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THE FLORIDA STATE UNIVERSITY
FAMU–FSU COLLEGE OF ENGINEERING
ANALYSIS AND CONTROL OF AN IN SITU HYDROGEN GENERATION
AND FUEL CELL POWER SYSTEM FOR AUTOMOTIVE APPLICATIONS
By
PANINI K. KOLAVENNU
A Dissertation submitted to theDepartment of Chemical Engineering
in partial fulfillment of therequirements for the degree of
Doctor of Philosophy
Degree Awarded:Spring Semester, 2006
The members of the Committee approve the dissertation of Panini K. Kolavennu defended
on December 8, 2005.
Srinivas PalankiProfessor Directing Dissertation
David CartesOutside Committee Member
John C. TelotteCommittee Member
Ravindran ChellaCommittee Member
Bruce R. LockeCommittee Member
The Office of Graduate Studies has verified and approved the above named committee members.
ii
To My Grandparents . . .
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ACKNOWLEDGEMENTS
I would like to express my deep sense of gratitude to my advisor Dr. Srinivas Palanki for
his guidance, help and encouragement throughout the course of this research. I am extremely
thankful to Dr. John Telotte for his help and invaluable suggestions and inspiring me with
his thoughtful insights into my research. I am indebted to Dr David Cartes who introduced
me to the adaptive control technique. I extend my heartfelt gratitude to Dr. Bruce R. Locke
and Dr. Ravindran Chella for their suggestions and continuing interest in my research. A
very very special thanks to my brother Dr. Soumitri Kolavennu who introduced me to the
concept of fuel cells and process control. He has been and will continue to be my guru and
a role model whose footprints have been my guiding lights.
A special thanks to Charmane Caldwell and Dr. Jyothy Vemuri for their help during
various stages of this research. I also thank my colleagues and friends in the department for
their help and constant support. A special thanks to all my roommates Nirup, Sasi, Vijay
and Sarma for their constant support and surviving my awe(some!)ful cooking.
I am grateful to my parents for their support and encouragement and instilling the
research spirit in me. I am thankful to my loving sister who helped me a lot right from
my childhood and thanks a lot for patiently listening to all the complaints my teachers had
about my mischief ( also for hiding them from my parents). A special thanks to Ananth
Ravi and Neelima. Last but not the least I would like to thank Supriya for her wonderful
love and support and for being there for me always and making my graduate life a pleasant
journey.
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TABLE OF CONTENTS
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Hydrogen Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Fueling Infrastructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3 Schematic Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.4 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2. LITERATURE SURVEY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1 Fuel Processing System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.1.1 Onboard Hydrogen Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.1.2 In situ Hydrogen Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.1.3 Development of Kinetic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 Fuel Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.2.1 Working Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.2.2 Types of Fuel Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 Fuel Cell Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.4 Thermal Management System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.5 Controller Design and Power Distribution System . . . . . . . . . . . . . . . . . . . . . . 28
2.5.1 Adaptive Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.5.2 Switching Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3. DESIGN OF FUEL PREPROCESSOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.1 Thermodynamic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.1.1 Feed Stream Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.1.2 Overall Heat Duty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.1.3 Combustor Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2 Steam to Carbon Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.3 Design of Fuel Processing Subsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.1 Kinetics of Steam Reformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.3.2 Water Gas Shift Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.3.3 Preferential Oxidation Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.3.4 Varying Feed Rates of Methane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
v
4. FUEL CELL DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.1 Design of Power Generation Subsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.1.1 Linear Fuel Cell Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.1.2 Nonlinear Fuel Cell Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5. ADAPTIVE CONTROLLER DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.1 Model Reference Adaptive Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745.1.1 Design Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745.1.2 Adaptive Controller with Deadzone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.2 PID Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775.3 Application to PEM Fuel cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.3.1 System Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 795.3.2 Realistic Power Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 815.3.3 Controller Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835.3.4 MRAC with Derivative Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 865.3.5 Design of Fuel Tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.4 Application to Phosphoric Acid Fuel Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6. BATTERY BACKUP MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.1 Battery Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1076.1.1 State of Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1076.1.2 Battery Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.2 Switching Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1096.3 MATLAB implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
7. CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
8. FUTURE WORK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
9. NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
APPENDIX A: MATLAB Programs used in Chapter 3 . . . . . . . . . . . . . . . . . 122
APPENDIX B: MATLAB Programs used in Chapter 4 . . . . . . . . . . . . . . . . . . 131
APPENDIX C: MATLAB Programs used in Chapter 5 . . . . . . . . . . . . . . . . . . 134
APPENDIX D: MATLAB Programs used in Chapter 6 . . . . . . . . . . . . . . . . . 137
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
BIOGRAPHICAL SKETCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
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LIST OF TABLES
1.1 Hydrogen production based on the type of fuel . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Pertinent physical properties of transportation fuels . . . . . . . . . . . . . . . . . . . . . 5
2.1 Salient features of the different types of fuel cells . . . . . . . . . . . . . . . . . . . . . . . 22
3.1 Standard heat of formations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2 Standard heat of reactions and type of reaction . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 Heat duty calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.4 Heat from the anode tail gas for different initial flow rates into the reformer. . . 38
3.5 Heat from the combustor when methane is fed at 25%, 30%, 35% in excess tothat fed to the reformer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.6 Effect of varying the steam to carbon ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.7 Kinetic parameters for the three reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.8 Parameters to calculate the equilibrium constant for the water gas shift reactor 49
3.9 Volume required for 90% conversion of CO in LTS reactor for differenttemperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.1 Regression fit data obtained from the Pukrushpan model . . . . . . . . . . . . . . . . . 66
4.2 Effect of varying the methane flow rate on the power output . . . . . . . . . . . . . . 72
5.1 Zeigler-Nichols Controller Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.2 Average ITAE error in kW obtained for the UDDS and US06-HWY profiles . . 84
5.3 ITAE error for the Adaptive controller with the derivative action designed forthe UDDS profile and also implemented on the USHWY06 . . . . . . . . . . . . . . . . 89
5.4 Performance of MRAC on different road profiles . . . . . . . . . . . . . . . . . . . . . . . . 94
5.5 Moles of methane required for a driving range of 300 and 400 miles for thedifferent cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.6 Average ITAE for the PAFC for a step pulse and band limited white noise input104
5.7 Steady State Average ITAE for the PAFC including the deadzone . . . . . . . . . . 104
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LIST OF FIGURES
1.1 Schematic diagram of the fuel cell system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 Cross section of a polymer electrolyte membrane fuel cell . . . . . . . . . . . . . . . . 19
3.1 Effect of operating temperature and oxygen excess ratio on heat duty . . . . . . . 39
3.2 PFD of Fuel Processing Subsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3 The concentration profiles obtained as a function of the reactor volume (a)CHEMCAD results (b)MATLAB results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.4 Concentration profiles along the volume of the reformer. . . . . . . . . . . . . . . . . . . 55
3.5 Conversion of CO inside the WGS reactor along the volume of the reactor fordifferent temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.6 Volume required for 90% conversion of CO inside the low temperature WGSreactor for different temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.7 Effect of change in methane flow rate on the hydrogen production . . . . . . . . . . 58
4.1 Methane feed Vs Power produced . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2 Representative fuel cell performance curve at 25 oC and 1 atm . . . . . . . . . . . . . 62
4.3 Effect of relative humidity on the fuel cell polarization curve. . . . . . . . . . . . . . . 68
4.4 Pressure dependence of the fuel cell polarization curve. . . . . . . . . . . . . . . . . . . . 69
4.5 Polarization curve for a fuel cell operating at 353 K, pressure 5 bar and relativehumidity 100%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.6 Power density vs. current density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.7 Effect of Methane Flow on Power Generated . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.1 Model Reference Adaptive Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.2 Implementation of Model Reference Adaptive Control . . . . . . . . . . . . . . . . . . . . 77
5.3 PID controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.4 System Identification using a step input in current . . . . . . . . . . . . . . . . . . . . . . 81
5.5 Speed Vs time profile and Force Vs time profile for UDDS . . . . . . . . . . . . . . . . 82
5.6 Power Vs time profile for UDDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.7 Simulink diagram of the adaptive controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.8 Error obtained(kW) for the PID and Adaptive controllers implemented on thenonlinear model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
viii
5.9 Speed and Power profiles for the US06-HWY driving cycle . . . . . . . . . . . . . . . 85
5.10 Adaptive controller with derivative action . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.11 Error Vs time plot for the adaptive controller with derivative action imple-mented on the UDDS power profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.12 Error Vs time plot for the Adaptive controller with derivative action imple-mented on the US HWY-06 power Profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.13 FTP Cycle: Speed Vs time and Power Vs time profiles . . . . . . . . . . . . . . . . . . . 91
5.14 FTP Cycle: Error Vs time plot for the Adaptive controller with derivative action. 92
5.15 US06 Cycle: Speed Vs time and Power Vs time profiles. . . . . . . . . . . . . . . . . . . 93
5.16 US06 Cycle: Error Vs time plot for the Adaptive controller with derivativeaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.17 HFET Cycle: Speed Vs time and Power Vs time profiles. . . . . . . . . . . . . . . . . . 95
5.18 HFET Cycle: Error Vs time plot for the Adaptive controller with derivativeaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.19 EUDC Cycle: Speed Vs time and Power Vs time profiles. . . . . . . . . . . . . . . . . . 97
5.20 EUDC Cycle: Error Vs time plot for the Adaptive controller with derivativeaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.21 EUDC-LOW Cycle: Speed Vs time and Power Vs time profiles. . . . . . . . . . . . . 99
5.22 EUDC-LOW Cycle: Error Vs time plot for the Adaptive controller withderivative action. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.23 IHP Cycle: Speed Vs time and Power Vs time profiles. . . . . . . . . . . . . . . . . . . . 101
5.24 IHP Cycle: Error Vs time plot for the Adaptive controller with derivative action.102
5.25 Error Vs time plot for the PID controller for a step of 100. . . . . . . . . . . . . . . . . 103
5.26 (a), (b) Errors for the adaptive controller for a white band noise of magnitudeof 100 and 1000. (c), (d) Errors for the PID controller at magnitudes of 100and 1000 respectively . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.27 (a) Error without dead zone for white noise of a magnitude 1000, (b) error inthe presence of dead zone for white noise of a magnitude 1000. . . . . . . . . . . . . . 105
5.28 (a) Steady state error for PID controller with pulse load (b) steady state errorfor adaptive controller with deadband. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.1 Power Requested, Fuel cell Power, Battery power profiles for a step increaseand decrease in Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.2 Speed profile for the Urban Dynamometer Driving Schedule (UDDS) . . . . . . . . 112
6.3 Power profile for the UDDS schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.4 State of Charge variation for different initial SOC. . . . . . . . . . . . . . . . . . . . . . . 114
ix
D.1 Simulink diagram to simulate the switching controller design . . . . . . . . . . . . . . 138
x
ABSTRACT
A new future in automotive transportation is approaching where vehicles are powered by
new, clean and efficient energy sources. While different technologies will contribute to this
future, many see fuel cells as the leading long term candidate for becoming the power source
for emissions-free, mass produced light vehicles.
The development of emissions-free vehicles, which run directly on hydrogen, is the true
long term goal. However significant difficulties exist in developing these vehicles, due to
hydrogen storage problems. For automotive applications, it is desirable to use a carbon-based
hydrogenous fuel. The focus of this research was to analyze a fuel cell system for automotive
applications, which generated hydrogen in situ using methane as a fuel source. This system
consists of four parts: (1) an in situ hydrogen generation subsystem, (2) a power generation
subsystem, (3) a thermal management subsystem and (4) a switching control subsystem.
The novelty of this research lies in the fact that the entire system was considered from a
systems engineering viewpoint with realistic constraints.
A fuel processor subsystem was designed and its volume optimized to less than 100 liters.
A relationship between the fuel fed into the fuel processor and the hydrogen coming out of
it was developed. Using a fuel cell model an overall relationship between the fuel feed rate
and the power output was established.
The fuel cell car must be fully operational within a minute or so of a cold-start and must
respond to rapidly varying loads. Significant load transitions occur frequently as a result
of changes in driving conditions. These engineering constraints were addressed by coupling
a battery to the fuel cell. A switching controller was designed and it was validated using
realistic power profiles. Finally, a model reference adaptive controller was designed to handle
nonlinearities and load transitions. The adaptive controller performance was enhanced by
adding dead zone compensation and derivative action. The enhanced adaptive controller
was validated for different power profiles.
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CHAPTER 1
INTRODUCTION
1.1 Overview
The beginning of the 19th century marked the advent of the modern automobile systems.
Fueled by hydrocarbons, automobiles utilizing the internal combustion engine technology
changed the way we travel. At the dawn of a new century, we are at the threshold of a new
future in automobile technology, where the emphasis is on clean and efficient energy sources.
While different technologies will contribute to this future, many see fuel cells as the leading
long term candidate for becoming the power source for emissions-free, mass produced light
vehicles [1].
For automotive applications, it is desirable to use a carbon-based hydrogenous fuel such as
methane or gasoline. Such fuels are particularly desirable as they are easy to store onboard a
vehicle and a nationwide infrastructure of service stations that supply this fuel already exists.
There are several important technological breakthroughs that are necessary to make a fuel
cell based automobile commercially viable. In the past, there has been significant research
effort in the development of new fuel cell membranes and catalysts [2]. However, it has only
recently been recognized [3] that for this technology to compete favorably with the internal
combustion engine technology, it is necessary to design and optimize the performance of the
entire operation in the face of dynamic constraints and uncertainty. Fuel cell power systems
for automotive applications are usually rated at 50 kW electrical power output. A power
plant of this size faces several performance constraints in an automotive environment. The
system must be fully operational within a minute or so of a cold-start and must be able to
respond rapidly to varying loads. Significant load transitions occur frequently as a result
of changes in driving conditions (e.g. acceleration while passing another vehicle, driving in
1
hilly conditions, highway vs. city driving etc.). These engineering constraints have to be
addressed properly for successful design of a vehicle powered by a fuel cell.
In this research, a virtual prototype of an integrated in situ hydrogen production and
fuel cell power system for automotive applications is developed and analyzed. This system
consists of four parts:
• An in situ hydrogen generation subsystem where the hydrocarbon fuel is converted to
hydrogen.
• A power generation subsystem where the hydrogen is converted to electrical energy via
a fuel cell.
• A thermal management subsystem that maintains the various subsystems at the desired
optimal temperature profiles.
• A switching control subsystem that switches between the fuel cell and a battery backup
depending on the power requirements of the vehicle.
For developing a commercially viable system, each of the above subsystems has to be properly
designed and evaluated. In this research, an overall systems level analysis, which is a key
component for making this technology feasible is proposed.
The novelty of this research lies in the fact that the entire system is being considered from
a systems engineering viewpoint with realistic constraints. Past work has typically focussed
on only one subsystem and the interaction between systems has been ignored. At the end of
this research, a virtual prototype of an integrated in situ hydrogen production and fuel cell
system that is capable of powering a small car will be developed. This research is a crucial
step for experimentally building a prototype vehicle.
The results of the proposed research will provide a key technology for developing an
economical fuel cell based automobile that provides a viable alternative to the conventional
automobiles based on an internal combustion engine. At present, automobiles based on
fuel cell technology promise the best opportunity to achieve near zero emissions of air
pollutants and greenhouse gases. Proper engineering design and optimization can result
in the development of a fuel cell system that is small enough to fit in a car, cheap enough to
be affordable by the masses and have sufficient driving range to replace conventional vehicles
2
based on the internal combustion engine. Most importantly, the use of an integrated fuel
cell system for an application as complex and demanding as an automobile would portend
a major paradigm shift in global energy consumption and supply. The potential would
exist to create new industries and allow people throughout the global community to enjoy
the benefits of access to an efficient, cost-effective, and reliable new technology [1]. The
virtual prototype developed in this research project will provide the key systems integration
parameters necessary for building a prototype vehicle. We expect that the development of
a viable virtual prototype will provide the necessary proof-of-concept for attracting research
and development investment in this important technological area from automotive and
mobile power generation companies and this will lead to a hydrogen economy.
1.2 Hydrogen Economy
Hydrogen is the most abundant element in the universe. However, not much is available
in pure form on earth and is available either as water (when combined with oxygen) or as
a hydrocarbon (when combined with carbon). For this reason, hydrogen is only an energy
carrier and not a primary energy source. While hydrogen is a very clean fuel and burning it
results in no greenhouse emissions or undesirable carbon compounds, its production ma still
have a considerable carbon footprint. It seems logical to produce hydrogen via electrolysis
of water. However, the electrolysis process is highly energy intensive and the electricity
needed for this process needs to be generated at another site. Most of the electricity in the
United States is currently produced by burning coal or oil which contributes significantly
to the greenhouse emissions. This scenario is unlikely to change in the near future and
considerable advances in alternative sources of energy (e.g. solar energy or nuclear energy)
are needed to change the scenario. Another alternative to produce hydrogen is to extract
it from a hydrocarbon source which also results in emission of greenhouse gases. For this
reason, the switch to the hydrogen economy is expected to occur gradually in the next several
decades rather than suddenly in the next few years.
Hydrogen production is a large, modern industry with commercial roots reaching back
more than a hundred years. Globally, hydrogen is widely used for two purposes. The first is
in the fertilizer industry where hydrogen has long been used for ammonia synthesis (NH3).
3
The second area is in oil refineries where hydrogen has been used for hydro-formulation,
or high-pressure hydro-treating, of petroleum in refineries. In the United States alone
hydrogen production is currently about 8 billion kg, roughly 90 billion Normal cubic meters
Nm3. Global annual production is about 45 billion kg or 500 billion Nm3. Hydrogen
is extracted from different sources as shown in Table 1.1 which breaks down the annual
hydrogen production depending on the fuel type and the main method of production.
Table 1.1. Hydrogen production based on the type of fuelFuel Amount percentage Method of
(billions of Nm3/year) ProductionNatural Gas 240 48% Steam Reforming
Oil 150 30% Partial Oxidation ReformingCoal 90 18% Coal gasification
Water 20 4% Electrolysis
Methane or natural gas is the fuel of choice and almost 50% of industrial hydrogen
production uses methane as a fuel. Steam reforming, which will be discussed in detail in the
next chapter, is generally used to obtain hydrogen from natural gas. For higher hydrocarbons
like gasoline or diesel partial oxidation reforming is generally used. During recent years
a combination of steam reforming and partial oxidation reforming known as autothermal
reforming is increasingly being employed. Hydrogen can also be obtained from gasification
of coal and currently 18% of the world’s hydrogen is produced from coal. Currently only 4% of
the total hydrogen production is produced via electrolysis of water and is generally used when
high purity hydrogen is required. This method can be made more environmentally friendly
by using renewable energy sources such as hydroelectric power systems, wind energy systems,
ocean thermal energy conversion systems, geothermal resources, and a host of direct solar
energy conversion systems including biomass production, photovoltaic energy conversion,
solar thermal systems, etc. However,at present the cost per kilowatt of producing energy
through these techniques is very high making the cost of producing hydrogen using these
energy sources prohibitive.
From the above analysis it is clear that in the current environment, the most practical
source for generating hydrogen is a hydrocarbon source. Some of the hydrocarbon fuels
4
Table 1.2. Pertinent physical properties of transportation fuelsFuel H/C Density Heating value Energy density CO2 CO2 emission
considered atom of fuel of fuel of fuel emissions relative- ratio kg/m3 MJ/kg MJ/m3 kg/kJ to CH4
gasoline 2.03 99.79 42.95 32781 69.18 1.4diesel 1.63 117.73 40.65 36612 72.06 1.46
propane 2.67 77.52 46.46 27539 59.89 1.21methanol 4 105.71 19.92 16105 63.29 1.28methane 4 56.70 50.163 21746 58.08 1hydrogen - 9.45 120.16 8681 - -
and their salient features [4] are given in Table 1.2. Fuels like gasoline and diesel have a
low hydrogen to carbon ratio whereas methane and methanol have a higher ratio. Even
though lower hydrocarbons have higher heating value(MJ/kg), higher hydrocarbons have
greater densities and hence have greater energy densities. Table 1.2 compares the amount of
CO2 produced for different fuels per unit energy production (kJ). Of all the hydrocarbons,
methane produces the least amount of CO2 and the relative ratio of CO2 production with
respect to methane is given in Table 1.2. For the same amount of energy using any other
hydrocarbon will produce at least 20 % more CO2 than methane. It is observed that methane
or natural gas would be the most suitable hydrocarbon for onboard hydrogen production.
1.2.1 Fueling Infrastructure
A pure hydrogen economy will require a sea change in the fueling infrastructure that has
been built over the past century to service the automobiles based on internal combustion
engine. Two key issues will determine the nature of that infrastructure: (1) where the
hydrogen is produced and (2) in what form is it stored on board the hydrogen vehicle.
Hydrogen could be produced at fueling stations located in cities and on highways by
reforming fossil fuels. This is sometimes called forecourt production. Hydrogen could also
be produced at centralized facilities nearer to potential fuel sources, such as coal plants or
windmills and transported to the fueling stations.
Both the methods mentioned above require significant economic investment and also
pose some technical problems. First, in order for a car to run on pure hydrogen, it must
5
be able to safely, compactly, and cost-effectively store hydrogen on board, which is a major
technical challenge. As seen from Table 1.2 hydrogen has a far lower energy to volume
ratio than hydrocarbon fuels such as methane, methanol, propane and octane. That is,
hydrogen contains much less energy per gallon than other fuels at the same pressure. At
room temperature and pressure, hydrogen takes up approximately 3,000 times more space
than gasoline containing an equivalent amount of energy. Hydrogen does have an exceptional
energy content per unit mass (120.16 MJ/kg), nearly triple that of gasoline (42.9 MJ/kg),
but the storage equipment on a car fitted for hydrogen use, such as pressurized tanks, adds
significant weight to the system and negates this advantage. Secondly, hydrogen storage
systems need to enable a vehicle to travel 300 to 400 miles and fit in an envelope that does not
compromise either passenger space or storage space. Current energy storage technologies are
insufficient to gain market acceptance because they do not meet these criteria. The driving
range requirement will probably require a tank holding about 5 kg of hydrogen or more,
depending on the size and weight of the vehicle. At the same time, the vehicle needs to be
fueled in a short time, with a storage system that is safe, leak proof, and also is lightweight
and affordable. These constraints have to be overcome before automobiles that operate on
pure hydrogen become commonly available.
The near term solution is onboard hydrogen generation using fossil fuels. Hydrogen could
be generated on the car or truck itself, most likely by a methane or gasoline reformer. If
onboard reforming of gasoline proves to be practical, the existing infrastructure of gasoline
can be used to power fuel cell based automobiles. This will provide a solid platform to launch
a more advanced hydrogen based car. As a starting point for this research a methane based
fuel reformer that can produce a hydrogen rich stream is studied.
1.3 Schematic Diagram
In this research, the primary components of an automotive fuel cell system are analyzed.
Fundamental chemical engineering principles are utilized to assess the role of thermody-
namics, heat transport, mass transport and reaction kinetics. In addition to the methane
reforming unit we need a CO removal section to protect the catalyst in the fuel cell from
6
CO poisoning. Furthermore, a fuel cell system should be designed such that it delivers upto
50 kW of power that is suitable for automotive applications. A power plant of this size
faces several performance constraints in an automotive environment. The system must be
fully operational within a minute or so of a cold-start and must respond to rapidly varying
loads. To address these issues, in addition to the fuel cell stack, the power generation
subsystem should also include a battery backup. A suitable thermal management control
system as well as a switching control system are proposed based on the dynamics of the
system. The dynamic analysis requires advanced tools from numerical methods and nonlinear
analysis. Furthermore, the control systems design and analysis is based on modern advanced
optimization tools and systems engineering approaches. A schematic of the fuel cell system
under consideration is shown in Fig. 1.1.
Figure 1.1. Schematic diagram of the fuel cell system
7
The fuel cell system is divided into the following four subsystems:
1. Fuel processing subsystem2. Power generation subsystem3. Thermal management subsystem4. Switching control subsystem
The fuel processing subsystem consists of three packed bed reactors:
• Steam Reformer (SR): In this reactor, the hydrocarbon fuel is converted to hydrogen
and carbon monoxide. The methane reacts with steam to form three moles of hydrogen
and a mole of carbon monoxide as given by Eq. 1.1. Part of the carbon monoxide
reacts with water to produce carbon dioxide and hydrogen as shown in Eq. 1.2. A
side reaction in which four moles of hydrogen are produced also takes place as shown
in Eq. 1.3.
CH4 +H2O CO + 3H2; ∆Ho298 = 205.81kJ/mol (1.1)
CO +H2O CO2 +H2; ∆Ho298 = −41.16kJ/mol (1.2)
CH4 + 2H2O CO2 + 4H2; ∆Ho298 = 164.64kJ/mol (1.3)
• Water Gas Shift Reactor (WGS): In this reactor, most of the remaining carbon
monoxide is converted to carbon dioxide via the water gas shift reaction given by
Eq. 1.4.
CO +H2O CO2 +H2; ∆H0298 = −41.1kJ/mol (1.4)
• Preferential Oxidation Reactor (PROX): In this reactor, the feed from the WGS is
reacted with air to reduce the carbon monoxide concentration to less than 100 ppm to
avoid damage to the fuel cell membrane. Some of the hydrogen reacts with the oxygen
8
to produce water.
CO +1
2O2 → CO2; ∆Ho
298 = −283kJ/mol (1.5)
H2 +1
2O2 → H2O; ∆Ho
298 = −242kJ/mol (1.6)
The power generation system consists of a Polymer Electrolyte Membrane (PEM) fuel
cell that utilizes the hydrogen coming from the fuel processing subsystem and converts it
into electricity that is used to power an electric motor for the automobile. In addition to the
fuel cell, there is a battery backup that the electric motor switches to when the fuel cell is
unable to deliver the necessary power.
The reforming reactions are endothermic while the water gas shift reaction and the
preferential oxidation reactor is exothermic. Furthermore, each reactor in the fuel processing
subsystem may have a different optimal temperature profile. Thus, it is necessary to design
an efficient thermal management system to effectively utilize the system energy and to
improve fuel economy. Furthermore, significant load transitions occur frequently as a result
of changes in driving conditions (e.g. acceleration while passing another vehicle, driving in
hilly conditions, highway vs. city driving etc.). For this reason, it is necessary to have a
battery backup that the electric motor has the option to switch to when the fuel processing
subsystem is unable to provide the necessary hydrogen to generate the necessary power. Since
the size of the battery in an automotive application is limited, it is necessary to develop an
effective switching control system that switches between the power generation system and
the battery backup depending on the supply and demand of hydrogen.
1.4 Thesis Overview
In this dissertation a fuel cell power system for automotive applications will be analyzed.
A block flow diagram of the system under consideration is shown in Fig. 1.1. Specifically,
the following issues will be addressed:
9
1. Assess the thermodynamic feasibility of the system.
2. Design and analyze the reactors necessary for the fuel processor subsystem.
3. Design and analyze the fuel cell system.
4. Develop a switching control system for effectively running the power generation sub-
system and the battery backup.
5. Develop an adaptive control algorithm to control reactant flow rate into the fuel cell
system to follow the power trajectory.
6. Implement the controllers on realistic power profiles.
In Chapter 2, methods for onboard hydrogen storage and various methods for reforming
hydrocarbons are reviewed. Kinetic models for the three reactors in the fuel processing
system are presented. The working principle, various areas of application and types of fuel
cells are discussed. A review of fuel cell models is presented. An introduction to process
control techniques, PID controller design and tuning, and adaptive control techniques is
presented.
In Chapter 3, the three different reactors of the fuel processing system are designed.
Operating parameters such as steam to carbon ratio, operating temperatures and pressures
and feed stream composition are established. A relationship between the methane flow rate
and the hydrogen output is obtained by varying the feed rate of methane.
In Chapter 4, the power generation subsystem is designed. Two different models for the
fuel cell are presented. The size of the polymer electrolyte fuel cell stack is calculated.
Chapter 5 discusses the adaptive control technique introduced in Chapter 2 in more
detail. Two different fuel cells the PEM fuel cell and the phosphoric acid fuel cell (PAFC)
models are studied. In the case of the PEM fuel cell the adaptive controller is implemented
on the nonlinear model and its performance is compared to that of a PID controller by
implementing the controllers on realistic power profiles.
In Chapter 6 a battery model suitable for control purposes is presented and a switching
controller is designed which effectively switches back and forth between the fuel cell and
10
battery. Finally, in Chapter 7 the main results of this dissertation are summarized and the
direction of future work is proposed in Chapter 8.
11
CHAPTER 2
LITERATURE SURVEY
The process flow diagram presented in Fig. 1.1 has many similarities to those in the
chemical process industry. The entire system can be divided into subsystems and most
research papers typically focus on the steady state analysis of a specific component of the
overall system. However, a review of the literature indicates that research on overall dynamic
behavior of fuel cell systems is sparse. The literature in this area can be classified as follows:
2.1 Fuel Processing System
Fuel cells need hydrogen and oxygen for operation while oxygen can be obtained from air
we need to develop a strategy to supply hydrogen. As discussed in Section 1.2 hydrogen is not
a primary fuel and it has to be extracted from hydrogen rich fuels. Hydrogen can be extracted
from these fuels at centralized plants and then distributed to the local fueling stations. In
such a scenario we need to develop an onboard hydrogen storage system which supplies the
hydrogen. Otherwise we can miniaturize the centralized plant to produce hydrogen through
in situ generation and then supply this hydrogen on an “as needed” basis.
2.1.1 Onboard Hydrogen Storage
It is challenging to store hydrogen safely in an automobile. The energy to volume ratio of
hydrogen is very low and if hydrogen is stored as a gas, a very large fuel tank is needed for a
relatively limited driving range. Hence, there is a lot of ongoing research on developing novel
methods for hydrogen storage. The success of these methods will depend on which method
is portable, affordable, can give the maximum driving range, can occupy a smaller volume
and is adjustable to fluctuations of the hydrogen demand. The five different methods often
quoted in the literature through which hydrogen can be stored are as follows [5]:
12
• Compression
• Liquefaction
• Physisorption
• Metallic hydrides
• Complex hydrides
Hydrogen can be stored in a pressurized cylinder with pressures up to 20 MPa, but the
energy density is too low to satisfy the fuel demand of current driving practice. Storing
hydrogen onboard in compressed gas cylinders has been investigated by Hwang et al. [6]
and they have successfully test run an experimental vehicle, but the range of the vehicle
is very low and needs refueling for every 100 miles. About four times higher pressure is
needed to meet the driving purpose; however, such high pressure cylinders are not available
commercially. Liquid hydrogen is widely used today for storing and transporting hydrogen
[7]. This method faces two significant challenges: (1) the efficiency of the liquefaction process
and (2) the boil-off of the liquid hydrogen.
Hydrogen can be adsorbed onto certain materials like nanotubes and the adsorbed gas
can be released reversibly. Zhang et al. [8] and Service [9] proposed storing hydrogen in
nanotubes or nanoballs and this has been a hot topic for research ([10], [11], [12]). Indications
are that hydrogen may be stored in nanotubes in quantities exceeding that of metal hydrides
and at a lower weight penalty [13], but no designs exist yet.
Some metals and alloys absorb hydrogen and form hydrides. Hydrogen diffused into
appropriate metal ions can achieve storage densities greater than that of liquid hydrogen.
There are two classes of hydrides, metallic hydrides and complex hydrides. The main
difference between them is the transition of metals to ionic or covalent compounds for the
complex hydrides upon absorbing hydrogen. Toyota [14] has been working on developing
high density metal alloys. Some of the metallic hydrides of interest for storage purpose
are listed in [5]. Group I, II, and III elements, (e.g. Li, Mg, B, Al) form a large variety
of metal−hydrogen complexes. NaAlH4 [15], LiBH4 [16] and NaBH4 [17] can reversibly
13
absorb/desorb hydrogen at moderate temperatures. While complex hydrides are a promising
solution of the hydrogen storage problem, the mass storage densities are still less than
10% of those of conventional fuels [18], making this method doubtful for economical mobile
applications. All the technologies listed above are still in their nascent stage of development
and require a lot of research work before they become commercial products. Even after
the hydrogen storage problem is solved, it is necessary to establish a hydrogen distribution
system which will take a lot more time and money.
2.1.2 In situ Hydrogen Generation
Hydrogen is a very difficult fuel to store onboard and there is a lack of infrastructure
for distribution of hydrogen. To make these cars commercially viable it is necessary to use
fuels like gasoline, diesel and natural gas as they already have a wide distribution network.
Hence, we need a reformer which can produce the required hydrogen onboard from these
hydrocarbons. When we use fuels like gasoline and diesel they have to be first broken down
to smaller molecules like methane. So as a starting point we chose methane as the fuel of
choice. There are different methods by which we can produce the hydrogen from methane
as described below
Steam Reforming (SR)
This is the process that is being used to produce hydrogen industrially. In this method
methane reacts with steam to produce CO and H2 as shown in Eq. 2.1. This is often
accompanied by a water gas shift reaction given by Eq. 2.2, in which CO and H2O react to
form CO2 and H2. In addition to this a side reaction also takes place where for each mole of
natural gas four moles of hydrogen are obtained as shown in Eq. 2.3. The overall reaction
is endothermic requiring an external heat source.
SR Initial Reaction
CH4 +H2O → CO + 3H2; ∆Ho298 = 205.81kJ/mol (2.1)
Water Gas Shift Reaction
CO +H2O → CO2 +H2; ∆Ho298 = −41.16kJ/mol (2.2)
14
SR Side Reaction
CH4 + 2H2O → CO2 + 4H2; ∆Ho298 = 164.64kJ/mol (2.3)
All the reactions occur at high temperature and the reacting temperature can be reduced
by the addition of a catalyst. Nickel, chromium-promoted iron oxide, copper, zinc catalysts
supported on alumina are the catalysts generally used. If the fuel is being supplied to a
polymer electrolyte fuel cell stack, further purification is required to reduce the concentration
of CO to less than 100 ppm [19].
Partial Oxidation Reforming (POX)
In partial oxidation reforming the feed consists of methane and oxygen. In the reformer
methane is partially oxidized to H2 and CO. The reaction is given in Eq. 2.4. The reaction
is exothermic and takes place at very high temperatures (> 1200oC).
POX Initial Oxidation Reaction:
CH4 + 0.5O2 → CO + 2H2; ∆H = −36kJ/mol (2.4)
The water gas shift reaction which is also seen in the SR method also takes pace converting
some of the CO to CO2. If catalysts are used the reaction temperature is reduced and the
process is known as catalytic POX. SR is more efficient than POX because for every mole of
methane more amount of hydrogen is produced in SR compared to POX method.
Autothermal Reforming (ATR)
This method is a combination of both the POX and SR methods. In this method the heat
generated by the POX method (exothermic) is used to supply the heat needed for the SR
reaction (endothermic). Since no external heat source is required it is called an autothermal
reformer. When the ratio of number of moles of CH4 reformed by SR to POX is n:m, the
total ATR reaction can be expressed as
ATR Total Reaction
(n+m)CH4 + (1/2m))O2 + (2n+m)H2O → (n+m)CO2 + (4n+ 3m)H2 (2.5)
15
2.1.3 Development of Kinetic Models
Steam reforming of hydrocarbons for hydrogen production has been studied for several
decades, mainly for applications in ammonia synthesis, methanol synthesis and for substitute
natural gas applications. In areas where natural gas is available in large quantities,
interest centered around steam reforming of methane and methane reforming technology
was pioneered by BASF in the first quarter of the 20th century [20]. Steam reforming of
higher hydrocarbons has been the focus in countries such as Japan and the U.S. where natural
gas is not as abundant. Rostrup-Nielson [21], Tottrup [22] and Christensen [23] used heptane
as a model feed for the investigation of steam reforming of higher hydrocarbons and they
found out that these reactors are too large to fit under the hood of a car. Xu and Froment
[24] developed a detailed reaction scheme for the steam reforming of methane, accompanied
by water gas shift reaction on a Ni/MgAl2O4 catalyst. Based on this reaction scheme they
developed Hougen-Watson-type equations for the reaction rates given by Eq. 2.6, Eq. 2.7
and Eq. 2.8.
r1 =
k1
P 2.5H2
(PCH4PH2O −
P 3H2PCO
K1
)
(1 +KCOPCO +KH2PH2 +KCH4PCH4 +KH2OPH2O/PH2)2(2.6)
r2 =
k2
PH2
(PCOPH2O − PH2
PCO2
K2
)
(1 +KCOPCO +KH2PH2 +KCH4PCH4 +KH2OPH2O/PH2)2(2.7)
r3 =
k3
P 3.5H2
(PCH4P
2H2O− P 4
H2PCO2
K3
)
(1 +KCOPCO +KH2PH2 +KCH4PCH4 +KH2OPH2O/PH2)2(2.8)
where r is the reaction rate, k is the Arrhenius rate constant, Px and Kx stands for the
partial pressure and adsorption coefficients of a component x. To avoid carbon formation
that poisons the catalyst, a high steam-to-carbon ratio in the range of 2-5 is commonly used
16
[25]. While industrial fixed-bed reactors operate at relatively high pressures (∼ 30 bar), fuel
cell applications typically operate at about 2-5 bar. To avoid excessive pressure drop, large
catalyst particles are used which result in an extremely low effectiveness factor in the range
10−2 − 10−3.
The water gas shift reaction, is an industrially important reaction that was first com-
mercialized for the manufacture of ammonia. Typically, iron based catalysts are used in
this process and a second catalyst based on copper is also used in order to achieve higher
conversion of carbon monoxide to carbon dioxide. Choi and Stenger [26] developed the
kinetic rate expressions for the water gas shift reaction based on a Cu/ZnO/Al2O3 catalyst.
They proposed an empirical rate expression for the amount of CO consumed as shown in
Eq. 2.9
rCO = kPCOPH2O(1− β) (2.9)
where β is the reversible factor given by
β =PCO2PH2
PCOPH2OKeq
where Keq is the equilibrium constant which can be obtained from thermodynamic
properties.
The water gas shift reaction results in a stream that is approximately 0.3% carbon
monoxide. However, it is necessary to reduce the carbon monoxide concentration in the
hydrogen stream to about 100 ppm before it can be sent to the fuel cell to avoid poisoning the
catalyst in the fuel cell membrane. The preferential oxidation (PROX) of carbon monoxide in
a hydrogen-rich atmosphere has long been of technical interest for purification of hydrogen. In
order to keep the overall energy conversion process as efficient as possible, the CO oxidation
has to be highly selective. Catalyst formulations for this reaction typically comprise of
platinum on alumina. Copper catalysts on alternative supports are also being developed
[27]. Kahlich et al.[28] developed a rate expression for selective CO oxidation based on a
platinum catalyst given by Eq. 2.10.
rCO = k1P0.42O2
λ0.82 (2.10)
17
where λ is a process parameter which represents the oxygen in excess with respect to the
amount of oxygen required for the oxidation of CO to CO2 as given by Eq. 2.11.
λ =2CO2
CCO=
2PO2
PCO(2.11)
The process parameter λ accounts for the amount of oxygen that is consumed by the
oxidation of hydrogen. A more detailed discussion of the kinetic rate expressions are
presented in the next chapter.
2.2 Fuel Cell
2.2.1 Working Principle
A fuel cell is an electrochemical device which combines a fuel (e.g. hydrogen, methanol)
and oxygen to produce a direct current. Unlike storage batteries fuel cells can be continuously
fed with a fuel so that the electrical power output is sustained for a longer period of time.
The fuel used is generally hydrogen which produces electrical energy and heat through the
reaction of hydrogen and oxygen to form water. The process is that of electrolysis in reverse.
The anode and cathode reactions are given in Eq. 2.12 and Eq. 2.13 respectively and the
overall cell reaction is given by Eq. 2.14.
H2 → 2H+ + 2e− (2.12)
2H+ + 2e− +1
2O2 → H2O (2.13)
H2 +1
2O2 → H2O (2.14)
The hydrogen comes in at the anode where it splits into hydrogen ions and electrons
in the presence of a catalyst. The hydrogen ions pass through the electrolyte towards the
cathode. The electrons which cannot pass through the electrolyte, pass through an external
circuit from the anode to the cathode thereby producing a current. At the cathode the
oxygen combines with the electrons and hydrogen ions in the presence of a catalyst to form
18
Figure 2.1. Cross section of a polymer electrolyte membrane fuel cell
water. Fig. 2.1 [29] shows a cross-sectional diagram of a single cell polymer electrolyte fuel
cell.
2.2.2 Types of Fuel Cells
There are numerous applications for fuel cells today and depending on the specific
application, different types of fuel cells are now available in the market. They differ mainly
in the type of membrane used, operating temperature, oxidant composition, reforming
technology etc. Some of the most common fuel cells are listed below and salient features of
the different types of fuel cells are listed in Table 2.1.
19
Phosphoric Acid Fuel Cell (PAFC)
As the name suggests the electrolyte in a phosphoric acid fuel cell is phosphoric acid.
PAFC is tolerant to carbon monoxide poisoning. The operating temperature is around 190
oC. These fuel cells are very sensitive to temperature changes. At lower temperatures the
water evolved by the fuel cell reaction is dissolved in the electrolyte thereby diluting the
electrolyte and reducing the efficiency of the fuel cell drastically. At higher temperatures the
phosphoric acid starts to decompose which also significantly decreases the efficiency of the
fuel cell. PAFC require nobel metal catalysts. Platinum and silicon carbide are generally
used as catalysts.
Molten Carbonate Fuel Cell (MCFC)
MCFC operate ata very high temperature of 650 oC. At these high operating temper-
atures the fuel cell acts as its own reformer. The electrolyte here is molten carbonate salt.
These fuel cells require carbon dioxide in the oxidant stream to regenerate the carbonate. The
main application areas of these fuel cells are large scale and stationary electricity production
for utility power generation. These cannot be used for transportation purposes because of
their bulk, thermal cycling, difficult start-up and complex control requirements.
Solid Oxide Fuel Cell (SOFC)
Solid oxide fuel cells are very useful when natural gas is used as a fuel because they are
very tolerant to sulphur and also they have better operating lives than the other fuel cells.
Operating temperature is around 1000 o C. Internal reforming is one of the main advantage of
using SOFC. High operating temperature causes slow start up and also start up/shut down
cycles are stressful to cell integrity. SOFC use nickel as a catalyst and have very narrow
operating temperature range.
Polymer Electrolyte Membrane Fuel Cell (PEM)
The electrolyte in a PEM fuel cell is a solid, organic polymer and is usually referred
to as a membrane. It consists of three parts: (1) the Teflon like, fluorocarbon backbone,
20
(2) side chains which connect the molecular backbone to the ionic part and (3) the ion
clusters consisting of sulfonic acid ions. In the presence of water the negative ions in the
membrane are held within the structure, but the positive ions (H+ ions) are mobile and
are free to carry positive charge through the membrane. The other important property of
the polymer electrolyte membrane is that the electrons cannot pass through them. Hence,
the electrons produced at the cathode pass through an external circuit thereby producing
current. Another advantage of these membranes is they act as effective gas separators. So
that the gases at the anode and cathode do not mix. The most popular PEM membrane is
Nafion 117 [30].
The reactions taking place at the anode and cathode given by Eq. 2.12 and Eq. 2.13
respectively. These reactions are normally very slow but in the presence of a catalyst like
platinum the reactions become fast. Platinum is costly and lowering the platinum catalyst
levels is an ongoing research effort [31]. Each electrode consists of porous carbon to which
small platinum particles are bonded. The combination of electrodes and membrane is called
the Membrane Electrode Assembly (MEA). The MEA is very thin (around 0.2 - 0.5mm in
thickness) and is generally sold as a single unit.
The MEA are enclosed in backing layers, flow fields and current collectors which are
designed to maximize the current that can be obtained from a MEA. Backing layers are
placed next to the anode and cathode. They are usually made of a porous carbon paper or
carbon cloth. Carbon conducts the electrons exiting the anode and entering the cathode and
the porous nature ensures effective diffusion of each reactant gas to the membrane electrode
assembly. The backing layers also help in water management by supplying the right amount
of water vapor to the membrane to prevent drying or flooding of the membrane. Adjacent
to the backing layers is a plate which serves the dual purpose of a flow field and a current
collector. The flow fields are used to carry reactant gas from the point it enters the fuel cell
to the point at which the gas exits. The plates also serve as current collectors. Electrons
produced at the anode pass through the backing layers and through the plate before exiting
the cell. After passing through an external circuit the electrons re-enter the fuel cell through
the cathode plate.
21
Fuel Cell Stack
The maximum voltage of a single fuel cell at 100 % efficiency is 1.23 V . As most
applications require higher voltages than this, the required voltage is obtained by connecting
individual fuel cells in series to form a fuel cell stack. To decrease the overall volume and
weight of the stack instead of two current collectors (one for the anode and one for the
cathode), a single plate is used with a flow field cut into each side of the plate. This type of
plate is called a bipolar plate.
For automotive applications it is desirable to have a fuel cell system with a low operating
temperature. MCFC operate at a very high temperature hence they are not used in this
application. One of the first fuel cell vehicles were developed using PAFC technology. PAFCs
have good designs as they had a lot of funding over the past 20 years, because they were
judged most tolerant of reformed hydrocarbon fuels. The operating temperature window is
small for PAFC systems and this is the major drawback. PEM fuel cells, because of their low
cost, ease of operation, lower operating temperature and higher energy density, are gaining
preference to PAFC systems. Many of the leading automotive manufactures have come up
with hybrid fuel cell cars using the PEM fuel cell. For a PEM fuel cell car a continuous
supply of hydrogen is neede which can be obtained by reforming of methane as discussed in
Section 2.1.
Table 2.1. Salient features of the different types of fuel cellsProperty PAFC PEMFC MCFC SOFC
Electrolyte Phosphoric acid Polymer Molten carbonate salt CeramicOperating Temperature 190 oC 80 oC 650 oC 1000 oC
Fuels H2 H2 H2/CO H2/CO/CH4/Reforming External External External/Internal External/InternalOxidant O2/air O2/air O2/air CO2/O2/air
2.2.3 Applications
Fuel cells have many applications today and the list is growing fast. The development of
the various technologies is application dependent with each fuel cell type having strengths
22
and weaknesses. There are three basic market segments for fuel cells: portable/battery
substitution, transportation and utility power.
Portable and Battery Substitution
Portable power is one of the areas where the first widespread application of fuel cell
technology is expected. Fuel cells as battery chargers are expected to be commercially viable
in the near future. Another exciting area is the world of consumer portable electronics.
Laptops, mobile phones, PDAs and many other electronic devices have shown better
performance and longer run times with fuel cells powering them in place of batteries.
Research is still in progress and issues such as heat management and space constraints
have to be resolved. There is a lot of interest shown by military over the use of fuel cell
battery packs. With the increase of sophisticated electronic equipment used by the military
a battery which runs for longer time while offering portability will be a good option. Many
novel applications such as powering small cycles and scooters have also been proposed and
are under development. All the major electronics companies such as Canon, Casi, Fujitsu,
Hitachi, Sanyo, Sharp, Sonyand Toshiba have ongoing research in this field.
Transportation
In terms of size, value and environmental impact, automotive markets represent the
biggest prize for fuel cells. Fuel cells were first used to power vehicles over forty years ago.
For many years development work was insignificant, and as a result until the mid nineties
only a handful of vehicles were developed. Fuel cell vehicles are now available in the light
and heavy duty vehicles category. The most successful area so far has been fuel cell buses
(FCBs). In 1993 Ballard powered the first fuel cell bus in the world. Recently in 2003
the Evobuses were introduced in Iceland and are being operated under the ECTOS project
[32]. In the U.S. the California Fuel Cell Partnership [33] is coordinating the deployment of
several FCBs at a number of californian transit agencies. Most of these buses run on direct
methanol fuel cells [34] which run directly on methanol instead of hydrogen.
In light duty vehicles such as cars and vans all the major automotive manufacturers have
shown interest, Honda and Toyota have already delivered vehicles to customers in California
and Japan. In 2004 Daimler Chrysler has also begun to deliver FCVs for limited fleet trials
23
and a number of other major manufacturers are gearing up to do the same. Nissan leased
its first FCV in 2004, Dihatsu, Ford and Hyundai are all expected to follow suit later this
year.
Stationary Power
The stationary applications can be divided into two groups small stationary power plants
(0.5-10 kW) and large stationary plants or utility generation (> 10 kW). In the small
stationary market main areas of focus over the past few years has been residential, UPS
or backup sector. A growing number of market segments including telecommunications,
emergency services such as hospitals and the banking industry have started to take an active
interest in fuel cell technology. Companies like Ballard, Plug Power, Fuji Electric, Kyocera
and ReliOn have limited commercialization of the 1kW PEM.
Large stationary power was one of the first applications for fuel cells. Most of the early
fuel cells were based on phosphoric acid and molten carbonate fuel cells. There are also a
number of companies developing SOFC and PEM fuel cells. In 2004 itself, more than 50
large stationary units were installed across the world, with North America and Japan leading
the way with the highest number of installations. UTC and Fuji Electric are the leaders
in terms of the total systems sold and they are based on phosphoric acid technology. Fuel
cell Energy and MTU CFC solutions have developed molten carbonate fuel cells. General
Motors, Siemens Westinghouse, Rolls Royce and Mitsubishi Electric have developed systems
based on SOFC and PEM fuel cells.
2.3 Fuel Cell Modeling
The PEM fuel cell is the most promising system currently available because of the
simplicity of its design and the low temperature of operation (around 80 oC). For this
reason, there have been several experimental and theoretical attempts in the past decade
to characterize the operation of PEM fuel cells. Rho et al. [35] utilized different mixtures
of oxygen and inert gases and studied mass transport phenomena across the PEM fuel cell
system. Beattie et al. [36] studied the effect of temperature and pressure on oxygen reduction
at the platinum and Nafion interfaces. Jordan et al. [37] studied the effect of diffusion layer
24
on the performance of the fuel cell. Motupally et al. [38] and Sridhar et al. [39] studied the
effect of water diffusion on these membrane reactors. Theoretical modeling of transport and
reaction in fuel cells is challenging due to the numerous design and operating parameters that
can influence its performance. The transport of water and ions in a PEM fuel cell has been
modeled at various levels of complexity by many groups. Mass transport of gas and water
was also studied with both one dimensional [40], [41], [42], [43] and two dimensional models
[44], [45], [46]. Verbrugge and Hill [47] developed a steady state fuel cell model to study
the transport properties of perfluorosulfonic acid membranes under electrolyte supported
conditions. Bernardi and Verbrugge [48] developed a one-dimensional steady state model
to study the effects of transport of gases in gas diffusion electrodes on the performance of
PEM fuel cells. Springer et al. [43] developed an isothermal, one-dimensional steady state
model for a complete polymer electrolyte fuel cell. Their model also predicted the net water
flow per proton through the membrane and the increase in membrane resistance due to the
membrane water content.
Nguyen and White [49] developed a two dimensional steady state model to describe the
heat transfer and mass transfer in the fuel cell. They also investigated the effectiveness of
various humidification designs. Thampan et al. [50] developed a steady state analytical
transport-reaction model by drawing parallels with membrane reactors. Fuller and Newman
[51] examined the water, thermal and reactant utilization of the fuel cell by developing a
two dimensional mass transport model of the membrane electrode assembly. Van Zee et
al. [52] presented a three dimensional numerical model that predicts the mass flow between
the cathode and anode channels. Several publications [53], [54], [55], [56] have focused on
fuel cell polarization curves and identification of the various fuel cell resistances that are
encountered at different operating conditions. The resistances are then used to predict the
fuel cell voltage-current characteristics or the fuel cell polarization curves.
The steady state models focus on developing the complex electrochemical, thermody-
namic and fluid mechanics principles and include spatial variations. These models are very
useful in designing the various components inside individual fuel cells like membrane electrode
assemblies, backing layers, flow fields etc. Design of these components is essential to establish
25
the feasibility of fuel cells and hence all the models that came out in the 1990s were steady
state models which were used to design the various components of the fuel cell. Once the
commercial viability of the fuel cells was realized, focus shifted from steady state models to
performance models which focus on the efficiency of the fuel cell under different operating
conditions. As the research became more application oriented the focus was on identifying
the current voltage characteristics which were useful in calculating the number of cells and
the area of cell depending upon the power demand, current required, operating voltage etc.
A single fuel cell cannot produce enough voltage and generally a group of cells are put
together and this arrangement is also known as the fuel cell stack. Several models were
developed to represent the behavior of fuel cell stacks [57], [58]. These models were used to
determine the operating configurations for the stack and for the stack flow field design. The
equal distribution of the gases to the various cells inside the stack is very critical for proper
functioning of the fuel cell.
In this dissertation analytical models of the fuel cell polarization curve will be used to
establish a good operating point for the fuel cell operation. Using the maximum power
demand the number of fuel cells in the stack, the cross sectional area of each fuel cell will
be calculated. Based on the results obtained by Nyugen and White [49] a linear model will
be developed and used to calculate the number of cells and operating points. Using these
values as initial guesses a more thorough estimate will be obtained using nonlinear model
given by Pukrushpan et al. [59] in Chapter 4.
2.4 Thermal Management System
The in situ hydrogen generation subsystem consists of a combination of exothermic and
endothermic reactions. The steam reforming reactions are endothermic and these reactions
take place at very high temperatures. Sufficient heat has to be supplied to the fuel and
steam to heat them to the reactor temperature and also maintain the reactor temperature.
Most of the literature on steam reforming thermodynamics is based on the large steam
reformers used industrially [60]. Lutz et al. [61] did a thermodynamic analysis of a compact
26
steam reformer using a diesel fuel and found out that both incomplete reaction and heat
transfer losses reduce the efficiency of the process. The gases leaving the reformer have to
be cooled to the operating temperature of the water gas shift reactor. The WGS reaction
is exothermic so there is excess heat available which can be redistributed to the reactors
requiring heat. The preferential oxidation reaction is also exothermic and produces heat.
Furthermore, the gases from the PROX coming out of the fuel processing subsystem have
to be cooled to the temperature at which the power generation subsystem operate. For
this reason, it is necessary to develop an efficient thermal management system for optimized
operation. This fact has been recognized in recent feasibility studies by Zalc and Loffler
[3] where the heat requirements for each reactor system were calculated based on overall
energy balances. Godat and Marechal [62] developed a model of a system including a proton
exchange membrane (PEM) fuel cell and its fuel processing section. They investigated the
process configurations to identify optimal operating conditions and optimal process structure
of the system by applying modeling and process integration techniques. They used pinch
technology techniques to model the integrated heat exchange system to get an estimate
of the net energy requirement for a PEM fuel system. Sorin and Paris [63] applied pinch
technology to the thermodynamic analysis of a process through the exergy load distribution
method. The focus of this study was on feasibility of operation, rather than on the dynamic
heat load of the operation, which is important from a control standpoint. In addition to the
fuel processing system we may need a combustor to provide the necessary heat for the steam
reformer. A thermal management system should be designed which can distribute the heat
among the different reactors. The design should take into consideration the dynamic effects
of the different processes.
In this dissertation the overall heat duty requirements for the three reactors in series will
be calculated for different flow rates of methane. Even though the WGS and PROX reactor
produce heat they operate at a lower temperature compared to SR and a heat source which
operates at a temperature higher than SR is needed. Hence a combustor which operates at
a higher temperature than SR will be designed. The thermal system design will be based on
steady state modeling.
27
2.5 Controller Design and Power Distribution System
For a fuel cell vehicle it is necessary to design a control system that can track the power
demand from the fuel cell. The reference for this control system is the power demand
of the automobiles, which changes with road conditions as well as driving characteristics.
Reference tracking problems are conventionally handled by PID controllers which are the
most commonly used controllers in the process industry. However, since the power demand
profile is not known a priori, a PID controller that is tuned to one set of conditions (e.g.
highway driving) may not work well under a different set of conditions (e.g. city driving).
It is necessary to design a controller that adapts to varying driving and road conditions.
2.5.1 Adaptive Controller
Interest in adaptive control techniques first started during the early 1950s when it was
used for the design of autopilots for high performance aircraft. This motivated an intense
research activity in adaptive control. High performance aircraft undergo drastic changes in
their dynamics when they fly from one operating point to another that cannot be handled by
constant-gain feedback control. A sophisticated controller, such as an adaptive controller,
that could learn and accommodate changes in the aircraft dynamics was needed. Model
Reference Adaptive Control (MRAC) was suggested by Whitaker et al. [64] to solve the
autopilot control problem. The sensitivity method and the MIT rule was used to design the
adaptive laws of the various proposed adaptive control schemes. An adaptive pole placement
scheme based on the optimal linear quadratic problem was suggested by Kalman [65]. During
1960s development of control theory and adaptive control in particular was facilitated by
the introduction of state space techniques and stability theory based on Lyapunov theory.
Developments in system identification and parameter estimation lead to the reformulation
and redesign of adaptive control techniques. The MIT rule-based adaptive laws used in the
MRAC schemes of the 1950s were redesigned by applying the Lyapunov design approach.
During this time the adaptive controllers designed were applicable only to a special class
of linear time invariant plants but nevertheless this provided a nice platform for further
rigorous stability proofs in adaptive control for more general classes of plant models. On
the other hand, the simultaneous development and progress in computers and electronics
28
that made the implementation of complex controllers feasible contributed to an increased
interest in applications of adaptive control. The 1970s witnessed several breakthrough results
in the design of adaptive control. MRAC schemes using the Lyapunov design approach
were improved. The concepts of positivity and hyperstability were used to develop a
wide class of MRAC schemes with well established stability properties [66]. At the same
time parallel efforts for discrete-time plants in a deterministic and stochastic environment
produced several classes of adaptive control schemes with rigorous stability proofs ([67],
[68]). The non-robust behavior of adaptive control became very controversial in the early
1980s when more examples of instabilities were published demonstrating lack of robustness
in the presence of unmodeled dynamics or bounded disturbances [69], [70]. This stimulated
many researchers, whose objective was to understand the mechanisms of instabilities and
find ways to counteract them. By the mid 1980s, several new redesigns and modifications
were proposed and analyzed, leading to a body of work known as robust adaptive control.
An adaptive controller is defined to be robust if it guarantees signal boundedness in the
presence of reasonable classes of unmodeled dynamics and bounded disturbances as well as
performance error bounds that are of the order of the modeling error [71].
The solution of the robustness problem in adaptive control led to the solution of the long
standing problem of controlling a linear plant whose parameters are unknown and changing
with time. By the end of the 1980s several breakthrough results were published in the area
of adaptive control for linear time-varying plants [72]. The focus of adaptive control research
in the late 1980s to early 1990s was on performance properties and on extending the results
of the 1980s to certain classes of nonlinear plants with unknown parameters. These efforts
led to new classes of adaptive schemes, motivated from nonlinear system theory [73] as well
as to adaptive control schemes with improved transient and steady state performance[74],
[71]. Adaptive control has a rich literature full with different techniques for design, analysis,
performance and applications. Several survey papers [75], [76] and books [77] have already
been published.
In this dissertation a model reference adaptive controller will be designed using the
Lyapunov method for tracking a time varying power profile in the fuel cell powered
29
automobile. To improve robustness a discontinuous dead zone and derivative action will be
added. The adaptability of the controller will be tested by implementing the controller on
different power profiles which simulate actual power requirement of different road conditions.
The performance of the adaptive controller is compared with a conventional PID controller
and the adaptive controller is shown to perform better than the PID.
2.5.2 Switching Controller
The fuel cell system requires time for the different reactors in the fuel processing system to
heat upto their respective optimum operating conditions. The fuel can be directly sent to the
combustor to produce the sufficient heat for this process. Nevertheless this may take several
minutes and thus an auxiliary power source is needed to supply the power in the meantime.
An auxiliary power source is also needed when the instantaneous power demand exceeds
the power supplied by the fuel cell. For the fuel cell to provide more power it is necessary
to process a higher flow rate of hydrocarbon fuel which results ina time lag in producing
the desired power. During this lag time the automobile has to operate on auxiliary power.
Instead of the lead-acid battery which has a energy density of 20-35 Wh/kg a Lithium-ion
battery can be used as it has a higher energy density of 100-200 Wh/kg [13]. Newman [78]
considered high power batteries for hybrid vehicles and developed a model for a lithium-ion
battery. A simpler model was developed by He et al. [79] who also were investigating battery
performance for a hybrid vehicle. Lee et al. [80] conducted experiments to study the effect
of load increase on a battery backup system and showed that it was necessary to have a
control system to switch effectively to the battery. Gokdere et al. [81] computed the power
requirements for rapid acceleration and deceleration to study the dynamics of the battery in
a hybrid electric car.
In this dissertation the simplified battery model proposed by He et al. will be used and a
switching controller will be designed which effectively switches between the fuel cell and the
battery. The factors to be considered in designing this switching controller are (a) ensure
power demand at all times, (b) ensure that the battery is not completely discharged and (c)
distribute excess power produced by the fuel cell to battery backup.
30
CHAPTER 3
DESIGN OF FUEL PREPROCESSOR
3.1 Thermodynamic Analysis
The fuel processor system designed should be small enough to fit under the hood of a
car and quick enough to produce the required hydrogen on an “as needed basis” to meet
the power demand. The steam reforming and the water gas shift reactions which take place
in the fuel processing subsystem are reversible reactions. The design of processes involving
reversible reactions, generally begins with a feasibility study or a thermodynamic analysis.
The thermodynamic analysis does not specify the sizes of the reactor or information about
how fast the reaction occurs, but it provides a theoretical limit on the conversion possible
based on the equilibrium conditions. This analysis is also useful in identifying whether the
overall process produces heat or requires heat. The fuel cell system schematic diagram as
shown in Fig. 1.1, consists of 3 packed bed reactors, a PEM fuel cell and a combustor. There
are different reactions that are taking place in the fuel processor and it is first necessary to
identify the reactions that require heat (endothermic) and the reactions that produce heat
(exothermic). This can be calculated easily based on the standard heat of reaction. If the
standard heat of reaction is positive then the reaction is said to be endothermic and if it
is negative the reaction is exothermic. The standard heat of reaction can be obtained from
the standard heat of formation of the individual species involved in the reaction by using
the Hess’s Law. The standard heat of formation shown in Table 3.1 were obtained from the
NIST Chemistry Webbook [82]. For oxygen and hydrogen the standard heat of formation
can be assumed to be zero [83].
31
Table 3.1. Standard heat of formationsSpecies Standard heat of formation (kJ/mol)CO -110.53CO2 -393.51H2O -242CH4 -74.5O2 0H2 0
Using the heat of formation data, the heat of reaction can be computed using Hess’s law.
Depending on the sign of the standard heat of reaction We can tell whether a reaction is
exothermic or endothermic.
Table 3.2. Standard heat of reactions and type of reactionReaction Standard heat of reaction Type
(kJ/mol)CH4 +H2O 3H2 + CO 205 endothermicCO +H2O CO2 +H2 -41 exothermic
CH4 + 2H2O 4H2 + CO2 164 endothermicCO + (1/2)O2 CO2 -283 exothermicH2 + (1/2)O2 H2O -242 exothermic
Table 3.2 indicates that the reforming reactions are endothermic while the water gas shift
reaction, preferential oxidation reactions are exothermic. It is necessary to design a heat
distribution system which will distribute the heat produced by the exothermic reactions to
the endothermic reactors. The heat produced by the exothermic reactors may or may not be
sufficient to provide the necessary heat to the endothermic reactors. A preliminary analysis
[84] for a fuel cell system powered by methane indicates that the methane feed stream does
not provide sufficient heat for high flow rates and it may be necessary to feed approximately
35% more methane than that required for the power generation subsystem to account for
the heat necessary for the fuel processor subsystem. Hence a combustor is needed to meet
the required heat demand.
32
3.1.1 Feed Stream Composition
To calculate the exact amount of hydrogen that is required inside the fuel cell, a
relationship between the hydrogen going into the fuel cell and the power produced by the
fuel cell is needed. This requires a fuel cell model which will be discussed in detail in the next
chapter. Once the amount of hydrogen required is known, the amount of methane to be fed
to the reformer can be calculated if a relationship between the methane fed to the reformer
and the hydrogen coming out of the series of reactors is known. As a starting guess it is
assumed that all the methane fed to the reactor is reacting by the main reformer reaction
given by Eq. 2.1, in which 3 moles of hydrogen are produced for every mole of methane.
A rough estimate of the hydrogen required to produce 50 kW (67 hp) of power is required.
The power produced by the fuel cell is given by Eq. 3.1.
P = IV (3.1)
Where P is the power (W) and I is the current (A) and V is the voltage (V). For every
molecule of hydrogen that reacts within a fuel cell, two electrons are liberated at the fuel cell
anode. This is most easily seen in the PAFC and PEM fuel cells, because of the simplicity
of the anode reaction given by Eq. 3.2.
H2 → 2H+ + 2e− (3.2)
One equivalence of electrons is 1 mol of electrons or 6.022 × 1023 electrons (Avogadro’s
number). This quantity of electrons has a charge of 96,487 C (Faraday’s constant). One
ampere of current is defined as 1 C/sec. Using the above information the moles of hydrogen
(nH2) needed to generate 1 A current can be calculated using Eq. 3.3.
nH2 = 1.0A
(1C/sec
1A
)(1eq. e−
96, 487C
)(1mol H2
2eq. e−)(
60sec
1min) = 3.1× 10−4mol/min (3.3)
The maximum theoretical voltage is 1.23 V. If it is assumed that the cell is operating at 50%
efficiency, a voltage of approximately 0.7 V results. The current required inside the fuel cell
to have a power output of 50kW is given in Eq. 3.4.
I =P
V=
50kW
0.7V= 71.43kA (3.4)
From Eq. 3.3 it can be seen that 3.1× 10−4 mol/min of H2 are required to produce 1A.
Using this factor the amount of fuel that must be provided to supply a desired fuel cell power
33
output can be determined. Not all the hydrogen that is sent into the fuel cell reacts and
some of the hydrogen comes out unreacted. The ratio of hydrogen reacted to the hydrogen
fed into the reactor is known as hydrogen utilization (U). If an 80% utilization is assumed,
then the hydrogen flow rate is given by Eq. 3.5
nH2t =nH2I
U=
3.1× 10−4mol/min× 71.43× 103A
0.8∼= 30mol/min (3.5)
where nH2t is the total amount of hydrogen required. Hence around 30 mol/min of H2 is
needed to get a power output of 50 kW. This is the maximum amount of hydrogen needed
as this corresponds to the maximum power. Assuming that the SR main reaction in which
3 moles of hydrogen is produced is the only reaction taking place, the maximum amount of
methane flow rate can be estimated to be 10 mol/min.
3.1.2 Overall Heat Duty
The fuel processing subsystem consists of the reformer, the water gas shift reactor and
the preferential oxidation reactor.
Steam Reformer
The reactions taking place in the reformer are
CH4 +H2O → CO + 3H2; ∆Ho298 = 205.81kJ/mol (3.6)
CO +H2O → CO2 +H2; ∆Ho298 = −41.16kJ/mol (3.7)
CH4 + 2H2O → CO2 + 4H2; ∆Ho298 = 164.64kJ/mol (3.8)
The reaction represented by Eq. 3.6 is the main reaction in which the methane reacts
with steam to give 3 moles of H2 and a mole of CO. This reaction is endothermic. In
addition to this reaction CO2 is also produced by a side reaction shown in Eq. 3.8, which is
also endothermic. Small amount of the CO produced in the main reaction reacts with steam
to form CO2 and H2 as shown in Eq. 3.7. This reaction is known as the water gas shift
reaction which is an exothermic reaction. A preliminary analysis was done to find the heat
requirements of the reformer. The amount of hydrogen required for the maximum power
output (50 kW) is around 30 mol/min. From the amount of hydrogen the approximate
34
amount of methane required is calculated by assuming that one mole of methane gives
approximately 3 moles of hydrogen, i.e., all the methane entering is reacting via Eq. 3.6
this corresponds to a maximum methane flow rate of 10 mol/min. To avoid the formation
of coke, the steam to methane ratio is maintained at 3:1 ratio.
Water Gas Shift Reactor (WGS)
The water gas shift reaction represented by Eq. 3.9 is an exothermic reaction.
CO +H2O −→ CO2 +H2; ∆Ho298 = −41.16kJ/mol (3.9)
This reactor is generally divided into two parts the high temperature shift reactor (HTS)
which is operated at a temperature of 700 K and the low temperature shift reactor (LTS)
which is operated at 490 K (The kinetic details and the details about how to obtain the
optimum temperature are discussed in the next section). The exhaust from the reformer is
sent as feed to the WGS reactor. The amount of heat liberated from the WGS reactor for
the different flow rates of methane into the reformer is calculated.
Preferential Oxidation Reactor(PROX)
The CO concentration is brought down to less than 100 ppm by preferentially oxidizing
CO with oxygen in air. The amount of oxygen present in air should be at least twice the
amount of CO present in the WGS exhaust. This reaction is also exothermic and the heat
liberated is calculated for an isothermal case of 473 K.
The overall heat duty was calculated for the three reactors. The heat requirement for
different flow rates of methane, where the methane flow rate is varied from 1 to 10 mol/min,
was calculated and is shown in Table 3.3. As can be seen from the heat duty calculation
we still need to supply some heat to the reactors and also we need a source of heat at
a temperature greater than 1000 K( i.e. the operating temperature of the reformer). To
supply this heat we added a combustor which can utilize any heat left in the anode tail gas.
If that heat is not sufficient more heat is supplied by feeding some methane directly to the
combustor. If the heat requirement is known for a given methane flow into the reformer,
35
the amount of methane to be fed to the combustor can be calculated as a percentage of the
methane being fed to the reformer.
Table 3.3. Heat duty calculationMethane flow rate Overall heat
into reformer required(mol/min) (kW)
1 4.572 9.133 13.304 17.655 22.776 26.647 31.038 35.419 39.5710 45.43
3.1.3 Combustor Calculations
The steam reformer is an exothermic reactor operating at a high temperature of 1000 K
and it needs a heat source which can supply the necessary heat. Some of the heat generated
in the water gas shift reactor and preferential oxidation reactor can be utilized. However,
both these reactors operate at a lower temperature than that of the steam reformer. The
combustor which has to be operated at a temperature higher than the operating temperature
of the reformer is used to supply the heat required. The reactions taking place inside the
combustor are the oxidation of, carbon monoxide as shown in Eq. 3.10, unreacted hydrogen
and methane as shown in Eq. 3.11, Eq. 3.12 respectively.
CO +1
2O2 → CO2 (3.10)
H2 +1
2O2 → H2O (3.11)
CH4 + 2O2 → CO2 + 2H2O (3.12)
The amount of heat liberated can be obtained form a simple energy balance around the
combustor as shown in Eq. 3.13.
36
∑i
N ini H
ini −
∑i
N outi Hout
i − Q = 0 (3.13)
where N ini , N out
i are the flow rate of species i coming into the combustor and leaving the
combustor respectively. The enthalpy of these streams is given by H ini , Hout
i and Q is the
amount of heat liberated. From the mass balance equation a relationship between the gases
coming into the reactor and leaving the reactor can be established and is given by Eq. 3.14.
N outi = N in
i +∑j
νij εj (3.14)
where νij is the stoichiometric constant of species i in reaction j (since there are three
reactions taking place j=1, 2, 3) and εj is the extent of reaction j. Substituting the mass
balance (Eq. 3.14) into the energy balance (Eq. 3.13) we can obtain an expression for Q as
given by Eq. 3.15.
Q =∑i
N ini H
ini −
∑i
(N ini +
∑j
νij εj)Houti (3.15)
which can be simplified as
Q =∑i
N ini (H in
i −Houti )−
∑i
∑j
νij εjHouti (3.16)
expanding the enthalpy terms we have
Q =∑i
N ini
∫ Tin
Tout
CpidT −∑j
εj∆Houtj (3.17)
where Cpi is the specific heat capacity of species i and ∆Houtj is the heat of reaction, of
reaction j at temperature Tout.
From the heat analysis it is clear that we still need to supply some heat to the reactors.
Some of the heat can be recovered from the gases leaving the anode section of the fuel cell.
If we assume 90% hydrogen utilization inside the fuel cell, the heat available from the rest
of the gases can be calculated assuming total combustion of the anode tail gases.
Table 3.4 lists the amount of heat available from the anode tail gases for different flow
rates of methane. It can be seen that this stream does not produce sufficient heat and it
37
Table 3.4. Heat from the anode tail gas for different initial flow rates into the reformer.Methane flow rate Overall heat duty Heat available from
mol/min kW anode tail gas(kW)1 4.57 1.482 9.13 2.973 13.30 4.444 17.65 5.945 22.77 7.456 26.64 9.037 31.03 10.678 35.41 12.419 39.57 14.2410 45.43 16.98
is necessary to supply methane to the combustor. The amount of excess methane required
depends on the available Q which itself depends on the operating temperature and the oxygen
excess ratio. Of the three reactors, the steam reformer operates at the highest temperature of
1000 K. To supply the heat to the reformer the combustor should operate at an even higher
temperature and to avoid pinch zones the combustor should supply heat at a temperature
which is at least 15-20 oC above that of the reformer temperature. The effect of change in
temperature as it is increased from 1020 to 1100 K on Q is shown in Fig. 3.1. Another
variable is the oxygen supplied in excess to that needed stoichiometrically to ensure complete
combustion. The effect of change in this ratio on Q is also presented in Fig. 3.1. A lower
excess ratio gives a higher Q as less energy is expended in heating up the nitrogen which
comes along with oxygen in air. Lowering the excess ratio may result in the combustion
reactions not going to completion. Based on the above analysis an operating temperature of
1020 K and an oxygen excess ratio of 15 % was selected. The amount of Q for different flow
rates when 25%, 30% and 35% of the methane fed to the reformer is fed to the combustor is
given in Table 3.1.3. From Table 3.1.3 it can be seen that35% excess methane is required in
the combustor.
3.2 Steam to Carbon Ratio
The steam to carbon ratio is an important operating parameter which can influence the
conversion inside the reformer. Steam supplied in the stoichiometric ratio facilitates the main
38
1020 1030 1040 1050 1060 1070 1080 1090 110036
37
38
39
40
41
42
43
44
45
TEMPERATURE(K)
Qdo
t (kW
)
15% excess O2
20% excess O2
25% excess O2
Figure 3.1. Effect of operating temperature and oxygen excess ratio on heat duty
reaction in which 3 moles of hydrogen are produced for every mole of methane. Supplying
steam in excess to the stoichiometric ratio has three advantages. First, in the presence of
excess steam the side reaction in which four moles of hydrogen are produced is favored.
Second, the excess steam pushes the water gas shift reaction equilibrium to the right thereby
producing more hydrogen and also reducing the carbon monoxide levels. Third, a high steam
to carbon ratio reduces the chances of coke formation inside the reformer as steam acts as a
coke inhibitor. In the absence of excess steam the active sites on the catalyst are occupied by
coke forming compounds instead of steam. Coke may be formed by methane decomposition
(Eq. 3.18), Bouduard reaction (Eq. 3.19) or carbon monoxide decomposition (Eq. 3.20).
CH4 C + 2H2 (3.18)
2CO CO2 + C (3.19)
CO +H2 C +H2O (3.20)
39
Table 3.5. Heat from the combustor when methane is fed at 25%, 30%, 35% in excess tothat fed to the reformer.
CH4 flow rate Overall Q from anode Q for 25% Q for 30% Q for 35%into reformer Heat duty tail gas excess CH4 excess CH4 excess CH4
(mol/min) (kW) (kW) (kW) (kW) (kW)1 4.57 1.48 3.66 4.09 4.522 9.13 2.97 7.33 8.19 9.143 13.30 4.44 10.99 12.27 13.554 17.65 5.94 14.67 16.38 18.085 22.77 7.45 18.36 20.50 22.646 26.64 9.03 22.12 24.69 27.257 31.03 10.67 25.96 28.95 31.948 35.41 12.41 29.88 33.30 36.729 39.57 14.24 33.90 37.74 41.5910 45.43 16.98 39.74 44.19 48.64
The carbon thus formed decreases the efficiency and longevity of the catalyst. Table
3.6 shows the increase in conversion of methane with the increase in steam to carbon ratio.
The volume of the reformer was kept constant at 10 litres and the amount of methane into
the reactor was maintained at the maximum flow rate. The steam flow rate was adjusted
according to the steam to carbon ratio. As seen from Table 3.6 the conversion increases as
the ratio increases. Industrial steam reformers often operate at high steam to carbon ratio.
However, a large steam to carbon ratio requires a large volume of steam or water tank. Since
the total volume available in an a automobile is limited, there is a constraint on the steam to
carbon ratio that is feasible for an automotive application. Moreover from the Table 3.6 it
can be observed that the increase in conversion is accompanied by a lot of unreacted steam.
Thus even though the amount of hydrogen in the reformer exhaust stream increases with
increasing steam to carbon ratio, the quality of hydrogen or the mole fraction of hydrogen
decreases. The steam has to be generated, heated to 1000 K and compressed to 5 atm. The
unreacted steam represents a lot of energy wasted. On the other hand decreasing the ratio
below 3:1 increases the coke formation and thereby reduces the amount of conversion and is
also detrimental to the longevity of the catalyst. Hence a steam to carbon ratio of 3:1 has
40
been chosen for this study.
Table 3.6. Effect of varying the steam to carbon ratioSteam to carbon H2 from reformer Methane conversion unreacted
ratio mol/min steam (mol/min)2:1 20.5 67% 9.33:1 24.2 77% 15.94:1 26.5 82% 23.25:1 28.2 86% 30.8
3.3 Design of Fuel Processing Subsystem
In this section, the design and operation of a fuel cell system for a rating of 50 kW is
considered. This value may seem low (50 kW = 67 hp) when compared to power ratings
of today’s internal combustion engines; yet because electric motors deliver maximum torque
at all rpms while internal combustion engines deliver maximum torque only at an optimal
rpm, internal combustion engines operate at a fraction of their nominal power rating while
electric motors operate at their rated power at all times [3].
As described in the previous section, the fuel processor subsystem consists of a train
of three tubular reactors. Each reactor is modeled as an isothermal plug-flow reactor. It
is assumed that no axial mixing or axial heat transfer occurs. Furthermore, the transit
times for all fluid elements through the reactor are assumed to be of equal duration. The
automotive application puts a constraint on the total volume of the reactor train since the
entire system has to fit under the hood of the automobile. In this section, it is assumed
that the maximum allowable volume of the fuel processor subsystem is 100 liters. The
initial focus was on the development of detailed dynamic models for each reactor in the
fuel processing subsystem. A time scale analysis of the reactor operations showed that in
the range of operating conditions for an automobile, the dynamic effects of changes to the
inlet conditions would be damped out by the thermal control system. In particular the gas
passing through the reactors had a typical residence time of the order of seconds. Changes
in the inlet feed to such a reactor presents short term responses, based on the residence
41
time, and long term transients seen in the bed temperature. Bell and Edgar [85] showed
that these effects occur in the time scale of 30 minutes. During practical vehicle operation,
these long term transients are overcome by the thermal control system. Consequently, it is
only necessary to determine the steady state relation between the methane going into the
steam reformer and the hydrogen coming out of the preferential oxidation reactor. Based
on the kinetic models available the optimum conditions for the reactor operation have been
found for the three packed bed reactors individually.
3.3.1 Kinetics of Steam Reformer
The reactions taking place in the SR are given in Eq. 3.6, 3.8, 3.7. Xu and Froment
[24] developed intrinsic rate expressions for the steam reforming of methane, accompanied
by the water gas shift reaction on a Ni/MgAl2O3 catalyst. The following reaction rate laws
were derived:
r1 =
k1
P 2.5H2
(PCH4PH2O −
P 3H2PCO
K1
)
(1 +KCOPCO +KH2PH2 +KCH4PCH4 +KH2OPH2O/PH2)2 (3.21)
r2 =
k2
PH2
(PCOPH2O −
PH2PCO2
K2
)
(1 +KCOPCO +KH2PH2 +KCH4PCH4 +KH2OPH2O/PH2)2 (3.22)
r3 =
k3
P 3.5H2
(PCH4P
2H2O− P 4
H2PCO2
K3
)
(1 +KCOPCO +KH2PH2 +KCH4PCH4 +KH2OPH2O/PH2)2 (3.23)
where r1 is the rate of formation of CO for the reaction represented by Eq. 3.6, r2 is
the rate of formation of CO2 for the reaction represented by Eq. 3.7 and r3 is the rate of
formation of CO2 for the reaction represented by Eq. 3.8. Pi are the partial pressures of the
reactants and Ki are the adsorption coefficients. The adsorption coefficients can be found
using the following relations for the respective species:
Ki = A(Ki)exp
(−∆Hoi
RT
), where i = H2, CO,CH4, H20 (3.24)
The rate constants are given by a similar Arrhenius type equation.
42
kj = A′(kj)exp
(−Ea,jRT
), where j = 1, 2, 3 (3.25)
The equilibrium constants for the three reactions are given by the following expression,
Kj = exp
(Aj +
Bj
T
)where j = 1, 2, 3 (3.26)
The parameter values of the various constants are given in Table 3.7.
These rate equations were then simulated using CHEMCAD [86] and also validated
using MATLAB [87]. The Process Flow Diagram (PFD) in CHEMCAD for the entire fuel
processing subsystem is given in Fig. 3.2.
Figure 3.2. PFD of Fuel Processing Subsystem
43
The KINETIC REACTOR model in CHEMCAD has the capability of rating or designing
plug flow reactors(PFR) and continuous stirred tank reactors (CSTR). Up to 20 simultaneous
reactions are permitted. In the Design mode, the user specifies the required fractional
conversion of a key component and CHEMCAD calculates the required volume of the reactor.
The rating mode allows the user to specify the available volume, and CHEMCAD calculates
the outlet composition and conditions. Either reactor (PFR or CSTR) may be applied to
the liquid or vapor phase. Mixed phase reactors are allowed, but the reactions take place
in only one phase. The PFR is a rigorous model which can simulate tubular reactors. The
basic assumptions of this model are:
1. No axial mixing or axial heat transfer occurs.
2. Transit times for all fluid elements through the reactor, from inlet to outlet, are of
equal duration
The plug flow reactor can be operated in five different thermal modes. isothermal,
adiabatic, specified heat duty, specified temperature profile and specified utility conditions.
The steam reformer and preferential oxidation reactors are simulated as isothermal. The
optimum temperature profile for the water gas shift reactor can be set using the specified
temperature profile option.
To simulate the reactor in MATLAB the following general mole balance equation for a
PFR is utilized:
dFjdV
= rj (3.27)
where V is the volume of the reactor and Fj, rj are the molar feed rate and rate of
reaction respectively. Here j represents the species present in the reactor. It is necessary
to determine the reaction rate for each species in the three reactors using the given rate
equations.
Since the rate expressions for the different reactions are given in terms of the partial
pressures of the reacting species the given molar feed rate of the gases “Fj” should be
44
converted to partial pressures. Using molar feed rates, we can calculate the mole fraction of
the feed which is then used to calculate the partial pressures as follows.
Xj = Fj/FT (3.28)
Pj = XjPT (3.29)
The partial pressures thus obtained are substituted into the rate expressions to calculate
the change in flow rate along the volume of the reactor.
The reaction rates in terms of the individual species involved can be expressed in terms
of the reaction rates represented by Eq. (3.21 - 3.23) as shown below.
rCH4 = −k1
P 2.5H2
(PCH4PH2O −
P 3H2PCO
K1
)
(1 +KCOPCO +KH2PH2 +KCH4PCH4 +KH2OPH2O/PH2)2
−k3
P 3.5H2
(PCH4P
2H2O− P 4
H2PCO2
K3
)
(1 +KCOPCO +KH2PH2 +KCH4PCH4 +KH2OPH2O/PH2)2
(3.30)
rCO =
k1
P 2.5H2
(PCH4PH2O −
P 3H2PCO
K1
)
(1 +KCOPCO +KH2PH2 +KCH4PCH4 +KH2OPH2O/PH2)2
−k2
PH2
(PCOPH2O −
PH2PCO2
K2
)
(1 +KCOPCO +KH2PH2 +KCH4PCH4 +KH2OPH2O/PH2)2
(3.31)
45
rCO2 =
k2
PH2
(PCOPH2O −
PH2PCO2
K2
)
(1 +KCOPCO +KH2PH2 +KCH4PCH4 +KH2OPH2O/PH2)2
+
k3
P 3.5H2
(PCH4P
2H2O− P 4
H2PCO2
K3
)
(1 +KCOPCO +KH2PH2 +KCH4PCH4 +KH2OPH2O/PH2)2
(3.32)
rH2O = −k1
P 2.5H2
(PCH4PH2O −
P 3H2PCO
K1
)
(1 +KCOPCO +KH2PH2 +KCH4PCH4 +KH2OPH2O/PH2)2
−k2
PH2
(PCOPH2O −
PH2PCO2
K2
)
(1 +KCOPCO +KH2PH2 +KCH4PCH4 +KH2OPH2O/PH2)2
−2
k3
P 3.5H2
(PCH4P
2H2O− P 4
H2PCO2
K3
)
(1 +KCOPCO +KH2PH2 +KCH4PCH4 +KH2OPH2O/PH2)2
(3.33)
rH2 = 3
k1
P 2.5H2
(PCH4PH2O −
P 3H2PCO
K1
)
(1 +KCOPCO +KH2PH2 +KCH4PCH4 +KH2OPH2O/PH2)2
+
k2
PH2
(PCOPH2O −
PH2PCO2
K2
)
(1 +KCOPCO +KH2PH2 +KCH4PCH4 +KH2OPH2O/PH2)2
+4
k3
P 3.5H2
(PCH4P
2H2O− P 4
H2PCO2
K3
)
(1 +KCOPCO +KH2PH2 +KCH4PCH4 +KH2OPH2O/PH2)2
(3.34)
The mole balance equations for the species in the steam reformer given in (Eq.3.30 - Eq.
3.34) can now be used to design the steam reformer. The steam reformer is simulated as an
46
Table 3.7. Kinetic parameters for the three reactorsParameter ValueA1 29.3014A2 -4.35369A3 25.225A′(k1) 9.886.1016, [mol.atm0.5/(m3.min)]
A′(k2) 4.665.107, [mol.atm−1/(m3.min)]
A′(k3) 2.386.1016, [mol.atm0.5/(ltr.min)]
A(KH2) 6.209.10−9, [atm−1]A(KCO) 8.339.10−5, [atm−1]A(KH20) 1.77.105
A(KCH4) 6.738.10−4, [atm−1]B1 -26248.4, [K−1]B2 4593.17, [K−1]B3 -21825.28, [K−1]Ea,1 240.1, [kJ/(mol.K)]Ea,2 67.13, [kJ/(mol.K)]Ea,3 243.9, [kJ/(mol.K)]∆H0
H2-82.90, [kJ/(mol.K)]
∆H0CO -70.65, [kJ/(mol.K)]
∆H0H20 +88.68, [kJ/(mol.K)]
∆H0CH4
-38.28, [kJ/(mol.K)]A′(k4) 6.195.108, [mol.atm−2/(m3.min)]
A′(k5) 2.333.1011, [mol.atm−0.4/(ltr.min)]
Ea,WGS 47.53, [kJ/(mol.K)]Ea,PROX 71, [kJ/(mol.K)]
isothermal packed bed reactor operating at 1000K and 5 atm. The feed to the reactor consists
of steam and methane in the ratio 3:1 and some traces of CO, CO2 and H2. As discussed
in Section 3.1.1 the highest expected methane flow rate is 10 mol/min. Since the ratio of
steam:carbon is 3 the total amount of feed is around 40 mol/min. To find the volume of the
reactor necessary to obtain a given conversion an initial volume for the reformer is guessed
and the mole balance equations are integrated numerically in MATLAB for this guessed
volume using the initial conditions specified above. The methane concentration exiting the
reformer is computed and the total methane conversion is calculated. The reactor volume
is iteratively adjusted till the computed conversion is equal to the desired percentage. The
mole fractions of various species as a function of reactor volume are shown in Fig. 3.3(a)
47
and 3.3(b). Fig. 3.3(a) shows the results obtained in CHEMCAD while Fig. 3.3(b) shows
the result obtained in MATLAB. It is observed that the results obtained in MATLAB and
CHEMCAD are the same. Fig. 3.3 represents the concentration profiles for a conversion
of 75%. As seen from Fig. 3.3 the concentration profiles almost reach a plateau for the
75% conversion case. When the reactor is simulated in design mode for volumes greater
than 10 liters there is no further increase in the outlet concentration of hydrogen and this
corresponds to the maximum conversion case. The maximum conversion possible in the
reformer comes to 77.5%. The amount of hydrogen produced for this flow rate is 28 mol/min.
The concentration profiles along the volume of the reactor are shown in Fig. 3.4.
3.3.2 Water Gas Shift Reactor
In the water gas shift reactor the CO in the reformate gas is converted to CO2 by the
reaction shown in Eq. 3.9. Numerous kinetic models have been proposed for this reaction
because of the different catalysts that are being used. Choi and Stenger [26] proposed a
kinetic model based on a Cu/ZnO/Al2O3 catalyst between 120o C and 450o C. The following
empirical rate expression given by Eq. 3.35 for the amount of CO consumed was proposed:
rCO = kPCOPH2O(1− β) (3.35)
where β is the factor of reversible reaction given by
β =PCO2PH2
PCOPH2OKeq
The Keq is the equilibrium constant which can be obtained from thermodynamic properties.
The equilibrium constant for the water gas shift reaction can be calculated using Eq. 3.36.
ln(Keq) =A
T+BlnT + CT −DT 2 − E
T 2− F (3.36)
where the constants are given in Table 3.8
A simpler equation for Keq was given by Moe [88] as shown in Eq. 3.37:
48
Table 3.8. Parameters to calculate the equilibrium constant for the water gas shift reactorA B C D E F
5693.5 1.077 5.44 10−4 1.125 10−7 49170 13.148
Keq = exp
(4577.8
T− 4.33
)(3.37)
There is only one reaction occurring in the water gas shift reactor. We can express the
reaction rate of each species in Eq. 3.9 in terms of the individual species.
rCO = −kPCOPH2O
(1− PCO2PH2
PCOPH2OKeq
)(3.38)
rH2O = −kPCOPH2O
(1− PCO2PH2
PCOPH2OKeq
)(3.39)
rCO2 = kPCOPH2O
(1− PCO2PH2
PCOPH2OKeq
)(3.40)
rH2 = kPCOPH2O
(1− PCO2PH2
PCOPH2OKeq
)(3.41)
Fig. 3.5 shows the effect of temperature on the equilibrium conversion of carbon monoxide
inside the water gas shift reactor. It is observed that at higher temperatures, the initial
reaction rate is very fast; however the equilibrium conversion is low. Conversely, at low
temperature, the reaction rate is slow but the equilibrium conversion is high.
49
To minimize the total volume necessary to achieve at least 90% conversion of carbon
monoxide, the water gas shift reactor is split into two zones: a high temperature zone
where the reaction rate is high and a low temperature zone where the conversion is high.
Simulations at 700 K indicate that an equilibrium conversion of 67% is achieved in a one liter
reactor. This is modeled as the high temperature zone of the water gas shift reactor. The
effect of changing temperature in the low temperature zone on the total volume to achieve
an overall conversion of 90% is shown in Fig. 3.6. The volume required for this conversion
decreases with increase in temperature from 440 K to 490 K. Increase in temperature beyond
490 K increases the volume again because of the conversion limitation. In fact if the
temperature is increased beyond 500 K we cannot obtain 90% conversion. It is observed
from Table 3.9 that operating the low temperature zone at 490 K results in a total volume
of about 41 liters. While it is possible to reduce the total volume further by utilizing a
continuously decreasing temperature profile, this optimal temperature profile calculation
was not attempted given the operational difficulties in experimentally implementing such a
temperature profile.
Table 3.9. Volume required for 90% conversion of CO in LTS reactor for differenttemperatures
Temperature Volume440 K 101.7 Ltrs450 K 78.92 Ltrs460 K 63.03 Ltrs470 K 51.43 Ltrs480 K 43.89 Ltrs490 K 40.8 Ltrs500 K 50.7 Ltrs
3.3.3 Preferential Oxidation Reactor
The following two oxidation reactions occur in the preferential oxidation reactor.
CO +1
2O2 → CO2, ; ∆Ho
298 = −283kJ/mol (3.42)
50
H2 +1
2O2 → H2O; ∆Ho
298 = −242kJ/mol (3.43)
The catalysts for CO selective oxidation are many and new catalysts have been found
recently. The most commonly used formulation is platinum or other precious metals on
alumina, at temperatures around 200oC. Also, gold based catalysts show good performance
at lower temperatures around 100oC which is close to PEM fuel cell operating temperatures.
Several common transition metals have been investigated to find a more economical CO
selective oxidation catalyst. Catalyst formulation, characterization, and activity and selec-
tivity of CO are few of the factors that determine the performance of the catalyst. Kahlich
et al. [28] derived a kinetic expression by introducing a process parameter λ which is the
oxygen in excess with respect to the amount of oxygen required for the oxidation of CO to
CO2.
λ =2CO2
CCO=
2PO2
PCO(3.44)
The analytical rate expression is given by
rCO = k1P0.42O2
λ0.82 (3.45)
From Eq. 3.45 we see that the reaction order with respect to CO and O2 is -0.4 and 0.82
respectively. In addition to the oxidation of the CO some hydrogen is also oxidized. The
rate of hydrogen oxidized can be found from the selectivity (S) of the catalyst given by Eq.
3.46.
S =rCO
rCO + rH2
(3.46)
For the catalyst used, Kahlich et al. [28] found out that even though the rate changes
with temperature, but the selectivity does not change and is constant at 0.4, i.e.,
S =rCO
rCO + rH2
= 0.4
51
Which implies that
⇒ rH2 = 1.5rCO
The feed to the preferential oxidation reactor consists of the hydrogen rich gas from the WGS
reactor and air. The oxygen in air is feeded at twice the amount of CO coming out of the
WGS reactor. A reactor volume of 0.35 liters was sufficient to reduce the carbon monoxide
to the desired level of 100 ppm.
3.3.4 Varying Feed Rates of Methane
In the previous subsections, the reactor train was designed assuming that the feed rate of
methane was 10 mol/min. In this subsection, the effect of change in feed rate on the overall
hydrogen produced, using the same reactor train, was studied. The methane feed rate to the
reformer was varied between 1 mol/min and 10mol/min. The corresponding steam flow rate
was adjusted so that the steam to methane ratio was maintained at 3. The relation between
hydrogen exiting the preferential oxidation reactor and the methane entering the reformer
is shown in Fig. 3.7. It is observed that the steady state hydrogen production rate varies
linearly with the methane feed and can be represented by Eq. 3.47 by fitting a straight line
through the data points in Fig. 3.7 as:
NH2 = 3.12NCH4 (3.47)
From the Eq. 3.47 we can infer that most of the methane reacting in the reformer is
because of the reaction represented by Eq. 3.6 as 3 moles of H2 are produced for every mole
of CH4 in this reaction. Even though there is a subsequent increase in the number of moles
of hydrogen as it passes through the WGS shift reactors some of the hydrogen is oxidized
in the PROX reactor. Hence, even though the flow rate is changed, the ratio of methane to
hydrogen remains at approximately the same value. Even though the relationship between
the amount of hydrogen coming out of the fuel processor and the amount of methane fed
to the reactor has been established for an overall relation between the methane fed to the
reactor and the power generated in the fuel cell stack, it is still necessary to address the issue
52
of how much power is generated per mole of hydrogen. This is addressed in detail in the
next chapter.
53
Figure 3.3. The concentration profiles obtained as a function of the reactor volume (a)CHEMCAD results (b)MATLAB results
54
0 0.002 0.004 0.006 0.008 0.010
5
10
15
20
25
30
35
Volume(m3)
flo
wra
te(m
ol/m
in)
H2
COCO
2CH
4H
2O
Figure 3.4. Concentration profiles along the volume of the reformer.
55
0 0.1 0.2 0.3 0.4 0.5 0.60
10
20
30
40
50
60
70
80
90
100
VOLUME(m3)
CO
NV
ER
SIO
N
400 K450 K500 K550 K600 K650 K700 K
Figure 3.5. Conversion of CO inside the WGS reactor along the volume of the reactor fordifferent temperatures
56
10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
90
100
Volume(Litres)
Co
nve
rsio
n
440450460470480490500
Figure 3.6. Volume required for 90% conversion of CO inside the low temperature WGSreactor for different temperatures
57
1 2 3 4 5 6 7 8 9 10
5
10
15
20
25
30
Methane feed rate (mol/min)
Hyd
roge
n P
rodu
ctio
n (m
ol/m
in)
Figure 3.7. Effect of change in methane flow rate on the hydrogen production
58
CHAPTER 4
FUEL CELL DESIGN
4.1 Design of Power Generation Subsystem
The power generation system consists of a PEM fuel cell that utilizes the hydrogen coming
from the fuel processing subsystem and converts it into electricity that is used to power an
electric motor for the automobile. In addition to the fuel cell, there is a battery backup that
the electric motor switches to when the fuel cell is unable to deliver the necessary hydrogen.
This battery backup is essential because significant load transitions occur frequently as a
result of acceleration, hilly conditions, highway cruising etc.
In this chapter the focus will be on the design of the fuel cell system. The number of
cells in the stack and the cross sectional area of the cell and the operating voltage of the fuel
cell are some of the design issues that have to be answered. The system should be able to
produce a maximum power output of 50 kW (67 hp). To design a fuel cell system a model
that relates the power output to the flow rate of hydrogen into the fuel cell is needed. Based
upon the voltage current characteristics of the fuel cell a linear model and nonlinear model
are presented. These models will be used for design, and a relationship between the fuel
flow rate into the fuel processing system and the power output of the fuel cell system will
be obtained.
4.1.1 Linear Fuel Cell Model
A fuel cell is a device that converts chemical energy to electrical energy. The electro-
chemical reactions occurring at the anode and cathode of a PEM fuel cell are given in Eq.
4.1 and Eq. 4.2 respectively.
Anode Reaction
59
H2 → 2H+ + 2e− (4.1)
Cathode Reaction
1
2O2 + 2H+ + 2e− → H2O (4.2)
The best attainable performance can be obtained from the thermodynamics of the system
using the Gibb’s free energy. The reversible standard potential Eo for the above cell reaction
is 1.23 Volts per mole of hydrogen at 25 oC, as determined from the change in the Gibb’s free
energy. The actual voltage depends upon the concentration of the species and temperature
at which the fuel cell is operating. The concentration dependence is given by the Nernst
equation as shown in Eq. 4.3.
E = Eo +
(RT
nF
)ln
(PH2)(PO2)0.5
PH2O
(4.3)
where PH2 , PO2 , PH2O are the partial pressures of the individual species, R is universal gas
constant, n is the number of electrons involved in the reaction and F is Faraday’s constant.
Since the fuel cell is generally operated at 80 oC we have to apply the temperature correction
for the standard reversible potential which is given by .
Eo2 − Eo
1 =∆S
T2 − T1
(4.4)
where Eo2 , Eo
1 are the reversible standard potentials at temperatures T2 and T1 respectively
and ∆S is the change in entropy.
When a load is applied to the cell current flows. The total current produced by the
cell in a given amount of time is directly proportional to the amount of products formed or
reactants consumed as expressed by Faraday’s Law,
I =mnF
sMt(4.5)
where I is the current, m is the mass of product formed or reactant consumed, s is the
stoichiometric constant which is defined as positive for products and negative for reactant
species. M is the molecular weight and t is time elapsed.
The current generated by the fuel cell is directly proportional to the hydrogen consump-
tion. The voltage generated by the cell is dependent on the current produced and can be
60
calculated for a given temperature, pressure and cell concentrations. Examination of the
results from Nguyen and White [49] show that a simple empirical model between current
density, i and voltage, V can be written as
V = 0.9− 0.4i (4.6)
This results in the following power generation model:
P = NA[0.9− 0.4i]i (4.7)
where N is the number of cells in the fuel cell stack and A is the active cell area. The current
density i can be written in terms of the flow rate of hydrogen as:
i = 2FεNH2 (4.8)
where ε is the conversion of hydrogen inside the fuel cell. It is assumed that 90% of hydrogen
is converted inside the fuel cell. The flow rate of hydrogen can be related to the flow rate of
methane into the reformer from Eq. 4.9 obtained in the previous chapter as follows:
NH2 = 3.12NCH4 (4.9)
The above expressions can now be used to correlate the power output to methane flow
rate. Fig. 4.1 shows this relation. It is observed that a methane flow rate of 9 mol/min
is needed to generate a power upto 50 kW. This value is close but slightly lower than the
hydrogen flow rate calculated based on the lower heating value of hydrogen in Section 3.1.1
which was 10 mol/min. This is because of the difference in hydrogen conversion assumed
(80% conversion was assumed in Section 3.1.1 whereas 90% conversion was assumed here).
This curve can be used to compute the steady state methane flow rate for a given power
requirement.
The fuel cell polarization curve is linear only for some ranges of the fuel cell operation. At
low and high current densities the voltage drop is not linear. Since the fuel cell will operate
a these high current densities especially when it is in the maximum power demand range, it
is important to take into consideration the nonlinear behavior.
61
Figure 4.1. Methane feed Vs Power produced
Figure 4.2. Representative fuel cell performance curve at 25 oC and 1 atm
62
4.1.2 Nonlinear Fuel Cell Model
A typical voltage-current polarization curve is shown in Fig. 4.2 [29]. The drop in voltage
as seen in the figure are due to different limitations that exist as described below:
Kinetic Limitations
This voltage loss is due to the slow reaction kinetics at the cathode and the anode and
is also called activation polarization (ηact,c and ηact,a). Activation polarization is due to
the activation energy barrier between the reacting species and is primarily a function of
temperature, pressure, concentration and electrode properties. Kinetic limitations dominate
the low current density regions of the polarization curve, where deviations from the
equilibrium conditions are small. At these conditions the reactants are plentiful; hence
there is very little mass transfer limitation. The current density is so small that the ohmic
losses defined as the product of the current density and resistance (iR) are also negligible .
The Tafel Equation [78] given by Eq. 4.10 represent the exponential fall in voltage in low
current density regions
ηact = Blog | i | −A (4.10)
where ηact is the voltage loss due to the activation polarization (mV), i is the current density
and constants A and B are kinetic parameters. Even though the activation polarization is
present at both the anode and cathode as seen in Fig.4.2 the cathode losses are much larger
than the anode losses and are often neglected.
Ohmic Limitations
There is resistance to the flow of electrons in the electrolyte and also through the
electrodes. The performance loss due to this resistance is called ohmic polarization (ηohm).
Ohmic polarization is given by the Ohm’s Law (V = IR), where i is the current and R is
the resistance. These losses dominate the linear portion of the current-density polarization
curve as shown in Fig. 4.2. These losses can be reduced by improving the ionic conductivity
of the solid electrolyte separating the two electrodes.
63
Transport Limitations
Transport limitations or Concentration polarization (ηconc,c and ηconc,a) occurs when a
reactant is consumed on the surface of the electrode, thereby forming a concentration gradient
between the bulk gas and the surface. Transport mechanisms within the gas diffusion layer
and electrode structure include the convection/diffusion and/or migration of reactants and
products in and out of the catalyst sites at the anode and cathode. The mass transfer limiting
region of the current-voltage polarization curve is apparent at high current density. Here,
increasing current density results in depletion of the reactants immediately adjacent to the
electrode. When the current is increased to a point where the concentration at the surface
falls to zero, a further increase in current is not possible. The current density at which this
happens is called the limiting current density (ilim). If the current density is lower than ilim
there is no concentration losses but for current densities greater than (ilim the concentration
or transportation losses cause rapid decrease in the performance of the fuel cell.
Pukrushpan Model
In this section the model developed by Pukrushpan and coworkers [59] will be summa-
rized. The actual cell voltage at any given current density is given by Eq. 4.11, which is
obtained by subtracting the activation, ohmic and concentration losses from the reversible
potential as expressed below.
νfc = E − νact − νohm − νconc (4.11)
Where E is the open circuit voltage and νact, νohm and νconc are activation, ohmic and
concentration overvoltages, which represent losses due to various physical or chemical factors
discussed in the starting of this section. The open circuit voltage is calculated from the Nernst
equation (Eq. 4.3) which is rearranged and the values of the various constants substituted
to get Eq. 4.12:
E = 1.229− 8.5× 104(Tfc − 298.15) + 4.3085× 10−5Tfc
[ln(PH2)− 1
2ln(PO2)
](4.12)
where the fuel cell temperature Tfc is in K, and reactant partial pressures PH2 and PO2
are expressed in atm. The relationship between the activation overvoltage and the current
density is described by the Tafel equation [89] which is approximated by:
64
νact = ν0 + νa(1− ec1i) (4.13)
where νact is the activation potential, i is the current density, ν0, νa and c1 are empirical
parameters determined from experimental data. The activation overvoltage depends on
temperature and oxygen partial pressure. The values of ν0, νa and c1 and their dependency
on oxygen partial pressure and temperature can be determined from nonlinear regression of
experimental data. The ohmic overvoltage, νohm, arises from the resistance of the polymer
membrane to the transfer of protons and the resistance of the electrodes and collector plates
to the transfer of electrons. The voltage drop is thus proportional to the stack current
density:
νohm = i.Rohm (4.14)
The resistance, Rohm, depends strongly on membrane humidity and cell temperature. The
ohmic resistance is proportional to membrane thickness tm and inversely proportional to the
membrane conductivity, σm given by Eq. 4.15:
Rohm =tmσm
(4.15)
The membrane conductivity is a function of membrane humidity and temperature as shown
in Eq. 4.16
σm = (b11λm − b12)exp
[b2
(1
303− 1
Tfc
)](4.16)
where λm represents the membrane water content, of tm, b11 and b12 are empirical parameters
which represent the characteristics of the membrane used. For this study, the characteristics
of Nafion 117 membrane were used [59]. The λm varies between 0 and 14, which corresponds
to relative humidity (RH) of 0% and 100%, respectively.
The concentration overvoltage, νconc, results from the increased losses at high current density,
e.g., a significant drop in reactant concentration due to both high reactant consumption and
head loss at high flow rate. Eq. 4.17 is used to calculate the concentration losses and is
given by
νconc = i
(c2
i
imax
)c3(4.17)
where c2, c3 and imax are empirical constants that depend on temperature and reactant
partial pressure. The coefficients are determined using nonlinear regression with polarization
65
data from an automotive propulsion-sized PEM fuel cell stack. By assuming that the data
is obtained from the fuel cell stack operating under a well-controlled environment, where
cathode gas is fully humidified and oxygen excess ratio( ratio of oxygen supplied to oxygen
reacted) is regulated at 2, the pressure terms in the activation and concentration overvoltage
terms can be related to oxygen partial pressure, PO2 , and saturated vapor pressure, Psat.
Eq. 4.18 - Eq. 4.20 represent the dependence of parameters ν0, νa, c2 on temperature
and oxygen partial pressures. Table 4.1 lists the other empirical parameters obtained by
regression analysis.
ν0 = 0.279− 8.5× 104(Tfc − 298.15)
+ 4.3085× 10−5Tfc
[ln
(Pca − Psat1.01325
)+
1
2ln
(0.1173(Pca − Psat)
1.01325
)]
(4.18)
νa = (−1.618× 10−5Tfc + 1.618× 10−2)
(PO2
0.1173+ Psat
)2
+ (1.8× 10−4Tfc − 0.166)
(PO2
0.1173+ Psat
)
+ (−5.8× 10−4Tfc + 0.5736)
(4.19)
Table 4.1. Regression fit data obtained from the Pukrushpan modelParameter Value
c1 10c3 2imax 2.2b11 0.05139b12 0.00326b2 350
66
c2 =
ifPO2
0.1173+ Psat < 2atm,
(7.16× 10−4Tfc − 0.622)(
PO2
0.1173+ Psat
)+ (−1.45× 10−3Tfc + 1.68)
else
(8.66× 10−5Tfc − 0.068)(
PO2
0.1173+ Psat
)+ (−1.6× 10−4Tfc + 0.54)
(4.20)
Using this model the pressure and humidity dependence of the fuel cell can be clearly
illustrated. Fig. 4.3 shows the dependence of the fuel cell voltage on the humidity of
the membrane for two different relative humidity values 50% and 100%. As the humidity
decreases the performance of the fuel cell falls down. The electrolyte membrane should be
saturated with water to allow the passage of the ions through the membrane. The absence of
water increases the resistance to the flow of ions and thereby increases the ohmic resistance
hence the drop in voltage. However at high humidity there is a danger of the fuel cell
membrane getting flooded but this aspect is not included in this model. Fig. 4.4 is the plot
for different pressures 1 bar , 2 bar, 3 bar for a constant temperature and relative humidity.
As we increase the pressure the curve shifts above i.e. for the same current density at higher
pressures you will have a greater voltage and hence greater power output is observed.
As the pressure is increased not only is the curve shifted up but also the slope of the curve
decreases, i.e., for a large range of the current densities the voltage remains nearly constant.
The increase in performance for pressures greater than 5 bar is very low and for pressures
higher than this a lot of the fuel cell power produced will be used up in compressing the gases
to higher pressure without a substantial increase in performance. For a fuel cell operating
at 353 K with air fed to the cathode at 5 bar and assuming a constant relative humidity of
100%, the empirical constants in Eq. 4.18 - Eq. 4.20 can be calculated. Substituting these
values and other empirical values given in Table 4.1 into Eq. 4.11 we can obtain an empirical
relationship between the current density and voltage.
V = 0.6405 + 0.3325e−10i − 0.03036i− 0.00355i3 (4.21)
This relation is plotted in Fig. 4.5. It should be noted that for these conditions that
there is a sharp drop-off in cell voltage at small current densities but a very flat region to the
polarization curve with cell voltages being nearly 0.6 V over a wide range of current densities.
This is desirable characteristic as this produces a power density that varies linearly with
current density, as seen in Fig. 4.6. For current densities less than 2 A/cm2 the polarization
67
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Current Density( Amp/cm2)
Vol
tage
(vol
ts)
50% RH100% RH
Figure 4.3. Effect of relative humidity on the fuel cell polarization curve.
curve is still in the ohmic losses zone and the concentration losses or transportation losses
have not yet become significant. Hence the voltage does not drop sharply at higher current
densities for this curve.
The design objective is to calculate the number of cells (Nc) and cross sectional area of
the fuel cell Ac for a 50 kW fuel cell stack. The number of cells in the stack determine
the total voltage (Vt = NcVc) and the cross sectional area of the cell gives the total current
(I = iAc). The power from the fuel cell which is the product of the current and voltage is
given by the following equation:
P = VtI = (NcVc)(iAc) (4.22)
From Eq. 4.21 the voltage for a particular current density can be obtained. As seen from
Fig. 4.6 the voltage stays around 0.6 V and for a current density of 1.15 A/cm2 the cell
68
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.2
0.4
0.6
0.8
1
1.2
Vol
tage
(vol
ts)
Pca=1 barPca=2 barPca=3 bar
Current Density (Amp/cm2)
Figure 4.4. Pressure dependence of the fuel cell polarization curve.
voltage is exactly 0.6 V. Hence in Eq. 4.22 we now know the values of Vc and i, but we still
need to calculate Nc, Ac. If one desires a system with a 300 V output [59], since we know
the voltage of each cell we can calculate the total number of cells as 500 cells in series. Since
the voltage is 500 V and the required power is 50 kW the current required is 166.67 A. Since
the current density is fixed the cross sectional area or active cell area is calculated from Eq.
4.22 to be 145 cm2. The required hydrogen flow per cell is calculate from
I = 2FεNH2 = 2(3.12)FεNCH4 (4.23)
where the conversion ε is assumed to be 90%, which yields a maximum required hydrogen
flow of 0.001 mol/s/cell. This corresponds to a total required methane flow of 9.2 mol/min.
The power curve for the combined fuel processor and fuel cell stack system is shown in Fig.
4.7. To construct this curve a methane flow rate was selected and the resultant hydrogen flow
69
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Current density(Amp/cm2)
Vo
ltag
e(V
olt
)
Figure 4.5. Polarization curve for a fuel cell operating at 353 K, pressure 5 bar and relativehumidity 100%.
from the fuel processor was calculated using Eq. 4.9. Using Eq. 4.23, the cell current was
then determined. With the cell area specified at 145 cm2, the current density is calculated.
The stack power is then calculated using Eq. 4.21. The variation of power output as a
function of the current density is shown in Fig. 4.6. Table 4.2 show the calculated values of
the hydrogen flow rate per cell, current density, voltage and power output as the methane
flow rate is varied from 0 to 10 mol/min. The overall power output versus methane flow into
the reformer is shown in Fig. 4.7.
70
0 0.5 1 1.5 20
0.2
0.4
0.6
0.8
1
Current density(Amp/cm2)
Po
wer
den
sity
(W/c
m2 )
Figure 4.6. Power density vs. current density
0 1 2 3 4 5 6 7 8 9 100
10
20
30
40
50
60
Methane flowrate(mol/min)
Sta
ck P
ow
er(k
W)
Figure 4.7. Effect of Methane Flow on Power Generated
71
Table 4.2. Effect of varying the methane flow rate on the power outputMethane Hydrogen Hydrogen Current Curr-Den Voltage Powermol/min mol/min mol/sec/cell Amp Amp/cm2 volts kW
0.00 0.00 0.00 × 10−3 0.00 0.00 0.97 0.000.20 0.62 0.02 × 10−3 3.61 0.02 0.90 1.620.40 1.25 0.04 × 10−3 7.22 0.05 0.84 3.040.60 1.87 0.06 × 10−3 10.84 0.07 0.80 4.310.80 2.50 0.08 × 10−3 14.45 0.10 0.76 5.491.00 3.12 0.10 × 10−3 18.06 0.12 0.73 6.611.20 3.74 0.12 × 10−3 21.67 0.15 0.71 7.701.40 4.37 0.15 × 10−3 25.29 0.17 0.69 8.771.60 4.99 0.17 × 10−3 28.90 0.20 0.68 9.821.80 5.62 0.19 × 10−3 32.51 0.22 0.67 10.872.00 6.24 0.21 × 10−3 36.12 0.25 0.66 11.933.00 9.36 0.31 × 10−3 54.19 0.37 0.64 17.254.00 12.48 0.42 × 10−3 72.25 0.50 0.63 22.665.00 15.60 0.52 × 10−3 90.31 0.62 0.62 28.066.00 18.72 0.62 × 10−3 108.37 0.75 0.62 33.417.00 21.84 0.73 × 10−3 126.43 0.87 0.61 38.678.00 24.96 0.83 × 10−3 144.50 1.00 0.61 43.839.00 28.08 0.94 × 10−3 162.56 1.12 0.60 48.8810.00 31.20 1.04 × 10−3 180.62 1.25 0.60 53.81
72
CHAPTER 5
ADAPTIVE CONTROLLER DESIGN
It is necessary for the fuel cell vehicle design a control system which can track the power
demand or power requested from the fuel cell. The set point for this control system is the
power demand which varies with time, depending on driving objectives and road conditions.
A conventional controller with fixed parameters (e.g. PID controller) designed for handling
city driving may not work for highway driving or for uphill driving. On the other hand a
controller which can adapt or change its controller settings online depending on the power
profile is desirable for automotive applications. A model reference adaptive controller is one
such controller which handles trajectory tracking problems even in the presence of parametric
and model uncertainty.
This chapter is divided into two parts. In the first part the design of a model reference
adaptive controller (MRAC) is illustrated and implemented on the PEM fuel cell. A
linearized model of the PEM fuel cell is obtained from the nonlinear model proposed by
Pukrushpan et al. [59] using standard system identification principles. The controller is
designed for a realistic power profile. The controller is then implemented on a different
power profile to demonstrate the adaptive nature of the MRAC controller. The controller
will be implemented on the original nonlinear model and the performance of the MRAC will
be compared with the PID controller. In the second part the adaptive controller design is
extended to a phosphoric acid fuel cell (PAFC). The model proposed by Rengaswamy et al.
[90] will be used for this purpose. This example deals with disturbance rejection. The aim
is to maintain the voltage of PAFC at a constant value in the presence of disturbance due
to the fluctuations in power demand.
73
Figure 5.1. Model Reference Adaptive Control
5.1 Model Reference Adaptive Controller
The objective of MRAC is to find the feedback control law that changes the structure
and dynamics of the plant so that its Input/Output (I/O) properties are exactly the same as
those of a reference model. The structure of a MRAC scheme for a Linear Time Invariant,
Single Input Single Output plant is shown in Fig. 5.1. Here Wm(s) is the transfer function
of the reference model, r(t) a given reference input signal, ym(t) the output of the reference
model and y(t) is the plant output. The feedback controller denoted by C(θ∗c ) is designed so
that all signals are bounded and the closed-loop plant transfer function from r to y is equal
to Wm(s). θc is the set of parameters that are adaptively estimated. This transfer function
matching guarantees that for any given reference input r(t), the tracking error e = y − ym,
which represents the deviation of the plant output from the desired trajectory ym, converges
to zero with time.
5.1.1 Design Procedure
Consider a first order dynamic system that can be represented as
V = aV + bu (5.1)
where V represents the system state, a and b are constants, u represents the control effort.
The reference model is chosen as
Vm = −amVm + bmr (5.2)
where r is the setpoint and am, bm are positive constants known a priori.
74
The control effort u is given by
u = −kV + lr (5.3)
Substituting the above equation into Eq. 5.1 yields
V = (a− bk)V + blr (5.4)
The objective is to find a feedback control law so that the plant I/O properties are exactly
the same as those of the reference model. In order to achieve this the error is defined as the
difference between the plant output and the reference model output.
e = V − Vm (5.5)
By taking the time derivative of e:
e = V − Vm = (a− bk)V + blr + amVm − bmr (5.6)
Eliminating Vm from Eq. 5.6 by substituting Vm = V − e we have
e = −ame+ (am + bk − a)V + (bl − bm)r (5.7)
For the adaptive controller an adaptation mechanism for k and l has to be developed such
that the error is minimized. Let the optimal values of k and l be represented by k∗ and l∗.
If we set:
k∗ =a− amb
l∗ =bmb
(5.8)
then, e will decay exponentially in Eq. 5.8. Since a and b are not precisely known, the
optimal values k∗ and l∗ cannot be calculated exactly. Thus, we start with an initial guess
k and l for the adaptive controller.
k = k − k∗
l = l − l∗ (5.9)
75
Now Eq. 5.7 can be rewritten as
e = −ame+ bkV + blr (5.10)
A Lyapunov candidate function is chosen so that it is positive definite and contains each of
the variables in Eq. 5.10. This equation is given by
V (e, k, l) =1
2e2 +
b
2γ1
k2 +b
2γ2
l2 (5.11)
where γ1 and γ2 are tuning parameters. The derivative of Eq. 5.11 gives
V = −ame2 +k
γ1
[γ1bV e+ b ˙k] +l
γ2
[γ2bre+ b ˙l] (5.12)
To ensure stability, Eq. 5.12 must be negative definite (1996). The only way to ensure
this is to set the second and third term of Eq. 5.12 to zero. This produces the adaptive law
˙k = −γ1eV
˙l = −γ2er (5.13)
where γ1, γ2 are tuning parameters. The MRAC control law Eq. 5.13 can be implemented
as shown in Fig. 5.2. The initial conditions l(0); k(0) are chosen by an a priori guess of the
unknown parameters k∗ and l∗ respectively.
5.1.2 Adaptive Controller with Deadzone
In cases were there are noisy outputs it is necessary to add some robustness to the
controller. In the presence of unmodeled disturbances there are several instability mecha-
nisms which have to be addressed like parameter drift, high gain instability and instability
resulting from fast adaption. Ioannou and coworkers [91] addressed the issue of instability
in the presence of unmodeled dynamics and bounded disturbances. Different methods like
leakage modification, parameter projection and deadzone are used as modifications to the
Lyapunov approach to ensure stability. To avoid phenomena such as bursting (i.e., large
errors relative to the level of the disturbance at steady state and over short intervals of
time) that may arise in the case of the leakage modification and projection, deadzone is
used. Another important property of the adaptive law with deadzone is that it guarantees
parameter convergence [72].
76
Figure 5.2. Implementation of Model Reference Adaptive Control
The Lyapunov design outlined above is modified such that the values of ˙k, ˙l remain same
as Eq. 5.13 as long as the disturbance is bounded. If the error e is less than the bounded
disturbance ˙k, ˙l equated to zero.
˙k = 0 |e| ≤ d0/am (5.14)
˙l = 0 |e| ≤ d0/am (5.15)
In the above equations, d0/am represents a bounded disturbance. The principal idea behind
the dead zone is to monitor the size of the estimation error and adapt only when the
estimation error is large relative to the modeling error. In essence, for some bounded
disturbance d0, the adaptation law can be turned on or off depending on the value of the
error. Moreover, the practical benefit for implementing a deadzone is that this procedure
saves actuator energy because the controller is not always in use.
5.2 PID Controller Design
Proportional integral derivative controllers or in short PID controllers are the most
ubiquitous controllers available in the process industry. In Feedback control the output
of the plant is fed back and compared with the setpoint and the deviation of the system
77
Table 5.1. Zeigler-Nichols Controller SettingType of Control Controller Kc τI τD
Proportional Kc 0.5Ku
Proportional Integral(PI) K(
1 + 1τIs
)0.45Ku
Pu1.2
Proportional Integral Derivative(PID) K(
1 + 1τIs
+ τDs)
0.6KuPu2
Pu8
from the setpoint is defined as error. In a proportional controller the gain in the controller
is set proportional to this error, the main drawback of the proportional controller is that it
is difficult to reach the steady state and there is always some offset or bias. This bias can
be removed by increasing the gain but it is not advisable to operate the system at high gain
especially when the set point has lot of fluctuations. So to overcome this problem we add the
integral action we removes the bias and reaches steady state by adding derivative control we
can reach steady state faster. Consider the design of a PID controller for the plant shown
in Fig. 5.3. A PID controller takes the form,
D(s) = K
(1 +
1
τIs+ τDs
)(5.16)
where (K,τI ,τD) denote the proportional gain, integral time and derivative time, respectively.
The parameters for PID controller are derived using the Ziegler Nichols method. This method
gives a first estimate of the different gains as shown in the Table 5.1. Where Ku is the ultimate
gain which would cause the system to be on the verge of stability and Pu is the ultimate
period and is defined as the period of the sustained cycling that would occur if the ultimate
gain Ku is used [92].
5.3 Application to PEM Fuel cell
In this section the design principles for an adaptive controller will be outlined and
implemented on PEM fuel cell control problem. The performance of this controller will
be performed to that of a conventional PID controller. The fuel cell should be able to supply
the requested power demand from the automobile and an adaptive controller will be designed
for this purpose.
78
Figure 5.3. PID controller Design
5.3.1 System Identification
The fuel cell power generation involves complex electrochemical, mass and heat transport
phenomena and hence there was a lot of emphasis on steady state modeling of fuel cells
initially and there were very few dynamic models. Pukrushpan [59] developed a dynamic
nonlinear model of a fuel cell stack. It is assumed that the stack is well designed so that
all the cells in the stack perform similarly, i.e., by analyzing the polarization curve of a
single cell, the stack performance can be estimated. The power from the fuel cell which is a
function of the current and voltage is given by the following equation:
P = VstI = (NcVc)(iAc) (5.17)
where P is the power produced by the fuel cell, Vst is the voltage of the stack which is the
product of the number of cells Nc and the individual cell voltage Vc, I is the current drawn
from the cell and is the same for each cell and depends on the area of cross section Ac, i is
the current density.
The reversible standard potential Eo for the above cell reaction is 1.23 V at 25 oC as
determined from the change in the Gibb’s free energy. The actual voltage depends upon
the concentration of the species and temperature at which the fuel cell is operating. The
concentration dependence is given by the Nernst equation.
79
E = 1.229− 8.5× 104(Tfc − 298.15) + 4.3085× 10−5Tfc
[ln(PH2)− 1
2ln(PO2)
](5.18)
where the fuel cell temperature Tfc is in K, and reactant partial pressures PH2 and PO2 are
expressed in atm. The actual cell voltage at any given current density is given by Eq. 5.19,
which is obtained by subtracting the activation, ohmic and concentration losses from the
reversible potential as expressed below.
νfc = E − νact − νohm − νconc (5.19)
where E is the open circuit voltage and νact, νohm and νconc are activation, ohmic and
concentration overvoltages. These losses are a function of the current density, pressure,
membrane humidity and also on the type of membrane and are represented by the empirical
equations given in Chapter 4. Using this model we can calculate the power produced by the
fuel cell based on the voltage current characteristics. For a given current demand the voltage
is calculated using Eq. 5.19 and thereby the power output of the fuel cell. Input output data
obtained from the nonlinear model was used for system identification purposes. For system
identification the system was linearized for a current demand of 100A which results in a stack
voltage of 247 Volts. A step input of 20 A was given and the voltage output was obtained as
shown in the figure below. At these operating conditions (Current = 100A, Voltage = 247V)
data from the nonlinear model was used to fit a second order model between the current
demand and the voltage produced by the fuel cell stack. The transfer function Gp is given
as
Gp =−390.78
s2 + 27.291s+ 2068.8(5.20)
When there is an increase in current demand the operating current density of the fuel cell
increases. From the fuel cell polarization curve [84] it is evident that with increase in current
density there is a decrease in voltage. Hence any increase in current demand results in a
decrease in the voltage of the stack and the negative sign in the numerator indicates this
relationship. The power output from the fuel cell is defined as the product of the current
and the voltage produced by the stack.
80
0 1 2 3 4 5 6 7 8 9 10240
242
244
246
248
VO
LTA
GE
(V
)
0 1 2 3 4 5 6 7 8 9 10100
105
110
115
120
CU
RR
EN
T (
A)
TIME−SECONDS
Figure 5.4. System Identification using a step input in current
5.3.2 Realistic Power Profile
To get a realistic power vs time profile the power profile for a small car was obtained
from an existing speed vs time profile using the ADVISOR software package [93]. The Urban
Dynamometer Driving schedule (UDDS), which is designed for light duty vehicle testing in
city driving conditions was used. The speed versus time and the corresponding force versus
time profiles are shown in Fig. 5.5.
The force profile has both positive and negative values denoting the acceleration and
deceleration phases of the car. The power requested by the engine is a product of the
speed and force. During acceleration the force is positive and since the speed is always
positive the power demand is positive and this power demand should be met by the power
generation system. During deceleration the force and hence the power requested is negative
and since this is handled by the braking system the power requested from the power
generation subsystem is zero. Hence the negative power demand is equated to zero and
the corresponding power profile is shown in Fig. 5.6. As seen from this figure the power
81
0 200 400 600 800 1000 1200 14000
10
20
30
40
50
60
SP
EE
D (
mile
s/hr
)
0 200 400 600 800 1000 1200 1400−2000
−1000
0
1000
2000
3000
FO
RC
E (
N)
TIME (SECONDS)
Figure 5.5. Speed Vs time profile and Force Vs time profile for UDDS
0 200 400 600 800 1000 1200 14000
5
10
15
20
25
30
TIME (SECONDS)
PO
WE
R(k
W)
Figure 5.6. Power Vs time profile for UDDS
82
profile changes continuously with time and a controller should be designed such that it follows
the trajectory of the power profile as closely as possible.
5.3.3 Controller Simulation
Two different types of controllers were designed to assure the trajectory tracking of the
power profile. The first controller is a PID controller and the second is an adaptive controller.
The linearized model used for the controller design is given by Eq. 5.20. The input to the
model is the current demand and the output from the model is the voltage. The power output
is obtained as a product of the current and the voltage. For the PID controller, parameters
Kc, τi, τd were varied for a range of 10−1-10−4 and the values for which the best performance
was obtained were Kc = 0.051, τi = 0.001, τd = 0.0001. To develop an adaptive controller
discussed in the above section we need a reference model in addition to the plant model. For
the reference model we need the desired time constant of the fuel cell process which can be
obtained from the nonlinear model and was calculated to be τref = 0.0230. The adaptive
controller was implemented, using the procedure outlined in Fig. 5.2, in MATLAB/Simulink
as shown in Fig. 5.7. The tuning parameters γ1, γ2 and the initial guesses for l(0) and k(0)
were calculated on a trial and error basis by varying the parameter values over a range and
obtaining the values which give the best performance. The tuning parameters γ14, γ2 are
set to 10−9, and the initial values for l(0) and k(0) are 0.01 and 0.001 respectively. For
implementing the deadzone the bounded disturbance is chosen to be 0.01kW .
To make a quantitative comparison between the adaptive controller and a PID controller the
Integrated Time Averaged Error (ITAE) was calculated by the following equation.
ITAE =n∑i=0
ti|ei(t)|n
(5.21)
where n stands for the number of time steps and ei is the error at time ti.
The PID controller and the adaptive controller were implemented on the nonlinear model.
The errors obtained for the UDDS profile are shown in Fig. 5.8. The adaptive controller
error has a larger undershoot compared to the PID controller but the error comes back
to zero quicker than the PID controller. The ITAE error obtained when implemented on
the nonlinear models for the two controllers is given in Table 5.2. It is observed that the
83
Figure 5.7. Simulink diagram of the adaptive controller
Table 5.2. Average ITAE error in kW obtained for the UDDS and US06-HWY profilesProfile PID MRACUDDS 91.46 40.5
US06-HWY unstable 55.6
MRAC performs better than the PID for the UDDS profile. Note that the parameters of
both controllers were fine tuned assuming the power profile was known a priori. However
an important aspect of designing a controller for an automotive purpose is we do not know
the trajectory of the power profile a priori and so the controller tuned for one profile should
work for several other typical road profiles. The controller designed for the UDDS profile
was implemented on a US06-HWY profile which simulates highway driving instead of city
driving represented by UDDS. This cycle has been created to provide a very short high speed
highway test cycle and the speed and power profiles are shown in Fig. 5.9.
When the US06- HWY profile is used on the controllers designed for the UDDS profile
the PID controller failed as the system became unstable whereas the adaptive controller
works well as shown in Table 5.2.
84
0 200 400 600 800 1000 1200 1400−2
−1.5
−1
−0.5
0
0.5
1
1.5
PID
ER
RO
R
0 200 400 600 800 1000 1200 1400−2
−1
0
1
2
AD
AP
TIV
E E
RR
OR
TIME−SECONDS
Figure 5.8. Error obtained(kW) for the PID and Adaptive controllers implemented on thenonlinear model
0 50 100 150 200 250 300 350 4000
20
40
60
80
100
SP
EE
D(m
iles/
hr)
0 50 100 150 200 250 300 350 4000
10
20
30
40
50
60
PO
WE
R(k
W)
TIME (SECONDS)
Figure 5.9. Speed and Power profiles for the US06-HWY driving cycle
85
5.3.4 MRAC with Derivative Action
The performance of the adaptive controller is better than that of the PID controller;
however the adaptive controller takes some time to adjust to the changes in the profiles.
This is because the adaptive controller tries to approximate the actual nonlinear model to a
linear first order model and the calculates appropriate control actions to make the closed loop
system follow the specified linear first order reference model. The actual nonlinear model
response more closely represents a second order process. The performance of the adaptive
controller can be improved by adding some derivative action, i.e., using a PD controller
in conjunction with the adaptive controller. Note that for the PD controller, the error is
defined as difference between the setpoint and the plant output. For the adaptive controller
the error is defined as deviation of the plant output from the reference model output.
The following analysis for the stability and adaptation law for the combined PD and
adaptive controllers is along the lines of Ioannou and Sun [72]. Consider the plant equation
given by a second order transfer function
yp = Gp(s)up where (5.22)
Gp(s) =b
s2 + a1s+ a2
(5.23)
If a PD controller is added to adaptive action as shown in Fig. 5.10, the new control input
to the system is given by
up = kyp + lr + kc(yp − r) +Kds(yp − r) (5.24)
Without loss in generality, this can be written as
up = k∗yp + l∗r + kdsyp − kdsr (5.25)
Substituting this value of up into Eq. 5.22, we can calculate the closed loop transfer function
between yp and r as
(s2 + a1s+ a2)yp = b(k∗yp + l∗r + kdsyp − kdsr) (5.26)
This impliesypr
=b(l∗ − skd)
s2 + (a1 − kdb)s+ (a2 − bk∗) (5.27)
86
Figure 5.10. Adaptive controller with derivative action
The control objective is to track the reference model output
ym =bm
s+ amr (5.28)
Equating Eq. 5.28 and Eq. 5.27 we get
b(l∗ − skd)s2 + (a1 − kdb)s+ (a2 − bk∗) =
bms+ am
r (5.29)
(−kdb)s2 + b(l∗ − amkd)s+ aml∗b = bms
2 + bm(a1 − kdb)s+ a2 − bk∗ (5.30)
Equating the coefficients of sn on both sides we have the optimal values for kd, l∗, k∗
kd =−bmb
(5.31)
l∗ =bmb
(a1 + bm − am) (5.32)
k∗ =a2 − aml∗b
b(5.33)
The optimal values of kd, l∗, k∗ when substituted in Eq. 5.26 ensure that the plant output
follows the model output. Hence if k∗ and l∗ are exactly known then yp = ym and we have
(s2 + a1s+ a2)ym = b(k∗yp + l∗r + kdsyp − kdsr) (5.34)
In reality, k∗ and l∗ are not known. If k and l are estimates of k∗ and l∗, then
(s2 + a1s+ a2)yp = b(kyp + lr + kdsyp − kdsr) (5.35)
87
Subtracting Eq. 5.34 from Eq. 5.35 and replacing yp − ym with e, we have
(s2 + a1s+ a2)e = b(kyp + lr), where k = k− k∗; l = l− l∗; (5.36)
This can be expressed in state space form as
X = AcX +BcθTω (5.37)
e = CTc X (5.38)
where
Ac =
(0 1−a2 −a1
);Bc =
(0b
);Cc =
(10
);
X =
(ee
); θ =
(k
l
);ω =
(ypr
)
Eq. 5.37 can be written as
X = AcX + Bcρ∗θTω; where Bc = Bcl
∗; ρ∗ = 1/l∗ (5.39)
e = CTc X (5.40)
Consider the Lyapunov-like function
V (θ, X) =XTPcX
2+θΓ−1θT
2|ρ∗| (5.41)
where Γ = ΓT > 0 and Pc = P Tc > 0 and satisfies the algebraic equations
PcAc + ATc Pc = −qqT − νcLc (5.42)
PcBc = Cc (5.43)
where q is a vector, Lc = LTc > 0 and νc > 0 is a small constant, that are implied by
the Meyer-Kalman-Yakubovich(MKY) lemma [72]. The time derivative V of V along the
solution of Eq. 5.39 is given by
V = −XT qqTX
2− νc
2XTLcX +XTPcBcρ
∗θTω + θTΓ−1 ˙θ|ρ∗| (5.44)
Since XTPcBc = XTCc = [CTc X]T = e and ρ∗ = |ρ∗|sgn(ρ∗), we can make V ≤ 0 by
choosing˙θ = θ = Γeωsgn(ρ∗) (5.45)
88
Table 5.3. ITAE error for the Adaptive controller with the derivative action designed forthe UDDS profile and also implemented on the USHWY06
Controller UDDS profile(ITAE) US06-HWY profile (ITAE)Adaptive 40.5 55.6
Adaptive with Derivative 15.6 31.94
which leads to
V = −XT qqTX
2− νc
2XTLcX (5.46)
which is negative definite. Note that Eq. 5.45 is same as the adaptation law Eq. 5.8 used
in the previous section. Hence, using the same adaptation mechanism as outlined in the
previous section we can ensure stability as well as improve the performance by adding the
PD controller.
The derivative controller is designed and implemented on the nonlinear model for the
two profiles discussed before, i.e., the UDDS and the US HWY06 profiles. The adaptive
controller with derivative action performs better than the adaptive controller as shown in
Fig. 5.11 which shows the error for the UDDS profile. Fig. 5.12 shows the adaptive controller
with the derivative action implemented on the US HWY06 profile.
0 200 400 600 800 1000 1200 1400−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
TIME−SECONDS
ER
RO
R
Figure 5.11. Error Vs time plot for the adaptive controller with derivative actionimplemented on the UDDS power profile.
89
0 50 100 150 200 250 300 350−3
−2
−1
0
1
2
3
TIME−SECONDS
ER
RO
R
Figure 5.12. Error Vs time plot for the Adaptive controller with derivative actionimplemented on the US HWY-06 power Profile.
The UDDS and US HWY06 profiles considered in the above sections were take from a
database of test procedures, developed by the Environmental Protection Agency, stored in
the ADVISOR. The Environmental Protection Agency(EPA) review and revise as necessary
the regulations governing the Federal Test Procedures (FTP)to insure that vehicles are
tested under circumstances which reflect the actual current driving conditions under which
motor vehicles are used, including conditions relating to fuel, temperature, acceleration,
and altitude. Present below are some of the profiles which were used to test the adaptive
controllers.
Federal Test Procedure(FTP)
The FTP is the test procedure used to determine compliance of light-duty motor vehicles
with federal emission standards. It is generally used for testing city driving conditions,
In fact the UDDS profile considered in the previous section is derived from this cycle and
consists of the first three bags of the FTP cycle. Fig. 5.13 shows the speed and power profile
obtained for this cycle.Using the same controller settings designed for the UDDS case the
90
adaptive controller with derivative action was implemented on this cycle and Fig. 5.14 shows
the error obtained.
0 500 1000 1500 2000 25000
10
20
30
40
50
60
SP
EE
D(m
iles/
hr)
0 500 1000 1500 2000 25000
0.5
1
1.5
2
2.5
3x 10
4
PO
WE
R(W
AT
TS
)
Figure 5.13. FTP Cycle: Speed Vs time and Power Vs time profiles
US06 Cycle
This cycle is one of the three included in the US EPA’s Supplemental Federal Test
Procedure to be used to measure vehicular tailpipe emissions. The US06 includes high speed
operation and demanding accelerations, the USHWY 06 is derived from this cycle. The
power and speed profiles obtained are shown in Fig. 5.15 and the error obtained are shown
in Fig. 5.16.
91
0 500 1000 1500 2000 2500−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
TIME−SECONDS
ER
RO
R
Figure 5.14. FTP Cycle: Error Vs time plot for the Adaptive controller with derivativeaction.
Highway Fuel Economy Test(HFET)
This data represents the Highway Fuel Economy Test driving cycle used by the US EPA
for Corporate Average Fuel Economy(CAFE) certification of passenger vehicles in the US.
Fig. 5.17 and Fig. 5.18 are the speed and error profiles respectively.
European Profiles( EUDC & EUDC LOW)
All the above profiles were developed by EPA for US conditions. The Extra Urban
Driving Cycle (EUDC) test cycle is performed on a chassis dynamometer. The cycle is
used for emission certification of light duty vehicles in Europe. It is also known as the
MVEG-A cycle. EUDC and EUDC-LOW profiles were chosen for this study. The speed and
92
0 100 200 300 400 500 6000
20
40
60
80
100
SP
EE
D(m
iles/
hr)
0 100 200 300 400 500 6000
1
2
3
4
5
6x 10
4
PO
WE
R(W
AT
TS
)
Figure 5.15. US06 Cycle: Speed Vs time and Power Vs time profiles.
error profiles for EUDC are given in Fig. 5.19, Fig. 5.20 and the corresponding profiles for
EUDC-LOW are given in Fig. 5.21, Fig. 5.22.
Indian Highway Profile(IHP)
This cycle contains a sample(unofficial) Indian highway driving cycle based on a study
in Madras, India. This cycle is characterized by moderate transients, with lower top speeds.
The speed and error profiles are shown in Fig. 5.23, Fig. 5.24.
The controller was designed for the UDDS profile and the same settings were employed for
the remaining profiles. The results are shown in Table 5.4. It is observed that the adaptive
controller with derivative action is able to handle a wide variety of profiles including high
acceleration highway profiles and also city driving conditions.
93
0 100 200 300 400 500 600−3
−2
−1
0
1
2
3
TIME−SECONDS
ER
RO
R
Figure 5.16. US06 Cycle: Error Vs time plot for the Adaptive controller with derivativeaction.
Table 5.4. Performance of MRAC on different road profilesProfile or Cycle ITAE error
FTP 42.76US06 55.13HFET 11.09EUDC 8.20
EUDC-LOW 18.50IHP 10.20
94
0 100 200 300 400 500 600 700 8000
10
20
30
40
50
60
SP
EE
D(m
iles/
hr)
0 100 200 300 400 500 600 700 8000
0.5
1
1.5
2
2.5x 10
4
PO
WE
R(W
AT
TS
)
TIME−SECONDS
Figure 5.17. HFET Cycle: Speed Vs time and Power Vs time profiles.
5.3.5 Design of Fuel Tank
One of the major design issue is the size of the fuel tank i.e. will the fuel tank size be
large enough to handle a driving range of 300 to 400 miles. A relationship between the
fuel feed rate and the current produced inside the cell has been established in Chapter 3.
Using the same relationship for a given current we can calculate the amount of methane
required can be calculated. By calculating the area under the curve of methane flow rate
and time the methane required per cell for the entire simulation can ba calculated. If this
area is multiplied with the total number of cells, e the total moles of methane required to
traverse the distance specified by the cycle can be calculated. The different cycles considered
present a range of average speeds ranging from 16 miles/hr to 60 miles/hr and the methane
95
0 100 200 300 400 500 600 700−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
TIME−SECONDS
ER
RO
R
Figure 5.18. HFET Cycle: Error Vs time plot for the Adaptive controller with derivativeaction.
consumption varies for the different profiles as seen in Table 5.5. In Table 5.5 the methane
required for a driving range of 300 and 400 miles is also calculated.
Table 5.5 lists the amount of methane required for a car following the UDDS profile to
travel 300 miles i.e. approximately 400 liters. A mole of methane at standard temperature
and pressure (1 atm and 298 K) occupies 22.4 liters. Thus, for a 300 miles driving range
a volume of 400x22.4 ∼= 9000 liters is required which is clearly not practical. Thus, it is
necessary to consider methane storage at a higher pressure. If we assume the size of the fuel
tank is 50 liters we can store upto 750 moles of methane at 340 atm (5000 PSI), which is
enough to ensure a range of 300 miles except for the USHWY and US06 and a range of 400
miles except for the USHWY, US06 and EUDC as shown in Table 5.5. From this it can be
inferred that the fuel cell vehicle designed in this research can handle city driving conditions
96
0 50 100 150 200 250 300 350 4000
20
40
60
80
SP
EE
D(m
iles/
hr)
0 50 100 150 200 250 300 350 4000
0.5
1
1.5
2
2.5
3
3.5x 10
4
PO
WE
R(W
AT
TS
)
TIME−SECONDS
Figure 5.19. EUDC Cycle: Speed Vs time and Power Vs time profiles.
Table 5.5. Moles of methane required for a driving range of 300 and 400 miles for thedifferent cycles
Distance Average CH4 CH4 Driving RangeCycle traveled Speed Required per mile 300miles 400miles
miles miles/hr moles mol/mile CH4 moles CH4 molesUDDS 7.45 19.58 9.64 1.29 388.19 517.58
USHWY 6.24 60.8 16.96 2.72 815.38 1087.18FTP 11.04 16.04 19.13 1.73 519.84 693.12US06 8.01 47.9 24.25 3.03 908.24 1210.99HFET 10.26 48.2 17.03 1.66 497.95 663.94EUDC 4.32 38.8 8.46 1.96 587.50 783.33
EUDC-LOW 6.58 19.33 9.73 1.48 443.62 591.49IHP 7.22 29.55 11.16 1.55 463.71 618.28
97
0 50 100 150 200 250 300 350 400−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
TIME−SECONDS
ER
RO
R
Figure 5.20. EUDC Cycle: Error Vs time plot for the Adaptive controller with derivativeaction.
easily but for higher velocities especially on the highways it is necessary to have a larger
tank.
Since the ratio of steam to carbon to be fed to the reformer is three, it is necessary to
design a water tank which can provide sufficient steam. Most of the water that is produced
from the fuel cell as well as the unreacted steam can be recovered and sent back to the water
tank. The average methane requirement for the 300 and 400 miles driving range is 578 and
770 moles respectively for the different profiles. Thus, for the 400 miles driving range the
minimum water requirement Vwater is
Vwater = NCH4 × r ×MH20/ρ = 42000cm3
98
0 200 400 600 800 1000 1200 14000
10
20
30
40
50
60
SP
EE
D(m
iles/
hr)
0 200 400 600 800 1000 1200 14000
0.5
1
1.5
2x 10
4
PO
WE
R(W
AT
TS
)
Figure 5.21. EUDC-LOW Cycle: Speed Vs time and Power Vs time profiles.
where NCH4 is the moles of methane, r is the ratio of steam to carbon, MH20 is the molecular
weight of water(18g/mol) ρ is the density of water(1gm/cc, the total volume of water is 42
liters. Thus the total size for the fuel tank and water tank combination is around 92 liters.
5.4 Application to Phosphoric Acid Fuel Cell
In this section a MRAC controller is implemented on a model of a phosphoric acid fuel
cell. The control problem is to maintain the voltage of a fuel cell at a constant value in the
presence of load disturbances using the oxygen flow rate as a manipulated variable. Some
fuel cells need to operate at a constant voltage in the presence of varying loads. When
there is a change in the load the operating current density changes. By changing the partial
pressure of oxygen at the cathode we can shift the polarization curve above and thereby
changing the operating voltage.
99
0 200 400 600 800 1000 1200−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
TIME−SECONDS
ER
RO
R
Figure 5.22. EUDC-LOW Cycle: Error Vs time plot for the Adaptive controller withderivative action.
To develop a controller for this problem a dynamic model of the fuel cell operation is
needed. Rengaswamy et al. [90] proposed a dynamic model given by the transfer functions
in Eq. and 5.48 which can be utilized for control study purposes.
Gp =0.0069s+ 0.1502
s2 + 5.377s+ 9.145(5.47)
Gd =0.01259s+ 0.00124
s2 + 1.684s+ 0.2109(5.48)
where Gp is the plant model that relates the output voltage to the input flow rate of oxygen
and Gd relates the voltage to the current disturbance. The control problem is to develop
a control system which maintains the voltage at a set point under the influence of varying
electric load by regulating the oxygen flow rate.
100
0 100 200 300 400 500 600 700 800 9000
10
20
30
40
50
SP
EE
D(m
iles/
hr)
0 100 200 300 400 500 600 700 800 9000
0.5
1
1.5
2
2.5x 10
4
PO
WE
R(W
AT
TS
)
TIME−SECONDS
Figure 5.23. IHP Cycle: Speed Vs time and Power Vs time profiles.
The ultimate gain Ku = 713 and period Pu = 0.13 are obtained using the Zeigler Nichols
method. This leads to the parameters.
K = 0.6Ku = 427.8
τI =1
2Pu = 0.15
τD =1
8Pu = 0.0375
These parameters are used as a starting point for fine tuning the PID controller. After,
fine tuning it is determined that the parameters K = 600, τI = 0.20, τD = 0.0375 are
necessary to achieve good tracking results. Fig.5.3 depicts the structure of the PID controller.
101
0 100 200 300 400 500 600 700 800 900−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
TIME−SECONDS
ER
RO
R
Figure 5.24. IHP Cycle: Error Vs time plot for the Adaptive controller with derivativeaction.
Controller Simulation
The control strategy outlined above was simulated for different load disturbances. The
oxygen flow rate was used as a manipulated variable and the voltage was set to 56.25 Volts.
First the ability of the controller to reject a step disturbance was tested. An error vs. time for
the PID controller is given in Fig. 5.25. However, a step input does not represent a realistic
disturbance scenario in an automobile application. To get a more realistic situation, the
system is simulated for a band limited white noise of varying magnitudes. For low magnitude
noise, the PID controller has a better transient response than the adaptive controller but
the steady state error is almost equal. When the magnitude of the white noise is increased
the adaptive controller out performs the PID controller in terms of the steady state error
as shown in Fig. 5.26. From Fig. 5.26(b) we can see that even though the steady state
102
error is small, the signal is very noisy. These fluctuations can be avoided by switching
off the adaptive controller when the error is less than a particular bounded disturbance.
This is accomplished with the dead zone compensation method described in the previous
section. After adding the dead zone compensation the disturbances were reduced drastically
as depicted in Fig. 5.27. The adaptive controller with dead zone is compared with the PID
controller for a pulse input of magnitude 1000. The steady state error for both the cases is
shown in Fig. 5.28. From Fig. 5.28 it is evident that the adaptive controller performs better
than the PID controller. In addition, the adaptive controller has a smaller overshoot and
comes to steady state faster than the PID controller.
Figure 5.25. Error Vs time plot for the PID controller for a step of 100.
The average errors obtained with the adaptive controller and the PID controller are given
in Table 5.6. For the step and pulse input, the PID controller has a lower ITAE, which suggest
that its performance is superior to that of the adaptive controller. There is a larger steady
state error for the PID controller with a noisy current load. However, the transient error is
large for the adaptive controllers. The steady state average errors for the pulse and white
noise of magnitude 1000 and a step of 100 are listed in Table 5.7. The adaptive controller
with dead zone has the lowest steady state error for both the pulse and noise cases.
103
Figure 5.26. (a), (b) Errors for the adaptive controller for a white band noise of magnitudeof 100 and 1000. (c), (d) Errors for the PID controller at magnitudes of 100 and 1000respectively
Table 5.6. Average ITAE for the PAFC for a step pulse and band limited white noise input- PID Adaptive Deadzone
Step 0.17 8.6 N/APulse 2.08 9.04 20.5Noise 51.4 11.69 9.87
Table 5.7. Steady State Average ITAE for the PAFC including the deadzone- PID Adaptive DeadZone
Step 0.008 2.12 N/APulse 3.09 2.36 2.09Noise 48.5 8.013 1.805
104
Figure 5.27. (a) Error without dead zone for white noise of a magnitude 1000, (b) error inthe presence of dead zone for white noise of a magnitude 1000.
105
Figure 5.28. (a) Steady state error for PID controller with pulse load (b) steady state errorfor adaptive controller with deadband.
106
CHAPTER 6
BATTERY BACKUP MODEL
6.1 Battery Modeling
In electric and fuel cell vehicles the battery is charged and discharged continuously and
thus knowledge of the transient behavior of the batteries is very important. Dynamic models
developed from electrochemical principles give the spatial distribution of potentials and
chemical compositions inside the cell as well as the transient behavior of cell potential and
temperature. However, for control oriented studies, models which can be simulated quickly
are required. Thus equivalent electric circuit models have been developed which give an
accurate prediction of state of charge of the battery [79].
6.1.1 State of Charge
He and coworkers [79] have observed that while discharging a battery over a period of time
there exists a cutoff or critical voltage beyond which the battery performance deteriorates
rapidly as the voltage begins to fall rapidly. To avoid operation near the critical voltage the
state of charge is set to zero at the cutoff voltage and is defined as
SOC = 1− V occutoffV ocfull
(6.1)
where V ocfull is the voltage of the battery at full capacity and V occutoff is the battery
terminal voltage at the critical point. From a practical viewpoint, it is difficult to measure
the open circuit voltage at each instant. Hence, SOC can be redefined by utilizing the
relationship between the SOC and the available battery capacity as
SOC = 1− Used Capacity
Total Capacity(6.2)
107
The total current drawn from the battery can be used as an indicator for the used capacity
and is given by Eq. 6.3.
CAPused =
∫ t
0
I.dt (6.3)
where CAPused is the used capacity and I is the current and t is time elapsed. Initially when
the battery is fully charged the CAPused is zero, hence, from Eq. 6.2 the SOC is one. On
the other hand when the battery is completely discharged i.e. the used capacity is equal to
the total capacity the SOC is zero. Thus now the SOC is equal to one when the battery is
fully charged and zero when discharged to the critical voltage. Even though ensuring SOC is
close to one ensures that the battery is not discharged completely, from a practical viewpoint
it is not possible to always maintain such high SOC. At low SOC the battery discharges
quickly when compared to higher SOC and reaches the cutoff voltage faster. Hence, it is
desirable to maintain the SOC around 0.5-0.7 [79].
6.1.2 Battery Model
A battery model which requires experimentally obtained open-circuit voltage and battery
resistance data and predicts the battery terminal voltage, current, and SOC as a dynamic
function of operator imposed power demand has been developed based on the model by He
et al. [79]. The model consists of the battery as an ideal voltage source with an internal
resistance. This battery model is characterized by the idealized open circuit voltage, Voc,
and the internal battery resistance, Rb. The terminal voltage can be expressed in terms of
Voc and Rb as
Vterm = Voc − I ×Rb (6.4)
where Vterm is the voltage of the battery at the terminal. The terminal voltage of a battery
during discharge is lower than the instantaneous open circuit voltage because of the internal
resistance inside the battery. Hence current I is given a positive sign when the cell is
discharging. Similarly when the cell is charging it is necessary to apply a voltage greater
than the Voc to overcome the internal resistance inside the cell so the current in this case is
chosen to be negative.
108
The open circuit voltage and the internal resistance of the battery are both functions of
SOC and temperature. For a battery operating at constant temperature the relationship
between Voc, Rb and the SOC can be determined experimentally.
The power available at the terminals of the battery is given by the product of voltage
and current and substituting the expression for voltage from Eq. 6.4. we have
Pwrterm = VtermI = IVoc − I2Rb (6.5)
where Pwrterm is the power produced by he battery. For a particular power demand we can
calculate the current by solving Eq. 6.5 which is a quadratic equation in I.
I =Voc − (V 2
oc − 4.Rb.Pwr)
2Rb
(6.6)
where Voc and Rb are both functions of SOC. It is assumed that the power is positive
during discharge and negative during charge. The current calculated from Eq. 6.6 is used
to calculate the used capacity from Eq. 6.3. The SOC is then calculated from Eq. 6.2. The
Voc and Rb are obtained for the new SOC from the experimental data. Using the new values
of Voc and Rb the current is estimated using Eq. 6.6.
6.2 Switching Controller
The switching controller is basically a logic based on off controller which switches back
and forth between the fuel cell and the battery to meet the power demand. The different
issues which the logic controller must take care of are as follows:
• The power produced by the fuel cell comes with a certain time delay and hence any
deficit in power demand is handled by switching to the battery until the fuel cell can
produce sufficient power.
• The excess power produced by the fuel cell during deceleration or decrease in power
demand should be routed to the battery.
• When the SOC of the battery falls below a specified target, the controller should direct
the fuel cell to produce power to charge the battery in addition to the power demand.
109
• Since the fuel processor and the fuel cell system were designed for a maximum power
output of 50 kW, the controller should make sure that the power demand is not greater
than 50 kW.
6.3 MATLAB implementation
The fuel processor, fuel cell system and battery model along with the switching controller
were setup in MATLAB-SIMULINK (shown in Appendix D) and simulated for different
power demands. A simple case where the power demand is a step increase followed by a
step decrease the power profiles are given in Fig. 6.1. It may be noticed that the fuel cell
supplies the power with a time delay of 4 seconds. In the meantime the battery supplies the
requested power demand. Once the fuel cell is able to meet the power demand the battery is
turned off until 15 seconds at which time the battery again is used to supply the necessary
power demand. At 30 seconds when there is a decrease in power demand the deficit power is
sent to the battery to charge it until the fuel cell reaches the level of the new power demand.
To get a more realistic power vs time profile the power profile for a small car was
obtained from an existing speed vs time profile using ADVISOR software package. The
Urban Dynamometer Driving Schedule (UDDS) which is designed for light duty vehicle
testing in city driving conditions has been used. The speed versus time profile is shown in
Fig. 6.2, power requested, fuel cell power and battery power profiles versus time are plotted
in Fig. 6.3.
The power supplied by the battery also depends on the initial SOC of the battery. For
the same cycle the system was simulated for different initial SOC as shown in Fig. 6.4. The
controller was designed to maintain the SOC above 0.5. For the initial conditions where
the battery is almost charged (SOC=0.9) and semi charged (SOC=0.64) the profiles look
similar.
For the case where the initial SOC is less than 0.5 the controller directs power from
the fuel cell to the battery and brings the SOC level to above 0.5. When the SOC is less
than 0.5 the fuel cell operates at its maximum rated power of 50 kW until the SOC of the
battery is greater than 0.5. Any power demand is met directly by the fuel cell and all the
excess power produced is directed to the battery. As seen from Fig. 6.4 it takes almost 100
seconds for the battery SOC to be brought above 0.5, but there is no chance of discharging
110
0 5 10 15 20 25 30 35 40 45 50−10
0
10
20
Time(sec)
0 5 10 15 20 25 30 35 40 45 500
10
20
pow
er(k
W)
0 5 10 15 20 25 30 35 40 45 5010
15
20power−req
power−fc
power−bat
Figure 6.1. Power Requested, Fuel cell Power, Battery power profiles for a step increaseand decrease in Power
the battery as the battery is only being charged and not discharged. The transport delay
only comes into picture when there is a change in the flow rate of methane. Since the fuel
cell is operating at the maximum methane flow rate there are no transient effects until the
SOC reaches 0.5. After the battery reaches the target SOC the fuel flow rate is decreased
and changed according to the power demand and the controller now switches to the battery
to handle any power deficit.
111
0 200 400 600 800 1000 1200 14000
10
20
30
40
50
60
Time(sec)
Spe
ed(m
ph)
UDDS speed Profile
Figure 6.2. Speed profile for the Urban Dynamometer Driving Schedule (UDDS)
112
0 200 400 600 800 1000 1200 1400−20
−10
0
10
20
time(sec)
0 200 400 600 800 1000 1200 1400−10
0
10
20
30
pow
er(k
W)
0 200 400 600 800 1000 1200 14000
10
20
30
battery power
fuel cell power
power requested
Figure 6.3. Power profile for the UDDS schedule
113
0 200 400 600 800 1000 1200 14000.46
0.48
0.5
0.52
Time(sec)
0 200 400 600 800 1000 1200 14000.63
0.64
0.65
Sta
te o
f Cha
rge(
SO
C) 0 200 400 600 800 1000 1200 1400
0.9
0.91
0.92
Figure 6.4. State of Charge variation for different initial SOC.
114
CHAPTER 7
CONCLUSIONS
The purpose of this work was to generate an integrated model for the steady-state
operation of a methane-fed PEM fuel cell for automotive operation. First it was shown
that the system is thermodynamically feasible. Then, an in situ fuel processor subsystem
was designed in combination with a fuel cell system. An adaptive control algorithm was
developed to control reactant flow rate into a fuel processor and fuel cell system to follow a
power trajectory. Then, a switching control system been developed for effectively running
the power generation subsystem and the battery backup. Finally, the controllers have
been implemented on realistic power profiles published by the US Environmental Protection
Agency.
The major focus of this work was on the fuel processing module. This was done to ensure
that the size of the necessary reactors would be reasonable for cars. The total reactor volume
required is approximately 60 liters, which can be accommodated under the hood of a car
along with some heat transfer equipment, small compressors and other auxiliary equipment.
If 500 fuel cells are stacked in series to generate significant voltage ( 300 V) and each cell
requires 144 sq centimeter of area then the overall volume of the cells is about 800 liters.
The entire unit should require roughly 1000 liters of space and can be accommodated under
the rear seat. The volume of the fuel tank and the steam tank combination was calculated
to be around 92 liters for a driving range of 300 miles. The methane tank can be considered
as a replaceable high pressure compressed gas cylinder. The batteries will likely be placed
in the trunk.
Thus an efficient in situ fuel cell and fuel processor system has been designed, satisfying
the real life constraints, delivering the desired performance comparable to the IC engine
based system, with significant increase in fuel economy. Crucial to the effective operation of
such a propulsion system is its overall energy efficiency. To satisfy the energy requirements
115
of the endothermic reactions a combustor is added which utilizes the heat available from the
anode tail gas. However, extra methane is required in addition to the anode tail gas. This
is a crucial design feature for real systems and is essential to understand for development of
the thermal control system.
As with the current trend in the automobile industry of introducing gasoline-electric
(battery) hybrid vehicles, the future of the fuel cell based vehicles lies in the development of
fuel cell - electric (battery) hybrid systems. In this work, such a fuel cell - battery hybrid
model has been studied. A simple battery model was presented and was integrated with the
fuel cell system with the help of a switching controller. The integrated system was simulated
for different initial state of charge of the battery and for different power profiles based on
realistic speed profiles.
Fuel cell technology provides an environmentally friendly, energy efficient process for
automobiles. A better understanding of the working of the fuel cell and a better control
structure will be instrumental in the production of fuel cell vehicles. In addition to the
design of the fuel processor reactors, another key objective of this work was the development
of a control scheme that can be used under varying load conditions.
It has been that a simple PID controller is sufficient for step changes in load and noisy
loads with lower magnitudes. However, for higher magnitude disturbances a simple PID
controller does not provide adequate performance. An adaptive controller based on MRAC
been developed that has both robust stability and robust performance for a wide range
of operating conditions. Robust performance was further improved through dead zone
compensation and addition of derivative action. The controller was then tested for a number
of real life profiles including the profiles published by the US EPA and equivalent government
agencies in the EU and India.
116
CHAPTER 8
FUTURE WORK
Water will one day be employed as fuel, that hydrogen and oxygen which
constitute it, used singly or together, will furnish an inexhaustible source of heat
and light, of an intensity of which coal is not capableI believe that when the
deposits of coal are exhausted, we shall heat and warm ourselves with water.
Water will be the coal of the future. -JULES VERNE in ”Mysterious Island”.
Hydrogen as a source of energy is not a new idea as the quote above made by Jules Verne
in 1870 suggests. Hydrogen produced from water will be the fuel of the future and fuel cells
will pave the way for hydrogen economy.
System Configuration
In this dissertation we used methane as the fuel to design the fuel processing subsystem
and we showed that it is possible to have an onboard reformer. The system configuration
presented is a flexible basic framework to build upon, i.e., if a more traditional fuel like
gasoline, diesel or jet fuel is used the methane reformer could be removed and replaced with
a more suitable reformer. Alternatively a pyrolysis unit could be added before the steam
reformer to break down the higher hydrocarbons to methane. Since these fuels have a high
sulphur content a desulphurizer unit is necessary before the reformer to avoid poisoning the
catalyst. If a catalyst can be found for the fuel cell which is more resistant to the CO
poisoning, the WGS and PROX reactors can be eliminated. If technology is developed to
handle and store hydrogen the fuel processing subsystem can be eliminated.
117
Thermal Management
In this dissertation a heat duty analysis of the individual reactors was done and it was
determined that we need a combustor to supply the required heat demand. It’s assumed
that a thermal management system exists which can distribute the heat among the reactors.
For a more thorough understanding a pinch technology analysis or an heat integration
analysis should be performed. All the reactors were designed as isothermal reactors . The
performance of the fuel processing subsystem can be improved by maintaining a spatially
varying temperature profile instead of a constant temperature. A dynamic heat integration
analysis will provide a good starting point for developing an advanced robust controller
which can maintain the temperature profile in the presence of disturbance and feed flow rate
fluctuations. Another important factor is the thermal management of the fuel cell itself. A
lot of heat is produced in the fuel cell and the thermal management system should be able
to keep the temperature at around 80 oC.
Water Management
Water management inside the fuel cell can be a major issue. The nonlinear model used
in this research partially addresses this issue. For relative humidity less than 100% it takes
into consideration the drop in performance as relative humidity drops but it does not take
into consideration the drawbacks of operating at higher humidity. At higher humidity there
is a greater chance of the fuel cell membrane being flooded. Using a model that takes this
into consideration can be used to calculate the optimum relative humidity of the fuel cell.
Fuel cell cars will be entering the market soon and this research is not a final solution
but a pathway towards a future based on hydrogen. Introduction of fuel cell cars based on
conventional fuels eases the transition from a hydrocarbon to a hydrogen based fuel system.
Exaggerating the potential of hydrogen fuel cell cars will not bring them to the market
sooner. In fact this may even create a backlash that will slow down their ultimate market
success. What is really needed is a steady research and development effort which will bring
major breakthroughs in all the key technological issues- hydrogen production, storage and
infrastructure,as well as fuel cells and carbon sequestration. Until then fuel cell cars based
on conventional fuels and having the capacity to generate hydrogen onboard will provide a
118
pathway to a hydrogen economy.
119
CHAPTER 9
NOMENCLATURE
A(K) pre-exponential factorAc active cell area, cm2
Cpi specific heat capacity of species i, kJ/mol/Ke errorEo reversible standard cell potential, VEa activation energy, kJ/molF Faraday’s constant, 96, 485C/molFi Molar flow rate of species i, mol/sHi enthalpy of species i, kJ/moli current density , A/cm2
I current, Ak rate constantK proportional gainKeq equilibrium constantKi adsorption coefficients of species iKu ultimate gainm mass of reactant, gM molecular weight, g/moln number of electronsNc number of cells in the stack
Ni flow rate of species i, mol/minP power, WPi partial pressure of species i, atmPsat saturation pressure, atmPu ultimate period, sr reaction rate mol/min/lR universal gas constant, kJ/mol/KRb internal resistance of the battery, ΩRohm resistance, Ω
120
NOMENCLATURE
S selectivity of the catalyst∆S entropy changet time, sT temperature, KV voltage, VVoc open circuit voltage, VVterm battery terminal voltage, VVr volume of the reactor, m3
β reversibility factorε conversion of hydrogen inside the fuel cellλ oxygen excess ratioρ density, kg/m3
τI integral timeτD derivative timeνfc fuel cell voltage, Vνact activation overvoltage, Vνohm ohmic overvoltage, Vνconc concentration overvoltage, V
121
APPENDIX A
MATLAB PROGRAMS USED IN CHAPTER 3
main simulation.m
0001 % file name main simulation.m
0002 % file created by Panini Kolavenu on December 15th 2003
0003 % program to calculate the conversion for a known volume of the steam reformer
0004 % program calculates conversion with respect to volume
0005
0006
0007 % for i=4:8:36,
0008 clc
0009 clear all
0010 close all
0011
0012 srparameters;
0013 x=[0.01 0.01 0.02 0.24 0.72];% ratio H2O CH4 3:1
0014 x1=[0.01 0.01 0.02 0.32 0.64];%2:1
0015 x2=[0.01 0.01 0.02 0.192 0.768];%4:1
0016 x3=[0.01 0.01 0.02 0.16 0.8];%5:1
0017 x4=[0.01 0.01 0.02 0.1371 0.8229];%6:1
0018 f=(10/x(4))*x % initial flowrates
0019
0020 %program for the reformer
0021 [V,X]=ode15s(@srfun,Vol,f);
0022
122
0023 figure(1)
0024 plot(V,X(:,1),V,X(:,2),’g+’,V,X(:,3),V,X(:,4),’y-’,V,X(:,5),’m.’);
0025 hold on
0026 % end
0027 X(end,:)
0028 %
0029 % program for the WGS REACTOR
0030
0031 Volwgs=[0.0001 50];
0032 [Vo,Xwgs]=ode15s(@wgsfun,Volwgs,X(end,:));
0033 figure(3)
0034 plot(Vo,Xwgs(:,1),’b^’,Vo,Xwgs(:,2),’g+’,Vo,Xwgs(:,3),...
0035 Vo,Xwgs(:,4),’y-’,Vo,Xwgs(:,5),’m.’);
0036
0037
0038 %program for PROX reactor
0039 VolP=[0.000001 0.34];
0040 Xp=Xwgs(end,:);
0041 Xp=[Xp,Xp(2)*2.2,Xp(2)*2.2*0.79/0.21];
0042 [Vo,Xprox]=ode15s(@PROXfun,VolP,Xp);
0043 figure(5)
0044 plot(Vo,Xprox(:,1),’b^’,Vo,Xprox(:,2),’g+’,Vo,Xprox(:,3),...
0045 Vo,Xprox(:,4),’y-’,Vo,Xprox(:,5),’m.’,Vo,Xprox(:,6),’b-’);
0046
0047 Xp
0048 Xprox(end,:)
0049 (f(4)-Xprox(end,4))*100/f(4) % total conversion
123
srfun.m
0001 function ddv = srfun(V,f)
0002 % SRFUN calculates the change in concentration along the reformer
0003 % For a given initial concentration calculates the concentration
0004 %of species along the volume of the reactor.
0005 %INPUTS
0006 % V is volume; f is flow rate
0007 % THE REACTIONS TAKING PLACE
0008 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0009 %% CH4 + H2O <====> CO + 3H2 %%
0010 %% CO + H2O <====> CO2 + H2 %%
0011 %% CH4 + 2H2O <====> CO2 + 4H2 %%
0012 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0013 srparameters;
0014 %concentration of individual species
0015 C=Pr*f/(Tr*0.0820575*sum(f));%concentration
0016
0017 f0=ft*(.24);
0018 conv=(f0-f(4))/f0;
0019 % figure(3)
0020 % plot(V,conv);
0021 % hold on;
0022
0023 y=f/sum(f);% mole fraction
0024
0025 % figure(2)
0026 % plot(V,y(1),’g*’,V,y(5),’b^’,V,y1(1),’y+’,V,y1(5),’r^’);
0027 % hold on;
0028
0029 Pj=y*Pr;% partial pressure
124
0030 Temp=Tr;
0031 P001=Pj(1);%H2
0032 P002=Pj(2);%CO
0033 P003=Pj(3);%CO2
0034 P004=Pj(4);%CH4
0035 P005=Pj(5);%H2O
0036
0037 %rate expressions r1,r2,r3
0038 r1 =9.886*10^16*exp(-240.1/(.008314*Temp)) /...
0039 (P001)^2.5*(P004*P005-P001^3*P002/exp(29.3014-26248.4/Temp))/...
0040 (1+8.339*10^-5*exp(70.65/(.008314*Temp))*P002+...
0041 6.209*10^-9*exp(82.90/(.008314*Temp))*P001+...
0042 6.738*10^-4*exp(38.28/(.008314*Temp))*P004+...
0043 1.77*10^5*exp(-88.68/(.008314*Temp))*P005/P001);
0044 r2 =4.665*10^7*exp(-67.13/(.008314*Temp)) /...
0045 (P001)*(P002*P005-P001*P003/exp(-4.35369+4593.17/Temp))/...
0046 (1+8.339*10^-5*exp(70.65/(.008314*Temp))*P002+...
0047 6.209*10^-9*exp(82.90/(.008314*Temp))*P001+...
0048 6.738*10^-4*exp(38.28/(.008314*Temp))*P004+...
0049 1.77*10^5*exp(-88.68/(.008314*Temp))*P005/P001);
0050 r3 =2.386*10^16*exp(-243.9/(.008314*Temp)) /...
0051 (P001)^3.5*(P004*P005^2-P001^4*P003/10^(10.955-9478.6/Temp))/...
0052 (1+8.339*10^-5*exp(70.65/(.008314*Temp))*P002+...
0053 6.209*10^-9*exp(82.90/(.008314*Temp))*P001+...
0054 6.738*10^-4*exp(38.28/(.008314*Temp))*P004+...
0055 1.77*10^5*exp(-88.68/(.008314*Temp))*P005/P001);
0056
0057 % rate expressions for the individual species
0058 dxdv(1)=(3*r1+4*r3+r2);%H2
0059 dxdv(2)=(r1-r2);%CO
0060 dxdv(3)=(r3+r2);%CO2
125
0061 dxdv(4)=-r1-r3;%CH4
0062 dxdv(5)=(-r1-r2-2*r3);%H20
0063
0064 ddv=dxdv(:);
126
wgsfun.m
0001 function ddv = wgsfun(V,f)
0002 % SRFUN calculates the change in concentration along the WGS reactor
0003 % For a given initial concentration calculates the concentration
0004 %of species along the volume of the reactor.
0005 % THE REACTION TAKING PLACE IS
0006 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0007 %% CO + H2O <====> CO2 + H2 %
0008 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0009 %INPUTS
0010 % V is volume; f is flow rate
0011
0012 Pr=2;%atm
0013 Tr=Trx(V);%adjusts the temperature according tho the temperature
0014 %concentration of individual species
0015 C=Pr*f/(Tr*0.0820575*sum(f));%concentration
0016
0017 y1=f/sum(f);
0018
0019 % figure(2)
0020 % plot(V,y(1),’g*’,V,y(5),’b^’,V,y1(1),’y+’,V,y1(5),’r^’);
0021 % hold on;
0022
0023 Pj=y*Pr;% partial pressure
0024
0025 P001=Pj(1);%H2
0026 P002=Pj(2);%CO
0027 P003=Pj(3);%%CO2
0028 P004=Pj(4);%CH4
0029 P005=Pj(5);%H2O
127
0030 r1=81.94*210*0.6*60*exp(-47500/(8.314*Temp))*...
0031 (P005*P002-(P003*P001)/exp((4577.8/Temp)-4.33))/1000;
0032 dxdv(1)=r1;%H2
0033 dxdv(2)=(-r1);%CO
0034 dxdv(3)=r1;%CO2
0035 dxdv(4)=0;%CH4
0036 dxdv(5)=-r1;%H2O
0037 ddv=dxdv(:);
0038
0039 function T=Trx(Vol)
0040 % TRX calculates the temperature depending upon the volume
0041 V=Vol;
0042 if V<=1
0043 Tv=700;
0044 else
0045 Tv=600;
0046 end
0047 T=Tv;
0048
128
PROXfun.m
0001 function ddv = PROXfun(V,f)
0002 % PROXFUN calculates the change in concentration along the PROX reactor
0003 % For a given initial concentration calculates the concentration
0004 % of species along the volume of the reactor.
0005 % THE REACTION TAKING PLACE IS
0006 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0007 %% CO + (1/2)O2 <====> CO2 %%
0008 %% H2 + (1/2)O2 <====> H2O %%
0009 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0010 %INPUTS
0011 % V is volume; f is flow rate
0012
0013 % V is volume f0 is flow rate
0014 Pr=2;%atm
0015 Tr=473;
0016 %concentration of individual species
0017
0018 C=Pr*f/(Tr*0.0820575*sum(f));%concentration
0019
0020 y1=f/sum(f); %molefraction
0021
0022 % figure(2)
0023 % plot(V,y(1),’g*’,V,y(5),’b^’,V,y1(1),’y+’,V,y1(5),’r^’);
0024 % hold on;
0025
0026 Pj=y*Pr;% partial pressure
0027 Temp=Tr;
0028 P001=Pj(1);%H2
0029 P002=Pj(2);%CO
129
0030 P003=Pj(3);%CO2
0031 P004=Pj(4);%CH4
0032 P005=Pj(5);%H2O
0033 P006=Pj(6);%O2
0034 P007=pj(7);%N2
0035 if f(2)<=0.00001 % this is to ensure concentration is positive
0036 r1=0;% the rate is set to zero for very very low conc of CO
0037 else
0038 r1 =2.333*10^8*exp(-8540/(Temp))*(P002)^0.4 *(P006/P002)^(0.82);
0039 end
0040 if f(6)<=0.00001
0041 r2=0;% the rate is set to zero for very very low conc of O2
0042 else
0043 r2 = 1.5*2.333*10^8*exp(-8540/(Temp))*(P002)^0.4 *(P006/P002)^(0.82);
0044 end
0045 dxdv(1)=-r2;%H2
0046 dxdv(2)=(-r1);%CO
0047 dxdv(3)=r1;%CO2
0048 dxdv(4)=0;%CH4
0049 dxdv(5)=r2;%H20
0050 dxdv(6)=-0.5*r1-0.5*r2;%O2
0051 dxdv(7)=0;%N2
0052 ddv=dxdv(:);
0053
130
APPENDIX B
MATLAB PROGRAMS USED IN CHAPTER 4
jtp fuelcellmodel.m
0001 % This program calculates and plots the fuel cell polarization curve
0002 % The dependence of the Polarization curve on Cathode Pressure
0003 % and Humidity will be illustrated
0004
0005 %%%%%%%%%%%%%%Stack Voltage model%%%%%%%%%%%%%%%
0006 close all
0007 clear all
0008
0009 %lambdam represents the relative humidity
0010 %lambdam varies from 0 to 14 as relative humidity varies from 0% and 100%.
0011
0012 for lambdam=7:7:14,
0013 %for Pca=1:1:3,
0014 %for tfc=70:10:100
0015 %lambdam=14
0016 Pca=1.1 % cathode pressure
0017 tfc=80;%temperature(oC)
0018 i=[0:.1:2]% current density
0019
0020
0021 % empirical parameters
0022
131
0023 c1=10;
0024 c3=2;
0025 imax=2.2;
0026 b11=0.05139;
0027 b12=0.00326;
0028
0029 tm=0.01275;
0030 b2=350;
0031
0032 Tfc=273+tfc;% temperature
0033 Psat=10^(5.20389-1733.926/(Tfc-39.485)) % saturation pressure
0034 %OR
0035 % Psat=10^(1.69e-10*Tfc^4+3.85e-7*Tfc^3-3.39e-4*Tfc^2+0.143*Tfc-20.92)
0036
0037 PH2=Pca;% hydrogen pressure at anode
0038 PO2=(Pca-Psat)*0.21;% oxygen pressure
0039
0040 % Voltage Calculation
0041 E=1.229-8.5e-4*(Tfc-298.15)+4.3085e-5*Tfc*(log(PH2)+0.5*log(PO2))
0042 sigm=(b11*lambdam-b12)*exp(b2*(1/303-1/Tfc));
0043 Rohm=tm/sigm;
0044
0045 v0=0.279-8.5e-4*(Tfc-298.15)+4.3085e-5*Tfc*(log((Pca-Psat)/1.01325)+...
0046 0.5*log(0.1173*(Pca-Psat)/1.01325));
0047 va=(-1.618e-5*Tfc+1.718e-2)*(PO2/0.1173+Psat)^2+(1.8e-4*Tfc-0.166)*...
0048 (PO2/0.1173+Psat)+(-5.5e-4*Tfc+0.5736);
0049
0050 k1=PO2/0.1173+Psat;
0051 if k1<2
0052 c2=(7.16e-4*Tfc-0.622)*k1+(-1.45e-3*Tfc+1.68)
0053 else
132
0054 c2=(8.665e-5*Tfc-0.068)*k1+(-1.6e-4*Tfc+0.54)
0055 end
0056
0057 vact=v0+va*(1-exp(-c1.*i)); % activation losses
0058 vohm=i.*Rohm;% ohmic losses
0059 vconc=i.*(c2*i./imax).^c3;%concentration losses
0060 vfc=E-vact-vohm-vconc;% fuel cell operating voltage
0061
0062 figure(1)
0063 plot(i,vfc)
0064 xlabel(’Current Density( Amp/cm2)’)
0065 ylabel(’Voltage(volts)’)
0066 legend(’50% RH’,’100% RH’)
0067 %legend(’Pca=1 bar’,’Pca=2 bar’,’Pca=3 bar’)
0068 %legend(’tfc=70 ^oC’,’tfc=80 ^oC’,’tfc=90 ^oC’,’tfc=100 ^oC’)
0069 hold on
0070
0071 end
133
APPENDIX C
MATLAB PROGRAMS USED IN CHAPTER 5
sysid.m
0001 % file name sysid.m
0002 % file created by Panini Kolavenu on November 10th 2003
0003 %system identification for the adaptive controller design.
0004 % using a simple step test
0005
0006
0007 %power-current
0008 % Plot the input and output
0009 t=outtime;
0010 y=outNETpower;
0011 u=outSTcurrent;
0012
0013 figure(1)
0014 subplot(2,1,1),plot(t,y),grid
0015 title(’STEP TEST OF FIRST ORDER SYSTEM’)
0016 ylabel(’POWER DATA’)
0017 subplot(2,1,2),plot(t,u),grid
0018 ylabel(’CURRENT DATA’),xlabel(’TIME - SECONDS’)
0019
0020 [tt,uu]=ginput(2)% get the the beginning and top of the step input.
0021
0022 subplot(2,1,1),
134
0023
0024 [ttt,yyy]=ginput(2)%beginning and the steady state of the output.
0025 %The gain is
0026 Kmodel=(yyy(2)-yyy(1))/(uu(2)-uu(1))
0027 a=yyy(1)+.632*(yyy(2)-yyy(1));
0028 figure(2)
0029 plot(t,y,[0 10],[a a]),grid on
0030 [tt,yy]=ginput(2)
0031 taumodel=tt(2)-tt(1)
0032
0033 sys1=tf([Kmodel],[taumodel,1]);
0034
0035 %voltage current
0036 y=outSTvoltage;
0037 figure(3)
0038 subplot(2,1,1)
0039 h=plot(t,y);
0040 grid on
0041 title(’SECOND ORDER SYSTEM’)
0042 ylabel(’VOLTAGE’)
0043
0044 subplot(2,1,2),plot(t,u),grid
0045 ylabel(’Current’),xlabel(’TIME SECONDS’)
0046
0047 % The points from the input are:
0048 subplot(2,1,2), [ttt,yyy]=ginput(2)
0049 grid
0050 ylabel(’INPUT’),xlabel(’TIME SECONDS’)
0051 subplot(2,1,1)
0052 [tt,yy]=ginput(3)
0053
135
0054 k=(yy(3)-yy(1))/(yyy(2)-yyy(1))
0055 a=(yy(2)-yy(3))/(yy(3)-yy(1));
0056 aa=(log(a)/pi)^2;
0057 zeta=sqrt(aa/(1+aa))
0058 omega=pi/(sqrt(1-zeta^2)*(tt(2)-tt(1)))
0059
0060 sys=tf([k*omega^2],[1 2*zeta*omega omega^2])
0061
136
APPENDIX D
MATLAB PROGRAMS USED IN CHAPTER 6
Simulink Diagram used for the battery modelling
137
Figure D.1. Simulink diagram to simulate the switching controller design
138
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144
BIOGRAPHICAL SKETCH
Panini K. Kolavennu
Kolavennu Krishna Panini received his Bachelors degree in Chemical Engineering with a
specialization in biotechnology from Andhra University, India in 2001. Upon graduation,
he joined the Chemical Engineering program at Florida State University to seek a doctoral
degree.
145
