Lino Guzzella · Antonio Sciarretta
`
`Vehicle Propulsion Systems
`
`1
`
`PAICE 2033
`BMW v. Paice
`IPR2020-01386
`
`

`

`Contents
`
`1
`
`1
`Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`1
`1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`2
`1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`5
`1.3 Upstream Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`1.4 Energy Density of On-Board Energy Carriers . . . . . . . . . . . . . . . 10
`1.5 Pathways to Better Fuel Economy . . . . . . . . . . . . . . . . . . . . . . . . . 12
`
`2 Vehicle Energy and Fuel Consumption – Basic Concepts . . . 13
`2.1 Vehicle Energy Losses and Performance Analysis . . . . . . . . . . . . 13
`2.1.1 Energy Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
`2.1.2 Performance and Drivability . . . . . . . . . . . . . . . . . . . . . . . . 18
`2.1.3 Vehicle Operating Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
`2.2 Mechanical Energy Demand in Driving Cycles. . . . . . . . . . . . . . . 21
`2.2.1 Test Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
`2.2.2 Mechanical Energy Demand . . . . . . . . . . . . . . . . . . . . . . . . 23
`2.2.3 Some Remarks on the Energy Consumption . . . . . . . . . . 27
`2.3 Methods and Tools for the Prediction of Fuel Consumption . . . 32
`2.3.1 Average Operating Point Approach . . . . . . . . . . . . . . . . . . 32
`2.3.2 Quasistatic Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
`2.3.3 Dynamic Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
`2.3.4 Optimization Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
`2.3.5 Software Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
`
`3
`
`IC-Engine-Based Propulsion Systems . . . . . . . . . . . . . . . . . . . . . . 43
`3.1 IC Engine Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
`3.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
`3.1.2 Normalized Engine Variables . . . . . . . . . . . . . . . . . . . . . . . . 44
`3.1.3 Engine Efficiency Representation . . . . . . . . . . . . . . . . . . . . 45
`3.2 Gear-Box Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
`3.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
`3.2.2 Selection of Gear Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
`
`2
`
`

`

`X
`
`Contents
`
`3.2.3 Gear-Box Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
`3.2.4 Losses in Friction Clutches and Torque Converters . . . . . 51
`3.3 Fuel Consumption of IC Engine Powertrains . . . . . . . . . . . . . . . . 54
`3.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
`3.3.2 Average Operating Point Method . . . . . . . . . . . . . . . . . . . . 54
`3.3.3 Quasistatic Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
`
`4 Electric and Hybrid-Electric Propulsion Systems . . . . . . . . . . 59
`4.1 Electric Propulsion Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
`4.2 Hybrid-Electric Propulsion Systems . . . . . . . . . . . . . . . . . . . . . . . . 60
`4.2.1 System Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
`4.2.2 Power Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
`4.2.3 Concepts Realized . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
`4.2.4 Modeling of Hybrid Vehicles . . . . . . . . . . . . . . . . . . . . . . . . 69
`4.3 Electric Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
`4.3.1 Quasistatic Modeling of Electric Motors . . . . . . . . . . . . . . 74
`4.3.2 Dynamic Modeling of Electric Motors . . . . . . . . . . . . . . . . 89
`4.3.3 Causality Representation of Generators . . . . . . . . . . . . . . 90
`4.4 Batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
`4.4.1 Quasistatic Modeling of Batteries . . . . . . . . . . . . . . . . . . . 95
`4.4.2 Dynamic Modeling of Batteries . . . . . . . . . . . . . . . . . . . . . 103
`4.5 Supercapacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
`4.5.1 Quasistatic Modeling of Supercapacitors. . . . . . . . . . . . . . 111
`4.5.2 Dynamic Modeling of Supercapacitors. . . . . . . . . . . . . . . . 115
`4.6 Electric Power Links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
`4.6.1 Quasistatic Modeling of Electric Power Links . . . . . . . . . 117
`4.6.2 Dynamic Modeling of Electric Power Links . . . . . . . . . . . 117
`4.7 Torque Couplers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
`4.7.1 Quasistatic Modeling of Torque Couplers . . . . . . . . . . . . . 119
`4.7.2 Dynamic Modeling of Torque Couplers . . . . . . . . . . . . . . . 120
`4.8 Power Split Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
`4.8.1 Quasistatic Modeling of Power Split Devices . . . . . . . . . . 121
`4.8.2 Dynamic Modeling of Power Split Devices . . . . . . . . . . . . 126
`
`5 Non-electric Hybrid Propulsion Systems . . . . . . . . . . . . . . . . . . . 131
`5.1 Short-Term Storage Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
`5.2 Flywheels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
`5.2.1 Quasistatic Modeling of Flywheel Accumulators . . . . . . . 137
`5.2.2 Dynamic Modeling of Flywheel Accumulators . . . . . . . . . 138
`5.3 Continuously Variable Transmissions . . . . . . . . . . . . . . . . . . . . . . . 140
`5.3.1 Quasistatic Modeling of CVTs . . . . . . . . . . . . . . . . . . . . . . 141
`5.3.2 Dynamic Modeling of CVTs . . . . . . . . . . . . . . . . . . . . . . . . 144
`5.4 Hydraulic Accumulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
`5.4.1 Quasistatic Modeling of Hydraulic Accumulators . . . . . . 146
`5.4.2 Dynamic Modeling of Hydraulic Accumulators . . . . . . . . 152
`
`3
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`Contents
`
`XI
`
`5.5 Hydraulic Pumps/Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
`5.5.1 Quasistatic Modeling of Hydraulic Pumps/Motors . . . . . 154
`5.5.2 Dynamic Modeling of Hydraulic Pumps/Motors . . . . . . . 156
`5.6 Pneumatic Hybrid Engine Systems . . . . . . . . . . . . . . . . . . . . . . . . 157
`5.6.1 Modeling of Operation Modes . . . . . . . . . . . . . . . . . . . . . . . 158
`
`6 Fuel-Cell Propulsion Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
`6.1 Fuel-Cell Electric Vehicles and Fuel-Cell Hybrid Vehicles . . . . . 165
`6.1.1 Concepts Realized . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
`6.2 Fuel Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
`6.2.1 Quasistatic Modeling of Fuel Cells . . . . . . . . . . . . . . . . . . . 179
`6.2.2 Dynamic Modeling of Fuel Cells . . . . . . . . . . . . . . . . . . . . . 193
`6.3 Reformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
`6.3.1 Quasistatic Modeling of Fuel Reformers . . . . . . . . . . . . . . 200
`6.3.2 Dynamic Modeling of Fuel Reformers . . . . . . . . . . . . . . . . 204
`
`7
`
`Supervisory Control Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
`7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
`7.2 Heuristic Control Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
`7.3 Optimal Control Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
`7.3.1 Optimal Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
`7.3.2 Optimization Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
`7.3.3 Real-time Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . 219
`
`8 Appendix I – Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
`8.1 Case Study 1: Gear Ratio Optimization . . . . . . . . . . . . . . . . . . . . 227
`8.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
`8.1.2 Software Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
`8.1.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
`8.2 Case Study 2: Dual-Clutch System - Gear Shifting . . . . . . . . . . . 231
`8.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
`8.2.2 Model Description and Problem Formulation . . . . . . . . . . 231
`8.2.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
`8.3 Case Study 3: IC Engine and Flywheel Powertrain . . . . . . . . . . . 234
`8.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
`8.3.2 Modeling and Experimental Validation . . . . . . . . . . . . . . . 236
`8.3.3 Numerical Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
`8.3.4 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
`8.4 Case Study 4: Supervisory Control for a Parallel HEV. . . . . . . . 241
`8.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
`8.4.2 Modeling and Experimental Validation . . . . . . . . . . . . . . . 241
`8.4.3 Control Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
`8.4.4 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
`8.5 Case Study 5: Optimal Rendez-Vous Maneuvers . . . . . . . . . . . . . 251
`8.5.1 Modeling and Problem Formulation . . . . . . . . . . . . . . . . . . 251
`
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`XII
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`8.5.2 Optimal Control for a Specified Final Distance . . . . . . . . 253
`8.5.3 Optimal Control for an Unspecified Final Distance . . . . 257
`8.6 Case Study 6: Fuel Optimal Trajectories of a Racing FCEV . . . 261
`8.6.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
`8.6.2 Optimal Control
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
`8.6.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
`8.7 Case Study 7: Optimal Control of a Series Hybrid Bus . . . . . . . 270
`8.7.1 Modeling and Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
`8.7.2 Optimal Control
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
`8.7.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
`8.8 Case Study 8: Hybrid Pneumatic Engine . . . . . . . . . . . . . . . . . . . 280
`8.8.1 HPE Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
`8.8.2 Driveline Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
`8.8.3 Air Tank Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
`8.8.4 Optimal Control Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . 284
`8.8.5 Optimal Control Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
`
`9 Appendix II – Optimal Control Theory . . . . . . . . . . . . . . . . . . . . 289
`9.1 Parameter Optimization Problems . . . . . . . . . . . . . . . . . . . . . . . . . 289
`9.1.1 Problems Without Constraints . . . . . . . . . . . . . . . . . . . . . . 289
`9.1.2 Numerical Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
`9.1.3 Minimization with Equality Constraints . . . . . . . . . . . . . . 293
`9.1.4 Minimization with Inequality Constraints . . . . . . . . . . . . . 296
`9.2 Optimal Control
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
`9.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
`9.2.2 Optimal Control for the Basic Problem . . . . . . . . . . . . . . . 298
`9.2.3 First Integral of the Hamiltonian . . . . . . . . . . . . . . . . . . . . 302
`9.2.4 Optimal Control with Specified Final State . . . . . . . . . . . 304
`9.2.5 Optimal Control with Unspecified Final Time . . . . . . . . . 305
`9.2.6 Optimal Control with Bounded Inputs . . . . . . . . . . . . . . . 306
`
`10 Appendix III – Dynamic Programming . . . . . . . . . . . . . . . . . . . . 311
`10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
`10.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
`10.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
`10.2.2 Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
`10.3 Implementation Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
`10.3.1 Grid Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
`10.3.2 Nearest Neighbor or Interpolation . . . . . . . . . . . . . . . . . . . 316
`10.3.3 Scalar or Set Implementation . . . . . . . . . . . . . . . . . . . . . . . 318
`
`References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
`
`5
`
`

`

`1 I
`
`ntroduction
`
`This introductory chapter shows how the problems discussed in this text are
`embedded in a broader setting. First a motivation for and the objective of the
`subsequent analysis is introduced. After that the complete energy conversion
`chain is described, starting from the available primary energy sources and
`ending with the distance driven. Using average energy conversion efficiency
`values, some of the available options are compared. This analysis shows the
`importance of the “upstream” processes. The importance of the selected on-
`board energy carrier (“fuel”) is stressed as well. In particular its energy density
`and the safety issues connected with the refueling process are emphasized. The
`last section of this first chapter lists the main options available for reducing
`the energy consumption of passenger vehicles.
`
`1.1 Motivation
`
`The main motivation to write this book is the inexorably increasing number
`of passenger cars worldwide. As Fig. 1.1 shows, some 800 million passenger
`cars are operated today. More interesting than this figure is the trend that
`is illustrated in this figure for the example of the United States of America
`(the same trend is observed in Japan and Europe): in wealthy societies the
`car density saturates at a ratio of approximately 400 to 800 cars per 1000
`inhabitants.
`It is corroborated empirically that the demand for personal transportation
`increases with the economic possibilities of a society [220]. Therefore, if the car
`density mentioned above is taken as the likely future value for other regions of
`the world, serious problems are to be expected. Countries such as China (1.3
`billion inhabitants) or India (1.1 billion inhabitants) in the year 2007 have car
`densities of around 30 cars per 1000 inhabitants. Accordingly, in the next 20
`years the car density in these countries will increase substantially, which will
`further increase the pressure on fuel prices and cause serious problems to the
`environment.
`
`6
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`

`2
`
`1 Introduction
`
`million cars
`800
`
`400
`
`all countries
`
`USA
`
`1980
`
`2000
`
`year
`
`Fig. 1.1. Schematic representation of the development of the number of passenger
`cars operated worldwide.
`
`In the face of these trends, it is clear that new fuel sources must be de-
`veloped and that the fuel consumption of passenger cars must be reduced
`substantially. This text focuses on the second approach.
`
`1.2 Objectives
`
`The main objectives of this text are to introduce mathematical models and
`optimization methods that permit a systematic minimization of the energy
`consumption of vehicle propulsion systems. The objects of this analysis are
`passenger cars, i.e., vehicles that
`• are autonomous and do not depend on fixed energy-providing grids;
`• have a refueling time that is negligible compared to the driving time be-
`tween two refueling events;
`• can transport two to six persons and some payload; and
`• accelerate in approximately 10 to 15 seconds from 0 to 100 km/h, or can
`drive uphill a 5% ramp at the legal top speed, respectively.1
`
`These requirements, which over the last one hundred years have evolved
`to a quasi-standard profile, substantially reduce the available options. Par-
`ticularly the first and the second requirement can only be satisfied by few
`on-board energy storage systems, and the performance requirements can only
`be satisfied by propulsion systems able to produce a maximum power that is
`substantially larger than the power needed for most driving conditions.
`A key element in all considerations is the on-board energy carrier system.
`This element must:
`1 These numerical values are only indicative. It goes without saying that the per-
`formance range is very wide.
`
`7
`
`

`

`1.2 Objectives
`
`3
`
`• provide the highest possible energy density2;
`• allow for the shortest possible refueling time; and
`• be safe and cause no environmental hazards in production, operation, and
`recycling.
`
`The number of components that are necessary to realize modern and in
`particular future propulsion systems is inexorably increasing. Improved per-
`formance and fuel economy can only be obtained with complex devices. Of
`course, these subsystems influence each other. The best possible results are
`thus not obtained by an isolated optimization of each single component. Opti-
`mizing the entire system, however, is not possible with heuristic methods due
`to the “curse of exponential growth.” The only viable approach to cope with
`this dilemma is to develop mathematical models of the components and to
`use model-based numerical methods to optimize the system structure and the
`necessary control algorithms. These models must be able to extrapolate the
`system behavior. In fact, such an optimization usually takes place before the
`actual components are available or requires the devices to operate in unex-
`pected conditions. For these reasons, only first-principle models, i.e., models
`that are based on physical laws, will be used in this text.
`Of course, some of the mathematical models and methods introduced in
`this text may be useful for the design of other classes of vehicles (trains,
`heavy-duty trucks, etc.). However, there are clear differences3 that render the
`passenger car optimization problem particularly interesting.
`At least three energy conversion steps are relevant for a comprehensive
`analysis of the energy consumption of passenger cars. As illustrated in Fig. 1.2,
`the actual energy source is one of the available primary energy carriers (chem-
`ical energy in fossil hydrocarbons, solar radiation used to produce bio mass
`or electric energy, nuclear energy, etc). In a first step, this energy is converted
`to an energy carrier that is suitable for on-board storage, i.e., to a “fuel”
`(examples are gasoline, hydrogen, etc.). This “fuel” is then converted by the
`propulsion system to mechanical energy that, in part, may be stored as ki-
`netic or potential energy in the vehicle. The third energy transformation is
`determined by the vehicle parameters and the driving profile. In this step,
`the mechanical energy produced in the second conversion step is ultimately
`dissipated to thermal energy that is deposited to the ambient. The terms
`“well-to-tank,” “tank-to-vehicle,” and “vehicle-to-miles” are used in this text
`to refer to these three conversion steps. Unfortunately, all of these conversion
`processes cause substantial energy losses.
`
`2 The energy density here is defined as the amount of net energy available for
`propulsion purposes divided by the mass of the energy carrier necessary to gen-
`erate that propulsion energy, including all containment elements but not the
`on-board energy transformation devices.
`3 For instance, the autonomy requirement and the dominance of part-load operation
`will be relevant for the optimization problems.
`
`8
`
`

`

`4
`
`1 Introduction
`
`primary energy
`sources
`
`upstream
`energy
`conversion
`
`on-board
`energy storage
`
`on-board
`energy
`conversion
`
`vehicle kinetic and
`potential energy
`
`vehicle
`energy
`consumption
`
`driving and
`altitude profile
`
`100
`
`50
`
`"well-to-tank"
`
`H2
`
`+ –
`
`"tank-to-vehicle"
`
`"vehicle-to-miles"
`
`Fig. 1.2. The main elements of the energy conversion scheme.
`
`0
`
`100
`
`200
`
`800
`
`900
`
`1000
`
`1100
`
`1200
`
`This text will not address any control problems pertaining to the “well-to-
`tank” energy conversion. The systems used for that conversion are very large
`power plants, refineries, or other process engineering systems. Of course, their
`average efficiency values and pollutant emission have an important impact on
`the economy and ecology. However, the problems arising in that area and the
`methods required to solve those problems belong to a different class.
`In the next section an overview of the most important energy conversion
`approaches is presented. With this information, a preliminary estimation of
`the total energy consumption is possible. Note that a correct comparison is
`not easy, if at all possible.4 Readers interested in a broader discussion are
`referred to [34].
`The main physical phenomena influencing the “vehicle-to-miles” energy
`conversion will be discussed in Chap. 2. That chapter will mainly introduce
`descriptions that are quasistatic (this term will be precisely defined below),
`
`4 For instance, the total “well-to-miles” carbon dioxide emissions are often used to
`compare two competing approaches. However, such a discussion is not complete
`unless the “gray” energy invested in the vehicles, refineries and plants is consid-
`ered. Even more difficult: how to take into account the problems associated with
`nuclear waste repositories, landscape degradation caused by windmills, or nitric
`oxide emission of coal-fired power plants?
`
`9
`
`

`

`1.3 Upstream Processes
`
`5
`
`but also dynamic models will be presented. In this context, it is important
`to understand the impact of the driving profile that the vehicle is assumed
`to follow. As mentioned above, only those effects are considered that have a
`substantial influence on the energy consumption.
`The main emphasis of this text is on the modeling and optimization of the
`“tank-to-vehicle” energy conversion systems. For this problem suitable math-
`ematical models of the most important devices will be introduced in Chaps. 3
`through 6. Chapter 7 presents methods with which the energy consumption
`can be minimized. All of these methods are model-based, i.e., they rely on
`the mathematical models derived in the previous chapters and on systematic
`optimization procedures to find (local) minima of precisely cast optimization
`problems. Eight case studies are included in Appendix I. Appendix II then
`summarizes the most important facts of parameter optimization and opti-
`mal control theory and Appendix III introduces the main ideas of dynamic
`programming.
`
`1.3 Upstream Processes
`
`As mentioned above, a detailed analysis of the “well-to-tank” energy conver-
`sion processes is not in the scope of this text. However, the efficiency and the
`economy of these systems are important aspects of a comprehensive analysis.
`For this reason a rather preliminary but nevertheless instructive overview of
`the main energy conversion systems is given in this section.
`Figure 1.3 shows a part of that complex network. The efficiency numbers
`given in that figure are approximate and are valid for available technology.
`The CO2 factors relate the amount of carbon dioxide emitted by using one
`energy unit of natural gas or coal to the amount emitted when using one
`energy unit of oil.5 Solar and nuclear primary energy sources are assumed to
`emit no CO2, i.e., the gray energy and the associated CO2 emission are not
`shown in that figure.
`Only three systems are considered in Fig. 1.3 for the conversion of “fuel”
`to mechanical energy: a spark-ignited (SI) or gasoline internal combustion
`engine (ICE), a compression-ignited (CI) or Diesel ICE, and an electric mo-
`tor. Average “tank-to-vehicle” efficiencies of these prime movers are shown in
`Fig. 1.3 as well.6 The mechanical energy consumption (the “vehicle-to-miles”
`efficiency) is approximated by an equation that is valid for the European test
`cycle (this expression will be introduced in Sect. 2.2). With the information
`shown in Fig. 1.3 it is easy to make some preliminary, back-of-the-envelope-
`style calculations that, despite the many uncertainties, are quite instructive.
`
`5 The CO2 factors reflect the different chemical composition and the different heat-
`ing values. The base line is defined in Table 1.1.
`6 The peak efficiencies of all of these devices are (substantially) higher. However,
`the relevant data are the cycle-averaged efficiencies, which are close to the values
`shown in Fig. 1.3.
`
`10
`
`

`

`6
`
`1 Introduction
`
`Fossil fuels
`Numbers: CO -factors
`2
`
`Oil
`1
`
` Nat. Gas
`0.75
`
`Coal
`1.5
`
`Solar energy
`
`Uranium
`
`Biomass
`0.2%
`
`Refinery, transportation
`
`90% 86%
`
`91%
`
`80%
`
`EU
`PP
`
`Diesel
`PP
`
`Combi
`PP
`
`47%
`
`48%
`
`55%
`
`Coal
`PP
`
`35%
`
`Hydro
`PP
`
`Solar
`PP
`
`Nuclear
`PP
`
`0.1%
`
`23%
`
`32%
`
`Compr.
`94%
`
`Diesel
`
`Gaso-
`line
`
`CH
`4
`
`Bio Methanol
`47%
`
`NG Methanol
`70%
`
`NG H
`2
`74%
`
`Reformer
`85%
`
`Grid
`94%
`
`Liquefaction
`75%
`
`H
`
`2
`
`H2
`
`Compr. with electricity
`94%
`
`Electrolysis
`76%
`
`Fuel cell 40%
`
`Battery, power
`electronics 80%
`
`SI engine 17% (for CNG 16%)
`Diesel 20%
`(incl. transmission losses)
`
`Electric
`drive 90%
`
`Vehicle
`
`4
`EMVEG-95 (cid:1) 1.9 10 (cid:2)
`(cid:2)
`
`A f
`
`cd(cid:2)
`
`+ 840 (cid:2)
`
`cr
`
`(cid:2) m + 10 (cid:2) m
`v
`
`v
`
`kJ /100 km
`
`Fig. 1.3. Different paths to convert a primary energy source to mechanical energy
`needed to drive a car in the MVEG-95 test cycle. Source: [69] and own data.
`
`For that purpose Table 1.1 summarizes some of the most important parame-
`ters of the fuels considered below.
`
`Table 1.1. Main parameters of some important energy carriers (lower heating value
`Hl, hydrogen-to-carbon ration H/C, and mass of CO2 emitted per mass fuel burned
`ν); CNG = compressed natural gas.
`
`oil
`CNG (≈ methane)
`coal (≈ carbon)
`hydrogen
`
`Hl (M J/kg)
`43
`50
`34
`121
`
`H/C
`≈ 2
`4
`0
`∞
`
`ν
`3.2
`2.75
`3.7
`0
`
`11
`
`

`

`1.3 Upstream Processes
`
`7
`
`Figure 1.4 shows the “well-to-miles” carbon dioxide emissions of three ICE-
`based powertrains. The vehicle assumed in these considerations is a standard
`mid-size passenger car. The efficiency values of the gasoline and Diesel engines
`are standard values as well. The efficiency of CNG engines is usually slightly
`smaller than the one of gasoline SI engines [12].
`Of course this analysis neglects several important factors, for instance the
`greenhouse potential of methane losses in the fueling infrastructure. Neverthe-
`less, the results obtained indicate that increasing the numbers of CNG engines
`could be one option to reduce CO2 emissions with relatively small changes in
`the design of the propulsion system. Unfortunately, as mentioned before, the
`“well-to-miles” CO2 emission levels are just one element of the problem space.
`In this case, the reduced energy density of CNG as on-board energy carrier
`has, so far, inhibited a broader market penetration of this vehicle class. The
`next section will show more details on this aspect.
`
`25 kg CO2 /100 km 21 kg CO2 /100 km
`oil
`
`20 kg CO2 /100 km
`natural gas
`
`refinery, transportation
`0.86
`
`gasoline
`
`0.90
`
`Diesel
`
`0.86
`
`CNG
`
`0.17
`
`SI-ICE
`
`0.20
`
`Diesel
`
`0.16
`
`SI-ICE
`
`vehicle
`50 MJ/100 km
`
`vehicle
`50 MJ/100 km
`
`vehicle
`50 MJ/100 km
`
`Fig. 1.4. “Well-to-miles” CO2 emission of three conventional powertrains. The ve-
`hicle is described by the parameters m = 1600 kg, cd · Af = 0.86 m2, andc r = 0.013
`(see Chap. 2). The fuel properties are defined in Table 1.1.
`
`Figure 1.5 shows what amount of CO2 emissions can be expected when a
`battery-electric propulsion system is employed. The base vehicle is assumed
`to have the same7 parameters as the one used to compute the values shown
`in Fig. 1.4. Several primary energy sources are compared in this analysis.
`The two CO2-neutral8 energy sources (solar and nuclear energy) produce no
`
`7 Of course the batteries substantially increase the vehicle mass. Here the (opti-
`mistic) assumption is adopted that the recuperation capabilities of the battery
`electric system compensate for the losses that are caused by this additional mass.
`8 As mentioned, only the CO2 emission caused by the operation of the power plants
`are considered.
`
`12
`
`

`

`8
`
`1 Introduction
`
`carbon dioxide emission. However, if the electric energy required to charge
`the batteries is generated using fossil primary energy sources, surprisingly
`different CO2 emission levels result.
`In the case of a natural-gas-fired combined-cycle power plant (PP) the CO2
`emission levels are substantially lower than those of traditional ICE-based
`propulsion systems. However, if the other limit case (coal-fired steam turbines)
`is taken into consideration, the “well-to-miles” carbon dioxide emission levels
`of a battery-electric car become even worse than those of the worst ICE-based
`propulsion system.9 Moreover, in the next section it will be shown that the
`energy density of batteries is so small that battery electric vehicles cannot
`satisfy the specifications of a passenger car as defined in Sect. 1.2.
`
`29 kg CO2 /100 km
`coal
`
`8 kg CO2 /100 km
`natural gas
`
`0 kg CO2/100 km
`solar
`nuclear
`
`transportation
`0.8
`
`0.91
`
`steam turbines PP
`0.35
`
`combined cycle PP
`0.55
`
`……
`
`0.23-0.32
`
`grid
`
`battery
`
`EM
`
`0.94
`
`0.80
`
`0.90
`
`vehicle
`50 MJ/100 km
`
`Fig. 1.5. “Well-to-miles” CO2 emission of a battery electric vehicle. Vehicle para-
`meters as in Fig. 1.4. Battery efficiency includes charging, discharging, and power
`electronic losses. The fuel properties are defined in Table 1.1.
`
`As a last example, the estimated “well-to-miles” CO2 emission levels of
`a fuel cell electric vehicle are shown in Fig. 1.6. Again, the vehicle parame-
`ters have been chosen to be the same as in the conventional case. The effi-
`ciency of the fuel cell system has been assumed to be around 0.40. Despite
`many more optimistic claims, experimental evidence, as the one published in
`
`9 Of course, low CO2 primary energy sources should first be used to replace the
`worst polluting power plants that are part of the corresponding grid. In this
`sense, each unit of additional electric energy used must be considered to have been
`produced by the power plant in the grid that has the worst efficiency. Accordingly,
`in the example shown in Fig. 1.5 the relevant CO2 emission number is the one
`valid for coal-fired power plants.
`
`13
`
`

`

`1.3 Upstream Processes
`
`9
`
`[212], has shown that the net efficiency of a fuel cell system will probably
`be close to that figure.10 Even more uncertain are the efficiencies of on-board
`gasoline-to-hydrogen reformers. Including all auxiliary devices, a net efficiency
`of approximately 60–70% may be expected.
`
`18 kg CO2 /100 km 12 kg CO2 /100 km
`natural gas
`oil
`
`21 kg CO 2 /100 km
`
`0.91
`
`combined cycle PP
`0.55
`electrolysis
`0.76
`
`0.90
`EM
`
`0.40
`
`FC
`
`2H
`
`compression
`0.94
`
`H tank
`2
`
`refinery, transportation
`0.91
`0.86
`
`steam ref.
`0.74
`
`gasoline tank
`
`OB reformer
`0.65 (?)
`
`vehicle
`
`50 MJ/100 km
`
`Fig. 1.6. “Well-to-miles” CO2 emission of a fuel cell electric vehicle. Vehicle para-
`meters as in Fig. 1.4. The efficiency of the on-board gasoline-to-hydrogen reformer
`is not experimentally verified. The fuel properties are defined in Table 1.1.
`
`The main insight that can be gained from Fig. 1.6 is that as long as fossil
`primary energy sources are used fuel cell electric vehicles have a potential to
`reduce the “well-to-miles” CO2 emission only if the hydrogen is produced in
`a steam reforming process using natural gas as primary energy source. As
`shown in Fig. 1.6, fuel-cell-based powertrains have excellent “tank-to-vehicle”
`but rather poor “well-to-tank” efficiencies. This fact will become very impor-
`tant once renewable primary energy sources are available on a large scale. If
`this comes true, then the “upstream” CO2 emission levels are zero and the
`only concern will be to utilize the available on-board energy as efficiently as
`possible. In this situation fuel-cell-based propulsion systems might prove to
`be the best choice.
`10 Fuel cells must be supercharged to achieve sufficient power densities and to exploit
`in the best possible way the expensive electrochemical converters. The compre