Design and Control of Bi-Directional Grid-Interactive Converter for Plugin Hybrid Electric Vehicle...

ABSTRACT

ZHOU, XIAOHU. Design and Control of Bi-Directional Grid-Interactive Converter for Plug-in Hybrid Electric Vehicle Applications. (Under the direction of Dr. Alex Q. Huang).

The plug-in hybrid electric vehicle (PHEV) is a promising technology which provides a

sustainable approach to transportation that is easily accessible to a large portion of the

population that already relies on gasoline-fueled cars. Although the larger scale adoption of

plug-in hybrid vehicles is still years away, politicians, electric utilities, and auto companies

are eagerly awaiting the opportunities that will arise from reduced emissions, reduced

gasoline consumption, new electric utility services, increased revenues, and new markets that

will lead to the creation of new jobs. In addition, the electrification of the transportation

system would lead to the creation of new avenues for researchers. In the case of power

electronics researchers, plug-in hybrid electric vehicles would provide a new candidate for

energy storage. Because energy storage is a component of so called “smart grids,” a topic of

growing interest to the power engineering research community, PHEVs could be

incorporated as a vital part of such a system. However, to enable this functionality, a power

electronics interface between the vehicle and grid is required. The motivation of this

dissertation is to design a grid-interactive smart charger to enable PHEV as distributed

energy storage device which will play an important role in smart grid applications.

For grid-connection applications of the proposed converter, adaptive virtual resistor control is

proposed to achieve high power quality for plug-in hybrid electric vehicles integration with

various grid conditions. High frequency resonance poses a challenge to controller design and

moreover the various impedances lead to the variation of the resonant frequency which will

make the control design more complicated. The proposed controller behaves as a controllable

resistor series with a filter capacitor but does not exist physically. It will be adjusted

automatically based on grid conditions in order to eliminate high frequency resonance. For

off-grid applications of the proposed converter, a new inductor current feedback controller

based on active harmonic injection is proposed. An active harmonics injection loop is

proposed to extract the harmonics from the load and add to the inductor current control loop.

This method effectively improves the harmonics compensation capability for the inductor

current feedback control and achieves a better output voltage with nonlinear loads.

For a Solid State Transformer (SST) based smart grid with multiple plug-in hybrid electric

vehicles, the instability issue is investigated. When the total demand power from the plug-in

vehicles exceeds the capability of one SST, a new power management strategy is proposed in

each vehicle to adjust its power demand in order to avoid voltage collapse of the SST. Gain

scheduling technique is proposed to dispatch power to each vehicle based on battery’s state

of charge. A comprehensive case study is conducted to verify the proposed method. The

proposed method can be used as a power electronics converter level control to improve the

stability of a solid state transformer.

For the DC/DC stage of the proposed converter a high order filter is proposed to be placed

between the battery and the converter. The objective is to reduce the filter size which will

further reduce the system cost and volume. Another major goal is to largely attenuate the

current ripple of the charging current which will yield ripple free charging for a battery.

Ripple free charging will eliminate the extra heat generated by the current ripple and will

increase the battery life. The new controller is proposed to resolve the potential instability

issue resulting from the high order filter. The control loop design and robustness analyses are

conducted.

Design and Control of Bi-Directional Grid-Interactive Converter for Plug-in Hybrid Electric Vehicle Applications

by Xiaohu Zhou

A dissertation submitted to the Graduate Faculty of North Carolina State University

in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

Electrical Engineering

Raleigh, North Carolina

2011

APPROVED BY:

_______________________________ ______________________________ Dr. Alex Q. Huang Dr. Mo-Yuen Chow Committee Chair ________________________________ ________________________________ Dr. Subhashish Bhattacharya Dr. Srdjan Lukic

ii

DEDICATION

To My Parents

Lili Huang and Zhigang Zhou

iii

BIOGRAPHY

The author, Xiaohu Zhou, was born in Harbin, China. He received the B.S. and the M.S.

degree from Harbin Institute of Technology, Harbin, China in 2004 and 2006, respectively,

both in electrical engineering. Since fall of 2006, he started to pursue a Ph.D. degree at

Semiconductor Power Electronics Center (SPEC) and later National Science Foundation

funded Engineering Research Center: Future Renewable Electric Energy Delivery and

Management Center (FREEDM), Department of Electrical and Computer Engineering, North

Carolina State University, Raleigh.

iv

ACKNOWLEDGMENTS

I would like to express my sincere appreciation to my advisor Dr. Alex Q. Huang for his

guidance, encouragement and support. Dr. Huang’s creative thinking, broad knowledge,

insightful vision and warm character always inspires my work and study. To explore

something new will always be rooted in my heart. Thank you for giving me this opportunity,

I enjoy my study and work in FREEDM Systems Center very much.

I am very grateful to my other committee members, Dr. Mo-Yuen Chow, Dr. Subhashish

Bhattacharya and Dr. Srdjan Lukic for their valuable suggestion and helpful discussion

during so many group and individual meetings. It is my great pleasure to work with you

during these five years. I would like also to thank Dr. Gracious Ngaile for serving as the

Graduate School Representative for my defense.

I want to thank ERC program of the National Science Foundation and Advanced

Transportation Energy Center for their financial support of my project and research.

I would like to thank all the staff members at FREEDM Systems Center who provide an

amazing environment for me to study and work. Special thanks go to Mr. Anousone

Sibounheuang and Mrs. Colleen Reid for their help.

I want to thank my student colleagues who have helped with many good discussions and

gave me so many joyful times: Dr. Chong Han, Dr. Yan Gao, Dr. Bin Chen, Dr. Wenchao

Song, Dr. Xiaojun Xu, Dr. Jinseok Park, Dr. Jeesung Jung, Dr. Yu Liu, Dr. Jun Wang, Dr.

Jiwei Fan, Dr. Liyu Yang, Dr. Sungkeun Lim, Dr. Xin Zhou, Dr. Tiefu Zhao, Dr. Jun Li, Dr.

Rong Guo, Dr. Xiaopeng Wang, Mr. Zhaoning Yang, Mr. Jifeng Qin, Mrs. Zhengping Xi,

Mr. Sameer Mundkur, Mr. Zhigang Liang, Mr. Yu Du, Mr. Qian Chen, Mr. Gangyao Wang,

v

Mr. Xunwei Yu, Mr. Edward Van Brunt, Mr. Babak Parkhideh, Mr. Arvind Govindaraj, Mr.

Sanzhong Bai, Mr. Zeljko Pantic, Mr. Xu She, Mr. Xingchen Yang, Mr. Yen-Mo Chen, Mr.

Pochin Lin, my Project Partner Mr. Philip Funderburk, Mr. Zhuoning Liu, Miss. Zhan Shen,

Miss. Mengqi Wang, Mr. Yalin Wang, Mr. Xing Huang, Mr. Li Jiang, Mr. Fei Wang, Mr.

Kai Tan, Mr. Xiang Lu.

Finally I want to give my heartfelt appreciation to my parents in China. You always

encourage me to pursue my dreams and help me get through tough times. I am so grateful to

you for your endless support, trust and love for all of these years.

vi

TABLE OF CONTENTS

LIST OF TABLES ................................................................................................................... ix

LIST OF FIGURES .................................................................................................................. x

Chapter One Introduction ......................................................................................................... 1

1.1 Research Background: Plug-in Hybrid Electric Vehicles ....................................... 1

1.2 State of the Art of Technology ................................................................................ 7

1.2.1 Survey of SAE Standards for Battery Chargers ............................................ 7

1.2.2 Battery Charger Classifications .................................................................... 9

1.2.3 Bi-directional Charger Topology and Charging Station ............................. 12

1.2.4 Overview of Vehicle to Grid (V2G) Technology ....................................... 15

1.3 Research Motivation: Enable Integration of Distributed Energy Storage Devices

(Plug-in Hybrid Electric Vehicles) with Smart Grid ...................................................... 16

1.4 Contributions and Dissertation Outline ................................................................. 19

Chapter Two Design a Grid-Interactive Converter for Plug-in Hybrid Electric Vehicles .........

.......................................................................................................................................... 23

2.1 Definition of Grid-Interactive Converter .............................................................. 23

2.2 Topology Selection of Proposed Grid-Interactive Converter ................................ 25

2.3 Power Stage Design of Proposed Converter ......................................................... 29

2.3.1 Passive Components Design ....................................................................... 29

2.3.2 Efficiency Test ............................................................................................ 34

2.4 Control Structure of Proposed Converter .............................................................. 36

2.5 Summary of Chapter Two ..................................................................................... 42

Chapter Three High Frequency Resonance Mitigation for Plug-in Hybrid Electric Vehicles’

Integration with a Wide Range of Grids ................................................................................. 43

3.1 High Order Filter Formation and its Negative Impacts ......................................... 43

3.2 Review of Active Damping Methods .................................................................... 45

3.3 Large Scale Penetration of Plug-in Hybrid Electric Vehicles into Various Grids 48

3.4 Modeling and Design of Adaptive Virtual Resistor Controller ............................ 50

vii

3.5 Adaptive Virtual Resistor Control for a Wide Range of Grids ............................. 62

3.6 Verification of Proposed Adaptive Virtual Resistor Controller with Different

Grids ............................................................................................................................... 77

3.7 Summary of Chapter Three ................................................................................... 87

Chapter Four New Inductor Current Control based on Active Harmonics Injection for Plug-in

Hybrid Electric Vehicles’ Vehicle to Home Application ....................................................... 88

4.1 Review of Control Methods for Single Phase Inverter ......................................... 88

4.2 Theoretical Analysis of the Proposed Control Method ......................................... 92

4.3 Steady State Operation and Dynamic Response of the Proposed Controller ........ 99

4.4 Investigation of Inductor Current Transient Response with Different Controllers ...

............................................................................................................................. 107

4.5 Summary of Chapter Four ................................................................................... 119

Chapter Five Power Management Strategy for Multiple Plug-in Hybrid Electric Vehicles in

FREEDM Smart Grid ........................................................................................................... 120

5.1 Architecture of PHEV Integration with Solid State Transformer based Smart Grid

............................................................................................................................. 120

5.2 The Issue of Multiple Plug-in Electric Vehicles Connected with Solid State

Transformer ................................................................................................................... 121

5.3 Proposed Power Management Strategy to Avoid Instability of Solid State

Transformer ................................................................................................................... 127

5.4 Gain Scheduling Technique to Dispatch Power based on State Charge of Vehicles

............................................................................................................................. 147

5.5 Load management of Solid State Transformer by Managing Power of PHEVs . 150

5.6 Summary of Chapter Five ................................................................................... 163

Chapter Six High-Order Filter for Compact Size and Ripple Free Charging ....................... 164

6.1 Design Goal—Compact Filter Size and Ripple Free Charging .......................... 164

6.2 Filter Design and Comparison with Conventional Filter .................................... 165

6.3 Controller Design ................................................................................................ 168

6.4 Controller Robustness Analysis .......................................................................... 177

viii

6.5 Simulation and Experiment Results .................................................................... 189

6.6 Summary of Chapter Six ..................................................................................... 195

Chapter Seven Conclusion and Future Work ........................................................................ 196

7.1 Conclusion ........................................................................................................... 196

7.2 Future Work ........................................................................................................ 199

REFERENCES ..................................................................................................................... 201

ix

LIST OF TABLES

Table 1-1 Plug-in Hybrid Electric vehicle charging level ................................................ 8

Table 2-1 Component count for H-bridge converter and three-leg converter ................ 27

Table 2-2 Power stage components in experimental setup ............................................. 33

Table 3-1 System configuration ...................................................................................... 65

Table 4-1 Output voltage with different types of load .................................................. 104

Table 4-2 Performance comparison of the capacitor current feedback, the inductor

current feedback and the proposed method .......................................................... 118

Table 6-1 Core volume and loss of L-type filters ......................................................... 167

Table 6-2 Core volume and loss of LCL-type filters .................................................... 167

x

LIST OF FIGURES

Figure 1.1 U.S oil consumption by sectors ............................................................................... 2

Figure 1.2 Oil production and consumption in U.S .................................................................. 2

Figure 1.3 Green house gas reductions with the adoption of PHEVs ....................................... 4

Figure 1.4 Predicted shares of new car sales in U.S market ..................................................... 6

Figure 1.5 Major models of PHEV and PEV ............................................................................ 7

Figure 1.6 Conductive EV/PHEV charging station and J1772 connector .............................. 10

Figure 1.7 structure of inductive charging system .................................................................. 12

Figure 1.8 integrated charger topology ................................................................................... 12

Figure 1.9 PHEV and PEV as distributed energy storage device (DESD) in FREEDM smart

grid .......................................................................................................................................... 18

Figure 1.10 PHEV and PEV in FREEDM Smart House ........................................................ 19

Figure 2.1 Infrastructure of PHEV’s integration with FREEDM smart grid .......................... 24

Figure 2.2 Topology of the proposed bi-directional charger .................................................. 25

Figure 2.3 Three-leg converter phase output voltage and spectrum at 10 kHz ...................... 28

Figure 2.4 H-bridge converter phase output voltage and spectrum at 10 kHz ....................... 28

Figure 2.5 Correlation of voltage ripple, input inductor and dc capacitor .............................. 32

Figure 2.6 Correlation of current ripple, input inductor and dc bus voltage .......................... 33

Figure 2.7 3D modeling of the proposed converter ................................................................ 34

Figure 2.8 Lab prototype of the proposed converter ............................................................... 35

Figure 2.9 Efficiency DC/AC Stage ....................................................................................... 36

Figure 2.10 Efficiency DC/DC Stage ..................................................................................... 36

Figure 2.11 Control Structure for Grid to Vehicle Function .................................................. 38

Figure 2.12 Control Structure for Vehicle to Grid Function .................................................. 38

Figure 2.13 Vehicle to grid with PR+HC controller ............................................................... 40

Figure 2.14 Controller performance comparison: PI, PR and PR+HC controller .................. 40

Figure 2.15 Grid to Vehicle with PR+HC controller .............................................................. 41

Figure 2.16 THD comparison: PI, PR and PR+HC controller ................................................ 41

xi

Figure 2.17 Vehicle to grid: comparison between vehicles’ input current and IEEE 1547

standard ................................................................................................................................... 42

Figure 2.18 Grid to Vehicle: comparison between vehicles’ output current and IEEE 1547

standard ................................................................................................................................... 42

Figure 3.1 Formation of high-order filter by converter LC filter and grid impedance ........... 44

Figure 3.2 Passive damping methods to eliminate high-frequency harmonics ...................... 45

Figure 3.3 Frequency characteristics of different grid conditions .......................................... 49

Figure 3.4 Grid current with the control loop having different virtual resistor values ........... 50

Figure 3.5 Variable virtual resistor based adaptive damping method .................................... 52

Figure 3.6 (a) Virtual resistor controller in synchronous frame ............................................. 52

Figure 3.6 (b) Measured one control cycle operation times for controller in synchronous

frame ....................................................................................................................................... 52

Figure 3.7 (a) Virtual resistor controller in stationary frame .................................................. 53

Figure 3.7 (b) Measured one control cycle operation times for controller in stationary frame

................................................................................................................................................. 53

Figure 3.8 Transfer function: converter output to grid current with/without virtual resistor . 59

Figure 3.9 Transfer function converter output to capacitor current with/without virtual

resistor ..................................................................................................................................... 59

Figure 3.10 Transfer function grid voltage to grid current with/without virtual resistor ....... 60

Figure 3.11 Transfer function grid voltage to capacitor current with/without virtual resistor 60

Figure 3.12 Block diagram of control plant and proposed controller ..................................... 61

Figure 3.13 Control loop modeling ......................................................................................... 61

Figure 3.14 Control Parameter Characteristics: adaptive gain Kad ........................................ 65

Figure 3.15 Block diagram of controller with adaptive virtual resistor loop .......................... 66

Figure 3.16 Frequency detection function block .................................................................... 66

Figure 3.17 Root locus of control plant with various impedances (0.2mH to 2.5mH) without

virtual resistor ......................................................................................................................... 66

Figure 3.18 Root locus of control plant with various impedances (0.2mH to 2.5mH) and fixed

virtual resistor ......................................................................................................................... 67

xii

Figure 3.19 Root locus of control plant with various impedances (0.2mH to 2.5mH) with

adaptive virtual resistor ........................................................................................................... 67

Figure 3.20 Root locus of control plant with 0.2mH adopts proper virtual resistor ............... 68

Figure 3.21 Root locus of control plant with 2.5mH adopts proper virtual resistor ............... 68

Figure 3.22 Grid impedance vs resonant frequencies ............................................................. 69

Figure 3.23 Resonant frequency vs proper adaptive gain Kad ............................................... 69

Figure 3.24 Relationship of adaptive gain Kad, control loop bandwidth and phase margin for

stiff grid ................................................................................................................................... 70

Figure 3.25 Relationship of adaptive gain Kad, control loop bandwidth and phase margin for

weak grid ................................................................................................................................. 70

Figure 3.26 Bode plot of control loop with 0.2mH impedance and with adaptive virtual

resistor control ........................................................................................................................ 73

Figure 3.27 Bode plot of control loop with 2.5mH impedance and with adpative virtual

resistor control ........................................................................................................................ 74

Figure 3.28 Bode plot of control loop with 1mH impedance and with adpative virtual resistor

control ..................................................................................................................................... 74

Figure 3.29 Controller robustness analysis for stiff grid control loop with grid impedance

20% variation .......................................................................................................................... 75

Figure 3.30 Controller robustness analysis for weak grid control loop with grid impedance

20% variation .......................................................................................................................... 75

Figure 3.31 Resonant frequency detection to determine grid impedance ............................... 76

Figure 3.32 Resonant frequency detection to determine grid impedance during impedance

transient ................................................................................................................................... 76

Figure 3.33 Converter-side current and grid-side current with the proposed controller enabled

................................................................................................................................................. 78


................................................................................................................................................. 79

Figure 3.35 Converter-side current and grid-side current without the proposed controller ... 79

Figure 3.36 Spectrum of grid-side current without the proposed controller ........................... 80

Figure 3.37 Converter-side current and grid-side current with the proposed controller ........ 80

xiii

Figure 3.38 Spectrum of grid-side current with the proposed controller enabled .................. 81

Figure 3.39 Spectrum comparison of grid-side current with IEEE 519 standard ................... 81


................................................................................................................................................. 83


................................................................................................................................................. 84

Figure 3.42 Converter-side current and grid-side current without the proposed controller ... 84

Figure 3.43 Spectrum of grid-side current without the proposed controller enabled ............. 85


................................................................................................................................................. 85

Figure 3.45 Spectrum of grid-side current with the proposed controller enabled .................. 86

Figure 3.46 Spectrum comparison of grid-side current with IEEE 519 standard ................... 86

Figure 4.1 Capacitor current feedback control ....................................................................... 91

Figure 4.2 Inductor current feedback control ......................................................................... 91

Figure 4.3 Inductor and load current feedback control method .............................................. 92

Figure 4.4 Control block of the proposed method based on active harmonics injection ........ 93

Figure 4.5 Harmonics detection and extraction block ............................................................ 96

Figure 4.6 Active harmonics injection before the inner current loop ..................................... 96

Figure 4.7 Nonlinear load tests with the proposed control method ........................................ 97

Figure 4.8 Nonlinear load tests with inductor current feedback control ................................. 97

Figure 4.9 Comparison of capacitor current spectrum: the proposed method and conventional

controller ................................................................................................................................. 98

Figure 4.10 Comparison of output voltage spectrum: the proposed method, conventional

controller and IEC62040-3 Standard ...................................................................................... 98

Figure 4.11 Simulation 1kW load test with the proposed method ........................................ 100

Figure 4.12 Experiment 1kW load test with the proposed method ....................................... 100

Figure 4.13 Simulation no load test with the proposed method ........................................... 101

Figure 4.14 Experiment no load test with the proposed method .......................................... 101

Figure 4.15 Simulation RL test 1kW resistive load and 2.5mH inductor with the proposed

method................................................................................................................................... 102

xiv

Figure 4.16 Experiment RL test 1kW resistor load with 2.5mH inductor test with the

proposed method ................................................................................................................... 102

Figure 4.17 Simulation nonlinear loads with the proposed method ..................................... 103

Figure 4.18 Experiment Nonlinear load test with the proposed method .............................. 103

Figure 4.19 Experiment nonlinear load test with the proposed method ............................... 104

Figure 4.20 Simulation a 1kW load transient for dynamic response test of the proposed

controller ............................................................................................................................... 105

Figure 4.21 Experiment a 1kW load transient for dynamic response test of the proposed

controller ............................................................................................................................... 106

Figure 4.22 Simulation a 1kW load transient for dynamic response test of the proposed

controller ............................................................................................................................... 106

Figure 4.23 Experiment a 1kW load transient for dynamic response test of the proposed

controller ............................................................................................................................... 107

Figure 4.24 Inductor current to load current with the proposed control method .................. 113

Figure 4.25 Inductor current to load current with the capacitor current feedback control ... 113

Figure 4.26 dynamic response: output voltage, load current, capacitor current and inductor

current ................................................................................................................................... 115

Figure 4.27 Inductor current overshoot during the load transient with the proposed control

method at L=1mH ................................................................................................................ 116

Figure 4.28 Inductor current overshoot during the load transient with the proposed control

method at L=0.5mH ............................................................................................................. 116

Figure 4.29 Inductor current overshoot during the load transient with the capacitor current

control at L=1mH .................................................................................................................. 117

Figure 4.30 Inductor current overshoot during the load transient with the capacitor current

control at L=0.5mH ............................................................................................................... 117

Figure 5.1 FREEDM smart grid and Solid State Transformer based Intelligent Energy

Management System ............................................................................................................. 120

Figure 5.2 Control loop model of inverter stage of solid state transformer .......................... 123

Figure 5.3 Bode plot of close loop of inner current loop ...................................................... 125

Figure 5.4 Bode plot of outer voltage loop open loop .......................................................... 125

xv

Figure 5.5 Bode plot of close loop of outer voltage loop ..................................................... 126

Figure 5.6 Bode plot of output impedance ............................................................................ 126

Figure 5.7 Controller architecture of PHEV charger ............................................................ 130

Figure 5.8 Proposed power dispatch method based on frequency restoration ...................... 130

Figure 5.9 Implementation of power-frequency control in inverter stage of SST ................ 131

Figure 5.10 SST operation frequency ................................................................................... 132

Figure 5.11 Charging Power of two vehicles ........................................................................ 133

Figure 5.12 Enlarged charging power of two vehicles ......................................................... 133

Figure 5.13 Voltage and current information of no.1 vehicle ............................................... 134



Figure 5.16 Charging power of two vehicles ........................................................................ 136

















Figure 5.33 Relationship of dispatched power and integration gain Ki with one vehicle at

urgent charging and another one with various conditions .................................................... 149

xvi


normal charging and another one with various conditions ................................................... 149


mild charging and another one with various conditions ....................................................... 150

Figure 5.36 System operation frequency .............................................................................. 155

Figure 5.37 Charging power of the vehicle .......................................................................... 155

Figure 5.38 Grid voltage, current and dc bus voltage of the vehicle .................................... 156



Figure 5.41 Injection current from renewable energy and possessive load current .............. 157



Figure 5.44 Injection current from renewable energy and possessive load current .............. 159


Figure 5.46 Charging and discharging power of the vehicle ................................................ 160

Figure 5.47 Grid current, voltage and dc bus voltage of the vehicle .................................... 160

Figure 5.48 Grid current, voltage and dc bus voltage of the vehicle (zoom-in) ................... 161


Figure 5.50 power of no.1 and no.2 vehicle ......................................................................... 162

Figure 5.51 grid voltage, current and dc bus voltage of no.1 vehicle ................................... 162

Figure 5.52 grid voltage, current and dc bus voltage of no.1 vehicle ................................... 163

Figure 6.1 volume comparison between LCL filter and L filter at 10A and 30A charging . 168

Figure 6.2 filter loss comparison between LCL filter and L filter at 10A and 30A charging

............................................................................................................................................... 168

Figure 6.3 System control loop model .................................................................................. 172

Figure 6.4 Bode plot of system open loop transfer function ................................................. 172

Figure 6.5 Bode plot of control plant and notch filter .......................................................... 173

Figure 6.6 System bode plot with proposed notch filter ....................................................... 173

Figure 6.7 Root locus of system with proposed method ....................................................... 174

Figure 6.8 System with proposed low pass filter .................................................................. 175

xvii

Figure 6.9 Comparison of system with low pass filter and without low pass filter .............. 176

Figure 6.10 Root locus of system with proposed low pass filter .......................................... 176

Figure 6.11 System Bode plot with its filter capacitor variation from 0.5 to 1.5 of original

value ...................................................................................................................................... 179

Figure 6.12 System Bode plot with its battery side inductance variation from 0.5 to 1.5 of

original value ........................................................................................................................ 180

Figure 6.13 System with 100uF and 120uF capacitance with notch filter controller ........... 180

Figure 6.14 System stable with 100uF capacitance and notch filter controller .................... 181

Figure 6.15 System stable with 120uF capacitance and notch filter controller .................... 181

Figure 6.16 System unstable with 60uF capacitance and notch filter ................................... 182

Figure 6.17 System unstable with 40uF capacitance and notch filter ................................... 182

Figure 6.18 Bode plots of different notch filter transfer functions to improve controller

robustness .............................................................................................................................. 183

Figure 6.19 System stable with 60uF capacitance and redesigned filter parameters ............ 183

Figure 6.20 System still unstable with 40uF capacitance and redesigned filter ................... 184

Figure 6.21 System with 40uF capacitor with different notch filter parameters to make loop

stable ..................................................................................................................................... 184

Figure 6.22 Notch filter and control plant with all capacitor values (0.5~1.5) ..................... 185

Figure 6.23 Control robustness test: charging current with the filter capacitance change from

80uF to 120uF ....................................................................................................................... 185


80uF to 100uF ....................................................................................................................... 186


80uF to 60uF ......................................................................................................................... 186


80uF to 40uF ......................................................................................................................... 187

Figure 6.27 Simulation waveforms of three currents without proposed control .................. 190

Figure 6.28 Simulation waveforms of three currents with proposed control ....................... 190

Figure 6.29 Zoom-in waveforms of three currents with proposed control ........................... 191

xviii

Figure 6.30 Experiment results of converter side current, charging current and capacitor

current with proposed control ............................................................................................... 191


current with proposed control (charging current AC coupled to show ripple) ..................... 192


current with proposed control (zoom-in) .............................................................................. 192

Figure 6.33 Experiment results of current transient response: 1A (0.1C) to 10A (1C) step

change ................................................................................................................................... 193

Figure 6.34 Experiment results of current transient response: 10A (1C) to 1A (0.1C) step

change ................................................................................................................................... 193

Figure 6.35 Experiment results of pulse charging with 100Hz ............................................ 194

Figure 6.36 Experiment results of pulse charging with 200Hz ............................................ 194

1

Chapter One Introduction

1.1 Research Background: Plug-in Hybrid Electric Vehicles

Currently, there are three significant issues challenging the conventional transportation

method in the United States. The first issue is the nearly 100% dependence on the imported

oil. The United States holds only 3% of global petroleum however it consumes one fourth of

the world’s oil supply. According to the U.S Department of Energy, the consumption figure

was 20.5 million barrels of oil per day in 2004, more than half of which came from imports

[1]. Figure 1.1 concludes that about two-thirds of this oil is refined into gasoline and diesel

fuel to power passenger vehicles and trucks in America. So we can see that most of this

imported oil is consumed by the transportation system. As can been in figure 1.2 U.S

domestic oil production has decreased 44% since the 1970s, the use of oil for transportation

has increased 83% and this gap is still widening. Therefore, transportation in today’s

America largely depends on the imported oil, and this vulnerability of relying on an unstable

part of the world continues to threaten national security. The second issue is that fuel price

has increased to a critical point; oil price has increased 200% from 1998 to 2006 [3]. It is

predicted by M. King Hubbert Center that world oil production will reach its peak within the

next 5~15 years [4]. Even though the price of oil may fall temporarily, over the long term the

price will continue to rise. The cost of transportation will also continue to increase. The last

but not the least issue is the environmental concern. Transportation is currently the single

largest source of carbon dioxide emissions in the U.S, contributing over 30% of total green

house gasses emissions. The growth rate of emissions from the transportation sector has

averaged 24% between 1993 and 2003, faster than the growth of any other sectors such as

2

electrical generation. In addition urban air pollutants brought by petroleum combustion such

as carbon monoxide, nitrogen oxides, and volatile organic compounds adversely affect public

health and air quality. To respond to these challenges a revolutionary, environment-friendly

safe and sustainable transportation approach is required.

Figure 1.1 U.S oil consumption by sectors [2]

Figure 1.2 Oil production and consumption in U.S [3]

0

5

10

15

20

25

1940 1950 1960 1970 1980 1990 2000 2010

Petr

oleu

m (m

mb/

day)

Domestic ProductionDomestic Consumption

Source: U.S. Department of Energy, Energy Information Administration

3

One of most promising transportation solutions is a newly emerging concept: Plug-in

Hybrid Electric Vehicle (PHEV). According to IEEE definition, a plug-in hybrid electric

vehicle is: any hybrid electric vehicle which contains at least: (1) a battery storage system of

4 Kwh or more, used to power the motion of the vehicle; (2) a means of recharging that

battery system from an external source of electricity; and (3) an ability to drive at least ten

miles in all-electric mode, and consume no gasoline [5]. In the future with the advance of

battery technology and electric motor design, the hybrid drive train may be replaced by a

pure electric drive train. Plug-in Electric Vehicle (PEV) a concept similar to EV (electric

vehicle) will also become a promising solution. Plug-in Hybrid Electric Vehicle introduces

significant usage of electricity as transportation fuel. Like hybrid vehicles on the market

today, these plug-in hybrids use battery power to supplement the power of its internal

combustion engine. However conventional hybrids obtain all of their propulsion power from

gasoline, PHEVs obtain most of their energy from an electric utility. Currently U.S energy

price for the cost of gasoline is $3 per gallon and the national average cost of electricity is 8.5

cents per kilowatt-hour. So a PHEV runs on an equivalent of 75 cents per gallon. Given that

50% of vehicles on U.S roads are driven 25 miles a day or less, a plug-in hybrid vehicle can

reduce petroleum consumption by about 60% [1]. There is another assessment from Pacific

Northwest National Laboratory, it claims by changing the transportation fuel from gasoline

to electricity the PHEV can reduce gasoline consumption by 85 billion gallons per year,

potentially displacing 52% of U.S oil imports, saving $270 billion in gasoline consumption

and reducing 27% of total U.S green house gas emissions [6, 7].

4

Regarding environmental benefits with a high penetration of PHEVs on the road, there is

one reasonable question: Is that possible using plug-in vehicles with increasing power

demand from power plant will reduce one source of pollution (burning fossil fuel) but

increase another (fuel based power generation). EPRI examined this possibility in a very

comprehensive way by assessing the environmental gain of using electric transportation in

most America regions in this century. In collaboration with Natural Resources Defense

Council (NRDC), the assessment focuses on the probable environmental impacts of bringing

a large number of PHEVs to roads over the next half century. The results show that the

cumulative green house gas emissions were reduced to 3.4 billion metric tons by 2050 [8].

The relationship of green house gas emissions reduction and the adoption of PHEV are

shown in figure 1.3 [12]. Moreover, this report addresses the point that for most regions of

the United States, the increased PHEV usage would result in modest but significant

improvements in air quality through the reduction of various pollutants and the substantial

reduction of ozone levels.

Figure 1.3 Green house gas reductions with the adoption of PHEVs [12]

5

An economic assessment has also been conducted by EPRI. Assuming that within six

major urban areas approximately about 50% of new-car sales are PHEVs. Substantial

increases in household incomes are predicted from $188.7 million/year in the Birmingham

region to $721.4 million/year in the Kansas region [8]. Based on the assumption of charging

a vehicle at off-peak time, PHEVs provide a valuable potential of providing load leveling to

utilities. By encouraging vehicle owners to recharge batteries at off-peak time, the grid could

support a high level of PHEV penetration without the need for generating more power, and

can improve power system efficiency by filling the generation valley at off-peak time.

However there are still concerns that charging at off-peak time may result in another peak

demand period if proper regulation is not adopted. This concern leverages the burgeoning

field of smart grid technology. The NREL study indicates that no new power plants are

required even with 50% PHEV market penetration [9], and according to Pacific Northwest

National Lab report [6] given the average drive range of a car is 33 miles per day, the current

U.S power grid capacity can fully supply approximately 70% of America’s passenger

vehicles, that is, roughly 217 million cars. The predicted market penetration of PHEV from

now to 2050 by EPRI is shown in figure 1.4 [10]. However whether the current utility

generation capability can meet the growth of PHEVs in the future remains highly

controversial. Finally, the auto industry and related research groups from national

laboratories in the U.S show a strong interest in the PHEV. Test versions and modified

versions of plug-in hybrids are already on the road. Some commercial versions will be

available on the market by late 2011 or thereabouts. Worldwide, main-stream vehicle

manufactures have joined in this new technology rapidly bringing many new products to the

6

market. In figure 1.5 the major models of PHEV and PEV in the current and near-future

market are illustrated. The electric drive range is from 30miles to 300miles [11]. The

booming market and new models show a bright tomorrow for PHEVs and PEVs.

Figure 1.4 Predicted shares of new car sales in U.S market [10]

From the above analysis we can see that PHEVs show great promise; they have the

potential to curb emissions decrease gasoline usage and reduce the cost of transportation.

Although large-scale adoption of plug-in vehicles is still a few years away, politicians,

electric utilities, and auto companies are eagerly awaiting the opportunities that may arise

from reduced emissions and gasoline consumption, new utility services and increased

revenues, and new markets that will create new jobs. This is particularly exciting to electric

utility companies, which can foresee substantial revenue growth through the electrification of

transportation market. For consumers, plug-in vehicles will lower their operational costs

when compared with traditional gasoline vehicles or today’s gasoline-electric hybrids. The

savings are potentially huge, as electricity cost per mile is calculated to be about one-quarter

to one-third the cost of gasoline, depending on the region and price of gasoline. Thus PHEV

7

is a promising, efficient and sustainable solution to today’s transportation challenge and a

driving force to electrification of the transportation system.

Audi A1 E-tron BMW ActiveE BYD F3DM Chevrolet Volt

Citroen Revolte Fisker Karma Ford Escape Ford Focus

Honda Fit Hyundai Blue-Will Kia Ray Mercedes S500 Vision

Nissan Leaf Renault Fluence Z.E. Suzuki Swift Tesla Motors Roadster

Tesla Motors Model S Toyota Prius Volvo V60Toyota 2nd Gen RAV4 Figure 1.5 Major models of PHEV and PEV

1.2 State of the Art of Technology

1.2.1 Survey of SAE Standards for Battery Chargers

SAE (North American Society of Automotive Engineer) is in charge of establishing all

standards related with electric and hybrid electric vehicles in North America. According to

SAE 2010’s newest version of J1772 standard which is specially revised for the charging

8

infrastructure of plug-in hybrid electric vehicles, the charging infrastructure to PHEVs is

classified into three levels, which is summarized in Table 1-1.

Table 1-1 Plug-in Hybrid Electric vehicle charging level [13]

Charge Method Nominal Supply Voltage (Volts)

Maximum Current (Amps-continuous)

Branch Circuit Breaker rating

(Amps) AC Level 1 120V AC, 1-phase 12A 15A AC Level 1 120V AC, 1-phase 16A 20A AC Level 2 208 to240V AC,

1-phase ≤80A Per NEC 625

DC Charging Under development

Definition of AC level I charging: a method of EV/PHEV charging that extends AC

power from the utility to an on-board charger from the most common grounded electrical

receptacle using an appropriate cord set. AC level I allows connection to existing electrical

receptacles in compliance with the National Electrical Code-Article 625. Definition of AC

level II charging: the primary method of EV/PHEV charging that extends AC power from the

electric supply to an on-board charger. The electrical ratings are similar to large household

appliances and can be utilized at home, workplace, and public charging facilities.The

definition of DC level III charging: for PHEV application DC charging is still under

development. It is cited in a previous version of J1772 that for EV level III charging is the

conductive charging system architecture that provides a method for the provision of energy

from an appropriate off-board charger to the EV in either private or public locations. The

power available for DC Charging can vary from power levels similar to AC Level 1 and 2 to

very high power levels that may be capable of replenishing more than ½ of the capacity of

the EV battery in as few as 10 minutes.

9

1.2.2 Battery Charger Classifications

There are several ways to classify battery chargers. Based on the type of connection there

are conductive charging and inductive charging (contactless charging). Based on the power

flow direction, there are uni-directional chargers and bi-directional chargers. Based on the

utilization of the drive train, there are integrated chargers and stand alone chargers. Based on

the location of battery charger, there are on-board chargers and off-board (stationary)

chargers. Based on the number of power stages, there are two-stage chargers and single-stage

chargers.

Conductive charging is a direct coupling method which requires direct electrical contact

between the charger and the batteries. It is achieved by connecting a charger to a power

source with plug-in pads. Contrary to conductive charging, inductive charging is a

contactless way of charging. It uses the electromagnetic field to transfer energy between the

power source and the battery. Because there is a small gap between the primary coil and the

secondary coil of the transformer, inductive charging can be considered one kind of short-

distance wireless energy transfer. It typically uses a primary coil to create an alternating

electromagnetic field within a charging base, and a secondary coil in the moveable device

picks up the power from the generated electromagnetic field and converts it back into

electrical current, and finally this high frequency AC current will converted to DC to charge

the battery. Inductive charging has the advantage of lower risk of electrical shock because the

users are not exposed to conductors. High frequency inductive charging methods have been

used in GM EV-1, Chevrolet S-10 EV and Toyota RAV4 EV. However, the disadvantage of

this charging method is obvious: efficiency is the number one concern that the large air gap

10

between the primary side and secondary side reduces the coupling factor of the transformer

and leads to lower efficiency. The reported efficiency of one industry product has achieved

86% [14] but still lower than conductive charging methods. In fact 2002 California Air

Resources Board selected SAE J1772 conductive charging interface for electric vehicles in

California. However high frequency inductive charging is still being investigated and

improved [15-19], because it is preferred in some special application fields such as materials

handling, clean factories for semiconductor manufacturing, liquid crystal displays, assembly

plants and automatic movers in particularly harsh environment. An illustration of a

conductive charging post and a 5-pin conductive connector in accordance to SAE J1772 is

presented in figure 1.5 and the structure of inductive charging is shown in figure 1.6.

Figure 1.6 Conductive EV/PHEV charging station and J1772 connector

Compared to the uni-directional charger the bi-directional battery charger is preferred in

future smart grid applications because it can achieve bi-directional power control, which is an

essential element to enable the use of a renewable energy based smart grid. However, a bi-

directional battery charger increases the cost of a whole vehicle and adds to control

complexity as well. Power electronics equipment needs more active semiconductor switches,

more gate drive circuits, and more powerful processors. The uni-directional battery chargers

11

available for PHEV in today’s market are built by companies such as Delta Energy, Delphi,

and Ford, etc. The Nissan Leaf has two charging ports [20], one AC charging port and one

DC charging port. The AC charging port is used to connect level II electric vehicle supply

equipment and a 6.6kW on-board charger. The DC charging port is connected to a DC off-

board charging station in order to fast charge the battery.

In order to reduce the cost of battery chargers for the whole vehicle system, the idea of

utilizing the vehicle drive train inverter as the integrated charger instead of adding an

additional charger is proposed [21-24]. When a vehicle is in an idle state, the inverter is not

used. So its use as a battery charger won’t affect the vehicle operation. Moreover the inverter

naturally has bi-directional capability, so an integrated charger can be easily modified into a

bi-directional charger. AC propulsion’s product AC-150 has an integrated 20 kW bi-

directional grid power interface, which allows the power electronics and motor windings to

be re-configured as a battery charger [21]. So far the concern to this integrated idea is

whether the frequent utilization of the motor and inverter will affect the life time of the drive

train. More test data regarding this impact are needed for the further analysis. However

integrated charging is a creative and cost effective method for the massive production of

plug-in hybrid vehicles. The integrated charger structure is shown in figure 1.7. The idea of

utilizing the drive train as the battery charger is called integrated charger. This concept is

implemented by AC Propulsion System and Oak Ridge National Lab and the charger system

is drawn in figure 1.8.

12

sL

pL

Figure 1.7 structure of inductive charging system

Figure 1.8 integrated charger topology [25]

1.2.3 Bi-directional Charger Topology and Charging Station

A bi-directional battery charger can be either a two-stage solution or a single-stage

solution. Two-stage indicates a bi-directional AC/DC stage and a bi-directional DC/DC

stage. For a bi-directional AC/DC converter within level 1 and level 2 power rating and

voltage level, an H-bridge based topology is usually adopted. The research area of converter

13

topology focuses on bi-directional DC/DC stage. In this stage, both non-isolated and isolated

topology can be used. Half-bridge, full-bridge and push-pull are three building blocks which

are used to construct the non-isolated topologies [26]. Half-bridge based buck boost topology

is utilized [27]. Multi-phase half bridge based battery charger is proposed for higher power

rating charging applications [28, 29]. The idea can also reduce the passive components. DCM

modulation has been used to reduce the size of the magnetic components to increase power

density [30]. With higher DC bus voltage, multilevel DC/DC converter is proposed to reduce

the power losses and reduce the size of passive components [31]. Four-switch buck boost

converter is proposed to handle a wide voltage range of battery [32]. For the non-isolated

topology one point needs to be addressed. Due to safety requirement [29], all of the charging

equipment must be isolated. So a charger with non-isolated DC/DC topology requires a line

frequency transformer at the AC/DC stage. This low frequency transformer increases the

weight and volume of the charger. A high frequency transformer is used in isolated

topologies to achieve galvanic isolation and soft switching as well. The basic topologies

include two sources at either primary side or secondary side: current source and voltage

source [26]. Dual active bridge based topology is very popular [33]. Dual half bridge circuit

is used in lower power rating applications [34]. For high power applications, a three phase

dual active bridge is proposed [35, 36]. An inductor is used to form a current source in one

side of the transformer and an active snubber is applied to reduce the voltage spike caused by

this inductor [37, 38]. For isolated topologies, its advantages are higher power density and

soft switching capable but the disadvantage is the loss of soft switching with different load

conditions. Contrary to a two-stage structure, single stage topology will be a promising

14

solution which will reduce cost and increase system density. The controller design for single-

stage topology will be also an interesting topic because the control structure is different

compared to the well defined two-stage converter control structure.

The charging station also called off-board charger is a concept for the fast charging

approach. Until now the majority of commercial products called charging stations are

actually level 2 charging equipment. The high power charging station for level 3 DC

charging is a charging station for the Nissan Leaf built by Tokyo Electric Power Company

(TEPCO). Besides the traditional method of using power from the utility to charge vehicles,

ideas for using renewable energy resources at charging stations are proposed. Charging

stations located in the public areas are designed for charging a large number of electric

vehicles simultaneously. Moreover fast charging poses a high power demand to the utility.

The current grid structure may not be suitable for such high power consumption units. By

using the energy from renewable energy resources, the power system’s burden is alleviated.

The idea of solar energy based charging station is proposed to achieve green charging for

vehicles [39-43] and the similar idea of using fuel cell to charge vehicles is proposed [44-48].

Municipal charging deck architecture [31] addresses the fast charging technique with the

integration of available renewable resources and the utilization of ultra-capacitor to

compensate for the power demand during the peak charging. In this dissertation based on

SAE J1772 standard and the need for smart grid integration capability; a two-stage bi-

directional stand alone conductive charger is proposed and its related control issues are

investigated.

15

1.2.4 Overview of Vehicle to Grid (V2G) Technology

The average vehicle usage in U.S is only about one hour a day (in 2001, the average US

driver drove 62.3 minutes/day) [49]. In other words, these cars are parked and idle most of

the time. Suppose those cars were energy storage sources for the remaining 23 hours, and

also suppose that the vehicle can discharge the battery’s power back to the grid. The power

system will have new service providers which are PHEVs. All of these techniques related to

battery discharging and grid interaction belong to Vehicle to Grid (V2G) technology [49-58].

To understand vehicle to grid one can compare this technology to a solar power system.

Vehicle to grid system is still in an early stage of research and development. The most

important similarity between solar power and V2G is that V2G will probably connect to the

grid in a highly distributed style at the same voltage level and with a similar power rating.

The important difference is that V2G is bi-direction capable and may behave either as a

source or a load. Solar power, for example, is only a source. Another important difference is

that the primary goal of solar power is to generate power and supply to the load while the

power generation function of V2G is only an additional function. With V2G capability,

PHEVs can provide several services: spinning reserve, which contracts with the available

PHEVs in order to provide power during unplanned outages of basic generators. Regulation

service collects either real power or reactive power to help regulate system’s voltage and

frequency. Back-up service is one or more plug-in vehicles connected together to form as an

autonomous grid during power outage in a certain area. Peak management is the service that

a large number of plug-in vehicles are connected to help reduce system peak power demand.

In addition, a large-scale adoption of PHEV V2G can be used to compensate for the

16

intermittent characteristics of renewable energy such as solar and wind by saving extra

energy during peak times and releasing energy during valley times. Besides these functions

PHEV should also have the capability to do islanding detection and have two-way

communication with the grid. These are also the major functions of distributed generation.

Moreover, the future vehicle should also have the low voltage ride through (LVRT)

capability because at high penetration levels without ride through the anti-islanding tripping

function will aggressively shut down many V2G vehicles. This will cause a momentary

voltage sage, loss of loads and result in economic losses.

The limitation for V2G technology is mainly due to the high cost of the plug-in hybrid

electric vehicles. Two main costs are the components, notably the batteries and power

electronics converter, and the labor for the conversion from gasoline power to electric power.

Currently these high costs are predominantly due to low production volumes. However,

unlike traditional power generation V2G can provide fast regulation service from clean

energy. This clean power capability in addition to oil-free personal transportation tool and the

future potential to support intermittent renewable energy sources will provide the

environmental, system reliability, and energy security benefits. Thus, there is a case for

finding policy support to initialize the fleets that are capable of V2G technology. Policy

mechanisms might include tax credits granted for the purchase of plug-in vehicles.

1.3 Research Motivation: Enable Integration of Distributed Energy Storage Devices (Plug-in

Hybrid Electric Vehicles) with Smart Grid

It is believed that in the future the power grid will undergo revolutionary change; the new

system will become more distributed with integration of large scale of renewable energy

17

sources and energy storage devices [59-61]. The widespread utilization of distributed energy

at residential and industrial levels is a major paradigm shift for the electric power industry,

moving away from today’s centralized power generation paradigm toward a distributed

generation based new grid [62]. With advanced communication methods and intelligent grid

control the distributed grid will be upgraded to a smart grid. The distributed energy storage

device (DESD) is an indispensible element in the formation of this future smart grid. It will

complement distributed renewable energy resources (DRER), enable various types of grid

regulation and supply backup power in islanding operations. The infrastructure of large scale

interconnection of PHEVs with a power grid and other renewable resources is shown in

figure 1.9. The interconnection of PHEVs with a home to form a smart home is shown in

figure 1.10.

It is critical to note that large scale penetration of PHEVs into the power grid cannot work

without help from information technology. Advanced metering infrastructure (AMI),

revenue-grade meters, various communications methods such as WIFI, cellular, Ethernet,

Power line carrier and Zigbee are very important for the power management of these

distributed storage devices. The smart grid impacts many of the operational and enterprise

information systems, including supervisory control and data acquisition (SCADA), feeder

and substation automation, customer service systems, planning, engineering and field

operations, grid operations, scheduling, and power marketing. It is expected that there will be

a significant number of plug-in vehicles and solar generation integrated into the distributed

grid around 2012~2014 [64]. This will result in system overloads, voltage distortion,

increased harmonics, increased line losses and unbalanced phase. To mitigate these issues

18

and to maintain system stability, coordinated voltage and reactive power control, automatic

switches and extensive monitoring will be needed. Moreover a combination of distributed

and centralized intelligent control, congestion management strategies, and market based

dynamic pricing strategy will also be needed. The integration of DESD (PHEV and PEV)

with the power grid is an absolute requirement in the future power system. The interface

between the power grid and PHEVs power electronics technology will play a key role in this

integration. Therefore the motivation of this dissertation is to design a power electronics

interface to treat the PHEV as a distributed energy storage device (DESD), and integrate

DESD with a future smart grid, and enhance the performance of this interaction, as well as

manage the power among multiple DESDs (vehicles).

Figure 1.9 PHEV and PEV as distributed energy storage device (DESD) in FREEDM smart grid [63]

19

Figure 1.10 PHEV and PEV in FREEDM Smart House [65]

1.4 Contributions and Dissertation Outline

There are several issues and challenges related to PHEVs interaction with the grid. The

challenges can be divided into two groups: the power electronics level for individual vehicle

and the power management level for multiple vehicles. At the power electronics level grid

connection, a high performance grid connection controller is required. High quality current

during either charging or discharging is essential to grid connection. However variable grid

impedances compromise the control performance and complicate the control loop design.

High frequency resonance appears on the grid charging/discharging current. Moreover the

grid impedance is unknown and will compromise the controller with fixed compensation

parameters. A new controller is needed to ensure high quality current in any kind of grid for

the future large penetration of PHEVs. During off-grid operation, a new controller is needed

to improve the quality of output voltage when connected with non-linear loads. In power

20

management level when multiple vehicles are connected together supplied under a power

electronics transformer (solid-state transformer), the power dispatch control is important to

the stability of the solid state transformer. If the total power demand of all the vehicles

exceeds the capacity of the transformer it will cause transformer voltage collapse. High speed

communication and system level intelligent control is the traditional method to address this

issue. However due to the communication delay, congestion and the rapid speed of power

electronics, the collapse may still happen. So a power electronics control scheme without

communication is proposed to automatically adjust power demand of each vehicle in order to

avoid voltage collapse. On the battery side, the charging current with low current ripple is

highly preferred because low current ripple will reduce the heat and lengthen the lifetime of a

battery. Normally, to reduce current ripple either passive components should be increased or

switching frequency need to be increased. However, this will either increase the system size

or reduce system efficiency. A method with compact size and low current ripple is desired. In

this dissertation, the research efforts are directed to deal with these issues and new solutions

are proposed to meet these challenges.

The dissertation is organized as below:

In Chapter I, the research background is introduced. State of the art of technology is

reviewed. The research motivation is given. The research contributions and dissertation

outline are presented.

In Chapter II a grid-interactive smart charger for plug-in hybrid electric vehicles in smart

grid applications is proposed. The proposed converter has three major functions: grid to

vehicle, vehicle to grid and vehicle to home. The system infrastructure of PHEVs with grid is

21

proposed. The converter power stage is designed. The control structure for three functions is

designed.

In Chapter III a new adaptive virtual resistor controller is proposed to achieve high

performance of power quality to assist large scale penetration of plug-in hybrid electric

vehicles into various power grids. The modeling of the proposed controller is derived and

analyzed. The control loop design for different grid conditions is proposed. The proposed

method acts as a controllable resistor at various grid impedances. The control loop robustness

is examined with control parameters mismatched at different grid impedances. The

simulation and experiment results verify the proposed controller.

In Chapter IV a new inductor current feedback control based on active harmonics

injection concept is proposed for vehicle to home application of PHEVs. The active injection

loop is designed and plugged into the loop to improve the harmonics compensation capability

for nonlinear loads. The inductor current overshoot during the load transient is investigated

for both inductor current feedback control and capacitor current feedback control. The

inductor current based control can limit the current overshoot with an even smaller inductor

value while the capacitor current based control cannot limit the current overshoot. The

capacitor current feedback control has the potential to cause core saturation with a smaller

inductor. So the proposed control method can be used to further reduce the passive

components and optimize the volume and weight of the converter.

In Chapter V a new power management strategy is proposed to solve the voltage

instability issue of the Solid State Transformer (SST) which supplies multiple PHEVs. When

multiple PHEVs are plugged into one SST based smart grid and the total demand power

22

exceeds the capability of SST, a new power dispatch method is proposed in each PHEV to

adjust its power demand in order to avoid voltage collapse of SST. Gain scheduling

technique is proposed to dispatch power to each vehicle based on battery’s state of charge.

The battery with low state of charge will get more power. A comprehensive case study is

conducted to verify the proposed method. The proposed method can be used as the power

electronics converter level control to improve the stability of solid state transformer.

In Chapter VI: a high order filter is proposed for use in DC/DC stage of the battery

charger. The objective is to reduce the filter size which will further reduce the system cost

and volume. Another major goal is to effectively attenuate the current ripple of the charging

current which will yield an almost ripple free charging for battery. Ripple free charging will

eliminate the extra heat caused by the current ripple and increase battery life. The filter based

controller is proposed to deal with the potential instability issue brought by the high order

filter. The control loop design and robustness analyses are conducted and presented. The

simulation and experiment results verify the proposed controller.

In chapter VII, the final conclusions are drawn and future research topics are discussed.

23

Chapter Two Design a Grid-Interactive Converter for Plug-in Hybrid Electric

Vehicles

2.1 Definition of Grid-Interactive Converter

The term smart converter in this discussion refers to the converter with bi-directional

power flow capability and the related functions. With bi-directional power flow capability

the proposed grid-interactive converter for plug-in hybrid electric vehicles in household

applications is presented [66]. The infrastructure of a PHEV integrated with an American

House is shown in figure 2.1. In [67, 68] the circuitry configuration for a traditional

American house is drawn in details, the AC mains and all connections are taken out of the

house in order to show the wiring connection of PHEV with the house. In the United States’

electrical distribution scheme, one house receives input power from a split-phase distribution

transformer that converts 13.2kV (line to line voltage) to a split-phase 240V/120V. The

center-tapped transformer supplies 120V to normal home loads and 240V to heavy duty

appliances such as electric oven and dryer. For a house installed with renewable energy

capabilities, the generated electricity can be sold back to the grid so a bi-directional smart

meter is used to calculate the net power consumption of this house and this meter is also

known as “net metering”[69-71].

Regarding V2G function, both real power and reactive power control can be implemented.

However, the grid code for PHEVs is not well established and reactive power control at

residential level is still controversial. So only the real power control is designed for the V2G

function, other functions related to reactive power such as power factor correction, reactive

24

power supplying and active power filter can be implemented but not included. Regarding the

real power control, the grid code IEEE 1547-2008 [72] for distributed generator (DG)

requires the disconnection of the DG from the house during the grid fault in order to provide

for the safety of the maintenance personnel. However by adding the extra electric breaker

and wire connection the DG can be still utilized to supply critical home loads during faults

such as an uninterrupted power supply (UPS). This function is very important considering the

power outage cases recently experienced due to natural disasters such as snow storms in the

Northeast and hurricanes or floods in the Southern region. Therefore this capability of

behaving as a UPS is also added in the proposed grid-interactive converter called Vehicle to

Home (V2H). In total, the major functions for the proposed converter are grid to vehicle,

vehicle to grid and vehicle to home.

Figure 2.1 Infrastructure of PHEV’s integration with FREEDM smart grid

25

2.2 Topology Selection of Proposed Grid-Interactive Converter

The topology of the proposed bi-directional battery charger is shown in figure 2.2. This

bidirectional charger has a two-stage topology: stage 1 is a grid-side converter; stage 2 is a

battery-side converter. A split-phase three-leg converter [73-77] is used as the grid-side

converter in order to fit the household circuitry configuration. Compared with a traditional

split-capacitor H-bridge, the center point of a three-leg converter is tapped to the middle

point of the third leg rather than the middle point of the dc capacitors. The two half-bridge

branches of the three-leg converter have the same uni-polar sinusoidal pulse width

modulation method as an H-bridge converter, and the third half-bridge is controlled to keep

the two 120V output voltage balance. Compared with a split-capacitor H-bridge converter,

the three-leg converter has the following advantages: 1) no DC capacitor voltage balance

issue; 2) comparatively smaller output filter size; 3) smaller DC bus current ripple; 4) higher

utilization of DC bus voltage. The topology for the battery-side converter is a bi-directional

buck-boost converter.

Figure 2.2 Topology of the proposed bi-directional charger

At grid to vehicle function, the converter transfers the power from the grid to charge the

battery. The grid-side converter uses different half-bridges to converter AC power based on

different input voltages. As shown in figure 2.2 if the input voltage is 240V the half-bridge

26

LA and LB will operate and if the input voltage is 120V AC the half-bridge LA or LB and

LN will operate. In the proposed charger the power rating is set to 120V/5kW and

240V/10kW. Although the current rating exceeds the rating of home circuitry branches,

higher power can help implement fast charging algorithms. The battery pack is composed of

90 lithium-ion battery cells and its terminal voltage is from 180V to 360V.

At V2G and V2H function, the power inside the battery is inversely fed back to either the

grid or the loads. At V2G mode, the grid-side converter operates in current-mode control

which regulates the grid current to be a low-harmonics sinusoidal current. While at V2H the

converter operates in voltage-mode control which regulates the output voltage to be

sinusoidal with any type of load. The battery-side converter in both modes regulates the DC

bus voltage by operation in the boost mode. The power feeding-back to grid is determined by

the state of charge of the battery monitored by the battery management system (BMS)

through CAN bus and the power demand from power system. Unlike the photovoltaic or fuel

cell system which are utilized as much as possible, it is not desirable to use V2G systems

continuously for a long time in order to preserve the health of the vehicle’s battery pack.

When the power system needs power from the vehicles in a certain area the operators should

choose vehicles with healthy batteries. Thus at V2G the duration of the service had better not

be too long like the time scale for frequency regulation and spinning reserve.

27

Table 2-1 Component count for H-bridge converter and three-leg converter

H bridge converter

Three-leg converter

IGBT Module(dual)

2 3

Gate Drivers(dual) 2 3 DC link capacitor (550V electrolytic

capacitor)

2 1

DC link voltage sensor

2 1

AC current sensor 2 2 Controller 1 1

A component count table for these two topologies is given in table 2-1. The current sensor

and voltage sensor number for these two topologies are almost the same. The H-bridge

converter needs two voltage sensors to monitor the DC link voltage to avoid unbalanced

voltage. The phase output voltages and spectrums of the three-leg converter and the H-bridge

converter at 10 kHz switching frequency are shown in figure2 and figure 3. The magnitude of

the three-leg converter’s 120V phase output voltage’s dominant harmonics are reduced from

74.9% to 49% compared to that of the H-Bridge due to the modulation of the neutral branch.

The neutral branch has the same switching frequency as the H-bridge branches and is

synchronized with the H-bridge branches. This is because of the additional modulation of the

neutral branch which supplies a zero-voltage level. The neutral branch will have the same

switching frequency as the H-bridge branches. Note that normally uni-polar PWM generates

harmonics at its multiple switching frequency however the neutral leg modulation generates

harmonics at the switching frequency.

28

0.05 0.052 0.054 0.056 0.058 0.06 0.062 0.064 0.066-500

-400

-300

-200

-100

0

100

200

300

400

500

Time

Figure 2.3 Three-leg converter phase output voltage and spectrum at 10 kHz

0.05 0.052 0.054 0.056 0.058 0.06 0.062 0.064 0.066-250

-200

-150

-100

-50

0

50

100

150

200

250

Time

Figure 2.4 H-bridge converter phase output voltage and spectrum at 10 kHz

Control effort for the two topologies is almost the same because the number of the voltage

and current sensors, the PWM ports and the control algorithms for these two converters are

similar. However, the control scheme differs with regards to the dc link capacitors’ voltage

balance for unbalanced loads. For the three-leg converter there is no need to balance the

capacitors, but in the case of the H-bridge converter it is very hard to balance the capacitors’

voltages unless there is an external circuit to charge the capacitors individually. In similar

applications such as Photovoltaic and fuel cell power conditioning systems, a high frequency

multi-winding transformer [78-82] in the dc/dc stage can be used to supply power to the

different capacitors to keep the voltage balanced.

29

2.3 Power Stage Design of Proposed Converter

2.3.1 Passive Components Design

The first step is to design dc bus capacitor. When designing the dc bus capacitor for a

single phase rectifier, the major disadvantage is the second-order harmonic on the dc bus,

which needs a fairly large bus capacitor to smooth the dc voltage. Considering this capacitor

an ‘energy buffer’ between input AC power and output dc power, the capacitor value can be

calculated and chosen based on its stored energy. Assuming the converter has unity power

factor, the input power is:

cos 22 2in g g

UI UIP u i tω= × = − (1)

Where the current and voltage are:

singu U tω= (2)

singi I tω= (3)

The energy stored in the input inductor is:

( )21 sin2

E L I tω= (4)

Instantaneous power stored in the input inductor is:

( )2 21( sin ) sin cos2LP E t L I t t LI t tω ω ω ω= ∂ ∂ = ∂ ∂ = (5)

The energy first passes through the input inductor and then the H-bridge finally charges

the dc capacitor. Without considering devices power loss, the energy stored in the dc

capacitor is the difference between the input energy and the energy stored in inductor:

2cos 2 sin cos2 2C in L

UI UIP P P t LI t tω ω ω ω= − = − − (6)

30

The dc component in (6) is supplied to the DC output, while the left second-order

components would charge and discharge the capacitor which leads to the DC bus voltage

ripple. By manipulating (6) to (7) and integrating the instantaneous power for a half cycle,

the ripple energy is derived in (8):

22

2 2 2 2 4

cos 2 sin cos cos 2 sin 22 2 2

sin(2 arctan )4 4

UI UI LIt LI t t t t

U I L I UtLI

ωω ω ω ω ω ω

ω ωω

+ = +

= + +

(7)

2 2 2 2 4

2 2 2 2 42

0

4 4sin 24 4

T

C

U I L IU I L IE tdt

ωω ω ω

+= + =∫ (8)

During one switching cycle the energy difference which equals the energy stored in the

capacitor is given in (9):

2 2 2 2 4

2 21 4 4[( ) ( ) ] 22C dc dc dc dc dc dc

U I L I

E c V V V V c V V

ω

ω+

= + Δ − −Δ = ⋅ ⋅Δ = (9)

From the ripple energy stored in capacitor we can derive the correlation between dc

capacitor, dc bus voltage ripple and input inductor, given by equation (10) and graphically

presented in figure 2.5.

2 2 2 2 4

4 42 dc dc

U I L I

CV V

ω

ω

+=

⋅ ⋅Δ ⋅ (10)

Set the dc bus voltage ripple cannot exceed more than 5% of the nominal dc bus voltage;

the dc capacitor value is selected as 2mF.

31

The second step is to choose the filter components. The filter inductor for the input/output

filter is designed based on the current ripple on that inductor. At any given time, the ripple

current can be calculated based on worst case ripple current.

( sin )2

DCpk

s

V U t DV tIL L f

ω− ⋅Δ ×Δ= =

⋅ (11)

Where the duty cycle D is determined in (12):

sinsin sinDC

DC DC

V M tU tD M tV V

ωω ω⋅ ⋅= = = (12)

Then the peak current can be represented by the function of dc bus voltage and modulation index M in (13):

(1 sin ) sin2

DCpk

f s

V M t M tIL f

ω ω⋅ − ⋅=

⋅ (13)

Set the current ripple to a proper percentage of the rated current, the inductor value is determined in (14):

(1 sin ) sin2

DCf

s pk

V M t M tLf I

ω ω⋅ − ⋅=

⋅ (14)

Here, UDC is the bus voltage with voltage ripple, Usinωt is the instantaneous value of AC

input voltage at the positive cycle, and fs is the switching frequency, U is the peak magnitude

of AC input voltage, and M is the PWM modulation index. Based on equation (14) the

correlation between the dc bus voltage, input inductor and current ripple is described the by

3-D drawing in figure 2.6. The inductor value is chosen to be 0.75mH and the ripple current

is 6.6A which is around 10% of the peak output current (58.9A). To calculate the filter

capacitor, the LC filter is to damp the harmonics of the output voltage. Equation (15) shows

it can achieve better performance with higher LC value. However, the output capacitor value

could not be too large otherwise too much power will be stored in the capacitor. It is

normally said that less than 10% of the rated power could be stored in the capacitor. The

32

filter capacitor value is calculated and chosen as 50uF. The power stage components and

parameters are listed in table 2-2.

2

1 12f

res f

Cf Lπ

⎛ ⎞= ⋅⎜ ⎟⎝ ⎠

(15)

Also the corner frequency of the LC filter, the capacitor value should not exceed 5% the

system base capacitance otherwise it will affect the power factor and absorb too much

reactive power on the capacitor

2

5% n

n n

PCVω

≤×

(16)

Here, nω is the fundamental frequency, nV is the output voltage and res

f is the filter corner frequency.

050

100150

200250

0

1

2

3

x 10-3

0

1

2

3

4

5

6

x 10-3

voltage ripple(Volt)

correlation of voltage ripple, input inductor and dc capacitor

input inductor(H)

dc c

apac

itor(F

)

Figure 2.5 Correlation of voltage ripple, input inductor and dc capacitor

33

01

23

45

x 10-3

0

5

10

15360

380

400

420

440

input inductor (H)

correlation of input inductor, current ripple and DC bus voltage

current ripple (A)

DC

bus

vol

tage

(V)

Figure 2.6 Correlation of current ripple, input inductor and dc bus voltage

Table 2-2 Power stage components in experimental setup

Power Rating 10kW (240V network)

5kW (120V network)

Power Devices CM150DY-12NF Powerex

IGBT Gate Driver BG2B Powerex

DC Bus Capacitor 2mF Electronics Concept

AC Filter Inductor 1mH/40mohm Magnetics Kool Mu

AC Filter Capacitor 50uF GE-Regal Capacitor

DC Filter Inductor 0.5mH/20mohm Magnetics Kool Mu

DC Filter Capacitor 220uF Epcos Corporation

34

2.3.2 Efficiency Test

The prototype is designed based on the structure of a commercial inverter. The 3-D

modeling is done by COSMOS SolidWorks and shown in figure 2.7. The hardware prototype

is constructed in laboratory and shown in figure 2.8.

Figure 2.7 3D modeling of the proposed converter

35

Figure 2.8 Lab prototype of the proposed converter

After the construction of the prototype, an efficiency test is performed to test the converter

reliability and measure efficiency. For the DC/AC stage the DC bus voltage is 400V,

switching frequency is 10 kHz and modulation index is 0.85. The DC/DC stage is tested in

the same way. Note that the efficiency data coincide with the value calculated by a software

package provided by Mitsubishi [83]. The only difference is that the passive components loss

is not included in the software. The measured efficiency for the DC/AC stage and DC/DC

stage is shown in figure 2.9 and figure 2.10 respectively.

36

93.00%

93.50%

94.00%

94.50%

95.00%

95.50%

96.00%

96.50%

1000W 2000W 5000W 6500W 8000W 10000W

AC/DC stage efficiency

Figure 2.9 Efficiency DC/AC Stage

94.50%

95.00%

95.50%

96.00%

96.50%

97.00%

97.50%

98.00%

98.50%

1000W 2000W 5000W 6500W 8000W 10000W

DC/DC stage efficiency

Figure 2.10 Efficiency DC/DC Stage

2.4 Control Structure of Proposed Converter

The control structures for both Grid to Vehicle and Vehicle to Grid belong to grid-tied

current mode controller [84-86]. Typically double-control-loop structure is used: inner

current loop and outer voltage loop. The inner current loop achieves good current tracking,

low current harmonics and fast transient response. The outer voltage loop regulates the DC

bus voltage. The control structure for grid to vehicle is shown in Figure 2.11; it is composed

of a double-loop structure for the AC/DC stage and a single loop for DC/DC stage. The

DC/DC stage has a single loop structure for grid to vehicle. Battery management system

37

monitors the battery pack and acquires a serial of parameters such as state of charge (SOC),

state of health (SOH), voltage and temperature. The controller will decide how to charge this

battery based on its condition. Different charging algorithms are implemented in the

controllers which are constant-current constant-voltage charging algorithm, pulse charging

algorithm and Reflex charging algorithm [87, 88]. These charging algorithms don’t pose a

challenge to power electronics controller because the battery is a very stiff plant with slow

response. Regarding pulse charging algorithm, it is believed to be the best charging algorithm

[89] because it uses battery AC impedance theory and tries to charge the battery at the lowest

impedance. Variable AC impedance theory has already been verified in the field of

Electrochemistry [90-94]. So to design a good charging algorithm it is essential to work

closely with batteries’ electrochemical characteristics.

Figure 2.12 shows the multi-loop structure for vehicle to grid function. Compared to

distributed generation controller, the outer voltage loop is regulated at the DC/AC stage and

only the inner current loop is needed. The current reference is generated by the power

system. When the power system needs vehicles to do the service such as frequency

regulation and load leveling, an operator will arrange a number of plug-in vehicles and send

the power requirement. The reason to use DC/AC to support the dc bus voltage is that during

the mode transfer between G2V and V2G, this control structure will lead to a smooth

transition.

38

*gi

gigridV

gridV

dcV

*dcV

gi

dci

dci

*dci

Figure 2.11 Control Structure for Grid to Vehicle Function

GFI BreakerBattery

AC Grid

PLL

-+

*gi

giCR SPWM

gridV

DC bus AC stageDC stage

PI

gridV

dcV

*dcV

-+ PWMPI

dci

dci

*dciBattery

Management System

CAN +-

feedback current

power system demand

Boostoperation

Figure 2.12 Control Structure for Vehicle to Grid Function

Regarding the current regulator, proportional plus Resonant (PR) controller [95-98] has

been proven that it has better performance than a proportional integral (PI) controller in

stationary frame. More theoretical analysis shows that the proportional plus resonant

controller in stationary frame is equivalent to proportional integral controller in rotating

frame. So in stationary frame a PR controller is more effective at achieving zero steady-state

error and improves the reference tracking capability. The controller equation is written in

equation (19):

0

2 2

2( )2

cc p i

c

sG s K Ks s

ωω ω

= + ⋅+ +

(17)

39

Here Kp determines the dynamic response of the controller, Ki adjusts the gain of the

setting frequency, with a higher gain the error is reduced, ωc is the cutoff frequency which is

much smaller than ω0, and ω0 is the resonant frequency which is set to 376.8 rad/s. Based on

PR controller, a series set of resonant blocks are utilized in particular to eliminate several

selected low order odd harmonics [99]. Similar to PR controller, a series of resonant

controller cascaded together are tuned to the desired low order odd frequencies to further

reduce current harmonics. The PR controller with selective harmonics elimination blocks are

shown in (20):

0

2 2 2 23,5,7 0

2 2( )2 2 ( )

c ch p i ih

hc c

s sG s K K Ks s s s h

ω ωω ω ω ω=

= + ⋅ ++ + + +∑ (18)

Here Kih determines the gains of the low order odd harmonic, h is the odd harmonics.

In this section the V2G function and G2V function are tested with three different types of

controller in stationary frame. First the V2G function is tested with PI, PR and PR+HC

controller with 1.2kW. The result with PR+HC controller is shown in figure 2.13. With

stationary frame PI the control error, especially the phase error, still exists. With stationary

PR controller the phase error is largely reduced because of the resonant gain at the

fundamental frequency, however the low-order harmonics such as 3rd, 5th and 7th harmonics

still exist. With PR+HC controller both the phase error and the low-order harmonics are

reduced. The detailed comparison for the individual harmonic among the three controllers is

shown in figure 2.14. With the spectrum of the output current shown in the figure the

PR+HC has the best performance.

40

Figure 2.13 Vehicle to grid with PR+HC controller (Purple curve: grid voltage; Red curve: output current)

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

3.50%

4.00%

4.50%

3rd 5th 7th 9th 11th 13th 15th 17th 19th

PR+HC PR PI

Figure 2.14 Controller performance comparison: PI, PR and PR+HC controller

After V2G test, the G2V experiment is conducted. The current controller is the same as

that used in V2G function. A steady-state operation for 1kW charging is shown in figure

2.15. In figure 2.16 the total harmonics for three controllers are used in G2V function with

different input current. Finally the current performance for both V2G function and G2V

function is listed and compared with the standard for distributed generation IEEE 1547-2008.

41

It can be seen from the figure 2.17 and figure 2.18 at 1.2kW the total harmonics and the

individual harmonic meet the standard.

Figure 2.15 Grid to Vehicle with PR+HC controller (Blue curve: dc bus voltage; Red curve: grid voltage; Purple

curve: input current)

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

9.00%

2.5A 5A 7.5A 10A 15A

PR+HC PR PI

Figure 2.16 THD comparison: PI, PR and PR+HC controller

42

0%

1%

1%

2%

2%

3%

3%

4%

4%

5%

3rd 5th 7th 9th 11th

13th

15th

17th

19th

21th

23th

25th

27th

29th

31th

33th

35th

37th

39th

IEEE1547 output current

Figure 2.17 Vehicle to grid: comparison between vehicles’ input current and IEEE 1547 standard

0%

1%

1%

2%

2%

3%

3%

4%

4%

5%

3rd 5th 7th 9th 11th

13th

15th

17th

19th

21th

23th

25th

27th

29th

31th

33th

35th

37th

39th

IEEE 1547 input current

Figure 2.18 Grid to Vehicle: comparison between vehicles’ output current and IEEE 1547 standard

2.5 Summary of Chapter Two

In this chapter, a bi-directional grid-interactive converter with multiple functions for

PHEV is proposed. It achieves three major functions: grid to vehicle (G2V), vehicle to grid

(V2G) and vehicle to home (V2H). The system infrastructure, operational principles are

illustrated. The hardware design and control structure for different functions are presented.

43

Chapter Three High Frequency Resonance Mitigation for Plug-in Hybrid

Electric Vehicles’ Integration with a Wide Range of Grids

3.1 High Order Filter Formation and its Negative Impacts

The proposed converter has an LC output filter to provide high quality current and

voltage, but with the connection of grid impedance the converter is connected with an LCL

filter. The inductor-capacitor-inductor (LCL) filter is widely utilized in the grid integration

application such as renewable energy interconnection, high performance regenerative

rectifier, etc. [100-103]. It is placed between a voltage source converter and the grid.

Normally, using L-type filter to fulfill existing grid codes such as IEEE 519-1992 [104],

IEC61000-3-4 [105] and IEEE 1547 [106], a large inductor value should be used. However,

the large inductor reduces the dynamic performance of the converter, also increases the

system cost and volume. The LCL filter is a third-order low-pass filter which effectively

attenuates the current ripples, with a smaller converter side inductor the current through the

grid is almost ripple free. Furthermore in high power application where the switching

frequency is limited due to the power losses, using LCL filter can help improve the output

current quality with lower switching frequency. To summarize the advantages of LCL-type

filter over L-type filter, two major aspects need to be addressed. First is higher attenuation of

the harmonics. The attenuation rate of LCL filter is 60dB per decade compared to 20dB per

decade of L-type filter. The second point is lower inductance compared to L-type filter and

better dynamic response. In the proposed converter, grid impedances will vary with different

grid conditions, i.e., the leakage inductance of isolated transformers and the inductance from

44

a long charging cable. The figure 3.1 also shows the converter is connected with the grid

through variable inductances and its LC filter.

fL

gL

fC

gifi

Figure 3.1 Formation of high-order filter by converter LC filter and grid impedance

Although an LCL filter has the advantages of low inductor value and current ripple, its

drawbacks are notable. Because of its high order resonance characteristics once excited by

high frequency harmonics, the filter will lead to resonant oscillation. At the natural resonant

frequency of the filter, a filter capacitor can be considered very low impedance almost to the

point of short circuit so it will draw harmonic currents around resonant frequency. It will lead

to high voltage oscillation on the capacitor voltage and the grid current. This oscillation will

distort the grid current, increase power losses, and trigger the converter protection and may

even lead to the system instability. The resonant frequency can come from both the converter

PWM voltage output and the grid voltage harmonics though the grid side harmonics will be

much lower than the converter output. To solve this low impedance issue at the resonant

frequency, passive damping methods are proposed. The passive damping method normally

utilizes a power resistor series with the filter capacitor to increase the impedance of this

branch at the resonant frequency. But it greatly increases system efficiency, for example with

120/1.5kW converter 10ohm damping resistor the power loss accounts to 3.41%. The

modification method shown in figure 3.2 has been proposed to replace the only resistor with

45

an inductor paralleled with a capacitor and then series with a resistor. In this way the power

loss on the resistor is largely reduced. But this will increase the system cost and volume and

more importantly the tuning frequency cannot be changed. Because of the simplicity and

high reliability, the passive solutions are adopted in industry. However, additional power

losses and the cost of inductor and resistor are the major drawbacks of this method. Another

notable drawback is that usually the passive damping method is effective in a certain range of

resonant frequency but cannot be effective in a large range of resonant frequency. But the

grid impedance cannot remain constant so the resonant frequency varies. A passive filter with

fixed frequency cannot effectively attenuate the resonant. Thus an active means of

attenuation with loss free and adaptive tuning capability is a preferred and promising method.

fL gL

fCconvV

gL

fCconvV

fL

Figure 3.2 Passive damping methods to eliminate high-frequency harmonics

3.2 Review of Active Damping Methods

Researchers have proposed lots of good active damping methods to address the unstable

problem. The filter based controller is proposed to extract and eliminate the resonant

components in the control loop. A genetic algorithm is proposed to be used as the tool to

choose the right parameters for the filter based controller [107]. Further development based

on the band-pass filter, virtual flux is used to eliminate addition current sensors [108]. A

46

digital infinite impulse type of filter is proposed to improve stability [109]. Different types of

filter based controllers are studied and compared [110]. The control parameters e.g., gain and

time constant are tuned to improve the phase margin at the resonant frequency in order to

make control loop stable [111]. The effect of the sampling frequency to the stability of the

control loop is analyzed. Compared to the resonant frequency, a much faster sampling

frequency is needed [111, 112]. A hybrid controller which has a virtual harmonic damper and

a three-step posicast compensator is proposed to damp the resonance resulting from the LC

input filter [113]. In order to maintain control loop stable, it is beneficial for the controller to

know as many control variables as possible. Beside the single grid current control loop, the

converter side current and the filter capacitor current or voltage can be used [114-123]. An

LCL filter had been altered to an LCCL filter so two control variable, the grid current and

part of filter capacitor current can be measured by one current sensor [124]. By sensing the

grid current and the filter capacitor voltage, an additional admittance feed-forward path is

added for fuel cell applications [125]. A direct power control (DPC) is modified to integrate

active damping control with sensing the capacitor filter voltage [126]. With multiple control

variables sensed and used in the controller, PI state space controller is proposed [112, 127-

130]. The state variable estimator is combined with state space controller [131-132].

Predictive current control has been applied with state space controller [133, 176-179]. A

robust controller based on H-infinity theory is proposed to tune the control parameters for

different grid impedances [180]. Passivity theory has been applied to examine the

convergence of the controller’s state trajectories [181]. Discrete sliding mode current

controller is proposed for active damping [182-184]. Compared to PI based controllers, these

47

controllers based on modern theories have not yet been well accepted in practical

applications. The LCL filter can be also utilized in microgrid applications which switch

between grid-connection operation and stand-alone operation [185, 186]. Virtual resistor

based damping method [118, 187-190] is very similar to the passive damping concept. The

controller senses either the filter capacitor current or voltage to emulate a resistor in series

with the filter capacitor to resolve the resonant issue. However, the virtual resistor based

controller has the drawback that its virtual resistor value highly relies on the value of LCL

filter. If the values of an LCL filter change, the performance of virtual resistor controller is

compromised. Moreover, in order to connect the PHEVs with a wide range of grids the

controller needs to be stable with different grid conditions. It means that the virtual resistor

controller should not only have variable resistor values to enhance the controller performance

at different grid conditions, but also the adaptive tuning capability to adjust the virtual

resistor value based on the grid conditions automatically. Some of the literature regarding the

virtual resistor controller has discussed about one set of controller at the different resonant

frequency mainly caused by filter capacitor. However, this type of controller has seldom

been adopted and examined in practical grid conditions for PHEV applications. The stability

of the virtual resistor controller at different grid conditions needs to be examined. The virtual

resistor controller with adaptive tuning capability behaves like a controllable resistor. This

method is desired for this type of application which is for a wide range of gird impedance. In

this chapter, an adaptive virtual resistor controller to achieve high power quality for plug-in

hybrid electric vehicles is proposed. Since current literature lacks the stability analysis of

48

controller of PHEVs under different grid conditions, this paper analyzes and designs the

controller to work with a large set of grids stably.

3.3 Large Scale Penetration of Plug-in Hybrid Electric Vehicles into Various Grids

With increased number of commercial plug-in vehicles available on the market, there

will be a large number of PHEVs connected to the power grid in the future. One remarkable

issue of the large scale penetration of PHEVs to the grid is the power balance issue. An

intelligent power allocation and management method leveraged with cyber technology is

proposed to alleviate this grid collapse [134]. The issue caused by the power electronics

converter needs to be addressed. When connected with the grid, the filter of the bi-directional

charger combining with the grid impedance forms a high order filter. This high order filter

will generate high frequency oscillation. When the PHEVs are largely adopted into the grid

the vehicles will be connected with a diversity of grids. For example in a remote area (rural

area) or in an isolated location far from the distribution transformer, the grid is highly

inductive and is also referred to weak grid [135-137]. The grid configuration becomes even

more complicated when the home appliances are considered. Because there is an equivalent

capacitance correcting power factor [138]. In figure 3.3 the Bode plot of control plant with

different grids is shown. The control plant means the transfer function of the control input to

the grid current. The grid impedance in this figure is 0.2mH, 0.5mH and 2.5mH respectively.

As we can see that with the variations of grid impedance, the control plant also changes.

Therefore, a single virtual resistor value which is specially designed for one grid impedance

cannot compensate for all the grid conditions. In figure 3.4, the grid current with control loop

having different virtual resistor values is shown. If the control loop designed for the grid

49

impedance 2.5mH is used at a 0.2mH grid, the control loop is not stable. The grid current

changes from stable operation to oscillation. The high frequency resonance appears on the

grid current. Thus, the control loop with a fixed virtual resistor value cannot be applied to a

wide range of grids.

-100

-50

0

50

Mag

nitu

de (d

B)

101

102

103

104

-270

-225

-180

-135

-90

Phas

e (d

eg)

Bode Diagram

Frequency (Hz)

L=0.2mHL=0.5mHL=2.5mH

Figure 3.3 Frequency characteristics of different grid conditions

50

0.24 0.26 0.28 0.3 0.32 0.34 0.36-15

-10

-5

0

5

10

15

Time

grid current

Figure 3.4 Grid current with the control loop having different virtual resistor values

3.4 Modeling and Design of Adaptive Virtual Resistor Controller

Inside a high order filter the capacitor path is the weakest path which always allows high

frequency current to flow through. To eliminate the weakest patch various passive damping

methods [139] place resistors, inductors and capacitors either series or parallel with the

capacitor in order to absorb the high frequency components. This idea will enlighten the

active controller design to come out with a variable virtual resistor to be placed in series with

the capacitor. The capacitor current is sensed and multiplied with an adaptive gain which

represents a variable resistor. The multiplication of capacitor current and the gain is added to

the input of the PWM generator to eliminate the resonant frequency components before they

go into the PWM generator to make a converter output as resonance excitation source. The

virtual resistor only exists in the control loop not physically connected in the converter

51

system. The virtual resistor value can be changed based on different grid impedances. In this

paper an adaptive virtual resistor method is proposed.

Figure 3.5 the idea of proposed adaptive virtual resistor method is drawn. As shown in this

figure the proposed controller emulates a variable resistor to be connected with the capacitor.

The LCL filter is in between with two voltage sources: converter PWM output voltage and

grid voltage. The virtual resistor based controller for the single phase application can be

divided into two types: Stationary Frame Control and Synchronous Frame Control. Figure

3.6 (a) describes the architecture of virtual resistor based controller in synchronous frame.

3.6(b) shows the measured one control cycle operation time for proposed controller in

synchronous frame. One control cycle takes around 34us. Figure 3.7 (a) describes the

architecture of virtual resistor based controller in stationary frame. 3.7 (b) shows the

measured one control cycle operation time for proposed controller in stationary frame. It

takes around 12us. So to compare the controller in these two control frames the stationary

frame has faster calculation and shorter time duration. So it occupies fewer of the digital

processors’ resources. Synchronous frame takes more time because it contains a single phase

d-q transformation. Regarding the performance the stationary frame with PI controller cannot

compete with synchronous frame because the control objective is at 60Hz not dc component.

But proportional resonant (PR) largely improves the gain at 60Hz and the steady-state error

for both the magnitude and phase can be eliminated theoretically. PR controller in [97] has

been proved to be equivalent to PI in synchronous frame. To save the resource of digital

process virtual resistor controller in stationary frame with PR and HC (harmonic

cancellation) control is used.

52

Figure 3.5 Variable virtual resistor based adaptive damping method

Figure 3.6 (a) Virtual resistor controller in synchronous frame

Figure 3.6 (b) Measured one control cycle operation times for controller in synchronous frame

53

PIVdc-ref

Vdc+ - ig-ref +

-ig

+

+PR+HC

icf

sinθ

Vgrid PLL

Stationaryframe

Ga

SPWM gatingsignals

Figure 3.7 (a) Virtual resistor controller in stationary frame

Figure 3.7 (b) Measured one control cycle operation times for controller in stationary frame

A. Modeling of Virtual Resistor Controller

For single phase stationary frame application the transfer functions can be derived directly

such variables are in dc format [191]. As shown in figure 3.5 that the grid current ig is the

control objective. It has two voltage sources affecting it based on superposition. The transfer

function for grid current to converter output voltage and grid voltage should be derived. The

capacitor current ic is also important to the virtual resistor based method because it emulates

a resistor in series with the capacitor. So the relationship of capacitor current to converter

output voltage and grid voltage is derived. The transfer function will be used in the next step

to help control loop design. Use the circuit shown in figure 3.1 and ignore the inductor

54

winding resistance. The equations show the relation between the grid voltage, grid current

and the converter output.

( )( ) ( )f

f conv cf

di tL u t u t

dt= − (1)

( )( ) ( )g

g cf g

di tL u t u t

dt= − (2)

( )( )cf

f c

du tc i t

dt= (3)

( ) ( ) ( )f c gi t i t i t= + (4)

Convert equations (1) ~ (4) from time domain to frequency domain to get equations (5) ~ (8):

( ) ( ) ( )f f conv cfs L i s u s u s⋅ = − (5)

( ) ( ) ( )g g cf gs L i s u s u s⋅ = − (6)

( ) ( )f cf cs c u s i s⋅ = (7)

( ) ( ) ( )f c gi s i s i s= + (8)

To consider the transfer function of grid current to converter output, the grid voltage is

considered constant without any disturbance. So in small signal model the grid voltage is

zero. So put (6) into (7) and (8) the grid current ig can be used to substitute capacitor voltage

and converter side current.

( ) ( )g g cfsL i s u s= (9)

55

2 ( ) ( )f g g cs c L i s i s= (10)

With the capacitor current and grid current derived, the converter side current can be

represented by grid current also.

2( 1) ( ) ( )f g g fs c L i s i s+ = (11)

Substitute equation (11) to (5) to get the transfer function of converter output to grid

current:

2 3( ) ( 1) ( ) ( ) ( ( )) ( )conv f g f g g g g f f g f gu s sL s L c i s sL i s s L L c s L L i s= + + = + + (12)

3

( ) 1( ) ( )

g

conv g f f g f

i su s L L c s L L s

=+ +

(13)

After derivation of converter output to grid current, the converter output to capacitor

current is easily derived:

32

2

( ( ))( ) ( 1) ( ) ( ) ( )g f f g f

conv f g f g g g cf g

s L L c s L Lu s sL s L c i s sL i s i s

s c L+ +

= + + = (14)

2

( )( )

g fc

conv g f f g f

L c si su s L L c s L L

=+ +

(15)

In the next step, the virtual resistor loop is plugged into the controller. The capacitor

current is sensed and multiplied with adaptive gain Kad, so the equation (5) will be rewritten

as:

( ) ( ) ( ) ( )f f conv ad c cfs L i s u s k i s u s⋅ = − ⋅− (16)

56

So to substitute (11) to (16), the transfer function with virtual resistor is included in (17):

2 2

3 2

( ) ( 1) ( ) ( ) ( )

( ( )) ( )conv f g f g g g ad g f g

g f f ad g f g f g

u s sL s L c i s sL i s s k L c i s

s L L c s k L c s L L i s

= + + +

= + + + (17)

The transfer of the converter output to the grid current with virtual resistor:

3 2

( ) 1( ) ( )

g

conv g f f g f ad g f

i su s L L c s L c k s L L s

=+ + +

(18)

Similar to equations (16), (17) and (18), the transfer function of converter output voltage

and capacitor current with virtual resistor Kad is derived in (19) and (20).

3 22

2

( ( ))( ) ( 1) ( ) ( ) ( ) ( )(19)g f f f g ad g f

conv f g f g g g ad c cf g

s L L c s c L k s L Lu s sL s L c i s sL i s k i s i s

s c L+ + +

= + + + =

2

( )( )

g fc

conv g f f g f ad g c

L c si su s L L c s L c K s L L

=+ + +

(20)

The next step is to analyze the impact from grid voltage to both grid current and capacitor

current. In addition to being excited by the converter output voltage, the excitation from the

grid voltage should also be taken into account. But it is obvious that grid voltage’s impact is

not significant because to meet the grid code the high frequency components of grid voltage

are much lower than the converter output voltage. Consider the converter output voltage to

be constant the relationship of grid voltage and grid current and capacitor current can be

derived.

( ) ( )f f cfs L i s u s⋅ = − (21)

( ) ( ) ( )g g cf gs L i s u s u s⋅ = − (22)

57

( ) ( )f cf cs c u s i s⋅ = (23)

( ) ( ) ( )f c gi s i s i s= + (24)

2

1( ) ( ) ( )1g g g g

f f

u s i s sL i sL c s

− = − −+

(25)

The transfer function of grid voltage to grid current is:

2

3

( ) 1( ) ( )

g f f

g g f f g f

i s L c su s L L c s L L s

+=

+ + (26)

After derivation of the grid voltage to grid current, the grid voltage to capacitor current is

easily derived:

2

1 1( ) ( 1) ( ) ( )g g c cf f f

u s sL i s i sL c s sc

− = − − − (27)

The transfer of the grid voltage to the capacitor current is:

2

( )( )

f fc

g g f f g f

L c si su s L L c s L L

=+ +

(28)

The virtual resistor loop is plugged into the controller. This proposed method cannot only

take effect with converter output voltage but also the grid voltage. The capacitor current is

sensed and multiplied with adaptive gain Kad, so the equation (5) will be rewritten:

( ) ( ) ( )f f ad c cfs L i s k i s u s⋅ = − − (29)

Simplify the equation (29) to (30):

( ) ( ) ( )f f f ad cf cfs L i s sc k u s u s⋅ = − − (30)

58

The relation of grid current and capacitor voltage is:

( 1) ( )( ) ( )f ad cf

g f cff

sc k u si s sc u s

s L− +

= −⋅

(31)

Substitute (31) to (22), the transfer function of grid voltage to grid current with virtual

resistor:

2

3 2

( ) 1( ) ( )

g f f f ad

g g f f g f ad g f

i s L c s c K su s L L c s L c K s L L s

+ +=

+ + + (32)

Use capacitor current to represent grid current:

2

( 1) ( )( ) ( )f ad c

g cf f

sc k i si s i s

s L c− +

= − (33)

Substitute (33) to (32), the transfer function of grid voltage to capacitor current with

virtual resistor:

2

( )( )

f fc

g g f f g f ad g f

L c si su s L L c s L c K s L L

=+ + +

(34)

The comparison of the transfer function with virtual resistor and without virtual resistor is

drawn in figures 3.8, 3.9, 3.10 and 3.11 respectively. As we can see from figures 3.8 and 3.10

that with virtual resistor control, the high frequency resonant from both converter output

voltage and grid voltage is eliminated. Figures 3.9 and 3.11 also prove that with virtual

resistor the capacitor current doesn’t have the resonant frequency. So from the circuit

perspective the capacitor path has increased its impedance to this specific resonant frequency

and no longer has low impedance.

59

-150

-100

-50

0

50

100

150

Mag

nitu

de (d

B)

102

103

104

105

-270

-225

-180

-135

-90

Phas

e (d

eg)

Bode Diagram

Frequency (Hz)

Figure 3.8 Transfer function: converter output to grid current with/without virtual resistor

-100

-50

0

50

100

150

Mag

nitu

de (d

B)

102

103

104

105

-90

-45

0

45

90

Phas

e (d

eg)

Bode Diagram

Frequency (Hz)

Figure 3.9 Transfer function converter output to capacitor current with/without virtual resistor

60

-200

-150

-100

-50

0

50

100

150

Mag

nitu

de (d

B)

101

102

103

104

-90

-45

0

45

90

Phas

e (d

eg)

Bode Diagram

Frequency (Hz)

Figure 3.10 Transfer function grid voltage to grid current with/without virtual resistor

-50

0

50

100

150

Mag

nitu

de (d

B)

102

103

104

105

-90

-45

0

45

90

Phas

e (d

eg)

Bode Diagram

Frequency (Hz)

Figure 3.11 Transfer function grid voltage to capacitor current with/without virtual resistor

61

B. Analysis of Control Loop of Virtual Resistor Controller

Virtual resistor loop only affects the inner current loop so the control loop is designed in

details especially for the current control loop. From the analysis above we know that LCL

filter is connected with two voltage sources, the converter output Uconv and grid Ug. Each of

them will have influence on both the grid current and capacitor current. The inner current

loop is designed to regulate grid current ig and capacitor current ic is used to damp the high

frequency resonance of the grid current loop. Based on the relationship among the converter

output, gird voltage, grid current and capacitor current, the diagram of control plant with

proposed controller is drawn in figure 3.12. To further simplify the block diagram the control

loop model is achieved in figure 3.13.

gu gi

ci

convu

Figure 3.12 Block diagram of control plant and proposed controller

Figure 3.13 Control loop modeling

1 2 32 2 2 2 2 2( )

20 20 (3 ) 20 (5 )i i i

comp pk s k s k sG s k

s s s s s sω ω ω⋅ ⋅ ⋅

= + + ++ + + + + +

(35)

62

1( )1d

s

G sT s

=+ ⋅

(36)

( )a adG s k= (37)

The current controller is stationary frame PR plus HC control. Kp is the proportional gain

and Ki1, Ki2, Ki3 is the integration gain and ω is the fundamental frequency. Harmonics

cancellation is used to eliminate low frequency odd order harmonics. According to Liserre

[86] that for single phase application the 3rd and 5th harmonics are more important so HC

controller is designed to reduce 3rd and 5th harmonics. The transport delay and

computational delay are also included. Ts is defined as one switching period. Kad is the

adaptive gain to represent virtual resistor. After the modeling of the control loop in the next

segment the control loop design will be presented. The adaptive virtual resistor controller

design will be narrated in detail.

3.5 Adaptive Virtual Resistor Control for a Wide Range of Grids

The major issue of large scale penetration of PHEVs into the grid has been described.

Since the issue is that various sets of grid impedances compromise the performance of the

damping control, the damping controller must have the capability of tuning its parameters

automatically. The grid impedance extraction method is proposed by using the resonant

frequency of LCL filter to calculate the grid impedance [140, 141]. In order to address a wide

range of grid impedances an effective way of damping is to ensure that the active damping

controller adaptive capability. The adaptive gain Kad performs as a controllable resistance in

series with the capacitor. To demonstrate why a variable Kad is important to the control loop

performance, the control plant with adaptive gain is drawn in figure 3.14. We can see from

63

this figure that the phase margin changes with the variation of Kad. The Kad acts like a

damping factor in the control loop, with different versions of Kad the Bode plot can be

lightly damped or heavily damped. However the phase margin and the gain margin are highly

dependent on this factor. If Kad is too high, the phase margin will be too low and the loop

may not be stable. If the phase margin is too high, such as 100 degree the loop response will

be very slow. If Kad is too low, the gain margin will be too low and the loop is close to its

stability boundary and any interference may cause it unstable

Next segment explains how to design an adaptive gain Kad based on the variation of grid

impedances. In this paper, grid impedances change with different grid conditions. Lower

impedance results in a stiff grid and higher impedance yields a weak grid. Based on system

power rating and converter parameters, the grid impedance is chosen to be between 0.2mH

(0.8% pu) and 2.5mH (9.8% pu). The system parameters and grid impedances are presented

in Table 3-1. The controller structure is shown in figure 3.15. In this figure the entire control

loop includes the outer dc bus regulation loop and the inner current synchronization loop.

Based on the sensed grid current, the resonant frequency is extracted and detected by a

frequency detection block. This function is edge triggered at every positive edge of the

detected frequency signal so that the time duration between the first positive edge and the

second positive edge is obtained. By inverting this time duration, we can get the frequency of

the measured signal. Zero crossing function can be also added to prevent the mistrigger and

increase the accuracy of the frequency detection. In figure 6.31 0.2mH grid impedance is

measured based on its resonant frequency. In figure 6.32 the transient of grid impedance is

tested.

64

In figure3.17, the pole-zero map for the dominant poles of the controller without virtual

resistor compensation is drawn. The lowest impedance is 0.2mH, and the highest impedance

is 2.5mH. The impedance increases incrementally with 0.1mH each time. In figure 3.18, the

dominant poles of the control loop with different grid impedance are used to show the

advantages of using adaptive virtual resistor over using fixed resistor value. We can see that

the controller’s dominant poles do not locate at the boundary or outside the unity circle, this

means the controller is stable with one fixed virtual resistor value, but even so, the control

loop performance is not good for some impedance because of the positions of the dominant

poles. Some dominant poles has lower phase margin especially for the lower impedance

cases. While for some higher impedance cases, the control loop can guarantee higher phase

margin but have lower gain margin concurrently. Use phase margin, bandwidth and gain

margin as the specification to design virtual resistor Kad. Virtual resistor at each impedance

point should locate the dominant poles at the proper locations. By saying proper locations, it

means that the control loop have the higher value of phase margin, gain margin and control

loop bandwidth. The pole-zero map for the dominant poles of the controller with adaptive

Kad is drawn in figure 3.19. In this figure, the dominant poles are located at the proper

positions to ensure the performance of the control loop. Figure 3.20 and figure 3.21 show the

cases of the stiffest and the weakest grid conditions, the control plant can achieve a good

phase margin with different Kad values. The relationship of grid impedance and resonant

frequency is shown in figure 3.22 and the relationship of grid impedance with proper resistor

value Kad is shown in figure 3.23.

65

Table 3-1 System configuration

Power rating 1.5kW

Voltage 120V

Filter inductor and capacitor 1mH, 50uF

Stiff grid condition 0.2mH (0.8% pu)

Weak grid condition 2.5mH (9.8% pu)

-100

-50

0

Mag

nitu

de (d

B)

101

102

103

104

105

-270

-225

-180

-135

-90

Phas

e (d

eg)

Bode Diagram

Frequency (Hz)

Kad=7.5Kad=2.0Kad=15.0Kad=0

Figure 3.14 Control Parameter Characteristics: adaptive gain Kad

66

Figure 3.15 Block diagram of controller with adaptive virtual resistor loop

Figure 3.16 Frequency detection function block

Figure 3.17 Root locus of control plant with various impedances (0.2mH to 2.5mH) without virtual resistor

Pole-Zero Map

Real Axis

Imag

inar

y Ax

is

-1.5 -1 -0.5 0 0.5 1 1.5-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.05/T

0.10/T

0.15/T

0.20/T0.25/T

0.30/T

0.35/T

0.40/T

0.45/T

0.50/T

0.05/T

0.10/T

0.15/T

0.20/T0.25/T

0.30/T

0.35/T

0.40/T

0.45/T

0.50/T

0.1

0.2

0.30.40.50.60.70.8

0.9

67

-1.5 -1 -0.5 0 0.5 1 1.5-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.05/T

0.10/T

0.15/T

0.20/T0.25/T

0.30/T

0.35/T

0.40/T

0.45/T

0.50/T

0.05/T

0.10/T

0.15/T

0.20/T0.25/T

0.30/T

0.35/T

0.40/T

0.45/T

0.50/T

0.1

0.2

0.30.40.50.60.70.8

0.9

Pole-Zero Map

Real Axis

Imag

inar

y Ax

is

Figure 3.18 Root locus of control plant with various impedances (0.2mH to 2.5mH) and fixed virtual resistor

-1.5 -1 -0.5 0 0.5 1 1.5-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.05/T

0.10/T

0.15/T

0.20/T0.25/T

0.30/T

0.35/T

0.40/T

0.45/T

0.50/T

0.05/T

0.10/T

0.15/T

0.20/T0.25/T

0.30/T

0.35/T

0.40/T

0.45/T

0.50/T

0.1

0.2

0.30.40.50.60.70.8

0.9

Pole-Zero Map

Real Axis

Imag

inar

y Ax

is

Figure 3.19 Root locus of control plant with various impedances (0.2mH to 2.5mH) with adaptive virtual

resistor

68

Pole-Zero Map

Real Axis

Imag

inar

y Ax

is

-1.5 -1 -0.5 0 0.5 1 1.5-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.05/T

0.10/T

0.15/T

0.20/T0.25/T

0.30/T

0.35/T

0.40/T

0.45/T

0.50/T

0.1

0.2

0.30.40.50.60.70.8

0.9

0.05/T

0.10/T

0.15/T

0.20/T0.25/T

0.30/T

0.35/T

0.40/T

0.45/T

0.50/T

Figure 3.20 Root locus of control plant with 0.2mH adopts proper virtual resistor

-1.5 -1 -0.5 0 0.5 1 1.5-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.05/T

0.10/T

0.15/T

0.20/T0.25/T

0.30/T

0.35/T

0.40/T

0.45/T

0.50/T

0.1

0.2

0.30.40.50.60.70.8

0.9

0.05/T

0.10/T

0.15/T

0.20/T0.25/T

0.30/T

0.35/T

0.40/T

0.45/T

0.50/T

Pole-Zero Map

Real Axis

Imag

inar

y Ax

is

Figure 3.21 Root locus of control plant with 2.5mH adopts proper virtual resistor

69

0 0.5 1 1.5 2 2.5

x 10-3

800

900

1000

1100

1200

1300

1400

1500

1600

1700

1800

grid impedance (mL)

reso

nant

freq

uenc

y (H

z)

grid impedance vs resonant frequency

Figure 3.22 Grid impedance vs resonant frequencies

800 900 1000 1100 1200 1300 1400 1500 1600 1700 18004

6

8

10

12

14

16

18

Resonant frequency

Res

isto

r val

ue K

ad

Figure 3.23 Resonant frequency vs proper adaptive gain Kad

70

63.5 62.5 61.6 60.6 59.8 58.9 58.1 57.3 56.5 55.5P.M

Bandwidth

0

100

200

300

400

500

600

700

800

0-100 100-200 200-300 300-400 400-500 500-600 600-700 700-800

Figure 3.24 Relationship of adaptive gain Kad, control loop bandwidth and phase margin for stiff grid

52.7 51 49.3 47.5 45.7 44 42.3 40 38.9 37.2P.M

Bandwidth

0

50

100

150

200

250

300

350

400

450

500

0-50 50-100 100-150 150-200 200-250 250-300 300-350

350-400 400-450 450-500

Figure 3.25 Relationship of adaptive gain Kad, control loop bandwidth and phase margin for weak grid

Regarding the selection virtual resistor values, there are tradeoffs between the control loop

bandwidth, phase margin and gain margin. If the virtual resistor is set too high, the phase

71

margin and bandwidth will increase, but the gain margin will decrease. So the value of

virtual resistor is chosen at different impedance to get proper bandwidth, phase margin and

gain margin with enough design margin for real system. These virtual resistor values become

a group of parameters which can guarantee the control loop stability and also improve the

control performance. Each of impedance from 0.2mH to 2.5mH corresponds to one

designated virtual resistor. The mathematical equation between the resonant frequency and

virtual resistor value (Ga) can be obtained by curve fitting and written in equation (38):

13 5 9 4 6 3 3 2( ) 1.383 10 0.91 10 2.381 10 3.088 101.997 508.6ad ak G f x freq x x x x

x

− − − −= = = = × − × + × − ×+ −

(38)

The next segment is to analyze and design the control loop for different grid conditions.

Here three grid impedances are used as example. The extreme case 0.2mH and 2.5mH are

used and 1mH are used as random impedances in the middle of the impedance range. Figure

3.24 shows the relationship of Kad with control loop bandwidth and phase margin at 0.2mH.

As Kad increases the gain margin increases, the bandwidth increases and phase margin

decreases. So the first case is to design the control loop for 0.2mH grid impedance. Figure

3.26 shows that the adaptive gain loop is added with the PR+HC current controller. The

control loop bandwidth is 700Hz less than 1/10 of the switching frequency. The phase

margin is 60 degree and gain margin is 5.37 dB. The magnitude at fundamental frequency

and 3rd and 5th order harmonics are well regulated. Figure 3.27 shows an adaptive gain loop

is added to the controller designed for 2.5mH. The control loop bandwidth is 441Hz, the

phase margin is 45.5 degree the stable margin for control system and gain margin is 5.21dB.

The reason the performance is not as good as 0.2mH is that with larger impedance the

72

resonant frequency moves to lower frequency so the bandwidth is limited to a lower

frequency. In figure 3.28, the Bode plot is drawn for the system with 1mH impedance.

It is very important to test the robustness of the controller to the variation of the grid

impedance. The proposed method uses the resonant frequency to determine the virtual

resistor gain. But practically, the grid impedance will not keep constant and always has

variations based on the load condition. If the variations of the grid impedance are still limited

by the virtual resistor set by the initial impedance, the adaptive tuning loop may not change

the virtual resistor value. In addition, if the damping gain is not precisely chosen based on the

derived equation the control parameter will not correspond to the grid impedance very well.

In other words, the virtual resistor gain Kad may not be the exact value for the grid

impedance. So the robustness of the proposed controller needs to be examined. In the

proposed system the grid impedances vary from 0.2mH to 2.5mH shown in Table I. Assume

+20% ~-20% variations of grid impedance and the control loop parameters are still the

parameters designed for 0.2mH and 2.5mH. The control loop performance for different grids

is investigated. For a stiff grid with 0.2mH impedance the grid impedance will change from

0.16mH to 0.24mH. For a weak grid with 2.5mH impedance the grid impedance will change

from 2mH to 3mH. In figure 3.29 the stiff grid control parameters designed for 0.2mH have

been applied to the control loop with 0.16mH and 0.24mH. Both control systems are still

stable. The control loop parameters for 0.16mH are phase margin 62.8 degree, bandwidth

718Hz and gain margin 5.20dB. For 0.24mH the control parameters are phase margin 58.4

degree, bandwidth 683Hz and gain margin 5.32dB. In figure 3.30 the weak grid control

parameters designed for 2.5mH have been applied to the control loops with 2mH and 3mH.

73

Both control systems are still stable. The control loop parameters for 2mH are phase margin

38.3 degree, bandwidth 534Hz and gain margin 3.93dB. For 3mH the control parameters are

phase margin 49.2 degree, bandwidth 377Hz and gain margin 6.32dB. Based on the above

controller design and robustness analyses we can predict that proposed adaptive resistor

controller can make the control loop stable even with the parameters mismatch or the

variation of the grid impedance. But the control loop performance is compromised, especially

at the weak condition. In the next section, the simulation and experimentation based on all

the grid conditions mentioned here will be conducted to verify the proposed control method.

Bode Diagram

Frequency (Hz)

-100

-50

0

50

100

System: GGain Margin (dB): 5.37At frequency (Hz): 1.57e+003Closed Loop Stable? Yes

Mag

nitu

de (d

B)

101

102

103

104

105

-360

-315

-270

-225

-180

-135

-90

-45

System: GPhase Margin (deg): 60.4Delay Margin (sec): 0.000239At frequency (Hz): 701Closed Loop Stable? Yes

Phas

e (d

eg)

Figure 3.26 Bode plot of control loop with 0.2mH impedance and with adaptive virtual resistor control

74

Bode Diagram

Frequency (Hz)

-200

-150

-100

-50

0

50

100System: GGain Margin (dB): 5.21At frequency (Hz): 776Closed Loop Stable? Yes

Mag

nitu

de (d

B)

101

102

103

104

105

-360

-315

-270

-225

-180

-135

-90

-45

System: GPhase Margin (deg): 45.5Delay Margin (sec): 0.000287At frequency (Hz): 441Closed Loop Stable? Yes

Phas

e (d

eg)

Figure 3.27 Bode plot of control loop with 2.5mH impedance and with adaptive virtual resistor control

Bode Diagram

Frequency (Hz)

-150

-100

-50

0

50

100

System: GGain Margin (dB): 5.13At frequency (Hz): 929Closed Loop Stable? Yes

Mag

nitu

de (d

B)

101

102

103

104

105

-360

-315

-270

-225

-180

-135

-90

-45

System: GPhase Margin (deg): 51Delay Margin (sec): 0.000284At frequency (Hz): 500Closed Loop Stable? Yes

Phas

e (d

eg)

Figure 3.28 Bode plot of control loop with 1mH impedance and with adaptive virtual resistor control

75

-200

-150

-100

-50

0

50

100

Mag

nitu

de (d

B)

101

102

103

104

105

-360

-315

-270

-225

-180

-135

-90

-45

0

Phas

e (d

eg)

Bode Diagram

Frequency (Hz)

L=0.2mHL=0.16mHL=0.24mH

Figure 3.29 Controller robustness analysis for stiff grid control loop with grid impedance 20% variation

Frequency (Hz)101 102 103 104 105-360

-315

-270

-225

-180

-135

-90

-45

0

Phas

e (d

eg)

-200

-150

-100

-50

0

50

100

Mag

nitu

de (d

B)

L=2.5mHL=2.0mHL=3.0mH

Figure 3.30 Controller robustness analysis for weak grid control loop with grid impedance 20% variation

76

Figure 3.31 Resonant frequency detection to determine grid impedance

Figure 3.32 Resonant frequency detection to determine grid impedance during impedance transient

77

3.6 Verification of Proposed Adaptive Virtual Resistor Controller with Different Grids

In this section, two grid conditions are examined which aims at investigating the

effectiveness of proposed controller. In case I the PHEV is connected with a stiff bus-0.2mH;

and in case II the PHEV is connected with a weak bus-2.5mH. The grid voltage is the actual

voltage from the feeder with THD around 3.8%~4%. The objective of using the actual

voltage is to test the ability of the proposed controller to reject disturbance from the grid side.

In case I, the grid is a stiff bus so the impedance, sets at 0.2mH, is very low. Note the grid

impedance can be even lower as in the case of an infinity bus but there will be no more

inductance and no resonance at all. The transformer’s leakage inductance is around 40uH

which does not affect the total impedance significantly. The simulation results with the

proposed adaptive resistor plugged into the control loop are shown in figure 3.33. In this

figure the converter-side current and grid-side current are shown. It can be seen that with the

damping function enabled in the control loop the high frequency resonance is mitigated

effectively.

The experimental results in figure 3.34 shows with proposed controller enabled in the loop

the resonance on the grid-side current and converter-side current is mitigated. In figure 3.35

the grid-side current and converter-side current without proposed method control are shown.

The spectrum of the grid-side current is analyzed and plotted in figure 3.36 and converter-

side current is not plotted because the grid-side current is the control objective. It can be seen

that the resonant frequency is around 25th~27th harmonics which matches with the grid

impedance value perfectly. The resonant frequency is calculated:

78

3 3

3 3 6

1 10 0.24 10 1618.67 26.9 601 10 0.24 10 50 10

f gres

f g f

L Lf Hz Hz

L L c

− −

− − −

+ × + ×= = = = ×

× × × × × × × (39)

In figure 3.37 the grid-side current and converter-side current with proposed control is

shown. In figure 3.38 the spectrum of the grid-side current is analyzed and it is obvious that

high frequency components (25th~27th harmonics) are eliminated. Finally in figure 3.39 the

grid current with proposed control method is compared with IEEE 519 harmonics standard.

The results show that both total harmonics and individual harmonic of grid current with the

proposed method meet the requirement of grid code.

0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2-15

-10

-5

0

5

10

15

0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2-15

-10

-5

0

5

10

15

converter current

grid current


79

Figure 3.34 Converter-side current and grid-side current with the proposed controller enabled (curve1:

converter-side current; curve2: grid-side current; curve3: command to enable the proposed control)

Figure 3.35 Converter-side current and grid-side current without the proposed controller (curve1: converter-side

current; curve2: grid-side current)

80

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%

1st 3rd 5th 7th 9th 11th 13th 15th 17th 19th 21th 23th 25th 27th 29th

Current Spectrum

Figure 3.36 Spectrum of grid-side current without the proposed controller

Figure 3.37 Converter-side current and grid-side current with the proposed controller (curve1: converter-side

current; curve2: grid-side current)

81

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%


Current spectrum

THD

Figure 3.38 Spectrum of grid-side current with the proposed controller enabled

0%

1%

1%

2%

2%

3%

3%

4%

4%

5%

3rd

5th

7th

9th

11th

13th

15th

17th

19th

21th

23th

25th

27th

29th

31th

33th

35th

37th

39th

IEEE 519 proposed controller

Figure 3.39 Spectrum comparison of grid-side current with IEEE 519 standard

82

In case II, the proposed controller is investigated with a weak bus. Here the weak bus

means very high value grid impedance which will make the resonance frequency very low. In

this paper the grid inductance is set at 2.5mH. Since the resonant frequency is in the low

frequency range and the crossover frequency must be set before the resonant peak, the

system bandwidth will be limited. The simulation results are shown in figure 3.40 with the

converter-side current and grid-side current. The experimental results in figure 3.41 show

that with the proposed control enabled in the loop, the resonance on the grid-side current and

converter-side current is eliminated. In figure 3.42 the grid-side current and converter-side

current without the proposed control are shown. The spectrum of the grid-side current is

analyzed and plotted in figure 3.43. The resonant frequency is around the 14th harmonics

which matches with the current grid impedance value.

3 3

3 3 6

1 10 2.54 10 840.69 14 601 10 2.54 10 50 10

f gres

f g f

L Lf Hz Hz

L L c

− −

− − −

+ × + ×= = = = ×

× × × × × × × (40)

In figure 3.44 the grid-side current and converter-side current with proposed control are

shown. In figure 3.45 the spectrum of the grid-side current is analyzed and the high

frequency components are eliminated after proposed control is enabled. Finally in figure 3.46

the grid current with proposed control method is compared with IEEE 519 harmonics

standard. The results show that total harmonics and individual harmonic of grid current with

the proposed method meet the requirement of grid code.

83

0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3-40

-20

0

20

40

0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3-30

-20

-10

0

10

20

30

Time

Grid current

Converter-side current


84

Figure 3.41 Converter-side current and grid-side current with the proposed controller enabled (curve1:

converter-side current; curve2: grid-side current; curve3: command to enable the proposed control)

Figure 3.42 Converter-side current and grid-side current without the proposed controller (Red curve: converter-

side current; Purple curve: grid-side current)

85

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%


THD

THD

Figure 3.43 Spectrum of grid-side current without the proposed controller enabled

Figure 3.44 Converter-side current and grid-side current with the proposed controller enabled (Red curve:

converter-side current; Purple curve: grid-side current)

86

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%


THD

THD

Figure 3.45 Spectrum of grid-side current with the proposed controller enabled

0%

1%

1%

2%

2%

3%

3%

4%

4%

5%

3rd

5th

7th

9th

11th

13th

15th

17th

19th

21th

23th

25th

27th

29th

31th

33th

35th

37th

39th

IEEE 519 proposed controller

Figure 3.46 Spectrum comparison of grid-side current with IEEE 519 standard

87

3.7 Summary of Chapter Three

In this chapter the challenge of integration of PHEVs with a large set of grid impedances

is described first. An adaptive virtual resistor control is proposed to solve the high frequency

resonance issue. The modeling of the control loop is derived. The controller design and

tuning guideline is presented. This virtual resistor loop can be plugged into the controller and

tuned automatically with the grid impedance. It can allow the PHEV controller to work with

a wide range of grid impedances. Symbolic case studies have been conducted to verify the

proposed controller. The stiff grid, weak grid and a grid in the medium have been examined.

The proposed control method eliminates the high frequency resonance effectively. This

proposed method greatly enhances the performance for large adoption of PHEVs into the

grid.

88

Chapter Four New Inductor Current Control based on Active Harmonics

Injection for Plug-in Hybrid Electric Vehicles’ Vehicle to Home Application

4.1 Review of Control Methods for Single Phase Inverter

An off-grid application (Vehicle to Home function) performs as a line-interactive UPS

[142]. The converter is shunt into the system to supply backup power during grid faults. So

control methods for a single phase inverter can be used. The first step is to analyze the

existing control methods for single phase inverter application.

Based on the control frame, the control method can be divided into two groups: stationary

frame which uses the instantaneous value and synchronous frame which uses DQ

transformation. For the DQ transformation, a faked imaginary axis can be used to form the

DQ together with a real axis [143]. Another way of doing this is to command the output

voltage and capacitor current to be DQ axis because these two values are naturally

perpendicular to each other. The new transformation in a three-dimension method for

multiple H-bridge legs is able to achieve good performance [144]. Without considering the

control frames, many control theories and methods have been applied to control single phase

or three phase inverter. A robust controller based on adaptive theory and dissipativity theory

is proposed in [145-147]. Dead-beat adaptive hysteresis current control is used as the current

loop for the inverter [148] and an improved deadbeat current controller is proposed in [149].

The control delay caused by digital processors is minimized to achieve high performance for

the inverter [150]. The repetitive controller is proposed to compensate for the harmonics of

the output voltage [151-153]. Multiloop structure with the digital predictive control is

89

proposed for inverter control [154]. A synchronous frame controller with the individual

compensation blocks is proposed to eliminate low-order harmonics of the output voltage

[155], and a similar method is proposed for the active filter application [156]. Beyond the

complex control theories, one good way to classify the control methods is based on their

feedback signals [157]. As we know, a perfectly sinusoidal output voltage is the ultimate goal

for an inverter. However, normally a double-loop control structure is adopted for the inverter

control. An outer voltage loop is used to regulate output voltage while the inner current loop

is intended to improve the dynamic speed for the load transient. To sense the control signal,

for the outer loop the output voltage should be measured and monitored with precision.

Regarding the inner current loop, several choices can be made, which bring us up to four

methods. Based on the sensed current signal, the control methods are inductor current

feedback control, capacitor current feedback control, load current feedback control and

combined inductor current and load current feedback control. The concept ‘back-EMF’

decoupling is also applied to these control methods [158]. This decoupling method can be

considered a type of feedforward control by adding the output voltage signal to the control

signal together to generate PWM signals. The advantage of this concept is that output voltage

is constant even during the load transient so the control parameters don’t need to be adjusted

drastically. This also allows the control to be easily tuned. This loop can be used to decouple

the impact of the DC bus on the controller. The last feedforward part plays a less important

role in the loop. It is added to the voltage command in order to compensate for the voltage

drop across the inductor especially when the load is heavy and voltage drop across the

inductor is not small. But the total value of this part only account for 1/1000 of the total

90

voltage command. Thus when a resonant type controller is used in the voltage loop and the

resonant gain is set to a higher value this feedforward part is unnecessary.

Among four control methods, the capacitor current feedback method is verified to be the

best control method with good steady-state and dynamic performance [159]. The capacitor

current feedback control is first proposed by Ryan [158]. This method uses an inexpensive

current transformer to sense the current through the filter capacitor and utilizes this signal as

the control feedback signal. A filter should be applied to filter out the high frequency

harmonics on the capacitor current otherwise these harmonics will be transmitted into the

current control and propagated thus polluting the entire loop. This method’s structure is

output voltage loop and capacitor current loop. One way to understand this method is without

considering high frequency harmonics, that the capacitor current is always a sinusoidal

current. This fundamental current does not change much when connected with any type of

load and if this current is well controlled, the output voltage which is the integration of the

capacitor current will be automatically regulated to a sinusoidal voltage. However, this

control method still has drawbacks in that this method cannot sense the inductor current to

protect the converter. An enhanced Luenberger observer is proposed in place of sensing the

capacitor current [157].

Inductor current feedback control senses the inductor current as the inner loop control

variable. Although the control performance is not as good as capacitor current based control,

this method provides superior protection. Whether there is a large current overshoot on the

inductor or a load short-circuit fault the control method can guarantee the converter stage is

safe. The load current control directly senses the load current as the control variable, but it

91

can not protect power devices if a fault occurs on the converter side e.g., resonant oscillation

or wrong control logic. When inductor current feedback is used disturbance input decoupling

also known as disturbance feedforward control, can be implemented. This method

incorporates with load current sensing to reject the load disturbance effectively. This method

senses both inductor current and load current as the feedback variables; its control

performance is promising. So this method can be considered an alternative to capacitor

current feedback, because capacitor current is the sum of the inductor current and load

current. With more current sensors the protection is also achieved but the cost of the total

system increases. This may compromise this method. To eliminate this extra sensor, a load

current prediction algorithm can be used [157]. Three basic control structures without

disturbance decoupling are shown in figures 4.1, 4.2 and 4.3 respectively.

outV1

sLfi 1

fscci

LrLoadi

( )cG s ( )PIG s

ci

outV

outV

*out

V

outV

Figure 4.1 Capacitor current feedback control

outV1

sL1

fscci

LrLoadi

( )cG s ( )PIG s outV

outV

*out

V

fi outV

fi

Figure 4.2 Inductor current feedback control

92

outV1

sL1

fscci

LrLoadi

( )cG s ( )PIG s outV

outV

*out

V

outV

fi

fi

sL

Figure 4.3 Inductor and load current feedback control method

In this chapter a new control method based on active harmonics injection and inductor

current feedback is proposed. The reason for choosing inductor current feedback is because

inductor current is the essential variable for protection. With the active harmonics injection,

control performance is improved especially for a nonlinear type of load. Moreover inductor

current feedback and capacitor current feedback are compared and the advantages of inductor

current are analyzed and verified. Inductor current feedback can limit the current overshoot at

the load transients which may cause the inductor core saturation. So with the inductor current

feedback control higher switching frequency and smaller passive components can be used to

provide an optimized design for the inverter stage.

4.2 Theoretical Analysis of the Proposed Control Method

Inductor current feedback control senses the inductor current as the inner control variable.

The outer voltage loop supplies a sinusoidal voltage reference to the inner loop; however,

when a nonlinear load such as a diode bridge rectifier is connected with the inverter the

inverter needs to provide high percentage of odd-order harmonics to the load. This odd-order

harmonics challenges the control loop design because the inner loop reference should have

the sinusoidal component for the output voltage and odd-order harmonics to cancel out the

harmonics brought by the inductor current. Theoretically, the output voltage loop can be

93

designed with a very high bandwidth which can cover higher order harmonics e.g. 15th, 17th

or even higher. However, in actual control loop design, the bandwidth is very limited,

especially for the outer voltage loop. The voltage loop is only above the fundamental

frequency. The inner current loop has a much faster bandwidth. So, according to this reason,

it is usually very easy to get good output voltage waveforms in simulation but the waveforms

are distorted in experiment. Since the outer loop is always very limited only dealing with the

fundamental frequency, the harmonics coming with the inductor current will pollute the

whole loop and output voltage as well. One effective way to reduce the harmonics on the

capacitor is to sense the capacitor current as the feedback signal which is the capacitor

current feedback control as discussed previously. Based on inductor current feedback control,

an extra harmonics injection loop is proposed as a plug-in to the original loop.

1sL

fi 1

fscci

Lr

( )vG s ( )iG s*

outV

Loadi

outVoutV

outV

outV( )PIG shV

*h

V

fi

Figure 4.4 Control block of the proposed method based on active harmonics injection

First the inductor current equals the sum of the load current and the capacitor current, and

the capacitor current contains the fundamental component and harmonics components.

L Load c Load cf chi i i i i i= + = + + (1)

94

The inverter output voltage equals the sum of the output voltage and the voltage drop on

the inductor.

1 1( ) ( ) ( ) ( )pwm L out Load cf ch cf ch Load cf chv i ls v i i i ls i i i ls i i lscs cs

= ⋅ + = + + ⋅ + + ⋅ = ⋅ + + ⋅ + (2)

With simple mathematic manipulation it can be seen that if the inverter output voltage can

generate harmonics voltage of the capacitor the output voltage will be sinusoidal. So a

harmonics extraction block is used to get the output voltage harmonics because these

harmonics are directly related to the harmonics current on the capacitor.

1 1( ) ( )pwm ch Load cfv i ls i ls i lscs cs

− ⋅ + = ⋅ + ⋅ + (3)

1h chv i

cs= ⋅ (4)

After the harmonics voltage is detected and extracted, these harmonics will go to the loop

which controls the amount of harmonics injection. Since the ultimate goal is to eliminate the

harmonics current on the capacitor so the harmonics voltage reference is set to zero. The

injection loop parameters are adjusted to make the loop output equal the additional item on

the left side of the equation (3). Based on the above analysis an active harmonics injection

loop can be added in Figure 4.4. This loop first extracts the harmonics from the output

voltage and forces the extracted harmonics to equal zero with the reference voltage setting at

zero. The generated harmonics are injected to be combined with the inner current loop output

as the modulation signal This harmonics output will cancel the load harmonics in such a way

95

that the capacitor current will have few or even no harmonics components. With no distortion

on the capacitor current the output voltage will be perfectly sinusoidal.

With this control method, one important function is to detect and extract the harmonics.

Similar to the process used in an active filter [160, 161] the voltage signal can be transformed

into the synchronous frame and transmitted through a high pass filter. This is a suitable

solution for three-phase applications. However for single phase applications another method

is used. An Enhanced PLL [162] is used to sense the output voltage and generate a sinusoidal

voltage reference which follows the output voltage instantaneously. A peak detection

function is used to detect and follow the peak value of the output voltage and multiplies it by

with the sinusoidal reference to form a modified output voltage reference. The voltage

difference between the instantaneous output voltage and the modified voltage reference is the

extracted harmonics. The reason to use peak diction is to make sure there are no fundamental

components in the injection loop to affect the control accuracy and Kp is used to compensate

the error from both the sensing and the conditioning process. The harmonics extraction block

is shown in figure 4.5. A similar idea can be designed and implemented in figure 4.6. Both of

the methods inject the harmonics to the control loop, and the harmonics are controlled by the

output voltage. The only difference is the point where the harmonics are injected. The good

thing is that this loop doesn’t have bandwidth limitation like the outer voltage loop. So it can

be designed be fast enough to cover high order harmonics.

The experiment is conducted with the conventional inductor current control and the

proposed control method. The nonlinear load is a single phase diode-bridge rectifier with the

filter inductor and dc load at the dc bus. The output voltage is 120V, and the load peak

96

current is 14A. The results with the conventional control and the proposed control method

are shown in figure 4.7 and 4.8 respectively. The output voltage THD with the conventional

control method is 6.11% while with the proposed control the output voltage THD has been

improved to 4.68%. Figure 4.9 shows the capacitor current spectrum comparison between

two control methods. The performance of the proposed controller is further examined by

comparing the harmonics with IEC standards for UPS: IEC 62040-3 [192, 193]. In figure

4.11, the harmonics of the output voltage regulated with conventional control method are

compared with IEC 62040-3.

pk

hVoutV

Figure 4.5 Harmonics detection and extraction block

1sL

fi 1

fscci

Lr

( )vG s ( )iG s*

outV

Loadi

outVoutV

outV

outV( )PIG shV

fi

Figure 4.6 Active harmonics injection before the inner current loop

97

Figure 4.7 Nonlinear load tests with the proposed control method (blue curve: output voltage 200V/dim; Purple

curve: voltage error between the reference and actual voltage; Green curve: load current 10A/dim)

Figure 4.8 Nonlinear load tests with inductor current feedback control (blue curve: output voltage 200V/dim;

Purple curve: voltage error between the reference and actual voltage; Green curve: load current 10A/dim)

Output

Load current

Voltage error

Output

Load current

Voltage error

98

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

THD 3rd 5th 7th 9th 11th 13th 15th 17th 19th 21th 23th 25th 27th 29th

with injection without injection

Figure 4.9 Comparison of capacitor current spectrum: the proposed method and conventional controller

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

3rd 5th 7th 9th 11th 13th 15th 17th 19th 21th 23th 25th 27th 29th

proposed controller conventional controller IEC 62040-3

Figure 4.10 Comparison of output voltage spectrum: the proposed method, conventional controller and

IEC62040-3 Standard

99

4.3 Steady State Operation and Dynamic Response of the Proposed Controller

According to the analysis in the previous section, the controller performance should be

superior to the inductor current feedback control method especially for nonlinear load. Four

types of loads have been used to examine the proposed control method. They are a 1kW

resistive load, no load, 1kW resistor and 2.5mH RL and nonlinear load. First the simulation

results are shown in figure 4.11, figure 4.13, figure 4.15 and figure 4.17 respectively. After

the simulations are conducted, the experiment is conducted based on the same loads

mentioned above. The experimental results are shown in figure 4.12, figure 4.14, figure 4.16

and figure 4.18 respectively. In figure 4.19 the actual output voltage and the output voltage

reference are shown. In this figure the purple curve is the voltage error between the actual

output voltage and the voltage reference. It can be seen that the voltage error only has the

high frequency components and the fundamental frequency component is hardly found. This

will prove the accuracy of the proposed control method. The output voltage THD for

different types of loads is summarized in table 4-1.

100

0.3 0.305 0.31 0.315 0.32 0.325 0.33 0.335 0.34 0.345 0.35-200

0

200

0.3 0.305 0.31 0.315 0.32 0.325 0.33 0.335 0.34 0.345 0.35-10

0

10

0.3 0.305 0.31 0.315 0.32 0.325 0.33 0.335 0.34 0.345 0.35-20

0

20

0.3 0.305 0.31 0.315 0.32 0.325 0.33 0.335 0.34 0.345 0.35-5

0

5

Figure 4.11 Simulation 1kW load test with the proposed method (curve 1: output voltage; curve 2: load current;

curve 3: inductor current; curve 4: capacitor current)

Figure 4.12 Experiment 1kW load test with the proposed method (Green curve: load current 20A/dim; Blue

curve: output voltage 200V/dim; Red curve: inductor current 20A/dim; Purple curve: capacitor current

10A/dim)

101

0.15 0.155 0.16 0.165 0.17 0.175 0.18 0.185 0.19 0.195 0.2-200

0

200

0.15 0.155 0.16 0.165 0.17 0.175 0.18 0.185 0.19 0.195 0.2-10

0

10

0.15 0.155 0.16 0.165 0.17 0.175 0.18 0.185 0.19 0.195 0.2-5

0

5

0.15 0.155 0.16 0.165 0.17 0.175 0.18 0.185 0.19 0.195 0.2-5

0

5

Figure 4.13 Simulation no load test with the proposed method (curve 1: output voltage; curve 2: load current;

curve 3: inductor current; curve 4: capacitor current)

Figure 4.14 Experiment no load test with the proposed method (Green curve: load current 20A/dim; Blue curve:

output voltage 200V/dim; Red curve: inductor current 20A/dim; Purple curve: capacitor current 10A/dim)

102

0.15 0.155 0.16 0.165 0.17 0.175 0.18 0.185 0.19 0.195 0.2-200

0

200

0.15 0.155 0.16 0.165 0.17 0.175 0.18 0.185 0.19 0.195 0.2-10

0

10

0.15 0.155 0.16 0.165 0.17 0.175 0.18 0.185 0.19 0.195 0.2-20

0

20

0.15 0.155 0.16 0.165 0.17 0.175 0.18 0.185 0.19 0.195 0.2-5

0

5

Figure 4.15 Simulation RL test 1kW resistive load and 2.5mH inductor with the proposed method (curve 1:

output voltage; curve 2: load current; curve 3: inductor current; curve 4: capacitor current)

Figure 4.16 Experiment RL test 1kW resistor load with 2.5mH inductor test with the proposed method (Green

curve: load current 20A/dim; Blue curve: output voltage 200V/dim; Red curve: inductor current 20A/dim;

Purple curve: capacitor current 10A/dim)

103

0.15 0.155 0.16 0.165 0.17 0.175 0.18 0.185 0.19 0.195 0.2-200

0

200

0.15 0.155 0.16 0.165 0.17 0.175 0.18 0.185 0.19 0.195 0.2-20

0

20

0.15 0.155 0.16 0.165 0.17 0.175 0.18 0.185 0.19 0.195 0.2-20

0

20

0.15 0.155 0.16 0.165 0.17 0.175 0.18 0.185 0.19 0.195 0.2-5

0

5

Figure 4.17 Simulation nonlinear loads with the proposed method (curve 1: output voltage; curve 2: load

current; curve 3: inductor current; curve 4: capacitor current)

Figure 4.18 Experiment Nonlinear load test with the proposed method (Red curve: DC bus voltage 200V/dim;

Purple curve: load current 10A/dim; Blue curve: output voltage 200V/dim; Green curve: capacitor current

10A/dim)

104

Figure 4.19 Experiment nonlinear load test with the proposed method (Purple curve: output voltage error; Blue

curve: output voltage 200V/dim; Red curve: output voltage reference; Purple curve: load current 10A/dim)

Table 4-1 Output voltage with different types of load

Load Condition Output Current THD [%] Output Voltage THD [%]

No Load - 2.90%

1kW resistive load - 2.68%

RL load 3.59% 3.01%

Nonlinear load 71.7% 4.68%

After the steady-state test the dynamic response of the proposed controller is examined

with a 1kW load transient. It should be mentioned that the proposed method belongs to the

inductor current based control group. The proposed method focuses on improving the

105

harmonics compensation capability for the inductor current feedback control but it is not

designed to improve the system dynamic response. However with the simulation results and

experimental results it can be seen that the response of the proposed controller is still good. A

1kW load transient test is first simulated in figure 4.20. Then the experimental results are

shown in figure 4.21, the response time for the output voltage after the load transient is

approximately 3~4 cycles. More results show the voltage error during the load transient in

figure 4.22 in simulation and figure 4.23 in experiment.

0.22 0.23 0.24 0.25 0.26 0.27 0.28-200

0

200

0.22 0.23 0.24 0.25 0.26 0.27 0.28-20

0

20

0.22 0.23 0.24 0.25 0.26 0.27 0.28-20

0

20

0.22 0.23 0.24 0.25 0.26 0.27 0.28

-10

0

10

Figure 4.20 Simulation a 1kW load transient for dynamic response test of the proposed controller (curve 1:

output voltage; curve 2: load current; curve 3: inductor current; curve 4: capacitor current)

106

Figure 4.21 Experiment a 1kW load transient for dynamic response test of the proposed controller (Green curve:

load current 10A/dim; Blue curve: output voltage 200V/dim; Red curve: inductor current 20A/dim; Purple

curve: capacitor current 10A/dim)

0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3-200

0

200

0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3-20

0

20

0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3-20

0

20

0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3-0.2

0

0.2

Figure 4.22 Simulation a 1kW load transient for dynamic response test of the proposed controller

107

Figure 4.23 Experiment a 1kW load transient for dynamic response test of the proposed controller (Green curve:

load current 20A/dim; Red curve: inductor current 20A/dim; Blue curve: output voltage 200V/dim; Purple

curve: output voltage error)

4.4 Investigation of Inductor Current Transient Response with Different Controllers

The proposed method is similar to the inductor current controller during transient because

its third loop compensates only the harmonics. So in this section the comparison focuses on

two major control methods: inductor current and capacitor current. Although it has been

already proven that the capacitor current feedback control has better steady-state and

dynamic state performance [159], an issue that needs to be addressed is that the inductor

current feedback control has the capability to limit the inductor current overshoot during the

load transient which has not yet been discussed. Although it is not addressed, the capability

to limit the inductor current overshoot during the load transient is very important, because

current overshoot may lead to the saturation of the magnetic cores. This issue becomes even

108

more critical with the claim that in a low power rating application (the power rating in the

range of tens of kW) the magnetic cores are required to operate close to the saturation point

on the B-H curve to reduce the cost and the size [163, 164].

To begin with, assume the stationary frame is used and the load transient happens at the

moment when the output voltage reaches the peak value because the capacitor voltage is 90

degree lag of the capacitor current. When the current goes to zero the voltage reaches the

peak value so at this time the load transient provides the highest current overshoot in of all

the transients. In the analysis the load is set as a resistive load for simplification. The detailed

analysis of capacitor current feedback control starts from the inner current loop. Assuming

the sampling frequency equals the switching frequency the load transient can be detected by

the digital processor immediately. After the transient goes into the interrupt of the processor

the inner loop feedback signal changes first, because during the load change it is the

capacitor that supplies the current. As seen in Figure 4.26 at the moment of transient the

capacitor current has a significant drop in the opposite direction due to discharge. The inner

loop reference is subtracted from the feedback signal to obtain an error and this error is sent

to the inner current loop. As the feedback signal decreases, the inner loop output increases

and the inverter output voltage increases. The next important event is that the output voltage

drops due to the discharge of the capacitor. So the outer loop generates an increased

reference signal for the inner loop this will even further increase the inner loop error which

will lead to a higher converter output. As we know the voltage on the inductor is the

difference between the converter output and the output voltage. With the converter output

increasing and the output voltage decreasing if the inductor value is further reduced the

109

current overshoot on the inductor will be further increased, because the nature of this control

does not provide any limitation on the inductor current. Note that the inner current loop with

different inductor value can be varied. A slow inner loop may be used to mitigate the current

overshoot however in this way the control will suffer from a slow response.

The next step is to analyze the transient for the inductor current feedback control. During

the transient, the inductor current cannot change immediately so the changing variable in the

control loop is only the output voltage drop due to the capacitor discharge. However when

the inner loop reference increases due to the outer voltage loop the inner current feedback

signal also increases because the inductor current increases. So these two increasing values

will compete to get an error which will go through the inner loop to generate the converter

output. Obviously the error will be increased rather than being decreased. Otherwise the

converter output won’t increase and the control loop becomes a positive feedback. But

compared to the capacitor current control the trend of this increasing is still low because of

an increasing feedback signal in the inner loop. In both control methods the outer voltage

loop provides an increasing reference for the inner current loop. The capacitor current control

makes the inner loop error increase, while the inductor current control counteracts this

increase to make the inner loop error rise at a slower rate because of the increasing inductor

current. With a smaller inductor the inductor current overshoot intends to rise higher however

this will in turn make the current feedback increase higher than the inner loop error becomes

lower, which in turn limits the rise of the inductor current. So with a smaller inductor the

inductor current control can limit the overshoot current. It also can be seen from another

angle that the dynamic response of the capacitor current feedback has already been proven to

110

be faster than the inductor current feedback because the inner loop error of the capacitor

current feedback is much greater than the inductor current feedback otherwise it cannot

respond faster than the inductor current feedback control. This can also be considered the

justification for the above analysis.

Similar to the concept ‘dynamic stiffness’ which is defined and derived by Ryan [157], the

relationship between the inductor current and the load current are derived using small signal

model. The same relationship has been used in the DVR application for dynamic response

analysis [165]. This relationship is used to evaluate the inductor current at the point of the

load current transient. The inductor current to the load current with proposed method is

derived in equation (5), while the relation for the capacitor current control is derived in (6).

1 2

1 2 1

4 3 2 1

6 5 4 3 2 1

1 1( ) ( ) ( ) ( )

1 1( ) ( ) ( ) ( ) ( )

pr pi H piL

Loadpr pi H pi pi

G s G s G s G si cs csi G s G s G s G s G s ls

cs csAs Bs Cs Ds E

Fs Gs A s B s C s D s E

⋅ + ⋅=

⋅ + ⋅ + +

+ + + +=

′ ′ ′ ′ ′+ + + + + +

(5)

1 2

1 1 1 1 2 2

2 21 1 1 1 1 1 2 2

2 2 21 1 1 1 2

21

;

;

;

;

pr p p

pr p c pr p h p r pr i p c i

pr p f pr p c h p r h pr i c pr i h r i p f i c

pr p h f pr i f pr i c h r i h i f

pr i h f

A k k k

B k k k k f k k k k k k

C k k k k f k k f k k k k f k k k k

D k k f k k k k f k k f k

E k k f

ω ω

ω ω ω ω ω

ω ω ω ω

ω

= +

= + + + + +

= + + + + + + +

= + + + +

=

111

21 2 1 1 1

21 1 1 1 2 2 1 1 1

21

2 21 1 1 1 1 1 2 2

;

;

pr p p p c p h i f c h

pr p c pr p h p r pr i p c i p f p c h i c

i h h f

pr p f pr p c h p r h pr i c pr i h r i p f i c

p

A k k k k c k f c k c lc lc f

B k k k k f k k k k k k k c k f c k c

k f c lcf

C k k k k f k k f k k k k f k k k k

k

ω ω ω

ω ω ω ω ω

ω

ω ω ω ω ω

′ = + + + + + +

′ = + + + + + + + +

+ +

′ = + + + + + + +

+ 2 21 1 1

2 2 2 21 1 1 1 2 1

21

1

;

;

;

h f i f i h c

pr p h f pr i f pr i c h r i h i f i h f

pr i h f

c h p

f c k c k f c

D k k f k k k k f k k f k k f c

E k k f

F lcG lc lcf k c

ω ω ω

ω ω ω ω ω

ω

ω

+ +

′ = + + + + +

′ =

== + +

Here prk and rk is the proportional and integration gain of the resonant controller for the

outer voltage loop, cω and fω is the cut-off frequency and the fundamental frequency of the

resonant controller respectively, 1pk and 1ik is the proportional and integration gain of the PI

controller for the inner current loop, 2pk and 2ik is the proportional and integration gain of the

PI controller for the harmonics injection loop hf is the cut-off frequency of the high-pass

filter.

From this equation we can see that F and G are so small that they can be ignored because

of the small value of inductor and capacitor. So the order for the denominator and the

numerator of this equation can be considered the same.

1 1

1 1

4 3 2 11 1 1 1

6 5 4 3 2 11 1 1 1 1 1 1

1 ( ) ( ) ( ) ( )

1 ( ) ( ) ( ) ( )

pr pi L piL

Loadpr pi L pi

G s G s G s G si csi G s G s G s G s ls

csA s B s C s D s

F s G s A s B s C s D s E

⋅ +=

⋅ + +

+ + +=

′ ′ ′ ′ ′ ′ ′+ + + + + +

(6)

112

1 1 1

1 1 1 1 1 1 1

2 2 21 1 1 1 1 1 1 1

2 21 1 1 1

;

;

;

pr p p L

pr p c pr p L p r pr i p L c i L

pr p f pr p c L p r L pr i c r i p L f i L f

pr p L f pr i L f pr i L

A k k k f c

B k k k k f k k k k k f c k f c

C k k k k f k k f k k k k k f c k f c

D k k f k k f k k f

ω ω

ω ω ω ω ω

ω ω

′ ′ ′= +

′ ′ ′ ′ ′ ′ ′ ′ ′ ′= + + + + +

′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′= + + + + + +

′ ′ ′ ′ ′ ′= + + 21 1 ;c r i L i L fk k f k f cω ω′ ′ ′+ +

21 1 1

1 1 1 1 1 1 1

2 2 21 1 1 1 1 1 1 1 1

1 1

;

;

;

pr p p L f c L

pr p c pr p L p r pr i p L c i L

pr p f pr p c L p r L pr i c pr i L f r i p L f i L c

pr p

A k k k f c lc lc f

B k k k k f k k k k k f c k f c

C k k k k f k k f k k k k f k k k f c k f c

D k k

ω ω

ω ω

ω ω ω ω ω ω

′ ′ ′ ′= + + +

′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′= + + + + +

′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′= + + + + + + +

′ ′ ′= 2 2 21 1 1 1

1

1

;

;;

L f pr i L f pr i L c r i L i L f

c L

f k k f k k f k k f k f c

F lcG lc lcf

ω ω ω ω

ω

′ ′ ′ ′ ′ ′ ′+ + + +

′=′ = +

Here prk′ and rk ′ is the proportional and integration gain of the resonant controller for the

outer voltage loop, cω and fω is the cut-off frequency and the fundamental frequency of the

resonant controller respectively, 1pk′ and 1ik′ is the proportional and integration gain of the PI

controller for the inner current loop, Lf is the cut-off frequency of the low-pass filter.

As we can see from the Bode plot drawn in Figure 4.24 the lower the inductor value used

the lower the inductor current overshoots will be. Inductor current overshoot is not directly

related to the inductor value. This is important because the trend is to have a smaller inductor

so that the current overshoot is not too high to cause core saturation. With the inductor

current as the feedback signal, the inductor current is well regulated. Note that this derivation

is not related with switching frequency. Even if the inductor is reduced and switching

frequency is kept unchanged the current overshoot can still be limited. In this way more

current ripples are generated which will cause more heating on the cables and loads. To avoid

the extra loss higher switching frequency can be applied.

113

Figure 4.24 Inductor current to load current with the proposed control method

Figure 4.25 Inductor current to load current with the capacitor current feedback control

114

Contrary to the Bode plot drawn in Figure 4.25 with the capacitor current the lower the

inductor value is used the higher the inductor current overshoot will be. This will impose a

challenge to the capacitor current based control because this method cannot limit the current

overshoot during the load transient. When advanced semiconductor devices which can handle

a higher switching frequency are applied to the inverter design, a lower inductor will be used

to optimize the system volume; however, with capacitor current control the current overshoot

will be increased with a smaller inductor and may cause core saturation. This is the drawback

of the capacitor current based controllers but the advantage of the inductor current based

controllers.

A 1kW load transient has been simulated and tested with the proposed controller using

three inductor values: 1mH, 0.5mH and 0.25mH. The illustrated simulation for the inductor

current overshoot during the load transient response is shown in figure 4.26. A 1mH and a

0.5mH inductor are tested. The inductor current overshoot with 1mH and 0.5mH are shown

in Figure 4.27 and Figure 4.28 respectively. As we can see, the current overshoot of both

cases are almost the same which is at about 15A. Using the capacitor current feedback

control method the same load transient test has been conducted. A 1mH and a 0.5mH

inductor are tested in the experiment. In Figure 4.29 and Figure 4.30 the same transient test is

conducted with the capacitor current feedback control. As we can see that at L=1mH the

inductor current overshoot is 17A however at L=0.5mH the inductor current overshoot has

been increased to 20A, which verifies the above analysis. Finally, based on the analysis, the

performance of the inductor current feedback control, capacitor current feedback control and

the proposed method is compared and summarized in table 4-2.

115

0.23 0.232 0.234 0.236 0.238 0.24 0.242 0.244 0.246-200

0

200

0.23 0.232 0.234 0.236 0.238 0.24 0.242 0.244 0.246-20

0

20

0.23 0.232 0.234 0.236 0.238 0.24 0.242 0.244 0.246

-10

0

10

0.23 0.232 0.234 0.236 0.238 0.24 0.242 0.244 0.246-20

0

20

Figure 4.26 dynamic response: output voltage, load current, capacitor current and inductor current (curve 1:

output voltage; curve 2: load current; curve 3: capacitor current; curve 4: inductor current)

116

Figure 4.27 Inductor current overshoot during the load transient with the proposed control method at L=1mH

Figure 4.28 Inductor current overshoot during the load transient with the proposed control method at L=0.5mH

117

Figure 4.29 Inductor current overshoot during the load transient with the capacitor current control at L=1mH

Figure 4.30 Inductor current overshoot during the load transient with the capacitor current control at L=0.5mH

118

Table 4-2 Performance comparison of the capacitor current feedback, the inductor current feedback and the

proposed method

Capacitor current

feedback

Inductor current

feedback

Proposed control

method

Steady-state

operation (linear

load)

Good Good Good

Harmonics

compensation

(nonlinear load)

Good Poor Good

Dynamic response Better Good Good

Current sensor

requirement

1 CT

1 LEM

1 LEM 1 LEM

Current overshoot

limitation

No Yes Yes

Further reduction of

Passive components

May cause core

saturation

Yes Yes

Over-current

protection

Needs an extra

current sensor

Integrated with

controller

Integrated with

controller

119

4.5 Summary of Chapter Four

In this chapter a new inductor current feedback controller based on active harmonics

injection is proposed for the stand-alone application of plug-in hybrid electric vehicle

application which can be also called vehicle to home application. This new controller can

improve the harmonics compensation capability for the controller which senses the inductor

current. The inductor current overshoot for both the capacitor current control and the

proposed controller is investigated. It is proven that the inductor current control can limit the

inductor current overshoot with an even smaller inductor. While using the capacitor current

control the current overshoot will be higher with a smaller inductor which may increase the

probability of core saturation. Therefore the proposed method will be used to optimize

passive components for the power stage design of the converter and further reduce the total

power stage volume and weight.

120

Chapter Five Power Management Strategy for Multiple Plug-in Hybrid Electric

Vehicles in FREEDM Smart Grid

5.1 Architecture of PHEV Integration with Solid State Transformer based Smart Grid

The Solid State Transformer (SST) is considered the key unit for power processing and

conversion in the distributed renewable energy internet—FREEDM system as shown in

figure 5.1. Within IEM (intelligent energy management) the role of SST is to interface with

and enable the active management of distributed energy resources, energy storage devices

and different types of loads at either household level or industry level. The basic idea of an

SST is to use a power electronics converter to replace the conventional bulky and non-

intelligent transformer. In addition the SST has the capability to deal with utility issues such

as voltage sag, power factor correction, etc [63]. At the household level one SST converts a

12 kV distribution level voltage to a 120V/240V split-phase voltage for a residence.

Figure 5.1 FREEDM smart grid and Solid State Transformer based Intelligent Energy Management System [63]

As the key element for distributed energy storage device (DESD) at level I and II

charging, PHEV will interface with the inverter stage of the SST. In this system a solid state

121

transformer supplies power to the chargers of PHEVs. The charger has two power stage

(AC/DC and DC/DC) and its model and control algorithm has been developed in the

previous chapters. So the scenario of this system is that the source of this system is the

inverter stage of SST and the loads are parallel operated PHEVs. Considering only PHEV

charging functions, power management strategy is needed when the total possessive power

requirement exceeds the limit of the inverter of the SST. The proposed method will be

analyzed and system modeling will be presented in the next sections.

5.2 The Issue of Multiple Plug-in Electric Vehicles Connected with Solid State Transformer

A smart transformer (solid state transformer) is used as intelligent energy management for

the FREEDM smart grid. Its primary goal is to enable power processing and management. A

distribution level solid state transformer is designed to supply power to 1~2 US families

based on power requirements and consumption. A SST (solid state transformer) is able to

supply power to multiple plug-in hybrid electric vehicles. However there is one problem for

the power management. If the power demand of plug-in vehicles is higher than the SST and

there is no effective communication and power allocation method, the SST voltage will

collapse. This will cause problems for other loads supplied by the same SST. This issue can

be resolved with two-way communication between the vehicle and the SST. In addition a

power allocation algorithm should be applied to ensure that the total demand power will not

exceed the safe operating limit of the SST. From the power electronics control point of view,

if a better control method is proposed without the need for communication, it will be a very

helpful and promising method. Because communication methods may not work or sometimes

experience delays. A power electronics converter operates rapidly (in kHz range), so a fast

122

control method is desired to deal with power management at the power converter level rather

than the system level. In other words, a smart grid such as FREEDM grid needs a hierarchy

controller which includes very high level control including a system plan and real time

allocation algorithm and also power electronics level control to guarantee the power

management. In this chapter, a new power management method for multiple PHEVs/PEVs

operating in FREEDM smart grid is proposed. It will achieve automatic power allocation

when the possessive power demand of the vehicles is higher than the power limitation of

SST. This method can be used as a converter level control strategy to deal with system

instability in the worst case scenario. The worst case means the system level control and

communication is disabled.

In summary, in this chapter the research focuses on resolving the following issues:

1) Voltage collapse when the possessive load (demand of charging PHEV) exceeds the

capability of SST. Power electronics level control strategy to avoid system collapse;

2) Power management relies on communication; its performance suffers from the delay

and congestion resulting from the communication method;

3) PHEV needs the guidance to adjust the power in a distributed manner, not based on

centralized command;

4) How to enable load management with the help of PHEV.

The interface between the SST and the PHEV chargers is the inverter stage of the SST.

The control loop model is shown in figure 5.2. The inverter controller includes an outer

voltage loop and an inner current loop. First the inner current loop is analyzed and modeled.

123

Figure 5.2 Control loop model of inverter stage of solid state transformer

In the inner current loop the Gcomp_c is the inner PI controller and L is the filer inductor,

r is the winding resistance of the inductor. So the closed loop transfer function for the inner

current is written as:

11

1 12

1 1 11

1 1( ) ( )( ) 1 1 ( )1 ( ) 1 ( )

ipi p

p iinner

i p ipi p

kG s k k s kLs r s Ls rG s k Ls k r s kG s kLs r s Ls r

⋅ + ⋅ ++ += = =+ + ++ ⋅ + + ⋅

+ +

(1)

The Bode plot is drawn in figure 5.3 and as we can see that it can be consider a first order

system with a corner frequency around 2kHz. This is also the bandwidth of the inner current

loop. The next step is drawn the Bode plot for both of inner and outer loop. In order for the

compensator of the outer voltage loop to increase the DC gain at 60Hz, a proportional

resonant controller is used as Gcomp_v. So the system open loop transfer function is written

as:

_1( ) ( ) ( ) ( )outer comp v inner d

f

G s G s G s G ssC

= ⋅ ⋅ ⋅ (2)

In this equation, the Gd is the system delay and Cf is output filter capacitor. The entire

system Bode plot is shown in figure 5.4. The bandwidth is 844Hz around 1/10 of the

switching frequency and phase margin is 50 degree. The dc gain at 60Hz is boosted to 49dB

124

which reduces the stead-state error. With the open loop transfer function derived the close

loop transfer function is plotted in figure 5.5. The output impedance is important for the

inverter because the lower the output impedance has less of an effect on load current impacts

on the output voltage. The output impedance is derived based on the passive components.

fconv f out

diL u i r u

dt= − ⋅ − (3)

outf f Load

duc i idt

= − (4)

From control loop another equation can be derived:

_( ) ( ) ( )conv ref out comp v inneru u u G s G s= − ⋅ ⋅ (5)

Substitute the equation (3) and (4) into equation (5) and the relationship of load current,

output voltage and voltage reference can be derived:

_2 2

_ _

( ) ( )( ) ( ) 1 ( ) ( ) 1

comp v innerout ref Load

comp v inner f comp v inner f

G s G s Ls ru u iG s G s Ls c s G s G s Ls c s

⋅ += ⋅ − ⋅

⋅ + + + ⋅ + + + (6)

As we can see from equation (6) that if the voltage loop has high magnitude and the

output impedance is very low the output voltage will equal the reference voltage. The output

impedance can be written as:

2_ ( ) ( ) 1out

comp v inner f

Ls rZG s G s Ls c s

+=

⋅ + + + (7)

125

-35

-30

-25

-20

-15

-10

-5

0

5

Mag

nitu

de (d

B)

100 101 102 103 104 105-90

-60

-30

0

Phas

e (d

eg)

Bode Diagram

Frequency (Hz)

Figure 5.3 Bode plot of close loop of inner current loop

Bode Diagram

Frequency (Hz)100 101 102 103 104 105

-270

-225

-180

-135

-90

-45

0

System: GvoltageFrequency (Hz): 844Phase (deg): -131

Phas

e (d

eg)

-120

-100

-80

-60

-40

-20

0

20

40

60

System: GvoltageFrequency (Hz): 60Magnitude (dB): 49

System: GvoltageFrequency (Hz): 844Magnitude (dB): -0.000867

Mag

nitu

de (d

B)

Figure 5.4 Bode plot of outer voltage loop open loop

126

-60

-50

-40

-30

-20

-10

0

10

Mag

nitu

de (d

B)

100

101

102

103

104

105

-180

-135

-90

-45

0

Phas

e (d

eg)

Bode Diagram

Frequency (Hz)

Figure 5.5 Bode plot of close loop of outer voltage loop

-80

-60

-40

-20

0

20

Mag

nitu

de (d

B)

100 101 102 103 104 105-180

-135

-90

-45

0

45

90

135

180

Phas

e (d

eg)

Bode Diagram

Frequency (Hz)

Figure 5.6 Bode plot of output impedance

127

The Bode plot of the output impedance of the inverter is shown in figure 5.6. The negative

peak at 60Hz is caused by the PR controller. The impedance is very low which means a good

decoupling from the load effect. However even the control loop shows the good dynamic and

voltage regulation performance there is no way the controller can make the system stable

when the load power is higher than its thermal capability.

5.3 Proposed Power Management Strategy to Avoid Instability of Solid State Transformer

Although the converters of PHEV are operating in parallel, the proposed method cannot

rely on droop control [166-169], because droop control can be only used in voltage source

parallel operations. However, during grid connected operation the converters are controlled

as current sources. It is also difficult to change the power demand from the inverter side

because as a voltage source, its output power is only decided by its loading information. So

the question comes to the point that to lower the power demand and avoid power collapse the

only possible solution is to reduce the charging rate of the chargers. Then another two

questions arise: first, how to inform all the chargers to reduce the power demand without

communication. Second is how to reduce the power demand if the chargers are informed. To

answer the first question, the frequency will be used as the medium for communication

between the inverter and the chargers, because all of the chargers are equipped with phase

lock loop (PLL) to measure the frequency and synchronize with grid. Similar idea of utilizing

the system frequency as the signal to communicate with others is proposed in [170] Even

though there is only one inverter to supply the loads; frequency droop can be applied to the

inverter control scheme. In this way the both inverter and chargers know the power

information even without communication. In this method only frequency droop is discussed

128

because the chargers all have power factor correction capability and only consume real

power. So the inverter output frequency will droop with the increase of the output power, the

frequency will change in a reasonable range (60.5Hz~59.5Hz) [72]. All of the equipment in

addition to the charger can operate within this frequency. Exceeding this range will trip the

protection of the inverter.

To answer the second question frequency restoration method is proposed. When the

frequency of the inverter falls below a certain point it will trigger another control loop inside

all of the chargers. Note that control loop is built inside the charger rather than in the inverter

because the voltage source cannot change its output power while the current source can. The

control loop will have frequency restoration capability which means it will control the

inverter’s output frequency back to a preset safe point. To move the frequency back to the

preset point the inverter power output will also reduce to the safe level. So the power

collapse crisis is resolved. The frequency restoration method is different from method of

Divan and Iravani [171, 172]. In their methods the frequency is used to push the frequency

back to the normal value after the frequency droop of several parallel inverters. In this

method frequency restoration is implemented in a current controlled source. The frequency

target is not the grid frequency but the preset save frequency.

The proposed frequency restoration controller is implemented in DC/DC stage of the

charger because the AC/DC stage of the charger cannot control the power demand. Normally

the AC/DC stage of the charger regulates the DC bus voltage and corrects the power factor.

DC/DC stage of the charger determines the charging rate which is the power demand. In

normal operation the PHEV user will choose a charging rate and charge the vehicle. When

129

multiple vehicles are connected and charged simultaneously, the total power demand equals

the power output of the inverter output. If the power demand exceeds the capability of this

inverter and triggers the frequency threshold, the proposed controller will be enabled and

reduce the power demand in order to move the frequency up to the predetermined value. All

the chargers connected with this inverter will be controlled by the proposed controller at the

DC/DC stage. The frequency will move gradually back to the predetermined value and

operate in stable state. In other words when multiple vehicles are connected with an inverter

and their power demand is higher than the inverter’s capability the power demand of each

vehicle will be reduced gradually to avoid the power collapse. The control architecture for

AC/DC and DC/DC stage of the charger is drawn in figure 5.7. The frequency restoration

method used in DC/DC stage is shown in figure 5.8. The frequency-power relationship is

implemented in the controller of the inverter in figure 5.9.

In this operation mode when some vehicles are unplugged from the feeder (inverter) and

the total power demand drops, the frequency will increase. The control scheme is designed to

let the frequency difference become negative and after the integrator of the proposed

controller works for sometime the frequency restoration controller output will drop to zero.

This means that the charging rate can return to the user defined value so at this time the

control mode goes back to normal operation. The inverter output frequency will not be kept

at the preset value but will be determined by its actual output power. Once again, if the loads

are increased higher than the limit, the control mode will switch to frequency restoration

mode to regulate the output power. Therefore the mode transfer can be automatically

achieved.

130

The test system is built with a detailed switching model in Matlab Simulink. The Solid

State Transformer is represented by its low-voltage inverter part. Its power rating is set to

10kW and output voltage is 240V. Two PHEVs are AC level II charger with rated power

6kW and are connected together to an SST. A comprehensive case study is conducted, which

includes normal operation, total power demand higher than SST power rating, and mode

transfer operation.

Figure 5.7 Controller architecture of PHEV charger

Figure 5.8 Proposed power dispatch method based on frequency restoration

o outk Pω ω= − ⋅ (8)

In this equation, oω is the initial frequency 60.5Hz and slope rate parameter K is defined

that the power increases from 0 to 10kW with the frequency decreasing from 60.5Hz to

59.5Hz. The K is selected 0.00008 Hz/W.

131

Figure 5.9 Implementation of power-frequency control in inverter stage of SST

Case Study I is the normal operation of charging PHEVs. One PHEV is charging at very

beginning with 4kW and another one is plugged into the grid at 0.2s randomly and charging

with 4kW. The total power equals to the power capability of SST so each vehicle is charged

with its required power. The frequency is measured by a single phase PLL. Although the

PLL has short time duration of dynamic response and during that duration the frequency

exceeds the frequency limit, a blanking function is used to delay the detection function and

prevent the mis-trigger of the power dispatch operation. In figure 5.10 the system operation

frequency is shown and this frequency exceeds the limit for around 0.2s and because of the

blanking function this frequency didn't trigger the proposed power dispatch method. The

frequency after the transient finally stabilized at 59.5Hz which means 10kW output for the

SST. In figure 5.11 the charging power for both vehicles is shown and the enlarged

waveform is shown in figure 5.12. The charging power for each vehicle is 6kW and for

normal operation charging power can be any value as long as the total power doesn’t exceed

the 10kW power limit. The grid voltage, current and dc bus voltage of no.1 and no.2 vehicle

is shown in figure 5.13 and figure 5.14 respectively. As we can see the grid current is in

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phase with the grid voltage and dc bus is well maintained at 400V. So the control objective

for both AC/DC and DC/DC stage is achieved.

0 0.2 0.4 0.6 0.8 1 1.259.4

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Figure 5.10 SST operation frequency

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0 0.2 0.4 0.6 0.8 1 1.20

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Figure 5.11 Charging Power of two vehicles

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.24980

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Figure 5.12 Enlarged charging power of two vehicles

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Figure 5.13 Voltage and current information of no.1 vehicle

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Case II is for power dispatch control. Initially, the first vehicle is charging at very

beginning with full power rating 6kW and the second one is plugged into the grid charging

also with full power rating 6kW at 0.2s. The total power rating exceeds the preset power

limit. The proposed power dispatch control is enabled. The dispatched power to each vehicle

is controlled to be equal and each vehicle is charging with 5kW. In figure 5.15 the system

operation frequency is shown. This frequency exceeds the limit after the blanking function so

the proposed power dispatch controller is enabled. The power for each vehicle is designed to

be equally shared with 5kW. The frequency is stabilized at 59.5Hz which represents the total

power for SST 10kW. The equal sharing power for no.1 and no.2 vehicle is shown in figure

5.16 and an enlarged waveform is shown in figure 5.17. The grid voltage, grid current and dc

bus voltage for no.1 and no.2 vehicle are shown in figure 5.18 and 5.19 respectively. As we

can see that the control performance is good. The dc bus regulation is very stable and the

variation is very low with the change of the power. So in this case, the plug-in vehicles have

the equal power sharing. Assuming that the vehicles are in a similar condition which means a

similar state of charge (SOC), state of health (SOH) and the charging priority, the proposed

method works well. For vehicles with different conditions the dispatched power can be

different.

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Charging power of No.2 vehicle

Figure 5.16 Charging power of two vehicles

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1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.54986

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Case III is for power dispatch control. The first vehicle is charging at very beginning with

6kW and the second one is plugged into the grid charging with 6kW at 0.2s. The total power

rating exceeds the preset power limit. The proposed power dispatch control is enabled. Since

the stage of charge (SOC) of two vehicle battery is different, the controller is designed to

dispatch more power to the vehicle with lower SOC. The first vehicle is dispatched 6kW and

the second one is dispatched 4kW. In figure 5.20 the system operation frequency is shown. In

this case the frequency also triggers the proposed controller and is stabilized at 59.5Hz.

Based on different control parameters the dispatched power for no.1 and no.2 vehicles is

shown in figure 5. 21 and enlarged waveform is shown in figure 5.22. The dispatched power

is controlled at 4kW and 6kW very accurately. The grid voltage, grid current and dc bus

voltage for no.1 and no.2 vehicles is shown in figures 5.23 and 5.24 respectively. As we can

139

see that the control performance is good. The dc bus regulation is very stable and the

variation is very low with the change of the power. So the vehicles can have unequal power

sharing based on the condition of SOC of batteries.

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1.4 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49 1.55990

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Case IV is for power dispatch control. Mode transfer is also examined. The first vehicle is

charging with 6kW initially and the second one is plugged into the grid charging with 6kW at

0.2s. The total power rating exceeds the preset power limit. The proposed power dispatch

control is enabled. After a while the first vehicle is unplugged by its user emulating a very

normal and random PHEV charging scenario. At that time the power demand is lower than

the SST power rating so the normal operation can be reactivated. The power dispatch control

at no.2 vehicle will move the charging power back to its setting value and here the power is

6kW. The system frequency will be determined by the power it supplies to the loads

according to the frequency and power curve in fig. 5.4. In figure 5.25 the frequency first is

controlled at 59.5Hz initially and then moved to 59.9Hz after the disconnection of no.1

vehicle. This proves that the proposed power dispatch method can be automatically switched

back to normal charging method. In figure 5.26 the charging power for no.1 vehicle is 6kW

at first and 5kW due to power dispatch and then 0kW, while for no.2 vehicle first is 6kW and

then 5kW due to power dispatch and finally return to the normal charging rate of 6kW. All

the grid voltage, grid current and dc bus voltage of no.1 and no.2 vehicle are shown in figure

5.27 and 5.28 respectively. After the disconnection of one vehicle, the total power drops to a

point lower than 12.5kW another vehicle can return to its normal charging rate.

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147

Case V is for power dispatch control. The first vehicle is charging at very beginning with

8kW and the second one is plugged into the grid charging with 6kW at 0.2s. The total power

rating exceeds the preset power limit. The proposed power dispatch control is enabled. After

a while the second vehicle is unplugged by its user attempting to emulate a very normal and

random PHEV charging scenario. At that time the power demand is lower than the SST

power rating so normal operation can be switched back. The power dispatch control at no.1

vehicle will move the charging power back to its setting value and, at this point the power is

8kW. The system frequency will be determined by the power it supplies according to the

frequency and power curve in fig. 5.4 and for this example it is 59.86Hz. In figure 5.29 the

frequency first is controlled at 59.7Hz and then moves to 59.86Hz after unplugging no.2

vehicle. 59.86Hz means the charging power of no.1 vehicle goes back to 8kW again. It

proves that the proposed power dispatch method can be automatically switched back to

normal charging method. In figure 5.30 the charging power for no.1 vehicle is 8kW and then

goes to 6kW because of power dispatch control and again back to 8kW, while for no.2

vehicle first is 6kW and then 4kW because of power dispatch control and finally 0kW. All of

the grid voltage, grid current and dc bus voltage of no.1 and no.2 vehicle is shown in figure

5.31 and 5.32 respectively. After the unplugging of one vehicle, the total power drops to

lower than 12.5kW another vehicle can come back to its normal charging rate.

5.4 Gain Scheduling Technique to Dispatch Power based on State Charge of Vehicles

Based on different state of charge of batteries the controller can be designed to charge the

battery with different charging rates during the proposed power dispatch operation. The

integration gain of the frequency restoration loop will affect the power dispatched to each

148

vehicle. With different vehicle states of charging tuning integration gain can make the

vehicle with less SOC dispatch more power. Since the proposed power dispatch method

doesn’t need any communication between vehicles the gain scheduling for the integration Ki

should be decided by each vehicle without knowing others’ information. Based on the battery

state of charge the integration gain can be simplified into three groups: urgent charge, regular

charge and mild charge. Urgent charge means the user needs to charge the vehicle as soon as

possible even the power limited by the feeder’s capability. Regular charge means the user is

not in a hurry and won’t need as much as power as possible. Mild charge means the vehicle

can wait and needs a small amount of power. In urgent charge integration gain Ki is defined

as 200, and in regular charge integration gain Ki is 800 and in mild charge integration gain Ki

is 1500. Then different integration gain values will be applied in order to find out the power

dispatched to each vehicle in six cases. The relationship of integration gain and dispatched

power will be used as guidance for each vehicle to share power. One vehicle is set at three

conditions, while the other one is controlled to let its state of change vary from 30% to 70%

and let its integration gain change in a wide range (100 to 4000). So the first condition is one

vehicle in urgent condition which assumes its state of charge is only 30% and its integration

gain is 200. The second condition is vehicle in normal condition with its state of charge 50%

and its integration gain 1000. The third condition is one vehicle in urgent condition with its

state of charge 70% and its integration gain 1500. In each case how to choose the proper

integration gain to dispatch the designated power will be shown. The first condition is

presented in figure 5.33, the second condition is presented in figure 5.34 and the third

condition is shown in figure 5.35.

149

0 500 1000 1500 2000 2500 3000 3500 40002000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

SOC=30%SOC=40%SOC=50%SOC=60%SOC=70%

Figure 5.33 Relationship of dispatched power and integration gain Ki with one vehicle at urgent charging and

another one with various conditions

0 500 1000 1500 2000 2500 3000 3500 40002000

3000

4000

5000

6000

7000

8000


Figure 5.34 Relationship of dispatched power and integration gain Ki with one vehicle at normal charging and


150

0 500 1000 1500 2000 2500 3000 3500 40003000

3500

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Figure 5.35 Relationship of dispatched power and integration gain Ki with one vehicle at mild charging and


5.5 Load management of Solid State Transformer by Managing Power of PHEVs

In the previous sections, a new power management strategy is proposed for multiple

PHEVs connected with a solid state transformer. This method is designed to regulate the

power of controllable loads e.g., PHEV. This method should be also examined with non-

controllable loads or loads whose power cannot be changed. So in this section, the proposed

method is applied to a system, which has an SST, non-controllable loads and a PHEV. The

proposed method will manage the power of the PHEV in order to assist the SST to do the

load management. Five cases are studied. Case I is the SST has both a non-controllable load

and the PHEV connected. The possessive power of the non-controllable load and the PHEV

is higher than the power capability of SST. The PHEV will reduce its charging power in

order to maintain the system operation frequency at 59.5Hz. In this way the power

151

requirement of the non-controllable load is fulfilled and the SST is fully utilized. This case

can be extended to the case, which has several PHEVs connected with SST. The operation

principle and control strategy is the same.

Case II and III are described that the SST has both a non-controllable load and the PHEV

connected. Concurrently, the SST gets the power from a renewable resource e.g. solar or fuel

cell generator. So in this case, the SST is not only the power generation unit. With the power

coming from external resources, the power requirement of the non-controllable load should

be met at first. Then the proposed method will control the PHEV to get the rest of the power.

If the rest of the power doesn’t meet the need of the PHEV, the frequency will be maintained

at 59.5Hz. If the rest of the power meets the need of the PHEV, the frequency will be

determined based on the power-frequency curve (figure 5.5).

Case IV is the SST has both a non-controllable load and the PHEV connected. In addition,

no external generator is connected into the system. However, the non-controllable load is

even higher than the power capability of the SST. In this case, the PHEV should discharge

rather than charge. It will discharge the power back to the load in order to maintain the

system frequency 59.5Hz. The assumption of this case is that the PHEV is willing to send

power back to the grid (vehicle to grid) and the vehicle has enough power inside its battery

pack. In the actual case, the PHEV’s battery may not be in good condition and may have low

state of charge; it may not send enough power back to the grid. But this is not the concern of

the proposed method. This case should be investigated together with battery management

system and system level intelligent control.

152

Case V is the SST has both a non-controllable load and two PHEVs connected. Contrary

to Case IV, the PHEVs in case V will share the discharging power. The discharging power

can be regulated by control the integration gain Ki in proposed frequency restoration loop.

The way of designing gain Ki is similar to the gain scheduling technique which is discussed

in previous section. With different integration gain, the vehicle can choose the amount of

power discharged to the grid. The total discharging power is determined by the system

frequency. In order to fully utilize the SST, the frequency should be maintained at 59.5Hz.

The following results demonstrate the three cases. In figure 5.36, the system operation

frequency is shown. The non-controllable load is 6kW at first and then the vehicle is plugged

into the system. The frequency drops lower than 59.5Hz and the proposed method is enabled.

Because the non-controllable load cannot adjust its own power, the vehicle will adjust its

power to maintain the system frequency 59.5Hz. At this point, the vehicle’s power is 4kW,

which is drawn in figure 5.37. Figure 5.38 shows the system voltage, input current and dc bus

voltage of the vehicle. With the proposed method, the vehicle’s input current and dc bus

voltage are regulated very well.

In figure 5.39, the operation system frequency is shown for case II. Since possessive

power of SST and renewable energy is higher than the power of load and vehicle, the vehicle

is fully charged. SST is not working at its full rating because it is determined by the

possessive load power subtracting the power of the renewable energy. If the renewable

energy’s power is higher than the load power, SST will send power back to the utility rather

than output any power to the load. In figure 5.40, the charging power of the vehicle is shown.

The charging power first tries to reach the rated power 6kW. But it trips the proposed method

153

and the power drops to 4kW to regulate the system frequency. After the power injection from

renewable energy, the charging power can go back to rated power again. In figure 5.41, the

possessive load current and current injected by renewable energy are shown. In figure 5.42,

the operation frequency is shown for case III. In this case, the possessive power of SST and

renewable energy is lower than the power of load and vehicle, the vehicle cannot be fully

charged. In figure 5.43, the charging power of the vehicle is shown. The non-controllable

load is 8kW and the charging power is 2kW without external power. After 2kW power

injection of the renewable energy, the charging power is regulated at 4kW to maintain

frequency 59.5Hz. SST is fully loaded in this case. In figure 5.44, the possessive load current

and current injected by renewable energy are shown.

The case IV is verified with the vehicle’s power discharged back to the grid. At first, SST

has no loads. Then the vehicle is plugged into the system and charged at 6kW. Then a 12kW

non-controllable load is plugged into the system. The vehicle will discharge the power back

to SST in order to keep it stable. The operation frequency is shown in figure 5.45, it is

60.5Hz at first and then 59.9Hz and finally regulated at 59.5Hz. The charging power is

shown in figure 5.46. It is 6kW at first and then changes to -2kW. The vehicle’s input current,

grid voltage and dc bus voltage are shown in figure 5.47 and the zoom-in waveform is shown

5.48. The dc bus is regulated very well. The current is synchronized with the grid voltage. At

first it is in phase with the voltage and then out-of phase with the voltage. The transition is

short and smooth. From the above cases, the proposed method can successfully enable the

load management for solid state transformer.

154

Finally the case V is verified with two vehicle’s power discharged back to the grid. At

first, two vehicles are charged at SST and the each vehicle is charged equally with 5kW.

Then a 15kW non-controllable load is plugged into the system, the vehicles have to change

the mode from charging to discharging. The mode transfer from charging to discharging is

determined by the current reference which is generated by the proposed frequency restoration

loop. When the frequency drops to a frequency point much lower than 59.5Hz, the current

reference will become negative which means the vehicle needs to discharging rather than

charge now. The charging loop needs to be disabled and the discharging loop is enabled. In

the actual operation, this case can rarely happen because the non-controllable load exceeds

the SST’s capability. However, from another aspect, the proposed method can extend the

operation range of SST with discharging PHEVs. In figure 5.49, the system operation

frequency is shown. In figure 5.50, the power for two vehicles is drawn. No.1 vehicle first

charges 5kW and then discharges 2kW. No.2 vehicle first charges 5kW and then discharge

3kW. In figure 5.51 and 5.52, the grid voltage, current and dc bus voltage for no.1 and no.2

vehicle is shown respectively. With discharging vehicles, SST can supply load which is

higher than its power capability without any voltage collapse. One thing needs to be

addressed that in this case the vehicles must have the capability to discharge and also the

health of the batteries are not affected. The decision-making method even game theory can

be used to combine the battery information to determine how much power should be

discharged to the grid for the vehicle.

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Figure 5.36 System operation frequency

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Figure 5.37 Charging power of the vehicle

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Figure 5.38 Grid voltage, current and dc bus voltage of the vehicle

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Figure 5.41 Injection current from renewable energy and possessive load current

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Figure 5.44 Injection current from renewable energy and possessive load current

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Figure 5.46 Charging and discharging power of the vehicle

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0

500Grid voltage of vehicle

0 0.5 1 1.5 2200

300

400

Time

DC bus voltage of vehicle

Figure 5.47 Grid current, voltage and dc bus voltage of the vehicle

161

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8-40

-20

0

20

40Current from vehicle

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8-500

0

500System AC bus voltage

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8380

400

420

440

Time

DC bus voltage of vehicle

Figure 5.48 Grid current, voltage and dc bus voltage of the vehicle (zoom-in)

0 0.5 1 1.5 2 2.558.4

58.6

58.8

59

59.2

59.4

59.6

59.8

60

60.2

Time



162

0 0.5 1 1.5 2 2.5-4000

-2000

0

2000

4000

6000

8000power of no.1 vehicle

0 0.5 1 1.5 2 2.5-4000

-2000

0

2000

4000

6000

8000

Time

power of no.2 vehicle

Figure 5.50 power of no.1 and no.2 vehicle

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3-50

0

50grid current of no.1 vehicle

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3-500

0

500grid voltage of no.1 vehicle

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3380

400

420

Time

dc bus voltage of no.1 vehicle

Figure 5.51 grid voltage, current and dc bus voltage of no.1 vehicle

163

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3-50

0

50grid voltage of no.2 vehicle

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3-500

0

500grid current of no.2 vehicle

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3380

400

420

Time

dc bus voltage of no.2 vehicle

Figure 5.52 grid voltage, current and dc bus voltage of no.1 vehicle

5.6 Summary of Chapter Five

In this chapter, a new power management strategy is proposed to solve the power collapse

issue of multiple PHEVs operating in a Solid State Transformer (SST) based smart grid.

When multiple PHEVs are plugged into one SST based smart grid and the total demand

power is higher than the power capability of SST, a frequency restoration based controller is

adopted in each PHEV to reduce its power demand to move the frequency back to a stable

point. Gain scheduling technique is proposed to dispatch power of each vehicle based on

battery’s state of charge. The battery with a low state of charge will be dispatched with more

power. The proposed power dispatch method is faster than a two-way communication

oriented system level control for the smart grid. So it can be used as a power electronics

converter level control to improve the stability of a solid state transformer.

164

Chapter Six High-Order Filter for Compact Size and Ripple Free Charging

6.1 Design Goal—Compact Filter Size and Ripple Free Charging

High order filter can not only be used in AC application to reduce the filter size but can

also be used in battery charging application. In using this type of filter, two primary goals are

achieved. First is the reduction of the filter size compared to conventional LC or L filter and

yield a compact battery charger. Second is the guarantee that the charging current has almost

zero switching ripples. The ripple free charging can avoid the negative effects brought by the

high frequency current ripples. Although there is no convincing evidence on the impact of

ripple current on batteries, it is widely believed that ripple current may harm the health of

batteries because it leads to temperature increases due to the additional internal heating and

power losses. Moreover, ripple currents may speed up positive grid corrosion and cause

premature failures. Therefore, most battery manufacturers recommend that the ripple current

should not exceed 5% of the battery Ahr capacity. Even though ripple currents may have

little impact on conventional charging, their effect will be quite notable for the higher current

charging or even fast charging [172-175]. Another important concern is the cooling system

for the battery bank. In automotive application, it is not practical to design an extra cooling

system for battery bank. So it is not easy to take out the heat of the battery. Ripple free

charging can reduce the heat of the battery, which alleviates the burden of the cooling

system. In this chapter ripple free current charging is achieved by applying an LCL filter and

this filter has a much lower value and size than conventional filter with ripple currents. So a

compact size and low volume charger can be achieved.

165

6.2 Filter Design and Comparison with Conventional Filter

The spectrum of the PWM output voltage of the dc/dc converter is written in (1)

1

2 sin( )cos( )( ) dc swdc

h

V h D h tu t D Vh

π ωπ

∞

=

= ⋅ +∑ (1)

Set 48V battery with dc bus 100V to design the converter side inductor, the charging

current is defined as 10A. The ripple current which is the half of the peak to peak current is

6A, so the converter side inductor can be chosen as a smaller value.

_1

( )2

dc battL PK

s

V Vi DL f−

= ⋅ (2)

batt

dc

VDV

= (3)

1 3_ _

( ) ( ) (100 48) 48 0.2082 2 2 6 10 10 100

dc batt dc batt batt

L PK s L PK s dc

V V V V VL D mHi f i f V− − −

= ⋅ = ⋅ = × =× × ×

(4)

The converter side current has ripple current 6A and then the ripple current flows through

a second order filter network composed by the capacitor C and battery side inductor L2. The

ripple current will greatly attenuate after this LC network. To design this L2 and C, the

transfer functions of converter side current to converter output and battery side current to

converter output are used. Without considering the resistance of both inductors the transfer

function are derived:

21 2

31 2 1 2

1( )conv

i L Csu L L Cs L L s

+=

+ + (5)

166

23

1 2 1 2

1( )conv

iu L L Cs L L s

=+ +

(6)

From these two transfer functions, the attenuate ratio between the converter side current

and the battery side current. In order to achieve ripple current lower than 0.5A, this ratio is

set to 1/12.

22

1 2

1 11 12

ii L Cs= =

+ (7)

So the multiplication of L2 and C is 11 and the value can vary but by reducing the L2

value the capacitor value can be higher. In this paper the inductor L2 is set 0.05mH and the

capacitor is calculated to be 55uF. Finally the actual value of the LCL filter is: L1=0.2mH,

L2=0.05mH, C=80uF. With this filter setup the actual current ripple will be further

attenuated to around 0.4A. The peak to peak current ripple to the charging current ratio is less

than 1%. While with the same ripple current 0.5A, the conventional L filter is calculate as:

1 3_ _

( ) ( ) (100 48) 48 2.4962 2 2 0.5 10 10 100

dc batt dc batt batt

L PK s L PK s dc

V V V V VL D mHi f i f V− − −

= ⋅ = ⋅ = × =× × ×

(8)

The conventional method must use 2.5mH inductor to get the same current ripple. And

this inductor is 10 times the total inductance of L1 an L2. The inductor size for converter side

inductor is actually larger than theoretical size because of large current ripple on the inductor.

The author used Kool Mu core from Magnetics to design these inductors, with different

charging current the comparison of LCL filter and L-type filter is shown in table 6.1 and 6.2.

First case the charging current equals 10A, all the inductors are designed with E cores.

Second case the charging current is increased to 30A. The comparison charts are shown in

167

figure 6.1 and 6.2. We can see that the volume reduction of using LCL filter is around 3~4

times and the loss reduction is around 2~3 times.

Table 6-1 Core volume and loss of L-type filters

L-type filter

10A

L=2.5mH

E-core

L-type filter

30A

L=2.5mH

E-core

Core volume

(mm3)

237000 Core volume

(mm3)

865000

Core loss (W) 19.5 Core loss (W) 181.2

Table 6-2 Core volume and loss of LCL-type filters

LCL-type filter

10A

L1=0.2mH

E-core

L2=0.05mH

E-core

Core volume

(mm3)

28600 5340

Core loss (W) 6.70 0.86

LCL-type filter

30A

L1=0.2mH

E-core

L2=0.05mH

E-core

Core volume

(mm3)

86500 86500

Core loss (W) 41.6 13.8

168

Figure 6.1 volume comparison between LCL filter and L filter at 10A and 30A charging

Figure 6.2 Filter loss comparison between LCL filter and L filter at 10A and 30A charging

6.3 Controller Design

A constant current charging algorithm is designed and implemented in digital controller.

Its design and modeling procedure is quite similar to the design of a grid-connected converter

with LCL filter. To avoid high frequency oscillation on the filter current, conventional

controller needs to be modified. Since high frequency oscillation is caused by the converter

PWM output and the resonant frequency of LCL filter, a filter which is designed to extract

and eliminate resonant frequency is plugged into the control loop. The merits of this filter are

that it functions without extra current or voltage sensor, and it is easy to implement. For the

filter type, either notch filter or low pass filter can be used. The control loop model is shown

in figure 6.3. The plant is derived as below:

0

20

40

60

80

100

120

140

160

180

200

1

loss of proposed filter a 30A charging loss of L filter at 30A charging

0

50000

100000

150000

200000

250000

1

volume of proposed filter at 10A charging volume of L filter at 10A charging

0

100000

200000

300000

400000

500000

600000

700000

800000

900000

1

volume of proposed filter at 30A charging volume of L filter at 30A charging

0

2

4

6

8

10

12

14

16

18

20

1

loss of proposed filter at 10A charging loss of L filter at 10A charging

169

11

22

1 2

conv c

c batt

c

diL u udtdiL u udt

duc i idt

⎧ ⋅ = −⎪⎪⎪ ⋅ = −⎨⎪⎪⋅ = −⎪⎩

(9)

In equation (9), L1 is the converter side inductor, L2 is the battery side inductor and C is

the filter capacitor. Uconv is the converter output voltage, Uc is the voltage on the filter

capacitor, Ubatt is the battery voltage. And i1 is the converter side current and i2 is the

battery side current and also the charging current. Transfer the equation (9) from time

domain to frequency domain to get equation (10):

1 1

2 2

1 2

conv c

c batt

c

L i s u uL i s u uc u s i i

⋅ = −⎧⎪ ⋅ = −⎨⎪ ⋅ = −⎩

(10)

To get the small signal model, the battery voltage is assumed to be constant. Equation (9)

can be further derived to:

1 1

2 2

2 1

conv c

c

c

u L i s uu L i si i c u s

= ⋅ +⎧⎪ = ⋅⎨⎪ = + ⋅⎩

(11)

From equation (11) substitute i1 and Uc with i2 and then derive the transfer function of

charging current to converter output:

23

1 2 1 2

1( )( )plant

conv

iG su L L Cs L L s

= =+ +

(12)

The compensator used here is PI controller in equation (13):

170

( ) iPI p

kG s ks

= + (13)

The sampling and propagation delay is modeled in equation (14)

1( )1dG s

T s=

+ ⋅ (14)

In equation (14), the delay T is the switching cycle.

So the open loop transfer function of the system is written in equation (15) and the bode

plot is drawn in figure 6.4

( ) ( ) ( ) ( )pi d plantG s G s G s G s= ⋅ ⋅ (15)

As we can see in figure 6.4 that Bode plot of the system with only PI compensation has a

negative gain margin and is not stable. The high frequency gain in the system will yield high

frequency resonant current on the charging current. In order to solve this issue, filter based

method is proposed. The method can extract the resonant frequency and eliminate this

frequency. Two types of filters are proposed. The first filter is a second order notch filter and

its ideal transfer function is:

2 2

2 2

1

resfilter

resres

sG ssQ

ωω ω

+=

⋅+ +

(16)

In the real system, this ideal transfer function will generate a very high negative

magnitude at the setting frequency. So the transfer function is modified to:

171

2 2

_2 2

resres

filter notchres

res

ssdG c ssd

ω ω

ω ω

⋅+ +

=⋅ ⋅

+ + (17)

The second filter used is a second order low pass filter and its transfer function is:

2

_2 2

2

resfilter low

resres

G ssQ

ωω ω

=⋅

+ + (18)

After plugging the notch filter transfer into the control loop the whole system transfer

function:

_( ) ( ) ( ) ( ) ( )pi d plant filter notchG s G s G s G s G s= ⋅ ⋅ ⋅ (19)

The control plant and notch filter are drawn in figure 6.5. The notch filter resonant

frequency matches the plant’s resonant frequency exactly. From figure 6.6 we can see that

after applying notch filter in the control loop, the phase margin is 55 deg close to 60 deg the

ideal phase margin for control system. The loop bandwidth is 700Hz a little less than 1/10 of

the switching frequency. The gain margin is 10.4 and the high frequency resonant peak is

eliminated. The dc gain of the system is almost infinity because of a pole placed at zero

frequency which forms a first order system. With this controller the system will have high dc

regulation accuracy and less steady-state error. The controller will have good dynamic

response and a short settling time because it is directly related to a high phase margin. In

figure 6.7 the root locus of the system also proves that the double-pole, which causes the

system instability, is compensated with two zeros.

172

2i*2i

Figure 6.3 System control loop model

-60

-40

-20

0

20

40

Mag

nitu

de (d

B)

103 104 105-270

-225

-180

-135

-90

Phas

e (d

eg)

Bode Diagram

Frequency (rad/sec)

Figure 6.4 Bode plot of system open loop transfer function

173

-150

-100

-50

0

50

Mag

nitu

de (d

B)

102

103

104

105

-270-225-180-135

-90-45

04590

Phas

e (d

eg)

Bode Diagram

Frequency (Hz)

Figure 6.5 Bode plot of control plant and notch filter

Bode Diagram

Frequency (Hz)

-150

-100

-50

0

50

100

150

System: Gout2c_dampGain Margin (dB): 10.4At frequency (Hz): 1.85e+003Closed Loop Stable? Yes

Mag

nitu

de (d

B)

10-2

10-1

100

101

102

103

104

105

-360

-315

-270

-225

-180

-135

-90

System: Gout2c_dampPhase Margin (deg): 55.5Delay Margin (sec): 0.000218At frequency (Hz): 708Closed Loop Stable? Yes

Phas

e (d

eg)

Figure 6.6 System bode plot with proposed notch filter

174

Pole-Zero Map

Real Axis

Imag

inar

y Ax

is

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.05/T

0.10/T

0.15/T

0.20/T0.25/T

0.30/T

0.35/T

0.40/T

0.45/T

0.50/T

0.1

0.2

0.30.40.50.60.70.8

0.9

0.05/T

0.10/T

0.15/T

0.20/T0.25/T

0.30/T

0.35/T

0.40/T

0.45/T

0.50/T

Figure 6.7 Root locus of system with proposed method

The low pass filter is the second proposed method. It aims at reducing all the magnitude

after its corner frequency. With its corner frequency tuned at the right value the high

frequency peak is largely reduced. The control system with low pass filter is written in

equation (20)

_( ) ( ) ( ) ( ) ( )pi d plant filter lowG s G s G s G s G s= ⋅ ⋅ ⋅ (20)

In figure 6.8 the Bode plot of the system is drawn. From this figure we can see that the

low pass filter based method has the serious drawback of low control bandwidth. The control

bandwidth is only 300Hz much slower than the notch filter based method. In addition with

the low pass filter the level shifts to all frequencies after only after its corner frequency but

does not compensate for the resonant frequency peak. So there is possibility of gain peaking

at the resonant frequency. As explained in figure 6.9, once amplified by improper gain or

175

system parameters the resonant gain will move higher than zero dB line which will lead to

negative gain margin and an unstable system. In figure 6.10 the root locus plot also proves

that the resonant frequency is not compensated for because the double-pole is very close to

the boundary of the unit circle and oscillation is easily generated.

Bode Diagram

Frequency (Hz)

-350

-300

-250

-200

-150

-100

-50

0

50

100

150


Mag

nitu

de (d

B)

10-2

10-1

100

101

102

103

104

105

106

-540

-495

-450

-405

-360

-315

-270

-225

-180

-135

-90


Phas

e (d

eg)

Figure 6.8 System with proposed low pass filter

176

Bode Diagram

Frequency (Hz)10

-210

-110

010

110

210

310

410

510

6-540

-495

-450

-405

-360

-315

-270

-225

-180

-135

-90

Phas

e (d

eg)

-350

-300

-250

-200

-150

-100

-50

0

50

100

150 System: Gout2c_undampGain Margin (dB): -12.5At frequency (Hz): 2.79e+003Closed Loop Stable? No

Mag

nitu

de (d

B)

Figure 6.9 Comparison of system with low pass filter and without low pass filter

Pole-Zero Map

Real Axis

Imag

inar

y Ax

is

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.05/T

0.10/T

0.15/T

0.20/T0.25/T

0.30/T

0.35/T

0.40/T

0.45/T

0.50/T

0.1

0.2

0.30.40.50.60.70.8

0.9

0.05/T

0.10/T

0.15/T

0.20/T0.25/T

0.30/T

0.35/T

0.40/T

0.45/T

0.50/T

Figure 6.10 Root locus of system with proposed low pass filter

177

Based on the analysis above the notch filter based method can achieve better performance

than the low filter based method. The notch filter based method is also more robust than the

low pass filter based method. In the next section the robustness analysis and dynamic

response for notch filter based controller will be examined.

6.4 Controller Robustness Analysis

The controller with the notch filter is proven to have better performance than the low pass

filter. But usually the notch filter is limited since it can only be designed to be effective at a

narrow frequency band. So if a system parameter such as inductance or capacitance has a

sudden change, the controller performance of this method is questionable. How to extend the

frequency range and whether the extended frequency range affects controller performance

will also be discussed. In this section, the controller robustness is analyzed and examined

with the variation of capacitance or inductance. In figure 6.11 the control system model with

capacitance variation from 0.5 to 1.5 of its original value. This is a very challenging test. In

figure 6.12 the control model with inductance variation from 0.8 to 1.2 of its original value is

tested. The variation of inductance should emulate the variation of battery internal

impedance.

In figure 6.13 the control loop with the notch filter set at the original value is connected

with both 120uF and 100uF capacitor. The individual Bode plot for 100uF and 120uF is

shown in figure 6.14 and 6.15 respectively. When the capacitance becomes larger the

resonant frequency moves to a lower frequency. As we can see that prior to the notch filter

resonant frequency there is a resonant peak and that peak will move across the zero dB line

because the notch filter gain at that frequency is not enough to compensate for that

178

frequency. But before this resonant frequency the phase has already passed -180 degree

gradually because of the slow phase drop of the notch filter. So at this resonant frequency,

even though the resonant peak crosses over the zero dB line, the phase has already dropped

significantly lower than -180. The gain margin of this system is 8.55dB with 100uF and

6.34dB with 120uF. With multiple zero dB crossings, the first crossing is used to measure the

bandwidth and phase margin. In figure 6.16 and 6.17 the capacitance is reduced to 60uF and

40uF respectively. With the reduction of the capacitance the resonant frequency has been

moved to a higher frequency range. As we can see from the Bode plots, after the

compensation from the notch filter the phase has a sudden jump above the -180 degree

because of the effect of resonant frequency. At the -180 degree crossing point the magnitude

of the system is higher than 0dB so the negative gain margin leads to an unstable system. The

notch filter has two parameters c and d in equation (17). They can be used to control the

magnitude and frequency range of the notch filter. By tuning c and d the frequency damping

range is widened. A notch filter with different c and d parameters is shown in figure 6.18.

With a redesigned notch filter, the capacitances 60uF and 40uF are examined again. In figure

6.19 system with 60uF capacitance is stable because with a wider frequency damping range

the magnitude is damped to be lower than 0dB even if the phase jumps back to -180 degree

line. So the gain margin is 4.34dB and system has returned to a stable state. The bandwidth

and phase of the system is determined by the first zero crossing point. But in figure 6.20 the

system with 40uF is still not stable because the frequency has moved to a higher level where

the notch filter is ineffective for damping its magnitude. So the gain margin becomes

negative again and system is not stable. One way to make it stable is to retune the parameters

179

to make the frequency damping range wider. However, as can be seen from figure 6.18, the

wider the damping range the lower the boosting phase. The phase will be reduced with a

wider damping range and in figure 6.19 we can see that although the system is stable the

phase margin has already dropped to 36 degree which may lead to longer settling time and

higher overshoot to the control loop.

-120

-100

-80

-60

-40

-20

0

20

40

Mag

nitu

de (d

B)

102

103

104

105

-270

-225

-180

-135

-90

Phas

e (d

eg)

Bode Diagram

Frequency (Hz)

C=80uFC=40uFC=120uF

Figure 6.11 System Bode plot with its filter capacitor variation from 0.5 to 1.5 of original value

180

-120

-100

-80

-60

-40

-20

0

20

40

Mag

nitu

de (d

B)

102

103

104

105

-270

-225

-180

-135

-90

Phas

e (d

eg)

Bode Diagram

Frequency (Hz)

L=50uHL=25uHL=75uH

Figure 6.12 System Bode plot with its battery side inductance variation from 0.5 to 1.5 of original value

Bode Diagram

Frequency (Hz)

-150

-100

-50

0

50

100

150


Mag

nitu

de (d

B)

10-2

10-1

100

101

102

103

104

105

-405

-360

-315

-270

-225

-180

-135

-90


Phas

e (d

eg)

Figure 6.13 System with 100uF and 120uF capacitance with notch filter controller

181

Bode Diagram

Frequency (Hz)

-150

-100

-50

0

50

100

150


Mag

nitu

de (d

B)

10-2

10-1

100

101

102

103

104

105

-450

-360

-270

-180

-90


Phas

e (d

eg)

Figure 6.14 System stable with 100uF capacitance and notch filter controller

Bode Diagram

Frequency (Hz)

-150

-100

-50

0

50

100

150


Mag

nitu

de (d

B)

10-2

10-1

100

101

102

103

104

105

-405

-360

-315

-270

-225

-180

-135

-90


Phas

e (d

eg)

Figure 6.15 System stable with 120uF capacitance and notch filter controller

182

Bode Diagram

Frequency (Hz)10

-210

-110

010

110

210

310

410

5-360

-315

-270

-225

-180

-135

-90

-45

System: Gout2c_dampPhase Margin (deg): 56.1Delay Margin (sec): 0.000224At frequency (Hz): 697Closed Loop Stable? NoPh

ase

(deg

)

-150

-100

-50

0

50

100

150

System: Gout2c_dampGain Margin (dB): -6.59At frequency (Hz): 3.26e+003Closed Loop Stable? No

Mag

nitu

de (d

B)

Figure 6.16 System unstable with 60uF capacitance and notch filter

Bode Diagram

Frequency (Hz)

-150

-100

-50

0

50

100

150


Mag

nitu

de (d

B)

10-2

10-1

100

101

102

103

104

105

-360

-315

-270

-225

-180

-135

-90

-45

System: Gout2c_dampPhase Margin (deg): 56.6Delay Margin (sec): 0.000229At frequency (Hz): 687Closed Loop Stable? No

Phas

e (d

eg)

Figure 6.17 System unstable with 40uF capacitance and notch filter

183

-60

-50

-40

-30

-20

-10

0

Mag

nitu

de (d

B)

101

102

103

104

105

106

-90

-45

0

45

90

Phas

e (d

eg)

Bode Diagram

Frequency (Hz)

Figure 6.18 Bode plots of different notch filter transfer functions to improve controller robustness

Bode Diagram

Frequency (Hz)

-250

-200

-150

-100

-50

0

50

100

150


Mag

nitu

de (d

B)

10-2

10-1

100

101

102

103

104

105

106

-360

-315

-270

-225

-180

-135

-90

-45

System: Gout2c_dampPhase Margin (deg): 36.2Delay Margin (sec): 0.00019At frequency (Hz): 531Closed Loop Stable? YesPh

ase

(deg

)

Figure 6.19 System stable with 60uF capacitance and redesigned filter parameters

184

Bode Diagram

Frequency (Hz)

-200

-150

-100

-50

0

50

100

150


Mag

nitu

de (d

B)

10-2

10-1

100

101

102

103

104

105

106

-360

-315

-270

-225

-180

-135

-90

-45

System: Gout2c_dampPhase Margin (deg): 36.5Delay Margin (sec): 0.000192At frequency (Hz): 527Closed Loop Stable? NoPh

ase

(deg

)

Figure 6.20 System still unstable with 40uF capacitance and redesigned filter

Bode Diagram

Frequency (Hz)

-250

-200

-150

-100

-50

0

50

100

150System: Gout2c_damp2Gain Margin (dB): -13.6At frequency (Hz): 3.98e+003Closed Loop Stable? No

Mag

nitu

de (d

B)

10-2

10-1

100

101

102

103

104

105

106

-360

-315

-270

-225

-180

-135

-90

-45

System: Gout2c_damp1Phase Margin (deg): 19.1Delay Margin (sec): 0.000174At frequency (Hz): 304Closed Loop Stable? Yes

Phas

e (d

eg)

Figure 6.21 System with 40uF capacitor with different notch filter parameters to make loop stable

185

-120

-100

-80

-60

-40

-20

0

20

40

60

Mag

nitu

de (d

B)

101

102

103

104

105

-270

-225

-180

-135

-90

-45

0

45

90

Phas

e (d

eg)

Bode Diagram

Frequency (Hz)

c=80uc=100uc=120uc=60uc=40ufilter

Figure 6.22 Notch filter and control plant with all capacitor values (0.5~1.5)

0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.164

6

8

10

12

14

16

0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.160

0.5

1

1.5

Time

Figure 6.23 Control robustness test: charging current with the filter capacitance change from 80uF to 120uF

186

0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.164

6

8

10

12

14

16

0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.160

0.5

1

1.5

Time


0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.164

6

8

10

12

14

16

0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.160

0.5

1

1.5

Time


187

0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.164

6

8

10

12

14

16

0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.160

0.5

1

1.5

Time


As we can see, that the controller works well with low resonant frequency but has some

drawbacks when the resonant frequency shifts to a higher frequency. By tuning the notch

filter’s parameters the performance at the high frequency can be improved. However, with

this procedure the phase margin is sacrificed. Tuning the notch filter can make the effective

damping range wider but concurrently, the control system loses phase margin because of the

notch filter. The controller is robust to the capacitance variation from 0.75 to 1.5 of its

original value. At 0.75 C, the phase margin is reduced to only 36 degree. In figure 6.21 an

unstable system with 40uF and a stable system with 40uF as well are compared. By further

extending the effective frequency range of the notch filter, the system with 40uF capacitor

can be made stable. The notch filter is tuned to widen the damped frequency range around

the resonant frequency. However, concurrently, the control loop phase margin drops

188

dramatically in the red curve and the phase margin is only 19 degree. This phase margin is

not reasonable in a practical design. So here is a tradeoff between the extension of the

effective damped frequency range and control loop performance. To make the control loop

robust to a wide range of parameters variation the control loop has too suffer from the phase

margin reduction. In figure 6.22 the notch filter transfer function and the transfer function of

control plant with all of the inductance (25uH to 75uH) is shown. From the control loop

design point of view, the variation of capacitance is the same as the variation of inductance

because both cases result in the movement of the resonant frequency. The inductance

variation mainly comes from the inductor change because the internal inductance of the

battery cannot be changed drastically. From figure 6.21 and 6.22 we can see that the

frequency variation resulting from the capacitance variation is wider than that of the

inductance variation. So the capacitance variation can represent both the inductance and

capacitance variation. The inductance variation analysis is the same as the capacitance

variation so it is not included. The simulation is conducted to prove the above analysis. In

figure 6.23 the capacitance changes from 80uF to 100uF the charging current almost doesn’t

change. This matches the Bode plot in that the controller for both 80uF and 100uF has the

same DC gain, phase margin and bandwidth. In figure 6.24 the capacitance changes from

80uF to 120uF the charging current is well regulated but some low current ripples can be

observed. With the resonant frequency moving toward an even lower frequency oscillation

may be aroused. In figure 6.25 with the redesigned notch filter the control system is stable.

The charging current is regulated at 10A the current ripples are higher because the filter

capacitance becomes smaller and absorbs less ripple currents. In figure 6.26 with the

189

capacitance change from 80uF to 40uF the control system is no longer stable and the

charging current begins to oscillate.

6.5 Simulation and Experiment Results

The simulation is conducted in Matlab Simulink with a 48V lead-acid battery pack. The

circuit parameters are converter side inductor 0.2mH, the battery side inductor 0.05mH and

the filter capacitor 80uF. The charging current is 10A, dc bus voltage is 100V and the

switching frequency is 10kHz. The simulation results first show the control without the

proposed filter in figure 6.27. As we can see the high frequency oscillation appears on all

currents. The blue curve is the converter side current, the purple curve is the capacitor current

and the red curve is the charging current. In figure 6.28 the proposed controller is plugged

into the control loop, all currents are stable. The zoom-in waveforms of three currents are

shown in figure 6.29. Experimental result for proposed control loop is shown in figure 6.30

and the measured ripple current is shown in figure 6.31. Zoom-in waveforms of all three

currents are shown in figure 6.32. So from the experiment results, we can see that converter

side current has the peak-to-peak current ripple 12A, the capacitor current is 6A and the

charging current has peak-to-peak current ripple 0.6 less than 1% of the charging current. So

the target of ripple free charging is achieved.

190

0.1 0.101 0.102 0.103 0.104 0.105 0.106 0.1070

10

20

30converter-side inductor current

0.1 0.101 0.102 0.103 0.104 0.105 0.106 0.107

-20

0

20

capacitor current

0.1 0.101 0.102 0.103 0.104 0.105 0.106 0.107-20

0

20

40

Time

battery-side inductor current

Figure 6.27 Simulation waveforms of three currents without proposed control

0.1 0.101 0.102 0.103 0.104 0.105 0.106 0.107 0.108 0.109 0.110

10

20Converter side inductor current

0.1 0.101 0.102 0.103 0.104 0.105 0.106 0.107 0.108 0.109 0.11-10

0

10Capacitor current

0.1 0.101 0.102 0.103 0.104 0.105 0.106 0.107 0.108 0.109 0.119

10

11

Time

Battery side inductor current

Figure 6.28 Simulation waveforms of three currents with proposed control

191

0.1 0.1001 0.1002 0.1003 0.1004 0.1005 0.10060

10

20Converter side inductor current

0.1 0.1001 0.1002 0.1003 0.1004 0.1005 0.1006-10

0

10Capacitor current

0.1 0.1001 0.1002 0.1003 0.1004 0.1005 0.10069.5

10

10.5

Time

Battery side inductor current

Figure 6.29 Zoom-in waveforms of three currents with proposed control

Figure 6.30 Experiment results of converter side current, charging current and capacitor current with proposed

control

192


control (charging current AC coupled to show ripple)


control (zoom-in)

converter side current

filter capacitor current

charging current

converter side current

filter capacitor current

charging current

peak to peak 12A

peak to peak 0.6A

193

Figure 6.33 Experiment results of current transient response: 1A (0.1C) to 10A (1C) step change

Figure 6.34 Experiment results of current transient response: 10A (1C) to 1A (0.1C) step change

194

Figure 6.35 Experiment results of pulse charging with 100Hz

Figure 6.36 Experiment results of pulse charging with 200Hz

195

In figure 6.33 and 6.34 the control loop dynamic response is tested. In figure 6.33 the

charging current is changed from a low charging rate 1A (0.1C) to a high charging rate 10A

(1C). The control objective is a battery bank which has a quite slow response but the control

response speed is quite good. The settling time is less than 1ms and the current overshoot is

less than 10%. In figure 6.34 the charging current is changed from a high charging rate 10A

to a low charging rate 2A. In figure 6.35 and 6.36, the pulse charging algorithm is

implemented in the control loop. Since the tested battery is a lead-acid battery bank the pulse

frequency only needs several hundred hertz. So both 100Hz and 200Hz current pulse charge

are tested.

6.6 Summary of Chapter Six

In this chapter, a high-order filter is proposed for dc/dc stage of interactive converter to

facilitate the charging function. The major achievement of this high-order filter is to reduce

the filter size and system volume and moreover significantly reduce the current ripples of the

charging current which yield ripple free charging. Ripple free charging can reduce the heat

generated by the ripple current and internal resistance of the battery so it can lengthen the

battery’s lifetime. To solve the resonance issue of the high-order filter, both the notch filter

and low-pass filter based controllers are proposed and compared. Comprehensive robustness

analysis is conducted on the notch filter based controller. Simulation and experiment results

verify the performance of the proposed filter and new controller.

196

Chapter Seven Conclusion and Future Work

7.1 Conclusion

In this dissertation a grid-interactive smart charger is proposed for plug-in hybrid electric

vehicle in the smart grid applications. The major contributions focus on improving the

performance of PHEV for both grid-connection application and off-grid application, and

power management strategies of multiple PHEVs in smart grid application.

In chapter II a bi-directional grid-interactive charger for plug-in hybrid electric vehicles in

household environment is proposed. The infrastructure of a PHEV integrated with the power

grid at an American home power circuitry is presented. The proposed converter has three

major functions: grid to vehicle (G2V), vehicle to grid (V2G) and vehicle to home (V2H).

The detailed converter power stage design for a 10kW lab prototype is reported including

passive components design, 3-D modeling of the power stage and the efficiency test of the

power stage. The control of three major functions is designed and experimental results verify

the performance of the controller.

In chapter III an adaptive virtual resistor controller to achieve high power quality for large

scale penetration of plug-in hybrid electric vehicles into various power grids is proposed. The

trend of high penetration of plug-in hybrid electric vehicles into the power grid of the future

seems to be imperative and is the best way to utilize PHEVs as energy storage devices.

However when largely connected to the grid the grid impedance varies tremendously and the

grid impedance with LC filter of the converter will form a high order filter which will lead to

high frequency resonance. This resonance will result in a serious power quality issue which

197

limits the grid-connection for PHEVs. Both the active damping method and passive damping

methods are effective ways to resolve this issue. The active damping method has more

advantages over the passive one in that it has no power consumption and more control

flexibility. Virtual resistor based series active damping method is proposed to solve the

resonance issue. A detailed design and control loop analysis is proposed. An auto-tuning

capability is proposed to be plugged into the controller to achieve automatic adjustment of

the damping parameter for various sets of grid impedances. The auto-tuning method uses the

filter capacitor current to extract the resonant current. Then the resonant frequency is

detected and is used as the tuning criterion. The proposed control method and auto-tuning

method are verified by the simulation and the experimental results.

In chapter IV a new control method is proposed as a stand-alone application for plug-in

hybrid electric vehicles. The inverter control methods are thoroughly reviewed and classified

into three groups. The inductor current feedback control and the capacitor current feedback

control are two most widely used control methods. A new method is proposed based on

inductor current feedback control. An active harmonics loop is proposed to be a third loop for

a double-loop control structure. This loop detects and extracts the harmonics from the output

voltage and uses this signal as the feedforward control for the whole loop. The proposed

method greatly enhances the harmonics compensation capability for the inductor current

feedback control. An experiment for steady-state and the transient is conducted to examine

the controller performance. The proposed control method has a better output voltage

especially with nonlinear loads. The capacitor current feedback control and inductor current

feedback control are compared with a different perspective. The capacitor current feedback

198

control cannot limit the inductor current overshoot during the load transient while the

inductor current feedback control can limit the inductor current overshoot even with a

smaller inductor. So we conclude that the inductor current based controller can be used to

optimize passive components and reduce the total volume and weight of the system. By using

the capacitor current based controller the current overshoot will become even higher with a

smaller inductor. This trend of increased inductor current overshoot will increase the

possibility of magnetic core saturation especially in the low power applications where the

cores are designed to operate close to saturation point. The simulation and experimental

results verify the proposed idea and analysis.

In Chapter V a new power management strategy is proposed to resolve the power collapse

issue of multiple PHEVs operating in the Solid State Transformer (SST) based smart grid.

When multiple PHEVs are plugged into one SST based smart grid and the total demand for

power is higher than the power capability of an SST, a new controller is adopted in each

PHEV to reduce its power demand in order to avoid power collapse of the SST. A gain

scheduling technique is proposed to dispatch power to each vehicle based on battery’s state

of charge. The battery with a low state of charge will get more power. This method doesn’t

require a communication method so it will reduce the dependence of the power electronics

converter on communication. It can be used as the converter level control strategy to deal

with voltage instability in the worst case scenario. The worst case means both

communication and system level control are disabled. The proposed power dispatch method

is faster than the two-way communication oriented system level control for the smart grid. So

199

it can be used as the power electronics converter level control to improve the stability of the

solid state transformer.

In Chapter VI: a high order filter is proposed to be use in DC/DC stage of bi-directional

battery charger. The objective is to reduce the filter size which will further reduce the system

cost and volume. Another major goal is to attenuate current ripple of the charging current

which will yield nearly ripple free charging for batteries. Ripple free charging will reduce the

extra heat caused by the current ripple and increase the battery life. The filter based controller

is proposed to deal with the potential instability issue brought by a high order filter. The filter

based method has the advantages of easily implementation and no need of extra current or

voltage sensors. Both low pass filter based controller and notch filter based controller are

analyzed and compared. The notch filter based controller has better performance. The control

loop design and robustness analyses are conducted and presented. The simulation and

experiment results verify the proposed controller.

7.2 Future Work

Future work I: a system level study of large scale of PHEV penetration into the power

grid. This work will focus on the harmonics interaction among a large number of plug-in

vehicles. Even though the individual vehicle meets the grid codes such as IEC61000 and

IEEE 519, there may still be some harmonics issues. The issues are caused by series and

parallel resonance of grid impedance, parasitic circuits of power electronics. The work

should first deliver a switching model of converter which meets the grid code and then large

numbers of this model will be integrated together with different grid impedances and grid

voltage. The power quality issue with a high penetration of PHEVs will be investigated. Then

200

system level solutions to this harmonics issue such as active filter and converter level

solution e.g., random harmonics cancellation should be studied and compared to find a better

approach.

Future work II: modern control theory such as H-Infinity theory and Sliding Mode theory

can be applied to grid connection control. Adaptive tuning based on different impedances can

be achieved. Better performance and less usage of sensing circuitry compared to PI voltage

oriented control (VOC) or PI state space control can be expected.

Future work III: define a frequency based standard for the connection of PHEVs with

solid state transformer. Based on this frequency, the voltage collapse protection and load

management will be achieved. Besides using the frequency, the voltage can be also used to

explore if the reactive power is needed by the loads. The reactive power sharing can be

supplied by both the solid state transformer and PHEVs.

201

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