KTH Chinese Dude Master Thesis About DAB Design
KTH Chinese Dude Master Thesis About DAB Design
KTH Chinese Dude Master Thesis About DAB Design
FAN YANG
Abstract
The EU has proposed an ambitious goal to achieve widespread E-mobility in
both the electrical and commercial sectors. To accomplish this, a substantial
number of DC fast-charging stations must be built. These power converters,
installed in the DC fast-charging stations (DCFC), differ from traditional DC-
DC converters as they exhibit high power density, reaching tens of kilowatts.
The thesis is organized into four distinct parts. The first part focuses
on conducting a comprehensive literature review to explore the challenges
prevalent in the current electrical field. Various DC-DC topologies
are compared based on different factors, including component analysis,
controllability, safety considerations, and cost-effectiveness. By examining
these aspects, potential solutions for Electric Vehicles (EVs) are identified. In
the second part, a specific DC-DC converter with a power rating of 10kW is
chosen, utilizing the DAB (Dual Active Bridge) topology. The selection is
based on the analysis conducted in the literature review. The thesis delves
into the issues and technical challenges associated with this choice, such as
reactive power, peak current, zero-voltage switching (ZVS), and phase shift
modulation. These topics are thoroughly explored and discussed within the
literature study.
In the final part of the thesis, conclusions are drawn based on the theoretical
findings and simulation results obtained throughout the study. These
conclusions reflect the overall outcomes and implications of the research
conducted. Furthermore, the future work section outlines the tasks that remain
unfinished or areas that can be explored in subsequent studies. This section
serves as a guide for future researchers, highlighting potential directions for
further investigation and improvement in the field of DAB-based DC-DC
converters for E-mobility applications. By presenting the conclusions and
future work, the thesis provides a comprehensive summary of the research
conducted, its contributions, and potential avenues for future research and
development.
Keywords
Converter Design, Dual Active Bridge, Single Phase Shift Modulation,
Extended Phase Shift Modulation, Efficiency Estimation
Abstract | iii
Sammanfattning
EU har föreslagit ett ambitiöst mål för att uppnå utbredd e-mobilitet
inom både den elektriska och kommersiella sektorn. För att åstadkomma
detta måste ett stort antal DC snabbladdningsstationer byggas. Dessa
effektomvandlare, installerade i DC-snabbladdningsstationerna (DCFC),
skiljer sig från traditionella DC-DC-omvandlare eftersom de uppvisar hög
effekttäthet och når tiotals kilowatt.
Phase Shift) i kretsen för att uppnå sluten-loop-styrning. Inom denna del
härleds förhållandet mellan ström, spänning och uteffekt och används för
konstruktionen av en sluten PI-regulator. För att ta itu med utmaningar
förknippade med SPS-kontroll, såsom eliminering av reaktiv effekt och
undertryckning av toppström, introduceras ett EPS-kontrollschema (Enhanced
Phase Shift). EPS-kontrollsystemet uppfyller inte bara det grundläggande
kravet på kraftöverföring utan optimerar också systemets totala effektivitet.
Nyckelord
Konverterdesign, Dual Active Bridge, Single Fas Shift Modulation, Extended
Phase Shift Modulation, Effektivitetsuppskattning
Abstract | v
Acknowledgments
I would like to express my deepest gratitude and appreciation to all those
who have contributed to the completion of this thesis project. Without
their support, guidance, and encouragement, this thesis would not have been
possible.
I am grateful to the members of the power lab of KTH, who have provided
me with a conducive experimental environment, cutting-edge resources, and
opportunities for intellectual growth. Large quantities of components are
bought with the help of Patrick Janus.
Contents
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Research Methodology . . . . . . . . . . . . . . . . . . . . . 4
1.5 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.6 Structure of the Thesis . . . . . . . . . . . . . . . . . . . . . 5
2 Literature Study 6
2.1 DC-DC Converters . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 DAB Converter . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Phase Shift Modulation . . . . . . . . . . . . . . . . . . . . . 14
5 Simulation Results 59
5.1 SPS Simulation Results . . . . . . . . . . . . . . . . . . . . . 60
5.1.1 Open Loop Simulation . . . . . . . . . . . . . . . . . 60
5.1.2 Closed Loop Simulation . . . . . . . . . . . . . . . . 64
5.2 EPS Simulation Results . . . . . . . . . . . . . . . . . . . . . 69
5.2.1 Open-Loop Simulation . . . . . . . . . . . . . . . . . 69
5.2.2 Closed Loop Simulation . . . . . . . . . . . . . . . . 71
5.2.2.1 Reactive Power Elimination . . . . . . . . . 71
5.2.2.2 Current Stress Suppression . . . . . . . . . 72
5.3 Efficiency Simulation . . . . . . . . . . . . . . . . . . . . . . 75
6 Conclusions 79
7 Future work 81
References 82
A Simulation Schematics 86
A.1 Simulink Schematic . . . . . . . . . . . . . . . . . . . . . . . 86
A.2 PLECS simulation . . . . . . . . . . . . . . . . . . . . . . . 88
viii | List of Figures
List of Figures
List of Tables
Chapter 1
Introduction
1.1 Background
Isolated bidirectional DC/DC power converters play an important role in
micro-grids, which serve as the interface of ESSs(Energy Storage Systems)
such as EV(Electric Vehicles) batteries and supercapacitors to allow energy
exchange between ESSs and the DC bus[1]. Figure (1.1) shows the structure
of a microgrid system. The DC-DC converter can be installed either between
the home DC bus or between the home DC bus and home appliances to provide
a stable power supply.
The power electronic transformers using DABs can reduce the weight, and
increase the energy power density. Compared with other IBDC topologies,
2 | Introduction
such as dual Flyback, Dual-Cuk, and Push-pull, DAB has the following
advantages[2]:
Based on the model including modulation methods, the control of DAB can
be implemented through the following control methods.
A. Feedback Control with a proportional-integral(PI) compensation is the
simplest method to stabilize the voltage. The PI compensation is used to
minimize the steady-state error[10].
B. To eliminate the nonlinear terms in DAB, a linearized control method is
proposed, which can reduce the sensitivity of the system stability to the load
condition and enlarge the stable margin.[11]
following part.
Output voltage ripple analysis and its alleviation in different applications is a
problem that is urgent to be solved. One ripple suppression technique has been
proposed, which can reveal the exact output voltage ripple. The parameter
analysis can be applied to the parameter design of the DAB converter to
decrease the amplitude of the voltage ripple[12].
In the literature study part, DC-DC converters, DAB converters,s, and control
methods are introduced in detail.
1.2 Purpose
The purpose of the thesis is to design a 10kW DAB converter that outputs
380V to 500V DC voltage. Controller design and simulation are performed
in Simulink. Specific details such as filter design, MOSFET selection, and
leakage inductor are introduced. Finally, the loss of switches and transformers
is estimated and efficiency is simulated in PLECS.
Through this thesis project, the student should be familiar with the process
of how to design and build a power electronics converter. The method of
performing a background investigation and research literature review should
be mastered. After the project, the student should be able to conduct a research
project individually and have the ability to perform the converter design and
modeling of the power electronics converter. The simulation should provide
solid theoretical support to the future work of lab experiments.
1.3 Goals
The goal of this project is to design a 10kW DAB converter. This has been
divided into the following four sub-goals:
4 | Introduction
The literature review provides solid information from both theoretical and
experimental aspects. Simulation provides a fast possibility to check the
assumption of the proposed models.
PLECS will be used for loss analysis and thermal simulation to calculate
the power losses. PLECS has a fast simulation speed and is useful in power
converter simulation.
1.5 Limitations
The modeling of DAB is a complex problem to be investigated. Some
simplifications are taken to obtain the reduced-order model of the converter,
such as the current dynamics of the leakage inductor. Besides, the modulation
of DAB has many control variables. However, only the external phase shift
ratio and internal phase shift ratio are considered in this report. Another
Introduction | 5
limitation of this project is the hardware design problems. It takes a long time
to prepare the components that we’re going to use.
Chapter (3) presents the analysis of the converter and design of the parameters.
The operation modes of the circuit are analyzed in section (3.1). The
design details and considerations are elaborated in section (3.2), such as the
leakage inductance, soft switching, output capacitance, switching frequency,
transformer, and MOSFET selection.
Chapter (4) set up the model of the converter and build the controller for
the voltage loop. The characteristics of the SPS modulation scheme are
derived in section (4.1). The model of SPS modulation scheme model is
built and a closed-loop PI compensation is designed. Section (4.2) gives
the characteristics and advantages of EPS compared to SPS, mainly from the
perspectives of reactive power and current stress.
Chapter (5) presents the simulation results to verify the theory. The simulation
results of SPS, EPS and efficiency are listed respctively in section (5.1),(5.2),
and (5.3) respectively.
Chapter (6) gives conclusions based on the former chapters. Chapter (7)
presents the work that will be implemented in the future.
6 | Literature Study
Chapter 2
Literature Study
First, the non-isolated DC-DC converters are introduced in the following part.
NIBDC (Non-isolated bidirectional DC converters) are converters that don’t
have galvanic isolation, which means the input and output are connected only
by electrical components. Figure (2.1) listed eight classical NIBDC power
converters that are widely used in both academic and industrial fields. A brief
introduction will be given to the Buck-Boost converter, Cascaded converter,
and Interleaved converter.
Buck-Boost is the most classical DC-DC converter that has the least number of
power devices. Figure(2.2) shows the topology of the power converter. There
are two switches S1 and S2 in the circuit. An input capacitor C1 and output
8 | Literature Study
capacitor C2 are set in the input side and output side as the rectifier to stabilize
the voltage.
D
V2 = − V1 (2.1)
1−D
The inductor L stores energy from the left side when S1 is on. And then the
energy is transferred to the right side when S2 is on. The circuit proposes a
simple method to achieve bidirectional energy transmission. However, the
power level is limited as the inductor cannot store too much energy. And
the output voltage has the opposite direction from the input direction as the
direction of the inductor current is opposite.
Compared with buck-boost topology, this converter has a higher voltage gain
ratio with the same duty cycle of the switch. Besides, the current ripples
and current stress of the inductor, switches have been reduced. An auxiliary
capacitor Ca can be used to reduce the output current ripples.
Literature Study | 9
The Flyback converter is widely used in the industrial field which combines the
advantage of galvanic isolation and relatively simple topology. Figure (2.6)
shows the topology of a flyback converter. The flyback is adapted from the
non-isolated buck-boost converter. The only difference is that a transformer
is used to change the voltage ratio by the factor of n : 1. When the switch S1
is on, the transformer is charged and the switch S2 is turned on to discharge
the inductor energy. Because the direction of the coupled inductor is opposite,
the output voltage V2 has the same direction as the input voltage V1 .Give the
equation of energy conversion of one switching duty cycle:
nD
nV1 D = V2 (1 − D) V2 = V1 (2.3)
1−D
safety insurance from the user side and protects the circuit. However, because
the input current is discontinuous, the circuit isn’t fully used to transmit the
power. The main usage of the flyback converter is UPS(uninterruptable power
supply) and,low-medium power application[17].
Owing to the advantages of high frequency, high energy density, electrical
isolation, low electromagnetic interference and harmonic pollution, and wide
output ranges, LLC resonant converters are widely used in various sectors of
the electronics-based industries.[18]. Figure (2.7) is the topology of a half-
bridge resonant converter. The most important part of the converter is the
resonant tank, which has a resonant capacitor Cr , resonant inductor Lr , and a
magnetic inductor Lm .
The half-bridge converter acts as an inverter that inverts the input DC voltage
into a high-frequency pulse signal. S1 and S2 are driven with 50% duty
cycle signals that are frequency modulated, which forms a square wave with
changing fundamental frequency. The resonant tank acts as a band-pass filter
that only leaves the dominant fundamental frequency component. Then the
diodes on the second side act as a rectifier that rectifies the AC voltage into
a DC signal with the output capacitor. By changing the switching frequency,
the impedance of the resonant tanks is also changed, resulting in a higher or
lower tank circuit current depending on the fundamental frequency. Finally,
the output voltage can be regulated by simply modulating the PWM frequency.
To be mentioned, there are two resonant peak frequencies in the LLC
converter, which are shown in the equation (2.4).
1 1
fr1 = p fr2 = √ (2.4)
2π (Lr + Lm )Cr 2π Lr Cr
12 | Literature Study
V2
Topology V1
Switches Characteristics Isolation
−D
Buck-Boost 1−D
2 Negative output voltage NIBDC
1
Cascaded 1−D
4 Higher voltage gain IBDC
1
Interleaved 1−D
4 Smaller EMI filter NIBDC
nD
Flyback 1−D
2 Discontinuous current IBDC
LLC PWM frequency 4 Frequency modulation IBDC
DAB Phase shift modulation 8 High power density IBDC
However, DAB converters haven’t been widely used in the industrial field
so far, which is because the control algorithm is more complicated and the
complexity of converter operation. Besides, the reactive power can impact
the efficiency of the converter. The high-frequency operation also brings
challenges to the power devices, such as MOSFETs and the transformer. In
the design process, these issues need to be considered.
14 | Literature Study
The phase shift is defined as the time delay between the switching events of the
primary and secondary bridges. By tuning the phase shift, the DAB converter
can control the direction and magnitude of the power flow.
Dividing by the controlling phase shift angles of either the primary side or
secondary side, PSM can be different modulation schemes such as single
phase shift control(SPS), extended phase shift control(EPS), dual phase shift
control(DPS), and triple phase shift control(TPS). Table (2.2) defines different
modulation scheme of a DAB converter.
D2 is the external phase shift ratio, defined as the phase shift ratio between
primary side voltage Vp and secondary side voltage Vs . D1 is the internal
phase sift ratio of the primary side, which is caused by the phase shift of the
primary side H bridge. D2 is the internal phase shift ratio of the secondary
Literature Study | 15
SPS only has 1 degree of freedom, which is the external phase shift ratio D2 .
EPS has 2 degrees of freedom, which is the external phase shift ratio D2 and
internal phase shift ratio D1 . DPS has 2 degrees of freedom, but the two
internal phase shift ratios of both sides are the same, which is D1 = D3 .
TPS has 3 degrees of freedom, which is the most complex PSM method of the
DAB converter. Figure (2.10) gives the definition of phase shift ratio. To be
mentioned, the value of D1 , D2 , D3 is the ratio between the phase shift and
half of the switching cycle, which is T2s .
If the internal phase shift ratio of the secondary side is 0, DPS modulation
scheme becomes EPS. In this project, the modulation scheme of SPS
modulation and EPS modulation are investigated and simulated.
16 | System Design Theory
Chapter 3
First, the operation modes of circuits are analyzed to derive the model of the
DAB converter. Based on the waveform of the inductor current, the operation
of the DAB converter can be divided into 6 states (8 states in EPS). The
relationship between inductor voltage and current is obtained.
The leakage inductor is designed from the transfer power perspective and also
satisfies the ZVS operation of the current. The capacitor is selected based on
the output voltage ripple requirement. With a certain switching frequency,
the transformer is designed and silicon carbide MOSFETs are chosen as the
switches.
Finally, the loss of the converter is analyzed by combining the switching loss
and transformer loss. The efficiency of the converter is estimated, which
satisfies the design requirement.
System Design Theory | 17
Ii is the input voltage, Io is the output current and L is the leakage inductor of
the transformer, which is the most important component in the DAB circuit.
The transformer ratio is n : 1(n > 1). S1 , S2 , S3 , S4 are the switches of
the primary side, each one is anti-parallel connected with a body diode and
a parasitic capacitor. S5 , S6 , S7 , S8 are the switches of the secondary side.
Vin is the input DC voltage source and Cin is the input capacitor.Vo is the
output voltage. Cout is the output capacitor and R is the load resistor. L is the
leakage inductor, and the voltage across the inductor is VL . Vs is the voltage
of the secondary side of the transformer, and Vs′ is the voltage converted to the
primary side. Vp is the voltage of the primary side.
To derive the voltage transmission equation of the primary side and secondary
side, the voltage and current of the inductor are analyzed. Figure(3.2) shows
the waveform of the inductor voltage VL , which equals the difference between
Vp and Vs′ . Vs′ is the secondary side voltage that multiplies the transformer
ratio n. To be mentioned, Vo′ is the value of output voltage Vo converted to the
primary side.
18 | System Design Theory
Because of the phase shift of the primary side and secondary side, there are
three values of the inductor voltage waveform. Equation (3.1) illustrates the
three values of inductor voltage under different cases.
Vin + Vo′ , Vp = Vin , Vs′ = −Vo
′
VL = Vin − Vo , Vp = Vin , Vs′ = Vo (3.1)
−Vin − Vo′ , Vp = −Vin , Vs′ = −Vo
The circuit mode can be divided into 6 working modes. The analysis is
performed in a steady state and all the switches are anti-parallel connected
with a body diode.
Mode 1(t0 − t1 ): Figure (3.3) shows the current flow direction of mode 1.
Before t0 , switches S2 , S3 are conducted, and the current of the inductor flows
in the negative direction. At the time of t0 , S1 , S4 are conducted which leads
to the positive value of Vp . As the current of the inductor is still negative,
diode D1 , D4 are conducted to freewheel the current. The reactive power is
produced from time t0 to t1 . As for the secondary side, switches S6 , S7 are
conducted. The current of the inductor is negative and gradually increases to
System Design Theory | 19
Mode 2(t1 − t2 ): Figure (3.4) shows the current flow direction of mode 2.
At the time of t0 , the current of the inductor increases from 0 to a positive
value. Primary side switches S1 , S4 keep conducting, secondary side switches
S6 , S7 keep conducting, and the voltage across the inductor is still (Vin + Vo′ ),
which is the same as mode 1. The expression of the inductor current of mode
1 and mode 2 is shown as equation (3.2).
Vin + Vo′
IL (t) = IL (t0 ) + (t − t0 ) (3.2)
L
Mode 3(t2 − t3 ): Figure (3.5) shows the current flow direction of mode 3. At
the time of t2 , S1 , S4 are still conducted, secondary side S5 , S8 are conducted
and S6 , S7 are switched off. The voltage across the inductor is (Vin − Vo′ ). The
current is stated as equation (3.3).
Vin − Vo′
IL (t) = IL (t2 ) + (t − t2 ) (3.3)
L
Mode 4(t3 − t4 ): Figure (3.6) shows the current flow direction of mode 4.
At the time of t3 , primary side switches S1 , S4 are turned off and S2 , S3 are
conducted, and diodes D2 , D3 are conducted to maintain the current flow. As
the primary side voltage and current have opposite directions, reactive power
is produced. Switches S5 , S8 of the secondary side are kept conducting. The
inductor current continued to decrease to 0. The voltage across the inductor is
(−Vin − Vo′ ).
−Vin − Vo′
IL (t) = IL (t3 ) + (t − t3 ) (3.4)
L
20 | System Design Theory
Mode 5(t4 − t5 ): Figure (3.7) shows the current flow direction of mode 5. At
the time of t4 , the inductor current decreases to a negative value. Primary side
S2 , S3 are conducted, secondary side S5 , S8 are conducted. The voltage across
the inductor is (−Vin − Vo′ ). The current expression of mode 4 and mode 5 is
shown as equation (3.4).
Mode 6(t5 − t6 ): Figure (3.8) shows the current flow direction of mode 6. At
the time of t5 , primary side S2 , S3 are conducted, and secondary side S5 , S8
are turned off. Switches S6 , S7 are conducted, and the current flows across
diodes D6 , D7 . The voltage across the inductor is (−Vin + Vo′ ). The current
expression of mode 4 and mode 5 is shown as equation (3.5).
−Vin + Vo′
IL (t) = IL (t4 ) + (t − t4 ) (3.5)
L
Assuming Vp is greater than Vs′ , the current through the inductor will change
depending on the voltage across the inductor. According to the relationship of
the inductor current and voltage, the following equations are obtained:
diL
L = VL = Vp − Vs′ (3.6)
dt
System Design Theory | 21
I1 + I2 Vin + Vo′
= (3.7)
D2 T L
In the second interval, equation(3.6) can be rewritten as equation (3.8).
I1 − I2 Vin − Vo′
= (3.8)
(1 − D2 )T L
Ts Ts
I1 = (Vin − Vo′ + 2Vo′ D2 ) I2 = (2Vin D2 − Vin + Vo′ ) (3.9)
4L 4L
From the geometry relationship of the output current Io waveform, the
relationship between I1 ,I2 and t1 ,t2 can be formed as equation (3.10).
I1 t1 1
= t1 + t2 = D2 T = D2 Ts (3.10)
I2 t2 2
Substituting I1 and I2 by equation (3.9), (3.10) can be reformulated as:
Finally, calculate the input and output current by integrating the area of
the current waveform and time, the input current and output current can be
formulated as equation (3.12).
D2 Ts ′ D2 T s
Ii = V (1 − D2 ) Io = Vin n(1 − D2 ) (3.12)
2L o 2L
If the load of the secondary side is a resistor, based on Ohm’s law Vo = Io R,
the transmission ratio between the primary side and the secondary side can be
written as equation (3.13).
(1 − D2 )D2 Ts Rn
Vo = Vi (3.13)
2L
22 | System Design Theory
The output power equals the product of the output current and output voltage,
which is equation (3.14).
Vin Vo D2 (1 − D2 )Ts n
Po = V o I o = (3.14)
2L
In the special case, if Vo′ = Vin , the RMS value of the input current, output
current, and inductor current are the smallest, shown as equation (3.15).
Vin + Vo′
I1 = I2 = D2 Ts (3.15)
4L
To derive the voltage and power transmission equations of EPS control, the
figures of inductor voltage and current are depicted as shown in figure (3.9).
Different from the SPS controlling, there are six stages of the inductor voltage,
which are Vo′ , (Vin + Vo′ ), (Vin − Vo′ ), −Vo′ , (−Vin − Vo′ ), and (−Vin + Vo′ ). D1
is the internal phase shift ratio of the primary side and D2 is the external phase
shift ratio between the primary and secondary sides.
System Design Theory | 23
Figure (3.9) shows that the inductor current waveform has half-wave
symmetry. Hence, only analyzing half of the current waveform can reveal
the whole process. The operation modes of EPS control can be divided into 8
modes, depending on the shape of the inductor current waveform.
Mode 1(t0 − t1 ): Figure (3.10) shows the current flow direction of mode 1.
Before time t0 , primary side switches S2 , S3 are conducted, and the current
flows in the negative direction. At the time of t0 , switch S1 is conducted,
the current is still negative, and switch S3 and diode D1 provide the current
with the freewheeling path. On the secondary side, D6 , D7 are conducted.
The voltage across the inductor is Vo′ . The current of mode 1 is expressed as
equation (3.16).
nVo
IL (t) = IL (t0 ) + (t − t0 ) (3.16)
L
Mode 2(t1 −t2 ): Figure (3.11) shows the current flow direction of mode 2. The
current at time t1 is −I1 , switch S3 is turned off and S4 is turned on. On the
secondary side, diodes D6 , D7 are conducted. The voltage across the inductor
is (Vin + Vo′ ). The inductor is discharged and the absolute value of the current
decrease to 0. The current of mode 2 is expressed as equation (3.17).
Vin + nVo
IL (t) = IL (t1 ) + (t − t1 ) (3.17)
L
Mode 3(t2 − t3 ): Figure (3.12) shows the current flow direction of mode
3. The inductor current increases from a negative value to a positive value.
S1 , S4 , S6 , S7 are conducted, the voltage across the inductor is (Vin + Vo′ ),
which is the largest positive voltage. The inductor current has the steepest
increasing slope. The current of the inductor is written as equation (3.17).
24 | System Design Theory
Mode 4(t3 − t4 ): Figure (3.13) shows the current flow direction of mode 4.At
time t3 , S6 , S7 are turned off, S5 , S8 are turned on. The voltage across the
inductor is (Vin − Vo′ ), and the inductor current will keep increasing as mode
3. The current of the inductor current is written as equation (3.18).
Vin − Vo′
IL (t) = IL (t2 ) + (t − t2 ) (3.18)
L
Mode 5(t4 − t5 ): Figure (3.14) shows the current flow direction of mode 5.
At the time of t4 , switch S1 is turned off and S2 is conducted. On the primary
side, D2 , S4 are conducted. On the secondary side, D5 , D8 are conducted.
The voltage across the inductor is −Vo′ . The current of the inductor gradually
decreases. The current of the inductor is written as equation (3.19).
−Vo′
IL (t) = IL (t4 ) + (t − t4 ) (3.19)
L
Mode 6(t5 − t6 ): Figure (3.14) shows the current flow direction of mode 6. At
time t5 , switch S4 is turned off and S5 is conducted. Diodes D2 , D3 , D6 , D7
are conducted. The inductor has the highest negative voltage, which is (−Vin −
Vo′ ). The current at time t6 is 0. The inductor current is written as equation
(3.20).
−Vin − Vo′
IL (t) = IL (t5 ) + (t − t5 ) (3.20)
L
Mode 7(t6 − t7 ): Figure (3.16) shows the current flow direction of mode 7.
The current becomes a negative value at time t6 . Switches S2 , S3 , S5 , S8 are
conducted, and the voltage of the inductor is the same as mode 6.
−Vin + Vo′
IL (t) = IL (t7 ) + (t − t7 ) (3.21)
L
Equation (3.23) gives the equation for the three inductor voltage and current
intervals.
I1 −I2
D1 T
= nVLo , 0 < t < D1
I2 +I3
= Vin +nV o
, 0 < t < D1 (3.23)
1−D1 T
I1 −I3
L
Vin −nVo
1−D2 T
= L
, D2 < t < T
26 | System Design Theory
has to make sure that the desired 10kW is less than the maximum transfer
power. If the inductance is set as 35µH, the maximum power is 52.24kW,
which is obtained when the external duty shift ratio D2 = 0.5.The design
requirement of the power level is 10kW, which is much smaller than the
maximum transfer power. Hence, the phase shift ratio can be set as a small
value, leading to less reactive power.
Vin Vo D2 (1 − D2 )Ts n
Pm = = 52.24kW (3.24)
2L
The leakage inductance value of 35µH is capable to transfer the 10kW power
from the primary side to the secondary side.
Figure (3.19) shows the output power varies with the duty shift ratio D2 . The
maximum value of output power is obtained when D2 = 0.5, which means the
duty shift ratio that obtains the maximum power is one-quarter of the switching
period. From the figure, it is inspected that the output power curve of the
SPS modulation scheme has a symmetrical structure. For one output power
operation point, there are two duty shift ratios correspondingly. The selection
between these two values leads to different values of current and losses.
28 | System Design Theory
k−1 1−k
D2 > D2 > (3.25)
2k 2
Figure (3.21) plots the boundary curve of the load and the ZVS condition.
The two black lines depict the ZVS working area of the DAB converter.
Putting L = 35µH, which is the value of the leakage inductor, the DAB
working area is plotted. The figure proves that it is possible to achieve ZVS
under the output voltage from 380V to 500V by setting the leakage inductance
as 35µH. The operation inside the black line area makes sure the positive value
of current I1 and I2 , which achieves the ZVS operation.
System Design Theory | 29
I1 Ts 1 D2 I 1 I 1 − I o 2
dQ1 = ( − Io )( − D2 ) dQ2 = ( I1 ) (3.26)
n 2 2 2 2 n
30 | System Design Theory
Operating at higher switching frequencies can reduce the size of the magnetic
components, thereby improving the power density of the converter. The
selection of switching frequency is a trade-off between the allowable heat
sink solution and transformer size for a given efficiency target. Besides, if the
output capacitance of MOSFET is very high, the selection of high switching
frequency leads to high switching losses at light load and affects efficiency.
The selection of switching frequency also affects the control loop bandwidth
implementation. Based on these factors, 100 kHz is used as the switching
frequency for this application.
Different from the traditional MOSFET, SiC MOSFET is chosen for the
following reasons:
The switching speed of SiC MOSFET is faster that can operate at 100kHZ.
The reverse recovery charge is significantly smaller in the SiC MOSFET for
the DAB application, resulting in reduced voltage and current overshoot. SiC
MOSFETs have lower state resistance that can reduce conduction loss. The
SiC switches can operate at high voltage levels without breakdown. Because
the secondary side has a lower voltage compared to the primary side, two
different types of MOSFET are selected for the two sides.
For this design, 1200-V Cree devices with on-state resistance of 16mΩ are
used on the primary side, and the 900V, voltage-blocking Cree devices
with on-state resistance of 30mΩ are used on the secondary side. The
actual conduction and switching loss calculations are shown in the following
sections.
source voltage VGS and drain-source voltage VDS . In the time interval tr the
current ID rises and the switch is on and VDS drops to 0.
Figures (3.25a) and (3.25b) show the switching curves of the MOSFETs.
The peak current of the primary side is 15A. The RMS and average values of
currents through the switches and diodes of the primary side are calculated as
equation (3.30).
r
1 2 Ts Ts Ts
Iswitchp RM S = (Ip tzero + Ip2 (D2 − tzero ) + ( − D2 ) × (Ip2 + Il2 + Il Ip ))
3Ts 2 2 2
= 10A
(3.30)
The diode conducts only during the switching period the dead time causing
ZVS. The average current of the diode is as equation (3.31).
Pconp = 4 × (Iswitch
2
p RM S
Rds + Idiodepavg Vf p) = 12.36W (3.32)
Using equation (3.33) and the conduction loss of switches, the secondary
conduction loss is calculated as equation (3.34).
Pcons = 4 × (Iswitch
2
s RM S
Rds + Idiodesavg Vf p) = 41W (3.34)
There are two physical phenomena that affect AC resistance, which is the skin
effect and the proximity effect. Figure (3.26) shows the figure of the skin depth
of a copper wire.
The skin effect has a huge impact on the AC resistance of the high operating
frequency. Because of the decrease of the cross-sectional area for current flow,
the AC resistance is increased. From equation (3.36), we can obtain the skin
depth of copper wire at 100kHz, which is 0.21mm.
" 1/2 #!1/2
1 1 µϵ σ2
δ= = 1+ 2 2 −1 (3.36)
β ω 2 ϵω
A good way to mitigate the skin effect is to use Litz wire instead of single-
strand copper wire. Litz wire consists of multiple individually insulated
strands that are twisted together. This arrangement helps to equalize the
current distribution among the strands and minimize the skin effect. Litz
wire of 800 strands is chosen for the windings. The parameters of the Litz
wire are provided by the manufacturer. The cross-section area of 800 strands
of copper wire is 6.28mm2 and 1mm2 can overflow 3.5A current. The 800
strands of copper wire can maintain a 22A current, which satisfies the design
requirement.
36 | System Design Theory
Figure (3.27a) and figure (3.27b) are taken from the datasheet of the SIFERRIT
material N87.
The volume of the core is 118cm3 , and the core loss at 100kHz is estimated
(a) Relative core losses versus AC field (b) Relative core losses versus temper-
flux density ature
as 300mW /cm3 . The total core loss at 100kHz is given by the equation (3.37).
the DAB converter can be derived, which will be elaborated in the chapter (4).
The input voltage Vin is set as 800V to meet the demand of the input DC bus
voltage. The duty shift ratio varies with the controlled output voltage and the
modulation scheme of the converter. Leakage inductance is decided by the
transferred power level and the soft switching operation range of the converter.
Output capacitance is chosen based on the requirement of voltage ripples.
The switching frequency is selected based on the consideration of power
density and switching losses. The transformer ratio of the power transformer
is selected depending on the best operation point, which is 500V.
Chapter 4
Based on the literature study and design parameters introduced above, the
model of the DAB converter is built up and a voltage closed-loop control
method is implemented in this section. Analyzing the steady state of the
inductor power flow, the voltage transmission ratio is derived, which is decided
by the circuit parameters and the duty shift ratio.
First, SPS and EPS control methods are selected to perform the modeling
and controller design. Different operation modes of the DAB converters are
analyzed to get the mathematical model of the DAB converter. Transfer
functions are obtained by using the small signal modeling method. The
reduced order models of SPS and EPS are built.
In this project, the secondary side is a load resistor leading to D2 > 0. The
energy is transferred from the primary side DC voltage source to the secondary
load resistor. To better illustrate the problem, the maximum power of SPS is
taken as the base power, which is obtained when the external duty shift ratio
is 0.5. Equation (4.1) gives the expression the base power. The unified output
power value of SPS is given as equation (4.2).
nVin Vo Ts
PB = (4.1)
8L
Po
Po ∗ = = 4D2 (1 − D2 ) (4.2)
PB
The reactive power of SPS control is calculated based on Mode 1 and Mode 5
by multiplying the primary side voltage and inductor current. Equation (4.3)
and (4.4) gives expressions of the reactive power.
40 | Modelling and Control
nVin Vo (k + (2D2 − 1)
Prs = (4.3)
16fs L(k + 1)
Prs (k + (2D2 − 1))2
Prs ∗ = = (4.4)
PB 2(k + 1)
Figure (4.1) plots the relationship between the external phase shift ratio D2
and the reactive power of SPS reactive power Prs . From the figure, it is shown
that when the duty shift ratio D2 is fixed, the reactive power is increased with
the increase of voltage transmission ratio k. If k is fixed, the reactive power is
increased with the duty shift ratio D2 . Hence, it is recommended to design the
voltage transmission ratio k as 1 and decrease the value of the external duty
shift ratio.
nVo Ts
Ims = I1 = (k + 2D2 − 1) (4.5)
4L
Modelling and Control | 41
To calculate the unified value of the peak current, the base value of the current
is chosen as the maximum output current of SPS, which is equation (4.6)
PB nVo Ts
IB = = (4.6)
Vin 8L
The peak current of SPS in per-unit value is equation (4.7), which has two
variables that are voltage transmission ratio k and external duty shift ratio D2 .
Ims
Ims ∗ = = 2(k − 1 + 2D2 ) (4.7)
IB
Similar to the reactive power analysis method, the figure of peak current and
duty shift ratio is plotted with different values of k to illustrate the factors that
influence the amplitude of the current. Figure (4.2) plots the figures of unified
current stress curves varied with k and D2 .
is specified), the peak current increases with the duty shift ratio. If the duty
shift ratio is specified, peak current increases with the voltage transmission k.
If k = 1, the converter has the least current stress, which gives the least loss
of components. Hence, the transformer ratio n needs to be well-designed to
make sure k has the optimized value.
42 | Modelling and Control
If D21 = 0.091, the peak value of the inductor current, input current and output
current can be calculated as (4.8):
Hence, the first step is to obtain the transfer function Gvd of the output voltage
and the duty shift ratio. Gvd is the voltage transfer function of the duty shift
ratio and the output voltage.
Equation (4.11) shows the parameters of the small signal equivalent circuit of
the DAB circuit.
44 | Modelling and Control
vˆo R
Gvd = = K3 (4.12)
d 1 + sCout R
The controller parameter is obtained as equation (4.13).
Kp s + Ki
GP I = (4.13)
s
According to the rule of thumb of power electronics converter controller
design, the gain at the crossing frequency is 1 and the phase margin should
be larger than 45◦ .
( Kp s+Ki
s
Gvd (s) =1
s=jωc (4.14)
̸ Gpi (s)Gvd (s) ≥ 180◦ − φ
Modelling and Control | 45
Figure (4.5a) is plotted based on the transfer function equation (4.13). Without
the PI controller, the crossing frequency is around 100kHz, which is almost the
same as the switching frequency. Setting the crossing frequency wc = 0.1ws ,
and the phase margin as 45◦ , the modified bode diagram with PI controller is
shown as figure (4.5b). Kp = 0.089 and Ki = 5.60 are the parameters of the
PI controller respectively.
Figure 4.5: Open loop and PI modified closed loop bode diagram of SPS
modulation scheme
In the controller loop, the output is the output voltage. The power devices
and output capacitor might be destroyed by the voltage overshoot. Hence, the
integral separation method is implemented to solve the problem. Figure (4.6)
gives the block diagram of an integration separation block. The integration
controller is disabled at the start point because the voltage difference is larger
than the threshold value. The proportional controller works to track the
reference. Once the output voltage is larger than the threshold, the integration
controller works to eliminate the steady-state error.
nVin Ts 1
Io = (D2 (1 − D2 ) + D1 (2D2 − D1 − 1)) (4.15)
2L 2
In the special case, if the voltage transmission k = 1, and internal phase shift
ratio D1 = 0, the output current Io = 2L Ts
D2 (1 − D2 Vin n), which is equation
(3.12). Finally, the output power Po is obtained by multiplying output voltage
Vo .
nVin Vo 1
Po = D2 (1 − D2 ) + D1 (2D2 − D1 − 1) (4.16)
2fs L 2
The figure of the per-unit value of output power is plotted as figure (4.8). From
the figure, it is inspected that if the internal phase shift ratio is 0, the 3D figure
becomes a figure (3.19). By adjusting the value of D1 and D2 , different output
power can be obtained. Hence, one more degree of freedom is provided to
optimize the DAB converter.
It is inspected that the reactive power is decided by three variables, which are
Modelling and Control | 51
the voltage transmission ratio k, internal duty shift ratio D1 and external phase
shift ratio D2 .The reactive power can be suppressed by setting the numerator
as 0. Equation (4.20) gives the expression of internal phase shift ratio D1 .
2 k−1
D1 = D2 + (4.20)
2+k k+2
The voltage transmission ratio k is set as 1 at the 500V output point. If k = 1,
the relationship between the phase shift D1 and D2 is that D1 = 23 D2 . The
controller design will be introduced in the modeling section.
In the DAB converter, the transformer leakage inductor is usually used as the
energy storage inductor. By minimizing the peak value of the inductor current,
the copper loss of the transformer windings can be decreased. Besides, the
conduction loss of switches can also be decreased. The peak value of the
inductor current is suppressed by tuning D1 and D2 . Figure (4.12) shows the
current waveform of EPS control.
Ts nVo
ILmax = [k(1 − D1 ) + (2D2 − 1)] (4.21)
4L
In the EPS control, the peak current is decided by both the internal phase
shift ratio D1 and the external phase shift ratio D2 . Equation (4.22) gives
the equation of EPS maximum inductor current. As the efficiency of DAB
converter is usually higher than 95%, an assumption is made that the output
power amount is the same as the input power amount. (i.e. the converter is an
ideal converter). Substituting the output voltage of the current equation, the
current is formed as an equation that is decided by the input voltage and duty
shift ratios.
nVin Vo Ts 1
Poeps = [D2 (1 − D2 ) + D1 (2D2 − D1 − 1)]
4L 2
nVo Ts
ILmax = [k(1 − D1 ) + (2D2 − 1)]
4L
Vin Ts n2 Vin RTs
Imeps = + (2D2 − 1)(−D12 − 2D22 − D1 + 2D2 + 2D1 D2 )
4L 8L
(4.22)
From the equation of equation (4.22), the equation of current stress of EPS
control is obtained. If the internal phase shift ratio D1 is fixed, the peak current
value will increase with D2 . Also, the peak current changes with the voltage
transmission ratio k, and the minimum value is obtained when k = 1. The
unified peak current expression is written as equation (4.23). Figure (4.13)
shows the current stress Imeps ∗ changing with D1 , D2 and k.
Imeps
Imeps ∗ = = 2(k(1 − D1 ) + (2D2 − 1)) (4.23)
IB
From the figure it is inspected that the current stress is proportional to the
voltage transmission ratio. The minimum value is obtained at k = 1. Hence,
to minimize the current stress, the value of D1 and D2 are calculated. The
external phase shift ratio D2 is calculated by the desired output power from
equation (4.22).
p
1 + D1 − 1 − Po ∗ −D12
D2 =
2 q (4.24)
Imeps = 2(k − (k − 1)D1 − 1 − Po ∗ −D12 )
Modelling and Control | 53
√
1+D1 − 1−Po ∗−D 2
The value of external phase shift ratio D2 can be either 1
or
√ 2
1+D1 + 1−Po ∗−D12
2
. As it is discussed in the above part, the duty shift ratio
should be as small as possible. Hence, the value of the external duty shift ratio
is chosen as equation (4.24).
To minimize the value of the peak current, calculating the derivative of Imeps
with D1 and the minimum point of peak current is obtained.
dImeps D1
= −2(k − 1) + p
dD1 1 − Po ∗ −D12
s
Po ∗
D1 = (k − 1)
4(k − 1)2 + 1
s s
1 − Po ∗ 3(k − 1)2 + 1
Imepsmin = 2[k − (k − 1)2 − (1 − P o ∗) ]
4(k − 1)2 + 1 4(k − 1)2 + 1
(4.25)
From the figure, it is clearly shown that the minimum current stress of EPS is
always smaller than that of SPS. If k = 1 (i.e. the output voltage is 500V) the
current stress curves of SPS and EPS are the same. If k = 1.3 (i.e. the output
voltage is 380V), the current stress of EPS is slightly smaller than that of SPS.
If k = 2(i.e. the output voltage is 250V), the current stress of EPS is much
smaller than that of SPS. Hence, it is concluded that the current stress of EPS is
always smaller than that of SPS, especially under a high voltage transmission
ratio k.
Figure (4.15) below is the reduced-order model of the EPS converter. To get
the transfer function of output voltage and external phase shift ratio D2 , small
signals are added to the equations of the output current. iˆo , dˆ1 , dˆ2 are the output
current signals and input duty shift ratio signals disturbance respectively. In
the reduced order method, the average input and output current values across
one switching cycle serve to explain the properties of the current. Finally, the
DAB is transformed into a first-order system by ignoring the dynamics of the
inductor current. The reduced order method is much easier and more accurate
enough to get the transfer function of the system.
The reduced order method is shown in figure (4.15). On the input side, the
input DC voltage source and capacitor are shown together with the average
input current. On the output side, the average output current from the converter
and load resistor are shown in parallel connection with it.
nTs Vin
Io + iˆo = [(D2 + dˆ2 )(1 − D2 − dˆ2 )]
2L (4.27)
1 ˆ ˆ ˆ
+ (D1 + d1 )[2(D2 + d2 ) − (D1 + d1 ) − 1]
2
The square of the small signal disturbance can be considered as 0. Eliminating
the steady state value, the small signal of the output current is written as
equation (4.28), which is the equation of the control variables, duty shift ratio
of both sides. The small signal of output current iˆo can be written as the
equation of dˆ1 and dˆ2 . The sum of these two parts makes up the output current.
1
iˆo = 2(1 − 2D2 + D1 )dˆ2 + (1 + D2 − D1 )dˆ1 (4.28)
2
56 | Modelling and Control
Separating the equation (4.28), the transfer function for current and external
phase sift ratio D2 is written as equation (4.29).
1
Gd2i = 2(1 − 2D2 + D1 ) Gd1i = (1 + D2 − D1 ) (4.29)
2
Figure (4.16) gives the reduced order control block diagram of EPS control.
The gain of the transfer function Gd2i and Gd1i is added together to get the
1 R
vˆo = (21 − 23D2 ) dˆ2 (4.32)
9 RCout s + 1
Figure (4.17) illustrates the control block diagram of the EPS modulation.
To be mentioned, the aim of designing a closed-loop voltage controller is to
modify the inaccuracy of the circuit parameters. The resistor and inductor
might be different from the set-up model which leads to the miscalculation of
the duty shift ratio. To maintain the constant output power, the closed-loop
controller is implemented. Besides, the closed-loop controller can stabilize
Modelling and Control | 57
Figure 4.18: Open loop and PI modified closed loop bode diagram of EPS
modulation scheme
Figure (4.19) shows the control block diagram of minimum current stress
control. The parameters of the PI regulators of minimum current stress control
Chapter 5
Simulation Results
In this chapter, the theoretical equations and models are verified via the
simulation models. First, the figures of SPS working under 380V and 500V
operation points are plotted to satisfy the 10kW power demand. Figures of the
closed-loop control are plotted under the load step test to verify the design of
the controller.
The power loss is simulated by inputting the datasheet of the power devices
into the circuit. The power device loss like conduction loss and switching loss
is calculated. The copper loss and magnetic loss of the transformer is also
considered. The efficiency of different operation points is simulated.
Finally, power loss such as switching loss, and transformer loss is taken into
consideration in the simulation. EPS increases the efficiency of the power
converter compared to SPS control.
60 | Simulation Results
Also, the figures of the output voltage and output power are plotted to verify
the desired requirements, which is shown in figure (5.3).
Figure (5.4) shows the waveform of the inductor current and primary side
voltage. To combine those two figures, unified values are used. It is inspected
Simulation Results | 61
that when the switches S2 and S4 are turned on, the current still flows in the
same direction, which means the voltage across the drain to the source is only
the voltage drop of the body diode. ZVS operation is realized.
Then the duty shift ratio D2 is set as 0.125, which gives the 500V output.
Same as the 380V output voltage, figures of voltage, current, output power,
and ZVS operation are plotted. Figure (5.5) shows the voltage waveform of
500V output. As it is stated in the theoretical part, the 500V output voltage is
62 | Simulation Results
If the output power is 500V, the converted secondary side voltage is 800V,
which means Vp = Vs′ , and the peak value of the inductor current is the same
as shown in figure (5.6). The inductor’s voltage only has two stages, which
are 0V and 1600V correspondingly. Figure (5.7) shows the output power and
Simulation Results | 63
The results of the open-loop simulation prove that the model of the converter
can give a 10kW output power of the output voltage varied from 380V to
500V. The design of the voltage loop works as expected leading to the current
and voltage values. The mathematical equations can describe the energy
conversion process of the DAB converter.
64 | Simulation Results
However, both the closed-loop simulation and the load step simulation have
one common problem, which is the overshoot caused by the integration
controller. The initial state of voltage is 0, leading to a huge difference between
the reference signal that saturates the integration controller.
66 | Simulation Results
From figure (5.14) and (5.15), it is shown that the overshoot is totally
eliminated. The figure of controller output has a narrow width that leads to
less output of the controller. In the steady state, the controller has the same
output as the normal PI controller, which tracks the voltage reference signal
perfectly.
Simulation Results | 69
The next step is to verify the results of the 380V voltage output. The voltage
transmission ratio k is calculated as k = Vin /nVo = 1.316. When the external
phase shift D2 = 0.175, the output voltage is almost 380V, and the output
power is 10kW. Simulation waveforms are shown in figure (5.18) and figure
(5.19). Caused by the unbalance of voltage of both sides, the inductor voltage
has 4 levels, which leads to a higher value of inductor current.
70 | Simulation Results
Figure 5.18: Primary and secondary side voltage of EPS control (380V)
From the waveform of EPS current and voltage, it can be verified that the
problem of reactive power and current stress can be solved by adjusting the
internal phase shift ratio D1 .
Simulation Results | 71
From the figures, the conclusion is that the reactive power of EPS can be totally
eliminated when the voltage transmission ratio k = 1. If k = 1.316, EPS
control still produced less reactive power than SPS control, which proves the
design is correct.
between SPS and EPS of the output voltage 250V. D1 = 0 is the SPS
modulation scheme, and D1 = 0.3 corresponds to the minimum current
value of EPS modulation. (250V voltage is only selected to draw an obvious
comparison. The design operation range of Vo is from 380V to 500V.)
From figure (5.24), it is inspected that the EPS control can greatly reduce the
current amplitude if the voltage transmission ratio is k = 2.
Different from the triangle wave of SPS current, the EPS current waveform
has 3 peaks, which are caused by the multi-levels of inductor voltage. The
maximum peak value of the inductor current is greatly reduced in this
modulation scheme.
Then, the control scheme is tested if the output voltage is 380V, which leads
to k = 1.316. Setting D1 = 0.2, the current is less than 20A, which is also
reduced compared to the SPS modulation.
74 | Simulation Results
Finally, the results of the inductor current are compared when the output
voltage is 500V, which corresponds to k = 1. At this operation point, D1 = 0
leads to the best efficiency. The minimum current stress is obtained by the
SPS modulation scheme. However, to make a comparison between SPS and
EPS control scheme, D1 = 0.2 is picked as a random value to modulate
the converter of the EPS scheme. In this special case, the optimum point is
Simulation Results | 75
obtained when the internal duty shift ratio is set to 0. (i.e. SPS control). From
figure (5.26), we can inspect that the minimum current is obtained by the SPS
control modulation as expected.
Compared figure (5.24), figure (5.25) and figure (5.26), several conclusions
can be drawn.
1. The inductor peak current increases with the voltage transmission ratio k,
the minimum value is obtained when k = 1.
2. EPS control scheme can greatly reduce the inductor current if k is much
greater than 1 by tuning the internal phase shift ratio D1 .
3. To minimize the inductor current, the designer should set the voltage
transmission ratio to operate around 1.
The parameters are the same as the Simulink. Thermal models of MOSFETs
are imported into the Simulink. A measurement subsystem consisting of
switching losses of primary FETs, switching losses of secondary FETs,
conduction losses of primary FETs, conduction losses of secondary FETs, and
transformer copper losses are taken into consideration. Figure (5.27) shows
the schematic in PLECS. The reference voltage is set as 500V, and the load
resistance is 25Ω, which leads to a 10kW output power. Figure (5.28) shows
the output voltage, output current, and output power of the DAB converter. A
500V output voltage, 10kW output power is set as the output power level.
The power loss is divided into switching loss of primary FETs, conduction
Simulation Results | 77
The efficiency of the DAB converter is tested at 380V and 500V to compare
the efficiency of the circuit. Table (5.2) and table (5.2) show the simulation
results.
78 | Simulation Results
In the EPS modulation scheme, the efficiency is increased if the input voltage
and converted output voltage are unequal. The value of the internal phase
shift ratio D1 can be calculated through the derivative of the inductor current.
Setting D1 to the optimized value, a closed-loop PI controller is built to
maintain the output power. In the steady state, the converter will have the
optimized performance as expected.
To be mentioned, as we can see from the table, the loss of 500V of the
EPS modulation scheme is much higher than that of SPS. This is because
the optimal point of EPS control at 500V is obtained when the internal duty
shift ratio is 0(i.e. SPS control), which is shown in figure(5.26). To make a
comparison, D1 = 0.2 is picked as a random value to simulate the EPS control.
As it is expected, the efficiency drops compared to the SPS control caused by
the conduction loss.
Conclusions | 79
Chapter 6
Conclusions
In the System Design Theory chapter, design details are presented. The DAB
converter is a sophisticated system comprising 8 switches, a high-frequency
transformer, an inductor, and an output capacitor. The circuit modes of
the SPS (single-phase shift) and EPS (extended phase shift) are analyzed to
facilitate better converter design. SPS has 6 operation modes based on the
waveform of the inductor current, while EPS has 2 additional states due to the
added internal phase shift ratio. The crucial component of the leakage inductor
is calculated to ensure zero-voltage switching (ZVS) operation of the power
circuit and efficient power transfer from the DC source. The output capacitor is
determined based on the requirement for output voltage ripple. The switching
frequency, transformer, and MOSFET are selected by considering the trade-off
between power density and efficiency, with calculations performed at the 500V
output voltage working point. The calculations primarily focus on switching
80 | Conclusions
and transformer losses, which are the most significant losses, to estimate the
overall efficiency.
Next, the modeling and control of SPS and EPS are addressed. A comparison
is made between the SPS and EPS modulation schemes based on reactive
power and current stress. By introducing a small disturbance to the steady-state
model, reduced-order dynamic models for SPS and EPS are obtained. Open-
loop bode diagrams are plotted, and a proportional-integral (PI) controller is
designed to compensate for system behavior, resulting in modified closed-
loop bode diagrams that provide the values for the PI controller. To address
the issue of integration saturation-induced overshoot, an integral separation
method is implemented in the closed-loop controller.
Chapter 7
Future work
Limited by the time and components, the hardware verification hasn’t been
finished. A 10kW DAB converter should be produced in the lab with the
ordered PCB boards and components. The control methods should be verified
on the hardware platform. Figure (7.1) shows the system overview of the
converter.
The DAB converter can be divided into 4 parts to ensure the flexibility and
scalability of the converter. The primary and secondary sensing cards collect
the voltage and current signals from the primary bridge and the secondary
bridge. Then those signals are converted to the range that the MCU can
process. The control card receives the signals from the sensor boards and
calculates the control signals to follow the reference value. Four control cards
are installed on the board that drives the four legs of the converter. A DAB
converter with the structure shown above will be produced.
82 | Future work
The control card will use the launch pad of Texas Instrument TMDSC-
NCD280049C or TMDSCNCD28379D. An HSEC 180pin connector is used
to connect the control card to the power board.
The control scheme will be verified based on the hardware platform to give
a more reliable conclusion.
References
[6] H. Bai, C. Mi, C. Wang, and S. Gargies, “The dynamic model and
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Appendix A
Simulation Schematics
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