1)
+i(n+2)
Ts/2φ AB
Figure 4.3: Oscillation in CCM mode in response to perturbation
i(n1) i(n)
m1
m2
m3
m4
δ i(n)
+i(n+1)
+i(n+2)
Ts/2φAB
ΔφAB
i(n+1)
ΔφAB
Figure 4.4: Oscillation in CCM mode in response to poor control scheme
steady state (cycle 0) operating point to another (cycle (n)) without causing oscilla
tion, ϕAB should be modified appropriately to address this issue. Assume, ϕAB(k)
represents the phase shift at the kth half switching cycle, and i(k) represents the lead
ing edge sampled current at this interval. The objective is to move from one steady
state current, i(0), to a new one, i(n) after n successive halfcycles. Therefore, the
trajectory of ϕAB begins from the initial steadystate ϕAB(0) and ends with the final
steadystate ϕAB(n) at which i(n) = i(n− 1) = iref .
Effect of Change in ϕAB on the current waveform
It is useful to examine the transient evolution of the current waveform in detail when
designing the control law. In order to design the control approach, we first have to
4.3. DIGITAL CURRENT CONTROL IN DAB CONVERTERSBASED ON NOVEL GEOMETRICSEQUENCE CONTROL (GSC)APPROACH 78
investigate how changes in ϕAB effects the current at TS/2. Figure 4.5 illustrates how
the current waveform changes in response to a change in ϕAB. ϕAB for every half
cycle is applied to the modulation at time interval T1. It is important to note that
the change in current waveform in response to ϕAB highly depends on the utilized
modulation scheme and the timing interval that the change in ϕAB is applied to the
modulation.
In Figure 4.5 (A) the dashed waveform corresponding to i(n) = i(n + 1) and the
solid line illustrates the current when a change in ϕAB occurs. It can be seen in
Figure 4.5 (A) that d1, d2, and d are equal to the change in the sampled current
δi(n+1). Therefore, we have:
d = δi(n+1) = i(n+ 1)− i(n) (4.3)
d1 = d2 = d (4.4)
The magnified figure of the designated area in Figure 4.5 (A) is depicted in Figure
ΔφAB
m2
m1
m3
ΔφAB
d1 d'
d''
d''
i(n)
d= δ i(n)
ΔφAB
Ts/2
m1
m2
m3m4
d1
d2
(A) (B)
+i(n+1)
Figure 4.5: Effect of Change in ϕAB on the current waveform
4.3. DIGITAL CURRENT CONTROL IN DAB CONVERTERSBASED ON NOVEL GEOMETRICSEQUENCE CONTROL (GSC)APPROACH 79
4.5 (B). In this Figure we will find the relationship between the change in phaseshift
(∆ϕAB) and d1. d1 can be written as
d1 = d′ − d′′ (4.5)
Therefore, we need to find d′
and d′′
in order to find phase shift d1.
To do this first it can be proven that the two highlighted triangles are congruent.
Therefore, it is evident that d′′
is equivalent to d′. d′′′
is calculated with
d′= d
′′′=
2
fSm1∆ϕABn (4.6)
∆ϕAB(n) = ϕAB(n)− ϕ∗AB(n) (4.7)
where ϕ∗AB(n) is the phase shift corresponding to the dotted waveform in Figure 4.5
that represents the steady state operation with in = i∗n+1 and m1 is the slope of the
current in time interval 1 which equals to
m1 =VA + kVB
LS(4.8)
also d′′
is calculated from
d′′
=1
2fSm3∆ϕABn (4.9)
where m3 is the slope of the current in time interval 3 which equals to
m3 =VA − kVB
LS(4.10)
4.3. DIGITAL CURRENT CONTROL IN DAB CONVERTERSBASED ON NOVEL GEOMETRICSEQUENCE CONTROL (GSC)APPROACH 80
By replacing (4.6) and 4.8 into (4.5), we have
d1 =1
2fS
(m1∆ϕAB −m3∆ϕAB
)−→ d1 =
1
2fS(m1 −m3)∆ϕABn (4.11)
and by replacing m1 and m2 from (4.7) and (4.9) into (4.10) we get
d1 =kVBLSfS
∆ϕAB(n) (4.12)
From (4.3) and (4.4) we know that d1 = d2 = d = δi(n+1). Therefore, the relation
between the change in phase shift (∆ϕAB) and the sampled current can be calculated
from
δi(n) =kVBLSfS
∆ϕAB(n) (4.13)
Figure 4.6 depicts three different current waveforms to show how the transient in a
DAB converter develops. The dashed waveforms illustrate two steady state operation
of the system where one corresponds to in = in+1 = i∗1 ϕAB(n+1) and the other
corresponds to in = in+1 = i∗0 ϕAB(n). The solid line represents the current
waveform in response to the change of phase shift from ϕ∗AB(n) to ϕAB(n).
The leading edge currents i∗0 and i∗1 can be written from (3.45):
i∗1 =1
2LSfS
((ϕ∗AB(n+ 1) + ϕA − 1
)kVB + ϕAVA
)(4.14)
i∗0 =1
2LSfS
((ϕ∗AB(n) + ϕA − 1
)kVB + ϕAVA
)(4.15)
4.3. DIGITAL CURRENT CONTROL IN DAB CONVERTERSBASED ON NOVEL GEOMETRICSEQUENCE CONTROL (GSC)APPROACH 81
i*(0)
d= δ i(n)
ΔφAB(n) = φAB(n)  φ*AB(n)
Ts/2
Δφ*AB(n) = φ*
AB(n+1)  φ*AB(n)
φ*AB(n)
φAB(n)
φ*AB(n+1)
d= δ i(n)
i*(1)
i*(0)i*(1)
Figure 4.6: Transient and steadystate waveforms in one halfcycle
By subtracting (4.15) from (4.14) we have
δin = i∗1 − i∗0 =kVB2LS
(∆ϕ∗AB(n)
)(4.16)
where
∆ϕ∗AB(n) = ϕ∗AB(n+ 1)− ϕ∗AB(n) (4.17)
4.3. DIGITAL CURRENT CONTROL IN DAB CONVERTERSBASED ON NOVEL GEOMETRICSEQUENCE CONTROL (GSC)APPROACH 82
Now by substituting δin from (4.13) into (4.16)
∆ϕ∗AB(n) = 2∆ϕAB(n) (4.18)
And by substituting (4.18) into (4.17), we get
ϕ∗AB(n+ 1) = ϕ∗AB(n) + 2∆ϕAB(n) (4.19)
From 4.7, ϕAB(n) can be written as
ϕAB(n) = ϕ∗AB(n) + ∆ϕAB(n) (4.20)
By combining the two (4.20) and (4.19), ϕ∗AB(n+ 1) is derived from
ϕ∗AB(n+ 1) = ϕAB(n) + ∆ϕAB(n) (4.21)
This equation can be rewritten as
ϕ∗AB(n) = ϕAB(n− 1) + ∆ϕAB(n− 1) (4.22)
By substituting ϕ∗AB(n) from the above equation back into (4.20), the control param
eter is calculated with the following equation
ϕAB(n) = ϕAB(n− 1) + ∆ϕAB(n− 1) + ∆ϕAB(n) (4.23)
Therefore, in order to design the control for the DAB converter with the designated
4.3. DIGITAL CURRENT CONTROL IN DAB CONVERTERSBASED ON NOVEL GEOMETRICSEQUENCE CONTROL (GSC)APPROACH 83
modulation, a discrete control function for ∆ϕAB(n) needs to be defined.
Proposed Discrete Control Law
So far we know how to change the phaseshift to achieve a desired current. The next
step is to design a control approach for the DAB converter.
Let us assume the converter is operating at steadystate that implies i(0) = i(1) =
i∗(0). The goal is to reach another steady state operating point at which the sample
current i(n) = i(n + 1) = i∗ref . Therefore, ϕAB(n) has to be controlled in such a
way that the current reaches its steadystate within a certain number of cycles. The
overall procedure can be seen as
i1 = i0 + δi(0) , δi(0) =kVBLfS
∆ϕAB(0)
i2 = i1 + δi(1) , δi(1) =kVBLfS
∆ϕAB(1)
i3 = i2 + δi(2) , δi(2) =kVBLfS
∆ϕAB(2)
.
.
.
in+1 = in + δi(n) , δi(n) =kVBLfS
∆ϕAB(n)
(4.24)
Figure 4.7 depicts the control approach presented in this thesis. In this control
algorithm the phase shift for every halfcycle is achieved by (4.23)
ϕAB(n) = ϕAB(n− 1) + ∆ϕAB(n− 1) + ∆ϕAB(n) (4.25)
4.3. DIGITAL CURRENT CONTROL IN DAB CONVERTERSBASED ON NOVEL GEOMETRICSEQUENCE CONTROL (GSC)APPROACH 84
i(0)i(1)
m1
m2
m3
m4
ΔφAB(1)
i(2)
ΔφAB(2)
iref
*
*Δi(2)
iref
φAB(0)
φAB(0)
φ*AB(0) = φAB(0)
φAB(1)=φAB(0)+ΔφAB(0)+ΔφAB(1)
*δ i(2)
Δi(2)
3, 4, 5 N1
iref
iref
*
*
φAB(n)
+i(3)
ΔφAB(0)=0 ΔφAB(1)
φ*AB(1)=φAB(1)+ΔφAB(1)
φAB(2)=φAB(1)+ΔφAB(1)+ΔφAB(2)
φ*AB(2)=φAB(2)+ΔφAB(2)
HalfCycle 0 HalfCycle 1 HalfCycle 2 HalfCycle n
ΔφAB(2)
φAB(n)=φAB(n1)+ΔφAB(n1)+ΔφAB(n)
φ*AB(n)=φAB(n)+ΔφAB(n)
ΔφAB(n)
*iref
Δi(1)
δ i(1)
Figure 4.7: Overall procedure of the applied control method
With the control discrete function
∆ϕAB(n) = aLSfSkVB
∆i(n) (4.26)
Where
a ∈ aa ∈ R , 0 < a < 2 (4.27)
∆i(n) = iref − i(n) (4.28)
The block diagram of the presented control is shown in Figure 4.8.
According to Table 4.1 for every a ∈ aa ∈ R , 0 < a < 2 the control
algorithm presented in (4.25) forces the error of the sampled current (∆i(n)) to reduce
with a geometricsequence trend in every halfcycle. (explained thoroughly in section
4.4)
Table 4.1: Elimination of the error current by a geometric progression procedure witha common ratio of 1
2
HalfCycle 0 1 2 . . . nCurrent Error ∆i(1) (1− a)∆i(1) (1− a)2∆i(1) . . . (1− a)n∆i(1)
4.3. DIGITAL CURRENT CONTROL IN DAB CONVERTERSBASED ON NOVEL GEOMETRICSEQUENCE CONTROL (GSC)APPROACH 85
+ +
Hold
LS
φAB(n)
ΔφAB(n+1)
ΔφAB(n)
φAB(n+1)
Modulation Scheme
×
fS
÷
kVB
iref +
i
+

Δ i
Control Law
fS
φA
φB
SA1 , SA2 , SA3 , SA4
SB1 , SB2 , SB3 , SB4
Figure 4.8: Inner control block diagram
Therefore, the control approach is called the geometricsequence control ap
proach. The common ratio in the GSC is (1− a).
This control approach is categorised into three different categories based on the
value of “a”
1. 0 < a < 1
2. a = 1
3. 1 < a < 2
In the first case where 0 < a < 1, the control parameter, ϕAB, increases in such way
that the error decreases in geometricprogression trend. Moreover, Since (1 − a) is
positive for this case, the current error polarity remains the same during transition.
Therefore, the current error does not exceed its reference value at any point and the
error converges to zero without overshoot in the control.
Figure 4.9 depicts the transient operation of the second case a = 1. This control
law states that if “a” is set to 1, then the inductor current will reach its reference value
in two halfcycle. As a result, the current error at t = TS will go to zero. Basically,
at this control algorithm, the first halfcycle is responsible for setting up the initial
4.3. DIGITAL CURRENT CONTROL IN DAB CONVERTERSBASED ON NOVEL GEOMETRICSEQUENCE CONTROL (GSC)APPROACH 86
conditions for the final steadystate operation and the second halfcycle increases the
phaseshift to the point where it reaches its final destination. It is worth mentioning
that in experiment “a” can not exactly be equal to 1 due to measurement precisions
and the changes in converter parameters with changes of temperature, etc.
In the third case where 1 < a < 2, the control parameter (ϕAB), similar to the first
case, increases such that the error decreases in geometricprogression trend. However,
in this case (1 − a) has a negative value and this results a change in the polarity of
the error in each halfcycle during the transient. Therefore, the current error will
exceed its reference value and overshoot of the control does happen. The transient
response time of the first and third case are the same. However, In the third case,
current exceeds the reference value and this ends up is high peak currents which may
saturate the transformer. Therefore, The third case has no advantages as compared
to the first case. Thus, This case is never used.
The advantage of the second case is very fast transient response in two half switch
ing cycles without causing any overshoot. This would be the optimal case to choose if
there was no perturbation and noise in the system. Parameter uncertainties, pertur
bation and noise can effect the control variable ϕAB such that the inductor current
waveform may lead to higher peak currents than anticipated; This phenomena makes
the second case a = 1 not desirable in practical cases. Therefore, we usually use
a value between 0 < a < 1 for the control law in order to achieve a fast dynamic
response as well as preventing high peak currents which may lead to transformer
saturation.
4.4. STABILITY 87
i(0) i(1)
m1
m2
m3
m4
δ i(1)
+i(2)+i(3)
Ts/2φAB i(2)
ΔφAB(2)=0ΔφAB(1)
δ i(2)=0
φAB(0)
ΔφAB(0)=0
HalfCycle 0
φAB(1)=φAB(0)+ΔφAB(1)
HalfCycle 1
)1((1)AB ikV
fL
B
SS
φAB(2)=φAB(1)+ΔφAB(1)
HalfCycle 2
ΔφAB(2)=0
+i(3)=i(2)
Figure 4.9: Overall procedure of the waveform when a = 1
4.4 Stability
In this section, the stability of the propose control is analysed. As explained before
the overall transient procedure of the system from one steady state operation to
another can be described by (4.24). The stability of the system for this transient
procedure is achieved when i(n) and i(n + 1) converge to iref as n goes towards
infinity meaning that δi(n) has to go towards zero. Therefore, The chosen discrete
function for ∆ϕAB(n) in (4.26) must fulfil the stability criteria which is
Stabilty Criteria −→ ∆i(n) = 0 as n becoms very big (4.29)
Therefore, a prediction of the error is required to investigate the stability of the
control law. This can be done using
∆i(n+ 1) = ∆i(n)− δi(n) (4.30)
4.5. ROBUSTNESS AND RELIABILITY 88
We can rewrite (4.13) in the form of
∆ϕAB(n) =LSfSkVB
δi(n) (4.31)
also from the discrete control discrete law:
∆ϕAB(n) = aLSfSkVB
∆i(n) (4.32)
By replacing (4.32) into (4.31), we get
δi(n) = a∆i(n) (4.33)
now we can replace the δi(n) from the above equation into (4.30)
∆i(n+ 1) = (1− a)∆i(n) (4.34)
In order for the control to be stable then ∆i(n+1) needs to be smaller than ∆i(n).
Therefore,
1− a < 1 −→ 0 < a < 2 (4.35)
To sum up if a = aa ∈ R , 0 < a < 2, Then the control system will be stable.
4.5 Robustness and Reliability
It can be seen from (4.26) that the control law depends on the transformer ratio, out
put voltage, switching period, and the transformer leakage inductance. In practice,
4.5. ROBUSTNESS AND RELIABILITY 89
the switching period is determined by the counter up limit created in the modula
tion inside the microprocessor system’s clock and its variations are relatively small.
The transformer ratio is fixed during all the operating conditions. However, the trans
former leakage inductance may show significant changes due to temperature variation,
operating conditions and age. In this section, the affect of tolerance in inductance on
the control performance is investigated.
By taking into account the tolerance ∆LS%
∆ϕAB(n) = a(1 + ∆LS%)LSfSkVB
∆i(n) (4.36)
where
∆LS% =∆LSLS
(4.37)
is achieved for the control law.
We know from the Stability analysis section that in order for the system to be stable
then
0 < a(1 + ∆LS%) < 2 −→ −1 < ∆LS% <2
a− 1 (4.38)
Then for a sample case where a = 0.5 in order to have a robust control the tolerance
of the converter should be
− 100% < ∆LS < 300% (4.39)
which means that the tolerance of the leakage inductance of the converter has to
increase more than the initial estimated inductance value before the control gets
unstable. This is way more than enough tolerance for the component variation during
4.6. OUTER CONTROL LOOP DESIGN 90
the converter operation. Therefore, in conclusion the presented converter depicts a
very fast control response and the show extremely high robustness and reliability for
the system.
4.6 Outer Control Loop Design
The control of the output voltage is obtained using a compensator that sets the inner
current loop reference. Theoretically, any classical compensator acting on the voltage
error can be used as long as they include some integral action. However, to benefit
from the high inner loop dynamics, a feedforward prediction of the reference current
along with a low gain PI compensator allows designers to maximize the bandwidth of
the controller. In this control, (3.52) is used to calculate ϕ and (3.45) is then utilized
to derive the feedforward prediction of the leading edge current. The block diagram
for the outer loop voltage is depicted in Figure 4.10 . In all the three control modes of
charging the traction battery of the converter: the voltage control mode, the current
control mode, and the power control mode, first the reference traction battery current
has to be estimated. then the adjustments of the inner control loop reference point
can be made by utilizing the error from the operating mode of the converter (Voltage
error, current error, and power error). This small modifications are made by passing
the errors to low gain PI controller.
4.7. SIMULATION 91
PI +
Nonlinear prediction
+ireferror
irefprediction
IBatref
V/I/P
+ +
+V*/I*/P*
Figure 4.10: Outer loop control in order to set the current reference for the innercurrent loop
4.7 Simulation
In order to evaluate the performance of the proposed control, simulations for different
loads and different voltage ranges are carried out. The simulations are performed in
PSIM 9.1 circuit simulator software from Powersim Inc.
In this simulation, the transient behaviour of the control system is examined for the
step load change at the output of the converter. In Figure 4.11, a negative step load
of 1.2 kW is applied at the output at t = 150µs for a = 1 and Figure 4.12 shows the
response when a negative step change of 1.2 kW is applied at the output at t = 150µs
for a = 1. These figures illustrate that the control system instantly adjusts the
phaseshift (ϕAB) in only twohalf cycles based on the new load condition. Whereas,
in conventional control method, the slow external control loop should first detect the
change in the output current and then change the peak of the instantaneous reference
value of the current loop and finally the current loop adjusts the ϕAB, accordingly.
Therefore, very fast response is achievable through the proposed GSC controller in
4.7. SIMULATION 92
45678
0
500
500
0.0001 0.00015 0.0002 0.00025Time (s)
0.08
0.12
0.16
0.2
ΨAB
Two halfcycles
I(BAT)
Figure 4.11: GSC control approach for 50% step change in current for Va=360 V andVb=400V
that the input power controller with a very high bandwidth acts instantly against
severe load changes. Figures 4.13 and 4.14 depict the transient response for different
25% step load change and different voltage bus levels, respectively. These figures also
demonstrate the fast transient superiority over different step load conditions and wide
voltage range operations of the DAB converter.
Figure 4.15 and Figure 4.16 show the behaviour of the closedloop control system
against uncertainties in the system parameters. In Figure 4.15 , the leakage induc
tance transformer is increased by 20% and in Figure 4.16 , the value of the input
inductor is decreased by 20%.
Figure 4.17 depicts the transient response of the case where the current is remained
constant and the input voltage VA changes its value from 360V to 400V . The figure
shows immediate response of the control variable ϕAB as the input voltage changes.
4.7. SIMULATION 93
4.55
5.56
6.57
0200400
200400
0.00015 0.0002 0.00025 0.0003Time (s)
0.1
0.12
0.14
0.16
I(BAT)
ΨABTwo halfcycles
Figure 4.12: GSC control approach for 50% step change in current for Va=360 V andVb=400V
6
6.5
7
7.5
8
0
400
400
0.00012 0.00014 0.00016 0.00018 0.0002 0.00022 0.00024 0.00026Time (s)
0.14
0.16
0.18
0.2
Two halfcyclesΨAB
I(BAT)
Figure 4.13: GSC control approach for 25% step change in current for Va=360 V andVb=400V
4.7. SIMULATION 94
8
10
12
14
0200400600
200400
0.0001 0.00015 0.0002 0.00025 0.0003Time (s)
0.1
0.2
0.3
0.4
Figure 4.14: GSC control approach for 50% step change in current for Va=400 V andVb=250V
4.55
5.56
6.57
0
400
400
0.00015 0.0002 0.00025Time (s)
0.080.1
0.120.140.16
I(BAT)
ΨAB
Figure 4.15: GSC control approach for 50% step change in current for Va=400 V andVb=250V with ∆LS% = 20%
4.7. SIMULATION 95
4.55
5.56
6.57
0
200
400
200400
0.00015 0.0002 0.00025 0.0003Time (s)
0.1
0.12
0.14
0.16
I(BAT)
ΨAB
Figure 4.16: GSC control approach for 50% step change in current for Va=360 V andVb=400V with ∆LS% = −20%
7.88
8.28.4
360
380
400
0
400
400
0.0001 0.0002 0.0003 0.0004Time (s)
0.170.180.19
0.2
I(BAT)
ΨAB
VA
Figure 4.17: GSC control approach for change in primary voltage: Va=360 V toVa=400 V and fixed Vb=400V
4.8. EXPERIMENTAL 96
4.8 Experimental
A 3kW prototype is implemented to verify the performance of the proposed converter.
The proposed high voltage DC/DC converter is a part of the 3KW AC/DC converter
depicted in Figure 4.18. The converter specifications are shown in Table 4.2. Table
4.3 shows the passive components used to implement the DAB converter.
Transient response for a step load change of the DAB converter is depicted in Figure
4.19, and 4.20.
Table 4.2: DAB converter Specifications
Symbol Parameter Value
Po Output Power 0  3.3 kW
VA Input Voltage 350  450 VDC
VB Traction Battery 250  430 VDC
fsw Frequency 200  350 kHz
Iin(max) Maximum input current 10 A
Table 4.3: DAB system parameters
Symbol Parameter Value
Ls Leakage Inductance 9 uH
k Transformer Turn’s Ratio 0.9:1
CA Filter Capacitance 2*80 uF
CB Filter Capacitance 2*80 uF
S Mosfets IPB65R110CFD
4.8. EXPERIMENTAL 97
Bidirectional DCDC ConverterBidirectional ACDC Converter
EMI Filter Auxilary Circuit
FPGA
Figure 4.18: 3kW bidirectional AC/DC converter prototype
Figure 4.19: transient response at VB = 100V , VA = 90V with achieved ZVS
4.8. EXPERIMENTAL 98
Figure 4.20: transient response at VB = 100V , VA = 120V with achieved ZVS
99
Chapter 5
Conclusions and Future Work
In this thesis, different control systems for bidirectional DCDC converters have been
examined. Based on the investigations, different difficulties and shortcomings of previ
ously proposed control systems for bidirectional dcdc converters have been identified.
Then, nonlinear control schemes have been proposed for bidirectional DCDC con
verters that can address the shortcomings of the conventional techniques.
The main contribution and summary of this thesis are as follows:
1. The design and development of bidirectional DCDC Dual Active Bridge (DAB)
converter with V2G/G2V capability is presented. The DAB converter consists
of two active Hbridge and a high frequency transformer which provides gal
vanic isolation for the traction battery of the electric vehicle. The converter is
designed to transfer power between the battery and the DC bus with the voltage
range of 350450 VDC and 250430 VDC, respectively. The power rating of the
converter is 03.3 kW.
2. Precise dynamical equations of the DAB converter is highly nonlinear. There
fore, linear control techniques are not able to provide satisfactory performance
5.1. FUTURE WORK 100
in wide range of operating conditions. In most literatures, linear control ap
proaches are utilized for a DAB converter. The proposed linear controllers are
not suitable for this application (Ev with V2G/G2V capability) due to the
emerging requirements on the system dynamics. In order to solve these issues,
nonlinear control schemes have been proposed which can address this problem.
3. Development of the precise discretetime domain model for steadystate oper
ation and during transients is derived. The change in the current waveforms
of the DAB converter with respect to the change in the control parameter is
carefully explored for each cycle.
4. A novel GeometricSequence Control (GSC) approach has been designed. This
method allows the DAB converter to operate under wide operating conditions
since it is based on the model of the process. It offers offers very fast dynamic
response as compared to the conventional control. The error in this control
converges to zero with a geometricprogression trend which results in only a
few halfcycles for the control to reach its reference value.
5. Stability analysis for the closedloop control of the system is evaluated. The
control sensitivity to the model parameters makes it also sensitive to the model
uncertainties. Nevertheless, it is proven that the proposed control offers strong
robustness against model uncertainties.
5.1 Future Work
The future work relating to this research can be conducted in the following:
5.1. FUTURE WORK 101
1. The loss analysis of the DAB converter can be explored to design an optimized
converter operating at each point. The two major switching sequences for DAB
converters are the DCM and the CCM techniques, which are for high load
and light load power transfer, respectively. The transition between these two
switching sequences can be calculated through a precise loss analysis of the
DAB converter.
2. An adaptive self sustained frequency control to better control the power transfer
for the DAB converter. As the switching frequency of the converter goes higher,
the passive components such as capacitors and inductors become smaller leading
to a higher power density. However, this also results to higher conduction due
to skin effect and core losses of the transformer. Therefore, and adaptive and
flexible frequency control can improve the effectiveness and operation of the
converter at any particular operating condition.
3. The breakpoint of which the operation of the converter has to convert from
DCM mode to CCM mode in order to achieve higher efficiency. finding the
right breaking point and evaluating the stability process could be tricky in the
DAB converter.
BIBLIOGRAPHY 102
Bibliography
[1] D. G. J. A. Fay, in Energy and the Environment: Scientific and Technological
Principles. Oxford University Press, Oxford University Press, 2012.
[2] P. Gevorkian, in Sustainable Energy System Engineering: The Complete Green
Building Design Resource, 2007.
[3] A. E. M. Ehsani, Y. Gao, in odern Electric, Hybrid Electric, and Fuel Cell Ve
hicles: Fundamentals, Theory, and Design, Second Edition. CEC Press, CEC
Press, 2009.
[4] S. S. W. A. Emadi and A. Khaligh, “Power electronics intensive solutions for
advanced electric, hybrid electric, and fuel cell vehicular power systems,” IEEE
Transactions on Power Electronics, vol. 21, no. 3, pp. 567–577, 2006.
[5] S. Basu, “Recent trends in fuel cell science and technology,” New York: Springer,
2007.
[6] M. Yilmaz and P. T. Krein, “Review of benefits and challenges of vehicletogrid
technology,” IEEE Energy Conversion Congress and Exposition (ECCE), pp.
3082–3089, 2012.
BIBLIOGRAPHY 103
[7] ——, “Review of the impact of vehicletogrid technologies on distribution sys
tems and utility interfaces,” IEEE Transactions on Power Electronics, vol. 28,
no. 12, pp. 5673–5689, Dec. 2013.
[8] M. D. Galus, “Integrating power systems, transport systems and vehicle technol
ogy for electric mobility impact assessment and efficient control,” IEEE Trans
actions on Smart Grid, vol. 3, no. 2, pp. 934–949, June 2012.
[9] P. Mitra and G. K. Venayagamoorthy, “Wide area control for improving stability
of a power system with plugin electric vehicles,” IET Generation, Transmission
and Distribution, vol. 4, no. 10, pp. 1151–1163, October 2010.
[10] Z. Duan, B. Gutierrez, and L. Wang, “Forecasting plugin electric vehicle sales
and the diurnal recharging load curve,” IEEE Transactions on Smart Grid, vol. 5,
no. 1, pp. 527–535, 2014.
[11] S. W. Hadley, “Evaluating the impact of plugin hybrid electric vehicles on re
gional electricity supplies,” Bulk Power System Dynamics and Control  VII. Re
vitalizing Operational Reliability, 2007 iREP Symposium, Charleston, SC, 2007,
pp. 1–12.
[12] K. S. M. KintnerMeyer and R. Pratt, “Impacts assessment of plugin hybrid
vehicles on electric utilities and regional u.s. power grids part 1: Technical anal
ysis,” Pacific Northwest Nat. Laboratory, Tech. Rep., 2007.
[13] J. Kliesch and T. Langer, “Plugin hybrids: An environmental and economic
performance outlook,” American Council for an EnergyEffi cient Economy,
Tech. Rep., 2006.
BIBLIOGRAPHY 104
[14] Z. Wang and S. Wang, “Grid power peak shaving and valley filling using vehicle
togrid systems,” IEEE Transactions on Power Delivery, vol. 28, no. 3, pp. 1822–
1829, July, 2013.
[15] L. Wang and M. Mazumdar, “Using a system model to decompose the effects of
influential factors on locational marginal prices,” IEEE Transactions on Power
Systems, vol. 22, no. 4, pp. 1456–1465, Nov. 2007.
[16] Y. J. L. A. Emadi and K. Rajashekara, “Power electronics and motor drives in
electric, hybrid electric, and plugin hybrid electric vehicles,” IEEE Transactions
on Industrial Electronics, vol. 55, no. 6, pp. 2237–2245, Jun, 2008.
[17] S. Z. Peng, H. Li, G.J. Su, J. S. L. Inoue, and H. Akagi, “A new zvs bidirectional
dcdc converter for fuel cell and battery application,” IEEE Transactions on
Power Electronics, vol. 19, no. 1, pp. 54–65, Jan. 2004.
[18] S. Inoue and H. Akagi, “A bidirectional dcdc converter for an energy storage sys
tem with galvanic isolation,” IEEE Transactions on Power Electronics, vol. 22,
no. 6, pp. 2299–2306, Nov. 2007.
[19] C. c. Lin, L. s. Yang, and G. W. Wu, “Study of a nonisolated bidirectional dcdc
converter,” IET Power Electronics, vol. 6, no. 1, pp. 30–37, 2013.
[20] K. Wang, C. Y. Lin, L. Zhu, D. Qu, F. C. Lee, and J. S. La, “Bidirectional dc
to dc converters for fuel cell systems,” Power Electronics in Transportation, pp.
47–51, 1998.
BIBLIOGRAPHY 105
[21] J. Walter and R. W. D. Doncker, “Highpower galvanically isolated dc/dc con
verter topology for future automobiles,” Proc. of the 34th IEEE Annual Power
Electronics Specialist Conference (PESC 2003), vol. 1, pp. 15–19, June 2003.
[22] S. Inoue and H. Akagi, “A bidirectional dcdc converter for an energy storage sys
tem with galvanic isolation,” IEEE Transactions on Power Electronics, vol. 22,
no. 6, p. 22992306, Nov. 2007.
[23] G. G. Oggier, G. O. Garca, and A. R. Oliva, “Switching control strategy to min
imize dual active bridge converter losses,” IEEE Transactions on Power Elec
tronics, vol. 7, no. 24, pp. 1826–1838, July 2009.
[24] D. M. D. M. N. Kheraluwala, R. W. Gascoigne and E. D. Baumann, “Perfor
mance characterization of a highpower dual active bridge dctodc converter,”
IEEE Transactions on Industry Applications, vol. 27, no. 1, pp. 63–73, Jan/Feb
1991.
[25] R. W. A. A. D. Doncker, D. M. Divan, , and M. H. Kheraluwala, “A threephase
softswitched highpowerdensity dc/dc converter for highpower applications,”
IEEE Transactions on Industry Applications, vol. 27, no. 1, p. Feb. 1991, Feb.
1991.
[26] R. L. Steigerwald, “A comparison of halfbridge resonant converter topologies,”
IEEE Transactions on Power Electronics, vol. 3, no. 2, p. 174182, April 1988.
[27] R.L.Steigerwald, “Highfrequency resonant transistor dcdc converters,” IEEE
Transactions on Industrial Electronics, vol. 1, no. 2, p. 181191, May 1984.
BIBLIOGRAPHY 106
[28] R. W. Erickson and D. Maksimovic, Fundamentals of Power Electronics, 2nd ed.
Norwell, MA: Kluwer, 2001.
[29] S. W. Anderson, R. W. Erickson, and R. A. Martin, “An improved automotive
power distribution system using nonlinear resonant switch converters,” IEEE
Transactions on Power Electronics, vol. 6, no. 1, pp. 148–54, 1991.
[30] F. Krismer, S. Round, and J. W. Kolar, “Performance optimization of a high cur
rent dual active bridge with a wide operating voltage range,” Power Electronics
Specialists Conference, 2006. PESC ’06. 37th IEEE, pp. 1 – 7, June 2006.
[31] S. B. K. Vangen, T. Melaa and R. Nilsen, “Efficient highfrequency softswitched
power converter with signal processor control,” Proc. of the 13th IEEE Interna
tional Telecommunications Energy Conference (INTELEC 1991), Kyoto, Japan,
p. 631639, Nov. 1991.
[32] H. Tao, A. Kotsopoulos, J. L. Duarte, , and M. A. M. Hendrix, “Transformer
coupled multiport zvs bidirectional dcdc converter with wide input range,” IEEE
Transactions on Power Electronics, vol. 23, no. 2, p. 771781, March 2008.
[33] H. L. Chan, K. W. E. Cheng, and D. Sutanto, “An extended load range zcszvs
bidirectional phaseshifted dcdc converter,” Proc. of the 8th IEE International
Conference on Power Electronics and Variable Speed Drives, London, UK, p.
7479, Sept. 2000.
[34] N. S. A.C. Rufer and C. Briguet, “A direct coupled 4quadrant multilevel con
verter for 16 2/3 hz traction systems,” Proc. of the 6th IEE Conference on Power
Electronics and Variable Speed Drives, Nottingham, UK, p. 448453, Sept. 1996.
BIBLIOGRAPHY 107
[35] C. Deisch, “Simple switching control method changes power converter into a
current source,” Proc. IEEE PESC78 Conf., p. 300306, 1978.
[36] S. S. Hsu, A. Brown, L. Rensink, and R. D. Middlebrook, “Modelling and anal
ysis of switching dctodc converters in constantfrequency current programmed
mode,” in Proc. IEEE PESC79 Conf., p. 284301, 1979.
[37] F. C. Lee and R. A. Carter, “Investigations of stability and dynamic perfor
mances of switching regulators employing currentinjected control,” in Proc.
IEEE PESC82 Conf., p. 316, 1982.
[38] R. Redl and N. O. Sokal, “Currentmode control, five different types, used with
the three basic classes of power converters: Smallsignal ac and largesignal
dc characterization, stability requirements, and implementation of practical cir
cuits,” in Proc. IEEE PESC85 Conf., p. 771785, 1985.
[39] R. Redl and B. Erisman, “Reducing distortion in peakcurrentcontrolled boost
power factor correctors,” in Proc. IEEE APEC94 Conf., p. 576583, 1994.
[40] R.Redl and B.Erisman, “Design of the clampedcurrent highpowerfactor boost
rectifier,” in Proc. IEEE APEC94 Conf, p. 584590, 1994.
[41] J. Lai and D. Chen, “Design consideration for power factor correction boost
converter operating at the boundary of continuous conduction mode and discon
tinuous conduction mode,” in Proc. IEEE APEC93 Conf., p. 267273, 1993.
[42] R. E. J. Chen and D. Maksimovic, “Averaged switch modelling of boundary
conduction mode dctodc converters,” in Proc. IEEE IECON01 Conf., 2001, p.
844849, 1993.
BIBLIOGRAPHY 108
[43] S. Chattopadhyay and S. Das, “A digital current mode control technique for dc
dc converters,” Twentieth Annual IEEE Applied Power Electronics Conference
and Exposition, 2005. APEC 2005, vol. 2, pp. 885–891, 2005.
[44] W. Tang, F. C. Lee, and R. B. Ridley, “Eliminate reactive power and increase
system effi ciency of isolated bidirectional dualactivebridge dcdc converters
using novel dualphaseshift control,” IEEE Transactions on Power Electronics,
vol. 8, no. 2, pp. 112–119, Apr 1993.
[45] W.Tang, F. Lee, and R. Ridley, “A general technique for derivation of average
current mode control laws for singlephase powerfactorcorrection circuits with
out input voltage sensing,” IEEE Transactions on Power Electronics, vol. 14,
no. 4, pp. 663–672, Jul 1999.
[46] M. P. G. Garcera and E. Figueres, “Robust average currentmode control of
multimodule parallel dcdc pwm converter systems with improved dynamic re
sponse,” IEEE Transactions on Industrial Electronics, vol. 48, no. 5, pp. 995–
1005, Oct 2001.
[47] H. L. Y. Qiu and X. Chen, “Digital average currentmode control of pwm dcdc
converters without current sensors,” IEEE Transactions on Industrial Electron
ics, vol. 57, no. 5, pp. 1670–1677, May 2010.
[48] B. Bryant and M. K. Kazimierczuk, “Modeling the closedcurrent loop of pwm
boost dcdc converters operating in ccm with peak currentmode control,” IEEE
Transactions on Circuits and Systems I: Regular Papers, vol. 52, no. 11, pp.
2404–2412, Nov. 2005.
BIBLIOGRAPHY 109
[49] J. P. Gegner and C. Q. Lee, “Linear peak current mode control: a simple active
power factor correction control technique for continuous conduction mode,” 27th
Annual IEEE Power Electronics Specialists Conference (PESC), vol. 1, pp. 196–
202, 1996.
[50] Y. S. Lai and C. A. Yeh, “Predictive digitalcontrolled converter with peak
currentmode control and leadingedge modulation,” IEEE Transactions on In
dustrial Electronics, vol. 56, no. 6, pp. 1854–1863, June 2009.
[51] M. Hallworth and S. A. Shirsavar, “Microcontrollerbased peak current mode
control using digital slope compensation,” IEEE Transactions on Power Elec
tronics, vol. 27, no. 7, pp. 3340–3351, July 2012.
[52] J.Chen, A.Prodic, R. W. Erickson, and D. Maksimovic, “Predictive digital cur
rent programmed control,” IEEE Transactions on Power Electronics, vol. 18,
no. 1, pp. 411–419, 2003.
[53] S.Bibian and H. Jin, “High performance predictive deadbeat digital controller
for dc power supplies,” IEEE Transactions on Power Electronics, vol. 17, no. 3,
pp. 420–427, May 2002.
[54] S. Bibian and H. Jin, “High performance predictive deadbeat digital controller
for dc power supplies,” Sixteenth Annual Applied Power Electronics Conference
and Exposition, (APEC), vol. 1, pp. 67–73, 2001.
[55] S. Saggini, W. Stefanutti, E. Tedeschi, and P. Mattavelli, “Digital deadbeat
control tuning for dcdc converters using error correlation,” IEEE Transactions
on Power Electronics, vol. 22, no. 4, pp. 1566–1570, July 2007.
BIBLIOGRAPHY 110
[56] S. B. S. Dutta and M. Chandorkar, “A novel predictive phase shift controller
for bidirectional isolated dc to dc converter for high power applications,” 2012
IEEE Energy Conversion Congress and Exposition (ECCE), pp. 418–423, 2012.
[57] S. Dutta and S. Bhattacharya, “Predictive current mode control of single phase
dual active bridge dc to dc converter,” 2013 IEEE Energy Conversion Congress
and Exposition, pp. 5526–5533, 2013.
[58] S. Dutta, S. Hazra, and S. Bhattacharya, “A digital predictive current mode
controller for single phase dual active bridge isolated dc to dc converter,” IEEE
Transactions on Industrial Electronics, vol. PP, pp. 1–1, April, 2016.
[59] J. Huang, Y. Wang, Z. Li, and W. Lei, “Predictive valleypeak current control
of isolated bidirectional dual active bridge dcdc converter,” 2015 IEEE Energy
Conversion Congress and Exposition (ECCE), pp. 1467–1472, 2015.
[60] F. Krismer and J. W. Kolar, “Accurate smallsignal model for the digital control
of an automotive bidirectional dual active bridge,” IEEE Transactions on Power
Electronics, vol. 24, no. 12, pp. 2756 – 2768, Dec. 2009.
[61] F.Krismer and J.W.Kolar, “Accurate smallsignal model for an automotive bidi
rectional dual active bridge converter,” 2008 11th Workshop on Control and
Modeling for Power Electronics, pp. 1–10, 2008.
[62] T. Patarau, D. Petreus, R.Etz, M. Cirstea, and S. Daraban, “Digital control
of bidirectional dcdc converters in smart grids,” Optimization of Electrical and
Electronic Equipment (OPTIM), pp. 1553 – 1558, May 2012.
BIBLIOGRAPHY 111
[63] R. T. Naayagi, A. J. Forsyth, and R. Shuttleworth, “Bidirectional control of
a dual active bridge dcdc converter for aerospace applicationsl,” IET Power
Electronics, vol. 5, no. 7, pp. 1104–1118, August 2012.
[64] H. Daneshpajooh, A. Bakhshai, and P. Jain, “Modified dual active bridge bidi
rectional dcdc converter with optimal efficiency,” 2012 TwentySeventh Annual
IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 1348–
1354, 2012.
[65] M. Pahlevaninezhad, H. DaneshPajooh, A. Bakhshai, and P. Jain, “A load/line
adaptive zero voltage switching dc/dc converter used in electric vehicles,” 2013
IEEE Energy Conversion Congress and Exposition, pp. 2065–2070, 2013.
[66] M. Pahlevaninezhad, H. Daneshpajooh, A. Bakhshai, and P. Jain, “A multi
variable control technique for zvs phaseshift fullbridge dc/dc converter,” Ap
plied Power Electronics Conference and Exposition (APEC), 2013 TwentyEighth
Annual IEEE, pp. 257–262, 2013.
[67] M. Pahlevani, A. Bakhshai, and P. Jain, “A novel digital peakcurrentmode self
sustained oscillating control (pcmssoc) technique for a dualactive bridge dc/dc
converter,” 2015 IEEE Applied Power Electronics Conference and Exposition
(APEC), pp. 3150–3156, 2015.
[68] M. Pahlevaninezhad, S. Eren, P. K. Jain, and A. Bakhshai, “Selfsustained os
cillating control technique for currentdriven fullbridge dc/dc converter,” IEEE
Transactions on Power Electronics, no. 11, pp. 5293–5310, Nov. 2013.
BIBLIOGRAPHY 112
[69] F. Krismer, “thesis on modeling and optimization of bidirectional dual active
bridge converter topologies.”