Pamvec PhD_Thesis Editado

Parametric Modelling Of Energy Consumption

In Road Vehicles

A thesis submitted for the degree of Doctor of Philosophy at

The University of Queensland in February 2005

Andrew G. Simpson

Sustainable Energy Research Group

School of Information Technology and Electrical Engineering

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Candidate's Statement of Originality

The work presented in this thesis is, to the best of my knowledge and belief, original, except

as acknowledged in the text, and has not been submitted, either in whole or in part, for a

degree at this university or any other university.

Andrew G. Simpson

……………………………………………………………

Dr Geoffrey R. Walker – Principal Advisor

……………………………………………………………

Copyright © 2005 by Andrew G. Simpson

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Acknowledgements

This research was conducted under a postgraduate research scholarship funded by the School

of Information Technology and Electrical Engineering.

Thanks to my advisory team – Dr Geoff Walker and Dr Gordon Wyeth – for their guidance

and faith in my ability to pursue this largely self-initiated research topic.

Thanks also to Prof. Simon Kaplan, Kathleen Williamson, Helen Lakidis and Maureen

Shields for their ongoing financial and administrative support.

Special thanks to close friends/colleagues for their interest and support of my research, their

thought-provoking discussions and feedback on my work, and contribution to my overall

development as a researcher and engineering professional:

• Dr Geoff Walker, Dr Andrew Dicks, Paul Sernia, David Finn, Matthew Greaves, Ben

Guymer, Justin Bray and Larry Weng – The University of Queensland

• Deborah Andrews – South Bank University, London

• Karin Öhgren – Lund University, Sweden

• Mark Northage and Campbell James – HybridAuto Pty Ltd

• Dr Conrad Stacey, Dr Peter Gehrke, Dr Nick Agnew, Colin Eustace, Dr Matthew

Bilson and Jodi Meissner – Maunsell Australia Pty Ltd

Finally, the greatest thanks to Mum, Dad, Catherine and Belinda for their love, understanding

and encouragement.

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List of Publications and Presentations

Publications and Presentations by the Candidate Relevant to the Thesis

Simpson A.G. (2004) “Modelling and Simulation of Vehicle Performance and Energy

Consumption”, presented at the US National Renewable Energy Laboratory, December 10,

Golden, CO, USA.

Simpson A.G. & Walker G.R. (2004) “A Parametric Analysis Technique for Design of Fuel

Cell and Hybrid-Electric Vehicles”, paper no. 2003-01-2300, Transactions of the SAE –

Journal of Engines, Society of Automotive Engineers International, Warrendale. Also printed

in “Hybrid Vehicle and Energy Storage Technologies”, publication no. SP-1789, Society of

Automotive Engineers International, Warrendale. Also presented at the 2003 SAE

International Future Transportation Technology Conference, June 23-25, Costa Mesa, CA,

USA.

Simpson A.G. (2004) “Full-cycle assessment of alternative fuels for light-duty road vehicles

in Australia”, Proceedings of the 2004 World Energy Congress – Youth Symposium,

September 5-9, Sydney, NSW, Australia.

Additional Publications and Presentations by the Candidate Relevant to the Thesis but not Forming Part of it

Simpson A.G. (2004) “Comparing Future Alternative Fuels and Powertrain Technologies for

Vehicles in Australia”, Proceedings of the ARC Centre for Functional Nanomaterials

Hydrogen Workshop, November 5, Brisbane, QLD, Australia.


Vehicles in Australia”, Environmental Engineering Division Seminar, 21 September, The

University of Queensland, Australia.

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in Australia”, Proceedings of the 7th Environmental Research Conference (EERE 2003),

Marysville, VIC, Australia.


Vehicles”, School of Information Technology and Electrical Engineering Seminar, November

6, The University of Queensland, Australia.


Vehicles”, presentation to the ANZSES Sustainable Transport Forum, October 20, Brisbane,

QLD, Australia.

Simpson A.G., Greaves M.C. & Walker G.R. (2003) “Electric Power Source Selection for the

UltraCommuter”, Proceedings of the Regional Inter-University Postgraduate Electrical and

Electronic Engineering Conference (RIUPEEEC), Hong Kong.

Simpson A.G. (2003) “Comparison of power source technologies for electric-drive vehicles”,

Sustainable Energy Research Group Seminar, May 27, The University of Queensland,

Australia.

Simpson A.G. & Andrews S.D. (2002) “Future Directions for the Sustainability of the

Australian Automobile”, Proceedings of the 6th Annual Environmental Engineering Research

Event, Blackheath, NSW, Australia.

Simpson A., Walker G., Greaves M., Finn D. & Guymer B. (2002) “The UltraCommuter: A

Viable and Desirable Solar-Powered Commuter Vehicle”, Proceedings of the 2002

Australasian Universities Power Engineering Conference, Melbourne, VIC, Australia.

Simpson A.G. (2001) “Automotive Propulsion Technology for the 21st century”, presentation

to Energy Systems Research Group Meeting, November 5, School of Information Technology

and Electrical Engineering, The University of Queensland, Australia.

Simpson A.G. (2001) “Design Approaches for Electric-drive Hybrid Vehicle Propulsion

Systems”, Ph.D Confirmation of Candidature Seminar, November 13, School of Information

Technology and Electrical Engineering, The University of Queensland, Australia.

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Abstract

This thesis presents a novel approach to modelling energy consumption in road vehicles – the

Parametric Analytical Model of Vehicle Energy Consumption (PAMVEC).

The technique is offered as a complement to existing vehicle modelling tools, the majority of

which are dynamic vehicle simulators such as ADVISOR. Dynamic vehicle simulators are

powerful modelling tools with high precision and accuracy (error typically <5%), and this

makes them ideally suited to detailed simulation, testing and refinement of vehicle designs as

part of a design process. However, they can be disadvantaged by their complexity, their need

for detailed powertrain component models (which often are not publicly available), and

excessive computational requirements due to their inherently iterative nature. In the context

of vehicle technology assessment where many vehicles or technologies may need to be

compared, these attributes can make dynamic simulators quite costly and time-consuming to

use. Furthermore, dynamic vehicle simulators rely upon deterministic driving cycles to

represent the driving pattern. Existing cycles have been shown in the literature to be quite

unrepresentative of real-world driving patterns, and this deterministic approach is particularly

unsuited to the modelling of uncertainty. Again, these attributes are not desirable for the

purposes of vehicle technology assessment.

In contrast, the PAMVEC tool is designed to be particularly well-suited to vehicle technology

assessment. Relative to dynamic simulators, the PAMVEC lumped-parameter models are

easier to analyse and interpret, requiring only minimal input data to produce a result, and the

calculations are performed nearly instantaneously. Furthermore, with its parametric

construction, PAMVEC is ideally-suited to performing sensitivity analyses and modelling of

uncertainty. Its features include:

• Parametric analytical expressions for predicting vehicle energy consumption that are

derived from the well-known road load equation

• Parametric analytical expressions to size powertrain components implicitly in terms of

specified performance targets that include driving range

• A novel parametric driving pattern description that encompasses the multiple

dimensions of real-world driving patterns, but is also well-suited to the modelling of

uncertainty

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• Simple component models based on parametric inputs for efficiency and specific

power/energy

• Transparent implementation in a Microsoft Excel spreadsheet with calculations that

occur almost instantaneously.

The convenience of the PAMVEC model is enabled by the central simplifying assumption

that tractive power flow that is reversible (due to vehicle inertia) can be modelled separately

from irreversible power flow (due to vehicle drag). However, this assumption is also the

primary cause of error in the predictions of vehicle energy consumption. PAMVEC

consistently overestimates vehicle energy consumption with errors of <20%. While this error

is large compared to that of dynamic simulators (<5%), it must be considered in the context of

vehicle technology assessment where uncertainties are so great. In contrast, PAMVEC’s

estimates of relative fuel economy are quite accurate, with errors typically <5%. Another

limitation of the PAMVEC tool is that it does not model powertrain component efficiencies

(since these are specified as inputs). Therefore, some important powertrain system

interactions such as the dependence of component efficiency on component size and/or the

driving pattern are not captured in the model.

However, the development of any vehicle modelling tool involve a compromise between

attributes, and the author believes that the development of PAMVEC is well-justified based

on the attributes of existing modelling tools. The thesis commences with a detailed review of

existing vehicle modelling tools and a discussion of their capabilities and limitations. It then

documents the derivation of the PAMVEC model including its key simplifications and

assumptions. The next chapter validates PAMVEC against vehicle test data and benchmarks

it against the ADVISOR dynamic vehicle simulator. In the final chapter, to demonstrate its

suitability to vehicle technology assessment, PAMVEC is applied in a well-to-wheel analysis

to predict the energy consumption of thirty-three vehicles with alternative fuels and

powertrain technologies.

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Table of Contents

1. INTRODUCTION 1

2. TOOLS FOR MODELLING VEHICLE ENERGY CONSUMPTION 5

2.1 Attributes of Vehicle Modelling Tools 5

2.2 Approaches to Modelling Vehicle Energy Consumption 8 2.2.1 Dynamic Vehicle Simulators 8 2.2.2 Lumped-Parameter Models 13

2.3 Approaches to Modelling Vehicle Performance 15 2.3.1 The Link between Vehicle Performance and Energy Consumption 15 2.3.2 Models of Vehicle Performance 16

2.4 Factors Affecting the Choice and Use of Vehicle Modelling Tools 22

2.5 Outcomes of Literature Review 25

3. THE PARAMETRIC ANALYTICAL MODEL OF VEHICLE ENERGY CONSUMPTION (PAMVEC) 27

3.1 The Parametric Road Load Equation 28 3.1.1 Average Road Load Power 28 3.1.2 Average Braking Losses 30

3.2 Driving Pattern Parameters 35

3.3 Powertrain Losses 42 3.3.1 Generic Powertrain Architecture 42 3.3.2 Fuel Cell Hybrid-Electric Vehicles 51 3.3.3 Fuel Cell Electric Vehicles 53 3.3.4 Series Hybrid-Electric Internal Combustion Engine Vehicles 54 3.3.5 Parallel Hybrid-Electric Internal Combustion Engine Vehicles 55 3.3.6 Conventional Internal Combustion Engine Vehicles 56 3.3.7 Battery Electric Vehicles 57

3.4 Vehicle Performance 58 3.4.1 Top Speed 59 3.4.2 Gradability 59 3.4.3 Driving Range 60 3.4.4 Acceleration 60

3.5 Powertrain Component Sizing Strategies and Mass Compounding 73 3.5.1 Fuel Cell Hybrid Electric Vehicles 74 3.5.2 Fuel Cell Electric Vehicles 76 3.5.3 Conventional Internal Combustion Engine Vehicles 76 3.5.4 Parallel Hybrid Electric Vehicles 77 3.5.5 Series Hybrid Electric Vehicles 78 3.5.6 Battery Electric Vehicles 78

3.6 Implementation of the PAMVEC Model 79

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4. PAMVEC VALIDATION 81

4.1 Validation with Published Vehicle Test Data 81 4.1.1 Acceleration performance for the GM HydroGen3 FCEV 81 4.1.2 Fuel consumption for the Holden Commodore ICV 82 4.1.3 Fuel consumption for the Virginia Tech. ZEburban FCHEV 83

4.2 Benchmarking against ADVISOR 84 4.2.1 Vehicle Platform and Driving Pattern 85 4.2.2 Benchmarking Results 87

4.3 Benchmarking for other driving patterns and vehicle platforms 96 4.3.1 Dependence of Error on Vehicle Platform and Driving Pattern 96 4.3.2 Benchmarking Results for Other Driving Patterns 99 4.3.3 Benchmarking Results for Other Vehicle Platforms 102

4.4 Validation Summary 103 4.4.1 Component Sizing and Total Vehicle Mass 103 4.4.2 Vehicle Energy Consumption 104

5. PAMVEC APPLICATION AND SENSITIVITY ANALYSIS 107

5.1 Energy Consumption Comparison 107 5.1.1 Powertrain Architectures 107 5.1.2 Vehicle Platform 108 5.1.3 Driving Pattern 108 5.1.4 Performance Specifications 109 5.1.5 Component Technologies and Energy Consumption Results 109

5.2 Sensitivity Analysis 113 5.2.1 Vehicle Platform Sensitivity 114 5.2.2 Component Specific Power/Energy Sensitivity 116 5.2.3 Component Efficiency Sensitivity 117 5.2.4 Driving Pattern Sensitivity 119 5.2.5 Vehicle Performance Sensitivity 120

5.3 Summary 125

6. CONCLUSION 127

6.1 Future Work 129

REFERENCES 131

APPENDIX A – DRIVING CYCLE PARAMETERS 139

APPENDIX B – VALIDATION STUDY RESULTS 141

Published Vehicle Data 141 Holden Commodore Sedan 141 Virginia Tech ZEburban 142

ADVISOR Benchmarking 143 NEDC 143 UDDS 155 HWFET 166 US06 179 NYCC 191

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NEDC – High MDR 203 HWFET – High MDR 215

APPENDIX C – TANK TO WHEEL ENERGY CONSUMPTION FOR VARIOUS FUELS/POWERTRAINS 227

Petrol ICV 227 LPG ICV 228 LNG ICV 229 CNG ICV 230 Diesel ICV 231 BioDiesel ICV 232 E10 ICV 233 E85 ICV 234 M85 ICV 235 GH2 ICV 236 LH2 ICV 237 Petrol PHEV 238 LPG PHEV 239 LNG PHEV 240 CNG PHEV 241 Diesel PHEV 242 Biodiesel PHEV 243 E10 PHEV 244 E85 PHEV 245 M85 PHEV 246 GH2 PHEV 247 LH2 PHEV 248 Petrol FCEV 249 Methanol FCEV 250 LH2 FCEV 251 GH2 FCEV 252 Petrol FCHEV 253 Methanol FCHEV 254 LH2 FCHEV 255 GH2 FCHEV 256 VRLA BEV 257 NiMH BEV 258 Li-Ion BEV 259

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List of Figures

Figure 2-1: A comparison of vehicle fuel economy of conventional and hybrid-electric

vehicles for various acceleration performances (Plotkin et al, 2001)............... 16

Figure 2-2: The explicit vs. implicit approaches to powertrain component sizing.............. 17

Figure 2-3: The effects of mass-compounding due to vehicle performance ....................... 18

Figure 2-4: The effects of mass-compounding due to vehicle performance including

driving range..................................................................................................... 19

Figure 2-5: The relative fuel economy of different BEV technologies for various driving

ranges calculated for a Ford Escort-style vehicle in Delucchi (2000) .............. 21

Figure 3-1: The PAMVEC model........................................................................................ 28

Figure 3-2: PAMVEC’s decoupling of drag and inertial power flows in the estimation of

braking losses.................................................................................................... 34

Figure 3-3: Overestimation of average braking losses in a representative vehicle platform

for a section of the UDDS driving cycle........................................................... 35

Figure 3-4: Errors in the estimate of outdriveP − (equation 3-19) over a range of mass-to-drag

ratios for several contrasting driving patterns................................................... 36

Figure 3-5: A hypothetical driving pattern with parameter values of vavg = 10m/s, Λ= 1.1

and a~ = 0.1m/s2................................................................................................. 37

Figure 3-6: A hypothetical driving pattern with parameter values of vavg = 10.5m/s (5%

increase), Λ= 1.1 and a~ = 0.1m/s2 ................................................................... 38

Figure 3-7: A hypothetical driving pattern with parameter values of vavg = 10m/s, Λ=

1.155 (5% increase) and a~ = 0.1m/s2................................................................ 39


and a~ = 0.105m/s2 (5% increase)...................................................................... 39

Figure 3-9: Velocity ratio (Λ ) vs. average velocity ( avgv ) for the driving cycles presented

in Appendix A................................................................................................... 41

Figure 3-10: Characteristic acceleration ( a~ ) vs. average velocity ( avgv ) for the driving

cycles presented in Appendix A ....................................................................... 41

Figure 3-11: Generic powertrain architecture........................................................................ 42


drivetrain losses ................................................................................................ 46

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Figure 3-13: Error in the estimate of indriveP − across a range of mass-to-drag ratios for several

different driving cycles......................................................................................47

Figure 3-14: Efficiency vs. load curves for some hypothetical HSED technologies.............49

Figure 3-15: Thermostatic losses due to the cycling of energy through the HSPD ...............50

Figure 3-16: Powertrain architecture for fuel cell hybrid-electric vehicle.............................51

Figure 3-17: Powertrain architecture for fuel cell electric vehicle.........................................53

Figure 3-18: Powertrain architecture for series hybrid-electric vehicle.................................54

Figure 3-19: Powertrain architecture for parallel hybrid-electric vehicle..............................55

Figure 3-20: Powertrain architecture for conventional internal combustion engine vehicle .57

Figure 3-21: Powertrain architecture for battery-electric vehicle ..........................................57

Figure 3-22: The generic shape of the torque-speed curve for a drivetrain ...........................62

Figure 3-23: Torque-speed characteristic of the UQM Technologies PowerPhase 100kW

drive system.......................................................................................................63

Figure 3-24: Modelled vs. actual torque-speed curves for the UQM Technologies drive.....66

Figure 3-25: Modelled vs. actual torque-speed curves using the effective power for the

UQM Technologies drive..................................................................................67

Figure 3-26: Torque-speed curves for (a) a Saturn 1.9L DOHC engine and (b) Siemens 33

kW permanent magnet motor/controller ...........................................................68

Figure 3-27: Torque-speed curve for a drivetrain consisting of the engine shown in Figure 3-

26a combined with a 5-speed transmission.......................................................69

Figure 3-28: Average torque approximation of the engine shown in Figure 3-26.................69


Saturn 1.9L engine (Figure 3-26a) and 5-speed transmission...........................71


Honda EV Plus drive.........................................................................................72

Figure 4-1: The New European Driving Cycle (NEDC)......................................................86

Figure 4-2: Error in the estimate of indriveP − (equation 3-22) for several different driving

patterns across a range of mass to drag ratios assuming (a) no regenerative

braking and (b) full regenerative braking..........................................................97

Figure 5-1: Comparison of equivalent fuel consumption for the 33 vehicles....................112

Figure 5-2: Net powertrain efficiency vs. total vehicle mass for the 33 vehicles ..............113

Figure 5-3: NSFs for vehicle platform parameters.............................................................115

Figure 5-4: NSFs for component specific power/energy parameters.................................116

Figure 5-5: Mass breakdowns for seven vehicles considered in the sensitivity analysis...117

Figure 5-6: NSFs for component efficiency parameters ....................................................118

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Figure 5-7: NSFs for driving pattern parameters............................................................... 119

Figure 5-8: NSFs for vehicle performance parameters...................................................... 121

Figure 5-9: Variation in BEV energy consumption across a range of battery specific

energies and driving range targets .................................................................. 123

Figure 5-10: Variation in H2 FCHEV energy consumption across a range of battery specific

energies and driving range targets .................................................................. 124

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List of Tables

Table 2-1: A range of existing vehicle modelling tools (listed alphabetically) ..................... 6

Table 2-2: Some prominent, recent vehicle technology assessment studies and the

modelling tools that were used (listed chronologically)....................................... 7

Table 2-3: Comparison of specific energy (Wh/kg) and energy density (Wh/L) values for

various fuel/energy storage systems ................................................................... 21

Table 3-1: Driving pattern parameters for some well-known driving cycles ...................... 40

Table 3-2: Values for E1 and E2 in equation 3-60 as presented by Delucchi (2000) ........... 61

Table 3-3: Errors in the estimates of acceleration power using equation 3-67.................... 64

Table 3-4: Predicted acceleration power requirements using various methods................... 73

Table 3-5: Component technology parameters used in PAMVEC’s model for powertrain

component sizes and mass compounding........................................................... 74

Table 4-1: Technical specifications for the GM HydroGen3 FCEV ................................... 81

Table 4-2: HydroGen3 parameter values assumed in the prediction of motor power ......... 82

Table 4-3: Vehicle parameters assumed for the Holden Commodore sedan ....................... 83

Table 4-4: Technical Specifications for the Virginia Tech. ZEburban FCHEV.................. 83

Table 4-5: Estimated technical parameters for the Virginia Tech. ZEburban FCHEV ....... 84

Table 4-6: Comparison between estimated and reported road load power requirements for

the Virginia Tech. ZEburban FCHEV................................................................ 84

Table 4-7: Predicted and reported fuel economies for the Virginia Tech. ZEburban.......... 84

Table 4-8: Vehicle platform parameters assumed for the ADVISOR benchmarking ......... 86

Table 4-9: Component technology parameters for the ICV................................................. 87

Table 4-10: Comparison of component size and vehicle mass predictions for the ICV........ 87

Table 4-11: Comparison of energy consumption predictions for the ICV............................. 88

Table 4-12: Component technology parameters for the PHEV ............................................. 89

Table 4-13: Comparison of component size and vehicle mass predictions for the PHEV .... 89

Table 4-14: Comparison of energy consumption predictions for the PHEV......................... 89

Table 4-15: Component technology parameters for the SHEV ............................................. 90

Table 4-16: Comparison of component size and vehicle mass predictions for the SHEV .... 90

Table 4-17: Comparison of energy consumption predictions for the SHEV......................... 91

Table 4-18: Component technology parameters for the FCEV ............................................. 91

Table 4-19: Comparison of component size and vehicle mass predictions for the FCEV .... 92

Table 4-20: Comparison of energy consumption predictions for the FCEV ......................... 92

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Table 4-21: Component technology parameters for the FCHEV...........................................93

Table 4-22: Comparison of component size and vehicle mass predictions for the FCHEV..93

Table 4-23: Comparison of energy consumption predictions for the FCHEV.......................93

Table 4-24: Component technology parameters for the BEV ................................................94

Table 4-25: Comparison of component size and vehicle mass predictions for the BEV .......94

Table 4-26: Comparison of energy consumption predictions for the BEV............................95

Table 4-27: Summary of validation results for the NEDC cycle ...........................................95

Table 4-28: Summary of validation results for the UDDS cycle ...........................................99

Table 4-29: Summary of validation results for the HWFET cycle.......................................100

Table 4-30: Summary of validation results for the US06 cycle ...........................................100

Table 4-31: Summary of validation results for the NYCC cycle .........................................101

Table 4-32: Powertrain component sizes (kW) for the various cycles.................................101

Table 4-33: Powertrain component efficiencies for the various driving cycles ...................102

Table 4-34: Validation results for the high MDR platform on the NEDC...........................103

Table 4-35: Validation results for the high MDR platform on the HWFET ........................103

Table 5-1: Transmission, electric motor and HEV battery technologies for the various

powertrain architectures considered in the comparison....................................108

Table 5-2: Physical parameters for the 2003 Holden VY Commodore sedan platform.....108

Table 5-3: Performance constraints for the vehicles in this comparison............................109

Table 5-4: Fuel/powertrain technology parameters and predicted energy consumption

results for the 33 vehicles in this comparison...................................................111

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List of Abbreviations

BEV battery electric vehicle

BioD biodiesel

CNG compressed natural gas

DC direct current

DOH degree of hybridisation

DOHC doubled overhead cam

EUCAR European Council for Automotive Research & Deveopment

EV electric vehicle (includes BEVs, SHEVs, FCEVs and FCHEVs)

E10 10% ethanol / 90% petrol fuel blend

E85 85% ethanol / 15% petrol fuel blend

FCEV fuel cell electric vehicle

FCHEV fuel cell hybrid-electric vehicle

FCV fuel cell vehicle (includes FCEVs and FCHEVs)

GH2 gaseous hydrogen

GM General Motors

HEV hybrid electric vehicle (includes PHEVs, SHEVs and FCHEVs)

HSED high specific energy device

HSPD high specific power device

HWFET Highway Fuel Economy Test

IEA International Energy Agency

ICE internal combustion engine

ICV conventional internal combustion engine vehicle

LBST L-B-Systemtechnik GmbH

LH2 liquid hydrogen

LNG liquefied natural gas

LPG liquefied petroleum gas

MDR mass to drag ratio

MeOH methanol

MPG miles per gallon

mpgge miles per gallon gasoline equivalent

M85 85% methanol / 15% petrol fuel blend

NEDC New European Driving Cycle

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NiMH nickel metal hydride (battery)

NSF normalised sensitivity factor

NYCC New York City Cycle

OEM (automotive) original equipment manufacturer

OTA Office of Technology Assessment

PAMVEC Parametric Analytical Model of Vehicle Energy Consumption

PC personal computer

PEM proton exchange membrane

PHEV parallel hybrid-electric vehicle

PKE positive kinetic energy

SHEV series hybrid-electric vehicle

SOC state of charge

UDDS Urban Dynamometer Driving Schedule

ULP unleaded petrol

US EPA United States Environmental Protection Agency

US FTP United States Federal Test Procedure

VRLA valve-regulated lead acid (battery)

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1. Introduction

The light-duty vehicle sector is mostly fuelled by liquid hydrocarbon fuels derived from crude

oil. However, growing concern over the environmental impacts and oil-dependence

associated with widespread automobile use has prompted the investigation of alternative

propulsion technologies for motor vehicles. A variety of candidate alternative fuels and

powertrain technologies are currently being considered for their ability to reduce emissions of

greenhouse gases and regulated air pollutants and promote energy independence through the

displacement of oil imports. Candidate fuels include petrol / gasoline, Diesel, liquefied

petroleum gas, natural gas, hydrogen, methanol, ethanol, biodiesel and electricity. Candidate

powertrains include advanced internal combustion engine vehicles, hybrid-electric vehicles,

fuel cell-electric vehicles and battery-electric vehicles, as well as many other novel

alternatives.

Each of these alternative transport energy pathways has unique characteristics in terms of its

potential for emissions reduction and promotion of energy independence. In performing

vehicle technology assessments to determine the potential for each technology, a central

variable is the vehicle energy consumption:

“Energy use is a central variable in economic, environmental, and engineering analyses of

motor vehicles. The energy use of a vehicle directly determines energy cost, driving range,

and emissions of greenhouse gases, and indirectly determines initial cost and performance. It

therefore is important to estimate energy use as accurately as possible.” Delucchi (2000)

Many studies have performed techno-economic comparisons of alternative fuels and

powertrain technologies for vehicles (see Table 2-2 for examples). A defining characteristic

of each study is the methodology used to estimate absolute or relative vehicle energy use for

the technologies concerned. Some studies have surveyed data in the literature to produce their

estimates of vehicle energy use (e.g. IEA (1999), Louis (2001), Wang (2002) and Ogden et al

(2004)), but by far the most common approach has been to calculate vehicle energy using

various modelling tools, with the most popular tools being dynamic vehicle simulators.

Dynamic simulators are powerful modelling tools offering high precision and accuracy and

this makes them ideally suited to detailed simulation, testing and refinement of vehicle

designs as part of a design process. However, they can be disadvantaged by their complexity,

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their need for detailed input data (which often is not publicly available), their reliance on

deterministic driving cycles to describe driving patterns, and excessive computational

requirements resulting from their inherently iterative nature. In the context of vehicle

technology assessment where many vehicles or technologies may need to be compared, these

attributes can make dynamic simulators costly and time-consuming to use and this thesis

argues that alternative modelling approaches may be better suited to the task.

Therefore, this thesis commences in Chapter 2 with a detailed review of existing vehicle

modelling tools and a discussion of their capabilities and limitations. In particular, this

chapter proposes that, relative to dynamic simulators, a tool that was better suited to the

purposes of technology assessment would:

1. Use a less deterministic description of driving patterns i.e. avoid driving cycles by

using a probabilistic/statistical description of driving patterns

2. Be tailored to the use of publicly available technology/component data i.e. utilise

simple input parameters to avoid the need for detailed component models.

3. Be less computationally intensive i.e. avoid iterative dynamic simulation by using

lumped-parameter style models of vehicle energy consumption and performance

To address these issues, this thesis presents a novel approach to modelling energy

consumption in road vehicles – the Parametric Analytical Model of Vehicle Energy

Consumption (PAMVEC). PAMVEC is a lumped-parameter-style model incorporating a

number of unique features that are designed to reduce its complexity, input data and

computational requirements relative to dynamic simulators, but also to provide greater

precision and accuracy than previous lumped-parameter approaches. These include:

• Parametric analytical expressions for predicting vehicle energy consumption that are

derived from the well-known road load equation

• Parametric analytical expressions to size powertrain components implicitly in terms of

specified performance targets that include driving range



uncertainty


power/energy



3

Chapter 3 documents the derivation of the PAMVEC model including its key simplifications

and assumptions. The simplicity of the PAMVEC model is enabled by the central assumption

that tractive power flow that is reversible (due to vehicle inertia) can be modelled separately

from irreversible power flow (due to vehicle drag). However, this assumption also introduces

error in the predictions of vehicle energy consumption. Therefore, Chapter 4 validates

PAMVEC against real vehicle test data and benchmarks it against the ADVISOR dynamic

vehicle simulator to test the accuracy of its predictions. While the errors are found to be

larger than those observed in dynamic simulators, this thesis argues that PAMVEC is still

sufficiently accurate for the purposes of technology assessment (where uncertainties tend to

be very large).

In the final Chapter 5, to demonstrate its suitability to vehicle technology assessment,

PAMVEC is applied in a well-to-wheel analysis to predict the energy consumption of 33

vehicles with alternative fuels and powertrain technologies. The results of this study are also

used to conduct an input-parameter sensitivity analysis that further highlights the capabilities

and limitations of the PAMVEC model.

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2. Tools for Modelling Vehicle Energy Consumption

The literature details a great many vehicle modelling tools that have been used for vehicle

design studies and technology assessment. A list of many of these tools is provided in Table

2-1, and Table 2-2 lists some prominent recent studies including the tools that were used.

This chapter provides a critical review of the capabilities of existing vehicle modelling tools.

It commences by outlining the attributes that qualify the capabilities of a vehicle modelling

tool. It then reviews approaches to modelling vehicle energy consumption and performance

that have been employed in existing tools, and discusses their suitability to the purposes of

technology assessment. Limitations of the existing approaches are identified, and this

provides justification for the development of the parametric approach presented in this thesis.

2.1 Attributes of Vehicle Modelling Tools

The qualities of vehicle modelling tools can be defined in terms of various attributes, such as:

• Accuracy – the error in a model’s predictions of vehicle energy consumption and

performance

• Precision – the level of detail employed in a model’s representation of physical effects

in the vehicle and its powertrain

• Computation – the computer hardware/software requirements for the use of a model

and the time taken to extract a result, which translate to costs for computer

hardware/software and the time of designers/analysts occupied in using a model.

• Input data – the amount of information required to characterise the vehicle and its

powertrain components and other aspects of a model

• Complexity/transparency – the amount of embedded functions and “hidden layers”

in a model that give rise to complex interactions that may not be obvious to the user.

Models that are less-complex/more-transparent are easier to “debug” and their results

are likely to be easier to analyse and interpret

• Versatility – the flexibility of a model in its ability to model different vehicles with

different performances utilising varying technologies operating over different regimes.

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Table 2-1: A range of existing vehicle modelling tools (listed alphabetically)

Vehicle Modelling Tool Type

ADVISOR (Wipke et al, 1999) Dynamic simulator (backward/forward)

Åhman (2001) Lumped parameter model

Delucchi (2000) Dynamic simulator (backward)

EVSIM (Chau et al, 2000) Dynamic simulator (backward/forward)

HPSP (Weber, 1998) Dynamic simulator (backward)

Louis (1999) Lumped parameter model

MARVEL (Marr & Walsh, 1992) Dynamic simulator (backward)

Moore (1996) Lumped parameter model

OSU-HEVSIM (Wasacz, 1997) Dynamic simulator (forward)

Plotkin et al (2001) Lumped parameter model

PSAT (ANL, 2004) Dynamic simulator (forward)

QSS Toolbox (Guzella & Amstutz, 1999) Dynamic simulator (backward)

Ross (1997) Lumped parameter model

SIMPLEV (Cole, 1993) Dynamic simulator (backward)

Sovran & Blaser (2003) Lumped parameter model

Sovran & Bohn (1981) Lumped parameter model

Steinbugler (1998) Dynamic simulator (backward)

Thomas et al (1998) Dynamic simulator (backward)

V-ELPH (Butler et al, 1999) Dynamic simulator (forward)

VSP (Van Mierlo & Maggetto, 1996) Dynamic simulator (backward)

Some of these attributes are obviously interrelated. Nevertheless it is important to recognise

the attributes of vehicle modelling tools since vehicle designers and technology analysts,

when they choose a particular tool for a particular problem, must inevitably compromise

between attributes. For example, the most precise and accurate models tend to have the

greatest input data and computation requirements, thereby being more costly to use. In the

following sections, existing approaches to modelling vehicle energy consumption and

performance are reviewed including a discussion of their relevant attributes.

7

Table 2-2: Some prominent, recent vehicle technology assessment studies and the modelling

tools that were used (listed chronologically)

Study (Reference) Modelling Tool

Advanced Automotive Technology: Visions of a Super-Efficient Family

Car (OTA, 1995)

Sovran & Bohn

(1981)

Analysis of the Fuel Economy Benefits of Drivetrain Hybridization

(Cuddy et al, 1997)

ADVISOR

Manufacturing and Lifecycle Costs of Battery Electric Vehicles, Direct-

Hydrogen Fuel Cell Vehicles, and Direct-Methanol Fuel Cell Vehicles

(Lipman, 2000)

Delucchi (2000)

On the Road in 2020: A Lifecycle Analysis of New Automotive

Technologies (Weiss et al, 2000)

QSS Toolbox

Well-to-wheel efficiency for alternative fuels from natural gas or biomass

(Ahlvik & Brandburg, 2001)

ADVISOR

A Lifecycle Emissions Analysis: Urban Air Pollutants and Greenhouse-

Gases from Petroleum, Natural Gas, LPG, and Other Fuels for Highway

Vehicles, Forklifts, and Household Heating in the U.S. (Delucchi, 2001)

Delucchi (2000)

Well-to-Wheel Energy Use and Greenhouse Gas Emissions of Advanced

Fuel/Vehicle Systems – North American Analysis (GM et al, 2001)

HPSP

Comparing the Benefits and Impacts of Hybrid Electric Vehicle Options

(Graham, 2001)

ADVISOR

Hybrid Electric Vehicle Technology Assessment: Methodology,

Analytical Issues, and Interim Results (Plotkin et al, 2001)

ADVISOR

GM Well-to-Wheel Analysis of Energy Use and Greenhouse Gas

Emissions of Advanced Fuel/Vehicle Systems – A European Study

(LBST, 2002)

HPSP

Well-to-Wheels Analysis of Future Automotive Fuels and Powertrains in

the European Context (EUCAR et al, 2003)

ADVISOR

A New Road: The Technology and Potential of Hybrid Vehicles

(Friedman, 2003)

ADVISOR

Comparative Assessment of Fuel Cell Cars (Weiss et al, 2003) QSS Toolbox

8

2.2 Approaches to Modelling Vehicle Energy Consumption

At the most fundamental level, there are two basic approaches to modelling vehicle energy

consumption. The first involves the use of dynamic simulation, whereas the second involves

the use of static “lumped-parameter” models.

2.2.1 Dynamic Vehicle Simulators

Dynamic vehicle simulators are by far the most widely-used tools for modelling vehicle

energy consumption. Popular examples from Table 2-1 include ADVISOR and PSAT.

These tools utilise hypothetical driving cycles (of vehicle velocity vs. time) to simulate

dynamic vehicle operation and the corresponding dynamic power flows and energy losses

within the powertrain. Dynamic simulators can be further classified into two generic groups –

forward facing and backward-facing simulators – based on the way in which the dynamic

calculations are performed. Excellent discussion of the two approaches is provided in Wipke

et al (1999), Miller et al (1999) and Guzella & Amstutz (1999), however, a brief summary is

also provided here.

Backward-facing simulators take the driving cycle as the actual vehicle speed and, using the

physical equations governing vehicle motion, calculate the tractive force required at the

vehicle wheels. The calculation then proceeds upstream (backwards relative to the flow of

tractive power) calculating the required output speed/torque/power of each component,

culminating in a calculation of the required energy input to the powertrain. In contrast,

forward-facing simulators take the driving cycle as the target vehicle speed and, using a

control loop or “driver model”, provide a throttle signal (and energy) input to the powertrain.

The calculation then proceeds downstream determining the output speed/torque/power of each

component, culminating in the calculation of a new vehicle speed, which is fed back to the

controller and compared to the target driving cycle. Both methods perform these calculations

over discrete time intervals.

As a result of their different calculation procedures, backward and forward facing simulators

have a number of contrasting attributes

9

• The backward facing approach is enabled by the availability of component

performance maps that detail efficiency or loss vs. output speed/torque/power, but

these are normally produced through steady-state testing of components and therefore

do not model dynamic effects. In contrast, proper dynamic models are readily utilised

by the forward approach.

• The backward approach assumes the speed vs. time trace is “followed”. Therefore it

is not suited to predicting best-effort performance under component limited

conditions. In contrast, the forward approach is ideal for this.

• The backward facing approach does not deal with real measurable quantities in a

vehicle (i.e. throttle position) so is not well suited to control system design, whereas,

forward approach models actual control signals and actual (not required)

torques/speeds/powers in the powertrain so it is ideally suited to development of

hardware and control system.

• The backward facing approach provides faster calculations using simpler integration

routines with larger time steps, whereas, the forward approach relies on calculation of

vehicle states that must be calculated through integration with higher-order routines

using smaller time steps and requiring more computation.

What both forward- and backward-facing simulators have in common is that they are capable

of great accuracy, and the validation of existing dynamic vehicle simulation tools has been

well documented in the literature. Guzella & Amstutz (1999) quote errors of <5% in the

estimation of vehicle fuel economy using QSS-Toolbox. Miller et al (1999) quote errors of

<3% for vehicle performance and <15% for vehicle fuel economy using OSU-HEVSIM. GM

et al (2001) report that HPSP predicts fuel economies that are “consistently within 1%” of

those measured in vehicles using a variety of powertrains. Several studies have validated

ADVISOR’s accuracy. Wipke et al (1999) quote errors of <1% for vehicle performance and

<2% for vehicle energy use. Senger et al (1998) and Ogburn et al (2000) quote errors in fuel

economy estimates of <10%. In EUCAR et al (2003), the validity of ADVISOR was checked

“against the in-house simulation codes of a number of European manufacturers and found to

deliver analogous results”. Similarly, Wipke et al (1999) have benchmarked ADVISOR

against a number of proprietary vehicle simulation models used by the automotive industry.

Unfortunately, despite their wonderful accuracy, the dynamic vehicle simulators have some

common limitations also.

10

Driving Cycles

Firstly, all dynamic vehicle simulators are reliant on driving cycles. The benefits that driving

cycles provide in being able to simulate powertrain dynamics over seemingly realistic driving

patterns cannot be overstated. Furthermore, standardised driving cycles are essential for

controlled dynamometer testing of vehicle fuel economy and emissions, and these same

cycles allow simulation tools to be validated with real-world results and provide a meaningful

basis for virtual comparison of vehicle technologies. However, “the choice of a suitable

driving cycle is not a trivial matter” states Rizzoni et al (1999). All driving cycles are totally

arbitrary and there is significant evidence to suggest that, despite over 30 years of driving

cycle research and development, existing cycles are quite unrepresentative of real-world

driving conditions (Milkins & Watson, 1983; Burba, 2000). This is particularly evidenced by

the “correction factors” used by the US EPA (2005) to estimate real-world fuel economies

based on dynamometer test results (tested urban/highway fuel economy values (MPG) are

reduced by 10%/22% respectively). Furthermore, it is common practice to scale the velocities

of existing cycles in order to “intensify” them such that they produce more realistic fuel

economies (Moore, 1996; Thomas et al, 1998; Friedman, 1999). It is likely that automotive

OEMs have developed their own proprietary cycles that are more-representative of real-world

conditions, but these are certainly not available in the public domain.

Another issue that arises from driving cycles is the concept of “off-cycle performance”. It is

quite possible for vehicle designs to be so optimised for a particular cycle that it becomes

detrimental to their operation in other conditions. Bullock (1982) suggests that this has in fact

occurred for production vehicles due to regulatory pressures and mandatory fuel consumption

labelling. The issue was explored through simulation by Wipke et al (2001) for the optimal

design of fuel cell hybrid vehicles, including the sizing of powertrain components and

determination of control strategy parameters. The results showed that the vehicle fuel

economy could increase by more than 30% when using designs optimised for another cycle.

Burba (2000) provides a convenient summary of the issues:

“Although the present practice in the industry is to utilise “driving cycles” as a metric, these

cycles are notoriously inaccurate and can lead to nonoptimized product design...The

engineering response to these errors has been to search for a better or correct drive cycle or

use “fudge factors” to adjust the results. These pursuits are neither scientific nor accurate.”

11

Ultimately, the problems inherent to driving cycles stem from the difficulty experienced in

creating them. Firstly, large quantities of data must be collected from instrumented vehicles

operating in real-world traffic conditions – a process that in itself is prone to significant

human error due to the presence of the driver (Johnson et al, 1975). Then by using

sophisticated statistical analysis, the real-world data (often hundreds or thousands of hours of

driving) must be distilled into cycles that, for practical purposes, rarely exceed 30 minutes in

length. Significant information may be lost and error potentially introduced throughout the

process. Despite all this effort, the resulting cycles “cannot account for the variability in

driving styles and locations encountered by a market population” (Burba, 2000).

Component Models

Another limitation of dynamic simulators stems from their need for detailed component

models. Existing simulators use a variety of component models to predict dynamic (time-

varying) component efficiencies and operating limits. A common approach is the use of

“quasi-static” performance maps to describe component efficiency or loss (Wipke et al,

1999). A more generic approach is the Willans Line Concept featured in QSS-Toolbox

(Rizzoni et al, 1999). However, the most-detailed models can be fully-scaleable, dynamic

models derived from first principles, such as the diesel engine model utilised by Assanis et al

(1999). Whichever component models are used, analysts have two possible avenues for

obtaining them:

1. Models can be developed and validated through testing of hardware by the analysts

themselves.

2. Models that are publicly available can be obtained from the literature or by contacting

component manufacturers.

Unfortunately, the availability of detailed, well-validated component models is somewhat

limited. Firstly, manufacturers of proprietary component technologies are understandably

reluctant to publish details of their technology, or provide component samples to allow

independent testing, modelling and verification. General Motors (2001) avoided publishing

any details of the powertrain technologies considered in their well-to-wheels studies for this

very reason. Analysts that do succeed in gaining access to proprietary information are

normally bound by confidentiality. For example, when Wipke et al (2001) published their

optimisation study for a fuel-cell hybrid vehicle they were unable to disclose the fuel cell or

12

motor/controller models used in the simulations. Furthermore, when component technology

data is released to the public domain, it is normally in the form of simple performance metrics

such as specific energy (Wh/kg), power density (W/L), specific cost ($/kW or kWh) or peak

efficiency. Data of this kind is good for publicising and comparing technologies, and

potentially for use in lumped-parameter models, but it does not lend itself to use of dynamic

vehicle simulation tools.

Secondly, the cost of obtaining powertrain components and test-bed facilities in order to

develop and validate component models presents a significant barrier to research groups with

limited resources. Furthermore, some research groups withhold their models from the public

domain in order to realise their commercial value or increase competitive advantage. For

example, the author’s primary source of powertrain component models was data files

provided with freely available versions of ADVISOR. However, the National Renewable

Energy Laboratory recently granted an exclusive license to AVL Powertrain Technologies to

commercialise ADVISOR, with the result that future component models will no longer be

freely available (PRNewswire, 2003).

If validated, up-to-date component models are not available to analysts, they may need to

limit the scope of their studies, or utilise inappropriate or out-of-date component models.

Either way, this constitutes a major inconvenience for the users of dynamic simulators.

Computational Requirements

A final limitation of dynamic simulation tools relates to their computational intensity. The

discrete time-step calculations performed by dynamic simulators are inherently iterative,

making them computationally intense. It has already been noted that forward-facing

simulators are more computationally intensive than backward simulators due to their need for

more-precise integration. However, there are other factors that may give rise to additional

computational requirements.

The ADVISOR simulation tool provides two convenient examples (Wipke et al, 1999).

Firstly, there is the need for state-of-charge (SOC) balancing. When a hybrid vehicle

completes a driving cycle, the delta-SOC of the energy storage may be non-zero and in

calculating the equivalent fuel use of the vehicle, this delta-SOC should be accounted for.

One approach is to adjust the fuel consumption based on the delta-SOC and the mean

13

efficiency of the powertrain components, such as the method proposed in Simpson (1999).

Alternatively, ADVISOR provides a convenient zero-delta-SOC routine that iterates on the

initial SOC until the final SOC is within some tolerance of it (e.g. 0.5%). Markel et al (2002)

report that 5-10 drive cycle iterations are typically required to meet the zero-delta SOC

tolerance, which essentially increases the computational requirements by an order of

magnitude. Secondly, there is the opportunity for control strategy optimisation in hybrid

vehicles. This thesis has discussed the issues associated with excessive control optimisation

and off-cycle performance, but for the same reasons, it is equally important that a control

strategy receive some fine tuning. Therefore, an analyst may choose to utilise ADVISOR’s

control strategy optimisation feature. On the author’s PC, the use of this feature required a

computation time of up to an hour. From these examples, it is easy to see how the

computation requirements can quickly add up when using dynamic simulators. Later

discussion in this thesis will also show how studies of component sizing and vehicle

performance can further increase the computational intensity of dynamic simulators.

Some might argue that, with the high processing power available in modern PC technology at

a relatively low cost, computational intensity is a trivial problem that may be readily

overcome. For the most part this may be correct, but there are several examples cited in the

literature where analysts have required the use of high-end workstations and/or parallel

computing to complete their vehicle simulations within a reasonable amount of time (Miller et

al, 1999; Wipke et al, 2001; Markel et al, 2002). Certainly, the greater investment in such

high-end computing would need to be weighed against the overhead & manpower costs of

longer-running vehicle simulations.

Overall, despite their limitations, dynamic simulators have proven to be immensely popular in

the vehicle design and analysis community, and this is evidenced by the large number of

vehicle simulators that have been developed around the world (Table 2-1).

2.2.2 Lumped-Parameter Models

The alternative approach to dynamic simulation is the use of lumped-parameter models for

vehicle energy consumption. These are much simpler models that avoid the need for dynamic

simulation by using “estimates of engine and motor characteristics and other variables that are

averages over a driving cycle” (OTA, 1995), and they often involve the use of empirical

14

correlations. Examples of lumped-parameter models include those employed by Moore

(1996), Åhman (2001), Louis (2001) and Sovran & Blaser (2003).

In contrast with dynamic simulators, lumped-parameter models are far less complex and much

easier to apply and interpret. They involve simple calculations that are readily implemented

in a spreadsheet and can often be performed quickly by hand. Since the models are usually

constructed in parametric form, they obviate the need for detailed component models or

performance maps.

Precision and Accuracy

However, the primary limitation of lumped-parameter models is their lack of precision and

resulting loss of accuracy. The inaccuracy can arise from simplifying assumptions that

facilitate a more convenient model but introduce error. Alternatively, inaccuracies can arise

since lumped-parameter models do not normally include a model of the driving pattern, and

therefore cannot model dynamic effects that would easily be reproduced with a driving cycle.

For example, the lumped-parameters models employed by Moore (1996), Åhman (2001),

Louis (2001) and Sovran & Blaser (2003) all require the energy consumption at the wheels of

the vehicle as an input and therefore cannot readily consider the dependence of this quantity

on the nature of the driving pattern.

Certainly, parametric models can be quite useful for demonstrating system trade-offs in

vehicle design, but their accuracy in making absolute predictions of energy consumption

cannot be compared to that of dynamic simulators. For example, Moore’s spreadsheet model

includes a notation to its user that the correlations employed are “not highly accurate”.

Unfortunately, to the author’s knowledge, the literature contains no documented validation

studies for lumped-parameter models to quantify their accuracy. However, errors in the range

of 10-20% (or even more) would certainly not be unexpected.

15

2.3 Approaches to Modelling Vehicle Performance

2.3.1 The Link between Vehicle Performance and Energy Consumption

Most tools for modelling vehicle energy consumption also include models for predicting

vehicle performance, and such tools allow vehicle designers and analysts to make trade-offs

between vehicle performance and energy consumption. This is necessary because vehicle

performance and energy consumption are inextricably linked through the sizing of powertrain

components. As a general rule, larger powertrain components lead to an improvement in

vehicle performance (although not always). However, the relationship between component

size and vehicle energy consumption is more complicated. Component sizes can affect

vehicle energy consumption in two ways:

1. Mass-related effects – increasing the size of a powertrain component increases its

mass. Furthermore, additional structural mass would normally be required to support

the extra mass of the component. The increase in total vehicle inertia increases the

road load with a resulting increase in energy consumption.

2. Component efficiency effects – a change in the size of a component changes its

loading fraction (the ratio of operating load to peak load) which affects its operating

efficiency. Whether this has a positive or negative influence on component efficiency

depends upon the shape of the component’s efficiency vs. load curve. There are also

higher-order effects to consider. For example, the change in road load that results

from a change of component size/mass will also produce a change in component

operating load fraction.

The link between vehicle performance and energy consumption is quite apparent for

conventional vehicle technologies. It is generally well-known that vehicles with larger

engines have better peak acceleration but worse fuel economy in ordinary driving conditions.

This is due to the combined efforts of the two effects described above. The larger engine is

obviously heavier. But since ICEs tend to operate with maximum efficiency near their peak

power, the larger engine also operates at a lower load fraction with substantially lower

efficiency. These tradeoffs are clearly demonstrated in the results of Plotkin et al (2001) who

compared fuel economy vs performance for both conventional and hybrid vehicles (Figure 2-

1). For other powertrain technologies, the link between vehicle performance and energy

16

consumption is less clear. For example, Friedman (1999) suggests that the fuel economy of a

fuel cell vehicle can be improved by using a larger fuel cell due to the natural shape of a fuel

cell’s efficiency vs. load curve. It is also possible that vehicle performance and energy

consumption can be simultaneously improved via hybridisation. These examples do however

serve to demonstrate the link between vehicle energy consumption and performance and the

need to model these in tandem.

Figure 2-1: A comparison of vehicle fuel economy of conventional and hybrid-electric

vehicles for various acceleration performances (Plotkin et al, 2001)

2.3.2 Models of Vehicle Performance

Each of the forward dynamic simulators reviewed in this thesis has an ability to predict

vehicle performances (including ADVISOR with its hybrid backward/forward approach

(Wipke et al, 1999)). Since vehicle performance tests are essentially full-throttle events, they

are easily replicated in forward simulators via a full throttle command to the powertrain

model. In contrast, backward simulators are particularly unsuited to simulating component-

limited operation and performance tests. As noted by GM et al (2001), it is possible to predict

vehicle performance with a backward simulator by iterating on the vehicle’s acceleration

response, but this is a relatively cumbersome approach that in the literature has only been

utilised with the HPSP model. All of the other backward simulators reviewed in this thesis do

not have a built-in capability to predict vehicle performance.

17

Other approaches to modelling vehicle performance include that employed by Moore (1996)

who included a forward-style calculation of acceleration time in his lumped-parameter

spreadsheet model. Delucchi (2000) has utilised approximate empirical formulae to predict

vehicle acceleration time in his spreadsheet model. However, many analysts have reversed

the component size/performance relationship in an effort to predict the component sizes that

are required to produce a certain level of performance. For example, Ehsani et al (1997) and

Plotkin et al (2001) have derived simple analytical expressions for predicting the drivetrain

power to produce a certain level of acceleration (and this approach has been developed

considerably further in this thesis). Some analysts have even chosen other metrics – such as

vehicle specific power or power-to-weight ratio – as surrogates for vehicle performance, with

examples being found in OTA (1995), Thomas et al (1998), Weiss et al (2000) and Sovran &

Blaser (2003).

On this basis, the various approaches to relating vehicle performance and component size can

be categorised according to whether the component sizes are defined explicitly or implicitly

(Figure 2-2). The explicit approach is that employed by dynamic simulators to predict the

vehicle performance based on a definition of the powertrain component sizes. The implicit

approach involves the powertrain component sizes being defined in terms of vehicle

performances or surrogate metrics. Of course, an explicit performance model becomes

implicit if it is mated with a routine to iterate the powertrain component sizes until a target

level of performance is achieved. An example of such a feature can be found in ADVISOR’s

Autosize routine (Wipke et al, 1999). However, for dynamic simulators this requires

additional computations that, as discussed in Section 2.2.1, may be undesirable.

Figure 2-2: The explicit vs. implicit approaches to powertrain component sizing.

Vehicle performance model Predicted vehicle performance(s)

Powertrain component sizes

Vehicle performance model Predicted component sizes

Target vehicle performance(s)

Explicit Approach

Implicit Approach

18

A feature of the implicit approach is that it results in the phenomenon commonly known as

mass compounding. Mass compounding occurs as follows: for better performance (say

increased acceleration), a vehicle requires a larger engine. But the larger engine is heavier

and also requires additional structural support. Therefore, the vehicle becomes heavier, and

the engine size must be further increased to achieve the target level of performance. The

process continues in an upward spiral with the mass compounding until the vehicle design

converges. Similarly, a reduction in a target level of vehicle performance can result in mass-

decompounding.

Figure 2-3 provides a diagrammatic representation of mass compounding for a model of

vehicle energy consumption using the implicit performance approach, and the feedback loop

that gives rise to mass compounding is clearly indicated. Obviously, this mass compounding

effect is most-pronounced for arduous performance goals and technologies with low specific

powers (W/kg).

Figure 2-3: The effects of mass-compounding due to vehicle performance

The Significance of Driving Range as a Performance Target

For those studies using an implicit approach to component sizing, the most common

performance targets have included acceleration, gradability and top speed. What is important

to note about these performance targets is that they determine the power output requirements

Performance targets

Vehicle platform

Component technologies

Driving pattern

Performance model & component sizing strategy

Component efficiency and vehicle energy consumption model

Mass balance Vehicle energy consumption

Total vehicle mass

Component sizes

Mass Compounding

19

for components in the powertrain. Several studies have also adopted a driving range target,

but this target is unique in that it determines an energy storage requirement for the

powertrain. Consequently, a driving range target will also result in mass-compounding

effects, but the feedback loop is different. Figure 2-4 demonstrates range-induced mass-

compounding effects. In addition to the original mass-compounding feedback loop due to

vehicle performance, note that there are now two additional feedback loops due to vehicle

energy consumption – one via the effects of component sizes on total vehicle mass, and

another via the effects of component sizes on powertrain efficiency.

Figure 2-4: The effects of mass-compounding due to vehicle performance including range

Despite this interaction, it is surprising to find that many studies have ignored range-induced

mass-compounding effects. Furthermore, many of the vehicle modelling tools surveyed by

this thesis do not have an ability to predict driving range, and only one (Delucchi, 2000) has

the built-in capability to size components and predict vehicle energy consumption based on

performance targets that include driving range. From the literature, it is not clear why this is

the case, but there is certainly a practical issue involved. As previously noted, dynamic

simulators are the most popular modelling tools and they use an explicit approach to

component sizing and must therefore be mated with iterative routines to enable the implicit

approach. These iterative routines would normally structure the component sizing problem as

a bounded optimisation, with the performance targets providing the constraints and the

objective being to minimise total vehicle mass or energy consumption. If driving range IS

Performance targets

Vehicle platform


Driving pattern


Component efficiency and vehicle energy consumption model


Total vehicle mass

Component sizes

Mass compounding

energy power

20

NOT included as a performance constraint, then the iterations to predict vehicle performance

and size powertrain components can be performed independent of the energy consumption,

and then a single driving cycle simulation can be performed to estimate the vehicle energy

consumption (and the resulting driving range). In addition, if a control strategy optimisation

is required, this can be performed separate to the component sizing. This is the approach

employed by ADVISOR with its Autosize routine, with each iteration taking approximately

20 seconds on the author’s PC. If driving range IS included as a performance constraint, then

each iteration of the optimisation routine must also include a prediction of the vehicle energy

consumption, which may need to be delta-SOC-corrected. Using ADVISOR on the author’s

PC, the result is an increase in time per iteration to up to 3 minutes. Furthermore, there is

now an additional optimisation variable (the size of the fuel/energy storage) and control

strategy parameters that might also need to be optimised (since they affect the energy

consumption), which could easily double the number of design variables. Due to these large

increases in computation requirements, analysts may have chosen to neglect range-induced

mass-compounding effects primarily for the sake of convenience when using existing

modelling tools.

But since so few studies have considered range-induced mass compounding effects, it is not

clear from the literature whether these can be legitimately neglected or not. Obviously, the

effect will be most pronounced for fuel/energy storage technologies with low specific

energies (Wh/kg). For example, Delucchi (2000) has examined the sensitivity of BEV energy

consumption to driving range and his results (reproduced in Figure 2-5) show a large

sensitivity to driving range. In contrast, the high specific energy of liquid hydrocarbon fuels

should make conventional vehicle technologies relatively insensitive to driving range. But,

apart from batteries, there are other fuel/energy storage technologies – most notably hydrogen

– which can have order-of-magnitude lower specific energy storage than that of conventional

fuels (Table 2-3). The sensitivity of energy consumption to driving range in vehicles using

these technologies should be explored much further. But such studies are not facilitated by

the existing dynamic simulation tools.

21

0%

100%

200%

300%

400%

500%

600%

700%

800%

0 50 100 150 200 250 300 350

Driving range (miles)

Rel

ativ

e fu

el e

cono

my

ICEPb-AcidNiMH Gen2NiMH Gen4Li-Ion

Figure 2-5: The relative fuel economy of different BEV technologies for various driving

ranges calculated for a Ford Escort-style vehicle in Delucchi (2000)

Table 2-3: Comparison of specific energy (Wh/kg) and energy density (Wh/L) values for

various fuel/energy storage systems. Fuel/Energy Storage Specific Energy (Wh/kg) Energy Density (Wh/L)

Gasoline/Petrol 1 10400 7000 Diesel 1 10400 8000 Biodiesel 1 8900 7000 LPG 1 5800 4600 LNG 1 7400 3900 CNG 1 2100-4300 2000 Ethanol 1 6300 4600 Methanol 1 5400 4000 Gaseous Hydrogen (5000psi) 2 3700 800 Gaseous Hydrogen (10000psi) 2 3300 1200 Liquid Hydrogen 2,3 2600-2700 1200 Sodium Boro-Hydride 2 1100 1100 Metal Hydride (high temp) 2,3 1000-1100 900-1500 Metal Hydride (low temp) 3 400 1000 Zinc-Air Battery5 200 220 Lithium-Ion Battery4 140 290 NiMH Battery4 70 165 VRLA Battery4 35 90 Table References:

1) IEA (1999)

2) TIAX (2002)

3) Wicke (2002)

4) Data from various papers presented at the 17th Electric Vehicle Symposium, Montreal.

5) Goldstein et al (1999)

22

2.4 Factors Affecting the Choice and Use of Vehicle Modelling Tools

The two primary uses of vehicle modelling tools are for 1) vehicle design studies and 2)

vehicle technology assessment, and it is interesting to consider how the requirements of a

vehicle modelling tool differ for each purpose.

Vehicle design studies are typically concerned with one (or at most only a few) vehicle design

concept(s) and the goal is normally for design simulation, testing and refinement. In terms of

the attributes listed in section 2.1, this naturally puts greater emphasis on precision and

accuracy in the modelling approach, even if this comes at the expense of greater complexity,

more-detailed input data requirements, greater computation or less versatility. Dynamic

simulators (especially forward simulators) are therefore ideally suited to this purpose.

In contrast, technology assessment often involves wide-ranging comparisons of many

different vehicles, powertrains and component technologies. This naturally puts greater

emphasis on versatility, simplicity, transparency and reduced input data requirements and

computation in the modelling approach, and analysts might be willing to forgo some precision

and accuracy for the sake of these other attributes. This suggests lumped-parameter models as

a better choice for the purposes of technology assessment, which is confirmed by the opinion

of analysts such as the OTA (1995):

“OTA’s projections of advanced vehicle performance used approximate vehicle models based

on well-known equations of vehicle energy use. These models are “lumped parameter”

models – that is, they use estimates of engine and motor characteristics and other variables

that are averages over a driving cycle. Ideally, a performance analysis of complex vehicles

such as hybrids should be based on detailed engine and motor maps that are capable of

capturing the second-by-second interactions of all of the components. Such models have been

developed by auto manufacturers and others. Nevertheless, OTA believes that the

approximate performance calculations give results that are adequate for our purposes. In

addition, the detailed models require a level of data on technology performance that is

unavailable for all but the very-near term technologies.”

Ross (1997) also argues the case for lumped parameter models:

23

“The spirit of the analysis is a physicist's, rather than that of an engineer who is responsible

for a vehicle's performance. I want to describe the energy flows accurately enough for

general understanding and perhaps conceptual design, not for designing an actual vehicle.

The approach is to develop simple algebraic expressions motivated by physical principles, in

contrast to the now pervasive analysis based on numerical arrays. Creating an energy

analysis in, hopefully, transparent terms should make the issues accessible to non-specialists

with technical background.”

But a survey of recent studies (Table 2-2) shows that the vast majority of analysts have

chosen dynamic simulators in preference to lumped-parameter models for the purposes of

technology assessment, presumably due to their greater accuracy. However, a number of

important issues arise when using dynamic simulators for technology assessment purposes.

Firstly, dynamic simulators are sophisticated engineering tools and policy makers will often

take the results from such tools as being “absolute” without appreciating the assumptions or

uncertainties embodied in the analysis. Approaches to promoting a better understanding of

uncertainties include conducting sensitivity analysis on key inputs and assumptions, or

propagating uncertainty through the entire analysis using, for example, fuzzy set theory

(Lipman, 1999). However, driving cycles create a particular challenge here due to their

deterministic nature. If existing driving cycles are unrepresentative of real-world conditions,

what cycle(s) should analysts choose to use for the base case “best estimate”? If a sensitivity

analysis is to be performed, how can analysts modify a driving cycle? Certainly, the “velocity

scaling” technique is an option, but this one-dimensional variation cannot possibly

encapsulate the multiple dimensions of real-world driving patterns. If driving pattern

uncertainty is to be carried through the entire analysis, how can analysts model the uncertainty

in a deterministic driving pattern?

It seems clear that deterministic driving cycles are particularly unsuited to the modelling of

uncertainty and that alternative representations of driving patterns might be considered. One

approach, suggested by Bullock (1982), Milkins & Watson (1983), Burba (2000) and others,

is to represent driving patterns as joint/cumulative probability functions of vehicle speed and

acceleration. However, it is difficult to see how these might be incorporated into a model of

vehicle energy consumption. Another approach might be to parameterise a driving pattern in

terms of meaningful physical metrics such as average speed or average acceleration, and use

these parameters to derive a lumped-parameter style model of vehicle energy consumption.

24

In the author’s view, this approach has considerable potential and is further explored in this

thesis as an alternative to modelling vehicle energy consumption in dynamic simulators using

deterministic driving cycles.

The second problem with using dynamic simulators for technology assessment is the amount

of costly resources that must be invested to produce a result. The resource intensity manifests

itself in three ways – computational requirements, input data requirements and sheer

manpower. This is best exemplified by three monumental well-to-wheels studies that have

been performed by automotive companies in recent years – GM et al (2001), LBST (2002)

and EUCAR et al (2003). These three studies are characterised by the large number of

vehicle technologies considered (GM – 15, LBST – 22 and EUCAR – 43) and the level of

detail in which the vehicles were modelled (all three studies used dynamic simulators).

Although it was not specifically reported in the studies’ documentation, it can reasonably be

assumed that all three studies involved large amounts of computation. This firstly stems from

the large number of cases considered and secondly from the use of dynamic simulators. To

further increase the computation requirements, each study notes that some degree of control

strategy optimisation was performed. Furthermore, all three studies utilised an implicit

approach to component sizing, increasing the computation even more. The control strategy

optimisation can be viewed as an optional component of these studies (in that it probably

wasn’t strictly necessary). In contrast, the implicit component-sizing approach seems to have

become a standard feature of recent vehicle technology assessment studies. This is because it

allows alternative vehicles to be compared on a basis of equal functionality, and as was

previously demonstrated, vehicle performance can have a major effect on vehicle energy

consumption. Overall, it seems clear that the manpower and computational resources needed

to complete such large numbers of simulations could have amounted to a significant cost.

The only option for reducing these costs is to consider alternative modelling tools that do not

have the inherent computational intensity of dynamic simulators i.e. lumped-parameter

models.

The input data required to support these studies must have also been large, since appropriate

component models and data needed to be provided for the dynamic simulation of each vehicle

technology. Fortunately, the automaker-funded studies could take advantage of their own

libraries of proprietary component models (GM et al, 2001). However, technology

assessment is an ongoing process, and as vehicle technologies evolve, studies will need to be

25

repeated. In future, it is unlikely that such large-scale studies as GM’s will be justified on a

regular basis. More likely, ongoing studies will be performed by smaller teams of researchers

with reduced technological scope and access to far less resources. They will probably not

have access to enormous libraries of detailed component models (such as those held by the

automakers). Therefore, obtaining suitable component data and models for use with dynamic

simulators will continue to be a challenge. Alternatively, through the use of appropriate

modelling tools, analysts could tap into the relative abundance of simple component

technology parameters available in the public domain and use this information to conduct

technology assessments of vehicle fuel economy. Again, this suggests a lumped-parameter

modelling approach.

2.5 Outcomes of Literature Review

In summary, compared to existing dynamic simulators, a tool that is better suited to the

purposes of technology assessment might have the following characteristics:

1. Use a less deterministic description of driving patterns i.e. avoid driving cycles by

using a probabilistic/statistical description of driving patterns

2. Be tailored to the use of publicly available technology/component data i.e. utilise

simple input parameters to avoid the need for detailed component models.

3. Be less computationally intensive i.e. avoid iterative dynamic simulation by using

lumped-parameter style models of vehicle energy consumption and performance

Each of these characteristics is consistent with the attributes of a lumped-parameter model.

However, if a new tool with these characteristics was developed, the key issue then becomes

accuracy. Existing lumped-parameter models have not been well-validated in the literature

but, with their simplifying assumptions and limited precision (in particular their lack of a

driving pattern model), they have potential to be far less accurate. Any new tool that was

developed would need to incorporate sufficient precision in its modelling approach for

analysts to be confident that key system interactions were being captured, and it would also

need to be well-validated to quantify its accuracy. These issues provide the justification for

the work presented in this thesis.

This thesis details a new vehicle modelling tool – the Parametric Analytical Model of Vehicle

Energy Consumption (PAMVEC). Its intended use is primarily for technology assessment,

26

although it could also be used to complement more detailed modelling tools as part of a

vehicle design process. Strictly speaking, PAMVEC is a lumped-parameter model. However,

it incorporates a number of unique features that, relative to dynamic simulators, are designed

to reduce its complexity and input data and computational requirements but also to provide

greater precision and accuracy than previous lumped-parameter approaches. These features

of PAMVEC include:

• A parametric driving pattern description that captures key attributes of the driving

pattern, but is also well-suited to the modelling of uncertainty


power/energy

• Implicit component sizing on the basis of specified performance parameters (which

include driving range)

• Derived analytical expressions for vehicle performance and energy consumption



The following chapters document the derivation of the PAMVEC tool and its validation

against test data and benchmarking against the ADVISOR modelling software. Lastly, an

example of the use of PAMVEC is provided to demonstrate its suitability for the purposes of

technology assessment.

27

3. The Parametric Analytical Model of Vehicle Energy Consumption (PAMVEC)

A schematic representation of the PAMVEC model is provided in Figure 3-1, which shows

that there are three main components to the model:

1. The energy consumption model that predicts vehicle energy consumption on the basis

of a parametric driving cycle description, total vehicle mass, other attributes of the

vehicle platform (such as drag coefficients and accessory loads) and the powertrain

component efficiencies. Note that component sizes do not feed into the energy

consumption model (i.e. the component efficiencies do not depend on their size). This

is the primary limitation of the PAMVEC tool discussed further in Section 5.2.

2. The vehicle performance and component sizing model that determines the powertrain

component sizes on the basis of input performance constraints, vehicle mass and drag,

and powertrain component efficiencies.

3. A mass balance that predicts total vehicle mass based on the powertrain component

sizes, the component specific powers/energies, and vehicle platform parameters (the

glider mass and passenger/cargo mass)

Figure 3-1: The PAMVEC model

Performance targets

Vehicle platform


Driving pattern


Vehicle energy consumption model


Total vehicle mass

Component sizes

MODEL OUTPUTS INPUTS

28

This chapter explains each component of the model in detail. Firstly, it outlines the derivation

of the energy consumption model, which includes a parametric formulation of the road load

equation, a novel parametric driving pattern description, and architecture-specific parametric

expressions for powertrain losses. It then details the model of vehicle performance, which

uses an implicit approach to predict the powertrain output powers and energy storage that are

required to achieve the target levels of performance. The implicit performance model is an

extension of the performance equations developed by Ehsani et al (1997). Finally, the

architecture-specific mass balances and component sizing strategies are outlined.

3.1 The Parametric Road Load Equation

3.1.1 Average Road Load Power

The parametric approach to modelling vehicle energy consumption is founded upon a

parametric description of the well-known road load equation (3-1):

roadP gradeaccelrollaero PPPP +++= (3-1a)

gZvmavmkgvmCAvC totaltotalmtotalRRD +++= 321 ρ (3-1b)

where roadP is the road load power (W), v is the vehicle speed (m/s), a is the vehicle

acceleration (m/s2), ρ is the density of air (~1.2kg/m3), DC is the aerodynamic drag

coefficient, A is the frontal area (m2), RRC is the rolling resistance coefficient, totalm is the

total vehicle mass (kg), g is the gravitational acceleration (9.81m/s2), Z is the road gradient

(%) and mk is a factor to account for the rotational inertia of the powertrain (Plotkin et al

(2001) use a value of km = 1.1 while Moore (1996) uses a value of km = 1.2).

The road load equation consists of four components as shown in Equation 3-1a. The first two

of these components represent the irreversible power losses due to aerodynamic and rolling

drag. However, the second two components – powers for vehicle acceleration and hill-

climbing – represent kinetic and potential energy storage in the vehicle inertia and in theory

are fully recoverable (subject to the availability and efficiency of energy recovery and storage

mechanisms in the vehicle). In order to parameterise the road load equation, the following

29

simplifying assumption is made: a vehicle’s journey is defined as including the return trip

to its point of departure. Following this assumption it can be assumed that over the journey

the terms accelP and gradeP in equation (3-1a) integrate to zero. Defining the total trip time as

T , this is written mathematically as:

00

=∫ dtavmkT

totalm (3-2)

00

=∫ dtgZvmT

total (3-3)

Expressions 3-2 and 3-3 are valid since over the journey the vehicle returns to its point of

departure and the net change in speed and elevation is zero. On this basis, it is therefore

possible to define the average road load power as follows:

avgtotalRRrmcDroad gvmCAvCP += 321 ρ (3-4)

In equation 3-4, rmcv and avgv represent the average and root-mean-cubed velocities,

respectively, over the driving pattern and are calculated as follows:

∫=T

avg vdtT

v0

1 (3-5)

30

31∫=

T

rmc dtvT

v (3-6)

Furthermore, the driving pattern velocity ratio (Λ ) can be defined:

avg

rmc

vv

=Λ (3-7)

A more-detailed discussion of these driving pattern parameters is given in Section 3.2. Using

equations 3-4 and 3-7, the average road load power can also be expressed as:

avgtotalRRavgDroad gvmCvACP +Λ= 3321 ρ (3-8)

30

Equations 3-4 and 3-8 represent a departure from conventional thought which normally

accounts for inertial and gravitational energy losses as a part of the vehicle road load. In fact,

these losses are actually due to inefficient energy recapture mechanisms in the vehicle

powertrain and should be considered as such. This point is well-illustrated by the parametric

expression which can be derived for the average vehicle braking losses.

3.1.2 Average Braking Losses

The function of friction brakes is to dissipate some of the kinetic and gravitational potential

energy stored within the inertia of the vehicle. Therefore, to calculate the average braking

losses we must determine the average rate of energy storage within the vehicle inertia which

is matched by an equal and opposite rate of energy dissipation and/or recapture. To derive an

expression for the average rate of energy storage, we begin with the recoverable component of

the road load:

( )vgZakmgZvmavmkP mtotaltotaltotalmerablere +=+=cov (3-9)

Note that the acceleration and gradient components can be represented by a single equivalent

acceleration term:

gZaka me += (3-10)

However, as a simplification, this thesis neglects gradient effects in its analysis and there are

several justifications for doing so:

1. Gradient data is rarely available for use in vehicle analysis (Bullock, 1982) and, to the

author’s knowledge, there are no standard driving cycles used for estimating and

comparing vehicle energy consumption that include road gradient data.

2. In comparing the relative fuel economy of different vehicle technologies, the inclusion

of gradient effects does not necessarily add much value to the comparison. Equation

3-10 suggests that likely gradient effects can be qualitatively inferred from the effects

produced by the acceleration characteristics of a driving pattern.

3. Finally, Bullock (1982) suggests that fluctuations in gradient tend to manifest

themselves as fluctuations in velocity anyway i.e. motorists tend to let speed fluctuate

over undulating terrain, rather than trying to hold the speed constant. This means that

31

gradient effects are most likely entrained within recorded velocity profiles, and the

error from neglecting gradient in the analysis is small.

By using equation 3-9 and assuming a gradient of zero, an expression for the average rate of

energy storage in the vehicle inertia can be written:

∫∫ ≥≥==

T

atotalmT

atotalminertia dtavTmk

dtavmkT

P0 00 0

1 (3-11)

However, to proceed further with the analysis requires that we develop a parametric

expression for the integral in equation 3-11. Fortunately, previous driving pattern research

provides a convenient solution. The average rate of energy storage in a vehicle mass can be

characterized by a parameter known as PKE – the positive acceleration kinetic energy per unit

distance – which is a measure of the acceleration work required in a driving pattern (Milkins

& Watson, 1983). PKE is defined as the sum of the differences between the squares of the

final and initial velocities in successive acceleration manoeuvres, divided by total trip

distance, and has units of acceleration (m/s2):

( ) ( )∫

∑∑ −=

−= T

initialfinalinitialfinal

vdt

vvD

vvPKE

0

2222

(3-12)

By making use of equation 3-5, equation 3-12 can be rearranged to give:

( )avg

initialfinal vPKET

vv×=

−∑ 22

(3-13)

Multiplying both sides of equation 3-13 by totalmmk21 gives:

( )PKEvmk

Tvmkvmk

avgtotalminitialtotalmfinaltotalm

21

2212

21

=−∑ (3-14)

By inspection we see that the left-hand-side of equation 3-13 represents the average rate of

kinetic energy storage in a vehicle mass during a driving pattern. Therefore, equation 3-11

can be written as:

32

PKEvmkP avgtotalminertia 21= (3-15)

Equation 3-15 is sufficient as a parametric expression for the average rate of energy storage

within the vehicle inertia; however, the author prefers a more meaningful form of 3-15 that is

consistent with the form of accelP in the road load equation (3-1a & 3-1b). This is achieved by

defining the characteristic acceleration ( a~ ) of the driving pattern:

( )Tv

vvPKEa

avg

initialfinal∑ −×==

22

21

21~ (3-16)

Equation 3-15 can now be written as:

avgtotalminertia vamkP ~= (3-17)

Again, see Section 3.2 for a detailed discussion of the driving pattern parameters. Equation 3-

17 provides a fully parametric expression for the average rate of energy storage in the vehicle

inertia over the driving pattern (assuming level road), which is matched by an equal and

opposite rate of energy dissipation and/or recovery. A fraction of this rate of energy

dissipation and/or recovery will be absorbed by the vehicle’s friction brakes. The average

braking losses can be defined using the regenerative braking fraction ( regenk ):

( ) ( ) avgtotalmregeninertiaregenbraking vamkkPkP ~11 −=−= (3-18)

The average road load (3-8) and average braking losses (3-18) can then be combined to give

the average power requirement at the output of the driveshaft(s) on the driven axle(s) of the

vehicle:

( ) avgtotalmregenavgtotalRRavgDbrakingroadoutdrive vamkkgvmCvACPPP ~13321 −++Λ=+=− ρ (3-19)

Note that as regenk tends to one the braking losses tend to zero. Under this scenario all of the

stored kinetic and potential energy is returned to the powertrain for recapture and, if the

energy recapture & storage mechanism were to be 100% efficient, there would be no energy

33

consumption due to inertial nor gravitational affects. However, powertrain inefficiencies and

inefficient braking technologies and strategies (with regenk <1) result in energy losses that are

more-appropriately attributed to the choice of powertrain technology rather than the vehicle

platform (which defines the road load).

Equation 3-18 is in fact only an approximate estimate of the braking losses since it assumes

that all vehicle deceleration is produced by braking. In reality a certain portion of vehicle

deceleration results from aerodynamic and rolling drag forces. The PAMVEC approach

models the irreversible drag losses and reversible inertial power flows as separate,

independent power flows in the powertrain, whereas in reality the two components add

together to give to net power flow (and when the net power flow is negative during

deceleration, its magnitude is reduced by the positive drag power). Therefore, equation 3-18

will always overestimate the average braking losses and in this manner is consistently

conservative.

This decoupling of irreversible and reversible power flows (Figure 3-2) is a central

assumption of the PAMVEC modelling approach, since it provides simplicity in the model

and enables the use of the novel parametric driving pattern description. However, it is also

the primary cause of modelling error. Figure 3-3 demonstrates the overestimation of average

braking losses for a section of the UDDS driving cycle, using a representative vehicle

platform with the following characteristics:

Mass: 1550kg

Drag-area (CDA): 0.8m2

Rolling resistance coefficient (CRR): 0.01

Regenerative braking fraction (kregen): 0.0

The braking loss error of 44% in the example in Figure 3-3 may seem large, but it must be

taken in the context of estimating the energy consumption for the entire vehicle. The braking

losses represent only a fraction of the total energy consumption and the significance of this

error in the total estimate will be reduced by the same fraction. Furthermore, the error in the

braking loss estimate is a function of the vehicle mass-to-drag ratio and the characteristics of

the driving pattern.

Owner

Underline

Owner

Underline

34


braking losses

0

10

20

30

40

50

60

Pow

er (k

W)

Estimated drive outputActual drive output

-60

-40

-20

0

20

40

60

Pow

er (k

W)

-60

-40

-20

0

20

40

60

Pow

er (k

W)

-60

-40

-20

0

20

40

60

Pow

er (k

W)

Road Load

Braking Losses

Inertial Power Drag Power

Drivetrain Output

Decoupling

0

10

20

30

40

50

60

Pow

er (k

W)

Estimated braking lossesActual braking losses

35

260 270 280 290 300 310 320 3300

50

100

Spe

ed (k

m/h

)

260 270 280 290 300 310 320 330-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5x 104

Time (s)

Pow

er (W

)

Proad

Paccel

Pdrag

Pdrag-avg = 2.23kW

Pbrake-avg = -1.60kW

Pbrake-avg-est = -2.30kW

Braking loss overestimated

Figure 3-3: Overestimation of average braking losses in a representative vehicle platform for

a section of the UDDS driving cycle

To demonstrate these interrelationships, Figure 3-4 presents errors in the estimate of outdriveP −

(equation 3-19) over a range of mass-to-drag ratios for several contrasting driving patterns.

This better illustrates the contribution of the error in the braking loss estimate to the error in

the estimate of total energy consumption, and the error in outdriveP − is generally less than 20%

across the full range of driving patterns and vehicle platforms. In practice, there are other loss

components such as powertrain inefficiencies and accessory loads which will further reduce

the contribution of the braking loss estimate error.

3.2 Driving Pattern Parameters

The previous section derived a parametric formulation of the road load equation. A novel

feature of this parametric approach is the use of only three parameters to fully characterise the

driving pattern – the average velocity (vavg), the velocity ratio (Λ ) and the characteristic

36

acceleration ( a~ ). Mathematical definitions of these three parameters are provided in

equations 3-5, 3-7 and 3-16 respectively.

1500 2000 2500 3000 3500 4000 4500 50008

10

12

14

16

18

20

22

UDDS

US06

HWFET

NYCC

NEDC

Vehicle mass-to-drag ratio (kg/m2)

Erro

r (%

)

Errors in the estimate of Pdrive-out for various driving patterns

Figure 3-4: Errors in the estimate of outdriveP − (equation 3-19) over a range of mass-to-drag

ratios for several contrasting driving patterns

In the context of driving pattern research, this set of parameters offers two important benefits.

Firstly, all three parameters can be calculated directly from a measured velocity profile. They

do not require the use of accelerometers (which are sensitive to higher-frequency vibration

onboard a vehicle) or differentiators (which are sensitive to noise in the measured velocity

profile) to provide acceleration data with which to quantify a driving pattern. The other key

benefit of this set of parameters is that they form an orthogonal (or independent) coordinate

set that quantify multiple dimensions of a driving pattern. In layman’s terms, these

dimensions are:

• Average velocity – the fundamental driving pattern attribute that describes how

quickly a vehicle will complete its journey.

• Velocity ratio – quantifies the range of speeds at which a vehicle has travelled during

its journey, but contains no information about the rate at which vehicle speed has

changed. A journey that includes periods of both low-speed, urban driving and high-

37

speed, highway driving will have a large velocity ratio. The minimum-possible value

for velocity ratio is unity, which corresponds to constant speed driving.

• Characteristic acceleration – quantifies the rate at which vehicle speed changes

throughout the journey, without providing any information regarding the range of

speeds at which the vehicle travels. The minimum-possible value for characteristic

acceleration is zero1, which corresponds to constant speed driving.

To better illustrate the physical meaning of each parameter, Figures 3-5 to 3-8 provide

examples of a hypothetical velocity profiles in the shape of a sine wave. Figure 3-5 presents

the base-case driving pattern with parameter values of vavg = 10m/s, Λ= 1.1 and a~ = 0.1m/s2.

Figures 3-6 to 3-8 show the resulting driving patterns when each parameter is increased by

5% independent of the other parameters. This ability to vary each parameter independent of

the others is a confirmation of their orthogonality, but also demonstrates their physical

meaning.

0

10

20

30

40

50

60

0 20 40 60 80 100 120

time (s)

spee

d (k

ph)


and a~ = 0.1m/s2

In Figure 3-6, avgv has been increased by 5%. However, to maintain the same value for Λ the

amplitude of the sine wave is also increased by 5%. But this increases the acceleration of the

1 By definition, a characteristic acceleration greater than zero implies a velocity ratio greater than unity, and vice versa.

38

vehicle (sine wave slope) by 5% - therefore the frequency of the sine wave must be decreased

(and the period increased) by 5% to keep a~ constant. In Figure 3-7, the amplitude of the sine

wave has been increased in order to increase Λ by 5%, whereas, the average speed is

unchanged. Therefore, the period of the sine wave is increased to produce the same a~ as the

base case. In Figure 3-8, the average speed and sine wave amplitude are unchanged such that

the values of avgv and Λ are the same. However, to increase a~ by 5% the frequency of the

sine wave must be increased (and the period decreased) by 5%.

0

10

20

30

40

50

60

0 20 40 60 80 100 120

time (s)

spee

d (k

ph)

Figure 3-6: A hypothetical driving pattern with parameter values of vavg = 10.5m/s (5%

increase), Λ= 1.1 and a~ = 0.1m/s2

Of course, the sine wave velocity profiles in Figures 3-5 to 3-8 are poor examples of realistic

driving patterns. They do serve, however, to demonstrate the physical meaning of the driving

pattern parameters. To demonstrate parameter values that might be expected in more-realistic

driving patterns, Table 3-1 presents the average velocities, velocity ratios and characteristic

accelerations for some well-known driving cycles. Further driving pattern parameters are

presented in Appendix A.

39

0

10

20

30

40

50

60

0 20 40 60 80 100 120

time (s)

spee

d (k

ph)


(5% increase) and a~ = 0.1m/s2

0

10

20

30

40

50

60

0 20 40 60 80 100 120

time (s)

spee

d (k

ph)


and a~ = 0.105m/s2 (5% increase)

40

Table 3-1: Driving pattern parameters for some well-known driving cycles

Average

velocity (km/h)

Root-mean-cubed

velocity (km/h)

Velocity ratio Characteristic

acceleration (m/s2)

Cycle

avgv rmcv Λ a~

NYCC 11.4 20.6 1.81 0.293

NEDC 33.0 53.6 1.62 0.112

UDDS 31.4 44.5 1.42 0.171

US06 76.9 91.2 1.19 0.190

HWFET 77.2 80.0 1.04 0.069

Figure 3-9 plots the velocity ratio (Λ ) versus the average velocity ( avgv ) for the driving cycles

presented in Appendix A. The curve fitted to this data suggests that there may be a definable

relationship between the velocity ratio and average speed. Qualitatively speaking, driving

cycles with a lower average speed tend to have a higher velocity ratio. This may be due to the

fact that during high-average-speed driving patterns (e.g. highway driving) a vehicle spends

most of its time travelling at velocities near the posted speed limit. In contrast, low-average-

speed driving patterns (e.g. stop-start urban driving) tend to involve significant periods of

travel at a wide range of speeds anywhere between standstill and the posted (albeit lower)

speed limit.

In contrast, there seems to be no relationship between average speed and characteristic

acceleration observed in driving patterns, as plotted in Figure 3-10. Driving patterns can have

large or small characteristic accelerations at both low and high average speeds.

41

Velocity ratio vs. Average velocity

1.00

1.20

1.40

1.60

1.80

2.00

2.20

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00

kph Figure 3-9: Velocity ratio (Λ ) vs. average velocity ( avgv ) for the driving cycles presented in

Appendix A

Characteristic acceleration vs. Average velocity

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.350

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00

kph

m/s

^2

Figure 3-10: Characteristic acceleration ( a~ ) vs. average velocity ( avgv ) for the driving

cycles presented in Appendix A

42

3.3 Powertrain Losses

The parametric approach can also be extended to model the powertrain losses in a vehicle.

However, there are subtle differences in the manner in which powertrain losses occur in

different powertrain architectures. Such powertrain architectures include:

• Conventional internal combustion engine vehicles (ICVs)

• Parallel hybrid-electric internal combustion engine vehicle (PHEVs)

• Series hybrid-electric internal combustion engine vehicles (SHEVs)

• Fuel cell-electric vehicles (FCEVs)

• Fuel cell hybrid-electric vehicles (FCHEVs)

• Battery electric vehicles (BEVs)

Therefore, this thesis firstly derives a model for the powertrain losses in generalised

powertrain architecture. Then, by using a series of simplifications and/or modifications, this

model is applied to the specific architectures listed above.

3.3.1 Generic Powertrain Architecture

A diagram of the generic powertrain architecture is shown in Figure 3-11.

Figure 3-11: Generic powertrain architecture

It is clearly a hybrid vehicle in that it includes two power sources:

• A high specific energy device (HSED) that provides the energy required to complete a

driving pattern. The HSED is typically capable of handling monodirectional power

flows only.

HSED

HSPD

DRIVE

FUEL

To axle/wheels

BRAKES

43

• A high specific power device (HSPD) that provides peak power capability in addition

to that of the HSED and also acts as a energy buffer/storage mechanism to smooth the

load experienced by the HSED. The HSPD is typically capable of handling bi-

directional power flows.

The generic powertrain architecture also includes a bi-directional drivetrain component that

transfers power between the power sources and wheels of the vehicle. With the bi-directional

power capabilities of the drivetrain and HSPD, the vehicle can achieve a certain fraction of its

braking via regenerative braking, with the remainder performed by friction brakes. In

accordance with equations 3-18 and 3-19, the average rate of power absorbed by the

powertrain due to regenerative braking will be:

avgtotalmregeninertiaregenregen vamkkPkP ~== (3-20)

However, due to inefficiencies in the drivetrain and HSPD, a certain fraction of this

regenerative power will be lost rather than being stored in the HSPD. Similarly, the

inefficiencies of the HSPD and drivetrain create losses during acceleration manoeuvres and

general cruising.

Drivetrain Losses

There are three components that must be considered in order to calculate the drivetrain losses:

• roadP – the average power required to overcome drag forces on the vehicle (equation

3-8). This component can be considered as representing the average drivetrain power

required for vehicle cruising.

• inertiaP – the average rate of kinetic energy storage in the vehicle inertia (equation 3-

17). This component represents the average drivetrain power required for vehicle

acceleration.

• regenP - the average rate of kinetic energy absorbed by the drivetrain (equation 3-20).

This component represents the average power absorbed by the drivetrain during

regenerative braking.

Each of these components cause losses in the drivetrain, however, it is important to note they

are not separate driving “modes” but rather are time-averaged quantities that must be

44

considered simultaneously. Furthermore, the direction of the regenP power flow is opposite to

that of the other components which results in a slightly different definition of the losses in that

component. The average drivetrain losses are given by

( ) ( ) regendriveinertiaroaddrive

drivelossdrive PPPP η

ηη

−++−

=− 11

(3-21)

where driveη is the mean efficiency of the drivetrain over the driving pattern. Again, the

PAMVEC model assumes a decoupling of the drag and inertial power flows (Figure 3-12) and

similar to the expression for braking losses, equation 3-21 is an approximate overestimate of

the drivetrain losses since in reality some fraction of vehicle braking is produced by vehicle

drag. To explore the significance of the error in the drivetrain loss estimate, we must first

define the average drivetrain input power:

indriveP − lossdriveoutdrive PP −− +=

( ) ( ) regendriveinertiaroaddrive

drivebrakingroad PPPPP η

ηη

−++−

++= 11

( )

drive

inertiaregendriveroad PkPηη 21−+

= (3-22)

Figure 3-13 plots the error in the estimate of indriveP − across a range of mass-to-drag ratios for

several different driving cycles (assuming CRR = 0.009, kregen = 50% and ηdrive = 80%). In all

cases the error in the estimate is less than 15%.

HSPD Losses

For a given vehicle platform and driving pattern, equation 3-22 calculates the average power

that must be supplied to the input of the drivetrain. This also represents the average power

that must be supplied by the vehicle’s power sources – the HSED and HSPD. However, as

previously noted, the function of the HSPD is to supply/absorb peak powers and filter the

loading on the HSED. The result is that small packets of energy are continuously being

transferred in and out of the HSPD, with losses occurring due to its inefficiencies. In

acknowledgement of this fact, the efficiency of HSPD technologies is commonly quoted in

terms of round-trip efficiency, rather than the throughput efficiency that is typical of other

45

powertrain components. Round-trip efficiency defines the losses in the HSPD as a fraction of

the energy that is temporarily stored in it. Therefore, to determine the average losses in the

HSPD, the average rate of energy storage in the HSPD must first be estimated.

Unfortunately, calculating the average rate of energy storage in the HSPD is a particularly

difficult task since it depends not only on the nature of the driving pattern, but also on the

power control strategy that shares the drivetrain power demands between the HSED and

HSPD. To overcome this difficulty, the PAMVEC model makes the following assumptions:

• The power control strategy is assumed to be charge-sustaining i.e. the net rate of

power flow from the HSPD is zero such that it is never discharged.

• The HSED supplies the average powertrain power requirement (including HSPD

losses) given as:

( )accessorylossHSPD

drive

inertiaregendriveroadHSED PP

PkPP ++

−+= −η

η 21 (3-23)

These assumptions may not be true in reality, but they provide a set of convenient

simplifications that allow the average rate of energy storage in the HSPD to be estimated.

Recall that the average drivetrain input power (equation 3-22) consists of three components –

the average road load, the average braking losses and the average drivetrain losses. Equation

3-23 implies that the HSED is dedicated to supplying the power for these components.

However, no account has been made for the power that must be supplied by the power sources

in order to store kinetic energy in the vehicle inertia. Similarly, a fraction of the stored kinetic

energy is returned to the powertrain via regenerative braking and this energy must be

absorbed by the power sources. Since the HSED is assumed to be otherwise occupied, the

natural consequence is to assume that these power demands are met by the HSPD.

The average power the HSPD must supply in order to store kinetic energy in the vehicle mass

at the rate of inertiaP is:

inertiaaccelHSPD PP =− (3-24)

46


drivetrain losses

-60

-40

-20

0

20

40

60

Pow

er (k

W)

-60

-40

-20

0

20

40

60

Pow

er (k

W)

-60

-40

-20

0

20

40

60

Pow

er (k

W)

0

1

2

3

4

5

6

Pow

er (k

W)

0

1

2

3

4

5

6

Pow

er (k

W)

Road Load

Inertial Losses Drag Losses

Inertial Power Drag Power

Total Losses

Decoupling

0

1

2

3

4

5

6

Pow

er (k

W)

Estimated LossActual Loss

47

1000 1500 2000 2500 3000 3500 4000 4500 50007

8

9

10

11

12

13

14

15


Erro

r (%

)

Errors in the estimate of Pdrive-in for various driving patterns

NEDC

NYCC

UDDS

HWFETUS06

Figure 3-13: Error in the estimate of indriveP − across a range of mass-to-drag ratios for

several different driving cycles

Equation 3-24 makes no allowance for drivetrain losses because these are already being

supplied by the HSED. Similarly, the average power the HSPD must absorb from

regenerative braking is:

inertiaregenbrakingHSPD PkP =− (3-25)

Ideally, the quantities calculated by equations 3-24 and 3-25 should be identical in order to

satisfy the constraint of a charge-sustaining control strategy. Therefore, to estimate the

average rate of energy charge/discharge in the HSPD we take the average:

inertiaregenbrakingHSPDaccelHSPD

HSPD PkPP

P2

12

+=

+= −− (3-26)

The average HSPD losses will then be:

48

( )( )inertia

regenHSPDlossHSPD P

kP

211 +−

=−

η (3-27)

where HSPDη is the HSPD round-trip efficiency.

Control Strategy Issues

For hybrid vehicles, the spectrum of powertrain control strategies is defined by two extremes:

1) a power-assist or load-following strategy where the HSED tries to follow the road load

whenever possible; and 2) a thermostatic control strategy where the HSED load is completely

buffered by the HSPD (Anderson & Pettit, 1995). The constant HSED power assumption in

equation 3-23 is clearly idealistic and realistic control strategies combine elements of the

thermostatic and load-following approaches. In developing an optimised control strategy, a

trade-off must be made between increased losses in the HSPD vs. reduced operating

efficiency of the HSED. A thermostatic approach makes the most sense when the HSED can

be operated at its optimum point (in terms of power or torque/speed). Therefore, the optimum

control strategies for FCHEVs and SHEVs tend to display a thermostatic characteristic, since

in these architectures the HSED is electrically de-coupled from the road load (Anderson &

Pettit, 1995; Cuddy & Wipke, 1997; Moore, 1997; Wipke et al, 2001). In PHEVs, the engine

is coupled to the wheels via the transmission and can rarely be operated at its optimum point –

therefore, the optimum control strategy tends to forgo some engine efficiency for the sake of

reduced losses in the battery by operating the engine over a wider range of torques/speeds

with more of a load-following approach (Anderson & Pettit, 1995; Cuddy & Wipke, 1997;

Moore, 1997). Practical differences in the control strategies of the difference HEV

architectures are discussed further in Sections 3.3.2, 3.3.3 and 3.3.5.

The thermostatic-style control strategy gets its name from the fact that for some HSED

technologies the average power requirement determined by equation 3-23 is so low that, if the

HSED were to operate at this power level, its efficiency would be prohibitively low. Figure

3-14 demonstrates for some hypothetical HSED technologies how there is typically an

optimum operating power level below which the HSED efficiency can fall quite rapidly.

In these situations, it is preferable to operate the HSED in a thermostatic manner, with the

HSED operating at its optimal power level when switched on. The duty ratio (D) of this

49

on/off cycle is chosen such that the average HSED output power equates to that calculated in

equation 3-23:

∗=HSED

HSED

PP

D (3-28)

where ∗HSEDP is the HSED optimal operating power level. Unfortunately, this thermostatic

operation results in additional HSPD losses as large packets of energy are cycled in and out of

the HSPD, as demonstrated in Figure 3-15.

Power

Effi

cien

cy

Figure 3-14: Efficiency vs. load curves for some hypothetical HSED technologies

In these cases, the HSPD losses include an additional term as follows:

( )( )icthermostatlossHSPDinertia

regenHSPDlossHSPD PP

kP −−− +

+−=

211 η

(3-29)

( )( )HSEDHSEDHSPDicthermostatlossHSPD PPDP −−= ∗−− η1 (3-30)

Therefore, thermostatic control strategies will produce larger HSPD losses, however, they do

have the advantage of allowing the HSPE to operate at higher efficiency. For further

50

discussion of the practical implications of various control strategies, the reader is directed to

the work of Anderson & Pettit (1995), Cuddy & Wipke (1997), Moore (1997) and Wipke et al

(2001).

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

-50

0

50

100

Time (s)

Pow

er (k

W)

PtotalPhsePhsp

0 10 20 30 40 50 60 70 80 90 100-0.02

0

0.02

0.04

0.06

Time (s)

HS

P S

OC

Figure 3-15: Thermostatic losses due to the cycling of energy through the HSPD

HSED Losses and Fuel/Energy Input to the HSED

The average output power requirement of the HSED is calculated using equation (3-23).

From this average output power, the HSED losses and fuel energy input requirements are

calculated as follows:

HSEDHSED

HSEDlossHSED PP

ηη−

=−

1 (3-31)

HSEDHSED

fuel PPη

1= (3-32)

where HSEDη is the driving pattern-averaged operating efficiency of the HSED.

51

This completes the derivation of a model for the losses of generalised powertrain architecture.

In the following sections, the generic powertrain energy loss model is applied to the following

specific powertrain architectures:

• Conventional internal combustion engine vehicles (ICVs)

• Parallel hybrid-electric internal combustion engine vehicle (PHEVs)

• Series hybrid-electric internal combustion engine vehicles (SHEVs)

• Fuel cell-electric vehicles (FCEVs)

• Fuel cell hybrid-electric vehicles (FCHEVs)

• Battery electric vehicles (BEVs)

The fuel cell hybrid-electric vehicle is considered first, as its architecture most-closely

resembles that of the generic powertrain. Then, through the use of appropriate analogies and

assumptions, the application of the generic model is extended to the other powertrain

architectures.

3.3.2 Fuel Cell Hybrid-Electric Vehicles

The powertrain architecture of a fuel cell hybrid-electric vehicle (Figure 3-16) is a close

match with the generic powertrain architecture. Therefore, the generic powertrain energy loss

model can be applied directly using the following equivalencies:

• HSED = fuel cell (and reformer if applicable)

• HSPD = battery (or sometimes an ultra capacitor)

• DRIVE = motor/controller and transmission

Figure 3-16: Powertrain architecture for a fuel cell hybrid-electric vehicle

For all powertrain architectures, the expression for drivetrain output power (3-19) is the same.

Therefore, we commence with the expression for drivetrain losses. Using the above

equivalencies, we may write:

Fuel Cell/ Reformer

Battery

Motor/ Controller

Fuel

To axle/ wheels Single-speed

Transmission

52

mctransdrive ηηη ×= (3-32)

where transη is the transmission efficiency and mcη is the combined motor/controller

efficiency. Using equation (3-21) the expression for drivetrain losses becomes:

( ) ( ) regenmctransinertiaroadmctrans

mctranslossdrive PPPP ηη

ηηηη

−++−

=− 11

(3-33)

For the battery, we may use its HSPD equivalency and assume a thermostatic control strategy

(equations (3-29) and (3-30)) to write the following expression for battery losses:

( )( )icthermostatlossbatteryinertia

regenbatterylossbattery PP

kP −−− +

+−=

211 η

(3-34)

( )( )FCFCbatteryicthermostatlossbattery PPDP −−= ∗−− η1 (3-35)

where batteryη is the battery efficiency, ∗FCP is the optimum fuel cell operating power, and FCP

is the average fuel cell power requirement, written as:

accessorylossbatterylossdriveoutdriveFC PPPPP +++= −−− (3-36)

Using the above HSED equivalency and equation (3-32), we may then write the following

expression for the average fuel energy flow:

FCFCreformer

fuel PPηη

1= (3-37)

where reformerη is the average reformer efficiency, and FCη is the average fuel cell efficiency.

53

3.3.3 Fuel Cell Electric Vehicles

The key difference in the powertrain architecture of a fuel cell electric vehicle (Figure 3-17)

and fuel cell hybrid-electric vehicle (Figure 3-16) is the lack of an HSPD component (battery

or ultra capacitor). Otherwise, the same equivalencies hold.

Figure 3-17: Powertrain architecture for a fuel cell electric vehicle

However, the lack of an HSPD component does have a significant impact on the expressions

for the losses in the powertrain, since it prevents the use of regenerative braking which forces

the values of regenk and regenP to zero. Firstly, using equation (3-19), this results in a different

expression for the average drivetrain output power:

avgtotalmavgtotalRRavgDoutdrive vamkgvmCvACP ~3321 ++Λ=− ρ (3-39)

Secondly, using equation (3-21) we may write the following expression for drivetrain losses:

( )inertiaroadmctrans

mctranslossdrive PPP +

−=− ηη

ηη1 (3-40)

There will obviously be no HSPD losses in a fuel cell electric vehicle. Therefore, the average

fuel cell power requirement will be:

accessorylossdriveoutdriveFC PPPP ++= −− (3-41)

The average fuel energy flow (power) will be as derived in equation (3-38).

Fuel Cell/ Reformer

Motor/ Controller

Fuel


Transmission

54

3.3.4 Series Hybrid-Electric Internal Combustion Engine Vehicles

Schematically, a series hybrid-electric vehicle (Figure 3-18) is nearly identical to a fuel cell

hybrid-electric vehicle, with the following exception:

• HSED = engine/generator

Otherwise the same equivalencies hold.

Figure 3-18: Powertrain architecture for a series hybrid-electric vehicle

Therefore, in a SHEV, the expression for drivetrain losses is the same as for the FCHEV:



ηηηη

−++−

=− 11

(3-42)

So too is the expression for battery losses, with the exception of the thermostatic battery loss

component:

( )( )icthermostatlossbatteryinertia

regenbatterylossbattery PP

kP −−− +

+−=

211 η

(3-43)

( )( )GenGenbatteryicthermostatlossbattery PPDP −−= ∗−− η1 (3-44)

where ∗GenP is the optimum generator output power, and GenP is the average generator power

requirement, written as:

accessorylossbatterylossdriveoutdriveGen PPPPP +++= −−− (3-45)

Engine/ Generator

Battery

Motor/ Controller

Fuel


Transmission

55

Lastly, the average fuel flow (power) will be:

GenGen

fuel PPη

1= (3-46)

where Genη is the combined efficiency of the engine/generator.

3.3.5 Parallel Hybrid-Electric Internal Combustion Engine Vehicles

While in theory the power flows within a PHEV (Figure 3-19) are similar to those in a SHEV,

in practice there are a few important differences. Firstly, the motor/controller only handles

power flows in/out of the battery. Furthermore, of all the hybrid-electric powertrain

architectures, the PHEV is unique in that the HSED speed is coupled to the wheel speed via

the transmission and for this reason a power-assist style control strategy is normally preferred

(see section 3.3.1).

Figure 3-19: Powertrain architecture for parallel hybrid-electric vehicle

Therefore, in PHEVs a substantial fraction of inertiaP tends to be provided by the engine with

the motor/battery providing power assist. During regenerative braking, the motor/battery is

still used to the maximum extent possible. These factors lead to some subtle differences in the

expression for drivetrain losses within a PHEV (equation 3-47). The drivetrain losses due to

regenerative braking ( regenP ) are unchanged. The change in losses due to drag forces ( roadP )

reflects the fact that motor/controller only handles power flows in/out of the battery. Lastly,

the losses due to vehicle acceleration ( inertiaP ) reflect the fact that the motor/controller only

handles part of this load component (with the remained provided by the engine). The exact

Engine/ Clutch

Battery

Motor/ Controller

Fuel

To axle/ wheels Multi-speed

Transmission

56

fraction of inertial load handled by the motor/controller is, of course, control strategy and

driving pattern dependent, but for convenience the PAMVEC model assumes that it is

proportional to the degree-of-hybridisation (DOH) defined in section 3.5.4.

( ) ( ) regenmctranstrans

inertia

mc

mcinertiaroad

trans

translossdrive P

PDOHPPP ηη

ηηη

ηη

−+−

×++−

=− 111

(3-47)

Similarly, there are subtle differences in the expression for battery losses:

( )( )inertia

regenbatterylossbattery P

kDOHP

21 +−

=−

η (3-48)

The average engine power requirement is given as:

accessorylossbatterylossdriveoutdriveICE PPPPP +++= −−− (3-49)

Lastly, the average fuel flow (power) will be:

ICEICE

fuel PPη

1= (3-50)

where ICEη is the average efficiency of the engine.

3.3.6 Conventional Internal Combustion Engine Vehicles

Just like the non-hybridised FCEVs, conventional internal combustion engine vehicles

(Figure 3-20) do not have a load-levelling HSPD component. Therefore, the expression for

the average drivetrain output power in an ICV is the same as for a FCEV:

avgtotalmavgtotalRRavgDoutdrive vamkgvmCvACP ~3321 ++Λ=− ρ (3-51)

57

Figure 3-20: Powertrain architecture for a conventional internal combustion engine vehicle

Furthermore, compared to a FCEV an ICV only has one component – the multi-speed

transmission – in its drivetrain. Therefore, the expression for drivetrain losses is:

( )inertiaroadtrans

translossdrive PPP +

−=− η

η1 (3-52)

The expression for the average engine power in an ICV is the same as for a FCEV:

accessorylossdriveoutdriveICE PPPP ++= −− (3-53)

The average fuel energy flow (power) will be as presented in equation (3-50).

3.3.7 Battery Electric Vehicles

Of all the powertrain architectures, the BEV (Figure 3-21) is unique in that its power source

(the battery) simultaneously fulfils the dual roles of HSED and HSPD.

Figure 3-21: Powertrain architecture for a battery-electric vehicle

Engine/Clutch

Fuel

To axle/ wheels Multi-speed

Transmission

Battery Motor/ Controller

Charger


Transmission

58

The expression for drivetrain losses is the same as for the other electric-drive vehicles:



ηηηη

−++−

=− 11

(3-54)

So too is the expression for HSPD losses, with the exception that there is no thermostatic

component:

( )( )inertia

regenbatterylossbattery P

kP

211 +−

=−

η (3-55)

However, equation (3-55) only accounts for the micro-cycling of power through the battery

during acceleration and braking manoeuvres. During a driving pattern, the battery in a BEV

also experiences a net rate of discharge:

accessorylossbatterylossdriveoutdriveBattery PPPPP +++= −−− (3-56)

At the end of the journey, the BEV will need to be recharged. Therefore, the expression for

the average electrical power input to a BEV includes parameters that account for the battery

and charger efficiencies during recharging:

BatteryBatteryerCh

elec PPηη arg

1= (3-57)

where erCh argη is the efficiency of the charger, and elecP is the average electric power for

charging the BEV.

3.4 Vehicle Performance

An important component of the parametric model developed by this thesis is the expressions

that relate vehicle performance to the size of powertrain components. These can be used to

predict vehicle performance on the basis of specified components (explicit method) or, more

importantly, to estimate the size of components are required to meet a series of vehicle

59

performance targets (implicit method). In this way, different powertrain technologies can be

compared on the level playing field of equivalent performance.

This thesis considers four separate performance metrics, although the approach can readily be

extended to include other performance criteria:

• Top Speed

• Gradability

• Driving Range

• Standing acceleration time (typically from 0-100kph/0-60mph)

3.4.1 Top Speed

For all vehicles, a simple expression relates the drivetrain output power to the top speed

performance criterion. Assuming the road load is represented by equation 3-1, and assuming

no road gradient, the required drivetrain output power at the top speed is:

topspeedtotalRRtopspeedDtopspeed

outdrive gvmCAvCP +=−3

21 ρ (3-58)

where topspeedv is the required continuous top speed of the vehicle.

3.4.2 Gradability

For all vehicles, a simple expression relates the drivetrain output power to the continuous

gradability performance criterion. Assuming the road load is represented by equation 3-1, and

assuming no acceleration, the required drivetrain output power for gradability:

gradegradetotalgradetotalRRgradeDgrade

outdrive vgZmgvmCAvCP ++=−3

21 ρ (3-59)

where gradeZ is the required gradability (as a fraction e.g. 1/10) at the speed of gradev .

60

3.4.3 Driving Range

The driving range constraint for a vehicle specifies the size of its fuel storage system. For

vehicles with a fuel tank, the size of the energy storage system (in Wh) is related to the

average flow of fuel (equations 3-37, 3-45 & 3-50) as follows:

( )kphavg

fuel

vP

RangeWhFuel−

×= (3-60)

where Range is the driving range constraint (km), and kphavgv − is the average speed of the

driving pattern (kph). For BEVs, the required energy storage relates to the average power

output of the battery as follows:

( )kphavg

battery

vP

RangeWhEnergy−

×= (3-61)

3.4.4 Acceleration

One novel aspect of the PAMVEC model is the parametric expression(s) used to determine

powertrain output power requirements due to vehicle acceleration performance. As noted in

Section 2.3.2, several analysts have previously developed parametric expressions of this kind,

with examples being found in Delucchi (2000), Plotkin et al (2001) and Ehsani et al (1997).

Assuming level road, Delucchi’s expression for the acceleration power required at the wheels

of the vehicle is:

k

vgmCAvCtv

mP

acceltotalRRaccelDaccel

acceltotal

2

241 ⎥

⎦

⎤⎢⎣

⎡++⎟⎟

⎠

⎞⎜⎜⎝

⎛

=

ρ (3-62)

where accelt is the time taken to accelerate to the terminal speed accelv , and k is an adjustment

factor to account for differences in the torque-speed characteristics of different technologies

(e.g. engines vs. electric motors), given as:

Owner

Underline

Owner

Underline

61

2

1,2

min1

E

accel

Ev

k ⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛= (3-63)

Values for E1 and E2 in equation 3-60 are provided in Table 3-2.

Table 3-2: Values for E1 and E2 in equation 3-60 as presented by Delucchi (2000)

ICE EV

E1 30 20

E2 0.55 0.20

Plotkin et al (2001) derived the following expression for the acceleration power required at

the wheels of the vehicle by assuming that the vehicle’s acceleration response (speed vs. time)

was a hyperbolic function.

bamP total += (3-64a)

accelRR

x

accel

accelaccel gvCt

ttt

va +

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛ ∆+∆

= 12

(3-64b)

321

accelD AvCb ρ= (3-64c)

where t∆ is some very small time increment (say 0.01s) and x ranges between 0.5-0.66 for

zero to 100kph/60mph acceleration times of 8-13 seconds. Plotkin et al use a value of x =

0.5 for all EVs and x = 0.56 for PHEVs. Presumably, a value of x = 0.66 corresponds to

ICVs, although this was not indicated in their documentation.

The equations used by Delucchi (2000) and Plotkin et al (2001) are quite reliant on empirical

factors to describe the torque-speed characteristics of a drivetrain. In contrast, Ehsani et al

(1997) handle this issue by assuming a generic shape for the torque-speed curve of a

drivetrain shown in Figure 3-22. This consists of a region of constant maximum torque up to

the “base speed”, followed by a region of constant power up to the maximum speed. The

shape is characterised by a parameter known as the over-speed ratio – define as the ratio of

the maximum and base speeds. In practice, this torque-speed characteristic is produced with

the use of a multi-speed transmission, or in some electric drives through field-oriented control

62

techniques (field weakening). Figure 3-23 demonstrates the “overspeed” torque-speed

characteristic for a 100kW UQM Technologies drive system (UQM, 2001).

Figure 3-22: The generic shape of the torque-speed curve of a drivetrain

For the ideal case where aerodynamic drag, rolling resistance and road gradient are zero,

Ehsani et al (1997) derived the following expression for vehicle acceleration power in terms

of the drivetrain overspeed ratio N :

accel

acceltotal

tvm

NNP

21 2

2

2

×+

= (3-65)

Intuitively, this expression makes a lot of sense in that the required peak drivetrain power

during the acceleration event is simply the maximum kinetic energy divided by the

acceleration time, corrected by an over-speed-ratio-dependent factor to account for the period

of acceleration at constant torque. (In the limit that ∞=N the entire acceleration would

occur at constant power and the required power would simply be the kinetic energy divided

by the acceleration time.) Unfortunately, the realistic case including drag losses cannot be

integrated analytically due to nonlinearities and this is one issue with this approach.

Furthermore, in reality the torque-speed characteristics of actual drivetrains (both electrical

and mechanical) deviate from the idealised curve in Figure 3-22. However, because of its

potential ability to model the different torque-speed characteristics of various drivetrain

technologies (rather than relying on empirical relationships), the author chose to develop the

approach of Ehsani et al (1997) further by attempting to address these issues. Another issue

that is unaddressed by any of the previous approaches is the effect that vehicle top speed can

Torque

Speed Base Speed

Max Torque

Max Speed

Constant power

Constant torque

63

have upon acceleration power requirements, but this has also been accounted for in the

PAMVEC model.

Figure 3-23: Torque-speed characteristic of the UQM Technologies PowerPhase 100kW

drive system

Vehicle Drag Effects

It is possible to devise a convenient approximation that accounts for drag effects (and any

other frictional loss mechanisms) in the acceleration power requirement. Firstly, it is noted

that the drag power at zero speed is zero. Secondly, at the terminal speed accelv the

drag/frictional losses will be at their maximum. If the drag/frictional losses are represented by

equation (3-1), then the power loss at the terminal speed will be:

acceltotalRRaccelDvdrag gvmCAvCPaccel

+=−3

21 ρ (3-66)

To incorporate these losses into equation (3-65), a simple approach is to assume that the drag

losses vary linearly with time between zero and accelvdragP − during the acceleration. This

implies that the average drag losses during the manoeuvre will be accelvdragP −2

1 , leading to the

following expression:

221 2

2

2accelvdrag

accel

acceltotalmacceloutdrive

Pt

vmkN

NP −− +×

+= (3-67)

64

Although equation (3-67) may seem a crude estimate of the required drivetrain power for

acceleration, it is surprisingly accurate. Table 3-3 compares errors in the estimates of

acceleration power using equation 3-67 for a mid-range value of N = 2 with CDA = 0.8 and

CRR = 0.01.

Table 3-3: Errors in the estimates of acceleration power using equation 3-67

6 8 10 121000 1.4% 1.8% 2.1% 2.4%2000 0.4% 0.6% 0.8% 1.0%3000 0.0% 0.0% 0.3% 0.5%

0-100kph acceleration time (s)

Mass to drag ratio (kg/m2)

The Effect of Top Speed Performance

It is normally the case that a vehicle’s top speed is greater than the terminal speed used to

define acceleration performance criteria (e.g. 180kph top speed vs. 0-100kph in 10 seconds).

The result is that only a lower portion of the drivetrain’s torque-speed curve is used to

complete the prescribed acceleration manoeuvre. The consequence is that the drive train over

speed ratio N in equation 3-67 must be reduced as follows:

topspeed

acceldriveaccel v

vNN ×= (3-68)

221 2

2

2accelvdrag

accel

acceltotalm

accel

accelacceloutdrive

Pt

vmkN

NP −

− +×+

= (3-69)

For example, consider a hypothetical drivetrain with driveN = 3. If the vehicle top speed

constraint (eg. 200kph) is double the terminal speed specified by the acceleration constraint

(eg. 100kph), then accelN = 1.5 in equations 3-68 and 3-69. Therefore, the top speed

performance criterion for a vehicle has a secondary influence on the acceleration

performance. For a fixed value of driveN , as the top speed criterion increases, the value of

accelN decreases which increases the drivetrain power output required to satisfy the

acceleration criteria.

65

To apply equation 3-69 to real vehicle powertrains, it must be considered how the torque-

speed curves of real drivetrains differ from the idealised model considered so far.

Drivetrains with Field Weakening

The powertrain architectures that fall under this category are the all-electric drives – the

BEVs, SHEVs, FCEVs and FCHEVs. Field-oriented control techniques (including field

weakening) can be utilised with some electric motor technologies to produce a torque-speed

characteristic similar to that of Figure 3-22. Motor technologies that are suited to this

approach include induction motors, switched-reluctance motors, and some brushless-DC

permanent magnet motors.

An example of a field-weakened torque-speed curve was provided for the UQM Technologies

drive shown in Figure 3-23. To apply equation 3-69, we must consider how this curve

deviates from the ideal (Figure 3-22) and calculate an effective over-speed ratio. The simplest

approach is as follows:

1. An effective base speed is calculated as the quotient of the motor’s peak power and

torque

2. The over speed ratio is then calculated as the ratio of the maximum and effective base

speeds

For the UQM Technologies drive, the maximum speed is maxω = 4400rpm, the peak torque is

maxT = 550.6 Nm and the peak power is maxP = 101.5kW (UQM, 2001). Therefore, the

effective base speed is calculated as 1761rpm corresponding to an effective over speed ratio

of effdriveN − = 2.5. Figure 3-24 plots the actual torque-speed curve against the effective torque

speed curve that is modelled with this approach. Note that the actual curve (the solid line) is

completely bounded by the modelled curve (the dotted line). Therefore, this approach

consistently underestimates the required motor power.

If torque-speed curves are available for an electric drive, then a better estimate of the

“effective” peak power and over-speed ratio can be produced. An effective maximum power

can be estimated by averaging the power-speed curve over all speeds greater than the

effective base speed. Then, by substituting the effective power for the maximum power, the

above procedure can be used to predict a new effective base speed and over-speed ratio. For

66

the UQM Technologies drive, this results in an effective peak power of effP = 93.9kW and an

effective over speed ratio of effdriveN − = 2.7. Figure 3-25 plots the actual torque-speed curve

against the effective torque speed curve that is modelled with these parameters. The values

can be used in equation 3-69, but the calculated power requirement must be adjusted by the

ratio of maximum and effective powers:

⎥⎥⎦

⎤

⎢⎢⎣

⎡+×

+= −

−

−− 22

1 2

2

2max accelvdrag

accel

acceltotalm

effaccel

effaccel

eff

acceloutdrive

Pt

vmkN

NPP

P (3-70)

For the example of the UQM Technologies drive considered here, effP

Pmax = 1.08.

0 500 1000 1500 2000 2500 3000 3500 4000 4500100

200

300

400

500

600

Speed (rpm)

Torq

ue (N

m)

ActualModel

0 500 1000 1500 2000 2500 3000 3500 4000 45000

20

40

60

80

100

120

Speed (rpm)

Pow

er (k

W)

ActualModel

Figure 3-24: Modelled vs. actual torque-speed curves for the UQM Technologies drive

Drivetrains with Multi-Speed Transmissions

Typically, multi-speed transmissions are used in conjunction with engines/motors that have a

torque-speed curve that is relatively flat. Examples are provided for an engine (Saturn 1.9L

DOHC engine – ADVISOR data file FC_SI95.m) and electric motor (Siemens 33 kW

67

permanent magnet motor/controller – ADVISOR data file MC_PM33.m) in Figure 3-26.

Through appropriate selection of ratios in the design of a transmission, a desirable torque-

speed profile similar to that of Figure 3-22 can be achieved. Figure 3-27 provides an example

for the engine shown in Figure 3-26, using a 5-speed transmission with a 5:1 ratio between 1st

and 5th gears.

0 500 1000 1500 2000 2500 3000 3500 4000 4500100

200

300

400

500

600

Speed (rpm)

Torq

ue (N

m)

ActualModel

0 500 1000 1500 2000 2500 3000 3500 4000 45000

20

40

60

80

100

120

Speed (rpm)

Pow

er (k

W)

ActualModel

Figure 3-25: Modelled vs. actual torque-speed curves using the effective power for the UQM

Technologies drive

The simple procedure for calculating the effective over-speed ratio of a drivetrain with multi-

ratio transmission is slightly more complicated than for an electric drive:

1. The over-speed ratio of the transmission alone is calculated as the ratio of the

maximum and minimum gear ratios.

2. The effective over-speed ratio of the engine/motor alone is calculated using the

procedure outlined for electric drives. This step accounts for the fact that the torque-

speed curve of the engine/motor may not be flat. This is particularly relevant to

parallel hybrid vehicles in which the combined torque-speed curve of the motor and

engine (without transmission) may exhibit an over-speed characteristic.

68

3. The effective over speed ratio of the total drivetrain is calculated as the multiple of the

two ratios calculated in steps 1 & 2 above.

0 1000 2000 3000 4000 5000 60000

20

40

60

80

100

120

140

160

180

200

Speed (rpm)

Torq

ue (r

pm)

0 1000 2000 3000 4000 5000 60000

10

20

30

40

50

60

70

80

90

100

Speed (rpm)

Torq

ue (r

pm)

(a) (b)

Figure 3-26: Torque-speed curves for (a) a Saturn 1.9L DOHC engine and (b) Siemens 33

kW permanent magnet motor/controller

As an example, consider the engine/transmission combination shown in Figure 3-27. The

transmission over speed ratio is already given as transN = 5. For the engine alone, maxω =

6000rpm, maxT = 165.4 Nm and maxP = 95.1kW. Using the quoted peak power and torque, the

effective base speed of the engine is calculated as 5491rpm. This gives an engine over speed

ratio of 1.09. Combining the two values calculates the over speed ratio of the drivetrain as a

whole to be effdriveN − = 5.45. Once again, note that the actual torque-speed curve is bounded

by the modelled curve, as shown in Figure 3-27. Again, this will underestimate the required

engine power.

To avoid underestimating the engine power, we must find an effective peak power for the

engine/transmission, similar to that which was developed above for electric drives. However,

there is the added complication of the step-changes in torque and power between gears.

Therefore, the author has devised the following procedure for approximating the shape of the

engine/transmission curve. Firstly, the torque-speed curve of the engine alone is

approximated by a flat line corresponding to the average torque, as shown in Figure 3-28. For

the example engine, this average torque is calculated as avgT = 153.3Nm. This value is then

used to calculate the peak power of the averaged torque-speed curve, maxω×= avgavg TP =

96.3kW.

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0 1000 2000 3000 4000 5000 60000

200

400

600

800

1000

Speed (rpm)

Torq

ue (N

m)

0 1000 2000 3000 4000 5000 60000

20

40

60

80

100

Speed (rpm)

Pow

er (k

W)

Figure 3-27: Torque-speed curve for a drivetrain consisting of the engine shown in Figure 3-

26a combined with a 5-speed transmission

0 1000 2000 3000 4000 5000 60000

20

40

60

80

100

120

140

160

180

200

Speed (rpm)

Torq

ue (r

pm)

ActualModel

Figure 3-28: Average torque approximation of the engine shown in Figure 3-26

70

To account for the step change in torque and power between gears, we assume the gear ratios

follow a geometric progression. For a geometric progression, the step change in power is the

same for each gear change, as shown in Figure 3-29. Therefore, a logical value to choose for

the effective power is the mid-way point in the step change, as shown in Figure 3-29. This

effective power can be calculated analytically as:

avgeff Pr

rP2

1+= (3-71)

where r is the ratio between gears which, assuming the gear ratios follow a geometric series,

is calculated as:

1−= GtransNr (3-72)

where G is the number of gears in the transmission. The effective over speed ratio of this

approximate power-speed curve can also be expressed in terms of r:

transeffdrive Nr

rN1

2+

=− (3-73)

For the example engine, the effective power was calculated as effP = 80.4kW and the effective

over-speed ratio was effdriveN − = 6.0. These values can be used in equation 3-70, including the

adjustment factor effP

Pmax = 1.18.

With multi-speed transmissions, another factor that must be considered is the time taken to

change gears. When the acceleration manoeuvre is subject to a certain time constraint, this in

effect reduces the time available to accelerate the vehicle inertia. Also, because vehicles tend

to have large mass-to-drag ratios, it is assumed that no speed is lost during the coasting time

when the gear is being changed. Therefore, to account for gear shifting, a slightly modified

form of equation 3-69 is used:

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( ) 221 2

2

2accelvdrag

shiftaccel

acceltotalm

effaccel

effaccelacceloutdrive

Ptt

vmkN

NP −

−

−− +

−×

+= (3-74)

where shiftt is the time occupied by gear changes. Obviously, shiftt depends on two factors –

the time taken per shift (which depends on the transmission technology), and the number of

gearshifts required during the acceleration manoeuvre. Mathematically, the number of

gearshifts is calculated as:

( ) 1log += accelr NtruncNumshifts (3-75)

0 1000 2000 3000 4000 5000 60000

10

20

30

40

50

60

70

80

90

100

Speed (rpm)

Pow

er (k

W)

ActualModel


Saturn 1.9L engine (Figure 3-26a) and 5-speed transmission

Comparison of Methods for Predicting Acceleration Power Requirements

Acceleration power predictions were performed for hypothetical ICVs and EVs to compare

the methods of Delucchi (2000), Plotkin et al (2001) and PAMVEC. The vehicle platform

assumed was representative of a large sedan, with the following parameters: mtotal = 1686kg;

CDA = 0.8m2; CRR = 0.01. The acceleration performance target was 0-100kph in 9.0 seconds.

72

For the ICVs, the assumed engine was that from the above example, but with a 5-speed

transmission with a realistic ratio between 1st and 5th gears of 4.74:1. The resulting

parameters for the drive were: effdriveN − = 6.0; effP

Pmax = 1.18. The ICV top speed was assumed

to be 200kph. For the EVs, two different drives were considered. The first was the 100kW

Unique Mobility drive from the above example. The second drive considered was the 49kW

BLDC drive used in the Honda EV Plus (ADVISOR data file MC_PM49.m) (Figure 3-30)

with the following parameters: effdriveN − = 5.0; effP

Pmax = 1.0. For the EVs, the top speed was

assumed to be less at 150kph.

0 1000 2000 3000 4000 5000 6000 7000 8000 900050

100

150

200

250

300

Speed (rpm)

Torq

ue (N

m)

ActualModel

0 1000 2000 3000 4000 5000 6000 7000 8000 90000

10

20

30

40

50

Speed (rpm)

Pow

er (k

W)

ActualModel


Honda EV Plus drive

The predicted acceleration power requirements from the three methods are shown in Table 3-

4. There is a good correlation between the predicted powers for the ICVs. There is also a

good correlation between the predicted powers for the EVs when using data for the Honda

drive, but the predicted EV power is clearly sensitive to the characteristics of the drive. The

73

UQM drive has a much lower over-speed ratio (2.7) than the Honda drive (5.0), and we can

only assume that the correlations used by Delucchi and Plotkin et al are based on EV drives

with large over-speed ratios. Regardless, the PAMVEC model is capable of accounting for

these differences in torque-speed characteristic, and this is a definite advantage over the other

models.

Table 3-4: Predicted acceleration power requirements using various methods

ICEPlotkin et al 110.1Delucchi 117.8PAMVEC 111.3 110.2 86.3

UQM Honda

Method EV87.083.0

Acceleration Power (kW)

3.5 Powertrain Component Sizing Strategies and Mass

Compounding

Total vehicle mass is an important factor in the road load equation (3-1) and a key contributor

to overall energy consumption. Therefore, a crucial element in the parametric modelling

technique is to relate the total vehicle mass to the performance criteria outlined in the previous

section. This allows mass-compounding effects to be captured in the sizing of powertrain

components and prediction of the overall energy consumption of the vehicle.

The key inputs to the model for component sizing and total vehicle mass are the component

technology attributes for specific power/energy and efficiency (Table 3-5), and the

performance-based drivetrain output powers calculated in the previous section.

The expression for the total mass of a vehicle is:

powertrainstructocglidertotal mkmmm ++= arg (3-76)

In equation 3-76, the parameters gliderm and ocm arg can be considered constant. However,

since different powertrain architectures utilise different components, the expressions for

powertrainm are clearly different. The parameter structk accounts for the mass of additional

structural support that may be required to support the powertrain. For structk , Ogden et al

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(1999) use a value of 115% while Delucchi (2000) uses a value of 110%, after citing values in

the literature ranging from 107-111%.

Table 3-5: Component technology parameters used in PAMVEC’s model for powertrain

component sizes and mass compounding

Component Specific power

(W/kg)

Specific energy

(Wh/kg)

Efficiency

(%)

Transmission transSP --- transη

Motor/Controller mcSP --- mcη

Generator genSP --- genη

Battery battSP battSE battη

Engine iceSP --- iceη

Fuel Cell fcSP --- fcη

Reformer refSP --- refη

Fuel Storage --- fuelSE ---

3.5.1 Fuel Cell Hybrid Electric Vehicles

The powertrain mass in a fuel cell hybrid electric vehicle includes contributions from the

energy storage (fuel tank), the fuel cell and (if applicable) the reformer, the battery, the

motor/controller and the transmission:

FCHEVpowertrainm transcmbattfcreffuel mmmmmm +++++= /

trans

trans

mc

mc

batt

batt

fc

fc

ref

ref

fuel

fuel

SPP

SPP

SPP

SPP

SPP

SEE maxmaxmaxmaxmax

+++++= (3-77)

The transmission power rating is defined as the maximum of the drivetrain output powers

(due to performance constraints) calculated in the previous section:

( )topspeedoutdrive

acceloutdrive

gradeoutdrivetrans PPPP −−−= ,,maxmax (3-78)

75

The motor/controller power is then calculated from the transmission power and efficiency:

trans

transmc

PP

η

maxmax = (3-79)

Similarly, the drivetrain input power is calculated from the motor/controller power and

efficiency:

mc

mcinputmc

PP

η

maxmax =− (3-80)

With hybridisation, there are many valid strategies for the sizing of the fuel cell and battery,

however, a universally conservative approach is to size the fuel cell to meet the maximum

continuous power requirement – either from gradability or top speed, combined with

accessory requirements.

( )accessory

mctrans

topspeedoutdrive

gradeoutdrive

fc PPP

P += −−

ηη,maxmax (3-81)

If applicable, the peak reformer power is calculated from the fuel cell peak power and

efficiency:

fc

fcref

PP

η

maxmax = (3-82)

The peak battery output power is that required to provide, in combination with the fuel cell,

the peak drivetrain input power:

maxmaxmaxfcaccessoryinputmcbatt PPPP −+= − (3-83)

76

3.5.2 Fuel Cell Electric Vehicles

The powertrain mass in a fuel cell electric vehicle includes contributions from the energy

storage (fuel tank), the fuel cell and (if applicable) the reformer, the motor/controller and the

transmission:

FCEVpowertrainm transmcfcreffuel mmmmm ++++=

trans

trans

mc

mc

fc

fc

ref

ref

fuel

fuel

SPP

SPP

SPP

SPP

SEE maxmaxmaxmax

++++= (3-84)

The expressions for transmission power and motor/controller power are the same as for the

FCHEV. But due to the lack of a battery, the peak fuel cell power is defined as:

accessoryipnutmcfc PPP += −maxmax (3-85)

The expression for the reformer peak power, if applicable, is also the same as for the FCHEV.

3.5.3 Conventional Internal Combustion Engine Vehicles

The powertrain mass in a conventional internal combustion engine vehicle includes

contributions from the energy storage (fuel tank), the engine and the transmission:

ICVpowertrainm transicefuel mmm ++=

trans

trans

ice

ice

fuel

fuel

SPP

SPP

SEE maxmax

++= (3-86)

The transmission size is as defined in equation 3-78. The peak engine output power will be

defined in terms of the transmission power and efficiency, and the accessory load:

accessorytrans

transice P

PP +=

η

maxmax (3-87)

77

3.5.4 Parallel Hybrid Electric Vehicles

The powertrain mass in a parallel hybrid electric vehicle includes contributions from the

energy storage (fuel tank), the engine, the battery, the motor/controller and the transmission:

PHEVpowertrainm transmcbatticefuel mmmmm ++++=

trans

trans

mc

mc

batt

batt

ice

ice

fuel

fuel

SPP

SPP

SPP

SPP

SEE maxmaxmaxmax

++++= (3-88)

The transmission size will be as defined in equation 3-78. Again, in this hybrid architecture,

the engine is sized to meet the maximum continuous power requirement:

( )accessory

trans

topspeedoutdrive

gradeoutdrive

ice PPP

P += −−

η,maxmax (3-89)

The motor/controller size will be that required, in combination with the engine, to meet the

peak power input to the transmission:

maxmax

maxiceaccessory

trans

transmc PP

PP −+=

η (3-90)

The model of powertrain losses for the PHEV refers to the degree of hybridisation (DOH),

which is defined here in terms of the engine and motor/controller powers:

maxmax

max

mcice

mc

PPP

DOH+

= (3-91)

The battery size will be defined by the peak input power requirement to the motor/controller:

mc

mcbatt

PP

ηmax

max−

− = (3-92)

78

3.5.5 Series Hybrid Electric Vehicles

The powertrain mass in a series hybrid electric vehicle includes contributions from the energy

storage (fuel tank), the engine and generator, the battery, the motor/controller and the

transmission:

SHEVpowertrainm transmcbattgenicefuel mmmmmm +++++=

trans

trans

mc

mc

batt

batt

gen

gen

ice

ice

fuel

fuel

SPP

SPP

SPP

SPP

SPP

SEE maxmaxmaxmaxmax

+++++= (3-93)

The transmission and motor/controller sizes will be as defined in equations 3-78 and 3-79,

and the maximum input power to the motor/controller will be as defined in equation 3-80.

Again, in this hybrid architecture, the generator is sized to meet the maximum continuous

power requirement – either from gradability or top speed, combined with accessory

requirements.

( )accessory

mctrans

topspeedoutdrive

gradeoutdrive

gen PPP

P += −−

ηη,maxmax (3-94)

The peak engine power is then defined in terms of the generator power and efficiency:

gen

genice

PP

ηmax

max−

− = (3-95)

The peak battery output power is as defined in equation 3-83.

3.5.6 Battery Electric Vehicles

The powertrain mass in a battery electric vehicle includes contributions from the energy

storage (the battery), the motor/controller and the transmission:

BEVpowertrainm transmcbatt mmm ++=

79

trans

trans

mc

mc

batt

batt

SPP

SPP

SEE maxmax

++= (3-96)

The transmission and motor/controller sizes are as defined in equations 3-78 and 3-79, and the

battery is sized based on the driving range constraint, as defined in equation 3-61.

3.6 Implementation of the PAMVEC Model

The expressions for vehicle performance and energy consumption outlined in previous

sections are coupled by total vehicle mass, and therefore must be solved simultaneously to

properly capture mass-compounding effects. A convenient approach is to utilize spreadsheet

software that allows circular referencing and iterative calculations, such as Microsoft Excel.

A spreadsheet implementation also allows parameters and expressions to be defined, modified

and solved quickly and the author has had great success with this method. Examples of the

implementation of PAMVEC in Microsoft Excel are provided in Appendices B & C. At the

time of writing, the author was working to make Microsoft Excel spreadsheet templates for

the PAMVEC model publicly available as soon as possible.

This concludes the description of the PAMVEC modelling approach. In the following

chapter, the accuracy of PAMVEC’s predictions of powertrain component sizes, total vehicle

mass and vehicle energy consumption is validated with published vehicle test data and

through benchmarking against the ADVISOR modelling tool.

80

81

4. PAMVEC Validation

This chapter documents the validation exercises that were performed to test the accuracy of

PAMVEC’s predictions of powertrain component sizes, total vehicle mass, and vehicle

energy consumption. PAMVEC was validated both from published vehicle test data and also

through benchmarking against the ADVISOR dynamic simulation software.

4.1 Validation with Published Vehicle Test Data

Published vehicle test data from the literature was used to validate PAMVEC’s predictions of

vehicle performance and energy consumption. Three examples are provided below.

4.1.1 Acceleration performance for the GM HydroGen3 FCEV

The GM HydroGen3 is a prototype fuel cell electric vehicle built on the Opel Zafira minivan

platform. Table 4-1 presents technical specifications for the HydroGen3 as given by Jost

(2002).

Table 4-1: Technical specifications for the GM HydroGen3 FCEV

Curb mass 1590kg

Top speed 150kph

Acceleration time: 0-100kph 16.0s

Peak motor power 60kW

Peak motor torque 215Nm

Peak motor speed 12,000rpm

Transmission ratio 8.67:1

The motor power required to achieve the acceleration performance given in Table 4-1 can be

predicted using equation 3-69. Firstly, the over-speed ratio for use in equation 3-69 is

calculated using the methods described in Section 3.4.4:

( ) 0.3215

6012000

150100

=×=Nm

kWrpm

kphkphNaccel

82

The motor power was then predicted using equation 3-69 and by assuming the parameter

values listed in Table 4-2. Using these values, the required motor power was predicted as

63kW – an error of 5%.

accel

outdriveP − ( ) ( )2

/8.27/81.9167001.0/8.278.02.15.0162

/8.2716701.13

13 2322

2

2 smsmkgsmms

smkg ×××+×××+

×××

×+

=

kW9.62=

Table 4-2: HydroGen3 parameter values assumed in the prediction of motor power

Drag area (CDA, estimated1) 0.8m2

Rolling resistance coefficient (CRR) 0.01

Vehicle inertia factor 1.1

Cargo mass 80kg (1 passenger)

Transmission efficiency 90% 1 Based on CD = 0.33, width = 1.74m, height = 1.63m (CARtoday.com, 2005) and area fill

factor = 85% to give frontal area = 2.41m2

4.1.2 Fuel consumption for the Holden Commodore ICV

The Holden Commodore sedan was the most popular passenger car sold in Australia in 2003

and has a published fuel consumption value of 11.1 L/100km (AGO, 2005). This value is

obtained through dynamometer testing on the NEDC according to Australian standards

(AGO, 2003).

The fuel consumption of a Holden Commodore over the NEDC was predicted using the

PAMVEC energy consumption model outlined in Chapter 3. Table 4-3 lists the vehicle

parameters that were assumed for the estimate. Driving pattern parameters for the NEDC

were provided in Table 3-1. Note that a range for engine efficiency was assumed based on

the author’s experience with similar vehicles operating over similar driving patterns. Using

the PAMVEC model, the predicted fuel consumption ranged from 11.8-12.5 L/100km – an

error of 6-12%.

83

4.1.3 Fuel consumption for the Virginia Tech. ZEburban FCHEV

The Virginia Tech. ZEburban fuel cell hybrid-electric vehicle is based upon the Chevy

Suburban platform, and is powered by a Honeywell PEM fuel cell, hybridized with a Hawker

Genesis battery pack (Gurski & Nelson, 2002). The vehicle has four-wheel-drive, driven by

GE induction motors on both the front and rear axles. Table 4-4 presents some selected

technical specifications for the Virginia Tech ZEburban.

Table 4-3: Vehicle parameters assumed for the Holden Commodore sedan

Curb mass 1560kg

Total vehicle mass 1640kg (one 80kg passenger)

Aerodynamic drag coefficient 0.32

Frontal area 2.5m2

Drag-area 0.8m2

Rolling resistance coefficient 0.01

Transmission efficiency 90%

Engine efficiency 17-18%

Table 4-4: Technical Specifications for the Virginia Tech. ZEburban FCHEV

Curb mass 3090kg

Fuel cell Honeywell PEM, 49kW net peak

Battery Hawker Genesis, 336V, 26Ah

Motor(s)/controller(s) 2 x GE induction motor/inverters (front/rear), 170kW total,

efficiency > 90%

Transmission 2 x single stage reduction (front/rear)

Hydrogen storage Quantum Technologies, 35MPa, 3kg H2, 7.5% by weight

To predict the energy consumption for the ZEburban, several other technical parameters were

estimated for the vehicle (Table 4-5).

The selected values for drag-area and coefficient of rolling resistance produced road-load

characteristics that showed a good correlation with those reported, as shown in Table 4-6.

The fuel cell efficiency of 45% was chosen based upon the efficiency map and operational

characteristics reported for the fuel cell system (Gurski & Nelson, 2002). Since no mention

84

was made of the braking characteristics of the vehicle, a mid-range estimate of 50% was

chosen for the regenerative braking fraction. Estimates for the other parameters were made

based upon the author’s experience.

Table 4-5: Estimated technical parameters for the Virginia Tech. ZEburban FCHEV

Drag-area (CDA) 1.3m2


Fuel cell efficiency 45%

Battery energy efficiency 80%

Transmission efficiency 90%

Regenerative braking fraction 50%

Average accessory load 1000W

Table 4-6: Comparison between estimated and reported road load power requirements for the

Virginia Tech. ZEburban FCHEV

Cruise velocity 65mph 81mph

Reported power 28.8kW 50.0kW

Estimated power 29.3kW 49.9kW

Gurski and Nelson (2002) present gasoline-equivalent (mpgge) fuel economy results for both

city (UDDS) and highway (HWFET) cycles and Table 4-7 compares these with the predicted

fuel economies resulting from the PAMVEC model. There is good correlation between the

results.

Table 4-7: Predicted and reported fuel economies for the Virginia Tech. ZEburban.

Driving cycle Reported fuel economy

(mpgge)

Predicted fuel economy

(mpgge)

Error

(%)

City (UDDS) 23.3 24.9 +6.9

Highway (HWFET) 25.2 27.6 +9.5

4.2 Benchmarking against ADVISOR

It proved difficult to validate PAMVEC against test data for a large number of vehicles since

very few publications included sufficient technical data to allow a precise comparison to be

85

made. Furthermore, published fuel/energy consumption data for vehicles rarely provides a

breakdown of losses in the powertrain that might be compared with the breakdown of losses

in the PAMVEC model to identify major sources of error. Therefore, the majority of the

PAMVEC validation process focused on benchmarking it against the ADVISOR advanced

vehicle simulation software. ADVISOR was chosen as the benchmarking too since it is well-

known and widely used, its accuracy has been well validated and it was freely available.

Validation runs were performed for a small sedan platform using six different powertrain

architectures – ICV, PHEV, SHEV, FCV, FCHEV and BEV. For each vehicle, the validation

procedure was as follows:

1. An ADVISOR simulation was performed to predict vehicle performance and

equivalent fuel consumption. SOC correction was used (zero-delta algorithm with

0.5% tolerance) to guarantee an accurate prediction of the equivalent fuel

consumption. Vehicle performance was predicted in terms of 0-100kph (0-60mph)

acceleration time, 88.5kph (55mph) gradability and continuous top speed. For hybrid

architectures, the gradability and continuous top speed performances were predicted

with the battery disabled. These vehicle performances were then used as performance

constraints in the PAMVEC model

2. Using input/output data from the ADVISOR simulation, the specific power (W/kg)

and net cycle operating efficiency of each powertrain component was calculated. For

drivetrain components (motor/controllers and/or transmissions), appropriate values for

over speed ratios were calculated as well. These values were then used as component

technology parameters in the PAMVEC model.

3. PAMVEC was used to predict powertrain component sizes, total vehicle mass and

vehicle energy consumption, based on the performance parameters and component

technology parameters obtained from steps 1 and 2.

4. The PAMVEC and ADVISOR results were compared including a detailed analysis of

sources of error.

4.2.1 Vehicle Platform and Driving Pattern

The six vehicles were simulated in operation over the New European Driving Cycle (NEDC),

shown in Figure 4-1.

86

The vehicle platform was a hypothetical small car, based on the 1994 Saturn SL1 vehicle

(ADVISOR data file: VEH_SMCAR.m). Relevant physical parameters for this platform are

presented in Table 4-8.

Table 4-8: Vehicle platform parameters assumed for the ADVISOR benchmarking

Glider mass (mglider) 592 kg

Drag area (CDA) 0.67 m2


Wheel radius 0.282 m

Cargo mass (mcargo) 136 kg

Accessory load 700 W

0 200 400 600 800 1000 12000

20

40

60

80

100

120

Time (s)

Spe

ed (k

m/h

)

Speed & Acceleration vs Time

0 200 400 600 800 1000 1200-0.2

-0.1

0

0.1

0.2

Acc

eler

atio

n (g

)

Time (s)

Figure 4-1: The New European Driving Cycle (NEDC)

87

4.2.2 Benchmarking Results

Conventional Internal Combustion Engine Vehicle (ICV)

The component technology parameters for the ICV are presented in Table 4-9. The predicted

vehicle performances from the ADVISOR simulation were as follows:

0-100 kph acceleration time: 10.0 s

88.5 kph gradability: 15.2 %

Continuous top speed: 194 kph

The predicted powertrain component sizes and total vehicle masses for the ICV are compared

in Table 4-10. The size and mass of the engine has been slightly underestimated (by approx.

6%) in the PAMVEC model. However, this result produces only a small underestimate of the

total vehicle mass of approx. 1%.

Table 4-9: Component technology parameters for the ICV. Component Specific power Efficiency Over-speed ADVISOR data file Notes

(W/kg) ratio

Engine 385 17% --- FC_SI41_emis based on Geo 1.0L (41kW) SI engine

Transmission --- 87% 4.74 TX_5SPD default 5-speed, 114kgFuel/Tank --- --- --- --- gasoline, 24.6kg

Table 4-10: Comparison of component size and vehicle mass predictions for the ICV Component

ADVISOR PAMVEC ADVISOR PAMVECEngine 82 77 213 199Transmission --- --- 114 114Fuel/Tank --- --- 25 25Glider --- --- 613 613Cargo --- --- 136 136Total --- --- 1101 1087

Power (kW) Mass (kg)

The predicted energy consumptions for the ICV are compared in Table 4-11, including a

detailed breakdown of the loss components and errors. Table 4-11 also indicates the

proportion each loss component contributes to the total energy consumption in the ADVISOR

model. The road load has been slightly underestimated - a result of PAMVEC’s slight

underestimation of total vehicle mass. The error in the braking losses is relatively large at

36%, although this is consistent with expectations based on the discussion in Section 3.1.2. In

88

contrast, the error in drive losses is quite small but there is no obvious explanation for this

accuracy. The error in the engine losses can be attributed to the cumulative errors of the

preceding four loss components (since the engine efficiency is the same in both models, the

engine losses can only differ due to the average engine load). Overall, at 10%, the total error

in the estimate of vehicle energy consumption is reasonable.

Table 4-11: Comparison of energy consumption predictions for the ICV

ADVISOR Proportion PAMVEC ErrorRoad load 67.7 9% 66.9 -1%Braking losses 24.9 3% 33.8 36%Drive losses 14.2 2% 14.5 2%Accesory load 21.1 3% 21.2 1%Engine losses 616.4 83% 682.1 11%Total 744.2 100% 818.5 10%

Energy consumption (Wh/km)ICV

Parallel Hybrid Electric Vehicle (PHEV)

The component technology parameters for the PHEV are presented in Table 4-12. The

predicted vehicle performances from the ADVISOR simulation were as follows:




The predicted powertrain component sizes and total vehicle masses for the PHEV are

compared in Table 4-13. Note that the size/mass of the engine has been underestimated by

approx. 2%. The motor/controller has been underestimated by 57%, however this is likely

due to differences in the component sizing strategies employed by the ADVISOR and

PAMVEC models. In contrast, the size/mass of the battery has been slightly overestimated –

one possible explanation for this result may be that the battery specific power (444W/kg)

reported in the ADVISOR data file is too low (battery power is often reported at low SOC,

but in practice batteries operate at higher SOC with more power available). In balance,

however, the error in the estimate of total vehicle mass is small at only -1%.

The predicted energy consumptions for the PHEV are compared in Table 4-14. Again, the

road load has been slightly underestimated as a result of PAMVEC’s slight underestimation

of total vehicle mass. The errors in the braking and drivetrain losses are significant at 34%

89

and 12%, respectively, although this is consistent with expectations based on the discussion in

Sections 3.1.2 and 3.3.1. These components contribute most of the total error. The error in

battery losses is very large, but these contribute a negligible amount to the total. Again, the

error in the engine losses can be attributed to the cumulative errors of the preceding five loss

components. Overall, at 6% the total error in the estimate of vehicle energy consumption is

quite acceptable.

Table 4-12: Component technology parameters for the PHEV Component Specific power Efficiency Over-speed ADVISOR data file Notes

(W/kg) ratio

Engine 385 24% 3.21 FC_SI41_emis based on Geo 1.0L (41kW) SI engine

Motor/Controller 1482 62% 3.21 MC_AC75based on Westinghouse 75-kW (continuous) AC induction motor/inverter

Battery 444 96% --- ESS_NIMH28_OVONIC based on Ovonic 28Ah NiMH HEV battery


Table 4-13: Comparison of component size and vehicle mass predictions for the PHEV Component

ADVISOR PAMVEC ADVISOR PAMVECEngine 29 28 75 74Motor/Controller 76 33 51 22Battery 46 53 104 119Transmission --- --- 114 114Fuel/Tank --- --- 25 25Glider --- --- 600 600Cargo --- --- 136 136Total --- --- 1105 1090


Table 4-14: Comparison of energy consumption predictions for the PHEV

ADVISOR Proportion PAMVEC ErrorRoad load 67.8 13% 66.9 -1%Braking losses 10.2 2% 13.7 34%Drive losses 33.2 6% 37.2 12%Accesory load 21.1 4% 21.2 1%Battery losses 0.5 0% 1.4 180%Engine losses 406.8 75% 434.2 7%Total 539.5 100% 574.6 6%

PHEV Energy consumption (Wh/km)

Series Hybrid Electric Vehicle (SHEV)

The component technology parameters for the SHEV are presented in Table 4-15. The


90




The predicted powertrain component sizes and total vehicle masses for the SHEV are

compared in Table 4-16. The sizes/masses of the engine/generator, motor/controller and

battery have been slightly underestimated (by approx. 14%, 7% and 20% respectively) in the

PAMVEC model. Overall, however, the error in the estimate of total vehicle mass is small at

only -4%.

Table 4-15: Component technology parameters for the SHEV Component Specific power Efficiency Over-speed ADVISOR data file Notes

(W/kg) ratio

Engine/Generator 257 29% --- FC_SI41_emis/GC_ETA95based on Geo 1.0L (41kW) SI engine, sample generator/controller




Table 4-16: Comparison of component size and vehicle mass predictions for the SHEV Component

ADVISOR PAMVEC ADVISOR PAMVECEngine/Generator 36 32 144 124Motor/Controller 70 66 48 45Battery 58 46 130 104Transmission --- --- 50 50Fuel/Tank --- --- 25 25Glider --- --- 601 601Cargo --- --- 136 136Total --- --- 1134 1084


The predicted energy consumptions for the SHEV are compared in Table 4-17. Again, the


of total vehicle mass. The error in the braking loss is relatively large at 30%, although this is

consistent with expectations based on the discussion in Section 3.1.2. The drive loss error is

much smaller at 10%. Together, these components contribute most of the total error. The

error in battery losses is very large, but contributes a negligible amount to the total. Again,

the error in engine/generator losses can be attributed to the cumulative errors of the preceding

91

five loss components. Overall, at 7% the total error in the estimate of vehicle energy

consumption is quite reasonable.

Table 4-17: Comparison of energy consumption predictions for the SHEV

ADVISOR Proportion PAMVEC ErrorRoad load 68.5 14% 66.8 -2%Braking losses 10.5 2% 13.6 30%Drive losses 37.5 8% 41.2 10%Accesory load 21.1 4% 21.2 1%Battery losses 5.4 1% 10.0 87%Generator losses 341.8 71% 365.9 7%Total 484.7 100% 518.7 7%

SHEV Energy consumption (Wh/km)

Fuel Cell Electric Vehicle (FCEV)

The component technology parameters for the FCEV are presented in Table 4-18. The





The predicted powertrain component sizes and total vehicle masses for the FCEV are

compared in Table 4-19. The size of the fuel cell has been predicted very accurately,

whereas, the motor/controller size has been slightly underestimated (5%). Overall, the error

in the estimate of total vehicle mass is small at less than 1%.

Table 4-18: Component technology parameters for the FCEV Component Specific power Efficiency Over-speed ADVISOR data file Notes

(W/kg) ratio

Fuel cell 309 43% --- custom based on Ballard 68kW (net) hydrogen fuel cell engine

Motor/Controller 812 86% 4.99 MC_PM49based on Honda 49 KW (continuous), permanent magnet motor/controller

Transmission --- 86% 1.00 TX_1SPD default 1-speed, 50kg

Fuel/Tank --- --- --- --- compressed hydrogen, 73.4kg

The predicted energy consumptions for the FCEV are compared in Table 4-20. Again, the


92

of total vehicle mass. The error in the braking loss is large at 53%, although this is consistent

with expectations based on the discussion in Section 3.1.2. The drive loss error is much

smaller at 9%, and together these components contribute most of the total error. The error in

fuel cell losses can be attributed to the cumulative errors of the preceding four loss

components. Overall, at 11% the error in the estimate of energy consumption is acceptable.

Table 4-19: Comparison of component size and vehicle mass predictions for the FCEV Component

ADVISOR PAMVEC ADVISOR PAMVECFuel Cell 77 77 249 249Motor/Controller 69 66 85 81Transmission --- --- 50 50Fuel/Tank --- --- 73 73Glider --- --- 592 592Cargo --- --- 136 136Total --- --- 1186 1181


Table 4-20: Comparison of energy consumption predictions for the FCEV

ADVISOR Proportion PAMVEC ErrorRoad load 69.7 20% 69.2 -1%Braking losses 24.0 7% 36.7 53%Drive losses 34.9 10% 38.0 9%Accesory load 21.1 6% 21.2 1%Fuel cell losses 195.4 57% 218.9 12%Total 345.2 100% 384.0 11%

FCEV Energy consumption (Wh/km)

Fuel Cell Hybrid Electric Vehicle (FCHEV)

The component technology parameters for the FCHEV are presented in Table 4-21. The





The predicted powertrain component sizes and total vehicle masses for the FCHEV are

compared in Table 4-22. Note that the sizes/masses of the engine/generator, motor/controller

and battery have been underestimated (by approx. 6%, 15% and 31% respectively) in the

93

PAMVEC model. Overall, however, the error in the estimate of total vehicle mass is small at

only -5%.

Table 4-21: Component technology parameters for the FCHEV Component Specific power Efficiency Over-speed ADVISOR data file Notes

(W/kg) ratio

Fuel cell 309 47% --- custom based on Ballard 68kW (net) hydrogen fuel cell engine




Fuel/Tank --- --- --- --- compressed hydrogen, 73.4kg

Table 4-22: Comparison of component size and vehicle mass predictions for the FCHEV Component

ADVISOR PAMVEC ADVISOR PAMVECFuel Cell 34 32 110 103Motor/Controller 74 63 51 43Battery 62 43 140 96Transmission --- --- 50 50Fuel/Tank --- --- 73 73Glider --- --- 601 601Cargo --- --- 136 136Total --- --- 1161 1103


The predicted energy consumptions for the FCHEV are compared in Table 4-23. Again, the


of total vehicle mass. The error in the braking loss is relatively large at 28%, although this is

consistent with expectations based on the discussion in Section 3.1.2. The drive loss error is

much smaller at 8%. Together, these components contribute most of the total error. The error

in battery losses is relatively small at 7%. Again, the error in fuel cell losses can be attributed

to the cumulative errors of the preceding five loss components. Overall, at 3% the total error

in the estimate of vehicle energy consumption is quite good.

Table 4-23: Comparison of energy consumption predictions for the FCHEV

ADVISOR Proportion PAMVEC ErrorRoad load 69.1 23% 67.3 -3%Braking losses 10.8 4% 13.8 28%Drive losses 38.4 13% 41.5 8%Accesory load 21.1 7% 21.2 1%Battery losses 2.1 1% 2.2 7%Fuel cell losses 158.8 53% 164.6 4%Total 300.3 100% 310.6 3%

FCHEV Energy consumption (Wh/km)

94

Battery Electric Vehicle (BEV)

The component technology parameters for the BEV are presented in Table 4-24. The





The predicted powertrain component sizes and total vehicle masses for the BEV are compared

in Table 4-25. Note that the size/mass of the motor/controller has been underestimated (by

approx. 20%) in the PAMVEC model. In contrast, the battery size/mass has been

significantly overestimated – again this may be due to an underestimate of the battery’s

specific power. The reader should also note that in BEVs, the battery is normally sized on the

basis of energy storage (for driving range), rather than power, therefore this inaccuracy would

not normally be present. Overall, however, the error in the estimate of total vehicle mass is

small at only 3%.

Table 4-24: Component technology parameters for the BEV Component Specific power Efficiency Over-speed ADVISOR data file Notes

(W/kg) ratio




Table 4-25: Comparison of component size and vehicle mass predictions for the BEV Component

ADVISOR PAMVEC ADVISOR PAMVECMotor/Controller 75 60 91 72Battery 56 76 143 193Transmission --- --- 50 50Glider --- --- 592 592Cargo --- --- 136 136Total --- --- 1012 1044


The predicted energy consumptions for the BEV are compared in Table 4-26. This time, the

road load has been slightly overestimated as a result of PAMVEC’s slight overestimate of

total vehicle mass. The errors in braking and drive losses are relatively large at 41% and 18%

95

respectively, although this is consistent with expectations based on the discussion in Section

3.1.2 and 3.3.1. The error in battery losses is also quite large at 30%. Together, these

components contribute a sizeable amount to the total error. Overall, at 10% the total error in

the estimate of vehicle energy consumption is acceptable.

Table 4-26: Comparison of energy consumption predictions for the BEV

ADVISOR Proportion PAMVEC ErrorRoad load 65.5 43% 65.8 0%Braking losses 9.2 6% 13.0 41%Drive losses 45.3 29% 53.4 18%Accesory load 21.1 14% 21.2 1%Battery losses 12.9 8% 16.7 30%Total 153.9 100% 170.1 10%

BEV Energy consumption (Wh/km)

Summary of Results

A summary of the results of the validation study is presented in Table 4-27. Generally, the

errors in the estimate of total vehicle mass are quite small at less than 5%. The errors in

vehicle energy consumption are also quite acceptable at approximately 10% or less. As was

noted for all six powertrain architectures, the major source of error in the energy consumption

estimate was due to the overestimation of braking and/or drivetrain losses. Table 4-27 also

presents the errors in the estimates of relative fuel economy, using the predicted ADVISOR

ICV as the reference. The relative errors across the six powertrains are quite good, at

approximately 5% or less.

Table 4-27: Summary of validation results for the NEDC cycle NEDC Relative

Mass L/100km Mass L/100km Mass L/100km errorConv ICE 1100 8.4 1087 9.2 -1% 10% ---Parallel HEV 1106 6.1 1090 6.5 -1% 6% -3%Series HEV 1134 5.5 1084 5.9 -4% 6% -3%Fuel Cell 1185 3.9 1181 4.3 0% 11% 1%Fuel cell HEV 1161 3.4 1103 3.5 -5% 3% -6%EV 1012 1.7 1044 1.9 3% 11% 0%

ADVISOR PAMVEC Error

96

4.3 Benchmarking for other driving patterns and vehicle platforms

The PAMVEC validation results presented thus far are valid for a specific small-sedan vehicle

platform operating on the NEDC. Therefore, it is pertinent to consider how the errors vary for

different vehicle platforms and driving patterns.

4.3.1 Dependence of Error on Vehicle Platform and Driving Pattern

Previous results have showed that errors in estimating inertial power flow are the primary

cause of error in PAMVEC’s energy consumption estimate. Two factors contribute to the

significance of this error:

1. The relative magnitude of drag power flow to inertial power flow – if the drag power

is large relative to the inertial power, the error in the estimate of inertial power will be

large

2. The relative magnitude of inertial power losses to the total power consumption – if the

inertial power loss constitutes a large fraction of the total power consumption, then

any error in the estimate of inertial power flow will result in significant error in the

energy consumption estimate. Conversely, if the inertial loss fraction is low, then

even if the inertial flow error is large, it will not result in significant error in the energy

consumption estimate.

To highlight the significance of these factors, Figure 4-2 plots the error in the estimate of

indriveP − (equation 3-22) for several different driving patterns across a range of mass to drag

ratios (MDRs). The small sedan platform used for the validation study has a relatively low

MDR of approx. 1640 kg/m2. Typical MDR values can be as high as 5000-6000 kg/m2 for

tractor-trailer combinations, or for the low-drag battery electric vehicles studied in Delucchi

(2000).

97

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

5

10

15

20

25Errors in the estimate of Pdrive-in for various driving patterns: kregen = 0


Erro

r (%

)

NEDC

NYCC

UDDS

US06

HWFET

(a)

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

2

4

6

8

10

12


Erro

r (%

)

Errors in the estimate of Pdrive-in for various driving patterns: kregen = 1

NEDC

NYCC

UDDS

US06

HWFET

(b)

Figure 4-2: Error in the estimate of indriveP − (equation 3-22) for several different driving

patterns across a range of mass to drag ratios assuming (a) no regenerative braking and (b)

full regenerative braking

98

Equation 3-22 can be used to derive a parametric expression for the ratio of the inertial and

total power components of indriveP − :

( )( )regendriveRR

avg

regendrive

kagCMDR

v

ka

223

2

1~2

1~

losspower Totallosspower Inertia

ηρ

η

−++Λ

−= (4-1)

where MDR is the mass-to-drag-ratio (kg/m2). Clearly, as MDR tends to zero, equation 4-1

also tends to zero. Looking at the curves in Figure 4-2, this is obviously the dominant factor

for low MDRs, since the errors all tend to zero for zero MDR. Similarly, equation 3-22 can

be used to derive a parametric expression for the ratio of the drag and inertial power flow

components of indriveP − :

a

gCMDR

vRR

avg

~2

flowpower Inertiaflowpower Drag

23

+Λ

=

ρ

(4-2)

As MDR tends to infinity, equation 4-2 tends to the following value:

agCRR

MDR~flowpower Inertia

flowpower Drag=

∞→

(4-3)

It can be seen that as the MDR tends to large values, the power losses become increasingly

dominated by the inertial component (equation 4-1), but the error in the estimate of inertial

power flow depends on the ratio of the rolling resistance coefficient and characteristic

acceleration (equation 4-3). For example, consider the HWFET which, of the five cycles

considered, has the lowest characteristic acceleration (0.069m/s2). This results in a ratio of

1.3 in equation 4-3, so it comes as no surprise that the error for the HFWET increases

significantly as the MDR increases. In contrast, the NYCC has the highest characteristic

acceleration (0.293m/s2) resulting in a ratio of 0.3 in equation 4-3, and its error falls

substantially as the MDR increases.

Finally, in comparing the plots of error in Figure 4-2 for different kregen values, note that the

absolute errors values for full regenerative braking (kregen = 1) are substantially lower. This is

99

because regenerative braking reduces the inertial loss fraction (equation 4-1) whereas the ratio

of drag to inertial power flow remains unchanged.

For differing MDRs, there can also be a peak error point resulting from the interplay of

aerodynamic and rolling drag losses and inertial power flows, however it is beyond the

capabilities of this simple parametric analysis to explain its location and/or relative

magnitude. Also, note that this simple parametric error analysis cannot explain the relative

magnitudes of errors between different cycles, as these are dependent on the transient

velocity/acceleration histories of each driving cycle.

4.3.2 Benchmarking Results for Other Driving Patterns

The results of Figure 4-2 suggested that PAMVEC would be most-accurate for the NEDC

cycle. Therefore, it was necessary to repeat the six-powertrain validation exercise for the

other four cycles in order to observe the (possibly larger) errors for these driving patterns.

UDDS

Compared to the NEDC, the UDDS is statistically quite similar (with a very similar average

speed and somewhat similar velocity ratios and characteristic accelerations). However, the

errors observed for the UDDS were slightly higher (around 15%) compared to the NEDC

(around 10%), while the relative errors were again low (<5%).

Table 4-28: Summary of validation results for the UDDS cycle UDDS Relative

Mass L/100km Mass L/100km Mass L/100km errorConv ICE 1100 8.4 1087 9.5 -1% 14% ---Parallel HEV 1106 6.0 1092 6.9 -1% 15% 1%Series HEV 1134 5.1 1095 5.7 -3% 13% -1%Fuel Cell 1185 3.9 1189 4.5 0% 16% 2%Fuel cell HEV 1161 3.3 1112 3.7 -4% 10% -3%EV 1012 1.8 1055 2.0 4% 12% -2%


HWFET

Compared to the NEDC, the HWFET represents a higher speed cycle with significantly lower

characteristic acceleration. Together with the UDDS, this cycle forms part of the US FTP

100

composite cycle for predicting vehicle fuel economy and emissions (55% UDDS, 45%

HWFET). The errors observed for the HWFET were slightly greater than those for the

NEDC, but slightly less than for the UDDS. Again, the relative errors were consistently low

(<5%).

Table 4-29: Summary of validation results for the HWFET cycle HWFET Relative

Mass L/100km Mass L/100km Mass L/100km errorConv ICE 1100 6.0 1087 6.6 -1% 10% ---Parallel HEV 1106 5.2 1075 5.5 -3% 5% -4%Series HEV 1134 4.6 1071 5.1 -6% 12% 2%Fuel Cell 1185 3.3 1174 3.8 -1% 14% 4%Fuel cell HEV 1161 3.1 1093 3.2 -6% 6% -4%EV 1012 1.6 1029 1.8 2% 11% 1%


US06

Compared to previous cycles, the US06 is quite aggressive as evidenced by its high average

speed and high characteristic acceleration. In the broad spectrum of driving patterns, it can be

considered one of the extremes. The errors observed for the US06 were similar to previous

cycles (<15%), but the relative errors were a bit larger. Also, ADVISOR modelling of the

PHEV over the US06 proved to be a challenge since the zero-delta-SOC-correction routine

was unable to find a solution. Therefore, the simulated PHEV operated as a charge-depleting

HEV and the result quoted is a gasoline-equivalent value hand-calculated by the author using

the ADVISOR results and the method outlined in Simpson (1999). Therefore, limited

significance should be given to this result.

Table 4-30: Summary of validation results for the US06 cycle US06 Relative

Mass L/100km Mass L/100km Mass L/100km errorConv ICE 1100 8.1 1087 9.2 -1% 14% ---Parallel HEV 1106 8.3 1053 8.0 -5% -3% -15%Series HEV 1134 7.7 1077 8.0 -5% 4% -9%Fuel Cell 1185 5.1 1173 5.8 -1% 14% 0%Fuel cell HEV 1161 5.0 1097 5.2 -5% 5% -8%EV 1012 2.5 1021 2.7 1% 10% -4%


NYCC

The NYCC is a low average speed, high characteristic acceleration cycle designed to simulate

stop-start driving in dense traffic in downtown New York. Therefore it can be considered

101

another “extreme” in the spectrum of driving cycles. The accuracy of PAMVEC was by far

the worst for the NYCC, showing the largest absolute and relative errors. Firstly, the non-

regenerative powertrains (ICV & FCEV) show a significant overestimation of vehicle energy

consumption, due to overestimation of braking losses. Secondly, the FCEV and BEV show a

significant overestimation of total vehicle mass, due to the over-sizing of their fuel

cell/battery as a result of uncharacteristically low motor/controller efficiency (see Tables 4-32

and 4-33). Finally, the PHEV shows an underestimate of energy consumption due to error in

the motor/controller efficiency (66%) specified in the PAMVEC model (ADVISOR quotes

two values for motor/controller efficiency under motoring [32%] and generating [78%] with

the author using an energy-weighted average of the two in the PAMVEC model).

Table 4-31: Summary of validation results for the NYCC cycle NYCC Relative

Mass L/100km Mass L/100km Mass L/100km errorConv ICE 1100 20.8 1087 25.8 -1% 24% ---Parallel HEV 1106 16.4 1081 15.2 -2% -7% -25%Series HEV 1134 9.5 1176 10.8 4% 13% -9%Fuel Cell 1185 7.8 1332 9.5 12% 21% -3%Fuel cell HEV 1161 6.5 1182 7.1 2% 9% -13%EV 1012 3.5 1178 4.1 16% 17% -6%


Table 4-32: Powertrain component sizes (kW) for the various cycles

ICV Engine 77 77 77 77 77 82

Engine 28 28 28 28 28 29Battery 49 53 54 47 38 46Motor/controller 33 33 33 32 32 76

Generator 44 32 33 30 31 36Battery 65 46 48 44 45 58Motor/controller 70 66 66 65 65 70

Fuel cell 121 77 79 75 75 77Motor/controller 73 66 66 65 65 69

Fuel cell 44 32 33 30 31 34Battery 60 43 45 41 42 62Motor/controller 67 63 63 62 63 74

Battery 126 76 80 70 67 56Motor/controller 66 60 60 59 59 75

ADVISOR

SHEV

FCEV

FCHEV

BEV

HWFET US06

PHEV

Driving Cycle

NYCC NEDC UDDS

102

Table 4-33: Powertrain component efficiencies for the various driving cycles

Engine 9% 17% 16% 22% 24%Transmission 86% 87% 87% 87% 87%

Engine 16% 24% 24% 26% 26%Battery 94% 96% 97% 96% 96%Motor/controller 66% 62% 61% 69% 85%Transmission 83% 87% 87% 87% 87%

Generator 31% 29% 31% 31% 29%Battery 91% 93% 92% 92% 92%Motor/controller 65% 85% 82% 89% 89%Transmission 88% 87% 87% 86% 86%

Fuel cell 41% 43% 43% 46% 46%Motor/controller 61% 86% 84% 88% 88%Transmission 86% 86% 86% 85% 85%

Fuel cell 44% 47% 47% 48% 48%Battery 95% 94% 95% 95% 95%Motor/controller 65% 85% 82% 89% 89%Transmission 88% 87% 87% 86% 86%

Battery 93% 92% 93% 91% 91%Motor/controller 53% 79% 75% 84% 84%Transmission 86% 86% 87% 86% 86%

US06

FCHEV

BEV

Driving Cycle

PHEV

SHEV

FCEV

NYCC NEDC UDDS HWFET

ICV

4.3.3 Benchmarking Results for Other Vehicle Platforms

The six-powertrain validation exercise was also repeated for a different vehicle platform to

examine its affect on PAMVEC’s accuracy. The original small sedan vehicle platform had a

relatively low MDR of approximately 1640kg/m2 (approx. 1100kg total vehicle mass and

CDA = 0.67). Therefore, the vehicle’s drag area was reduced by a factor of 4 to simulate a

vehicle with a relatively high MDR. This new vehicle was validated for two driving cycles –

firstly, the NEDC to compare with the original results, and secondly the HWFET since Figure

4-1 suggests that much larger errors can be expected for high MDR vehicles on this cycle.

The high MDR validation results for the NEDC are presented in Table 4-34. Compared to the

original low MDR results, the errors have varied slightly, but overall the accuracy of

PAMVEC has not changed for better or worse for the high MDR platform on this cycle. The

high MDR validation results for the HWFET are presented in Table 4-35. For this cycle,

there is an observable increase in the errors for the high MDR case relative to the low MDR

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case (as expected), but even for this extremely high MDR platform the errors remain less than

approximately 20%.

Table 4-34: Validation results for the high MDR platform on the NEDC NEDC Relative

Mass L/100km Mass L/100km Mass L/100km errorConv ICE 1100 7.5 1056 8.0 -4% 7% ---Parallel HEV 1106 4.9 1080 5.3 -2% 9% 1%Series HEV 1134 4.1 1069 4.2 -6% 2% -5%Fuel Cell 1185 3.2 1196 3.6 1% 10% 2%Fuel cell HEV 1161 2.7 1091 2.7 -6% -1% -8%EV 1012 1.4 1038 1.5 3% 3% -4%


Table 4-35: Validation results for the high MDR platform on the HWFET NEDC Relative

Mass L/100km Mass L/100km Mass L/100km errorConv ICE 1100 4.6 1056 5.2 -4% 14% ---Parallel HEV 1106 3.3 1084 3.9 -2% 19% 5%Series HEV 1134 3.1 1061 3.4 -6% 10% -3%Fuel Cell 1185 2.4 1200 2.9 1% 21% 7%Fuel cell HEV 1161 2.0 1084 2.2 -7% 9% -4%EV 1012 1.1 1032 1.2 2% 16% 2%


4.4 Validation Summary

4.4.1 Component Sizing and Total Vehicle Mass

Generally speaking, PAMVEC’s predictions of powertrain component sizes are less accurate

than the estimates of total vehicle mass and vehicle energy consumption. This can be partly

attributed to inaccuracies in the PAMVEC model, however, it is also important to note that

the powertrain component sizing strategy employed by PAMVEC is not necessarily the same

as that of ADVISOR (or any other model). Even when performance constraints are satisfied,

there are still degrees of freedom in the sizing of powertrain components. For example, in a

SHEV architecture, the acceleration performance of the vehicle may be limited by the

motor/controller size, or alternatively, by the battery size. If the performance is limited by the

motor/controller, then the battery may be “oversized” without affecting the vehicle

performance (apart from the 2nd-order effect of the added mass), or vice versa. Therefore, the

difference in component sizes between the two models does not necessarily constitute an

“error”.

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The PAMVEC predictions of total vehicle mass are quite good, generally within 5% of the

ADVISOR values. This is despite the differences in component sizes, which have a limited

effect due to the high specific power of powertrain components and the low powertrain-mass-

fraction (the total powertrain mass as a fraction of total vehicle mass) of the vehicles in

general.

4.4.2 Vehicle Energy Consumption

The PAMVEC predictions of vehicle energy consumption are consistently overestimated

relative to the ADVISOR values, however, the errors are consistently less <20% and mostly

<15%. This overestimation is to be expected, based on PAMVEC’s approach to modelling

inertial power flows within the powertrain, which inevitably leads to an overestimation of

braking and drivetrain losses. The results presented above for the six powertrain architectures

confirm that, for the most part, it was errors in the braking and drivetrain losses that resulted

in the errors in vehicle energy consumption. The sensitivity of PAMVEC’s accuracy was also

tested across a wide range of driving patterns and vehicle platforms. Even for extreme cases,

the accuracy of PAMVEC remained quite tolerable at <20%.

Adopting the predicted ICV energy consumption as the reference value, the error in

PAMVEC’s predictions of relative fuel economy are normally quite low at <5%. This

suggests that PAMVEC is better suited as a tool for performing comparative studies of

relative fuel economy for multiple vehicles, rather than to produce absolute estimates of fuel

economy for individual vehicles.

The errors in PAMVEC’s predictions of vehicle performance and energy consumption are

clearly larger than those produced by dynamic simulation tools. This is not unexpected since

the PAMVEC model was designed to sacrifice some precision and accuracy in favour of

greater convenience in use. However, in the context of vehicle technology assessment,

consideration must be given to the uncertainty in estimates of vehicle energy consumption.

To predict vehicle energy consumption, analysts must make so many assumptions about

driving patterns, vehicle performances, vehicle platforms and component technologies that the

result is a high degree of uncertainty. For example, the PAMVEC model requires the

definition of approximately 30 technical parameters – each with their own uncertainty – so it

105

can be argued that errors <20% are well-within the bounds of the combined uncertainty. On

this basis, the author maintains that PAMVEC, despite its reduced accuracy compared to

dynamic simulators, is still sufficiently accurate for the purposes of vehicle technology

assessment.

106

107

5. PAMVEC Application and Sensitivity Analysis

In Simpson (2004), PAMVEC was used to perform a detailed energy consumption

comparison of 33 vehicles using different alternative fuels and powertrain technologies. This

comparison of vehicle energy consumptions constituted the “tank-to-wheel” stage of a larger

well-to-wheel comparison performed by the author. In this chapter, the comparison from

Simpson (2004) is reproduced2 as an example of the application of PAMVEC to a real-world

problem, and to demonstrate its suitability to the purposes of technology assessment. This

chapter also presents an input parameter sensitivity analysis for a selected group of the 33

vehicles in order to provide better insight into the inner-workings of the PAMVEC tool and

highlight its capabilities and limitations.

5.1 Energy Consumption Comparison

PAMVEC was used to compare 33 different vehicle technologies on the basis of equivalent

performance, using a common vehicle platform and driving pattern.

5.1.1 Powertrain Architectures

The powertrain architectures included in the comparison included internal-combustion-engine

vehicles (ICVs), internal-combustion-engine parallel hybrid-electric vehicles (PHEVs), fuel

cell electric vehicles (FCEVs), fuel cell hybrid-electric vehicles (FCHEVs) and battery

electric vehicles (BEVs).

Transmission, electric motor and HEV battery technologies were kept consistent for all

vehicles, and the relevant technical parameters for these components are presented in Table 5-

1. These technical parameters were derived from previous modelling conducted by the author

using ADVISOR. All EVs and HEVs were assumed to have 60% regenerative braking.

2 Some revisions have occurred in the PAMVEC model since the publication of this study so, although the same input data were used, there are some minor differences between the results in Simpson [REF] and those presented here.

108

5.1.2 Vehicle Platform

The 2003 Holden VY Commodore sedan (Holden, 2003) was chosen as a representative

Australian passenger vehicle platform for the comparison. Table 5-2 presents relevant

physical data for this platform.

Table 5-1: Transmission, electric motor and HEV battery technologies for the various

powertrain architectures considered in the comparison Component Powertrain Architecture Specific Power (W/kg) Efficiency

ICVs and HEVs (5 speed) 13001 87%4 Transmission

FCEVs, FCHEVs and BEVs (1 speed) 16251 87%4

ICVs --- ---

HEVs 14003 70%4

Electric Motor

& Controller

FCEVs, FCHEVs and BEVs 10273 86%4

ICVs, FCEVs and BEVs --- ---

HEVs 4442 96%4

HEV Battery

FCHEVs 4442 95%4

Notes: 1 From Plotkin et al (2001) 2 Based on Ovonic 28Ah NiMH HEV battery (ADVISOR data file ESS_NIMH28_OVONIC.m) 3 From EUCAR et al (2003) 4 Author estimates

Table 5-2: Physical parameters for the 2003 Holden VY Commodore sedan platform

Curb mass 1550 kg

Glider mass (estimated) 830 kg

Aerodynamic drag coefficient 0.32

Frontal area (estimated) 2.5 m2

Rolling resistance coefficient 0.01

Wheel radius 320 mm

Accessory load 1000 W

5.1.3 Driving Pattern

The driving pattern assumed for the comparison was the New European Driving Cycle

(NEDC) from test procedures specified in United Nations Economic Commission for Europe

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Regulation 83 (Figure 4-1). From January 2003, these test procedures have been used to

measure fuel consumption and emissions for the purposes of labelling production vehicles for

the Australian market (AGO, 2003).

5.1.4 Performance Specifications

All vehicles in the comparison were intended to have identical performance capabilities, in

accordance with the specifications for acceleration, gradability, top speed and driving range

presented in Table 5-3 which have been assumed as being representative of a Holden

Commodore sedan. This approach distinguishes this comparison from previous work, in

which certain performance constraints have often been relaxed for particular vehicle

technologies. There are, however, two exceptions in this study. The NiMH and VRLA BEVs

have reduced driving ranges (250km and 125km respectively) since the achievement of

500km driving range is not technically feasible for these technologies.

Table 5-3: Performance constraints for the vehicles in this comparison

Top speed 180 km/h

Acceleration 0-100 kph in 9.0s

Gradability 6.5% at 100 kph

Driving range 500km

5.1.5 Component Technologies and Energy Consumption Results

Table 5-4 presents the 33 powertrain technologies included in the comparison. The data was

collected from a variety of sources and represents predictions of component technical

specifications for the 2010 timeframe. The technologies include:

• Spark-ignition ICVs fuelled with unleaded petrol (ULP), liquid petroleum gas (LPG),

compressed natural gas (CNG) at 3600psi, liquid natural gas (LNG), compressed

gaseous hydrogen (GH2) at 5000psi, liquid hydrogen (LH2), an 85% methanol / 15%

petrol blend (M85), an 85% ethanol / 15% petrol blend (E85), and a 10% ethanol /

90% petrol blend (E10)

• Compression-ignition ICVs for Diesel and biodiesel (BioD)

• Spark-ignition PHEVs for ULP, LPG, CNG, LNG, GH2, LH2, M85, E85 and E10

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• Compression-ignition PHEVs for Diesel and Biodiesel

• Fuel cell/reformer EVs for ULP and pure methanol (MeOH)

• Fuel cell EVs for GH2 and LH2

• Fuel cell/reformer HEVs for ULP and MeOH

• Fuel cell HEVs for GH2 and LH2

• BEVs with lithium-ion (Li-Ion), nickel-metal hydride (NiMH) and valve-regulated

lead-acid (VRLA) batteries

In Table 5-4, the results of the PAMVEC modelling are presented in terms of curb mass, net

powertrain efficiency and vehicle energy consumption. The ULP ICV is chosen as the

reference vehicle technology for the comparison.

The curb masses of the ICVs are somewhat similar, with some variation (~10%) due to

differences in the specific energy of fuels and specific power of engines. The HEVs are

slightly heavier than their ICV counterparts, which reflect the lower specific power of HEVs’

motor plus battery combination relative to engines. The non-hybrid FCEVs are relatively

heavy due to the low specific power of fuel cell systems (particularly reformers), whereas the

FCHEVs are less heavy due to the higher specific power of batteries relative to fuel cells. As

expected, the BEVs are particularly heavy due to their low specific energy battery packs.

The net powertrain efficiency correlates closely with engine/fuel cell efficiency, although the

non-hybridised ICVs and FCEVs do have the additional efficiency penalty of no regenerative

braking. On average, the HEVs are approximately 40% more efficient than their ICV

counterparts. The reformer-based, non-hybrid FCEVs show no efficiency advantage over

HEVs using the same fuels, whereas the H2-fuelled FCEVs are approximately 25% more

efficient than H2-fuelled HEVs. FCHEVs with reformers are approximately 15% more

efficient than their FCEV counterparts, whereas the H2-fuelled FCHEVs are only 8% more

efficient than non-hybrid variants. The battery EVs’ high efficiencies (more than three times

that of the reference vehicle) must be considered in light of the fact that no fuel conversion

occurs onboard the vehicle.

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Table 5-4: Fuel/powertrain technology parameters and predicted energy consumption results

for the 33 vehicles in this comparison Fuel Powertrain Fuel

specific

energy

(MJ/kg)

Engine / Fuel

Cell / Battery

specific power

(W/kg)

Engine / Fuel

Cell / Battery

efficiency (%)

Curb Mass

(kg)

Powertrain

efficiency

(%)

Energy

Consumption

(MJ/km)

ULP ICV 37.3 1 642 7 22.5 8 1260 10.6 2.78

LPG ICV 20.7 1 642 7 23.7 8,9 1299 11.2 2.69

CNG ICV 15.6 1 531 7 25.8 8 1371 12.1 2.54

LNG ICV 26.6 1 531 7 25.8 8 1320 12.2 2.49

GH2 ICV 12.7 2 642 7 27.7 8 1337 13.0 2.33

LH2 ICV 9.5 2 642 7 27.7 8 1383 13.0 2.37

M85 ICV 22.2 3 642 7 24.5 8,9 1290 11.5 2.59

E85 ICV 24.8 3 642 7 23.9 8,9 1282 11.3 2.64

E10 ICV 35.8 3 642 7 22.5 8 1262 10.6 2.79

Diesel ICV 37.3 1 510 7 28.5 8 1307 13.4 2.24

BioD ICV 31.9 1 510 7 28.5 8 1315 13.4 2.25

ULP HEV 37.3 1 642 7 30.5 8 1378 15.0 2.05

LPG HEV 20.7 1 642 7 32.1 8,9 1403 15.8 1.96

CNG HEV 15.6 1 531 7 33.0 8 1455 16.2 1.95

LNG HEV 26.6 1 531 7 33.0 8 1422 16.2 1.92

GH2 HEV 12.7 2 642 7 37.7 8 1427 18.5 1.69

LH2 HEV 9.5 2 642 7 37.7 8 1455 18.5 1.70

M85 HEV 22.2 3 642 7 33.2 8,9 1397 16.3 1.90

E85 HEV 24.8 3 642 7 32.4 8,9 1393 16.0 1.94

E10 HEV 35.8 3 642 7 30.5 8 1380 15.0 2.05

Diesel HEV 37.3 1 510 7 34.8 8 1416 17.1 1.82

BioD HEV 31.9 1 510 7 34.8 8 1421 17.1 1.82

ULP FCEV 37.3 1 259 7 37.8 8 1810 15.2 2.31

MeOH FCEV 19.5 1 259 7 41.5 8 1857 16.6 2.14

GH2 FCEV 12.7 2 375 7 56.6 8 1568 23.1 1.42

LH2 FCEV 9.5 2 375 7 56.6 8 1601 23.0 1.43

ULP FCHEV 37.3 1 259 7 39.2 8 1679 17.3 1.95

MeOH FCHEV 19.5 1 259 7 42.6 8 1712 18.8 1.81

GH2 FCHEV 12.7 2 375 7 55.6 8 1541 24.7 1.31

LH2 FCHEV 9.5 2 375 7 55.6 8 1570 24.7 1.32

Li-Ion BEV 0.50 4 420 4 95.0 4 2325 39.6 1.01

NiMH BEV 0.26 5 393 5 92.0 5 2406 37.9 1.08

VRLA BEV 0.13 6 300 6 90.0 6 2466 36.8 1.13

Notes:

1. From International Energy Agency (1999)

2. From TIAX (2002)

3. For fuel blends, values are calculated in proportion to the constituent fuels.

4. Based on 140Wh/kg and 420W/kg lithium-ion (Li-Ion) batteries (SAFT, 2003)

5. Based on 70Wh/kg and 220W/kg nickel-metal-hydride (NiMH) batteries (Ovonic Battery Co., 2000)

6. Based on 35Wh/kg and 300W/kg valve-regulated lead-acid (VRLA) batteries (Japan Storage Battery Co., 2000)

7. From EUCAR et al (2003)

8. From L-B-Systemtechnik (2002)

9. Efficiency adjusted for octane rating of fuel based on data in International Energy Agency (1999)

112

Overall, the vehicle energy consumption (which combines the effects of curb mass and

powertrain efficiency) is the most-important comparison (Figure 5-1). The higher efficiency

of HEVs relative to ICVs is slightly offset by their greater mass, with a reduction in energy

consumption of approximately 25%. Relative to ICVs, the higher efficiency of reformer

FCEVs is substantially offset by their much-higher mass (reduction in energy consumption of

only 15%), whereas the H2 FCEVs offer a 40% reduction in energy consumption from their

ICV counterparts. In contrast, the hybridisation of FCEVs offers both efficiency and mass-

reduction benefits – the reformer FCHEVs and H2 FCHEVs offer 15% and 8% less energy

consumption, respectively, than their non-hybrid counterparts. The large curb mass of the

BEVs is more-than compensated for by their superior efficiency, resulting in approximately

60% less energy consumption than the reference vehicle.

From these results it seems clear that improvements in vehicle energy consumption are

primarily due to greater powertrain efficiency, although large increases in curb mass can

substantially detract from efficiency gains. Furthermore, the energy consumption of non-

hybrid vehicles shows a heightened sensitivity to curb mass due to their lack of regenerative

braking. These factors are explored more thoroughly in the sensitivity analysis in the

following section.

Equivalent Fuel Consumption of Various Fuel/Powertrain Technologies

8.65 8.658.34 8.20 8.05

7.88 7.727.37 7.24

6.98 6.96

6.36 6.376.10 6.05 6.01 5.98 5.89

5.66 5.655.29 5.24

7.17

6.64

4.45 4.40

6.04

5.62

4.11 4.07

3.50 3.353.14

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

PULP IC

V

E10 IC

V

LPG IC

V

E85 IC

V

M85 IC

V

CNG ICV

LNG IC

V

LH2 I

CV

GH2 ICV

BioD IC

V

Diesel

ICV

PULP H

EV

E10 H

EV

LPG H

EV

CNG HEV

E85 H

EV

LNG H

EV

M85 H

EV

BioD H

EV

Diesel

HEV

LH2 H

EV

GH2 HEV

PULP FCEV

MeOH FCEV

LH2 F

CEV

GH2 FCEV

PULP FCHEV

MeOH FCHEV

LH2 F

CHEV

GH2 FCHEV

VRLA BEV

NiMH B

EV

Li-Ion

BEV

Pet

rol-e

quiv

alen

t fue

l con

sum

ptio

n (L

/100

km)

Figure 5-1: Comparison of equivalent fuel consumption for the 33 vehicles

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5.2 Sensitivity Analysis

An analysis of the sensitivity of these vehicle energy consumption results to input parameters

in the PAMVEC model is important because 1) it shows technology analysts which

parameters need to be most-accurately specified in the comparison, and 2) it shows vehicle

designers which component technologies to target in order to produce designs with minimised

energy consumption. Furthermore, by comparing the sensitivity results across a range of

powertrain architectures and component technologies, we can also obtain greater

understanding of the inner-workings of the PAMVEC model and highlight its benefits and

limitations.

It was beyond the scope of this thesis to perform an input parameter sensitivity analysis for all

of the vehicles compared in the previous section. Rather, a selection of technologies were

included that spanned the full extents of the design space. The earlier analysis of energy

consumption results identified two key factors in determining overall vehicle energy

consumption – net powertrain efficiency (including regenerative braking effects) and total

vehicle mass. Figure 5-2 plots these factors against one another for the 33 vehicles compared

in the previous section.

Figure 5-2: Net powertrain efficiency vs. total vehicle mass for the 33 vehicles

Mass vs Efficiency

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

35.0%

40.0%

45.0%

1200 1400 1600 1800 2000 2200 2400 2600Total vehicle mass

Net powertrain efficiency ICVsPHEVsFCEVsFCHEVsBEVs

BEVs

ICVs

HEVs

H2 FCVs

Reformer FCVs

114

The different powertrain architectures can be seen to group roughly into five clusters.

Therefore, the following seven vehicles were chosen for the sensitivity analysis as a

representative selection from the five groups (both FCEV and FCHEV variants were included

from the H2 FCV and Reformer FCV groups to consider the effects of regenerative braking

and FCV hybridisation):

• Petrol ICV

• Petrol HEV

• Petrol FCEV

• GH2 FCEV

• Petrol FCHEV

• GH2 FCHEV

• Li-Ion BEV

In the following sections, these seven vehicles are used to test the sensitivity of vehicle energy

consumption to PAMVEC input parameters for 1) the vehicle platform, 2) component specific

powers/energies, 3) component efficiencies, 4) the driving pattern and 5) vehicle

performance. The sensitivities are expressed as normalised sensitivity factors (NSFs), defined

as:

⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆

⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆

=

inputinput

outputoutput

NSF (5-1)

By definition, a NSF of 1 means that a 1% change in the input parameter produces a 1%

change in the output (in this case vehicle energy consumption).

5.2.1 Vehicle Platform Sensitivity

The vehicle platform parameter sensitivities are shown in Figure 5-3. Sensitivity to glider

mass ranges between values of 0.35-0.5. In contrast, sensitivity to drag-area (CDA) is slightly

lower ranging between 0.3-0.45. The non-hybrid vehicles (ICVs and FCEVs) show a greater

sensitivity to glider mass than drag-area because of their lack of regenerative braking and

115

resulting braking losses. For regenerative vehicles, sensitivities to glider mass and drag-area

are somewhat similar. The FCEVs show the highest sensitivity to glider mass because of

their low specific power powertrain and mass-compounding effects through acceleration

performance requirements.

Vehicle Platform Sensitivities

0.00

0.10

0.20

0.30

0.40

0.50

0.60

ULP ICV ULP HEV ULP FCEV H2 FCEV ULP FCHEV H2 FCHEV Li BEV

Mglider

CdA

Crr

Kregen

Pacc

Figure 5-3: NSFs for vehicle platform parameters

The sensitivity to rolling resistance coefficient is typically lower, ranging between 0.2-0.3,

except for the BEV which has a heightened sensitivity (0.5) to rolling resistance because of its

impact on battery energy storage requirements due to driving range. The BEV also has a

higher sensitivity (0.2) to regenerative braking fraction because of its large mass. For other

vehicles, the sensitivity to kregen is low at approximately 0.1. For all vehicles, the sensitivity

to accessory load is generally low at around 0.15.

In discussing these sensitivity factors, it is important to consider which vehicle system effects

are captured by the model. Firstly, changes to the vehicle platform will affect powertrain

component sizes through the vehicle performance model. The resulting change in total

vehicle mass, in conjunction with changes to the vehicle platform, will vary the road load.

The direct consequence of this variation in the road load is a change in the vehicle energy

consumption, which is captured by the model. However, a higher-order effect that is NOT

captured by the PAMVEC model is the change in the mass-to-drag ratio of the vehicle and the

affect this has on component efficiency. For example, consider an increase in the glider mass.

Assuming vehicle acceleration is the dominant performance constraint, the powertrain

116

component sizes will increase roughly in proportion to the increase in mass (since

acceleration power is dominated by the inertial component proportional to vehicle mass).

Furthermore, the road load will increase roughly in proportion to vehicle mass also, since the

transient road load power requirements also tend to be dominated by the inertial component.

Therefore, in this situation, both the component sizes and their operating torques/powers are

increasing roughly in proportion with vehicle mass such that their operating load fraction

should not change significantly. On this basis, it can be argued that the higher-order affects of

vehicle platform on component efficiency are probably not significant, and that the vehicle

platform sensitivity factors produced by the PAMVEC model are representative values for

what occurs in reality. As a confirmation of this, the vehicle platform sensitivities presented

here are generally consistent with those determined by Cuddy & Wipke (1997).

5.2.2 Component Specific Power/Energy Sensitivity

The component specific power/energy parameter sensitivities are shown in Figure 5-4. For

most powertrain components in most vehicles, the energy consumption is relatively

insensitive (NSF<0.1) to changes in component technology specific power/energy. This can

generally be attributed to the relatively high specific power/energy of the vehicle powertrain

components, resulting in component masses that are a low fraction of total vehicle mass (see

the mass breakdowns presented in Figure 5-5).

Component Specific Power/Energy Sensitivities

0.00

0.10

0.20

0.30

0.40

0.50

0.60


Fuel Wh/kg

HSE W/kg

HSP W/kg

MC W/kg

Trans W/kg

Figure 5-4: NSFs for component specific power/energy parameters

117

Total vehicle mass breakdown for various powertrains

0

500

1000

1500

2000

2500


Mas

s (k

g)

StructureTransmissionMotor/controllerBatteryEngine/Fuel cellFuel storageCargoGlider

Figure 5-5: Mass breakdowns for the seven vehicles considered in the sensitivity analysis

The exceptions, however, are the specific energy storage (Wh/kg) for the BEV and the fuel

cell/reformer specific power (W/kg) for the FCVs. The specific energy of the Li-Ion batteries

is more than an order of magnitude lower than the other fuel technologies, resulting in the

large sensitivity. Similarly, the low specific power of fuel cell systems (particularly those

including reformers) gives rise to the large sensitivity for the FCVs.

For the component specific power/energies, PAMVEC’s predictions of NSF should be quite

valid. Again, the changes in total vehicle mass (including mass compounding effects), the

road load and component sizes are captured by the model. There will be some higher-order

effects (relating to component efficiency) but again these can be assumed to be relatively

insignificant.

5.2.3 Component Efficiency Sensitivity

The component efficiency parameter sensitivities are shown in Figure 5-6. Generally

speaking, the component efficiency sensitivities are quite high for all vehicles. The HSED

sensitivities are approximately 1 which is to be expected since all fuel consumed is subject to

the HSED efficiency. In hybrid vehicles, the HSPD sensitivity is only a fraction of 1, since

only part of the power flow is subject to this efficiency. Similarly, in the PHEV, the

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motor/controller efficiency sensitivity is much less than 1. However, for other vehicles it is

greater than 1, which reflects not only the motor/controller’s contribution to net powertrain

efficiency, but also its affect on component sizing and subsequent mass compounding.

Similarly, the transmission sensitivities are greater than 1. The BEV energy consumption

shows high sensitivities (of almost 2) to all component efficiencies, which reflects mass

compounding effects in the battery energy storage, in addition to the effects on powertrain

efficiency and drivetrain component sizing. Overall, these component efficiency sensitivities

are generally consistent with the findings of Cuddy & Wipke (1997).

Component Efficiency Sensitivities

0.00

0.50

1.00

1.50

2.00

2.50


HSE

HSP

MC

Trans

Figure 5-6: NSFs for component efficiency parameters

In the PAMVEC model, component efficiencies are specified as an input, but in reality

component efficiency depends upon many factors, which amongst other things include the

driving pattern, the component technologies and sizes and the powertrain control strategy.

Therefore, the component efficiency NSFs provide the most value by identifying which

efficiency parameters need to be specified most-accurately to produce accurate predictions

from the PAMVEC tool. For example, the NSFs suggest that hybrid vehicle energy

consumption is relatively less sensitive to battery efficiency (and also motor/controller

efficiency in the PHEV). Therefore, analysts can define these parameters with less precision

because an error is not likely to have a major bearing on the result. However, all the other

component efficiencies show NSFs ≥ 1, which means that care must be taken when specifying

these parameters. Ultimately, when specifying component efficiencies, the analysts must

exercise a degree of technical judgement that accounts for subtleties of the driving pattern,

119

component technologies, etc. However, it does not need to be pure guesswork. As

demonstrated in this thesis, the analyst can be guided by the results of dynamic simulators or

by the many studies in the literature that quote component efficiencies under realistic

operating conditions. Nevertheless, in light of these large component efficiency NSFs, the

inability of PAMVEC to model component efficiency is its primary limitation and analysts

should be mindful of it.

5.2.4 Driving Pattern Sensitivity

The driving pattern parameter sensitivities are shown in Figure 5-7. Since the driving pattern

parameters contribute directly to the road load (and vehicle energy consumption), it comes as

no surprise to find that their NSFs are generally high. The sensitivity to average velocity

ranges between 0.4-0.6, and the sensitivity to characteristic acceleration between 0.25-0.45.

The sensitivity to average velocity is lowest in the heavy fuel cell vehicles since their energy

consumption is more-dominated by mass-dependent loss components such as rolling

resistance. In contrast, the sensitivity to average velocity is high in the electric vehicle

because of mass-compounding in the sizing of the battery. Not surprisingly, the sensitivity to

characteristic acceleration is lowest for the vehicles with regenerative braking, except for the

BEV which shows the highest sensitivity to characteristic acceleration due to mass-

compounding effects in the battery sizing.

Driving Pattern Sensitivities

0.00

0.20

0.40

0.60

0.80

1.00

1.20


Vavg

Vratio

Achar

Figure 5-7: NSFs for driving pattern parameters

120

The sensitivity to velocity ratio is consistently high for all vehicles with values approaching

NSF = 1 for most vehicles (expect for the BEV with NSF = 1.15). This is no doubt due to the

cubic dependence of aerodynamic drag on vehicle velocity.

These driving pattern sensitivities do account for the direct effects of driving pattern on

vehicle energy consumption, but they do not include effects on component efficiency. Unlike

parameters for the vehicle platform and component specific power/energy, driving pattern

parameters do not affect component sizing (apart from fuel/energy storage). Therefore, the

changes in road load resulting from changes in the driving pattern can have a significant

impact upon component efficiency, and as was demonstrated in the previous section, vehicle

energy consumption can be quite sensitive to component efficiency.

Fortunately, the results in Table 4-33 provide an opportunity to test the sensitivity of

component efficiency to the driving pattern. Clearly, the efficiency of some powertrain

components was not very dependent on the driving cycle. For example, the transmission

efficiency varied little across cycles and the use of a constant, representative value (e.g. 87%)

would introduce very little error into the estimates of vehicle energy consumption (the error

magnitude can be estimated using the NSFs presented in Figure 5-6). The same can be said

for battery efficiency in the PHEV, FCHEVs and BEV. The engine/fuel cell efficiencies in

SHEV, FCEV and FCHEV architectures showed a reduced dependence on driving pattern

because these components are decoupled from the road load by the all-electric powertrain. In

contrast, for engines and motor/controllers, different driving patterns force these components

to operate in different regions of their torque-speed envelope, resulting in substantial

variations in efficiency. However, it is interesting to note that the efficiency of these

components generally improved for the higher average speed cycles, and this would act to

reduce the average velocity sensitivities shown in Figure 5-7. In contrast, increasing the

characteristic acceleration (e.g. moving from the NEDC to the UDDS) tended to reduce the

efficiency of motor/controllers (due to operation at higher torques) and this would act to

increase the characteristic acceleration NSFs shown in Figure 5-7.

5.2.5 Vehicle Performance Sensitivity

The vehicle performance parameter sensitivities are shown in Figure 5-8. The sensitivity to

various performance constraints is quite varied across the vehicles examined. Acceleration

121

sensitivities vary by an order of magnitude from <0.05 for the PHEV to almost 0.5 for the

ULP FCEV. Sensitivity to top speed varies from <0.05 for the ULP ICV to almost 0.4 for the

ULP FCHEV. However, the influence of the component sizing strategy can be seen quite

clearly in these results. Acceleration is clearly the dominant performance target for the non-

hybrid vehicles, and acceleration sensitivity is highest for low specific power components

(e.g. ULP FCEV). For the hybrid vehicles, where the HSED is not sized according to

acceleration requirements, top speed becomes the dominant constraint. Gradability was not

an active constraint for any of the vehicles considered; therefore its NSFs are all zero.

Vehicle Performance Sensitivities

0.00

0.10

0.20

0.30

0.40

0.50

0.60


Top speed

Acceleration

Gradability

Range

Figure 5-8: NSFs for vehicle performance parameters

Apart from the BEV, the vehicles are consistently insensitive to the range target with NSFs <

0.05. Range is clearly the most significant constraint for the BEV (NSF ~0.5), while the other

constraints are relatively insignificant given that its battery has been sized for energy storage,

and not power delivery.

In calculating these performance sensitivities, the main system effect captured by the

PAMVEC model is mass-compounding, since the model is unable to capture the effects of

performance constraints on component efficiency (via the component sizing). Unfortunately,

several studies have shown that vehicle energy consumption can be quite sensitive to

performance requirements via component efficiency effects. For example, the analysis of

Plotkin et al (2001) (Figure 2-1) suggests that ICV sensitivity to acceleration should be

approximately 0.8, not 0.1, due to the poor-part load efficiency of internal combustion

122

engines. For PHEVs, the same study predicts sensitivity to acceleration of NSF = 0.2 (not

0.05). Simple statistical analysis of reported fuel economy predictions by Santini et al (2002)

predicts sensitivities to acceleration of NSF = 0.9 for ICVs and NSF = 0.5 for HEVs. Clearly,

the PAMVEC model does not capture key system effects relating to the efficiency of engines

and the result is a significant underestimation of the sensitivity to acceleration for both ICVs

and PHEVs.

In contrast, the PAMVEC tool is ideally suited to predicting sensitivities to driving range,

since these are predominantly due to mass-compounding effects. Figure 5-9 shows the

variation in energy consumption for the BEV across a range of battery specific energies and

driving range targets. The minimum energy consumption in Figure 5-9 is 2.42 L/100km and

note that, for the vehicle (acceleration) performance assumed in this analysis, the vehicle

energy consumption is quite insensitive to the driving range for battery specific energies

greater than approx. 250 Wh/kg. In these cases, the battery would be sized according to

power rather than energy requirements. Unfortunately, most battery technologies have

specific energies much lower than 250Wh/kg (see Table 2-3) therefore it can be concluded

that BEV energy consumption will typically be quite sensitive to the driving range target.

Figure 5-10 presents an identical comparison for a H2 FCHEV. For this vehicle, the

minimum energy consumption is 4.0 L/100km and the energy consumption is also quite

insensitive to driving range for hydrogen specific energy storages greater than approx. 1000

Wh/kg (3% by weight H2). Most hydrogen storage technologies have specific energies

greater than this value (see Table 2-3) so it can be concluded that, despite the low specific

energy storage of hydrogen relative to conventional fuels, H2 FCHEV energy consumption

will typically be relatively insensitive to the driving range target. Such comparisons are not

easy to perform using existing vehicle modelling tools, but they are readily performed with

the PAMVEC model.

123

0

100

200

300

400

500

0100

200300

400500

0

2

4

6

8

10

Specific energy storage (Wh/kg)

Battery EV: Energy Consumption vs. Driving Range and Specific Energy Storage

Driving range (km)

Equ

ival

ent f

uel c

onsu

mpt

ion

(L/1

00km

)

(a)

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500

Driving range (km)

Spe

cific

ene

rgy

stor

age

(Wh/

kg)

Battery EV: Energy Consumption (L/100km) vs. Driving Range and Specific Energy Storage

2.5

2.5

2.5

2.5

3

3

3

4

4

5

5

10

(b)

Figure 5-9: Variation in BEV energy consumption across a range of battery specific energies

and driving range targets

124

0

100

200

300

400

500

01000

20003000

40005000

0

2

4

6

8

10

Specific energy storage (Wh/kg)

Fuel Cell HEV: Energy Consumption vs. Driving Range and Specific Energy Storage

Driving range (km)

Equ

ival

ent f

uel c

onsu

mpt

ion

(L/1

00km

)

(a)

0 50 100 150 200 250 300 350 400 450 5000

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Driving range (km)

Spe

cific

ene

rgy

stor

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(Wh/

kg)

Fuel Cell HEV: Energy Consumption (L/100km) vs. Driving Range and Specific Energy Storage

4.1

4.1

4.1

4.1

4.5

4.5

4.5

55

5

66

10

(b)

Figure 5-10: Variation in H2 FCHEV energy consumption across a range of battery specific

energies and driving range targets

125

5.3 Summary

This chapter has demonstrated the use of PAMVEC in a topical and relevant vehicle

technology assessment: the prediction of vehicle energy consumption as part of a well-to-

wheels study. The versatility of the PAMVEC model allowed it to be applied to seven

different powertrain architectures utilising a variety of alternative fuels (33 vehicles in total).

Despite this large number of vehicles, the study was completed in a relatively small amount of

time since the PAMVEC model avoided the significant computation time that would

otherwise have been incurred using existing dynamic vehicle simulation tools. Furthermore,

the input data for the modelling (particularly relating to component technologies) was

obtained relatively easily from public-domain sources. Lastly, PAMVEC’s unique modelling

capabilities allowed the use of a driving range constraint for the comparison, which was

particularly valuable since the scope of the study included BEVs for which the vehicle energy

consumption was shown to be quite sensitive to driving range.

An input parameter sensitivity analysis was also performed for the PAMVEC model using

data from the well-to-wheels study. This revealed the parameters that were of greatest

significance to the study outcomes (and also to vehicle energy consumption in general) and in

many cases the sensitivity coefficients correlated well with those reported in other studies.

However, the analysis also highlighted the primary limitation in PAMVEC’s modelling

capabilities, which is its inability to model the dependence of powertrain component

efficiency on the driving pattern and/or component sizes. This aspect of the PAMVEC model

may limit its applicability to some studies.

126

127

6. Conclusion

This thesis has presented a novel approach to modelling energy consumption in road vehicles

– the Parametric Analytical Model of Vehicle Energy Consumption (PAMVEC).

PAMVEC is fundamentally a lumped-parameter model, but it offers a unique combination of

attributes intended to occupy a niche between the capabilities of existing dynamic simulators

and previous lumped-parameter models. PAMVEC’s unique features include:



uncertainty.

• Parametric analytical equations for predicting vehicle energy consumption that are

derived from the well-known road load equation. These models have the simplicity

and minimal input data requirements of a lumped-parameter model but, in

combination with the novel driving pattern description, can model some driving-

pattern-dependent phenomena (such as braking losses) without the need for the

iterative computations of dynamic simulators.

• Parametric analytical equations to size powertrain components implicitly in terms of

specified performance targets that include driving range, without the need for the

iterative component sizing routines of dynamic simulators. The model takes full

account of the mass-compounding effects that arise through the sizing of powertrain

components due to various performance constraints. The component sizing equations

also include a novel acceleration performance model that accounts for differences in

the torque/power vs. speed characteristics of various drivetrain technologies.

The simplicity of the PAMVEC model is enabled by a central simplifying assumption that

tractive power flow that is reversible (due to vehicle inertia) can be modelled separately from

irreversible power flow (due to vehicle drag). This assumption can arguably be justified

based on the fact that transient inertial power flows are typically an order of magnitude larger

than drag powers. However, this assumption does introduce error into the energy

consumption model (particularly in the estimate of drivetrain losses) and this was quite

apparent in the benchmarking against the ADVISOR advanced vehicle simulator. Errors in

predicted vehicle energy consumption of <20% (typically <15%) were observed across a wide

range of vehicle platforms and driving patterns, and the overestimation of drivetrain losses (in

128

the brakes, transmission and/or motor/controller) was identified as the major contributor to

this error. While this error is large compared to that of dynamic simulators (<5%), it can still

be considered satisfactory in the context of vehicle technology assessment where uncertainties

are so great. Generally speaking, the errors in PAMVEC’s predictions of relative fuel/energy

consumption were much lower (typically <5%), suggesting that the tool is better suited to

relative predictions, such as those that might be required in a comparative vehicle technology

assessment.

From a systems perspective, the primary limitation in the capabilities of the PAMVEC model

is that it does not model component efficiencies, but rather, requires the user to specify mean

component efficiencies as an input. The model is therefore unable to predict variations in

component efficiencies due to changes in component sizes or driving pattern. Fortunately for

the user, there are large amounts of published data in the literature to indicate the operating

efficiency of powertrain components under various conditions. When coupled with some

engineering judgement, this source of data is sufficient to support the use of a tool such as

PAMVEC. However, the component efficiency model limitation will inevitably be

experienced when conducting parametric sensitivity analysis such as those presented in

Chapter 5.

This thesis has provided at least five examples of the use of the PAMVEC model to predict

vehicle energy consumption for various purposes:

1. To estimate the performance and energy consumption of existing production-model

and prototype vehicles with a variety of powertrain technologies based on published

data for those vehicles.

2. To benchmark PAMVEC’s predictions of component sizes, total vehicle mass and

vehicle energy consumption against those of ADVISOR

3. To predict the energy consumption of 33 hypothetical vehicles as part of a well-to-

wheels analysis

4. Parametric studies such as the input parameter sensitivity analysis in Chapter 5, and

5. An examination of the sensitivity of vehicle energy consumption in BEVs and

FCHEVs to their specific energy storage and driving range.

These examples demonstrate the suitability and versatility of the PAMVEC model and it is

the author’s hope that this modelling approach will become a valued complement to existing

tools in the vehicle technology research community.

129

6.1 Future Work

For a modelling tool such as PAMVEC to benefit the research community, it must be

distributed to other users so they may gain experience in order to appreciate its capabilities

and limitations. At the time of writing, the PAMVEC spreadsheet model was not publicly

available. Therefore, the author’s next task will be to release a public version of PAMVEC

containing MS Excel spreadsheet templates for various powertrain architectures. Further

journal publications are also currently being written to promote PAMVEC and demonstrate its

uses, and to disseminate the novel concepts embodied in its modelling approach. Hopefully,

other researchers and analysts will choose to apply PAMVEC to their own vehicle technology

studies, or adapt novel elements of the model (such as the parametric driving pattern

description) for other purposes.

While the validation exercise documented in this thesis was quite thorough, it is by no means

complete. Further, ongoing validation of PAMVEC can definitely be justified, especially as

more published data becomes available for various prototype and production vehicles with

alternative powertrain technologies. In particular, the applicability of PAMVEC to heavy-

duty vehicles (e.g. buses and trucks) should be verified even though, based on the validation

presented in this thesis, there are no reasons to doubt its suitability for these vehicle platforms.

To try to address PAMVEC’s inability to model component efficiency, the author hopes to

investigate alternative modelling approaches that offer this capability while retaining some of

PAMVEC’s beneficial attributes (such as non-time-iterative calculations). Empirical

correlations can readily be used to model the relationships between component size and

efficiency, but the dependence of component efficiency on the driving pattern presents a

greater challenge. One possible approach was alluded to in Section 2.4, which is to model

driving patterns as joint velocity-acceleration probability distributions that can then be

mapped to a powertrain torque-speed distribution and coupled with component efficiency

maps to predict component efficiency with much greater precision. When combined with the

powerful matrix-algebra capabilities of software such as MATLAB, this approach could lead

to energy consumption models with high accuracy and fast calculation relative to dynamic

simulators. Such an energy consumption model could also be mated with an implicit

performance model such as that employed by PAMVEC to limit the need for iterative

130

component sizing against performance constraints (although iteration cannot be avoided if

driving range is employed as a constraint).

Finally, the capabilities of PAMVEC inspire many interesting parametric vehicle studies that

the author hopes to pursue on an ongoing basis.

131

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Weiss M.A., Heywood J.B., Drake E.M., Schafer A. & AuYeung, F. (2000) “On the Road in

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139

Appendix A – Driving Cycle Parameters Source: ADVISOR 2002 driving cycle data files

Average

velocity

(km/h)

Root-mean-

cubed velocity

(km/h)

Velocity

ratio

Characteristic

acceleration

(m/s2)

Cycle

avgv rmcv Λ a~

MANHATTAN 10.93 19.11 1.75 0.269

NYCC 11.36 20.61 1.81 0.293

NYCTRUCK 12.10 25.99 2.15 0.234

NYCCOMP 14.03 24.89 1.77 0.186

WVUCITY 13.53 26.20 1.94 0.155

NURMBERGR36 14.28 24.09 1.69 0.235

CSHVR_VEHICLE 21.74 34.91 1.61 0.162

INDIA_URBAN_SAMPLE 23.28 32.07 1.38 0.170

1015 25.69 38.80 1.51 0.125

WVUSUB 25.75 39.89 1.55 0.138

UDDSHDV 30.17 51.88 1.72 0.124

UDDS 31.35 44.49 1.42 0.171

NEDC 33.04 53.62 1.62 0.112

SC03 34.36 46.81 1.36 0.200

LA92 39.40 57.72 1.47 0.217

UNIF01 40.88 62.39 1.53 0.172

IM240 47.00 58.15 1.24 0.198

INDIA_HWY_SAMPLE 47.33 52.02 1.10 0.149

WVUINTER 54.50 70.11 1.29 0.067

ARB02 69.68 85.90 1.23 0.187

US06 76.88 91.20 1.19 0.190

HWFET 77.23 79.99 1.04 0.069

REP05 82.45 91.87 1.11 0.138

HL07 85.44 97.02 1.14 0.143

US06_HWY 97.60 102.56 1.05 0.113

140

141

Appendix B – Validation Study Results

Published Vehicle Data

Holden Commodore Sedan

Fuel type n/a Top Speed n/a kphFuel spec energy n/a Wh/kg Acceleration: 0 to n/a kph in n/a secFuel energy density n/a Wh/L Gradability: maintain n/a kph on a grade of n/aFuel energy storage n/a Wh Driving range n/a kmFuel mass n/a kgFuel volume n/a L glider mass n/a kg

CdA 0.8HPU type n/a Crr 0.01HPU specific power n/a W/kg R n/a mHPU power n/a W G n/aHPU mass n/a kg Trans. efficiency 90%HPU efficiency 17.0% Kregen 0

Powertrain mass n/a kgLLD type none Curb mass 1560 kgLLD specific power n/a W/kg cargo mass (1 person) 80 kgLLD max power n/a W Total mass 1640 kgLLD mass n/a kgLLD efficiency n/a Drive Cycle NEDC

Average speed 33.04 kphRoot-mean-cubed speed 53.62 kph

MC type none Characteristic acceleration 0.112 m/s^2MC specific power n/a W/kgMC max power n/a W Average wheel power 3063 W 92.7 WhpkmMC mass n/a kg Average brake power 1686 W 51.0 WhpkmMC efficiency n/a Average drive losses 528 W 16.0 WhpkmMC base speed n/a rpm Accessory power 1000 W 30.3 WhpkmMC max speed n/a rpm Average LLD losses 0 W 0.0 WhpkmMC N (overspeed ratio) n/a Average HPU power 6276 W 190.0 WhpkmMC N for accel spec n/a Average HPU losses 30641 W 927.4 Whpkm

Average fuel flow 36917 W 1117.4 Whpkm12.49 L/100km_eq18.8 MPG_eq

142

Virginia Tech ZEburban

Urban (UDDS) Fuel type n/a Top Speed n/a kphFuel spec energy n/a Wh/kg Acceleration: 0 to n/a kph in n/a secFuel energy density n/a Wh/L Gradability: maintain n/a kph on a grade of n/aFuel energy storage n/a Wh Driving range n/a kmFuel mass n/a kgFuel volume n/a L glider mass n/a kg

CdA 1.3HPU type Fuel Cell Crr 0.012HPU specific power n/a W/kg R n/a mHPU power n/a W G n/aHPU mass n/a kg Trans. efficiency 90%HPU efficiency 45.0% Kregen 0.5

Powertrain mass n/a kgLLD type Pb-Acid Curb mass 3090 kgLLD specific power n/a W/kg cargo mass (1 person) 80 kgLLD max power n/a W Total mass 3170 kgLLD mass n/a kgLLD efficiency 80% Drive Cycle UDDS


MC type GE Characteristic acceleration 0.171 m/s^2MC specific power n/a W/kgMC max power n/a W Average wheel power 4728 W 150.6 WhpkmMC mass n/a kg Average brake power 2364 W 75.3 WhpkmMC efficiency 90% Average drive losses 2667 W 84.9 WhpkmMC base speed n/a rpm Accessory power 1000 W 31.8 WhpkmMC max speed n/a rpm Average LLD losses 1167 W 37.2 WhpkmMC N (overspeed ratio) n/a Average HPU power 11927 W 379.8 WhpkmMC N for accel spec n/a Average HPU losses 14577 W 464.2 Whpkm


Highway (HWFET) Fuel type n/a Top Speed n/a kphFuel spec energy n/a Wh/kg Acceleration: 0 to n/a kph in n/a secFuel energy density n/a Wh/L Gradability: maintain n/a kph on a grade of n/aFuel energy storage n/a Wh Driving range n/a kmFuel mass n/a kgFuel volume n/a L glider mass n/a kg

CdA 1.3HPU type Fuel Cell Crr 0.012HPU specific power n/a W/kg R n/a mHPU power n/a W G n/aHPU mass n/a kg Trans. efficiency 90%HPU efficiency 45.0% Kregen 0.5

Powertrain mass n/a kgLLD type Pb-Acid Curb mass 3090 kgLLD specific power n/a W/kg cargo mass (1 person) 80 kgLLD max power n/a W Total mass 3170 kgLLD mass n/a kgLLD efficiency 80% Drive Cycle HWFET


MC type GE Characteristic acceleration 0.069 m/s^2MC specific power n/a W/kgMC max power n/a W Average wheel power 16562 W 214.5 WhpkmMC mass n/a kg Average brake power 2346 W 30.4 WhpkmMC efficiency 90% Average drive losses 5431 W 70.3 WhpkmMC base speed n/a rpm Accessory power 1000 W 12.9 WhpkmMC max speed n/a rpm Average LLD losses 1159 W 15.0 WhpkmMC N (overspeed ratio) n/a Average HPU power 26498 W 343.1 WhpkmMC N for accel spec n/a Average HPU losses 32387 W 419.4 Whpkm


143

ADVISOR Benchmarking (Various Powertrain Architectures)

NEDC

ICV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 12800 Wh/kg glider mass 613 kg Top Speed 194 kphFuel energy storage 409239 Wh Km 1 Acceleration: 0 to 100 kph in 10.0 secFuel mass 24.60 kg CdA 0.67 Gradability: maintain 88.5 kph on a grade of 15.2%

Crr 0.009 Driving range 500 kmHybrid Power Unit R 0.282 m Top speed ICE limited 240.73 kphHPU specific power 385 W/kg G 2.52HPU efficiency 16.7% Kregen 0%HPU power 76719 W Kstruct 1 Drive Cycle NEDCHPU mass 199.5 kg Powertrain mass 338 kg Average speed 33.04 kph

Curb mass 951 kg Root-mean-cubed speed 53.62 kphTotal Propulsion system cargo mass (1 person) 136 kg Characteristic acceleration 0.112 m/s^2

Total mass 1087 kgMass 338 kg Effective inertial mass 1087 Average wheel power 2209 W 66.9 WhpkmPower 76019 W Average brake power 1117 W 33.8 WhpkmEnergy 59602 Wh Transmission Average drive losses 479 W 14.5 Whpkm

Trans. efficiency 87% Accessory power 700 W 21.2 WhpkmSpec power 225 W/kg Trans spec power 1000 W/kg Average HPU power 4505 W 136.4 WhpkmSpec energy 176 Wh/kg Trans power 76019 W Average HPU losses 22537 W 682.1 Whpkm

Trans mass 114.0 kg Average fuel flow 27043 W 818.5 WhpkmICE max speed 5,700 rpm 9.24 L/100km_eqNo of gears 5 25.4 MPG_eqtime per shift 0.2 INPUTSTrans N (overspeed ratio) 4.74 OUTPUTSTrans N accel for shifts 1.97Inter-gear ratio 1.47520028No. of shifts 2.00Shifting time 0.4N drive eff 5.6N accel eff 2.35Pmax/Peff 1.1215

0.15 0.15

0.2

0.25 0.25

0.250.3

144

145

PHEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 12800 Wh/kg glider mass 600 kg Top Speed 135 kphFuel energy storage 287294 Wh Km 1 Acceleration: 0 to 100 kph in 9.9 secFuel mass 24.60 kg CdA 0.67 Gradability: maintain 88.5 kph on a grade of 6.7%

Crr 0.009 Driving range 500 kmHybrid Power Unit R 0.282 m Top speed due ICE speed 246.20HPU specific power 385 W/kg G 2.46HPU efficiency 24.4% Kregen 60%HPU power 28428 W Kstruct 1 Drive Cycle NEDCHPU mass 73.9 kg Powertrain mass 354 kg Average speed 33.04 kph

Curb mass 954 kg Root-mean-cubed speed 53.62 kphLoad-Leveling Device cargo mass (1 person) 136 kg Characteristic acceleration 0.112 m/s^2LLD specific power 444 W/kg Total mass 1090 kgLLD efficiency 96% Effective inertial mass 1090 Average wheel power 2212 W 66.9 WhpkmLLD max power 53021 W Average brake power 452 W 13.7 WhpkmLLD mass 119.3 kg Transmission Average drive losses 1229 W 37.2 Whpkm

Trans. efficiency 87% Accessory power 700 W 21.2 WhpkmTotal Propulsion system Trans spec power 1000 Average LLD losses 47 W 1.4 Whpkm

Trans power 60601 Average HPU power 4640 W 140.4 WhpkmMass 354 kg Trans mass 114.0 Average HPU losses 14345 W 434.2 WhpkmPower 60601 W Trans max speed 5,700 rpm Average fuel flow 18984 W 574.6 WhpkmEnergy 61087 Wh No. of gears 5 6.48 L/100km_eq

time per shift 0.2 36.2 MPG_eqSpec power 171 W/kg Trans N (overspeed ratio) 4.74 INPUTSSpec energy 173 Wh/kg Trans N for shifts calc 1.92 OUTPUTS

Inter-gear ratio 1.47520028Motor/Controller No. of shifts 2.00MC type Shifting time 0.4MC specific power 1482 W/kg ICE/motor overspeed 3.21MC max power 32873 W N drive eff 15.20MC mass 22.2 kg N accel eff 6.17MC efficiency 62% Pmax/Peff 1.0685Min DOH 30%DOH 54%

0.15 0.15

0.2

0.25 0.25

0.25

0.3

146

147

SHEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 12800 Wh/kg glider mass 601 kg Top Speed 132 kphFuel energy storage 259355 Wh Km 1 Acceleration: 0 to 100 kph in 9.6 secFuel mass 24.60 kg CdA 0.67 Gradability: maintain 88.5 kph on a grade of 6.9%

Crr 0.009 Driving range 500 kmHybrid Power Unit R 0.282 m Top speed due EM 188.98HPU specific power 257 W/kg G 5.63HPU efficiency 29.5% Kregen 60%HPU power 31725 W Kstruct 1 Drive Cycle NEDCHPU mass 123.6 kg Powertrain mass 347 kg Average speed 33.04 kphHPU frac 16% Curb mass 948 kg Root-mean-cubed speed 53.62 kphHPU opt frac 50% cargo mass (1 person) 136 kg Characteristic acceleration 0.112 m/s^2HPU opt power 15862 Total mass 1084 kgHPU duty 31.8% Effective inertial mass 1084 Average wheel power 2207 W 66.8 Whpkm

Average brake power 449 W 13.6 WhpkmTransmission Average drive losses 1360 W 41.2 Whpkm

Load-Leveling Device Trans. efficiency 87% Accessory power 700 W 21.2 WhpkmLLD specific power 444 W/kg Trans spec power 1000 Average LLD losses 84 W 2.6 WhpkmLLD efficiency 93% Trans power 65600 Average bus power 4801LLD max power 46152 W Trans mass 50.0 LLD thermo losses 246 7.5 WhpkmLLD mass 103.9 kg Total LLD losses 330.9 10.0 WhpkmLLD energy Motor/Controller Average HPU power 5047 W 152.8 WhpkmLLD specific energy MC type Average HPU losses 12091 W 365.9 Whpkm

MC specific power 1463 W/kg Average fuel flow 17138 W 518.7 WhpkmTotal Propulsion system MC max power 65600 W 5.85 L/100km_eq

MC mass 44.9 kg 40.1 MPG_eqMass 347 kg MC efficiency 85% INPUTSPower 65600 W MC max speed 10,000 rpm OUTPUTSEnergy 56288 Wh MC N (overspeed ratio) 3.81

MC N for accel spec 2.01Spec power 189 W/kg Pmax/Peff 1.0003Spec energy 162 Wh/kg

0.150.150.2

0.25 0.25

0.25

0.3

148

149

FCEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 2000 Wh/kg glider mass 592 kg Top Speed 157 kphFuel energy storage 192000 Wh Km 1 Acceleration: 0 to 100 kph in 10.0 secFuel mass 73.40 kg CdA 0.67 Gradability: maintain 88.5 kph on a grade of 20.0%

Crr 0.009 Driving range 500 kmHybrid Power Unit R 0.282 m Top speed due EM 159.31 kphHPU specific power 309 W/kg G 5.67HPU efficiency 43.0% Kregen 0%HPU power 76898 W Kstruct 1 Drive Cycle NEDCHPU mass 248.9 kg Powertrain mass 453 kg Average speed 33.04 kph



Trans. efficiency 86% Accessory power 700 W 21.2 WhpkmSpec power 145 W/kg Trans spec power 1000 Average HPU power 5456 W 165.1 WhpkmSpec energy 134 Wh/kg Trans power 65530 Average HPU losses 7232 W 218.9 Whpkm

Trans mass 50.0 Average fuel flow 12687 W 384.0 Whpkm4.33 L/100km_eq

Motor/Controller 54.2 MPG_eqMC type INPUTSMC specific power 812 W/kg OUTPUTSMC max power 65530 WMC mass 80.7 kgMC efficiency 86%MC max speed 8,500 rpmMC N (overspeed ratio) 4.99MC N for accel spec 3.13Pmax/Peff 1.0005

150

151

FCHEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 2000 Wh/kg glider mass 601 kg Top Speed 130 kphFuel energy storage 155310 Wh Km 1 Acceleration: 0 to 100 kph in 10.3 secFuel mass 73.40 kg CdA 0.67 Gradability: maintain 88.5 kph on a grade of 6.8%

Crr 0.009 Driving range 500 kmHybrid Power Unit R 0.282 m Top speed due EM 188.98 kphHPU specific power 309 W/kg G 5.63HPU efficiency 47.0% Kregen 60%HPU power 31839 W Kstruct 1 Drive Cycle NEDCHPU mass 103.0 kg Powertrain mass 366 kg Average speed 33.04 kphHPU frac 15% Curb mass 967 kg Root-mean-cubed speed 53.62 kphHPU opt frac 10% cargo mass (1 person) 136 kg Characteristic acceleration 0.112 m/s^2HPU opt power 4824 Total mass 1103 kgHPU duty 100.0% Effective inertial mass 1103 Average wheel power 2222 W 67.3 Whpkm


Load-Leveling Device Trans. efficiency 87% Accessory power 700 W 21.2 WhpkmLLD specific power 444 W/kg Trans spec power 1000 Average LLD losses 74 W 2.2 WhpkmLLD efficiency 94% Trans power 62857 Average bus power 4824LLD max power 42810 W Trans mass 50.0 LLD thermo losses 0 0.0LLD mass 96.4 kg Total LLD losses 74 2.2

Motor/Controller Average HPU power 4824 W 146.0 WhpkmTotal Propulsion system MC type Average HPU losses 5439 W 164.6 Whpkm

MC specific power 1447 W/kg Average fuel flow 10263 W 310.6 WhpkmMass 366 kg MC max power 62857 W 3.51 L/100km_eqPower 62857 W MC mass 43.4 kg 67.0 MPG_eqEnergy 53856 Wh MC efficiency 85% INPUTS

MC max speed 10,000 rpm OUTPUTSSpec power 172 W/kg MC N (overspeed ratio) 3.81Spec energy 147 Wh/kg MC N for accel spec 2.01

Pmax/Peff 1.0003

152

153

BEV

Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy Wh/kg glider mass 592 kg Top Speed 169 kphFuel energy storage Wh Km 1 Acceleration: 0 to 100 kph in 9.9 secFuel mass kg CdA 0.67 Gradability: maintain 88.5 kph on a grade of 18.9%

Crr 0.009 Driving range 81 kmHybrid Power Unit R 0.282 m Top speed due EM 188.98HPU specific power W/kg G 5.63HPU efficiency Trans. efficiency 90%HPU power W Kregen 60% Drive Cycle NEDCHPU mass kg Kstruct 1 Average speed 33.04 kph

Powertrain mass 316 kg Root-mean-cubed speed 53.62 kphLoad-Leveling Device Curb mass 908 kg Characteristic acceleration 0.112 m/s^2LLD specific power 393 W/kg cargo mass (1 person) 136 kgLLD specific energy 71 Wh/kg Total mass 1044 kg Average wheel power 2174 W 65.8 WhpkmLLD efficiency 92% Effective inertial mass 1044 Average brake power 429 W 13.0 WhpkmLLD max power 75911 W Average drive losses 1765 W 53.4 WhpkmLLD energy 13756 Wh Transmission Accessory power 700 W 21.2 WhpkmLLD mass 193.2 kg Trans. efficiency 86% Average LLD losses 102 W 3.1 WhpkmCharger 95% Trans spec power 1000 Average LLD power 5170 W 156.5 WhpkmTotal Propulsion system Trans power 59666 Average LLD losses 450 W 13.6 Whpkm

Trans mass 50.0 Total LLD losses 551 16.7Mass 316 kg Average electricity 5619 W 170.1 WhpkmPower 47208 W Motor/Controller 1.92 L/100km_eqEnergy 8555 Wh MC type 122.4 MPG_eq

MC specific power 824 W/kg INPUTSSpec power 150 W/kg MC max power 59666 W OUTPUTS ChargerSpec energy 27 Wh/kg MC mass 72.4 kg 179.0 Whpkm

MC efficiency 79% 2.00 L/100km_eqMC max speed 10,000 rpm 117.4 MPG_eqMC N (overspeed ratio) 3.81MC N for accel spec 2.01Pmax/Peff 1.0003

0.7

0.7

0.75

0.75

0.8

0.8

0.8

0.8

0.85

0.85

0.85

0.85

0.9

0.9

154

155

UDDS


Crr 0.009 Driving range 500 kmHybrid Power Unit R 0.282 m Top speed ICE limited 240.73 kphHPU specific power 385 W/kg G 2.52HPU efficiency 16.5% Kregen 0%HPU power 76719 W Kstruct 1 Drive Cycle UDDSHPU mass 199.5 kg Powertrain mass 338 kg Average speed 31.347 kph





0.15 0.15

0.2

0.25 0.25

0.250.3

156

157


Crr 0.009 Driving range 500 kmHybrid Power Unit R 0.282 m Top speed due ICE speed 246.20HPU specific power 385 W/kg G 2.46HPU efficiency 23.9% Kregen 55%HPU power 28474 W Kstruct 1 Drive Cycle UDDSHPU mass 74.0 kg Powertrain mass 356 kg Average speed 31.347 kph



Trans power 60712 Average HPU power 4595 W 146.6 WhpkmMass 356 kg Trans mass 114.0 Average HPU losses 14615 W 466.2 WhpkmPower 60712 W Trans max speed 5,700 rpm Average fuel flow 19210 W 612.8 WhpkmEnergy 64058 Wh No. of gears 5 6.92 L/100km_eqSpec power 170 W/kg time per shift 0.2 34.0 MPG_eqSpec energy 180 Wh/kg Trans N (overspeed ratio) 4.74 INPUTS

Trans N for shifts calc 1.92 OUTPUTSMotor/Controller Inter-gear ratio 1.47520028MC type No. of shifts 2.00MC specific power 1482 W/kg Shifting time 0.4MC max power 32938 W ICE/motor overspeed 3.21MC mass 22.2 kg N drive eff 15.20MC efficiency 61% N accel eff 6.17Min DOH 30% Pmax/Peff 1.0685DOH 54%

0.15 0.15

0.2

0.25 0.25

0.25

0.3

158

159


Crr 0.009 Driving range 500 kmHybrid Power Unit R 0.282 m Top speed due EM 188.98HPU specific power 257 W/kg G 5.63HPU efficiency 31.4% Kregen 55%HPU power 33101 W Kstruct 1 Drive Cycle UDDSHPU mass 129.0 kg Powertrain mass 358 kg Average speed 31.347 kphHPU frac 15% Curb mass 959 kg Root-mean-cubed speed 44.4939318 kphHPU opt frac 50% cargo mass (1 person) 136 kg Characteristic acceleration 0.1705 m/s^2HPU opt power 16551 Total mass 1095 kgHPU duty 30.2% Effective inertial mass 1095 Average wheel power 1600 W 51.1 Whpkm






0.150.150.2

0.25 0.25

0.25

0.3

160

161


Crr 0.009 Driving range 500 kmHybrid Power Unit R 0.282 m Top speed due EM 159.31 kphHPU specific power 309 W/kg G 5.67HPU efficiency 43.4% Kregen 0%HPU power 79186 W Kstruct 1 Drive Cycle UDDSHPU mass 256.3 kg Powertrain mass 461 kg Average speed 31.347 kph






162

163


Crr 0.009 Driving range 500 kmHybrid Power Unit R 0.282 m Top speed due EM 188.98 kphHPU specific power 309 W/kg G 5.63HPU efficiency 46.6% Kregen 55%HPU power 33180 W Kstruct 1 Drive Cycle UDDSHPU mass 107.4 kg Powertrain mass 375 kg Average speed 31.347 kphHPU frac 14% Curb mass 976 kg Root-mean-cubed speed 44.4939318 kphHPU opt frac 10% cargo mass (1 person) 136 kg Characteristic acceleration 0.1705 m/s^2HPU opt power 4731 Total mass 1112 kgHPU duty 100.0% Effective inertial mass 1112 Average wheel power 1614 W 51.5 Whpkm






Pmax/Peff 1.0003

164

165

BEV

Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy Wh/kg glider mass 592 kg Top Speed 169 kphFuel energy storage Wh Km 1 Acceleration: 0 to 100 kph in 9.9 secFuel mass kg CdA 0.67 Gradability: maintain 88.5 kph on a grade of 18.9%

Crr 0.009 Driving range 83 kmHybrid Power Unit R 0.282 m Top speed due EM 188.98HPU specific power W/kg G 5.63HPU efficiency Trans. efficiency 90%HPU power W Kregen 55% Drive Cycle UDDSHPU mass kg Kstruct 1 Average speed 31.347 kph





0.7

0.7

0.75

0.75

0.8

0.8

0.8

0.8

0.85

0.85

0.85

0.85

0.9

0.9

166

167

HWFET







0.15 0.15

0.2

0.25 0.25

0.250.3

168

169







0.15 0.15

0.2

0.25 0.25

0.25

0.3

170

171








0.150.150.2

0.25 0.25

0.25

0.3

172

173








174

175








Pmax/Peff 1.0003

176

177

BEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy Wh/kg glider mass 592 kg Top Speed 169 kphFuel energy storage Wh Km 1 Acceleration: 0 to 100 kph in 9.9 secFuel mass kg CdA 0.67 Gradability: maintain 88.5 kph on a grade of 18.9%






0.7

0.7

0.75

0.75

0.8

0.8

0.8

0.8

0.85

0.85

0.85

0.85

0.9

0.9

178

179

US06







0.15 0.15

0.2

0.25 0.25

0.250.3

180

181







0.15 0.15

0.2

0.25 0.25

0.25

0.3

182

183








0.150.150.2

0.25 0.25

0.25

0.3

184

185








186

187








Pmax/Peff 1.0003

188

189







0.7

0.7

0.75

0.75

0.8

0.8

0.8

0.8

0.85

0.85

0.85

0.85

0.9

0.9

190

191

NYCC







0.15 0.15

0.2

0.25 0.25

0.250.3

192

193







0.15 0.15

0.2

0.25 0.25

0.25

0.3

194

195








0.150.150.2

0.25 0.25

0.25

0.3

196

197








198

199








Pmax/Peff 1.0003

200

201







0.7

0.7

0.75

0.75

0.8

0.8

0.8

0.8

0.85

0.85

0.85

0.85

0.9

0.9

202

203

NEDC – High MDR


Crr 0.009 Driving range 500 kmHybrid Power Unit R 0.282 m Top speed ICE limited 240.73 kphHPU specific power 385 W/kg G 2.52HPU efficiency 14.6% Kregen 0%HPU power 64706 W Kstruct 1 Drive Cycle UDDSHPU mass 168.2 kg Powertrain mass 307 kg Average speed 33.04 kph





0.15 0.150.2

0.25 0.25

0.25

0.3

204

205


Crr 0.009 Driving range 500 kmHybrid Power Unit R 0.282 m Top speed due ICE speed 246.20HPU specific power 385 W/kg G 2.46HPU efficiency 23.5% Kregen 61%HPU power 28177 W Kstruct 1 Drive Cycle UDDSHPU mass 73.3 kg Powertrain mass 344 kg Average speed 33.04 kph





0.150.150.2

0.25 0.25

0.25

0.3

206

207


Crr 0.009 Driving range 500 kmHybrid Power Unit R 0.282 m Top speed due EM 188.98HPU specific power 257 W/kg G 5.63HPU efficiency 31.4% Kregen 61%HPU power 31719 W Kstruct 1 Drive Cycle UDDSHPU mass 123.6 kg Powertrain mass 332 kg Average speed 33.04 kphHPU frac 12% Curb mass 933 kg Root-mean-cubed speed 53.62 kphHPU opt frac 50% cargo mass (1 person) 136 kg Characteristic acceleration 0.112 m/s^2HPU opt power 15859 Total mass 1069 kgHPU duty 24.4% Effective inertial mass 1069 Average wheel power 1199 W 36.3 Whpkm






0.15 0.150.2

0.250.25

0.25

0.3

208

209


Crr 0.009 Driving range 500 kmHybrid Power Unit R 0.282 m Top speed due EM 159.31 kphHPU specific power 309 W/kg G 5.67HPU efficiency 42.0% Kregen 0%HPU power 81072 W Kstruct 1 Drive Cycle UDDSHPU mass 262.4 kg Powertrain mass 468 kg Average speed 33.04 kph






210

211


Crr 0.009 Driving range 500 kmHybrid Power Unit R 0.282 m Top speed due EM 188.98 kphHPU specific power 309 W/kg G 5.63HPU efficiency 46.0% Kregen 61%HPU power 32434 W Kstruct 1 Drive Cycle UDDSHPU mass 105.0 kg Powertrain mass 354 kg Average speed 33.04 kphHPU frac 11% Curb mass 955 kg Root-mean-cubed speed 53.62 kphHPU opt frac 10% cargo mass (1 person) 136 kg Characteristic acceleration 0.112 m/s^2HPU opt power 3599 Total mass 1091 kgHPU duty 100.0% Effective inertial mass 1091 Average wheel power 1217 W 36.8 Whpkm






Pmax/Peff 1.0003

212

213


Crr 0.009 Driving range 106 kmHybrid Power Unit R 0.282 m Top speed due EM 188.98HPU specific power W/kg G 5.63HPU efficiency Trans. efficiency 90%HPU power W Kregen 61% Drive Cycle UDDSHPU mass kg Kstruct 1 Average speed 33.04 kph





0.7

0.7

0.750.75

0.8

0.8

0.8

0.8

0.85

0.85

0.85

0.

0.90.9

214

215

HWFET – High MDR


Crr 0.009 Driving range 500 kmHybrid Power Unit R 0.282 m Top speed ICE limited 240.73 kphHPU specific power 385 W/kg G 2.52HPU efficiency 18.0% Kregen 0%HPU power 64706 W Kstruct 1 Drive Cycle HWFETHPU mass 168.2 kg Powertrain mass 307 kg Average speed 77.23 kph





0.15 0.15

0.2

0.25 0.25

0.250.3

216

217


Crr 0.009 Driving range 500 kmHybrid Power Unit R 0.282 m Top speed due ICE speed 246.20HPU specific power 385 W/kg G 2.46HPU efficiency 26.2% Kregen 68%HPU power 28280 W Kstruct 1 Drive Cycle HWFETHPU mass 73.5 kg Powertrain mass 348 kg Average speed 77.23 kph





0.150.150.2

0.25 0.25

0.25

0.3

218

219


Crr 0.009 Driving range 500 kmHybrid Power Unit R 0.282 m Top speed due EM 188.98HPU specific power 257 W/kg G 5.63HPU efficiency 31.4% Kregen 67%HPU power 30512 W Kstruct 1 Drive Cycle HWFETHPU mass 118.9 kg Powertrain mass 324 kg Average speed 77.23 kphHPU frac 24% Curb mass 925 kg Root-mean-cubed speed 79.99 kphHPU opt frac 50% cargo mass (1 person) 136 kg Characteristic acceleration 0.069 m/s^2HPU opt power 15256 Total mass 1061 kgHPU duty 47.6% Effective inertial mass 1061 Average wheel power 3112 W 40.3 Whpkm






0.15 0.150.2

0.250.25

0.25

0.3

220

221


Crr 0.009 Driving range 500 kmHybrid Power Unit R 0.282 m Top speed due EM 159.31 kphHPU specific power 309 W/kg G 5.67HPU efficiency 44.0% Kregen 0%HPU power 82346 W Kstruct 1 Drive Cycle HWFETHPU mass 266.5 kg Powertrain mass 472 kg Average speed 77.23 kph






222

223


Crr 0.009 Driving range 500 kmHybrid Power Unit R 0.282 m Top speed due EM 188.98 kphHPU specific power 309 W/kg G 5.63HPU efficiency 47.0% Kregen 67%HPU power 31277 W Kstruct 1 Drive Cycle HWFETHPU mass 101.2 kg Powertrain mass 347 kg Average speed 77.23 kphHPU frac 22% Curb mass 948 kg Root-mean-cubed speed 79.99 kphHPU opt frac 10% cargo mass (1 person) 136 kg Characteristic acceleration 0.069 m/s^2HPU opt power 7008 Total mass 1084 kgHPU duty 100.0% Effective inertial mass 1084 Average wheel power 3156 W 40.9 Whpkm






Pmax/Peff 1.0003

224

225


Crr 0.009 Driving range 121 kmHybrid Power Unit R 0.282 m Top speed due EM 188.98HPU specific power W/kg G 5.63HPU efficiency Trans. efficiency 90%HPU power W Kregen 67% Drive Cycle HWFETHPU mass kg Kstruct 1 Average speed 77.23 kph





0.7

0.7

0.750.75

0.8

0.8

0.8

0.8

0.85

0.85

0.85

0.

0.90.9

226

227

Appendix C – Tank to Wheel Energy Consumption for Various Fuels/Powertrains

Petrol ICV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 10360 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 7010 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 386633 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 37.32 kg Crr 0.01 Driving range 500 kmFuel volume 55.2 L R 0.32 m

G 3.82Hybrid Power Unit Kregen 0%HPU specific power 642 W/kg Kstruct 1.15 Drive Cycle NEDCHPU efficiency 22.5% Powertrain mass 294 kg Average speed 33.04 kphHPU power 98306 W Curb mass 1124 kg Root-mean-cubed speed 53.62 kphHPU mass 153.2 kg cargo mass (1 person) 136 kg Characteristic acceleration 0.112 m/s^2

Total mass 1260 kgTotal Propulsion system Effective inertial mass 1372 Average wheel power 2720 W 82.3 Whpkm

44.09850828 Average brake power 1411 W 42.7 WhpkmMass 294 kg Transmission Average drive losses 617 W 18.7 WhpkmPower 84656 W Trans. efficiency 87% Accessory power 1000 W 30.3 WhpkmEnergy 75683 Wh Trans spec power 1300 W/kg Average HPU power 5748 W 174.0 Whpkm

Trans power 84656 W Average HPU losses 19800 W 599.3 WhpkmSpec power 288 W/kg Trans mass 65.1 kg Average fuel flow 25549 W 773.3 WhpkmSpec energy 257 Wh/kg ICE max speed 5,700 rpm 8.65 L/100km_eq

No of gears 5 27.2 MPG_eqVSP 67.18783906 time per shift 0.2 INPUTS

Trans N (overspeed ratio) 4.74 OUTPUTS 10.6%PMF 0.261559303 Trans N for shift calcs 2.63

Inter-gear ratio 1.47520028No. of shifts 3.00Shifting time 0.6N drive eff 5.6N accel eff 3.14Pmax/Peff 1.1215

228

LPG ICV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 5760 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 4550 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 373069 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 64.77 kg Crr 0.01 Driving range 500 kmFuel volume 82.0 L R 0.32 m



Average brake power 1454 W 44.0 WhpkmMass 289 kg Transmission Average drive losses 629 W 19.0 WhpkmPower 87101 W Trans. efficiency 87% Accessory power 1000 W 30.3 WhpkmEnergy 76872 Wh Trans spec power 1300 W/kg Average HPU power 5839 W 176.7 Whpkm


No of gears 5 28.2 MPG_eqtime per shift 0.2 INPUTSTrans N (overspeed ratio) 4.74 OUTPUTS 11.2%Trans N for shift calcs 2.63Inter-gear ratio 1.47520028No. of shifts 3.00Shifting time 0.6N drive eff 5.6N accel eff 3.14Pmax/Peff 1.1215

229

LNG ICV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 7400 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 3890 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 345426 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 46.68 kg Crr 0.01 Driving range 500 kmFuel volume 88.8 L R 0.32 m






230

CNG ICV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 4320 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 1950 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 352411 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 81.58 kg Crr 0.01 Driving range 500 kmFuel volume 180.7 L R 0.32 m






231

Diesel ICV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 10360 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 7970 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 311106 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 30.03 kg Crr 0.01 Driving range 500 kmFuel volume 39.0 L R 0.32 m






232

BioDiesel ICV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 8860 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 7010 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 312054 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 35.22 kg Crr 0.01 Driving range 500 kmFuel volume 44.5 L R 0.32 m






233

E10 ICV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 9952 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 6773 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 386980 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 38.88 kg Crr 0.01 Driving range 500 kmFuel volume 57.1 L R 0.32 m






234

E85 ICV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 6892 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 4995.5 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 366732 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 53.21 kg Crr 0.01 Driving range 500 kmFuel volume 73.4 L R 0.32 m






235

M85 ICV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 6170 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 4434.5 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 359978 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 58.35 kg Crr 0.01 Driving range 500 kmFuel volume 81.2 L R 0.32 m






236

GH2 ICV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 3520 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 970 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 323910 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 92.02 kg Crr 0.01 Driving range 500 kmFuel volume 333.9 L R 0.32 m






237

LH2 ICV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 2650 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 1190 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 329751 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 124.43 kg Crr 0.01 Driving range 500 kmFuel volume 277.1 L R 0.32 m






238

Petrol PHEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 10360 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 7010 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 284511 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 27.46 kg Crr 0.01 Driving range 500 kmFuel volume 40.6 L R 0.32 m


Total mass 1378 kgLoad-Leveling Device Effective inertial mass 1503 Average wheel power 2827 W 85.6 WhpkmLLD specific power 444 W/kg 61.84203474 Average brake power 618 W 18.7 WhpkmLLD efficiency 96% Transmission Average drive losses 1244 W 37.6 WhpkmLLD max power 50812 W Trans. efficiency 87% Accessory power 1000 W 30.3 WhpkmLLD mass 114.4 kg Trans spec power 1300 Average LLD losses 46 W 1.4 Whpkm

Trans power 82272 Average HPU power 5734 W 173.6 WhpkmTotal Propulsion system Trans mass 63.3 Average HPU losses 13066 W 395.5 Whpkm

Trans max speed 5,700 rpm Average fuel flow 18801 W 569.0 WhpkmMass 412 kg No. of gears 5 6.36 L/100km_eqPower 82272 W time pershift 0.2 36.9 MPG_eqEnergy 75495 Wh Trans N (overspeed ratio) 4.74 INPUTSSpec power 200 W/kg Trans N for shifts calc 2.63 OUTPUTS 15.0%Spec energy 183 Wh/kg Inter gear ratio 1.47520028VSP 59.69195905 No. of shifts 3.00PMF 0.331873776 Shifting time 0.6Motor/Controller ICE/motor overspeed 3.21MC type N drive eff 15.20MC specific power 1484 W/kg N accel eff 8.45MC max power 35568 W Pmax/Peff 1.0685MC mass 24.0 kgMC efficiency 70%Min DOH 30%DOH 30%

239

LPG PHEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 5760 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 4550 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 272743 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 47.35 kg Crr 0.01 Driving range 500 kmFuel volume 59.9 L R 0.32 m


Total mass 1403 kgLoad-Leveling Device Effective inertial mass 1530 Average wheel power 2849 W 86.2 WhpkmLLD specific power 444 W/kg Average brake power 629 W 19.0 WhpkmLLD efficiency 96% Transmission Average drive losses 1262 W 38.2 WhpkmLLD max power 50902 W Trans. efficiency 87% Accessory power 1000 W 30.3 WhpkmLLD mass 114.6 kg Trans spec power 1300 Average LLD losses 46 W 1.4 Whpkm


Trans max speed 5,700 rpm Average fuel flow 18023 W 545.5 WhpkmMass 380 kg No. of gears 5 6.10 L/100km_eqPower 83653 W time pershift 0.2 38.5 MPG_eqEnergy 76181 Wh Trans N (overspeed ratio) 4.74 INPUTSSpec power 220 W/kg Trans N for shifts calc 2.63 OUTPUTS 15.8%Spec energy 201 Wh/kg Inter gear ratio 1.47520028

No. of shifts 3.00Shifting time 0.6

Motor/Controller ICE/motor overspeed 3.21MC type N drive eff 15.20MC specific power 1484 W/kg N accel eff 8.45MC max power 35632 W Pmax/Peff 1.0685MC mass 24.0 kgMC efficiency 70%Min DOH 30%DOH 30%

240

LNG PHEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 7400 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 3890 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 267253 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 36.12 kg Crr 0.01 Driving range 500 kmFuel volume 68.7 L R 0.32 m




Trans max speed 5,700 rpm Average fuel flow 17660 W 534.5 WhpkmMass 397 kg No. of gears 5 5.98 L/100km_eqPower 84753 W time pershift 0.2 39.3 MPG_eqEnergy 76728 Wh Trans N (overspeed ratio) 4.74 INPUTS

Trans N for shifts calc 2.63 OUTPUTS 16.2%Spec power 214 W/kg Inter gear ratio 1.47520028Spec energy 193 Wh/kg No. of shifts 3.00

Shifting time 0.6Motor/Controller ICE/motor overspeed 3.21MC type N drive eff 15.20MC specific power 1484 W/kg N accel eff 8.45MC max power 35682 W Pmax/Peff 1.0685MC mass 24.1 kgMC efficiency 70%Min DOH 30%DOH 30%

241

CNG PHEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 4320 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 1950 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 270455 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 62.61 kg Crr 0.01 Driving range 500 kmFuel volume 138.7 L R 0.32 m







242

Diesel PHEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 10360 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 7970 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 252823 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 24.40 kg Crr 0.01 Driving range 500 kmFuel volume 31.7 L R 0.32 m







243

Biodiesel PHEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 8860 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 7010 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 253303 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 28.59 kg Crr 0.01 Driving range 500 kmFuel volume 36.1 L R 0.32 m







244

E10 PHEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 9952 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 6773 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 284660 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 28.60 kg Crr 0.01 Driving range 500 kmFuel volume 42.0 L R 0.32 m







245

E85 PHEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 6892 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 4995.5 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 268849 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 39.01 kg Crr 0.01 Driving range 500 kmFuel volume 53.8 L R 0.32 m







246

M85 PHEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 6170 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 4434.5 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 263574 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 42.72 kg Crr 0.01 Driving range 500 kmFuel volume 59.4 L R 0.32 m







247

GH2 PHEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 3520 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 970 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 234302 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 66.56 kg Crr 0.01 Driving range 500 kmFuel volume 241.5 L R 0.32 m







248

LH2 PHEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 2650 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 1190 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 236705 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 89.32 kg Crr 0.01 Driving range 500 kmFuel volume 198.9 L R 0.32 m







249

Petrol FCEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 10360 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 7010 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 320842 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 30.97 kg Crr 0.01 Driving range 500 kmFuel volume 45.8 L R 0.32 m



126.5757444 Average brake power 2032 W 61.5 WhpkmMass 844 kg Transmission Average drive losses 1766 W 53.5 WhpkmPower 103451 W Trans. efficiency 87% Accessory power 1000 W 30.3 WhpkmEnergy 90740 Wh Trans spec power 1625 Average HPU power 8014 W 242.6 Whpkm

Trans power 103451 Average HPU losses 13187 W 399.1 WhpkmSpec power 123 W/kg Trans mass 63.7 Average fuel flow 21201 W 641.7 WhpkmSpec energy 108 Wh/kg 7.17 L/100km_eq

Motor/Controller 32.8 MPG_eqVSP 57.16050806 MC type INPUTS

MC specific power 1027 W/kg OUTPUTS 15.2%PMF 0.504133702 MC max power 118910 W

MC mass 100.6 kgMC efficiency 86%MC max speed 8,500 rpmMC N (overspeed ratio) 4.99MC N for accel spec 2.77Pmax/Peff 1.0005

250

Methanol FCEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 5430 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 3980 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 296930 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 54.68 kg Crr 0.01 Driving range 500 kmFuel volume 74.6 L R 0.32 m



Average brake power 2086 W 63.1 WhpkmMass 775 kg Transmission Average drive losses 1799 W 54.4 WhpkmPower 106044 W Trans. efficiency 87% Accessory power 1000 W 30.3 WhpkmEnergy 92198 Wh Trans spec power 1625 Average HPU power 8143 W 246.5 Whpkm


Motor/Controller 35.4 MPG_eqMC type INPUTSMC specific power 1027 W/kg OUTPUTS 16.6%MC max power 121890 WMC mass 103.2 kgMC efficiency 86%MC max speed 8,500 rpmMC N (overspeed ratio) 4.99MC N for accel spec 2.77Pmax/Peff 1.0005

251

LH2 FCEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 2650 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 1190 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 199090 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 75.13 kg Crr 0.01 Driving range 500 kmFuel volume 167.3 L R 0.32 m



Average brake power 1796 W 54.4 WhpkmMass 552 kg Transmission Average drive losses 1623 W 49.1 WhpkmPower 92013 W Trans. efficiency 87% Accessory power 1000 W 30.3 WhpkmEnergy 84311 Wh Trans spec power 1625 Average HPU power 7446 W 225.4 Whpkm


Motor/Controller 52.8 MPG_eqMC type INPUTSMC specific power 1027 W/kg OUTPUTS 23.0%MC max power 105762 WMC mass 89.5 kgMC efficiency 86%MC max speed 8,500 rpmMC N (overspeed ratio) 4.99MC N for accel spec 2.77Pmax/Peff 1.0005

252

GH2 FCEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 3520 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 970 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 196714 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 55.88 kg Crr 0.01 Driving range 500 kmFuel volume 202.8 L R 0.32 m



90.28850372 Average brake power 1759 W 53.2 WhpkmMass 602 kg Transmission Average drive losses 1601 W 48.4 WhpkmPower 90223 W Trans. efficiency 87% Accessory power 1000 W 30.3 WhpkmEnergy 83305 Wh Trans spec power 1625 Average HPU power 7357 W 222.7 Whpkm


Motor/Controller 53.4 MPG_eqVSP 57.54306234 MC type INPUTS

MC specific power 1027 W/kg OUTPUTS 23.1%PMF 0.420360039 MC max power 103705 W

MC mass 87.8 kgMC efficiency 86%MC max speed 8,500 rpmMC N (overspeed ratio) 4.99MC N for accel spec 2.77Pmax/Peff 1.0005

253

Petrol FCHEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 10360 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 7010 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 270299 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 26.09 kg Crr 0.01 Driving range 500 kmFuel volume 38.6 L R 0.32 m

G 5.70Hybrid Power Unit Kregen 60%HPU specific power 259 W/kg Kstruct 1.15 Drive Cycle NEDCHPU efficiency 39.2% Powertrain mass 713 kg Average speed 33.04 kphHPU power 92246 W Curb mass 1543 kg Root-mean-cubed speed 53.62 kphHPU mass 356.7 kg cargo mass (1 person) 136 kg Characteristic acceleration 0.112 m/s^2HPU frac 8% Total mass 1679 kgHPU opt frac 10% Effective inertial mass 1833 Average wheel power 3098 W 93.8 WhpkmHPU opt power 9225 106.9702809 Average brake power 754 W 22.8 WhpkmHPU duty 75.9% Transmission Average drive losses 1962 W 59.4 Whpkm

Trans. efficiency 87% Accessory power 1000 W 30.3 WhpkmTrans spec power 1625 Average LLD losses 101 W 3.0 Whpkm

Load-Leveling Device Trans power 96304 Average bus power 6914LLD specific power 444 W/kg Trans mass 59.3 LLD thermo losses 88LLD efficiency 95% Average HPU power 7002 W 211.9 WhpkmLLD max power 37469 W Motor/Controller Average HPU losses 10860 W 328.7 WhpkmLLD mass 84.4 kg MC type Average fuel flow 17861 W 540.6 Whpkm

MC specific power 1027 W/kg 6.04 L/100km_eqTotal Propulsion system MC max power 110695 W 38.9 MPG_eq

MC mass 93.7 kg INPUTSMass 713 kg MC efficiency 86% OUTPUTS 17.3%Power 96304 W MC max speed 8,500 rpmEnergy 79277 Wh MC N (overspeed ratio) 4.99


VSP 57.35350721

PMF 0.462133974

254

Methanol FCHEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 5430 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 3980 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 251357 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 46.29 kg Crr 0.01 Driving range 500 kmFuel volume 63.2 L R 0.32 m

G 0.00Hybrid Power Unit Kregen 60%HPU specific power 259 W/kg Kstruct 1.15 Drive Cycle NEDCHPU efficiency 42.6% Powertrain mass 746 kg Average speed 33.04 kphHPU power 92464 W Curb mass 1576 kg Root-mean-cubed speed 53.62 kphHPU mass 357.5 kg cargo mass (1 person) 136 kg Characteristic acceleration 0.112 m/s^2HPU frac 8% Total mass 1712 kgHPU opt frac 10% Effective inertial mass 1870 Average wheel power 3128 W 94.7 WhpkmHPU opt power 9246 Average brake power 769 W 23.3 WhpkmHPU duty 76.5% Transmission Average drive losses 1990 W 60.2 Whpkm






255

LH2 FCHEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 2650 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 1190 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 183926 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 69.41 kg Crr 0.01 Driving range 500 kmFuel volume 154.6 L R 0.32 m

G 0.00Hybrid Power Unit Kregen 60%HPU specific power 375 W/kg Kstruct 1.15 Drive Cycle NEDCHPU efficiency 55.6% Powertrain mass 604 kg Average speed 33.04 kphHPU power 91528 W Curb mass 1434 kg Root-mean-cubed speed 53.62 kphHPU mass 244.1 kg cargo mass (1 person) 136 kg Characteristic acceleration 0.112 m/s^2HPU frac 7% Total mass 1570 kgHPU opt frac 10% Effective inertial mass 1713 Average wheel power 2999 W 90.8 WhpkmHPU opt power 9153 Average brake power 704 W 21.3 WhpkmHPU duty 73.8% Transmission Average drive losses 1868 W 56.5 Whpkm






256

GH2 FCHEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy 3520 Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy density 970 Wh/L Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel energy storage 182183 Wh CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%Fuel mass 51.76 kg Crr 0.01 Driving range 500 kmFuel volume 187.8 L R 0.32 m

G 5.70Hybrid Power Unit Kregen 60%HPU specific power 375 W/kg Kstruct 1.15 Drive Cycle NEDCHPU efficiency 55.6% Powertrain mass 575 kg Average speed 33.04 kphHPU power 91340 W Curb mass 1405 kg Root-mean-cubed speed 53.62 kphHPU mass 243.6 kg cargo mass (1 person) 136 kg Characteristic acceleration 0.112 m/s^2HPU frac 7% Total mass 1541 kgHPU opt frac 10% Effective inertial mass 1681 Average wheel power 2973 W 90.0 WhpkmHPU opt power 9134 86.24485751 Average brake power 691 W 20.9 WhpkmHPU duty 73.3% Transmission Average drive losses 1843 W 55.8 Whpkm






VSP 57.59313021

PMF 0.409238254

257

VRLA BEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy storage Wh Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel mass kg CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%

Crr 0.01 Driving range target 125Hybrid Power Unit R 0.32 m Driving range 125 kmHPU specific power W/kg G 0.00HPU efficiency Kregen 60%HPU power W Kstruct 1.15 Drive Cycle NEDCHPU mass kg Powertrain mass 1500 kg Average speed 33.04 kph

Curb mass 2330 kg Root-mean-cubed speed 53.62 kphLoad-Leveling Device cargo mass (1 person) 136 kg Characteristic acceleration 0.112 m/s^2LLD specific power 300 W/kg Total mass 2466 kgLLD specific energy 35 Wh/kg Effective inertial mass 2698 Average wheel power 3806 W 115.2 WhpkmLLD efficiency 90% Average brake power 1110 W 33.6 WhpkmLLD max power 187188 W Transmission Average drive losses 2633 W 79.7 WhpkmLLD energy 37183 Wh Trans. efficiency 87% Accessory power 1000 W 30.3 WhpkmLLD mass 1062.4 kg Trans spec power 1625 Average LLD losses 297 W 9.0 WhpkmCharger 95% Trans power 139306 Average LLD power 8845 W 267.7 WhpkmTotal Propulsion system Trans mass 85.7 Average LLD losses 983 W 29.7 Whpkm

Average electricity 9828 W 297.5 WhpkmMass 1304 kg Motor/Controller 3.33 L/100km_eqPower 126049 W MC type 70.7 MPG_eqEnergy 25038 Wh MC specific power 1027 W/kg INPUTS

MC max power 160122 W OUTPUTS ChargerSpec power 97 W/kg MC mass 155.9 kg 313.1 WhpkmSpec energy 19 Wh/kg MC efficiency 86% 3.50 L/100km_eq

MC max speed 8,500 rpm 67.1 MPG_eqMC N (overspeed ratio) 4.99MC N for accel spec 2.77 36.8%Pmax/Peff 1.0005

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NiMH BEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy storage Wh Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel mass kg CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%

Crr 0.01 Driving range target 250 kmHybrid Power Unit R 0.32 m Driving range 250 kmHPU specific power W/kg G 0.00HPU efficiency Kregen 60%HPU power W Kstruct 1.15 Drive Cycle NEDCHPU mass kg Powertrain mass 1440 kg Average speed 33.04 kph

Curb mass 2270 kg Root-mean-cubed speed 53.62 kphLoad-Leveling Device cargo mass (1 person) 136 kg Characteristic acceleration 0.112 m/s^2LLD specific power 220 W/kg Total mass 2406 kgLLD specific energy 70 Wh/kg Effective inertial mass 2633 Average wheel power 3752 W 113.6 WhpkmLLD efficiency 92% Average brake power 1083 W 32.8 WhpkmLLD max power 223556 W Transmission Average drive losses 2582 W 78.2 WhpkmLLD energy 71131 Wh Trans. efficiency 87% Accessory power 1000 W 30.3 WhpkmLLD mass 1016.2 kg Trans spec power 1625 Average LLD losses 231 W 7.0 WhpkmCharger 95% Trans power 136044 Average LLD power 8649 W 261.8 WhpkmTotal Propulsion system Trans mass 83.7 Average LLD losses 752 W 22.8 Whpkm



MC max speed 8,500 rpm 70.2 MPG_eqMC N (overspeed ratio) 4.99MC N for accel spec 2.77 37.9%Pmax/Peff 1.0005

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Li-Ion BEV Fuel Storage System Vehicle Platform Performance TargetsFuel spec energy Wh/kg glider mass 830 kg Top Speed 180 kphFuel energy storage Wh Km 1.1 Acceleration: 0 to 100 kph in 9.0 secFuel mass kg CdA 0.8 Gradability: maintain 100 kph on a grade of 6.5%

Crr 0.01 Driving range target 500 kmHybrid Power Unit R 0.32 m Driving range 500 kmHPU specific power W/kg G 5.70HPU efficiency Kregen 60%HPU power W Kstruct 1.15 Drive Cycle NEDCHPU mass kg Powertrain mass 1359 kg Average speed 33.04 kph

Curb mass 2189 kg Root-mean-cubed speed 53.62 kphLoad-Leveling Device cargo mass (1 person) 136 kg Characteristic acceleration 0.112 m/s^2LLD specific power 420 W/kg Total mass 2325 kgLLD specific energy 140 Wh/kg Effective inertial mass 2544 Average wheel power 3679 W 111.4 WhpkmLLD efficiency 95% 203.8023166 Average brake power 1046 W 31.7 WhpkmLLD max power 400361 W Transmission Average drive losses 2513 W 76.1 WhpkmLLD energy 133454 Wh Trans. efficiency 87% Accessory power 1000 W 30.3 WhpkmLLD mass 953.2 kg Trans spec power 1625 Average LLD losses 140 W 4.2 WhpkmCharger 95% Trans power 131603 Average LLD power 8378 W 253.6 WhpkmTotal Propulsion system Trans mass 81.0 Average LLD losses 441 W 13.3 Whpkm



MC max speed 8,500 rpm 74.8 MPG_eqVSP 128.8564959 MC N (overspeed ratio) 4.99

MC N for accel spec 2.77 39.6%PMF 0.620776359 Pmax/Peff 1.0005

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Pamvec PhD_Thesis Editado