an improved battery/ultracapacitor … · storage system management strategy for electric vehicles...
TRANSCRIPT
A
AN IMPROVED BATTERY/ULTRACAPACITOR HYBRID ENERGY
STORAGE SYSTEM MANAGEMENT STRATEGY FOR
ELECTRIC VEHICLES
SO KAI MAN
(B.Eng. (Hons.), NUS)
A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
DEPARTMENT OF MECHANICAL ENGINEERING
NATIONAL UNIVERSITY OF SINGAPORE
2017
Supervisors:
Associate Professor Hong Geok Soon, Main Supervisor
Associate Professor Lu Wen Feng, Co-Supervisor
Examiners:
Associate Professor Lee Kim Seng
Associate Professor Chen Chao Yu, Peter
Associate Professor Chen Xiaoqi, University of Canterbury
ii
DECLARATION PAGE
I hereby declare that this thesis is my original work and it has been written by me in its
entirety. I have duly acknowledged all the sources of information which have been used in
the thesis.
This thesis has also not been submitted for any degree in any university previously.
_______________________________________
So Kai Man
22 December 2017
iii
ACKNOWLEDGMENTS
Firstly, the author would like to express his sincere gratitude to his supervisors – Assoc. Prof
Hong Geok Soon, Assoc. Prof Lu Wen Feng and Prof Wong Yoke San – for their
supervision, guidance and advice throughout the project.
Secondly, the author would like to extend his appreciation to his laboratory mates for their
help, suggestions and recommendations. They are Mr Kawsar Ali and Ms Sindhu Shetty from
Electrical Machines and Drives Lab, Department of Electrical & Computer Engineering, Mr
Lihil Uthpala Subasinghe and Mr Manikandan Balasundaram from Thermal Process Lab,
Department of Mechanical Engineering, Dr Zhang Ming, Ms See Hian Hian, Mr Ch’ng Chin
Boon, and Mr Yedige Tlegenov from Control Lab, Department of Mechanical Engineering.
Thirdly, the author would like to thank the staff at Control Labs 1 & 2, and Thermal Process
Lab 1, Department of Mechanical Engineering for their kind assistance rendered.
Lastly, special mention must be given to the author’s friends for their moral support.
iv
TABLE OF CONTENTS
DECLARATION PAGE ......................................................................................................... ii
ACKNOWLEDGMENTS ..................................................................................................... iii
TABLE OF CONTENTS ....................................................................................................... iv
SUMMARY .............................................................................................................................. x
LIST OF TABLES ................................................................................................................. xii
LIST OF FIGURES .............................................................................................................. xiv
LIST OF SYMBOLS ............................................................................................................. xx
LIST OF ACRONYMS ........................................................................................................ xxi
1 INTRODUCTION............................................................................................................ 1
1.1 Problems of Electric Vehicles ..................................................................................... 1
1.2 Battery/UC HESS ........................................................................................................ 2
1.3 Energy Management Strategy & Power Management Strategy .................................. 3
1.4 Criticism of Battery/UC HESS ................................................................................... 4
1.5 Objective ..................................................................................................................... 4
1.6 Scope ........................................................................................................................... 5
1.7 Structure of Thesis ...................................................................................................... 6
1.8 Contributions ............................................................................................................... 8
1.9 Publications ................................................................................................................. 9
2 LITERATURE REVIEW ............................................................................................. 10
2.1 Overview ................................................................................................................... 10
2.2 Hardware: HESS Topologies .................................................................................... 11
2.3 Software: HESS Management Strategies .................................................................. 14
2.3.1 Energy Management Strategies ......................................................................... 14
2.3.2 Power Management Strategies ........................................................................... 16
v
2.4 Case Studies .............................................................................................................. 18
2.4.1 Dixon, Ortuzar & Moreno.................................................................................. 18
2.4.2 Avelino, Garcia, Ferreira & Pomilio.................................................................. 20
2.4.3 Choi, Lee & Seo ................................................................................................. 20
2.5 Limitations of Existing Works and Proposed Approach ........................................... 21
3 VEHICLE & HESS MODELLING ............................................................................. 23
3.1 Selected HESS Topology .......................................................................................... 23
3.2 Drive Cycle ............................................................................................................... 24
3.3 Simulation Approach................................................................................................. 26
3.4 Motor & Inverter Model ............................................................................................ 27
3.5 Auxiliary Loads ......................................................................................................... 30
3.6 Vehicle Model ........................................................................................................... 30
3.7 Battery Model ............................................................................................................ 37
3.8 Ultracapacitor Model................................................................................................. 40
3.9 DC/DC Converter Model .......................................................................................... 42
3.9.1 Boost Mode Duty Cycle..................................................................................... 43
3.9.2 Boost Mode Efficiency ...................................................................................... 46
3.9.3 Buck Mode Duty Cycle ..................................................................................... 47
3.9.4 Buck Mode Efficiency ....................................................................................... 50
3.9.5 Combined Duty Cycle and Efficiency ............................................................... 51
3.10 Battery Cycle Life Model .......................................................................................... 52
3.11 Parameters for Modelling .......................................................................................... 54
3.11.1 General ............................................................................................................... 54
3.11.2 Using UR18650W Batteries .............................................................................. 57
vi
4 HESS: IMPROVED ENERGY & POWER MANAGEMENT STRATEGIES ...... 59
4.1 Power Management Strategy Pt. 1: Battery Limits ................................................... 59
4.1.1 Battery Power at Constant Speeds ..................................................................... 60
4.1.2 Final Battery Limit Curve .................................................................................. 61
4.2 Energy Management Strategy ................................................................................... 63
4.2.1 Sufficient Space in UC for Regenerative Braking ............................................. 64
4.2.2 Sufficient Energy in UC for Acceleration ......................................................... 70
4.2.3 Selected Braking and Acceleration Torque Values ........................................... 74
4.2.4 Target UC Energy Band..................................................................................... 79
4.2.5 Summary ............................................................................................................ 85
4.3 Power Management Strategy Pt. 2: Implementation ................................................. 85
4.4 Summary ................................................................................................................... 88
5 HESS SIMULATIONS .................................................................................................. 91
5.1 Implementation.......................................................................................................... 91
5.2 EMS Comparison: Target UC Energy Band ............................................................. 93
5.3 PMS Comparison: Battery Power Limits .................................................................. 96
5.4 Drive Cycles .............................................................................................................. 97
5.4.1 LA92 Drive Cycle .............................................................................................. 97
5.4.2 EUDC ............................................................................................................... 103
5.4.3 FTP-75 City Drive Cycle ................................................................................. 104
5.5 Battery Cycle Life ................................................................................................... 107
5.5.1 Description ....................................................................................................... 107
5.5.2 Drive Cycle Comparison.................................................................................. 107
5.5.3 Simulation ........................................................................................................ 108
5.5.4 Drive Cycle Selection for Experiment 2 .......................................................... 112
vii
5.6 Summary ................................................................................................................. 112
6 HESS EXPERIMENTS ............................................................................................... 114
6.1 Setup ........................................................................................................................ 114
6.1.1 Energy Storage Components............................................................................ 117
6.1.2 DC/DC Converter ............................................................................................ 117
6.1.3 Sensors ............................................................................................................. 120
6.1.4 Safety Components .......................................................................................... 124
6.2 Scaling ..................................................................................................................... 126
6.3 Scale Factor k .......................................................................................................... 127
6.3.1 Selecting k Based on Drive Cycle ................................................................... 127
6.3.2 Selecting k Based on Simulation/Experiment Energy Ratio ........................... 128
6.3.3 Selecting k Based on Battery Limitations ........................................................ 129
6.3.4 Consequences of k = 160 ................................................................................. 130
6.4 Experiment 0 ........................................................................................................... 132
6.4.1 Objective .......................................................................................................... 132
6.4.2 Procedure ......................................................................................................... 132
6.4.3 Results .............................................................................................................. 134
6.4.4 Summary .......................................................................................................... 140
6.5 Software Implementation ........................................................................................ 140
6.5.1 Algorithm Curve Fitting .................................................................................. 140
6.5.2 Syncing Speed with Power .............................................................................. 144
6.5.3 Problems with Maccor ..................................................................................... 144
6.5.4 Battery Power vs. Current Thresholds ............................................................. 145
6.5.5 Integral Controller for UC Voltage Control..................................................... 146
6.6 Experiment 1 ........................................................................................................... 149
viii
6.6.1 Objective .......................................................................................................... 149
6.6.2 EUDC Drive Cycle .......................................................................................... 149
6.6.3 FTP-75 City Drive Cycle ................................................................................. 153
6.6.4 Average Currents ............................................................................................. 158
6.6.5 Summary .......................................................................................................... 159
6.7 Experiment 2 ........................................................................................................... 160
6.7.1 Objective .......................................................................................................... 160
6.7.2 Description ....................................................................................................... 160
6.7.3 Procedure ......................................................................................................... 161
6.7.4 Battery Discharge Capacity Test ..................................................................... 162
6.7.5 Battery-only Setup ........................................................................................... 165
6.7.6 Initial Results ................................................................................................... 166
6.7.7 Battery-only Undervoltage During Demanding Sections ................................ 167
6.7.8 Battery-only Contact Resistance ...................................................................... 168
6.7.9 Battery-only Setup, Revised ............................................................................ 172
6.7.10 Final Results..................................................................................................... 174
6.7.11 Summary .......................................................................................................... 176
7 HESS REDUCED-SCALED SIMULATIONS ......................................................... 177
7.1 Differences between Full and Reduced-scale Simulation ....................................... 177
7.2 EUDC ...................................................................................................................... 178
7.3 FTP-75 City Drive Cycle ........................................................................................ 179
7.4 Total Energy Use ..................................................................................................... 181
7.5 Summary ................................................................................................................. 183
8 CONCLUSION & FUTURE WORKS ...................................................................... 184
8.1 Conclusion ............................................................................................................... 184
ix
8.2 Future Works ........................................................................................................... 186
8.2.1 Optimization to Extend Battery Cycle Life ..................................................... 186
8.2.2 Full-scale Implementation ............................................................................... 187
8.2.3 SuPower Battery Cycle Life Curve Fitting ...................................................... 188
8.2.4 Cost-Benefit Analysis of UCs .......................................................................... 189
8.2.5 Improvement to Experiments ........................................................................... 189
BIBLIOGRAPHY ................................................................................................................ 190
APPENDIX ........................................................................................................................... 201
A Charging Procedure .................................................................................................... 201
B Scaling......................................................................................................................... 202
C Sensor Circuits ............................................................................................................ 206
x
SUMMARY
Electric Vehicles (EVs) still have not been adopted by the masses yet. Common grievances
include the high cost of EVs as well as the limited driving range. The EV battery is an
expensive component, so it is desirable to extend the batteries’ cycle life. One reason which
shortens battery lifespan is high charge and discharge rates. A solution is to adopt a Hybrid
Energy Storage System (HESS), with an Ultracapacitor (UC) assisting the battery. The high
power density of the UC can relieve the battery of high charge and discharge rates, extending
the battery’s cycle life.
There are two parts to the HESS – energy management strategy (EMS) and power
management strategy (PMS). Most existing works focus on PMS. The existing EMS are quite
empirical, such as a fixed target UC energy level regardless of loading conditions. This can
be further improved.
In this work, a novel HESS management strategy is proposed. The EMS involves a more
comprehensive method of setting the target UC energy level using a speed-dependent band,
which considers worst case scenarios and real-life drive cycles. This is the first contribution
of this work. With the proposed EMS, the UC can achieve two goals – to contain sufficient
energy required for future accelerations, and to have sufficient space to store energy captured
from future regenerative braking.
The PMS has two goals – to ensure the EMS (target UC energy level) is followed, and to
ensure the battery charge/discharge rates do not exceed the limits. A novel method of setting
the battery power limit based on speed is proposed, which is the second contribution of this
work. This also has two goals – better utilisation of the UC and to ensure that when the EV
travels at constant speed, the power is supplied mainly by the battery.
xi
Simulations were performed using the proposed battery/UC HESS management strategy on a
mid-sized EV sedan. The results show that the proposed strategy achieves the four goals of
the EMS and PMS mentioned above, as well as the two speed-dependent battery limit goals.
Further simulations show that existing published works cannot achieve all the goals
simultaneously unless their UCs are sized twice as large, increasing weight and costs.
Subsequently, battery cycle life simulations were performed to observe the battery capacity
fade for the proposed battery/UC HESS, and for a battery-only system. Almost 30%
reduction in capacity loss due to cycling was seen for the proposed battery/UC HESS as
compared to the battery-only system when running three FTP-75 city drive cycles daily over
10 years.
Afterwards, a reduced-scale experiment was constructed. This experiment verified the
proposed strategy could work physically as intended. Then the experiment was compared to a
reduced-scale simulation. They behave similarly time-wise and in terms of energy consumed.
Lastly, another set of experiment was performed to compare the battery cycle life of the
battery/UC HESS to a battery-only system. Each setup was cycled continuously with the
FTP-75 city drive cycle. As only 190 cycles have been completed, the results are too close to
call.
xii
LIST OF TABLES
Table 3-1 Simulation parameters for the vehicle model. ......................................................... 55
Table 3-2 Simulation parameters for the EV motor................................................................. 56
Table 3-3 Parameters of new components to be installed in the EV. ...................................... 57
Table 3-4 Parameters of Nissan Leaf and modified batteries. ................................................. 58
Table 3-5 Parameters for battery voltage and battery cycle life curve fitting. ........................ 58
Table 5-1 Comparison of no. of drive cycles to hit 50km. .................................................... 108
Table 5-2 Simulated cycle life capacity losses over 10 years. ............................................... 110
Table 5-3 Simulated cycle life for 20% capacity losses. ....................................................... 111
Table 5-4 Simulated cycle life for 80% capacity losses, including calendar loss. ................ 112
Table 6-1 Energy storage components. .................................................................................. 117
Table 6-2 DC/DC converter components. ............................................................................. 119
Table 6-3 Sensors and supporting components. .................................................................... 121
Table 6-4 Safety & miscellaneous components. .................................................................... 125
Table 6-5 Symbols and their meanings for scaling derivation. ............................................. 127
Table 6-6 Battery and UC energy specifications. .................................................................. 129
Table 6-7 Value of k which allows 3x FTP-75 city drive cycle to complete. ....................... 130
Table 6-8 UC scaling specifications. ..................................................................................... 131
Table 6-9 Battery scaling specifications. ............................................................................... 132
Table 6-10 DC/DC converter efficiency test for one data point. ........................................... 133
Table 6-11 Reduced-scale simulation parameters. ................................................................ 137
Table 6-12 Average of absolute battery currents for experiments ......................................... 159
Table 6-13 Discharge capacity test procedure. ...................................................................... 162
Table 6-14 FTP-75 city drive cycles before battery undervoltage. ....................................... 169
Table 7-1 Experiment battery energy use. ............................................................................. 182
xiii
Table 7-2 Comparison of battery energy use between experiments and reduced-scale
simulations. ............................................................................................................................ 182
Table A-1 Symbols and their meanings for scaling derivation. ............................................. 202
xiv
LIST OF FIGURES
Figure 1-1 Ragone plot illustrating power and energy densities [9]. ......................................... 2
Figure 2-1 Passive configuration [32]...................................................................................... 11
Figure 2-2 Nissan Leaf Li-ion battery pack discharge curve [34]. .......................................... 12
Figure 2-3 Partially-decoupled configuration [32]. ................................................................. 12
Figure 2-4 Partially-decoupled configuration 2 [32]. .............................................................. 13
Figure 2-5 Fully-decoupled cascaded configuration [32]. ....................................................... 13
Figure 2-6 Fully-decoupled multiple converter configuration [32]. ........................................ 14
Figure 2-7 Power management strategies [11]. ....................................................................... 16
Figure 2-8 Target UC SOC values [47]. .................................................................................. 19
Figure 3-1 Single DC/DC converter between battery and UC. ............................................... 23
Figure 3-2 FTP-75 city drive cycle (Transient) [55]. .............................................................. 24
Figure 3-3 FTP-75 HWFET drive cycle (Transient) [55]. ....................................................... 25
Figure 3-4 LA92 drive cycle (Transient) [55]. ........................................................................ 25
Figure 3-5 ECE-15 drive cycle (Modal) [55]. ......................................................................... 26
Figure 3-6 EUDC (Modal) [55]. .............................................................................................. 26
Figure 3-7 2011 Nissan Leaf combined motor/inverter efficiency [59]. ................................. 28
Figure 3-8 Combined motor/inverter efficiencies.................................................................... 29
Figure 3-9 Block diagram for vehicle model updating. ........................................................... 31
Figure 3-10 EUDC input. ......................................................................................................... 35
Figure 3-11 Forces over EUDC: intermediate output from model. ......................................... 36
Figure 3-12 Torque over EUDC: intermediate output from model. ........................................ 36
Figure 3-13 Power over EUDC: model output. ....................................................................... 36
Figure 3-14 Battery model. ...................................................................................................... 37
Figure 3-15 Block diagram for battery model updating. ......................................................... 37
xv
Figure 3-16 UC model. ............................................................................................................ 40
Figure 3-17 Block diagram for UC model updating. ............................................................... 40
Figure 3-18 Electrical model of DC/DC converter. ................................................................. 42
Figure 3-19 Boost mode, Q2 on. .............................................................................................. 43
Figure 3-20 Boost mode, Q2 off. ............................................................................................. 44
Figure 3-21 Buck mode, Q1 on................................................................................................ 47
Figure 3-22 Buck mode, Q1 off. .............................................................................................. 48
Figure 3-23 Combined buck-boost duty cycle. ........................................................................ 51
Figure 3-24 Combined buck-boost efficiency. ........................................................................ 51
Figure 4-1 Battery power required at constant vehicle speed. ................................................. 61
Figure 4-2 Speed-dependent PMS battery limit curve. ............................................................ 62
Figure 4-3 Block diagram of overall EMS design ................................................................... 64
Figure 4-4 EMS block diagram to anticipate UC space required or energy generated. .......... 65
Figure 4-5 (a) Kinematics (b) torques (c) powers (d) SOCs during regenerative braking. ..... 69
Figure 4-6 (a) Kinematics (b) torques (c) powers (d) SOCs during acceleration. ................... 73
Figure 4-7 Target UC SOC for varying brake torques and start velocities. ............................ 76
Figure 4-8 Brake torques corresponding to max. recovered UC energy for each velocity. .... 76
Figure 4-9 Target UC SOC for varying brake torques and start velocities. ............................ 78
Figure 4-10 Target UC SOC band vs. speed, 6 UC modules. ................................................. 80
Figure 4-11 Target UC SOC band vs. speed, 5 UC modules. ................................................. 81
Figure 4-12 Target UC SOC for varying brake torques and start velocities, 5 UC modules. . 82
Figure 4-13 Target UC SOC band vs. speed, no battery power loosening .............................. 83
Figure 4-14 Block diagram of PMS algorithm. ....................................................................... 86
Figure 5-1 Complete simulation block diagram. ..................................................................... 92
Figure 5-2 Target UC SOC band vs. speed, 6 UC modules. ................................................... 93
xvi
Figure 5-3 Target UC SOC band vs. speed, 13 UC modules. ................................................. 95
Figure 5-4 Speed-dependent PMS battery limit curve comparison. ........................................ 96
Figure 5-5 LA92 drive cycle power required. ......................................................................... 98
Figure 5-6 LA92 torque profile for the mid-sized EV. ............................................................ 98
Figure 5-7 LA92 power distribution of battery and UC. ......................................................... 99
Figure 5-8 LA92 UC SOC (target and actual) and battery SOC. ............................................ 99
Figure 5-9 LA92 torque profile for the mid-sized EV, zoomed 820-920s. ........................... 100
Figure 5-10 LA92 power distribution of battery and UC, zoomed 820-920s. ....................... 100
Figure 5-11 LA92 UC and battery SOC, zoomed 820-920s. ................................................. 101
Figure 5-12 EUDC power distribution of battery and UC. .................................................... 103
Figure 5-13 EUDC UC and battery SOC. .............................................................................. 103
Figure 5-14 FTP-75 city power distribution of battery and UC. ........................................... 105
Figure 5-15 FTP-75 city UC and battery SOC. ..................................................................... 105
Figure 5-16 FTP-75 city power distribution of battery and UC, zoomed 150-250s. ............. 106
Figure 5-17 FTP-75 city UC and battery SOC, zoomed 150-250s. ....................................... 106
Figure 5-18 Battery capacity loss curve for battery/UC system over FTP-75 city. ............... 109
Figure 6-1 Electrical diagram of experiment setup................................................................ 115
Figure 6-2 Photo of experiment setup (front). ....................................................................... 115
Figure 6-3 Photo of experiment setup (top). .......................................................................... 116
Figure 6-4 Photo of experiment setup (side, auxiliary equipment). ...................................... 116
Figure 6-5 Photo of DC/DC converter. .................................................................................. 118
Figure 6-6 Voltage sensor calibration. ................................................................................... 123
Figure 6-7 Current sensor calibration. ................................................................................... 124
Figure 6-8 Experiment 0 setup. .............................................................................................. 133
Figure 6-9 DC/DC converter boost efficiency. ...................................................................... 134
xvii
Figure 6-10 DC/DC converter buck efficiency. ..................................................................... 135
Figure 6-11 Interpolated DC/DC converter efficiency from experiment. ............................. 136
Figure 6-12 DC/DC converter efficiency from simulation. ................................................... 139
Figure 6-13 DC/DC converter efficiency, experimental minus simulation output. ............... 139
Figure 6-14 Reduced-scale combined motor/inverter efficiency. .......................................... 141
Figure 6-15 Battery power to maintain EV at constant speed for k=160. ............................. 141
Figure 6-16 Target UC SOC band for k=160. ....................................................................... 142
Figure 6-17 EUDC speed profile after scaling with k=160. .................................................. 149
Figure 6-18 Battery & UC currents from experiment, EUDC. .............................................. 150
Figure 6-19 Battery & UC voltages from experiment, EUDC. ............................................. 151
Figure 6-20 Target UC voltage addition term vuc,tar,add, EUDC. ............................................ 151
Figure 6-21 Power and time sync check, EUDC. .................................................................. 153
Figure 6-22 FTP-75 city speed profile after scaling with k=160. .......................................... 153
Figure 6-23 Battery & UC currents from experiment, FTP-75 city. ..................................... 154
Figure 6-24 Battery & UC voltages from experiment, FTP-75 city. ..................................... 154
Figure 6-25 Target UC voltage addition term vuc,tar,add, FTP-75 city. .................................... 155
Figure 6-26 Battery & UC currents from experiment, FTP-75 city, zoomed 180-280s. ....... 155
Figure 6-27 Battery & UC voltages from experiment, FTP-75 city, zoomed 180-280s. ...... 156
Figure 6-28 Target UC voltage addition term vuc,tar,add, FTP-75 city, zoomed 180-280s. ..... 156
Figure 6-29 Power and time sync check, FTP-75 city. .......................................................... 157
Figure 6-30 Battery-only setup. Currents from experiment, FTP-75 city run 1. ................... 158
Figure 6-31 (a) Discharging current from ACS3 (b) coulomb counting. .............................. 164
Figure 6-32 Discharging voltage. .......................................................................................... 164
Figure 6-33 Battery discharging capacity. ............................................................................. 164
Figure 6-34 Battery discharge capacity tests over 60 cycles. ................................................ 166
xviii
Figure 6-35 Battery-only voltage for FTP-75 city, tripped, k=160. ...................................... 167
Figure 6-36 Battery-only current for FTP-75 city, tripped, k=160. ....................................... 167
Figure 6-37 Contact resistance experiment connections diagram. ........................................ 170
Figure 6-38 Current profile to find voltage drop. .................................................................. 171
Figure 6-39(a) Measured voltages (b) voltage drop. ............................................................. 171
Figure 6-40 Equivalent resistance (contact resistance and other losses). .............................. 171
Figure 6-41 Photo of battery-only setup. ............................................................................... 172
Figure 6-42(a) Measured voltages (b) voltage drop. ............................................................. 173
Figure 6-43 Equivalent resistance (contact resistance and others). ....................................... 173
Figure 6-44 Battery capacity of battery-only and battery/UC setup. ..................................... 174
Figure 6-45 Relative capacity. Cycle capacity divided by initial capacity. ........................... 174
Figure 6-46 Capacity “gained” due to high contact resistance .............................................. 175
Figure 7-1 Battery & UC currents from simulation, EUDC (compare with experiment in
Figure 6-18). .......................................................................................................................... 178
Figure 7-2 Battery & UC voltages from simulation, EUDC (compare with experiment in
Figure 6-19). .......................................................................................................................... 178
Figure 7-3 Battery & UC currents from simulation, FTP-75 city (compare with experiment in
Figure 6-23). .......................................................................................................................... 179
Figure 7-4 Battery & UC voltages from simulation, FTP-75 city (compare with experiment in
Figure 6-24). .......................................................................................................................... 180
Figure 7-5 Battery & UC currents from simulation, FTP-75 city, zoomed 180-280s (compare
with experiment in Figure 6-26). ........................................................................................... 180
Figure 7-6 Battery & UC voltages from simulation, FTP-75 city, zoomed 180-280s (compare
with experiment in Figure 6-27). ........................................................................................... 181
Figure A-1 Charging current (b) coulomb counting. ............................................................. 201
xix
Figure A-2 Charging voltage. ................................................................................................ 201
Figure A-3 Voltage sensors and filters. ................................................................................. 206
Figure A-4 Current sensor filters, precision voltage reference and thermistor. ..................... 207
Figure A-5 Relays. ................................................................................................................. 208
xx
LIST OF SYMBOLS
ρ Air density g Gravitational acceleration
ωx Angular velocity h Height of CG
A, B, K,
Vbatt,0
Battery constants Rx Internal resistance, where x =
batt / uc / etc.
a, b, c, d, e Battery cycle life constants m Mass
C Capacitance of UC Px Power, where x = batt / uc / etc.
Qx Capacity, where x = batt /
uc / etc.
μs Static friction coefficient
Ahthroughput Charge used SOCx State of Charge, where x = batt
/ uc / etc.
ix Current, where x = batt /
uc / etc.
T Temperature
Lb Distance from rear wheel
to CG
t, j, k Time / Loop iteration
Cd Drag coefficient τx Torque
ηx Efficiency vwh Velocity of wheel
Ex Energy, where x = batt / uc
/ etc.
vx Voltage, where x = batt / uc /
etc.
Af Frontal area rwh Wheel radius
Gr Gear ratio L Wheelbase length
θ Gradient angle of road
xxi
LIST OF ACRONYMS
BMS Battery Management System
CC Constant Current
CV Constant Voltage
DoD Depth of Discharge
ECE Economic Commission for Europe
EMS Energy Management Strategy
EUDC Extra-Urban Driving Cycle
EV Electric Vehicle
FTP Federal Test Procedures
HESS Hybrid Energy Storage System
IGBT Insulated-gate bipolar transistor
Li-ion Lithium-ion
MOSFET Metal-oxide-semiconductor field-effect transistor
NEDC New European Driving Cycle
OCV Open Circuit Voltage
PMS Power Management Strategy
PMSM Permanent Magnet Synchronous Motor
SOC State of Charge
UC Ultracapacitor
1
1 INTRODUCTION
1.1 Problems of Electric Vehicles
Electric Vehicles (EVs) have already been commercially available for a number of years.
Well-known models include the Nissan Leaf, Mitsubishi i-MiEV, and the high-performance
Tesla Model S. However, they have not been adopted by the masses yet – most of the EVs
today are only used for trial or research purposes. Reasons for this situation include the high
costs of EVs, as well as their limited driving range.
In Singapore, a brand new Nissan Leaf for private use costs S$200k with Certificate of
Entitlement (COE) at May 2014 prices (EVs for research purposes are exempted from COEs)
[1]. As a comparison, the petrol powered equivalent Nissan Sylphy 1.6L costs S$110k [1],
making the Nissan Leaf almost twice as expensive. In the United States, the Nissan Leaf
costs US$21.5k [2] while a Nissan Sentra 1.8L (a rebadged Sylphy) costs US$16k [3] as of
December 2014, making the Nissan Leaf still 35% more expensive.
The Lithium-ion (Li-ion) battery is an expensive component of the EV. As commercial EVs
are still relatively new, there is not much data on the reliability of EV batteries yet. But in the
reasonably mature hybrid car scene, consumers often complain about the costs of replacing
the battery, which usually last only about 10 years, sometimes even shorter [4] [5]. The
Nissan Leaf battery pack costs US$5.5k (and has an eight year warranty) [6], a quarter of a
brand new US$21.5k Nissan Leaf, which is a substantial amount.
Therefore, it is desirable to extend the lifespan of the battery in order to reduce replacement
costs. One reason which causes a reduction of battery lifespan is high charge and discharge
rates [7] [8].
2
1.2 Battery/UC HESS
A solution is to adopt a Hybrid Energy Storage System (HESS), with an additional energy
storage device to assist the battery. A good choice for the additional device is the
Ultracapacitor (UC), also known as the Supercapacitor, which has a higher capacitance than
traditional electrolytic capacitors, but lower voltage limits.
The UC has a high power density, but a low energy density. The Li-ion battery has
contrasting specifications – low power density but high energy density. This is illustrated in
Figure 1-1 with a Ragone plot.
Figure 1-1 Ragone plot illustrating power and energy densities [9].
Therefore, the UC and battery complement each other perfectly in an HESS. Furthermore, the
UC has a longer cycle life. Generally, Li-ion batteries achieve 500 to 1000 full
charge/discharge cycles, while UCs achieve 1 million cycles [10]. Therefore, the UC can
handle the high charging and discharging power peaks due to its high power density and
longer cycle life, resulting in lower battery charge and discharge rates, and therefore longer
battery cycle life.
3
There are no commercial vehicles with a battery/UC HESS at the moment as much research
still needs to be done to address the energy and power management issues in the HESS.
As a side note, there are two main purposes of a battery/UC HESS system. The first purpose
is to extend battery cycle life (which this thesis focuses on). In this case, the battery is sized
such that the battery can solely meet the required energy and power of the EV design. Then
the UC is added to the system to reduce the peak battery power so that the battery cycle life
can be extended.
The second purpose is to provide additional power that the battery is unable to provide on its
own. For example, the battery of the EV could be halved, and the UC provides the other half
of the power. The benefits of this purpose as compared to the first purpose is that weight and
costs have been reduced, as only half the original battery is required. However, the drawback
is that battery cycle life is not extended, and since the battery is halved, the EV range is also
halved. As range is a big concern of EVs today, it is not suggested to reduce the range
further. Therefore, this work focuses on the first purpose, which is to extend battery cycle
life.
1.3 Energy Management Strategy & Power Management Strategy
Although energy management strategy (EMS) and power management strategy (PMS) are
sometimes used interchangeably in the literature, they are actually two distinct concepts [11].
EMS involves managing the energy levels in the HESS, while PMS means managing the
power flow within the HESS. Both management strategies must be implemented together for
an HESS to work.
There are many such battery/UC HESS strategies discussed in the literature. Most works
focus on PMS. The EMS are generally empirical or quite rudimentary, such as attempting to
maintain a constant energy level in the UC, regardless of loading. Therefore, the UC has to be
4
sized larger in order to contain sufficient energy for acceleration, and have sufficient
remaining space to store energy recovered from regenerative braking (which are two goals
the UC should have).
UCs of today are relatively expensive, with the UC suggested in this proposed work – six
Maxwell general purpose UC modules [12] – costing approximately US$7.2k (as of
December 2017) [13]. Therefore, it is desirable to minimize the UC size.
1.4 Criticism of Battery/UC HESS
Some critics of the battery/UC HESS argue the extra money could be used to buy more
battery modules instead of a UC to relieve battery stress. However, this would greatly
increase the EV’s weight for a similar power density. The battery pack in this proposed work
(similar to a Nissan Leaf battery) is 294kg and rated for 90kW, while the six Maxwell UC
bank is 62kg and rated for 331kW. The supporting components (e.g. inductor, DC/DC
converter, etc.) are 22kg, resulting in a theoretical combined rating of 421kW at 378kg. If a
duplicate battery pack were added instead of the UC, the twin battery packs would have a
combined rating of 180kW at 588kg (still far from the 421kW).
Despite the extra range the second battery pack offers, it is far heavier than the battery/UC
HESS option. The extra weight is equivalent to almost three passengers (assuming each
passenger is 75kg). This results in sluggish vehicle performance and larger energy
consumption from hauling the extra weight. Therefore, the battery/UC HESS combination is
better for relieving battery stress and increasing the battery cycle life, while not significantly
affecting vehicle performance.
1.5 Objective
The objective of this work is to develop a new HESS management strategy, consisting of an
EMS and a PMS, which performs better than existing works in terms of achieving four goals.
5
The first two goals are that the UC should have sufficient energy in case of future
accelerations, and should have sufficient space in case of future regenerative braking. These
two goals would be realized by the EMS. The next two goals are that the battery should
supply the steady state constant speed power, and that the UC should be utilized even during
low power demands to extend battery cycle life. These two goals are realized by the PMS.
Existing works do not ensure these goals are met.
The reasons why these four goals are necessary are described in Chapter 2 Literature Review
and Chapter 4, which explains the EMS and PMS design. Ultimately, the goal of the HESS is
to extend battery cycle life.
1.6 Scope
First, a literature review is performed to examine the current state of the art. Second, the new
HESS management strategy for EVs is developed. In order to demonstrate the new HESS
management strategy, simulations and experiments are carried out. To run the simulations,
models have to be built. So the third step consists of examining and selecting existing models
for use in the simulations. Modifications are carried out where necessary to make it suitable
for this work.
The fourth step consists of running the simulations. One simulation each compares the EMS
and PMS to existing works and shows why the proposed strategy is better. Another
simulation demonstrates running the proposed HESS management strategy over drive cycles
and that the four HESS goals are met. The last simulation compares the battery cycle life
degradation of the battery/UC HESS system to a battery-only system. The purpose of this last
simulation is to show that the ultimate goal of the HESS is achieved, which is to extend
battery cycle life.
6
The fifth step consists of running reduced-scale experiments. One experiment verifies the
algorithm is able to work as intended physically. Another experiment compares the battery
cycle life of actual batteries for the proposed battery/UC HESS to a battery-only system.
As it is difficult to compare the reduced-scale experiments with the full-scale EV simulations
directly, the last step involves creating a reduced-scale simulation. This allows direct
comparison of the reduced-scale experiment with the reduced-scale simulation to determine if
they perform similarly.
1.7 Structure of Thesis
The structure of this thesis is as follows.
Chapter 2 comprises a review of existing works. Firstly, an overall view of HESS is
presented, covering various other applications besides EVs. Subsequently, the scope is
narrowed to EVs, where the hardware is discussed, specifically, various battery/UC HESS
topologies. Afterwards, software is discussed, specifically, various battery/UC HESS EMS
and PMS. Drawbacks in existing works are also highlighted.
Chapter 3 discusses the models used for simulating the proposed strategy in Matlab. This
includes the dynamics of the car, as well as models of the electrical components used. The
battery cycle life model is also illustrated. The models are mostly from existing works.
Chapter 4 describes the EMS and PMS in detail with full mathematical formulation. First, the
proposed EMS is described. The method of calculating the speed-dependent target UC energy
band is explained in detail. It is based on averaged worst case (most) energy recovered during
braking, worst case energy requirement during acceleration, as well as with real-life drive
cycles. This type of justification is not seen in existing works. Since it already considers the
worst case scenarios, the proposed EMS does not need future knowledge of the route or drive
profile.
7
In the chapter, the PMS is also explained in detail. The PMS ensures the EMS works
correctly by controlling the power flow between the battery and UC to regulate the UC
energy level, and also enforces speed-dependent battery charge/discharge limits, with priority
placed in the latter. A speed-dependent battery limit is not seen in existing works.
Chapter 5 comprises the simulation results. Two main simulations were performed in Matlab.
A specific design case study was considered in the simulations, where the models were based
on equipping a mid-sized EV sedan with an HESS. This EV sedan is based on a Nissan Leaf.
A mid-sized EV sedan was chosen for this work as it is designed for regular everyday use by
the masses (as opposed to high performance racing) and will therefore have a bigger
audience.
The first two simulations compare the EMS and PMS with existing works, showing that they
cannot achieve the goals simultaneously. A third simulation shows that the proposed strategy
works over a drive cycle and can achieve the EMS and PMS goals.
A fourth simulation on battery cycle life was performed to observe the fall in battery capacity
due to cycling the proposed battery/UC HESS. This was subsequently compared to a battery-
only system.
Chapter 6 explains the experiment setup and the scaling. The experiments are reduced-scale
bench setups and only considers the electrical components, specifically, the battery, UC and a
custom-built DC/DC converter. This setup is connected directly to a programmable load to
represent the motor loading.
Two main experiments were performed. The first experiment was to verify the algorithm
works as designed on a physical setup. The second experiment compares the battery cycle life
of the battery/UC HESS to a battery-only system.
8
In Chapter 7, a reduced-scale simulation was created and compared to the experiment. They
are compared in terms of energy consumption and how they behave time-wise.
Lastly, Chapter 8 contains the conclusion and future works.
1.8 Contributions
The main contribution of this work to the state of the art is a new management strategy for a
battery/UC HESS.
As mentioned earlier, the EMS has two goals for the UC – ensuring sufficient space in the
UC for capturing energy during future regenerative braking, and ensuring the UC has
sufficient remaining energy for future accelerations. The first contribution in this work is a
new method involving a speed-dependent target band to ensure the two goals are met, where
multiple factors are considered, such as worst case (most) energy recovered during braking,
worst case energy requirement during acceleration, and real-life drive cycles. In existing
works, no such justification and rigorous calculations have been performed. Most are based
empirically or on experience, resulting in situations where the two goals may not be met.
Also, the EMS design and procedures are explained in detail, providing a framework for
designing such a system.
As mentioned earlier, the PMS has two goals – to ensure the EMS is followed, and that
battery limits are not exceeded. However, this is not the contribution as existing PMS works
already perform this. The PMS contribution lies in the speed-dependent battery limit, which
is not seen in existing literature. It is a simple but useful method to ensure better utilisation of
the UC, and this is compared with other rule-based deterministic battery limits to show the
benefits of the proposed algorithm.
9
1.9 Publications
An early version of the proposed EMS was simulated and presented in a conference [14]. The
full proposed HESS management strategy (EMS and PMS) including both simulation and
experimental results, but excluding cycle life results, have been submitted to a journal [15]
and is under review at the time of submission of this thesis.
10
2 LITERATURE REVIEW
In this chapter, existing works in HESS development are highlighted. First, a broad overview
of HESS is provided. Second, common topologies on battery/UC HESS (hardware) specific
to EVs are introduced. Third, existing EMS and PMS works (software) for EVs from current
researchers are discussed. Subsequently, some specific cases are considered. Lastly, the
limitations of existing works are examined, leading to the motivation of the work proposed in
this thesis.
2.1 Overview
Although this work focuses on battery/UC HESS for EVs, there have been other research
applications of a battery/UC HESS. One common application is for a power grid with
renewable energy sources [16] [17] [18]. For example, wind energy is an intermittent energy
source, with varying wind speeds encountered throughout the day. Therefore, the UC in the
HESS handles transients from the energy generated from wind turbines, while the batteries
handle the main load. There has also been research for battery/UC HESS in other types of
transportation, for example, ships [19] [20] [21] or tramways [22] [23].
Specific to the EV case, the battery/UC HESS is sometimes supplemented by other energy
generating devices, such as fuel cells [22] [23] [24] [25] [26] or solar cells [27]. The HESS
algorithm attempts to control the power and energy flow in all the components.
HESS can also be found in traditional internal combustion engine (ICE) vehicles with a non-
electric drive train. In these cases, ICEs are integrated with other energy storage devices, such
as batteries for hybrid vehicles, or a flywheel energy storage for Formula One racing [28]
[29] [30]. A hydraulic axial piston unit has also been paired with a diesel engine in one case
[31], known as a hybrid hydraulic vehicle.
11
2.2 Hardware: HESS Topologies
Next, some of the common HESS topologies encountered in the literature specific to
battery/UC HESS EVs [32] [33] are discussed.
Figure 2-1 Passive configuration [32].
Figure 2-1 shows a passive connection, where the battery and UC are connected directly in
parallel, without any DC/DC converters. The voltages of the battery and UC must always be
equal, and the UC essentially acts as a low pass filter. Advantages for this method are its
simplicity and avoidance of expensive DC/DC converters. The disadvantage is that the UC
cannot vary its voltage sufficiently to deliver its stored energy. This is because the battery and
UC voltages have been clamped together, despite having vastly different charge/discharge
voltage profiles.
The Li-ion battery voltage profile is relatively flat throughout its operating region (see Figure
2-2), while the UC voltage profile varies proportionally to the amount of charge remaining
(Quc = C Vuc).
Subsequent topologies are active configurations, involving at least one DC/DC converter,
allowing controllability in power flow between the battery and UC. In simple terms, a
DC/DC converter can be thought of as a transformer for DC circuits (in these cases, an
multiple-tap transformer controlled by a microprocessor).
12
Figure 2-2 Nissan Leaf Li-ion battery pack discharge curve [34].
Figure 2-3 is the most common single DC/DC converter configuration used in the literature,
with the battery directly connected to the DC link, and a DC/DC converter between the
battery and UC. This allows the UC to vary its voltage sufficiently within its operating range.
A drawback of this method is difficulty in balancing the battery cells. Since the battery is
connected to the high voltage dc-link, the balancing of the cells will have to be done at high
voltages. Another drawback is that the battery is directly exposed to the current and power
fluctuations from the inverter if the DC/DC converter is not controlled well.
Figure 2-3 Partially-decoupled configuration [32].
Swapping the battery and UC positions produces Figure 2-4. The benefit in this configuration
is that the battery can be connected at a lower voltage, allowing easier cell balancing. In
addition, the UC is directly exposed to the current fluctuation instead of the battery, which is
13
desired. However, there is a big variation in the DC link voltage, so the inverter must be able
to accept such large variations with reasonable efficiency levels.
Figure 2-4 Partially-decoupled configuration 2 [32].
Figure 2-5 shows a cascaded configuration with two DC/DC converters. Here, the battery and
UC are both fully decoupled from the DC link. In this situation, the battery can be balanced at
a lower voltage, and the UC can have large variations in voltage without affecting the DC
link. Therefore, the design and specifications of the battery and UC can have more flexibility.
The drawback is an additional DC/DC converter, which is expensive, and requires another
layer of control. There will also be further power losses due to the additional DC/DC
converter. The battery and UC positions in Figure 2-5 can be swapped to create another
configuration.
Figure 2-5 Fully-decoupled cascaded configuration [32].
The most popular twin DC/DC converter configuration in the literature is shown in Figure
2-6. The advantages and disadvantages are similar to the cascaded configuration in Figure
14
2-5, but the topology in Figure 2-6 has an additional advantage – independent control of the
battery and UC, providing more flexibility and more accurate control, as compared to the
cascaded configuration.
Figure 2-6 Fully-decoupled multiple converter configuration [32].
In recent times, there has been research on integrating the various components (instead of
using discrete components) to get a higher efficiency. In [35], the battery, inverter, and
DC/DC converter are merged. While [36] has a topology which bypasses the DC/DC
converter when regenerating energy to the UC.
2.3 Software: HESS Management Strategies
In this section, existing EMS in the literature are discussed, followed by existing PMS.
2.3.1 Energy Management Strategies
In general, EMS can be classified into three strategies, where the target UC energy is – a
constant level, a constant band, or a variable level.
2.3.1.1 Constant Target UC Energy Level
Existing EMS are generally quite rudimentary, such as maintaining a constant energy level in
the UC, regardless of loading [22] [23] [25] [26] [37] [38] [39] [40] [41] [42] [43] [44]. After
handling high power peaks, the UC energy level is restored to the pre-determined constant
target. The pre-determined target level varies between different works, for example, a UC
15
state of charge (SOC) of 75% in Torreglosa, et al.’s work [22] or 87.5% in Avelino, et al.’s
work [37] or 25% in Yu, et al.’s work [42].
Usually, a medium SOC value is chosen empirically for two goals – such that the UC can
capture energy if regenerative braking is encountered in future, as well as supply energy if
acceleration is required in future. However, in the simulations section, this medium SOC is
shown to be unable to meet the two goals for certain situations, unless their UC is sized twice
as large as that in this proposed work.
2.3.1.2 Constant Target UC Energy Band
Another work, Cao & Emadi propose a target energy band [32], which is known as the
thermostat on-off strategy, where the UC is kept within a fixed band of 25.5V to 28.5V
(approx. 78% to 88% SOC). When the UC energy reaches the bottom of the band, it is
charged until it reaches the top of the band. Again, it is unable to meet the two goals in
certain situations, unless their UC is sized larger.
2.3.1.3 Variable Target UC Energy Level
Other works propose a variable target UC energy level [45] [46] [47] [48] [49] dependent on
speed. In general, at higher vehicle speeds, capturing energy recovered from regenerative
braking is more probable in the future. Therefore, more room in the UC is required, and the
target UC energy level is set lower. In contrast, at lower vehicle speeds, supplying energy for
acceleration is more probable. Therefore, the target UC energy level is set higher. The
relationship between target UC energy level and speed is usually set empirically or by
intuition, such as the target UC energy level being inversely related to speed due to the
kinetic energy equation E=0.5mv2 [46] [47] [48]. However, not all kinetic energy can be
recovered in braking. Also, during acceleration, more than just kinetic energy is needed to
overcome friction losses.
16
Carter, et al. [48] use an empirical formula,
𝑉𝑡𝑎𝑟 = 𝑉𝑢𝑐,𝑚𝑎𝑥√1 − 0.01875 𝑣𝑚𝑎𝑥 (2-1)
where Vtar is the target UC voltage level, Vuc,max is the maximum UC voltage level and vmax is
the maximum speed of the car, which is 40mph. When the car is stopped, Vtar = Vuc,max, while
if the car is at maximum speed, then Vtar = 0.5Vuc,max. The 0.5 value was selected to prevent
the UC voltage from falling too low, leading to large DC/DC converter inefficiencies.
A more advanced variable target UC energy level strategy is seen in the works of Choi, et al.
[45], which estimates the energy recovered from future regenerative braking, ensuring the UC
always has sufficient space to store that energy. However, in their algorithm, all energy is
anticipated to be charged to the UC – none to the battery – increasing UC size. As mentioned
earlier, UCs of today are relatively expensive, so it is desirable to minimize UC size.
Moreover, they do not consider the worst case scenarios.
2.3.2 Power Management Strategies
PMS can be divided into rule-based and optimization-based strategies [11] [33] [50] [51] as
shown in Figure 2-7. These strategies apply not only to EVs with an HESS, but also to hybrid
vehicles.
Figure 2-7 Power management strategies [11].
17
2.3.2.1 Rule-based
Rule-based algorithms are effective for real-time implementation in a vehicle as they are
simple and do not require much online computation power. The rules can be determined
based on heuristics, intuition, human expertise or mathematical models and simulations [33].
Usually the driving profile is not known in advance. The output of the rule-based approach
determines the mode of operation for the battery and UC. Rule-based approaches can be
deterministic or fuzzy.
In deterministic methods, the rules are usually derived from the present power demanded, the
velocity of the vehicle and the SOC of the battery and UC. For instance, a rule may be – if
driving power demanded is more than maximum battery power threshold, and the SOC of UC
is high, use the UC to assist the battery. They are generally implemented via look-up tables.
Works include [25] [32] [36] [47]. This technique is also implemented in many commercial
hybrid cars of today [50]. Some incorporate this idea into a model-predictive control based
approach, for example [22] [23] [26] [41] [44], while others use a low-pass/high-pass power
split approach, such as [35] [37] [38] [40].
Present works have a fixed maximum battery power threshold. For example, Cao & Emadi
[32] use a fixed battery limit of 12kW. If the power required exceeds 12kW, the battery
supplies 12kW while the UC supplies the remainder. The simulations in Chapter 5 later show
that this does not have good utilisation of the UC.
In fuzzy-based techniques, two or more operating modes are used to control the power
management between the battery and UC in a fuzzy logic manner. Therefore, the transition
between one mode and another does not happen at a specific moment of time, but in a
continuous time manner. It can be considered an extension of deterministic rule-based
methods. The advantages of fuzzy logic are that they are robust and tolerant to imprecise
measurements. They can also be easily tuned. Works include [23] [24] [39].
18
The problem with rule-based strategies is that the drivetrain may not be optimized for
efficiency, as there may be substantial power loss in the power electronic converters.
2.3.2.2 Optimization-based
On the other hand, optimization-based algorithms can account for power losses.
Optimization-based algorithms can be divided into real-time and global optimization. Here,
well-known optimization techniques are used to optimize the system. Common objectives are
to minimize losses in the system, as well as minimize battery power variation and magnitude.
Real-time optimization is based on the system variables at that current point of time, which is
an instantaneous cost function. This does not require knowledge of the future driving profile.
Works include [43] [45]. However, a large amount of online computation is required, so there
has not been any experimental work directly implementing this strategy.
On the other hand, global optimization requires knowledge of the future drive profile in order
to find the global optimum. So this technique can only be used if the vehicle is driven the
same route repeatedly with similar driving patterns, such as garbage collection vehicles or
public buses. Otherwise, it can only be used as a basis for designing rules for online
implementation, or for comparison with other strategies [51], such as in [52]. Some works
implement this strategy as a neural network, where the results of an offline global
optimization are used to train an online network [46] [53].
2.4 Case Studies
Next, some interesting examples are examined in detail.
2.4.1 Dixon, Ortuzar & Moreno
The grandfathers of the battery/UC HESS are probably Dixon & Ortuzar [47]. Although they
were not the first to suggest the battery/UC HESS idea, they were one of the first to
19
successfully implement it on a full-size Chevrolet LUV truck in 2002. Their EMS is
dependent on speed – the higher the speed of the vehicle and the battery SOC, the lower the
target voltage level of the UC. It ranges from SOC 100% to 15% (300V to 45V) as shown in
Figure 2-8. However, no detail was given in their work on how the curves were derived.
Figure 2-8 Target UC SOC values [47].
Their PMS is a simple rule-based approach. When the vehicle accelerates, the battery delivers
the required amount of current. If this current exceeds a threshold, the UC provides the
difference. Regenerative braking is similar, where the current is delivered into the battery. If
that current exceeds a threshold, then the UC captures the rest of the current. They used a
partially-decoupled configuration (Figure 2-3).
The strength of their technique is that it is simple to implement. The weakness is that the UC
is underutilized. The UC is only used when the battery exceeds the thresholds, leading to the
UC being idle during low power phases. In this work’s proposed algorithm, the UC is utilised
even during lower power phases to relieve the battery stress as much as possible.
Subsequently in 2006 and 2007, they published further works with an additional author,
Moreno, where they implemented global optimization using neural networks [46] [54]. The
objectives were to reduce battery current, reduce losses, and ensure the UC SOC at the end of
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the drive cycle is equal to the SOC at the start (i.e. unchanged). The last goal is related to
EMS, while the first two goals are related to PMS.
2.4.2 Avelino, Garcia, Ferreira & Pomilio
Avelino, et al. (2013) have built a working go-kart using a battery/UC HESS [37] with a
fully-decoupled configuration (Figure 2-6). Their EMS is a fixed target UC voltage level at
42V (SOC 87.5%). Their PMS is a rule-based strategy, where the UC takes the fast transients
as long as the UC SOC is within a target band, and the battery takes the rest. This was
implemented via two controllers with differing bandwidths. The UC controller reacts faster to
the desired power changes. The battery controller reacts slower, reducing the battery current
fluctuation, and slowly restoring the UC to the target voltage level. The advantage is simple
real-time implementation. However, they used a fixed UC target energy level. This will be
shown to be insufficient in subsequent simulations in this thesis.
A similar work has been done independently by Hredzak, et al (2014) [40], where a low-pass
filter (rule-based) was used to divide the power flow between the battery and UC in a
reduced-scale experiment. The EMS again consists of a fixed target UC voltage level at 5V
(SOC 41.6%). They used a fully-decoupled configuration (Figure 2-6).
2.4.3 Choi, Lee & Seo
In the work of Choi, et al (2014) [45], a real-time optimization strategy was simulated using a
partially-decoupled configuration (Figure 2-3). Their EMS is not a fixed UC level, but
variable, dependent on the speed of the vehicle. Their algorithm estimated the amount of
regenerative braking energy that would be generated if the vehicle braked at the maximum
deceleration at the next moment. Then it ensures sufficient space in the UC such that the UC
is able to fully capture this energy.
21
Their PMS involved a real-time optimization strategy, where the objectives were to minimize
battery power magnitude and variation, reduce power losses, and to ensure the UC follows
the target energy level. Their work is one of the latest and most comprehensive strategies in
the literature today.
However, there are still some problems. In the EMS for example, the vehicle is always
assumed to brake with maximum deceleration, which is not the worst case scenario for
energy regeneration as energy is lost to friction brakes. Since real-time optimization was
used, it is expected to be computationally expensive. Only simulations were performed
without experiments. There will be more discussion on the shortcomings of Choi’s strategy in
later sections of this thesis, where it will be compared with this work’s proposed strategy.
2.5 Limitations of Existing Works and Proposed Approach
As mentioned earlier, most of the existing EMS are quite rudimentary, such as attempting to
maintain a fixed target voltage level in the UC. This target SOC was usually determined by
intuition, with no explanation on why that specific SOC was selected. These strategies will be
shown to be insufficient in simulations later.
In this work, a more comprehensive and rigorous method of setting the target UC energy
level is used. A new variable target UC energy band is proposed which varies with the speed
of the car. In the simulations later, when using the proposed strategy, the UC size can be
halved in terms of energy stored as compared to the fixed UC energy level strategies, saving
costs, yet still achieving the two goals. The proposed EMS can be considered an extension
and improvement of Choi’s EMS [45].
In addition, a new PMS with a speed-dependent battery limit is proposed, which is not seen in
existing works. It is a simple but useful method to ensure better utilisation of the UC. A rule-
based deterministic PMS is developed as it allows simple real-time implementation for a
22
physical setup. In the simulations later, the proposed PMS is compared with other rule-based
deterministic PMS to show the benefits of the proposed work.
23
3 VEHICLE & HESS MODELLING
In order to demonstrate the proposed novel HESS management strategy, foremost, a model of
the car and the powertrain components needs to be created. In this chapter, the modelling,
which was implemented in Matlab, is discussed.
First, the selected hardware topology is explained, then the concept of drive cycles is
introduced. Subsequently, the modelling of each component is explained, such as the vehicle
model, the battery model, etc. In addition, simulation demonstrations of the more complicated
models are provided to facilitate easier understanding. Lastly, the battery cycle life model is
discussed, which is used for characterizing the battery capacity loss over time.
These models are derived or modified from existing works in the literature.
3.1 Selected HESS Topology
This work proposes adding the UC to a mid-sized sedan EV as a specific design case study,
using the partially-decoupled single DC/DC converter topology. The mid-sized sedan EV is
modelled on a 2013 Nissan Leaf. To avoid major changes to the powertrain design from
conventional EV norms, the original battery is left connected to the DC link. Then a DC/DC
converter is connected to the DC link, and the UC is connected to the DC/DC converter as
shown in Figure 3-1.
Figure 3-1 Single DC/DC converter between battery and UC.
Bidirectional
DC/DC
Converter
Bidirectional
DC/AC
Converter
M
Battery UC
Braking
Chopper
DC Link
New Parts Existing Parts
24
Using a single DC/DC converter saves costs, and allows the conventional existing EV
hardware to be relatively intact (as opposed to using the twin converter topologies). In
addition, as the Li-ion battery voltage is relatively constant throughout most of the operating
range, connecting it directly to the DC link is suitable. The UC voltage will fluctuate
significantly during usage, so it is better to place it after the DC/DC converter to reduce
voltage fluctuations in the DC link.
3.2 Drive Cycle
Drive cycles are created by various countries and organizations to test the performance of
vehicles, for example, fuel consumption or emissions. A drive cycle is defined by a series of
data points which represent the velocity of the vehicle over a period of time. There are two
types of drive cycles – transient and modal. Transient cycles involve much fluctuation in
speed and represent real-world driving scenarios. Examples include the American Federal
Test Procedures FTP-75 city, FTP-75 HWFET highway and LA92 drive cycles [55].
Figure 3-2 FTP-75 city drive cycle (Transient) [55].
25
Figure 3-3 FTP-75 HWFET drive cycle (Transient) [55].
Figure 3-4 LA92 drive cycle (Transient) [55].
On the other hand, modal drive cycles are highly stylized drive cycles, involving constant
accelerations and constant speeds, which are hard to achieve in the real world. Examples
include the Economic Commission for Europe ECE-15 and Extra-Urban Driving Cycle
(EUDC) [55]. The New European Driving Cycle (NEDC) consists of four repeated ECE-15
followed by one EUDC.
26
Figure 3-5 ECE-15 drive cycle (Modal) [55].
Figure 3-6 EUDC (Modal) [55].
3.3 Simulation Approach
There are two types of simulation approaches – backward approach and forward approach.
In the backward facing approach, the performance of a vehicle is evaluated over a drive
cycle, assuming the vehicle follows the drive cycle perfectly [56]. There is no driver model.
Instead, the force required to accelerate the vehicle based on the drive cycle is calculated
first. The calculations move backwards through the drivetrain, computing the torques at each
upstream component such as at the motor shaft. Then finally, the total motor power, the total
battery and UC power required to follow the drive cycle is determined.
27
This is a convenient, simple and fast way to calculate power required. Most, if not all,
literature on battery/UC HESS use this approach. However, the drawback of this approach is
that the drive cycle is assumed to be followed perfectly and there are no transients in the
system. If the car is underpowered such that it cannot follow the drive cycle, then the
simulation becomes invalid.
In contrast, a forward-facing approach includes a driver model [56]. The driver gives
appropriate throttle and brake commands to follow the drive cycle (usually implemented with
a Proportional-Integral (PI) controller). The calculations go forward through the drivetrain,
computing the resulting acceleration and velocity due to the driver’s input, as well as the
power consumption. This is a more realistic scenario as transients are included, but is
extremely time-consuming in simulations. Also, the drive cycle may not be perfectly
followed due to the transients, making it difficult for comparison across different works.
Therefore, a backward approach is implemented in this work. Later in the EMS description in
section 4.2, there will be some elements of the forward approach for offline calculations.
3.4 Motor & Inverter Model
The motor used on a Nissan Leaf is an AC Permanent Magnet Synchronous Motor (PMSM).
In a backward approach, the dynamics of the motor and inverter and how they operate is not
crucial. Instead, these two units are viewed together as a whole. Only the physical limits of
the motor and the combined efficiencies of the motor and inverter are required. Specifically,
the maximum torque τm,max or minimum torque τm,min of the motor is computed from the
angular motor velocity ωm. In addition, the motor efficiency ηm is found from ωm and the
motor torque τm.
28
From official Nissan data [57], the 2013 Nissan Leaf motor is rated at 80kW, with 254Nm
maximum torque and a base speed of 3008rpm. Thus, the maximum motor torque/speed
curve under variable speed operation for first quadrant motoring can be derived easily.
However, the speed at which the motor transitions from constant power to constant torque
during braking in the second quadrant is not known. This speed depends on the speed
regulation of the motor. The better the speed regulation, the closer it is to base speed. From
data in a technical book [58], this speed is estimated to be 10rpm higher than the base speed
of 3008rpm.
A technical magazine has the combined motor/inverter efficiency of an older 2011 Nissan
Leaf motor [59] as shown in Figure 3-7. However, there is no curve-fitted data, so the
efficiency map is recreated with some approximations.
Figure 3-7 2011 Nissan Leaf combined motor/inverter efficiency [59].
From Figure 3-7, the efficiency peaks near the centre of the figure, so it is approximated with
a hump equation given by (3-1) to (3-3). The efficiency for both the forward motoring
(upper) and forward braking (lower) quadrants are assumed symmetrical about the speed
axis.
29
𝜂 = (𝜂𝑚𝑎𝑥)(ℎ) [𝑟
2 − (𝜔 − 𝜔𝑐𝑒𝑛)2 + (
𝜔𝑚𝑎𝑥𝜏𝑚𝑎𝑥
𝜏𝑠𝑐𝑎𝑙𝑒)2
(𝜏 − 𝜏𝑐𝑒𝑛)2]
(3-1)
𝜏𝑐𝑒𝑛 = 𝜏𝑚𝑎𝑥2
+ 𝜏𝑎𝑑𝑗 𝑖𝑓 𝜏 ≥ 0
−𝜏𝑚𝑎𝑥2
− 𝜏𝑎𝑑𝑗 𝑖𝑓 𝜏 < 0
(3-2)
𝜔𝑐𝑒𝑛 = 𝜔𝑚𝑎𝑥2
+ 𝜔𝑎𝑑𝑗 (3-3)
Equation (3-4) defines the maximum torque (edge of curve). Below base speed, maximum
torque is constant, while above base speed, maximum torque decreases inversely with angular
velocity.
𝜏𝑚𝑎𝑥 =
𝑃
𝜔 𝑖𝑓 𝜔 ≥ 𝜔𝑏𝑎𝑠𝑒
𝑃𝑚𝑎𝑥𝜔𝑏𝑎𝑠𝑒,𝑝𝑜𝑠
𝑖𝑓 𝜏 ≥ 0
𝑃𝑚𝑎𝑥𝜔𝑏𝑎𝑠𝑒,𝑛𝑒𝑔
𝑖𝑓 𝜏 < 0
𝑖𝑓 𝜔 < 𝜔𝑏𝑎𝑠𝑒
(3-4)
Figure 3-8 Combined motor/inverter efficiencies.
30
The parameters of the hump equation have been tuned to match the 2011 Nissan Leaf
motor/inverter efficiency in Figure 3-7 as closely as possible. As the parameters are
decoupled, each parameter was tuned iteratively in a process similar to the bisection method.
The resultant parameters used are given in Table 3-2 in section 3.11, and the resultant
efficiency chart is shown in Figure 3-8, which gives a reasonable match. For example, the
maximum and minimum for both charts are at 95% and 85% (Note: 1rad/s = 9.55rpm ~
10rpm).
3.5 Auxiliary Loads
Auxiliary loads in a car include power steering, headlights, the radio, etc. It also includes the
heater and air-conditioning, which consumes the most power. Fleetcarma [60] performed
some experiments on a Nissan Leaf to evaluate the auxiliary power loads. The load varies
from 0.2kW to 5kW, depending on driver habits as well as the surrounding temperature.
However, for the drive cycle specifications, auxiliary loads are ignored. Therefore, in the
model, although there is a provision for the auxiliary load, it is set to zero.
3.6 Vehicle Model
In this section, the vehicle dynamic model is discussed, which is based on the works of [61].
As this work focuses mainly on the HESS and powertrain, the vehicle model is restricted to
one-dimensional movement – driving forwards or backwards. Other movement, such as the
lateral forces involved when cornering are not considered. This vehicle dynamic model uses
all the models discussed previously, from sections 3.2 to 3.5.
The drive cycles mentioned earlier contains the vehicle velocity v(j) (where j is the drive
cycle time in seconds) and is fed into this model at 1Hz [55]. v(j) is differentiated to get
vehicle acceleration a(j). In the drive cycles discussed earlier, the gradient is zero, so θ(j) = 0.
31
Therefore, the inputs to the vehicle model are v(j) and θ(j). The output of the vehicle model is
the power required to follow the drive cycle Pdr+aux(j) at that instant. Figure 3-9 shows the
vehicle model block diagram. The numbers inside the blocks refer to the equation numbers,
which will be discussed subsequently.
Figure 3-9 Block diagram for vehicle model updating.
The aerodynamic drag Fw(j), rolling resistance Fr(j), and grading resistance Fg(j) can be
calculated from v(j), a(j) and θ(j), using the following formulas,
𝐹𝑤(𝑗) = 0.5 𝜌 𝐶𝑑 𝐴𝑓 (𝑣(𝑗))2 (3-5)
𝐹𝑟(𝑗) = 𝑚 𝑔 cos(𝜃(𝑗)) 𝐶𝑟(𝑗) 𝑜𝑛(𝑗) (3-6)
𝐹𝑔(𝑗) = 𝑚 𝑔 sin(𝜃(𝑗)) 𝑜𝑛(𝑗) (3-7)
Motor torque/speed,
efficiency
(Figure 3-8)
ηm(τm,ωm)
Compute max.
tractive effort
(3-14)
Compute
tractive effort
(3-5) to (3-13)
Ensure no
slipping
(3-15)
Compute motor
torque
(3-16), (3-17)
Clip braking
motor torque
(3-19)
Compute motor
ang. velocity
(3-20), (3-21)
Compute drive
cycle power
(3-22)
Compute total power
(3-23)
v(j)
θ(j) Ft(j) Ft(j)
τm(j)
ωm(j)
τm(j)
Pdr(j) Pdr+aux(j)
Ft,f,slip(j)
m, mk, ρ,
Cd, A, g
rwh, Gr
rwh, Gr, ηp
m, μ, Lb, h, rwh, g
Cr(j)
If regen. If acc.
Output
Ensure valid
motor torque
(3-18)
32
where on(j) ensures the grading resistance and rolling resistance are involved only if the
vehicle is moving or starts to move (the brakes should hold the vehicle stationary on a
gradient instead of the motor),
𝑜𝑛(𝑗) =
0 𝑖𝑓 (𝑣(𝑗) = 0 𝑎𝑛𝑑 𝑎(𝑗) = 0)1 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
(3-8)
and rolling resistance coefficient Cr(j) is dependent on velocity,
𝐶𝑟(𝑗) = 𝐶𝑟,𝑎 (1 +
3.6
100 𝑣(𝑗))
(3-9)
Constant m is the gross vehicle weight, so this means the mid-sized EV is fully loaded in the
simulation. Other parameters such as the air density ρ, etc. can be found in Table 3-1 in
section 3.11.
The total resistance force Fv(j) is calculated by summing the three forces together,
𝐹𝑣(𝑗) = 𝐹𝑤(𝑗) + 𝐹𝑟(𝑗) + 𝐹𝑔(𝑗) (3-10)
Next the acceleration force Fa(j) is calculated by,
𝐹𝑎(𝑗) = (𝑚 +𝑚𝑟)(𝑎(𝑗)) (3-11)
where the effect of the rotating component inertias in the power train is translated to the car
body as mr. A rough approximation of mr is
𝑚𝑟 = 0.04 𝑚𝑘 (3-12)
where mk is the kerb weight (unloaded weight) of the car.
Total tractive effort Ft(j) is calculated by,
𝐹𝑡(𝑗) = 𝐹𝑎(𝑗) + 𝐹𝑣(𝑗) (3-13)
33
Next, the car should not slip or skid. Otherwise, the backward approach would be inaccurate
as the drive cycle cannot be followed and the dynamic equations above would be invalid. The
maximum tractive effort can be derived from a free body diagram.
For a front wheel drive car, the maximum tractive effort is defined as
𝐹𝑡,𝑓,𝑠𝑙𝑖𝑝(𝑗) =
𝜇 𝑚 𝑔 cos 𝜃(𝑗) [𝐿𝑏 + 𝐶𝑟(𝑗) (ℎ − 𝑟𝑤ℎ)]
𝐿 + 𝜇 ℎ
(3-14)
The following equation (3-15) must hold true, otherwise slipping occurs and the simulation is
invalid.
|𝐹𝑡(𝑗)| ≤ 𝐹𝑡,𝑓,𝑠𝑙𝑖𝑝(𝑗) (3-15)
After accounting for the wheel radius rwh, the torque at the wheel is calculated by,
𝜏𝑤ℎ(𝑗) = 𝑟𝑤ℎ 𝐹𝑡(𝑗) (3-16)
After accounting for the gear ratio Gr and drivetrain mechanical losses ηp due to friction, etc.,
the torque which the motor must deliver is calculated by,
𝜏𝑚(𝑗) =
𝜏𝑤ℎ
(𝑗)
𝐺𝑟 𝜂𝑝 𝑖𝑓 𝜏𝑤ℎ(𝑗) ≥ 0
𝜏𝑤ℎ(𝑗) 𝜂𝑝
𝐺𝑟 𝑖𝑓 𝜏𝑤ℎ(𝑗) < 0
(3-17)
During acceleration, the torque required by the drive cycle should be less than the maximum
motor torque. The maximum torque/speed curve of the motor was shown in Figure 3-8.
Therefore, given a motor speed ωm(j), the maximum torque τm,max(ωm(j)) can be found. If
(3-18) is violated, then the car is underpowered and the backward approach simulation is
invalid.
𝜏𝑚(𝑗)+ ≤ 𝜏𝑚,𝑚𝑎𝑥(𝜔𝑚(𝑗)) (3-18)
34
Deceleration is more complex. There are three different brake control strategies for
regenerative braking – series braking with optimal feel, series braking with optimal energy
recovery, and parallel braking [61].
The Nissan Leaf has an Electric Driven Intelligent Brake (EDIB) system [62], which is a
brake-by-wire system. According to Nissan’s description, it uses a series braking strategy. A
computer splits the braking torque between the motor and mechanical brakes electrically.
This is more complicated than parallel braking, where a physical link exists between the
brake pedal and the mechanical brakes.
Series braking with optimal energy recovery is the best case scenario for energy recovery
among the three brake control strategies, so this strategy was selected. The motor provides as
much braking torque as possible. If the braking torque exceeds the maximum torque that the
motor can handle, then the motor produces the maximum braking torque, and the remaining
braking torque is met by the mechanical braking system.
Again, the maximum braking torque (or alternatively, minimum motor torque) τm,min(ωm(j))
(which is a negative number) can be found from Figure 3-8. Therefore, the motor provides
the following braking torque,
𝜏𝑚(𝑗)− = max (𝜏𝑚(𝑗)−, 𝜏𝑚,𝑚𝑖𝑛(𝜔𝑚(𝑗))) (3-19)
At this point, the torque experienced by the motor τm(j) has been computed. Next, the motor
speed ωm(j) is calculated. Subsequently, these two terms are multiplied to determine the
power required.
First, the angular velocity of the wheel is calculated,
𝜔𝑤ℎ(𝑗) =
𝑣(𝑗)
𝑟𝑤ℎ
(3-20)
Next, the angular velocity of the motor is calculated,
35
𝜔𝑚(𝑗) = 𝜔𝑤ℎ(𝑗) 𝐺𝑟 (3-21)
Finally, by considering the motor/inverter efficiency ηm(j) at that instant, the power required
by the drive cycle Pdr(j) can be calculated. ηm(j) can be read from Figure 3-8.
𝑃𝑑𝑟(𝑗) =
𝜏𝑚(𝑗) 𝜔𝑚(𝑗)
𝜂𝑚(𝑗) 𝑓𝑜𝑟 𝜏𝑚(𝑗)+
𝜏𝑚(𝑗) 𝜔𝑚(𝑗) 𝜂𝑚(𝑗) 𝑓𝑜𝑟 𝜏𝑚(𝑗)−
(3-22)
The total power which the HESS must supply Pdr+aux(j) includes both the power required by
the drive cycle and the auxiliary load,
𝑃𝑑𝑟+𝑎𝑢𝑥(𝑗) = 𝑃𝑑𝑟(𝑗) + 𝑃𝑎𝑢𝑥 (3-23)
Note that a positive Pdr+aux(j) value means the HESS must supply power to the car, while a
negative Pdr+aux(j) value means the HESS captures power from the car during regenerative
braking.
The four following figures illustrate a working example of the vehicle model. Figure 3-10
shows the drive cycle inputs v(j) and a(j) for the EUDC. Figure 3-11 and Figure 3-12 show
the forces and torques computed by the model, while Figure 3-13 shows the model output,
Pdr+aux.
Figure 3-10 EUDC input.
36
Figure 3-11 Forces over EUDC: intermediate output from model.
Figure 3-12 Torque over EUDC: intermediate output from model.
Figure 3-13 Power over EUDC: model output.
37
3.7 Battery Model
The battery model consists of a battery with open circuit voltage (OCV) vbatt,ocv in series with
the internal resistance as shown in Figure 3-14.
Figure 3-14 Battery model.
The inputs to the battery model are battery power demanded Pbatt(j) and battery open circuit
voltage (OCV) vbatt,ocv(j) at that moment. It also requires the starting charge in the battery
Qbatt,start, as well as the maximum possible charge Qbatt,max.
The outputs are the terminal voltage vbatt(j) and current flow ibatt(j) of the battery at that
moment, as well as the remaining charge in the next instant Qbatt(j+1) after discharging the
present ibatt(j), and battery OCV in the next instant vbatt,ocv(j+1).
Figure 3-15 shows a block diagram of the battery model.
Figure 3-15 Block diagram for battery model updating.
vbatt,ocv
Rbatt
vbatt, Pbatt
ibatt
vbatt(j)
Qbatt(j+1) Compute
SOC at
(j+1)
(3-31) Pbatt(j)
vbatt,ocv(j)
Rbatt
ibatt(j)
vbatt,ocv(j+1) Qdis(j+1) SOCbatt(j+1)
Qdis(j) Qbatt,max,
Qbatt,start,
Vbatt,0, K,
A, B
Qbatt,max
Compute terminal
volt. & current at (j)
(3-26), (3-27)
Compute OCV &
charge at (j+1)
(3-28) to (3-30)
Output
38
Now, the model is explained in detail. Based on Figure 3-14, the battery current demanded
can be calculated from the power demanded,
𝑖𝑏𝑎𝑡𝑡(𝑗) =
𝑃𝑏𝑎𝑡𝑡(𝑗)
𝑣𝑏𝑎𝑡𝑡(𝑗)=
𝑃𝑏𝑎𝑡𝑡(𝑗)
𝑣𝑏𝑎𝑡𝑡,𝑜𝑐𝑣(𝑗) − 𝑅𝑏𝑎𝑡𝑡 𝑖𝑏𝑎𝑡𝑡(𝑗)
(3-24)
Rearranging, a quadratic equation is obtained,
𝑅𝑏𝑎𝑡𝑡 𝑖𝑏𝑎𝑡𝑡(𝑗)2 − 𝑣𝑏𝑎𝑡𝑡,𝑜𝑐𝑣(𝑗) 𝑖𝑏𝑎𝑡𝑡(𝑗) + 𝑃𝑏𝑎𝑡𝑡(𝑗) = 0 (3-25)
𝑖𝑏𝑎𝑡𝑡(𝑗) =
𝑣𝑏𝑎𝑡𝑡,𝑜𝑐𝑣(𝑗) − √𝑣𝑏𝑎𝑡𝑡,𝑜𝑐𝑣(𝑗)2 − 4 𝑅𝑏𝑎𝑡𝑡 𝑃𝑏𝑎𝑡𝑡(𝑗)
2 𝑅𝑏𝑎𝑡𝑡
(3-26)
Note that the more negative root of the quadratic equation is always used. During charging,
Pbatt(j) is negative. Therefore, ibatt(j) consists of one negative root and one positive root. Since
the battery voltage vbatt(j) is always positive, the negative ibatt(j) root is always selected such
that Pbatt(j) is negative, based on (3-24).
On the other hand, during discharging, Pbatt(j) is positive. There will be two positive ibatt(j)
roots. Again, the more negative (smaller) root is used to ensure the power losses due to ibatt(j)2
Rbatt are minimized.
If imaginary roots are present in the solution, it means the required battery power cannot be
delivered. For example, the internal resistance Rbatt might be so large that all the power is lost
in the internal resistance.
Subsequently, the battery voltage at the present instant is calculated by,
𝑣𝑏𝑎𝑡𝑡(𝑗) = 𝑣𝑏𝑎𝑡𝑡,𝑜𝑐𝑣(𝑗) − 𝑅𝑏𝑎𝑡𝑡 𝑖𝑏𝑎𝑡𝑡(𝑗) (3-27)
Next, the OCV vbatt,ocv(j), which varies with charging and discharging, is calculated. This is
based on a model by Tremblay, et al. [63]. In their work, an easy-to-use battery model was
described. They also presented a method of extracting parameters from the battery
39
manufacturer’s discharge curve, such that the discharge curve can be replicated in a
simulation.
The US Department of Energy, Vehicle Technologies Program has performed experiments
with a Nissan Leaf battery to obtain the battery discharge curve as well as internal resistance
(see earlier Figure 2-2) [34]. Therefore, Tremblay’s methods have been applied to extract the
battery parameter constants A, B, K, and Vbatt,0 from the discharge curve.
Now, the battery model updating based on Tremblay’s work is discussed. First, the total
battery discharge since the start of the simulation Qdis(j+1) in the next instant after
discharging the present ibatt(j) is calculated. Then, the remaining charge in the battery
Qbatt(j+1) is calculated,
𝑄𝑑𝑖𝑠(𝑗 + 1) = ∫ 𝑖𝑏𝑎𝑡𝑡(𝑗) 𝑑𝑗
𝑗
0
= 𝑄𝑑𝑖𝑠(𝑗) + 𝑖𝑏𝑎𝑡𝑡(𝑗) ∆𝑗 (3-28)
𝑄𝑏𝑎𝑡𝑡(𝑗 + 1) = 𝑄𝑏𝑎𝑡𝑡,𝑠𝑡𝑎𝑟𝑡 − 𝑄𝑑𝑖𝑠(𝑗 + 1) (3-29)
where Qdis (1) = 0. Next, the battery OCV is calculated by,
𝑣𝑏𝑎𝑡𝑡,𝑜𝑐𝑣(𝑗 + 1) = 𝑉𝑏𝑎𝑡𝑡,0 − 𝐾
𝑄𝑏𝑎𝑡𝑡,𝑚𝑎𝑥
𝑄𝑏𝑎𝑡𝑡(𝑗 + 1)+ 𝐴 𝑒−𝐵(𝑄𝑏𝑎𝑡𝑡,𝑚𝑎𝑥−𝑄𝑏𝑎𝑡𝑡(𝑗+1))
(3-30)
Now, the battery model has been updated over a time instant. vbatt(j), ibatt(j), Qbatt(j+1) and
vbatt,ocv(j+1) have been calculated. The SOC of the battery can also be easily calculated by,
𝑆𝑂𝐶𝑏𝑎𝑡𝑡(𝑗) =
𝑄𝑏𝑎𝑡𝑡(𝑗)
𝑄𝑏𝑎𝑡𝑡,𝑚𝑎𝑥
(3-31)
40
3.8 Ultracapacitor Model
The UC model consists of a capacitor with OCV vuc,ocv in series with the equivalent series
resistance (internal resistance) [64], similar to the previous battery model.
Figure 3-16 UC model.
The inputs to the UC model are UC power demanded Puc,ocv(j) and UC OCV vuc,ocv(j) at that
instant. It also requires the starting UC energy Euc,start. The outputs are the UC current at that
moment iuc(j), as well as the remaining energy Euc(j+1) and UC OCV vuc,ocv(j+1) in the next
moment.
Figure 3-17 shows a block diagram of the UC model.
Figure 3-17 Block diagram for UC model updating.
From the power demanded, the required UC current can be calculated by,
𝑖𝑢𝑐(𝑗) =
𝑃𝑢𝑐,𝑜𝑐𝑣(𝑗)
𝑣𝑢𝑐,𝑜𝑐𝑣(𝑗)
(3-32)
Compute
SOC at
(j+1)
(3-36)
Compute OCV &
energy at (j+1)
(3-33) to (3-35) Puc,ocv(j)
vuc,ocv(j)
Compute current
at (j)
(3-32)
iuc(j) vuc,ocv(j+1) Euc(j+1) SOCuc(j+1)
Euc(j),
Euc,start
C, Ruc Vuc,ocv,max
Output
Ruc
vuc,ocv, Puc,ocv vuc, Puc
iuc
41
In the earlier battery model, battery internal resistance was included. But in this model, the
UC internal resistance Ruc is ignored, as it will be included in the next section, 3.9 DC/DC
Converter Model.
Next, the OCV vuc,ocv(j+1), which varies with charging and discharging, is calculated. The
energy of the UC Euc(j) at the present instant is given by,
𝐸𝑢𝑐(𝑗) = 0.5 𝐶 𝑣𝑢𝑐,𝑜𝑐𝑣(𝑗)2 (3-33)
After that, the energy in the UC at the next instant is calculated,
𝐸𝑢𝑐(𝑗 + 1) = −∫ 𝑃𝑢𝑐,𝑜𝑐𝑣(𝑗) 𝑑𝑗
𝑗
0
= 𝐸𝑢𝑐(𝑗) − 𝑃𝑢𝑐,𝑜𝑐𝑣(𝑗) ∆𝑗 (3-34)
where Euc (1) = Euc,start. Finally, vuc,ocv(j+1) is calculated,
𝑣𝑢𝑐,𝑜𝑐𝑣(𝑗 + 1) = √2 𝐸𝑢𝑐(𝑗 + 1)
𝐶
(3-35)
Now, the UC model has been updated over a time instant. iuc(j), Euc(j+1), and vuc,ocv(j+1) has
been calculated. The SOC of the UC can also be easily calculated by,
𝑆𝑂𝐶𝑢𝑐(𝑗) =
𝑄𝑢𝑐(𝑗)
𝑄𝑢𝑐,𝑚𝑎𝑥=𝐶 𝑣𝑢𝑐,𝑜𝑐𝑣(𝑗)
𝐶 𝑉𝑢𝑐,𝑚𝑎𝑥=𝑣𝑢𝑐,𝑜𝑐𝑣(𝑗)
𝑉𝑢𝑐,𝑚𝑎𝑥
(3-36)
As the DC/DC converter becomes inefficient at low voltages (see next section), the minimum
voltage of the UC is limited to be approximately half that of the maximum, i.e.
𝑉𝑢𝑐,𝑚𝑖𝑛 ≈ 0.5 𝑉𝑢𝑐,𝑚𝑎𝑥 (3-37)
This allows 75% of the energy in the UC to be utilised.
42
3.9 DC/DC Converter Model
The bidirectional two-quadrant buck-boost DC/DC converter is shown in Figure 3-18. The
converter operates in buck mode (step down) when transferring power from the DC link to
the UC, and in boost mode (step up) when transferring power from the UC to the DC link.
Figure 3-18 Electrical model of DC/DC converter.
The power input on the high-side (left side) of the DC/DC converter Puc,H is the difference
between the required power and battery power,
𝑃𝑢𝑐,𝐻(𝑗) = 𝑃𝑑𝑟+𝑎𝑢𝑥(𝑗) − 𝑃𝑏𝑎𝑡𝑡(𝑗) (3-38)
Just like the motor/inverter model previously, knowledge of the DC/DC converter’s internal
operation is not critical. Only the efficiency of the DC/DC converter is required, such that the
drivetrain power flow can be modelled accurately.
After accounting for DC/DC converter losses (ɳDC/DC,bo for boost or ɳDC/DC,bu for buck) , the
power that the UC encounters Puc,ocv(j) (right side of the DC/DC converter in Figure 3-18) is
given by,
Puc,ocv
Puc,H DC Link
Pdr+aux
Q1 D1
Q2 D2
Pbatt
43
𝑃𝑢𝑐,𝑜𝑐𝑣(𝑗) =
𝑃𝑢𝑐,𝐻(𝑗)
𝜂𝐷𝐶/𝐷𝐶,𝑏𝑜(𝑗) 𝑖𝑓 𝑃𝑢𝑐,𝐻(𝑗) ≥ 0
𝜂𝐷𝐶/𝐷𝐶,𝑏𝑢(𝑗) 𝑃𝑢𝑐,𝐻(𝑗) 𝑖𝑓 𝑃𝑢𝑐,𝐻(𝑗) < 0
(3-39)
The models are based on the works of [65]. The required duty cycle of the converter at each
instant j needs to be computed first, before the efficiency can be determined.
3.9.1 Boost Mode Duty Cycle
First, boost mode is considered. In boost mode, there are two subintervals of operation –
when insulated-gate bipolar transistor (IGBT) switch Q2 is on and when it is off (Q1 operates
complementary to Q2).
Figure 3-19 Boost mode, Q2 on.
In the subinterval when Q2 is on, the equivalent circuit is seen in Figure 3-19. From
Kirchhoff’s Voltage Law (KVL), the following can be formed,
𝑣𝐿(𝑡) = 𝑉𝑢𝑐,𝑜𝑐𝑣 − 𝑉𝑖𝑔𝑏𝑡 − 𝐼𝐿(𝑅𝐿 + 𝑅𝑢𝑐 + 𝑅𝑖𝑔𝑏𝑡) (3-40)
44
Figure 3-20 Boost mode, Q2 off.
In the subinterval when Q2 is off, the equivalent circuit is seen in Figure 3-20. From KVL,
the following can be formed,
𝑣𝐿(𝑡) = 𝑉𝑢𝑐,𝑜𝑐𝑣 − 𝑉𝑑 − 𝑉𝑏𝑎𝑡𝑡 − 𝐼𝐿(𝑅𝐿 + 𝑅𝑢𝑐 + 𝑅𝑑) (3-41)
Then the principle of inductor volt-second balance is invoked. By averaging the two
subintervals with the duty cycle D2, the average inductor current IL can be determined,
𝑉𝐿 =1
𝑇𝑠∫ 𝑣𝐿(𝑡) 𝑑𝑡
𝑇𝑠
0
= 0
(3-42)
𝐷2 [𝑉𝑢𝑐,𝑜𝑐𝑣 − 𝑉𝑖𝑔𝑏𝑡 − 𝐼𝐿(𝑅𝐿 + 𝑅𝑢𝑐 + 𝑅𝑖𝑔𝑏𝑡)]
+ 𝐷2′ [𝑉𝑢𝑐,𝑜𝑐𝑣 − 𝑉𝑑 − 𝑉𝑏𝑎𝑡𝑡 − 𝐼𝐿(𝑅𝐿 + 𝑅𝑢𝑐 + 𝑅𝑑)] = 0
(3-43)
𝐼𝐿 =
𝑉𝑢𝑐,𝑜𝑐𝑣 − 𝐷2𝑉𝑖𝑔𝑏𝑡 − 𝐷2′(𝑉𝑑 + 𝑉𝑏𝑎𝑡𝑡)
𝑅𝐿 + 𝑅𝑢𝑐 + 𝐷2𝑅𝑖𝑔𝑏𝑡 + 𝐷2′𝑅𝑑
(3-44)
45
As IGBT switches Q1 and Q2 are complementary (i.e. Q1 is off when Q2 is on, and vice-
versa), the following equation can be attained, where D1 and D2 are the duty cycles of
switches Q1 and Q2 respectively.
𝐷2′ = 𝐷1
𝐷2 = 𝐷1′
(3-45)
Next, switching losses are considered. Again, two subintervals are present, when Q2 is on
and when it is off.
When Q2 is on, switch Q1 needs to block the following voltage Vblock,bo,1,
𝑉𝑏𝑙𝑜𝑐𝑘,𝑏𝑜,1 = 𝑉𝑏𝑎𝑡𝑡 − 𝑉𝑖𝑔𝑏𝑡 − 𝑅𝑖𝑔𝑏𝑡𝐼𝐿 (3-46)
When Q2 is off, switch Q2 needs to block the following voltage Vblock,bo,2,
𝑉𝑏𝑙𝑜𝑐𝑘,𝑏𝑜,2 = 𝑉𝑏𝑎𝑡𝑡 + 𝑉𝑑 + 𝑅𝑑𝐼𝐿 (3-47)
By averaging the blocking voltage with the duty cycle, the average blocked voltage by the
switches is Vblock,bo,
𝑉𝑏𝑙𝑜𝑐𝑘,𝑏𝑜 = 𝐷2𝑉𝑏𝑙𝑜𝑐𝑘,𝑏𝑜,1 + 𝐷2′𝑉𝑏𝑙𝑜𝑐𝑘,𝑏𝑜,2
= 𝑉𝑏𝑎𝑡𝑡 − 𝐷1′𝑉𝑖𝑔𝑏𝑡 + 𝐷1𝑉𝑑 + 𝐼𝐿[𝐷1𝑅𝑑 − 𝐷1
′𝑅𝑖𝑔𝑏𝑡]
(3-48)
The total switching power loss is given by Psw,bo, which depends on the switching frequency
fs and IGBT turn on and off times,
𝑃𝑠𝑤,𝑏𝑜 = 𝑉𝑏𝑙𝑜𝑐𝑘,𝑏𝑜𝛼𝐼𝐿 (3-49)
𝛼 = 𝑓𝑠(𝑡𝑠𝑤,𝑜𝑛 + 𝑡𝑠𝑤,𝑜𝑓𝑓) (3-50)
Equation (3-51) is achieved by including the switching loss into the original inductor current
IL in (3-44). Subsequently, the required duty cycle D1 can be found by (3-52) if the voltages
46
at the two ends of the DC/DC converter (Vuc,ocv, Vbatt), as well as the current IL flowing
through it are known.
𝐼𝐿 =
𝑉𝑢𝑐,𝑜𝑐𝑣 − 𝐷1𝑉𝑏𝑎𝑡𝑡 − (𝐷1′𝑉𝑖𝑔𝑏𝑡 + 𝐷1𝑉𝑑) − 𝑉𝑏𝑙𝑜𝑐𝑘,𝑏𝑜𝛼
(𝑅𝐿 + 𝑅𝑢𝑐) + 𝐷1𝑅𝑑 + 𝐷1′𝑅𝑖𝑔𝑏𝑡
(3-51)
𝐷1𝐼𝐿[𝑅𝑑(1 + 𝛼) − 𝑅𝑖𝑔𝑏𝑡(1 − 𝛼)] + 𝑉𝑏𝑎𝑡𝑡 + 𝑉𝑑(1 + 𝛼) − 𝑉𝑖𝑔𝑏𝑡(1 − 𝛼)
+ 𝐼𝐿[(𝑅𝐿 + 𝑅𝑢𝑐) + 𝑅𝑖𝑔𝑏𝑡(1 − 𝛼)] + 𝑉𝑖𝑔𝑏𝑡(1 − 𝛼) − 𝑉𝑢𝑐,𝑜𝑐𝑣
+ 𝑉𝑏𝑎𝑡𝑡𝛼 = 0
(3-52)
3.9.2 Boost Mode Efficiency
To obtain the efficiency, the inductor current term IL should be replaced, because this is not
known. As the power on the high-side of the DC/DC converter Puc,H is known, (3-53) is
substituted into the boost duty cycle equation (3-52), resulting in (3-54) and (3-55).
𝐼𝐿 =
𝑃𝑢𝑐,𝐻𝑉𝑢𝑐,𝑜𝑐𝑣 𝜂𝐷𝐶/𝐷𝐶,𝑏𝑜
=𝑃𝑢𝑐,𝐻𝑉𝑏𝑎𝑡𝑡𝐷1
(3-53)
𝐷1
=−
𝑃𝑢𝑐,𝐻𝑉𝑏𝑎𝑡𝑡𝐷1
[(𝑅𝐿 + 𝑅𝑢𝑐) + 𝑅𝑖𝑔𝑏𝑡(1 − 𝛼)] − 𝑉𝑖𝑔𝑏𝑡(1 − 𝛼) + 𝑉𝑢𝑐,𝑜𝑐𝑣 − 𝑉𝑏𝑎𝑡𝑡𝛼
𝑃𝑢𝑐,𝐻𝑉𝑏𝑎𝑡𝑡𝐷1
[𝑅𝑑(1 + 𝛼) − 𝑅𝑖𝑔𝑏𝑡(1 − 𝛼)] + 𝑉𝑏𝑎𝑡𝑡 + 𝑉𝑑(1 + 𝛼) − 𝑉𝑖𝑔𝑏𝑡(1 − 𝛼)
(3-54)
𝐷12𝑉𝑏𝑎𝑡𝑡 + 𝑉𝑑(1 + 𝛼) − 𝑉𝑖𝑔𝑏𝑡 (1 − 𝛼)
+ 𝐷1 𝑉𝑖𝑔𝑏𝑡 (1 − 𝛼) − 𝑉𝑢𝑐,𝑜𝑐𝑣 + 𝑉𝑏𝑎𝑡𝑡𝛼
+𝑃𝑢𝑐,𝐻𝑉𝑏𝑎𝑡𝑡
[𝑅𝑑(1 + 𝛼) − 𝑅𝑖𝑔𝑏𝑡(1 − 𝛼)]
+ 𝑃𝑢𝑐,𝐻𝑉𝑏𝑎𝑡𝑡
[(𝑅𝐿 + 𝑅𝑢𝑐) + 𝑅𝑖𝑔𝑏𝑡(1 − 𝛼)] = 0
(3-55)
47
The boost efficiency can be found by taking the positive root of D1 in (3-55), and then
substituting D1 into (3-56),
𝜂𝐷𝐶/𝐷𝐶,𝑏𝑜 =
𝑃𝑜𝑢𝑡𝑃𝑖𝑛
=𝑃𝑢𝑐,𝐻𝑉𝑢𝑐,𝑜𝑐𝑣𝐼𝐿
=𝑉𝑜𝑢𝑡𝐼𝑜𝑢𝑡𝑉𝑢𝑐,𝑜𝑐𝑣𝐼𝐿
=𝑉𝑏𝑎𝑡𝑡𝐷1𝐼𝐿𝑉𝑢𝑐,𝑜𝑐𝑣𝐼𝐿
=𝑉𝑏𝑎𝑡𝑡𝐷1𝑉𝑢𝑐,𝑜𝑐𝑣
(3-56)
3.9.3 Buck Mode Duty Cycle
Next, buck mode is considered, which is analysed in a similar way. Again, there are two
subintervals of operation – when IGBT switch Q1 is on and when it is off.
Figure 3-21 Buck mode, Q1 on.
In the subinterval when Q1 is on, the equivalent circuit is seen in Figure 3-21. From KVL, the
following can be formed,
𝑣𝐿(𝑡) = 𝑉𝑢𝑐,𝑜𝑐𝑣 + 𝑉𝑖𝑔𝑏𝑡 − 𝑉𝑏𝑎𝑡𝑡 − 𝐼𝐿(𝑅𝐿 + 𝑅𝑢𝑐 + 𝑅𝑖𝑔𝑏𝑡) (3-57)
48
Figure 3-22 Buck mode, Q1 off.
In the subinterval when Q1 is off, the equivalent circuit is seen in Figure 3-22. From KVL,
the following can be formed,
𝑣𝐿(𝑡) = 𝑉𝑢𝑐,𝑜𝑐𝑣 + 𝑉𝑑 − 𝐼𝐿(𝑅𝐿 + 𝑅𝑢𝑐 + 𝑅𝑑) (3-58)
Then the principle of inductor volt-second balance is invoked. By averaging the two
subintervals with the duty cycle, the average inductor current IL is determined,
𝑉𝐿 =1
𝑇𝑠∫ 𝑣𝐿(𝑡) 𝑑𝑡
𝑇𝑠
0
= 0
(3-59)
𝐷1 [𝑉𝑢𝑐,𝑜𝑐𝑣 + 𝑉𝑖𝑔𝑏𝑡 − 𝑉𝑏𝑎𝑡𝑡 − 𝐼𝐿(𝑅𝐿 + 𝑅𝑢𝑐 + 𝑅𝑖𝑔𝑏𝑡)]
+ 𝐷1′ [𝑉𝑢𝑐,𝑜𝑐𝑣 + 𝑉𝑑 − 𝐼𝐿(𝑅𝐿 + 𝑅𝑢𝑐 + 𝑅𝑑)] = 0
(3-60)
49
𝐼𝐿 =
𝑉𝑢𝑐,𝑜𝑐𝑣 + 𝐷1(𝑉𝑖𝑔𝑏𝑡 − 𝑉𝑏𝑎𝑡𝑡) + 𝐷1′𝑉𝑑
𝑅𝐿 + 𝑅𝑢𝑐 + 𝐷1𝑅𝑖𝑔𝑏𝑡 + 𝐷1′𝑅𝑑
(3-61)
Next, switching losses are considered. Again, two subintervals are present, when Q1 is on
and when it is off.
When Q1 is on, switch Q2 needs to block the following voltage Vblock,bu,1,
𝑉𝑏𝑙𝑜𝑐𝑘,𝑏𝑢,1 = 𝑉𝑏𝑎𝑡𝑡 − 𝑉𝑖𝑔𝑏𝑡 + 𝑅𝑖𝑔𝑏𝑡𝐼𝐿 (3-62)
When Q1 is off, switch Q1 needs to block the following voltage Vblock,bu,2,
𝑉𝑏𝑙𝑜𝑐𝑘,𝑏𝑢,2 = 𝑉𝑏𝑎𝑡𝑡 + 𝑉𝑑 − 𝑅𝑑𝐼𝐿 (3-63)
By averaging the blocking voltage with the duty cycle, the average blocked voltage by the
switches is Vblock,bu,
𝑉𝑏𝑙𝑜𝑐𝑘,𝑏𝑢 = 𝐷1𝑉𝑏𝑙𝑜𝑐𝑘,𝑏𝑢,1 + 𝐷1′𝑉𝑏𝑙𝑜𝑐𝑘,𝑏𝑢,2
= 𝑉𝑏𝑎𝑡𝑡 + 𝐷1′𝑉𝑑 − 𝐷1𝑉𝑖𝑔𝑏𝑡 + 𝐼𝐿[𝐷1𝑅𝑖𝑔𝑏𝑡 − 𝐷1
′𝑅𝑑]
(3-64)
The total switching power loss is given by Psw,bu, where α was calculated earlier in (3-50).
𝑃𝑠𝑤,𝑏𝑢 = 𝑉𝑏𝑙𝑜𝑐𝑘,𝑏𝑢𝛼𝐼𝐿 (3-65)
Equation (3-66) is achieved by including the switching loss into the original inductor current
IL in (3-61). Subsequently, the required duty cycle D1 can be found by (3-67) if the voltages
at the two ends of the DC/DC converter (Vuc,ocv, Vbatt), as well as the current IL flowing
through it are known.
𝐼𝐿 =
𝑉𝑢𝑐,𝑜𝑐𝑣 + 𝐷1𝑉𝑖𝑔𝑏𝑡 + 𝐷1′𝑉𝑑 − 𝐷1𝑉𝑏𝑎𝑡𝑡 + 𝑉𝑏𝑙𝑜𝑐𝑘,𝑏𝑢𝛼
(𝑅𝐿 + 𝑅𝑢𝑐) + 𝐷1𝑅𝑖𝑔𝑏𝑡 + 𝐷1′𝑅𝑑
(3-66)
50
𝐷1𝐼𝐿[𝑅𝑖𝑔𝑏𝑡(1 − 𝛼) − 𝑅𝑑(1 + 𝛼) − 𝑅𝑡ℎ𝛼] + 𝑉𝑏𝑎𝑡𝑡 − 𝑉𝑖𝑔𝑏𝑡(1 − 𝛼)
+ 𝑉𝑑(1 + 𝛼)
+ 𝐼𝐿[(𝑅𝐿 + 𝑅𝑢𝑐) + 𝑅𝑑(1 + 𝛼)] − 𝑉𝑑(1 + 𝛼) − 𝑉𝑢𝑐,𝑜𝑐𝑣
− 𝑉𝑏𝑎𝑡𝑡𝛼 = 0
(3-67)
3.9.4 Buck Mode Efficiency
To get the buck efficiency, similar to the earlier boost case, the inductor current IL should be
replaced. (3-68) is substituted into the buck duty cycle (3-67), resulting in (3-69) and (3-70).
𝐼𝐿 =
𝑃𝑢𝑐,𝐻 𝜂𝐷𝐶/𝐷𝐶,𝑏𝑢
𝑉𝑢𝑐,𝑜𝑐𝑣=
𝑃𝑢𝑐,𝐻𝑉𝑏𝑎𝑡𝑡𝐷1
(3-68)
𝐷1
=−
𝑃𝑢𝑐,𝐻𝑉𝑏𝑎𝑡𝑡𝐷1
[(𝑅𝐿 + 𝑅𝑢𝑐) + 𝑅𝑑(1 + 𝛼)] + 𝑉𝑑(1 + 𝛼) + 𝑉𝑢𝑐,𝑜𝑐𝑣 + 𝑉𝑏𝑎𝑡𝑡𝛼
𝑃𝑢𝑐,𝐻𝑉𝑏𝑎𝑡𝑡𝐷1
[𝑅𝑖𝑔𝑏𝑡(1 − 𝛼) − 𝑅𝑑(1 + 𝛼)] + 𝑉𝑏𝑎𝑡𝑡 − 𝑉𝑖𝑔𝑏𝑡(1 − 𝛼) + 𝑉𝑑(1 + 𝛼)
(3-69)
𝐷12𝑉𝑏𝑎𝑡𝑡 − 𝑉𝑖𝑔𝑏𝑡 (1 − 𝛼) + 𝑉𝑑(1 + 𝛼)
+ 𝐷1 −𝑉𝑑 (1 + 𝛼) − 𝑉𝑢𝑐,𝑜𝑐𝑣 − 𝑉𝑏𝑎𝑡𝑡𝛼
+𝑃𝑢𝑐,𝐻𝑉𝑏𝑎𝑡𝑡
[𝑅𝑖𝑔𝑏𝑡(1 − 𝛼) − 𝑅𝑑(1 + 𝛼)]
+ 𝑃𝑢𝑐,𝐻𝑉𝑏𝑎𝑡𝑡
[(𝑅𝐿 + 𝑅𝑢𝑐) + 𝑅𝑑(1 + 𝛼)] = 0
(3-70)
The buck efficiency can be found by making D1 the subject in (3-70), and then substituting
D1 into (3-71),
𝜂𝐷𝐶/𝐷𝐶,𝑏𝑢 =
𝑃𝑜𝑢𝑡𝑃𝑖𝑛
=𝑉𝑢𝑐,𝑜𝑐𝑣𝐼𝐿𝑉𝑏𝑎𝑡𝑡𝐷1𝐼𝐿
=𝑉𝑢𝑐,𝑜𝑐𝑣𝑉𝑏𝑎𝑡𝑡𝐷1
(3-71)
51
3.9.5 Combined Duty Cycle and Efficiency
Figure 3-23 shows the duty cycle of Q1 for both buck and boost modes combined into a
single chart for the case of Vbatt = 370V. This figure was achieved by varying the high-side
UC power Puc,H and UC voltage Vuc,ocv and then computing the resulting efficiency for the
buck and boost case separately using the equations earlier. Then the two charts were
combined. Similarly, Figure 3-24 shows the combined buck-boost efficiency in a single
diagram.
Figure 3-23 Combined buck-boost duty cycle.
Figure 3-24 Combined buck-boost efficiency.
52
A positive Puc,H value means the UC is being discharged (boost), while a negative value
means the UC is being charged (buck). In general, the DC/DC converter is more efficient
around the 0kW mark (low demand) and at high UC voltages.
The top left corners in Figure 3-23 and Figure 3-24 have missing data. In that region,
equation (3-55) has no real solution. This means that all power discharged by the UC is lost
in the DC/DC converter, therefore the UC is unable to supply power to the HESS.
As a side note, the battery voltage (i.e. high-side DC/DC converter voltage) has minimal
effect on the efficiency, e.g. a large change in battery voltage Vbatt leads only to a marginal
change in efficiency. For a simple demonstration, an ideal synchronous converter has the
following properties, Rd – Rigbt = 0 and Vd – Vigbt = 0. Substituting this to solve the efficiency
equations in (3-55), (3-56), (3-70) and (3-71) and ignoring switching losses (α = 0), it is
found that the Vbatt term disappears from the equations altogether, so the efficiency does not
depend on Vbatt. However, in real-life, Rd – Rigbt and Vd – Vigbt are not equal to zero, but is
very small. Therefore, Vbatt only has a small effect on DC/DC converter efficiency.
In summary, the various models of the car and the powertrain have been discussed. These are
building blocks for the proposed HESS management strategy.
3.10 Battery Cycle Life Model
Next the battery cycle life model is considered, which is used to simulate the battery capacity
loss. The battery cycle life model is a modified version of the works of Wang, et al (2014)
[7]. In their works, they have cycled commercially available 1.5Ah Sanyo UR18650W (2007
technology) batteries to monitor their capacity loss. From fitting the resultant data, they have
created a semi-empirical model. Although the term battery cycle life is used as a generic term
to mean the battery lifetime, there are actually two components in their battery capacity loss
model – calendar life and cycle life. These are the equations,
53
𝑄𝑙𝑜𝑠𝑠,%,𝑐𝑎𝑙𝑒𝑛𝑑𝑎𝑟 = 𝑓 √𝑡 𝑒
[−𝐸𝑎𝑅 𝑇
]
(3-72)
𝑄𝑙𝑜𝑠𝑠,%,𝑐𝑦𝑐𝑙𝑒 = (𝑎 𝑇2 + 𝑏 𝑇 + 𝑐) 𝑒[(𝑑 𝑇+𝑒) 𝐶𝑟𝑎𝑡𝑒)] 𝐴ℎ𝑡ℎ𝑟𝑜𝑢𝑔ℎ𝑝𝑢𝑡 (3-73)
𝑄𝑙𝑜𝑠𝑠,% = 𝑄𝑙𝑜𝑠𝑠,%,𝑐𝑎𝑙𝑒𝑛𝑑𝑎𝑟 + 𝑄𝑙𝑜𝑠𝑠,%,𝑐𝑦𝑐𝑙𝑒 (3-74)
Equation (3-72) is the percentage capacity loss due to calendar life, while (3-73) is the
percentage capacity loss due to cycle life. Equation (3-74) is the total percentage capacity
loss. Parameters a to f are empirical fit parameters, while t represents time in days, T for
temperature in Kelvin, and Ahthroughput for total charge used. Ea and R are the activation
energy and gas constant respectively.
For the calendar life equation (3-72), they have adopted a square root of time relation to
account for the diffusion limited capacity loss, and an Arrhenius correlation to capture the
influence of temperature. For the cycle life equation (3-73), the C-rate is exponential, while
that of time (or charge throughput) is linear.
In their tests, the C-rates were constant throughout, i.e. a constant 0.5C discharge rate. In this
work, the EV is simulated over drive cycles, which are far from constant C-rates. Therefore,
the cycle life equation is modified to have an incremental capacity loss for every incremental
change in time. This is similar to the works of [66], which modifies an earlier 2011 cycle life
model by the same authors, Wang, et al. [67] to work incrementally. These are the resultant
equations,
𝑄𝑙𝑜𝑠𝑠,%,𝑐𝑦𝑐𝑙𝑒(𝑡) =
𝑑𝑄𝑙𝑜𝑠𝑠,%,𝑐𝑦𝑐𝑙𝑒(𝑡)
𝑑𝑡∆𝑡 + 𝑄𝑙𝑜𝑠𝑠,%,𝑐𝑦𝑐𝑙𝑒(𝑡 − 1)
(3-75)
𝑑𝑄𝑙𝑜𝑠𝑠,%,𝑐𝑦𝑐𝑙𝑒(𝑡)
𝑑𝑡= (𝑎 𝑇2 + 𝑏 𝑇 + 𝑐) 𝑒[(𝑑 𝑇+𝑒) 𝐶𝑟𝑎𝑡𝑒(𝑡))]
𝑑𝐴ℎ𝑡ℎ𝑟𝑜𝑢𝑔ℎ𝑝𝑢𝑡(𝑡)
𝑑𝑡
(3-76)
𝑑𝐴ℎ𝑡ℎ𝑟𝑜𝑢𝑔ℎ𝑝𝑢𝑡(𝑡)
𝑑𝑡=𝐼(𝑡) ∆𝑡
3600
(3-77)
54
𝐶𝑟𝑎𝑡𝑒(𝑡) =
𝐼(𝑡)
𝑄𝑏𝑎𝑡𝑡
(3-78)
From equations (3-76) to (3-78), I(t) and ∆t are required to compute the incremental cycle-
life loss dQloss,%,cycle(t)/dt over ∆t. Then, the incremental losses are summed to compute the
total loss using (3-75).
The model does not distinguish between charge and discharge. So the absolute value is taken
for charging currents, which is negative in the convention in this work, resulting in both
discharge and charge currents being positive for running the cycle life model.
3.11 Parameters for Modelling
3.11.1 General
The next two tables comprise the parameters used for modelling the EV and its various
components as discussed in the earlier sections.
55
Table 3-1 Simulation parameters for the vehicle model.
Parameter Value Source
Car Properties
Gross vehicle weight m 1962 kg Kerb weight + new components
Kerb weight mk 1503 kg [57]
Weight of driver & 4
passengers
75 * 5 kg [55]
Gear ratio Gr 8.1938 [57]
Wheel radius rwh 0.31595 m Tyre size: 205/55R16 [57]
Frontal area Af 2.31 m2 [68]
Wheelbase L 2.7 m [57]
Height of CG h 0.54 m Estimated from another sedan,
Hyundai Sonata [69]
Distance from rear wheel to
CG Lb
1.6 m Estimated from another sedan,
Hyundai Sonata [69]
Top speed 144 km/h [57]
Drag coefficient Cd 0.29 [57]
Rolling resistance coefficient
parameter Cr,a
0.006 Tuned from [61]
Drivetrain efficiency ηp 0.98 Estimated from [61]
Auxiliary power Paux 0 -
Environment Properties
Gravitational acceleration g 9.81 m/s2 -
Air density ρ 1.2041 kg/m3 At 20oC
Static friction coefficient μs 0.85 Asphalt & Concrete Road [61]
56
Table 3-2 Simulation parameters for the EV motor.
Parameter Value Source
Type AC PMSM [34]
Base speed (positive torque) ωbase,pos 3008 rpm [57]
Base speed (negative torque) ωbase,neg 3018 rpm Estimated from [58]
Max speed ωmax 10500 rpm [57]
Max torque τmax 254 Nm [57]
Max power 80 kW [57]
Radius of hump r (21000)(2π/60) Tuning parameter
Height of hump h 1/r2 Tuning parameter
Maximum efficiency ɳmax 1 Tuning parameter
Centre of hump, angular velocity-wise ωcen
(rad/s)
- Tuning parameter
Centre of hump, torque-wise τcen (Nm) - Tuning parameter
Shifts centre of hump up/down τadj 25 Nm Tuning parameter
Shifts centre of hump left/right ωadj 250 rad/s Tuning parameter
Compresses/elongates hump up/down τscale 1.1 Tuning parameter
The following table on the next page contains the parameters of the new components to be
installed in the mid-sized EV. The selected UC are six Maxwell 48V general purpose
modules, connected in series, totalling 288V, 13.8F [12].
57
Table 3-3 Parameters of new components to be installed in the EV.
Parameter Value Source
UC Properties
Rated voltage Vuc,max 288 V [12]
Rated capacitance C 13.83 F [12]
Internal resistance Ruc 0.06 Ω [12]
Weight 62 kg [12]
DC/DC Converter Properties
IGBT forward voltage drop
Vce = Vigbt + IL Rigbt
Vigbt + IL Rigbt =
0.857 + IL(0.00285) V
[70]
IGBT reverse voltage drop
Vec = Vd + IL Rd
Vd + IL Rd =
0.88 + IL(0.00184) V
[70]
Inductor internal resistance RL 0.037 Ω [54]
Weight 22 kg [47]
3.11.2 Using UR18650W Batteries
Table 3-4 shows the parameters for the original Nissan Leaf battery. However, the parameters
cannot be used directly if battery cycle life simulations are to be included in this work. Earlier
in section 3.10, the battery cycle life model from Wang, et al [7] was discussed. They
performed cycle life experiments using Sanyo UR18650W batteries and empirically fitted a
model with their data. Therefore, the empirical parameters only suit the UR18650W batteries.
However, there is no data on the Nissan Leaf battery cycle life. Therefore, for the mid-sized
EV in this work, the 1.5Ah Sanyo UR18650W batteries are assembled into a 98S44P
configuration to have a similar capacity and nominal voltage to the original Nissan Leaf
battery. The modified configuration values are also shown in Table 3-4.
Table 3-5 lists the battery voltage curve and battery cycle life model parameters.
58
Table 3-4 Parameters of Nissan Leaf and modified batteries.
Parameter Value Source Modified Value for
UR18650W
Type Li-ion
Cathode: LiMn2O4 with
LiNiO2
Anode: Graphite
[34] Li-ion
Cathode: LiMn1/3Ni1/3Co1/3
+ LiMn2O4 Anode:
Graphite
Cell configuration 96S 2P [34] 98S 44P
Maximum voltage 403.2 V [34] 411.6 V
Nominal voltage 364.8 V [34] 362.6 V
Minimum voltage 240 V [34] 245 V
Rated capacity Qmax 66.2 Ah (24 kWh) [34] 66 Ah (23.93 kWh)
Table 3-5 Parameters for battery voltage and battery cycle life curve fitting.
Parameter Value Source
Battery Voltage Curve
Constant A 16.89 V Calculated with [63]
Constant B 6.0423e-05 (Ah)-1 Calculated with [63]
Constant K 8.919 V Calculated with [63]
Constant Vbatt,0 395.229 V Calculated with [63]
Internal resistance Rbatt 0.14 Ω [34]
Battery Cycle Life Curve
Constant a 8.6124e-06; Ah-1 K-2 [7]
Constant b -5.1252e-03 Ah-1 K-1 [7]
Constant c 7.6292e-01 Ah-1 [7]
Constant d -6.7150e-03 K-1 C-rate-1 [7]
Constant e 2.3467 C-rate-1 [7]
Constant f 14876 day-0.5 [7]
Activation energy Ea 24.5 kJ mol-1 [7]
Gas constant R 8.31446; J mol-1 K-1 [7]
Temperature T 323.15 K -
59
4 HESS: IMPROVED ENERGY & POWER MANAGEMENT
STRATEGIES
As mentioned earlier, there are two parts to an HESS management strategy – energy
management strategy (EMS) and power management strategy (PMS). In this chapter, the
algorithms of the proposed EMS and PMS are discussed. In order to discuss these algorithms,
the models derived in Chapter 3 earlier are used.
As a side note, the EMS and PMS were designed in an iterative fashion, i.e. EMS was
designed first, then PMS designed second. Subsequently, the EMS was revised to suit the
PMS, and PMS was also further revised to suit the new EMS. And the cycle continued.
Therefore, it is challenging to explain the EMS and PMS in a linear fashion in this thesis. Part
of the PMS is discussed first to introduce the concept of battery limits, before the EMS is
described in full. Finally, the remainder of the PMS is discussed, which focuses on its
implementation.
4.1 Power Management Strategy Pt. 1: Battery Limits
The PMS decides how the power flow should be split between the battery and UC. The PMS
has two goals,
To ensure the actual UC energy level follows the target UC energy level
To ensure the battery power limits are not exceeded
By ensuring the first PMS goal is met, the two EMS goals will also be met. The two EMS
goals and the method of calculating this target UC energy level is explained later in EMS
section 4.2.
The focus in this section is on the second and more urgent goal, which is to ensure that
battery power is restricted to self-imposed limits [Pbatt,min, Pbatt,max]. Based on the works of
60
Wang, et al. [7], a lower battery charge/discharge rate leads to a longer battery cycle life. So
by reducing battery power with the self-imposed limits, the battery cycle life can be extended.
The following sections explain how the limits were calculated.
Note that as mentioned earlier in section 1.8, the contribution of this work to the state of the
art is the speed dependent battery limits, not the two PMS goals, as these two goals are
common in existing works.
4.1.1 Battery Power at Constant Speeds
In general, the battery is used to supply the steady state power, while the UC handles the
transients. For example, if the mid-sized EV is maintaining a constant speed of 100km/h, the
battery needs to supply all the power required at steady state. This is because the UC does not
have enough energy to supply power for an extended time, so it only assists during the
transients (acceleration or braking).
From this logic, a speed-dependent battery power limit was developed, and it is based on the
power required to maintain the mid-sized EV at a constant speed. A speed-dependent battery
power limit achieves two functions – to utilise the UC even during low power demands (such
as low speeds) to further reduce battery use, and to allow the battery to supply power during
steady state.
First, the power required to maintain the EV at a constant speed is studied. This is calculated
using the vehicle model simulation discussed in section 3.6. By setting the acceleration to
zero, and varying the velocity input v(j), the power required to maintain the EV at the
specified velocity inputs can be computed. The result is shown in Figure 4-1.
An upward sloping curve with increasing gradient is observed. This is expected as the
aerodynamic drag Fw(j) in equation (3-5) earlier is dependent on velocity squared. The
maximum power required occurs at the EV’s top speed, 40.3kW at 144km/h, which
61
corresponds to 1.69C. This is far under the 90kW rated Nissan Leaf battery, as the Nissan
Leaf battery needs to handle transients as well. Limiting the battery power to approximately
half its rated power would benefit battery cycle life.
Figure 4-1 Battery power required at constant vehicle speed.
In short, Figure 4-1 shows what the maximum battery discharge power limit should be for the
proposed algorithm design, where the battery supplies enough power to maintain the mid-
sized EV at constant speed, and the UC supplies the extra transient acceleration power.
4.1.2 Final Battery Limit Curve
However, upon further simulations, the UC needs to be much larger in order to supply the
required transient power. This is further explained when discussing the EMS in section
4.2.4.3. Therefore, the battery discharge power limit restriction was loosened by a factor of
Pbatt,max,scale = 3. How this factor of 3 was calculated is also discussed in section 4.2.4.3.
By reflecting Figure 4-1 across its x-axis (making it upside down), the minimum allowed
battery power (or maximum charge power) is attained. On a Nissan Leaf, the maximum
allowed regenerative braking is a constant 30kW (1.25C), as seen on its digital Energy
Information dashboard screen [71]. Therefore, this -30kW is set as the absolute minimum
value.
62
Figure 4-2 shows the final battery limit curve of the proposed algorithm design, which is
solely dependent on speed. The maximum battery limit has been loosened by a factor of
Pbatt,max,scale = 3. However, it has been clipped to a maximum of 40.6kW or 1.7C (slightly
more than the original 1.69C to give a buffer). Similarly, the minimum battery limit has been
clipped to the -30kW or 1.25C.
Figure 4-2 Speed-dependent PMS battery limit curve.
At lower speeds, the limits have been opened up to 0.4C (9.6kW). This allows the battery to
charge or discharge the UC to the required target UC energy level at those speeds. For
example, if the battery limits were zero at zero speed (as shown by the original curve in
Figure 4-1), then the UC would be unable to charge when the vehicle is not moving. 0.4C
was chosen as it is a gentle discharge on the battery, yet able to top-up the UC from 90%
SOC to full in about 10 seconds (the difference in SOC is due to deviation from the EMS
algorithm, which uses average values).
With this proposed speed-dependent band, the higher the vehicle speed, the more battery
power can be used.
The final speed-dependent battery limit curve can be expressed mathematically by,
63
𝑃𝑏𝑎𝑡𝑡,𝑚𝑎𝑥(𝑣(𝑡)) = max(9.56,𝑚𝑖𝑛(𝑃𝑏𝑎𝑡𝑡,𝑚𝑎𝑥,𝑠𝑐𝑎𝑙𝑒 𝑃𝑏𝑎𝑡𝑡,𝑐𝑜𝑛𝑠𝑡(𝑣(𝑡)) , 40.6)) (4-1)
𝑃𝑏𝑎𝑡𝑡,𝑚𝑖𝑛(𝑣(𝑡)) = min(−9.56,𝑚𝑎𝑥(−𝑃𝑏𝑎𝑡𝑡,𝑐𝑜𝑛𝑠𝑡(𝑣(𝑡)),−30)) (4-2)
To summarise, Figure 4-2 shows the speed-dependent battery limit curve of the proposed
algorithm design, which is a simple rule-based deterministic design. The higher the vehicle
speed, the higher the limits, and more battery power can be used. This speed-dependent
battery power limit permits two goals to be achieved – to utilise the UC even during low
power demands to reduce battery use, and to allow the battery to supply power during steady
state. This will be further illustrated in the simulations in section 5.3. The simulations also
show that existing constant battery limits from literature are unable to meet these two goals
simultaneously.
4.2 Energy Management Strategy
The self-imposed battery power limits in the PMS was introduced in the previous section. In
this section, the EMS is discussed. There are two goals in the proposed EMS,
To ensure sufficient space in the UC to absorb energy during future regenerative
braking.
To ensure sufficient energy remaining in the UC for future accelerations.
These two goals are achieved by setting a target UC energy band. The upper limit of the band
defines the maximum allowed UC energy, which is calculated from the space required to
capture regenerative braking energy. The lower limit defines the minimum allowed UC
energy, which is calculated from the energy required for future accelerations. As long as the
actual UC energy level is within the band, then the two goals are achieved.
The contribution of this proposed EMS to the state of the art is the rigorous methods for
determining this band, which considers multiple factors, such as worst case scenarios and
64
real-life drive cycles. In other works, the band, or mostly, just a target UC energy level is set
based on experience.
In the following sections, the upper and lower limits of the UC energy band are calculated
and explained. Figure 4-3 shows the overall flow of the proposed EMS design. From the
vehicle speed, the target UC energy band can be calculated.
Figure 4-3 Block diagram of overall EMS design
4.2.1 Sufficient Space in UC for Regenerative Braking
In this section, the ‘Anticipate UC space required for regen.’ block in Figure 4-3 is discussed.
Figure 4-4 presents a detailed diagram of this block. The ‘Anticipate UC energy required for
acc.’ block is shared in Figure 4-4 as they are similar. It will be discussed later in section
4.2.2.
The first EMS goal is to ensure sufficient space (i.e. sufficiently low energy or SOC) in the
UC for regenerative braking, by estimating the energy absorbed by the UC during
regenerative braking and therefore generating the initial maximum allowed starting UC SOC.
Upper
band limit
Lower band
limit
Anticipate UC space
required for regen.
(section 4.2.1, Figure
4-4)
Consider worst case
scenario
(section 4.2.3.2) UC sizing
(section
4.2.4.2) Worst case brake torque
Target UC
band
(section
4.2.4.1) Anticipate UC energy
required for acc.
(section 4.2.2, Figure
4-4)
Consider worst case
scenario
(section 4.2.3.3)
Worst case acc. torque
Battery
limits from
PMS
(section 4.1,
Figure 4-2)
Vehicle
Speed
65
The general idea of the algorithm is a forward approach simulation – a constant braking
torque is applied, and then kinematic equations are used to predict the future velocity profile
of the car and the motor. With the motor velocity and torque, the power and energy generated
during regenerative braking can be computed. Now, the algorithm is explained in detail.
Figure 4-4 EMS block diagram to anticipate UC space required or energy generated.
The inputs to this algorithm are present motor speed ωm(j), target braking torque at the motor
τbr,tar, battery power at previous instant Pbatt(j-1). The output of this algorithm is the estimated
Motor torque/speed,
efficiency
(Figure 3-8)
ηm(τm,ωm)
τm,tar,
ωm,tar
Ptar+aux
Compute
motor ang.
velocity
(4-8)
Compute
motor
torque
(4-9)
Compute total
power
(4-10), (4-11)
Compute batt./UC
power split
(4-12) to (4-14)
Compute energy
generated
(4-15)
Compute energy
required
(4-18)
If regen. If acc.
If regen. If acc.
Puc,H,tar
Euc,regen,tar(j)
Euc,acc,tar(j)
Pbatt(j-1)
rwh, Gr
ωm,tar
ωm,tar
SOCuc,regen,tar(j)
SOCuc,acc,tar(j)
Compute max.
UC SOC
(Figure 3-17)
Compute min.
UC SOC
(Figure 3-17)
ηDC/DC(k)
ωm(j)
τbr,tar
τacc ratio
vwh,tar
τwh,tar(k)
Compute wheel
torque
(4-3)
Compute wheel
& motor torque
(4-16), (4-17)
m, mr, rwh,
Gr, ηp
If regen. If acc.
τwh,tar(k)
vwh,tar(k)
For k, loop until target speed
reached
τm,tar
Compute wheel
velocity
(4-4) to (4-7)
DC/DC converter
efficiency
(Figure 3-24)
Output
66
energy sent to the UC on the low-side of the DC/DC converter Euc,regen,tar(j) and the maximum
initial UC SOC SOCuc,regen,tar(j).
In the first instant at k=1, the target brake torque τbr,tar at the motor is applied (The reason and
value for this target brake torque is explained later in section 4.2.3). The brake torque at the
wheel τwh,tar(k) is computed as follows,
𝜏𝑤ℎ,𝑡𝑎𝑟(𝑘) =
𝐺𝑟 𝜏𝑏𝑟,𝑡𝑎𝑟𝜂𝑝
(4-3)
The tractive effort Ft,tar(k=1) and resistance force Fv,tar(k=1) at that point of time is also
calculated. Then the acceleration awh,tar(k=1) can be determined as follows,
𝐹𝑡,𝑡𝑎𝑟(𝑘) =
𝜏𝑤ℎ,𝑡𝑎𝑟(𝑘)
𝑟𝑤ℎ
(4-4)
𝐹𝑣,𝑡𝑎𝑟(𝑗) = 𝐹𝑤,𝑡𝑎𝑟(𝑗) + 𝐹𝑟,𝑡𝑎𝑟(𝑗) + 𝐹𝑔,𝑡𝑎𝑟(𝑗) (4-5)
𝑎𝑤ℎ,𝑡𝑎𝑟(𝑘) =
𝐹𝑡,𝑡𝑎𝑟(𝑘) − 𝐹𝑣,𝑡𝑎𝑟(𝑘)
𝑚 +𝑚𝑟
(4-6)
The future velocity vwh,tar(k) can be computed with the acceleration from the previous instant
as follows,
𝑣𝑤ℎ,𝑡𝑎𝑟(𝑘) = 𝑣𝑤ℎ,𝑡𝑎𝑟(𝑘 − 1) + 𝑎𝑤ℎ,𝑡𝑎𝑟(𝑘)∆𝑡 (4-7)
Now, computations for the first iteration k=1 have been completed. Subsequently, equations
(4-3) to (4-7) are looped for iterations of k until the vehicle velocity vwh,tar drops to zero,
where the car has stopped moving and no further regenerative braking can occur.
As a side remark, k corresponds to the inner loop forward approach kinematic equation
iterations until the car has reached the desired velocity (zero in this case), while j corresponds
to the outer loop drive cycle in the backwards approach simulation (see Figure 4-4).
At the end of the loop, the motor speed ωm,tar at every iteration k is computed by,
67
𝜔𝑚,𝑡𝑎𝑟 =
𝐺𝑟 𝑣𝑤ℎ,𝑡𝑎𝑟𝑟𝑤ℎ
(4-8)
The target braking torque as mentioned previously is τbr,tar. But before the power generated by
regenerative braking can be computed, the motor must be checked to see if it can handle the
high braking torques encountered.
As discussed in section 3.6 Vehicle Model, the maximum braking torque (alternatively,
minimum motor torque) τm,min(ωm(k)) (which is a negative number) as well as the
motor/inverter efficiency ηm,tar(k) can be found from a specified motor speed ωm,tar(k) using
Figure 3-8. Therefore, the motor provides the following braking torque,
𝜏𝑚,𝑡𝑎𝑟(𝑘)− = max (𝜏𝑏𝑟,𝑡𝑎𝑟(𝑘), 𝜏𝑚,𝑚𝑖𝑛(𝜔𝑚(𝑘))) (4-9)
The rest of the braking torque comes from the mechanical brakes. Now, the total power
generated during regenerative braking operation can be computed after considering
motor/inverter efficiencies,
𝑃𝑡𝑎𝑟(𝑘) =
𝜏𝑚,𝑡𝑎𝑟(𝑘) 𝜔𝑚,𝑡𝑎𝑟(𝑘)
𝜂𝑚,𝑡𝑎𝑟(𝑘) 𝑓𝑜𝑟 𝜏𝑚,𝑡𝑎𝑟(𝑘)+
𝜏𝑚,𝑡𝑎𝑟(𝑘) 𝜔𝑚,𝑡𝑎𝑟(𝑘) 𝜂𝑚,𝑡𝑎𝑟(𝑘) 𝑓𝑜𝑟 𝜏𝑚,𝑡𝑎𝑟(𝑘)−
(4-10)
Note that in regenerative braking, Ptar(k) is a negative value. After including the auxiliary
loads Paux, the total regenerative power becomes,
𝑃𝑡𝑎𝑟+𝑎𝑢𝑥(𝑘) = 𝑃𝑡𝑎𝑟(𝑘) + 𝑃𝑎𝑢𝑥 (4-11)
Some of this power is charged to the UC and some to the battery. This power split is decided
by the self-imposed battery power limits [Pbatt,min, Pbatt,max] discussed in section 4.1 earlier.
The regenerative power is charged to the battery as long as the anticipated battery power
Pbatt,tar is within limits, i.e. Pbatt,max(k) > Pbatt,tar(k) > Pbatt,min(k). The remaining power which
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cannot be captured by the battery will be charged to the UC (high-side UC power Puc,H,tar).
This can be expressed mathematically as follows,
𝑃𝑏𝑎𝑡𝑡,𝑡𝑎𝑟(𝑘) =
min(𝑃𝑏𝑎𝑡𝑡,𝑡𝑎𝑟(𝑘), 𝑃𝑏𝑎𝑡𝑡,𝑚𝑎𝑥(𝑘)) 𝑖𝑓 𝑃𝑏𝑎𝑡𝑡,𝑡𝑎𝑟 ≥ 0
max(𝑃𝑏𝑎𝑡𝑡,𝑡𝑎𝑟(𝑘), 𝑃𝑏𝑎𝑡𝑡,𝑚𝑖𝑛(𝑘)) 𝑖𝑓 𝑃𝑏𝑎𝑡𝑡,𝑡𝑎𝑟 < 0
(4-12)
𝑃𝑢𝑐,𝐻,𝑡𝑎𝑟(𝑘) = 𝑃𝑡𝑎𝑟+𝑎𝑢𝑥(𝑘) − 𝑃𝑏𝑎𝑡𝑡,𝑡𝑎𝑟(𝑘) (4-13)
where the starting value of Pbatt,tar(1) is,
𝑃𝑏𝑎𝑡𝑡,𝑡𝑎𝑟(1) = 𝑃𝑏𝑎𝑡𝑡(𝑗 − 1) (4-14)
Note that for the regenerative braking case, only Pbatt,tar < 0 is considered. Pbatt,tar > 0 is also
shown above for completion. It will be used in the acceleration case later.
Now, the anticipated (target) battery power Pbatt,tar and high-side UC power (before DC/DC
converter losses) Puc,H,tar has been computed for one instant of j, which comprises multiple
instances of k. Figure 4-5 shows a demonstration of this algorithm, where the mid-sized EV
was braked from 120km/h (33m/s) to zero. Figure 4-5(a) shows the kinematics, Figure 4-5(b)
shows the torques, Figure 4-5(c) shows the powers, and Figure 4-5(d) shows the
corresponding UC and battery SOC values.
The target braking torque τbr,tar in this demonstration is 244Nm (more on how this value was
selected later). The motor cannot handle this torque above the base speed, so the mechanical
brakes assist in the braking as seen in the first 6s of Figure 4-5(b). Note that in reality, the
mechanical brake torque acts on the wheel, but the torque in Figure 4-5(b) shows the
mechanical brake torque as if it occurred at the motor shaft for an easier comparison with the
motor torque.
In Figure 4-5(c), the power split is shown. As the total regenerative power Ptar+aux exceeds the
Pbatt,min battery limit, the battery charges at the limit while the UC handles the rest of the
power, given by Puc,tar (low-side power) and Puc,H,tar (high-side power).
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Figure 4-5 (a) Kinematics (b) torques (c) powers (d) SOCs during regenerative braking.
Assuming the UC is fully charged at the end of braking, the maximum corresponding UC
energy level or SOC in order to absorb this energy can be calculated by working backwards.
70
Note, fully charged is defined as 98.8% UC SOC. In the experiment setup later, the UC was
not charged to 100% for safety reasons, but to 98.8%. So the simulation here was revised to
standardise the conditions.
By integrating the high-side UC power Puc,H,tar(k) over time k, as well as considering the
DC/DC converter losses, the energy Euc,regen,tar(j) sent to the UC can be computed for the
above demonstration,
𝐸𝑢𝑐,𝑟𝑒𝑔𝑒𝑛,𝑡𝑎𝑟(𝑗) =
∫
𝑃𝑢𝑐,𝐻,𝑡𝑎𝑟(𝑘)
𝜂𝐷𝐶/𝐷𝐶,𝑏𝑜(𝑘)𝑑𝑘
𝑘
0
𝑖𝑓 𝑃𝑢𝑐,𝐻,𝑡𝑎𝑟(𝑘) ≥ 0
∫ 𝜂𝐷𝐶/𝐷𝐶,𝑏𝑢(𝑘) 𝑃𝑢𝑐,𝐻,𝑡𝑎𝑟(𝑘)𝑘
0
𝑑𝑘 𝑖𝑓 𝑃𝑢𝑐,𝐻,𝑡𝑎𝑟(𝑘) < 0
(4-15)
Therefore, the UC needs to have this amount of space available to absorb the regenerative
braking if the car were to brake to a standstill from 120km/h with a braking torque of 244Nm.
Inserting these values into the UC model discussed in section 3.8, the corresponding
maximum UC SOC values can be computed.
Figure 4-5(d) shows the SOCs of the battery and UC. The maximum allowed starting
SOCuc,regen,tar value is 48.9% for this demonstration (as shown by the orange arrow) to ensure
sufficient space in the UC.
4.2.2 Sufficient Energy in UC for Acceleration
The second EMS goal is to ensure sufficient energy in the UC for acceleration, by estimating
the energy required from the UC during acceleration and therefore generating the minimum
allowed initial starting UC SOC. The general idea of this algorithm is similar to the previous
regenerative braking algorithm, where kinematic equations are used to predict the future
velocity profile of the car and the motor. Then the required power can be calculated.
The difference between this algorithm and the regenerative braking algorithm is that the
regenerative braking algorithm allows a brake torque which is both constant and exceeds the
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motor limits since the mechanical brakes can assist. But in this acceleration algorithm, the
acceleration torque is solely provided by the motor, so it will not exceed the motor limits. In
addition, the torque may not be constant when the motor is operating in the constant power
region. Therefore, instead of specifying a constant acceleration torque, a constant acceleration
torque ratio τacc ratio = τm,tar(k)/τm,max(ωm(k)) is specified, where τm,max(ωm(k)) is obtained from
Figure 3-8. What this means is that by holding the accelerator pedal steady (constant τacc ratio),
the torque output τm,tar(k) will be directly proportional to the maximum torque of the motor
τm,max(ωm(k)) at that specific speed.
Now, the algorithm is explained in detail. The inputs to the algorithm are present motor speed
ωm(j), target acceleration torque ratio τacc ratio, battery power at previous instant Pbatt(j-1). The
output is the estimated energy required by the UC on the low-side of the DC/DC converter
Euc,acc,tar(j) and the minimum initial UC SOC SOCuc,acc,tar(j) (see Figure 4-4).
In the first instant k=1, the target acceleration torque τm,tar(k) at the motor is applied. Then the
acceleration torque at the wheel τwh,tar(k) is computed by,
𝜏𝑚,𝑡𝑎𝑟(𝑘) = 𝜏𝑎𝑐𝑐 𝑟𝑎𝑡𝑖𝑜 𝜏𝑚,𝑚𝑎𝑥(𝜔𝑚(𝑘)) (4-16)
𝜏𝑤ℎ,𝑡𝑎𝑟(𝑘) = 𝐺𝑟 𝜏𝑚,𝑡𝑎𝑟(𝑘) 𝜂𝑝 (4-17)
Then, the tractive effort Ft,tar(k) and resistance force Fv,tar(k) at that point of time are
calculated using earlier equations (4-4) and (4-5). Subsequently, the acceleration awh,tar(k) is
calculated using (4-6). Finally, the future velocity vwh,tar(k) is computed using equation (4-7).
Equations (4-16), (4-17), (4-4), (4-5), (4-6), (4-7), in this specific order, are looped until the
vehicle velocity vwh,tar increases to 120km/h (33m/s). A highway speed of 120km/h has been
selected instead of the top speed of the mid-sized EV, 144km/h, as under normal driving
conditions, the top speed would not be attained. Therefore, the algorithm ensures the UC has
sufficient energy just to get the car to highway speeds (more on limitations later).
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At the end of the loop, the motor speed ωm,tar at every iteration k can be computed with (4-8).
Next, the total power required for acceleration after considering motor/inverter efficiencies is
calculated using (4-10) and (4-11).
Some of this power will be supplied by the UC and some by the battery, where the battery
power is restricted to the speed-dependent limit discussed in section 4.1. The remaining
power which cannot be supplied by the battery due to the restriction will be supplied by the
UC, and this is expressed mathematically using equations (4-12) to (4-14).
Figure 4-6 shows a demonstration of this algorithm, where the car was originally travelling at
30km/h (8m/s) and suddenly required an acceleration torque ratio of 0.5.
Figure 4-6(c) shows the power split. As the total required acceleration power Ptar+aux exceeds
the Pbatt,max battery limit, the battery discharges at the limit while the UC handles the rest of
the power.
Assuming the UC SOC is at the minimum level (50%) at the end of the acceleration, the
minimum corresponding initial UC energy level or SOC to provide this acceleration can be
calculated by working backwards.
By integrating the high-side UC power Puc,H,tar(k) over time k, as well as considering the
DC/DC converter losses, the energy Euc,acc,tar(j) required from the UC for the demonstration
can be computed by,
𝐸𝑢𝑐,𝑎𝑐𝑐,𝑡𝑎𝑟(𝑗) =
∫
𝑃𝑢𝑐,𝐻,𝑡𝑎𝑟(𝑘)
𝜂𝐷𝐶/𝐷𝐶,𝑏𝑜(𝑘)𝑑𝑘
𝑘
0
𝑖𝑓 𝑃𝑢𝑐,𝐷𝐶/𝐷𝐶,𝑡𝑎𝑟(𝑘) > 0
∫ 𝜂𝐷𝐶/𝐷𝐶,𝑏𝑢(𝑘) 𝑃𝑢𝑐,𝐻,𝑡𝑎𝑟(𝑘)𝑑𝑘𝑘
0
𝑖𝑓 𝑃𝑢𝑐,𝐷𝐶/𝐷𝐶,𝑡𝑎𝑟(𝑘) < 0
(4-18)
Therefore, the UC needs to have this amount of energy if the car were to accelerate from
30km/h to 120km/h with an acceleration torque ratio of 0.5. Inserting these values into the
UC model discussed in section 3.8, the corresponding SOCuc,acc,tar values can be computed.
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Figure 4-6 (a) Kinematics (b) torques (c) powers (d) SOCs during acceleration.
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Figure 4-6(d) shows the SOCs of the battery and UC. The minimum allowed starting
SOCuc,acc,tar value is 94.8% for this demonstration (as shown by the orange arrow) to ensure
sufficient energy in the UC for acceleration.
4.2.3 Selected Braking and Acceleration Torque Values
In this section, the braking torque τbr,tar and acceleration torque ratio τacc ratio values mentioned
in the previous sections are discussed.
The general idea here is to select the worst case regenerative braking scenario (recovers most
UC energy, therefore requires most space), and the worst case acceleration scenario
(consumes most UC energy). This is only done once and is not part of the simulation loop.
4.2.3.1 Worst Case Braking Torque
To recover the most energy during braking, the car should be stopped as quickly as possible,
with a braking torque just before the wheel skids. This is because less energy would be lost to
the resistance forces Fv if the distance d that the car travels is shorter,
𝐸𝑣,𝑙𝑜𝑠𝑠 = 𝐹𝑣 𝑑 (4-19)
However, this means the mechanical brakes need to be used, and energy will be dissipated, so
the braking forces need to be restrained to within the motor limits. Therefore, the most energy
can be recovered during regenerative braking when the braking torque is controlled to follow
the maximum torque/speed curve in Figure 3-8 (i.e. follow the edge).
However, there are a few problems with following the curve. Firstly, it is difficult for a driver
to operate the brake pedals such that it follows the curve exactly. Secondly, this goes against
conventional driving techniques. In driving school, learners are usually taught to brake harder
and firmer at the start of the deceleration to bring the speed of the car down quickly, and then
ease up on the brakes as the car slows. In contrast, to recover the most energy, the driver
75
needs to apply a small braking torque at the start of the deceleration, and then progressively
increase the brake torque to the motor maximum as the car slows. This may be dangerous as
the driver may underestimate the braking effort required and overshoot.
In addition, the motor/inverter efficiency has not been considered yet. So in fact, following
the edge of the motor torque/speed curve does not give the worst case braking torque. The
worst case braking torque consists of a path within the torque/speed curve which attains the
highest overall efficiency. This further adds to the difficulty, and it is highly unlikely that a
driver would apply the brakes in such a pattern.
4.2.3.2 Worst Case Constant Brake Torque
To simplify the problem, the strategy in this proposed work is restricted to a constant brake
torque value, which is also more realistic in terms of driving patterns. Next, the constant
brake torque value that corresponds to the maximum energy absorbed by the UC is found.
The forward approach simulation discussed in section 4.2.1 is run repeatedly, varying the
braking torque value τbr,tar, as well as the starting vehicle velocity vwh. The battery power at
the previous instant Pbatt(j-1) is calculated to be the power required for maintaining the initial
starting vehicle velocity vwh (shown earlier in Figure 4-1). Then a target UC SOC value
SOCuc,regen,tar for every τbr,tar and vwh is obtained, and this is represented by a contour plot in
Figure 4-7. In general, the higher the starting velocity of the car, the more UC regenerative
braking energy it can recover.
At each velocity vwh, the brake torque τbr,tar that recovers the most energy (i.e. lowest starting
target UC SOC) is found, and this is highlighted by the red line in Figure 4-7. Figure 4-8
shows this line isolated.
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Figure 4-7 Target UC SOC for varying brake torques and start velocities.
Figure 4-8 Brake torques corresponding to max. recovered UC energy for each velocity.
In Figure 4-8, at high starting velocities, a smaller (less negative) constant braking torque
generates more energy. In contrast, at low starting velocities, a larger (more negative)
constant braking torque generates more energy. This seems counter intuitive, but can be
explained easily.
At high velocities, especially in the constant power region of the motor, the amount of
braking torque that the motor can absorb is low as shown in Figure 3-8. Therefore, a smaller
constant braking torque is used to reduce energy dissipated by the mechanical brakes.
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Conversely, when the starting velocity is low, the motor would be in the constant torque
region, providing more braking torque. Therefore, a braking torque value close to the motor
limits can be used.
Since regenerative braking is most often used in city start-stop driving, where the top speed is
at most 60km/h, the selected constant brake torque for this proposed strategy is 244Nm,
which is an average of the 0 – 60km/h section of Figure 4-8. Therefore, below 60km/h, there
will be sufficient space in the UC for regenerative braking. But at speeds above 60km/h, if
the driver coincidentally applies the corresponding worst case braking torque to stop the car,
the UC will not be able to absorb the energy completely. The excess will be directed to the
battery instead. If the driver is travelling above 60km/h, he is likely to be travelling on a
highway and the use of brakes is not as frequent as city driving. Furthermore, in normal
situations, he is unlikely to brake to a standstill in the middle of the highway. Therefore, this
is a good compromise to ensure minimal sizing of the UC (more on this in section 4.2.4.2 UC
Sizing). Although there are some compromises, it will be shown in the simulations later that
this is not a problem as the algorithm can tolerate harsh driving for short durations.
This was how the target braking torque τbr,tar = 244Nm was selected in section 4.2.1.
4.2.3.3 Worst Case Constant Acceleration Torque
In this section, the constant acceleration torque ratio that corresponds to the maximum energy
which needs to be supplied by the UC is determined.
Again, a constant acceleration torque ratio is used for simplicity. Similar to the previous
section, the forward simulation discussed in section 4.2.2 is run repeatedly, varying the
acceleration torque ratio τacc ratio, as well as the starting vehicle velocity vwh. Then a target UC
SOC value SOCuc,acc,tar for every τacc ratio and vwh is obtained, shown in Figure 4-9.
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Figure 4-9 Target UC SOC for varying brake torques and start velocities.
In general, the higher the desired acceleration and the lower the initial car speed, the more
UC energy is required to bring the car to a highway speed of 120km/h.
The white line in Figure 4-9 demarcates the UC 100% SOC crossing. To the bottom right of
the line with high acceleration ratios and low initial vehicle speeds, the UC needs to be
charged beyond 100% to enable that acceleration (i.e. insufficient energy in the UC). This
will not be a problem as explained later (Although the algorithm is not designed for
aggressive acceleration, it can tolerate it).
Again, at each velocity vwh in Figure 4-9, the acceleration torque ratio τacc ratio that consumes
the most UC energy is found. This corresponds to the right most edge, τacc ratio = 1 for all
speeds, i.e. to floor the accelerator.
However, in normal driving conditions, it is highly uncommon to floor the accelerator pedal
from 0 to 120km/h in a single shot. Therefore, the region in the bottom right corner is
unlikely to occur. Other methods of determining the worst case acceleration energy under
normal driving conditions are considered instead.
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Comparing the NEDC, FTP-75 city and FTP-75 HWFET regular driving cycles, the
maximum (worst case) torque for acceleration occurs in the FTP-75 city drive cycle with
123Nm at 37.2 km/h, corresponding to a motor speed of 2557rpm on the Nissan Leaf (below
motor base speed). Using these figures, the acceleration torque ratio was calculated as
follows,
𝜏𝑎𝑐𝑐 𝑟𝑎𝑡𝑖𝑜(𝑘) =
𝜏𝑚,𝑡𝑎𝑟𝜏max(2557 𝑟𝑝𝑚)
= 123 𝑁𝑚
254 𝑁𝑚= 0.48
(4-20)
Therefore, τacc ratio was selected at 0.5 (to allow some buffer). The implication is that the UC
only has sufficient energy to get to 120km/h for acceleration torque ratios below 0.5. This is a
good compromise as it ensures minimal sizing of the UC, while allowing sufficient
acceleration under normal driving conditions, such as those seen in the standard drive cycles.
It will be shown later that the algorithm can tolerate aggressive driving cycles such as the
LA92, as there is no flooring the accelerator from 0 to 120km/h.
This was how the target acceleration torque ratio τacc ratio = 0.5 was selected in section 4.2.2.
4.2.4 Target UC Energy Band
In this section, the creation of the target UC energy band is discussed. In earlier sections 4.2.1
and 4.2.2, the maximum and minimum target UC SOC values – SOCuc,regen,tar(j) and
SOCuc,acc,tar(j) respectively were calculated.
4.2.4.1 Target UC SOC Band
These maximum and minimum target SOC values define a UC SOC band. If the present UC
SOC SOCuc(j) is within the band, i.e.
𝑆𝑂𝐶𝑢𝑐,𝑎𝑐𝑐,𝑡𝑎𝑟(𝑗) ≤ 𝑆𝑂𝐶𝑢𝑐(𝑗) ≤ 𝑆𝑂𝐶𝑢𝑐,𝑟𝑒𝑔𝑒𝑛,𝑡𝑎𝑟(𝑗) (4-21)
then there would always be sufficient space and energy in the UC, meeting the goals of the
proposed EMS. As the braking torque τbr,tar and acceleration torque ratios τacc ratio have already
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been determined and fixed in the previous section, the band limits only depend on vehicle
velocity vwh.
Figure 4-10 shows the final result of the target UC SOC band versus vehicle velocity curve,
with the upper limit (calculated from regenerative braking) in blue and the lower limit
(calculated from acceleration) in red.
Figure 4-10 Target UC SOC band vs. speed, 6 UC modules.
It is observed that both curves slope downwards. For the blue regenerative braking curve, the
higher the vehicle speed, the more energy will be captured during regenerative braking,
resulting in the downward sloping curve. Similarly, for the red acceleration curve, the higher
the vehicle speed, the less energy required to get it to the highway speed of 120km/h.
A substantial change in the gradient is observed at about 90km/h for the red acceleration
curve. This corresponds to the flat section for the blue Pbatt,max curve in Figure 4-2. Speeds
above 45km/h correspond to the constant power region of the motor. At speeds above
90km/h, as the battery power limit is at the maximum (flat section), less UC energy is
required for a constant power. Therefore, the gradient of the red acceleration curve flattens
out.
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The following sections explain how Figure 4-10 was finalised.
4.2.4.2 UC Sizing
Six Maxwell 48V general purpose UC modules in series, totalling 288V and 13.8F were
used. The UC was sized based on being able to capture regenerative braking energy. The
lowest point of the blue regenerative braking curve in Figure 4-10 is 48.9% as shown by the
orange arrow. Earlier in section 3.8 Ultracapacitor Model, it was mentioned that the UC
should not be discharged below 50% SOC as the DC/DC converter becomes inefficient at
low UC voltages. Although 48.9% is slightly below 50%, it is still acceptable as it is not a
hard rule.
Another perspective was shown in earlier Figure 4-7, which was simulated with six UC
modules. In that figure, the white arrow points to the maximum starting 48.9% SOC with a
selected brake torque of 244Nm.
If only five UC modules were used, Figure 4-11 shows the results (ignore the red curve for
now). From the orange arrow, the lowest point of the blue regenerative braking curve is
37.0%, which is too low. Another perspective is shown in Figure 4-12.
Figure 4-11 Target UC SOC band vs. speed, 5 UC modules.
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Figure 4-12 Target UC SOC for varying brake torques and start velocities, 5 UC modules.
The white arrow in Figure 4-12 points to the maximum starting 37.0% SOC with a selected
brake torque of 244Nm. The white semi-circle at the top centre is a part which is
unachievable (imaginary roots to the DC/DC converter quadratic equations), where the
starting UC SOC drops too low, and has insufficient power to compensate for the DC/DC
converter losses.
Therefore, six UC modules is the minimum number of UC modules to fully capture the
regenerative braking energy.
In Figure 4-10, the two limits cross at about 115km/h. That means beyond 115km/h, one of
the two UC goals (sufficient energy for acceleration or space for braking) cannot be achieved.
An additional UC module would widen the band such that they no longer cross. But as it is a
very short section, six UC modules is a good compromise to avoid another UC module,
which costs approximately US$1.2k [13]. An alternative is to define the minimum of the red
acceleration curve as 48.9% SOC in earlier section 4.2.2, i.e. to shift the red acceleration
curve downwards slightly, such that the two curves no longer cross.
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4.2.4.3 Tuning Battery Limits
Earlier in section 4.1.2 on battery limits, loosening the battery restriction by a factor of
Pbatt,max,scale = 3 was mentioned. The reason for that is discussed here. If the battery power at
constant speed curve from Figure 4-1 was used directly as the battery limits, Figure 4-13
shows the result.
Figure 4-13 Target UC SOC band vs. speed, no battery power loosening
In Figure 4-13, the red acceleration curve shoots off the top of the figure at low speeds,
meaning more than 100% UC SOC is required to perform the acceleration. This is because
more energy is required for acceleration to a certain speed than energy generated from
braking from that speed, due to electrical losses (DC/DC converter, motor/inverter, etc.) and
mechanical losses (friction, etc.). There are two ways to solve this. The first is to increase the
UC size. However, this is an expensive solution. The second way is to loosen the self-
imposed battery restriction (i.e. sacrificing some cycle life), which allows the battery to be
used more.
In order to fit the red acceleration curve under the blue regenerative curve, the self-imposed
battery restriction was loosened by increasing Pbatt,max,scale iteratively in an approach similar to
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the bisection method. The value which fits the acceleration curve just under the regenerative
curve is Pbatt,max,scale = 3, resulting in the band shown in Figure 4-10.
In short, this loosening compensates for the differences in energy required for acceleration
and energy generated from braking. It allows the UC to be sized appropriately for both
regenerative braking and acceleration.
4.2.4.4 Target UC SOC Level
In Figure 4-10, the target UC SOC band was shown. As long as the actual UC SOC is within
the band, the two UC goals of sufficient energy for acceleration and space for braking are
satisfied. In this section, a specific point within the band is selected to reduce the band to a
target UC SOC level for implementation.
The maximum possible SOC of the two limits is selected, i.e.
𝑆𝑂𝐶𝑢𝑐,𝑡𝑎𝑟(𝑣𝑤ℎ(𝑡)) = max (𝑆𝑂𝐶𝑢𝑐,𝑎𝑐𝑐,𝑡𝑎𝑟(𝑣𝑤ℎ(𝑡)), 𝑆𝑂𝐶𝑢𝑐,𝑟𝑒𝑔𝑒𝑛,𝑡𝑎𝑟(𝑣𝑤ℎ(𝑡))) (4-22)
This results in SOCuc,tar following the blue SOCuc,regen,tar curve in Figure 4-10 below 115km/h
and the red SOCuc,acc,tar curve above 115km/h. This implies that more emphasis is placed on
acceleration as the EMS acceleration goal is always met. The UC has both sufficient space
for braking and energy for acceleration at speeds below 115km/h. Above 115km/h, the UC
has the minimum energy required for acceleration but slightly insufficient space for braking.
When travelling above 115km/h, the EV is likely to be on a highway and braking would not
be frequent, so this is not a major concern.
The reason for placing emphasis on acceleration is because acceleration power comes solely
from the battery and UC. While for braking, in the worst case scenario, the excess energy can
be dumped to the braking chopper or the mechanical brakes.
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4.2.5 Summary
In summary, comprehensive calculations which consider the worst case scenarios have been
provided to justify the proposed EMS. The upper limit of the target UC SOC band is
determined by the amount of energy which would be generated in the averaged worst case
regenerative braking. The lower limit of the band is determined by the amount of energy
required for the averaged worst case future acceleration and real-life drive cycles. Since the
worst case scenarios have already been considered, knowledge of future drive profile is not
required. This is an advantage as the proposed HESS management strategy can work on any
route, even new ones (In contrast, PMS based on global optimization as discussed in the
literature review require the drive profile beforehand).
As long as the actual UC SOC is within the proposed target UC SOC band, the UC will
always have sufficient space for regenerative braking and sufficient energy for acceleration,
meeting the two EMS goals (except for a very short section above 115km/h). An added
benefit is that during the algorithm design process, the UC is also sized appropriately to
reduce costs.
Although the algorithm has been designed using averaged worst case drive cycles and some
compromises have been made to reduce UC size, the algorithm can still tolerate harsh driving
cycles as shown in the simulation results later. The proposed target UC SOC band will also
be compared with other EMS works in the simulations.
4.3 Power Management Strategy Pt. 2: Implementation
The concept of the target UC energy (or SOC) level has been explained in the previous
section. Here, the implementation of the PMS is discussed. To recap, the PMS decides how
the power flow should be split between the battery and UC. It has two goals,
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To ensure the actual UC energy level follows the target UC energy level
To ensure the battery power limits are not exceeded
The PMS prioritises the second goal. That means it will ensure the UC follows the target UC
energy level normally, but if the self-imposed battery limits are exceeded, it will override
following the target UC energy level and get the battery to be within limits. As the target UC
energy level has been designed for averaged worst case scenarios in section 4.2, there will be
instances such as during hard acceleration or hard braking where the target UC voltage is
insufficient to keep the battery within its limits. Therefore, the second goal is used to always
keep the battery within the limits.
With the knowledge from the previous sections, the PMS is expressed mathematically here.
The inputs to the algorithm are target UC energy Euc,tar(j-1), actual UC energy level Euc(j-1) at
previous instant, power required for drive cycle Pdr+aux(j-1), and actual battery power Pbatt(j-
1). The outputs are battery power Pbatt(j), high-side UC power Puc,H(j).
Figure 4-14 Block diagram of PMS algorithm.
The PMS implementation algorithm is summarised in Figure 4-14. In earlier equation (4-22),
the target UC energy level was stated in terms of SOC. The corresponding energy levels is
calculated by,
𝐸𝑢𝑐,𝑡𝑎𝑟 =
1
2𝐶(𝑆𝑂𝐶𝑢𝑐,𝑡𝑎𝑟 𝑉𝑢𝑐,𝑚𝑎𝑥)
2
(4-23)
Puc,ocv,1(j) UC power
required
(4-24)
Battery power
restriction
(4-25) to (4-33)
System Euc,tar(j) Euc(j) Puc,H(j) +
_
Euc(j-1)
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In order to bring Euc(j) to the desired level Euc,tar(j), power should be channelled into the UC.
This required low-side UC power is calculated by,
𝑃𝑢𝑐,𝑜𝑐𝑣,1(𝑗) = [𝐸𝑢𝑐,𝑡𝑎𝑟(𝑗 − 1) − 𝐸𝑢𝑐(𝑗 − 1)]/𝑑𝑡 (4-24)
Then the output faces a restriction block which enforces the battery power limits. First, the
DC/DC converter losses are accounted for to get the high-side UC power,
𝑃𝑢𝑐,𝐻,1(𝑗) =
𝜂𝐷𝐶/𝐷𝐶,𝑏𝑜(𝑗) 𝑃𝑢𝑐,𝑜𝑐𝑣,1(𝑗) 𝑖𝑓 𝑃𝑢𝑐(𝑗) ≥ 0
𝑃𝑢𝑐,𝑜𝑐𝑣,1(𝑗)
𝜂𝐷𝐶/𝐷𝐶,𝑏𝑢(𝑗) 𝑖𝑓 𝑃𝑢𝑐(𝑗) < 0
(4-25)
Second, the battery power Pbatt,1(j) that ensures the target UC energy level is perfectly met is
determined by,
𝑃𝑏𝑎𝑡𝑡,1(𝑗) = 𝑃𝑑𝑟+𝑎𝑢𝑥(𝑗) − 𝑃𝑢𝑐,𝐻,1(𝑗) (4-26)
Third, the battery power is brought within the limits. Similar to equations (4-12) and (4-13)
earlier, it is enforced by,
𝑃𝑏𝑎𝑡𝑡(𝑗) =
min(𝑃𝑏𝑎𝑡𝑡,1(𝑗), 𝑃𝑏𝑎𝑡𝑡,𝑚𝑎𝑥(𝑗)) 𝑖𝑓 𝑃𝑏𝑎𝑡𝑡,1 ≥ 0
max(𝑃𝑏𝑎𝑡𝑡,1(𝑗), 𝑃𝑏𝑎𝑡𝑡,𝑚𝑖𝑛(𝑗)) 𝑖𝑓 𝑃𝑏𝑎𝑡𝑡,1 < 0
(4-27)
Fourth, the UC power Puc,H(j) is recalculated after the battery restriction is enforced,
𝑃𝑢𝑐,𝐻(𝑗) = 𝑃𝑑𝑟+𝑎𝑢𝑥(𝑗) − 𝑃𝑏𝑎𝑡𝑡(𝑗) (4-28)
Now, the desired UC and battery powers have been determined.
Fifth, two exceptions to the rule are considered. If the UC is fully charged, yet regenerative
braking is required (e.g. driving downhill or under a harsh driving cycle), then the
regenerative energy will be charged to the battery only, which may exceed the battery limits.
Therefore, priority is placed in not wasting energy (short term goals) over battery cycle life
(long term goals). This is expressed mathematically by,
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𝑃𝑢𝑐,𝐻(𝑗) =
0 𝑖𝑓 (𝑃𝑢𝑐,𝐻(𝑗) ≤ 0 𝑎𝑛𝑑 𝑆𝑂𝐶𝑢𝑐(𝑗) ≥ 1)
𝑃𝑢𝑐,𝐻(𝑗) 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
(4-29)
𝑃𝑏𝑎𝑡𝑡(𝑗) = 𝑃𝑑𝑟+𝑎𝑢𝑥(𝑗) − 𝑃𝑢𝑐,𝐻(𝑗) (4-30)
The second exception is if the battery is also fully charged (driving a long distance downhill),
then rheostatic braking will be used. The power generated from the motor will be dumped
into a braking chopper, so that the braking power of the motor is still utilized and not
switched off completely. This can be expressed mathematically as
𝑃𝑏𝑎𝑡𝑡,𝑜𝑛(𝑗) =
0 𝑖𝑓 (𝑃𝑏𝑎𝑡𝑡(𝑗) ≤ 0 𝑎𝑛𝑑 𝑆𝑂𝐶𝑏𝑎𝑡𝑡(𝑗) ≥ 1)1 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
(4-31)
𝑃𝑏𝑎𝑡𝑡(𝑗) = 𝑃𝑏𝑎𝑡𝑡,𝑜𝑛 𝑃𝑏𝑎𝑡𝑡(𝑗) (4-32)
𝑃𝑏𝑐(𝑗) =
𝑃𝑏𝑎𝑡𝑡(𝑗) 𝑖𝑓 𝑃𝑏𝑎𝑡𝑡,𝑜𝑛 = 0
0 𝑖𝑓 𝑃𝑏𝑎𝑡𝑡,𝑜𝑛 = 1
(4-33)
Now, the power split has been computed, namely, battery power Pbatt(j), high-side UC power
Puc,H(j), and braking chopper power Pbc(j), which are the outputs of the proposed power
management algorithm. Examples will be shown in the simulations section later.
4.4 Summary
To summarise this chapter, the proposed HESS management strategy which comprises the
EMS and PMS has been explained.
The EMS computes the target UC energy band and has two goals – to ensure sufficient UC
space to absorb energy during future regenerative braking, and to ensure sufficient UC energy
for future accelerations. Comprehensive calculations and justifications based on averaged
worst case scenarios have been provided to explain how this target UC energy band was
developed, which is not seen in existing works, and is one of the contributions of this thesis.
As the calculations have already considered the worst case scenarios, knowledge of the future
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drive profile is not required, which allows the proposed strategy to work on any route,
including new ones.
The PMS decides the power split between the battery and UC and also has two goals, which
are to ensure the actual UC energy level follows the target UC energy level, and to ensure the
battery power limits are not exceeded, with priority placed in the latter.
The speed-dependent self-imposed battery power limit is the second contribution of this
thesis, which was calculated based on the power required by the EV to maintain a constant
speed. It achieves two functions – to utilise the UC even during low power demands to
reduce battery use, and to allow the battery to supply power during steady state. Later, in the
simulations, it will be clear how the two goals are achieved.
In short, a framework for designing the HESS has been provided. This framework includes
the appropriate sizing of the UC to reduce costs. In this case, six UC modules have been used.
As mentioned earlier, the EMS and PMS were not designed linearly. The EMS was designed
first, followed by the PMS, and the EMS was revised again, and so on. For example, only
five UC modules were used in the original PMS design. This was found to be insufficient for
the EMS. So the number of UC modules was revised to six, and the simulations were re-run
to include the additional energy, voltage, weight, etc. Also, further revisions were performed
after the experiments in Chapter 6 were run, for example the maximum UC SOC was limited
to 98.8% in the experiments for safety reasons. So the maximum UC SOC in the simulation
was revised to 98.8% to standardise the conditions.
Unless stated otherwise, all the plots and figures from this chapter were from the final
simulation configuration.
Before the simulations are presented, the author has some final remarks about the proposed
HESS management strategy. Although a mid-sized EV sedan based on the Nissan Leaf was
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used to develop the HESS management strategy, the strategy is not limited to a sedan. The
parameters for modelling in section 3.11 can be updated to reflect non-sedans, such as
electric buses or electric goods vehicles.
As this work provides a framework for HESS designing, the procedures mentioned in this
chapter for creating the EMS and PMS can be repeated for the new vehicle. For example, the
minimum braking torque for an electric bus may not be τbr,tar = 244Nm, so the target UC
energy band will look different but will suit the electric bus specifications.
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5 HESS SIMULATIONS
In this chapter, simulation results of the HESS are presented. There are four simulations. The
first simulation compares the proposed EMS to that of other works, and shows why the
proposed EMS is better. The second simulation compares the proposed PMS to that of other
works. Similarly, it shows how the proposed PMS is better than other rule-based
deterministic strategies.
The third simulation involves running the mid-sized EV over drive cycles using the proposed
HESS management strategy to show that it can achieve all the desired goals. The fourth
simulation is a battery cycle life simulation to show the improvement of battery cycle life of
the proposed battery/UC HESS setup as compared to a battery-only setup.
5.1 Implementation
Before discussing the simulation results, first an overview of the simulation setup is shown.
The models and algorithms discussed earlier have been integrated to form Figure 5-1, which
shows the complete backward approach simulation, with separate blocks for EMS and PMS
algorithms, models, and drive cycle.
One data point of the drive cycle (v(j) and θ(j)) is fed into the vehicle model to calculate the
total power required for that data point. The EMS generates the target UC energy level based
on the vehicle speed to meet the two goals of sufficient energy for acceleration and sufficient
space for regenerative braking. Subsequently, these data are fed into the PMS, which decides
on the power split between the battery and UC. It performs the two goals of following the
target UC energy level and limiting battery power, with priority in the latter. Once the power
split has been determined, the battery and UC models are updated to reflect the loss or gain in
energy for that data point j. Then this cycle is repeated for the subsequent drive cycle j data
points.
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Figure 5-1 Complete simulation block diagram.
In the experiments later in Chapter 6, a similar approach is used, except that the electrical
models have been replaced with the actual hardware, as can be seen in the ‘output to’ and
‘input from’ hardware boxes in Figure 5-1.
Input from
Simulation
Model/
Hardware
SOCbatt(j-1)
SOCuc(j-1)
Pbatt(j-1)
DC/DC Converter
Model
(Figure 3-24)
Puc,ocv(j)
SOCbatt(j)
SOCuc(j) UC Model
(Figure 3-17)
Battery Model
(Figure 3-15)
Electrical Models
Euc,regen,tar(j) Acc./Regen.
UC Energy
(Figure 4-4)
Loop for k
Euc,acc,tar(j)
Target UC
Energy
(4-22),
(4-23)
Euc,tar(j)
EMS
Loop for j
PMS
(Figure 4-14)
Output to
Hardware
Pbatt(j)
Puc,H(j)
v(j)
θ(j) Vehicle
Model
(Figure 3-9)
Loop for j
ωm
Pdr+aux
Drive
Cycle
Pbc(j)
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5.2 EMS Comparison: Target UC Energy Band
In this section, the proposed target UC energy band is compared to other works and shown to
be better.
Figure 5-2 Target UC SOC band vs. speed, 6 UC modules.
Earlier in Figure 4-10, the proposed target UC SOC band against speed curve was presented.
Figure 5-2 shows the target UC SOC band again, where the blue line represents the upper
limit and the red line the lower limit. Comparisons are made with other works, where the
EMS algorithm of others are applied onto this work’s mid-sized EV. As mentioned earlier in
the literature review, there are a few types of EMS algorithms, such as a constant target UC
energy level or a speed-dependent target UC energy level. The exact value of the target UC
energy level differs between different works.
For example, Avelino, et al. use a constant 87.5% target SOC level [37] coloured green in
Figure 5-2. It exceeds the upper limit at speeds above 55km/h, meaning the UC has
insufficient space if the worst case τbr,tar = 244Nm of regenerative braking is applied at those
Above band
Below band
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speeds. A similar case can be seen for Torreglosa’s constant 75% target SOC [22] in light
blue, which falls under the lower limit below 70km/h, meaning the UC has insufficient
energy for an acceleration of τacc ratio = 0.5 at those speeds.
Choi, et al. use a speed-dependent target UC energy curve [45]. It is coloured orange and
rises above the upper limit at speeds above 45km/h. Below 45km/h, Choi’s curve stays within
or close to the band. However, their method of computation is different from the proposed
work, with the proposed method being more realistic. Choi uses the maximum deceleration
rate to anticipate energy recovered from future regenerative braking. However, the maximum
deceleration rate does not correspond to the worst case energy recovered. This is because
mechanical friction brakes activate at high deceleration rates, dissipating energy as explained
earlier in section 4.2.3, where the worst case scenarios was discussed. In addition, they
charge all regenerative power to the UC. In the proposed algorithm, a constant deceleration
brake torque τbr,tar which recovers the most energy is used, and that energy is charged to both
the battery and UC, reducing required UC size.
It turns out that these two design decisions by Choi reduce the effect of each other. As the
worst case energy was not used, less UC space is required as compared to this work. But
since they charge all regenerative power to the UC, more UC space is required as compared
to this work. This results in Choi’s curve being quite close to the upper limit of the proposed
target UC energy band.
Carter, et al. also use a speed-dependent target UC energy curve [48], coloured purple (Their
design was based on the works of [47]). It falls below and rises above the band at different
points. As discussed earlier in section 2.3.1.3 their curve was computed based on the
assumption that all kinetic energy is recovered to the UC. Similar to the Choi case, this is not
true as not all kinetic energy can be recovered, as some will be dissipated via the mechanical
brakes and some are lost as electrical losses or mechanical losses. In contrast, the proposed
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EMS algorithm in this work uses a far more rigorous method of computation, which
considers the worst case (averaged) scenarios and realistic drive cycles.
Although not shown in Figure 5-2, the constant target UC band of Cao & Emadi [32] suffers
from the same problem as the constant target UC level designs, where the two goals cannot
be satisfied at all times as it is speed-independent. The UC in their work is charged when the
bottom of the band is reached, and stops charging at the top of the band, which is not
dependent on speed.
As shown in Figure 5-3, if the UC energy storage size was increased by 2.2 times to 13
modules, the height of the band would increase and a constant target UC SOC of 76.5% can
be fitted within the band at all times. Only then would the constant UC SOC strategy meet the
two goals. But this would be an expensive and inconvenient solution due to the UC cost and
size.
Figure 5-3 Target UC SOC band vs. speed, 13 UC modules.
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5.3 PMS Comparison: Battery Power Limits
In this section, the proposed speed-dependent battery limit is compared to existing constant
battery limit works and is shown to be better.
To recall, the proposed speed-dependent battery power limit allows two goals, to utilise the
UC even during low power demands to reduce battery use, and to allow the battery to supply
power during steady state. Other deterministic rule-based designs discussed earlier in
literature review section 2.3.2.1, for example [22] [25] [32] [47], have a fixed (non-speed-
dependent) battery limit, and the battery limits differ between different works. In those cases,
the UC only activates when the battery exceeds a certain threshold. For example, in Cao &
Emadi’s work [32] where a simulation was performed, the battery was limited to 12kW
(0.39C), and the UC handles the excessive power beyond 12kW. While in Thounthong, et
al’s work [25] where both simulation and experiment were performed, the discharge battery
current was limited to 20A (0.29C), and the UC handles the excessive power beyond that.
Figure 5-4 Speed-dependent PMS battery limit curve comparison.
Earlier in Figure 4-2 in PMS section 4.1.2, the final proposed speed-dependent battery limit
was presented. Here in Figure 5-4, the limits are presented again, but only considering the
discharge power (positive, upper half only) as it is sufficient to show this comparison. It also
shows a constant 0.39C threshold from Cao & Emadi [32], and a 1.7C threshold at the other
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extreme for comparison purposes. Other works have a threshold which lies between these two
extremes.
If the 0.39C (9.3kW for this work’s mid-sized EV) threshold was used, the battery would not
be able to supply enough power for steady state at speeds above 45km/h. For example, from
earlier Figure 4-1, 20kW is required to maintain a constant 100km/h, and 9.3kW is far from
enough. Since the UC would need to constantly supply 20 – 9.3 = 10.7kW of power at steady
state, it would be drained of energy quickly.
On the other hand, if the 1.7C (40.6kW) threshold was used, the UC would be underutilized
during low power demands. As long as the battery usage does not exceed 40.6kW, the UC
will not be used. However, in the proposed algorithm, the UC is used even at low power
demands to reduce the battery usage to extend the battery cycle life. For example, at 20kmh,
the proposed algorithm uses the UC once the power demanded exceeds 9.6kW, as compared
to 40.6kW for the 1.7C threshold.
5.4 Drive Cycles
In this section, the mid-sized EV was simulated driving over three drive cycles – LA92,
EUDC and FTP-75 city. The two EMS goals of sufficient space and energy in the UC, and
the two PMS goals of enforcing the EMS and enforcing the battery limits are shown to be
met. Also, the two goals of the proposed speed-dependent battery limit are shown to be
achieved.
5.4.1 LA92 Drive Cycle
Earlier in EMS section 4.2.3, where the algorithm brake torque and acceleration torques were
selected, there were some compromises. For example, if the driver coincidentally applies the
corresponding worst case braking torque at speeds above 60 km/h to stop the car, there is
insufficient space in the UC and it will not be able to absorb the energy completely.
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Alternatively, if the driver accelerates harsher than an acceleration torque ratio of 0.5, he may
not have sufficient energy to get to highway speeds.
Therefore, an aggressive LA92 drive cycle (Figure 5-5) has been used to demonstrate that
although there are some compromises in the algorithm design, it can still tolerate an
aggressive drive cycle as the aggressive parts are usually short and not continuous.
Figure 5-5 LA92 drive cycle power required.
Figure 5-6 LA92 torque profile for the mid-sized EV.
Figure 5-6 shows the torque profile for the mid-sized EV running the LA92 drive cycle.
Some parts of the required torque (blue) are more than 0.5 of the motor limit (yellow). This
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means that the car is accelerating with more than the designed acceleration torque ratio τacc
ratio = 0.5, although just for short periods. Figure 5-7 shows the corresponding power profile
and the power split between the battery and UC using the proposed HESS management
strategy, and Figure 5-8 shows the SOC values of the UC and the UC band.
Figure 5-7 LA92 power distribution of battery and UC.
Figure 5-8 LA92 UC SOC (target and actual) and battery SOC.
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As the LA92 is a transient drive cycle, it is difficult to read the plots, so a zoomed-in section
from 820s to 920s with high torque and power demand is presented in the following figures.
Figure 5-9 LA92 torque profile for the mid-sized EV, zoomed 820-920s.
Figure 5-9 shows the zoomed-in torque profile, where the required torque exceeds the
selected acceleration torque ratio τacc ratio = 0.5 at approximately 855s.
Figure 5-10 LA92 power distribution of battery and UC, zoomed 820-920s.
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Figure 5-11 LA92 UC and battery SOC, zoomed 820-920s.
Figure 5-10 shows the corresponding power profile Pdr+aux and the power split between the
battery and UC using the proposed HESS management strategy. As the power demanded is
above the self-imposed battery limits (Pbatt,max), the battery power Pbatt is clipped to its
maximum Pbatt,max, with the excess power being handled by the UC (Puc,ocv for DC/DC
converter low-side power and Puc,H for DC/DC converter high-side power). This is one of the
goals of the PMS – to restrict battery current to its limits.
Figure 5-11 shows the target UC SOC band (defined by SOCuc,regen,tar and SOCuc,acc,tar), the
target UC SOC level SOCuc,tar and the actual UC SOC SOCuc, which stays within the band
most of the time. This is another goal of the PMS – to enforce the EMS by following the
target UC energy level. It also shows the actual battery SOC SOCbatt.
At approximately 855 seconds, the red SOCuc curve deviates from the target SOC SOCuc,tar in
Figure 5-11. This is because the battery limit Pbatt,max is exceeded in Figure 5-10. Since the
algorithm prioritises preventing the battery limits from being exceeded, the UC supplies the
extra power initially, resulting in its SOC dipping below the band. Once power demand is not
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as heavy, the UC SOC is recovered to the target SOC level as seen at approximately 875s
where the UC is charged (power is negative).
From these figures, the two PMS goals were shown to be met, which are to follow the target
UC energy level and to enforce battery limits, with priority placed in the latter. By
successfully following the target UC energy level, the UC would always have sufficient space
for future braking and sufficient energy for future acceleration, meeting the two EMS goals.
In addition, the aggressive LA92 drive cycle has shown the proposed HESS management
strategy can tolerate heavy demands (τacc ratio > 0.5) despite not being designed specifically for
the absolute worst case scenarios as the heavy demands are mostly short. Although not shown
here, heavy regenerative braking behaves similar to the heavy acceleration, just that the UC
SOC would rise above the target UC band to capture more energy instead of below the target
UC band in this heavy acceleration scenario.
It must be noted that in the event the driver attempts to do the absolute worst case
acceleration, that is to floor the vehicle from zero to full speed in a single sustained run, it
does not mean that the EV is unable to meet the power demand. When the UC is emptied
midway through the acceleration, the algorithm takes the power from the battery instead,
worsening its cycle life, but still satisfying the required power demand. This is a reasonable
compromise to reduce the UC size. In a conventional petrol-powered vehicle, it is understood
that flooring the car constantly leads to high fuel consumption and high wear and tear, so it
should be avoided. Similarly, for a battery/UC HESS EV, it would be accepted that
constantly flooring the car would lead to a shorter battery cycle life.
Lastly, another point to note is that future drive profile knowledge was not required. The
proposed HESS management strategy had no information on the next instance of the drive
cycle. It responded based on present data only.
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5.4.2 EUDC
In this section, the simulation is run with the Extra-Urban Driving Cycle (EUDC). This drive
cycle is used to demonstrate the proposed speed-dependent battery limit.
Figure 5-12 EUDC power distribution of battery and UC.
Figure 5-13 EUDC UC and battery SOC.
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Figure 5-12 shows the corresponding EUDC power profile Pdr+aux and the power split
between the battery and UC using the proposed HESS management strategy. Figure 5-13
shows the various SOC values.
Earlier in section 4.1, it was mentioned that the speed-dependent battery power limit achieves
two functions – to utilise the UC even during low power demands to reduce battery use, and
to allow the battery to supply power during steady state.
As the EUDC is a modal cycle with constant speed or acceleration sections, these two goals
can be seen clearly. From 250s to 290s in Figure 5-12, the battery limits are not exceeded as
Pdr+aux < Pbatt,max. However, the UC is still utilised (Puc,H > 0), which satisfies the first goal of
using the UC even during low demands to reduce battery usage.
From 290s to 320s in Figure 5-12, a constant speed of 100km/h is maintained (see Figure 3-6
for speed profile), and it is observed that the battery is supplying all the power at steady state,
satisfying the second goal of the speed-dependent battery limit.
5.4.3 FTP-75 City Drive Cycle
The four goals of the proposed HESS management strategy have already been demonstrated
in the LA92 drive cycle above. The LA92 drive cycle has also shown that the proposed
strategy is able to tolerate aggressive drive cycles despite not being designed for it.
Also, the EUDC has shown the two goals of the proposed speed-dependent battery limits.
Here, the FTP-75 city drive cycle is run for reference only, as the FTP-75 city drive cycle is
used for the cycle life tests in the experiments. Figure 5-14 shows the corresponding power
profile and the power split between the battery and UC using the proposed HESS
management strategy. Figure 5-15 shows the various SOC values.
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Figure 5-14 FTP-75 city power distribution of battery and UC.
Figure 5-15 FTP-75 city UC and battery SOC.
As the FTP-75 city is a transient drive cycle, a zoomed in section between 150s and 250s is
shown in the following two figures, where there is high power demand.
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Figure 5-16 FTP-75 city power distribution of battery and UC, zoomed 150-250s.
Figure 5-17 FTP-75 city UC and battery SOC, zoomed 150-250s.
Similar to the earlier LA92 drive cycle simulation, Figure 5-16 shows the battery power Pbatt
clipped to its maximum Pbatt,max around the 200s mark, with the excess power being handled
by the UC.
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In Figure 5-17, the red SOCuc curve deviates from the target SOC SOCuc,tar near the 200s
mark as the battery limit Pbatt,max is exceeded. Since the algorithm prioritises preventing the
battery limits from being exceeded, the UC supplies the extra power initially, resulting in its
SOC dipping below the target, but remains within the band. A smaller deviation is seen here
as compared to the earlier aggressive LA92 case, as the algorithm was designed with the
worst case scenario of the FTP-75 city drive cycle. Therefore, the deviation remains within
the band.
5.5 Battery Cycle Life
5.5.1 Description
Ultimately, the goal of a battery/UC HESS is to extend battery cycle life. So in this section,
the battery cycle life of the battery/UC HESS system is compared to that of a battery-only
system.
Earlier in section 3.10, the battery cycle life model was presented. In section 3.11.2,
configuring Sanyo UR18650W batteries to a 98S44P formation to approximate a Nissan Leaf
battery in terms of energy and nominal voltage was discussed. This allows the battery cycle
life model and the curve-fitted parameters to be used directly from Wang, et al [7].
From the drive cycle simulations in section 5.4 earlier, the battery currents were shown. The
battery currents are the required input to the battery cycle life model.
5.5.2 Drive Cycle Comparison
First, the best approach to represent a daily driving scenario is decided. In Singapore, a drive
from the suburbs (e.g. Jurong) to the city centre (e.g. Orchard) and back is approximately
50km. This represents a daily driving scenario of a person travelling between home and his
workplace. So 50km is set as the target distance to be driven. Table 5-1 shows the distances
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of the common drive cycles and the number of such repeated cycles to get as close as
possible to the 50km target.
Table 5-1 Comparison of no. of drive cycles to hit 50km.
FTP-75 City FTP-75 HWFET LA92 NEDC
Distance (km) 17.77 16.51 15.80 10.93
Time (min) 31.23 12.75 24.08 19.67
No. of cycles to hit
50km per day
3 3 3 5
Total distance (km) 53.31 49.52 47.40 54.65
5.5.3 Simulation
Next, the drive cycle simulations for each of the drive cycles mentioned in Table 5-1 is run,
and the battery current data is logged. At the end of each day, the battery is charged back to
its starting SOC of 80% at 0.5C and this data is appended to the original battery current data.
For example, a set of battery current data for the FTP-75 city drive cycle consists of three
consecutive FTP-75 city cycles, followed by charging the battery back to 80% SOC in
preparation for the next day’s driving.
This battery current data was divided by 44 as each parallel branch of the 98S44P battery
pack configuration is only subject to 1/44th the total current. Then it was fed into the battery
life model for 10 years of driving. The ambient temperature was set at 50oC to represent a
relatively hot battery compartment with frequent usage under the sun.
Figure 5-18 shows an example of the capacity loss curve for the case of three FTP-75 city
drive cycles per day over 10 years for the proposed battery/UC system.
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Figure 5-18 Battery capacity loss curve for battery/UC system over FTP-75 city.
From the chart, the capacity loss due to cycling is 17.9% and the capacity loss due to calendar
life is 98.5%, resulting in a total capacity loss of 116.5% over 10 years, i.e. the battery is
more than dead. A quick verification was performed to see if the calendar life model was
implemented correctly.
In Wang, et al’s work, the Sanyo UR18650W battery cycled at 46oC (the closest condition to
this work) over 1 year lost 30% of capacity due to calendar losses, and was extrapolated to
lose 40% over 2 years. Re-examining this work’s simulation in Figure 5-18, losing 98.5%
capacity in terms of calendar life over 10 years is a reasonable output of the model.
The reason for such large losses may be because the tested Sanyo UR18650W batteries are
from 2007, which is older technology. Another reason is the selected temperature of 50oC. If
the temperature was reduced to 20oC, the calendar losses would be halved.
Since the battery/UC system and battery-only system are subject to the same 10 years of
aging, the capacity loss due to calendar life would be the same for both cases (neglecting
minor temperature differences). In addition, calendar life loss is not within the algorithm’s
control – it is only dependent on time. Because of these reasons, the calendar loss is excluded
from the results. Only the capacity loss due to cycling is considered, which is controllable by
the proposed HESS algorithm.
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Table 5-2 Simulated cycle life capacity losses over 10 years.
FTP-75
City x3
FTP-75
HWFET x3
LA92
x3
NEDC
x5
Battery/UC Q-loss (%) 17.9 19.7 21.7 21.4
Avg. of absolute C-rate 0.25 0.46 0.36 0.27
Ah Throughput (Ah) 2735 2964 3226 3197
Battery-only Q-loss (%) 25.5 21.4 29.5 25.5
Avg. of absolute C-rate 0.35 0.50 0.45 0.32
Ah Throughput (Ah) 3770 3178 4232 3770
% Reduction in Q-loss 29.5 7.7 26.4 16.3
Table 5-2 shows the results, where the battery cycle life is quantified by the capacity loss
over 10 years. The best reduction of capacity loss occurs for the FTP-75 city drive cycle,
where the battery in the battery/UC system loses only 17.9% of its capacity due to cycling,
while the battery-only system loses 25.5% of its capacity. This is a 29.5% improvement when
using the proposed HESS algorithm.
It is observed the proposed HESS algorithm works best for city drive cycles, where there are
many transients and start-stop driving, such as the FTP-75 city and LA92 drive cycles. The
FTP-75 HWFET is a highway driving cycle. If the car is maintained at high speeds at steady
state, then there is not much utilization of the UC as the battery supplies the steady state
power. Similarly, the NEDC is a modal drive cycle, which is very ideal with smooth
accelerations and much constant speed driving, so there is less utilization of the UC as well.
Therefore, the proposed HESS system works best for city driving.
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Table 5-3 Simulated cycle life for 20% capacity losses.
FTP-75
City x3
FTP-75
HWFET x3
LA92
x3
NEDC
x5
Battery/UC Days 4070 3705 3364 3420
Ah Throughput (Ah) 3048 3008 2971 2995
Battery-only Days 2868 3419 2474 2860
Ah Throughput (Ah) 2961 2976 2867 2953
% Battery Cycle Life Extension 41.9% 8.4% 36.0% 19.6%
Table 5-3 offers another perspective, where the battery cycle life is quantified by the number
of days until 20% capacity loss due to cycling. Again, the longest battery cycle life extension
occurs for the FTP-75 city drive cycle, where the battery in the battery/UC system lasts 4070
days (11.1 years) until 20% capacity loss is experienced, while the battery-only system lasts
2868 days (7.9 years). This is a 41.9% extension of battery cycle life when considering only
cycling losses.
Note that if calendar life losses are also included, the improvements would be reduced
because the battery/UC system lasts longer, therefore experiencing more calendar losses also.
Table 5-4 shows such a scenario, which counts the number of days until 80% total loss (cycle
+ calendar) is experienced. It has been extended to 80% to allow for a longer cycling time for
a better comparison so that calendar life losses are less dominating.
As the calendar life of the Sanyo UR18650W is poor, the best battery cycle life improvement
(FTP-75 city case) is now 8.5% (over 5 years). In future works section 8.2.3, it is suggested
to extract model parameters from more modern batteries, which have better calendar life.
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Table 5-4 Simulated cycle life for 80% capacity losses, including calendar loss.
FTP-75
City x3
FTP-75
HWFET x3
LA92
x3
NEDC
x5
Battery/UC Days 1883 1846 1805 1812
Ah Throughput (Ah) 1410 1498 1594 1586
Battery-only Days 1735 1812 1666 1734
Ah Throughput (Ah) 1791 1577 1931 1790
% Battery Cycle Life Extension 8.5% 1.9% 8.3% 4.5%
5.5.4 Drive Cycle Selection for Experiment 2
To summarise the simulation results, when considering cycling losses only, the FTP-75 city
drive cycle shows the greatest improvement to battery life for the battery/UC system as
compared to the battery-only system. In terms of capacity loss due to cycling over 10 years,
an almost 30% reduction was seen for the battery/UC system. In terms of time to reach 20%
capacity loss due to cycling, a 40% improvement was seen for the battery/UC system.
Therefore, the FTP-75 city drive cycle was selected for the battery cycle life experiments in
Experiment 2 later.
5.6 Summary
To summarise, from the first simulation on EMS comparison, it was demonstrated that if six
UC modules are used, only the proposed EMS achieves the two goals of sufficient energy for
acceleration and sufficient energy for braking. Other existing works cannot always achieve
the two UC goals simultaneously unless their UCs are sized up to twice as large, increasing
weight and costs.
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In the second simulation, the proposed PMS speed-dependent battery limit allows better UC
utilization and allows the battery to be the main energy provider during constant speed
driving. Again, it was shown that other rule-based deterministic PMS are unable to achieve
these two goals simultaneously.
In the third simulation, the mid-sized EV equipped with the proposed HESS management
strategy was driven over various drive cycles.
The four goals of the proposed HESS management strategy were demonstrated in the LA92
drive cycle. The two EMS goals are to ensure sufficient space in the UC for future
regenerative braking and to ensure sufficient energy in the UC for future accelerations. The
two PMS goals are to ensure the target UC energy level (EMS) is followed, and to enforce
battery power limits, with priority on the latter. The LA92 drive cycle has also shown that the
proposed strategy is able to tolerate aggressive drive cycles despite not being designed for it.
Also, knowledge of the future drive profile was not required.
In addition, the EUDC demonstrated the two goals of the proposed speed-dependent battery
limit, which are UC utilization even during low power demands and that the battery should be
the main energy provider during constant speed driving.
Lastly, battery cycle life simulations were performed to observe the fall in battery capacity
for the proposed battery/UC HESS, and for the battery-only system. Almost 30% reduction in
capacity loss due to cycling was seen for the battery/UC HESS as compared to the battery-
only system when running the FTP-75 city drive cycle over 10 years.
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6 HESS EXPERIMENTS
As there was no budget to purchase an actual EV to implement the HESS, a reduced-scale
experiment was built instead. There are three distinct experiments, each with different
objectives. Experiment 0, a preliminary experiment, was used to investigate the efficiency of
the custom-built DC/DC converter. Experiment 1 was used to prove the proposed algorithm
worked as intended by running the algorithm over a drive cycle. Experiment 2 was used to
compare the battery cycle life for the battery/UC HESS configuration to a battery-only
configuration.
In this chapter, first the setup is described, then the scaling is discussed. Subsequently, each
of the three experiments are explained and analysed individually.
6.1 Setup
Figure 6-1 shows a detailed electrical diagram of the setup, while Figure 6-2 to Figure 6-4 are
photos of the setup. To simplify the setup, a programmable load replaced the EV motor and
inverter. This programmable load is a Maccor Series 4000 battery tester. Drive cycles in
terms of power were programmed into the Maccor tester, and it would sink or source power
accordingly. This machine has a maximum output of 1.6kW, versus 80kW of the mid-sized
EV. Therefore, a reduced-scale experiment has to be implemented. Scaling is discussed in a
subsequent section.
In general, the experiment setup was designed for a maximum of 20V and 30A. The Maccor
tester is limited to 20V, while current sensors above 30A are not as common and a substantial
increase in price.
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Figure 6-1 Electrical diagram of experiment setup.
Figure 6-2 Photo of experiment setup (front).
Fan for DC/DC
converter Switches
for relays
Power supply for aux.
equipment, e.g. sensors
Battery
Maccor
Thermistor
vuc
vbatt
to μC
to μC
to μC
to μC
to μC
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Figure 6-3 Photo of experiment setup (top).
Figure 6-4 Photo of experiment setup (side, auxiliary equipment).
UC
Battery
Ferrite
cores
DC/DC
converter Current
sensors
Ferrite
cores
Arduino
Voltage
sensor
filters
Current
sensor
filters
Power supply for aux.
equipment, e.g. sensors
Precision
voltage
reference
Ceramic
capacitors
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6.1.1 Energy Storage Components
The specifications for the reduced-scale battery and UC are listed in Table 6-1. Three
identical batteries were purchased, labelled 1 to 3. Battery 1 was used for preliminary testing
of the setup, and for running Experiment 1. Battery 2 was used for the battery-only
configuration and battery 3 for the battery/UC configuration in the Experiment 2 cycle life
tests.
Table 6-1 Energy storage components.
Component Model Specifications Quantity
Battery SuPower Li-Ion
18650 18V
7.8Ah, 5S3P, Li(NiCoMn)O2
14V (min) - 18.5V (nom) - 21V (max)
With built-in PCB protection
3
Ultracapacitor Tecate PowerBurst
PBD-58/16.2K
16.2V, 58F 1
6.1.2 DC/DC Converter
Initially, it was desired to purchase a controllable bidirectional DC/DC converter off the
shelf, as DC/DC converter development is not the highlight of this work. However, there are
no such DC/DC converters available in the market with the desired specifications at the
moment. Therefore, the bidirectional two-quadrant buck-boost DC/DC converter (Figure 6-5)
was self-made, powered with two MOSFETs and controlled by an Arduino microcontroller.
The microcontroller produces an 8-bit Pulse Width Modulation (PWM) signal, which
controls the two MOSFETs in a complementary manner. A dead time of 852ns was
programmed, where both MOSFETs are in off state to prevent a short between switching.
The 852ns value was calculated from the turn-on and turn-off times from the MOSFET
datasheet. The specifications for the DC/DC converter components are listed in Table 6-2.
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MOSFETs were used here instead of IGBTs in the full-scale simulations as MOSFETs are
better suited to low power applications such as this reduced-scale experiment, and IGBTs for
high power applications like an actual EV.
Figure 6-5 Photo of DC/DC converter.
Inductor
(part)
Electrolytic
Capacitor
(part)
MOSFET
driver
MOSFET &
heat sink
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Table 6-2 DC/DC converter components.
Component Model Quantity Specifications
Microcontroller Arduino MEGA 2560 1 Based on Atmel
ATmega2560
MOSFET Vishay IRFP048PBF N-channel,
enhancement mode
2 60V, 70A
MOSFET
driver
Cree CRD-001 2 -
Inductor Coilcraft AGP4233-333ME 2 in series 33µH, 24A
Capacitors
(Electrolytic)
TDK B41560A9158M000 2 100V, 1500µF
Panasonic 5306C1 1 500V, 330µF
Switching
capacitors
(Ceramic)
Vishay K102K15X7RH5UH5 2 50V, 1000pF
TDK FG28X7R1H334KRT06 2 50V, 0.33µF
TDK FK26X7R1H225K 2 50V, 2.2µF
TDK FK20X7R1H335K 2 50V, 3.3µF
Murata
RDEC71H106K3K1H03B
2 50V, 10µF
(Unknown models) 11 3.3pF, 10pF, 33pF, 68pF,
100pF, 220pF, 680pF,
3300pF, 6800pF, 0.01µF,
0.022µF, 0.047µF, 0.1µF,
0.22µF, 0.47µF, 1µF
Ferrite cores Fair-Rite 2675821502 4 200kHz – 30MHz, 75
material
Fair-Rite 2675102002 6 200kHz – 30MHz, 75
material
Fair-Rite 2631101902 6 1MHz – 300MHz, 31
material
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6.1.3 Sensors
There are two voltage sensors, one each for measuring the battery and UC voltages (vbatt and
vuc respectively). They are custom-built 1.8kΩ//6.8kΩ resistor voltage dividers, with output
over the 1.8kΩ resistor. The signal is fed into a 3-pole active Sallen-Key topology low-pass
filter, built from an operational amplifier (op-amp). The cutoff frequency is set at 40Hz. Then
this signal is sent to the Arduino microcontroller, and to a personal computer (PC) over
Universal Serial Bus (USB) where it is logged at 10Hz. Originally, the op-amp was only to be
used as a voltage follower due to the high output impedance of the voltage divider
(recommended maximum input impedance of Arduino ADC is 10kΩ), so it was
underutilised. Later, it was reconfigured as a Sallen-Key topology low-pass filter to fully
utilise the op-amp.
There are three Hall-effect current sensors, for measuring the current consumed by the drive
cycle idr (labelled ACS1 in Figure 6-1), UC current on the low-side of the DC/DC converter
iuc (ACS2), and battery current ibatt (ACS3). The sensor for the high-side UC current iuc,H
(ACS4) is disused, but it can easily be computed by,
𝑖𝑢𝑐,𝐻 = 𝑖𝑑𝑟 − 𝑖𝑏𝑎𝑡𝑡 (6-1)
The signals from the current sensors are fed into a single pole passive RC low-pass filter with
a 40Hz cutoff frequency. As the hall-effect sensor already contains a built-in op-amp to
amplify the signal, no voltage follower was necessary. Therefore, no Sallen-Key topology
was implemented here. Then this signal was fed into the Arduino just like the voltage sensor.
These sensors and filters are powered by two 230V AC to 9V DC isolation transformer
adapters, and then further regulated to the required voltages by LM78xx series linear
regulators. The components used for the sensors are listed in Table 6-3. These components
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were soldered onto stripboards seen in Figure 6-4. The sensor electrical connection diagrams
are found in Appendix C.
Table 6-3 Sensors and supporting components.
Component Model Quantity Specifications
Current sensor Allegro ACS712ELCTR-30A-T 3 Hall-effect, ±30A
Voltage sensor Custom-built voltage divider 2 1:4.78 step down.
Max input of 23.9V
Temperature sensor Vishay NTCLE400E3103H 1 NTC Thermistor
DC/DC converter for
op-amp
TI DCP020515DP 2 5V input, unregulated
±15V output,
isolated, 2W
Op-amp Intersil CA3140E 2 -
Capacitors for op-amp AVX TAP105K035SCS 8 Tantalum, 35V, 1 µF
Precision micropower
shunt voltage
reference
TI LM4040A50I 1 5V
6.1.3.1 Sensor Noise Problems
As it was a self-made DC/DC converter, initially there was a lot of switching noise generated
and observed in the sensor readings. In the voltage and current measurements, ringing would
appear at the DC/DC converter switching frequency of 31.3kHz, with the ringing frequency
peaking at about 60MHz.
This was solved with three methods. First, star grounding was implemented to avoid ground
loops. Following the suggestions of [72], the ground circuits of analogue and digital signals
were separated and each star grounded. Also, the ground of the power supplies to the sensors
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and filters were floated by using isolation transformer adapters to avoid having too many
connections to ground.
Second, numerous ceramic capacitors were added in parallel to the circuit to avoid
differential mode (DM) noise, following the suggestions of [73] and [74]. DM noise occurs
between the converter’s output and the return line. Ideally, ceramic capacitors with an
impedance null (self resonance) that is the same as the ringing frequency should be added.
The impedance null is explained as follows. The impedance of an ideal capacitor ZC
decreases as frequency ω increases, as indicated by ZC = (jωC)-1. However, a real and non-
ideal capacitor also has some internal resistance and some inductance, given by Z = (jωC)-1 +
R + (jωL). The impedance null occurs at frequency ωn given when the impedance Z is
minimum. Below ωn, the capacitance term dominates, while above ωn, the inductance term
dominates.
However, this impedance null frequency ωn is usually not specified in the manufacturer’s
data. It requires performing experiments, where the capacitor is swept over a frequency range
while the impedance is recorded. Due to the lack of relevant equipment, 21 ceramic
capacitors with capacitances from 3.3pF to 10µF (approximately 2 for each order, listed in
Table 6-2) were installed instead for a quick fix, with one set of 21 for the DC/DC converter
high-side and another set of 21 for the low-side. This is an overkill solution. If a minimum
component or cost design is required in future, some optimisation can be performed here.
The third solution to overcome switching noise was to install chokes, in the form of ferrite
cores, to overcome common mode (CM) noise. CM noise occurs in both output and return
lines. Following the suggestions of [73], ferrite cores were installed. Two types of ferrite
cores were used – 75 material for rejecting noise in the 200kHz to 30MHz range, and 31
material for rejecting noise in the 1MHz to 300MHz range (listed in Table 6-2). The output
and return lines were wound round the ferrite cores with a 1:1 turns ratio on both the high and
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low-sides of the DC/DC converter. Further ferrite cores were installed on the voltage sensor
signal output lines, in case the cores on the output and return lines were unable to reject the
noise. Again, this is an overkill solution, and optimisation can be performed to minimise
components and costs in the future.
6.1.3.2 Sensor Calibration
Firstly, before any experiment was performed, the current and voltage sensors were calibrated
to two multimeters. Two multimeters of different models (Fluke 115 & Fluke 19) were used
as they produced slightly different results, so the sensors were calibrated to the average of the
two multimeters.
For voltage sensor calibration, a Thurlby Thandar Instruments (TTI) EX354T bench DC
power supply was connected to a small resistive load (to stabilise the voltage), and the two
voltage sensors and two multimeters were connected in parallel to the load to measure the
voltage drop across the load. Figure 6-6 shows the multimeter voltage versus the 10-bit data
logged on the Arduino. Using Microsoft Excel, a least squares best fit line was created. The
best fit line equations (V1 & V2, shown in the figure) were implemented in Arduino.
Figure 6-6 Voltage sensor calibration.
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For current sensor calibration, the TTI EX354T power supply was connected to the high-side
of the custom-built DC/DC converter. The three hall-effect current sensors and the two
multimeters were connected in series with a small resistive load at the low-side of the DC/DC
converter. The purpose of using the DC/DC converter was to step-up the current output to
15A as the EX354T power supply could only give a maximum of 4A output. Ideally, it
should be calibrated to 30A, but the multimeters could only measure up to 10A, with
overload up to ~15A for a few seconds. Figure 6-7 shows the results. Again, a best fit line
was created for the three sensors and the equations (shown in the figure) were loaded into
Arduino.
Figure 6-7 Current sensor calibration.
6.1.4 Safety Components
In addition, there are various safety components in the setup. There are two relays, one for
the entire setup and one for the UC. To turn on these relays, a physical switch must be turned
on, and the Arduino must give a turn-on command.
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Fast acting 20A fuses were also installed in multiple locations. Although the components can
withstand 30A, a 20A fuse was used instead as the 20A fuse does not blow immediately at
20A. According to the manufacturer’s datasheet [75], 20A passing through 20A fuses would
take more than 100s to blow. The time to blow decreases exponentially with increasing
current.
These fuses were installed after programming errors for the Arduino caused a short in the
DC/DC converter, destroying the MOSFETs and current sensors during an early testing stage.
A 12V fan was also installed above the DC/DC converter MOSFETs, sucking air away from
the MOSFETs to ensure it remained cool.
Table 6-4 Safety & miscellaneous components.
Component Model Quantity Specifications
Safety relay TE Connectivity T9AS1D22-5 2 240VAC, 30A
Safety fuse Cooper Bussmann AGC-20-R 3 20A, 32V, fast acting
Fuse holder Cooper Bussmann HKP 3 30A
Optoisolators
for relay
Vishay 4N35 2 -
Transistors for
relay
2N222A 2 -
Main wiring Pro-power 12AWG multiple 600V, 41A
Linear
Regulators
Fairchild LM7805ACT, Fairchild
LM7810ACT, ST LM7812
multiple -
LEDs for visual
reference
HP HLMP1700, HLMP1719,
HLMP1790
5 -
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In addition, a thermistor was installed to monitor the temperature of the battery. If the battery
temperature exceeded 50oC, the Arduino would stop the experiment by switching off the
relays. These components are listed in Table 6-4 and earlier Table 6-3 (for the thermistor).
Furthermore, the UC voltage was monitored closely. If it exceeded 16V (98.8% SOC), the
Arduino would trigger the relays to disconnect the UC to prevent overcharging. 100% UC
SOC (16.2V) was not used to give a small buffer in case of any programming or sensor
errors.
6.2 Scaling
In this section, scaling is discussed. First, a reduced-scale mechanical model should be
created. A concept known as similitude was applied, common in fluid dynamic reduced-scale
models. The reduced-scale model is said to have similitude with the full-scale setup if both
share geometric similarity, kinematic similarity and dynamic similarity. Geometric similarity
occurs when the model is the same shape as the full-scale setup, only scaled. Kinematic
similarity occurs when fluid flow of both the reduced-scale model and full-scale setup
undergo similar motions. Dynamic similarity occurs when ratios of all forces acting on
corresponding fluid particles and boundary surfaces in both systems are constant.
Dimensional analysis was performed and the following scaling law was derived,
𝐿𝑚𝐿𝑎
=𝑣𝑎𝑣𝑚
=𝜏𝑚𝜏𝑎= √
𝜔𝑎𝜔𝑚
=𝑃𝑎𝑃𝑚
=𝑚𝑚
𝑚𝑎= 𝑘
(6-2)
and the meaning of each symbol is shown in Table 6-5. The full dimensional analysis
workings can be found in Appendix B.
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Table 6-5 Symbols and their meanings for scaling derivation.
Symbol Meaning Symbol Meaning
k Scaling ratio. >1 for reduced-
scale
P Power
τ Torque m Mass
v Velocity Xa a subscript for full-size ‘actual’
L Length Xm m subscript for reduced-scale
‘model’
ω Angular velocity
A Maccor Series 4000 battery tester was used to simulate drive cycles. This machine has a
maximum output of 1.6kW, versus the 80kW motor of the mid-size EV.
To scale down the power while achieving similitude, k should be larger than 1 in equation
(6-2) (k = Pa/Pm > 1). This means the reduced-scale model has lower power, velocity and
angular velocity, but has larger dimensions, mass and torque generated. The force remains
constant (the same) for both cases.
6.3 Scale Factor k
In this section, the scale factor k is chosen.
6.3.1 Selecting k Based on Drive Cycle
First, the drive cycles are examined to select an appropriate scale factor. As the FTP-75 city
drive cycle showed the greatest improvement for the battery/UC system in the cycle life
simulations in section 5.5, the FTP-75 city drive was selected for the cycle life tests in
Experiment 2. The FTP-75 city drive cycle peaks at 42kW as shown in earlier Figure 5-14.
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However, the most aggressive official drive cycle is the LA92 drive cycle, which peaks at
60kW as shown earlier in Figure 5-5. The more aggressive LA92 is used here for scaling in
case it needs to be run for some reason in future. Since the circuit components can only
handle 30A, while the Maccor can only manage 20V, the maximum power which the
experiment can face is (30A)(20V) = 600W. This leads to k > Pa/Pm = 60000/600 = 100, i.e. k
cannot be smaller than 100, otherwise the components cannot handle the required power.
6.3.2 Selecting k Based on Simulation/Experiment Energy Ratio
Due to a limited budget, the UC was donated from a previous project in the university. The
battery was bought quite early while budget was still available, before the algorithm was
finalised. Therefore, the energy ratio of the actual battery and UC are different from what was
used in the HESS management strategy in the full-scale simulations.
Table 6-6 shows the energy specifications of the battery and UC used in the simulation and
the actual battery and UC for the experiments. The battery energy/UC energy ratio for the
simulation is 151, while that for the experiment is 68. So for the experiment setup, it can be
said either the battery is undersized, or the UC is oversized. For the former case, where the
battery is undersized in terms of energy and the UC is correctly sized, it means the battery
would be become flat faster, and given a specified fixed current, the C-rate would be higher
and the battery would be stressed more. This case would result in the scale factor k = 75 as
seen by the full-scale simulation vs. reduced-scale experiment UC energy ratio in Table 6-6.
While in the latter case, the battery is correctly sized, while the UC is oversized. This means
it is not necessary to use the entire UC SOC range. This case would result in the scale factor k
= 166.
Therefore, k should be picked in the range 75 < k < 166. However, k > 100 as limited by the
components. The appropriate values of k become 100 < k < 166.
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Table 6-6 Battery and UC energy specifications.
Full-scale simulation
specifications
Reduced-scale experiment
specifications
Battery
Capacity (Ah) 66 7.8
Nominal voltage (V) 362.6 18.5
Energy (kJ) (66)(362.6)(3600/1000) =
86153
(7.8)(18.5)(3600/1000) = 519
UC
Max voltage (V) 288 16.2
Capacitance (F) 13.8 58
Energy (kJ) (0.5)(13.8)(288)2 = 572 (0.5)(58)(16.2)2 = 7.61
Overall
Battery energy/UC energy
ratio
86153/572 = 151 519/7.61 = 68
Full-scale/reduced-scale
battery energy ratio
86153/519 = 166
Full-scale/reduced-scale UC
energy ratio
572/7.61 = 75
6.3.3 Selecting k Based on Battery Limitations
As an accelerated capacity drop for the cycle life tests is preferred, it is ideal to push the
battery harder, i.e. closer to the undersized battery k = 100 case. So the battery was cycled
with k = 100 (1/100th original mid-sized EV power) with three consecutive FTP-75 city drive
cycle. The battery was charged to 20.2V.
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However, it is unable to complete the drive cycles. This is because at demanding sections of
the drive cycles when the power drawn is too large, it causes the battery voltage to dip below
14V, leading to the built-in battery management system (BMS) to trip and disconnect the
battery (discussed further in section 6.7.7 Battery-only Undervoltage During Demanding
Sections). This is not surprising as the battery is undersized. Therefore, the scale was
increased further, until the drive cycles could successfully complete. This is summarised in
Table 6-7.
Table 6-7 Value of k which allows 3x FTP-75 city drive cycle to complete.
Scale factor k 100 130 140 150 160
Battery only x x x x √
Battery/UC x x x √ √
Both setups are able to complete the three FTP-75 drive cycles only when k = 160.
Interestingly, the battery/UC configuration can handle k = 150 while the battery-only
configuration cannot. This shows the UC is able to provide sufficient current during high
demands to prevent the battery voltage from dipping significantly.
From the table, k = 160 was selected, where both configurations are able to complete the
drive cycles. Since k = 160, this is closer to the case of UC being oversized. This means, only
part of the UC energy will be used.
6.3.4 Consequences of k = 160
From Table 6-8, after scaling the UC by k = 160, the experiment UC should only contain
3.58kJ. Therefore, the 7.61kJ experiment UC is oversized. Since in the full-scale simulation,
only 75% of the UC energy can be used, this results in only 2.68kJ of the 3.58kJ in the
experiment UC being used. This 2.68kJ corresponds to using only 35.2% energy or 19.5%
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charge. Therefore, to compensate for the oversized UC, the UC is restricted to using only a
19.5% Depth of Discharge (DoD) instead of 50%.
Table 6-8 UC scaling specifications.
Full-scale simulation
specifications
Reduced-scale experiment
specifications
UC energy (kJ) 572 7.61
Scaled UC energy (kJ) - 572/160 = 3.58
Usable Depth of Energy (DoE) 0.75 2.68/7.61 = 0.352
Usable energy (kJ) (0.75)(572) = 429 (0.75)(3.58) = 2.68
Usable Depth of Discharge
(DoD)
0.5 1-√(1-0.352) = 0.195
(computed with (6-3) & (6-4))
𝑈𝐶𝑆𝑜𝐸 =
𝐸
𝐸𝑚𝑎𝑥=
0.5 𝐶 𝑉2
0.5 𝐶 𝑉𝑚𝑎𝑥2 = (
𝑉
𝑉𝑚𝑎𝑥 )2
= 𝑈𝐶𝑆𝑜𝐶2
(6-3)
𝑈𝐶𝐷𝑜𝐷 = 1 − 𝑈𝐶𝑆𝑜𝐶 = 1 − √𝑈𝐶𝑆𝑜𝐸 = 1 − √1 − 𝑈𝐶𝐷𝑜𝐸 (6-4)
Next, the battery parameter scaling is examined. The battery is still slightly undersized (k =
160 instead of 166), therefore, the reduced-scale experiment battery will experience slightly
higher C-rates than the full-scale simulation battery. Table 6-9 summarises the scaling results.
From earlier section 4.1.2, the maximum power the car will consume at constant speed is
40.6kW. Scaling it would mean the reduced-scale experiment battery discharge power should
be limited to 0.254kW, which is 1.76C, slightly larger than 1.7C in the full-scale simulation.
Similarly, the charge power in the reduced-scale experiment is scaled to be 0.188kW, or
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1.30C, which is slightly larger than the original 1.25C. This is normal as the battery is slightly
undersized (k = 160 instead of 166).
Table 6-9 Battery scaling specifications.
Full-scale simulation
specifications
Reduced-scale experiment
specifications
Battery energy (kWh) (66)(362.6)/1000 = 23.9 (7.8)(18.5)/1000 = 0.144
Power at max speed (kW)
(self-limited)
40.6 40.6/160 = 0.254
Max discharge rate (C)
(self-limited)
40.6/23.9 = 1.7 0.254/0.144 = 1.76
Max regen power (kW) 30 30/160 = 0.188
Max charge rate (C) 30/23.9 = 1.25 0.188/0.144 = 1.30
6.4 Experiment 0
6.4.1 Objective
As mentioned in the previous section, experiments 1 and 2 are run at 1:160 scale. However,
the DC/DC converter power losses and inefficiencies are not able to scale perfectly.
Therefore, a preliminary experiment, Experiment 0, is run to investigate the efficiency of the
custom-built DC/DC converter. This is important as it allows the differences to be
compensated during scaling for more accurate results.
6.4.2 Procedure
Similar to section 3.9 DC/DC Converter Model, a plot of efficiency vs. high-side power vs.
low-side voltage is required. The buck and boost case are performed separately.
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For the buck case, the high-side of the DC/DC converter was connected to the Maccor, while
the low-side was connected to a bank of resistors as shown in Figure 6-8.
Figure 6-8 Experiment 0 setup.
Three values are varied in this experiment – the resistor bank value, the Maccor output
current, and the DC/DC converter duty cycle. Table 6-10 shows one data point as an
example.
Table 6-10 DC/DC converter efficiency test for one data point.
Variables Measured Computed
Resistance Duty
Cycle
Current Voltage Power Efficiency
ɳ IH
(Maccor)
IL VH VL PH
(input)
PL
(output)
0.5Ω 40% 1.69A 4.28A 5.98V 2.05V 10.11W 8.77W 86.8%
For that data point, a resistor bank value of 0.5Ω was selected. The Maccor was commanded
to output 1.69A to the DC/DC converter high-side, and then a DC/DC converter duty cycle of
40% was selected.
The voltages and currents on both the high and low-side were measured, and the powers
calculated. The input power (high-side) was 10.11W and the output power (low-side) was
8.77W, resulting in an efficiency of 86.8%.
The three variables were varied to get more data points.
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For the boost case, the same procedure was performed, except that the DC/DC converter was
connected in reverse, where the low-side of the DC/DC converter was connected to the
Maccor, and the high-side connected to a bank of resistors. In this case, IL corresponds to the
Maccor current, while IH, VL and VH are the measured values. Again, Maccor current IL, the
duty cycle, and the resistor bank values were varied to get data points.
6.4.3 Results
6.4.3.1 Missing Data Discussion
Figure 6-9 DC/DC converter boost efficiency.
Figure 6-9 shows the DC/DC converter efficiency for the boost case. Each blue circle
represents a data point, and the data points were interpolated. The efficiency values are
difficult to read right now; this will be addressed in a later figure. First, some concerns are
addressed. From the figure, the surface is triangular, and not square, this means that not all
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possible combinations of IH and VL were covered. This is because of limitations of the
experimental setup.
At large IH values, there is limited data. This is because large IH requires an even larger IL due
to the boost mode of operation. However, the setup is only designed for 30A, so it is not
possible to get data for large IH values.
At large VL values, there is also limited data. A large VL requires an even larger VH due to the
boost mode of operation. However, the setup is designed for 35V maximum. Also, the
Maccor can only operate at a maximum of VL = 20V.
At low VL values, there is also limited data. This is because the resistor bank needs to have a
smaller overall resistance (i.e. more resistors in parallel), based on the DC/DC converter
formulas, VL = DVH = DRIH, where R is the resistance and D is the duty cycle. However, all
the resistors of the required sizes in the laboratory were already in use (by the author). Also,
as the resistance decreases, the current increases (high IH values). The resistors do not have
sufficient power dissipation rating.
Figure 6-10 DC/DC converter buck efficiency.
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Similarly, Figure 6-10 shows the DC/DC converter buck efficiency. Again, there are some
missing data sections.
A large VL requires an even larger VH due to the buck mode of operation. However, the
Maccor is only able to operate at a maximum of VH = 20V. A low VL value, requires the
resistor bank to have a smaller overall resistance, based on the DC/DC converter formula VL
= RIL (A low VL value also corresponds to a large IL value due to the buck mode of
operation).
However, these missing sections are not a concern because these are outside the operating
range.
6.4.3.2 Flattened Results
Figure 6-11 shows a flattened 2D view of the combined boost and buck efficiency
experimental results, which is easier to read. The y-axis has been converted to power from
current by multiplying the high-side voltage.
Figure 6-11 Interpolated DC/DC converter efficiency from experiment.
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Reasonably good performance is observed for the self-made DC/DC converter, with at least
85% efficiency for most parts, dropping to 75% for low VL UC voltages (below 8V on the
left). This is not a concern because the UC will be operated above 12.2V due to the UC being
oversized as discussed in the earlier scaling section 6.3.4 and later section 6.5.1.
6.4.3.3 Matching Simulation to Experimental Values
Next, a model for the custom-built DC/DC converter was created, using the DC/DC converter
model discussed in section 3.9, parameters from the data sheets, and some tuning based on
the experimental data.
Table 6-11 shows the parameters used for the full-scale simulation, and the custom-built
DC/DC converter parameters, extracted from the data sheets of the MOSFET and inductor.
Table 6-11 Reduced-scale simulation parameters.
Parameter Full-scale
simulation
From data
sheets
Experimental Tuned
Vigbt (V) 0.857 0 N.A.
Rigbt (Ω) 0.00285 0.018
Vd (V) 0.88 0
Rd (Ω) 0.00184 0.018
RL (mΩ) 37 2.95
Turn on time (ns) 800 250 45 35
Turn off time (ns) 1000 250 45 35
As the data given in the Vishay IRFP048 MOSFET data sheet was for specific test conditions
which were not encountered during the experiment, some tuning was necessary for the
simulation model to match the experiment data.
The biggest difference to the test conditions in the experiment setup was the turn-on and turn-
off times, which was tested with 72A MOSFET drain current in the data sheet (the setup only
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reached 30A). So a further experiment was performed to observe the turn on and turn off
times.
A Tektronix TDS2012 oscilloscope was hooked to the DC/DC converter output before the
electrolytic capacitors, so the waveform seen on the oscilloscope was a square wave. The rise
and fall section of the square wave was zoomed in, and the rise and fall was observed to take
approximately 45ns each. Because of the ringing in the square wave, it was difficult to
determine the start and end of the rise or fall. So this parameter was further tuned to match
the experimental values as close as possible.
Figure 6-12 shows the efficiency of the reduced-scale DC/DC converter as produced from the
simulation model and tuned. Next, the simulation output was subtracted from the
experimental output (i.e. Figure 6-11 minus Figure 6-12) to see how well it was tuned,
resulting in Figure 6-13.
Eventually, the turn on and turn off time was tuned to 35ns to minimize the difference in
efficiency between the experiment and simulation. From Figure 6-13, there is less than 4%
difference in most parts. The difference hits 8% at low UC voltages (below 10V on the left).
Again, this is not a great concern as the UC will operate above 12.2V.
As a comparison, the full-scale DC/DC converter efficiency map was seen earlier in Figure
3-24. As the components used are different, it is expected the efficiency map would be
different.
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Figure 6-12 DC/DC converter efficiency from simulation.
Figure 6-13 DC/DC converter efficiency, experimental minus simulation output.
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6.4.4 Summary
In summary, the efficiency of the custom-built DC/DC converter has been investigated in
experiment 0. In general, it performs with an efficiency above 80%, which is reasonably good
for a self-made DC/DC converter. Then, a reduced-scale DC/DC converter model was
created to match the experimental values. This model is used later in the reduced-scale
simulations.
6.5 Software Implementation
As mentioned earlier, the microcontroller controls the duty cycle of the DC/DC converter.
This allows it to control the current flow or the voltage output. The Arduino microcontroller
is loaded with a reduced-scale algorithm, which is discussed in this section.
6.5.1 Algorithm Curve Fitting
To avoid the Arduino performing complex calculations on the fly to determine the battery
limits for the PMS and target UC bands for the EMS, polynomial curve-fitted equations have
been implemented instead. This reduces the processing power required. In this section, the
curve-fitting is explained.
In the Matlab simulation, k = 160 was implemented to create a reduced-scale simulation. The
DC/DC converter has been scaled separately as discussed in the previous section and is
incorporated into this simulation too.
For simplicity, the combined motor/inverter efficiency map profile is assumed to be scaled
perfectly as shown in Figure 6-14, stretched from the full-scale Figure 3-8.
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Figure 6-14 Reduced-scale combined motor/inverter efficiency.
Figure 6-15 Battery power to maintain EV at constant speed for k=160.
The reduced-scale simulation is run to get the battery power required to maintain the EV at a
constant speed, resulting in the curve as shown in Figure 6-15 (full-scale version earlier in
Figure 4-1). The data points are represented by the blue diamonds (very close together).
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Curve fitting was performed using Microsoft Excel’s least squares, shown by the thin black
line. The lowest order polynomial was chosen that fits the curve well, which is
𝑃𝑏𝑎𝑡𝑡 𝑎𝑡 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑠𝑝𝑒𝑒𝑑 = 368.928𝑣2 − 72.106𝑣 + 8.382 (6-5)
As explained earlier in the PMS description, this battery power at constant speed is used to
determine the self-imposed battery power limits. Then the battery discharge power was
loosened by a factor of 3, and clipped to the maximum of 1.76C (254W). Similarly, the
battery charge power was clipped to -1.30C (-188W) according to earlier Table 6-9 Battery
scaling specifications. (Note that as given by equation (6-2), speed has also been reduced by a
factor of k = 160.)
Next, the target UC SOC bands for k = 160 are calculated and are shown in Figure 6-16
(Figure 4-10 for full-scale version). The band limits are defined by the red squares for the
upper limit and blue diamonds for the lower limit. Here, it is expressed in terms of UC
voltage instead of SOC or energy level as the sensor reads the UC voltage directly.
Figure 6-16 Target UC SOC band for k=160.
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Again, a curve fitting was performed with Microsoft Excel, shown by the thin black lines.
The best fit regenerative braking curve and best fit acceleration curve are given by (6-6) and
(6-7) respectively. Then, the maximum at each point of the two curves is taken as the target
UC voltage level, similar to what was discussed in the EMS section 4.2.4 earlier.
𝑣𝑢𝑐,𝑡𝑎𝑟,𝑟𝑒𝑔𝑒𝑛 = 10.391𝑣3 − 15.015𝑣2 + 1.0395𝑣 + 15.999 (6-6)
𝑣𝑢𝑐,𝑡𝑎𝑟,𝑎𝑐𝑐 = −195.15𝑣5 + 351.36𝑣4 − 194.14𝑣3 + 27.277𝑣2 + 1.8655𝑣
+ 15.881
(6-7)
In Figure 6-16, the minimum UC voltage value observed is 12.6V, corresponding to a DoD of
22.0%. However, it is mentioned earlier in the UC scaling of section 6.3.4 that the UC is
oversized and that only 19.5% DoD of the UC will be used. The reason for this difference is
that the DC/DC converter efficiencies of the full-scale and reduced-scale had not been
considered earlier when computing the 19.5% value. After inputting the interpolated DC/DC
converter efficiency from Experiment 0 into the simulation, the actual UC DoD should be
22.0%.
Therefore, to compensate for the differences in DC/DC converter efficiency scaling, more
UC energy is used, which is not a problem as the UC is oversized anyway.
In short, instead of the Arduino performing complex calculations on the fly to determine the
battery limits and target UC bands, the three simple polynomial equations (6-5) to (6-7) were
implemented in the Arudino. The three polynomial equations only require vehicle speed as
the input.
144
6.5.2 Syncing Speed with Power
However, as there are no wheels in the reduced-scale experiment, there is no ‘speed’ value. In
real-life, the speed can be tapped from the speedometer. Therefore, for the experiments, the
FTP-75 city drive cycle’s reduced-scale speed vs. time data was loaded into the Arduino.
The proposed HESS management strategy requires the power drawn by the motor (in this
case, the Maccor) and the vehicle speed to function. The Maccor is loaded with a power vs.
time data, so it will automatically draw the specified power at the specified timing. Therefore,
the speed vs. time data loaded into the Arudino must be synced with the Maccor. For
simplicity, a manual sync at the start was used, where both Arduino and the Maccor are
turned on together.
6.5.3 Problems with Maccor
However, a problem was observed. When running highly transient drive cycles like the FTP-
75 city, the Maccor is unable to keep up and therefore runs slower. Three consecutive FTP-75
drive cycles were run on the Maccor. Instead of taking (1875s)(3) = 5625s, the Maccor was
timed to take 6156s, which is 9.44% slower. Therefore, the speed vs. time profile in the
Arduino was also slowed down by 9.5% to match the Maccor. The Arudino is only able to
handle milliseconds in integers, so 1000ms was not translated to 1094.4ms, but 1095ms
instead to avoid interpolation of the drive cycle. (1094ms was tested at first, but resulted in
the Arduino ending earlier than the Maccor (as expected), which was bad as the setup was
programmed to be turned off for safety reasons at the end, which was before the Maccor
drive cycles had actually ended).
The consequence of this is that the drive cycle is not perfectly scaled down. But since this
slowed drive cycle is applied to both battery-only and battery/UC setups, it is still a fair
comparison between the two.
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Interestingly, when running modal drive cycles such as the EUDC or ECE drive cycles, the
Maccor had no slowdowns. This showed the Maccor is unable to keep up only for highly
transient drive cycles.
Also, the current sensor and voltage sensor of the Maccor machine are out of calibration. It
costs an excessive amount to fix as a technician is required to be flown from the United
States, and his flight and accommodation have to be paid for, in addition to the calibration
services. Therefore, in the experiment, sensors separate from the Maccor have been used for
data logging as discussed in 6.1.3.
Intriguingly, the Maccor underreports voltages, while it overreports current. Since the Maccor
is programmed in power vs. time, the underreported voltage and overreported current cancel
each other out, resulting in the power calibration being reasonably accurate. This is shown in
more detail in the next section, 6.6 Experiment 1.
For safety reasons, the Arduino was also programmed to turn off the relays and stop the
experiment if the battery temperature exceeded 50oC, or if the UC was charged beyond 16.2V
(100% SOC), or when three consecutive FTP-75 city drive cycles were over.
6.5.4 Battery Power vs. Current Thresholds
To recall, the goal of the PMS is to ensure the UC voltage follows the target UC voltage and
to prevent the battery power thresholds from being exceeded. However, there were problems
implementing battery power thresholds. During demanding sections, due to high contact
resistance in the circuit, a substantial voltage drop was encountered between the Maccor and
battery (This problem is discussed in detail later in sections 6.7.7 and 6.7.8). Due to the
voltage drop, the Maccor attempts to pull more current to compensate, causing the battery
voltage to drop even further.
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If a battery power threshold is used, the Arduino is slow to respond because when the current
increases, the battery voltage also drops, so the battery power threshold may not be exceeded.
However, since the current is increased, the battery is experiencing a higher than expected C-
rate discharge, which is not good for the cycle life.
Therefore, for experiment implementation, a battery current threshold was used instead to
avoid the transient voltage dips from affecting the C-rate too heavily. The battery current
threshold is calculated by dividing the battery power threshold by a fixed voltage, 18.5V, the
nominal voltage of the battery.
Ideally, if the contact resistance is minimized in the experiment setup, there would not be a
significant difference whether battery current or battery power threshold was used, as the
battery voltage would not change much in the short-term. Even in the literature, this is not
standardised. For example works of [32] [45] [48] attempt to limit battery power, while
works of [25] [40] [47] attempt to limit battery current.
6.5.5 Integral Controller for UC Voltage Control
As mentioned earlier in section 3.3 Simulation Approach, a backward facing approach was
used for the simulations. In the backward facing approach, transients are not considered. So
in the simulations earlier, the algorithm is able to calculate the exact amount of power which
the UC should generate/absorb to relieve the battery at every instant. In order to do this, the
algorithm was programmed with the DC/DC converter efficiency map to compensate for the
actual UC power required.
However, physically, transients are unavoidable. Also, from Experiment 0, although the
DC/DC converter efficiency model was empirically fit based on data from the actual
efficiency, there are still some inaccuracies.
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Therefore in the physical setup, an integral controller was implemented, mathematically
expressed with the following equations. This controller ensures the battery current threshold
is not exceeded, even with transients, and without knowledge of the DC/DC converter
efficiency map.
𝐼𝑏𝑎𝑡𝑡,𝑜𝑣𝑒𝑟(𝑡)
=
𝐼𝑏𝑎𝑡𝑡,𝑚𝑎𝑥(𝑡) − 𝐼𝑏𝑎𝑡𝑡(𝑡) 𝑖𝑓 𝐼𝑏𝑎𝑡𝑡(𝑡) ≥ 0 𝑎𝑛𝑑 𝐼𝑏𝑎𝑡𝑡(𝑡) > 𝐼𝑏𝑎𝑡𝑡,𝑚𝑎𝑥(𝑡)
𝐼𝑏𝑎𝑡𝑡,𝑚𝑖𝑛(𝑡) − 𝐼𝑏𝑎𝑡𝑡(𝑡) 𝑖𝑓 𝐼𝑏𝑎𝑡𝑡(𝑡) < 0 𝑎𝑛𝑑 𝐼𝑏𝑎𝑡𝑡(𝑡) < 𝐼𝑏𝑎𝑡𝑡,𝑚𝑖𝑛(𝑡)
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
(6-8)
𝑣𝑢𝑐,𝑡𝑎𝑟,𝑎𝑑𝑑(𝑡) =
𝐾𝑣 ∗ 𝐼𝑏𝑎𝑡𝑡,𝑜𝑣𝑒𝑟(𝑡) + 𝑣𝑢𝑐,𝑡𝑎𝑟,𝑎𝑑𝑑 (𝑡 − 1) 𝑖𝑓 𝐼𝑏𝑎𝑡𝑡,𝑜𝑣𝑒𝑟(𝑡) ≠ 0
(1 − 𝛾) 𝑣𝑢𝑐,𝑡𝑎𝑟,𝑎𝑑𝑑 (𝑡 − 1) 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
(6-9)
𝑣𝑢𝑐,𝑡𝑎𝑟,𝑎𝑑𝑗(𝑡) = 𝑣𝑢𝑐,𝑡𝑎𝑟(𝑡) + 𝑣𝑢𝑐,𝑡𝑎𝑟,𝑎𝑑𝑑(𝑡) (6-10)
The purpose of these equations are as follows. If the battery current (on current sensor ACS3)
exceeds its positive threshold (i.e. discharging more than the threshold), the UC should assist
by discharging as well. Therefore, the target UC voltage should be adjusted lower so the UC
will discharge more. The converse is true also. If the battery current is exceeding its negative
threshold (i.e. charging more than the threshold), the target UC voltage should be raised so
more current enters the UC instead.
However, if no battery limits have been exceeded, then the target UC voltage should be
followed as per normal and no adjustments are required.
Equation (6-8) checks if the battery limits (Ibatt,max or Ibatt,min) have been exceeded. If it has
been exceeded, Ibatt,over is the error term. Equation (6-9) calculates the target UC voltage
addition term (Kv is a tuning parameter), while equation (6-10) is the final adjusted target UC
voltage.
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As an example, by considering the case of exceeding the positive battery current limit (i.e.
discharging too much). If the discharge limit Ibatt,max has been exceeded, the error term Ibatt,over
is a negative number. This causes the vuc,tar,add term to be negative, leading to the target UC
voltage being adjusted downwards as vuc,tar,adj < vuc,tar. After a few iterations, the error
coefficient Kv was tuned to 0.2 for best performance.
The addition (integral) term allows the output to be held at the value which prevents the
battery currents from being exceeded. Once the battery limits are no longer exceeding the
limits, the addition term should be switched off and the original target UC voltage followed.
However, there are problems for a sudden switch off.
A sudden switch off is only suitable if the battery limit is no longer exceeded because the
drive cycle current demand has fallen. But if the battery limit is no longer exceeded because
the output is giving an appropriate addition term, causing the error term to fall to zero, a
sudden switch off would cause the addition term to fall to zero, leading to the battery currents
being exceeded again, and the addition term must ramp up again, leading to oscillations.
The solution is a decaying addition term, so the switch off is not sudden. The decay rate is set
by ɣ in equation (6-9). If ɣ = 0, there will be no decay and the addition term will never die. If
ɣ = 1, the addition term decays to zero in one instant, leading to oscillations as mentioned
above.
ɣ was tuned such that the effects of the decay term are non-observable within the 10Hz data-
logging. The addition term decayed within 0.1s if the drive cycle current demand fell. But
when a sustained control output was required to prevent the battery current limits from being
exceeded, no decay was observed at 0.1s intervals. Eventually, ɣ was tuned to 0.05 iteratively
in a manner similar to the bisection method to achieve the non-observable decay effect.
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Once the adjusted target UC voltage vuc,tar,adj has been computed from equation (6-10), a
Proportional-Integral (PI) controller is used to bring the actual UC voltage to the adjusted
target UC voltage. The PI controller outputs an 8-bit PWM, which controls the DC/DC
converter duty cycle, and the PI controller was tuned iteratively for best performance.
6.6 Experiment 1
6.6.1 Objective
The purpose of Experiment 1 is to demonstrate the algorithm works in a physical setup and
performs as intended. For the PMS, the target UC voltage should be followed, except when
the battery current exceeds the speed-dependent limit, where the UC should produce/absorb
the excess current. For the EMS, as long as the target UC voltage is followed, the two EMS
goals of sufficient space and sufficient energy are met. Battery 1 was used for this test.
6.6.2 EUDC Drive Cycle
Although the FTP-75 city drive cycle is used for the cycle life test (Experiment 2), the EUDC
is demonstrated here for easier observation as the EUDC is a modal cycle.
The EUDC power vs. time data were loaded into the Maccor, and the speed vs. time were
loaded into the Arduino, and the EUDC was run (at normal speed). The following figures
show the results.
Figure 6-17 EUDC speed profile after scaling with k=160.
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Figure 6-17 shows the scaled EUDC speed profile as loaded into the Arduino. Figure 6-18
shows the drive cycle, battery and UC currents as measured by the current sensors (high-side
UC current iuc,H is computed with (6-1)). It also shows the battery current limits as computed
by the Arduino using the curve fit equations discussed in section 6.5.1.
Figure 6-18 Battery & UC currents from experiment, EUDC.
Here, the UC takes over when the battery exceeds the current limits. At 320s to 340s, when
the vehicle is accelerating to high speeds, the total drive cycle current idr exceeds the upper
battery limit ibatt,max. So the algorithm limits the battery current ibatt to ibatt,max, and the UC
handles the rest of the current as shown by iuc,H (iuc is the UC current at the DC/DC converter
low-side, while iuc,H is the UC current at the DC/DC converter high-side). A similar case can
be seen during high regenerative braking from 120s to 130s.
Note: The Arduino loop runs at 100Hz, while the data is logged and plotted at 10Hz.
Figure 6-19 shows the battery and UC voltages. There are 3 UC voltages – the actual UC
voltage vuc, the target UC voltage (as computed by the curve fit equations in section 6.5.1)
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vuc,tar, and the adjusted target UC voltage to prevent excessive battery currents vuc,tar,adj. It is
observed that vuc follows vuc,tar,adj very closely, such that they overlap. This shows that the
voltage tracking of the PI controller is very good.
Figure 6-19 Battery & UC voltages from experiment, EUDC.
It can also be observed that vuc,tar,adj deviates from vuc,tar at 320s to 340s, at the same place
where the battery current was going to exceed its limits. With earlier equation (6-10), vuc,tar,add
= vuc,tar,adj – vuc,tar, the deviation (addition term vuc,tar,add) can be seen more carefully in Figure
6-20. To prevent the battery current from exceeding the limits, the algorithm lowers the UC
target voltage as designed, therefore causing the UC to discharge more, and assisting the
battery during high power phases.
Figure 6-20 Target UC voltage addition term vuc,tar,add, EUDC.
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The opposite case is seen from 120s to 130s, where high regenerative braking is encountered.
The algorithm raises the target UC voltage to ensure the UC is charged more.
During non-demanding sections, vuc follows vuc,tar quite closely. So it has been shown that the
two PMS goals have been achieved – to ensure the actual UC voltage follows the target UC
voltage, and to limit battery currents – with priority on the latter. When the actual UC voltage
follows the target UC voltage, the two EMS goals of sufficient space and energy are also
achieved.
Similar to the full-scale simulations, the EUDC also demonstrates the two goals of the speed-
dependent battery current limit. From 250s to 290s in Figure 6-18, it is observed that the
battery limits are not exceeded as idr < ibatt,max. However, the UC is still being utilised (iuc,H >
0), which satisfies the first goal of using the UC even during low demands to reduce battery
usage. From 290s to 320s in Figure 6-18, a constant speed is being maintained, and it can be
seen that the battery is supplying all the power at steady state, satisfying the second goal of
the speed-dependent battery limit.
As mentioned earlier in section 6.5.3, there are two problems with the Maccor machine – the
machine runs slow for transient drive cycles, and the sensors are out of calibration. As the
EUDC is a modal drive cycle, the Maccor is able to run at the correct timing, so the Arduino
was not purposely slowed to compensate.
As discussed earlier, although the Maccor sensors are out of calibration, the resulting power
output is reasonably accurate as the voltage is underreported and the current is overreported,
cancelling each other out. This is shown in Figure 6-21, where the blue curve is the actual
power drawn by the Maccor, measured by the setup’s separate current sensors and voltage
sensors and multiplied together. The red Pdc curve is the power vs. time profile programmed
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into the Maccor. It was added later in post-processing after the experiment was finished (i.e.
it was not logged). It can be seen that the two curves do not differ much from each other.
Figure 6-21 Power and time sync check, EUDC.
6.6.3 FTP-75 City Drive Cycle
The four HESS and two battery limits goals have already been demonstrated in the EUDC
run above. Here, the FTP-75 city drive cycle was loaded into the setup and also tested. This is
provided for reference as the cycle life tests in experiment 2 use the FTP-75 city drive cycle.
It was run at reduced speed as discussed in section 6.5.3. The following figures show the
results.
Figure 6-22 FTP-75 city speed profile after scaling with k=160.
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Figure 6-23 Battery & UC currents from experiment, FTP-75 city.
Figure 6-24 Battery & UC voltages from experiment, FTP-75 city.
Figure 6-22 shows the scaled FTP-75 city speed profile as loaded into the Arduino. Figure
6-23 shows the drive cycle, battery and UC currents. Figure 6-24 shows the battery and UC
voltages. Figure 6-25 shows the target UC voltage adjustment values.
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Figure 6-25 Target UC voltage addition term vuc,tar,add, FTP-75 city.
As it is transient drive cycle, it may look ‘messy’, so a zoomed-in section from 180 to 280s is
shown in the following figures, where high acceleration is required. Figure 6-26 shows the
zoomed in section of currents. During the section from 205s to 220s, it is observed the drive
cycle current idr exceeds the upper battery limit ibatt,max. The algorithm has correctly limited
the battery current ibatt to the limits, and the UC iuc,H handles the excess current, just like the
earlier EUDC case.
Figure 6-26 Battery & UC currents from experiment, FTP-75 city, zoomed 180-280s.
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Figure 6-27 shows the battery and UC voltages. Again, it can be seen that actual UC voltage
vuc follows the adjusted target UC voltage vuc,tar,adj very closely such that they overlap,
showing good control of UC voltage.
Figure 6-27 Battery & UC voltages from experiment, FTP-75 city, zoomed 180-280s.
Also, the adjusted target UC voltage vuc,tar,adj deviates from target UC voltage vuc,tar at 205s to
220s, at the same place where the battery current was going to exceed its limits. Figure 6-28
shows this target UC voltage addition term more clearly. Similar to the earlier EUDC case,
the algorithm lowers the UC target voltage to further discharge the UC, assisting the battery.
Figure 6-28 Target UC voltage addition term vuc,tar,add, FTP-75 city, zoomed 180-280s.
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As mentioned earlier in section 6.5.3, the Maccor is unable to keep up with transient drive
cycles. Figure 6-29 shows the actual power drawn vs. the expected power drawn.
Figure 6-29 Power and time sync check, FTP-75 city.
The Maccor is running slow, taking 2052s instead of 1875s for a single FTP-75 drive cycle.
Also, within the cycle, some sections run faster, while others run slower, as can be seen from
the blue actual power drawn curve sometimes leading and sometimes lagging the red
expected curve (The expected curve was added in post-processing. It is slowed by a fixed
9.5% throughout, just like the Arduino).
On the positive side, the Maccor was consistent between cycles. When the FTP-75 city cycle
was run again, the same sections would lead or lag, so it was repeatable.
Although some sections lead or lag, this was not a major concern. Ultimately, the battery-
only and battery/UC setup are both subject to the same leading/lagging drive cycle in the
cycle life tests in Experiment 2, so a fair comparison can still be made (though the battery/UC
setup is at a slight disadvantage due to the speed vs. time being slightly out of sync with the
power vs. time).
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Also as discussed earlier, the actual power drawn and expected power drawn are reasonably
similar in terms of magnitude, despite the Maccor sensors being out of calibration.
6.6.4 Average Currents
In this section, the average of absolute values of the battery current in the battery/UC
experiments above is computed and compared to that in a battery-only system. It will be
shown that the battery in the battery/UC HESS outputs a lower average current as compared
to a battery-only system. A lower average current (or lower C-rate) results in a longer battery
cycle life.
Figure 6-30 shows the logged current data from running a battery-only system over the FTP-
75 city drive cycle. It can be seen this battery-only system exceeds the battery current limits
numerous times as there is no UC to assist.
Figure 6-30 Battery-only setup. Currents from experiment, FTP-75 city run 1.
Table 6-12 shows the average of absolute battery current values from experiment data. Three
runs of the EUDC and FTP-75 city drive cycles were performed, and the results were
averaged.
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Table 6-12 Average of absolute battery currents for experiments
EUDC FTP-75 City
Run No. 1 2 3 Avg. 1 2 3 Avg.
Battery-only setup (A) - - - - 2.19 2.20 2.25 2.21
Battery/UC setup (A) 3.44 3.51 3.59 3.51 1.81 1.86 1.86 1.84
The EUDC battery-only setup was unable to complete for the selected scale factor of k = 160,
as the demanding sections of EUDC caused the battery voltage to dip below 14V and tripped
the BMS (see section 6.3.3 for a similar case). Interestingly, the battery/UC setup could
complete the EUDC. This shows the UC is able to provide sufficient current during high
demands to prevent the battery voltage from dipping too much.
From Table 6-12, the battery/UC system reduces the battery current (or C-rate) from 2.21A to
1.84A over the FTP-75 city drive cycle. Based on the works of Wang, et al. [7], a lower C-
rate leads to a longer battery cycle life. This is explained further in Experiment 2.
6.6.5 Summary
Therefore, from this section, it has been shown that the proposed HESS management strategy
works in a physical setup and performs as intended. Similar to the simulation results earlier,
the EUDC experiment has shown that the four HESS goals and two battery limit goals have
been achieved.
Specific to the experiment (i.e. not simulation), it was observed the target UC voltage is well
tracked. And when battery current exceeds the limit, the target UC voltage is adjusted and the
UC will absorb/generate the extra power.
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In addition, it was shown that the proposed HESS management strategy reduces the average
C-rate of the battery in a battery/UC setup as compared to that of the battery-only setup,
extending the battery cycle life.
Although there are some problems with the Maccor machine as discussed in 6.5.3, these have
already been compensated or are not a major concern.
In addition, when using a scale of k = 160, the EUDC is only able to run in a battery/UC
setup. During peak power demands, the battery-only setup is unable to supply enough current
and undervoltage occurs. In contrast, the UC in the battery/UC setup is able to assist the
battery in supplying current, so the undervoltage condition does not occur.
6.7 Experiment 2
6.7.1 Objective
The purpose of experiment 2 is to compare the cycle life of battery 2 in the battery-only setup
to battery 3 in the battery/UC setup. Each setup is cycled continuously for an accelerated
cycle life test, and the capacities of the batteries in the two setups are compared. This would
verify the ultimate HESS goal, which is to extend battery cycle life.
6.7.2 Description
As mentioned in section 5.5.2, three FTP-75 city drive cycles comprise one full day of
driving. To estimate how many cycles should be performed, existing works in the literature
are examined.
In [7], Wang, et al. performed constant charge and discharge accelerated cycling tests with
Sanyo UR18650W batteries. With 0.5C as the charge and discharge rate, approximately 5000
cycles were required for a 30% drop in battery capacity, which took about two years, while at
least 200 cycles were required to observe a noticeable drop of 5%.
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As the average C-rate for the battery/UC setup under the FTP-75 city drive cycle is only
0.24C (less than their 0.5C), it is expected to take even longer. Running thousands of cycles
for three or four years is not feasible within the authors’ PhD candidature. Instead, as many
cycles as possible were run within a six-month period (during office hours only due to safety
concerns) until the final version of this thesis was submitted.
6.7.3 Procedure
Two brand new 5S3P SuPower battery packs (from China) were used for this experiment –
battery 2 for the battery-only setup and battery 3 for the battery/UC setup. First, it was
required to find the two batteries’ initial capacity by performing a capacity test.
Secondly, each battery was cycled for 20 daily cycles (i.e. 60 FTP-75 city cycles), one for the
battery-only setup and one for the battery/UC setup. This was effectively repeating
Experiment 1 multiple times. Charging at 0.5C was performed when the battery fell below
17V or was unable to get through the demanding sections of the FTP-75 city cycle (more on
this in section 6.7.7 later).
After the 20 daily cycles, another capacity test was performed to determine the capacity loss.
This was repeated, where a capacity test would be performed every 20 daily cycles. The
value of 20 daily cycles was selected in order to perform about 6 to 8 capacity tests in over
the first three months. This would provide sufficient data points to observe a capacity drop
trend. In the subsequent three months, it was spaced to 30 cycles instead, to allow more drive
cycles to be run.
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6.7.4 Battery Discharge Capacity Test
6.7.4.1 Procedure
The battery capacity test is performed similar to that found in [7]. The battery is placed into
the green box as seen in the photo in Figure 6-2 for data logging, but with the UC and DC/DC
converter disconnected.
First the battery is charged at constant current (CC) to maximum voltage, then charged at
constant voltage (CV) to make sure it is fully charged. Then the battery is discharged at CC
and the data is logged to determine the discharge capacity. The discharge capacity procedure
is summarised in Table 6-13.
Table 6-13 Discharge capacity test procedure.
Step Procedure Run Until Data
1 4.7A CC charge Voltage reaches 20.2V Discarded
2 20.2V CV charge Current falls below 0.7A Discarded
3 Rest For 3 mins Discarded
4 4.7A CC discharge Voltage falls below 14V Logged
5 Post-processing to limit voltage range to
[18.9V, 15.3V]
- -
The maximum voltage of the battery is 21V, however, the Maccor is only rated for 20V.
Therefore, the upper charging limit was set at 20V on Maccor. As the Maccor sensor was out
of calibration, it was actually 20.2V. The lower discharge limit is set to 14V, which is when
the battery built-in BMS trips the battery due to undervoltage occuring.
Ideally, a small CC charging/discharging rate should be used to get the true maximum battery
capacity (to reduce losses) and to avoid the capacity test affecting the cycle life results.
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Wang, et al. in [7] use 0.5C. However, since the purpose of the experiment was to observe the
capacity fade, the true maximum capacity was not that important, but rather the relative
capacity between the two batteries. Therefore, the maximum discharge current given by the
manufacturer of 5A was used to speed up the experiment. The Maccor was commanded to
charge/discharge at 5A, but because its calibration was off, it produced 4.7A instead,
corresponding to 0.6C.
The CV charging section should be stopped when the current falls below a threshold. Ideally,
this threshold should be as small as possible. Wang, et al. in [7] used a threshold of 0.075A,
sometimes taking up to a maximum of two days to charge. Again, as only the relative
capacity is important, and to speed up the experiment, the threshold was set at 0.7A
(commanded to 1A on Maccor), resulting in the CV charging section taking slightly more
than an hour.
6.7.4.2 Post-processing Calculations
Once the discharge cycle had finished, there was further post-processing to calculate the
battery capacity. This is illustrated by the first discharge test of battery 3.
Figure 6-31(a) shows the CC discharge of 4.7A as logged by current sensor ACS3. The
charging starts at about 1700s and ends at 6600s (ignore the dashed lines for now). The curve
in Figure 6-31(a) is integrated over time (known as coulomb counting) to give Figure
6-31(b), which is the amount of charge which has been discharged from the battery so far.
Figure 6-32 shows the battery voltage over time as logged by the sensor. It decreases over
time to 14V, when the BMS trips the battery due to undervoltage, disconnecting and dropping
the voltage to 0V at the end.
Since the UC and DC/DC converter are disconnected (iuc,H = 0), from equation (6-1), idr = ibatt,
and there are two current sensors – ACS3 & ACS1 – logging the same data. However, there
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are some minor differences in the two readings (up to ~0.1A), so the average was taken from
both sensors. Figure 6-33 shows the battery capacity with respect to battery voltage, for each
of the sensors. Time is implicit in that plot.
Figure 6-31 (a) Discharging current from ACS3 (b) coulomb counting.
Figure 6-32 Discharging voltage.
Figure 6-33 Battery discharging capacity.
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The total battery discharge capacity can be determined by the right-most value on Figure
6-33, which is 6.44Ah on ACS3 and 6.31Ah on ACS1, giving an average of 6.37Ah.
In Table 6-13 earlier, the discharge capacity procedure was presented, where the first two
steps are for charging the battery to 20.2V. However, due to contact resistance and other
losses (discussed in section 6.7.8), some voltage drop is present, and once the battery stops
charging, the open circuit battery voltage is lower than 20.2V.
In the fourth step, the battery discharge is performed until the in-built BMS trips the battery
at 14V. However, it is not known how consistent the BMS is.
Since the upper 20.2V and lower 14V limits cannot be fully relied on, further post-processing
was done on the resultant data. Only the data between 18.9V and 15.3V was retained as
shown by the dashed lines in the previous three figures. The two values were selected to
ensure a small distance from the edges, to avoid the uncertainty at the limits.
Subtracting the capacity from the two ends, this results in 6.06Ah on ACS3 and 5.93Ah on
ACS1, giving an average of 6.00Ah. This is the discharge capacity test procedure result.
For completeness, the plots for the first two steps of Table 6-13, which is to charge the
battery, are shown in Appendix A.
6.7.5 Battery-only Setup
There are two independent channels in the Maccor, so it is possible to run both the battery-
only and battery/UC experiments at the same time.
To run the battery-only cycle life experiment, ideally, the green box setup in the photo in
Figure 6-2 should be duplicated, for example, all the sensors, data logging equipment and
safety switches, only without the DC/DC converter and UC. However, there was limited
budget and time to construct a new setup for the battery-only system, so the Maccor was
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directly connected to the battery through wires only, without any sensors, for running the
cycle life test.
But for the capacity test, the battery (battery 2) would be placed in the green box setup in
Figure 6-2 (with the UC and DC/DC converter disconnected) in order to log the current and
voltage.
6.7.6 Initial Results
Figure 6-34 Battery discharge capacity tests over 60 cycles.
Figure 6-34 shows the discharge capacity tests results over 60 cycles for battery 2 (battery-
only system) and battery 3 (battery/UC system). They are the averaged results from the two
current sensors.
As the number of cycles performed is small, the battery capacity is not expected to drop
much. The variation in the results above seem to be noise due to experiment variations.
However, it seemed that battery 2 was more consistent than battery 3, which has some drop in
battery capacity when comparing cycle 0 to cycle 60 (or even cycle 40). This is contrary to
the predictions, so further investigation was necessary.
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6.7.7 Battery-only Undervoltage During Demanding Sections
Before explaining why the battery/UC system seemed to perform worse, an observation from
the experiments is discussed first.
In section 6.3 Scale Factor k, and more specifically Table 6-7, it was shown that the battery-
only and battery/UC system were able to complete the FTP-75 city drive cycle only when k =
160. That was when the battery was charged to 20.2V. After going through a few more
cycles, naturally the battery would be more discharged and its voltage would drop.
As an example, the battery-only setup was run with the FTP-75 city drive cycle, where the
initial battery voltage was 19.1V (Nominal battery voltage is 18.5V).
Figure 6-35 Battery-only voltage for FTP-75 city, tripped, k=160.
Figure 6-36 Battery-only current for FTP-75 city, tripped, k=160.
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Figure 6-35 shows the battery voltage profile and Figure 6-36 shows the current profile. At
212s real-time (corresponding to 193s drive cycle time due to the slow Maccor), the FTP-75
city drive cycle experiences a peak in power. The Maccor attempts to draw higher current,
which causes the battery voltage to dip because of internal resistance and other unwanted
resistive losses in the circuit. As the battery voltage dips, the Maccor draws even higher
current to hit the required power, which causes the battery voltage to dip even further. From
Figure 6-36, the last recorded non-zero current was 30A (the limit of the current sensor),
which caused the battery voltage to dip excessively, leading to the BMS to trip the battery,
resulting in 0V at 212s in Figure 6-35.
In this example, the battery-only system is unable to complete the drive cycle not because it
is flat, but because it cannot meet the required power demands.
As a side-note, in the battery/UC system, the FTP-75 city drive cycle is able to complete
when the initial battery voltage was less than 19V. Figure 6-24 in section 6.6.3 of Experiment
1 showed this. This is because the UC is able to provide sufficient current during high
demands and prevents the battery voltage from dipping too low.
6.7.8 Battery-only Contact Resistance
To recap, from earlier section 6.7.6, it was found that the battery/UC system performed worse
in terms of capacity loss. The reason is explained in this section.
6.7.8.1 No. of Drive Cycles Completed
Some observations were noticed in the experiment and summarised in Table 6-14. If initially
charged to 20.2V, the battery/UC system could complete approximately 11 FTP-drive cycles
before battery undervoltage occurred as discussed in the previous section. On the other hand,
the battery-only setup could complete approximately 10 FTP-75 city drive cycles.
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Table 6-14 FTP-75 city drive cycles before battery undervoltage.
Direct connection (section
6.7.5 Battery-only Setup)
Placed into green box
(Figure 6-2)
Battery-only system
(battery 2)
10 3
Battery/UC system
(battery 3)
- 11
However, if battery 2 from the battery-only setup was placed in the green box setup (Figure
6-2) with the DC/DC converter and UC disconnected, it would last for only three FTP-75 city
drive cycles before undervoltage occured.
It was suspected there was high voltage drop due to contact resistance in the green box setup,
leading to a higher possibility of undervoltage occurring. From the Maccor to the battery in
the green box, the current had to pass through two connectors, two fuses, two current sensors
and a relay as shown earlier in the electrical diagram Figure 6-1. The current sensors were
connected via nuts and bolts, and the fuses and relays were connected via quick connect
crimp connectors, so there may be substantial contact resistance.
In contrast, for the directly connected battery-only setup, the current only had to pass through
two connectors, resulting in smaller voltage losses.
6.7.8.2 Contact Resistance Experiment
The voltage losses due to contact resistance (and others) were verified in an experiment as
follows. The two voltage sensors of the setup were disconnected. One was placed as close to
the battery as possible, by making cuts on the battery lead insulation. The other sensor was
placed as close to the Maccor as possible, at the connection between the Maccor and the
experiment setup. This is shown in Figure 6-37.
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Figure 6-37 Contact resistance experiment connections diagram.
A step current profile was programmed into the Maccor, from 10A to 0A (discharging), then
-10A to 0A (charging) as shown in Figure 6-38. As mentioned earlier, there are two sensors
measuring current, so there are two curves, one for each sensor (ACS1 and ACS3), almost
overlapping.
Figure 6-39(a) shows the voltage measurement of the two sensors, while Figure 6-39(b) is the
difference of the two curves in Figure 6-39(a), showing the voltage drop between the Maccor
and the battery.
Figure 6-40 shows the equivalent resistance between the Maccor and battery, due to contact
resistance and other losses. This was calculated by dividing the voltage drop (Figure 6-39(b))
by current (Figure 6-38).
The section from 67s to 77s is blank because current is zero, and voltage divided by zero
current is undefined. The sections from 57s to 67s and from 117s to 127s are very noisy and
have high peaks. This is because during that section, the current is small (0.7A), resulting in
only a small voltage drop. As the voltage drop is very small and close to zero (see Figure
6-39(b)), there is a low signal-to-noise ratio in that section, so it is ignored.
to μC
to μC
to μC
to μC
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Figure 6-38 Current profile to find voltage drop.
Figure 6-39(a) Measured voltages (b) voltage drop.
Figure 6-40 Equivalent resistance (contact resistance and other losses).
It is observed from this experiment, that the equivalent resistance in the battery/UC green box
setup is on average, approximately 0.07Ω, which is significant. Earlier Figure 6-26 shows the
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current demanded hits 15A at 212s in the FTP-75 city drive cycle. A 15A current over 0.07Ω
results in a 1.05V voltage drop, enough to push the battery to undervoltage conditions.
To summarise, although the battery stress is relieved by the UC in the battery/UC setup, it
also has to overcome an extra voltage drop due to contact resistance and other losses, which
increases battery stress again.
6.7.9 Battery-only Setup, Revised
Therefore, the battery-only setup was revised after the first 60 cycles. The additional voltage
drop was included to ensure the cycle life tests between the battery-only and battery/UC setup
are fair. After a few trials, 0.06Ω of resistance was added in series to the direct connection of
the battery-only setup as shown in Figure 6-41.
Figure 6-41 Photo of battery-only setup.
The voltage drop and equivalent resistance were tested in the new setup. The same current
profile in Figure 6-38 was cycled. Figure 6-42 shows the voltage measurements and the
voltage drop between the Maccor and the battery.
Figure 6-43 shows the equivalent resistance between the Maccor and battery. Again, the
noisy sections from 50s to 60s and from 110s to 120s were ignored. Although only 0.06Ω of
Battery
0.06Ω of
resistance
To Maccor
Connector
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resistors were used, it can be seen from the plot that the total resistance is approximately
0.07Ω. The extra 0.01Ω is likely due to actual contact resistance present.
Figure 6-42(a) Measured voltages (b) voltage drop.
Figure 6-43 Equivalent resistance (contact resistance and others).
Now, the contact resistance of the battery-only setup has been matched to the battery/UC
setup.
The FTP-75 city drive cycles were run again in this revised battery-only setup, and as
expected, the battery completed only three FTP-75 city drive cycles before undervoltage
occurred, matching the situation in the green box as shown earlier in Table 6-14.
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6.7.10 Final Results
Eventually, 220 cycles of the battery-only setup and 190 cycles of the battery/UC setup were
completed in the six-month period. Figure 6-44 shows the battery capacity versus cycle
number. Figure 6-45 shows the battery capacity as a percentage of the initial battery capacity.
Figure 6-44 Battery capacity of battery-only and battery/UC setup.
Figure 6-45 Relative capacity. Cycle capacity divided by initial capacity.
From Figure 6-45, both battery capacities are hovering around the 97-100% mark. As each
cycle is equivalent to a day of driving, only 60% of a year of driving has been completed. As
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only a small number of cycles have been completed, the results are too close to call and still
inconclusive at this point.
The variation in the data points seem to be more of noise due to experiment variations. For
example, the additional ‘contact’ resistance in the battery-only setup was introduced only
after 60 cycles. In the 100 to 130 cycles section, there was a rise in capacity. This was due to
an increase in contact resistance for both setups. The connectors were found to be corroding
due to the extra flux used in soldering the wire and connectors. The rise in capacity was due
to the smaller gradient at the start of the discharge versus the steeper gradient at the end as
shown in Figure 6-46. Therefore, a larger section of capacity was gained as compared to the
capacity lost. The connectors were eventually replaced after 130 cycles, and no extra flux was
used, only the solder rosin core.
Figure 6-46 Capacity “gained” due to high contact resistance
In short, the contact resistance causes some minor capacity gain to be logged. As a side note,
at first glance, it might seem there is some conflict, because earlier in section 6.7.6 Initial
Results, it was said that the contact resistance worsens the capacity loss for the battery/UC
system. There is no conflict, because in section 6.7.6, the extra contact resistance stresses the
battery in the battery/UC setup more during the drive cycle tests, leading to higher C-rates
High contact resistance
Low contact resistance
Capacity gained Capacity lost Capacity (Ah)
Volt
age
(V)
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and more capacity loss. But in this section, only the capacity test is discussed, not the drive
cycle tests, and it is applied to both setups.
As mentioned earlier in section 6.7.2, when Wang, et al. performed constant 0.5C charge and
discharge accelerated cycling tests, they took 200 cycles to observe a noticeable drop of 5%,
and 5000 cycles (two years in real-time) for a 30% drop. As the average C-rate for this
battery/UC setup under the FTP-75 city drive cycle is only 0.24C (half of their 0.5C), it
would take even longer for similar results.
6.7.11 Summary
In Experiment 2, the battery/UC setup and the battery-only setup was cycled to compare the
cycle life. The purpose was to verify the ultimate HESS goal of extended battery cycle life.
After 190 cycles, the results are still inconclusive. However, based on the works of Wang, et
al, they showed that a lower C-rate leads to a longer battery cycle life. From earlier
Experiment 1, section 6.6.4, it was shown that the proposed battery/UC setup indeed has a
lower averaged absolute C-rate for the battery as compared to that in the battery-only setup.
If the experiment was run over a longer period, the capacity drop of the battery-only system
should be more severe than that of the battery/UC HESS setup.
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7 HESS REDUCED-SCALED SIMULATIONS
Earlier in section 6.5 Software Implementation, the scale factor k = 160 for a reduced-scale
experimental implementation was discussed. In this section, k = 160 was implemented to
create a reduced-scale simulation. The purpose was to allow a comparison between the results
of Experiment 1 and the reduced-scale simulation. They are compared in terms of behaviour
over time and in terms of energy consumption for the EUDC and FTP-75 city drive cycles.
7.1 Differences between Full and Reduced-scale Simulation
There are some differences between the reduced-scale simulation and full-scale simulation.
First, the additional contact resistance was added to the reduced-scale simulation. Although
the measured resistance was 0.07Ω, 0.2Ω was used instead as it was a better fit to match the
experiment and simulation. In general, the larger the contact resistance in the simulation, the
more the battery voltage would dip during drive cycle peaks, leading to the current drawn
surging. So with some iterative tuning, 0.2Ω matched the current surge better.
Second, the battery power limits in the full-scale simulation was replaced by battery current
limits to match the experiment as explained in section 6.5.4.
Thirdly, in the full-scale battery-only simulation, the maximum regenerative braking was
clipped to -30kW to match the Nissan Leaf. However, no clipping was performed in the
experiment. Therefore, this clipping was removed in the reduced-scale simulation.
Lastly, the FTP-75 city drive cycle in the reduced-scale simulation was stretched by 1.095 to
match the slow running Maccor, as explained in section 6.5.3. However, as illustrated by
earlier Figure 6-29, the Maccor does not stretch the drive cycles linearly, some sections are
stretched more than others.
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7.2 EUDC
Figure 7-1 Battery & UC currents from simulation, EUDC (compare with experiment in
Figure 6-18).
Figure 7-2 Battery & UC voltages from simulation, EUDC (compare with experiment in
Figure 6-19).
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Figure 7-1 and Figure 7-2 show the reduced-scale simulation results for the EUDC. It can be
seen that they are quite similar to the experiment results shown earlier (Figure 6-18 and
Figure 6-19) in terms of behaviour (shape) with respect to time.
From the figures, the battery current has been clipped to the limits from 320s to 340s, and the
UC voltage deviates from the target voltage to handle the excessive power required, just like
what was seen in the experiment in section 6.6.2. Therefore, both the experiment and
reduced-scale simulation behave similarly time-wise.
For an additional reference, the full-scale simulation results were presented in Figure 5-12
and Figure 5-13 in section 5.4.2. They are also similar in terms of battery and UC behaviour.
7.3 FTP-75 City Drive Cycle
The following figures show the reduced-scale FTP-75 city drive cycle simulations, with a
zoomed-in section just like the experiments. Again, they are quite similar to the experiments
in terms of their behaviour with respect to time.
Figure 7-3 Battery & UC currents from simulation, FTP-75 city (compare with experiment in
Figure 6-23).
180
Figure 7-4 Battery & UC voltages from simulation, FTP-75 city (compare with experiment in
Figure 6-24).
Figure 7-5 Battery & UC currents from simulation, FTP-75 city, zoomed 180-280s (compare
with experiment in Figure 6-26).
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Figure 7-6 Battery & UC voltages from simulation, FTP-75 city, zoomed 180-280s (compare
with experiment in Figure 6-27).
Again, the battery current is clipped to the limits from 205s to 220s, and the UC deviates
from the target voltage to handle the excessive power, just like what was seen in the
experiment in section 6.6.3. Therefore, both the experiment and reduced-scale simulation
behave similarly time-wise.
For an additional reference, the full-scale simulation results were presented in Figure 5-14 to
Figure 5-17 in section 5.4.3. They are also similar in terms of battery and UC behaviour.
7.4 Total Energy Use
Here, the energy consumption of the battery in the experiments is compared to that of the
reduced-scale simulations. The energy consumption was calculated by multiplying the logged
battery voltage and current data, and then integrating it over time. Three runs were performed
for both the EUDC and FTP-75 city drive cycles and the results were averaged as shown in
Table 7-1.
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Table 7-1 Experiment battery energy use.
EUDC FTP-75 City
Run no. 1 2 3 Avg. 1 2 3 Avg.
Battery-only setup (kJ) - - - - 38.88 38.78 39.12 38.93
Battery/UC setup (kJ) 21.17 21.37 21.52 21.35 38.31 38.89 39.38 38.86
Then the averaged results was compared to the reduced-scale simulation results in Table 7-2.
There is a percentage difference of at most 10.6% (seen in the battery-only FTP-75 city case),
so the simulation is a reasonable estimation of the energy consumption of the experimental
setup. Note that as mentioned earlier in section 6.6.4, the EUDC battery-only setup was
unable to complete due to undervoltage occurring.
Table 7-2 Comparison of battery energy use between experiments and reduced-scale
simulations.
EUDC FTP-75 City
Battery-only setup Experiment (Avg.) (kJ) - 38.93
Simulation (kJ) - 43.04
Battery/UC setup Experiment (Avg.) (kJ) 21.35 38.86
Simulation (kJ) 21.56 42.15
From the results, the FTP-75 city drive cycle exhibits a bigger difference between the
reduced-scale simulation and experiment results as compared to the EUDC. This is not
surprising as the FTP-75 city drive cycle suffers from the Maccor speed problems discussed
in 6.5.3 and 6.6.3 and illustrated in Figure 6-29 earlier, where the actual power drawn by the
Maccor drifts in and out of sync with the programmed power.
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As a side note, the battery energy consumption when comparing the battery-only and
battery/UC case are very similar for both the experiment and simulation (i.e. battery-only
simulation consumes 43.04kJ vs. 42.15kJ in the battery/UC simulation). This is because the
UC only has a slight contribution to the total energy use. The UC is fully charged at the start
of the drive cycle, varies during the drive cycle, and is fully charged again at the end of the
drive cycle. Ultimately, the battery provides the energy to move the car from one location to
another location, so the energy consumption should be similar.
There are three possible reasons why the experiment results differ from the reduced-scale
simulation results. The first is the Maccor sync problems mentioned above, and the second
may be due to the DC/DC converter. The simulation uses an interpolated DC/DC converter
efficiency chart as discussed in 6.4 Experiment 0, so there is still some difference between
the actual DC/DC converter efficiency and simulated efficiency. The third reason may be due
to the simulation being a backward approach, where transients of the electrical components
such as the MOSFETs, inductors, capacitors, etc. are not considered.
7.5 Summary
To summarise, the reduced-scale drive cycle simulations give a reasonably accurate
prediction of the behaviour of the actual battery and UC currents and voltages time-wise. The
proposed HESS management strategy in both the experiment and reduced-scale simulations
perform similar manoeuvres to utilise the UC to prevent the battery from exceeding its limits.
In addition, the reduced-scale simulation is a reasonably accurate representation of the
experiment in terms of battery energy usage, where only an 11% difference was observed.
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8 CONCLUSION & FUTURE WORKS
8.1 Conclusion
In this work, a novel HESS management strategy was proposed. The proposed EMS involved
a more rigorous method of setting the target UC energy level using a speed-dependent band,
which is the first contribution of this thesis. This allows the UC to achieve two goals – to
contain sufficient energy required for future accelerations, and to have sufficient space to
store energy captured from future regenerative braking. Such rigorous calculations and
justifications based on averaged worst case scenarios and real-life drive cycles are not seen in
existing literature. As the calculations were based on worst case scenarios, knowledge of the
future drive profile is not required.
The proposed PMS also has two goals – to ensure the EMS (target UC energy level) is
followed, and to ensure the battery charge and discharge rates do not exceed specified limits
in order to extend the battery cycle life. The second contribution of this thesis is that the
specified battery limits are speed-dependent. This allows it to achieve two goals – better
utilization of the UC and allowing the battery to supply the steady state constant speed power.
In addition, by using the proposed HESS design methodology, the UC can be appropriately
sized to reduce weight and costs.
From simulations, by running the mid-sized EV over the EUDC and LA92 drive cycles, it has
been demonstrated that the proposed strategy achieves the two EMS goals, the two PMS
goals, and the two battery limit goals mentioned above. Furthermore, despite the algorithm
being designed with averaged worst case scenarios, it was able to tolerate harsh drive cycles.
In addition, the simulations showed that existing works cannot always achieve the two EMS
goals simultaneously unless their UCs are sized twice as large (especially for those with fixed
target UC energy levels), increasing weight and costs. Similarly, it was shown the proposed
185
speed-dependent battery power limit allows the battery to supply the steady state power and
achieves better UC utilization as compared to other rule-based deterministic PMS.
Subsequently, battery cycle life simulations were performed to observe the fall in battery
capacity for the proposed battery/UC HESS, and for a battery-only system. Almost 30%
reduction in capacity loss due to cycling was seen for the battery/UC HESS as compared to
the battery-only system when running three FTP-75 city drive cycles daily over 10 years.
This is because the battery/UC HESS is subject to a smaller C-rate as compared to the
battery-only system.
Afterwards, a reduced-scale experiment was created. A preliminary Experiment 0 was
conducted to evaluate the DC/DC converter efficiency. Then Experiment 1 verified the
proposed strategy could work physically and satisfy the four HESS goals and the two battery
limit goals. Also, the results showed that the battery/UC HESS has a lower average of
absolute current as compared to the battery-only system.
In addition, the experiment showed that the EUDC cycle is only able to run in the battery/UC
HESS setup for the selected scale. The battery-only setup was unable to run as it could not
supply the required current demand, demonstrating an extremely useful application of the
battery/UC HESS.
Subsequently, a reduced-scale simulation was created and compared to the experiments. The
results from both are reasonably similar in terms of energy consumption, where only an 11%
difference was observed. Also, they behaved similarly time-wise, for example, the battery
was about to exceed its limits in the same section for both the experiment and reduced-scale
simulations, and the algorithm in both the experiment and simulations performed similar
manoeuvres to utilise the UC to prevent the battery from exceeding its limits.
186
Lastly, Experiment 2 was performed to compare the battery cycle life of the battery/UC
HESS to the battery-only system. Each setup was continuously cycled with the FTP-75 city
drive cycle. The results are too close to call due to the small number of cycles run. However,
based on the works of Wang, et al., a smaller charge/discharge current (which the battery/UC
HESS achieves) leads to a longer battery cycle life.
8.2 Future Works
There are still further research works which can be done to expand or improve the work.
8.2.1 Optimization to Extend Battery Cycle Life
In section 5.5, battery cycle life simulation results were presented for the proposed algorithm.
However, this may not be the best performance from the proposed algorithm. Optimization
can be performed to further improve the battery cycle life.
There are many variables which can be adjusted, for example in the PMS discussed in section
4.1.1 regarding the battery limits, the selected values of maximum battery power of 1.7C or
the battery power scaling of Pbatt,max,scale = 3 could be optimized to get the longest cycle life.
Similarly for the EMS, the selected brake torque of τbr,tar = 244 Nm and acceleration torque
ratio τacc ratio = 0.5 in section 4.2.3 could also be optimized.
This would be a multi-objective optimization, where the objectives are to extend battery cycle
life, and to ensure the two EMS and two PMS goals are met. Satisfying the EMS and PMS
goals would allow the algorithm to tolerate harsh drive cycles outside its design range, like
the LA92 as discussed in section 5.4.1. Also, multiple drive cycles would need to be
considered, as the optimal solution for one drive cycle may not be the optimal for another
drive cycle.
187
8.2.2 Full-scale Implementation
In this work, only a reduced-scale experiment was performed. Further research can be done
with a full-scale implementation in an EV, such as a Nissan Leaf. For a full-scale
implementation, here are some suggestions by the author.
Sensor readings are expected to be noisy when implemented in a real EV, with many
disturbances. As the algorithm responds in real-time to the power demanded, for example,
limiting the battery power, care must be taken in selecting the filter cutoff values. A low
cutoff will lead to more stable readings, but will also cause excessive lag.
Also, as the battery power or current limiting is hugely dependent on the battery current
sensor, it might be wise to have a duplicate sensor for redundancy. In the experiment, wrong
sensor readings were occasionally encountered, resulting in the UC unable to assist the
battery at the appropriate times and blowing the circuit fuses. Furthermore, as the Hall-effect
current sensors used in the experiment were rather sensitive to disturbances, other techniques
of measuring current could be considered, for example, using shunt resistors.
In addition, effort should be spent studying contact resistance. Due to the vibrations
experienced by a real vehicle, contact resistance is expected to be a bigger concern as
compared to the stationary experiment performed in this work, as connections may become
loose over time.
Lastly, a gradient sensor and weight sensor are required for more accurate implementation. In
the simulations and experiments in this work, all drive cycles were for flat terrain. The
gradient sensor will feed the present gradient θ(j) into the vehicle model in section 3.6.
Similarly, the simulations and experiments were performed with constant weight. Weight
sensors, in the form of strain gauges, could be installed on the suspension to weigh the
loading on the EV. The sensor does not need to continually weigh the loading. A good
188
suggestion would be to perform the weighing every time the doors close as the loading is
most likely to change then.
The different weight or gradient encountered by the EV would produce a different target UC
band. Therefore, each weight or gradient would have its own curve-fitting polynomial. The
author suggests dividing all the combinations into a few bands, e.g. a load of 50-80kg would
have its own curve-fitting polynomial, while 80-110kg would have another polynomial to
reduce the number of options.
8.2.3 SuPower Battery Cycle Life Curve Fitting
Earlier in section 3.11.2, assembling Sanyo UR18650W batteries to a 98S44P configuration
to match the Nissan Leaf battery capacity was discussed. The reason for doing this is because
an empirically fitted battery cycle life model was available for the Sanyo UR18650W
batteries from Wang, et al [7], but not for the Nissan Leaf batteries.
In future, a cycle life curve fitting can be performed on the SuPower batteries used in the
experiments. As only 190 cycles have been performed in Experiment 2, there is not enough
data to extract the required parameters to fit the model at this moment.
When an appropriate number of cycles have been performed and the battery capacity fade
curve shape is clearly visible, a battery cycle life model for the SuPower batteries could be
created, and its cycle life could be simulated. This could be used to predict the cycle life of
the SuPower batteries, and there could be less emphasis on running the cycle life experiments
since a simulation is available.
Also, the SuPower batteries are more modern, and may not suffer the severe calendar life
losses faced by the 2007 Sanyo UR18650W. Therefore, the mid-sized EV in the full-scale
simulation can be modified to use SuPower batteries instead of the Sanyo batteries for an
improved cycle life simulation.
189
8.2.4 Cost-Benefit Analysis of UCs
After understanding the cycle life of modern batteries, a cost benefit analysis could be
performed to determine what circumstances would favour a battery/UC HESS as compared to
a battery-only setup in terms of costs in the long run.
From the author’s analysis, the most cost beneficial scenario is when the EV has heavy city
start-stop driving, for example, a public bus. From the cycle life simulations earlier, a city
drive cycle extends the battery cycle life the most. In addition, with heavy daily usage, the
battery capacity loss due to cycle life would dominate the capacity loss due to calendar life.
This is beneficial as the battery/UC HESS can only control battery capacity loss due to cycle
life.
8.2.5 Improvement to Experiments
Further improvements can be made to the experiment, which is specific to this work. To
make the experiment measurements more accurate, instead of adding resistors to the battery-
only experiment setup to match the contact resistance of the battery/UC HESS experiment
setup, effort should be spent on reducing the contact resistance in the green box battery/UC
setup. For example, quick connect crimp connectors were used for easy troubleshooting and
swapping out of parts. For convenience, existing quick connect crimp connectors in the
laboratory were used. However, some connectors have been idle for many years, such that the
surface is no longer shiny, but slightly oxidised. New connectors should have been bought
instead.
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BIBLIOGRAPHY
[1] J. Xue, “Electric vehicles ‘not economically feasible yet’,” TODAY, p. 2, 9 December
2014.
[2] Nissan USA, “Nissan Leaf Electric Car: 100% Electric. 100% Fun.,” 2014. [Online].
Available: http://www.nissanusa.com/electric-cars/leaf/. [Accessed 10 December 2014].
[3] Nissan USA, “2014 Nissan Sentra Sedan,” 2014. [Online]. Available:
http://www.nissanusa.com/cars/sentra. [Accessed 10 December 2014].
[4] C. Gaylord, “Hybrid cars 101: How long should batteries last?,” 6 March 2012.
[Online]. Available: http://www.csmonitor.com/Innovation/2012/0306/Hybrid-cars-101-
How-long-should-batteries-last. [Accessed 18 December 2017].
[5] T. Bradley, “Replacing A Dead Prius Hybrid Battery Doesn't Have To Cost Thousands
Of Dollars,” 9 April 2014. [Online]. Available:
http://www.forbes.com/sites/tonybradley/2014/04/09/replacing-a-dead-prius-hybrid-
battery-doesnt-have-to-cost-thousands-of-dollars/. [Accessed 18 December 2017].
[6] J. Voelcker, “Nissan Leaf New Battery Cost: $5,500 For Replacement With Heat-
Resistant Chemistry,” 28 June 2014. [Online]. Available:
http://www.greencarreports.com/news/1092983_nissan-leaf-battery-cost-5500-for-
replacement-with-heat-resistant-chemistry. [Accessed 18 December 2017].
[7] J. Wang, J. Purewal, P. Liu, J. Hicks-Garner, S. Soukazian, E. Sherman, A. Sorenson, L.
Vu, H. Tataria and M. W. Verbrugge, “Degradation of lithium ion batteries employing
graphite negatives and nickel-cobalt-manganese oxide + spinel manganese oxide
191
positives: Part 1, aging mechanisms and life estimation,” Journal of Power Sources, vol.
269, pp. 937-948, 2014.
[8] J. C. Burns, D. A. Stevens and J. R. Dahn, “In-Situ Detection of Lithium Plating Using
High Precision Coulometry,” Journal of The Electrochemical Society, vol. 162, no. 6,
pp. A959-A964, 2015.
[9] Q. Cai, D. J. L. Brett, D. Browning and N. Brandon, “A sizing-design methodology for
hybrid fuel cell power systems and its application to an unmanned underwater vehicle,”
Journal of Power Sources, vol. 195, no. 19, pp. 6559-6569, 2010.
[10] Battery University, “BU-209: How does a Supercapacitor Work?,” 21 April 2017.
[Online]. Available:
http://batteryuniversity.com/learn/article/whats_the_role_of_the_supercapacitor.
[Accessed 18 December 2017].
[11] A. Khajepour, S. Fallah and A. Goodarzi, Electric and Hybrid Vehicles: Technologies,
Modeling and Control - A Mechatronic Approach, West Sussex: John Wiley & Sons,
2014.
[12] Maxwell Technologies, “48 Volt Module Ultracapacitor General Purpose Module,”
2014. [Online]. Available: http://www.maxwell.com/products/ultracapacitors/48v-
modules. [Accessed 18 December 2017].
[13] Mouser Electronics, “BMOD0083 P048 B01 Maxwell Technologies,” 2017. [Online].
Available: http://www.mouser.com/ProductDetail/Maxwell-Technologies/BMOD0083-
P048-B01/. [Accessed 18 December 2017].
[14] K. M. So, Y. S. Wong, G. S. Hong and W. F. Lu, “An Improved Energy Management
192
Strategy for a Battery/Ultracapacitor Hybrid Energy Storage System in Electric
Vehicles,” in IEEE Transportation Electrification Conference and Expo, Detroit, MI,
2016.
[15] K. M. So, G. S. Hong, W. F. Lu and Y. S. Wong, “An Improved Speed-dependent
Battery/Ultracapacitor Hybrid Energy Storage System Management Strategy for Electric
Vehicles,” IEEE Transactions on Transportation Electrification, [Under Review].
[16] Q. Xu, X. Hu, P. Wang, J. Xiao, P. Tu, C. Wen and M. Y. Lee, “A Decentralized
Dynamic Power Sharing Strategy for Hybrid Energy Storage System in Autonomous
DC Microgrid,” IEEE Transactions on Industrial Electronics, vol. 64, no. 7, pp. 5930-
5941, 2017.
[17] S. K. Kollimalla, M. K. Mishra, A. Ukil and H. B. Gooi, “DC Grid Voltage Regulation
Using New HESS Control Strategy,” IEEE Transactions on Sustainable Energy, vol. 8,
no. 2, pp. 772-781, 2017.
[18] U. Manandhar, A. Ukil, H. B. Gooi, N. R. Tummuru, S. K. Kollimalla, B. Wang and K.
Chaudhari, “Energy Management and Control for Grid Connected Hybrid Energy
Storage System under Different Operating Modes,” IEEE Transactions on Smart Grid,
vol. PP, no. 99, 2017.
[19] M. M. S. Khan, M. O. Faruque and A. Newaz, “Fuzzy Logic Based Energy Storage
Management System for MVDC Power System of All Electric Ship,” IEEE
Transactions on Energy Conversion, vol. 32, no. 2, pp. 798-809, 2017.
[20] J. Hou, J. Sun and H. F. Hofmann, “Mitigating Power Fluctuations in Electric Ship
Propulsion With Hybrid Energy Storage System: Design and Analysis,” IEEE Journal of
Oceanic Engineering, vol. PP, no. 99, pp. 1-15, 2017.
193
[21] J. P. Trovão, F. Machado and P. G. Pereirinha, “Hybrid electric excursion ships power
supply system based on a multiple energy storage system,” IET Electrical Systems in
Transportation, vol. 6, no. 3, pp. 190-201, 2016.
[22] J. P. Torreglosa, P. Garcia, L. M. Fernández and F. Jurado, “Predictive Control for the
Energy Management of a Fuel-Cell-Battery-Supercapacitor Tramway,” IEEE
Transactions on Industrial Informatics, vol. 10, no. 1, pp. 276-285, 2014.
[23] P. García, J. P. Torreglosa, L. M. Fernándeza and F. Jurado, “Control strategies for high-
power electric vehicles powered by hydrogen fuel cell, battery and supercapacitor,”
Expert Systems with Applications, vol. 40, no. 12, pp. 4791-4804, 2013.
[24] A. A. Ferreira, J. A. Pomilio, G. Spiazzi and L. de Araujo Silva, “Energy Management
Fuzzy Logic Supervisory for Electric Vehicle Power Supplies System,” IEEE
Transactions on Power Electronics, vol. 23, no. 1, pp. 107-115, 2008.
[25] P. Thounthong, S. Raël and B. Davat, “Energy management of fuel
cell/battery/supercapacitor hybrid power source for vehicle applications,” Journal of
Power Sources, vol. 193, no. 1, pp. 376-385, 2009.
[26] Amin, R. T. Bambang, A. S. Rohman, C. J. Dronkers, R. Ortega and A. Sasongko,
“Energy Management of Fuel Cell/Battery/Supercapacitor Hybrid Power Sources Using
Model Predictive Control,” IEEE Transactions on Industrial Informatics, vol. 10, no. 4,
pp. 1992-2002, 2014.
[27] P. Thounthong, V. Chunkag, P. Sethakul, S. Sikkabut, S. Pierfederici and B. Davat,
“Energy management of fuel cell/solar cell/supercapacitor hybrid power source,”
Journal of Power Sources, vol. 196, no. 1, pp. 313-324, 2011.
194
[28] S. F. Tie and C. W. Tan, “A review of energy sources and energy management system in
electric vehicles,” Renewable and Sustainable Energy Reviews, vol. 20, pp. 82-102,
2013.
[29] S. Collins, “Flywheel hybrid systems (KERS),” 4 April 2011. [Online]. Available:
http://www.racecar-engineering.com/articles/f1/flywheel-hybrid-systems-kers/.
[Accessed 18 December 2017].
[30] M. I. Masouleh and D. J. N. Limebeer, “Fuel Minimization for a Vehicle Equipped With
a Flywheel and Battery on a Three-Dimensional Track,” IEEE Transactions on
Intelligent Vehicles, vol. 2, no. 3, pp. 161-174, 2017.
[31] F. A. Bender, M. Kaszynski and O. Sawodny, “Drive Cycle Prediction and Energy
Management Optimization for Hybrid Hydraulic Vehicles,” IEEE Transactions on
Vehicular Technology, vol. 62, no. 8, pp. 3581-3592, 2013.
[32] J. Cao and A. Emadi, “A New Battery/UltraCapacitor Hybrid Energy Storage System
for Electric, Hybrid, and Plug-In Hybrid Electric Vehicles,” IEEE Transactions on
Power Electronics, vol. 27, no. 1, pp. 122-132 , 2011.
[33] A. Ostadi, M. Kazerani and S.-K. Chen, “Hybrid Energy Storage System (HESS) in
vehicular applications: A review on interfacing battery and ultra-capacitor units,” in
IEEE Transportation Electrification Conference and Expo (ITEC), Detroit, MI, 2013.
[34] U.S. Department of Energy Vehicle Technologies Program, “Advanced Vehicle Testing
- Beginning-of-Test Battery Testing Results,” 2012. [Online]. Available:
http://media3.ev-tv.me/DOEleaftest.pdf. [Accessed 18 December 2017].
[35] S. Hu, Z. Liang and X. He, “Ultracapacitor-Battery Hybrid Energy Storage System
195
Based on the Asymmetric Bidirectional Z-Source Topology for EV,” IEEE Transactions
on Power Electronics, vol. 31, no. 11, pp. 7489-7498, 2016.
[36] F. Naseri, E. Farjah and T. Ghanbari, “An Efficient Regenerative Braking System Based
on Battery/Supercapacitor for Electric, Hybrid, and Plug-In Hybrid Electric Vehicles
With BLDC Motor,” IEEE Transactions on Vehicular Technology, vol. 66, no. 5, pp.
3724-3738, 2017.
[37] W. O. Avelino, F. S. Garcia, A. A. Ferreira and J. A. Pomilio, “Electric go-kart with
battery-ultracapacitor hybrid energy storage system,” in IEEE Transportation
Electrification Conference and Expo, Detroit, MI, 2013.
[38] F. S. Garcia, A. A. Ferreira and J. A. Pomilio, “Control Strategy for Battery-
Ultracapacitor Hybrid Energy Storage System,” in Applied Power Electronics
Conference and Exposition (APEC), Washington, DC, USA , 2009.
[39] S. Dusmez and A. Khaligh, “A Supervisory Power-Splitting Approach for a New
Ultracapacitor-Battery Vehicle Deploying Two Propulsion Machines,” IEEE
Transactions on Industrial Informatics, vol. 10, no. 3, pp. 1960-1971 , 2014.
[40] B. Hredzak, V. G. Agelidis and G. D. Demetriades, “A Low Complexity Control System
for a Hybrid DC Power Source Based on Ultracapacitor-Lead-Acid Battery
Configuration,” IEEE Transactions on Power Electronics, vol. 29, no. 6, pp. 2882-2891,
2014.
[41] B. Hredzak, V. G. Agelidis and M. Jang, “A Model Predictive Control System for a
Hybrid Battery-Ultracapacitor Power Source,” IEEE Transactions on Power
Electronics, vol. 29, no. 3, pp. 1469-1479, 2014.
196
[42] Z. Yu, D. Zinger and A. Bose, “An innovative optimal power allocation strategy for fuel
cell, battery and supercapacitor hybrid electric vehicle,” Journal of Power Sources, vol.
196, no. 4, pp. 2351-2359, 2011.
[43] C. Romaus, J. Böcker, K. Witting, A. Seifried and O. Znamenshchykov, “Optimal
energy management for a hybrid energy storage system combining batteries and double
layer capacitors,” in IEEE Energy Conversion Congress and Exposition, San Jose, CA,
2009.
[44] P. Golchoubian and N. L. Azad, “Real-Time Nonlinear Model Predictive Control of a
Battery–Supercapacitor Hybrid Energy Storage System in Electric Vehicles,” IEEE
Transactions on Vehicular Technology, vol. 66, no. 11, pp. 9678-9688, 2017.
[45] M.-E. Choi, J.-S. Lee and S.-W. Seo, “Real-Time Optimization for Power Management
Systems of a Battery/Supercapacitor Hybrid Energy Storage System in Electric
Vehicles,” IEEE Transactions on Vehicular Technology, vol. 63, no. 8, pp. 3600-3611,
2014.
[46] J. Moreno, M. E. Ortúzar and J. W. Dixon, “Energy-management system for a hybrid
electric vehicle, using ultracapacitors and neural networks,” IEEE Transactions on
Industrial Electronics, vol. 53, no. 2, pp. 614-623, 2006.
[47] J. W. Dixon and M. E. Ortúzar, “Ultracapacitors + DC-DC converters in regenerative
braking system,” IEEE Aerospace and Electronic Systems Magazine, vol. 17, no. 8, pp.
16-21, 2002.
[48] R. Carter, A. Cruden and P. J. Hall, “Optimizing for Efficiency or Battery Life in a
Battery/Supercapacitor Electric Vehicle,” IEEE Transactions on Vehicular Technology,
vol. 61, no. 4, pp. 1526-1533, 2012.
197
[49] J. Armenta, C. Núñez, N. Visairo and I. Lázaro, “An advanced energy management
system for controlling the ultracapacitor discharge and improving the electric vehicle
range,” Journal of Power Sources, vol. 284, pp. 452-458, 2015.
[50] F. R. Salmasi, “Control Strategies for Hybrid Electric Vehicles: Evolution,
Classification, Comparison, and Future Trends,” IEEE Transactions on Vehicular
Technology, vol. 56, no. 5, pp. 2393-2404, 2007.
[51] K. Ç. Bayindir, M. A. Gözüküçük and Ahmet Teke, “A comprehensive overview of
hybrid electric vehicle: Powertrain configurations, powertrain control techniques and
electronic control units,” Energy Conversion and Management, vol. 52, no. 2, pp. 1305-
1313, 2011.
[52] E. D. Tate and S. P. Boyd, “Finding Ultimate Limits of Performance for Hybrid Electric
Vehicles,” in SAE Future Transportation Technology Conference, Costa Mesa, CA,
2000.
[53] J. Shen and A. Khaligh, “A Supervisory Energy Management Control Strategy in a
Battery/Ultracapacitor Hybrid Energy Storage System,” IEEE Transactions on
Transportation Electrification, vol. 1, no. 3, pp. 223-231, 2015.
[54] M. E. Ortúzar, J. Moreno and J. W. Dixon, “Ultracapacitor-Based Auxiliary Energy
System for an Electric Vehicle: Implementation and Evaluation,” IEEE Transactions on
Industrial Electronics, vol. 54, no. 4, pp. 2147-2156 , 2007.
[55] United States Environmental Protection Agency, “Dynamometer Drive Schedules,” 1
August 2013. [Online]. Available: https://www.epa.gov/vehicle-and-fuel-emissions-
testing/dynamometer-drive-schedules. [Accessed 18 December 2017].
198
[56] T. Markel, A. Brooker, T. Hendricks, V. Johnson, K. Kelly, B. Kramer, M. O'Keefe, S.
Sprik and K. Wipke, “ADVISOR: a systems analysis tool for advanced vehicle
modeling,” Journal of Power Sources, vol. 110, no. 2, pp. 255-266, 2002.
[57] Nissan Newsroom Europe, “New Nissan Leaf Technical Specification,” 8 April 2013.
[Online]. Available: http://www.newsroom.nissan-europe.com/EU/en-
gb/NEW_LEAF/Product/TechnicalSpecs.aspx. [Accessed 10 December 2014].
[58] Z. Stević, New Generation of Electric Vehicles, Rijeka: InTech, 2012.
[59] SAE International, “Power from Within,” Vehicle Electrification, p. 17, 23 February
2011.
[60] M. Allen, “Real-world range ramifications: heating and air conditioning,” 22 January
2014. [Online]. Available: http://www.fleetcarma.com/electric-vehicle-heating-
chevrolet-volt-nissan-leaf/. [Accessed 18 December 2017].
[61] M. H. Rashid, Modern Electric, Hybrid Electric and Fuel Cell Vehicles - Fundamentals,
Theory and Design, Boca Raton: CRC Press LLC, 2005.
[62] Nissan Motor Corporation, “EDIB (Electric Driven Intelligent Brake),” n.d.. [Online].
Available: http://www.nissan-global.com/EN/TECHNOLOGY/OVERVIEW/edib.html.
[Accessed 18 December 2017].
[63] O. Tremblay, L.-A. Dessaint and A.-I. Dekkiche, “A Generic Battery Model for the
Dynamic Simulation of Hybrid Electric Vehicles,” in IEEE Vehicle Power and
Propulsion Conference, Arlington, TX, 2007.
[64] L. Shi and M. L. Crow, “Comparison of ultracapacitor electric circuit models,” in IEEE
Power and Energy Society General Meeting - Conversion and Delivery of Electrical
199
Energy in the 21st Century, Pittsburgh, PA, 2008.
[65] R. W. Erickson and D. Maksimovic, Fundamentals of Power Electronics, New York:
Springer Science+Business Media, LLC, 2001.
[66] J. Shen, S. Dusmez and A. Khaligh, “Optimization of Sizing and Battery Cycle Life in
Battery/Ultracapacitor Hybrid Energy Storage Systems for Electric Vehicle
Applications,” IEEE Transactions on Industrial Informatics, vol. 10, no. 4, pp. 2112-
2121, 2014.
[67] J. Wang, P. Liu, J. Hicks-Garner, E. Sherman, S. Soukiazian, M. Verbrugge, H. Tataria,
J. Musser and P. Finamore, “Cycle-life model for graphite-LiFePO4 cells,” Journal of
Power Sources, vol. 196, no. 8, pp. 3942-3948, 2011.
[68] EcoModder, “Vehicle Coefficient of Drag List,” 12 September 2014. [Online].
Available: http://ecomodder.com/wiki/index.php/Vehicle_Coefficient_of_Drag_List.
[Accessed 18 December 2017].
[69] U.S. Department of Transportation, National Highway Traffic Safety Administration,
“Laboratory Test Procedure for Rollover Stability Measurement for NCAP: SSF
Measurement,” March 2013. [Online]. Available:
http://www.safercar.gov/staticfiles/safercar/NCAP/SSF_Test_Procedure-
March2013.pdf. [Accessed 18 December 2017].
[70] Powerex, “PM400DV1A060 Intellimod Module Data Sheet,” 2012. [Online]. Available:
http://www.pwrx.com/Product/PM400DV1A060. [Accessed 18 December 2017].
[71] S. Blanco, “Second Drive: 2011 Nissan Leaf - Some things you probably didn't know,”
22 October 2010. [Online]. Available: https://www.autoblog.com/2010/10/22/2011-
200
nissan-leaf-review-drive-second/. [Accessed 18 December 2017].
[72] H. Zumbahlen, “Staying Well Grounded,” Analog Dialogue, vol. 46, no. 06, 2012.
[73] Crane Aerospace & Electronics Power Solution, “Measurement and Filtering of Output
Noise of DC-DC Converters,” 29 August 2016. [Online]. Available:
http://www.interpoint.com/product_documents/DC_DC_Converters_Output_Noise.pdf.
[Accessed 18 December 2017].
[74] A. Martin, M. Davis-Marsh, G. Pinto and I. Jorio, “Capacitor Selection for DC/DC
Converters,” 2012. [Online]. Available:
http://www.kemet.com/Lists/TechnicalArticles/Attachments/5/Avnet2012PowerForum_
CapacitorsSelection.pdf. [Accessed 18 December 2017].
[75] Cooper Bussmann, “1/4" x 1-1/4" Fuses, AGC Series, Fast Acting, Glass Tube,” May
2017. [Online]. Available:
http://www.cooperindustries.com/content/dam/public/bussmann/Electronics/Resources/p
roduct-datasheets/Bus_Elx_DS_OC-2543_AGC_Series.pdf. [Accessed 18 December
2017].
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APPENDIX
A Charging Procedure
This is the charging procedure for the first two steps of the battery capacity tests in section
6.7.4, which was summarised earlier in Table 6-13. The following figures show battery 3
charging to 20.2V as an example.
Figure A-1 Charging current (b) coulomb counting.
Figure A-1(a) shows the charging current as logged by sensor ACS3. CC 4.7A charging
occurs from 0s to about 3900s, while the remaining section is CV charging. Figure A-1 (b) is
the amount of charge which has been charged to the battery so far (The plot is in the negative
region because charging has a negative convention).
Figure A-2 Charging voltage.
202
Figure A-2 shows the battery voltage over time. Again, the CC region is from 0s to about
3900s, and 20.2V CV charging takes up the remainder of the time.
B Scaling
In section 6.2, dimensional analysis for scaling the experiment was discussed. The full
dimensional analysis workings are found here.
The torque is dependent on 7 variables (n=7), with 3 base dimensions (m=3).
𝑇 = 𝑓(𝜌, 𝜇, 𝑣, 𝐿, 𝜔, 𝐹) (A-1)
The meaning of the symbols are shown in the following table,
Table A-1 Symbols and their meanings for scaling derivation.
Symbol Meaning Symbol Meaning
k Scaling ratio M Mass, basic dimension
τ Torque L Length, basic dimension
ρ Density T Time, basic dimension
µ Dynamic viscosity CD Drag Coefficient
v Velocity Re Reynolds Number
L Length Xa a subscript for ‘actual’
ω Angular velocity Xm m subscript for small-scale
‘model’
F Force
203
The dimensional analysis is performed as follows,
Choosing ρ, v, L
Π1 = 𝜏𝜌𝑎1𝑣𝑏1𝐿𝑐1
Π2 = 𝜇𝜌𝑎2𝑣𝑏2𝐿𝑐2
Π3 = 𝜔𝜌𝑎3𝑣𝑏3𝐿𝑐3
Π4 = 𝐹𝜌𝑎4𝑣𝑏4𝐿𝑐4
Π1 = [𝑀𝐿2𝑇−2][𝑀𝐿−3]𝑎1[𝐿𝑇−1]𝑏1[𝐿]𝑐1 = 𝑀1+𝑎1𝐿2−3𝑎1+𝑏1+𝑐1𝑇−2−𝑏1
= 𝑀0𝐿0𝑇0
𝑆𝑜𝑙𝑣𝑖𝑛𝑔, 𝑎1 = −1, 𝑏1 = −2, 𝑐1 = −2 + 3𝑎1 − 𝑏1 = −3
Π1 =𝜏
𝜌𝑣2𝐿3
Π2 =𝜌𝑣𝐿
𝜇= 𝑅𝑒
Π3 = [𝑇−1][𝑀𝐿−3]𝑎3[𝐿𝑇−1]𝑏3[𝐿]𝑐3 = 𝑀𝑎3𝐿−3𝑎3+𝑏3+𝑐3𝑇−1−𝑏3 = 𝑀0𝐿0𝑇0
𝑎3 = 0, 𝑏3 = −1, 𝑐3 = 3𝑎3 − 𝑏3 = 1
Π3 =𝜔𝐿
𝑣
Π4 =2𝐹
𝜌𝑣2𝐿2= 𝐶𝐷
𝑇
𝜌𝑣2𝐿3= 𝑓 (
𝜌𝑣𝐿
𝜇,𝜔𝐿
𝑣,2𝐹
𝜌𝑣2𝐿2)
(A-2)
204
For complete similarity,
𝜌𝑎 = 𝜌𝑚 , 𝜇𝑎 = 𝜇𝑚
(𝜌𝑣𝐿
𝜇)𝑎
= (𝜌𝑣𝐿
𝜇)𝑚
𝐿𝑚𝐿𝑎
=𝑣𝑎𝑣𝑚
(2𝐹
𝜌𝑣2𝐿2)𝑎
= (2𝐹
𝜌𝑣2𝐿2)𝑚
𝐹𝑎𝐹𝑚
=𝑣𝑎2𝐿𝑎2
𝑣𝑚2 𝐿𝑚2= (
𝐿𝑚𝐿𝑎)2
(𝐿𝑎𝐿𝑚)2
= 1 (𝐷𝑟𝑖𝑣𝑖𝑛𝑔 𝑓𝑜𝑟𝑐𝑒 𝑑𝑜𝑒𝑠 𝑛𝑜𝑡 𝑐ℎ𝑎𝑛𝑔𝑒)
(𝜔𝐿
𝑣)𝑎= (
𝜔𝐿
𝑣)𝑚
𝜔𝑎𝜔𝑚
=𝑣𝑎𝑣𝑚
𝐿𝑚𝐿𝑎
= (𝐿𝑚𝐿𝑎)2
(𝜏
𝜌𝑣2𝐿3)𝑎
= (𝜏
𝜌𝑣2𝐿3)𝑚
𝜏𝑎𝜏𝑚
=𝑣𝑎2𝐿𝑎3
𝑣𝑚2 𝐿𝑚3 = (
𝐿𝑚𝐿𝑎)2
(𝐿𝑎𝐿𝑚)3
=𝐿𝑎𝐿𝑚
This results in the scaling law,
𝐿𝑚𝐿𝑎
=𝑣𝑎𝑣𝑚
=𝜏𝑚𝜏𝑎= √
𝜔𝑎𝜔𝑚
= 𝑘
(A-3)
Further calculations are performed to get the power scaling into the equation,
𝜏𝑎 = 𝜏𝑚
√𝜔𝑚
√𝜔𝑎
(A-4)
205
𝑃𝑎𝑃𝑚
=𝜏𝑎𝜔𝑎𝜏𝑚𝜔𝑚
=𝜏𝑚√𝜔𝑚 𝜔𝑎
𝜏𝑚𝜔𝑚√𝜔𝑎= 𝑘
(A-5)
It turns out that the force scaling is a 1:1 ratio as shown by,
𝐹𝑚𝐹𝑎=𝑚𝑚𝑎𝑚𝑚𝑎𝑎𝑎
=𝑚𝑚𝑣𝑚𝑚𝑎𝑣𝑎
=𝑚𝑚
𝑚𝑎
1
𝑘= 1
𝑚𝑚
𝑚𝑎= 𝑘
(A-6)
This results in the final scaling law as,
𝐿𝑚𝐿𝑎
=𝑣𝑎𝑣𝑚
=𝜏𝑚𝜏𝑎= √
𝜔𝑎𝜔𝑚
=𝑃𝑎𝑃𝑚
=𝑚𝑚
𝑚𝑎= 𝑘
(A-7)
206
C Sensor Circuits
These are the sensor circuits used for the experiment as discussed in section 6.1.3
Figure A-3 Voltage sensors and filters.
to voltage measurement to voltage measurement
to μC
9V power
supply input
Voltage divider
1st order RC filter
2nd order Sallen-
key filter
1st order RC filter
207
Figure A-4 Current sensor filters, precision voltage reference and thermistor.
to μC
to current
sensor
to μC
to
thermistor
1st order RC filter
Precision voltage
reference
9V power
supply input
208
Figure A-5 Relays.
to μC
to fan
Optoisolators
Main relay
to MOSEFT
drivers
15V power
supply input
UC relay
Switches for user