Control Strategies for Series

Hybrid Electric Vehicles

Wassif Shabbir

A thesis submitted for the degree of

Doctor of Philosophy
August 2015

Control and Power Group

Electrical and Electronic Engineering
Imperial College London
I declare that this thesis is the result of my own work, and that any ideas or quotations from the
work of other people are appropriately referenced.

The copyright of this thesis rests with the author and is made available under a Creative Commons
Attribution Non-Commercial No Derivatives licence. Researchers are free to copy, distribute or
transmit the thesis on the condition that they attribute it, that they do not use it for commercial
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researchers must make clear to others the licence terms of this work.
 Abstract
This thesis deals with the energy management problem of series hybrid electric
vehicles (HEVs), where the objective is to maximize fuel economy for general driving.
The work employs a high-fidelity model that has been refined to deliver appropriate
level of dynamics (for the purposes of this research) at an acceptable computational
burden. The model is then used to design, test and study established conventional
control strategies, which then act as benchmarks and inspiration for proposed novel
control strategies.

A family of efficiency maximizing map strategies (EMMS) are developed based on a

thorough and holistic analysis of the powertrain efficiencies. The real-time variants
are found to deliver impressive fuel economy, and the global variant is found to out-
perform the conventional global benchmark. Two heuristic strategies are developed
(exclusive operation strategy (XOS) and optimal primary source strategy (OPSS))
that are found to deliver significantly better fuel economy results, compared to con-
ventional alternatives, and further desirable traits. This is found to be particularly
related to the better use of modern start stop systems (SSSs) that has not been
considered sufficiently in the past.

A global heuristic strategy (GHS) is presented that successfully outperforms the

conventional global benchmark without any particularly complex analysis. This
exposes some of the limitations of optimization-based techniques that have been
developed for simple vehicle models. Lastly, the sensitivity of the performance of the
control strategies has been studied for variations in tuning accuracy, SSS efficiency,
vehicle initial conditions, and general driving conditions. This allows a deeper insight
into each control strategy, exposing strengths and limitations that have not been
apparent from past work.
 Acknowledgments
First and foremost, I would like to thank my supervisor Dr. Simos Evangelou, who
has offered timely support and guidance whenever needed. He encouraged me to
explore a wide range of research interests, which kept expanding from our stimulating
conversations, contributing greatly to my productivity as well as how much I enjoyed
my research. Aside from the happy times at Imperial, I will cherish the memories
of our amazing time in South Carolina, Hawaii and South Africa together.

It has also been a privilege to work with Prof. Meisel, whose immense practical
knowledge of vehicles has been invaluable to me. Working and publishing together
with him has undoubtedly made me a better researcher, and made me appreciate
my research in a broader context.

A special thanks to Carlos, who has been taking his PhD journey alongside me.
When I got stuck or had a problem, he would be the first person I would discuss
it with. Apart from the research, I have also really enjoyed our frequent breaks,
together with Hadi and Zohaib, discussing anything between heaven and earth.
Every day has been a joy.

These years would have been less incredible, if it was not for all the friends I met
in London. A lot of great memories with Andy, Atsushi, Cheng and Saad through-
out the Imperial days, always providing perspective. I am also grateful for all the
amazing people I got to work with through ICCS and ICG: these times have been
an integral part of my life at Imperial.

Finally, I am deeply grateful for my family and their unconditional love and en-
couragement. Particular thanks to Saddaf who offered valuable feedback in the
completion of this thesis. My visits back home were always refreshing, in particular
when seeing my niece and nephews Isabella, Fawad and Noah.
Contents

Abstract 3

Acknowledgments 5

List of Figures 11

List of Tables 15

List of Publications 17

Abbreviations 19

1 Introduction 21
1.1 Rationale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.2 Scope and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2 Vehicle Model 27
2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.1.1 Brief History . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.1.2 Electrification . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.1.3 Architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.2 Propulsion Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.2.1 Car dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.2.2 Permanent Magnet Synchronous Motor . . . . . . . . . . . . . 35
2.2.3 Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.2.4 Continuously Variable Transmission . . . . . . . . . . . . . . . 39
2.3 Primary Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.3.1 Internal Combustion Engine . . . . . . . . . . . . . . . . . . . 41
2.3.2 Permanent Magnet Synchronous Generator . . . . . . . . . . . 43
2.3.3 Rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.3.4 Overall Operation . . . . . . . . . . . . . . . . . . . . . . . . . 45

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2.4 Secondary Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.4.1 Battery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.4.2 DC-DC Converter . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.5 System Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.5.1 Overall Powertrain . . . . . . . . . . . . . . . . . . . . . . . . 51
2.5.2 Supervisory Control System . . . . . . . . . . . . . . . . . . . 53
2.5.3 Start Stop System . . . . . . . . . . . . . . . . . . . . . . . . 55
2.5.4 Overall Model Characteristics . . . . . . . . . . . . . . . . . . 56
2.6 Simulation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.6.1 Driving Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.6.2 Fuel Economy Evaluation . . . . . . . . . . . . . . . . . . . . 62
2.6.3 Simulation Speed Improvements . . . . . . . . . . . . . . . . . 68
2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

3 Conventional Strategies 75
3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.1.1 Rule-based Strategies . . . . . . . . . . . . . . . . . . . . . . . 76
3.1.2 Real-time Optimization-based Strategies . . . . . . . . . . . . 80
3.1.3 Global Optimization-based Controllers . . . . . . . . . . . . . 84
3.2 Thermostat Control Strategy . . . . . . . . . . . . . . . . . . . . . . 88
3.2.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.2.2 Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.2.3 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.3 Power Follower Control Strategy . . . . . . . . . . . . . . . . . . . . . 96
3.3.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.3.2 Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.3.3 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.4 Global Equivalent Consumption Minimization Strategy . . . . . . . . 105
3.4.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.4.2 Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.4.3 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

4 Efficiency Maximizing Map Strategies 115

4.1 Design Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.2 Powertrain Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.2.1 Primary Source . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.2.2 Secondary Source . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.2.3 Total Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.3 Efficiency Maximizing Map Strategy 0 . . . . . . . . . . . . . . . . . 124
4.3.1 Control Approach . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.3.2 Efficiency Maximizing Map . . . . . . . . . . . . . . . . . . . 125
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4.3.3 Charge Sustaining Operation . . . . . . . . . . . . . . . . . . 129

4.3.4 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.4 Efficiency Maximizing Map Strategy 1 . . . . . . . . . . . . . . . . . 138
4.4.1 Modified Efficiency Maximizing Map . . . . . . . . . . . . . . 138
4.4.2 Charge Sustaining Operation . . . . . . . . . . . . . . . . . . 143
4.4.3 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
4.5 Global Efficiency Maximizing Map Strategy . . . . . . . . . . . . . . 153
4.5.1 Global Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
4.5.2 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
4.5.3 Relation to GECMS . . . . . . . . . . . . . . . . . . . . . . . 161
4.6 Efficiency Maximizing Map Strategy 2 . . . . . . . . . . . . . . . . . 163
4.6.1 Real-time Adaption of GEMMS . . . . . . . . . . . . . . . . . 163
4.6.2 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
4.7 Comparison of Optimization-based Strategies . . . . . . . . . . . . . 171
4.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

5 Heuristic Strategies 177

5.1 Design Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
5.1.1 Fuel Economy Optimizing Mechanisms . . . . . . . . . . . . . 178
5.1.2 Charge Sustaining Mechanisms . . . . . . . . . . . . . . . . . 180
5.1.3 Implementation Mechanisms . . . . . . . . . . . . . . . . . . . 184
5.2 Exclusive Operation Strategy . . . . . . . . . . . . . . . . . . . . . . 186
5.2.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
5.2.2 Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
5.2.3 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
5.3 Optimal Primary Source Strategy . . . . . . . . . . . . . . . . . . . . 197
5.3.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
5.3.2 Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
5.3.3 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
5.4 Comparison of Heuristic Strategies . . . . . . . . . . . . . . . . . . . 207
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

6 Global Optimality 213

6.1 Global Heuristic Strategy . . . . . . . . . . . . . . . . . . . . . . . . . 214
6.1.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
6.1.2 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
6.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
6.2.1 Causes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
6.2.2 Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
6.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
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7 Control Sensitivity Analysis 231

7.1 Tuning Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
7.2 Start Stop System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
7.3 Initial Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
7.4 Driving Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

8 Conclusion 247
8.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
8.2 Future Research Direction . . . . . . . . . . . . . . . . . . . . . . . . 250

Bibliography 253
List of Figures

2.1 Overall model block diagram . . . . . . . . . . . . . . . . . . . . . . . 28

2.2 PMSM efficiency map . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.3 Inverter efficiency profile . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.4 CVT implementation block diagram . . . . . . . . . . . . . . . . . . . 40
2.5 ICE break specific fuel consumption (BSFC) map . . . . . . . . . . . 42
2.6 PMSG efficiency map . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.7 Rectifier efficiency profile . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.8 PS break specific fuel consumption (BSFC) map . . . . . . . . . . . . 46
2.9 Look-up profile for preferred engine speed . . . . . . . . . . . . . . . 46
2.10 Fuel consumption profile . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.11 DC-DC converter efficiency profile . . . . . . . . . . . . . . . . . . . . 50
2.12 Electric connection of powertrain . . . . . . . . . . . . . . . . . . . . 51
2.13 Control loops for overall model . . . . . . . . . . . . . . . . . . . . . 52
2.14 Simulink implementation of the SCS . . . . . . . . . . . . . . . . . . 54
2.15 Simulink implementation of the SSS . . . . . . . . . . . . . . . . . . . 56
2.16 Speed profile of driving cycles . . . . . . . . . . . . . . . . . . . . . . 60
2.17 Correlations between electrical and fuel energy for wide range . . . . 65
2.18 Correlations between electrical and fuel energy for narrow range . . . 66
2.19 Simulink implementation of the reduced model . . . . . . . . . . . . . 70
2.20 Simulink implementation of the overall model . . . . . . . . . . . . . 71

3.1 TCS: operation schematic . . . . . . . . . . . . . . . . . . . . . . . . 89

3.2 TCS: stateflow diagram . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.3 TCS: normalized EFC and final SOC . . . . . . . . . . . . . . . . . . 90
3.4 TCS: normalized total EFC . . . . . . . . . . . . . . . . . . . . . . . 91
3.5 TCS: first iteration of power profiles . . . . . . . . . . . . . . . . . . . 93
3.6 TCS: second iteration of power profiles . . . . . . . . . . . . . . . . . 94
3.7 PFCS: operation schematic . . . . . . . . . . . . . . . . . . . . . . . . 97
3.8 PFCS: stateflow diagram . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.9 PFCS: normalized EFC and final SOC . . . . . . . . . . . . . . . . . 99
3.10 PFCS: normalized total EFC . . . . . . . . . . . . . . . . . . . . . . . 100
3.11 PFCS: first iteration of power profiles . . . . . . . . . . . . . . . . . . 101
3.12 PFCS: second iteration of power profiles . . . . . . . . . . . . . . . . 102

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3.13 PFCS alternative design: power profiles . . . . . . . . . . . . . . . . . 103

3.14 GECMS: normalized EFC and final SOC for wide range . . . . . . . . 107
3.15 GECMS: normalized EFC and final SOC for narrow range . . . . . . 108
3.16 GECMS: power share profile . . . . . . . . . . . . . . . . . . . . . . . 110
3.17 GECMS: Simulink implementation . . . . . . . . . . . . . . . . . . . 111
3.18 GECMS: first iteration of power profiles . . . . . . . . . . . . . . . . 112

4.1 PS efficiency map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

4.2 SS efficiency map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.3 Simulink implementation of EMMS . . . . . . . . . . . . . . . . . . . 125
4.4 Non-CS EMMS0: power share profiles and corresponding efficiency . 127
4.5 Non-CS EMMS0: normalized EFC and final SOC . . . . . . . . . . . 128
4.6 Non-CS EMMS0: normalized total EFC . . . . . . . . . . . . . . . . 129
4.7 EMMS0: charge sustaining function . . . . . . . . . . . . . . . . . . . 130
4.8 EMMS0: power share profiles and corresponding efficiency . . . . . . 131
4.9 EMMS0: normalized EFC and final SOC . . . . . . . . . . . . . . . . 133
4.10 EMMS0: normalized total EFC . . . . . . . . . . . . . . . . . . . . . 134
4.11 EMMS0: first iteration of power profiles . . . . . . . . . . . . . . . . 135
4.12 EMMS0: final iteration of power profiles . . . . . . . . . . . . . . . . 136
4.13 Non-CS EMMS1: power share profiles and corresponding efficiency . 141
4.14 Non-CS EMMS1: normalized EFC and final SOC . . . . . . . . . . . 142
4.15 Non-CS EMMS1: normalized total EFC . . . . . . . . . . . . . . . . 143
4.16 EMMS1: Replenishing efficiency profiles . . . . . . . . . . . . . . . . 144
4.17 EMMS1: power share profiles and corresponding efficiency . . . . . . 145
4.18 EMMS1: normalized EFC and final SOC . . . . . . . . . . . . . . . . 147
4.19 EMMS1: normalized total EFC . . . . . . . . . . . . . . . . . . . . . 148
4.20 EMMS1: first iteration of power profiles . . . . . . . . . . . . . . . . 149
4.21 EMMS1: final iteration of power profiles . . . . . . . . . . . . . . . . 150
4.22 EMMS1: WL-E power profiles . . . . . . . . . . . . . . . . . . . . . . 152
4.23 GEMMS: normalized EFC and final SOC . . . . . . . . . . . . . . . . 155
4.24 GEMMS: power share profiles . . . . . . . . . . . . . . . . . . . . . . 156
4.25 GEMMS: first iteration of power profiles . . . . . . . . . . . . . . . . 158
4.26 GEMMS: final iteration of power profiles . . . . . . . . . . . . . . . . 159
4.27 Comparison of GECMS and GEMMS power share profiles . . . . . . 162
4.28 EMMS2: normalized EFC and final SOC . . . . . . . . . . . . . . . . 165
4.29 EMMS2: normalized total EFC . . . . . . . . . . . . . . . . . . . . . 166
4.30 EMMS2: power share profiles and corresponding efficiency . . . . . . 167
4.31 EMMS2: first iteration of power profiles . . . . . . . . . . . . . . . . 168
4.32 EMMS2: final iteration of power profiles . . . . . . . . . . . . . . . . 169
4.33 Comparison of SOC profiles for EMMS . . . . . . . . . . . . . . . . . 172
4.34 Comparison of fuel economy for EMMS . . . . . . . . . . . . . . . . . 174
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5.1 Power share profile for load leveling strategy . . . . . . . . . . . . . . 179

5.2 Power share profile for load following strategy . . . . . . . . . . . . . 179
5.3 Power share profile when employing threshold changing mechanism . 181
5.4 Power share profile when employing power changing mechanism . . . 182
5.5 XOS: operation schematic . . . . . . . . . . . . . . . . . . . . . . . . 186
5.6 Efficiency profiles for PS and SS . . . . . . . . . . . . . . . . . . . . . 188
5.7 XOS: power share profile . . . . . . . . . . . . . . . . . . . . . . . . . 189
5.8 XOS: Simulink implementation . . . . . . . . . . . . . . . . . . . . . 190
5.9 XOS: normalized EFC and final SOC . . . . . . . . . . . . . . . . . . 191
5.10 XOS: normalized total EFC . . . . . . . . . . . . . . . . . . . . . . . 192
5.11 XOS: first iteration of power profiles . . . . . . . . . . . . . . . . . . 194
5.12 XOS: final iteration of power profiles . . . . . . . . . . . . . . . . . . 195
5.13 OPSS: operation schematic . . . . . . . . . . . . . . . . . . . . . . . . 198
5.14 OPSS: power share profile . . . . . . . . . . . . . . . . . . . . . . . . 199
5.15 OPSS: Simulink implementation . . . . . . . . . . . . . . . . . . . . . 200
5.16 OPSS: normalized EFC and final SOC . . . . . . . . . . . . . . . . . 201
5.17 OPSS: normalized total EFC . . . . . . . . . . . . . . . . . . . . . . . 202
5.18 OPSS: first iteration of power profiles . . . . . . . . . . . . . . . . . . 204
5.19 OPSS: final iteration of power profiles . . . . . . . . . . . . . . . . . . 205
5.20 Comparison of SOC profiles for heuristic strategies . . . . . . . . . . 208
5.21 Comparison of fuel economy for heuristic strategies . . . . . . . . . . 210

6.1 GHS: power share profile . . . . . . . . . . . . . . . . . . . . . . . . . 215

6.2 GHS: normalized EFC and final SOC . . . . . . . . . . . . . . . . . . 217
6.3 GHS: first iteration of power profiles . . . . . . . . . . . . . . . . . . 219
6.4 GHS: final iteration of power profiles . . . . . . . . . . . . . . . . . . 220

7.1 Sensitivity of normalized EFC to tuning parameters . . . . . . . . . . 233

7.2 Sensitivity of normalized EFC to SSS trade-off time . . . . . . . . . . 236
7.3 Sensitivity of normalized EFC to initial SOC conditions . . . . . . . . 238
7.4 Sensitivity of EFC to initial SOC conditions . . . . . . . . . . . . . . 240
7.5 Sensitivity of EFC to choice of driving cycle . . . . . . . . . . . . . . 243
7.6 Sensitivity of relative EFC to choice of driving cycle . . . . . . . . . . 243
7.7 Sensitivity of final SOC to choice of driving cycle . . . . . . . . . . . 245
List of Tables

2.1 Parameter values for friction torques Tf m (and Tf g ) . . . . . . . . . . 36

2.2 Parameters for PMSM (and PMSG) . . . . . . . . . . . . . . . . . . . 36
2.3 Parameter values of the Li-Ion battery . . . . . . . . . . . . . . . . . 49
2.4 Parameter values for PI controllers . . . . . . . . . . . . . . . . . . . 53
2.5 Physical states in the vehicle model . . . . . . . . . . . . . . . . . . . 58
2.6 Features of the speed profiles for the four driving cycles . . . . . . . . 61
2.7 EFC factors as determined by the correlation between Ef and Ee . . 66
2.8 Comparison of simulation speeds . . . . . . . . . . . . . . . . . . . . 72
2.9 Comparison of simulation errors . . . . . . . . . . . . . . . . . . . . . 72

3.1 Fuel economy results for TCS . . . . . . . . . . . . . . . . . . . . . . 95

3.2 Fuel economy results for PFCS . . . . . . . . . . . . . . . . . . . . . 104
3.3 Optimal equivalence factor values . . . . . . . . . . . . . . . . . . . . 111
3.4 Fuel economy results for GECMS . . . . . . . . . . . . . . . . . . . . 113
3.5 Overview of control strategies for series HEVs . . . . . . . . . . . . . 114

4.1 Definition of CS function kcs . . . . . . . . . . . . . . . . . . . . . . . 130

4.2 Fuel economy results for EMMS0 . . . . . . . . . . . . . . . . . . . . 137
4.3 Fuel economy results for EMMS1 . . . . . . . . . . . . . . . . . . . . 152
4.4 Optimal replenishing efficiency values for GEMMS . . . . . . . . . . . 154
4.5 Fuel economy results for GEMMS . . . . . . . . . . . . . . . . . . . . 160
4.6 Fuel economy results for EMMS2 . . . . . . . . . . . . . . . . . . . . 170
4.7 Choice of correction factor v . . . . . . . . . . . . . . . . . . . . . . . 175

5.1 Fuel economy results for XOS . . . . . . . . . . . . . . . . . . . . . . 196

5.2 Fuel economy results for OPSS . . . . . . . . . . . . . . . . . . . . . 206
5.3 Possible design principles for control of HEVs . . . . . . . . . . . . . 211

6.1 Fuel economy results for GHS . . . . . . . . . . . . . . . . . . . . . . 221

7.1 Additional driving cycles tested . . . . . . . . . . . . . . . . . . . . . 242

15
List of Publications

Journal Articles
• M. Roche, W. Shabbir, and S. A. Evangelou, “Voltage control for enhanced power electronic
efficiency in series hybrid electric vehicles,” IEEE Transactions on Vehicular Technology,
in review.
• W. Shabbir and S. A. Evangelou, “Exclusive operation strategy for the supervisory control
of series hybrid electric vehicles,” IEEE Transactions on Control Systems Technology, in
press.
• W. Shabbir and S. A. Evangelou, “Real-time control strategy to maximize hybrid electric
vehicle powertrain efficiency,” Applied Energy, vol. 135, pp. 512–522, 2014.

Conference Articles
• S. A. Evangelou and W. Shabbir, “Dynamic modeling platform for series hybrid electric
vehicles,” in Advances in Automotive Control (AAC), IFAC, in review.
• J. Meisel, W. Shabbir, and S. A. Evangelou, “Control of PHEV and HEV parallel power-
trains using a sequential linearization algorithm,” in SAE World Congress, SAE Technical
Paper, 2015.
• W. Shabbir and S. A. Evangelou, “Efficiency analysis of a continuously variable transmis-
sion with linear control for a series hybrid electric vehicle,” in IFAC World Congress, vol.
19, pp. 6264–6269, 2014.
• J. Meisel, W. Shabbir, and S. A. Evangelou, “Evaluation of the through-the-road archi-
tecture for plug-in hybrid electric vehicle powertrains,” in International Electric Vehicle
Conference (IEVC), pp. 1–5, IEEE, 2013.
• J. Meisel, W. Shabbir, and S. A. Evangelou, “A practical control methodology for parallel
plug-in hybrid electric vehicle powertrains,” in Vehicle Power and Propulsion Conference
(VPPC), pp. 1–6, IEEE, 2013.
• W. Shabbir and S. A. Evangelou, “Efficiency maximizing and charge sustaining supervisory
control for series hybrid electric vehicles,” in Conference on Decision and Control (CDC),
pp. 6327–6332, IEEE, 2012.
• W. Shabbir, C. Arana, and S. A. Evangelou, “Series hybrid electric vehicle supervisory con-
trol based on off-line efficiency optimization,” in International Electric Vehicle Conference
(IEVC), pp. 1–5, IEEE, 2012.

17
Abbreviations

AL Algebraic Loop
BSFC Break Specific Fuel Consumption
CS Charge Sustaining
CSI Charge Sustaining Intensity
CVT Continuously Variable Transmission
DP Dynamic Programming
ECMS Equivalent Consumption Minimization Strategy
EFC Equivalent Fuel Consumption
FLC Fuzzy Logic Controller
EMMS Efficiency Maximizing Map Strategy
GECMS Global Equivalent Consumption Minimization Strategy
GEMMS Global Efficiency Maximizing Map Strategy
GHS Global Heuristic Strategy
HEV Hybrid Electric Vehicle
ICE Internal Combustion Engine
MPC Model Predictive Control
NN Neural Networks
OPSS Optimal Primary Source Strategy
PFCS Power Follower Control Strategy
PHEV Plug-in Hybrid Electric Vehicle
PL Propulsion Load
PMP Pontryagin’s Minimum Principle

19
20

PMSG Permanent Magnet Synchronous Generator

PMSM Permanent Magnet Synchronous Motor
PS Primary Source of energy
SCS Supervisory Control System
SOC State Of Charge
SS Secondary Source of energy
SSS Start Stop System
TCS Thermostat Control Strategy
WLTP Worldwide harmonized Light vehicles Test Procedure
XOS Exclusive Operation Strategy
Chapter 1

Introduction

1.1 Rationale

The world is facing tremendous challenges ahead: CO2 levels are alarmingly high
and are steadily rising; consumption of the finite supply of oil is increasing; and world
energy consumption is unreservedly on the rise. These issues are critically relevant
in addressing the threat of climate change, which is by many seen as the greatest
challenge for this generation. A concerted push by NGOs, scientists and activists
has seen these challenges receive an increasing amount of attention from regulators,
industry and consumers. In particular, the personal transport industry has been
recognized as a major area of improvement. Since the 1970s the greenhouse gas
(GHG) emissions from transport have doubled, and the rapid adoption of personal
vehicles in India and China has made the necessity of sustainable transport more
urgent.

An essential step towards addressing these stated problems has to be a reduction

of energy consumed by cars. Shifting from fossil fuels to electric energy is quite
useful, as the macro-level generation of energy is going to be more efficient than a
small engine in each car (even with consideration for the transmission of energy).
However, the average consumer is not willing to sacrifice the convenience of easy
and quick refueling for a limited gain in fuel economy. A balance can be found in
the design of hybrid electric vehicles (HEVs), which enjoys both the convenience

21
22 Chapter 1

and range (due to fuel density) from engines, and the cleaner and cheaper energy of
electric motors.

This pursuit of HEVs has seen commercial success for the past decade, with Toyota
and Honda leading the way at the turn of the millennium. However, there is an
ongoing effort to push for even better fuel economy from these vehicles and make
them more competitive. This can be done by refining the component design, choice
of materials and aerodynamics. However, an essential and cost effective measure is
to improve upon the supervisory control system (SCS) of the HEV, such that the
powertrain is operated more efficiently. The key decision for the SCS is to determine
how the load power should be split between the multiple energy sources of the
powertrain. There is scope to significantly improve the fuel economy of a vehicle at
some developmental cost but a negligible variable cost for each manufactured car.

The academic research in this field has been active for the past two decades and has
seen several significant developments. Tools and frameworks have been developed
that help the design, implementation or validation of SCSs. A majority of the
techniques being used recently are established concepts from other applications, such
as dynamic programming (DP), model predictive control (MPC), game theory (GT),
genetic algorithms (GA) and neural networks (NN). However, the research on control
of HEVs has seen the development of the equivalent consumption minimization
strategy (ECMS) and the concept of equivalent fuel consumption (EFC) which are
novel and powerful. This area of research is thus not simply applying old techniques
to new problems, but fundamentally developing new tools to address these new
problems.

However, a vast majority of the research so far has been done with quite simple static
models. The few publications that have experimental data often show a larger error
between simulation and experimental data, than between the various studied control
strategies. As the research community has pursued the more advanced control theory
concepts, it has often been at the expense of the model complexity and accuracy.
The validity of a control strategy will ever only be as good as the model it is tested
on. Also, with regard to heuristic or rule-based strategies (which are still dominant
in commercial HEVs) the research has been quite stagnant. The main heuristic
strategies are from the mid-1990s.
Introduction 23

Despite this being an active research topic, there has been several calls for further
research in this field. The IEEE Control Systems Society published a document
on the most important areas of research for control theory and control engineering,
and the SCS for HEVs was among the recommended focus areas [1]. Several recent
review papers on the control of HEVs have highlighted the stagnant nature of recent
work, and the need for control strategies to be designed and tested on more realistic
models [2, 3].

1.2 Scope and Objectives

This work builds on past work by Dr. Evangelou that has involved developing a
high-fidelity HEV model [4–6]. This model can be employed to test and analyze
the conventional control strategies from the literature, as well as to develop novel
control strategies. The richness of the model is expected to not only allow for more
reliable results, but to also expose different dynamics which lead to new control
requirements. Also, as the model is of a series architecture, it allows the study and
design of SCSs for series HEVs that have received less attention in the academic
literature than the parallel or power-split architecture.

The research conducted as part of this PhD, has involved a very wide range of
problems being studied. A significant portion of the research activity was on control
of through-the-road (TTR) parallel plug-in hybrid electric vehicles (PHEVs). This
research was done together with Prof. Meisel from Georgia Institute of Technology,
and has led to three publications [7–9]. However, being a PHEV, with a TTR
architecture, this research meant a very different control problem. The vehicle used
for that research was a hybridized Ford Explorer and the model was very different
as well. As such, it was considered best to limit the scope of this thesis to only my
work on series HEVs.

For the work on series HEVs, an additional fifteen projects were pursued together
with final year undergraduate and postgraduate students. This included: four
projects on controlling the voltage of the DC bus (some results being published
in [10]); four projects on modeling and controlling emissions; four projects on mod-
eling and controlling the battery health; two projects on optimal control; and one
project on model predictive control (MPC). The work on each of these research
24 Chapter 1

paths have evolved quite far over the past four years, mainly by the students them-
selves but with significant guidance from me. These work packages could have been
a chapter each, but they still have many remaining loose ends. This work will need
to be refined and consolidated at a later stage.

A few additional research paths were also explored, almost as a necessity to facilitate
the main objectives of this project. In particular, significant efforts were put into
refining the vehicle model that is at the core of this project. Some of these contri-
butions are mentioned in Chapter 2 where appropriate, but have not been expanded
upon in detail. This modeling work is being published in [6]. Quite related to this,
an efficiency study was done on the continuously variable transmission (CVT) used
in the vehicle model, which was published separately in [11]. This has not been
included in this thesis either.

Thus, this thesis will be exclusively focused on the supervisory control of series
HEVs with the objective to improve the fuel economy. The efficiency maximizing
map strategy 0 (EMMS0) has been previously published [12–14], but all the results in
this thesis are new and based on an updated model (from the past few months). Also,
the control strategy has been evolved further, which will be presented as EMMS1
and EMMS2 in Chapter 4. Similarly, the exclusive operation strategy (XOS) in
Chapter 5 is being published in [15] but the results in this thesis have been updated.
The approach has been to reimplement and resimulate all past work to ensure that
all results are obtained for the same vehicle model, thus allowing valid comparison.

The main objectives of this thesis can be stated as follows:

1. To employ a high-fidelity HEV model that is suitable to test control strategies

2. To study and learn from existing work on control strategies

3. To design control strategies for HEVs based on analysis of the powertrain

4. To design heuristic control strategies that are suitable for modern HEVs

5. To expose the benefits of a high-fidelity model when testing control strategies

6. To understand the sensitivity of control strategies

These objectives can in order loosely be associated with each of the chapters from
Chapter 2 to Chapter 7.
Introduction 25

1.3 Outline

This thesis will begin by describing the vehicle model, which will be used throughout
the rest of the thesis. Thereafter the conventional strategies from the literature will
be described and a few will be implemented into Simulink. This will be followed by
the design of a family of novel control strategies that aim to maximize the powertrain
efficiency. The insights gained from these strategies, as well as the conventional
strategies, will be used to design two novel heuristic strategies, which are found to
perform well. The remarkable performance of the heuristic strategies will lead to a
discussion about the nature of global optimal solution for HEVs and their reliability.
Finally, a sensitivity study will be done to test the various designed strategies. Each
chapter is described briefly below.

Chapter 2 The modeling of the powertrain components are described together

with their interconnection. Emphasis is given on core operational behavior related to
the efficiency and performance of the components, as well as the significant changes
and updates from the original model. Simulation methods and how they are applied
within latter chapters of the thesis are also introduced and clarified.

Chapter 3 The conventional strategies are introduced by a brief literature review,

covering separately the heuristic strategies, the real-time optimization-based strate-
gies and the global optimization-based strategies. This is followed by the description,
tuning and implementation of three conventional control strategies: thermostat con-
trol strategy (TCS), power follower control strategy (PFCS) and global equivalent
consumption minimization strategy (GECMS).

Chapter 4 A family of control strategies are developed, with the objective of max-
imizing powertrain efficiency. The powertrain efficiency is analyzed, which includes
the use of replenishing efficiencies to consider the battery usage more holistically.
Based on the definition of the replenishing efficiencies, three different real-time con-
trol strategies are developed: EMMS0, EMMS1 and EMMS2. These outperform the
conventional rule-based strategies and approach the GECMS performance. A global
version of the developed strategies, GEMMS, is found to be more effective than the
GECMS.
26 Chapter 1

Chapter 5 Insights from past control strategies are discussed and formalized into
design principles, which are then used to design two distinct heuristic strategies: the
exclusive operation strategy (XOS) and optimal primary source strategy (OPSS).
Both of these are found to deliver good performance, with the latter approaching
the fuel economy realized by GECMS.

Chapter 6 The impressive performance of OPSS is developed further with the

global heuristic strategy (GHS), which allows two tunable parameters with advance
knowledge of the driving cycle. This heuristic strategy is found to outperform the
GECMS and GEMMS by a significant margin. The causes for this unexpected result
are explored and its impact on the wider body of work is discussed.

Chapter 7 The sensitivity of the real-time strategies presented in this work is

studied. This includes the sensitivity of the strategies to: correct tuning; effective-
ness of the start stop system (SSS); initial conditions of the battery; and changes
in driving cycle. It is found that the proposed novel strategies are more suitable for
modern HEVs with good SSSs.

Chapter 8 Conclusions are made for the whole thesis and contributions are sum-
marized. This is followed by an outline of future directions for this research.
Chapter 2

Vehicle Model

The vehicle model used in this work is based on work by Dr. Evangelou and Dr. Shukla
[4–6]. When referring to earlier versions of the model, this work will often refer to
Model0 and Model1. Model0 refers to the model inherited at the start of this re-
search (September 2012), and is documented in [4]. Model1 refers to an improved
model, which has been used for most of the past publications during this research,
and is documented in [6]. However significant changes have been made since Model1
for the work presented in this thesis that will be discussed in this chapter.

The vehicle model represents a general-purpose passenger car with a series hybrid
powertrain as shown in Fig. 2.1. This dynamic model is capable of realistic transient
response in the frequency range appropriate for standard driving. The powertrain of
the vehicle comprises three branches: the Propulsion Load (PL), which is an inverter
driven Permanent Magnet Synchronous Motor (PMSM), mechanically connected to
the wheels of the car via a continuously variable transmission (CVT); the Primary
Source of energy (PS) which consists of a turbocharged 2.0L diesel internal com-
bustion engine (ICE), mechanically coupled to a Permanent Magnet Synchronous
Generator (PMSG) which is electrically connected to a three-phase rectifier; and the
Secondary Source of energy (SS) which contains a lithium-ion battery connected to a
bi-directional dual active bridge DC-DC converter. Regenerative braking is possible
by the PMSM behaving as a PMSG while capturing the kinetic energy from the
wheels and converting it to electrical energy, which then gets stored in the SS.

27
28 Chapter 2

Mechanical Power Flow

Secondary Source Electrical Power Flow
Drive Information Signal
SCS Battery DC-DC Cycle
Converter Driver
DC Model
Link
Engine PMSG Rectifier Inverter PMSM CVT+Car
/PMSG
Primary Source Propulsion Load

Figure 2.1: Overall structure of the series HEV model. Thin and thick arrows cor-
respond to electrical and mechanical energy flow respectively, while the direction of the
arrows shows the direction of the flow.

The PL is powered by the PS and SS, all connected to a common DC bus through
which energy transfer takes place, giving

PP S + PSS = PP L , (2.1)

where PP S and PSS are the output powers of the PS and SS respectively, and PP L is
the load power requested by the PL. Given the power ratings of the components, the
PS and SS are constrained to operate within their rated limits, which are defined to
be PP S ∈ [0, 58] kW and PSS ∈ [−21, 42] kW.

The vehicle also includes a supervisory control system (SCS) that manages the power
split of the powertrain by following a control strategy (of which the design is the
main focus of this work). In parallel with the SCS, the powertrain makes use of
a start-stop system (SSS) that enables the ICE to be switched off to reduce idling
losses. These kinds of systems are becoming standard in commercial vehicles and
significantly improve the fuel economy.

This chapter will provide some background on hybrid vehicles before describing the
component models of the PL (car dynamics, PMSM, inverter and CVT), PS (ICE,
PMSG and rectifier) and SS (battery and DC-DC converter), and then describing
their interconnection and overall control (including the use of a SSS). Lastly, the
applied methods of simulations will be discussed.
Vehicle Model 29

2.1 Background

2.1.1 Brief History

There have been several historical attempts to bring HEVs to the market, with lim-
ited success. The first HEV, the Lohner-Porsche of 1900 , was a series HEV designed
by Ferdinand Porsche. It was impressive, but too expensive for popular consump-
tion. A revival in the 1970s seemed imminent, following the Arab oil embargo of
1973 which resulted in a hike in fuel prices. The pioneering work of Victor Wouk,
who has been called the “godfather of the hybrid”, saw several promising hybrid
prototypes developed but would eventually be controversially stopped by the US
Environmental Protection Agency. The American car industry would thereafter not
pursue any further hybrid technology, and with the exception of a few European
projects (by Audi and Volvo) the technology would enter a long hiatus.

The true HEV revival occurred in the late 1990s when the Japanese car manufac-
turers produced affordable, efficient and practical HEVs. The Toyota Prius was
the first mass-market hybrid to be launched in 1997 (originally in only Japan), and
Honda Insight was first to the American market in 1999. There has since then been
an effort by most major manufacturers to include HEVs in their vehicle fleet, but
Toyota remains the leader as they now sell more than 1 million new hybrid cars
each year (in a world where global total accumulated sales for all hybrids reached
10 million just this year).

2.1.2 Electrification

As cars are becoming more electrified, there is a large range of possible arrangements,
and degrees of electrification. The closest to a conventional car would be a mild
hybrid which only has a small motor to enable quick restarts of the car, allowing the
engine to be switched off rather than waste fuel idling. They may also be capable
of recovering energy through regenerative braking, further improving fuel economy.
Hybrids with a larger hybridization factor (relative size of the motor to the engine),
are referred to as full hybrids (or strong hybrids) and make much more use of the
electric motor even during normal driving. These can typically operate in pure
electric mode during low-speed urban driving.
30 Chapter 2

The next level of electrification is a hybrid which has a larger battery and can be
charged from the electric grid. These plug-in hybrid electric vehicles (PHEVs) are
often operated in pure electric mode most of the time, but use the engine as a
back-up option in case the battery is approaching depletion. However, it is also
possible to use the engine and the motor in a blended mode at all times. This latter
approach tends to be optimal only for longer journeys. The fact that electric energy
is available from the grid is a fundamental difference from ordinary HEVs, where
even the electric energy of the battery has to come from either direct charging by
the engine or through regenerative braking.

Lastly the pure electric vehicle (EV), also often called battery electric vehicle (BEV),
is a fully electrified vehicle. The engine has been removed from the PHEV and the
battery capacity is typically increased, to allow for a decent range. Although, the
EV is considered the most environmental friendly (zero emissions, and no fossil fuel
consumption), it is still not considered cost effective. Also, if the battery runs out
of charge, a significant amount of recharge time is required.

According to experts, and judging by adoption trends, the electric vehicles are still
not ready for the mass-market. Significant innovation in battery technology will be
required for the battery capacity to increase, and for recharge times to be more palat-
able. Also, the charging infrastructure is developing fast but is still not widespread.
PHEVs on the other hand have been gaining traction and are expected to overtake
the conventional HEVs, which are by many seen as a stepping stone towards further
electrification.

It is worth mentioning that hybrid powertrains are not limited to electric motors and
engines. A significant amount of research is happening in the area of fuel cell electric
vehicles (FCEVs), which uses compressed hydrogen to produce energy by reacting
with oxygen, resulting in only heat and water as by-products. Also, fuel cells have
been shown to be more efficient than combustion engines. However, there are major
challenges for mass-market adoption, including the requirement of completely new
infrastructure to allow refueling of hydrogen. A handful of commercial FCEVs are
currently available, but are practically limited to a few select regions with developed
hydrogen infrastructure.
Vehicle Model 31

2.1.3 Architectures

Series

A HEV with a series powertrain is sometimes referred to as a range-extended elec-

tric vehicle. This reflects the fact that it can be operated purely as a BEV, with
the battery powering the motor to drive the wheels. Although such operation (with
no emissions) is great during urban driving, the battery offers a limited range for
highway driving. This is addressed by the series architecture with an internal com-
bustion engine (ICE) connected to a generator that can either charge the battery
or power the motor driving the vehicle. Due to the high energy density of fuel, this
addition greatly benefits the range of the vehicle. The fact that the ICE is not me-
chanically connected to the wheels decouples the engine speed from the wheel speed,
allowing the ICE to operate at its optimal point persistently. Furthermore, it allows
the ICE to be located flexibly and simplifies packaging, as it is unconstrained by
any mechanical connections. Also, as the motor singlehandedly provides the torque
for the propulsion of the vehicle, both transmission and control can be kept quite
simple.

However, these benefits come at the expense of an additional electrical machine. The
generator not only adds to weight, bulk and cost but also introduces another stage
of energy conversion. The mechanical energy of the ICE is converted to electrical
energy by the generator before being reconverted to mechanical energy by the motor
to drive the wheels. These conversions are particularly significant during sustained
highway driving. Lastly, as the series powertrain is solely powered by the motor,
it needs to be sized for peak power requirements. Additionally, both the ICE and
generator need to be sized for maximum sustained road load to allow full battery
redundancy. Consequently the series powertrain is quite bulky, and mainly suitable
for heavy and large vehicles. However, as components are becoming more compact,
the architecture is becoming more attractive.

Parallel

As the name suggests, a parallel powertrain allows the HEV to be propelled by the
ICE and motor in parallel, simultaneously. This not only eliminates the need of a
generator, but also reduces size of ICE and motor due to the synergistic operation.
32 Chapter 2

This power share also improves performance, as both ICE and motor can provide
propulsion during heavy acceleration. The direct connection between the ICE and
the wheels (through transmission) avoids the conversion losses associated with the
series architecture, and it thus offers superior efficiency for sustained highway driv-
ing.

However, the mechanical connection between the ICE and the wheels couples their
speed through finite number of gear ratios, limiting the ICE efficiency. This is partic-
ularly significant during urban driving when both requested power and wheel speed
vary across a wide range. The parallel architecture faces more complicated control
and transmission compared to the series architecture as it requires torque blend-
ing. There are many approaches to connecting the ICE, motor and transmission
system so the parallel architecture is often sub-categorized into pre-transmission,
post-transmission and through-the-road configurations.

Pre-transmission In the pre-transmission configuration, both the motor and ICE

are located before the transmission system. This allows the ICE to drive the motor
like a generator (as with regenerative braking) to charge the battery, even during
stand-still. More importantly, as the motor is driven at a higher speed than the
wheels, it can operate at a lower torque which results in a smaller sized motor.
However, it also means that the ICE and the motor have to operate at the same
speeds as they both share the same transmission system. This configuration is
primarily used in mild hybrid passenger cars.

Post-transmission In the post-transmission configuration, the motor is coupled

to ICE branch after the transmission system. Therefore the power is delivered to and
from the motor without suffering transmission losses, and the transmission system
is kept relatively simple. However, with the motor coupled to the wheels, it must
be specified to operate across all vehicle speeds. Consequently, it is also required to
operate at higher torques, resulting in a larger sized motor. It is therefore typically
used in full hybrids of passenger cars and light-duty trucks.

Through-the-road As the previous two configurations have the ICE and motor
driving the same axle in the vehicle, they have to use speed or torque couplers to
connect the power flow of the ICE and motor. Through-the-road is an alternative
Vehicle Model 33

configuration where the motor and ICE are acting on separate axles, avoiding any
kind of direct coupling. Instead, the road acts as a speed coupling device, fixing
both sets of wheels to the same rotational speed, enabling power flow from the ICE
to the motor/generator. This configuration has a low mechanical complexity, with a
simple transmission, no coupling device and is essentially identical to a conventional
powertrain for one of the axles. It is therefore very suitable for hybridization of
conventional vehicles. Also, it benefits from improved traction due to the four-wheel
drive. However, consequently, it requires more complex control as the two axles are
driven simultaneously by two indirectly coupled machines.

Split power

The increasingly popular split power architecture delivers the benefits of both the
series and parallel architectures. It decouples the ICE speed from vehicle speed,
but still allows some of the ICE power to transfer mechanically to the wheels. Such
operation enables the split power powertrain to perform efficiently in urban as well
as highway driving conditions.

These benefits come at the expense of complexity. Not only does it require an
additional electrical machine (like the series architecture) but it also needs a power
split device, typically a planetary gear set, which couples the ICE, the motor, the
generator and the transmission shaft. This adds weight, bulk, cost and complexity
(mechanical as well as control). There are many configurations of this architecture,
which have evolved from the single-mode of Toyota Prius to the latest three-mode
configuration of GM Volt. The increasing complexity is pushing the boundary of
realized efficiency across wide ranges of operation, but again it is at the expense of
bulk and cost as multiple planetary gears and other components are required.
34 Chapter 2

2.2 Propulsion Load

As mentioned, the PL comprises the car dynamics, PMSM, inverter and CVT. Each
of these will be briefly described and discussed in this subsection, with emphasis on
the differences from previous versions of the model.

2.2.1 Car dynamics

This work is mainly focused on the control of the powertrain, but this necessitates a
sufficiently accurate model of not only the powertrain but also the car response. The
modeled car describes the longitudinal vehicle dynamics and employs a mechanical
multibody system model based on [16]. The constituent masses are introduced in
a tree structure with the freedoms and forces between them specified. Thus the
main body of the vehicle is allowed forward and vertical translation, and pitch
rotation. The front and rear hub carriers are attached to it with vertical translation
freedoms, with their motion restricted by spring and damper suspension forces. The
model also has spinning wheels attached to the hub carriers. The rear wheel is
connected via a crown wheel and pinion, and a CVT to the motor shaft. The model
employed here includes also aerodynamic lift and drag forces which are proportional
to the square of the speed. The tires are treated as vertically compliant, with
associated spring and damper forces, and the tire longitudinal force is generated
from normal load and longitudinal slip using standard ‘magic formulas’ [17]. Tyre
rolling resistance proportional to tire normal load is also included. The vehicle
is decelerated by regenerative braking only, via the rear wheels and transmission,
and the useful energy is captured. The parameter values used in the model are
representative of a contemporary European family saloon and are taken from [16]
where the total mass is 1475.6 kg, the pitch inertia is 2152.1 kgm2 , and the drag
coefficient is 0.35. Further vehicle parameters are presented in [6]

Model0 and Model1 implemented these vehicle dynamics in LISP with the multi-
body modeling code VehicleSim R , formerly called Autosim [18]. The VehicleSim
model was then imported into the Simulink environment as an S-Function. However,
this implementation was restrictive in several aspects. Any change to the vehicle
dynamics (including the CVT, which used to be implemented in VehicleSim as well)
Vehicle Model 35

required changes to the VehicleSim code, followed by stages of compiling and in-
tegration with the remaining Simulink vehicle model. Having the model split up
between Simulink and VehicleSim also increased computational load, resulting in
slower simulations. Furthermore, the use of an imported S-function prohibited the
use of simulation accelerators within Simulink that can potentially reduce simula-
tion time into a fraction of the original. Therefore, all of the car dynamics were
reimplemented in Simulink directly, using the SimMechanics library.

2.2.2 Permanent Magnet Synchronous Motor

The model uses a surface mounted PMSM, which offers a high torque-to-inertia ratio
and power density. It is a 3-phase system with a star-connection to the inverter that
links it with the DC bus of the powertrain. However, rather than dealing with
the three phases individually, the model converts these into a standard 2-phase
d-q rotating reference system, using the non-power-invariant Park Transform [19],
greatly simplifying its control. The resulting nonlinear coupled differential equations
for the electrical dynamics of the PMSM [19] are thus as follows:

didm
= (vdm − Rm idm + ωsm Lqm iqm )/Ldm , (2.2)
dt
diqm
= (vqm − Rm iqm − ωsm (Ldm idm + λf m ))/Lqm , (2.3)
dt

where idm and iqm are the d- (direct) and q- (quadrature) axis components of stator
current, vdm and vqm are the d- and q-axis components of stator voltage, and Ldm and
Lqm are the d- and q-axis stator inductances. The electromagnetic torque produced
by the motor is given by [19]

3
Tem = pm (λf m iqm + (Ldm − Lqm )idm iqm ) (2.4)
2

which in the case of Ldm = Lqm (surface-mounted PMSM) is simplified to

3
Tem = pm λf m iqm . (2.5)
2

This torque is reduced by a friction torque, Tf m , to produce a load toque, Tlm ,

according to
Tlm = Tem − Tf m . (2.6)
36 Chapter 2

Table 2.1: Parameter values for friction torques Tf m (and Tf g )

Constant Value
a1 10
a2 4
a3 0.3
p0 1.779
p1 −1.116 × 10−2
p2 1.307 × 10−4
p3 −1.321 × 10−6
p4 6.699 × 10−9
p5 −1.300 × 10−11
p6 8.685 × 10−15

Table 2.2: Parameters for PMSM (and PMSG)

Parameter Symbol Value

Nominal rated power Pn 75 kW
Maximum speed ωn 5000 rpm
Stator resistance R 0.04 Ω
D-axis stator inductance Ld 0.20 mH
Q-axis stator inductance Lq 0.20 mH
Rotor magnetic flux λf 0.125 Wb
Moment of inertia J 0.05 kgm2
Number of pole pairs p 6

The proposed friction torque is identified to be a function of rotor speed as follows

6
!
2 X
i
Tf m = tan−1 (a1m ωrm ) · a2m exp(−a3m ωrm ) + pim ωrm (2.7)
π i=0

with parameter values given in Table 2.1. Tlm is applied on the rotor shaft that is
connected to the car transmission, thereby driving the car forward. Therefore, Tlm
is an output of the motor model and an input to the transmission model of the car,
while the rotor speed, ωrm , is calculated in the transmission model of the car and
fed back to the motor as an input.

The remaining parameter values for the PMSM are given in Table 2.2. The basis
of this selection is the EVO Electric AFM-140 motor [20]. The chosen parameters,
together with the tuned friction torque, are found to deliver a qualitatively correct
representation of the efficiency based on experimental results from the manufacturer.
The PMSM efficiency is presented in Fig. 2.2.
Vehicle Model 37

400 75%
85%
300 90%
93%
200 94%
95%
Load Torque, Tlm (Nm)

96%
100

-100

-200

-300

-400
0 1000 2000 3000 4000 5000
PMSM Rotor Speed, ωrm (rpm)
Figure 2.2: PMSM steady-state power efficiency map for variations in load torque, Tlm ,
and rotor speed, ωrm for the PMSM model. As only forward vehicle motion is of interest,
the rotor speed is always non-negative and the PMSM can operate in two quadrants: a)
positive Tlm (motoring) and b) negative Tlm (regenerating). The contours correspond to
constant efficiencies in the range 75%-96%.

2.2.3 Inverter

The PMSM is connected to the DC bus through a bi-directional inverter (operating

as a rectifier during regenerative braking). This component is described with an
averaged model. The converter switches are first treated like voltage and current
sources, making the circuit topology time-invariant, before averaging the signals.
The negligible (for the purposes of energy management of the overall powertrain)
high frequency switching harmonics are thus removed, balancing precision with com-
putational load. The resulting average model of the PWM inverter in the d-q frame
is described by the following equations [21, 22]:

3
i′P L = (dqm iqm + ddm idm ), (2.8)
2
vdm = ddm vdc , (2.9)
vqm = dqm vdc , (2.10)
38 Chapter 2

in which vdc is the DC-link voltage, i′P L is the modified (before inverter losses are
applied) DC current drawn by the inverter from the DC-link, and ddm , dqm are
continuous duty cycle functions in the d- and q-axis respectively.

Model0 and Model1 used a constant efficiency term for the inverter (ηinv = 95%).
However, unlike the assumption of using an averaged model, this choice does im-
pact the overall energy flow of the powertrain. Therefore, additional dynamics are
included to consider the conduction and switching losses of the inverter based on
the work in [23]. The conduction losses of the inverter are given by [24, 25]:
    
1 M 1 M
Pcond = 6 ipk vf 0 − + i2pk rf −
2π 8 8 3π
    
2 1 M 1 M
+ 6 rce ipk + + vc0 ipk − , (2.11)
8 3π 2π 8

where ipk is the peak AC current from the inverter, vf 0 is the diode forward voltage
corresponding to zero current, rf is the diode forward resistance, rce is the IGBT
(insulated-gate bipolar transistor) collector emitter resistance and vc0 is the IGBT
forward voltage corresponding to zero collector current. The switching losses of the
inverter are given by [25]:

fi vdc ipk
Psw = 6 (Eon,ref + Eof f,ref + Err,ref ) (2.12)
vref iref π

where fi is the switching frequency (carrier signal frequency) of the inverter; Eon,ref
and Eof f,ref are the reference IGBT turn on and turn off energy losses respectively;
vref and iref are the voltage and current respectively at which reference energy loss is
measured; and Err,ref is the reference diode reverse recovery energy loss. Reference
values are obtained from the device datasheet of Infineon for F S150R12KT 4 [26].
The dynamic efficiency expression of the inverter is implemented as

i′P L vdc

 i′P L vdc +Pcond +Psw iP L ≥ 0
′

ηinv = , (2.13)
 i′P L vdc +Pcond +Psw i′ < 0

PLi′ vdc PL
Vehicle Model 39

100
Inverter Efficiency, ηinv (%)

90

80

70

60

50
0 25 50 75 100
Propulsion Load, PP L (kW)

Figure 2.3: Inverter efficiency for varying values of propulsion load.

which can also be expressed more simply as


PP L −Pcond −Psw

 PP L
PP L ≥ 0
ηinv = . (2.14)
PP L


PP L −Pcond −Psw
PP L < 0

The simulated steady state inverter efficiency is presented in Fig. 2.3, where it can
be seen to gradually rise towards about ηinv = 97%. The efficiency is however quite
low at very low power loads. The efficiency dynamics are very symmetrical, so a
similar but mirrored profile is applied during regenerative braking when the inverter
is engaged in AC to DC conversion. However, note that this steady state efficiency
map is only included for illustrative purposes. The actual inverter model deals with
transients and is dependent on the state of the vehicle (mainly PMSM rotor speed
ωrm ).

2.2.4 Continuously Variable Transmission

Lastly, the model uses a toroidal CVT to connect the PMSM to the wheels. The
stepless gear ratios offered by the CVT enables the PMSM to rotate at its optimum
speed while driving the wheels of the car at any speed. This is done by defining the
appropriate final drive ratio N , as ωrm = N ωwc (where ωwc is the rotational speed
of the wheel). However, this is compromised to some extent due to the fine range of
final drive ratios that are realizable (N ∈ [1.47, 10.67] in this work).
40 Chapter 2

The CVT control strategy pursued is to operate it in a straight line through the
PMSM torque-speed map such that

′
Tlm = kCV T ωrm , (2.15)

in which kCV T is a constant and Tlm′

is the PMSM load torque after the CVT losses.
This is not only easy to implement but also allows the line of operation to intersect
with the most efficient region of the PMSM. This is realized by setting the reference
final gear reduction ratio to:

|Tlm
′
|
Nref = . (2.16)
kCV T ωwc

Here Nref is the total (requested) gear reduction from the motor shaft to the rear
wheels of the car (N = Nref in steady-state).

The dynamic response of the CVT is characterized by a first order lag with a cor-
responding time constant, τ , of 200 ms [27]. The CVT losses are simplified to be
expressed as a constant efficiency of ηCV T = 93%, which was found to be the average
efficiency for a toroidal CVT [28–31]. The CVT model is shown in Fig. 2.4.

ωrm
x

ωwc
Nref 1 N
Ratio sτ +1
Tlm
Losses ′
Tlm

Figure 2.4: CVT implementation block diagram, with Ratio defined in Eq. 2.16 while
Losses is the application of a constant ηCV T = 93%.
Vehicle Model 41

2.3 Primary Source

The PS consists of three components: an internal combustion engine (ICE), a Per-

manent Magnet Synchronous Generator (PMSG), and a three-phase rectifier. Each
of these will be described here, together with some analysis of the PS as a whole.

2.3.1 Internal Combustion Engine

The ICE is the main energy source of the HEV, and the only source of a conven-
tional vehicle. It converts the chemical energy of the fuel into mechanical energy to
power the propulsion of the vehicle. The ICE model in the work represents a tur-
bocharged 2.0L Puma diesel engine. It is based on mean-value torque maps for the
engine cylinders, turbocharger turbine and turbocharger compressor, but includes
dynamics for the filling and emptying of the inlet and outlet manifolds; the inter-
action of engine and turbocharger inertia; and fuel-injection valve dynamics. These
dynamics consider the pressures, temperatures and mass flows through the various
parts of the engine. As such, this model can partly capture transient dynamics
that are essential for the application of HEVs, where the operating state changes
from one second to another. This is in contrast to other vehicle models that will
typically use static look-up tables for either fuel consumption or engine efficiency.
The ICE model used thus allows a more accurate representation of a real engine.
Furthermore, the steady-state operation of the model have been validated against
Ricardo WAVE full computational fluid dynamics (CFD) model simulation results,
which were previously validated against experimental results. This model has been
fully detailed in [4].

The ICE model used in this work has implemented a few significant changes from
Model0. The initial fuel injection constraints were restricting the ICE to operate
with a maximum power rating of 42 kW, which is lower than the validated region
of operation and the maximum rating of the Puma 2.0L engine. These constraints
have therefore been eased, such that the ICE can operate up to PICEmax = 64.7 kW.
In fact, the constraint has been made a function of the reference PS power PP Sref
such that higher reference loads to the ICE allows higher fuel injection. The key
purpose of this is to avoid open throttle fuel injection during sudden changes from
42 Chapter 2

70

60
Power of ICE, PICE (kW)

50

0
250

25
40

30 230
222
250
20 230
250 230 250
10 250
300 300
500 500
0 1000 500 1000 1000
800 1200 1600 2000 2400 2800 3200
Engine Speed, ωICE (rpm)

Figure 2.5: BSFC of ICE, BSF CICE (g/kWh), for varying ICE power demand and
engine speed. Minimum is marked with a cross.

very low to low power requirements. As part of these changes, the PID control (with
anti-windup) for the fuel-injection has been retuned as well.

The brake specific fuel consumption (BSFC) of the ICE is defined as

ṁf uel
BSF CICE = , (2.17)
PICE

where ṁf uel is the mass rate of fuel consumption and PICE is the output power of
the ICE that is defined as
PICE = TICE ωICE , (2.18)

where ωICE is the engine speed (in rad/s) and TICE is the output torque of the ICE.
To determine the BSFC at various operating points, the ICE model is simulated
for PICE ∈ [0, PICEmax ] kW in 0.1 kW steps and ωICE ∈ [800, 3200] rpm in 10 rpm
steps. The resulting BSFC map is presented in Fig. 2.5. It can be seen that the
minimum BSFC (marked with a cross in the figure) is found in the island around
ωICE = 1620 rpm and PICE = 25.2 kW. The envelope of the efficiency map is
determined by feasibility of the ICE. The omitted data points at very low power
requirements are either not operationally feasible or the model is not validated in
that range. Furthermore, the engine has an internal control constraint for the air fuel
ratio that essentially limits the power output at any engine speed (the uppermost
diagonal limit), in order to reduce emissions [5].
Vehicle Model 43

2.3.2 Permanent Magnet Synchronous Generator

The ICE is connected to a PMSG, which is based on the same equations and pa-
rameter values as the PMSM in Section 2.2.2. However, it is only operated with a
negative torque. Thus, the energy flow is reversed and the machine converts me-
chanical energy to electrical energy (similar to the regenerative braking case of the
PMSM). The efficiency of this process is given by

3
(v i
2 qg qg
+ vdg idg )
ηg = , (2.19)
TICE ωICE

where vdg , idg , vqg and iqg represent d-q voltages and currents respectively corre-
sponding to the three-phase output of the PMSG. The efficiency plot of the PMSG
is presented in Fig. 2.6. Note that the output power is expressed as a negative value,
due to the aforementioned negative torque convention.

In Model0 and Model1 the PMSG was sized at 95 kVA, due to legacy reasons.
However, as the PMSG is connected to an ICE barely capable of 65 kW, the PMSG
was clearly oversized. Therefore, the old PMSG has been reduced, and now employs
the same machine as is used for the PMSM (with parameters given in Table 2.2).
This should be beneficial when the project is expanded to include hardware-in-the-
loop simulations.

While the PMSM rotor shaft was connected to the wheels through a CVT, the
PMSG connects to the ICE through a fixed gear ratio G, such that ωrg = GωICE . In
this work G = 1.2 is used, as it was found to deliver improved overall efficiency (the
efficient ICE operation island around ωrg ∈ [1600, 1800] rpm is matched up with
the efficient PMSG operation around ωICE ∈ [1900, 2150] rpm). The mechanical
dynamics of this connection are given by

dωrg
GTICE + G2 (Teg − Tf g ) = (JICE + G2 Jg ) , (2.20)
dt

with TICE the mechanical torque applied by the ICE on its inertia, Teg the elec-
tromagnetic torque applied by the PMSG on its shaft, Tf g the friction torque in
the generator, and JICE and Jg the moments of inertia of the ICE and generator
respectively.
44 Chapter 2

Output Power, Poutg (kVA) 0

-40

Continuous Power
-80 75%
85%
90%
-120 93% Peak Power
95%
96%
-160
0 1000 2000 3000 4000 5000
PMSG Rotor Speed, ωrg (rpm)
Figure 2.6: PMSG steady-state power efficiency contours ηg (%) for varying output
power and rotor speed.

2.3.3 Rectifier

Lastly, the energy flows through the rectifier, which is modeled identically (with con-
duction and switching losses) to the inverter in Section 2.2.3, as opposed to the fixed
efficiency model in Model0 and Model1. However, the expression for the rectifier
efficiency is not the same as that of the inverter in Eq. 2.13 as the rectifier operates
in a single direction and the PMSG makes use of the negative sign convention, but
the PS does not. The rectifier efficiency is thus implemented as

i′P S vdc − Pcond − Psw

ηrec = , (2.21)
i′P S vdc

which can also be expressed more simply as

PP S
ηrec = , (2.22)
PP S + Pcond + Psw

which is the ratio between the input power of the DC link to the output power of
the PMSG.

The simulated rectifier efficiency is presented in Fig. 2.7. Unlike the inverter effi-
ciency in Fig. 2.3, the rectifier achieves good performance even at very low loads.
As the efficiency is indirectly dependent on the rotor speed of the connected ma-
chine, the rectifier always enjoys high-speed operation with the engine-generator set
(which always operates at ≥800 rpm). However, as the PMSM is delivering low
Vehicle Model 45

100
Rectifier Efficiency, ηrec (%)

95

90

85

80
0 15 30 45 60
PS Power, PP S (kW)

Figure 2.7: Rectifier efficiency for varying values of PS power.

loads, or the wheel speed is very low, the inverter experiences quite inefficient oper-
ation. Furthermore, the correlation between the rectifier efficiency and the operating
engine speed is clearly visible when comparing the profile of the rectifier efficiency
in Fig. 2.7 with the profile of the operating engine speed for varying PP S in Fig. 2.9
later in this section.

2.3.4 Overall Operation

As each component of the PS has been modeled, the combined operation can be
analyzed to determine the optimal operating points. This analysis and optimization
was originally performed as part of the EMMS in Chapter 4 but was later adopted
for all strategies. It is therefore briefly presented here.

By considering the ICE, PMSG and rectifier together, the BSFC of the PS can be
expressed as
ṁf uel (PP S , ωICE )
BSF CP S (PP S , ωICE ) = , (2.23)
PP S
in which PP S is the PS power flowing to the DC-link. Thus, for any given PP S the
BSFC of the PS can be determined by measuring the fuel rate ṁf uel . This is done
for PP S ∈ [0, PP Smax ] with ωICE ∈ [800, 3200] rpm to produce the BSFC map in
Fig. 2.8. It demonstrates that the PS is generally more efficient at higher levels
of power demand and medium speeds. Note that the minimum BSFC is found at
20.1 kW at 1870 rpm and is marked with a cross in the chart. This point has moved
46 Chapter 2

60

50
Power of PS, PP S (kW)

270
40
270
30 270
250
3 270
20 24
250
270 300
250
10 270
300
500 500
0 1000 500 1000 1000
800 1200 1600 2000 2400 2800 3200
Engine Speed, ωICE (rpm)

Figure 2.8: BSFC of PS, BSF CP S (g/kWh), for varying PS power demand and engine
speed. Minimum is marked with a cross.

3200
Engine Speed, ωICE (rpm)

2800

2400

2000

1600

1200

800
0 10 20 30 40 50 60
PS Power, PP S (kW)

Figure 2.9: Look-up profile for preferred engine speed for varying power requirements
of the PS.

to a higher speed and lower power as compared to the optimal BSF CICE due to the
efficiency profiles of the PMSG and rectifier.

It can be noted that BSF CP S in Eq. 2.23 is a function of ωICE as well as PP S .

However, with the obtained BSFC map in Fig. 2.8 we can now determine the optimal
ωICE for a given PP S such that BSF CP S is minimized (with some adjustments to
ensure smooth transitions). This relationship, as shown in Fig. 2.9 is independent of
any choice by the SCS and can therefore be used in the optimization problem later.
Vehicle Model 47

Fuel consumption, ṁf uel (g/s) 5

0
0 10 20 30 40 50 60
PS Power, PP S (kW)

Figure 2.10: Steady-state fuel consumption for varying power requirements of the PS.

With ωICE (PP S ) defined, the expression for BSF CP S can simply be expressed as

ṁf uel (PP S )

BSF CP S (PP S ) = , (2.24)
PP S

Consequently, the control problem of the powertrain is reduced by one degree of

freedom and the steady state fuel consumption of the PS can be treated (neglecting
transient behavior) as a one-dimensional look-up table for control purposes, as shown
in Fig. 2.10. Note that the vehicle model is still using the full dynamics of the engine
model, and this fuel consumption profile is only to be used for control designs in
later chapters.
48 Chapter 2

2.4 Secondary Source

2.4.1 Battery

The Li-ion battery model in this work is based on the battery model from the
SimPowerSystems library in Simulink that has been described in [32, 33]. It uses
the physical parameters of the battery in electrochemical equations to describe the
battery dynamics. It is able to capture the generic dynamic response of a Li-ion
battery. The battery voltage is defined as

vbat = Ebat − Rbat · ibat (2.25)

where Rbat is the battery internal resistance and ibat is the average current drawn
from the battery. The open circuit voltage Ebat is given by
( Q ∗
·K2 ibat )
Qmax ·K1 Q
E0 − Qmax −Q
− max
Qmax −Q
+ A exp(−B · Q) i∗bat ≥ 0
Ebat = Qmax ·K1 Q Qmax ·K2 i∗bat ) (2.26)
E0 − 0.1Qmax +Q
− Qmax −Q + A exp(−B · Q) i∗bat < 0

where Q represents the consumed charge and the i∗bat variable is a filtered version of
ibat flowing through the polarization resistance, and are defined as
Z t
Q = (1 − SOCinit ) · Qmax + ibat dt (2.27)
0

1
i∗bat = ibat , (2.28)
τr s + 1
where ‘s’ is the standard Laplace variable. However, rather than considering the
absolute level of consumed charge Q, the key state variable of interest for the battery
is the state of charge (SOC) given by

Q
SOC = 1 − . (2.29)
Qmax

Model0 and Model1 employed a battery with a maximum battery capacity of 20

Ah and nominal voltage of 215 V, with further parameters populated through the
experimental look-up tables provided by the Simulink library. This battery was then
operated within the range of PSS ∈ [−30, 30] kW. However, the battery has now been
resized and is based on a stack of Kokam SLPB11043140H cells (3.7 V and 4.8 Ah)
Vehicle Model 49

Table 2.3: Parameter values of the Li-Ion battery

Parameter Symbol Li-Ion Battery

Rated capacity Qmax 14.4 Ah
Nominal Voltage Vnom 296 V
Initial state of charge SOCinit 65%
Battery constant voltage E0 320.6795 V
Polarization constant K1 0.116 V/(Ah)
Polarization resistance K2 0.116 Ω
Internal resistance Rbat 0.2056 Ω
Time constant for filtered current (i∗bat ) τr 10 s
Exponential zone amplitude A 25.1477 V
Exponential zone time constant inverse B 4.2404 (Ah)−1

[34], with three parallel connected modules of 80 cells in series, giving a nominal
voltage of 296 V and rated capacity of 14.4 Ah. This gives a power capacity of
4.26 kWh, which is practically identical to that of the old model. The power rating
of the battery is defined by limiting the battery to C ratings of 5 C during charging
and 10 C during discharging, which would correspond to Pbat ∈ [−21, 42] kW. For
simplicity, these have been applied as power ratings for the SS. The remaining model
parameters are found through the mentioned experimental look-up tables of the
Simulink library, and these have been summarized in Table 2.3.

The efficiency of the battery is conventionally based on charge and discharge cycles,
but this will not be done in this work. Instead, the aim is to express the charging
and discharging efficiencies separately. This will be done in Section 4.2.2.

2.4.2 DC-DC Converter

To connect the battery, which has a variable voltage, to the 700 V DC link requires a
bi-directional DC-DC converter. Model0 and Model1 utilized a half-bridge converter
based on the work in [35]. However, the model in this work has instead considered
a dual active bridge (DAB) converter (as shown in Fig. 2.12 in the next section).
This is based on the investigation and modeling in [23], which identified the DAB
architecture to be suitable. However, much of the modeling work, which required
in-depth modeling of the converter to assess its losses, is very detailed and thus too
heavy in terms of computational load for our purposes. Therefore, the dynamics of
the DC-DC converter model have been simplified. The main converting dynamic is
50 Chapter 2

100
DC-DC Efficiency, ηdcdc (%)

90

80

70

60

50
-50 -25 0 25 50
DC-DC Converter Load, Pdcdc (kW)

Figure 2.11: DC-DC converter efficiency for varying values of load power.

governed by the following equation for the average power flow [36, 37]:

vbat vdc φ(π − φ)

Pdcdc = , (2.30)
2nπ 2 Ldcdc fdcdc

where φ is the phase shift between the primary and secondary switch gating signals
of the DAB converter, determining the direction of power flow (positive phase shift
results in power flow from battery to DC link, and negative in the opposite direction);
n is the transformer turns ratio; Ldcdc is the primary referred leakage inductance of
the intermediate isolation transformer; and fdcdc is the switching frequency of the
DC-DC converter.

The model individually models the average current flows through the inductors,
capacitors, transistors (IGBTs) for a large set of operating modes. This is the most
computationally intensive part of the model. These signals are then used to compute
the conduction, switching and core losses of the transistors as well as component
losses for diodes and snubber capacitors. However, rather than employing the full
model, this work has first implemented the model and thereafter determined the
steady-state efficiencies at different loads through simulation. This data has been
used to produce a look-up table for the DC-DC converter efficiency as shown in
Fig. 2.11. It can be seen that the efficiency is very low at low loads but quickly rises
to peak around 96.4% for positive flow (at Pdcdc = 23 kW) and 95.4% for negative
flow (at Pdcdc = −28 kW). The efficiency is generally quite flat around 95%, but it
is clear that the SS should not be operated at very low loads.
Vehicle Model 51

2.5 System Integration

This section describes the integration and control of the the PL, PS and SS branches;
the overall control by the SCS and SSS; as well as an overview of model time con-
stants and states.

2.5.1 Overall Powertrain

Each of the described branches (PL, PS and SS) of the powertrain are connected
together at the DC link, as shown in Fig. 2.12. This diagram illustrates the electrical
integration of the powertrain branches.

PMSG Rectifier iP S iP L Inverter PMSM

Rg Rm

Lbg Lbm

ebg eag Co eam ebm

Lag Rg Rm Lam
ecg ecm
Lcg Lcm

Rg Rm

PP S ucar
- -
PP S,ref+ Gating Gating + ucar,ref
PI Signals Signals
PI

vdc
-
vdc,ref+ Gating
PI Signals

Battery iSS

L
Rbat
Ebat
1:n
+
-
DAB
Converter

Figure 2.12: The electric connection of the powertrain includes the PMSG, rectifier,
battery, DAB converter, inverter and PMSM. Symbols R, L and e represent phase resis-
tances, inductances and induced emfs; subscripts a, b and c correspond to the individual
phases; and subscripts g, m and ref correspond to ‘generator’, ‘motor’ and ‘reference’.
52 Chapter 2

idg,ref – idm
ωICE PI ωwc

Rectifier
+ vdg idm,ref –
PI

PMSG
idg + vdm

PMSM
ωICE,ref –

DC link

Inverter
ṁf uel TICE iP S
PI ICE

CVT
′

Car
+ ωrm Tlm Tlm
iqg +
+ vdc iP L
iqg,ref
PP S,ref vqg N
+
PI +
PI – ucar,ref iqm,ref
vqm
PP S
– –
+
PI +
PI
– –
iqm
X
ucar

DC/DC
iP S vdc,ref –
φ
+
PI iSS

Batteryvbat ibat

W
Figure 2.13: Block diagram showing the interconnection of the ICE, PMSG, rectifier,
battery, DC/DC converter, inverter, PMSM, CVT and car, and the related control loops.

The DC link comprises a capacitor (Co = 3 mF) that is operated at a constant

voltage, with vdc,ref = 700 V, by controlling the power flowing from the SS into the
DC link. The voltage is governed by the standard capacitor differential equation:

dvdc
iP S + iSS − iP L = Co , (2.31)
dt

where the directions of the currents involved are consistent with the direction of
power flow. For example, when iSS < 0 the battery is being charged and when
iP L > 0 the PMSM is being driven.

The powertrain is managed by controlling the converters. The inverter is controlled

such that the the forward speed of the car ucar is following the reference speed ucar,ref ,
defined by a specified driving cycle (discussed further in Section 2.6.1). This results
in the necessary energy being pulled from the DC link to power the propulsion of
the vehicle. The rectifier is controlled by the SCS which determines the reference PS
power PP S,ref . Lastly, as mentioned, the DC-DC converter is controlled such that the
DC link voltage is operated at its reference voltage, meaning that the inflowing and
outflowing current of the DC link, as described in Eq. 2.31, are balanced (resulting in
the power balance described in Eq. 2.1). A block diagram of the overall powertrain
control can be seen in Fig. 2.13.

In addition to the overarching control loops, it can be seen that the vehicle model
employs PI control schemes at eight instances. The values for these have largely been
determined through trial and error and have been summarized in Table 2.4. These
are slightly different from Model1, as the components have been sized differently.
Vehicle Model 53

Table 2.4: Parameter values for PI controllers

Block KP KI
Engine speed ωICE 10−5 2 · 10−5
Generator power PP S 0 −0.04
Generator direct current idg 5 100
Generator quadrature current iqg 5 100
DC-link voltage vdc 0.08 0.008
Motor direct current idm 5 40
Motor quadrature current iqm 5 40
Car speed ucar 1000 500

Note that the PMSM and PMSG are described with their three individual phases (a,
b and c) in Fig. 2.12, representing the physical nature of the components, while they
are described using the d-q frame convention in Fig. 2.13, representing the control
signals employed.

2.5.2 Supervisory Control System

The control diagram in Fig. 2.13 clearly shows the interconnected nature of the
powertrain. It can be noted that all the control loops are closed apart from the
necessity to provide PP S,ref , ωICE,ref , vdc,ref and ucar,ref . From these, the car speed
reference ucar,ref is set as the driving cycle profile, which is discussed in the next
section. The DC link voltage reference is always defined as vdc,ref = 700 V in
this work, although it has been controlled in real time in [10]. Furthermore, in
Section 2.3.4 the preferred engine speed was determined to be a function of PP S
(as shown in Fig. 2.9), meaning that the reference engine speed can be given as
ωICE,ref = f (PP S,ref ). Thus, the only control signal that needs to be determined
externally is PP S,ref . This is the role of the SCS. However, as the control strategies
often deal with both the PS and SS in their optimization process, the control variable
is often defined to be the power share factor u as:

PP S
u= . (2.32)
PP L

Several SCSs will be presented in this work, but they all operate under certain
common constraints. In terms of inputs for the SCS, it will depend on the nature
of the choice of control strategy. In this work, only the load power PP L and SOC
54 Chapter 2

1 f(u)
w_ICE
u-P_SSmin min up
P_PL P_PSmax
2 P_PL
P_PSref u y 1
3 SOC 1-D T(u) P_PS,ref
SOC 2
SCS
w_ICE,ref
lo
w_ICE(P_PS) 0

Figure 2.14: Simulink implementation of the SCS and its constraints. Note that f (u)
implements Eq. 2.36 to limit PP S,ref .

will be used, but it is not uncommon for control strategies in the literature to also
use the vehicle speed (ucar ). In the work on regulating the DC link voltage in [10],
even vdc is a required input (and output).

The SCS output in each case is the reference PS power PP S,ref , but it needs to be
checked to meet four different constraints. The first three of these are quite simple:
the PS can not be required to deliver negative power; the PS power demand can
not exceed its maximum rating; and finally the PS can not be allowed to exceed
the load power of the PL by such a margin that the SS can not absorb the surplus
power. The fourth constraint concerns the maximum realizable PS power for the
current engine speed. Essentially, the PS should not be loaded with more power than
it is capable of at the current engine speed. An alternative understanding of this
constraint is that the increasing of engine speed is prioritized in order of execution
over the increasing of PS power. In summary:

PP S,ref (t) ≥ 0 (2.33)

PP S,ref (t) ≤ PP Smax (2.34)
PP S,ref (t) ≤ PP L (t) + PSSmin (2.35)
PP S,ref (t) ≤ max(PP S (ωICE (t))) (2.36)

These constraints, together with the required inputs/outputs, form the surrounding
structure for each SCS. This is implemented in Simulink as shown in Fig. 2.14.
Vehicle Model 55

2.5.3 Start Stop System

As the SCS instructs the PS to operate at different power levels, it will quite often
request the PS to deliver no power at all (PP S,ref = 0 kW). Such a request would have
the net effect of the PS producing 0 kW overall, but the ICE would need to “idle”
at 800 rpm with enough torque to overcome the losses within the ICE and PMSG.
This state of operation requires about ṁf uel = 0.11 g/s. This waste of fuel is not
desirable, but switching off the engine has several drawbacks. Once the ICE has been
switched off, some amount of fuel is consumed (and emissions are emitted) to turn
on the ICE again. Furthermore, this turn-on is not instantaneous, compromising
the vehicle’s ability to follow a driving cycle, compromising the drivability of the
vehicle. The drivability is further affected by the jerk and vibrations involved in the
turn-on of the ICE. Nevertheless, drivers of conventional cars have often used the
rule of thumb that it is worth turning off the engine any time the duration of the
stop is greater than 10 seconds.

However, a HEV is not as restricted as a conventional car. The availability of electric

power to drive the car, allows the powertrain to deliver instantaneous power even
if the engine has been switched off. Furthermore, modern SSSs are highly efficient,
with the associated fuel consumption becoming negligible. There are industrial
reports that show that a modern SSS allows the ICE to break even with the idling
losses for short stops of 0.7 seconds [38].

As these types of SSSs are installed by default in most modern HEVs, it is essential to
include this capability within the model to allow relevant design of control strategies.
However these are rarely seen within models employed in the literature. Either the
losses associated with turning on the ICE are neglected altogether or the ICE is
kept idling when not in use. This can partly be attributed to the very complex
dynamics involved in modeling the turning on of an engine. Including such dynamics
are not only beyond the scope of this work, but would also negatively impact the
computational speed of the model.

Instead, the model used makes use of a simplified SSS, as shown in Fig. 2.15, which
crudely considers the fuel losses of switching the engine on. This subsystem is
installed in the cylinder model of the ICE and modifies the base fuel consumption
ṁf uel∗ with a penalty. The SSS takes the reference engine speed ωICE,ref as input,
and as long as the ICE model is idling, the fuel consumption is zero. However, the
56 Chapter 2

Penalty (kg)
0.00011
Detect Increase Scale
U > U/z 20
Fall: 0.1sec 1
m_fuel (kg/s)
1 > 800
w_ICE,ref 2
m_fuel* (kg/s)
Figure 2.15: Simulink implementation of the SSS. Note that the threshold of 801 rpm
corresponds to the idling speed of the ICE.

instance the signal exceeds 800 rpm (the idling speed) this signals that the ICE
has been turned on. This event results in a spike of magnitude 1 by the “Detect
Increase” block, but is scaled by a gain of 20 immediately afterwards. To make use
of this spike, the slew rate of the falling signal is restricted to -200 units/second, such
that the fall from 20 to 0 takes 0.1 seconds, producing a triangular signal with an
area of 1 unit. This signal is multiplied by the defined “Penalty” and finally added
to the base fuel consumption to produce the modified fuel consumption ṁf uel . In
this work the penalty has been defined such that it corresponds to the fuel consumed
by idling the ICE for 1 second (mpenalty = 0.11 g). However, a sensitivity study of
this parameter is presented later in Section 7.2.

The main limitation of this simplified SSS is the lack of delay for the availability
of the PS and the distinction between the actual engine speed ωICE and the refer-
ence ωICE,ref (the reference typically reaches the idling speed faster than the actual
speed). Furthermore, the effects on emissions have not been studied within this
work and that will affect the break-even time of idling. However, the use of this SSS
is nevertheless an improvement upon Model0 and other work in the literature.

2.5.4 Overall Model Characteristics

For the purposes of this work an appropriately high fidelity has been achieved,
balanced by the level of complexity and computational load. The model is simulated
with a fine sample time (0.1 ms) and requires 35 (model and control) states.
Vehicle Model 57

The overall model is non-linear and has come together with consideration of what
dynamics are of interest for each component. The PL is mainly affected by the
vehicle dynamics with time constants of about 100-500 ms and the CVT, which has
a time constant of 200 ms. At least one of the PS and SS need to keep up with
these transients. The PS is mainly governed by the ICE, which is quite slow. The
combustion in the cylinder is a very fast process and has been replaced by a map
that is accessed instantaneously. The fuel injection has a time constant of 5 ms,
but due to the slower air flow and mechanical inertia the output power has a time
constant of about 200-500 ms. Consequently, the PS often struggles to keep up with
the changing load requirements from the PL, and thus the faster SS is often called
into action during faster transients.

The battery and the electric dynamics of the PMSM and PMSG have time constants
in the order of 1 ms, so they have an easy time keeping up with the required transient
loads. These dynamics were considered significant enough to justify being included
in the model, but this requires the simulations to be run at sample time steps of
just 0.1 ms. The DC-DC converter, rectifier and inverter have even faster switching
dynamics (time constants of 0.05 ms). However, with consideration of the balance
between the benefits of faster dynamics and the negative impact on simulation time,
these very fast dynamics have been averaged in this model.

As the model has been modeled in great detail, it consists of a large number of
states. While most models employed in literature to study control strategies have
3-5 states (typically vehicle speed, SOC and gear ratio), the presented model com-
prises 27 physical states and 8 control states (PI component controllers within the
model, as shown in Table 2.4). Furthermore, there are also a number of additional
output states (typically seven of these), due to integrators being introduced to pro-
cess output signals (for example, to measure total fuel consumed by integrating
the fuel consumption rate). These are not strictly speaking part of the model, but
would nevertheless affect simulation speed. All states discussed above are continu-
ous states that are evaluated at each time step. In contrast, there are an additional
14 delay states introduced to resolve algebraic loops and reduce component inter-
dependencies, with the aim to increase simulation speed. Each delay state is a dis-
crete state that stores the value of some continuous state at the previous simulation
time step (delayed by one sampling time step).
58 Chapter 2

Of the 27 model states, 13 describe the powertrain components while the remaining
14 describe the vehicle dynamics (car body, suspensions and wheels). Each of these
states are listed in Table 2.5. For the purposes of designing control strategies, the
vehicle dynamics are not playing a significant role, in particular with consideration
of how many states are dedicated towards it. However, the upcoming section will
discuss methods to retain some of these detailed vehicles dynamics while removing
the corresponding states from the model. Thus, allowing the model to enjoy high
accuracy without compromising simulation speed. However, when studying the de-
signed control strategies, these dynamics and the corresponding states are retained.

Table 2.5: Physical states in the vehicle model

Symbol Component Description

ωICE ICE Engine speed
ωtc ICE Turbocharger speed
ṁae ICE Air exhaust mass flow rate
ṁai ICE Air inlet mass flow rate
ṁf ICE Fuel mass flow rate
idg PMSG Direct current
iqg PMSG Quadrature current
idm PMSM Direct current
iqg PMSM Quadrature current
Q Battery Charge
i∗bat Battery Filtered current
vdc DC link Bus voltage
Ncvt CVT Final drive ratio
pxc Car body Longitudinal displacement, x-axis
vxc Car body Longitudinal speed, x-axis
pyc Car body Vertical displacement, y-axis
vyc Car body Vertical speed, y-axis
θrc Car body Pitch angle, r-axis
ωrc Car body Pitch angular speed, r-axis
pf s Suspensions Deflection, front
vf s Suspensions Deflection rate, front
prs Suspensions Deflection, rear
vrs Suspensions Deflection rate, rear
θf w Wheels Rotational angle, front
ωf w Wheels Angular speed, front
θrw Wheels Rotational angle, rear
ωrw Wheels Angular speed, rear
Vehicle Model 59

2.6 Simulation Methods

With the vehicle model described, it is important to discuss the simulation methods
that will be applied in this work. Even with a good model, the validity of the
developed control strategies rely on them being tested on representative driving
cycles and that the fuel economy is evaluated in a robust way. There are thus three
important aspects that will be explored in this section: the speed profile of the
driving cycles; the method of assessing fuel economy; and approaches to improve
simulation speed. Each of these will be discussed in turn in this section.

2.6.1 Driving Cycles

To run the simulation model, it is necessary to test it for a specific driving cycle,
which essentially defines the speed profile for the vehicle to follow. The choice of
driving cycle heavily influences the operation and fuel economy of the driving and
it is therefore essential to have an arsenal of driving cycles to apply for the results
to be representative.

The standard European driving cycles are the ECE15 (low-speed urban), EUDC
(medium speed rural/highway) and NEDC (composite of ECE15 and EUDC). These
are quite common in the literature, as they are very simple and the European reg-
ulators apply these to test commercial vehicles and assign official fuel economies.
These type of driving cycles are called modal cycles, and consist of acceleration and
speed profiles of straight lines. These features make them easy to define and, more
importantly, easy to implement. However, both academic work and the industry
have pointed out the significant flaws in these designs. They are overly smooth and
not representative of real-world driving. Also, the load during acceleration stages
of these driving cycles are not representative of modern vehicles, which tend to be
lighter and more powerful. The Japanese driving cycles are also modal cycles.

In contrast, the American driving cycles by the EPA (Environmental Protection

Agency) do not use modal cycles. These cycles, which include the NYCC (low-
speed urban), UDDS (medium-speed urban), HWFET (medium-speed highway),
FTP (medium-speed urban) and US06 (aggressive high-speed rural/highway), are
defined with transient data and are thus much more realistic. However, there is a
60 Chapter 2

150
Vehicle Speed, ucar (km/h) WL-L WL-M WL-H WL-E

120

90

60

30

0
0 450 900 1350 1800
Time (t) (s)

Figure 2.16: Speed profile of the WLTP, with the four different stages (WL-L, WL-M,
WL-H and WL-E) demarcated.

large number of cycles with no intuitively clear choice of cycles to be tested. Fur-
thermore, the driving cycles are US-centric in their speed and acceleration profiles.
Nevertheless, these American cycles were considered the most suitable ones in the
past, and all previously published results are based on these (with some usage of the
EUDC).

However, there is a new driving cycle in development that is called the WLTP
(worldwide harmonized light vehicles test procedure). This project is led by the
United Nations, but has had wide international support and participation. It has
been noted that the deviation between laboratory-based results (based on cycles
like the NEDC) and real-world driving have been increasing over the past decades,
and the effect is particularly pronounced for hybrid vehicles [39]. The WLTP pro-
files are therefore based on internationally collected data of real driving to be as
representative as possible.

The cycle is being developed right now and will be adopted by the EU in 2017 to
replace current cycles [39]. The WLTP is a single driving cycle with four stages that
can be considered as independent driving cycles of their own. These are defined by
their speeds: low (WL-L), medium (WL-M), high (WL-H) and extra high (WL-E).
These speed profiles are shown in Fig. 2.16. Some particular features of the profiles
are given in Table 2.6 (note that the power features are specific for the vehicle design
in this work).
Vehicle Model 61

Table 2.6: Features of the speed profiles for the four driving cycles

WL-L WL-M WL-H WL-E

Duration (s) 589 433 455 323
Stationary time (s) 156 48 31 7
Distance (m) 3095 4756 7158 8254
Maximum Speed (km/h) 56.5 76.6 97.4 131.3
Average Speed excl. stops (km/h) 25.7 44.5 60.8 94.0
Average Speed incl. stops (km/h) 18.9 39.5 56.6 92.0
Minimum acceleration (m/s2 ) -1.47 -1.49 -1.49 -1.21
Maximum acceleration (m/s2 ) 1.47 1.57 1.58 1.03
Maximum load, PP Lmax (kW) 25.69 35.97 41.59 50.36
Average load, P̄P L (kW) 1.96 4.52 7.36 17.32

In this work, it is often necessary to simulate multiple iterations of a particular driv-

ing cycle to exhibit or reliably measure the features of interest. Therefore, whenever
driving cycles are repeated, the notation ×N will be used to indicate N iterations.
For example WL-H×4 refers to a driving cycle comprising four repetitions of the
WL-H driving cycle. It was found that the most useful number of iterations to run
is WL-L×8, WL-M×8, WL-H×4 and WL-E×4, which in total takes just more than
three hours to drive. Although this makes the WL-L part of the simulations much
longer and more time consuming, it keeps the fuel consumption reasonably balanced
across the different driving cycles. Also, it is sufficient to expose most relevant
long-term characteristics (in particular SOC evolution) of the control strategies.

A vast majority of the results in this thesis are based on the above number of
iterations, so whenever WL-L, WL-M, WL-H and WL-E are mentioned without any
explicit information about the number of iterations, then 8, 8, 4 and 4 iterations
have been used for each driving cycle respectively.
62 Chapter 2

2.6.2 Fuel Economy Evaluation

The essence of this work relates to the fuel economy achieved by various control
strategies for a series HEV. However, the definition of fuel economy is not trivial for
a vehicle with multiple energy sources. This subsection will consider various possible
methods to assess the fuel economy of the vehicle for a driving cycle, before pursuing
a particular method in more depth.

The first approach is to only consider the fuel consumed by the ICE, and ignore
the usage of the SS. This can be justified by the fact that all the energy of the
SS ultimately originates from the PS anyway (either through direct charging or
through regenerative braking). Thus, the fuel is the only true energy source of the
vehicle while the battery acts merely as a buffer and temporary storage. However,
this perspective neglects the short-term effects of the battery. A low-speed urban
driving cycle is often quite short (WL-L is 589 s, NYCC is 599 s and ECE15 is 195
s) and can often be driven purely by the SS. With this method of assessing the fuel
economy, the vehicle would be assigned a fuel consumption of zero, and thus an
infinite fuel economy. Thus, this method is clearly flawed for shorter driving cycles.

A second approach is to apply the first method (of only measuring the fuel consumed)
but complement it with the following SOC constraint: SOCf inal = SOCinitial . As
this forces the control strategy to be strictly charge sustaining, with zero charge
consumed over a full driving cycle, the fuel consumed by the ICE is the only rel-
evant parameter left. This is a very popular approach in the academic literature
when investigating and proposing optimization based control strategies. However,
this method requires prior knowledge of the driving cycle for the control strategy to
ensure that the artificially strict SOC constraint is met. This is not representative
of real driving and thus this approach of assessing fuel economy loses validity. Fur-
thermore, many SCSs operate in a charge sustaining but charge oscillatory manner
(e.g. TCS (thermostat control strategy) in Section 3.2). Forcing such a control
strategy to meet the SOC constraint might not only be unrealizable, but would
severely compromise the integrity of the fuel-saving nature of the control strategy.
This approach is therefore not suitable, with the possible exception of evaluating
global optimization-based strategies for benchmarking purposes.

The third approach also applies the first method but with repeated iterations of the
driving cycle being studied. Thus, if the control strategy initially applies SS-only
Vehicle Model 63

driving for a low-speed urban driving cycle, it will not be able to do so indefinitely.
After a few iterations, the SOC will reach its lower limit and the control strategy
will have to operate in a CS manner. Furthermore, as the number of iterations
is increased, the contribution of the ICE fuel to the fuel economy increases. For
example, if a single driving cycle requires 0.1 kg of fuel, and consumes 5% of the
battery charge, the control strategy will need to adjust for the coming two driving
cycles such that the constraint of SOC ≥ SOCL is not violated. The vehicle may
therefore consume 0.3 kg of fuel and 15% (SOCinitial − SOCL ) of the battery charge
over 3 iterations, with no further ability to consume charge over another driving
cycle. However, it remains problematic to determine how 0.3 kg and 15% of battery
charge can be evaluated overall (e.g. against 0.4 kg fuel and 10% battery charge).
But this can be resolved by increasing the number of iterations. After 100 iterations
of the driving cycle, the vehicle will have consumed 10 kg fuel and 15% battery
charge. At this point the battery charge becomes negligible and only considering the
fuel consumption is sufficient. However, running such a high number of iterations is
not desirable from a computational point of view. Not only will running simulations
become onerous, it will be outright prohibitive for tuning processes.

The fourth approach is therefore to evaluate the fuel and charge consumption under
a single paradigm. It is possible to consider the efficiency of the components, the
cost of operation, or any other factor which both fuel and charge can be translated
to. However, the most suitable approach that is often used in the literature is to
convert the consumed charge into an equivalent fuel consumption (EFC). It allows
comparison of the overall fuel economy by considering the actual fuel consumption
as well as the shortage/surplus of final SOC. Many analytical methods have been
described in the literature to define such an equivalence between SOC and fuel
consumption [40–42]. For the purposes of analyzing the results in this work, the
line-chart approach described in [42] is adopted as it is a natural extension of the
GECMS (which will be described in Section 3.4). The total EFC is defined as

 mf + Sd,ef c · ∆SOC Qmax vb,OC ∆SOC ≥ 0
QLHV
mef c = Qmax vb,OC
, (2.37)
 m +S
f c,ef c · ∆SOC QLHV ∆SOC < 0

where ∆SOC = SOCinitial − SOCf inal , Qmax is the battery capacity and vb,OC is the
battery open-circuit voltage. The two equivalence factors Sd,ef c and Sc,ef c need to
be identified for each driving cycle by determining the correlation of the electrical
64 Chapter 2

energy Ee and the fuel energy Ef required to drive the driving cycle in question,
where
Ef = mf QLHV (2.38)

Ee = ∆SOCQmax vb,OC . (2.39)

To run these simulations it is necessary to operate with some control strategy, and
this choice will influence the resulting equivalence factors. The SCS suggested in
[42] is to apply a simple proportional control strategy as

PP Sref = uef c PP L (2.40)

where uef c is a constant.

A sweep is therefore performed for uef c ∈ [0, 2], in steps of 0.05 units, to obtain a
wide set of power shares between the PS and SS. The obtained values of Ee and Ef
(for WL-L×2, WL-M×2, WL-H×1 and WL-E×1) are plotted against each other in
Fig. 2.17. It can be seen that the slopes of the correlation has two distinct sections
for each driving cycle, separated by the reference electric energy Ee0 . This term is
the value of Ee for the case when the SS is only used during regenerative braking
(corresponding to uef c = 1). The slope of the Ee -Ef charts for Ee ≤ Ee0 gives the
negative values of Sd,ef c , while the case of Ee ≥ Ee0 gives the negative values of
Sc,ef c . These can intuitively be understood as the conversion factors between fuel
energy and electrical energy, for the cases of discharging (data marked as plus signs)
and charging (data marked as circles) respectively.

However, the lines are not completely linear. For higher uef c values, the results
are distorted as the battery approaches SOC = 100% and for lower values the
inefficient use of the PS, and the SSS begin influencing the operation. The latter
is particularly true for WL-L where low load combined with low uef c results in the
PS being operated very inefficiently (in a way it would never operate during real
driving). The applied method for determining the equivalence factors, as suggested
in [42], has limitations in which points to consider when calculating the slope. The
suggestion of setting the lower and upper limit by the values corresponding to SOCU
and SOCL respectively is only appropriate if the Ee0 is quite close to the center of
the sloped lines. This can best be understood by considering the case of WL-M×2,
where the Ee0 appears quite close to the lower constraint (checked line corresponding
Vehicle Model 65

40 40
uef c ≥ 1
uef c ≤ 1

30 30
SOC = 80% SOC = 50%
Ef (MJ)

20 SOC = 50% 20
SOC = 80%

10 10

0 0
-4 -2 0 2 4 -10 -5 0 5
40 40
SOC = 80%

30 30 SOC = 50%

SOC = 80%
Ef (MJ)

20 SOC = 50% 20

10 10

0 0
-4 -2 0 2 4 -5 0 5 10
Ee (MJ) Ee (MJ)
Figure 2.17: Correlations between electrical energy Ee and fuel energy Ef with uef c ∈
[0, 2] for WL-L, WL-M, WL-H and WL-E (left to right, top to bottom).

to SOCU = 80% in Fig. 2.17), only allowing five points to be considered when
determining the slope and Sd,ef c . A more extreme case can be considered with WL-
M×4 for which all the tested points within the span SOCL < SOCf inal < SOCU
would have Ee > Ee0 , thereby making it impossible to determine Sd,ef c .

An alternative approach is to limit the testing range in terms of uef c rather than
SOC. By only plotting and considering the slopes of uef c ∈ [1 − α, 1 + α] the testing
points will always be symmetric around Ee0 (corresponding to uef c = 1). This
method is applied here with α = 0.5 and the resulting Ee -Ef charts are presented
in Fig. 2.18.

The lines of best fit are also shown in the charts, and the resulting equivalence
factors can be obtained my measuring their slopes. To confirm the validity of this
method, these values are applied to assess the fuel economy of a strategy (GECMS,
which is described in Section 3.4) which is known to produce optimal result such
66 Chapter 2

18 30
uef c ≥ 1
16 uef c ≤ 1
25
14
Ef (MJ)

12 20

10
15
8

6 10
-3 -2 -1 0 1 2 -4 -2 0 2
20 30

18
25
16
Ef (MJ)

20
14

12 15
10
10
8
6 5
-3 -2 -1 0 1 2 -4 -2 0 2 4
Ee (MJ) Ee (MJ)
Figure 2.18: Correlations between electrical energy Ee and fuel energy Ef with uef c ∈
[0.5, 1.5] for WL-L (top left), WL-M(top right), WL-H (bottom left) and WL-E (bottom
right), together with the line of best fit for both charging and discharging cases.

Table 2.7: EFC factors as determined by the correlation between Ef and Ee

Driving cycle Sd,ef c Sc,ef c

WL-L 2.80 2.59
WL-M 2.98 2.46
WL-H 3.09 2.45
WL-E 3.54 2.91

that SOCf inal ≈ SOCinitial . Badly selected equivalence factors will not yield this
result. However, it is possible to have false positives, so this criterion is a necessary
condition but not sufficient. The equivalence factors obtained by the mentioned
line-chart method for α = 0.5 satisfied these tests (although the Sd,ef c value for
WL-L×2 had to be modified from 2.77 to 2.80), and the final equivalence factors
are presented in Table 2.7.
Vehicle Model 67

Recognizing the fallibility of these equivalence factors, the fuel economy results in
this work will apply these together with the approach of running multiple iterations
of each driving cycle. Even if the equivalence factor for a particular driving cycle
is off by 0.1, the worst case scenario (SOCf inal = 50% with WL-L) would result in
a an error in fuel economy assessment of 1.1%, while for normal driving conditions
(60% ≤ SOCf inal ≤ 70% the error would be less than 0.36%.

It is useful to be able to evaluate the fuel economy of several driving cycles together.
In this work, when evaluating the total fuel economy of a particular control strat-
egy, the four mentioned driving cycles will be used (WL-L, WL-M, WL-H, WL-E).
However, the defined number of iterations (8, 8, 4 and 4 respectively) is found to
bias the summed fuel economy too heavily towards the WL-E driving cycle, which
consumes a significant amount of fuel. Therefore the total fuel economy will only
consider half the EFC contribution from WL-E, as follows:

mtot = mef c,W L−L + mef c,W L−M + mef c,W L−H + mef c,W L−E /2. (2.41)

Furthermore, the fuel economy results will typically be normalized against the opti-
mal performing strategy or tuning parameter selection as follows (unless explicitly
defined otherwise):
mef c
Mef c = , (2.42)
mef c,opt
mtot
Mtot = . (2.43)
mtot,opt

Finally, for all the control strategies implemented in this work, the GECMS will be
used as a benchmark to express the fuel economy. Thus, the relative performance
to the GECMS will often be used, which is defined as:

mef c
∆GECM S = (2.44)
mef c,GECM S

where mef c is the EFC of the control strategy being evaluated and mef c,GECM S is
the EFC of the GECMS for the same driving conditions.
68 Chapter 2

2.6.3 Simulation Speed Improvements

The developed high-fidelity model captures detailed dynamics of the hybrid power-
train and offers more accurate results compared to other models in the literature.
However, this depth and accuracy comes at the expense of computational burden
and simulation time. Whilst other models can simulate a second of driving within
a few milliseconds, this used to take about 14 seconds for Model0. This is a serious
bottle-neck for any work on the model, and thus measures were taken to speed up
simulations.

The conventional approach would be to simply reduce the model by removing some
of the model dynamics. This is indeed the reason why most control strategy work
is done on very simplistic models. However, a core part of the motivation for this
work is to study control strategies when applied to high-fidelity models. Thus, it
is essential to maintain at least one full-scale version of the model. The approach
taken here is therefore to speed up the full model as much as possible with negligible
effect on simulation results, and then accompany it with a significantly faster model
with limited deviation in simulation results. The reduced model will be particularly
useful for various debugging and tuning processes where hundreds of iterations might
be required, translating into months of simulation time, which is unacceptable.

The first technique that is applied to speed up simulations is to re-implement the

model with simpler and leaner tools in Simulink, to realize the same dynamics with
lower computational burden. Rather than implementing an equation with a dozen
graphical mathematical blocks, it can be expressed with a single user-defined func-
tion. These are not only more efficient in terms of computational burden, but also
make the model more user-friendly and concise. Furthermore, nested subsystems
adversely affect simulation time and have therefore been minimized as much as rea-
sonable without compromising clarity.

A second technique that has been applied is the reduction of required memory. Al-
though the required memory has small impact on simulation time, it affects the
ability to run multiple simulations in parallel. If each simulation (the longest types)
requires 4 GB of RAM to complete and there is only 8 GB spare RAM, then only
two parallel simulations can be run. However, if the required memory is reduced to
2 GB per simulation, then four parallel simulations can be run. This can practically
Vehicle Model 69

be considered as doubling the simulation speed. This is primarily achieved by re-

moving superfluous signals, scopes and outputs, but it is also necessary to reduce
the sampling frequency of some of the data collection. Furthermore, attention is
given to the data type of signals stored and time-arrays are not collected for each
individual signal, but instead as a single array overall.

A third technique is to resolve any algebraic loop (AL) within the model. ALs occur
when a signal A is needed to compute a signal B, but at the same time signal A
needs signal B to be defined. Simulink can generally solve these iteratively but
the process is very inefficient. Therefore, each of the ALs within the model were
solved, using the following three approaches: redefining the dynamic to avoid the
loop; introducing an “initialization value” for one of the signals; or introducing a
unit delay (0.1 ms) between the signals. Each of these changes had negligible effect
on the simulation results, but significantly sped up simulations.

A fourth technique is to introduce unit delays in other parts of the model to reduce
the interconnectivity of the model blocks. This allows Simulink to compute the
model and its components with fewer interdependencies, again resulting in faster
simulations. However, these need to be applied carefully and appropriately. Thus,
unit delays were included for reference signals (e.g. ωICEref and PP Sref ) which would
experience a minor lag in a real vehicle as well. The DC link voltage vdc is practically
constant at 700 V and connects to most components in the vehicle. It is therefore a
prime candidate for a unit delay. However, the SS is somewhat sensitive to the vdc in
determining PSS , which if disturbed would affect the simulation results noticeably.
As a result, vdc has only been delayed within the PS and PL).

A fifth technique is to apply accelerators within Simulink. This is related to the

earlier point about removing ALs. A model without any ALs can make use of ac-
celeration tools within Simulink. When running the model, Simulink will generate
a C-MEX S-function to perform the simulation external to the Simulink environ-
ment. This significantly speeds up the simulation, while only taking a few seconds
of additional compilation and build time. Additional drawbacks, such as limited
interactivity during run-time, are not very relevant for our purposes.

All of the mentioned techniques can be applied with negligible loss of precision in
results and deliver significant improvements in simulation speed. However, the simu-
lation speed has only been sped up by a factor of about five. To truly begin speeding
70 Chapter 2

V_dc
1
1
I_PL

Reduced: P_PL P_PL/V_dc

Figure 2.19: Simulink implementation of the reduced model, where a pre-recorded PP L
signal is used to produce the iP L signal for the model.

up the model, a separate reduced model is considered, where we will compromise on

precision to a slightly larger extent.

The vast majority of simulations that are performed within this work are interested
in the fuel economy of the vehicle for a particular driving cycle for a particular
control strategy. The main signals of interest are therefore the accumulated fuel
consumption (mf ) and final value of battery SOC (SOCf inal ), which will provide the
EFC (mef c ), as described in the previous section. By studying the series powertrain
in Fig. 2.1, or the control diagram of the model in Fig. 2.13, it can be understood
that the operation of the PL is independent of the control strategy being used. The
PL simply determines the PL current iP L that flows into the DC link, after which
the SCS determines how the PS and SS should share in meeting this load. The PL
only depends on the driving cycle ucar,ref (and on the DC bus voltage to a negligible
extent).

It thus follows that the PL can be replaced by a pre-defined signal. The full model
can be simulated for all driving cycles of interest, and the resulting PP L for each case
is recorded. Then a separate reduced model can be produced where the recorded
PP L signal is a pre-defined input, as shown in Fig. 2.19. This block replaces the
PL and driver model in the overall model, as shown in Fig. 2.20. Note that the
Propulsion Load and Driver models have been “commented out” (as indicated by
the % sign) and are not simulated. The removal of the inverter, PMSM, driver and
CVT models are very helpful, but it is particularly the car dynamics that are worth
removing. Even though the car dynamics have been made faster by implementing
them with SimMechanics within Simulink (as opposed to with VehicleSim in Model0
and Model1), this remains one of of the most computationally heavy blocks of the
model. Consequently, the simulation speed is dramatically improved.
Vehicle Model 71

Driver
SOC SOC
P_PS,ref T_lm,ref u_car
V_dc
w_ICE
I_SS
w_ICE,ref
I_PL T_car,ref u_car
Secondary Source
Supervisory Controller
V_dc I_PL

I_PL
V_dc Propulsion Load
w_ICE
I_SS V_dc
P_PS,ref V_dc I_PL

I_PS I_PS Reduced PL

w_ICE,ref
DC Link
Primary Source Merge

Figure 2.20: Overall Simulink model where the Reduced PL is integrated to override
the full PL and driver that have been commented out (as indicated by the % symbol).

To quantify the benefits and costs of these procedures, simulations are run for various
versions of the model and simulation speed Ssim (seconds of simulated driving in
1 real second) and EFC mef c are measured. The results for Ssim and Eef c (the
error in mef c relative to the “Full model”) are presented in Table 2.8 and Table 2.9
respectively for WLTP as well as separate simulation of its individual stages (WL-L,
WL-M, WL-H and WL-E). Note that the “Full model” does not have all the ALs
that were present in Model0 and that the latter can not be compared in terms of
EFC due to differences in component sizing.

The speed results are quite consistent across driving cycles, but it can be noted that
the speed tends to be higher for longer driving cycles. This is mainly due to the
effect of the building and compilation times becoming increasingly negligible as a
proportion for longer simulations. Thus, the WLTP results can be considered most
representative for simulations required in this work. The EFC results on the other
hand are very dependent on the individual driving characteristics of the driving
72 Chapter 2

Table 2.8: Comparison of simulation speeds Ssim for original, full and reduced models
for various driving cycles (all results for Model0 were obtained for NEDC). Simulations
with acceleration mode are marked with “Acc”.

Model WLTP WL-L WL-M WL-H WL-E

Model0 0.0714 0.0714 0.0714 0.0714 0.0714
Full model 0.1217 0.1175 0.1226 0.1232 0.1227
Full model, Acc 0.4401 0.4401 0.4375 0.4227 0.4150
Reduced model 0.3039 0.2928 0.2971 0.2974 0.2965
Reduced model, Acc 3.7336 3.6555 3.4456 3.5747 3.3936

Table 2.9: Comparison of error in EFC Eef c (%) with regards to the Full model results
for various driving cycles. Simulations with acceleration mode are marked with “Acc”.

Model WLTP WL-L WL-M WL-H WL-E

Full model 0.0000 0.0000 0.0000 0.0000 0.0000
Full model, Acc -0.0004 -0.0005 0.0001 -0.0003 -0.0005
Reduced model -0.0352 -0.1227 -0.0658 -0.0488 -0.0111
Reduced model, Acc -0.0355 -0.1226 -0.0657 -0.0489 -0.0111

cycles and thus vary significantly. However, the WLTP (which comprises the four
other driving cycles) can be considered to include a variety of all these driving
dynamics and is quite representative of all types of driving. Nevertheless, many
upcoming simulations will include repetitions of a particular type of driving, so the
worst case scenario is of most interest.

Comparing the models for WLTP, it is clear that the Full model improved the simu-
lations significantly (+70% in speed) over Model0, just by reimplementing the blocks
and introducing some minor delays (the first four techniques mentioned above) de-
spite the new model having more complex converter models. As the accelerator
mode is used, the full model increased simulation speed by another 262% while hav-
ing a negligible impact on EFC. This is the model that will be used to generate
final results within this work. Lastly, the reduced model with acceleration mode is
able to improve the simulation speed by another 748% while compromising the mef c
precision by about 0.12% at worst (0.04% for WLTP overall). This reduced model
will be used for the tuning processes for all control strategies in this work.
Vehicle Model 73

2.7 Summary

This chapter has described the vehicle model that will be used within this work. It is
a series HEV, where the PL comprises an inverter, PMSM, CVT and car dynamics;
the PS includes a turbo-charged diesel engine, PMSG and rectifier; and the SS
consists of a Li-ion battery and a DAB DC-DC converter. The three branches are
connected together at the DC link where energy is exchanged. The SCS determines
how the load power PP L should be distributed between the PS and SS.

The model has been changed and improved upon in several respects since Model0.
Several of the components have adjusted power ratings (e.g. ICE from 34 kW
to 58 kW, PMSG from 92kVA to 75 kVA, battery from 30 kW to 42 kW), new
loss dynamics have been included (e.g. detailed loss models for inverter, rectifier
and DC-DC converter, rather than fixed efficiencies), and the overall control of the
powertrain has been redesigned (e.g. introducing a SSS, retuning most PI loops,
and optimizing engine speed as a function of PP S ).

This chapter has also presented the driving cycles that will be employed within this
work: WL-L, WL-M, WL-H and WL-E (the four stages of WLTP). Each of these will
typically be repeated multiple times in each simulation to allow more reliable results
and to investigate dynamics that only appear over longer time frames. Furthermore,
the concept of EFC is introduced as a means to express the fuel economy of the
vehicle with consideration for the charge consumed by the SS over a driving cycle.
To this end, the equivalence factors Sd,ef c and Sc,ef c have been identified for each
driving cycle, to be used to evaluate fuel economy results in upcoming chapters.

These changes to the model dynamics have been accompanied with significant im-
provements in modeling implementation, allowing simulations to run more than six
times faster than Model0. In addition a reduced model has been designed that en-
ables simulations at more than 50 times the speed of Model0 with only minor loss
in precision. This reduced model has allowed this work to progress much faster, as
the time spent on the tuning and debugging processes for each control strategy have
been dramatically reduced. This will benefit all future work as well.
Chapter 3

Conventional Strategies

The research area of SCSs for HEVs has been quite active for the past two decades,
and a handful of techniques and strategies have established themselves as the de-
fault choice for benchmarking, prototyping or inspiration for novel strategies. These
conventional strategies are the topic of this chapter.

The chapter will begin by describing past work in the literature, exploring rule-based
strategies, real-time optimization-based strategies, and global optimization-based
strategies. The aim is to briefly introduce the reader to a wider body of work in this
research area, and set this work in both its research and historical context. Particular
attention will be given to the thermostat control strategy (TCS), power follower
control strategy (PFCS), equivalent consumption minimization strategy (ECMS),
its globally tuned version GECMS, and dynamic programming (DP), as these have
been most influential in this research area.

Based on this review, the TCS, PFCS and GECMS will be implemented for the
purpose of study and benchmarking. Each of the three control strategies is designed,
implemented and tuned before its operation and performance is evaluated. These
strategies (the GECMS in particular) will serve as both inspiration and benchmarks
for novel control strategies in upcoming chapters.

75
76 Chapter 3

3.1 Background

As mentioned in the last chapter, the earliest HEVs employed series architecture,
and practically operated as an electric vehicle with an engine-generator set aboard
to recharge the battery. There was thus barely any designed control strategy. As the
concept of hybrid vehicles evolved, and the engine-generator set would increasingly
power the propulsion motor at the same time as the battery, the role of the control
system became more important. However, this proved to be a challenging task, and
the interaction between the battery, engine and the control system remained one of
the biggest challenges for these early HEVs (in addition to cost) [43].

The early implementation of simple rules to control the powertrain, was arguably
more concerned with meeting the operational constraints of the components than any
type of optimization of the fuel economy. However, in the early 1990s the academic
research on SCSs accelerated significantly [44], developing and consolidating several
key control strategies that are popular even today. It is worth noting that this boom
in control strategy research happened years before the Toyota Prius was released in
Japan in 1997 and was later brought to the US market in 2000.

This section will discuss some of the most conventional control strategies in the
literature from the past two decades. Although the thesis overall deals primarily
with series HEVs, there has been such a rich exchange of ideas and concepts between
HEVs of varying architectures that this section will explore the evolution of control
strategies without limiting the scope to just series HEVs (although this will be
given some prominence). The section will begin by discussing rule-based controllers,
followed by real-time control strategies and finally the global optimization-based
strategies.

3.1.1 Rule-based Strategies

Most commercial vehicles apply rule-based control strategies due to their ease of use
and reliability. For series HEVs the two most conventional strategies are the TCS
and PFCS. The evolution of these two will be discussed, followed by some alternative
heuristic strategies.
Conventional Strategies 77

Thermostat and Power Follower Control Strategy

In 1995, Anderson and Petit discussed several concepts for the design of control
strategies for series HEVs in [45], where the essential features of the TCS are defined.
This was followed up by work in 1996 by Hochgraf et al., that made a more detailed
study of the TCS in [46]. Since then, the TCS has been established as the most
conventional control strategy for series HEVs and is used as a benchmark to this day
[47–50]. It operates the powertrain in two distinct modes: battery only mode and
active engine mode. The default mode of operation is with the battery only, making
the propulsion of the vehicle completely electrical. However as the battery depletes
its charge and reaches a defined lower limit, the engine-generator set is activated
and is thereafter operated at its optimal operating point. This point of operation
of the engine-generator set is typically higher than the load of the vehicle during
driving, so the surplus energy is directed to the battery, which is thus gradually
recharged. As the battery SOC reaches a defined upper limit, the engine-generator
set is switched off, and the vehicle operates in pure electric mode once again. This
control strategy is implemented later in Section 3.2.

Two years later, in 1997, Cuddy and Wipke implemented a PFCS in a series HEV
[51], just a few months before Jalil et al. would do the same in [52]. These were
the first implementations for a series HEV, but early work on control strategies
operating on the same principles can be found as early as 1987 for parallel HEVs
[53]. This control system has several modes of operation, but the two main ones are:
battery only mode and power following mode. At very low loads (sometimes also
constrained to low speeds) the battery is used to drive the powertrain. However,
above a minimum load, the PS is responsible for meeting the full load of the driving.
Later developments of the PFCS include a small deviation from pure power following
that is proportional to the change in SOC of the battery [54]. This deviation ensures
that the battery is charged for lower SOC and discharged at higher SOC values,
thus making the strategy charge sustaining (CS). The PFCS has been used for
series HEVs but has seen particular success when implemented in HEVs of parallel
architecture. Most importantly, the control strategies of most commercial HEVs so
far are based on this control strategy [55, 56]. This control strategy is implemented
later in Section 3.3.
78 Chapter 3

The principle of operating the PS at a constant load and using the battery as an
equalizer, like the TCS, is commonly referred to as load leveling. In contrast, the
principle of having the PS power follow the load power, like the PFCS, is called
load following. Each of these will be explored further in Section 5.1, discussing the
design principles of heuristic strategies. The advantages and disadvantages of the
load leveling and load following methods have been further understood over the past
two decades and several control strategies have been proposed to exploit the best
of each. This is exemplified by the more recent work by Kim et al. [57], which
proposed the hybrid thermostat strategy (HTS) which has its basis in the TCS,
but applied concepts from the PFCS to achieve improved performance. A similar
approach was also taken in [58] by Ko et al. This more comprehensive approach is
particularly relevant when considering multi-objective control. For example, Zhang
et al. designed a control strategy in [59] which is based on TCS to achieve good
fuel economy but, recognizing the resulting harsh usage of the battery, the control
is modified to not operate the engine-generator set strictly at its most efficient point
at all times. In this particular case a sliding mode controller is applied to achieve
this result.

Maximum SOC-of-PPS

Although the TCS and PFCS can be considered the parents of most deterministic
rule-based strategies, there are a few exceptions. One noteworthy alternative to
the TCS for series HEVs, is the Maximum SOC-of-PPS (MSP) that is presented in
[47]. It aims to keep the SOC at a high level persistently by often operating with
only the engine-generator set to meet the load. In doing so, it often operates the
engine-generator set inefficiently, which is why it is not as popular. However, it
offers benefits beyond fuel economy.

MSP recognizes a few limitations of the TCS in terms of reliability. Firstly, the TCS
does not guarantee CS operation for any driving cycle (as will be demonstrated
later in Section 3.2) [47]. If the average load exceeds the optimal operating point
of the engine-generator set, the SOC will keep on decreasing even when the engine
is on. Secondly, as the SOC of the battery oscillates between its lower and upper
bound, the performance of the powertrain will be compromised at the lower bound
[47]. The lower battery voltage at this stage will reduce the battery efficiency and
possibly (if no DC-DC converter is present) reduce the voltage level (and thus power
Conventional Strategies 79

rating) of the electric machines in the powertrain. Both of these limitations can be
unacceptable in mission critical situations, such as for a military vehicle (which is
one of the common applications of series architecture) [47]. The MSP addresses
these issues by maintaining the SOC high, and operating the engine-generator set
more flexibly.

Other

The heuristic strategies mentioned so far have all been deterministic. A second cat-
egory of heuristic strategies include the fuzzy logic controllers (FLCs), which apply
fuzzy logic to handle different operating modes, as opposed to discrete thresholds.
This makes the control strategy more robust to disturbances and less sensitive to im-
precise data input [56]. Like the PFCS, these control systems have historically and
typically been developed for parallel HEVs, but have seen implementation in series
HEVs as well [60, 61]. Although the FLCs are rule-based, they are not as heuristic
as the previously mentioned strategies. As FLCs excel at handling multiple inputs
and outputs, it is not uncommon for them to work with additional inputs, such as
GPS data in [60].

A third category of heuristic control strategies that is often mentioned is the State
machine controllers (SMCs), with the only prolific contribution being by Phillips et
al. in 2000 in [62]. It involves a set of dynamic rules to govern the hybrid powertrain
in numerous different conditions and ten distinct states. With such clear operating
conditions and well defined state transitions, the resulting control strategy is very
robust. However, arguably, this category of systems is not a separate category of
rules, but rather a different method of implementation. In fact, control strategies
such as TCS and PFCS might have historically been implemented with simple logic
gates or if-else statements, but they are now often implemented with state machines.

Overall, two decades from inception, the TCS and PFCS remain the go to control
strategies for both prototype and benchmarking purposes. Not only are they simple
to implement but they have historically performed quite well. The advancement of
fuzzy logic based controllers is seen to hold high potential but the impact so far
has mainly been within academic circles. Among commercial vehicles, the heuristic
strategies are still more prevalent than optimization based strategies due to their
simplicity and effectiveness [55, 63].
80 Chapter 3

3.1.2 Real-time Optimization-based Strategies

This subsection explores various real-time optimization-based control strategies that

have been applied for the supervisory control of HEVs. As the dominant approach
in this field is the ECMS, this will be treated first separately. Thereafter the model
predictive control (MPC) approach will be explored and lastly some alternative
techniques will be mentioned briefly.

Equivalent Consumption Minimization Strategy

Although the heuristic strategies are able to deliver good performance with a simple
approach they are unlikely to deliver fuel economies (or any other control objective)
close to the global optimal. Thus, to achieve improved results, researchers have
applied concepts from optimal control theory in the context of a hybrid powertrain.

The first step is to determine a cost function. The general problem for a vehicle is
to minimize the fuel consumption:
Z tf
J= ṁf (t, u(t)) dt (3.1)
0

However, such an objective would result in persistent use of the battery (to achieve
J = 0). It is thus necessary to include a penalty for the discharging of the battery
(as well as a reward for charging it):
Z tf
J= ˙
ṁf (t, u(t)) + w · SOC(t) dt (3.2)
0

As pointed out in [44], this approach has often been used with an arbitrary weight
w [64–66].

The ECMS takes the approach of defining w by an analytical equivalence between

fuel and charge. The concept of such an equivalent fuel consumption (EFC) factor
was introduced by Kim et al. in 1999 [67] and it established the foundation for the
real-time strategy presented by Paganelli et al. in 2000 [68]. This work evolved over
several years in Ohio with several publications [69–72], and gained traction around
2004 when several influential publications developed the ECMS further. Pisu, Riz-
zoni and the team at Ohio State University would continue and build on the work
Conventional Strategies 81

of Paganelli, and apply the ECMS to series HEVs as well [73, 74]. This also resulted
in the development of an adaptive ECMS (A-ECMS), which added an estimating
algorithm onto the ECMS, to adapt the equivalence factor based on the propulsion
load during driving [75]. This work also compares the optimally tuned ECMS to
a DP solution, and finds the results to be practically identical. However, the work
notes that the DP solution were executed on a simpler quasi-static model to allow
reasonable computation time. This makes the comparison of results less valid, but
nevertheless suggests that the ECMS technique is potent.

At the same time in ETH Zurich, the ECMS is being applied and refined by Scia-
rretta, Guzzella and their team. In [42], the equivalence factor is redefined to be
applied at each time instant as:

J(t, u) = ∆Ef (t, u(t)) + s(t) · ∆Ee (t, u(t)) (3.3)

where ∆Ef and ∆Ee are the used amount of fuel and electrical energy respectively.
Unlike previous versions of ECMS, this definition does not rely on average efficiencies
for the powertrain components [56]. Also, it considers each operating condition and
control input when defining the equivalence factor at each time instant. Intuitively,
this can be considered as the association of use of electrical energy to the future
change in fuel consumption (as the battery is merely an energy buffer). However,
during implementation, the equivalence factor is actually simplified to

s(t) = p(t)Sdis + (1 − p(t))Schg (3.4)

where Sdis and Schg are the discharging and charging equivalence factors (that are
either tuned or defined by the process described in Section 2.6.2) respectively. The
probability function p(t) expresses the probability of the final amount of electrical
energy Ee being positive. Thus, it is unable to precisely implement the optimal
equivalence factor s(t) that would yield the best possible fuel economy. However,
simulation results have shown that the resulting performance is very close to the
global optimal results (as obtained through DP solutions), with a gap of 0.1 to 2%.
Considering the relative simplicity of this method, it is very powerful.

The next evolution of the ECMS was the association to the Pontryagin’s minimum
principle (PMP), which offers a set of necessary conditions for the optimal control,
allowing a reduction of the search space for candidate solutions. The PMP was
82 Chapter 3

applied in two separate control strategies proposed in 2008: [76] for a parallel HEV
and [77] for a series HEV. It was thereafter evaluated in relation to the ECMS
for a series HEV in 2009 by Serrao et al. at Ohio [78]. It was shown that the
ECMS, under certain circumstances, is equivalent to the global optimal solution
offered by the application of PMP. But while the PMP requires prior access to the
whole driving cycle, the ECMS allows a real-time and straightforward approach
for implementation. One of the assumptions in this work is a constant battery
efficiency as it simplifies the problem significantly. The conclusion of this work
is that ECMS allows the identification of the global optimal solution. However,
this equivalence between ECMS and PMP was re-evaluated in 2011 by Kim et al.
in [79]. Although the strong link between the two approaches is re-affirmed, it
emphasizes the simplifications required for the ECMS to be equivalent to the PMP.
One of the possible suggestions to improve performance would be to consider multiple
equivalence factors (e.g. S1 , S2 , S3 , S4 and S5 ) rather than just two (e.g. Sdis
and Schg ) when determining the overall equivalence factor s(t). Nevertheless, by
comparing to DP, it found that the solutions are practically identical. However, it is
worth noting that some of the PMP results were superior to the DP solutions (which
should be impossible). This was attributed to truncation and numerical errors in
the simulations, which were run for a static model.

More recent developments for the ECMS have been incremental rather than con-
ceptual. The framework of the ECMS has not changed in concept, but has rather
expanded to deal with a larger set of control objectives. The nature of the problem
formulation of the ECMS lends itself towards including additional variables and con-
straints with additional equivalence factors. Several contributions have been made
that also consider emissions, battery health [80, 81] and drivability. Other work has
expanded the ECMS by considering additional input information, by using a GPS
[82] or telematics [83]. This has led to more work taking the MPC approach to the
control problem.

In 2013, the collaborative paper [3] (authors include Serrao and Sciarretta) was
published to discuss open issues within supervisory control of HEVs, from the per-
spective of the ECMS and PMP framework. One of the main issues raised was that
the simplicity of the models (quasi-static, isothermal) used to design ECMS (and
other optimal control strategies) are unrealistic. Typically, the SOC is considered
the only state of the powertrain. In particular engine temperatures are identified as
Conventional Strategies 83

having a significant impact on the resulting fuel economy. Interestingly, it is found

that heuristic strategies might perform better than ECMS strategies that are based
on engine models that do not consider engine temperature (as heuristic strategies
are less dependent on engine models).

Model Predictive Control

The MPC approach has a great track record in industrial applications and has been
applied to HEVs as well over the past decade. It is a success story for optimal
control theory, as it was adopted in chemical plants and oil refineries already in the
1980s and has expanded to other areas since then. The basic principle is to design
a predictive model that allows you to determine the impact of your control input.
By solving such an optimization problem over a finite time horizon, it allows the
determination of a the optimal control input at the immediate time instant, which is
then implemented. The time horizon is chosen such that the problem can be solved
in real-time. The approach is particularly useful when it is essential to avoid certain
types of operation (typically due to system instability or regulation).

The earliest example of the use of MPC for the supervisory control of HEVs can be
found in [84] in 2004, although a few other earlier work had considered the use of
predictive data. MPC was also being used for other purposes: [85] used it to prevent
depletion of hydrogen in hybrid fuel cell vehicles; [86] applied it to steer autonomous
vehicles; and [87] applied it for adaptive cruise control in vehicles. The consequence
of bad control in the two latter applications is a collision of vehicles which is clearly
essential to avoid. However, it has become increasingly more common to apply MPC
solely for the purpose of improving the fuel economy of the HEV.

The publication of the paper [88] by Johannesson et al. in 2007 (based on the paper
with the same name in 2005 [89]), might be considered an important moment in the
development of MPCs for HEVs. The emphasis of the paper was to evaluate the
potential of predictive control for HEVs, assuming that accurate data could be ob-
tained through GPS and telematics. The results were promising and were followed
by a significant amount of research the coming years. This has also been boosted
further by the trend of navigation systems becoming standard in new commercial
vehicles, and developments towards communication between vehicles and infrastruc-
ture [90]. Also, as computational power is becoming cheaper and more available on
84 Chapter 3

vehicles, the MPC becomes more attractive. MPC techniques have become partic-
ularly popular for power split HEVs [2], but [91] presented a stochastic MPC for a
series HEV.

However, the suitability of MPC for HEV application has limitations. Wang and
Boyd state in [92] that MPC is only suitable for systems with slow dynamics, which
a HEV wouldn’t really qualify as. Also, the benefits offered by MPC might be more
useful as a safety system rather than an energy management system.

Other

One of the weaknesses of DP (see next subsection) is that it produces a driving

cycle specific control policy that is not generally applicable. This has been dealt
by the development of stochastic DP, where the driving load is determined by a
random Markov process [93, 94]. The same effect has also been achieved by training
neural networks (NN) with various driving profiles [50, 95]. In each of these cases
a significant amount of offline analysis is required, but the resulting control policy
can be implemented in real-time.

3.1.3 Global Optimization-based Controllers

Finally, this subsection will present a few global control strategies. Here, global refers
to the available data: a global controller is acausal and has access to the full driving
cycle at all times. Such an infinite-horizon problem is not real-time implementable,
but serves other purposes (benchmarking, inspiration, etc.). The first technique to
be discussed will be DP, which has established itself as the default global optimal
approach for HEV control systems. This will be followed by the GECMS, which is
the global solution preferred in this work, and will be followed by briefly mentioning
alternative strategies.

Dynamic Programming

DP is a numerical optimization technique based on the Bellman’s principle of op-

timality [96], which has been expressed in [97] as: “An optimal control policy has
Conventional Strategies 85

the property that no matter what the previous decisions (i.e. controls) have been,
the remaining decisions must constitute an optimal policy with regard to the state
resulting from those previous decisions.” This allows the problem to be solved in
a backwards fashion, based on a defined final state. This requires the evolution of
states to be incremental:
x(t + 1) = f (x(t), u(t)). (3.5)

The essence of the DP method is to discretize the problem (time-domain, states and
control inputs), such that the solution space is made finite. Naturally, the precision
of the optimality of the DP solution is proportional to how finely these spaces are
discretized. As the technique requires access to the whole driving cycle in advance
to determine the optimal solution, the process is acausal and not implementable in
real time. Furthermore, it is worth noting that the computational time increases
linearly with the drive cycle duration, but increases exponentially with the number
of model states [44]. Thus, the main restriction of DP is that it can only be applied
to relatively simple models.

The first DP implementation was done for a series HEV, due to the fewer number
of decision variables in this architecture, by Brahma et al. in 2000 [98]. The model
used a single state, a sampling time of 1 second and a power discretization of 5 kW.
This simple model yielded useful results in about 10 minutes on a general purpose
PC. This inspired the work of Lin et al. in 2001 for a parallel truck [99], which
was further improved and developed in 2003 in [100]. A model with three states
was used: SOC, vehicle speed and transmission gear. They simplified their normal
vehicle mode such that Eq. 3.5 is abided for each state. Despite these simplifications,
the optimization process required a sampling time of 1 second, and resulted in errors
in vehicle speed of up to 3 km/h. However, the solution was useful enough to provide
insights to design a refined rule-based controller that outperformed a conventional
heuristic strategy.

Many further implementations of DP have been made since then, but they have
always been limited to simplified models. However, techniques have been suggested
to reduce the computational burden by, for example, reducing the control space
without compromising the optimality of the solution [101]. Nevertheless, it has
been very popular as a benchmark [42, 75, 102], inspiration for control design [99],
and inspiration for powertrain design [103].
86 Chapter 3

Although DP is one of the most robust optimization techniques available it is still

being held back by the “curse of dimensionality”. It is definitely not realizable in
real-time, and even as a benchmark it is not great as it is only able to operate on
very simple models. Considering the high-fidelity model being considered in this
work, implementing a DP is beyond feasibility.

Global Equivalent Consumption Minimization Strategy

It was mentioned in the previous subsection that the ECMS has been shown to
be equivalent to the PMP (under certain conditions), which in turn is practically
equivalent to DP [75, 78, 79, 104]. This has been shown to be the case for both
optimally tuned and adaptive equivalence factors for the ECMS. It is therefore pos-
sible to consider a GECMS, which has been tuned for each individual driving cycle
separately, as a close approximation of the global optimal solution. Considering
the foundation on the ECMS, which is the most established framework of analysis
within the control strategy literature, it can be considered a reliable benchmark for
this work.

The GECMS is relatively easy to implement. The determination of the equivalence

factors can be done either through the line-method described in Section 2.6.2 or
through a brute force approach. Although the line-method offers a good selection
of equivalence factors, they have not been found to be optimal. Instead, a variety of
combinations of equivalence factors are tested for each driving cycle, and the EFC
is measured to determine the best set of equivalence factor that yield the optimal
fuel economy. This solution can be considered to be a close approximation of the
global optimal. The production of optimal control inputs for each set of equivalence
factors can be somewhat tedious but is easy to automate. The implementation of
the GECMS in this work is based on [78] and is described more fully later in Section
3.4.

Another advantage of the GECMS is the medium computational requirements. The

testing of each candidate set of equivalence factors can take an hour for repeated
iterations of a driving cycle. Nevertheless, identifying the optimal set of equivalence
factors to three significant digits (beyond which the impact is quite small) is a process
that will typically take a few days for our model, as opposed to times greater than
the age of the universe (for DP). Thus the global benchmarking solution can be
Conventional Strategies 87

obtained for the same vehicle model as the other proposed control strategies, unlike
DP which is typically implemented on simplified models.

Other

Several other established control theory methods have also been tested and applied
on HEVs. Genetic algorithms (GAs) search for the optimal solution by allowing
each candidate solution to evolve towards its minimum. Implementations have been
published frequently, from as early as 2001 [105, 106]. It is based on biological
evolution and is useful for complex non-linear optimization problems [56]. However,
they are not considered suitable for constrained optimization, and are generally not
considered suitable to be applied to the control of HEVs [63].

A second approach has been to apply game theory to HEVs [107, 108], where the
vehicle operation is evaluated as a non-cooperative game between the driver and
the powertrain. Recent results have been quite positive but the literature is still
quite limited. Other applied approaches include linear programming (LP) [109] and
convex optimization (CO) [110–112].
88 Chapter 3

3.2 Thermostat Control Strategy

The thermostat control strategy (TCS) is a simple, robust SCS that achieves a
good fuel economy and is the most conventional control strategy for series HEVs. It
oscillates between battery-only operation (with the engine off), and using the engine
at its most efficient point of operation (with the battery leveling out the load).

3.2.1 Design

The basic principle is to run the PS at its optimal point and have the SS act as an
equalizer, as
PSS = PP L − PP S,cop (3.6)

where PP S,cop is the selected constant operating point of the PS. Typically this is set
to be the most power efficient point of operation of the PS (PP S,cop = PP S,opt ). This
mode of operation is valid until the SOC reaches its upper threshold (SOCU = 80%),
at which point it enters a mode of SS-only operation. This mode quickly depletes
the SS and once the SOC hits the lower threshold (SOCL = 50%) it returns to
operate the PS at its optimal point. This logic is implemented by S(t), which is
the state determining whether the PS is generally (with the exception of insufficient
power) active (S(t) = 1) or not (S(t) = 0):

 0
 SOC(t) ≥ SOCU
S(t) = 1 SOC(t) ≤ SOCL . (3.7)

S(t ) SOCL < SOC(t) < SOCU
 −

Here, S(t− ) is the state S in the previous time sample. The rules and different modes
of operation of the TCS are presented graphically in Fig. 3.1. Note that the PS will
be requested to supplement power (at PP S = PP S,cop ) if the load power exceeds the
capability of the SS (PP L > PSSmax ), without changing S(t) to 1. For the purpose
of stable operation an additional rule is also introduced: the PS reduces its supply
of power if the battery is about to be charged beyond its power capacity (typically
occurs during the event of regenerative braking), to avoid damage to the battery.

This two-state SCS is best implemented using a state machine, which can easily be
designed using the Stateflow tool in Simulink, as shown in Fig. 3.2.
Conventional Strategies 89

SOC
1
PP S = 0
SOCU
PP S = 0 if S = 0
PP S = PP S,cop if S = 1
SOCL

PP S = PP S,cop PP S = PP L − PSSmax

PP L
PSSmax PP S,cop PP Smax
+PSSmax +PSSmax
Figure 3.1: The TCS operates in two different modes, depending on given SOC and
PP L : SS-only or hybrid-mode with PS operating at a constant operating point.

Start SS_mode [P_PL>(42+TCS_opt)]

P_PSref=0; Max_mode
[SOC>0] S=0; during: P_PSref=P_PL-42;
[SOC<50 [P_PL<(42+TCS_opt)]
[P_PL<30 &&(SOC>79 || P_PL>42] [P_PL>(42+TCS_opt)]
|| (S==0 && SOC>51))] [SOC>80]
PSopt_mode PS_mode
P_PSref=TCS_opt; P_PSref=TCS_opt;
[SOC<51 || (S==1 && SOC<79)] S=1;
Figure 3.2: Stateflow diagram of the TCS, illustrating the control laws governing this
SCS. TCS opt is the optimal value for PP S,cop .

3.2.2 Tuning

The TCS has a single control parameter, PP S,cop , that needs to be set appropriately.
By design, this should be the optimal operating point of the PS (although certain
work in literature looks solely on the engine), which corresponds to PP S,opt = 20.1 kW
in the case of the vehicle model used in this work. However, although this intuitively
is an appropriate selection, it is worth validating this choice with an objective tuning
process.

Simulations are therefore run for the four driving cycles (WL-L, WL-M, WL-H and
WL-E) with a range of PP S,cop values. Tuning results are presented in Fig. 3.3. It can
be seen that the ideal value of PP S,cop varies between each driving cycle (19.6 kW,
17.8 kW, 17.0 kW and 23.8 kW for the four driving cycles respectively). It is
interesting to observe that the optimal power level is reduced as the average power
consumption increases from WL-L to WL-M to WL-H. This can be explained by the
90 Chapter 3

1.03 65

1.02 64

SOC (%)
Mef c (-)

1.01 63

1 62
15 20 25 15 20 25
1.04 90

1.03 80

SOC (%)
Mef c (-)

1.02 70

1.01 60

1 50
15 20 25 15 20 25
1.04 80

75
1.03
SOC (%)
Mef c (-)

70
1.02
65

1.01
60

1 55
15 20 25 15 20 25
1.15 80

60
1.1
SOC (%)
Mef c (-)

40

1.05
20

1 0
15 20 25 15 20 25
PP S,cop (kW) PP S,cop (kW)
Figure 3.3: Normalized EFC (left) and final SOC (right) for varying PP S,cop when
driving WL-L, WL-M, WL-H and WL-E (from top to bottom) with TCS.
Conventional Strategies 91

1.03
Fuel Economy, Mef c (-)

1.02

1.01

1
15 17.5 20 22.5 25
PS operating point, PP S,cop (kW)
Figure 3.4: Normalized total EFC Mtot for varying PP S,cop with TCS.

benefits gained from reducing the amount of SS operation at high loads (where it is
inefficient). A lower power level PP S,cop results in longer duration of PS operation,
meaning that the SS can avoid a large part of its high load operation. However,
if the average power load is high enough (like the WL-E) then the SS is typically
required to be active and discharging during PS mode as well. Thus, the control
strategy can’t be CS for lower values of PP S,cop (the SOC can be seen to drop to
20% for PP S,cop = 15 kW). Instead, by increasing the power levels of the PS, the
burden on the SS is reduced.

To determine a single value for PP S,cop to be used during real-time driving, the
four driving cycles are considered together (as described in Section 2.6.2). The
normalized total EFC results are presented in Fig. 3.4, where the optimal tuning
value is found to be PP S,cop = 19.8 kW. It can thus be seen that the preliminary
guess of PP Sopt = 20.1 kW is a very good estimate of the most suitable choice. For
the purposes of this work, PP S,cop = 19.8 kW will be used to allow the TCS to
perform at its best when benchmarking against other control strategies.

It is worth mentioning that the parameter PP S,cop could be defined as an adaptive

variable to persistently remain close to the optimal value for each driving cycle that
yields the best fuel economy results, but such a variable would add undesirable
complexity as well as move away from the heuristic nature intended for the TCS.
Nevertheless, it is worth considering further why a single constant PP S,cop is not a
universally suitable parameter value (as evidenced by the WL-E simulations).
92 Chapter 3

Selecting PP S,cop to correspond with the peak efficiency operating point of the PS
ensures optimal performance of the PS in the powertrain. However, the efficiency
of the SS is not accounted for by any means, and is completely dictated by the
propulsion load required to meet the driving cycle. If a driving cycle typically
requires power loads comparable to the optimal power supply of the PS, then the SS
efficiency does not significantly impact the overall fuel economy of the powertrain
during PS mode. However, if the propulsion load greatly exceeds the optimal power
supply of the PS (PP L >> PP S,cop ) then the magnitude of power from the SS becomes
significant and its efficiency dynamics impact the overall fuel economy. Conversely,
if the propulsion load is very low (and PP L << PP Sopt ), then the battery is being
charged at a very high C-rating, and thus a lower efficiency, again resulting in reduced
overall powertrain efficiency. Also, there are further non-linear effects of PP Sopt on
the timing of the on-set of PS (S(t) = 1) that are very driving cycle specific (you
would ideally like to have the PS switch on just before high loads within the driving
cycle).

3.2.3 Operation

Based on above findings, PP S,cop = 19.8 kW is found to be the most suitable choice
and will be used hereafter for all driving cycles. To understand the operation of the
TCS, it is useful to study its power profiles. Figures 3.5 and 3.6 show the power
profiles for the first and second iteration respectively of the four driving cycles.

For WL-L and WL-M, the vehicle is only powered by the SS in the first iteration of
the cycles (as the TCS is in its charge depleting state S = 0). As the required load is
quite low, it takes a long time for the SOC to drop sufficiently for the TCS to enter
charging mode. This happens in the second iteration (Fig. 3.6) for both of these
driving cycles. It can be seen that the SS is charged rapidly once the PS is on as
typically the load is much lower than the PS power being delivered (PP L < PP S,cop ).
The TCS will actually return to charge depleting mode very soon after finishing
the second iteration of the cycle. It’s also worth noting that the PS deviates from
its steady operation during significant regenerative braking, to respect the battery
limits (PSSmin = −21 kW).

In contrast, WL-M and WL-E both enter charging mode within the first iteration
of the cycles (in fact, in less than a quarter of the time it took WL-L). However,
Conventional Strategies 93

30

15
Power (kW)

-15 PS S
PP S
PP L
-30
0 100 200 300 400 500 589
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 433
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 455
60

45

30
Power (kW)

15

-15

-30
0 100 200 300 323
Time (s)

Figure 3.5: Power time histories for PS, SS and PL for the first iteration of driving
WL-L, WL-M, WL-H and WL-E (top to bottom) with the TCS.
94 Chapter 3

30

15
Power (kW)

-15 PS S
PP S
PP L
-30
0 100 200 300 400 500 589
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 433
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 455
60

45

30
Power (kW)

15

-15

-30
0 100 200 300 323
Time (s)

Figure 3.6: Power time histories for PS, SS and PL for the second iteration of driving
WL-L, WL-M, WL-H and WL-E (top to bottom) with the TCS.
Conventional Strategies 95

this change of state could not have arrived soon enough, as it can be seen that
the SS was being exposed to very heavy loads, which is inefficient and accelerates
battery degradation. The PS is in fact required to briefly assist the SS during peak
loads for the WL-E, as the load exceeds the SS limits (PP L > PSSmax ). It can also
be seen in both iterations of the WL-E cycle that the SS is often being discharged
despite the TCS operating in charging mode (S = 1). Thus, for any driving cycle
that frequently or persistently uses more power than the steady supply of the PS
(PP L < PP S,cop ), the TCS will not be able to be CS (in the case WL-E for the vehicle
design being tested, the TCS is just barely CS).

Overall, it can be seen that the TCS is able to operate the PS quite steadily in a
very efficient manner, but at the expense of extreme types of operation by the SS.
The latter is often charged at its limit PSSmin , and it is also often required to deliver
very heavy loads (at times matching PSSmax ). This stems from the PS-centric design
of the TCS and does not serve the overall powertrain very well.

The resulting fuel economy for the four driving cycles for the TCS is shown in
Table 3.1. It can be seen that the final SOC varies considerably, as could be expected
from the oscillating nature of the control. The fuel economy is also compared to the
GECMS (presented in Section 3.4) which can be considered an approximate global
optimal solution. Thus, the TCS is found to lag the GECMS results by 7.13-17.89%,
with a combined difference (as computed for Mtot ) of 14.35%. This leaves plenty of
room for improvement.

Table 3.1: Fuel economy results for TCS

Driving Cycle SOCf inal (%) mf (kg) mef c (kg) ∆GECM S (%)
WL-L 62.84 0.8115 0.8350 +17.89
WL-M 73.71 1.4174 1.3345 +17.18
WL-H 76.03 1.1912 1.0865 +14.34
WL-E 49.21 1.4818 1.6983 +7.13
96 Chapter 3

3.3 Power Follower Control Strategy

The power follower control strategy (PFCS) is the second most conventional control
strategy for series HEVs. Its key characteristic is having the engine deliver the
required power to drive the car, unless high loads are required, in which case the
battery adds support.

3.3.1 Design

The PFCS follows a set of rules. Generally, the PS follows the load of the PL, with
some deviation to correct and consider the varying SOC. When the load from the
PL (PP L ) is low and SOC is high, the SS is selected to deliver the power to the
vehicle (S(t) = 0). Conversely, when PP L is high or SOC is low, the PS is selected
to meet the load (S(t) = 1). These states are defined as follows:

 0
 SOC(t) ≥ SOCU and PP L < Pmin
S(t) = 1 SOC(t) ≤ SOCL or PP L > PSSmax . (3.8)

S(t ) SOC(t) ≥ SOCL and PP L < PSSmax
 −

For S(t) = 0, we always have PP S = 0. For S(t) = 1, the operation of the PS is

defined as 
 Pmin
 SOC(t) ≥ SOCU
PP S (t) = Pm (t) SOCL < SOC(t) < SOCU (3.9)

PP Smax SOC(t) ≤ SOCL


where Pm is given by
 
SOCU + SOCL
Pm (t) = PP L + Pch − SOC(t) . (3.10)
2

It can be understood that the PS power is essentially following the load PP L when
the SOC is at the midpoint between SOCL and SOCU , but biases the operation in
favor of charging or discharging the SS in the cases of low and high SOC respectively.
The bias is scaled by Pch to achieve CS operation. Note that in general PSS 6= 0
when S(t) = 1. These rules are shown visually in Fig. 3.7 and the implementation
of the rules within a state-flow diagram is shown in Fig. 3.8. Note that the PS
is constrained to operate within Pmin ≤ PP S ≤ PP Smax (where Pmin is a tunable
Conventional Strategies 97

SOC
1
PP S = 0 if S = 0
PP S = 0 PP S = Pmin
PP S = Pmin if S = 1
SOCU
PP S = Pm
PP S = 0 if S = 0
SOCL
PP S = Pm if S = 1

PP S = PP Smax

PP L
Pmin PSSmax PP Smax
+PSSmax
Figure 3.7: The PFCS has two distinct states, dependent on given SOC and PP L (as
defined in (3.8)), and has an area of hysteresis in between where the PS delivers zero, Pmin
or Pm power. Note that the vehicle can’t deliver maximum power for SOC > SOCU .

[(P_PL+P_ch*(65-SOC))<PFCS_min Min_mode
|| (SOC>80 && P_PL>PFCS_min)] during: P_PSref=PFCS_min;
[(P_PL+P_ch*(65-SOC))>PFCS_min
[SOC>80 && P_PL<PFCS_min] || (SOC>80 && P_PL<PFCS_min)]
Start SS_mode Pm_mode
P_PSref=0; during: P_PSref=P_PL+P_ch*(65-SOC);
[SOC>0] [P_PL>42 || SOC<50] [((P_PL+P_ch*(65-SOC))<58
&& SOC>50) || SOC>80]
[(P_PL+P_ch*(65-SOC))>58 Max_mode
|| SOC<49] during: P_PSref=58;
Figure 3.8: Stateflow diagram of the PFCS, illustrating the control laws governing this
SCS. PFCS min is the minimum power Pmin .

parameter whilst PP Smax = 58 kW is a physical constraint of the PS) when it is on,

thus resulting in the diagonal boundaries (with slope 1/Pch ) in Fig. 3.7.

The PFCS therefore has two tunable parameters: the charging factor Pch and the
minimum power Pmin . The charging factor needs to be positive to contribute to-
wards making the control strategy more CS, but Pch = 0 is permissible as well.
Furthermore, as the charging factor scales the amount the battery is recharged, it
should respect the maximum power the battery can absorb, such that

100(SOCL − SOCU )
Pch ≤ PSSmin . (3.11)
2

Note that the factor of 100 is to convert the SOC units to percentage, as this is the
convention when defining Pch . Thus, for PSSmin = −21 kW the charging factor Pch
98 Chapter 3

should be defined such that it’s limited to Pch ∈ [0, 1.4] kW. Similarly, the charging
factor is also limited by the maximum power limit of the SS, such that

100(SOCU − SOCL )
Pch ≤ PSSmax . (3.12)
2

Thus, for PSSmax = 42 kW the charging factor Pch should be defined such that it’s
limited to Pch ∈ [0, 2.8] kW. To allow the charging factor to achieve all its potential
influence, it will be explored in the range Pch ∈ [0, 3] kW, but limits in the model
will ensure that the SS is not overloaded.

In the literature, the minimum power Pmin is sometimes defined by a physical con-
straint of the engine-generator set, but the magnitude of this parameter varies widely
across different work. The powertrain used in this work can operate at very low
power levels, and the PFCS inherently imposes Pmin < PSSmax (as can be understood
by Fig. 3.7). Thus the feasible range for the minimum power is Pmin ∈ [0, 42] kW.

3.3.2 Tuning

The implemented PFCS is simulated for various driving cycles with different Pch
and Pmin values and the resulting normalized EFC and final SOC values for these
tests are presented in Fig. 3.9. The optimal selection of parameters for each driving
cycle is marked with a cross sign.

As can be seen in the charts, the optimal tuning for each driving cycle is unique.
However, in each case the optimal Pmin is found to be close to 20 kW, which is
the PS peak efficiency operating point, or just below it. Considering the fact that
the PFCS often operates at PP S = Pmin , it is not a surprising outcome, although
it is not a typical setup in the literature (where lower values are typically used).
Furthermore, in the first three of the driving cycles, Pch = 0 is found to be the
ideal selection, thus having the PFCS truly operate such that the PS follows the
load power (PP S = PP L ) with no additional CS action. Instead, the control strategy
remains CS through switching between it’s charge depleting state (S(t) = 0) and
charge replenishing state (S(t) = 1). However, it can be seen that the control
strategy is operating close to the upper bound of the SOC for WL-E if Pch = 0 is
used.
Conventional Strategies 99

3 3

2.5 2.5

64
1.0
2

63

62.
64

622. .5
1.0

6
2 2

3
Pch (kW)

Pch (kW)
1.01

64
1.5 1.5

.7
1 5 1

1.0
1.00

62
1.0

64.7
02

64

.5
0.5 05 0.5

0 0
15 17 19 21 23 15 17 19 21 23
3 3

80
80
1.
2.5 04 2.5

1.04
2 2
Pch (kW)

Pch (kW)
1.03
1.5 1.5 80

80
1 3 1
1.0
1.0

75
1.0 .01

80
70
2

0.5 05 0.5
65
0 0
15 17 19 21 23 15 17 19 21 23
3 3 67505
780

5
1.0

60
2.5 1.0 2.5
5
2 2 80
Pch (kW)

Pch (kW)

1.5 1.03 1.5

1.03
1 1
70
65 5
1.

75

1.01
02

0.5 1.0 0.5

2 70
0 0
15 17 19 21 23 15 17 19 21 23
3 3
76
1.005

2.5 2.5 73
1.01

1.00

77
1.002

2 2 74
1
Pch (kW)

Pch (kW)

75
1.5 1.5 76
1.005 77 78
1 1 7 8
1.01 79
0.5 0.5 80
79
80
0 0
15 17 19 21 23 15 17 19 21 23
Pmin (kW) Pmin (kW)
Figure 3.9: Normalized EFC Mef c (left) (Mef c = 1 is marked with a cross) and final
SOC (right) for varying Pmin and Pch when driving WL-L, WL-M, WL-H and WL-E
(from top to bottom) with PFCS.
100 Chapter 3

03
5
Charging Factor, Pch (kW)
2.5 02

1.
.02
5 1. 1.025
1
2
1.02 1.02

1.5 1.02
5
1.01 1.015
1
01 1.015
1. 1.

1.015
00

1.01
0.5 5

0
15 17 19 21 23
Minimum Power, Pmin (kW)
Figure 3.10: Normalized total EFC Mtot for varying Pmin and Pch with PFCS.

To obtain the optimal tuning parameters for implementation during real-time driv-
ing, a single set is found by evaluating the total fuel economy of the four driving
cycles combined. The results are presented in Fig. 3.10, and the total EFC is found
to be at its minimum for Pch = 0 and Pmin = 16.8 kW. This selection will therefore
be used henceforth within this work.

3.3.3 Operation

Using the tuned values for the control parameter it is now possible to look closer
at the resulting operation. Figure 3.11 shows the power profiles of the powertrain
when driving the first iteration of the four driving cycles, and Fig. 3.12 shows the
second iteration.

For WL-L, the PFCS operation is very similar to the operation of TCS from Figs.
3.5 and 3.6. As it opens with pure SS operation it operates identically to the TCS
until halfway through the second iteration, when the PS is switched on. The PFCS
operates at Pmin quite persistently as the required load is very low. The power
level is however different, as Pmin is of a lower magnitude than the PP S,cop of the
TCS. Consequently, the PFCS can expect to operate in a charge replenishing mode
(S = 1) for a longer duration than the TCS, while exposing the SS for less intensive
charging.
Conventional Strategies 101

30

15
Power (kW)

-15 PS S
PP S
PP L
-30
0 100 200 300 400 500 589
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 433
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 455
60

45

30
Power (kW)

15

-15

-30
0 100 200 300 323
Time (s)

Figure 3.11: Power time histories for PS, SS and PL for the first iteration of driving
WL-L, WL-M, WL-H and WL-E (top to bottom) with the PFCS.
102 Chapter 3

30

15
Power (kW)

-15 PS S
PP S
PP L
-30
0 100 200 300 400 500 589
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 433
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 455
60

45

30
Power (kW)

15

-15

-30
0 100 200 300 323
Time (s)

Figure 3.12: Power time histories for PS, SS and PL for the second iteration of driving
WL-L, WL-M, WL-H and WL-E (top to bottom) with the PFCS.
Conventional Strategies 103

45 PS S
PP S
PP L
30
Power (kW)

15

-15

-30
0 100 200 300 400 500 600 700 800 910
Time (s)

Figure 3.13: Power time histories for PS, SS and PL for the first two iterations of
driving WL-H with the PFCS with Pc h = 1 kW and Pmin = 10 kW.

The operation for WL-M is the same as the TCS for the first iteration, but it begins
to display its power following characteristics in the second iteration. As the PS is
switched on (as SOC has dropped to its lower limit), the PS will operate typically
at Pmin , but whenever the required load exceeds this threshold, the PS will adjust
and meet the load fully.

This operation becomes even clearer for WL-H and WL-E, where a higher amount of
time is spent with PP L > Pmin , allowing the PFCS to operate in its power following
mode for a significant part of the driving cycle. As the SS is not discharged in
this mode of operation, the SOC can be expected to recover quite fast, which is
comparable to TCS for WL-H, despite Pmin < PP S,cop . It also worth noting that the
PFCS enters charge replenishing mode already around t = 60 s, which is earlier than
the TCS. This is an effect of the power conditions that are given in Eq. 3.8, which
makes the PFCS change state if the load becomes high. This allows the PFCS to
enable the PS at an earlier stage than the TCS, which is clearly advantageous for
WL-E.

The resulting operation from the optimal tuning parameters is not the typical PFCS
operation (although it arguably is more “power following”), which would have a
higher Pch and lower Pmin . To illustrate this, Fig. 3.13 shows the power profile for
WL-H×2 with Pch = 1 kW and Pmin = 10 kW. The PFCS starts the driving cycle
starts with SS-only mode, just like the optimal setting in Fig. 3.11. As the PS is
switched on around t = 200 s (because SOC reaches SOCL ), the power from the
104 Chapter 3

PS generally follows the shape of the load power but exceeds it with some margin
(PP S > PP L ) resulting in the SS being charged. This offset is due to the contribution
from the charging factor Pch as seen in Eq. 3.10.

However, with time (as SOC increases), the margin between PP S and PP L is grad-
ually reduced, resulting in the SS being charged at a slower rate, until the PS is
briefly following the load power quite precisely (as SOC = SOCU +SOC
2
L
). As the SS
is generally charged (and the SOC thus increases), the SS begins supplementing the
PS in meeting the load power. This type of operation is clearly more CS (rather
than just rapid charging) than the operation shown in Fig. 3.12, and thus keeps
the PS on even at the end of the two iterations of WL-L. However, having the SS
operate at very low power levels is not efficient due to the high DC-DC converter
losses for this type of operation. Consequently, the PFCS setting of Pch = 0 and
Pmin = 16.8 kW is find to be the best. As the nature of the PFCS is dependent
on the particular powertrain in which it is implemented, it is expected to exhibit
some variance in behavior. Thus, the appropriate way to proceed is to use the tuned
parameters that were found to be optimal for the PFCS in terms of equivalent fuel
economy, despite its somewhat unconventional operation (albeit within the power
follower framework).

Lastly, the fuel economy of the PFCS is presented in Table 3.2 for the four driving
cycles. Similar to the TCS, it can be seen that the final SOC varies considerably, as
the high setting of Pmin has the PFCS partly mimic the operation of the TCS. The
fuel economy is also compared to the GECMS (presented in the next section) which
can be considered an approximate global optimal solution. The PFCS is found to
lag the GECMS results by 6.57-18.60%, with a combined difference of 13.55%. This
is a small improvement on the TCS, but further improvements can be expected for
better designed strategies.

Table 3.2: Fuel economy results for PFCS

Driving Cycle SOCf inal (%) mf (kg) mef c (kg) ∆GECM S (%)
WL-L 63.88 0.8278 0.8400 +18.60
WL-M 62.02 1.2824 1.3145 +15.43
WL-H 69.49 1.1198 1.0772 +13.35
WL-E 80.86 1.8681 1.6894 +6.57
Conventional Strategies 105

3.4 Global Equivalent Consumption Minimization

Strategy

The GECMS is a globally tuned ECMS. The strategy determines the equivalent fuel
consumption (EFC) of the powertrain for various driving conditions to produce an
offline control map, instructing how to best share the power between engine and
battery. To compute the EFC, the equivalence factors Sd and Sc need to be esti-
mated, but the GECMS operates with the luxury of being allowed to use optimally
tuned equivalence factors, in order to achieve close to optimal fuel economy.

3.4.1 Design

The ECMS has been widely described in the literature, both as a proposed SCS as
well as for benchmarking [70, 78, 113]. There are many variants, but the presented
work implements a GECMS (globally tuned ECMS), based on [78]. It has been
shown that the GECMS is able to realize operation almost identical to the global
optimal solution as determined through DP [104]. This makes the GECMS a very
suitable benchmark, as it provides a close to optimal solution to benchmark any
proposed SCS without employing DP, which might be unfeasible to implement for
a complex and dynamic vehicle model. As the principles of GECMS, and its foun-
dation on PMP, have been discussed previously in this chapter (and in more depth
in the literature), this section will solely focus on the implementation of this SCS.

The objective of a GECMS is to minimize the EFC meq , which is defined as

Z tf
meq = ṁeq (t, u(t)) dt, (3.13)
o

where 
 ṁf (PP S ) − Sd PSS PSS ≥ 0
QLHV
ṁeq = , (3.14)
 ṁ (P ) − S PSS PSS < 0
f PS c QLHV

where ṁf is the fuel consumption rate of the ICE in the PS and QLHV is the lower
heating value of the fuel. The two constants Sd and Sc are equivalence factors that
translate the energy discharged/charged by the SS into a corresponding amount of
106 Chapter 3

fuel consumed/stored. The values of these constants can be determined by trial-

and-error or numerical optimization, to identify the optimal selection of equivalence
factors for each driving cycle being tested. Although such tuning can be time-
consuming for very complex vehicle models, it’s likely to be faster and simpler than
implementing alternative global SCSs (such as DP solutions).

The optimization problem can now be reduced to a local minimization problem as

follows: 
 min ṁeq (t, u) ∀t ∈ [0, tf ]

 u
PGECM S 0 ≤ u ≤ PPPSmax (3.15)
 PL

 SOC ≤ SOC ≤ SOC
L U

Thus, for each time instant t of a given driving cycle (for which we obtain the PP L
profile), an optimal power share factor uopt can be defined for each set of equivalence
factors Sd and Sc . Using a map of fuel consumption mf (PP S ), as shown in Fig. 2.10,
a sweep can be performed for Eq. 3.14 with u ∈ [0, PPPSmax PL
] for PP L (t) to produce
an optimal control input. This process is repeated for each candidate set of Sd and
Sc . For m number of Sd values investigated and n number of Sc values investigated,
there are m×n number of control maps produced for each driving cycle investigated.
Consequently, to identify the optimal selection of equivalence factors, within a range
of e.g. Sd ∈ [2.9, 3.1] and Sc ∈ [2.6, 2.9] with intervals of 0.01 for the four driving
cycles would require approximately 2000 hours of driving simulation.

3.4.2 Tuning

To tune the GECMS, the computational time needs to be reduced. A coarser search
(with 0.02 intervals) is therefore performed on a quarter of the number of iterations
that are typically used in this work for each driving cycle (i.e. WL-L×2, WL-M×2,
WL-H×1 and WL-E×1). As the GECMS control variable is independent of SOC,
or any other model state, the applied control is identical for each iteration of each
driving cycle. Thus, these initial simulations will yield quite accurate equivalence
factor values. The fuel economy results for these tests, together with final SOC
values, are shown in Fig. 3.14.

It can be seen that the optimality of the driving cycle is highly sensitive to the
selected equivalence factors Sd and Sc (e.g. an error of 2% in Sc could cause a 20%
Conventional Strategies 107

2.86 2.86 90
75
1.05 70 85
1 80
2.84 1..002 1.1 2.84
6
1 60 5
2.82 2.82 75
1.0
Sc (-)

Sc (-)
2.8 1 2.8 70
1.0
1.0

2.78 1.0 03 2.78

03 65
2

2.76 2.76 55
60
2.74 2.74
2.9 2.92 2.94 2.96 2.98 3 2.9 2.92 2.94 2.96 2.98 3

2.85 1.1 2.85

85
1 80 95
1.2
1.0.05 7
65 75 90
2 0
1.0

2.8 2.8 85
2
Sc (-)

Sc (-)
1.1
1. 80
01
2.75 1.0 2.75 75
5
1.05

1.0 60
1 70

55
50
1.02

65
2.7 2.7
2.9 2.95 3 3.05 3.1 2.9 2.95 3 3.05 3.1

1.0 75
2.85 2.85 80
5 70
1. 1.1 65
02
2.8 2.8
1.0
Sc (-)

Sc (-)
2

1.0
1.0

5
1.
5

01
2.75 2.75 70
1.0
1
60
55

1.0
2 65
2.7 2.7
2.9 2.95 3 3.05 3.1 2.9 2.95 3 3.05 3.1
2.9 2.9

2.88 2.88
1.05 70
1.02
2.86 2.86 65
Sc (-)

Sc (-)

1.0002
1.0
01

2.84 2.84
1.001
2.82 2.82
64 65
2.8 2.8
3.4 3.42 3.44 3.46 3.48 3.5 3.4 3.42 3.44 3.46 3.48 3.5
Sd (-) Sd (-)
Figure 3.14: Normalized EFC Mef c (left) (Mef c = 1 is marked with a cross) and final
SOC (right) for varying Sd and Sc coarsely when driving WL-L, WL-M, WL-H and WL-E
(from top to bottom) with GECMS.
108 Chapter 3

2.82 2.82 75
1.0
1 1.0 1.0 70 80 85 90 95
2 4
1.00 65
5
2.81 2.81 6
0
Sc (-)

Sc (-)
2.8 2.8 55
1.0 75
1 50 70
1.0
2.79
05 2.79 65
1. 45
00 60
5
2.78 2.78
2.94 2.95 2.96 2.97 2.98 2.94 2.95 2.96 2.97 2.98
2.77 2.77 80
1.0 75
1. 60 70

65
00 1
5
2.76 2.76

55
Sc (-)

Sc (-)
2.75 2.75 5
0

2.74 1.
00 2.74 45 65
1. 5 60
01
2.73 2.73
2.96 2.97 2.98 2.99 3 2.96 2.97 2.98 2.99 3
2.76 2.76 65 75
1.0 1.0 70
05 1
2.75 2.75
60
Sc (-)

Sc (-)
1.

2.74 2.74
00
5

1.0 65
2.73 1 2.73
1.005 55
1.01 60
2.72 1.02 2.72
2.98 2.99 3 3.01 3.02 2.98 2.99 3 3.01 3.02
2.88 2.88
85

1.
2.87
06 2.87
80 80
1.02 70
Sc (-)

Sc (-)

70
2.86 1.0005 2.86 65 64
1.0

63
005

65

2.85 1.0 2.85

00
5
2.84 2.84
3.41 3.42 3.43 3.44 3.45 3.41 3.42 3.43 3.44 3.45
Sd (-) Sd (-)
Figure 3.15: Normalized EFC Mef c (left) (Mef c = 1 is marked with a cross) and final
SOC (right) for varying Sd and Sc when driving WL-L, WL-M, WL-H and WL-E (from
top to bottom) with GECMS.
Conventional Strategies 109

drop in fuel economy for WL-M), although the approximate optimal values (marked
by the cross) are often found in close proximity to each other, in particular for the
three first driving cycles. Furthermore, by comparing each set of subplots, it appears
that each approximate optimal solution appears nearby the SOCf inal = SOCinitial
line (where SOCinitial = 65%). This is a desirable trait, as it tends towards making
the GECMS CS. However, it is worth noting that this behavior is not inherent to the
ECMS alone, but relies on appropriately defined Sd , ef c and Sc , ef c when evaluating
the EFC mef c (as discussed in Section 2.6.2). A badly defined EFC would not have
the GECMS exhibit these CS tendencies.

Now further simulations can be run (for the full number of iterations of the driving
cycles and with intervals of 0.01) in the proximity of the obtained approximate
equivalence factors. The fuel economy results for these tests, together with final
SOC values, are shown in Fig. 3.15.

At this precision level, it becomes apparent that the fuel economy is less sensitive
than the final SOC to the equivalence factors (the fuel economy is still more sensitive
for the GECMS than for the TCS or PFCS). In fact, this feature can be exploited
to design a real-time ECMS. By tuning the equivalence factors in real-time based
on the SOC, the real-time ECMS will remain CS for any driving cycle and achieve a
fuel economy comparable to the GECMS. Although a real-time ECMS has not been
implemented, this concept will be used in the next chapter.

The equivalence factor values obtained from this optimization process for the four
driving cycles are given in Table 3.3 and the resulting optimal control maps are
shown in Fig. 3.16. In all four cases it can be seen that the strategy includes a
pure electric operation at low powers, which should be expected considering that
the PS doesn’t perform very efficiently at low loads. Equally, once the PS is turned
on, it delivers more power than the required load and thus ends up charging the
SS. This is followed by generally hybrid operation for higher power loads. The mix
of u < 1 and u > 1 operation allows driving to be more CS than only relying on
regenerative braking. These are all insights that will be used in designing further
control strategies in the coming chapters.

The GECMS is implemented into the vehicle model in Simulink through a simple
look-up table that uses the produced map (shown in Fig. 3.16) and the requested PP L
to select the optimal power share factor, that is then multiplied by PP L to provide
110 Chapter 3

3 60

PS Power, PP S (kW)
Power Share, u (-)

2 40

1 20

0 0
0 20 40 60 80 100 0 20 40 60 80 100
3 60

PS Power, PP S (kW)
Power Share, u (-)

2 40

1 20

0 0
0 20 40 60 80 100 0 20 40 60 80 100
3 60
PS Power, PP S (kW)
Power Share, u (-)

2 40

1 20

0 0
0 20 40 60 80 100 0 20 40 60 80 100
3 60
PS Power, PP S (kW)
Power Share, u (-)

2 40

1 20

0 0
0 20 40 60 80 100 0 20 40 60 80 100
Power Requirement, PP L (kW) Power Requirement, PP L (kW)
Figure 3.16: Power share factor and PS power for varying power requirements, for
WL-L, WL-M, WL-H and WL-E (from top to bottom) with GECMS.
Conventional Strategies 111

Table 3.3: Optimal equivalence factor values

Driving cycle Sd Sc
WL-L 2.96 2.80
WL-M 2.98 2.75
WL-H 3.00 2.74
WL-E 3.43 2.86

1-D T(u)
1 f(u) 1
P_PL P_PSref

Lookup Table 1D
Figure 3.17: Implementation of the GECMS in Simulink.

the optimal PP Sref . This implementation is shown in Fig. 3.17. An alternative

implementation would be to generate a power share ratio profile u(t) for each driving
cycle and implement it without any input from the model. However, such a method
is less robust for changes in vehicle operation and requires more pre-simulation
processing time (to generate the power share profile). Lastly, and maybe the most
common method of implementation, would be to compute the power share ratio
u (using globally tuned, pre-computed equivalence factors) at each sample time.
Although this process is feasible in real time, it would result in increased simulation
time and is thus not preferred.

3.4.3 Operation

The implemented GECMS, with optimally tuned Sd and Sc values, has been sim-
ulated and the resulting power profiles are shown in Fig. 3.18 for the four driving
cycles. As the GECMS is state-independent, it operates exactly the same way for
every iteration of the driving cycles. Therefore, only the first iteration is presented
here.

For WL-L and WL-M, the control can be characterized by its frequent switching of
the PS. It is not used more than 20 s continuously. It is consequently much more
responsive to changes in required load, as compared to the TCS or PFCS that could
112 Chapter 3

30

15
Power (kW)

-15 PS S
PP S
PP L
-30
0 100 200 300 400 500 589
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 433
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 455
60

45

30
Power (kW)

15

-15

-30
0 100 200 300 323
Time (s)

Figure 3.18: Power time histories for PS, SS and PL for the first iteration of driving
WL-L, WL-M, WL-H and WL-E (top to bottom) with the GECMS.
Conventional Strategies 113

keep on operating the SS close to its maximum limit rather than turn on the PS.
In fact, while the TCS and PFCS would switch on the PS twice each during WL-L,
the GECMS does it 144 times (corresponding to one switch per 33 s). Although this
incurs a penalty in fuel consumption, it is quite likely that the improved power share
will more than compensate for this (as is shown later). The GECMS experiences
somewhat more continuous operation for WL-H and WL-E. For the latter, the PS
operates in some sense even steadier than the PFCS. The PS is operated between
20 and 25 kW with a few spikes for very high loads.

More generally, it can be seen that the GECMS is quite “blocky” and often operates
the PS quite steadily, despite having the possibility to operate with much more
variance. This also corresponds with the nature of the series powertrain, where the
ability to operate the PS quite freely (to operate close to its optimal operating point)
is seen as the biggest advantage. However, the nature of these “blocks” are different
from the TCS or PFCS, in the sense that they are often of a very short duration.
In fact, some of these switches are just for about a second, which are unlikely to be
optimal. Such operation is not ideal and would not occur in a truly global optimal
solution. It is these kinds of discrepancies that separate the solutions obtained by
methods such as DP and a GECMS. However, as mentioned, works in the literature
suggest that the fuel economy differences between these approaches are very small.

The fuel economy results for the four driving cycles are presented in Table 3.4. It is
immediately apparent that the GECMS is able to maintain the SOC very close to
SOCinitial = 65%. The absolute EFC results are not of great importance yet, but
these GECMS results will be used to benchmark all other strategies in this work (as
was done for TCS and PFCS earlier in this chapter).

Table 3.4: Fuel economy results for GECMS

Driving Cycle SOCf inal (%) mf (kg) mef c (kg) ∆GECM S (%)
WL-L 65.17 0.7100 0.7083 +0
WL-M 64.34 1.1317 1.1388 +0
WL-H 64.18 0.9404 0.9503 +0
WL-E 64.05 1.5723 1.5853 +0
114 Chapter 3

3.5 Summary

This chapter has introduced past work on control strategies for HEVs. This has
included a review of both rule-based and optimization-based control strategies,
with the latter further subdivided into real-time and global control strategies. An
overview of these strategies from the literature is shown in Table 3.5.
Table 3.5: Overview of control strategies for series HEVs

Rule-based Real-time Optimization Global Optimization

Strategies -based Strategies -based Strategies
TCS ECMS DP
PFCS MPC GECMS
MSP SDP GA
FLC NN GT
SMC CO

The TCS and PFCS are the most conventional rule-based strategies for series HEVs,
and have therefore been adopted as benchmarking strategies in this work. While the
ECMS and DP are the most common approaches in optimization-based strategies,
the GECMS was found to be most suitable. It enjoys the simplicity and effectiveness
of the ECMS while achieving a fuel economy performance comparable to DP.

The implementation of a real-time ECMS would have been useful as another bench-
mark, but there is a wide range of approaches that would have achieved a wide
range of results. Based on work in the literature, the real-time implementation is
typically a few percentage points behind the GECMS (assuming no GPS or telem-
atic information is used). DP, on the other hand, has not been pursued due to it
being unfeasible for the used model. The approach of creating a significantly reduced
model for the application of DP (the conventional approach in literature) does not
appear worthwhile, as any benchmarking where the candidate strategies are tested
on different vehicle models has questionable validity.

The chapter also included the design, implementation and operation of the TCS,
PFCS and GECMS. The TCS takes a load leveling approach while the PFCS applies
load following, but both their operation and fuel economy results were similar. The
GECMS outperformed these with 14.35% and 13.55% respectively in terms of fuel
economy, and demonstrated consistently CS operation. The GECMS will be acting
as the fuel economy benchmark for the proposed strategies in the coming chapters.
Chapter 4

Efficiency Maximizing Map

Strategies

This chapter will propose a set of novel efficiency maximizing map strategies (EMMS).
These will include the EMMS0, EMMS1 and EMMS2 that are real-time control
strategies, as well as the the Global EMMS (GEMMS), which is a globally tuned
variant. The core idea behind each of these strategies is to utilize a thorough under-
standing of the powertrain efficiencies to maximize the fuel economy during driving
with precomputed control maps.

The chapter will begin by laying out the design principles of the proposed control
strategies, before thoroughly evaluating the powertrain efficiencies, with the objec-
tive to control the powertrain in upcoming sections. Efficiencies for both the PS
and SS are derived before a total efficiency is expressed. Thereafter, the EMMS0,
which we have published in [12–14], is presented. Some minor adjustments have
been made to the control strategy as compared to these publications and new re-
sults are presented. This is developed further with the EMMS1 by including a more
intuitive and effective method to accomplish CS operation, in addition to delivering
improved fuel economy. The EMMS1 is modified and converted into the globally
tuned strategy GEMMS (similar to the GECMS in the previous chapter). Lastly, the
GEMMS will be modified into EMMS2 to allow real-time implementation. For each
of the proposed control strategies, the tuning process, the resulting control maps,
and representative power profiles of operation will be presented and discussed.

115
116 Chapter 4

4.1 Design Principles

The control strategies discussed and presented in Chapter 3 included a mix of rule-
based and optimization-based strategies. It was mentioned that the latter type tend
to deliver better performance but at the expense of simplicity, robustness and ease of
tuning. In particular, the ECMS was emphasized, as it is the most popular approach
within the research community today.

However, the success of the ECMS is quite sensitive to the equivalence factors, con-
verting between fuel and battery charge, that depend on driving cycle and other
time-variant factors. An alternative approach to minimizing equivalent fuel con-
sumption is to maximize the powertrain efficiency. This has the advantage of not
only being more intuitive but also less sensitive to tuning, as the component efficien-
cies are often readily available unlike equivalence factors. Also, this method is more
transparent in the sense that it can be understood where the various losses are oc-
curring in the powertrain. Furthermore, this control method does not rely on future
driving information but only on the instantaneous power demanded for the vehicle
to follow any given speed profile, as well as the SOC of the battery. Therefore, it
can be implemented in real-time at low computational cost.

Past work that has taken the approach of considering the powertrain efficiency has
often focused on the optimization of the internal combustion engine (ICE) or the
engine-generator set, as a vast majority of the powertrain losses occurs there. Con-
sequently, this often results in the battery dynamics and losses being considered
very crudely, if not neglected. Instead the battery is only considered when applying
constraints on the control, typically to ensure the SOC remains between a defined
upper and lower bound. Some work investigates the overall powertrain efficiency
but uses it to derive heuristic control rules rather than an efficiency-maximizing
objective function [114–116]. Other work studies the powertrain efficiency in depth
to inform the control algorithm (without specifically optimizing efficiency) and then
evaluates simulation results rigorously [117, 118].

The work proposed in this chapter takes a holistic approach and investigates the
efficiency of the whole powertrain in depth before producing a control map such
that the total efficiency is continuously locally maximized during driving (subject to
SOC constraints). The implementation of SCSs using control maps has been done
in the past as well [119]. These maps are easy to implement and can be read during
Efficiency Maximizing Map Strategies 117

driving in real-time with very limited processing requirements. Also, as the maps
are precomputed off-line, there is practically no time-constraint on the optimization
algorithm to maximize the efficiency.

Particular attention is also given to charge sustaining mechanisms. Any optimization

that solely focuses on optimizing the fuel economy will tend to deplete the battery
quite rapidly (or overcharge in rare cases). It is therefore essential to balance short-
term gains in fuel economy with long-term sustainability of such driving. The first
two real-time strategies (EMMS0 and EMMS1) will take two distinct approaches
to address this problem, while the GEMMS has the luxury of knowing its route in
advance and is thus inherently designed to be CS. The permissible range of SOC will
be the same as in Chapter 3 (SOCL = 50% and SOCU = 80%) but further emphasis
will exist on maintaining the SOC reasonably close to SOCinitial = 65%. This differs
vastly from the TCS and PFCS, which both are designed to reach their extreme
points of SOC before alternating the operation such that the SOC drifts in the
opposite direction. This type of driving has certain benefits in terms of robustness
and lack of engine start-stop events, but is very inefficient and has detrimental effects
on the battery.

Lastly, an effort has been made to keep the control strategies practical. There are
always possibilities to include additional factors or corrections that add new tuning
parameters. Such choices tend to make the control design a tuning exercise, and often
render the control system impractical for any other vehicle design. Thus, each of
the control strategies proposed have been limited to use only two tuning parameters.
The approach also aims to be general enough to allow the same optimization process
to be successfully applied to a different series HEV design.
118 Chapter 4

4.2 Powertrain Efficiency

This section studies and identifies the efficiency of the powertrain with the objective
to control it in upcoming sections. Efficiencies for both the PS and SS are presented
before a total efficiency is expressed.

4.2.1 Primary Source

The study of the PS efficiency has already been partly presented as part of the
overall PS operation description in Section 2.3.4. This subsection will therefore
only briefly identify the component efficiencies of the engine, the generator and the
rectifier before presenting the resulting combined PS efficiency ηP S .

The energy of the PS originates from the fuel powering the ICE, where the chemical
energy is converted to mechanical energy. The efficiency of this process is defined
by
TICE ωICE
ηICE = , (4.1)
ṁf uel · QLHV
where TICE and ωICE are the torque and speed of the ICE respectively, ṁf uel is
the fuel mass flow rate and QLHV is the lower heating value of the fuel. The PS
then uses the PMSG to convert the above to three-phase electrical energy, and the
efficiency of this process is given by
3
(v i
2 qg qg
+ vdg idg )
ηg = , (4.2)
TICE ωICE

where vdg , idg , vqg and iqg represent d-q voltages and currents respectively corre-
sponding to the three-phase output of the PMSG. Lastly, the energy flows through
the rectifier to make the energy available as DC power, and its efficiency is defined
as
PP S
ηrec = 3 . (4.3)
(v i + vdg idg )
2 qg qg

The overall energy of the PS is therefore defined as the product of these three
efficiencies
PP S
ηP S (PP S ) = . (4.4)
ṁf uel (PP S ) · QLHV
Efficiency Maximizing Map Strategies 119

60

50
Power of PS, PP S (kW)

3
0.
40

30
0.34
0.346 2 0.3
20 0.3
0.34
0.
10
32 0.3
0.25
0.25
0 0.1 0.1 0.1
800 1200 1600 2000 2400 2800 3200
Engine Speed, ωICE (rpm)
Figure 4.1: PS efficiency, ηP S , for varying PS power demand and engine speed.

Thus, for any given PP S the efficiency ηP S can be determined by measuring the fuel
rate ṁf uel , which will only depend on PP S (as the optimal selection of engine speed
ωICE is utilized as shown in Fig. 2.9). Based on the BSFC data from Section 2.3.4,
the PS efficiency ηP S is presented in Fig. 4.1 as a function of PP S . It demonstrates
that the PS is generally more efficient at higher levels of power demand and medium
speeds. As discussed in Section 2.3.4, the dotted border is defined by the operational
limits of the ICE (due to feasibility or lack of validation). Note that the maximum
efficiency is found at 20.1 kW at 1870 rpm and is marked with a cross in the chart.

4.2.2 Secondary Source

Strictly speaking, the SS is an energy buffer, rather than an energy source. It receives
energy from the PS either directly (by charging) or indirectly (by regenerative brak-
ing). It is therefore not straightforward to express the efficiency as an instantaneous
value. The conventional approach is to express it as the energy charge-discharge
efficiency [41], defined as
Edischarge
ηbat,c−d = , (4.5)
Echarge
where the two energies are defined for the same SOC. Other alternatives include
the expression of efficiency as the coulombic efficiency or the voltaic efficiency [120].
However, they all suffer from an inaccuracy: the underlying assumption of these
types of efficiency is that the battery will be charged and discharged at the same
120 Chapter 4

power level. Consequently, when evaluating the efficiency of the battery at a dis-
charge of, e.g. 10 kW as compared to 20 kW, it is not the actual instantaneous
efficiency being compared, but rather it is a comparison with two different assump-
tions being made for the two cases. The assumptions are that the battery was
charged with 10 kW in the past if discharging at 10 kW, and 20 kW if discharging
at 20 kW. Clearly the past charging should be already fixed, and not determined
by present and future discharging levels. To address this, the efficiency is separated
into charging efficiency and discharging efficiency, where the former is defined as

Pbat−charge vbat,OC · ibat vbat,OC

ηbat,c = = = , (4.6)
Pbat−in vbat · ibat vbat

in which Pbat−charge is the power being stored in the battery. This power is obtained
by multiplying the current, ibat , with the open-circuit voltage of the battery, vbat,OC .
Pbat−in corresponds to the power sent to the battery at its ports, while vbat is the
voltage at the same ports. Similarly the discharging efficiency can be formulated as

Pbat−out vbat · ibat vbat

ηbat,d = = = , (4.7)
Pbat−discharge vbat,OC · ibat vbat,OC

where Pbat−out is the power delivered by the battery at its ports, and Pbat−discharge
is the power consumed by the battery internally. The latter power is obtained by
multiplying the current with the open-circuit voltage of the battery.

The efficiency of the DC-DC converter ηdcdc can now be included, which is defined
through a look-up table (as given in Section 2.4.2). Thus the overall efficiency of
the SS can be expressed as

vbat,OC

vbat
ηdcdc PSS < 0
ηSS = . (4.8)
vbat
 η
vbat,OC dcdc
PSS ≥ 0

To allow simplification of Eq. 4.8 and make it more usable for the optimization
in the next section, battery voltage can be substituted with current. The battery
voltage is modeled to be a function of ibat and SOC. However, vbat,OC has ibat = 0
so we can determine that vbat,OC = f (SOC). Similarly, ibat is a function of SOC
Efficiency Maximizing Map Strategies 121

and vbat , which can however be expressed as a function of PSS as follows:


PSS ·ηdcdc

vbat
PSS < 0
ibat = . (4.9)
PSS

vbat ·ηdcdc
PSS ≥ 0

Now, by considering Eqs. 4.8 and 4.9 the overall efficiency of the SS is given by

vbat,OC ibat

PSS
PSS < 0
ηSS (PSS , SOC, ibat ) = , (4.10)
PSS

vbat,OC ibat
PSS ≥ 0

The defined SS efficiency can now be determined experimentally, analytically or

through simulations. Both of the two latter methods have been performed and
published in [12, 14], but only the analytical method will be presented in this thesis.

The battery model used is described in Section 2.4.1 where parameter values are
also given. It has minor differences in dynamics between charging and discharging
operation to account for differences in the polarization resistance. However, below
only the discharging dynamics are presented, although the dynamics of each mode of
operation were considered when performing the analysis and producing the efficiency
map in this section. The key discharging dynamics of the battery model are given
by Eqs. 2.25-2.29.

To make the efficiency model time-invariant, it is assumed that i∗bat = ibat , so that
we obtain the efficiencies for steady-state operation. To obtain vbat−OC , Eqs. 2.25
and 2.26 should be substituted with ibat = 0 to create open circuit conditions. To
express this as a function of SOC, we substitute with Eq. 2.29 to give

K1 · Qmax (1 − SOC)
vbat,OC (SOC) = E0 − (4.11)
SOC
−B·Qmax (1−SOC)
+ Ae .

Lastly, ibat can be determined by combining Eqs. 4.9, 2.25,2.26 and 2.29 to produce
the following quadratic equation

2
aIbat + bibat + c = 0, (4.12)
122 Chapter 4

where

K2
a= + Rbat ,
SOC
K1 Qmax (1 − SOC)
b= − E0 − Ae−B·Qmax (1−SOC) ,
SOC
PSS
c= .
ηdcdc

Thus, we obtain the battery current as

√
−b ± b2 − 4ac
ibat (PSS , SOC) = , (4.13)
2a

where it is only a function of PSS and SOC. This allows the expression of Eq. 4.10
as follows: 
 vbat,OC ibat PSS < 0
PSS
ηSS (PSS , SOC) = , (4.14)
PSS

vbat,OC ibat
PSS ≥ 0

Equations 4.11 and 4.13 are then iteratively solved for SOC ∈ [SOCL , SOCU ] and
PSS ∈ [PSSmin , PSSmax ] in steps of 1% and 0.1 kW respectively before being sub-
stituted into Eq. 4.14 to provide the efficiency of the SS. The obtained results are
presented in Fig. 4.2.

Battery efficiencies are typically high at low magnitudes of power and get gradually
lower for higher loads. However, as the powertrain includes a DC-DC converter,
the efficiency is very low at very low loads. These two features together result in
an efficiency profile with a peak around 10 kW for discharging and -10 kW for
charging. Furthermore, it is interesting to note that the charging becomes slightly
more efficient at lower SOC levels, while discharging becomes slightly more efficient
at higher SOC levels. Thus, if efficient operation is encouraged, CS is indirectly
taking place to a limited extent.

4.2.3 Total Efficiency

Having obtained the efficiencies for both the PS and the SS in Eqs. 4.4 and 4.14
respectively, these can now be merged into a single expression. However, as we
consider the complete powertrain, we need to make a correction to the SS efficiency.
As mentioned, the battery is not a source of energy by itself but must ultimately
Efficiency Maximizing Map Strategies 123

80

5
91
State of Charge, SOC (%)

75

0.

0.91
0.8
0.3

0.88

0.85
0.9

0.8
70

0.7
0.9

0.91
65

60
0.88

0.3
0.8
0.9
0.9

55

50
-25 -12.5 0 12.5 25 37.5 50
Power of SS, PSS (kW)
Figure 4.2: SS efficiency ηSS for varying charging (negative) and discharging (positive)
SS power demand and SOC.

receive its energy through the PS. Therefore, a correction factor v is included to
account for the PS losses involved in facilitating the SS to operate (the term is
defined further in upcoming sections). Thus, the combined total efficiency (for
PP L ≥ 0) can be expressed as

PP S +PSS
 PP S P η PSS < 0
PP L 
ηP S
+ SSv SS
ηtot (PP S , PSS , SOC) = = , (4.15)
Pin 
 PP S +PSS
PP S P PSS ≥ 0
ηP S
+ vηSS
SS

As the SS efficiency (in Eq. 4.10) during discharging is the inverse of itself during
charging, the expression can by simplified by using

 1/ηSS PSS < 0
∗
ηSS = . (4.16)
 η PSS ≥ 0
SS

Essentially, ηSS
∗
expresses the bi-directional efficiency as a single term. To simplify
further, the individual powers of the sources can be expressed using the power share
factor u, defined in Eq. 2.32, giving a single decision variable to determine both PP S
and PSS . Thus the total efficiency can be formulated as

ηP S ηSS
∗
v
ηtot (u, PP L , SOC) = . (4.17)
vηSS u + ηP S (1 − u)
∗
124 Chapter 4

4.3 Efficiency Maximizing Map Strategy 0

This section presents the general design of the EMMS approach as well as the
specifics of the EMMS0. It begins by introducing the problem formulation and
the control map approach that can be used to solve this. The fist attempt, the
non-CS EMMS0, is presented before being improved further by including a mech-
anism to ensure CS operation, to produce the EMMS0. Lastly, the operation and
performance is evaluated.

4.3.1 Control Approach

The fundamental principle of the EMMS is to operate the energy sources such that
the efficiency ηtot is maximized. As it is clear from the definition of this variable in
the previous section, it depends on two defined variables (PP L and SOC) and one
decision variable (u). The optimization problem can be expressed as the following
local maximization problem:
(
max ηtot (t, u) ∀t ∈ [0, tf ]
P u
PP Smax
(4.18)
0≤u≤ PP L

However, the total efficiency at any time instant is determined by the power re-
quested by the PL, the SOC and the power split between PS and SS, and therefore
the optimization problem can be reformulated as:
(
max ηtot (PP L , SOC, u) ∀PP L ∈ [0, PP Lmax ], SOC ∈ [SOCL , SOCU ]
PEM M S u
PP Smax
0≤u≤ PP L
(4.19)
where PP Lmax = PP Smax + PSSmax .

This reformulation has many benefits. It reduces the time to perform the optimiza-
tion offline and allows the same control map to be used for different driving cycles.
Furthermore, the memory used to store the maps is often reduced. However, the
EMMS approach has some additional processing requirements during operation, as
it needs to read the PP L and SOC in real-time to select the appropriate operating
point. However, this type of real-time feedback also makes the control more robust,
should there be any unexpected variation in operating conditions.
Efficiency Maximizing Map Strategies 125

2 f(u)
1
P_PL
1 P_PSref
SOC
Lookup Table (2D)
Figure 4.3: Implementation of the EMMS in Simulink.

The objective is thus to produce a map for the optimal decision variable given the
defined variables, according to

uopt = f (PP L , SOC). (4.20)

This control map is then implemented within the Simulink model as shown in
Fig. 4.3. The SOC and load power PP L signals are read into the map, which
produces the optimal power share ratio that can simply be multiplied by the load
power to generate a reference signal for the PP S . Note that the f (u) function block
converts the input to the same precision as the generated control map.

The objective function can then be solved through a simple iterative process, within
the search space of SOC ∈ [SOCL , SOCU ], PSS ∈ [PSSmin , PSSmax ] and PP S ∈
[0, PP Smax ]. Note that the search for ωICE is not needed due to the pre-computation
of ωICE,opt = f (PP S ) as shown in Fig. 2.9, thus significantly reducing computational
time (which is not a significant issue though, as optimization is performed off-line).
The efficiency is therefore computed for every feasible combination of values for the
defined and the decision variables and the optimal u is selected in each case (the
range of u is set by the PP L of interest as u ∈ [0, PP Smax /PP L ] and is appropriately
discretized). Once this optimization is performed, the efficiency maximizing control
map is obtained.

4.3.2 Efficiency Maximizing Map

This first design attempt will only consider the efficiencies of the powertrain to
produce the control map, without consideration for CS operation. To implement
the control map it is first necessary to further define the total efficiency of the
powertrain. As mentioned in the previous section, the SS efficiency needs to be
126 Chapter 4

adjusted by a factor v to account for the PS losses incurred in the charging of the
battery. The definition used in [14] is as follows:

 1 PSS < 0
v= . (4.21)
 η
re PSS ≥ 0

where ηre is the replenishing efficiency. This term is applied only during discharging,
and can be intuitively understood as a correction with consideration for the PS
efficiency involved in replenishing the battery after it has been discharged. This can
also be related to practically by considering the fact that the SS efficiency is often
in the region of 90% while the PS efficiency is around 34%. Without any correction,
the efficiency maximizing strategy would almost always operate using only the SS,
ending up depleting the battery. By multiplying the SS discharging efficiency with
the replenishing efficiency, the complete energy cycle involved in discharging the
power from the battery is considered.

In reality, the replenishing efficiency is a variable that is dependent on both past and
future operating conditions and is difficult to compute. However, as its dynamics
can be considered very slow, it can be treated as a constant for a particular driving
cycle without much loss in optimality. This is the approach taken in this work, and
a unique control map can be produced for each selection of ηre .

The optimal power share factor uopt for varying power demand is shown in Fig. 4.4
for ηre = 34%, together with the realized efficiency ηtot . It can be seen that the SCS
chooses to operate SS-only mode during low PP L and almost PS-only mode during
mid-range PP L . For higher power requirements the non-CS EMMS0 uses a blended
mode to drive the powertrain. It is worth noting that the dependence of uopt on
SOC-levels is quite limited, as could be expected from the efficiency plot of the SS
in Fig. 4.2. The total efficiency ηtot that is realized by this selection of u is quite
steady above 30% for most power requirements.

Simulations are run for the four different driving cycles to tune the replenishing
efficiency ηre ∈ [26, 36]% to maximize the fuel economy. Results with normalized
EFC and final SOC levels are presented in Fig. 4.5, and it can be seen that the
optimal value is found as low as ηre = 29% for WL-E but higher than ηre = 36% for
WL-L. Higher values for the replenishing efficiency were not tested as the battery
SOC was dropping too low. However, by looking at the fuel economy of the four
Efficiency Maximizing Map Strategies 127

3
SOC=50%
2.5
Power Share, u (-)

SOC=65%
2 SOC=80%

1.5

0.5

0
0 10 20 30 40 50 60 70 80 90 100
60
PS Power, PP S (kW)

50

40

30

20

10

0
0 10 20 30 40 50 60 70 80 90 100
35
Efficiency, ηtot (%)

30

25

20

15
0 10 20 30 40 50 60 70 80 90 100
Power Requirement, PP L (kW)
Figure 4.4: Optimal power share and PS power, and corresponding total efficiency for
varying power requirements and SOC for ηre = 34% for non-CS EMMS0.

driving cycles combined, as shown in Fig. 4.6, it can be determined that ηre = 34%
is the optimal selection. This corresponds to the typical efficiency of the PS, as
shown in Fig. 4.1.

It is also evident that for all the driving cycles the SOC drops to low levels, and
the control strategy is not CS. In fact, even for extremely low ηre values (which
discourages the use of the SS), the final SOC is only higher than 70% for WL-M.
This can be attributed to the unwillingness of the strategy to use the PS to charge
the SS directly, and instead being overly reliant on regenerative braking.
128 Chapter 4

1.1 70

1.08 60

SOC (%)
Mef c (-)

1.06 50

1.04 40

1.02 30

1 20
26 28 30 32 34 36 26 28 30 32 34 36
1.08 90

80
1.06
70

SOC (%)
Mef c (-)

1.04 60

50
1.02
40

1 30
26 28 30 32 34 36 26 28 30 32 34 36
1.04 70

1.03 60
SOC (%)
Mef c (-)

1.02 50

1.01 40

1 30
26 28 30 32 34 36 26 28 30 32 34 36
1.03 70

60
1.02
SOC (%)

50
Mef c (-)

40
1.01
30

1 20
26 28 30 32 34 36 26 28 30 32 34 36
Replenishing Efficiency, ηre (%) Replenishing Efficiency, ηre (%)
Figure 4.5: Normalized EFC (left) and final SOC (right) for varying ηre when driving
WL-L, WL-M, WL-H and WL-E (from top to bottom) with non-CS EMMS0.
Efficiency Maximizing Map Strategies 129

1.06

1.05
Fuel Economy, Mef c (-)

1.04

1.03

1.02

1.01

1
26 28 30 32 34 36
Replenishing Efficiency, ηre (%)
Figure 4.6: Normalized total EFC Mtot for varying ηre with non-CS EMMS0.

4.3.3 Charge Sustaining Operation

The non-CS EMMS0 has no inherent constraints in terms of SOC, so the battery
could end up depleted or overcharged and permanently damaged. To address this,
a CS function kcs (SOC) is included in the control design, which encourages the
battery to be charged at low SOC values and discharged at high SOC values. This
bias is introduced in the expression of total efficiency, by weighting the input power
of the SS as follows:

ηP S ηSS
∗
v
ηCS (u, PP L , SOC) = . (4.22)
vηSS u + kcs ηP S (1 − u)
∗

For kcs > 1, the SS discharging power becomes heavier, causing it to be reduced by
the optimization algorithm. Simultaneously the SS charging power becomes heavier,
but since it is a negative quantity, this actually encourages further charging of the
battery (as ηCS is always positive and we are aiming to minimize the denominator).
Conversely, for smaller kcs values, the discharging of the SS becomes more attractive
and charging less desirable. The new objective is not only to maximize the efficiency
but also to keep the SOC levels within a certain range. The upper and lower limits
of SOC are the same as for TCS and PFCS (with SOCL = 50% and SOCU = 80%).
This allows a buffer for regenerative braking, as well as avoids very low or high SOC
that accelerates degradation of the battery. Thus, the new optimization problem to
130 Chapter 4

Table 4.1: Definition of CS function kcs

kcs (SOC%) Defined such that

kcs (80) u = 0 for PP L ≤ PSSmax
kcs (75) 1 − (1 − kcs (80))/Kcsi
kcs (70) No correction
kcs (60) No correction
kcs (55) 1 + (kcs (50) − 1)/Kcsi
kcs (50) u ≥ 1 for 0 < PP L ≤ PP Smax

3
Kcsi =1
2.5 Kcsi =2
Kcsi =3
CS Function, kcs (-)

Kcsi =4
2 Kcsi =5
Kcsi =6
1.5 Kcsi =7
Kcsi =8

0.5

0
50 55 60 65 70 75 80
State of Charge, SOC (%)
Figure 4.7: Charge sustaining function kcs (SOC) for various CSI factors Kcsi for
EMMS0.

be solved can be expressed as


 max ηCS (PP L , SOC, u) ∀PP L ∈ [0, PP Lmax ], SOC ∈ [SOCL , SOCU ]

 u
PEM M S0 0 ≤ u ≤ PPPSmax
 PL

 SOC ≤ SOC ≤ SOC L U
(4.23)

To ensure operation within this SOC range the CS function kcs is shaped according
to the rules presented in Table 4.1. During operation at high SOC, the PS is used to
a minimal extent while at lower SOC the PS is often charging the SS. The resultant
profile for the charge sustaining factor kcs is shown in Fig. 4.7. It can be seen that
the lower values of SOC are associated with a high kcs value, encouraging the SCS
to charge the battery, as discussed above. Similarly, at high SOC values, the kcs
value is low and thus encourages the battery to be discharged. There is a flat region
between 60% and 70% where no modification is desired. The intensity of the charge
Efficiency Maximizing Map Strategies 131

3
SOC=50%
2.5
Power Share, u (-)

SOC=55%
2 SOC=65%
SOC=75%
1.5 SOC=80%

0.5

0
0 10 20 30 40 50 60 70 80 90 100
60
PS Power, PP S (kW)

50

40

30

20

10

0
0 10 20 30 40 50 60 70 80 90 100
35
Efficiency, ηtot (%)

30

25

20

15
0 10 20 30 40 50 60 70 80 90 100
Power Requirement, PP L (kW)
Figure 4.8: Optimal power share and PS power, and corresponding total efficiency for
varying power requirements and SOC with ηre = 34% and Kcsi = 8 for EMMS0.

sustaining modification at moderately low or high SOC levels is adjusted by the

charge sustaining intensity factor Kcsi . When published in [14], Kcsi = 4 was used
without any thorough tuning, but for the purpose of completion, and consistency
with other control strategies being evaluated, it should be a tunable parameter as
there is no intrinsic reason to choose any particular value.

As an example, the CS function is implemented for ηre = 34% and Kcsi = 8, and new
maps are produced for optimal power share factor and total efficiency in Fig. 4.8.
Clearly the power share factor is consistently higher for lower SOC (often larger
132 Chapter 4

than one) and quite low (often zero) for higher SOC. The charge sustaining factor
thus seems successful in maintaining the SOC within the desired thresholds and the
resulting power share is in accordance with the rules defined in Table 4.1. However,
it is clear from Fig. 4.8 that this charge sustaining correction comes at the expense
of efficiency in the case of extreme SOC values. Arguably, it is better to suffer some
reduced efficiency immediately rather than damaging the battery or for that matter
suffer heavy inefficiency later. Thus, over longer periods of driving, the EMMS0
could be more efficient.

With the CS function included, new power share maps are produced for each com-
bination of values of ηre ∈ [26, 36]% and Kcsi ∈ [1, 8] in steps of 1% and 1 unit
respectively. Each of these are then tested for the four driving cycles to tune the
parameters to maximize the fuel economy. Results with normalized EFC and final
SOC levels are presented in Fig. 4.9, and it can be seen that the optimal value
is still found around 34% or lower, similar to the non-charge sustaining results of
Fig. 4.5. However, it can be seen that the simulation results, for all ηre values,
are within the defined SOC limits (between 50% and 80%) for each driving cy-
cle. The CS function kcs (SOC) thus appears successful in its objective to maintain
SOCL ≤ SOC ≤ SOCU .

To determine the optimal selection overall, the total fuel economy for the four driving
cycles is evaluated and is presented in Fig. 4.10. It can be seen that the optimal
selection is found to be ηre = 34% (which coincides with the optimal from the
non-CS EMMS0) and Kcsi = 8 (the maximum tested). As the CSI factor Kcsi is
increased, the effects of the CS function kcs (SOC) are reduced, thus resulting in a
lower final SOC. As a consequence, the fuel economy is generally improved by the
increasing Kcsi , as the kcs (SOC) interferes less with the control decision. There is
thus a trade-off between fuel economy and CS ability.

There is a case to be made for choosing a more CS set of tuning parameters, at

the expense of half a percent of fuel economy. However, for the purposes of this
work it is most useful to pursue the strategy that yields a higher fuel economy while
delivering an acceptable CS ability. The EMMS0 will therefore be using ηre = 34%
and Kcsi = 8 for all result from here onwards.
Efficiency Maximizing Map Strategies 133

8 8

1..00
02

1
7 7

01 5
1.0

1.01

58
6 6 55

59
1.00
Kcsi (-)

Kcsi (-)
5 5 5
56
1.01
4 1. 4
02 57

1.0 1.05
3 3
1.02

64
62
60
58
5

2 2
1.0

1 1 59
26 28 30 32 34 36 26 28 30 32 34 36
8 8
7 7

60
2
6 1.00 6
1.05

58
Kcsi (-)

Kcsi (-)
5 5

74
4 4
1.005

05
1.0
1.01
1.02

3 3

66
62
70
72
2 1.01 2
1.02
1 1 60
26 28 30 32 34 36 26 28 30 32 34 36
8 8

56
02
1.002

7 7
001
1.0

1.
6 6
Kcsi (-)

Kcsi (-)

5 5
1.005

4 5 4 58
00
1.
1.02
1.01

3 3
68
66
64
62

1
2 1.0 2
60
1 1
26 28 30 32 34 36 26 28 30 32 34 36
8 8
7 7
05

05
1.00

6 6
1.0

60
Kcsi (-)

Kcsi (-)

5 5 58
4 4
1.0005
1.005
1.01

3 3
66
62

2 2 60
1 1.01 1
26 28 30 32 34 36 26 28 30 32 34 36
ηre (%) ηre (%)
Figure 4.9: Normalized EFC Mef c (left) (Mef c = 1 is marked with a cross) and final
SOC (right) for varying ηre and Kcsi when driving WL-L, WL-M, WL-H and WL-E (from
top to bottom) with EMMS0.
134 Chapter 4

8
1.0
7
05
1.001

1.
00
1.01

2
6
1.002
Kcsi (-)

4 1.005
1.0
05
1
3 1.0

1.
1.02

01
2 1.01 1.
02
1.02
1
26 28 30 32 34 36
Replenishing Efficiency, ηre (%)
Figure 4.10: Normalized total EFC Mtot for varying ηre and Kcsi with EMMS0.

4.3.4 Operation

The power profiles of the operation corresponding to this selection are presented for
the first and final iterations of the tested driving cycles in Fig. 4.11 and Fig. 4.12
respectively. Note that final iterations correspond 8th , 8th , 4th and 4th iteration for
WL-L, WL-M, WL-H and WL-E respectively.

For the first iteration of WL-L and WL-M, the operation of the EMMS0 is quite
similar to the GECMS in when the PS is active. However, the difference is that
the EMMS0 will often follow the load at these times rather than operate the PS
as steadily as the GECMS. Nevertheless, resembling the GECMS rather than TCS
or PFCS should be reassuring for the EMMS0, based on the fuel economy results
from the previous chapter. It is also worth noticing that the SS is practically only
recharged through regenerative braking. This is clear from the figure, as the SS
is never charged (light shading that is negative) unless the vehicle is experiencing
regenerative braking (PP L < 0). Also, although the power share is normally either
u = 0 (only SS delivering load) or u = 1 (only PS delivering load) there are a few
times (when the load is somewhat high) when the SS and PS act together. This
hybrid type of operation becomes more prevalent for WL-H and WL-E, as the load
level is generally higher. However, even for these driving cycles, the PS is often
switched on and off to adapt to the changing loads.

For the final iteration of each of these driving cycles the operation is quite different
as the EMMS0 is SOC dependent, unlike the GECMS. Most visibly, the PS is used
Efficiency Maximizing Map Strategies 135

30

15
Power (kW)

-15 PS S
PP S
PP L
-30
0 100 200 300 400 500 589
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 433
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 455
60

45

30
Power (kW)

15

-15

-30
0 100 200 300 323
Time (s)

Figure 4.11: Power time histories for PS, SS and PL for the first iteration of driving
WL-L, WL-M, WL-H and WL-E (top to bottom) with EMMS0.
136 Chapter 4

30

15
Power (kW)

-15 PS S
PP S
PP L
-30
0 100 200 300 400 500 589
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 433
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 455
60

45

30
Power (kW)

15

-15

-30
0 100 200 300 323
Time (s)

Figure 4.12: Power time histories for PS, SS and PL for the final iteration of driving
WL-L, WL-M, WL-H and WL-E (top to bottom) with EMMS0.
Efficiency Maximizing Map Strategies 137

to a much larger extent for each of the driving cycles. This can be attributed to the
drop in SOC that has occurred over the repeated iterations of driving. The EMMS0
is now actively discouraging the use of SS and the driving is thus dominated by PS
operation. There is however still no direct charging by the PS of the SS, as the SOC
has not dropped low enough to trigger this type of operation (as seen in Fig. 4.8).
This is probably an area for improvement.

Finally, the fuel economy of the EMMS0 is given in Table 4.2 for the four driving
cycles. The actual fuel consumption of the engine mf of the vehicle is actually much
lower than the GECMS for each driving cycle. This is a result of significant driving
with the SS, which is why it is followed by a significant drop in SOC (but still
within the constraints). Looking at the fuel economy comprehensively, the EFC of
the EMMS0 is consistently outperformed by the GECMS, with margins between 4
and 11%. The total fuel economy for the driving cycles combined (as defined for
Mtot ) has the EMMS0 5.68% behind the GECMS. This is a significant improvement
on the TCS and PFCS, which were lagging the GECMS by 14.35% and 13.55%
respectively. However, the urban driving is still a significant issue for EMMS0, as it
needs to be able to use the SS more effectively.

Table 4.2: Fuel economy results for EMMS0

Driving Cycle SOCf inal (%) mf (kg) mef c (kg) ∆GECM S (%)
WL-L 54.54 0.6700 0.7835 +10.61
WL-M 57.25 1.1128 1.1963 +5.04
WL-H 56.67 0.8901 0.9897 +4.15
WL-E 55.97 1.5254 1.6492 +4.03
138 Chapter 4

4.4 Efficiency Maximizing Map Strategy 1

This section presents the non-CS EMMS1, which is an evolution of the non-CS
EMMS0 discussed in the previous section. The strategy is then further developed
into the EMMS1 that accomplishes charge sustaining operation more intuitively and
effectively, in addition to delivering improved fuel economy.

4.4.1 Modified Efficiency Maximizing Map

The non-CS EMMS0 employs the efficiency expressed in Eq. 4.17 to produce the
control map shown in Fig. 4.4. It can be observed that for all power requirements,
we always have u ≤ 1, meaning that the PS is never used to charge the SS. Conse-
quently, the powertrain is limited to operate the SS with only as much energy as is
recuperated through regenerative braking. This works out reasonably well, as the
SS is particularly useful in urban settings (where proportion of regenerative brak-
ing is high) and less important when cruising at highways (where a limited amount
of regenerative braking is applied). However, considering the heavy investment in
electrifying the powertrain, it makes sense to have the ability to utilize the SS to a
larger extent and accomplish an even greater fuel economy.

The reason why the non-EMMS0 never opts for the “charging mode” (PS charging
the SS directly) can be attributed to the severe drop in efficiency due to increased
usage of the PS, which is the least efficient component in the powertrain. To illustrate
the impact that the mode of operation has on efficiency, it is worth looking at a
simplified example (values do not correspond exactly to the vehicle model being
used). If the powertrain has to deliver 20 kW, we can explore three different modes
of operation: PS only (PS mode); PS operation with SS supplementing (hybrid
mode); or PS operation with the SS simultaneously being charged (charging mode).
In this example we are using ηP S (15 kW)= ηP S (20 kW)= ηP S (25 kW)=33%, ηSS (-
5 kW)= ηSS (5 kW)= 90% and ηre = 33%.

The powertrain efficiency (as given in Eq. 4.15) can be simplified for PS mode and
computed for PP S = 20 kW as follows:

PP S + PSS 20 20
ηtot = PP S PSS
= 20 0 = = 33%. (4.24)
ηP S
+ vηSS ηP S
+ ηSS ηre 60 + 0
Efficiency Maximizing Map Strategies 139

The expression is reduced to ηtot = ηP S , which is obvious as we are only using the
PS. For hybrid mode, the efficiency in the case of PP S = 15 kW and PSS = 5 kW is
expressed and computed as:

PP S + PSS 20 20
ηtot = PP S PSS
= 15 5 = = 32.43%. (4.25)
ηP S
+ vη ηP S
+ ηSS ηre 45 + 16.67
SS

The chosen format is used to emphasize the PS and SS components of the input
power (denominator). It can be seen that any increase in contribution from the SS
will slightly decrease the total efficiency. However, it can be imagined that in a case
where ηP S (15 kW)> ηP S (20 kW) there would be scope for the hybrid mode to be
more efficient than PS only mode. Lastly, the efficiency for the charging mode in
the case of PP S =25 kW and PSS =-5 kW is expressed and computed as:

PP S + PSS 20 20
ηtot = = 25 = = 28.37%. (4.26)
PP S
ηP S
+ PSSvηSS ηP S
− 5 · ηSS 75 − 4.5

The charging mode clearly has a dramatically lower efficiency as compared to the
two former modes. In particular, it can be seen that the input power of the PS
(the first term in the denominator) has increased significantly with only a limited
amount of power being absorbed by the SS (the second term in the denominator).
This explains why this mode is seldom used for the non-CS EMMS0.

However, although the above efficiency expression might be true locally in real-
time, it doesn’t yield the maximum efficiency over a longer period of driving. An
alternative understanding of the SS efficiency during charging would be to include
a correction factor in the same way the replenishing efficiency ηre is applied during
discharging. Similar to how the discharging efficiency of the battery needs to be
penalized with the efficiency of the PS involved in replenishing the battery, any
charging should be “rewarded” for offsetting future needs to be replenished. To
include this consideration, the correction factor v from Eq. 4.21 needs to be modified
to:
v = ηre . (4.27)

This new formulation yields a different efficiency for the charging mode case with
PP S = 25 kW and PSS = −5 kW:

PP S + PSS 20 20
ηtot = PP S PSS ηSS
= 25 5·ηSS = = 32.52%. (4.28)
ηP S
+ v ηP S
− ηre 75 − 13.5
140 Chapter 4

It can be seen that the magnitude of the second term in the denominator is increased
such that the overall impact of charging the battery is amplified. Consequently,
the obtained efficiency is now comparable to that of the hybrid mode, and it can
similarly be imagined that in a case of efficient use of the PS, the charging mode
could outperform the other two modes of operation and end up being the optimal
solution.

Based on the new efficiency expression, the optimization problem can be formulated
in the same way as for the non-CS EMMS0 (in Eq. 4.19) with the updated correc-
tion factor v. The process to solve this problem is identical as well (described in
Subsection 4.3.1), allowing the formation of the EMMS1 control map.

The optimal power share factor uopt for varying power demand is shown in Fig. 4.13
together with the realized efficiency ηtot . It can be seen that the SCS chooses to
operate SS-only mode during low PP L , similar to the non-CS EMMS0. However,
once the PS starts to be used, it is used at u > 1 (charging mode), which would
not occur previously. Thereafter, at lower mid-range PP L , a lot of the operation is
almost PS-only mode. For higher power requirements the map uses hybrid mode to
drive the powertrain. It is worth noting that the dependence of uopt on SOC-levels
is still quite limited, although the added charging mode operation can be expected
to impact the SOC profile of the resulting driving. The total efficiency ηtot that is
realized by this selection of u is slightly higher during the charging mode compared
to the non-CS EMMS0, but this can currently only be attributed to the efficiency
being redefined as opposed to superior performance.

Simulations are run for the four different driving cycles to tune the replenishing
efficiency to maximize the fuel economy. Results with normalized EFC and final
SOC levels are presented in Fig. 4.14. Simulations were run for the same range of
ηre as non-CS EMMS0, but only ηre ∈ [33, 36]% were successfully completed. As
can be seen from the results, the final SOC is extremely sensitive to the replenishing
efficiency with variations from 100% to around 40% for WL-L, WL-M and WL-H.
Even the WL-E sees significant changes in SOCf inal for varying ηre .

It can be seen that the optimal value is often found around ηre = 35%, and this
is confirmed by looking at the normalized total EFC in Fig. 4.15. The data is
quite sparse but the optimal value for ηre is likely to be in close proximity to ηre =
35%. However, these results are sufficiently precise to realize that there is a need
Efficiency Maximizing Map Strategies 141

3
SOC=50%
2.5
Power Share, u (-)

SOC=65%
2 SOC=80%

1.5

0.5

0
0 10 20 30 40 50 60 70 80 90 100
60
PS Power, PP S (kW)

50

40

30

20

10

0
0 10 20 30 40 50 60 70 80 90 100
35
Efficiency, ηtot (%)

30

25

20

15
0 10 20 30 40 50 60 70 80 90 100
Power Requirement, PP L (kW)
Figure 4.13: Optimal power share and PS power, and corresponding total efficiency for
varying power requirements and SOC for ηre = 35% for non-CS EMMS1.

to improve upon this control strategy by designing a charge sustaining mechanism.

The SOCf inal values for ηre = 35% are 50%, 60%, 62% and 34% for the four driving
cycles. Thus, similar to the non-CS EMMS0, the non-CS EMMS1 will require some
modification to ensure CS operation. However, the non-CS EMMS1 might be in a
better position to do so.

As mentioned, the SOC range of the non-CS EMMS1 stretches from very high to
very low with a very limited range of ηre , while the non-CS EMMS0 can not even
match the same SOC range with five times the range for ηre . This difference can
142 Chapter 4

1.2 100

1.15 80

SOC (%)
Mef c (-)

1.1 60

1.05 40

1 20
33 34 35 36 33 34 35 36
1.4 100

1.3 80

SOC (%)
Mef c (-)

1.2 60

1.1 40

1 20
33 34 35 36 33 34 35 36
1.08 100

90
1.06
80
SOC (%)
Mef c (-)

1.04 70

60
1.02
50

1 40
33 34 35 36 33 34 35 36
1.05 55

1.04 50

45
SOC (%)
Mef c (-)

1.03
40
1.02
35
1.01 30

1 25
33 34 35 36 33 34 35 36
Replenishing Efficiency, ηre (%) Replenishing Efficiency, ηre (%)
Figure 4.14: Normalized EFC (left) and final SOC (right) for varying ηre when driving
WL-L, WL-M, WL-H and WL-E (from top to bottom) with non-CS EMMS1.
Efficiency Maximizing Map Strategies 143

1.16
Fuel Economy, Mef c (-)

1.12

1.08

1.04

1
33 34 35 36
Replenishing Efficiency, ηre (%)
Figure 4.15: Normalized total EFC Mtot for varying ηre with non-CS EMMS1.

be attributed to the modification of the correction factor v which now encourages

charging mode operation. Although the achievement of high final SOC comes at
the expense of the fuel economy, it is a great characteristic that can be utilized to
make the control strategy CS without designing an external function to perform this
function.

4.4.2 Charge Sustaining Operation

As has been shown in Fig. 4.14, the non-CS EMMS1 is capable of controlling the
final SOC over a wide range by simply adjusting the replenishing efficiency ηre for
the control strategy. As ηre is reduced, the final SOC is increased, and a higher ηre
results in a drop for the final SOC. Thus, if the control strategy is designed such that
a low ηre is employed when the SOC is low (to increase the SOC) and a high ηre is
used when the SOC is high (to decrease the SOC), then the control strategy would
be inherently CS. Designing such an SOC-dependent ηre function is very simple, as
a linear relationship would be sufficient for our purposes. Some possible designs,
with varying CSI factors Dcsi , are presented in Fig. 4.16 (where the optimal ηre,opt
is chosen to be 35%).

Each line represents a unique design that intersects with the optimal solution of
ηre,opt at SOC = SOCinitial . The CSI factor Dcsi determines the deviation from
the optimal ηre,opt . For example, with ηre,opt = 34% and Dcsi = 4, the extreme
points of SOCL and SOCU will correspond to ηre (50%) = 34% − 4% = 30% and
144 Chapter 4

45
Replenishing Efficiency, ηre (%) Dcsi =1 Dcsi =5
Dcsi =2 Dcsi =6
Dcsi =3 Dcsi =7
40
Dcsi =4 Dcsi =8

35

30

25
50 55 60 65 70 75 80
State of Charge, SOC (%)
Figure 4.16: Replenishing efficiency ηre (SOC) for various values of CSI factor Dcsi with
ηre,opt = 35%.

ηre (80%) = 34% + 4% = 38% respectively. This is expressed analytically as

SOC − SOCmid
ηre = ηre,opt + Dcsi (4.29)
SOCrange

where
SOCU + SOCL
SOCmid = = 65% (4.30)
2
and
SOCU − SOCL
SOCrange = = 15%. (4.31)
2
Thus, Dcsi determines how intensely CS operation should be pursued.

The SOC-dependent ηre is then considered to produce new control maps, using the
same approach as taken in the previous section for EMMS0. The generated map for
optimal power share is presented in Fig. 4.17 together with the corresponding power-
train efficiencies. It can clearly be seen that the control strategy is relying heavily on
the PS during low SOC, with significant amount of charging mode operation as well.
Conversely, for higher SOC, the SS is used much more significantly. The contrast
is less extreme compared to EMMS0 in Fig. 4.8, as it is beyond practical necessity
to require complete SS mode for high SOC. It is worth noting that the operation
for the cases of SOC = 55% and SOC = 75% are quite close to the operation of
SOC = 50% and SOC = 80% respectively. This is in contrast to the EMMS0
where even these very low and high values of SOC would result in operation only
marginally different from the SOC = 65% case. Thus, a more aggressive charge
Efficiency Maximizing Map Strategies 145

6
SOC=50%
5
Power Share, u (-)

SOC=55%
4 SOC=65%
SOC=75%
3 SOC=80%

0
0 10 20 30 40 50 60 70 80 90 100
60
PS Power, PP S (kW)

50

40

30

20

10

0
0 10 20 30 40 50 60 70 80 90 100
50

45
Efficiency, ηtot (%)

40

35

30

25

20
0 10 20 30 40 50 60 70 80 90 100
Power Requirement, PP L (kW)
Figure 4.17: Optimal power share and PS power, and corresponding total efficiency for
varying power requirements and SOC for ηre = 35% and Dcsi = 7 for EMMS1.

sustaining operation can be expected. Also, the EMMS1 utilizes the charging mode
not only for low power requirements but also at higher levels, where the EMMS0
would use hybrid mode.

The resulting efficiency is even more different. The inclusion of the replenishing effi-
ciency for charging, which boosts the SS efficiency term, allows very high efficiency
values to be achieved. This is particularly visible at very low power requirements
where the use of charging mode results in efficiencies higher than the peak PS ef-
ficiency (around 35%), which has often been the upper limit for previous control
146 Chapter 4

strategies. However, it is problematic to compare the efficiencies of each control

strategy, as although the EMMS1 is still using the total powertrain efficiency ηtot
as defined in Eq. 4.15 earlier in this chapter, the meaning is quite different. The
definition of the total efficiency has changed as we use a new understanding of
the replenishing efficiency ηre (within the correction factor v) which is now SOC-
dependent rather than a constant and both boosts and penalizes the SS efficiencies
during charging and discharging respectively. Consequently, this new efficiency for
the EMMS1 does not relate to the instantaneous physical efficiency of the power-
train, but it allows the optimization process to identify suitable operating points for
longer durations of driving.

To test the EMMS1 with its CS features, new power share maps are produced for
each combination of values of ηre,opt ∈ [34, 36]% and Dcsi ∈ [1, 9]% in steps of 0.2%
and 1% respectively. Each of these are then tested for the four driving cycles to tune
the parameters such that the fuel economy is maximized. Results with normalized
EFC and final SOC levels are presented in Fig. 4.18.

The optimal selection of ηre,opt and Dcsi varies considerably between driving cycles,
and is in fact typically outside the investigated region (thus appearing on the edge of
the plots). However, it can be seen for the first three driving cycles that the final SOC
is found to be sustained best within the investigated range (in particular just below
ηre,opt = 35% where SOCf inal ≈ SOCinitial ). Also, an overall evaluation of Mtot , as
shown in Fig. 4.19, gives ηre,opt = 35% and Dcsi = 7% as the optimal selection. This
selection was manually favored over an alternative solution at ηre,opt = 36% and
Dcsi = 8% as it yields practically identical fuel economy results (<0.02% difference)
but delivers improved CS ability.

As the investigated range of the tuning parameters is quite narrow, relative to the
EMMS0, it might be thought that this control strategy is highly sensitive to precise
tuning. However, there are two reasons why this is not true. Firstly, even though the
optimal tuning parameters for various driving cycles are very different, the resulting
fuel economy for varying tuning parameters are quite similar. Secondly, and most
importantly, due to the nature of the charge sustaining mechanism, the control
strategy will often tend to drift towards the optimal ηre value for the particular
type of driving. For example, as was shown in Fig. 4.14, the WL-E driving cycle
performs optimally for ηre = 33% while the other driving cycles prefer operation
closer to ηre = 35%. With the EMMS1, it can be seen that the optimal selection (of
Efficiency Maximizing Map Strategies 147

9 9
1

1.002
8 1.0 8

1.01
1.005

05
1.005

1 .0
7 7

64
1.0
6 6
Dcsi (%)

Dcsi (%)
05
1.005
5 5

66
4 4
60

2
1.00
3 3
58
2 2 56
62
1 1 50
34 34.5 35 35.5 36 34 34.5 35 35.5 36
9 9
1.
1.0
00

8 8
5

1.0
1

05

05

66
5

64
7 7
1.0
1.00

6 6
Dcsi (%)

Dcsi (%)
5 5
4 4 62
68
3 3
1.0 02 70 60
2 1 1.0 2 58
1 1 56
34 34.5 35 35.5 36 34 34.5 35 35.5 36
9 9
8 1.002 8
1.00

1.0

1.003
66

64
7 7
03
2

6 6
Dcsi (%)

Dcsi (%)
1.001

5 5
4 4 62
02
1.0

68
1.001

1.0

3 3
05

0 3
.0 5 60
2 1 0 2
1.0 58
1 1
34 34.5 35 35.5 36 34 34.5 35 35.5 36
9 9
62
8 8
7 7 58
5
1.00
6 6
Dcsi (%)

Dcsi (%)

02 56
5 1.0 5 60

4 1.01 4 58
5
3 1.00 3 50
56
4 5
2 2 40
1 1.02 1 50 35
34 34.5 35 35.5 36 34 34.5 35 35.5 36
ηre,opt (%) ηre,opt (%)
Figure 4.18: Normalized EFC Mef c (left) (Mef c = 1 is marked with a cross) and final
SOC (right) for varying ηre,opt and Dcsi when driving WL-L, WL-M, WL-H and WL-E
(from top to bottom) with EMMS1.
148 Chapter 4

1.003
04

1
1.10.003
8 2

1.00
2
02
1.0 0

1.00
01 1.0

1.0
7 1.002

01
6

1.0
Dcsi (%)

5
1.003 1.001
4
2
1.0
02 1.00
3 1.004 1.003
1.005 1.004
2 1 1.003 1.005
1.0.00706 1.004
1 1.005 1.006 1.007 1.008
34 34.5 35 35.5 36
Replenishing Efficiency, ηre,opt (%)
Figure 4.19: Normalized total EFC Mtot for varying ηre,opt and Dcsi with EMMS1.

ηre,opt = 35% and Dcsi = 7%) will result in a final SOC of 60% for WL-E. By using
Eq. 4.29 we can calculate that this corresponds to operation with ηre = 32.7%.
Thus, for most types of driving, the SOC will often drift and become reasonably
steady close to the point that yields the best ηre value such that the fuel economy
is maximized.

It is also worth noting that for the first three driving cycles the final SOC is close
to SOCinitial = 65%. This has several benefits. Firstly, this mean that the SOC
will rarely deviate significantly from the base SOC value. This reduced depth of
discharge leads to improved battery health. Secondly, the limited need to apply
CS adjustments speaks to the effective design of the core control strategy that is
applicable to a wide range of driving cycles. Thirdly, the control strategy is quickly
able to reach the optimal ηre value to maximize the fuel economy for the given driving
cycle. If a particular driving cycle had its optimal operation with ηre = 28%, the
EMMS1 would need to drive sub-optimally for quite a while until the SOC drops
down to 50% (as given by Eq. 4.29) to make the control strategy effectively operate
with ηre = 28%. Thus, the closer the final steady SOC value for a driving cycle is
to SOCinitial , the faster it will reach its ideal fuel economy.

4.4.3 Operation

The power profiles resulting from the operation of EMMS1 with ηre,opt = 35% and
Dcsi = 7% are presented in Fig. 4.20 and Fig. 4.21, for the first and final iteration
Efficiency Maximizing Map Strategies 149

30

15
Power (kW)

-15 PS S
PP S
PP L
-30
0 100 200 300 400 500 589
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 433
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 455
60

45

30
Power (kW)

15

-15

-30
0 100 200 300 323
Time (s)

Figure 4.20: Power time histories for PS, SS and PL for the first iteration of driving
WL-L, WL-M, WL-H and WL-E (top to bottom) with the EMMS1.
150 Chapter 4

30

15
Power (kW)

-15 PS S
PP S
PP L
-30
0 100 200 300 400 500 589
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 433
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 455
60

45

30
Power (kW)

15

-15

-30
0 100 200 300 323
Time (s)

Figure 4.21: Power time histories for PS, SS and PL for the final iteration of driving
WL-L, WL-M, WL-H and WL-E (top to bottom) with the EMMS1.
Efficiency Maximizing Map Strategies 151

of the driving cycles respectively. There are three major differences between the
operation of EMMS0 and EMMS1: the use of charging mode operation; the amount
of PS operation; and the differences between the first and final iteration.

Firstly, it is quite clear from the EMMS1 results that the SS is quite often charged
directly by the PS (shown as light shading in the negative region, while PP L is
positive). This occurs frequently for every single driving cycle, normally in quite
small magnitudes. However, as is seen towards the end of WL-E, the EMMS1 even
opts to charge the SS at about 15 kW during driving. This not only boosts the SOC
but also allows the PS to operate at a more efficient power level. Consequently,
the power share can be seen to exhibit a mix of load following and load leveling
characteristics.

Secondly, the PS is used more frequently for the EMMS1. There are many instances
where the SS on its own is more efficient than the PS on its own. However, in many
of these cases an even more preferred option is to have the PS deliver power in excess
of the required load and thus charge the SS. As this is allowed by the EMMS1, it can
be seen that the PS is used to deliver reasonably low loads. The operation around
t = 120 s for WL-E can be compared with the operation of EMMS0 in Fig. 4.11.
The two valleys in PP L are operated by the SS in EMMS0, while the EMMS1 decides
to use the PS to deliver power (efficiently) in excess of the required load and thus
charge the SS at the same time.

Thirdly, it can be seen that the difference between the first and final iteration for
EMMS1 for each driving cycle is relatively low. The differences for WL-L, WL-
M and WL-H are barely noticeable, while the WL-E clearly has more PS usage.
Nevertheless, the differences are much smaller than EMMS0. This can be explained
by the previous two differences mentioned, which both result in a higher SOC. As
the EMMS0 struggled to maintain its SOC (having final SOC values around 55% for
each driving cycle), it needed to apply control decisions that deviated significantly
from its base operation (at SOC = SOCinitial ). EMMS1 on the other hand maintains
SOC ≈ SOCinitial for most of its driving and does thus not need to deviate from
its operation. In fact, the limited deviation that does occur is desirable, as this is
the mechanism that allows the EMMS1 to identify the ideal control policy for the
particular driving conditions.
152 Chapter 4

60

45

30
Power (kW)

15

PS S
-15 PP S
PP L
-30
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1292
Time (s)

Figure 4.22: Power time histories for PS, SS and PL for all four iterations of driving
WL-E with the EMMS1.

The WL-E is the only driving cycle where the SOCf inal drops by more than 1.5%,
which is why it has some clearly visible differences between the first and final itera-
tion. It is however worth emphasizing that the EMMS1 operates quite steadily even
for WL-E. To demonstrate this further, the power profiles for all four of the WL-E
iterations are shown in Fig. 4.22. It is quite clear that the control strategy is quick to
learn about the driving conditions, and adapts already by the second iteration. The
differences in control between the second and fourth iteration are very small. Thus,
it can be understood that the EMMS1 will “find” the preferred mode of operation
within a short time frame and then settle into consistent operation.

The fuel economy results corresponding to these driving cycles are shown in Ta-
ble 4.3. As observed and mentioned earlier, the EMMS1 is quite successful in main-
taining its SOC (in contrast to the EMMS0). The EFC results are quite impressive
as they are at worst less than 5% behind the GECMS, and at best less than 1%
behind. Overall, for all driving cycles considered together, the GECMS outperforms
the EMMS1 by only 2.34%, which essentially cuts the margin to EMMS0 by half.

Table 4.3: Fuel economy results for EMMS1

Driving Cycle SOCf inal (%) mf (kg) mef c (kg) ∆GECM S (%)
WL-L 63.63 0.7258 0.7406 +4.57
WL-M 65.18 1.1701 1.1684 +2.59
WL-H 65.30 0.9679 0.9651 +1.56
WL-E 59.60 1.5257 1.5997 +0.91
Efficiency Maximizing Map Strategies 153

4.5 Global Efficiency Maximizing Map Strategy

As the EMMS framework is delivering good performance, it is of interest to produce

a globally tuned variant that is comparable to the GECMS. This section will present
such a control in the form of the GEMMS, which will be designed, tuned and studied,
as well as compared to the GECMS.

4.5.1 Global Design

The GEMMS is a globally tuned EMMS (similar to the relationship between the
GECMS and ECMS). However, the GEMMS not only tunes the EMMS1 optimally
with prior knowledge of the driving cycle, it also refines the definition of the objective
function. The EMMS1 refined the total efficiency expression used by the EMMS0, to
include a correction to the battery charging operation as well (the EMMS0 only cor-
rected discharging operation), and also made the correction factor SOC-dependent
(rather than being a constant). However, the correction factors are the same for
charging and discharging operation. Although this is a good approximation, the re-
plenishing efficiency ηre is not identical for charging and discharging operation and
a more precise expression can be obtained by modifying the correction factor v from
Eq. 4.27 to: 
 ηre,c PSS < 0
v= (4.32)
 η P ≥ 0
re,d SS

where ηre,c and ηre,d are the replenishing efficiencies for charging and discharging
respectively.

Based on the new efficiency expression, the optimization problem can be formulated
as the local maximization problem given in Eq. 4.19. However, for the GEMMS
the correction factor v can be globally tuned for each driving cycle. Thus, for any
given positive power requirement PP L , an optimal power share factor uopt can be
defined for each set of replenishing efficiencies ηre,c and ηre,d . Using the efficiency
maps for the PS and SS, a sweep can be performed for Eq. 4.15 with u ∈ [0, PPPSmax PL
],
PP L ∈ [0, PP Lmax ] and SOC ∈ [SOCL , SOCU ] to produce an optimal control map.
This process is repeated for each candidate set of ηre,c and ηre,d .
154 Chapter 4

Table 4.4: Optimal replenishing efficiency values for GEMMS

Driving cycle ηre,d (%) ηre,c (%)

WL-L 37.7 31.9
WL-M 37.9 31.9
WL-H 36.7 32.8
WL-E 34.7 31.0

This optimization process is now applied to produce power share maps for each
combination of values of ηre,c ∈ [31.5, 33]% and ηre,d ∈ [36.5, 38]% (the WL-E solution
was however later found by studying ηre,c ∈ [30, 32]% and ηre,d ∈ [34, 36]%) in steps
of 0.1% for each. Each of these are then tested for the four driving cycles to tune
the parameters to maximize the fuel economy. Results with normalized EFC and
final SOC levels are presented in Fig. 4.23. The optimal selection of replenishing
efficiencies for each of the four driving cycles is presented in Table 4.4.

The optimal selections of replenishing efficiency values are unique for each driving
cycle, but they are very similar for the first three of them. In fact, using ηre,d = 37.7%
and ηre,c = 31.9% yields fuel economies that are less than 0.2% inferior to the optimal
solution for these three driving cycles. The GEMMS is thus less sensitive to varying
driving cycles when compared to the GECMS. So despite that the optimal set of
tuning parameters for WL-H is found at ηre,d = 36.7% and ηre,c = 32.8%, which is
far from the values mentioned above, the performance is negligibly small. In general,
for each of the driving cycles, the performance of the control strategy is strongest
along the SOCf inal = SOCinitial line of operation (similar to GECMS).

However, it can be seen that the optimal value for WL-L and WL-M is not very
close to SOCf inal = SOCinitial = 65%, which can be expected from a global optimal
solution. This can be attributed to the limited precision of the tuning. For example,
for WL-L at ηre,d = 37.6% and ηre,c = 31.8% the fuel economy is only worsened
by <0.04%, while achieving SOCf inal = 65.67%. It is quite likely that there is
another solution in between these that achieves a better fuel economy (with very
small margin) while approaching SOCf inal = SOCinitial even more. When a similar
situation appeared for the EMMS1, the more charge sustaining option was selected,
as it was the preferred solution for a real-time control strategy (that is expected to
operate well for varying driving conditions). However, for the GEMMS the solution
with the better fuel economy will be selected, as the priority is to minimize EFC
such that it can be used as benchmark of what is realizable.
Efficiency Maximizing Map Strategies 155

33 1.005 33 50
1.

1.
01

02
60

30
32.5 1.0 32.5
ηre,c (%)

ηre,c (%)
0 40
1.0 5 70
1 1.00
1.0 5
2 50

1 .0
32 32
0.0051
1.1
2
1.05

02
60
80
100 90 70
31.5 31.5
36.5 37 37.5 38 36.5 37 37.5 38
1.00

33 33
1.0 60
2

05
1.0
05

30
32.5 1.0 32.5 70 40
1
ηre,c (%)

ηre,c (%)
1.0 50
2
32 32
1.0 60
02 51
1.110..0052
1.0 90 80 70
1.05 100
31.5 31.5
36.5 37 37.5 38 36.5 37 37.5 38
33 33
1. 1.0 1.0 60
00 05 1
1.

2
02

1.0

40
32.5 1.0 05 32.5 70
1
ηre,c (%)

ηre,c (%)

1.0 50
2
32 32
05

60
.01
1.0

11.02
80 70
31.5 1.05 31.5
90
36.5 37 37.5 38 36.5 37 37.5 38
32 32 58 54
1.01 6
60 56
1.005 2
658
0
31.5 31.5
1.00
1.0012 64 62
1.
ηre,c (%)

ηre,c (%)

00
31 1.0001 2 31
1.0 64
01 66
1.0
01
30.5 30.5

1.00 1.001 66
30 2 30 68
34 34.5 35 35.5 36 34 34.5 35 35.5 36
ηre,d (%) ηre,d (%)
Figure 4.23: Normalized EFC Mef c (left) (Mef c = 1 is marked with a cross) and final
SOC (right) for varying ηre,c and ηre,d when driving WL-L, WL-M, WL-H and WL-E
(from top to bottom) with GEMMS.
156 Chapter 4

3 60
SOC=50%

PS Power, PP S (kW)
SOC=65%
Power Share, u (-)

SOC=80%
2 40

1 20

0 0
0 20 40 60 80 100 0 20 40 60 80 100
3 60

PS Power, PP S (kW)
Power Share, u (-)

2 40

1 20

0 0
0 20 40 60 80 100 0 20 40 60 80 100
3 60
PS Power, PP S (kW)
Power Share, u (-)

2 40

1 20

0 0
0 20 40 60 80 100 0 20 40 60 80 100
3 60
PS Power, PP S (kW)
Power Share, u (-)

2 40

1 20

0 0
0 20 40 60 80 100 0 20 40 60 80 100
Power Requirement, PP L (kW) Power Requirement, PP L (kW)
Figure 4.24: Optimal power share and PS power for varying power requirements and
SOC for WL-L, WL-M, WL-H and WL-E (top to bottom) with GEMMS.
Efficiency Maximizing Map Strategies 157

The optimal set of replenishing efficiencies for each of the four driving cycles, corre-
spond to the control maps presented in Fig. 4.24. As can be seen, the optimal power
share uopt has similar trends to most of the previous optimization-based control
strategies in this work: pure PS operation at very low power requirements; charging
mode operation at mid-low power requirements; and hybrid operation for medium
and high power requirements. However it differs from the previous control strate-
gies in key respects. Firstly, it is interesting that the general shape of the GEMMS
control map is more similar to the GECMS than it is to the EMMS1. The flexibility
offered by having two tuning parameters allows both the GEMMS and GECMS to
adopt more precisely the truly optimal power share. However, in terms of its SOC
dependence, the GEMMS is more similar to the EMMS1 than the GECMS. Note
that the spike in power share around PP L = 0.5 kW, is an effect of the extremely
low DC-DC converter efficiency. However, this spike is not implemented in the real
control.

4.5.2 Operation

The operation based on the globally tuned parameter values is presented further in
Fig. 4.25 and Fig. 4.26, showing the power profiles for the first and final iterations
of the driving cycles respectively.

The operation for WL-L and WL-M is very similar to the GECMS. However, it can
be seen that the GEMMS experiences fewer false starts, i.e. the PS being switched
on for a brief moment before being switched off. This is particularly visible for
the WL-L, where the GECMS suffers from a large quantity of false starts. However,
rather than being a particular trait of the GEMMS, it has most likely been fortunate
with the driving conditions and its own rules at these particular times. The GEMMS
is using the PS to a lesser extent (as evidenced by the drop in final SOC discussed
earlier) and fewer false starts would be a consequence for these driving cycles with
low loads. Another difference between the GEMMS and GECMS, which is clearer
in WL-M and WL-E, is that the GEMMS is using the PS much more flexibly. As
was remarked earlier, the GECMS operates in a quite “blocky” manner, with the
PS often operating quite steadily. In contrast, the PS operation of the GEMMS is
much more uneven as it adapts to the changing load.
158 Chapter 4

30

15
Power (kW)

-15 PS S
PP S
PP L
-30
0 100 200 300 400 500 589
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 433
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 455
60

45

30
Power (kW)

15

-15

-30
0 100 200 300 323
Time (s)

Figure 4.25: Power time histories for PS, SS and PL for the first iteration of driving
WL-L, WL-M, WL-H and WL-E (top to bottom) with the GEMMS.
Efficiency Maximizing Map Strategies 159

30

15
Power (kW)

-15 PS S
PP S
PP L
-30
0 100 200 300 400 500 589
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 433
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 455
60

45

30
Power (kW)

15

-15

-30
0 100 200 300 323
Time (s)

Figure 4.26: Power time histories for PS, SS and PL for the final iteration of driving
WL-L, WL-M, WL-H and WL-E (top to bottom) with the GEMMS.
160 Chapter 4

With regards to the GEMMS performance for the first and final iterations of the
driving cycles, it can be seen that the PS is used to a larger extent for WL-L and
WL-M (and WL-H to a limited extent). This can be attributed to the drop in
SOC that was noted earlier that causes the SS efficiency to drop, making the PS the
preferred energy source more often. This results in an indirect form of CS operation.
The WL-E, on the other hand practically operates identically for all iterations.

It is worth noting that there is a significantly larger amount of charging mode op-
eration when compared to the EMMS1 (in Fig. 4.21). The frequency or duration
of charging mode operation is comparable but the magnitude is much higher with
the GEMMS. This can be attributed to the fact that the EMMS1 has ηre,c = ηre,d ,
and is thus unable to include intense charging mode operation without detrimental
impact on the optimization of the balance during hybrid mode operation. Thus, the
ability to tune the replenishing efficiencies of charging and discharging separately
makes the GEMMS much more nuanced in making its decisions.

Finally, the fuel economy results for the GEMMS are presented in Table 4.5. As
mentioned earlier, the focus of the GEMMS is on minimizing EFC and thus the
lower final SOC is less relevant. It can be seen that the GEMMS has outperformed
the GECMS for every single driving cycle, with margins of 0.06-0.38%. For the
driving cycles combined, the net improvement is 0.2%. Considering the additional
analysis of the powertrain that was done to be able to implement this strategy, these
gains can be considered quite modest. The GECMS has a simple implementation
stage, and also results in relatively simple operation of the PS, which is operated
quite steadily. In fact, maybe the GECMS performed well because of its simplicity
rather than despite it. This will be explored further in Chapter 6.

Nevertheless, as the objective of both the GECMS and GEMMS is to act as bench-
marks, representing approximate global optimal solutions, the 0.2% improvement is
significant.

Table 4.5: Fuel economy results for GEMMS

Driving Cycle SOCf inal (%) mf (kg) mef c (kg) ∆GECM S (%)
WL-L 59.36 0.6451 0.7063 -0.28
WL-M 59.13 1.0750 1.1382 -0.06
WL-H 64.82 0.9465 0.9487 -0.17
WL-E 64.96 1.5788 1.5793 -0.38
Efficiency Maximizing Map Strategies 161

4.5.3 Relation to GECMS

It might be apparent from the comparisons between the GEMMS and GECMS in
this section that the two control strategies are similar. By looking closer at the
objective function of each of these control strategies, their connection can be further
understood.

The objective of the GEMMS (as given in Eq. 4.19) is to maximize the total power-
train efficiency for each possible power requirement. However, as the output power
for a particular driving cycle is fixed, the problem can be reformulated as a mini-
mization of the input power of the powertrain instead, giving:

 min Pin (PP L , SOC, u) ∀PP L ∈ [0, PP Lmax ], SOC ∈ [SOCL , SOCU ]

 u
PGEM M S 0≤u≤ PP Smax
 PP L

 SOCL ≤ SOC ≤ SOCU
(4.33)
where 
PP S ηSS
PP S PSS 
ηP S
+ P
ηre,c SS
PSS < 0
Pin = + ∗ = , (4.34)
ηP S ηSS  PP S
+ 1
P PSS ≥ 0
ηP S ηre,d ηSS SS

which corresponds to the denominator of the efficiency expression in Eq. 4.15. This
can then be expressed in terms of fuel consumption using

PP S = ṁf QLHV ηP S (4.35)

which yields 
 ṁf + ηSS PSS
Pin ηre,c QLHV
PSS < 0
= . (4.36)
QLHV  ṁf + 1 PSS
PSS ≥ 0
ηre,d ηSS QLHV

This is equivalent to the GECMS cost function (in Eq. 3.14), with the equivalent
factors as PSS and SOC sensitive variables, rather than constants, as follows:

ηSS (PP L , u, SOC)

Sc (PP L , u, SOC) = (4.37)
ηre,c

1
Sd (PP L , u, SOC) = (4.38)
ηre,d ηSS (PP L , u, SOC)
The GEMMS can thus, in some sense, be considered equivalent to the GECMS, even
though this was not the original intention.
162 Chapter 4

3 3
GEMMS (SOC=65%)
GECMS
Power Share, u (-)

2 2

1 1

0 0
0 20 40 60 80 100 0 20 40 60 80 100
3 3
Power Share, u (-)

2 2

1 1

0 0
0 20 40 60 80 100 0 20 40 60 80 100
Power Requirement, PP L (kW) Power Requirement, PP L (kW)
Figure 4.27: Comparison of optimal power share profiles for GECMS and GEMMS (for
SOC = 65%) for WL-L, WL-M, WL-H and WL-E (left to right, top to bottom).

However, note that the traditional GECMS, which pre-computes the control input,
would find it difficult to solve above cost function as it would struggle to deal with
the SOC dependence. However, any implementation that pre-computers tools (like
the control maps of the GEMMS) rather than control inputs, would be able to solve
the problem as the driving and state conditions are available at each time instance.

It is interesting to compare the GECMS control maps from Fig. 3.16 directly with
GEMMS. This has been done in Fig. 4.27, where the GECMS is compared to the
GEMMS with SOC = 65%. It can be seen that the two control strategies produce
similar control maps in general, but the GEMMS is less smooth. This can be at-
tributed to the inclusion of the SS efficiency in the evaluation, due to the inefficient
region of operation at very low SS power levels, resulting in sudden changes in power
share. Also, at mid-high power requirements, the GEMMS is more inclined to use
the PS, exhibiting another clear difference between the control strategies.
Efficiency Maximizing Map Strategies 163

4.6 Efficiency Maximizing Map Strategy 2

This section presents the fourth and final EMMS. It aims to emulate the GEMMS
operation, but with the constraint of being real-time realizable. It will therefore use
the efficiency definition (and its tuned parameters) of GEMMS together with the
CS mechanism of the EMMS1 to produce the EMMS2.

4.6.1 Real-time Adaption of GEMMS

The developed GEMMS is great at delivering excellent fuel economy, and is probably
close to the global optimal solution as it outperformed the GECMS, but it is not
realizable in real time and thus mainly serves as a great benchmark. However, it is
possible to make use of the globally tuned selections of ηre,c and ηre,d of the GEMMS
to produce a real-time version based on the EMMS process.

Similar to EMMS1, it will be necessary to make the the replenishing efficiencies

SOC-dependent as ηre,c (SOC) and ηre,d (SOC) to allow the powertrain management
to adjust depending on operating conditions. For the EMMS1 there was only one
factor to be defined (in Eq. 4.29) while the EMMS2 will require the definition of
two replenishing efficiencies as

SOC − SOCmid
ηre,c = ηre,c,opt + Dcsi,c (4.39)
SOCrange

SOC − SOCmid
ηre,d = ηre,d,opt + Dcsi,d (4.40)
SOCrange
where ηre,c,opt and ηre,d,opt are optimal base values for the charging and discharging
replenishing efficiencies respectively, while Dcsi,c and Dcsi,d determine how intensely
CS operation should be pursued for each respectively.

Having four different tuning parameters might make this control strategy appear
excessively laborious. Investigating a range of 10 values for each parameter would
require 10,000 simulations to determine the optimal combination, which would be
prohibitively time-consuming. However, half the tuning is completed indirectly by
producing the GEMMS where the optimal replenishing factors are given for each
driving cycle in Table 4.4. Rather than selecting the values for a particular driving
cycle, ηre,c,opt and ηre,d,opt were selected such that the deviation from optimality is
164 Chapter 4

minimized. It was found that ηre,c,opt = 31.9% and ηre,d,opt = 37.7% delivered fuel
economies that were within 0.2% of the optimal solution for the first three driving
cycles and are therefore chosen. An alternative method to determine ηre,c,opt and
ηre,d,opt would be to define them as the set of values that optimizes the total fuel
economy of all four driving cycles together, or that minimizes the total distance to
all preferred solutions. The EMMS2 therefore only has to tune Dcsi,c and Dcsi,d .

Combinations of tuning parameters in the range of Dcsi,c ∈ [0, 1]% and Dcsi,d ∈
[0, 5]% in steps of 0.1% are used to produce control maps, based on the process
described in Section 4.3.1. Each of these are then tested for the four driving cycles
to tune the parameters such that the fuel economy is maximized. Results with
normalized EFC and final SOC levels are presented in Fig. 4.28.

The most striking feature is the straight lines of the profiles of the fuel economy
and SOC results for the first three driving cycles. This can attributed to the dis-
cretization process where the realized ηre,c,opt and ηre,d,opt values are implemented
in 0.1% intervals. Thus, for example, there would be no change in ηre,d,opt with
Dcsi,d = 3%, for any changes in SOC ∈ [64.5, 65.5) (as this would yield values of
ηre,d,opt ∈ [37.65, 37.75)%, which would be rounded to ηre,d,opt = 37.7%). Thus, for
the first three driving cycles which operate within a very narrow band of SOC, the
effects of discretization are very prominent, unlike the WL-E where the operation
over a wider range of SOC conceals this effect.

In general, the results have low sensitivity to changes in CSI factors Dcsi,c and
Dcsi,d . This is an expected outcome, if we consider the results of Fig. 4.23 for
the GEMMS. The selected ηre,c,opt and ηre,d,opt values do not only yield close to
optimal fuel economy results for the first three driving cycles, but also very close to
SOCf inal = SOCinitial . Consequently, these driving cycles are immediately operated
in a close to optimal strategy such that the SOC remains steady. The Dcsi,c and
Dcsi,d factors mainly influence the control behavior at low and high SOC values and
are thus barely needed for the three mentioned driving cycles.

In contrast, the WL-E relies heavily on the CSI factors Dcsi,c and Dcsi,d to achieve
its optimal fuel economy. In fact, it would prefer a very high Dcsi,d so that the
ηre,d,opt = 37.7% can be adjusted to ηre,d = 34.7% (as given in Table 4.4) as quickly
as possible. However, the ηre,c,opt = 31.9% needs to be adjusted to a lesser extent to
reach its preferred ηre,c = 31.0%, which is why a small Dcsi,c factor will suffice.
Efficiency Maximizing Map Strategies 165

1 1

64
1.1
0.8 0.8 64.5
1.05
1.01
Dcsi,c (%)

Dcsi (%)
0.6 0.6
5 1.1

0.4 0.4
63
1.0

01

64
1. 62
0.2 1.002 0.2

0 1 2 3 4 5 0 1 2 3 4 5
1 1
1.02
0.8 2 1.0 0.8
00 02

65 5.4
1.

.5
6
1.0
Dcsi,c (%)

Dcsi (%)
001

0.6 0.6

0.4 0.4

65.5
65.4
0.2 0.2

0 1 2 3 4 5 0 1 2 3 4 5
1 1
6655
1.02

.8.65.5

0.8 0.8
6

1.002 65
1.00
Dcsi,c (%)

Dcsi (%)

0.6 0.6
05

65.6
1.002

0.4 0.4
64.5

0.2 0.2

0 1 2 3 4 5 0 1 2 3 4 5
1 1
1
56

1.00
58
54

0.8 1. 0.8
00
5 1.00
1

1
Dcsi,c (%)

Dcsi (%)

1.002
1.

0.6 0.6
52 50

0.4 0.4
56
48
1.0 54
1.

05
4644

0.2 0.2
01

0 1 2 3 4 5 0 1 2 3 4 5
Dcsi,d (%) Dcsi,d (%)
Figure 4.28: Normalized EFC Mef c (left) (Mef c = 1 is marked with a cross) and final
SOC (right) for varying ηre,c and ηre,d when driving WL-L, WL-M, WL-H and WL-E
(from top to bottom) with EMMS2.
166 Chapter 4

1.03

1.02

1.03
0.8
1.01 1.0 1.02
1.001 1.01

1.01
03
Dcsi,c (%)

1.01
0.6

1.003
1.001
1.032
1.0

0.4

1.01
0.2 1.0
03
1
1.0

0 1 2 3 4 5
Dcsi,d (%)
Figure 4.29: Normalized total EFC Mtot for varying Dcsi,c and Dcsi,d with EMMS2.

As can be seen, the ideal selection of the CSI factors for the WL-E would compro-
mise the fuel economies of the remaining three driving cycles. Therefore, the total
normalized EFC Mtot is found and is shown in Fig. 4.29. The optimal selection, such
that the overall fuel economy of all driving cycles together is optimized, is delivered
with the selection Dcsi,c = 0.7% and Dcsi,d = 3.7%.

The resulting control map of optimal power share (and corresponding efficiency) for
the case of Dcsi,c = 0.7% and Dcsi,d = 3.7% is shown in Fig. 4.30. It can be seen that
the power share at medium SOC is very similar to the GEMMS for WL-L, WL-M
and WL-H. Also, at lower SOC, the power share is similar to the GEMMS for WL-E.
This control can therefore be expected to perform close to the optimal fuel economy
solution. It also clearly resembles the EMMS1 with regards to its SOC dependence,
although it is less aggressive in its CS pursuits. This is most evident at medium-high
load levels, where charging mode would be enabled already at around PP L = 32 kW
for SOC = 50% with EMMS1 but at around PP L = 47 kW with EMMS2. The
gentler CS intensity means less diversion from the optimal power share.

4.6.2 Operation

The resulting power profiles from this selection are presented in Fig. 4.31 and
Fig. 4.32 for the first and final iterations of the driving cycles respectively. For WL-
L, the operation in the final iteration is very similar to the first iteration, suggesting
Efficiency Maximizing Map Strategies 167

6
SOC=50%
5
Power Share, u (-)

SOC=55%
4 SOC=65%
SOC=75%
3 SOC=80%

0
0 10 20 30 40 50 60 70 80 90 100
60
PS Power, PP S (kW)

50

40

30

20

10

0
0 10 20 30 40 50 60 70 80 90 100
40
Efficiency, ηtot (%)

35

30

25

20
0 10 20 30 40 50 60 70 80 90 100
Power Requirement, PP L (kW)
Figure 4.30: Optimal power share and PS power, and corresponding total efficiency for
varying power requirements and SOC for ηre,c,opt = 31.9%, ηre,d,opt = 37.7%, Dcsi,c =
0.7% and Dcsi,d = 3.7% for EMMS2.

that the control finds its stride quickly and operates quite consistently. Further-
more, by comparing to the GEMMS results in Fig. 4.25 and Fig. 4.26, it can be seen
that the operation is very similar. The EMMS2 is thus successful in adopting the
approximate global optimal solution in real time and does it quickly and effectively.

For WL-M and WL-H, the EMMS2 delivers very similar operation for the first and
final iterations of the driving cycles as well, as they both start and end around
SOCf inal = SOCinitial . When comparing with the GEMMS, the results are qutie
similar, but there are some distinct differences as well. For both the WL-M and
168 Chapter 4

30

15
Power (kW)

-15 PS S
PP S
PP L
-30
0 100 200 300 400 500 589
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 433
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 455
60

45

30
Power (kW)

15

-15

-30
0 100 200 300 323
Time (s)

Figure 4.31: Power time histories for PS, SS and PL for the first iteration of driving
WL-L, WL-M, WL-H and WL-E (top to bottom) with the EMMS2.
Efficiency Maximizing Map Strategies 169

30

15
Power (kW)

-15 PS S
PP S
PP L
-30
0 100 200 300 400 500 589
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 433
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 455
60

45

30
Power (kW)

15

-15

-30
0 100 200 300 323
Time (s)

Figure 4.32: Power time histories for PS, SS and PL for the final iteration of driving
WL-L, WL-M, WL-H and WL-E (top to bottom) with the EMMS2.
170 Chapter 4

WL-H, the PS is active more often for the EMMS2 than for the GEMMS. However,
when used, the PS is generally used in a similar manner as the GEMMS (although
there is some additional charging mode operation with the PS in WL-H).

Lastly, for the WL-E, the EMMS2 operation is quite different for the first and final
iterations of the driving cycle. The base operation (corresponding to SOC = 65%)
of the EMMS2 uses the SS a lot, before its SOC drop and it needs to react by
adopting a more rural type of driving. As the SOC drops further, it adapts further
and takes on a more highway type of operation. Thus, it can be seen that the final
iteration uses the PS more frequently and often uses it to a larger extent. This type
of operation is expected, as the principle of the EMMS2 is that it should seek its way
to an optimal manner of operation. Comparing its operation to the GEMMS, it can
be seen that their first iterations are quite different. However, their final iterations
are very similar, with the EMMS2 applying just a bit more charging mode operation.

The ability of the EMMS2 to realize operation that is quite similar to the GEMMS
suggests that it should achieve great fuel economy results. To look at this further,
the fuel economy results for the four driving cycles are presented in Table 4.6. It can
be seen that the EMMS2 performs very similarly to the GECMS, despite being a
real-time control strategy. In fact, it outperforms the GECMS for two of the driving
cycles. Comparing to the GEMMS instead, EMMS2 results for WL-L, WL-M and
WL-H are only behind by 0.11%, 0.17% and 0.15% respectively. A better choice of
ηre,c,opt and ηre,c,opt might have delivered even better results.

The WL-E results are slightly worse. Considering the fact that the EMMS2 needed
to spend some time to find the desired control policy, and thus had to operate in
an inefficient way for a while, the results are quite impressive. The final SOC is
somewhat low, but this is by design, as the EMMS2 essentially needed to locate the
control policy that matched the WL-E type of driving. Overall, for all driving cycles
considered together, the EMMS2 results were 0.18% behind the GECMS.

Table 4.6: Fuel economy results for EMMS2

Driving Cycle SOCf inal (%) mf (kg) mef c (kg) ∆GECM S (%)
WL-L 64.24 0.6988 0.7071 -0.17
WL-M 65.53 1.1452 1.1402 +0.12
WL-H 65.60 0.9558 0.9501 -0.02
WL-E 57.16 1.4909 1.5983 +0.83
Efficiency Maximizing Map Strategies 171

4.7 Comparison of Optimization-based Strategies

Having developed the four EMMS (EMMS0, EMMS1, EMMS2 and GEMMS) it is
of interest to compare them internally, as well as with the GECMS from Section 3.4.
This section will compare their operation by studying their SOC profiles as well as
compare their fuel economy results.

The SOC profiles for each of the five optimization-based strategies are presented in
Fig. 4.33 for the four driving cycles. It can be seen that a majority of the control
strategies maintain their SOC quite steady around SOCinitial across the driving
cycles. This could have been expected based on the SOCf inal values that have been
presented for each SCS earlier in this chapter. However the EMMS0 does stand out
from this pattern, as it can be seen to experience a fall in SOC before steadying,
resulting in final values lower than 60%. Interestingly enough, it is joined by the
GEMMS for the WL-L and WL-M, where the SOC drops and steadies. As mentioned
earlier, this is not typical for a global optimization strategy, but it did yield the best
fuel economy among the tested parameters.

In addition, it is worth noting that the operation of all five strategies is gener-
ally smooth, as opposed to the oscillatory operation (where SOC oscillates between
SOCL and SOCU ) that is associated with conventional strategies like TCS and
PFCS. This is a result of each of these strategies operating with a single state.
There is however an element of repetition in the profiles, which is a result of the
repeated iterations for each driving cycle.

This general pattern of dropping and steadying applies to all the presented control
strategies here, apart from GECMS. All the EMMS strategies have a charge sus-
taining element such that they will tend to flatten their SOC profile as they deviate
from SOCinitial . This is not true for the GECMS though, for which the error will
accumulate and get progressively worse. This is not very visible in the present chart
as the SOC deviation is very small for each driving cycle. Nevertheless it can be
seen for WL-H and WL-E in particular that the GECMS keeps dropping in SOC
relative to other strategies with a steady SOC.

The GECMS and GEMMS are the only strategies that remain close to SOCinitial
for the WL-E. This is easily understood as an effect of their global tuning. The
EMMS0 drops and steadies, due to the charge sustaining factor KCSI , but would
172 Chapter 4

66

64

62
SOC (%)

60

58 EMMS0
EMMS1
EMMS2
56
GEMMS
GECMS
54
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
66 Time (s)

64
SOC (%)

62

60

58

56
0 500 1000 1500 2000 2500 3000 3500
70 Time (s)

65
SOC (%)

60

55
0 200 400 600 800 1000 1200 1400 1600 1800 2000
70 Time (s)

65
SOC (%)

60

55

50
0 200 400 600 800 1000 1200 1400
Time (s)
Figure 4.33: SOC profiles for EMMS0, EMMS1, EMMS2, GEMMS and GECMS when
driving WL-L, WL-M, WL-H and WL-E.
Efficiency Maximizing Map Strategies 173

have preferred to operate close to SOC ≈ SOCinitial . However, the other real-time
control strategies, EMMS1 and EMMS2, have both mechanisms that encourage the
SOC to drop such that it can reach control rules that are more suited for the WL-E
type of driving. The drop in SOC for these SCSs is thus not a failure, but rather a
tool that is actively employed to seek the optimal type of operation and to deliver
great fuel economy.

It is also worth noting that all of these control strategies have either kept a flat
SOC profile, or have dropped. Considering the fact that the SOC band between
SOCL = 50% and SOCU = 80% is at the disposal of the control strategies, none of
them make use of the upper half of this band. This could possibly have been due
to badly tuned equivalence factors Sd,ef c and Sc,ef c , such that any stored charged by
the end of a driving cycle is not proportionally rewarded, compared to the penalty of
having a net discharge. However, apart from the fact that the process for obtaining
these equivalence factors was rigorous, it can also be observed that the fuel economy
results for the tuning process of most control strategies have been quite symmetrical
about the SOCf inal = SOCinitial lines (e.g. the GEMMS tuning results in Fig. 4.23).

A more plausible explanation might be that the repetitive and short nature of the
driving cycles biases the results to be more short-term oriented. Although it would
in reality be ideal for a medium-speed rural driving cycle to charge the SS while
driving, such that more SS energy is available at a later date for either a lot of
low-speed urban driving or high-speed highway driving, the simulations results do
not consider this. Instead, the optimization process is about a single cycle being
repeated. The use of the equivalence factors is supposed to address this, but it
considers the average case for each driving cycle separately, so the benefits of having
a well-charged battery for WL-E is not considered in the EFC calculation for the
WL-L.

An additional consideration is that the general approach of HEV operation is to

use the SS as much as it will allow sustainably (this is even more true for PHEVs).
Most control strategies are greedy in the sense that “sustainably” is seen to mean
“without depleting or damaging the battery”. Such an approach is inherently biased
towards either discharging or maintaining the battery SOC.

Finally, the fuel economy performance relative to the GECMS (∆GECM S ) for all
these strategies is presented in Fig. 4.34. It can clearly be seen that the EMMS0
174 Chapter 4

12
EMMS0
10 EMMS1
Fuel economy, ∆GECM S (%)

EMMS2
8 GEMMS

-2
WL-L WL-M WL-H WL-E

Figure 4.34: Comparison of fuel economy for EMMS0, EMMS1, EMMS2 and GEMMS
against GECMS when driving WL-L, WL-M, WL-H and WL-E.

is the least impressive among these. Its results are consistently behind the other
strategies. The same can not be said for the EMMS1 as it becomes progressively
better for driving cycles with higher loads. In fact it is comparable to the EMMS2
for WL-E. The EMMS2 is however the most impressive, as it is able to outperform
the GECMS on WL-L and WL-H (and is not far behind on the other strategies),
despite being a real-time control strategy.

The performance should however be considered in relation to the complexity of the

strategy. The GEMMS is somewhat more difficult to implement than the GECMS
(as it requires the powertrain analysis) but achieves a marginal improvement. How-
ever, for any solution that claims to approximate the global optimal solution, im-
provements in the order of 0.38% (as for WL-E) are quite significant. Between
the real-time strategies the performance is, as expected, improved gradually from
EMMS0 to EMMS1 to EMMS2. Considering the minor change in complexity from
EMMS0 to EMMS1, and the major difference in fuel economy performance, the
EMMS0 is not a worthwhile alternative (at least for the vehicle design for the model
in this work). However, in contrast, there is a significant increase in complexity from
EMMS1 to EMMS2, with more modest differences in fuel economy (in particular
for driving cycles with higher load). Therefore, the EMMS1 serves a function as an
easier implementation with decent performance.
Efficiency Maximizing Map Strategies 175

4.8 Summary

This chapter has presented a family of novel control strategies based on the objective
of maximizing the powertrain efficiency, which was determined by studying each
component comprising the powertrain sources: ICE, PMSG and rectifier for the PS,
and battery and DC-DC converter for the SS. In addition, a correction factor v
was considered to account for the losses involved in replenishing the battery after
it is discharged (or the gains involved in avoiding future replenishing after being
charged). The four control strategies EMMS0, EMMS1, GEMMS and EMMS2 used
this correction factor differently and a summary is provided in Table 4.7.

Table 4.7: Choice of correction factor v

Correction factor v EMMS0 EMMS1 GEMMS EMMS2

For PSS < 0 1 ηre (SOC) ηre,c ηre,c (SOC)
For PSS ≥ 0 ηre ηre (SOC) ηre,d ηre,d (SOC)

Each of the control strategies was implemented through a control map, which pro-
vides the optimal power share uopt as a function of the operating conditions (SOC
and PP L ). This method is not only simple and computationally light, but it also
easily allows effective use of state dynamics (such as SOC) that are difficult to assess
offline for global control strategies. The fuel economy became progressively better
from the EMMS0, EMMS1 to the EMMS2 as the correction factor became more
nuanced and effective. The EMMS0 adopted a CS function kcs (SOC) to penalize
and reward the use of the SS, while the EMMS1 (and EMMS2) made the replen-
ishing efficiency ηre (and ηre,c and ηre,d ) a function of SOC to achieve CS operation.
The GEMMS achieved the same inherently through global tuning, which required
no modification to its optimization procedure. Interestingly, the GEMMS was found
to be equivalent to a SOC dependent GECMS with consideration for SS efficiency.

In terms of fuel economy, the GEMMS was found to outperform the GECMS consis-
tently (by 0.2% overall), while the real-time EMMS2 was better than the GECMS
for half the driving cycles (but was 0.18% worse overall). The results demonstrate
how a more detailed understanding of the powertrain can contribute toward bet-
ter performance by the control strategies. Nevertheless, the GECMS has compared
quite favorably despite its simplicity (or maybe because of it).
Chapter 5

Heuristic Strategies

This chapter will propose two novel heuristic strategies: the exclusive operation
strategy (XOS) and the optimal primary source strategy (OPSS). Each of these
makes use of insights from previous chapters to deliver good performance with very
simple rule-based control. In some sense, these two strategies can be considered to
be improved versions of the TCS and PFCS from Chapter 3. The XOS presented in
this thesis has been partly modified since being published in [15], but has the same
essence (differences will be discussed within the chapter).

Although it is increasingly easier to make use of optimization-based strategies in

real HEVs, it is still useful to produce effective rule-based strategies. Not only are
these appropriate for prototypes and preliminary studies of powertrains (evaluating
architecture choice or component sizing), but they can also be the preferred choice
when simple and intuitive operation is a higher priority than an optimized fuel
economy. In fact, most commercial HEVs so far have opted to use heuristic energy
management strategies [55, 63].

The chapter will first explore the design principles that have been derived through
insights from previous chapters and discuss their applicability in designing heuristic
strategies for series HEVs. Thereafter, the XOS will be introduced in the context of
discussed design principles. This will be followed by the presentation of the OPSS.
For both the proposed control strategies the implementation, the tuning process,
representative power profiles of operation, and the fuel economy are presented and
discussed. Finally, the performance of the XOS and OPSS will be compared to the
conventional heuristic strategies.

177
178 Chapter 5

5.1 Design Principles

The essence of heuristic strategies is to apply design rules based on knowledge of

and experience with the system to be controlled. For the series HEV that is the
subject of this work, several insights have been gained over the past two chapters
that will here be condensed into a handful of such rules.

5.1.1 Fuel Economy Optimizing Mechanisms

There are three distinct approaches to determine the power share within the power-
train to achieve fuel efficient driving: load leveling, load following and load blending.

Load leveling refers to the strategy of operating the PS steadily and using the SS to
“level” the load as a buffer, as

PP S (t) = PP S,cop (5.1)

PSS (t) = PP L (t) − PP S,cop (5.2)

where PP S,cop is a constant operating point of the PS. This is most clearly applied in
the TCS where the PS is operated at its optimal point of operation (PP S,cop = PP Sopt )
and the SS takes care of the difference between the PS and the propulsion load.
This approach typically optimizes the PS efficiency but suffers higher SS losses. The
general shape of the control input, both in terms of power share and PS power, is
presented in Fig. 5.1 (with PP S,cop = 20 kW).

This technique is also partly used by the GEMMS and GECMS, where it can partly
be seen in the smooth curves (corresponding to constant PP S levels) of the power
share charts in 4.27. However, it is more clearly visible in the operational power
profiles where the PS can be seen to operate quite steadily around 20 kW whenever
it is used in Fig. 3.18 and 4.25.

Load following on the other hand takes the opposite approach. It uses the PS to
“follow” the load power while the SS is ideally used at zero power levels, as

PP S (t) = PP L (t), (5.3)

Heuristic Strategies 179

4 40

PS Power, PP S (kW)
3 30
Power share, u (-)

2 20

1 10

0 0
0 10 20 30 40 0 10 20 30 40
Power requirement, PP L (kW) Power requirement, PP L (kW)
Figure 5.1: Power share and PS power for varying load for a load leveling strategy.

4 PS Power, PP S (kW) 40

3 30
Power share, u (-)

2 20

1 10

0 0
0 10 20 30 40 0 10 20 30 40
Power requirement, PP L (kW) Power requirement, PP L (kW)
Figure 5.2: Power share and PS power for varying load for a load following strategy.

PSS (t) = 0. (5.4)

This is the core approach behind the PFCS, where the above expression holds exactly
true for SOC = SOCinitial . However, to ensure charge sustaining operation, the
PFCS deviates from strict load following operation and instead allows the SS to
charge or discharge in proportion to its SOC deviation. Having the SS operate at
low power levels ensures higher SS efficiencies but this leaves the PS efficiency to be
determined by the varying load. The resulting control input, both in terms of power
share and PS power, is illustrated in Fig. 5.2.

This type of operation is also apparent in non-CS EMMS0 where the strategy often
uses u = 1 in Fig. 4.4. To a lesser extent the same technique can also be seen within
180 Chapter 5

non-CS EMMS1 in Fig. 4.13 (during PP L ∈ [17, 28] kW and PP L ∈ [50, 57] kW.

Lastly, the load blending mode of operation concerns itself with optimizing both
the power source branches of the powertrain. The operation is thus not as clearly
defined as the load leveling and load following modes, but instead encompasses all
techniques that blend the use of the PS and SS such that the overall performance
of the powertrain is benefited. This would clearly include the EMMS strategies of
the previous chapter that display a varied choice of operation with consideration of
both the PS and SS. For example, the EMMS2 in Fig. 4.30 has elements that would
fit either of the load leveling and load following modes, as well as some power share
choices that would fit neither. This approach is typically required to achieve global
optimal solutions, but it does not lend itself to be expressed as simple rules.

As shown, each of the fuel economy optimizing mechanisms discussed has been
employed in various control strategies within this work. However, as was just men-
tioned, the load blending operation does not easily translate into a rule-based control
strategy. Therefore, this chapter will aim to deliver one strategy based on load fol-
lowing and another on load leveling.

5.1.2 Charge Sustaining Mechanisms

From the presented work, four approaches have emerged to make control strategies
charge sustaining: state changing, threshold changing, power changing and emer-
gency handling.

The state changing approach does not have inherently CS rules, but rather switches
between two (or more) sets of rules depending on the SOC. These changes in state
are often triggered as the SOC reaches its lower (SOCL ) or upper (SOCU ) limit,
with a hysteresis area in between, as

 0
 SOC(t) ≥ SOCU
S(t) = 1 SOC(t) ≤ SOCL , (5.5)

S(t ) SOCL < SOC(t) < SOCU
 −

where S(t− ) is the state in the previous time instance. This approach is followed
precisely with the TCS (as defined in Eq. 3.7) and is implemented with some
additional conditions with the PFCS (as defined in Eq. 3.8). These changing states
Heuristic Strategies 181

2 SOC=50%
SOC=55%
SOC=60%
1.5 SOC=65%
Power share, u (-)

SOC=70%
SOC=75%
SOC=80%
1

0.5

0
0 5 10 15 20 25 30 35 40
Power requirement, PP L (kW)
Figure 5.3: Optimal power share for varying power requirements and SOC when em-
ploying the threshold changing mechanism to encourage charge sustaining operation.

are often relatively easy to define and none of them need to be CS in themselves.
In fact, the only necessary constraint is that at least one of the states is charge
depleting and at least one is charge increasing. Furthermore, these changes in states
can easily be connected to whether the PS is active or not (as is done for both TCS
and PFCS), such that the engine is only turned on or off when there is a change in
state. This reduces the number of start-stop events of the engine.

Threshold changing refers to the definition of a SOC dependent threshold to govern

whether the PS is active or not. Such a lower limit of the PS can be defined as
 
SOC − SOCmid
PP Smin (SOC) = Pth + Pcsi (5.6)
SOCrange

where Pth is the base power threshold and Pcsi (which does not necessarily need to be
a constant) regulates the CSI of the strategy by defining the range as PP Smin (SOC) ∈
[Pth − Pcsi , Pth + Pcsi ]. This is shown in Fig. 5.3 with an illustrative example. It can
be seen that the threshold operates such that the PS is activated at lower load levels
(and thus more frequently) if the SOC is low and is activated at higher load levels
if the SOC is high. This encourages the use of the SS when the SOC is high, and
discourages it when the SOC is low, thus tending towards making the operation CS.
It is however essential that the threshold and its range is defined appropriately to
ensure CS operation in all kinds of realistic operation.

The use of threshold changing operation is very clearly visible in EMMS0 (Fig. 4.8),
182 Chapter 5

2
SOC=50%
SOC=55%
1.5 SOC=60%
Power share, u (-)

SOC=65%
SOC=70%
SOC=75%
1 SOC=80%

0.5

0
0 5 10 15 20 25 30 35 40
Power requirement, PP L (kW)
Figure 5.4: Optimal power share for varying power requirement and SOC when em-
ploying the power changing mechanism to encourage charge sustaining operation.

EMMS1 (Fig. 4.17) and EMMS2 (Fig. 4.30), with a wide range for the threshold. In
all of these cases the range of the threshold stretches all the way down to PP L = 0 kW
which guarantees that the SOC will not drop below SOCL . This mechanism is
present to a limited extent in the GEMMS as well due to the SOC sensitive efficiency
expression (as shown in Fig. 4.24) but the range is very limited.

The power changing approach modifies the PS operating point to be SOC dependent.
This can be applied to a load leveling strategy as
 
SOC − SOCmid
PP S,op (SOC) = Pcop − Pcsi (5.7)
SOCrange

where PP S,op is the operating point of the PS and is defined in the range of PP S,op ∈
[Pcop −Pcsi , Pcop +Pcsi ]. Alternatively, the power changing mechanism can be applied
to a load following strategy as
 
SOC − SOCmid
PP S,op (PP L , SOC) = PP L − Pcsi . (5.8)
SOCrange

The power changing mechanism is shown visually in Fig. 5.4 for the load following
case (where u = 1 corresponds to exact power following operation).

The PFCS uses the power changing method (with the load following alternative) to
bias operation in favor of maintaining the SOC close to SOCmid , as expressed in Eq.
3.10. The EMMS on the other hand can be considered to employ a blended version
Heuristic Strategies 183

of the power changing mechanism. For example, in Fig. 4.30 for EMMS2, it can be
seen that a higher power share is selected in general for lower SOC cases, and lower
power share for higher SOC. In fact, typically u > 1 (charging mode) is used for
very low SOC values, thus encouraging charge sustaining operation.

However, this particular CS mechanism has a few vulnerabilities. If the power

changing mechanism is applied all the way down to PP L = 0 kW, the PS will have
to be operated at very low power levels which would be highly inefficient. The
solution could be to use a threshold above which the power changing (together with
load following or load leveling) is active. However, even in this case, if the powertrain
is operated at a low load level where the PS is not active, the fact that the PS power
levels at higher load levels are being adjusted by the power changing mechanism as
the SOC decreases will have no CS effect. Thus, this CS mechanism is generally
insufficient by itself.

Finally, as a last resort, it is useful to include emergency handling. These are rules
that are activated only if the SOC bounds are violated. These can in some sense be
considered a subset of the state changes discussed earlier, with the difference that
the emergency handling rules are only active while the SOC bounds are violated, and
normal mode is restored as soon as SOCL < SOC < SOCU . However, note that the
TCS does not make use of emergency handling rules, as Eq. 3.7 does not provide
separate instructions for how to operate if the SOC constraints are continuously
transgressed. This is later demonstrated in Fig. 5.20, where the SOC profile for the
TCS when driving the WL-E can be seen to fall to SOC = 45% before recovering. In
contrast, the PFCS clearly has defined emergency handling rules in Eq. 3.9 in case
the SOC limits are exceeded. The emergency handling rules need to be CS at the
very least, or possibly charge increasing for SOC < SOCL and charge depleting for
SOC > SOCU . It is however important to emphasize that the emergency handling
rules are typically not very fuel efficient. Thus, if the main CS mechanism employed
is badly designed, the benefits of the main fuel economy optimization mechanism
will be lost.

From these charge sustaining techniques, the threshold changing mechanism is con-
sidered to be the most suitable one for a modern series HEV. The state changing
approach has many attractive features (e.g. its simplicity and lack of engine start-
stop events), but these are increasingly less relevant today. As modern HEVs use
very efficient start-stop systems (SSSs), the cost of turning the engine on is very low,
184 Chapter 5

compared with a decade ago. The objective of minimizing the number of start-stop
events is thus much less of a priority (although it still matters to some extent for
the purposes of drivability). Furthermore, computational power is easily available
in any modern HEV and the automotive companies have the resources to develop
and test more advanced strategies (although robustness remains imperative). The
threshold changing approach on the other hand is the primary benefactor of the more
efficient SSSs, and can be expected to sustain the charge without compromising the
fuel economy too much. However, it will be sensible to include some emergency
handling rules nevertheless to handle exceptional driving circumstances.

Thus, the rule-based strategies presented in this chapter will mainly make use of a
threshold changing approach together with some emergency handling rules.

5.1.3 Implementation Mechanisms

Two different real-time implementation mechanisms have been used in the control
strategies presented so far: state machines and control maps. The GECMS can
also use precomputed control inputs to implement its strategy but this option is
only available for global strategies with prior knowledge of the driving route and
is thus not an option for the rule based strategies being considered in this chapter.
However, an additional approach that has not been considered so far is the algebraic
implementation with logic gates.

The state machines are particularly suitable for state changing strategies, as they
naturally involve multiple states with varying rules. This would include the TCS
and PFCS. In these cases a state-machine implementation is almost unavoidable.
However, for other rule based strategies with a single set of rules, the state machine
can be used by treating various operating conditions (such as low and high load
powers, or low and high SOC) as different states. However, this often requires certain
rules to be repeated in multiple states, making the expression of some strategies less
concise. Also, it often comes with a higher computational load (which is quite
negligible anyway).

The control maps on the other hand are look-up tables that are essentially flexible
enough to express any type of rules or optimizations. These were used for all the
EMMS and have also been implemented for the GECMS. They are also easy to
Heuristic Strategies 185

design and have the benefit of being easily visualized. Although they are particu-
larly suitable for single-state strategies, it is possible to implement multiple-states
strategies like the TCS and PFCS using multiple control maps. However, the control
maps don’t shine when used to express simple rules. The precision of the control is
only as good as its sampling interval. Thus, a simple logical or algebraic relation
(or a state machine) could follow the intended strategy perfectly while the control
map has to compromise based on the imperfect precision arising from the finite size
of the map.

The third approach, which hasn’t been presented so far is the algebraic implemen-
tation with logic gates. Most rule-based controllers rely on simple arithmetical
and logical relations between inputs and outputs. These relations can be directly
expressed by equations and logic blocks in Simulink and most other design environ-
ments. Not only is this approach computationally efficient and easy to design, it also
delivers perfect precision when interpreting the intended strategy. For these reasons,
the algebraic implementation will be used for the rule-based strategies presented in
this chapter.
186 Chapter 5

5.2 Exclusive Operation Strategy

The exclusive operation strategy (XOS) is based on the load following technique
and uses the threshold changing mechanism to ensure CS operation. This design
uses insights gained from the PFCS and EMMS0 in particular, but also attempts to
emulate parts of the operation of the global strategies GECMS and GEMMS.

5.2.1 Design

Investigation of the power-split between the PS and SS in a powertrain shows that

the optimal selection is often to operate with the SS at lower powers and the PS
at higher load requirements. This agrees roughly with previously developed control
systems [14] as well as the GECMS and GEMMS presented here. Thus, the principle
of XOS is quite simple: operate with only SS at low load requirements (or if SOC >
SOCU ), and operate with only PS at medium loads. The two energy sources are
only used together if the load power exceeds the maximum rating of the source in
operation (or SOC < SOCL , in which the SS is charged). These rules are shown
visually in Fig. 5.5.

The XOS is inspired by the PFCS as can be seen by its “power following” behavior
during PS-only mode. However, the XOS does not adjust PS power to correct SOC
deviation as done by Pm with the PFCS in Eq. 3.10. Such a deviation tends to
use the SS at very low powers, which is quite inefficient due to the high amount of

1
SOC
PP S = 0
SOCU

PP S = PP L

SOCL

PP S = PP Smax

PP L
Pth PSSmax PP Smax PP Smax
+PSSmax
Figure 5.5: The XOS operates in three distinct ways depending on given SOC and PP L :
SS-only (white), PS-only (light gray) and hybrid operation (dark gray).
Heuristic Strategies 187

DC-DC converter losses at these operating points. Instead the SOC correction is
performed by using the threshold changing approach discussed in Section 5.1.2.

The XOS requires three parameters: PP Smin (SOC), PP Smax and PSSmax . The two
latter are readily available for any powertrain, but the former needs some further
attention. The threshold PP Smin (SOC) is the load at which the SCS switches from
using the SS to PS, and is defined as Eq. 5.6. However, it is preferable to consider
the case of Pcsi = Pth . Not only does this eliminate one tuning parameter from the
control strategy, but it also ensures that the strategy is CS for continuous operation
at low power levels. For example, if Pcsi < Pth , then a low persistent load PP L > 0
will gradually drain the battery until the emergency handling rules are activated
at SOC = SOCL . However, if Pcsi = Pth , then the PS will always be activated
before SOC = SOCL , practically always avoiding the need to trigger the emergency
handling rules. Therefore, the following PS activation threshold is used instead:
 
SOC − SOCinitial
PP Smin (SOC) = Pth + Pth . (5.9)
SOCrange

To determine the optimal value for Pth , the efficiencies of the SS and PS could
be compared. However, as the SS efficiency by itself does not consider the PS
losses required to replenish the SS, the replenishing efficiency ηre = 35% (based
on the findings for EMMS1 in Section 4.4.2) is also included. Figure 5.6 shows a
comparison of PS and SS efficiencies based on the components used in this work, but
similar shapes would be found for most series HEVs. As expected, the SS efficiency
is high at low loads and drops for higher loads, while the PS starts with a lower
efficiency and moves towards a higher efficiency (peaking at PP Sopt = 20.1 kW).
Thus the threshold at which the PS becomes more efficient than the SS is found
to be between 11.1 and 11.5 kW depending on SOC. In this work, Pth values of
between 10.4 and 15.0 kW are found to deliver optimal fuel economy results for
tested driving cycles.

A particular benefit of driving with each energy source exclusively is the linear
correlation between PL power request and PS power supply. Drivers have developed
a sense of intuition with regards to the speed and acceleration of the vehicle based
on auditory cues from the ICE in a conventional car. The unfamiliar, and sometimes
counterintuitive, cues provided by a hybrid powertrain remain a significant challenge
in terms of drivability for adopters of HEVs. The XOS addresses this particular
188 Chapter 5

35

30

25
Efficiency (%)

20

15

10
PS
SS (SOC=50%)
5
SS (SOC=80%)
0
0 5 10 15 20 25 30
Power (kW)
Figure 5.6: Efficiency profiles for PS and SS (corrected by ηre = 35%). The intersection
between the profiles can be considered as Pth .

issue, but the switching between PS and SS mode, as the engine is switched on and
off, remains a challenge in terms of drivability. However, drivers are increasingly
becoming familiar with this sensation as SSSs are introduced in conventional vehicles
or mild hybrids. The XOS therefore helps in making the driver experience for a HEV
more similar to a conventional vehicle.

It is interesting to compare and contrast the operation of the GECMS and the XOS.
Each SCS has the same task: to determine the optimal power split of the load
request between the PS and SS. This task is reduced to the selection of the power
share factor u, as shown for the GECMS and GEMMS in Fig. 4.27. The equivalent
chart for XOS is presented in Fig. 5.7, for operation with SOCL ≤ SOC ≤ SOCU .

It can be seen that the XOS has three simple stages of operation: the first stage
(low PP L and medium or high SOC) is SS-only; the second stage (medium PP L )
is PS-only; and the third stage (high PP L ) is hybrid mode with the PS delivering
maximum power. The transition between the first and second stage is dependent
upon the SOC, such that battery use is encouraged at high SOC and discouraged
at low SOC. This type of transition is also visible for the GEMMS and GECMS
in Fig. 4.27 to a lesser extent. Although the latter is not sensitive to SOC directly,
it can be seen that the transition occurs at higher PP L for WL-L to encourage the
use of the SS during urban driving, while the transition is at lower PP L for WL-E
where PS operation is preferred for highway driving. In the second stage, where
XOS applies u = 1, the GECMS and GEMMS are somewhat higher towards the
Heuristic Strategies 189

2 SOC=50% 60
SOC=55%
SOC=60%

PS Power, PP S (kW)
SOC=65%
Power Share, u (-)

SOC=70% 40
SOC=75%
SOC=80%
1

20

0 0
0 20 40 60 80 100 0 20 40 60 80 100
Power Requirement, PP L (kW) Power Requirement, PP L (kW)
Figure 5.7: Power share factor and PS power for varying load and SOC (with Pth =
12.2 kW) for XOS.

start of this stage, and somewhat lower towards the end of the stage. Operation
above the u = 1 line is charge increasing operation while operation below this line
is charge depleting. Thus, the operation of XOS can be considered a smoothened
version of the GECMS and GEMMS operation, to balance out charging and charge
depleting operations. Although not optimal, the simplified control policy of XOS
roughly reflects the general behavior of the GECMS and GEMMS, and can thus be
expected to perform well.

Unlike the TCS and PFCS that operate in two distinct states, and are thus imple-
mented with state machines, the XOS has a single state of operation and can be
implemented algebraically with the use of logic gates. The Simulink implementation
of the XOS is shown in Fig. 5.8. It can be seen that only simple arithmetic and logic
blocks are required for this implementation.

5.2.2 Tuning

The only tuning parameter for the XOS is the base threshold Pth . It is varied in
the range of Pth ∈ [10, 17] kW in steps of 0.2 kW. Each of these values are then
tested for the four driving cycles to tune the parameters such that the fuel economy
is maximized. Results with normalized equivalent fuel consumption and final SOC
levels are shown in Fig. 5.9.
190 Chapter 5

< SOC_L P_PSmax

1 >= SOC_L
SOC <= SOC_U
f(u) 1
2 <
P_PSref
P_PL

> SOC_U
> P_SSmax

Figure 5.8: Implementation of the XOS in Simulink. Note that f (u) implements Eq.
5.9 to define PP Smin (SOC).

As can be seen, each of the driving cycles have different thresholds Pth (the optimal
threshold Pth for WL-L, WL-M, WL-H and WL-E are 15.0 kW, 12.6 kW, 11.6 kW
and 10.4 kW respectively). The pattern of having higher thresholds for WL-L (of-
ten low loads) and lower thresholds for WL-E (often high loads) is consistent with
previously presented strategies, including the GECMS and GEMMS presented in
Fig. 4.27. However, for all of those previous strategies, low-medium loads meant
charging of the SS and medium-high loads meant discharging of the SS. Thus, driv-
ing cycles that often operate at medium-high loads would need to have a lower
transition threshold to ensure CS operation. However, this explanation is not valid
for the XOS. When the PS is active, whether at low-medium or medium-high load,
the SS is neither charged nor discharged. Thus, the driving cycles with low loads
are discharging the SS the most, and are thus in most need of a lower transition
threshold.

This apparent contradiction can be resolved by understanding the inverse relation-

ship between the propulsion load and the need to apply CS correction. As the SOC
drifts over the duration of the driving cycle, the effective transition threshold PP Smin
tends to be quite different from the base threshold Pth . It is therefore more useful
to consider the PP Smin (SOCf inal ) (by using the optimal values of Pth and SOCf inal
from Fig. 5.9 and use with Eq. 5.9) which yields values of 6.5 kW, 8.4 kW, 7.8 kW
and 10.5 kW for the four driving cycles. These agree better with the mentioned
expectations.
Heuristic Strategies 191

1.01 62

1.008
60

SOC (%)
Mef c (-)

1.006
58
1.004

56
1.002

1 54
8 10 12 14 16 18 8 10 12 14 16 18
1.004 66

64
1.003

SOC (%)
Mef c (-)

62
1.002
60

1.001
58

1 56
8 10 12 14 16 18 8 10 12 14 16 18
1.004 64

1.003 62
SOC (%)
Mef c (-)

1.002 60

1.001 58

1 56
8 10 12 14 16 18 8 10 12 14 16 18
1.005 68

1.004
66
SOC (%)
Mef c (-)

1.003
64
1.002

62
1.001

1 60
8 10 12 14 16 18 8 10 12 14 16 18
Pth (kW) Pth (kW)
Figure 5.9: Normalized EFC (left) and final SOC (right) for varying Pth when driving
WL-L, WL-M, WL-H and WL-E (from top to bottom) with XOS.
192 Chapter 5

1.003
Fuel Economy, Mef c (-)

1.002

1.001

1
9 11 13 15 17
Base Threshold, Pth (kW)
Figure 5.10: Normalized total EFC Mtot for varying Pth with XOS.

Despite the variations in threshold across the driving cycles, it can be noted that
the compromise in fuel economy for a badly tuned threshold is lower than 1% in
each case. It is also worth noting that the final SOC values are typically quite
lower than SOCinitial , even for quite low thresholds. This control strategy has the
same limitations as the EMMS0 with regards to being overly reliant on regenerative
braking to recharge the SS. Nevertheless, the operation is well within the SOC
bounds of the vehicle.

To identify the optimal base threshold Pth with consideration for the varying results
for the different driving cycles, the EFC of each driving cycle is combined (as dis-
cussed in Section 2.6.2) and normalized, and is presented in Fig. 5.10. As can be
seen, there is a very flat region for Pth ∈ [12, 14] kW, but the optimal value is found
at Pth = 13.4 kW. However, as it is possible to choose a lower threshold value at
negligible impact to fuel economy, while realizing a higher final SOC (a lower base
threshold translates to a high final SOC, as shown in Fig. 5.9), this is preferred.
Thus, for the purposes of this work, Pth = 12.2 kW is selected instead (sacrificing
0.0024% in fuel economy relative to the optimal selection). The overall fuel economy
is only affected by about 0.2% for changes of 25% in Pth . With such a low tuning
sensitivity, the realized fuel economy can not be expected to be comparable to the
EMMS, but the aim is to keep the XOS extremely simple and still deliver superior
fuel economies to the conventional heuristic strategies.
Heuristic Strategies 193

5.2.3 Operation

Using the selected base threshold value, the power profiles for the XOS when driv-
ing the first and final iteration of the driving cycles are presented in Fig. 5.11 and
Fig. 5.12 respectively. The operation is clearly applying the load following mecha-
nism, as the PS, when used, is always matching the load requirement PP L precisely.
However rather than resembling the PFCS, which would use the PS persistently at
Pmin at low loads and operate the PS much more steadily, the operation is more
similar to the EMMS0 in Fig. 4.11 and 4.12. It is also evident that the PS and SS
are never used together, but rather used exclusively (as the name suggests). This
has, as mentioned, great benefits for drivability as the auditory cues of the engine
are more intuitive and comparable to conventional vehicles. However, as a result
there is no direct charging of the SS, which has to rely on regenerative braking to
increase its charge.

The operation for WL-L is almost exactly like the EMMS0, for both the first and
final iteration, as the load is generally low and the threshold at when to activate
the PS is the main decision. For WL-M and WL-H, there are some differences at
higher loads. Whenever the load increases beyond about 25 kW, the EMMS0 will
supplement the PS with the SS in hybrid mode, while the XOS persists in using
PS only operation. Interestingly, the changes that occur from the first to the final
iteration of driving with the XOS are very similar to the changes that occur for
the EMMS0, as both of these strategies see the SOC gradually decrease before
steadying.

The differences are most clear for the first iteration for the WL-E, where the EMMS0
will rarely use the PS beyond 25 kW, while the XOS is operating the PS close to
50 kW. There is a significant difference in operation here, and it might be unclear
which operation should be preferred. However, by looking at the final iteration of the
WL-E driving, it can be seen that even the EMMS0 adopts the same approach as the
XOS and uses the PS at much higher power levels (as high as 50 kW). Essentially, the
EMMS0 needed to operate for quite a while (until SOC had dropped significantly)
before it recognized what type of operation was desirable and sustainable, while the
XOS figured this out much faster. However, even the XOS will be using the PS to
a larger extent for all driving cycles in the final iteration, as its SOC has dropped
somewhat.
194 Chapter 5

30

15
Power (kW)

-15 PS S
PP S
PP L
-30
0 100 200 300 400 500 589
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 433
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 455
60

45

30
Power (kW)

15

-15

-30
0 100 200 300 323
Time (s)

Figure 5.11: Power time histories for PS, SS and PL for the first iteration of driving
WL-L, WL-M, WL-H and WL-E (top to bottom) with the XOS.
Heuristic Strategies 195

30

15
Power (kW)

-15 PS S
PP S
PP L
-30
0 100 200 300 400 500 589
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 433
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 455
60

45

30
Power (kW)

15

-15

-30
0 100 200 300 323
Time (s)

Figure 5.12: Power time histories for PS, SS and PL for the final iteration of driving
WL-L, WL-M, WL-H and WL-E (top to bottom) with the XOS.
196 Chapter 5

Lastly, the fuel economy of the XOS is evaluated in Table 5.1 for the four different
driving cycles. Although the charge has been sustained in each case (with good
margins between SOCf inal and SOCL or SOCU ), the XOS is unable to maintain
the SOC steady at SOCf inal ≈ SOCinitial for any of the driving cycles. Also, the
inability to actively adjust the SOC by charging the SS clearly reduces the flexibility
of the strategy to operate efficiently without compromising the CS operation. The
resulting EFC is thus not great, but lags the GECMS results by 4.45-11.53%, with
a combined difference (for all four driving cycles together) of 6.29%.

This is however quite favorable if compared to the TCS and PFCS, which were
outperformed by the GECMS by 14.35% and 13.72% respectively. The results are
particularly good for high-speed driving cycles, where the regenerative braking is
sufficient to balance the SS load over the driving cycles. Also, as another benchmark,
the XOS performs almost as well the EMMS0 (which is 5.68% behind the GECMS)
while using simpler rules and implementation.

Table 5.1: Fuel economy results for XOS

Driving Cycle SOCf inal (%) mf (kg) mef c (kg) ∆GECM S (%)
WL-L 57.36 0.7070 0.7899 +11.53
WL-M 60.79 1.1568 1.2022 +5.56
WL-H 60.44 0.9414 0.9959 +4.80
WL-E 63.91 1.6409 1.6559 +4.45
Heuristic Strategies 197

5.3 Optimal Primary Source Strategy

The OPSS employs the load leveling approach for the powertrain management and
operates the PS at its optimal operating point (in terms of efficiency), like the
conventional TCS. However, rather than using the state changing technique like the
TCS, the OPSS uses the threshold changing mechanism to ensure that charge is
sustained. This type of operation is strongly inspired by the global solutions found
through GECMS and GEMMS.

5.3.1 Design

One of the key characteristics of the series HEV is the ability to operate the engine-
generator set independent of the wheel speed, thus allowing continuously optimal
operation if desired. Although such an optimization strategy neglects the SS losses,
it is worth considering that all energy delivered by the SS ultimately originates from
the PS through either regenerative braking or direct charging. Thus, even the SS,
when considered holistically, is greatly benefited by operating the PS optimally. Fur-
thermore, this could enable further optimization of the engine and generator design,
sizing, coupling and control to perform optimally at a single point of operation,
as opposed to the more complex consideration of all the various possible operating
points in a load following strategy.

Although the name of the OPSS makes emphasis on the optimal operation of the
PS, the TCS does not. The key characteristic of the TCS is the “thermostat” type
of operation, oscillating between charge increasing and charge depleting operation
through a hysteresis mechanism. As mentioned earlier in this chapter in Section
5.1.2, this state changing approach allows the number of start-stop events of the
engine to be minimized. However, within a modern HEV the cost of start-stop
events is much lower than it used to be, and it is therefore possible to reduce SS
losses (by switching off the PS at appropriate times) such that they outweigh the cost
of the start-stop events involved. The OPSS therefore uses the threshold changing
mechanism to not only ensure CS operation, but also to reduce the typical magnitude
of the charging and discharging operation of the SS. The implementation of the
threshold changing mechanism is the same as for the XOS, as given in Eq. 5.9 (and
described in Section 5.1.2).
198 Chapter 5

1
SOC
PP S = 0
SOCU

PP S = PP Sopt

SOCL

PP S = PP Smax

PP L
Pth PSSmax PP Smax PP Smax
+PSSmax
Figure 5.13: The OPSS operates in three modes depending on given SOC and PP L :
SS mode (white), optimal PS mode (light gray) and maximum PS mode (dark gray).

The complete set of rules governing the OPSS is best illustrated graphically, as shown
in Fig. 5.13, where the assigned PS power is shown for various operating conditions
(varying load power and SOC). It can be seen that the “shell” of the strategy, in
the form of its emergency handling rules (for SOC < SOCL or SOC > SOCU ), is
practically identical to the XOS (in Fig. 5.5). The simple difference exists only in
the center of the chart, where the PS power is defined as PP S = PP Sopt .

It is also useful to compare the simple nature of these rules to the setup of the TCS
and PFCS (in Section 3.2.1 and Section 3.3.1 respectively). The TCS arguably has
the simplest rules, followed by the XOS, OPSS and PFCS in this particular order.
The TCS has a single tunable parameter PP S,cop that can readily be estimated as
PP S,opt , while both the XOS and OPSS have to tune the base threshold Pth with
some guidance. The PFCS on the other hand has two tunable parameters in Pch and
Pmin . However, the TCS and PFCS have two states of operation as opposed to the
single-state operation of the XOS and OPSS. Furthermore, there are significantly
fewer rules and modes of operation within the XOS and OPSS as compared to the
PFCS.

To further clarify the design of the OPSS, the resulting power share has been pre-
sented in Fig. 5.14 (with PP Sopt = 20 kW) in the same form as previously presented
strategies. The strategy uses only SS at low powers but turns on the PS to its op-
timal operating point once it passes the threshold PP Smin . Only as the load reaches
the maximum power of the PS PP Smax does the PS begin to contribute more power
(in fact its maximum power) to meet the load.
Heuristic Strategies 199

8 60
7 SOC=50%
SOC=55% 50

PS Power, PP S (kW)
6 SOC=60%
Power Share, u (-)

SOC=65% 40
5 SOC=70%
SOC=75%
4 SOC=80% 30

3
20
2
10
1
0 0
0 20 40 60 80 100 0 20 40 60 80 100
Power Requirement, PP L (kW) Power Requirement, PP L (kW)
Figure 5.14: Power share factor and PS power for varying load PP L and SOC (with
Pth = 10.4 kW) for OPSS.

Comparing these profiles to those of the GECMS and GEMMS in Fig. 4.27, it can be
seen that they are almost identical up until about PP L = 50 kW (for SOC = 65%).
The main exception is a small region around PP L = 20 kW where u = 1 is used
instead (like the XOS). This deviation is expected, as the GECMS and GEMMS have
considered the extremely low DC-DC converter efficiency at low SS power levels and
have opted to use PSS = 0, rather than PSS = 1 kW or PSS = −1 kW. Such
consideration or nuance does not exist for the OPSS which persistently uses the PS
at PP Sopt . The implementation of the OPSS is practically the same as the XOS, as
might be expected from the similarities between the control schematics in Fig. 5.5
and Fig. 5.13. Figure 5.15 shows the OPSS Simulink implementation, where the
second of the three terms being added is now a constant (PP Sopt ), unlike the XOS.

5.3.2 Tuning

To tune the OPSS, the threshold power is varied in the range of Pth ∈ [4, 15] kW in
steps of 0.2 kW. Each of the values is then tested for the four driving cycles to tune
the parameter such that the fuel economy is maximized. Results with normalized
EFC and final SOC levels are shown in Fig. 5.16.

The optimal threshold Pth varies for each of the driving cycles. The fuel economy
is maximized when Pth is defined as 9.2 kW, 10.2 kW and 10.4 kW for WL-L,
WL-M and WL-H respectively (although not very clear from the figure). The ideal
200 Chapter 5

> P_PSmax
< SOC_L P_PSmax

1 >= SOC_L
SOC <= SOC_U
f(u) 1
2 <
P_PSref
P_PL P_PSopt

> SOC_U
> P_SSmax

Figure 5.15: Implementation of the OPSS in Simulink. Note that f (u) implements Eq.
5.9 to define PP Smin (SOC).

threshold for WL-E is outside the investigated region (the minimum at Pth = 5.4 kW
is just a local minimum), but is found separately to be at -0.8 kW. Similar to the
EMMS and GECMS, the threshold is higher for the driving cycles with lower load
(e.g. WL-L) and lower for higher loads (e.g. WL-E). The exception of the XOS
results in Section 5.2.2, is thus not applicable as the OPSS operation is more similar
to optimization-based strategies in the sense that the SS is charged at medium-low
loads and discharged at medium-high loads (the SS is neither charged or discharged
in either of these cases for the XOS). Furthermore, the distinction between the base
threshold Pth and the effective transition threshold PP Smin is less relevant for the
OPSS results as there is barely any SOC deviation (SOCf inal ≈ SOCinitial ), giving
PP Smin (SOCf inal ) (as given by Eq. 5.9) values of 9.02 kW, 10.26 kW, 10.47 kW and
1.00 kW for WL-L, WL-M, WL-H and WL-E respectively (with SOCf inal values of
64.81%, 65.06%, 65.08% and 53.64%).

It is also interesting to contrast the final SOC values of the OPSS results with those
of the XOS. As the XOS relied solely on regenerative braking to charge the SS, the
strategy was essentially only able to reduce the discharging of the SS to maintain
CS operation. The OPSS, on the other hand, is able to actively charge the SS more
by reducing the power threshold Pth . Consequently it can be seen that the SOC
reaches its upper limit SOCU = 80% for the first three driving cycles at low values
of Pth . Such threshold selections cause the emergency handling rules, as displayed
Heuristic Strategies 201

1.2 80

75
1.15

SOC (%)
Mef c (-)

70
1.1
65

1.05
60

1 55
4 8 12 16 4 8 12 16
1.2 85

80
1.15

SOC (%)
Mef c (-)

75
1.1
70

1.05
65

1 60
4 8 12 16 4 8 12 16
1.08 85

80
1.06
SOC (%)
Mef c (-)

75
1.04
70

1.02
65

1 60
4 8 12 16 4 8 12 16
1.004 53.8

1.003
53.7
Mef c (-)

SOC (%)

1.002

53.6
1.001

1 53.5
4 8 12 16 4 8 12 16
Pth (kW) Pth (kW)
Figure 5.16: Normalized EFC (left) and final SOC (right) for varying Pth when driving
WL-L, WL-M, WL-H and WL-E (from top to bottom) with OPSS.
202 Chapter 5

Fuel Economy, Mef c (-) 1.1

1.08

1.06

1.04

1.02

1
4 7 10 13 16
Base Threshold, Pth (kW)
Figure 5.17: Normalized total EFC Mtot for varying Pth with OPSS.

in Fig. 5.13, to intervene to prevent the SOC from increasing further. However, this
intervention comes at the expense of fuel economy, where a clear spike is visible, in
particular for WL-L and WL-M. It is thus clearly desirable to set an appropriate
value for Pth to avoid the emergency handling rules on the upper range of SOC.

The consequences of triggering the emergency handling rules in the lower SOC range
are quite different. The case of the WL-E shows the SOC flattening off around
SOC = 54%, which still has a decent gap to SOCL = 50%. However, as will be
shown later in Fig. 5.20, the SOC actually reaches this lower threshold during the
driving cycle, before recovering somewhat by the end of the cycle to yield SOCf inal =
54%. Most importantly, it can be seen that the fuel economy also flattens out
around Pth = 10 kW. Thus, the fuel economy in some sense benefits by triggering
the emergency handling rules, as it prevents the operation from becoming even more
suboptimal. This is the ideal type of emergency handling rules. However, for this
work the emergency handling rules at higher SOC have prioritized simplicity, which
is why a spike in fuel economy can be observed for badly tuned threshold values.

To determine the optimal tuning of the OPSS, the overall fuel economy is evalu-
ated for the four driving cycles combined. The normalized results are presented in
Fig. 5.17. The optimal power threshold is found at Pth = 10.4 kW, which is very
close to the ideal selection for WL-M and WL-H (which arguably represents the
most common type of driving). Although the OPSS is more sensitive to tuning than
the XOS, even if the Pth is off by 25%, it would only affect the fuel economy by less
than 0.4%.
Heuristic Strategies 203

5.3.3 Operation

The resulting power profiles are shown in Fig. 5.18 and Fig. 5.19, for the first and final
iteration of the driving cycles respectively. It is clear that the OPSS is relying on the
load leveling approach as the PS, whenever used, is always used at PP Sopt = 20 kW.
Although this approach might sound or even look primitive, it is worth comparing
the resulting power profiles to the GECMS and GEMMS in Fig. 4.27.

The operation for WL-L is very similar to the GECMS, which operates the PS with
slightly more variation. However, both the GEMMS and GECMS generally use the
PS for the same durations as the OPSS. These variations in power levels for the
PS by the GECMS and GEMMS become larger for the WL-M and WL-H, while
the OPSS maintains its steady operation, but generally uses the PS at the same
occasions. It is also worth noting that the OPSS is operating almost identically in
its first and final iteration, suggesting that its operation is charge sustaining from
the very beginning.

The same can not be said for the WL-E, where the OPSS uses the SS more often at
high magnitudes, as compared to the GECMS and GEMMS. As can be expected,
this results in a lower SOC and the operation in the final iteration is therefore quite
different. Apart from generally having the PS on at all times (except during regen-
erative braking), the OPSS experiences some extreme oscillatory behavior towards
the second half of the final iteration of WL-E. Essentially the SOC drops below
SOCL , requiring the emergency handling rules to be kicked in. This results in the
PS being requested to deliver its maximum rated power (as illustrated in Fig. 5.13),
causing the PS load to exceed the required load, thus charging the SS and increasing
the SOC. This in turn, results in the OPSS returning to normal mode (i.e. exiting
emergency handling rules), causing the PS to return to delivering PP Sopt and the
SS supplementing the difference to the load as the SOC drops again. This causes
high-speed oscillations in the operation of the PS such that it on average follows the
load (PP S = PP L ). Although this operation is sensible, these oscillations are highly
undesirable. They can however be removed by either redefining the emergency han-
dling rules or by including a hysteresis effect between the emergency handling rules
to prevent the oscillations. This will be done in the next version of this control
strategy.
204 Chapter 5

30

15
Power (kW)

-15 PS S
PP S
PP L
-30
0 100 200 300 400 500 589
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 433
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 455
60

45

30
Power (kW)

15

-15

-30
0 100 200 300 323
Time (s)

Figure 5.18: Power time histories for PS, SS and PL for the first iteration of driving
WL-L, WL-M, WL-H and WL-E (top to bottom) with the OPSS.
Heuristic Strategies 205

30

15
Power (kW)

-15 PS S
PP S
PP L
-30
0 100 200 300 400 500 589
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 433
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 455
60

45

30
Power (kW)

15

-15

-30
0 100 200 300 323
Time (s)

Figure 5.19: Power time histories for PS, SS and PL for the final iteration of driving
WL-L, WL-M, WL-H and WL-E (top to bottom) with the OPSS.
206 Chapter 5

Finally, the fuel economy of the OPSS is evaluated in Table 5.2 for the four different
driving cycles. It can be seen that the SOC has been closely sustained (SOCf inal ≈
SOCinitial ) for the first three of the studied driving cycles, while it has dropped
significantly for WL-E×4. Considering the simplicity of the rules, this CS ability is
very impressive. The achieved fuel economy is equally impressive, being only 0.00-
3.52% behind the GECMS (the GECMS outperforms the OPSS with 0.0042% for
WL-L). If the four driving cycles are considered together (as calculated for Mtot ),
the difference is 0.95%. Considering the analytical effort invested in the GECMS,
the OPSS delivers exceptional utility in terms of results per effort.

Table 5.2: Fuel economy results for OPSS

Driving Cycle SOCf inal (%) mf (kg) mef c (kg) ∆GECM S (%)
WL-L 63.16 0.6884 0.7083 +0.00
WL-M 64.78 1.1404 1.1428 +0.34
WL-H 65.08 0.9532 0.9525 +0.23
WL-E 53.64 1.4853 1.6410 +3.52
Heuristic Strategies 207

5.4 Comparison of Heuristic Strategies

Having presented the XOS and OPSS, and their individual designs and perfor-
mances, it is interesting to compare their operation to the two conventional heuristic
strategies: the TCS and PFCS. Results of the GECMS are also included as a refer-
ence point.

The SOC profiles for each of the four heuristic strategies are presented in Fig. 5.20
for the four driving cycles. It should be noted that the selection of tuning parameters
for the PFCS in Section 3.3.1 makes this strategy operate quite similarly to the TCS
for PP L ≤ PP Sopt . As this is often true for WL-L (and somewhat true for WL-M
and WL-H), the SOC profiles of the PFCS and TCS are very similar (and somewhat
similar for WL-M and WL-H) in the presented results. This similarity is also visible
in comparing the power profiles of TCS and PFCS in Fig. 3.5 and Fig. 3.11. The
difference of 3 kW between PP S,cop = 19.8 kW and Pmin = 16.8 kW results essentially
in a change in period for the SOC profiles.

There is also a distinct difference between the operational pattern between the state
changing strategies (TCS and PFCS) and threshold changing strategies (XOS and
OPSS). The former can be seen to oscillate between the lower and upper SOC limits,
alternating between charge depleting and charge replenishing modes of operation.
This is also true for WL-E, although the oscillations occur at the limits rather than
between them.

The TCS can be seen to discharge quite sharply at the start of the driving cycle,
but even as the operation changes to charging mode, the charge keeps depleting for
some further time. This occurs due to the high level of load for the WL-E, such
that PP L ≥ PP Sopt , meaning that the SS has to supplement the PS to meet the load
power. Thus the SOC drops to 42.65% before beginning to recover. The TCS then
remains in charging mode (with the SS occasionally entering discharging mode) for
the rest of the driving cycle as the progress of increasing SOC towards the upper
limit of SOC is essentially flat due to the generally high load power. However, if
the PP S,cop was slightly higher, the SOC would reach its upper limit and the TCS
would enter the charge depleting mode again. This operation is consistent with the
observation that the period of the state changes (Ttcs ) for the TCS is proportional
to the average load power of the driving cycle (P̄dc ). As shown in Table 2.6, we have
208 Chapter 5

90
TCS
80 PFCS
XOS
OPSS
SOC (%)

70 GECMS

60

50

40
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
90

80
SOC (%)

70

60

50

40
0 500 1000 1500 2000 2500 3000 3500
90

80
SOC (%)

70

60

50

40
0 200 400 600 800 1000 1200 1400 1600 1800 2000
90

80
SOC (%)

70

60

50

40
0 200 400 600 800 1000 1200 1400
Time (s)
Figure 5.20: SOC profiles for XOS, PFCS, OPSS, TCS and GECMS when driving
WL-L, WL-M, WL-H and WL-E. Note that the TCS and PFCS profiles often overlap.
Heuristic Strategies 209

P̄W L−L < P̄W L−M < P̄W L−H < P̄W L−E . Thus, it follows (and matches the results in
Fig. 5.20) that TW L−L < TW L−M < TW L−H < TW L−E .

The PFCS operation is however quite different for WL-E. While the TCS can only
change its mode by having the SOC reach its lower or upper limits, the PFCS has
some additional possibilities, as shown in Eq. 3.8. The PFCS will also activate
the charging mode operation if the load power exceeds the maximum SS power
(PP L > PSSmax ), which occurs quite frequently for the WL-E. Thus, it can be seen
that the PFCS enters charging mode operation already around t = 60 s, without
needing to operate the SS at very high loads (as TCS has do). Thereafter, the
PFCS often operates in a load following manner but ends up charging the SS during
low loads (and regenerative braking). The SOC is thus gradually increased, before
reaching its upper limit around t = 670 s As the PFCS switches mode to operate
with SS only, the SOC begins dropping. However, quite soon the load power briefly
exceeds the maximum SS power (PP L > PSSmax ), making the strategy return to its
load following mode. As a result, the PFCS keeps on operating at a quite high SOC,
oscillating between around SOC = 81% and SOC = 76%.

In contrast, both XOS and OPSS operate much more steadily, quite similarly to the
GECMS. In fact, the OPSS is always operating within the following SOC bands for
WL-L, WL-M and WL-H: 62.75-65%, 63.76-65.15% and 63.39-65.59% respectively.
Such a limited depth-of-discharge (DOD), as opposed to the 50-80% cycles of TCS
and PFCS, is not only beneficial for the fuel economy of the vehicle, but also helps to
reduce battery degradation. Similarly, the XOS also has a small DOD, but operates
within a band of SOC that has deviated further from SOCinitial . It can be seen
that it takes the XOS less than a quarter of the simulated driving cycles to reach
its steady and CS operation, while the OPSS is very well positioned from the very
start. However, the simulation results for WL-E demonstrate the opposite relation.
Here, the XOS is operating within the SOC band of 62.43-64.33%, which is very
close to SOCinitial , while the OPSS is operating at 49.99-55.06%. In fact, the OPSS
is briefly activating the emergency handling rules to remain within the SOC bounds.

As the operation of both XOS and OPSS (and in particular the latter) is very
similar to the GECMS, which significantly outperformed the TCS and PFCS in
Chapter 3, it is not surprising to have these new heuristic strategies achieve better
fuel economies than the conventional heuristic strategies. The relative fuel economy
performance is shown in Fig. 5.21 for the four driving cycles. It can be seen that the
210 Chapter 5

20
TCS
PFCS
Fuel economy, ∆GECM S (%)

XOS
15 OPSS

10

0
WL-L WL-M WL-H WL-E

Figure 5.21: Comparison of fuel economy for PFCS, TCS, XOS and OPSS, relative to
the performance of the GECMS, when driving WL-L, WL-M, WL-H and WL-E.

novel proposed heuristic strategies are consistently outperforming the conventional

ones. It is also clear that the XOS tends to perform better for higher loads, while
the OPSS performs at its best at lower loads (note that that OPSS bar for WL-L is
at ∆GECM S = 0 so is not visible).

It is useful to compare the load following and load leveling strategies internally. The
XOS reduces the EFC by 6.83% relative to the PFCS for the four driving cycles
considered together, while the OPSS improves the fuel economy by 13.28% relative
to the TCS for the four driving cycles combined. These results demonstrate the
ineffective nature of the state changing mechanism for modern HEVs for which the
frequent, but intelligent, use of a SSS for the ICE is essential to achieve great fuel
economy. Although the XOS is a significant improvement over the conventional
heuristic strategies, it is the OPSS that is the most impressive one, achieving fuel
economy comparable (in fact identical for WL-L) to the GECMS.

The fact that the OPSS only has made use of a single tunable parameter and is
matching the fuel economy of the GECMS, raises some new questions. How much
further can the fuel economy of heuristic strategies be pushed? How close to the
truly global optimal solution are these strategies operating? These questions will be
discussed further in Chapter 6.
Heuristic Strategies 211

5.5 Summary

This chapter has discussed insights gained from past chapters that can serve as
design principles for heuristic control strategies. These have been formulated as
distinct design principles, which are summarized in Table 5.3.
Table 5.3: Possible design principles for control of HEVs

Fuel Economy Charge Sustaining Implementation

Optimizing Mechanisms Mechanisms Mechanisms
Load leveling State changing State machine
Load following Threshold changing Control map
Load blending Power changing Algebraic
Emergency handling

The XOS used the load following technique together with a threshold changing
mechanism. It thus operated as: SS-only mode at low load power; PS-only mode at
medium load; and hybrid mode at higher loads. This generally exclusive operation
of each power source allows more intuitive auditory feedback for the driver, and
makes the experience more similar to driving a conventional vehicle. The XOS out-
performed the PFCS (the conventional implementation of load following) by 6.83%.
However, the fuel economy results were still lagging the GECMS by 6.29%.

The OPSS, on the other hand, used the load leveling technique together with a
threshold changing mechanism. The resulting strategy operated as follows: SS-only
mode at low load power; PS operating at its optimal level at medium load; and PS
operating at its maximum level at higher loads. This type of operation is very similar
to the operation of GECMS and GEMMS, and thus the performance of the OPSS
was very impressive. It lags the GECMS by only about 1.4%, and consequently
outperformed the TCS (the conventional implementation of load leveling) by 12.7%.

The dramatic improvements of XOS and OPSS, over PFCS and TCS respectively,
clearly demonstrated the advantage that threshold changing has over state changing
mechanisms to enable charge sustaining operation in a modern HEV. The benefit
of fewer ICE start-stop events that the state changing mechanism enjoys, is less
relevant if an efficient SSS is installed. This result would translate to modern HEVs
with parallel architecture as well. However, the extraordinary performance of the
OPSS, with its load leveling strategy, can only be expected to be effective for series
HEVs where the ICE can be operated independently of the vehicle speed.
Chapter 6

Global Optimality

This work has proposed several novel control strategies, including both optimization-
based (EMMS0, EMMS1 and EMMS2) and rule-based strategies (XOS and OPSS).
Their performance relative to conventional control (TCS and PFCS) strategies has
been impressive and the results have often approached the performance of GECMS,
which supposedly is close to the global optimal solution [75, 78, 79, 104]. The fact
that GEMMS narrowly outperformed the GECMS might support this claim, as the
room for improvement seems quite limited. However, the extraordinary performance
of the OPSS, albeit inferior to GECMS, suggests that there might be a global optimal
solution out there that has not been considered in the search space of the investigated
control strategies so far.

To investigate this possibility, ideally a DP or brute force approach should be applied

to explore the control space more exhaustively. However, the previously mentioned
computational issues make any such attempt unfeasible. The best practical choice
is thus to take a “brute force light” approach, where a suitable heuristic control
structure is setup with multiple tunable parameters. This chapter will thus design
a global heuristic strategy (GHS) with the aim to outperform the GECMS and
GEMMS. The larger the margin, the less validity can be asserted to the claim that
the GECMS is practically identical to the DP solution.

This chapter will begin by introducing the design of the GHS, followed by a demon-
stration of its operation and analysis of its fuel economy. Thereafter the results
will be discussed in the context of claims of global optimality among other control
strategies.

213
214 Chapter 6

6.1 Global Heuristic Strategy

6.1.1 Design

The objective of the GHS is to apply heuristic rules that can be globally tuned to
achieve fuel economy results that are superior to GECMS with as large a margin
as possible. There are a wide range of heuristic insights that can be considered,
including those mentioned in the Design Principles section in Section 5.1. However,
rather than investigating new heuristic rules it makes sense to apply the OPSS rules,
which were shown to deliver fuel economies comparable to the GECMS results in
Section 5.3.3. This tried and tested approach will thus be further improved in this
section by allowing for a significantly larger amount of tuning.

Firstly, the tuning process will be made driving cycle specific. The global nature of
the control allows it access to the whole driving cycle in advance, so that it can be
tuned separately for each driving cycle, as has been the case for the GECMS and
GEMMS. This allows the control strategy to perform at its optimum rather than
needing to have a compromised nature of policies that are not excellent on any one
driving cycle but are instead good at all of them.

Secondly, a few additional tuning parameters are included. Rather than just tuning
the power threshold Pth , like the OPSS, the GHS will also tune Pcsi and PP S,cop
(previously defined as Pcsi = Pth and PP S,cop = PP Sopt = 20 kW for OPSS). This
wide range of tuning will result in control policies that have not been tested before,
and have not been replicated by the GECMS or GEMMS either. It is expected
that this somewhat blind tuning process will yield improvements on OPSS (unless
Pcsi = Pth and PP S,cop = PP Sopt happen to be the truly optimal tuning). The actual
implementation of the GHS is identical to the OPSS (as shown in Fig. 5.15).

However, result from the tuning process show that the initial selection for Pcsi = Pth
is already selected quite well, and the potential gains in fuel economy are smaller
than 0.05%. Therefore, this chapter will not describe the tuning of this variable
further, focusing instead on PP S,cop . This also makes the presentation of the tuning
results more readable. It should be noted that the use of only two tuning parameters
is quite restrictive, and the ideal approach would be to consider at least three or
four variables.
Global Optimality 215

3 60
SOC=50%

PS Power, PP S (kW)
SOC=65%
Power Share, u (-)

SOC=80%
2 40

1 20

0 0
0 20 40 60 80 100 0 20 40 60 80 100
3 60

PS Power, PP S (kW)
Power Share, u (-)

2 40

1 20

0 0
0 20 40 60 80 100 0 20 40 60 80 100
3 60
PS Power, PP S (kW)
Power Share, u (-)

2 40

1 20

0 0
0 20 40 60 80 100 0 20 40 60 80 100
3 60
PS Power, PP S (kW)
Power Share, u (-)

2 40

1 20

0 0
0 20 40 60 80 100 0 20 40 60 80 100
Power Requirement, PP L (kW) Power Requirement, PP L (kW)
Figure 6.1: Optimal power share and PS power for varying power requirements and
SOC for WL-L, WL-M, WL-H and WL-E (from top to bottom) for GHS.
216 Chapter 6

The resulting control policy (based on the tuning process described in the upcoming
subsection) for each of the four driving cycles is shown in Fig 6.1. This corresponds
to: Pth = 10.4 kW and PP S,cop = 24.2 kW for WL-L; Pth = 11.8 kW and PP S,cop =
23.8 kW for WL-M; Pth = 11.2 kW and PP S,cop = 23.6 kW for WL-H; and Pth =
2.8 kW and PP S,cop = 24.2 kW for WL-E. The control policy can generally be
considered a vertical shift of the OPSS control from Fig. 5.14, while maintaining
close resemblance to the GECMS and GEMMS in Fig. 4.27.

6.1.2 Operation

The tuning process for the GHS involves simulating the control strategy with a wide
range of Pth and PP S,cop for the four driving cycles. The presented tuning result for
the three first driving cycles will be in the range Pth ∈ [10, 12] kW and PP S,cop ∈
[22, 25] kW in intervals of 0.2 kW. However, the optimal tuning parameter for WL-E
was found elsewhere and the tuning results are presented for Pth ∈ [1, 4] kW and
PP S,cop ∈ [22, 25] kW in intervals of 0.2 kW. The resulting tuning graphs for all
driving cycles are presented in Fig. 6.2 with normalized EFC and final SOC values.

It can be seen that none of the optimal power levels are found at PP S,cop = 20 kW,
as was assumed for OPSS. Instead the ideal power levels are found at 24.2 kW,
23.8 kW, 23.6 kW and 24.2 kW for the four driving cycles. By noting that the final
SOC for each driving cycle is very close to SOCf inal = SOCinitial = 65%, it can be
understood that the GHS can use the PS constant operating point PP S,cop to affect
the charge sustaining ability of the control strategy. The ideal base thresholds are
found at 10.4 kW, 11.8 kW, 11.2 kW and 2.8 kW. Each of these has seen an increase
compared to the OPSS (which had optimal thresholds at 9.2 kW, 10.2 kW, 10.4 kW
and 5.4 kW), with the exception of WL-E. This final driving cycle didn’t finish with
SOCf inal = SOCinitial for OPSS, and should therefore be corrected by Eq. 5.9 to
find PP Smin . This value for OPSS if found to be at 1.32 kW. Thus, for each driving
cycle, the effective threshold PP Smin was increased for GHS, and the power level
PP S,cop was increased as well.

While the OPSS determines the PP S,cop = PP Sopt with the aim to operate the PS
efficiently and tunes the base threshold Pth to make the control strategy charge
sustaining, the GHS uses both parameters to make the strategy charge sustaining
and to improve overall powertrain efficiency. By having a higher PP S,cop level, the
Global Optimality 217

24.4 24.4
PP S,cop (kW) 1.0001.0
5
01

PP S,cop (kW)
23.8 23.8
0 1
1.0 1.002

23.2 23.2

64.5

63.5
1.005

64

63
22.6 22.6
10 10.5 11 11.5 12 10 10.5 11 11.5 12
24.4 1.005 24.4

1.001
2
1.00
PP S,cop (kW)

PP S,cop (kW)
23.8 23.8

1.0005

67
23.2 1.001 23.2

5
65.
66.

64.5
66

65
1.002
1.00
5
22.6 22.6
10 10.5 11 11.5 12 10 10.5 11 11.5 12
24.4 24.4
67

1.002
PP S,cop (kW)

PP S,cop (kW)

23.8 1.00 23.8

1
1.00
02

05

66.5

23.2
02

23.2
1.0

65.5

64.5
1.001
1.0

66

65

64
22.6 22.6
10 10.5 11 11.5 12 10 10.5 11 11.5 12
25 25
74 68
1.005
24.5 2 24.5 72
00 1.001 66
1.
PP S,cop (kW)

PP S,cop (kW)

005
5

1.0 1.001 70
00

64
1.002
1.0

24 24
68
1.005
23.5 23.5 66

64 62 60
23 23
1 2 3 4 1 2 3 4
Pth (kW) Pth (kW)
Figure 6.2: Normalized EFC Mef c (left) (Mef c = 1 is marked with a cross) and final
SOC (right) for varying Pth and PP S,cop when driving WL-L, WL-M, WL-H and WL-E
(top to bottom) with GHS.
218 Chapter 6

base threshold level can be kept higher without compromising the charge sustaining
ability. This allows the SS to be used to a larger extent.

Despite the global nature of tuning, the fuel economy is not very sensitive (relative
to the sensitivities of the optimization-based strategies) to the tuning parameters.
Even the final SOC values are very close to SOCf inal = SOCinitial for the first three
driving cycles for practically the whole investigated search space. This speaks to the
general robustness that often comes with heuristic strategies, and is further discussed
in the next chapter.

It is also worth noting that the generally vertical nature of the SOC profiles (meaning
that the SOCf inal is not very dependent on PP S,cop ) for the first three driving cycles
explains why the OPSS is able to achieve SOCf inal = SOCinitial without an optimal
selection of tuning parameters. In these cases the base threshold Pth is the critical
tuning parameter. However, for WL-E the SOC profiles are more horizontal (or
diagonal), meaning that the SOCf inal is quite dependent on PP S,cop . Thus, for WL-
E, the OPSS is not able to achieve SOCf inal = SOCinitial .

To study the operation of the GHS, the power profiles for the first and final iterations
of the driving cycles are shown in Fig. 6.3 and Fig. 6.4 respectively. The operation
clearly resembles the OPSS operation, but with more intense use of the PS, and
somewhat less frequent. It is also remarkable how similar the first and final iteration
is for every single driving cycle: they are practically identical. This suggests that
the GHS enters its efficient stride from the very start and is able to perform well
through all the iterations, and is able to maintain a steady SOC. Nevertheless, the
control and operation looks deceptively simple.

It is not until the fuel economy results are studied, that the performance of the
GHS is appreciated. The fuel economy of the GHS is presented in Table 6.1 for the
four different driving cycles. As can be seen, this control strategy has outperformed
the GECMS for every single driving cycle, while maintaining the SOC sustained
(SOCf inal ≈ SOCinitial ). The GHS is particularly successful at slower driving cycles,
but keeps an edge even at the highway. There is quite likely an alternative heuristic
strategy that could serve as the core structure for another GHS that would excel
for highway driving only. Overall, if the four driving cycles are considered together,
the GHS improves the fuel economy by 0.83% compared to GECMS (and 0.58%
compared to GEMMS).
Global Optimality 219

30

15
Power (kW)

-15 PS S
PP S
PP L
-30
0 100 200 300 400 500 589
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 433
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 455
60

45

30
Power (kW)

15

-15

-30
0 100 200 300 323
Time (s)

Figure 6.3: Power time histories for PS, SS and PL for the first iteration of driving
WL-L, WL-M, WL-H and WL-E (top to bottom) with the GHS.
220 Chapter 6

30

15
Power (kW)

-15 PS S
PP S
PP L
-30
0 100 200 300 400 500 589
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 433
45

30
Power (kW)

15

-15

-30
0 100 200 300 400 455
60

45

30
Power (kW)

15

-15

-30
0 100 200 300 323
Time (s)

Figure 6.4: Power time histories for PS, SS and PL for the final iteration of driving
WL-L, WL-M, WL-H and WL-E (top to bottom) with the GHS.
Global Optimality 221

This impressive performance has been achieved with very simple rules and quite
limited tuning. As the GECMS is outperformed by up to 1.8%, it suggests that the
GECMS might not be as close to the global optimal solution as originally thought.

Table 6.1: Fuel economy results for GHS

Driving Cycle SOCf inal (%) mf (kg) mef c (kg) ∆GECM S (%)
WL-L 64.45 0.6895 0.6954 -1.82
WL-M 64.87 1.1227 1.1241 -1.34
WL-H 65.11 0.9453 0.9442 -0.64
WL-E 64.94 1.5826 1.5834 -0.12
222 Chapter 6

6.2 Discussion

This section will discuss the findings of the previous section, where the GHS was
found to outperform the GECMS and GEMMS. It will begin by exploring various
causes for this unexpected result, before discussing the impact and conclusions for
the wider body of work.

6.2.1 Causes

Precision of Implementation

The first possible, but trivial, suspect for the cause of the GECMS and GEMMS
being outperformed by the GHS is the precision of implementation. Both of these
strategies were implemented with three significant digits. However, these control
strategies are very sensitive to changes in the equivalence factors, where a change
of 0.3% (roughly double the error margin of three significant digits) in just one of
the equivalence factors can change the SOCf inal with more than 2%. However, by
studying the tuning plots for both the GECMS and GEMMS, it can be seen that the
general area around the optimal policy selection in terms of fuel economy is quite
flat, and any hidden solution between the studied points is unlikely to be more than
a 0.1% improvement.

However, there are a few additional imprecisions. The whole process of designing
these strategies has involved discretizing each space. The PS fuel consumption and
efficiency has been measured for engine speeds and power levels that have been
discretized in 10 rpm and 0.1 kW intervals respectively. The SS efficiency has been
determined for SOC and power levels that have been discretized in 1% and 0.1 kW
intervals respectively. Also, the input for the control system, the load power PP L
is discretized in 0.1 kW intervals before being processed. Altogether, these minor
imprecisions can be accumulated into a somewhat larger error. Nevertheless, these
imprecisions are unlikely to account for the whole difference between the GHS and
the studied global strategies. Also, the discretization in this work has been quite
narrow, relative to other work and implementations in the literature.
Global Optimality 223

Limited Search Space

There are many limitations in the search space for the proposed global strategies
in this work. A DP solution allows for the controller to apply different control
inputs for two instances t1 and t2 where the load requirement and vehicle states are
identical. This is not possible for GECMS or GEMMS, for which the control input
is essentially a mapping between load power PP L (and SOC for GEMMS) and the
control input. Thus, at any two instances t1 and t2 , where the load power is identical
(as well as the SOC for GEMMS), the power share ratio u as determined by the
GECMS and GEMMS will always be identical, independent of where in the driving
cycle these two instances are.

It is also important to understand the role of the equivalence factors in determining

the control policy for the GECMS (and replenishing efficiencies for GEMMS). Each
GECMS control policy assumes a constant Sd and Sc for the duration of the driving
cycle. Furthermore, the same set of equivalence factors are considered for a particular
policy for all power requirements. Thus, an optimal policy, such that it requires
different equivalence factors at different power levels, would never be able to be
discovered by the GECMS. This can be visually understood as follows. As the
equivalence factors are tuned, every single point of the control map in Fig. 3.16 is
adjusted. For the ideal selection of equivalence factors, certain parts of the control
policy match the optimal policy. Any further tuning would make some additional
points match up with the optimal policy but a larger number of points would fall out
of alignment with the optimal policy, with a net negative impact on fuel economy.
Thus, despite the tens of thousands of control policies that were tested for GECMS
and GEMMS, none of these matched the better control policies that GHS produced.

To quantify some of these limitations, we can look at the number of control decisions
that are designed. For the GECMS, a control decision is defined for each load power
PP L ∈ [0, 100] kW in increments of 0.1 kW. In each case, the PS can take on a value
of PP Sref ∈ [0, 58] kW in increments of 0.1 kW, although this will be restricted
in many cases due to the limited ability of the SS to be charged. For simplicity,
300 different possible control decisions can be considered. Thus, 1001 scenarios are
considered with 300 possible decisions in each case. A brute force approach would
allow 3001001 different control policies, while the GECMS would at most have tested
100 × 100 (assuming 100 values each of Sd and Sc are trialled). This constitutes a
224 Chapter 6

negligible part of the control space (which is mostly junk). In the case of GEMMS,
the SOC is also considered as SOC ∈ [50, 80]% in 1% increments, resulting in a
total of 31,031 control scenarios, and thus 30031,031 different control policies. Of
course, any intelligent approach to optimization would not consider each of these
cases, but the necessary computational time would become prohibitive long before
we can consider additional factors such as engine temperatures or battery voltage.

Complexity of Model

The fallibility of the global optimal benchmark has not been considered an issue in
previous work, where a simplified and reduced model is used to apply DP to identify
the global optimal solution. This solution has been found by exhaustively searching
the feasible points of operation, and truly represents the global optimal solution
of that particular model. Thus, in the case of an ECMS (or any other real-time
strategy) being tested on a quite simple model and the DP on a very simple model,
the benchmarking can be considered quite valid. This explains why in general the
DP results are marginally better than the real-time control strategies, as should
be expected. However, in the case of a real-time control strategy being applied to
detailed dynamic model, and being compared to a DP solution on a very simple
model, the results can’t be considered valid.

In fact, considering a normal distribution of any systematic deviation between the

full and simplified model, it should be expected that the DP is outperformed by an
excellent real-time control strategy almost half the times. There are some reported
cases of the DP being outperformed, but these have typically been attributed to
numerical errors. Also, such negative results might be held back from publication.
However, considering that most real-time strategies are at least 1-2% inferior to the
DP, any results with a simplified model that produces fuel economy errors (relative
to the full model) within ±1% would produce results consistent with the expectation
of DP beating the real-time strategy. However, the accuracy of the simplified models
are never disclosed in the published works.

Apart from the inaccuracy of the simplified model, it is worth recognizing the inac-
curacy of the full models as well. These are very often vehicle models with a handful
of states (maybe some of SOC, engine speed, transmission gear and vehicle speed).
However, a real vehicle would be greatly affected by many more states and would
Global Optimality 225

experience transient behavior that can’t be modeled. This discrepancy can easily
be observed in any work that publishes experimental data together with simulation
data. The error in the full model is typically larger than the 1-2% that were pre-
viously mentioned for the simplified model. The vehicle model in this particular
work has been modeled in greater detail than most previously published work, and
includes states and transients that give a better representation of a real vehicle.
Thus, the greatly simplified analysis of GECMS (assuming constant component ef-
ficiencies, steady state fuel consumption, instantaneous engine speed changes, etc.)
is not as successful as it would be on a simpler model.

6.2.2 Impact

Simulation vs Reality

In the published body of work on SCSs, the vast majority of proposed control strate-
gies have been demonstrated on vehicle simulations only. This is reasonable enough,
considering the costs involved in real vehicle validation. However, it is important to
recognize the compromise in accuracy when dealing with simulation results.

Based on the findings in this work, as well as some experience with other vehicle
models, it could be claimed that the complexity of the ideal control policy is in-
versely proportional to the complexity of the vehicle model. A very simple model
can make use of optimization techniques such as DP to obtain the optimal control
policy. A medium-level model wouldn’t allow DP solutions, but has simple enough
dynamics to be analyzed to design an optimization-based control strategy that would
perform very well. A high fidelity vehicle model or a real vehicle would only allow
the optimization-based control strategy to analyze a fraction of the vehicle and com-
ponent dynamics and would thus design a competent control strategy (recognizing
that most of the assumptions going into the design would not hold during actual
operation), which might be comparable to a well-designed heuristic strategy.

However, at this point the distinction between an optimization-based and a heuristic

strategy becomes somewhat blurred. The ideal heuristic strategy could be derived
either by brute force tuning (similar to numerical optimization approaches like DP
or GA) or by heuristics derived from analysis of the powertrain (similar to ECMS or
EMMS). Nevertheless, as it is not feasible to execute an extensive tuning process on
226 Chapter 6

a real vehicle, and quite difficult for a high fidelity model, the best approach might
be to use the analysis behind optimization-based strategies to inform the control
structure for the heuristic strategy, which can then be tuned on a high-fidelity model,
with further minor adjustments by tests on a real vehicle.

A final example of this point can be made by considering the optimal engine speed
map that was produced in Section 2.3.4. The standard method to design this map
is to determine the most efficient engine speed for each possible load requirement,
and use the corresponding point of operation for each given load during driving.
However, recognizing that the change in engine speed is not instantaneous in our
model, or in reality, it was found that the vehicle performed better if a smoother
engine speed map was implemented, although this would result in suboptimal points
of operation. Essentially, it was preferable to operate on a slightly suboptimal engine
speed consistently, rather than have significant changes in engine speed every second
in the pursuit of achieving the “optimal” engine speed, as defined by its steady state
efficiency. This illustrates how simplistic analysis that performs well on simpler
models might be bad for high fidelity model and real vehicles.

Better benchmarking practices

As discussed, the validity of DP solutions executed on a simplified model is question-

able. The application of theoretically sound analysis on a bad model of reality will
not yield sound control policies or good benchmarking results. There is thus a need
to develop tools that allow the determination of the global optimal performance,
or at least an approximate solution, for high-fidelity models for benchmarking pur-
poses. There are many possible paths towards this, but based on this work, it is
probably a good idea to be open-minded about what the balance should be between
pre-design analysis and tuning. The former might be more rigorous, elegant and
transferable (to be applied on other powertrains), but the value of a richer and more
vast search space might be useful. This is not to argue for a brute force method, but
possibly something like the GHS, where a competent heuristic strategy is defined
and then multiple aspects are opened up for tuning. Any such tuning will explore
control space that would have been ignored by optimization-based strategies.

A variation of this approach could be to further tune the control policy of the
GECMS. Having found the ideal set of equivalence factors, further control space
Global Optimality 227

can be explored by strategically increasing or decreasing the power share ratio for
various power requirements. The easiest approach might be to smoothen the control
policy and remove occurrences of very low SS power being charged or discharged.
Depending on computational load, more advanced tuning could be done. The essen-
tial principle would be to treat the original GECMS control policy as a competent
“initial guess” rather than as the actual optimal policy.

In fact, the objective of actually achieving a guaranteed global optimal policy might
be impossible for a high-fidelity model or a real vehicle. Not only is the search space
incredibly vast, but the complexity of the model, and the significant amount of
interconnectivity between powertrain components, makes the system exhibit certain
chaotic features. The effects of a particular control decision cannot be predicted well
enough, despite the system being deterministic. This limits any analytical approach
to the problem, thus prohibiting any rigorous proof of optimality. Thus, it might
be more productive to determine a different benchmarking target; possibly defined
by the searched control space. For example, a numerical optimization approach
might be applied to obtain the optimal control policy such that the control decision
u is defined for each load power PP L . Thus, for any two time instances t1 and t2
where the load power PP L is identical, the control decisions u1 and u2 will also be
identical. Although this is a compromise on optimality, it would be a well-defined
solution that would be more informative as a benchmark than a DP solution on a
simplified model.

Powerful heuristic strategies

The findings of this work also emphasize the potential of heuristic strategies. The
rule-based strategies are often overlooked as a simplistic approach that exist for his-
toric reasons or are at best useful as baseline benchmarks. However, it is important
to appreciate the significant value they offer. Not only are they very effective (as-
suming well designed rules), they are in fact remarkably robust against modeling
inaccuracies. For example, Serrao et al. in [3] found that heuristic strategies out-
performed ECMS if applied to models which included temperature dynamics for the
engine. This advantage would be significantly stronger on a real vehicle where all
kinds of additional dynamics come into play.
228 Chapter 6

The most appropriate method for designing SCSs for real-time implementation might
therefore be to produce good suboptimal control policies (preferably by previously
mentioned method) and then extract simpler rules to produce a real-time control
strategy. There have been some works in the literature taking this approach of
converting DP solutions into rule-based strategies as well. This might be the best
approach until more powerful tools exist to design optimization-based control strate-
gies for high fidelity models. However, strong candidate methodologies for producing
good suboptimal solutions would include the NN (neural network) approach, which
is applied in [50]. It demonstrates many of the desired features, including the ability
to deal with larger search spaces (considering state space, control space and decision
space).
Global Optimality 229

6.3 Summary

Based on the surprisingly impressive results of the previous chapter, this chapter
has investigated the claim that the GECMS delivers results that are close to the
global optimal solution. The most suitable approach was identified to be the global
tuning of a heuristic strategy, producing the GHS, in an attempt to outperform the
GECMS. The GHS in this work was based on the OPSS. Several control parameters
were investigated, but finally only the power level was treated as a tunable param-
eter. This control strategy was found to outperform the GECMS by 0.83% (the
improvement for WL-L was 1.82%), thereby discrediting the claim to approximate
global optimality of the GECMS.

The causes for this failure of the GECMS are multiple, including the precision of
implementation, the limited search space, and the complexity of the model. How-
ever, the latter might be most relevant. Optimization-based control strategies (and
benchmark implementations like DP) have often been implemented on simple mod-
els, where they are most effective. The vehicle dynamics are simple enough to be
analyzed and controlled effectively, and simple assumptions might either hold true
for the model or affect the performance negligibly. However, a real vehicle, or a high-
fidelity model as the one used in this work, will have significantly richer dynamics
that are not as easy to analyze, and practically impossible to control optimally.
Thus, the GECMS, which might perform close to the global optimal solution for a
simple model, is less effective on the vehicle model in this work.

Consequently, it raises the importance of appreciating the differences between sim-

ulation results and reality. These differences can be partly reduced by using high-
fidelity models. However, this in turn will require the development of better bench-
marking practices to be applied to high-fidelity models, as the current benchmarking
tools require excessive computational load. A potential solution could be in the form
of a tunable heuristic strategy, like the GHS, but with a more robust method of tun-
ing and defining the control space. Lastly, the point from the previous chapter was
further strengthened: heuristic strategies (with inspiration from optimization-based
strategies) might be the most suitable category of control strategies for commercial
vehicles.
Chapter 7

Control Sensitivity Analysis

The past chapters have presented both conventional and novel control strategies,
and have evaluated their results in terms of fuel economy. However, it is of interest
to consider the performance of each control strategy more broadly. Other work
in the literature may consider additional performance metrics, such as emissions,
battery degradation or drivability, but there is a very limited body of work on the
sensitivity of the strategies to various design or operating conditions. Ignorance of
such considerations may lead to the design of control strategies that only perform
well under very particular operating conditions (realized in a simulation setting),
such as driving profile or initial battery SOC. A control strategy that excels on
two driving cycles, but performs terribly at ten other driving cycles, might appear
very impressive if only tested on the “right” set of driving cycles. Furthermore,
the performance of control strategies might be significantly affected by technological
developments, such as improvements in the performance of start stop systems (SSSs)
or batteries. It is important to appreciate these sensitivities to determine how the
optimal strategy might change with time.

This chapter will analyze and compare the sensitivities of the six presented real-
time control strategies (TCS, PFCS, XOS, OPSS, EMMS1 and EMMS2) to four
different factors: correct tuning of the control parameters; effectiveness of the SSS;
initial conditions of the vehicle; and the driving cycles being tested. Each of these
will be considered in a separate section. The objective of this study is to further
understand the strengths and weaknesses of the different control strategies, so they
can be selected more appropriately.

231
232 Chapter 7

7.1 Tuning Parameters

This section compares the six real-time control strategies that have been presented
in this work, in terms of the sensitivity of the fuel economy results to the tuning of
the control parameters.

To make any such comparison possible, it is necessary to normalize the fuel economy
results as well as the tuning parameters. The former can be dealt by the normalized
EFC Mef c that has been used throughout this work already, with the distinction
that each control strategy will be normalized separately. Thus, each control strategy
will have Mef c = 1 at its optimal point. Also, the total fuel economy results are
considered (for all four driving cycles together). This ensures Mef c ≥ 1 at all points,
and the results are more readable.

Normalizing the tuning parameters is less straightforward, but the most appropriate
method was found as:
xtune
Xtune = (7.1)
xtune,opt
where xtune is the tuning parameter for the SCS in question, and xtune,opt is the opti-
mal value that yields the best fuel economy results. For control strategies with two
tuning parameters (PFCS, EMMS1 and EMMS2), the more influential parameter is
considered. For PFCS, the fuel economy results are mainly driven by Pmin , whereas
Pch only has a minor role (in fact Pch = 0 is used in this work). For EMMS1, the
performance is governed primarily by ηre , while Dcsi is for CS purposes. Lastly, for
EMMS2 Dcsi,d and Dcsi,c (modifying ηre,d and ηre,c respectively) have equal concep-
tual influence. However, as the range of variation in ηre,d for various driving cycles
is much greater than ηre,c , the Dcsi,d parameter is found to be the most influential.

The tuning results for TCS, PFCS, XOS, OPSS, EMMS1 and EMMS2 from previ-
ous chapters are then processed and normalized as discussed, and are presented in
Fig. 7.1. Here, the optimal results for each control strategy is found at Xtune = 1
(where Mef c = 1). The results are shown in the range Xtune ∈ [0.6, 1.4], meaning
that the tuning parameter is considered within ±40% of its optimal value.

It can be seen that the TCS and PFCS are most sensitive to the correct tuning
of its control parameters, with the latter producing 1% inferior fuel economy for a
10% error in tuning. Both the XOS and OPSS are significantly less sensitive, with
a 20% tuning error only compromising the fuel economy by about 0.2%. The XOS
Control Sensitivity Analysis 233

in particular is impressive, allowing up to 40% tuning error while the fuel economy
only drops by 0.2%. The EMMS1 results are defined within a narrow range (but
represents the relevant tuning space) where the fuel economy is compromised 0.2-
0.3% for bad tuning. EMMS2 is tuned for a much larger range, and show extremely
low sensitivity for the lower range of the tuning parameter (less than 0.1% drop in
fuel economy for tuning error of 35%), while there is a significant error for the higher
range (1% drop in fuel economy for tuning error of 5%).

Many of the tuning sensitivity profiles are somewhat asymmetrical, meaning that
the sign of the tuning error is relevant. In general, it can be seen that it is preferable
to overestimate the value for the tuning parameters, rather than underestimate, with
the EMMS2 being the only clear exception (and the TCS in very close range of the
optimally tuned value). A larger set of control strategies would be needed though,
to study such a bias further.

It can also be seen that the range for the various control strategies is different:
the EMMS1 results are defined for roughly Xtune ∈ [0.97, 1.03] (as ηre ∈ [34, 36])
while EMMS2 is defined for Xtune ∈ [0, 1.37] (as Dcsi,d ∈ [0, 5]). It can thus be
seen that lower values of xtune will produce relatively larger values of Xtune (e.g.
xtune = 6 and xtune,opt = 5 will give Xtune = 1.2, while xtune = 51 and xtune,opt = 50
will give Xtune = 1.02). Thus, the Xtune parameter might mean quite different
things for each control strategy. Nevertheless, this definition of Xtune together with
the presented range (which gives an indication of the relevant search space), gives
sufficient information to evaluate the sensitivity of the tuning process.

1.03
TCS
Normalized EFC, MEF C (-)

1.025 PFCS
XOS
OPSS
1.02
EMMS1
EMMS2
1.015

1.01

1.005

1
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
Tuning parameter, ptune (-)
Figure 7.1: Fuel economy sensitivity profiles for the tuning of control strategies.
234 Chapter 7

7.2 Start Stop System

This section investigates the SSS impact on the fuel economy results of the six real-
time control strategies presented in this work. In particular, it looks at how effective
each control strategy would have been for a SSS with a different turn-on penalty.

It has been suggested earlier in this work that the conventional heuristic SCSs, which
aim to minimize the number of engine turn-on events, are based on outdated ideas
of the tradeoff between engine idling and switching. In the 1980s, the rule-of-thumb
used to be that the engine should be switched off if the vehicle is expected to idle for
30 seconds or more. This tradeoff has become updated with time, and it has been
commonly advised in the past decade that the tradeoff is 10 seconds. However, as
mentioned earlier in Section 2.5.3, modern HEVs use very efficient SSSs that have
reduced this tradeoff to less than 1 second. The vehicle model in this work uses a
SSS that penalizes each engine turn-on event by a fuel penalty mpen , defined as

mpen = TSSS · ṁidling (7.2)

where TSSS is the tradeoff time between switching off and idling, and ṁidle is the
rate of fuel consumption during idling operation. In this work TSSS = 1 second has
been used (corresponding to mpen = 0.00011 kg).

It would be interesting to find how the fuel economies determined in the previous
chapters would be affected by a different selection of TSSS . To proceed with this
analysis, the number of engine turn-on events Nturn−on for each control strategy
(when optimally tuned) are measured, and the overall fuel economy is defined as:

mef c = m′ef c + Nturn−on · mpen (7.3)

where m′ef c is the pre-correction value for the EFC (which can be calculated from
the previously obtained results by computing m′ef c = mef c −Nturn−on ·0.00011). Fur-
thermore, as the EMMS2 results are the best for each driving cycle, it is appropriate
to normalize all the fuel economy values for the mpen = 0 case of EMMS2 operation,
as:
m′ef c + Nturn−on · mpen
Mef c = . (7.4)
m′ef c,EM M S2
This would give Mef c ≥ 1 for all control strategies, for all positive values of TSSS .
Control Sensitivity Analysis 235

The normalized fuel economy results for TSSS ∈ [0, 30] seconds are presented in
Fig. 7.2 for the four driving cycles. It is important to understand that the slope of
the lines are proportional to Nturn−on . Thus, a control strategy with a low value for
Nturn−on would have a flat profile (like TCS and PFCS), whereas a higher Nturn−on
value would lead to an increasing profile. Also, as mentioned, the actual fuel economy
results for the vehicle in this work are those that correspond with TSSS = 1 second.

The most striking feature of these charts is the flat nature of the TCS and PFCS. As
these control strategies make use of a state changing charge sustaining mechanism
(as discussed in Section 5.1.2), the aim is to minimize the number of engine switch-
ing events. This used to be a sensible policy two decades ago when these control
strategies were developed, but is clearly less effective today. As can be seen, the XOS
outperforms the PFCS for TSSS < 4, TSSS < 7.5, TSSS < 11 and TSSS < 17 seconds,
for the four driving cycles respectively. The other control strategies outperform the
TCS and PFCS with an even more generous margin for TSSS . This clearly suggests
that the aim to minimize Nturn−on should not be a priority once the SSSs are good
enough to deliver about TSSS = 5 seconds, which happened many years ago.

This largely explains why the XOS and OPSS have been able to outperform the con-
ventional heuristic control strategies (TCS and PFCS) with very large margins (up
to 20%). These novel control strategies are designed in a paradigm where significant
engine switching is a necessary requirement to achieve good fuel economy results. In
fact, it is interesting to observe that the optimization-based strategies (EMMS1 and
EMMS2) typically have a higher slope (larger Nturn−on values) than XOS and OPSS.
Consequently, the EMMS are more sensitive to TSSS , and are actually outperformed
by the OPSS for high TSSS values for most driving cycles. This is particularly pro-
nounced for WL-E where the EMMS2 is the best strategy for TSSS = 0 and the
worst strategy for TSSS = 30 seconds.

However, it is worth emphasizing that the reduction of Nturn−on is not only a matter
of fuel economy. Any such switching causes undesirable jerks in operation that need
to be kept low for the comfort of the driver. Also, there might be considerations
in terms of component degradation, as frequent engine switching has a negative
impact on the engine life. However, most modern engines will fail for other reasons,
long before the switching becomes a dominant influence. Thus, although extremely
frequent engine switching might be undesirable, it is likely to become less of an issue
with time.
236 Chapter 7

2
TCS
1.8 PFCS
XOS
OPSS
Mef c (-)

1.6 EMMS1
EMMS2
1.4

1.2

1
0 5 10 15 20 25 30
1.6

1.5

1.4
Mef c (-)

1.3

1.2

1.1

1
0 5 10 15 20 25 30
1.4

1.3
Mef c (-)

1.2

1.1

1
0 5 10 15 20 25 30
1.1

1.08
Mef c (-)

1.06

1.04

1.02

1
0 5 10 15 20 25 30
SSS trade-off time, TSSS (s)
Figure 7.2: Normalized EFC Mef c for varying tradeoff time between engine switching
and idling, when driving WL-L, WL-M, WL-H and WL-E (from top to bottom) with six
different real-time control strategies.
Control Sensitivity Analysis 237

7.3 Initial Conditions

This section investigates the influence of simulation initial conditions on the final
state of the vehicle and its fuel economy. It focuses on determining how sensitive
each of the presented real-time control strategies are to the setting of the initial SOC
value, SOCinitial .

All the simulation results presented in this work so far have consistently used the
same initial conditions. The state of the vehicle at the start of the simulation is
identical for when testing each control strategy. This is essential to allow a fair
comparison between various control strategies, which has been an essential part of
this work. However, this comes with a few limitations. To measure the performance
of the control strategies for the same initial conditions every time, might not be
indicative of actual performance in a real vehicle, where initial conditions vary for
every single journey. There are several initial conditions that could be considered.
However, most states have quite fast dynamics and would quickly return to some
reference value (e.g. DC Link voltage, battery voltage, etc.), so any variation in
initial condition would have a negligible effect. Instead, it is more useful to consider
states like ambient temperature, engine temperature and battery SOC, as these
change more slowly and can impact simulation results to a larger extent.

In this chapter, only the battery SOC will be considered. The ambient temperature
should affect both the battery and engine performance, but as the vehicle model
in this work does not include battery temperature dynamics, the results of such a
study would not be valid. A sensitivity study of engine temperature could be done,
but considering that most real journeys, and most commercials tests, are done with
a cold start of the engine, this is probably an appropriate assumption for all tests.
The battery SOC, however, is distinct in the sense that it does not tend towards
a reference or ambient value with time. As such, each journey with a real vehicle
might start with any battery SOC value, depending on the past history of driving
of the vehicle. Therefore, the influence of the initial setting of SOC on the fuel
economy and final SOC for each journey will be studied.

To investigate this, new simulations are run for the optimal setting of the six real-
time control strategies presented in this work, with the following three initial SOC
values: SOCinitial ∈ {50, 65, 80}% (as SOCL = 50% and SOCU = 80%). Results of
normalized EFC and final SOC for the four driving cycles are shown in Fig. 7.3.
238 Chapter 7

1.1 90
TCS
PFCS
XOS 80

SOCf inal (%)

1.05 OPSS
Mef c (-)

EMMS1
EMMS2
70

1
60

0.95 50
50 60 70 80 50 60 70 80
1.06 SOCinitial (%) 75 SOCinitial (%)

1.04 70

SOCf inal (%)

Mef c (-)

1.02 65

1 60

0.98 55

0.96 50
50 60 70 80 50 60 70 80
1.06 SOCinitial (%) 80 SOCinitial (%)
75
1.04
SOCf inal (%)

70
Mef c (-)

1.02 65

60
1
55

0.98 50
50 60 70 80 50 60 70 80
1.03 SOCinitial (%) 90 SOCinitial (%)
1.02 80
SOCf inal (%)

1.01
Mef c (-)

70
1
60
0.99

0.98 50

0.97 40
50 60 70 80 50 60 70 80
SOCinitial (%) SOCinitial (%)
Figure 7.3: Normalized EFC Mef c and final SOC for varying values of initial SOC at the
start of simulations when driving WL-L, WL-M, WL-H and WL-E (from top to bottom)
with six different real-time control strategies.
Control Sensitivity Analysis 239

Note that the EFC is calculated based on the new initial SOC values, and that the
EFC of each control strategy has been normalized with respect to the EFC results
corresponding to the case of SOCinitial = 65% of the same strategy:

mef c
Mef c = . (7.5)
mef c,SOCinitial=65%

Also, note that the lines are based on only three values of SOCinitial for each control
strategy and line charts have been used to allow easier distinction between the
strategies. Interpolating these results would not be valid (for TCS and PFCS in
particular).

It can clearly be seen that the impact of varying SOCinitial on the fuel economy
of each control strategy is very significant, with fuel economy typically improving
for higher SOCinitial values. This is the expected result, as the battery gets more
efficient for higher SOC levels. The conventional rule-based strategies TCS and
PFCS are least affected, as their operation tend to by cyclical, and no particular
SOCf inal is preferred (as is clear from the SOCf inal plots). However, WL-E is an
exception as both the TCS and PFCS are forced to use their emergency handling
rules and operate consistently around SOC = 50% and SOC = 80% respectively.
In this case the TCS benefits from being able to operate in its steady mode as long
as possible, and it thus has better fuel economy at lower SOC levels.

The EMMS1 and EMMS2 are slightly more sensitive to the initial SOC setting in
terms of fuel economy, but it can be seen that the final SOC values remain consistent
for all settings, for all driving cycles (apart from the drop for SOCinitial = 50%
for WL-E for EMMS2). This is an effect of the charge sustaining mechanisms of
these strategies, meaning that they will seek themselves towards SOCf inal = 65%,
independent of the initial setting of SOCinitial . As a consequence, the fuel economy is
compromised for any deviation from the SOCinitial = 65%, as they have to struggle
their way towards this operating point. Again, the WL-E is an exception as the
EMMS strategies have their optimal operating point below SOC = 65% for this
driving cycle, and thus the SOCinitial = 50% setting ends up being favorable, for
EMMS2 in particular.

The OPSS performs quite similar to the EMMS, and is actually less sensitive than
EMMS2 to SOCinitial variations in terms of SOCf inal values. But it is slightly less
successful in keeping the SOC close to the SOCf inal = 65%. However, the XOS has
240 Chapter 7

0.9 1.4
TCS
PFCS
XOS
OPSS
EMMS1 1.3
mef c (kg)

EMMS2
0.8

1.2

0.7 1.1
50 60 70 80 50 60 70 80

1.2 1.8

1.1 1.7
mef c (kg)

1 1.6

0.9 1.5
50 60 70 80 50 60 70 80
SOCinitial (%) SOCinitial (%)
Figure 7.4: Equivalent fuel consumption mef c for varying values of initial SOC at the
start of simulations when driving WL-L (top left), WL-M (top right), WL-H (bottom
left) and WL-E (bottom right) with six different real-time control strategies.

the most distinct profiles. In terms of fuel economy, it is the most sensitive to varying
SOCinitial values. This can easily by understood by its limited ability to control its
SOC trajectory, as it is unable to recharge the battery directly and has to rely on
regenerative braking to increase the SOC. Most importantly, the XOS is not ever
supposed to operate at its extreme SOC limits, as its charge sustaining mechanism
gets progressively more extreme from towards the boundaries. The operation at
either end of the SOC band has quite extreme control decisions to push the SOC
away from its limits and this will inevitably have a negative impact on the fuel
economy.

To further study the impact on fuel economy, the sensitivity plot for the absolute
values of mef c are presented in Fig. 7.4 for the four driving cycles. It can be seen
that, in general, each of the control strategies have somewhat similar sensitivity to
Control Sensitivity Analysis 241

variations in SOCinitial , with the exception of the XOS. In fact, the effect on the
XOS is so pronounced that it is actually outperformed by both the TCS and PFCS
for WL-L, and it is outperformed by TCS and almost matched by the PFCS for
WL-E.

This limitation of the XOS was not visible in previous simulation results in this work,
but has been discovered in this sensitivity analysis. However, considering the design
and performance of the XOS, it is quite unlikely that it would ever get itself into a
position of SOCinitial = 50% in the first place (due to the mentioned progressively
more extreme charge sustaining behavior towards the SOC limits). However, for
example, a HEV that has not been used for a very long time might find the SOC
dropping to these levels through natural charge leakage. Nevertheless, the variations
in SOCinitial that would occur for each journey in a real vehicle would affect the XOS
and compromise its fuel economy (even if not to the extent to be outperformed by
the TCS and PFCS).
242 Chapter 7

7.4 Driving Cycles

This section will be testing the performance of the control strategies for a new set of
driving cycles, that have not been part of the tuning process. The aim is to assess
how sensitive each control strategy is to varying driving conditions.

It is quite common for SCSs presented in the literature to be developed and tested for
two or three driving cycles. This always raises the question of how effective the SCS
in question might be for alternative driving cycles. This work has actively sought
to develop, design, tune and test the control strategies for a wide range of driving
cycles, as discussed in Section 2.6.1, which is why the driving cycle segments of the
WLTP were employed. This has allowed the testing of each control strategy on low-
speed urban (WL-L), medium-speed urban (WL-M), rural (WL-H), and high-speed
highway (WL-E) driving cycles.

To further test the developed control strategies, they will be used to simulate six
additional driving cycles. These driving cycles consist of the NYCC, HWFET,
FTP-75 and US06 that are the most standard American driving cycles, as well as
the EUDC and the NEDC that are the most conventional European driving cycles.
These will be run for multiple iterations to allow the study of SOC deviation and
fuel economy over longer period of driving. However, the EFC equivalence factors
Sd,ef c and Sc,ef c have not been evaluated for these new driving cycles. Therefore,
as an approximate solution, the equivalence factors from WL-L, WL-M, WL-H and
WL-E will be used and assigned based on which driving cycle is most similar. While
this compromises the precision of the study to some extent, the results are still quite
reliable due to the repeated iterations and the reasonably narrow range of SOC
deviation (as shown later). A brief summary of the driving cycles are presented in
Table 7.1.
Table 7.1: Additional driving cycles tested

Driving Cycle Iterations EFC factors from Description

NYCC 8 WL-L Low-speed urban
NEDC 4 WL-M Low-speed urban and high-speed rural
FTP75 4 WL-M Medium-speed urban
EUDC 8 WL-H High-speed rural
HWFET 4 WL-H Medium-speed highway
US06 4 WL-E Aggressive highway
Control Sensitivity Analysis 243

3
TCS
2.5 PFCS
XOS
Fuel economy, mef c (kg)

OPSS
2 EMMS1
EMMS2

1.5

0.5

0
WL-L WL-M WL-H WL-E NYCC NEDC FTP75 EUDC HWFET US06

Figure 7.5: EFC mef c for multiple iterations (see Table 7.1) of ten different driving
cycles with six different real-time control strategies.

30
TCS
25 PFCS
XOS
Fuel economy, ∆ef c (%)

OPSS
20 EMMS1
EMMS2

15

10

0
WL-L WL-M WL-H WL-E NYCC NEDC FTP75 EUDC HWFET US06

Figure 7.6: Relative EFC ∆ef c for multiple iterations (see Table 7.1) of ten different
driving cycles with six different real-time control strategies.

Fuel economy results for the four WLTP driving cycles as well as the six additional
driving cycles are presented in Fig. 7.5, where the absolute EFC results are given for
each of the presented real-time control strategies, for each driving cycle. In addition,
for further clarity, Fig. 7.6 shows the relative difference in EFC ∆ef c compared to
the best strategy for that particular driving cycle. It can be seen for the first four
sets of data (for WL-L, WL-M, WL-H and WL-E) that the results are reasonably
consistent. The TCS and PFCS are the worst, followed by the XOS, followed by the
OPSS and EMMS1, and finally the EMMS2 that yields the best fuel economy for
each of these driving cycles.
244 Chapter 7

However, the results for the additional six driving cycles are quite different. Quite
remarkably, the EMMS2 is the worst-performing strategy for NEDC and EUDC. The
results for the NEDC could have been expected, as it consists partly of low-speed
urban driving and partly of high-speed rural driving. This prevents the EMMS2 from
settling into an optimal mode of operation and it has to keep changing its desired
mode of operation. However, the negative impact of such switching wouldn’t have
needed to be as high if the strategy had also considered the NEDC in the tuning
process and the CSI factors had been chosen more appropriately. The weak results
for the EUDC are somewhat more surprising, as the EMMS2 should have handled
such repetitive driving cycles quite well. However, this result might be attributed to
the distinct type of operation the EUDC exhibits, which is different from both WL-
H and WL-E. Again, a better tuning process might have addressed this issue, but
the point has been made: an optimization-based strategy will always be vulnerable
to driving conditions that have not been part of the designing and tuning process.

It is also worth noting that the EMMS1 performance is much more reliable than
the EMMS2. As the tuning process of EMMS1 is essentially based on powertrain
analysis, its results are quite consistent. In contrast, the tuning of the EMMS2 is
partly based on the global tuning of the GEMMS, which is much more susceptible
to bias the control strategy based on the particular driving conditions for which it
was tuned. Thus, EMMS1 not only performs consistently, but actually is the best
control strategy for EUDC. This can partly be attributed to the artificially plain
speed and acceleration profiling of the EUDC, which is always piecewise linear. Such
operation allows plenty of steady state operation, allowing the EMMS1 to excel with
its steady-state analysis of the powertrain efficiencies.

However, the most impressive results are achieved by the OPSS, which achieves the
best results for four out of the six additional driving cycles being tested. Although
the OPSS is also based on a tuning process involving only WL-L, WL-M, WL-H
and WL-E, there is only a single tuning parameter and it is not very sensitive to
driving conditions (apart from very aggressive driving). Consequently, the OPSS
achieves excellent fuel economy results for all driving cycles apart from WL-E and
US06 (where it still performs decently).

It is also worth noting that the XOS delivered the best results for the US06. In
contrast to the OPSS, the XOS excels with aggressive driving, as it allows plenty
of opportunities for regenerative braking and has a good balance between the use
Control Sensitivity Analysis 245

85
TCS
80 PFCS
State of Charge, SOC (%)

XOS
75 OPSS
EMMS1
70 EMMS2

65

60

55

50

45
WL-L WL-M WL-H WL-E NYCC NEDC FTP75 EUDC HWFET US06

Figure 7.7: Final SOC values for multiple iterations (see Table 7.1) of ten different
driving cycles with six different real-time control strategies.

of battery and engine. The latter is not true for urban driving with this particular
vehicle model. The XOS can be expected to perform better for a powertrain where
the battery power rating is more limited, such as in [15]. Nevertheless, even for all
the other driving cycles, it always outperforms the conventional heuristic control
strategies TCS and PFCS.

Finally, it is also of interest to check the charge sustaining ability of the control
strategies under new driving conditions. The final SOC values from simulations with
each of the control strategies are shown for each of the driving cycles in Fig. 7.7. It
can be seen that the TCS and PFCS remain as erratic as ever, as they are based on
state changing operation. Most of the other final SOC results are around 60-65%,
which is quite good.

The EMMS strategies are the most capable ones in maintaining their SOC such
that SOCf inal ≈ SOCinitial . The fact that the EMMS2 is able to do so, despite
the poor performance for EUDC and NEDC, is somewhat surprising. The OPSS
profile is more in line with expectations where the aggressive driving cycles WL-E
and US06 are seeing a dip in SOCf inal , but other results are more charge sustaining.
Conversely, the XOS generally has a lower SOCf inal value for most driving cycles,
but is boosted for the aggressive driving cycles WL-E and US06, where it was shown
to perform best. This chart, is quite effective in contrasting the nature of the XOS
and OPSS, where the SOC will increase and decrease respectively for more aggressive
driving.
246 Chapter 7

7.5 Summary

This chapter has conducted a brief control sensitivity analysis of six real-time con-
trol strategies (TCS, PFCS, XOS, OPSS, EMMS1 and EMMS2), investigating the
impact on changes in: tuning parameters; effectiveness of SSS; initial battery SOC;
and selection of driving cycles.

It was found that the conventional heuristic strategies (TCS and PFCS) are most
sensitive to correct tuning, with a 10% error causing a drop of 1% in fuel economy.
This can be contrasted with the novel heuristic strategies (XOS and OPSS) which
could suffer a 20% tuning error but only lose 0.2% in fuel economy. Thus, the novel
heuristic strategies have more robust designs and might be easier to design.

The influence of the SSS on the preference among control strategies was found to be
very significant. A poor SSS resulted in the conventional heuristic strategies being
preferred, while a strong SSS overwhelmingly favored the novel heuristic strategies,
as well as the EMMS. The results verified the earlier stated hypothesis that the
TCS and PFCS are based on an outdated concept of the undesirability to switch the
engine on or off. Thus, the control principles put forward with the XOS and OPSS
can be expected to be successful in most modern HEVs.

By studying the impact of the initial battery SOC on the resulting fuel economy,
it was found that the XOS in particular is more sensitive to deviations in initial
conditions (in particular low supplies of charge). In fact, it is so sensitive that it was
at times outperformed by the TCS and PFCS. The other novel strategies presented
were not only quite robust in terms of fuel economy, but were also quite successful
in returning the SOC to medium levels by the end of the driving cycles.

Lastly, the study of an additional six driving cycles exposed the strong sensitivity
to driving conditions of the EMMS2 in particular. It failed miserably for two of
the tested driving cycles, and was generally less effective when facing new types of
driving. However, this could probably be addressed by better tuning. In contrast,
the OPSS, for which the design is less tuning-dependent, excels at the new driving
cycles (finishing top for four out of six).

Overall, the sensitivity analysis provided much deeper insights into the operation of
each control strategy, and exposed limitations that were not visible in previous fuel
economy results. In consideration of these results, the OPSS is the top performer.
Chapter 8

Conclusion

This thesis has gone though three distinct stages: Chapters 1 to 3 introduced the
problem, the vehicle model and conventional control strategies; Chapters 4 and 5
presented several novel control strategies; and Chapters 6 and 7 have provided novel
analysis and perspective of control strategies.

It has been found that the conventional control strategies are lacking in several
regards. The heuristic strategies are based on outdated ideas of engine switching,
making room for the novel heuristic strategies XOS and OPSS to outperform these
conventional strategies by a good margin. As SSSs get better, this effect becomes
more pronounced. The most established optimization-based strategy (ECMS) lacks
knowledge about the powertrain it operates on. The design of the EMMS, based
on a thorough understanding of the powertrain efficiencies, allowed the GEMMS to
outperform the GECMS (suggesting that the EMMS2 would outperform the ECMS).

Also, overall, the optimization-based strategies have been found to be less effective
than expected, due to the use of a high-fidelity model. The optimization-process
often requires significant assumptions, which might hold true in a simple model, but
not in a real vehicle. This was further aggravated when driving on fresh driving
cycles, where heuristic strategies like the OPSS excelled.

This final chapter will not further summarize the findings of these past chapters,
as it has been done quite concisely by the end of each chapter. Instead, the key
contributions of this thesis will be listed. This will be followed and finished by an
outlook on future research directions.

247
248 Chapter 8

8.1 Contributions

This section will list the key contributions from each chapter of this work.

Chapters 2 and 3: Vehicle Model and Conventional Strategies

1. A high-fidelity model was further developed to enable more reliable study and
design of control strategies.

2. A reduced model was developed to allow more than 50 times faster simulations
at a very limited loss of precision. This enabled the implementation of control
strategies with higher tuning requirements.

3. Conventional strategies (TCS, PFCS and GECMS) were implemented and

tested for this high-fidelity model, providing new insights about their operation
and effectiveness.

Chapter 4: Efficiency Maximizing Map Strategies

1. A framework for designing control strategies is proposed, such that the partic-
ular powertrain in question is optimized. Control objectives and cost functions
are expressed in terms of component efficiencies, in an intuitive, measurable
(replenishing efficiencies being the only non-measurable parameter), and com-
prehensive way (in contrast to the ECMS that typically assumes constant
battery efficiency).

2. The concept of replenishing efficiency is proposed, that is not only more in-
tuitive than equivalence factors, but also more compatible when dealing with
battery efficiencies. Multiple uses of the replenishing efficiencies are consid-
ered (in EMMS0, EMMS1 and EMMS2), leading to varying advantages and
disadvantages, which are explored.

3. Simulation results suggest that EMMS1 and EMMS2 are effective (but the
latter will require more thorough tuning). The global version, the GEMMS,
delivers superior performance than GECMS and is thus a better benchmark
for future work.
Conclusion 249

Chapter 5: Heuristic Strategies

1. A useful classification is given for design principles for fuel economy optimizing,
charge sustaining and implementation mechanisms. These can be mixed and
matched to create a wide range of control strategies.

2. The XOS is proposed, which is found to deliver good fuel economy (7% im-
provement on PFCS), with very simple rules. Also, the exclusive operation of
each power source allows intuitive auditory feedback from the engine, improv-
ing drivability, and reducing barriers to adoption of HEVs.

3. The OPSS is proposed, which is found to deliver excellent fuel economy (13%
improvement on TCS), with very simple and intuitive rules. The results are
found to be consistent across varying driving conditions.

Chapter 6: Global Optimality

1. The developed GHS outperforms the GECMS (with up to 1.82% margin), thus
disproving the notion of approximate optimal solution for the GECMS.

2. Results, from both this work and literature, are used to make the case for the
limited validity of designing advanced control strategies on simplistic models.

3. Alternative benchmarking methods and concepts are proposed, whereof only

the GHS is implemented.

Chapter 7: Control Sensitivity Analysis

1. A sensitivity study of control strategies, the first of its kind, was conducted for:
tuning parameters; effectiveness of SSSs; initial battery conditions; and varying
driving cycles. This provided a deeper insight into each control strategy.

2. The superiority of the novel heuristic strategies (XOS and OPSS) over the
conventional heuristic strategies (PFCS and TCS) is further shown by demon-
strating more robustness to tuning errors.

3. The significant impact of the SSS on the fuel economy and the relative perfor-
mance of control strategies is exposed. The results justify the superiority of
the novel heuristic strategies for a modern HEV.
250 Chapter 8

8.2 Future Research Direction

This section highlights some of the suggested future paths of research.

Chapter 2: Vehicle Model

1. Many components should be further refined, in particular the DC-DC converter

and the CVT. The engine and battery models should be developed further, to
allow the modeling of emissions and battery degradation.

2. Components with various power ratings should be modeled, allowing control

strategies to be tested on different powertrains.

3. It would be useful to conduct hardware in the loop (HiL) simulations, or even

implement control strategies in real vehicles.

Chapter 3: Conventional Strategies

1. A real-time ECMS should be implemented to act as a better benchmark for

the EMMS, as well as to inform the discussion in Chapter 6.

2. Fuzzy logic controllers (FLCs) should be implemented to provide a fuller pic-

ture of the rule-based strategies.

3. More generally, wide types of strategies should be implemented for a large

benchmarking exercise.

Chapter 4: Efficiency Maximizing Map Strategies

1. The concept of replenishing efficiency should be further refined, ideally allowing

real-time estimation during driving in an intuitive way.

2. The strategies should be tuned more broadly (especially EMMS2), as exposed

in Section 7.4. The base values for the replenishing efficiencies for EMMS2
should be selected more rigorously.

3. It would be interesting to try to use more dynamic expressions for the efficien-
cies rather than the steady state maps.
Conclusion 251

Chapter 5: Heuristic Strategies

1. Further heuristic strategies can be designed based on the design principles

presented in Section 5.1. An exhaustive benchmarking exercise might be in-
sightful.

2. The performance results of the XOS were not as impressive for the model
used in this work, as compared to the previous results in [15]. The impact of
powertrain sizing on control strategies would be a very useful study.

3. The use of fuzzy logic control (FLC) should be explored.

Chapter 6: Global Optimality

1. It would be useful if DP solutions on varying model complexities could be

systematically compared to result of a high-fidelity model or a real vehicle.

2. A more powerful GHS (or alternative) should be designed to provide a better

indication of how much the GECMS is lagging the global optimal solution.

3. New concepts of control space-constrained optimal solutions should be pro-

posed (building on the brief discussion in Section 6.2.2), as they might be
more valuable as benchmarks.

Chapter 7: Control Sensitivity Analysis

1. There are several other factors for which a sensitivity study would be of inter-
est: component sizing, hybridization, or component temperatures.

2. The influence of the SSS on control strategies is dramatic, and definitely merits
further study. This should also consider emissions and drivability though.

3. Sensitivity to driving conditions (including road slopes) should be studied fur-

ther, including tests with mixed driving cycles, as opposed to repeating the
same for multiple iterations. The EMMS2 performance on the NEDC in par-
ticular raises this flag.
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