Digital Geometric-Sequence Control Technique for

Digital Geometric-Sequence Control Technique

for Bidirectional Dual Active Bridge DC-DC

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 DC-DC 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 DC-DC 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 non-linear behaviour of the converter. In this thesis, the precise

mathematical model of the converter is derived and non-linear control schemes are

proposed for the control system of bidirectional DC-DC converters based on the de-

rived model. The proposed inner current control technique is developed based on a

novel Geometric-Sequence 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 DC-DC 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) DC-DC Con-verters 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 Steady-State 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 Geometric-Sequence 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 Geometric-Sequence Control.

vi

HF High Frequency.

PEV Purely Electric Vehicle.

PHEV Plug-in Hybrid Electric Vehicle.

PSM Phase-Shift 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 Non-fossil energy sources for the utility grid . . . . . . . . . . . . . . 2

1.2 Typical Electricity load variation of the utility grid during 24 hours . 3

1.3 AC-DC 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 DC-DC 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 SSOC-PCM 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


B for triangular current mode modulator when VA < kVB . . . . . . 34


A for triangular current mode modulator when VA < kVB . . . . . . 35


B for trapezoidal current mode modulator when VA > kVB . . . . . . 36


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 2D-ZVS 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


to I=6 A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65


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 steady-state waveforms in one half-cycle . . . . . . . . 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


and Vb=400V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93


and Vb=400V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93


and Vb=250V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94


and Vb=250V with ∆LS% = 20% . . . . . . . . . . . . . . . . . . . . 94

xi


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



xii

List of Tables

2.1 PERIOD-DOUBLING 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 phase-shift . . . . . . . . . 40

3.3 Phase-shift 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 CO2-caused 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: Non-fossil energy sources for the utility grid

internal combustion engine vehicle, especially auto-mobiles. 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 so-called 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 valley-filling 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 AC-DC converter used

for the purpose of power transfer between the grid and the EV. The AC-DC con-

verter used in this thesis is comprised of a full-bridge AC-DC converter followed by

a bidirectional DC-DC 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

AC-DC Converter DC-DC Converter

CFB

Lg

Figure 1.3: AC-DC Converter used in G2V/V2G applications

voltage to the input of the AC-DC converter. The inductor Lg makes the AC-DC

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 DC-DC 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 DC-DC 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 DC-DC converter with V2G/G2V ca-

pability

2. Development of the precise discrete-time domain model for steady-state 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 Geometric-Sequence 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 DC-DC convert-

ers are explored. The benefits and drawbacks of the conventional control structures

are also discussed.

chapter 3, Bidirectional DAB DC-DC 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 geometric-sequence 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 semi-conductors. Simulation and experimen-

tal results are provided to verify the behaviour of the proposed geometric-sequence

control approach.

chapter 6, Conclusion

A conclusion of the thesis along with future work in the field.

7

Chapter 2

Literature Review

Bidirectional DC-DC converters with galvanic isolation are used in Plug-in 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 DC-DC 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

DC-DC converters [23–25]. In this chapter, a literature review of DAB converters

and their control schemes are explained.

2.1 Overview of Bidirectional DAB DC-DC Converters

Figure 2.1 depicts a typical full-bridge 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 DC-DC 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 DC-AC 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 AC-DC 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 phase-shift, 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 phase-shift between the

two active bridges, ϕ, as the only control parameter out of the 4 control parameters

mentioned above. This method is called the Phase-Shift 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 phase-shifts. 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


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 (1-D) optimization problem to improve the converter

efficiency since either D1 or D2 changes [23].

[32–34] represent a 2-dimensional (D1 and D2 change simultaneously) optimiza-

tion approach in which highly efficient operation of the DAB converter is reported.

However, compared to the 1-d problem, the 2-d 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 DC-DC power converters is

to maintain a constant output voltage/ current, in spite of the disturbances in the


Switching Dual Active Bridge(DAB) DC-DC 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


and consequently resulting in simple and robust wide-bandwidth control in DC-

DC converter. Moreover, the peak current control provides an over-current

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


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 micro-controllers (e.g. Digital

Signal Processing (DSP) and/or Field Programmable Gate Arrays (FPGA)) can com-

promise control performance, especially in high-frequency 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


Table 2.1: PERIOD-DOUBLING OSCILLATIONS OCCUR FOR THE INDI-CATED 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, buck-boost. 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

current-programmed control, where usually a slope-compensation 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 DC-DC

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 DC-DC 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 valley-peak 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 valley-peak current control


+ 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 over-current switch protection, and meanwhile eliminates the

possible saturation of the high-frequency transformer.

In [60,61] an accurate small-signal model for a galvanic isolated, bidirectional DC-DC

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 DC-DC 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 Li-ion cell), after that in the second state

the voltage is kept constant and the current decreases. At the end of the charging


+ +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 DC-DC converter


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 ultra-capacitors. (figure 2.8)

[30] analyses the performance of a high current DAB DC-DC 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


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 multi-variable control system for an efficient Zero Voltage

Switching (ZVS) full-bridge DC-DC converter used in a (Plug-in Hybrid Electric Ve-

hicle (PHEV)). This converter processes the power between the high voltage traction

battery and low voltage (12V) battery. Generally, Phase-shift between the two legs of

the full-bridge converter is the main control parameter to regulate the output power.

However, the zero voltage switching cannot be guaranteed by merely controlling the

phase-shift 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


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 DC-DC 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 multi-variable 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 DC-DC 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


Voltage andcurrent

controllers

Multiplier

D1Lookuptable for(VA,VB)

D2Lookuptable for(VA,VB)

?Lookuptable for(VA,VB)

Measure

DC-DCConverter

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 (PCM-SSOC)

technique for DAB DC-DC converter. The proposed control improves the performance

of the bidirectional DAB DC-DC converter over wide operating conditions. Basically,

the proposed PCM-SSOC 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).


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 current-driven full-bridge DC-DC 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|

+ -Dead-timeGenerator

Dead-timeGenerator

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: SSOC-PCM control system

2.3 Summary

Overall, the dynamical equations of DAB converter has non-linear 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) DC-DC

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 full-bridge circuits can be replaced by the respective square-wave

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)


k .VAC-B

LsiL=iAC-A

+

-

iAC-B / k+

-VAC-A

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,


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 phase-shift, 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 phase-shift

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 phase-shift

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 steady-state operation, the phase-shift time Tϕ and the DC supply voltage VA and

VB remain constant during one cycle. This property results in vACA(t), vACB

(t), and


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 half-cycle

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

phase-shift 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


t

I III IV

TS

t1

VAC-A

K VAC-B

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 phase-shift needed to obtain a given power transfer

is derived by rearranging (3.10):

ϕ =π

2

(1−

√1− 8fsL|P |

kVAVB

)sgn(p) ∀ |P | < |PPS,max| (3.12)

The wide usage of phase-shift modulation is because of its simplicity to adjust the

transferred power. Drawbacks of DAB converters operated under phase-shift 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


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 phase-shift modulation problems. The alternative mod-

ulation schemes bring the following advantages as compared to the phase-shift 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)


t

I II

TS

t1

VAC-A

K VAC-B

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 full-bridge 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)


t

III

TS

t1

VAC-A

K VAC-B

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 phase-shift. 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.


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 phase-shift 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


tTS

t1

VAC-A

K VAC-B

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)


tTS

t1

VAC-A

K VAC-B

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


t

T1

TS

t1

VAC-A

K VAC-B

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 − 2|ϕ2|

))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,


t

T1

TS

t1

VAC-A

K VAC-B 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 , phase-shifts required to obtain specific power levels, and

the inductor RMS current (IL) for different voltage sequences are given in Table 3.2,


t

VAC-A

k VAC-B

iL

TS

t

VAC-A

k VAC-B

iL

TS

t

VAC-A

k VAC-B

iL

TS

t

VAC-A

k VAC-B

iL

TS

t

VAC-A

k VAC-B

iL`

`

TS

VAC-A

k VAC-B

TS

iL

tt

k VAC-B

TS

iL

t

VAC-A

k VAC-B

iL

VAC-A

TS

Sequence 5 Sequence 6





t

VAC-A

k VAC-B

iL

t

k VAC-B

iL

VAC-A

TS

t

VAC-A

k VAC-B

iL

TSt

VAC-A

k VAC-B

iL



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


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 phase-shift

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


Table 3.3: Phase-shift required to achieve a certain power level

Mode ϕ

1 ϕ = πLfSPkDAVAVB

9 ϕ = πLfSPkDBVAVB

2, 8 ϕ = πsgn(P ).

(DA +DB − 2

√DADB − L|P |fS

kVAVB

)

10, 12 ϕ = πsgn(P ).

(12−√DA(1−DA) +DB(1−DB)− 1

4− 2fSL|P |

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. STEADY-STATE 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 Cur-rent Mode (CCM) with Zero Voltage Switching (ZVS)

3.3 Steady-State 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 half-cycle 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)


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


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)


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);

• voltage-time 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.


Conduction losses of each switch is determined based on their respective RMS

current. Due to the half-cycle 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


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, turn-on 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


of the leg) lags the voltage of the pole.. A short amount of time should be set aside

between the turn-off and turn-on 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 turn-on 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 turn-off), and with the assumption of sufficient Tdeadtime, SA2

is turned on with vDS,T2 = −vD ≈ 0 (zero voltage turn-on; 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.


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 turn-off and turn-on 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 phase-shifts 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 2-D 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)


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)


Figure 3.15: 2D-ZVS 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 closed-loop PI control loop is introduced for the DAB converter. The

control loop consist of a modulator, look-up table, linear compensator, and a feedback

which are explained in more detail in this section. Moreover, the digitalization of the

control will be explained.


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, look-up 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 look-up 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


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 look-up 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 s-transfer function to

z-domain 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 micro-controller (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 phase-shift 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


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 dead-time. 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.


Table 3.5: DAB waveform details for VA = 360 VDC and VB = 400 VDC with differ-ent 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


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 phase-shift 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 phase-shift 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.


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)


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 non-linearity of the system-dynamics, it is not always stable over a wide voltage

range and load range. Figure 3.29 depicts a case of instability in the system.


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


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 condi-tions: VA = 360, VB = 400, iBat = 6A


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 condi-tions: 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


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


0

5

10

5e-005 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


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,


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.


ip

Vp

Vs

ZVS not achieved

Figure 3.32: steady state operation at VA = 100V , VB = 120V without ZVS


ipVp

VsIBAT

Figure 3.33: steady state operation at VA = 100V , VB = 120V , I = 2.2A withachieved ZVS


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 2-loop

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

Geometric-Sequence 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 geometric-progression 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. Phase-shift 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 micro-controller 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 GEOMETRIC-SEQUENCE 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


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 geometric-sequence 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 half-cycle (i(n)). Therefore, perturbation of the current can be denoted as ∆i

at the beginning of any half-cycle. In can be seen from Figure 4.3 that if −∆i oc-

curs, provided that the phase-shift remains constant during the whole switching cycle

(open-loop), 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 half-cycle results in oscillation of the current waveform.

To avoid these oscillations, the progression of the current waveform in response to

a change in the phase-shift is investigated. Through that, a digital control approach

is proposed to improve the state space current waveforms and remove/ attenuate

oscillations.

4.3.2 Geometric-Sequence 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


-i(n-1) -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(n-1) -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 half-cycles. Therefore, the

trajectory of ϕAB begins from the initial steady-state ϕAB(0) and ends with the final

steady-state 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


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


4.5 (B). In this Figure we will find the relationship between the change in phase-shift

(∆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)


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)


-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 steady-state waveforms in one half-cycle

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)


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


modulation, a discrete control function for ∆ϕAB(n) needs to be defined.

Proposed Discrete Control Law

So far we know how to change the phase-shift 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 steady-state 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 steady-state 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 half-cycle is achieved by (4.23)

ϕAB(n) = ϕAB(n− 1) + ∆ϕAB(n− 1) + ∆ϕAB(n) (4.25)


-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 N-1

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)

Half-Cycle 0 Half-Cycle 1 Half-Cycle 2 Half-Cycle n

ΔφAB(2)

φAB(n)=φAB(n-1)+ΔφAB(n-1)+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 ∈ a|a ∈ 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 ∈ a|a ∈ R , 0 < a < 2 the control

algorithm presented in (4.25) forces the error of the sampled current (∆i(n)) to reduce

with a geometric-sequence trend in every half-cycle. (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

Half-Cycle 0 1 2 . . . nCurrent Error ∆i(1) (1− a)∆i(1) (1− a)2∆i(1) . . . (1− a)n∆i(1)


+ +

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 geometric-sequence 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 geometric-progression 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 half-cycle. As a result, the current error at t = TS will go to zero. Basically,

at this control algorithm, the first half-cycle is responsible for setting up the initial


conditions for the final steady-state operation and the second half-cycle increases the

phase-shift 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 geometric-progression trend. However,

in this case (1 − a) has a negative value and this results a change in the polarity of

the error in each half-cycle 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

Half-Cycle 0

φAB(1)=φAB(0)+ΔφAB(1)

Half-Cycle 1

)1((1)AB ikV

fL

B

SS

φAB(2)=φAB(1)+ΔφAB(1)

Half-Cycle 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 = a|a ∈ 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 feed-forward 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 feed-forward 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

iref-prediction

IBat-ref

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

phase-shift (ϕAB) in only two-half 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 half-cycles

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 closed-loop 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

0-200-400

200400

0.00015 0.0002 0.00025 0.0003Time (s)

0.1

0.12

0.14

0.16

I(BAT)

ΨABTwo half-cycles


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 half-cyclesΨAB

I(BAT)


4.7. SIMULATION 94

8

10

12

14

0-200-400-600

200400

0.0001 0.00015 0.0002 0.00025 0.0003Time (s)

0.1

0.2

0.3

0.4


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


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


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


Bidirectional DC-DC ConverterBidirectional AC-DC Converter

EMI Filter Auxilary Circuit

FPGA

Figure 4.18: 3kW bidirectional AC/DC converter prototype




99

Chapter 5

Conclusions and Future Work

In this thesis, different control systems for bidirectional DC-DC converters have been

examined. Based on the investigations, different difficulties and shortcomings of previ-

ously proposed control systems for bidirectional dc-dc converters have been identified.

Then, non-linear control schemes have been proposed for bidirectional DC-DC 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 DC-DC Dual Active Bridge (DAB)

converter with V2G/G2V capability is presented. The DAB converter consists

of two active H-bridge 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 350-450 VDC and 250-430 VDC, respectively. The power rating of the

converter is 0-3.3 kW.

2. Precise dynamical equations of the DAB converter is highly non-linear. 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,

non-linear control schemes have been proposed which can address this problem.

3. Development of the precise discrete-time domain model for steady-state 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 Geometric-Sequence 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 geometric-progression trend which results in only a

few half-cycles for the control to reach its reference value.

5. Stability analysis for the closed-loop 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.

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