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
Figure 3.34 Converter-side current and grid-side current with the proposed controller enabled
................................................................................................................................................. 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
Figure 3.40 Converter-side current and grid-side current with the proposed controller enabled
................................................................................................................................................. 83
Figure 3.41 Converter-side current and grid-side current with the proposed controller enabled
................................................................................................................................................. 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
Figure 3.44 Converter-side current and grid-side current with the proposed controller enabled
................................................................................................................................................. 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 5.14 Voltage and current information of no.2 vehicle ............................................... 134
Figure 5.15 SST operation frequency ................................................................................... 136
Figure 5.16 Charging power of two vehicles ........................................................................ 136
Figure 5.17 Enlarged charging power of two vehicles ......................................................... 137
Figure 5.18 Voltage and current information of no.1 vehicle ............................................... 137
Figure 5.19 Voltage and current information of no.2 vehicle ............................................... 138
Figure 5.20 SST operation frequency ................................................................................... 139
Figure 5.21 Charging power of two vehicles ........................................................................ 140
Figure 5.22 Enlarged charging power of two vehicles ......................................................... 140
Figure 5.23 Voltage and current information of no.1 vehicle ............................................... 141
Figure 5.24 Voltage and current information of no.2 vehicle ............................................... 141
Figure 5.25 SST operation frequency ................................................................................... 143
Figure 5.26 Charging power of two vehicles ........................................................................ 143
Figure 5.27 Voltage and current information of no.1 vehicle ............................................... 144
Figure 5.28 Voltage and current information of no.2 vehicle ............................................... 144
Figure 5.29 SST operation frequency ................................................................................... 145
Figure 5.30 Charging power of two vehicles ........................................................................ 145
Figure 5.31 Voltage and current information of no.1 vehicle ............................................... 146
Figure 5.32 Voltage and current information of no.2 vehicle ............................................... 146
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
Figure 5.34 Relationship of dispatched power and integration gain Ki with one vehicle at
normal charging and another one with various conditions ................................................... 149
Figure 5.35 Relationship of dispatched power and integration gain Ki with one vehicle at
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 5.39 System operation frequency .............................................................................. 156
Figure 5.40 Charging power of the vehicle .......................................................................... 157
Figure 5.41 Injection current from renewable energy and possessive load current .............. 157
Figure 5.42 System operation frequency .............................................................................. 158
Figure 5.43 Charging power of the vehicle .......................................................................... 158
Figure 5.44 Injection current from renewable energy and possessive load current .............. 159
Figure 5.45 System operation frequency .............................................................................. 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 5.49 System operation frequency .............................................................................. 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
Figure 6.24 Control robustness test: charging current with the filter capacitance change from
80uF to 100uF ....................................................................................................................... 186
Figure 6.25 Control robustness test: charging current with the filter capacitance change from
80uF to 60uF ......................................................................................................................... 186
Figure 6.26 Control robustness test: charging current with the filter capacitance change from
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
Figure 6.31 Experiment results of converter side current, charging current and capacitor
current with proposed control (charging current AC coupled to show ripple) ..................... 192
Figure 6.32 Experiment results of converter side current, charging current and capacitor
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
Figure 3.33 Converter-side current and grid-side current with the proposed controller enabled
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%
1st 3rd 5th 7th 9th 11th 13th 15th 17th 19th 21th 23th 25th 27th 29th
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
Figure 3.40 Converter-side current and grid-side current with the proposed controller enabled
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%
1st 3rd 5th 7th 9th 11th 13th 15th 17th 19th 21th 23th 25th 27th 29th
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%
1st 3rd 5th 7th 9th 11th 13th 15th 17th 19th 21th 23th 25th 27th 29th
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
132
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
59.5
59.6
59.7
59.8
59.9
60
60.1
60.2
Time
system operation frequency
Figure 5.10 SST operation frequency
133
0 0.2 0.4 0.6 0.8 1 1.20
1000
2000
3000
4000
5000
6000Charging power of No.1 Vehicle
0 0.2 0.4 0.6 0.8 1 1.20
1000
2000
3000
4000
5000
6000
Time
Charging power of No.2 Vehicle
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
4985
4990
4995
5000Charging power of No.1 Vehicle
0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.24980
4985
4990
4995
5000
Time
Charging power of No.2 Vehicle
Figure 5.12 Enlarged charging power of two vehicles
134
0 0.2 0.4 0.6 0.8 1 1.2-50
0
50Grid current of No.1 Vehicle
0 0.2 0.4 0.6 0.8 1 1.2-500
0
500Grid voltage of No.1 Vehicle
0 0.2 0.4 0.6 0.8 1 1.2200
300
400
Time
DC bus voltage of No.1 Vehicle
Figure 5.13 Voltage and current information of no.1 vehicle
0 0.2 0.4 0.6 0.8 1 1.2-50
0
50Grid current of No.2 vehicle
0 0.2 0.4 0.6 0.8 1 1.2-500
0
500Grid voltage of No.2 vehicle
0 0.2 0.4 0.6 0.8 1 1.2200
300
400
Time
DC bus voltage of No.2 Vehicle
Figure 5.14 Voltage and current information of no.2 vehicle
135
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.
136
0 0.5 1 1.559.2
59.3
59.4
59.5
59.6
59.7
59.8
59.9
60
Time
System operation frequency
Figure 5.15 SST operation frequency
0 0.5 1 1.50
2000
4000
6000
8000Charging power of No.1 vehicle
0 0.5 1 1.50
2000
4000
6000
8000
Time
Charging power of No.2 vehicle
Figure 5.16 Charging power of two vehicles
137
1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.54986
4988
4990
4992
4994
4996Charging power of No.1 vehicle
1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.55006
5008
5010
5012
5014
5016
Time
Charging power of No.2 vehicle
Figure 5.17 Enlarged charging power of two vehicles
0 0.2 0.4 0.6 0.8 1 1.2-50
0
50Grid current of No.1 vehicle
0 0.2 0.4 0.6 0.8 1 1.2-500
0
500Grid voltage of No.1 vehicle
0 0.2 0.4 0.6 0.8 1 1.2200
300
400
Time
DC bus voltage of No.1 vehicle
Figure 5.18 Voltage and current information of no.1 vehicle
138
0 0.2 0.4 0.6 0.8 1 1.2-50
0
50Grid current of No.2 vehicle
0 0.2 0.4 0.6 0.8 1 1.2-500
0
500Grid voltage of No.2 vehicle
0 0.2 0.4 0.6 0.8 1 1.2200
300
400
Time
DC bus voltage of No.2 vehicle
Figure 5.19 Voltage and current information of no.2 vehicle
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.
0 0.5 1 1.559.2
59.3
59.4
59.5
59.6
59.7
59.8
59.9
60
Time
System operation frequency
Figure 5.20 SST operation frequency
140
0 0.5 1 1.50
2000
4000
6000
8000Charging power of No.1 vehicle
0 0.5 1 1.50
2000
4000
6000
8000
Time
Charging power of No.2 vehicle
Figure 5.21 Charging power of two vehicles
1.4 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49 1.55990
5995
6000
6005
6010Charging power of No.1 vehicle
1.4 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49 1.54010
4015
4020
4025
4030
Time
Charging power of No.2 vehicle
Figure 5.22 Enlarged charging power of two vehicles
141
0 0.5 1 1.5-50
0
50Grid current of No.1 vehicle
0 0.5 1 1.5-500
0
500Grid voltage of No.1 vehicle
0 0.5 1 1.5100
200
300
400
Time
DC bus voltage of No.1 vehicle
Figure 5.23 Voltage and current information of no.1 vehicle
0 0.5 1 1.5-50
0
50Grid current of No.2 vehicle
0 0.5 1 1.5-500
0
500Grid voltage of No.2 vehicle
0 0.5 1 1.5100
200
300
400
Time
DC bus voltage of No.2 vehicle
Figure 5.24 Voltage and current information of no.2 vehicle
142
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.
143
0 0.5 1 1.559.2
59.3
59.4
59.5
59.6
59.7
59.8
59.9
60
60.1
Time
system operation frequency
Figure 5.25 SST operation frequency
0 0.5 1 1.50
1000
2000
3000
4000
5000
6000
7000Charging power of No.1 vehicle
0 0.5 1 1.50
2000
4000
6000
8000
Time
Charging powre of No.2 vehicle
Figure 5.26 Charging power of two vehicles
144
0 0.5 1 1.5-50
0
50Grid current of No.1 vehicle
0 0.5 1 1.5-500
0
500Grid voltage of No.1 vehicle
0 0.5 1 1.5100
200
300
400
Time
DC bus voltage of No.1 vehicle
Figure 5.27 Voltage and current information of no.1 vehicle
0 0.5 1 1.5-50
0
50Grid current of No.2 vehicle
0 0.5 1 1.5-500
0
500Grid voltage of No.2 vehicle
0 0.5 1 1.5100
200
300
400
Time
DC bus voltage of No.2 vehicle
Figure 5.28 Voltage and current information of no.2 vehicle
145
0 0.5 1 1.559.3
59.4
59.5
59.6
59.7
59.8
59.9
60
60.1
Time
system operation frequency
Figure 5.29 SST operation frequency
0 0.5 1 1.50
1000
2000
3000
4000
5000
6000Charging power of No.1 vehicle
0 0.5 1 1.50
100020003000
4000500060007000
Time
Charging power of No.2 vehicle
Figure 5.30 Charging power of two vehicles
146
0 0.5 1 1.5-50
0
50Grid current of No.1 vehicle
0 0.5 1 1.5-500
0
500Grid voltage of No.1 vehicle
0 0.5 1 1.5100
200
300
400
Time
DC bus voltage of No.1 vehicle
Figure 5.31 Voltage and current information of no.1 vehicle
0 0.5 1 1.5-50
0
50Grid current of No.2 vehicle
0 0.5 1 1.5-500
0
500Grid voltage of No.2 vehicle
0 0.5 1 1.5100
200
300
400
Time
DC bus voltage of No.2 vehicle
Figure 5.32 Voltage and current information of no.2 vehicle
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
SOC=30%SOC=40%SOC=50%SOC=60%SOC=70%
Figure 5.34 Relationship of dispatched power and integration gain Ki with one vehicle at normal charging and
another one with various conditions
150
0 500 1000 1500 2000 2500 3000 3500 40003000
3500
4000
4500
5000
5500
6000
6500
7000
7500
8000
SOC=30%SOC=40%SOC=50%SOC=60%SOC=70%
Figure 5.35 Relationship of dispatched power and integration gain Ki with one vehicle at mild charging and
another one with various conditions
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.
155
0 0.5 1 1.559.2
59.3
59.4
59.5
59.6
59.7
59.8
59.9
60
Time
system operation frequency
Figure 5.36 System operation frequency
0 0.5 1 1.50
1000
2000
3000
4000
5000
6000
7000
Time
Figure 5.37 Charging power of the vehicle
156
0 0.5 1 1.5-50
0
50
0 0.5 1 1.5-500
0
500
0 0.5 1 1.5200
300
400
Time
Figure 5.38 Grid voltage, current and dc bus voltage of the vehicle
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.659.1
59.2
59.3
59.4
59.5
59.6
59.7
59.8
59.9
60
Time
Figure 5.39 System operation frequency
157
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60
1000
2000
3000
4000
5000
6000
7000
Time
Figure 5.40 Charging power of the vehicle
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6-500
0
500Gird voltage
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6-50
0
50Current injection from renewable energy
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6-100
0
100
Time
Possesive load current
Figure 5.41 Injection current from renewable energy and possessive load current
158
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 258.8
59
59.2
59.4
59.6
59.8
60
60.2
Time
system operation frequency
Figure 5.42 System operation frequency
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
1000
2000
3000
4000
5000
6000
Time
Figure 5.43 Charging power of the vehicle
159
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-500
0
500Grid voltage
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-20
0
20Current injection from renewable energy
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-100
0
100
Time
Possesive load current
Figure 5.44 Injection current from renewable energy and possessive load current
0 0.5 1 1.5 2 2.558.8
59
59.2
59.4
59.6
59.8
60
60.2
60.4
60.6
Time
system operation frequency
Figure 5.45 System operation frequency
160
0 0.5 1 1.5 2 2.5-3000
-2000
-1000
0
1000
2000
3000
4000
5000
6000
7000
Time
powre from vehicle
Figure 5.46 Charging and discharging power of the vehicle
0 0.5 1 1.5 2-50
0
50Grid current of vehicle
0 0.5 1 1.5 2-500
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
system operation frequency
Figure 5.49 System operation frequency
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
System: Gout2c_dampGain Margin (dB): 16.9At frequency (Hz): 1.13e+003Closed Loop Stable? Yes
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
System: Gout2c_dampPhase Margin (deg): 52.5Delay Margin (sec): 0.000481At frequency (Hz): 303Closed Loop Stable? Yes
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
System: Gout2c_dampGain Margin (dB): 6.34At frequency (Hz): 1.82e+003Closed Loop Stable? Yes
Mag
nitu
de (d
B)
10-2
10-1
100
101
102
103
104
105
-405
-360
-315
-270
-225
-180
-135
-90
System: Gout2c_dampPhase Margin (deg): 54.9Delay Margin (sec): 0.000212At frequency (Hz): 719Closed Loop Stable? Yes
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
System: Gout2c_dampGain Margin (dB): 8.55At frequency (Hz): 1.83e+003Closed Loop Stable? Yes
Mag
nitu
de (d
B)
10-2
10-1
100
101
102
103
104
105
-450
-360
-270
-180
-90
System: Gout2c_dampPhase Margin (deg): 54.9Delay Margin (sec): 0.000212At frequency (Hz): 719Closed Loop Stable? Yes
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
System: Gout2c_dampGain Margin (dB): 6.34At frequency (Hz): 1.82e+003Closed Loop Stable? Yes
Mag
nitu
de (d
B)
10-2
10-1
100
101
102
103
104
105
-405
-360
-315
-270
-225
-180
-135
-90
System: Gout2c_dampPhase Margin (deg): 54.2Delay Margin (sec): 0.000205At frequency (Hz): 732Closed Loop Stable? Yes
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
System: Gout2c_dampGain 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
-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
System: Gout2c_dampGain Margin (dB): 4.47At frequency (Hz): 3.26e+003Closed Loop Stable? Yes
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
System: Gout2c_dampGain Margin (dB): -2.95At frequency (Hz): 3.99e+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_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
Figure 6.24 Control robustness test: charging current with the filter capacitance change from 80uF to 100uF
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 6.25 Control robustness test: charging current with the filter capacitance change from 80uF to 60uF
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
Figure 6.26 Control robustness test: charging current with the filter capacitance change from 80uF to 40uF
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
Figure 6.31 Experiment results of converter side current, charging current and capacitor current with proposed
control (charging current AC coupled to show ripple)
Figure 6.32 Experiment results of converter side current, charging current and capacitor current with proposed
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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