stand-alone power systems for the future: s3. · pdf filethe work of this thesis is divided...

STAND-ALONE POWER SYSTEMS FOR THE FUTURE: OPTIMAL DESIGN, OPERATION & CONTROL OF

SOLAR-HYDROGEN ENERGY SYSTEMS

ØYSTEIN ULLEBERG

December 1998

Ph. D. dissertation Department of Thermal Energy and Hydropower

Norwegian University of Science and Technology Trondheim

i

PREFACE

My first real encounter with the field of solar energy was in 1991, during the last semester of my undergraduate studies at the University of Texas at El Paso (UTEP), United States of America. The person who introduced me to this fascinating science was Prof. Peter Golding, who was my advisor on a semester project at the UTEP Solar Pond Project. That project sparked my interest for continuing in the field of solar energy.

After carefully looking at several options for graduate studies, I ended up at the solar energy laboratory (SEL) at the University of Wisconsin–Madison, and the Professors William A. Beckman, Sanford A. Klein, John W. Mitchell, and John A. Duffie (Emeritus Professor). After a very educational and personally rewarding one and a half-year at SEL in Madison I returned to Norway. Six years of university life in the USA had ended. Today, I always look back at my stay in Madison with a very particular sentiment, because that was also the place were I met my wife Eirin.

We returned together to Oslo, Norway, in late summer of 1993. I spent the next year at the Army Material Command (HFK) in Oslo, were I did my compulsory military service. At HFK I began looking for jobs, preferably in the field of renewable energy (energy is not renewable so I really prefer to use the term natural energy). I contacted Kjell Solberg, who at the time was the head of a research section at the Institute for Energy Technology (IFE), to find out if there were any job opportunities in the area. Unfortunately, there were none, and I therefore got a job in the HVAC business instead. However, about two weeks before I was to begin in my new job, Kjell Solberg called and offered me a Ph.D. scholarship in the area of stand-alone power systems (SAPS) based on renewable energy. That was the beginning of a four-year long journey that finally led to this Ph.D. dissertation.

This dissertation is not only a result of my own dedication and perseverance, but is largely a credit to a number of patient and helpful people that I have lived and worked with over these past four years. In addition to my wife Eirin, these include my sisters, my parents and their families, and many good friends. Furthermore, I would particularly like to thank my advisor Prof. Odd Andreas Asbjørnsen at the Norwegian University of Science and Technology (NTNU), Trondheim, for his never-ending enthusiasm, encouraging attitude, and guidance on fundamentally and theoretical important matters. I would also like to thank the people at the research center (FZ) in Jülich, Germany, for letting me visit and study their photovoltaic-hydrogen (PV–H2) energy plant (PHOEBUS) in detail.

The visit at PHOEBUS in the fall of 1996 came about after I had presented a paper on PV–H2 systems with dr. ing. Svein O. Mørner at the ISES-1996 Congress in Harare, Zimbabwe. I would like to thank Svein for introducing me to the field of solar-hydrogen and for letting me use some of his models. Among the people at FZ– Jülich, I would particularly like to thank Dr. Heinz Barthels for making my visit possible, Dr. Wennemar Brocke for his assistance and advice on modeling, and Jürgen Mergel for providing indispensable experimental data.

Finally, I would like to thank IFE and all my colleagues at the department of Energy Systems (ENSYS) for letting me work here, and the Norwegian Research Council (NFR) for sponsoring the study through a strategic institute program (SIP).

ii

Explore everything around you, penetrate to the furthest limits

of human knowledge, and always you will come up with something inexplicable

in the end.

It is called life.

Albert Schweitzer

iii

ABSTRACT

A stand-alone power system (SAPS) is defined as an autonomous system that supplies electricity without being connected to the electric grid. The work of this thesis is divided into two parts. The first part deals with the fundamentals of stand-alone power systems, while the second part deals with the simulation of integrated based on solar-hydrogen energy technology.

The first part of the thesis is a systematic review of the fundamentals of energy systems, the governing physical and chemical laws related to energy, inherent characteristics of energy system, and the availability of the earth’s energy. The purpose of this review is to clarify and make it easier to select practical SAPS that can fulfill the user needs and corresponding system operational and functional requirements. In this context, the most realistic technological options are reviewed and a few general design guidelines about generically optimal SAPS for the future are given. The systematic approach presented in this part of the study demonstrates in a factual way why solar–hydrogen systems are one of the most viable options for the future.

The second part, and main bulk, of the thesis deals with the modeling of SAPS, with focus on photovoltaic–hydrogen (PV–H2) energy systems. Simulation models for a transient simulation program (TRNSYS) are developed for PV–H2 components. These include detailed models for key technologies such as photovoltaics (PV), water electrolysis, hydrogen storage (compressed gas or metal hydrides), fuel cells, and secondary batteries. All of the developed models are based on physical and chemical principles, as well as empirical parameters.

A PV–H2 demonstration plant (PHOEBUS) located at the research center in Jülich, Germany, was studied in detail and served as a reference plant. This plant has been in operation since 1993, but most of the data used in this thesis were based on measurements made in 1996—a year with extraordinary consistent operation and regular minutely measurements. The developed TRNSYS models were tested and verified up against operational data from the reference plant, as well as separate experiments performed on individual system components. The results from these analyses showed that all of the key component models were in good to excellent agreement with the measured values. The conclusion was that most of the developed models were sufficiently accurate to perform short-term system simulation studies, while all of the models were more than accurate enough to perform long-term simulations.

In the last part of the study, the verified simulation models were used to find the optimal operation and control strategies of an existing PV–H2 system (the reference plant). A set of realistic control actions related to the on/off-switching of components, such as the electrolyzer and fuel cell, were simulated, so that both the short-term and long-term system effects could be analyzed. System constraints related to state of charge of the battery, pressure in the hydrogen storage, run time (or standby time) components, and so forth, were considered. The main conclusion was that the simulation methods could successfully be used to find optimal operation and control strategies for a system with a fixed design. The simulation results also illustrated that a similar method could be used to find alternative system designs. A methodology on how to perform a combined optimization of the system design and operation was outlined and recommended for future work.

v

TABLE OF CONTENTS

Preface i

Abstract iii

Table of Contents v

Acronyms xi

1 Introduction 1 1.1 Stand-Alone Power Systems .............................................................................1

1.1.1 Definition of SAPS ...............................................................................1 1.1.2 Factors Influencing SAPS .....................................................................1 1.1.3 Externalities...........................................................................................2 1.1.4 Global Perspective.................................................................................4 1.1.5 Local Perspective ..................................................................................6

1.2 Scope of The Study ...........................................................................................7 1.2.1 Objective 7 1.2.2 Organization of Thesis ..........................................................................7

2 Fundamentals of Energy Systems 11 2.1 Introduction .....................................................................................................11

2.1.1 Definition of Energy............................................................................11 2.1.1.1 Extensive Variables ............................................................12 2.1.1.2 Intensive Variables .............................................................12

2.1.2 Classification of Energy ......................................................................12 2.1.3 Energy Units........................................................................................13

2.2 Energy Forms ..................................................................................................13 2.2.1 Mechanical Energy..............................................................................13

2.2.1.1 Gravitational Energy...........................................................13 2.2.1.2 Accelerational Work ...........................................................14 2.2.1.3 Rotational Work..................................................................14 2.2.1.4 Spring Work........................................................................14 2.2.1.5 Energy of a Fluid (Boundary Work) ...................................14

2.2.2 Electrical and Electromagnetic Energy ...............................................14 2.2.2.1 Electrostatic Energy............................................................15 2.2.2.2 Energy in a Capacitor..........................................................15 2.2.2.3 Energy of Electromagnetic Induction .................................15 2.2.2.4 Energy of Electromagnetic Field Wave ..............................15 2.2.2.5 Magnetic Energy.................................................................16

2.2.3 Chemical Energy .................................................................................16 2.2.3.1 Molecular Bonding .............................................................16 2.2.3.2 Hydrogen Bonding..............................................................17 2.2.3.3 Metallic Bonding ................................................................17 2.2.3.4 Ionic Bonding .....................................................................17 2.2.3.5 Covalent Bonding ...............................................................17

vi

2.2.3.6 Energy in Solutions (Chemical Potential) ..........................18 2.2.4 Thermal Energy...................................................................................18 2.2.5 Photon Energy (Radiation Energy)......................................................19 2.2.6 Potential Energy Forms &Terminology ..............................................20

2.2.6.1 Voltaic Cell Potentials ........................................................20 2.2.6.2 Nuclear Energy ...................................................................20 2.2.6.3 Bernoulli’s Theorem...........................................................21 2.2.6.4 Thermodynamic Potentials .................................................21

2.3 Energy Systems ...............................................................................................21 2.3.1 Quality of Energy (Exergy) .................................................................22 2.3.2 Energy Conversion ..............................................................................23

2.3.2.1 Ranking of Energy Forms...................................................23 2.3.2.2 Exergy Conversion Efficiency (Theoretical Maximum) ....25 2.3.2.3 Actual System Conversion Efficiencies..............................27

2.3.3 Energy Storage ....................................................................................28 2.4 Traditional Energy Resources .........................................................................29

2.4.1 Fossil Fuel Energy...............................................................................29 2.4.1.1 Coal.....................................................................................30 2.4.1.2 Petroleum............................................................................30 2.4.1.3 Natural Gas .........................................................................30

2.4.2 Nuclear Energy....................................................................................31 2.4.2.1 Nuclear Fission ...................................................................31 2.4.2.2 Nuclear Fusion....................................................................32

2.5 Natural Energy Resources ...............................................................................32 2.5.1 Solar Energy........................................................................................34 2.5.2 Hydro Energy ......................................................................................36 2.5.3 Wind Energy........................................................................................37 2.5.4 Bioenergy 40 2.5.5 Ocean Energy ......................................................................................42

2.5.5.1 Ocean Current Energy.........................................................42 2.5.5.2 Ocean Thermal Energy .......................................................42 2.5.5.3 Ocean Wave Energy (Wave Power) ...................................43 2.5.5.4 Ocean Salinity Gradient Energy .........................................43

2.5.6 Ocean Tidal Energy.............................................................................44 2.5.7 Geothermal Energy..............................................................................44

2.6 Summary .........................................................................................................45

3 Stand-Alone Power Systems 47 3.1 Generic SAPS .................................................................................................47

3.1.1 Feasible Systems .................................................................................47 3.1.2 General Design Guidelines..................................................................49 3.1.3 Hydrogen Energy Systems ..................................................................50

3.2 Practical SAPS ................................................................................................51 3.2.1 Size of Systems ...................................................................................51 3.2.2 Mini-grid Systems (Fixed Size) ..........................................................52 3.2.3 Modular Systems (Flexible Size) ........................................................52

3.3 Hydrogen Energy Technology.........................................................................53 3.3.1 Hydrogen Production (Water Electrolysis) .........................................53

3.3.1.1 Conventional Alkaline Electrolyzers ..................................54

vii

3.3.1.2 Advanced Alkaline Electrolyzers .......................................55 3.3.1.3 Acidic Electrolyzers............................................................56 3.3.1.4 Solar Photoproduction of Hydrogen ...................................56

3.3.2 Hydrogen Storage................................................................................57 3.3.3 Hydrogen Utilization (Fuel Cells) .......................................................58

3.3.3.1 Other Fuel Cell Systems .....................................................59 3.4 Energy Technologies for SAPS.......................................................................60

3.4.1 Recommended SAPS Configurations .................................................60 3.4.2 Characteristics of SAPS Technology ..................................................61 3.4.3 Photovoltaic Cells ...............................................................................61 3.4.4 Secondary Batteries .............................................................................63

3.4.4.1 Classification of Battery Systems .......................................64 3.4.4.2 Lead-acid Batteries .............................................................65 3.4.4.3 Valve-Regulated Lead-Acid (VRLA) Batteries..................66 3.4.4.4 Nickel-Cadmium Batteries .................................................67 3.4.4.5 Advanced Battery Systems .................................................68

3.4.5 Power Converters (Power Conditioners).............................................70 3.5 Recommended SAPS for the Future ...............................................................71

3.5.1 Hydrogen Systems...............................................................................71

4 Modeling 75 4.1 SIMULATION of PV–H2 Systems .................................................................76

4.1.1 Simulation Programs...........................................................................76 4.1.2 TRNSYS 77

4.2 Simulation Input..............................................................................................78 4.2.1 Solar Radiation....................................................................................78

4.2.1.1 Weather Data Generator .....................................................79 4.2.1.2 Solar Radiation Processor...................................................79

4.2.2 User Load ............................................................................................79 4.3 PV-Generator ..................................................................................................79

4.3.1 General Description.............................................................................79 4.3.2 Mathematical Modeling ......................................................................80

4.3.2.1 Electrical Model (I–U Characteristic)................................81 4.3.2.2 Thermal Model ...................................................................85 4.3.2.3 Numerical Methods ............................................................87

4.3.3 Other PV Models.................................................................................87 4.3.3.1 Two-diode Model ...............................................................87 4.3.3.2 Detailed Thermal Model.....................................................88

4.4 Wind Energy Generator ..................................................................................89 4.5 Electrochemical Reactors................................................................................90

4.5.1 Chemical Reaction Principles .............................................................90 4.5.2 Standard State......................................................................................91 4.5.3 Thermodynamics .................................................................................91 4.5.4 Electrode kinetics ................................................................................94 4.5.5 Transport Phenomena..........................................................................95

4.6 Electrolyzer .....................................................................................................96 4.6.1 General Description.............................................................................96 4.6.2 Mathematical Modeling ......................................................................97

viii

4.6.2.1 Relation between Change in Gibbs Energy and Cell Potential ..............................................................................97

4.6.2.2 I–U Characteristics .............................................................98 4.6.2.3 Hydrogen Production (Faraday Efficiency) ........................99 4.6.2.4 Energy Efficiency .............................................................101 4.6.2.5 Thermal Model .................................................................101 4.6.2.6 Overall Heat Transfer Coefficient–Area Product .............103 4.6.2.7 Numerical Methods ..........................................................104

4.7 Hydrogen Storage and Auxiliary Equipment ................................................104 4.7.1 Gas Storage (Pressure Vessel)...........................................................104 4.7.2 Compressor........................................................................................105 4.7.3 Metal Hydride....................................................................................105

4.8 Fuel Cell ........................................................................................................107 4.8.1 General Description...........................................................................107 4.8.2 Mathematical Modeling ....................................................................109

4.8.2.1 I–U Characteristics ...........................................................109 4.8.2.2 Faraday Efficiency ............................................................111 4.8.2.3 Energy Efficiency .............................................................112 4.8.2.4 Thermal Model .................................................................113

4.9 Secondary Battery .........................................................................................114 4.9.1 General Description...........................................................................114 4.9.2 Mathematical Modeling ....................................................................116

4.9.2.1 Literature Survey ..............................................................116 4.9.2.2 Equivalent Circuit .............................................................117 4.9.2.3 Current Model...................................................................117 4.9.2.4 Voltage Model ..................................................................118 4.9.2.5 Battery Capacity................................................................119 4.9.2.6 Thermal Model .................................................................119

4.10 Power Conditioning Equipment....................................................................119 4.10.1 General Description...........................................................................119 4.10.2 Mathematical Description .................................................................120

4.11 Summary .......................................................................................................120

5 Testing & Verification of Models 121 5.1 PV–Generator................................................................................................122

5.1.1 Verification of I–U Characteristic.....................................................122 5.1.1.1 Comparison between One-Diode and Two-Diode Model 122 5.1.1.2 Comparison with Operational Data ..................................123

5.1.2 Maximum Power Point Tracker ........................................................124 5.1.2.1 Performance of MPPT ......................................................124 5.1.2.2 Temperature Dependence of the MPP ..............................125

5.1.3 Analysis of a Detailed Thermal Model .............................................125 5.1.4 Verification of Thermal Models........................................................127

5.2 Electrolyzer ...................................................................................................130 5.2.1 I–U Characteristic .............................................................................130 5.2.2 Hydrogen Production ........................................................................132

5.2.2.1 Faraday Efficiency ............................................................132 5.2.2.2 Comparison between Simulated and Experimental Data .133

5.2.3 Thermal Model..................................................................................134

ix

5.2.3.1 Overall Heat Transfer Coefficient–Area Product .............134 5.2.3.2 Comparison between Simulated and Measured Data .......135

5.3 Fuel Cell ........................................................................................................137 5.3.1 I–U Characteristic .............................................................................137 5.3.2 PEMFC Stack Performance ..............................................................138 5.3.3 Hydrogen Consumption ....................................................................138 5.3.4 Thermal Model..................................................................................139

5.4 Secondary Battery .........................................................................................139 5.4.1 Voltage Model...................................................................................139 5.4.2 I–U Characteristic .............................................................................140

5.4.2.1 Comparison with Operational Data from the SAPS at Lyklingholmen..................................................................141

5.4.2.2 Comparison with Operational Data from PHOEBUS ......143 5.5 Power Conditioning Equipment....................................................................144

5.5.1 Efficiency Curves ..............................................................................144 5.6 Conclusions & Recommendations ................................................................145

5.6.1 PV–Generator....................................................................................145 5.6.2 Electrolyzer .......................................................................................145 5.6.3 Fuel Cell 146 5.6.4 Battery 146 5.6.5 Power Conditioning Equipment ........................................................146

6 Simulation of Stand-Alone PV–H2 Systems 147 6.1 Simulation Setup ...........................................................................................147

6.1.1 Reference System ..............................................................................147 6.1.2 Simulated System..............................................................................148 6.1.3 Assumptions & Simplifications ........................................................148

6.1.3.1 Oxygen Handling System .................................................148 6.1.3.2 Hydrogen Losses...............................................................150 6.1.3.3 Parasitic Loads..................................................................150 6.1.3.4 Protective Current for the Electrolyzer .............................151

6.2 Control Strategies for PV–H2 Systems .........................................................152 6.2.1 Basic Control Strategy.......................................................................152 6.2.2 Electrolyzer Controller ......................................................................153

6.2.2.1 Mode of Operation............................................................153 6.2.2.2 Standby Mode & Seasonal On/Off-Switching..................156 6.2.2.3 Additional Controls ..........................................................156 6.2.2.4 Numerical Solutions in TRNSYS.....................................157

6.2.3 Fuel Cell Controller...........................................................................157 6.2.3.1 Mode of Operation............................................................159 6.2.3.2 Seasonal Switching...........................................................159

6.2.4 Compressor Controller ......................................................................159 6.3 Typical Control Actions................................................................................159

6.3.1 Electrolyzer .......................................................................................159 6.3.1.1 March 10–12.....................................................................159 6.3.1.2 Scenario 1 .........................................................................160 6.3.1.3 Scenario 2 .........................................................................160 6.3.1.4 June 7 ................................................................................162 6.3.1.5 Scenario 3 .........................................................................162

x

6.3.1.6 Scenario 4 .........................................................................162 6.3.2 Compressor........................................................................................164

6.3.2.1 Scenario 5 .........................................................................164 6.3.3 Fuel Cell 164

6.3.3.1 January 1–4 .......................................................................164 6.3.3.2 Scenario 6 .........................................................................165 6.3.3.3 Scenario 7 .........................................................................165

6.4 System Simulations.......................................................................................166 6.4.1 Typical Week ....................................................................................166 6.4.2 Typical Year ......................................................................................168

6.4.2.1 Solar Radiation & User Load............................................168 6.4.2.2 Battery Conditions ............................................................169 6.4.2.3 Fuel Cell and Electrolyzer Operation ...............................169 6.4.2.4 Hydrogen Storage .............................................................169 6.4.2.5 Total System .....................................................................170

6.5 Optimal Control Strategies............................................................................172 6.5.1 Controller Set Points .........................................................................172

6.5.1.1 Electrolyzer Mode of Operation .......................................173 6.5.1.2 Basic Control Strategy for the Electrolyzer ......................173 6.5.1.3 Additional Controls ..........................................................174 6.5.1.4 Seasonal On/Off-Switching for the Electrolyzer ..............174 6.5.1.5 Hydrogen Supply Flow Set Point for the Fuel Cell ..........176 6.5.1.6 Basic Control Strategy for the Fuel Cell...........................177 6.5.1.7 Seasonal Settings of Fuel Cell Thresholds .......................178

6.5.2 Discussion of Results ........................................................................178 6.5.2.1 Sensitivity Analysis ..........................................................181 6.5.2.2 Two Extreme Scenarios ....................................................181

6.5.3 Conclusions & Recommendations ....................................................182 6.6 Optimal System Designs ...............................................................................183

6.6.1 Direct Coupling of Components .......................................................183 6.6.2 High-pressure Electrolyzer................................................................184 6.6.3 Metal Hydride Storage ......................................................................184 6.6.4 PV–Wind–H2 System........................................................................185 6.6.5 Recommendations .............................................................................185

6.7 Summary .......................................................................................................186

7 Conclusions & Recommendations 187 7.1 Sustainable Stand-Alone Power System (SAPS) for the Future (Part I).......187 7.2 Simulation of Stand-Alone PV–H2 Systems (Part II) ...................................188

7.2.1 Modeling of PV–H2 Components .....................................................188 7.2.2 Optimization of the Operation of PV-H2 Systems ............................190 7.2.3 Recommendations for Improved Designs .........................................190

References 192

Appendix 203

xi

ACRONYMS

AC Alternating Current AFC Alkaline Fuel Cell AGM Absorbed Glass Mat AM Air Mass ASME American Society of Mechanical Engineers CHP Combined Heat and Power plant CPV Common Pressure Vessel DACS Data Acquisition and Control System DC Direct Current DMFC Direct Methanol Fuel Cell DOD Depth of discharge EC External Combustion EEC European Economic Community emf electromotive force ENEA Ente per le Nuove tecnologie, l'Energia e l'Ambiente EV Electrical Vehicle FhG-ISE Fraunhofer Institut für Solare Energiesysteme FZ Jülich ForschungsZentrum Jülich GEO Geosynchronous Earth Orbit H2–SAPS Hydrogen based Stand-Alone Power System H2PHOTO H2–PHOTOvoltaic simulation program HYSOLAR HYdrogen SOLAR project IC Internal Combustion IFE Institutt for Energy Teknikk INTA Instituto Nacional de Technica Aerospacial IPCC Intergovernmental Panel on Climate Change IPV Individual Pressure Vessel ISES International Solar Energy Society JULSIM JUelich SIMulation program LEO Low Earth Orbit LH2 Liquid Hydrogen MCFC Molten Carbonate Fuel Cell MEA Membrane Electrode Assembly MH Metal Hydride mmf magnetomotive force MO Molecular Orbital MPP Maximum Power Point MPPT Maximum Power Point Tracker NAS National Academy of Sciences NOCT Nominal Operating Cell Temperature OTEC Ocean Thermal Energy Conversion PAFC Phosphoric Acid Fuel Cell PEC PhotoElectroChemical

xii

PEM Proton Exchange Membrane PEMFC Proton Exchange Membrane Fuel Cell PHOEBUS PHOtovoltaik-Elektrolyse-Brennstoffzelle Und Systemtecknik PH2 Pressurized Hydrogen PTFE PolyTetraFluorEthylene PV Photovoltaic PV1 PV-array at PHOEBUS oriented to the southwest at a tilt of 40° R&D Research & Development RAPS Remote-Area Power System redox oxidation-reduction RMS Root Mean Square rpm revolutions per minute SAPHYS Stand-Alone Photovoltaic HYdrogen energy System SAPS Stand-Alone Power System SCADA Supervisory Control and Data Acquisition SE SouthEast SI le Système International d’unités SIMELINT SIMulaton of ELectrolyzers in INTermittent operation SIMNON SIMulation program for NON-linear systems SOC State of Charge SOFC Solid Oxide Fuel Cell SOV State of Voltage SPE Solid Polymer Electrolyte SW SouthWest SWB Solar-Wasserstoff-Bayern TRNSYS TRaNsient SYstem Simulation program UN United Nations UNESCO United Nations Educational, Scientific, and Cultural Organization USSR Union of Soviet Socialist Republics VRB Vanadium Redox Battery VRLA Valve-Regulated Lead-Acid WCED World Commission on Environment and Development WECS Wind Energy Conversion System WMO World Meteorological Organization WRC World Radiation Centre

1 INTRODUCTION

The overall objective of this thesis is to study and optimize the design and operation of stand-alone power system (SAPS). The purpose of this chapter is to properly define SAPS and to give an overview of the main factors influencing stand-alone power systems. The topic of SAPS is viewed from both a global and local perspective. The chapter also gives an overview of the scope of the study and the organization of the thesis.

1.1 STAND-ALONE POWER SYSTEMS

1.1.1 Definition of SAPS

A stand-alone power system (SAPS) is defined as an autonomous system that supplies electricity without being connected to the electric grid. These kinds of decentralized systems can also be referred to as remote-area power systems (RAPS) because they are frequently located in remote and inaccessible areas. However, in this thesis the terminology SAPS will be used. The definition also includes small electric grids, or mini-grids, which are common for large types of stand-alone power systems.

1.1.2 Factors Influencing SAPS

A global view of the main factors influencing SAPS is given conceptually in Figure 1.1. These factors—the user needs and requirements, the climate, the energy resources, the physical laws of nature, and the environment—are regarded as external processes and are therefore indicated by squares with rounded corners. The system boundary around the SAPS is indicated by the doted circle while the factors that influence processes or the system itself are drawn with lines pointing in the direction of cause and effect. Solid lines indicate a direct cause while doted lines indirect non-definite cause.

A comprehensive study of SAPS is best done by first investigating each of the individual factors separately. If this is done in a thorough and exhaustive manner, the limitations, or constraints, are once and for all established. Furthermore, the chances of overlooking possible solutions are minimized. A key issue in relation to design and operation of SAPS are the two independent factors: (1) location and (2) time span (i.e., lifecycle).

The location, defined as the exact physical position in terms of latitude, longitude, and altitude, is a natural starting point for any analysis of SAPS. The reason for this is that leads directly to information about the climate, energy resources, and user needs. Along with local environmental constraints, these factors are, as it will be demonstrated during the course of this study, essential inputs to the first stage of the design of SAPS.

In relation to SAPS there are several issues related to the aspect of time—both long-term and short-term considerations must be made. The long-term time aspects are clearly illustrated by

2

the seasonal changes in the climate, where the magnitude of the change of course depends on the location. User needs and energy availability might also be seasonal. These long-term time effects are bound to influence the design of SAPS.

The short-term time scale is defined in this thesis as day, hours, minutes or seconds. The external conditions such as climate and user needs are continuously dependent on time while the physical laws on energy conversion are independent of time. An analysis of SAPS at a quasi-instantaneous level gives insight to how actual systems should be operated.

SAPS

user needs

energy resources

climate

physical laws

time & location

environment

System boundary of research

Figure 1.1 The main factors influencing a stand-alone power system (SAPS).

1.1.3 Externalities

A true life-cycle analysis of a SAPS can only be complete if all factors, both global and local, are investigated over a very long period of time (e.g., 50 years or more). According to the Intergovernmental Panel on Climate Change (IPCC) of the United Nations (UN), there is a balance of evidence that suggests that anthropogenic (human-induced) greenhouse gases, inter alia carbon dioxide (CO2), methane (CH4), and nitrous oxide (N2O), are interfering with the global climate system (IPCC, 1995). In other words, there is a discernible human influence on the global climate.

According to the World Commission on Environment and Development (WCED), the principle of a sustainable development implies that the human consumption of resources (e.g., water, food, and energy) on earth must in the longer term be in harmony with the environment (WCED, 1987). In this context, the main global environmental problems to be avoided in the development and dissemination of SAPS are:

Chapter 1 Introduction

3

• Air pollution (e.g., CO2 and other greenhouse gases) • Ground water pollution (e.g., toxic waste) • Destruction of plant and animal life (e.g., land degradation, deforestation) • Creation of fallow land (e.g., landfills with manufacturing and end-of-use waste)

Environmental problems with possible retroactive effects on the global climate are not an integral part of this study. This explains why no link between the environment and climate is indicated in Figure 1.1. Nevertheless, the SAPS considered will aim to minimize the damage on the environment.

From an energy point of view, it is possible to calculate a so-called energy payback time—the time it takes for an energy system to generate (during operation) the amount of energy that was required to produce (in manufacturing) the energy system in the first place. In other words, the energy payback time is a measure of how resource friendly an energy system is in the long term. Although the energy payback time is not explicitly analyzed in this study, the concept is used as a guideline in the selection of possible SAPS technologies for the future.

In addition to the global constraints mentioned so far, practical SAPS must satisfy a set of local constraints. Some of the most important of these “real world” constraints are:

Local environmental constraints:

• Air pollution (e.g., noise, smell) • Ground pollution (e.g., toxic waste) • Aesthetics

Monetary (financial) constraints:

• Capital costs • Operational costs

Social & public constraints:

• Manpower and technical expertise • Physical infrastructure (e.g., roads, water utilities, telecommunications) • Organizational infrastructure (e.g., energy bureaus and departments) • Conflicts of interest between energy and other resources (e.g., water, food, land)1

The financing of SAPS is naturally of prime importance in liberated economies of today. However, the lists above indicate that there are also a number of other, less quantifiable, but important constraints. For instance, the issue of manpower, technical expertise and infrastructure might be of prime importance, as a comparison between industrial and developing countries might illustrate:

In industrialized countries, where the infrastructure and technological development has come the furthest, complex SAPS can be installed. The supply of spare part, repair, maintenance, and so forth, is generally not a problem. Conversely, in developing countries, where access to

1Also a global problem which frequently leads to wars.

4

sophisticated technical equipment and professional technical expertise is scarcer, simple SAPS are more viable.

Although no detailed analysis of local constraints such as the ones mentioned above are included in this thesis, they are, similarly to the global environmental constraints, used as general guidelines in the selection of sustainable SAPS for the future.

1.1.4 Global Perspective

First of all, it is important to establish some fundamental facts about SAPS. A systematic method on how to determine the needs and requirements of a properly defined system can be found by asking simple questions beginning with the words why, where, and what about the defined system (Asbjørnsen, 1992). A good starting point for the discussion of is therefore to ask questions such as: Why is there a need for SAPS? Where is there a need for SAPS? and What are the SAPS user requirements?

Electrical energy, or electricity, is defined as high quality energy (Section 2.3). In the past century all modern societies in the world have grown increasingly dependent on electricity for continual growth and development. Towards the end of this century, also people in the developing countries have shown that they are becoming more and more dependent on electrical power. With the advent of the information society this trend is not likely to change. On the contrary, people living without electricity today will most likely require electricity in the future, simply because they want to take part of the global development.

In the industrialized countries, the countries with the greatest technological developments, most of the consumers’ electricity demand is met by power from electric transmission lines. These kind of electrical systems, or grid-connected systems, link consumers to large and distant power plants. In most industrialized countries both urban and rural areas have become almost fully electrified. However, there are some regions that have not been and cannot be electrified by the grid due to obvious physical constraints, e.g., remote islands and areas deep into the forests or high up in the mountains.

In recent decades developing countries have sought to provide power for communications and education, as well as to boost productivity of industry and agriculture. According to researchers at the Worldwatch Institute (Flavin and O’Meara, 1997) an estimated 1.3 billion people have received power in the last 25 years. Today about 2 billion people—one-third of the world’s population—still lack access to electricity.

Table 1.1 specifies for various countries and regions the number and percentage of the population living off-grid. Africa, India, China, Asia, Oceania, and parts of South America are regions where large fractions of the total population live off-grid. Many of these people live in rural and remote areas, but in the future it is likely that many will move in to urban areas—similarly to what the trend has been in the industrialized nations the past century.

The rate at which people in the developing countries will move into the urban areas will depend on politics, sosio-economics, and technical developments, both on a global and local level. However, in the future it is likely that large numbers of people will continue to live in rural and remote areas. The rate at which these people will be given power from the grid is also dependent on the factors mentioned above.


5

According to Table 1.1, the fraction of the population in the industrialized countries living off-grid is very low. In North America, North and Central Europe, Former USSR, Japan, and Australia most people are connected to the grid. Hence, the need for SAPS for residential applications in these regions is relatively low.

Table 1.1 Population in various regions of the world living off-grid a.

Region Total millions

Off-grid %

Off-grid millions

Canada 25 4 1 USA 240 2 5 Mexico 80 20 16 Latin America 190 40 76 Brazil 145 23 33 Northern Europe 30 2 1 Central Europe 115 5 6 Southern Europe 80 15 12 EEC-Europe 320 2 6 Former USSR 280 5 14 Middle East 110 45 50 India 770 78 601 China 1,070 37 396 North Africa 135 56 76 Nigeria & Gabon 95 63 60 South Africa 35 17 6 Africa 310 90 279 Japan 120 2 2 South Korea 70 4 3 Indonesia 175 80 140 Asia & Oceania 520 72 374 Australia & New Zealand 20 5 1

a. Source: Dessus et al. (1992)

In addition to the domestic potential, there are a number of commercial and public applications that require off-grid power and fall into the category of SAPS. Some typical areas and potential applications (listed in parenthesis) are:

• Telecommunication (e.g., satellite stations) • Meteorology (e.g., weather stations) • Navigation (e.g., lighthouses) • Light industry (e.g., fisheries) • Tourism (e.g., lodges, huts, cabins, and camps) • Agriculture (e.g., water pumping) • Public (e.g., schools and hospitals) • Emergency (e.g., field hospitals and refugee camps)

6

The above list is by no means exhaustive, but does indicate that the needs and requirements for these applications are very different. The design and operation of a SAPS that satisfies the power demand for a specific application can only be understood by detailed analyses.

1.1.5 Local Perspective

The needs and requirements, which in this case are defined as the electrical power demand, or the load, depends on several factors (Figure 1.1), but mainly on the climate and the users’ need for electricity and their consumption habits.

The climate and location has a significant impact on the size and shape of the load because it directly influences the way people use electricity for lighting, cooling, heating, and so forth. For instance, in cool temperate and cold climates (high latitudes), where there are great seasonal variations between summer and winter, the demand varies significantly over the year. In comparison, tropical and dry climates (low latitudes), where the seasonal changes are smaller, the demand is likely to be more constant.

However, the need for electricity is also closely linked to people’s habits of electricity consumption. In the residential sector, for example, there are some minimum power requirements that people in industrialized countries have become accustomed to expect. If this power demand is to be reduced new and more efficient energy technologies must be introduced and users might have to change their habits.

The situation is quite different in the developing countries. Here peoples’ need for electricity is quite small, but is likely to increase, as also they become accustomed to the modern necessities in life. In any case, independent of country, there is a need for off-grid electricity for domestic purposes.

In order to differentiate between SAPS a convenient classification system, where the systems are classified according to the required power demand, is proposed in this thesis. Table 1.2 gives an example on what such a categorization system might look like. Note that the power ranges in the table are approximate and that an application could be listed in more than one of the three categories. For instance, in the case of industrialized countries, SAPS for holiday cabins can probably be categorized as both small and medium-sized.

One reason for why it might be helpful to organize SAPS in the manner demonstrated above (Table 1.2) is that it can be instrumental in determining the shape of the load, which largely depends on the application. For instance, the load for a typical rural village in a developing country will be quite low during day time compared to night time (Harvey, 1995). This is because the electricity needed is primarily for lighting and running appliances (e.g., TV, radio, and cooking) that are used (after work) in the evenings. In comparison, a telecommunication or meteorological station is likely to have a relatively constant load.

Based on the above facts on population living off-grid (Table 1.1) and the classification system proposed (Table 1.2), it can be inferred that the largest and probably fastest growing marked for SAPS are the ones with small power requirements—in the range of a few watts.

Nevertheless, the scope and focus of this study will be on medium and large SAPS because they cover the electricity needs for a wide range of applications. Thus, the research and development (R&D) of such systems will benefit people in all parts of the world. The


7

philosophy here is that R&D of medium to large SAPS applicable for niche markets in industrialized countries eventually will lead to systems that satisfy and benefit the much larger markets in the developing countries.

Table 1.2 Classification system for SAPS according to power demand.

Category Rated Power W

Country a type

Application example

Small 10–100 D Dwelling I Holiday cabinb D,I Weather station D,I Navigation system

Medium 100–10,000 D School D Hospital D Tourist lodge D Agricultureb I Dwelling D,I Field hospitalc D,I Telecom. station

Large 10,000–100,000 D Village D Light industryb I Agricultureb D,I Tourist lodge D,I Refugee campb, c

a. D = Developing country, I = Industrialized country b. Special requirement: Do not need continuous power. c. Special requirement: Need to be portable

1.2 SCOPE OF THE STUDY

1.2.1 Objective

The general objective of this thesis is to analyze stand-alone power systems (SAPS) based on technologies that satisfy and abide by the principle of efficient energy conversion and storage of sustainable energy resources. Thus, the main focus will be on alternative fuels and energy technologies for SAPS for the relative near future—say the next 20 years.

1.2.2 Organization of Thesis

The thesis is divided into two parts. Part I (Chapters 2–3) deals with the fundamentals of stand-alone power systems, while Part II (Chapters 4–7) deals with the simulation of integrated based on solar-hydrogen energy technology.

Chapter 2 is a systematic review of the fundamentals of energy systems, the governing physical and chemical laws related to energy, inherent characteristics of energy system, and

8

the availability of the earth’s energy. The purpose of this review is to clarify and make it easier to select practical SAPS that can fulfill the user needs and corresponding system operational and functional requirements. In Chapter 3 a number of practical SAPS are recommended. Thus, Part I sets the precedence for the detailed simulations on solar-hydrogen energy systems in Part II.

The individual system components required in a SAPS based on solar hydrogen energy technology are modeled in detail in Chapter 4. A thorough testing and verification of these models are provided in Chapter 5. Finally, the results from the simulations of integrated systems are presented in Chapter 6. The conclusions and recommendations of the thesis are given in Chapter 7.

PART I

FUNDAMENTALS

OF

STAND-ALONE POWER SYSTEMS

2 FUNDAMENTALS OF ENERGY SYSTEMS

The concept of energy in society seems to be quite independent of what is meant by energy in scientific terms. Most people in society think of energy from an economical point of view. The cost of petroleum, coal, natural gas, nuclear energy, hydroelectric power, and so forth is usually the main concern, but recently also energy problems such as global air pollution—including climatic change—has been a concern. The solution to these problems is energy conservation, whose leading principles can be derived from physics and chemistry.

This chapter focuses on the fundamental principles of energy and energy systems in general, as SAPS ultimately depend on these principles. The chapter introduces by properly defining, classifying, and describing the concept of energy (Section 2.1). Next, follows a brief description of the five main forms of energy (Section 2.2). Then some fundamentally important issues related to energy conversion and energy storage are discussed (Section 2.3). Finally, the traditional and natural energy resource base on earth are assessed (Sections 2.4 and 2.5). The natural energy resources, which later are demonstrated to be particularly relevant for SAPS, are discussed in quite some detail.

This chapter is a review of the fundamentals of energy systems, and provides therefore no new basic knowledge. However, it is included because it provides important and indisputable facts about energy resource availability, energy conversion, and energy storage. In today’s society this information is too often overshadowed by economic considerations. It is therefore hoped that the material presented in this chapter will clarify some of these issues and that it will help the reader to make the right energy decisions in the future.

2.1 INTRODUCTION

2.1.1 Definition of Energy

The origination of the term energy is the Greek word ergon meaning work. In other words, energy is a generic term and is defined as the capacity of a body or a system of bodies of doing work. Therefore, work is the same physical quantity as energy. In practice, this means that work and energy have the same dimensions or units (Table 2.2).

A scientific definition of energy is possible by introducing a set of generalized variables; if the force F acts over the displacement x, then the corresponding work W can be expressed on differential form as (Ohta, 1994):

dW = Fdx or dW = pAdx = p dV 2.1

where p is the pressure and acting over the area A, and dV is the change in volume. There is an important observation to be made about Equation 2.1, and that is that the generalized force flux, or pressure, p is an intensive variable, while dV = Adx is an extensive variable.

12

Intensive and extensive variables can never be added. However, an extensive property can be multiplied by an intensive property to produce a new extensive property (Asbjørnsen, 1989).

2.1.1.1 Extensive Variables

Extensive variables are variables associated with the size of the system, and they must be measured by spatial integration. Some examples of extensive variables are total volume, total number of moles, total mass, and total energy.

The total volume and total number of moles are basic extensive variables (with basic units). Other extensive variables, such as total mass or total energy, can be derived from basic extensive variables and intensive variables. For instance, the total mass can be derived from density or molar weight, while total energy can be derived from an energy intensive variable.

2.1.1.2 Intensive Variables

Intensive variables are point variables, or field variables in a system. They are independent of size of the system and can only be measured at a point. The purpose of intensive variables is to characterize the spacious field of a system. Some examples of intensive variables are:

• Vector quantities characterizing mass movement (e.g., force flux, velocity, acceleration). • Vector quantities characterizing energy movement (e.g., heat flux, radiation flux). • Vector quantities characterizing electrical fields (e.g., electrical current flux, magnetic

flux). • Quantities characterizing the speed and direction of chemical reactions (e.g., reaction rates

per unit volume, per unit mass, or per mass of catalyst). • Properties characterizing thermodynamic state (e.g., temperature, pressure, density,

concentration). • Properties characterizing transport phenomena (e.g., viscosity, thermal and electrical

conductivity, molecular diffusivity). • Properties characterizing radiation (e.g., absorption, reflection, scattering) • Properties characterizing materials (e.g., porosity, permeability, crystalline structure)

2.1.2 Classification of Energy

Energy can be classified into three distinct groups (Table 2.1). The primary energy resources are simply defined as the energy resource. In an energy systems primary energy is converted via secondary energy (often in another form) into tertiary energy, which is cleaner and easier to utilize.

Table 2.1 Classification of Energy.

Energy Resource primary energy

Energy Form primary or secondary energy Energy System

• Fossil fuel energy • Mechanical energy • Nuclear energy • Electric and electromagnetic energy • Natural energy • Chemical energy • Thermal energy • Photon energy (radiation energy)

• primary energy → secondary energy → tertiary energy

Chapter 2 Fundamentals of Energy Systems

13

2.1.3 Energy Units

The physical dimensions of energy can be represented in many ways—per unit time, per unit mass, per unit area, per unit volume, per unit charge, per weight, or combinations of these units. The energy terminology used throughout this thesis, unless otherwise stated, is summarized in Table 2.2, where the Standard International (SI) units are also indicated. Some times, it is also convenient to give the energy units in kilowatt-hours (kWh), a derived unit frequently used in relation to electrical systems.

Table 2.2 Energy terminology.

Energy term Alternative term Description SI-Units

Energy basic energy unit J Energy flux energy per unit area J m-2 Energy density energy per unit volume J m-3 Power Energy rate energy per unit time W Power flux energy per unit time per unit area W m-2 Power density energy per unit time per unit volume W m-3 Specific energy energy per unit mass J kg-1 Molar energy energy per unit mol J mol-1

2.2 ENERGY FORMS

This section describes the five basic forms of energy. It should be noted that in cases were the energy expressions describe transitional forms of energy, the correct terminology is power and not energy as indicated in the text.

2.2.1 Mechanical Energy

Five basic forms of mechanical energy, or work, exist: (1) Gravitational energy (PE), (2) Accelerational energy (KE), (3) Rotational energy (KE), (4) Spring energy (PE), and (5) Energy of a fluid (boundary work) (KE). These five forms of mechanical energy can also be defined as kinetic energy (KE) or potential energy (PE). Usually, these forms of energy are presented as a change in kinetic energy (∆KE) or as a change in potential energy (∆PE). In the expressions below (Equations 2.2–2.6) the initial conditions in the integrated work ∫W were assumed equal to zero.

2.2.1.1 Gravitational Energy

The gravitational energy Wg is found from Newton’s universal law of gravity, which shows that a body with mass m placed at a height h in a gravitational field g is:

Wg = mgh (J) 2.2

14

2.2.1.2 Accelerational Work

Accelerational energy is the resulting energy when a force is exerted on a body and moves it a distance along the direction of the force. From Newton’s second law of motion it can be shown that the kinetic energy Wt for a translating body with a mass m and a velocity v is:

2t 2

1 mvW = (J) (translating body) 2.3

2.2.1.3 Rotational Work

Rotational energy Wr is defined as a rotational body with moment of inertia I and angular velocity ω. This kind of kinetic energy is expressed as:

2r 2

1 ωIW = (J) (rotational body) 2.4

2.2.1.4 Spring Work

The potential energy of an elastic spring Ws is related to the spring constant k and the displacement x by the expression:

2s 2

1 kxW = (J) 2.5

2.2.1.5 Energy of a Fluid (Boundary Work)

The energy associated with the expansion and compression of a fluid (in liquid or gas form) is usually referred to the moving boundary work, or simply the boundary work Wb (Çengel and Boles, 1989). The differential boundary work dWb is derived from thermodynamics and is expressed as:

dWb = ρAdh or dWb = pdV (J) 2.6

where ρ is the density of the fluid, A is the cross-sectional area and of the expansion and/or compression cycle, h is enthalpy (Equation 2.28), and V is the volume. The energy Wb from this process can be found by integration.

The result that is found by integrating Equation 2.6 will depend on the fluid used in the process (gas or liquid) and on the process itself, which may be dynamic or static. An example of a dynamic process is the expansion of an air-fuel mixture in a combustion chamber, while the pressure exerted by column water is an example of a static fluid system.

2.2.2 Electrical and Electromagnetic Energy

Electrical current is defined as the time rate of change of charge passing through a specified area. The moving charge may be positive or negative and the area may be the cross-sectional area of a wire or some other suitable spatial area where charges are in motion (Del Toro,


15

1986). The instantaneous current i can be expressed mathematically as the time rate of change of charge1:

tqi

dd= (A) 2.7

Electrical and electromagnetic energy can essentially be classified into five categories: (1) Electrostatic energy, (2) Energy of electric charge in a parallel plate capacitor, (3) Energy of electromagnetic induction, (4) Energy of electromagnetic field wave, and (5) Magnetic energy.

2.2.2.1 Electrostatic Energy

Coulomb’s law describes the electrostatic forces of repulsion between two positively charged electrical particles. Electrostatic energy is the work required overcoming these repulsive forces. The work required moving a charge in an electric field is called voltage. An electric field with a differential voltage dV is often called the potential difference because of its potential to do work on a charge q. Hence, the work W on differential form is

dW = q dV (J) 2.8

2.2.2.2 Energy in a Capacitor

A parallel plate capacitor, or condenser, placed in a potential field is able to store electrostatic energy. The capacitance C of a capacitor is defined as the ratio of the magnitude of the charge Q on either conductor to the magnitude of the potential difference V. That is, C = Q/V. Thus, by substituting this expression into Equation 2.8 and integrating, it can be shown that the energy required to charge the capacitor from q = 0 to q = Q is

W QC

=2

2 (J) 2.9

2.2.2.3 Energy of Electromagnetic Induction

Faraday’s law of induction states that the electromotive force (emf) induced in a circuit is directly proportional to the time rate of change of magnetic flux through the circuit. From this it can be demonstrated that the emf of self-induction ε is directly related to the time rate of change of current di/dt by a proportionality factor L called the inductance (ε = Ldi/dt). Hence, the electromagnetic energy of induction is

W Li= 12

2 (J) 2.10

2.2.2.4 Energy of Electromagnetic Field Wave

An electromagnetic wave is described as a propagating electric field wave combined with a magnetic field wave. The unified theory of electromagnetism is described in Maxwell’s

1 In this context lower case letters are used to emphasize the time-varying nature of current i and potential differences. Conversely, upper case letters and are used to emphasize constant currents I and voltages V.

16

equations (Serway, 1990). If one assumes that the electromagnetic waves are plane waves (travel in one direction) the following is true:

• The electric field E and magnetic field B both satisfy the same wave equation. • In free space (vacuum) electromagnetic waves are related by the speed of light,

c =1 0 0/ ε µ , where ε0 is the permittivity and µ0 is the permeability. • The electric and magnetic field components of plane electromagnetic waves are

perpendicular to each other and also perpendicular to the direction of wave propagation. • The relative magnitudes of E and B in empty space are related by E/B = c.

From the above it can be shown that for an electromagnetic wave the instantaneous energy density associated with the electric field We equals that of the magnetic field Wm. Thus, the electromagnetic energy density is given by:

W W W E B E Be m= + = = = +

ε

µε

µ02

2

00

22

0

12

(J m-3) 2.11

2.2.2.5 Magnetic Energy

Ampère’s law states that in order to produce an average force (or torque) in an electromagnetic device—a magnetomotive force (mmf)—there must be exist a magnetic flux and an ampere-conductor distribution that are stationary to each other and a favorable pattern for the magnetic field. The magnetic field intensity is related by the relationship H = B/µ, where µ is the permeability of the medium. Thus, from Equation 2.11 it is seen that the magnetic energy density can be expressed as

W BHm = 12

(J m-3) 2.12

2.2.3 Chemical Energy

Chemical energy is essentially the bonding energy required to hold atoms or molecules together in stable materials—solids, liquids, or gases (Zumdahl, 1995). Five basic types of chemical energy due to cohesive forces exist: (1) Molecular bonding, (2) Hydrogen bonding, (3) Metallic bonding, (4) Ionic bonding, and (5) Covalent bonding. Another type of chemical energy is the work potential of solutions (or gas mixtures). The work associated with ion transport in solutions is caused by differences in the chemical potential (Bockris and Reddy, 1998).

2.2.3.1 Molecular Bonding

Molecular bonding due to van der Waal’s potential between two molecules of the same material. Organic compounds, such as hydrocarbons found in fossil fuels (Section 2.4.1), belong to this category. The chemical bonded energy of fuels can be released in a combustion process by maintaining an ignition temperature. The energy required to vaporize the fuel is a function of the temperature Ti and can be estimated by

Et = kBTi (J) 2.13


17

where kB is Boltzmann’s constant. Most molecular bonding materials have an Et in the order of 1eV2, which corresponds to a Ti around 1,000–1,500 K. A combustion process is an exothermic reaction—it releases an amount of thermal energy Q and transfers electrons from the fuel (the reactant), to the oxidation material (the product). Reactions like this, where one or more electrons are transferred, are called oxidation-reduction reactions, or redox reactions. On general form, the combustion reaction of hydrocarbons CnHm in pure oxygen, where n is the number of carbon atoms and m is the number of hydrogen atoms, is given by

C H (4

)O CO H On m 2 2 2+ + → + +n m n m Q 2.14

2.2.3.2 Hydrogen Bonding

Hydrogen bonding is due to strong dipole-dipole forces seen among molecules in which hydrogen in bound to a highly electronegative atom, such as nitrogen, oxygen or fluorine. Bonding of water molecules is the most common type of hydrogen bonding in nature. The hydrogen bonding energy is smaller than that of molecular bonding.

2.2.3.3 Metallic Bonding

Metallic bonding is strong and nondirectional. A molecular orbital (MO) model that describes the molecules in terms of quantum mechanics can be used to explain the bonding energy of metals. In this model the electrons are assumed to travel around the metal crystal in the MOs formed from the valence atomic orbitals of the metal atoms. In metal crystals a large number of closely spaced MO energy levels exists. Thus, metallic-bonding energy is relatively strong—it is the third strongest type of chemical bonding.

2.2.3.4 Ionic Bonding

In ionic compounds there exist forces of attraction between opposite charged ions. The most known ionic compound is salt, or sodium chloride (NaCl). Since no free electrons exist in such compounds, the bonding is strong. According to Coulomb’s law, the energy of interaction between a pair of ions is related to the ion charges Q1 and Q2, the distance r between the ion centers, and a proportionality factor k (which depends on the lattice structure of the solid) by the equation

E k Q Qr

= 1 2 (J) 2.15

2.2.3.5 Covalent Bonding

Covalent bonding is due to the exchange of electron pairs in the component molecule. The energy associated with covalent bonds in a molecule depends on the number of pairs of electrons that are shared between the atoms. Those that share one pair of electrons form a single bond, those with two pairs form a double bond, and those with three pairs form a triple bond. In general, multiple bonds are stronger than single bonds. However, the energy of

2 This quantity is close to the ionization energy, i.e., the energy required to remove an electron from a gaseous atom or ion.

18

organic material, for example, a single C–H bond varies in a nonsystematic way depending on the type of molecule. Covalent bonds of inorganic crystals, such as diamonds, are among the strongest types of chemical bonds.

2.2.3.6 Energy in Solutions (Chemical Potential)

In an ideal solution, the work required transferring one mole of species i (in the x-direction) from an initial concentration cI to a final concentration cF (where both cI and cF are equi-concentration surfaces in the yz-plane) is related to the change in chemical potential ∆µ by the expression3:

I

FIF ln

ccRTw =−=∆= µµµ (J mol-1) 2.16

where R is the universal gas constant, T is the temperature, and µI and µF are the initial and final chemical potentials, respectively. The chemical potential µ and Gibbs energy G (Equation 2.30) is related by the theory of thermodynamics. The chemical potential µi of component i is defined as the partial molar Gibbs energy of the system:

ji,,i

i

≠∂∂=

nTpnGµ (J mol-1) 2.17

where nj is amount of substance i at constant pressure p, temperature T, and amount of all the other components except the ith (Koryta et al., 1993). Thus, from Equation 2.17 it is seen that in an isothermal, constant-pressure reversible process the net work done on the system is equal to the change in chemical potential (w = ∆ µ).

2.2.4 Thermal Energy

Thermal energy, or heat, is defined as energy transferred between two systems (or a system and its surroundings) by virtue of a temperature difference. This is in agreement with the 2nd law of thermodynamics as stated in general terms by Kelvin–Planck and Clausius (Boles and Çengel, 1989). The second law of thermodynamics is, according to the Clausius inequality, expressed as the cyclic line integral

0d ≤∫ TQ 2.18

where dQ is the heat loss through a contour. This inequality is valid for all reversible or irreversible cycles. Based on Equation 2.18 the heat for a reversible process can on differential form be expressed as

dQ = T dS (J) 2.19

3 The use of concentration c rather than activity a (defined in Section 4.5.1) implies that the solution is assumed to behave ideally (Bockris et al., 1998).


19

where S is the entropy. The concept of entropy is on a microscopic level explained as molecular disorder and leads to the third law of thermodynamics which states that entropy is zero (i.e., zero molecular disorder) for a pure crystalline substance at absolute zero temperature. Statistical thermodynamics provides a quantitative definition of entropy:

S = kB ln Ω (J K-1) 2.20

where kB is Boltzmann’s constant and Ω is the number of microstates (i.e., number of molecular arrangements) corresponding to a given state (Zumdahl, 1995). Hence, the entropy of a gas is greater than for a liquid or solid because the number of microstates is greater for gases than for liquids and solids. Similarly, the entropy is higher for liquids than for solids. The physical interpretation of Equation 2.20 is that at absolute zero temperature (0 K) no molecular movements in a substance exist, thus the number of microstates is 1.

2.2.5 Photon Energy (Radiation Energy)

Photon energy, or radiation energy, can be explained by Planck’s quantum theory of light which states that light and matter can interact only through the exchange of discrete amounts of energy, called quantum units or quanta (Anderson, 1982). In other words, the energy of very short wave radiation cannot be explained by classical theory of electromagnetic waves (Equation 2.11), but rather by considering small energy units called photons—particles with zero mass and zero charge. The energy of the photon is given by

E = hv (J) 2.21

where h is Planck’s constant and v is the frequency of the radiation. A blackbody is a perfect absorber and emitter of radiation. Planck’s radiation law4 gives the wavelength distribution of radiation emitted by a blackbody (Duffie and Beckman, 1991):

( )E hchc k TB

λπλ λ, exp /b =

−2 1

102

50

(W m-2⋅µm-1) 2.22

where h is Planck’s constant, kB is Boltzmann’s constant, c0 is the speed of light in vacuum, λ is the wavelength, and T is the blackbody temperature. The wavelength λmax corresponding to the maximum intensity of the blackbody radiation distribution can be found by differentiating Equation 2.22 and equating to zero. This leads to Wien’s displacement law, which states that λmax decrease with increasing temperature T according to the expression

λmax T = 0.2898 × 10-2 (µm⋅K) 2.23

Finally, integrating Equation 2.22 over all wavelengths yields the total photon energy emitted by a blackbody

4 The symbol Eλ,b is the energy per unit area per unit time per unit wavelength interval at wave length λ. The subscript b denotes blackbody.

20

4

0b d TEE σλ == ∫

∞

(W m-2) 2.24

where σ is the Stefan-Boltzmann constant, which appears in essentially all radiation equations. Equation 2.24 is particularly useful in thermal radiation calculations.

2.2.6 Potential Energy Forms &Terminology

Potential energy is the capacity of a system to do work. The form of potential energy depends on the five basic energy forms described above (Sections 2.2.1–2.2.5). For instance, potential energy can be on the form of gravitational energy, pressurized gas, electrostatic fields, chemical bonds, electrochemical energy (voltaic cell potentials), nuclear energy, or thermal energy (thermodynamic potentials).

2.2.6.1 Voltaic Cell Potentials

In a galvanic cell chemical energy from a spontaneous oxidation-reduction (redox) reaction is converted into electrical energy to produce an electromotive force (emf) in form of a voltaic cell potential (cell voltage). Physically, the galvanic cell consists of two solutions with different concentrations that can be separated by an electrolyte or membrane (a porous disk) that allows for the passage of ions (Oldham and Myland, 1994). A relationship between the cell potential E and concentration is given by the Nernst equation

QzFRTEE ln−= o (V) 2.25

where E° is the voltaic cell potential at standard state R is the universal gas constant, T is the temperature, z is the charge number (i.e., the number of moles of electrons), F is the Faraday constant, and Q is the reaction quotient. According to Equation 2.8 this cell potential can be converted into work. A more detailed description of electrochemical devices is provided in Section 4.5.

2.2.6.2 Nuclear Energy

In a nuclear reaction an atomic nucleus is broken into its individual nucleons (protons and neutrons). For this reaction to start an amount of energy, at least equivalent to the mass defect δm, is necessary. The mass defect in atomic mass units is defined as

( )δ m Zm A Z m m= + − −p n a 2.26

where Z is the atomic number, A the atomic mass number, mp the proton mass, mn the neutron mass, and ma the atomic mass. Note that nuclear symbols are conventionally written as Z

A X , where X is the chemical symbol, Z is the atomic number (number of protons), and A is the mass number (total number of nucleons, i.e., protons and neutrons).


21

In Einstein’s theory of special relativity energy E is related to mass m by the equation E = mc2, where c is the speed of light in vacuum. The energy equivalent to the mass defect is called the total nuclear binding energy5 (Anderson, 1982)

2.2.6.3 Bernoulli’s Theorem

Bernoulli’s equation in fluid dynamics illustrates how the change in potential, momentum, and kinetic energy of a fluid are interrelated. Thus, on a per weight basis, the energy balance for two points on a streamline becomes

02

KEMEPE22

2121

21 =−+−+−=∆+∆+∆gvvppzz

γ (m) 2.27

where z is the relative elevation, p is the flow pressure, γ is the specific weight, v is the flow velocity, and g is gravitational acceleration (Streeter and Wylie, 1985).

2.2.6.4 Thermodynamic Potentials

Thermal energy potentials can be found by using five fundamental thermodynamic functions, where three are so-called combined property functions. The internal energy U, a microscopic type of energy, relates to the molecular structure of a system and the degree of molecular activity. The definition of entropy S is given by Equations 2.18 and 2.20. Enthalpy H is a property that combines internal energy U with pressure p and volume V of a control volume. Helmholtz function F combines internal energy U with temperature T and enthalpy S. Gibbs function relates enthalpy with temperature T and enthalpy S. In summary, these three combination functions, or system variables, are defined as

H = U + pV (J) 2.28

F = U – TS (J) 2.29

G = H – TS (J) (Exergy) 2.30

2.3 ENERGY SYSTEMS

The term energy system is ambiguously used. In general, an energy system is described as the search for primary energy sources and its subsequent development, refining, conversion, transportation, storage, distribution, utilization, pollution, etc. An energy system can also describe a system that consists of elemental subsystems. This section provides the principles of energy conversion systems and energy storage systems. A schematic of a generic energy system is given in Figure 2.1.

Energy storage and energy transport systems are needed in order to supply stable amounts of secondary energy. This is because primary energy resources are intermittent and/or unevenly

5 From Einstein’s E = mc2: m = 1 atomic mass unit = 1 u = 1.660 540 × 10-27 kg ⇒ E = 931 MeV

22

distributed, and because the need for secondary energy is subject to heavy fluctuation (e.g., variable user demand). In general, the costs (energy and monetary), associated with the transport of energy (e.g., fuel or electricity) increase with the distance between the energy source (or energy supplier) and the end user.

Primary Energy

Secondary Energy

Tertiary Energy

transportstorageconversion

transportstorageconversion

1. Fossile fuel energy2. Nuclear energy3. Natural Energy

1. Electrical energy2. Chemical energy (gas, liquid, solid)

1. Transport2. Industry3. Domestic

Figure 2.1 A generic energy system.

2.3.1 Quality of Energy (Exergy)

It is important to remember that the energy content of the universe is constant, as mass and energy in the universe are equivalent forms of energy. Thus, energy can neither be created nor destroyed, but can only be converted into other forms. However, there exist no processes, artificial or natural, that are entirely reversible. Therefore, the concept of exergy—a measure for quality of energy—becomes important when converting energy resources on earth into useful energy such as electricity.

A scientific method to determine the actual value of energy is to evaluate its exergy. Exergy is defined as the maximum possible work that can be extracted from a system as it undergoes a reversible process from a specified initial state to the state of the its environment, i.e., dead state (Çengel and Boles, 1989)6.

As it will be demonstrated in the next two sections, the quality of energy depends on its ability to be converted, stored, and transmitted. A conceptual illustration of how the quality of energy is decreased for any process involving conversion, transmission, or storage of energy is shown in Figure 2.2. The figure also shows how a process with low energy quality requirements can utilize energy from a process with relatively higher energy quality requirements.

6 Availability is an alternative term frequently used (in the US) instead of the term exergy.


23

2.3.2 Energy Conversion

2.3.2.1 Ranking of Energy Forms

Since the quality of energy, or exergy, is closely related to its ability to be converted, a simple ranking principle can be used to determine the relative quality of the five basic energy forms: If conversion of energy A to energy B is relatively “easier” than conversion from energy B to energy A, then energy A has a higher quality than energy B (Ohta, 1994). This yields the following exergy ranking according to conversion:

1. Electrical 2. Mechanical 3. Photon or radiation 4. Chemical 5. Thermal

Source(s)

End use 1End use 2

End use n

Process 1Process 2

Process n

Decrease inenergy quality

(exergy)

Decrease inenergy qualityrequirement

Figure 2.2 Decrease in energy quality (exergy) due to processes involving conversion, storage, and transmission of energy.

For all practical purposes electrical, mechanical and radiation energy can be assumed to be pure exergy, i.e., all of the energy can theoretically be converted into useful energy. In the case of mechanical energy, this can be illustrated with a fluid flow. If a fluid stream (e.g., a wind stream) has a velocity v (with direction normal to the gravitational field), the exergy on a per unit mass basis is simply equal to the kinetic energy (Equation 2.3) of the fluid:

2mechmax, 2

1 vw = (J kg-1) (fluid stream) 2.31

Conversion between mechanical energy and electrical energy is achieved with very high efficiencies. This is also true for the opposite process. In nature, electrical energy only exists as lightning while mechanical energy exists in many forms. Thus, electrical energy is ranked before mechanical energy.

24

Photon or radiation energy can be produced by electrical energy, but the process requires heat with high temperatures. Mechanical energy can hardly be converted to photon energy, while the opposite is true in the universe. However, in terrestrial circumstances mechanical energy is ranked higher than photon energy. Radiation energy can easily be converted to thermal energy.

Chemical energy is almost pure exergy and its potential to do work is best illustrated by the principles of chemical reactions. The theoretical work potential of a chemical reaction depends on the conditions, such as temperature, pressure, and concentration of the products and reactants. The maximum possible useful work obtainable from a chemical reaction at constant conditions is equal to the change in Gibbs energy:

Wmax,chem = ∆G (J) (chemical reaction) 2.32

The exergy of thermal energy is related to second law of thermodynamics and is best illustrated by the principle of a reversible heat engine. The Carnot cycle, a reversible thermal process, is a measure of the maximum amount of work Wmax,therm that is possible to generate by transferring heat QH from a high temperature TH reservoir (heat source) to a low temperature TL reservoir (surroundings). The maximum efficiency of a thermally reversible process of this sort is called the Carnot efficiency ηC. Thus, thermal exergy can be expressed by

Wmax,therm = ηCQH (J) (heat engine) 2.33

and the Carnot efficiency is given by

ηCTT

= −1 L

H

2.34

where TH and TL are absolute temperatures. From Equations 2.33 and 2.34 it is observed that the exergy in a reversible thermal process is equal to the Carnot efficiency times the heat supplied. Thus, for a fixed TL and an increasing TH the Carnot efficiency increases and so does the exergy. This is in agreement with the notion that high-temperature thermal energy has a higher value and quality than low-temperature heat. The constraint on thermal energy conversion due to the Carnot efficiency also explains why thermal energy is ranked last among the five forms of energy.

In practice, chemical energy can always be converted into thermal energy, but not so easily into other energy forms. Thus, chemical energy is ranked higher than thermal energy. Any kind of energy eventually becomes heat with low temperature. Hence, thermal energy has the lowest ranking.

A few interesting observations regarding the relationship between radiation energy and the temperature of a blackbody can be made. According to the Stefan-Boltzmann equation (Equation 2.24), the maximum spectral emissive power from a blackbody Eλmax,b increase with temperature. Hence, the quality of the radiation also increases.

Furthermore, according to Wien’s displacement law (Equation 2.23), it can be demonstrated that the wave length λmax corresponding to Eλmax,b, decreases with increasing temperature. This indicates also that the quality of blackbody radiation energy increases with decreasing


25

wavelengths of the radiation. This is in good agreement with the observations made in nature. For instance, the sun, with its very high temperatures (about 6000 K), emits high quality energy at short wavelengths.

2.3.2.2 Exergy Conversion Efficiency (Theoretical Maximum)

In addition to the energy efficiency associated with an actual conversion process, it is also important to bear in mind the maximum theoretical conversion efficiency, the exergy conversion efficiency, of a process. This point is illustrated by the two examples below.

_____________

Example 2.1: Combustion of methane

This example finds the exergy losses due irreversibilities in a typical combustion of methane by comparing reversible work of an adiabatic combustion to that of an isothermal. The balanced equation for the complete combustion of methane with 50% excess air is

( )CH O N CO + 2H O + O N2 2 24 2 2 23 3 76 11 28( ) . .g + + → + 2.35

(a) Adiabatic combustion

Methane (CH4) gas enters a steady-flow adiabatic combustion chamber at 25°C and 1 atm and is burned in air (O2 and N2), also at 25°C and 1 atm. The products (CO2, H2O, O2, and N2) are assumed to leave the combustion chamber in gas form at 1 atm pressure. The ambient temperature T0 = 25°C (298 K). The energy balance on a combustion chamber is for steady-flow processes given by

Q – W = ∆H = HP – HR 2.36

where Q is the heat released, W is the work produced, and HR and HP are the reaction enthalpies of the products and reactants, respectively. In a constant volume chamber no work is performed (W = 0), while for an adiabatic chamber no heat is released (Q = 0). Thus, by inserting the reaction enthalpies and sensible enthalpy changes of the reactants and products in Equation 2.36, it can be shown that the temperature of the products is TP = 1789 K.

In general the total entropy generated Sgen in a reaction is the sum of the entropy change of the reaction system and surroundings ∆Ssys and ∆Ssurr, respectively, and is expressed as

Sgen = ∆Ssys + ∆Ssurr 2.37

In an adiabatic process no heat is transferred to the surrounding, hence from the 2nd law of thermodynamics, where Qsurr = T∆Ssurr (Equation 2.19), it is seen that ∆Ssurr = 0. A calculation based on Equation 2.37 and ideal gas values for entropy gives

Sgen = 969.02 kJ/(kmol·K) CH4

(b) Isothermal combustion

For an isothermal combustion reaction a similar procedure as in (a) can be used. However, at 25°C part of the H2O formed (Equation 2.35) will condense, thus water exist both in liquid

26

and vapor phase and requires the calculation of partial pressures. The change in reaction enthalpy ∆H (Equation 2.36 with W = 0) is in an isothermal combustion transferred as heat to the surrounding, which consequently results in an entropy change in the surroundings ∆Ssurr (Equation 2.19). Along with the entropy change of the system ∆Ssys, it is then possible to find the total entropy generation (Equation 2.37), which in this case is

Sgen = 2,748.84 kJ/(kmol·K) CH4

(c) Exergy losses

Since no work is performed by the system (W = 0) in this example, the reversible work for the reaction can be expressed by

Wrev = T0∆Sgen 2.38

Thus, inserting the values for temperature and entropy from (a) and (b) in Equation 2.38 gives the following reversible work potentials for the adiabatic and isothermal reactions:

Wrev, adiabatic = 298 × 969.02 = 288,768 kJ/kmol CH4

Wrev, isothermal = 298 × 2,748.84 = 819,154 kJ/kmol·CH4

A comparison of these two values reveals that the exergy of the reactants (819,154 kJ/kmol CH4) decreased by 288,768 kJ/kmol due to the adiabatic combustion process alone. That is, the exergy of the hot combustion gases at the end of the adiabatic combustion process is 818,154 – 288,768 = 530,386 kJ/kmol. In other words, the exergy of the hot combustion gases (TP = 1789 K) is about 65% of the exergy of the reactants (Figure 2.3).

Adiabaticcombustion

chamber

25°CReactants(CH4, air)

Exergy = 819,154 kJ/kmol(100%)

1789 KProducts

Exergy = 530,386 kJ/kmol(65%)

Figure 2.3 Exergy decrease of methane as a result of an irreversible combustion

process.

The above result is of great importance because it indicates that 35% of the work potential of CH4 (chemical exergy) is lost even before it is utilized as thermal energy.

_____________

Example 2.2: Exergy efficiency of electrochemical conversion of methane

This example finds the maximum theoretical efficiency, or exergy efficiency, of an electrochemical process that converts chemical energy directly into electrical energy in the form of a voltaic cell potential (Section 2.2.6.1). The specific reaction selected is the fuel cell reaction of methane (CH4), an exothermic reaction which can be expressed by

CH O CO H O4 2+ → +2 22 2 2.39


27

The theory of electrochemical energy conversion combines the basic laws of electrochemistry and thermodynamics and shows that the maximum voltaic cell potential is related to Gibbs energy by the expression

∆G° = – nFE° 2.40

where n is the number of moles of electrons transferred per mol of reactants and products, F is the Faraday constant, E ° is the cell potential at standard state, and ∆G° is the difference in Gibbs energy between the reactants and the products (Tilak et al., 1981). From the basic relation ∆G = ∆H – T∆S (Equation 2.30) it is seen that the irreversibilities of the reaction is equal to T∆S (Equation 2.19). Thus, the exergy efficiency of an electrochemical reaction is on general form

η max = ∆∆

GH

2.41

Hence, based on thermodynamic data for Gibbs energy and enthalpy at standard state (in kJ/kmol), the exergy efficiency of the fuel cell reaction of CH4 is

η max,,951

= −−

815 519890

= 91.5%

This result shows the attractiveness of electrochemical conversion as opposed to regular combustion (Example 2.1).

_____________

2.3.2.3 Actual System Conversion Efficiencies

From the discussion above it is clear that in any real system, each individual conversion process will, due to irreversibilities, decrease the system efficiency. In general, energy systems can transfer energy both in parallel and series. This is often the case in multipurpose and multistage plants. In the electricity producing systems, energy is usually converted through a series of processes. The final efficiency—the overall efficiency from the primary energy (energy source) to tertiary energy (utilizable energy)—is simply the product of all the individual subsystem efficiencies ηi, and is for n number of processes in series expressed as

η ηf ==

∏ ii

n

1

2.42

The purpose of multistage energy conversion is to maximize the use of energy available (exergy) in the primary source. This is done by using the remainder of the available energy after one process as input to a new process (series) or several other processes (parallel). In general, the overall efficiency of a multistage process connected in series is

( )η ηo = − −=

∏1 11

ii

n

2.43

where ηi is the efficiency of each individual conversion process and n is the number of processes in series (Ohta, 1994). From Equation 2.43 it is clearly seen that the overall

28

efficiency ηo increases with the number of successive energy conversion processes and/or with increasing efficiencies of the individual processes.

2.3.3 Energy Storage

An energy storage system is defined as a sustainable structure of materials or structures in a non-equilibrium state, and is consequently a form of potential energy. Energy can essentially be stored as microscopic or macroscopic potential energy. Microscopic energy storage comes in the form of chemical energy (e.g., batteries and fuels), while macroscopic storage comes in the form of mechanical energy created by physical structures (e.g., water dams, flywheels, elastic bodies, and vessels with compressed gas).

Some of the most important parameters in relation to any kind of energy storage are energy density or specific energy and the time factor. If the size of storage volume is a limitation, then it is necessary to maximize the energy density. Similarly, if the storage weight is a limitation, then the specific energy must be maximized.

If energy is to be stored over long periods of time (e.g., hours, days, and months), the time factor might be the predominant parameter. The rate at which the stored energy is lost to the environment depends heavily the kind of energy storage selected. Two typical examples are the losses in potential in chemical stores due to inherent chemical reactions or the heat losses associated with thermal energy stores.

Based on the description of the five main forms of energy in Section 2.2, a ranking of the kind of energies that are adaptable to storage can be found:

1. Chemical energy 2. Mechanical (potential and kinetic) energy 3. Electromagnetic energy 4. Electric current 5. Thermal energy 6. Electromagnetic wave energy 7. Photon energy

Chemical energy is exceptionally adaptable to storage because chemical substances have cohesive energies that are confined in a stable form within them and are obtained by relatively small ignition energy. Electric energy is usually converted to mechanical potential energy or to chemical energy. The storage of thermal energy is difficult because it disperses by heat conduction, convection, and radiation. Electromagnetic wave energy and photon energy are usually converted and stored in other energy forms.

An overview of the specific energies for various materials (microscopic storage) and practical systems (macroscopic storage) is given in Table 2.3. The storage of energy in materials is generally more flexible than the storage of energy in systems. One the left side in Table 2.3 it can be observed that hydrogen is the non-nuclear material with the highest specific energy. The specific energy of hydrogen is 2.7 times that of gasoline (a petroleum product). Among the storage systems (right side of Table 2.3), the metal hydrides, such as nickel-hydrogen batteries, have the highest specific energies, but are mostly suitable for medium size storage. Water pumped up in a dam situated at an elevation yields a much lower specific energy, but is one of the best options for large-scale energy storage.


29

Table 2.3 Types of energy storage—materials and systems.

Material (microscopic)

Specific energy kJ kg-1

System (macroscopic)


Scale of system

Deuterium 3.5 × 1011

Silver oxide zinc battery 437 Medium

U-235 7.0 × 1010

Nickel-hydrogen batteryd 160 Medium

Pu-238 (80% Pu) 1.8 × 106 Lead-acid battery 119 Medium Hydrogen (LHV) 1.2 × 105 Compressed gas 71 Large Methanec 5.0 × 104 Hydro power dam (∆z =100 m) 9.80 Large Gasolinec 4.4 × 104 Torsion spring 0.24 Small Oil 2.8 × 104 Condenser 0.016 Small

Source: Culp (1991).

2.4 TRADITIONAL ENERGY RESOURCES

The energy resources available to man on earth are usually divided into two main classes: (1) Traditional energy resources and (2) Alternative energy resources. In this thesis the traditional energy resources include fossil fuel and nuclear energy. However, it should be noted that although nuclear fusion is discussed in this section, it is in reality not a traditional energy source, but rather an alternative energy source.

The alternative energy resources are in this thesis defined as resources based on natural energy processes on earth, often called renewable energy. However, the term renewable energy is slightly misleading because no form of energy is renewable. Natural energy (Section 2.5) is therefore a more appropriate and concise term. It should be noted that some natural energy resources, such as wind and hydropower, also could have been referred to as traditional energy resources, as man has used them for ages.

2.4.1 Fossil Fuel Energy

The production of fossil fuels on earth is a result of the very slow decomposition and chemical conversion of organic material produced via photosynthesis (a continuous process). It is believed that the whole process takes approximately 500 million years. The material produced from this very slow process is therefore referred to as fossil fuel and is categorized as so-called non-renewable energy. This reflects the fact that they require a very long time to be recycled or renewed.

The fossil fuels come in three basic forms: (1) Coal (s), (2) Petroleum (l), and (3) Natural gas (g). Another group of fossil fuels are the synthetic fuels, or synfuels, which are liquids and gases derived largely from coal, oil shale, and tar sands (El-Wakil, 1984). The first stage of the production of fossil fuels, is the production of biomass produced via photosynthesis. However, since the production of biomass is a relatively fast process, it is categorized as a renewable or natural energy source (Section 2.5.4).

30

A convenient measure for the value of fossil fuel energy is to find its enthalpy of combustion, or heating value. In general the heating value of a fuel is defined as the amount of energy released when a fuel is burned completely in a steady-flow process at a specified temperature and pressure, usually 25°C and 1 atm, respectively.

However, the heating value also depends on the phase of the H2O in the in the products. The heating value is called the higher heating value HHV when the H2O in the in the products is in the liquid form, and is called the lower heating value LHV when the products are in the vapor form. The two heating values are related by

HHV LHV n h= + H O fg,H O2 2 (kJ -1

fuelkg ) 2.44

where nH2O is the amount of H2O in the products and hfg,H2O is the enthalpy of vaporization of pure water at standard state (Çengel and Boles, 1989).

Table 2.4 gives an overview the most common fossil fuel energy resources, organized according to their specific energies. The total confirmed reserves and estimated corresponding lifetimes are also indicated in Table 2.4. There also exist various estimates for the ultimate reserves, but these are not listed due to their inherent uncertainties.

2.4.1.1 Coal

The oldest and most petrified coal, anthracite, has a higher specific energy than the younger coal, lignite, which includes more moisture and volatile matter. The heating value of coal is mainly dependent on its mass fractions of carbon, hydrogen, oxygen, and sulfur. Typical heating values are indicated in Table 2.4 and illustrate how the HHV for coal increases with increasing mass fractions of carbon. The coal reserves in the world are extremely large. In addition, the coal resources are fairly evenly distributed all over the world, which is an explanation for its widespread use worldwide. A simple calculation based on the confirmed reserves and production rate of today shows that the coal reserves will last about 230 years.

2.4.1.2 Petroleum

Crude oil, or crude petroleum, is a thick dark liquid composed mostly of hydrocarbons, denoted CnHm, where m is a function of n that depends on the “family” of the hydrocarbons (Zumdahl, 1995). The hydrocarbons found in petroleum can be divided into groups according to the number of carbon atoms in the molecule—thick oils have high number of carbon atoms and high heating values (Table 2.4). However, liquid fuels from petroleum have fairly similar heating values. The petroleum reserves in the world are fairly unevenly distributed, where almost 60% of the total are found in the Middle East. According to the life cycle model proposed by Hubbert (NAS, 1969), the ultimate petroleum reserves (about 350×1012 kg with a crude oil density of 0.9 kg L-1) will, at the utilization and consumption rates of today, last until about year 2060.

2.4.1.3 Natural Gas

Natural gas that is produced together with petroleum is classified as petroleum gas. However, there are gases that exist everywhere on the earth and are produced independently of petroleum. Methane is an example of a gas that exists everywhere on earth. The petroleum gases are in a liquid state at the high pressures that exist underground, but become gaseous at


31

standard state due to their low boiling points below 0°C. In general, the heating value of natural gas depends on the n/m-ratio of the hydrocarbon. Table 2.4 shows how HHV increases with increasing n/m-ratios. The confirmed world reserves of methane is in the same order of magnitude as the confirmed oil petroleum reserves, but is a little more evenly distributed around the world. The ultimate reserves for methane gas (about 450×1012 kg) will, based Hubbert’s life cycle model and the utilization and consumption rates of today, last until about year 2070.

Table 2.4 Specific energy data for various fossil fuels.

Type Details HHVa kJ kg-1

Reservesb kg

Life.timec years

Coal Elemental compositiond 730×1012 230 Anthracite C(92), H2(3), O2(3) 32,331 Bituminous C(80), H2(6), O2(8) 32,564 Sub-bituminous C(77), H2(5), O2(16) 29,308 Lignite C(71), H2(4), O2(23) 25,586 Petroleum No. of Carbon atoms 125×1012 60-70 Heavy oil >C25 45,740 Fuel oil C15–C25 42,680 Kerosene C10–C18 40,850 Natural gas Chemical formula, CnHm 150×1012 70-80 Methane CH4 60,780 Ethane C2H6 56,590 Propane C3H8 56,406 n-Butane C4H10 54,062 a. Higher heating values. b. The confirmed reserves: Coal (World Energy Conference, 1976), petroleum (British Petroleum Co., 1985),

and methane (World Gas Conference, 1985). Note that normal conditions (25°C and 1 atm) were assumed in the fuel and gas mass calculations. The density of crude oil was assumed to be 0.9 kg L-1. The natural gas density of was calculated from ρ = 0.0409 Mr (kg m-3 or g L-1), where Mr is the molecular weight

c. The calculations for coal were based on the confirmed reserves while the calculations for oil and gas were based on the ultimate reserves.

2.4.2 Nuclear Energy

In principle nuclear binding energy can be released through: (1) Nuclear fission or (2) Nuclear fusion.

2.4.2.1 Nuclear Fission

In a nuclear fission, bonding energy can be released by irradiating neutrons on fissionable isotopes, such as U-235, Pu-239 and U-233, which are fissionable by neutrons of all energies. An example of a fission reaction is

92235

01

4694

58140

01

bU ... Zr Ce 2+ → → + + +n n E 2.45

where U-235 is the uranium isotope (radioactive reactant), n is the neutron, Zr and Ce are nuclear stable products, and Eb is the released binding energy. As seen in Equation 2.45 the

32

reaction produces two neutrons. By applying these neutrons to another uranium atom a nuclear chain reaction is possible (El-Wakil, 1984).

Another type of nuclear fission process, commonly known as breeding, involves the conversion of fertile isotopes into fissile isotopes. The characteristic of fertile isotopes is that they need to be irradiated by high-energy neutrons in order to release nuclear energy. Hence, they cannot be used directly as nuclear fuels. In a breeder reaction system more nuclear fuel is produced than what is used. An example of breeding is the conversion of U-238 (fertile isotope) into Pu-239 (fissile isotope), which produces more Pu-239 than the quantity of U-238 used.

The only chemical elements in nature that readily can be used as fuel is uranium or thorium. The natural uranium resources consists of the isotopes U-235 (0.7%) and U-238 (99.3%) while thorium consists entirely of Th-232. Today the commercially most important fissile isotopes is U-235 and Pu-239, the latter which is produced by breeding U-238. However, also Th-232 could be used for breeding. Both uranium and thorium are relatively evenly distributed on the surface of the earth and in the oceans. To estimate the lifetime of the nuclear energy resources available for fission is difficult because it requires accurate geological mapping of the deposits. The lifetime of the resource also depends greatly on how the nuclear fuel is utilized. With the thermal reactor systems of today the resources are likely to last around 60-70 years while with a breeder reactor system they can last for a significantly longer period of time, probably for several centuries (Murray, 1993).

2.4.2.2 Nuclear Fusion

The other method to release nuclear binding energy is fusion—the process of forming a heavy nucleus from two or more lighter nuclei. One example of a nuclear fusion reaction is

12

12

23

01

bH H He+ → + +n E 2.46

where the combination of a deuterium-pair produces one helium atom and a neutron and releases the binding energy. The ignition temperature for fusion reactions is in the order of 108 K. This means that the reactants are in the plasma state, which can only be achieved by bombarding the fuel with high-energy particles or with a high-power laser. A much more difficult problem is to confine the heated plasma long enough to sustain the fusion reaction until all the fuel is spent. Another serious problem is to couple the energy produced by fusion to an external load without getting large radiation losses (Anderson, 1982).

The fuels of most interest for fusion reaction is the hydrogen isotopes deuterium and tritium, where deuterium exist in seawater (at densities around 0.015%) while tritium must be produced from lithium which exists underground caves and seawater. Hence, the resources for nuclear fusion are practically unlimited.

2.5 NATURAL ENERGY RESOURCES

Natural energy is defined as energy that drives or activates natural phenomena. The natural energy sources are continuous, intermittent, and non-depletable and are therefore often referred to as renewable energy sources. There are three categories of natural energy, which in turn can be broken down further into types commonly referred to as renewables. These are


33

summarized in Table 2.5. The availability of the natural energy resources, along with some of the key issues involved when determining their local and global potentials, is discussed in Section 2.5.1–2.5.7.

Table 2.5 The natural energy resources available on earth.

Solar energy and its derivatives

Energy due to planetary motions Energy from the earth

• Solar Energy • Ocean Tidal Energy • Geothermal Energy • Hydro Energy • Wind Energy • Bioenergy • Ocean Energy

Most of the natural energy on earth is solar energy or derivatives of solar energy. The continuous nuclear fusion reactions that take place at the sun yield huge amounts of emitted energy. About 30% of the total solar energy (1.73 × 1017 W) incident on the atmosphere of the earth is directly reflected back into space as short-wave radiation. The rest (1.2 × 1017 W) is distributed onto the earth’s surface, where it is either utilized in artificial (man-made) energy conversion or transferred to natural energy conversion processes (Ohta, 1994).

Man-made (artificial) solar energy devices are essentially based on two different concepts: (1) Direct utilization of solar radiation (photon energy) or (2) Indirect utilization solar radiation via solar thermal processes. Most of the natural energy processes on earth are a result of solar radiation. The solar driven natural processes occur in three areas: (1) on land (photolysis), (2) in the atmosphere (climate), and (3) in the ocean. An overview of the distribution of solar energy on the earth’s surface and some of its areas of utilization is presented in Figure 2.4.

Solar Energy

NaturalArtificial

Photon Thermal Photolysis Climate Ocean

PhotovoltaicPhotolysisIllumination

HydroWind

ThermalCurrent

Wave

Heat engineDryingCookingRefrigerationDistillationHeating

Solar Furnace FoodFertilizerCarbon fix

Figure 2.4 Distribution of solar energy and its derivatives on the surface of the earth.

34

2.5.1 Solar Energy

The rate of energy from the sun received on a unit area perpendicular to the direction of propagation of the radiation, at mean earth-sun distance, outside of the atmosphere is called the solar constant Gsc. The solar constant varies slightly over the year due to the earth’s elliptical orbit around the sun (the distance from the earth to the sun varies about 1.7% over the year). A solar constant of 1367 W/m2, adopted by the World Radiation Center (WRC), and recommended by Duffie and Beckman (1991), is used in this thesis.

The solar radiation from the sun incident on the earth’s atmosphere, or extraterrestrial irradiance, is short wave radiation with wavelengths λ in the range of 0.3–3 µm, often called the solar spectrum or visible light. The solar spectrum is divided into three main regions, according to wavelengths (Table 2.6).

Table 2.6 The solar spectrum.

Type Wavelength, λ µm

Fraction of Irradiance %

Ultraviolet (UV) region < 0.4 9 Visible region 0.4–0.7 45 Infrared region > 0.7 46 Source: Twidell and Weir, 1986

The solar radiation consists of two components: (1) Beam radiation and (2) Diffuse radiation. In this thesis, the terminology solar radiation, which often is called total or global solar radiation, includes both beam and diffuse unless otherwise specified.

The spectral radiation incident on the earth’s surface is different from the extraterrestrial radiation mainly due to scattering and absorption in the atmosphere. Scattering of radiation as it passes through the atmosphere is caused by interaction of the radiation with air molecules, water (vapor and droplets), and aerosols (e.g., smoke, dust, salt, and pollen).

Absorption of radiation in the atmosphere is primarily due to the absorption of solar radiation in O3 (ozone), H2O, and CO2. The x-rays and other very short-wave radiation of the solar spectrum are absorbed high in the ionosphere (50–600 km) by nitrogen, oxygen and other atmospheric components, while most of the ultraviolet radiation is absorbed by ozone7 in the stratosphere (10–50 km) (Pleym, 1992).

7 The amount of ozone in the stratosphere (10–50 km) is kept constant by various processes that form and break down ozone. The main formation of O3 (ozone) occurs at altitudes above 30 km. First, oxygen is split into two single oxygen atoms in the presence of ultraviolet (UV) radiation hv with wavelength λ < 242 µm. Next, the oxygen atoms re-combine on another molecule (M) and forms ozone. In the third (and last) reaction ozone is broken down by UV-radiation in the range λ = 240–320 µm. In summary these three reactions are:

1) O2 + hv → O + O 2) O + O2 + M → O3 + M 3) O3 + hv → O2 + O.


35

At wavelengths longer than 2.5 µm very little energy reaches the ground due to a combination of low extraterrestrial radiation and strong absorption by CO2 in the atmosphere. Thus, for practical terrestrial solar energy applications, only radiation of wavelengths between 0.29 and 2.5 µm need to be considered (Duffie and Beckman, 1991).

The amount of beam solar radiation absorbed in the atmosphere is for convenience lumped into a quantity called the air mass. Figure 2.5 illustrates the concept of air mass (Zweibel, 1990). It is defined as the ratio of the mass of atmosphere through which the beam radiation passes to the mass it would pass through if the sun were at the zenith. Since the earth’s orbit around the sun is elliptical, the sun-earth distance varies over the year. This causes the air mass zero (AM0)8 to vary ± 3.4% over the year. A frequently used air mass reference condition for testing solar energy devices is AM1.5 (Imamura et al., 1992).

Atmosphere

Zenith

Solar noon

Sunrise/sunset

AM 1.5AM 3.0

AM 1. 0

48.2°70.7°

Earth Figure 2.5 Air mass (AM) — the path length of sunlight through the atmosphere.

The availability of solar energy is best found from radiation data measurements. If these data are not available it is possible to estimate the average solar radiation by using empirical equations and simulation programs (Section 4.2).

The total theoretical solar energy potential for the world is enormous—more than enough to satisfy the total energy demand in the world, today and in the foreseeable future. However, a more interesting view of the global potential of solar energy is to look at the radiation levels for different parts of the world, which naturally vary considerably depending on the geographic location, the time of the year and time of the year. The position of the overhead sun varies over the year because the earth rotates around its own axis at a 23.5° tilt (with respect to the sun). Hence, four dates of the year have a particular significance:

• Equinox: Spring (March 21) and Fall (September 21)—The sun is directly above the Equator at noon; day and night duration is exactly 12 hours at any point on the earth’s surface.

• Solstice: Summer (June 21) and Winter (December 21)—The sun is directly over the Tropic of Cancer (23.5°N) at noon on June 21 and directly over the Tropic of Capricorn (23.5°S) on December 21.

8 Air mass zero (AM0) is the air mass at the top of the earth’s atmosphere.

36

The monthly average daily radiation on a horizontal surface varies over the year, depending on the location. This is illustrated in Figure 2.6 by selecting a few very different locations, which is based on solar radiation data from the World Meteorological Organization (WMO, 1985), summarized in Duffie and Beckman (1991).

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9 10 11 12

Month

Mon

thly

ave

age

daily

radi

atio

n on

a

horiz

onta

l sur

face

, MJ/

m2

Fairbanks, Alaska 64.8°NKarachi, Pakistan 24.8°NSingapore 1.0°NPretoria, South Africa 25.8°S

Jan Dec

Figure 2.6 Examples of monthly average daily solar radiation on a horizontal surface.

The following can be inferred from Figure 2.6: At high latitudes, e.g., the Arctic Circle (66.57°N) and the Antarctic Circle (66.57°S), there are great seasonal variations in the solar radiation levels. This is seen in the plot for Fairbanks, Alaska (64.8°N). The opposite is true for locations close to the Equator, which receive almost constant radiation year round, as seen in the plot for Singapore (1.0°N). In Karachi, Pakistan (24.8°N), close to the Tropic of Cancer, the summer solstice is followed by a two-month rainy season which causes a slight slump in the otherwise high insolation levels while in Pretoria, South Africa (25.8°S), close to the Tropic of Capricorn, no such slump is observed.

In summary, several factors need to be mapped in order to estimate the solar energy potential for a particular location on region. Solar energy, due to the earth’s orbit around the sun and the earth’s rotation around its own axis, is an intermittent source of energy. Furthermore, because of local climatic conditions, such as rain, snow, fog, and clouds, solar energy is also very stochastic. In general, solar energy is very evenly distributed around the globe, but the regions where there are relatively small seasonal variations have the best conditions for utilizing solar energy. Many countries in South America, most of Africa, the Subcontinent (India), and Southeast Asia and Oceania fall into this category. The largest solar energy potentials are found in dry climates in the Tropics.

2.5.2 Hydro Energy

Hydro energy, or hydropower, depends ultimately on the natural evaporation of water by solar energy. The evaporated water precipitates at high elevations and is stored as potential energy in water reservoirs, before it runs off in streams and rivers towards lower elevations as kinetic energy.


37

On a global basis, the total amount of water precipitated over time is equal to the amount returned to the atmosphere by evapotranspiration. On land precipitation exceeds evapotranspiration (60%), but the difference is eliminated by the runoff (40%) from rivers (and groundwater) to the ocean. The opposite process occurs in the oceans. Table 2.7 gives a summary of the annual water balance and shows that the average precipitation, evaporation, and runoff in South America exceeds that of other continents by a factor of two while Asia accounts for the largest total runoff. In mountainous regions and cold climates, where hydro energy is stored in form of snow during winter, the evaporative losses are small and the conditions for hydro storage very favorable.

Table 2.7 Annual world water balancea. Surface Precipitation Evaporation Runoff

b Region area average total 106 km2 mm 1012 m3 1012 m3 1012 m3

Europe 10.5 790 8.3 5.3 3.0 Asia 43.5 740 32.2 18.1 14.1 Africa 30.1 740 22.3 17.7 4.6 North America 24.2 756 18.3 10.1 8.2 South America 17.8 1,600 28.4 16.2 12.2 Australia & Oceania 8.9 791 7.1 4.6 2.5 Antarctica 14.0 165 2.3 0 2.3 Total land area 149 800 119 72 47 Pacific Ocean 178.7 1,460 260.0 269.7 -14.8 Atlantic Ocean 91.7 1,010 92.7 124.4 -20.8 Indian Ocean 76.2 1,320 100.4 108.0 -6.1 Arctic Ocean 14.7 361 5.3 8.2 -5.2 Total ocean area 361 1,270 458 505 -47

Globe 510 1,130 577 577 0 a. Adapted from UNESCO (1977). b. Outflow of water from continents into ocean (rivers and groundwater).

By building artificial dams it is possible to collect and store large amounts of hydro energy. The volume of runoff water and the distance it falls before reaching the ocean determines the theoretical energy potential of hydropower9. The runoff energy is not evenly distributed around the globe, but varies due to different altitudes on the continent and due to seasonal variations. According to Moreira and Poole (1993) the global theoretical potential for hydropower is in the range from 36,000 to 44,000 TWh.

2.5.3 Wind Energy

On a global scale the circulation of air in the atmosphere is in principle a gigantic heat exchange system and a consequence of unequal heating of the earth’s surface by the sun. In

9 From Equation 2.2: E = ρVgh , where V is the water flow rate, ρ is the density of water, g is the gravitational acceleration, and h is the hydrostatic head.

38

the equatorial regions solar energy heats the air near the ground causing it to expand and rise and creates a permanent low-pressure belt (the doldrums). The light and warm air then cools, sometimes causing rain and spreads north and south. Some of this air sinks around latitudes 30°N and 30°S (the horse latitudes) and forms high pressure belts while the rest continues to the poles where it cools, sinks, and forms polar high-pressure zones. The high and low pressure belts are calm areas with light to non-existent winds, but between them air is blowing from high to low pressure (Herrmann, 1992).

The most stable prevailing winds are the winds blowing from the horse latitudes towards the equator (the tradewinds), a pattern known as the Hadley circulation. In comparison, the regions between latitudes 30° and 65° north and south have more changeable weather due to the intermingling of cold polar air currents (the polar easterlies) and warm subtropical air currents (the westerlies). Due to the rotation of the earth the easterlies and westerlies are deflected to the right of their natural direction in the northern hemisphere and to the left in the southern hemisphere (the Coriolis effect), creating a wavelike pattern known as the Rossby circulation.

The paths of the prevailing winds and the positions of the dominant high- and low-pressure systems also undergo seasonal changes. This has to do with the changing position of the overhead sun over the year (see section on solar energy). For instance, at equinox the sun is directly over the equator and the solar radiation is equally balanced between the two hemispheres. The overall effect of the changes in heating is that the wind and pressure belts move north and south throughout the year.

On a smaller scale, local thermal effects create winds. In hot regions, temperature differences between land and sea can create strong thermal winds. Another important factor is the local topography. Valleys and mountains, for instance, can serve as channels to amplify the thermal winds.

In the atmospheric boundary layer, which on the average extends about one kilometer above the earth’s surface, air is slowed down by surface friction. The extent to which it is slowed down depends on the height above the ground and the surface roughness. Near the ground it is mostly the terrain that influences the wind speeds. Winds are strongest over grassland and open water, moderate over scrub, and weakest over forests. Clearly, the best conditions are found in coastal areas and open plains (e.g., prairies and deserts).

Due to the surface roughness of the ground the wind slows down as it gets closer to the ground. It is therefore important to capture this kinetic energy, or wind energy, at reasonably high elevations above the ground. A power law is frequently used to extrapolate wind speeds v from one height h to the other:

v v hh2 1

2

1

= ×

α

(m s-1) 2.47

where α is the height exponent. A value of α = 1/7 is often used to approximate very smooth surfaces while values of 1/3 or higher are appropriate for obstructed sites (Grubb and Meyer, 1993). This behavior is in accordance with the general theory of fluid flow across external surfaces—the gradient of the free stream velocity profile in the low part of the boundary layer


39

(close to the surface) is higher for laminar flow than for turbulent flow (Incropera and DeWitt, 1990).

Wind speeds v are highly variable, but their distribution at any given site can be described reasonably by a two-parameter probability density function known as the Weibull function:

−

=

− b

c

b

cc vv

vv

vbv exp)f(

1

(b > 1, v ≥ 0, vc > 0) 2.48

where vc is the characteristic wind speed, or Weibull scaling parameter, and b is the Weibull shape parameter (Cavallo et al., 1993). If b equals 2 the function is known as the Rayleigh distribution.

Weibull statistics provide a convenient way of summarizing wind regimes for a location. For variable wind regimes the probability density function f(v) is relatively flat (b ≅ 1) while for wind regimes that are relatively constant f(v) is more peaked (b ≅ 2). In areas that are generally calm, but sometimes interrupted by typhoon winds (e.g., the Caribbean), b varies from 1 to 3, while in areas with more constant winds, (e.g., the tradewinds around the Equator) b is about 4 (Grubb and Meyer, 1993).

The energy flux of an air stream moving with a velocity through a bounded area (perpendicular to the air stream) per unit time is called the wind power density, and is proportional to the wind velocity raised to the third power. Since the power density depends on the form of the Weibull distribution, the relation between mean wind speed and mean power density can vary greatly. Hence, wind resources for a particular site should be expressed in terms of power density rather than in terms of wind speeds.

The classes of wind power density used in the United States wind atlas is given in Table 2.8. These categories are based on wind power densities at elevations of 50 m. The corresponding mean wind speeds can be estimated from the power densities assuming a Rayleigh distribution (b = 2) and standard sea-level air density.

Table 2.8 Classes of wind power density in the United States wind atlas.

Wind power class Wind power density

at 50 meters Wm-2

Wind Speeds at 50 meters

m s-1

1 0–200 0–5.6 2 200–300 5.6–6.4 3 300–400 6.4–7.0 4 400–500 7.0–7.5 5 500–600 7.5–8.0 6 600–800 8.0–8.8 7 800–2,000 8.8–11.9

The global wind energy resources classified according to the U.S. wind class system are summarized in Table 2.9 (Grubb and Meyer (1993)). Note that the land area with wind power

40

densities in wind classes 3 to 7 is, for each continent, given both in terms of absolute values (thousands of square kilometers) and relative values (percent of total land area). North America and Eastern Europe & former USSR have the largest land areas with wind classes 5 to 7 while Africa has the largest land areas with wind classes 3 and 4. Globally, the largest wind energy potential is found in land areas with wind class 3.

Table 2.9 World wind energy resources according to power densities.

Land area in Class 5–7

Land area in Class 4

Land area in Class 3

Region 103 km2 % 103 km2 % 103 km2 %

Africa 200 1 3,350 11 3,750 12 Australia 550 5 400 4 850 8 North America 3,350 15 1,750 8 2,550 12 Latin America 950 5 850 5 1,400 8 Western Europe 371 22 416 10 345 9 Eastern Europe/former USSR 1,146 5 2,260 10 3,377 15 Rest of Asia 200 5 450 2 1,550 6

Total 8,350 6 9,550 7 13,650 10

2.5.4 Bioenergy

Biomass for energy, or bioenergy, is a result of photosynthesis. It is by far the most important renewable energy process on earth, because living organisms are made from material fixed by photosynthesis and, at the same time, they rely on the oxygen stored in the organic material.

In photosynthesis, sunlight is absorbed by chlorophyll in the chloroplasts of green plant cells and utilized by the plant to produce carbohydrates, proteins, and fats from CO2 and H2O taken from the atmosphere. The process can be presented in simplified form by the equation

[ ]CO H O O + CH O + H O2 2sunlight

2 2 2+ →2 2.49

where [CH2O] is the generalized symbol for carbohydrates, proteins, and fats. As a result of absorption of photons the energy in the products are about 5 eV per carbon atom higher than the energy in the initial material (Twidell and Weir, 1986).

The biomass produced by photosynthesis consists mainly of carbohydrates (e.g., glucose C6H12O6). Thus, the energy content of a carbohydrate is equal to the solar energy absorbed by the plant in photosynthesis. This amount of energy depends on its physical and chemical properties of the specific carbohydrate, but can be estimated by the heating value (Equation 2.44) of the material. On a dry-weight basis, heating values range from about 17,500 kJ/kg for typical herbaceous plants (e.g., bagasse, wheat straw, grass,) to about 20,000 kJ/kg for wood (Jenkins, 1989).

The potential for field production of biomass is in principle dependent on two factors:

• The ambient conditions for the photosynthesis.


41

• The photosynthetic efficiency.

The ambient conditions that affects the photosynthesis is predominantly the temperature, CO2 concentration in the atmosphere (affects the CO2 uptake), the availability of water and nutrients, and the intensity and wavelength distribution of the incident light (e.g., solar spectrum). The photosynthetic efficiency is defined as the overall efficiency from solar energy to chemical bound organic material via photosynthesis.

From a global point of view, most of the biomass (95%) is C3 plants10 (e.g., wheat, rice, soybeans, and trees). These are mainly found in the temperate climates while the C4 plants (e.g., maize, sorghum, and sugarcane) grow best in relatively hot climates (Hall et al. 1993). Globally, the amount of biomass is tremendous, in the order of hundreds of billion tons, with equivalent energy values several times the world’s energy consumption today. However, the distribution of these resources varies from region to region, depending on the factors mentioned above.

The maximum photosynthetic efficiency is about 6.7% for C4 plants. In comparison, C3 plants lose about 30% CO2 during photorespiration (which does not occur in C4 plants) and have a light-utilizing capacity 30% lower than C4 plants. Thus, the maximum photosynthetic efficiency for C3 plants is 3.3% (0.7 × 0.7 × 6.7), or about half that of C4 plants. The example below illustrate the constraints on biomass (C3 plants) for energy purposes for an arbitrarily selected location.

_____________

Example 2.3: Maximum yearly recoverable amount of biomass for energy purposes

In this example the production rate of a typical herbaceous plant (HHV = 17.5 MJ/kg) grown in a field in Oslo, Norway (59.9°N), a location with low yearly average daily solar radiation (G = 10.2 MJ/m2), is calculated. A photosynthetic efficiency η of 6.7% for C4 plants and 3.3% for C3 plants can be assumed.

The total biomass production rate (in dry mass per surface area per year) for a particular region needs to be calculated from the photosynthetic efficiency η, the higher heating value HHV, and solar radiation G. Thus, for Oslo, the theoretical maximum biomass production rate on a yearly basis is 10.2 / 17.5 × 0.067 × 365 = 14.3 kg/m2. This is equivalent to 143 tons per hectare. For a C3 plant (the most common type of biomass), with half the photosynthetic efficiency, the production rate is about 70 tons per hectare.

The temperature affects the photosynthesis. In temperate climates, where there are significant seasonal variations, this must be accounted for. The optimal temperature for uptake of water and nutrients by the roots for C3 plants is between 20 and 30°C. In Oslo one can assume a growing season between May and September. This 5-month period receives an average daily solar radiation of about 1.77 times the yearly average. Thus, the adjusted maximum annual biomass production rate is 5/12 × 1.77 × 70 = 52 tons per hectare.

10 Sugars are the most important carbohydrates. In C4 plants the first product of synthesis is a 4 carbon sugar while in C3 plant the first product is a 3 carbon sugar.

42

Not all of the biomass grown can be recovered for energy purposes. In the case of trees (C3 plants), for example, only trunk and large branches can be utilized and not the roots, twigs, and foliage. According to Hall et al. (1993) about 58% of wood can be utilized as bioenergy. Thus, the maximum yearly recoverable amount of biomass for energy in Oslo is 0.58 × 52 = 30 tons per hectare

_____________

In the above calculations it was assumed that the trees got the right amounts of water and nutrients during the growing season. In general, producing biomass at a yield of 25 tons per hectare per year requires water for transpiration11 equivalent to 770 to 2,500 millimeters of annual rainfall (Table 2.7 for details on precipitation).

The most significant potential sources to biomass for energy are residues, wood resources from natural forests, and biomass from managed plantations. Biomass residues are organic byproducts from food, fiber (e.g., crops, animal manure), and forest production.

Biomass produced in photosynthesis is organic material in solid form, but there also exist natural processes (with fast or slow time constants) that produce organic gases and liquids. Gases, such as methane (CH4) and liquids, such as methanol (CH3OH) and ethanol (CH3CH2OH), can be derived from biomass and are therefore considered as renewable energy sources, even though they often are produced artificially in biological conversion processes driven by non-renewable energy. In relation to bioenergy these are often called biogas and biofuels, and have heating values comparable to natural gas and petroleum, respectively.

2.5.5 Ocean Energy

Ocean energy is essentially solar energy stored in the oceans and comes in the 5 basic forms: (1) Ocean current energy, (2) Ocean wave energy, (3) Ocean thermal energy, (4) Ocean salinity gradient energy, and (5) Marine biomass. All of these are discussed in the sections below, except marine biomass, which for energy purposes can treated similarly to biomass.

2.5.5.1 Ocean Current Energy

The circulation of water in the oceans is, similarly to the circulation of air in the atmosphere, a gigantic heat exchanger and a consequence of unequal heating of the ocean surface by the sun. This causes main ocean currents, such as the ones that originate at the poles where cold water sinks and travels (slowly) at large depths towards the tropical regions. The kinetic energy in the ocean currents, or ocean current energy, is a renewable energy source as they follow predictable seasonal flow patterns, similar to that of the prevailing winds. However, the potential of ocean current energy is difficult to estimate.

2.5.5.2 Ocean Thermal Energy

Since there is relatively little mixing of the upper and lower water streams in the oceans, there exists a temperature difference between the surface waters and those at depth. According to

11 Water is used to transport nutrients throughout the plant and large amounts are lost via transpiration through the stomata—the openings in the leaves or needles that allow the CO2 to enter the plant.


43

the second law of thermodynamics this natural temperature gradient can be utilized in a heat engine and is therefore termed ocean thermal energy. If one assumes that a practical ocean thermal energy conversion (OTEC) system requires about 20°C temperature difference to operate, the total area in the world with a potential for ocean thermal energy would be about 60 million km2. On a global basis, the theoretical potential for ocean thermal energy has been estimated to be about two orders of magnitude greater than that of wind, wave, or tidal energy (Cavanagh et al. 1993).

2.5.5.3 Ocean Wave Energy (Wave Power)

Ocean waves, created by interactions between winds and the sea surface, contain both kinetic (due to the velocity of water particles) and potential energy (function of the height displaced from sea level). Ocean wave energy, the amount of energy transferred to the ocean from the winds, depends ultimately on the wind regimes (e.g., wind speed, wind-water interaction area, wind duration).

The power density of a wave is defined as the rate at which its energy is transferred across a unit length at right angles to its direction, i.e., power per wave front, and can be estimated by the equation

′ =P g a Tρπ

2 2

8 (W m-1) 2.50

where ρ is the water density, g is the gravitational acceleration, a is the wave amplitude, and T is the wave period (Twidell and Weir, 1986). From Equation 2.50, which includes both kinetic and potential energy, it is seen that the wave power increases with increasing wave periods and wave amplitudes. The amplitude of the surface wave is essentially independent of the velocity, wavelength, or period of the wave.

It is difficult to predict the wave energy potential for a particular location because of the complex climatic and physical mechanisms involved, but a few general comments can be made. The power in a wave remains relatively constant in deep water and long smooth swells can persists for hundreds of kilometers, whereas shorter steeper seas decay more rapidly. In shallow waters (about half a wavelength deep) energy is lost to friction on the seabed. Along a coast with a shelving seabed (water depth progressively reduced towards the coastline) the waves slow down and change direction, and are sometimes even refracted. Landmasses can also obstruct waves.

On a global basis, the highest concentration of wave energy occurs between latitudes 40° and 60° in each hemisphere and at latitudes 30° with prevailing tradewinds. The west coasts of Europe and the United States, and coasts of New Zealand and Japan are particularly suitable for wave energy extraction (Cavanagh et al. 1993).

2.5.5.4 Ocean Salinity Gradient Energy

The last kind of ocean energy considered here is salt-gradient energy—a result of differences in osmotic pressure that exists between freshwater and salt seawater. The flow of solvent (freshwater) into a solution (seawater) through a semipermeable membrane is called osmosis and the pressure that just stops this process is equal to the osmotic pressure of the solution.

44

Experiments show that the dependence on osmotic pressure on the solution concentration is given by the equation

Π = MRT (atm) 2.51

where Π is the osmotic pressure in atm, M is the molarity of the solute, R is the universal gas constant, and T is the temperature in Kelvin (Zumdahl, 1995). Seawater has an approximate concentration of 0.6 M NaCl yields an osmotic pressure of 30 atm, which is equal to a hydrostatic head of 300 meters. Based on the values in Table 2.7 and assuming that 10% of the total precipitation goes to ground water, the annual river runoff to the oceans is estimated to 35 × 1012 m3. Hence, on the assumption that all the rivers in the world could be harnessed, the global theoretical salt-gradient energy potential is about 28,600 TWh12

2.5.6 Ocean Tidal Energy

Ocean tides are created by the gravitational attraction of the moon and the sun acting on the oceans and by the rotation of the earth. It is the relative motion of these bodies that cause the level of water in the large oceans to rise and fall according to predictable patterns. The main periods of these tides, created by the rotation of the earth within the gravitational field of the moon, are diurnal at 24 h and semidiurnal at about 12 h 25 min. Every 14 days the combined gravitational field of the sun and the moon produces maxima and minima in the tides called spring and neap tides, respectively. Every half-year, due to the inclination of the moon’s orbit, another maxima in the tides can be observed. These high spring tides occur in March and September (Herrmann, 1992)

The change in height between the successive high and low tides is in the range R. At open sea R is maximum about 1 m while closer to shore R can be much larger, depending on local effects such as shelving, funneling, reflection, and resonance. (These local effects may also increase the flow rates of the tidal streams). For a specific site the average ocean tidal power P can be approximated by

( )

P Ag R R≅

+ρτ2 2

2 2max min (W) 2.52

where ρ is the water density, A is the surface area of the water basin, g is the gravitational acceleration, τ is the intertidal period, and Rmax and Rmin the maximum and minimum tidal ranges, respectively. Globally, the annual theoretical potential for ocean tidal energy dissipated in shallow sea areas is estimated to about 8,760 TWh (Twidell and Weir, 1986).

2.5.7 Geothermal Energy

The inner core of the earth holds temperatures of about 4000°C and stems from the formation of the earth some 5 billion years ago. The temperature difference between the earth’s inner core and surface causes heat to flow from the inner core (6,370 km) through the outer core (5,150 km), mantle (2,900 km), and crust (30 km), before it is dissipated to the ambient at the

12 From Equation 2.2: E = ρVgh = (1000 kg/m3)(35×1012 m3) (9.8 m/s2)(300 m)(1 Wh /3,600 J) = 28,583 TWh


45

surface. In the earth’s crust heat is also generated by ongoing nuclear and chemical reactions (e.g. radioactive decay of unstable elements such as uranium and thorium) with long time constants. For this reason it is not possible to know if the earth’s temperature is increasing or decreasing.

Geothermal energy is defined as the heat that passes through the upper layer of the earth’s crust. Most of this heat is passed on by conduction, but a small part of it is also passed on by convection currents of water, steam, gas, or magma that flows up to the earth’s surface (e.g., geysers, spas, volcanoes). The conductive component of the heat flux varies from 0.03 to 0.50 W/m2, depending on the location. There are six regions in the world where the total heat flow and concentration of geothermal energy are highest. They are the Circum-Pacific, the Mid-Atlantic Ridge, the Alpine Himalayan mountain chain, much of eastern Africa and the Arabian peninsula, central Asia, and a few archipelagos in the central and south Pacific. All these zones coincide with the discontinuities in the earth’s crust and are tectonically very active. Therefore, from a practical point of view, they do not necessarily render the best sites for geothermal extraction.

On a global basis, the amount of heat that could theoretically be tapped within a depth of 5 km (the accessible resource base) is on the order of 140 × 1024 J. Because much of the in situ heat is dispersed or too low in temperature, a more realistic estimate of the geothermal resource is 5 × 1021 J (Palmerini, 1993). However, it should be noted that if terrestrial heat flow is increased artificially it can, on a long time scale, not be regarded as renewable energy.

2.6 SUMMARY

This chapter is a review of the basic principles related to energy conversion and energy storage. An extensive and factual assessment of the energy resources available on earth was also provided, where particular attention was drawn to the natural energy resources. Thus, the chapter should include the most essential information needed to evaluate and select viable stand-alone power systems (SAPS) for the future.

3 STAND-ALONE POWER SYSTEMS

This chapter is the link between the theory and fundamentals presented in Chapter 2 and the detailed modeling and simulation studies performed in Part II (Chapters 4–6). First, a systematic approach on how to arrive at optimal generic stand-alone power systems is given. The purpose here is to illustrate how one can—based on the fundamental laws and facts about energy resources, energy conversion, and energy storage (Chapter 2)—limit the discussion to relatively few generic types of SAPS.

The second part of this chapter is more practical and describes the energy technologies related to SAPS. However, the main focus is on solar-hydrogen energy technology, as this was demonstrated to be a particularly attractive option. All of the energy technologies used in the modeling and simulation work of this thesis (Part II) are discussed in this chapter.

3.1 GENERIC SAPS

3.1.1 Feasible Systems

A compilation of all the energy resources on earth with corresponding applicability in relation to SAPS is summarized in Table 3.1. The purpose here is to provide a compact view of all the options for on-site conversion of energy resources into electricity, along with the corresponding on-site storage and/or to-the-site transport requirements. A few comments about Table 3.1 are listed below:

• According to the definition of SAPS the energy resources can only be converted on-site, either directly into electricity or indirectly from a fuel.

• A traditional fuel is another term for fossil fuel. They require little to no pre-processing and are therefore defined here as primary.

• Alternative fuels are derived from renewables. They require pre-processing and are therefore defined here as secondary.

• The alternative fuels may or may not be produced on site. • The alternative fuels can be converted to electricity via traditional or alternative energy

conversion processes. • Traditional energy conversion is based on known, proven, and well-established processes. • Alternative energy conversion is based on known, less proven, and non-established

processes. • In an internal combustion (IC) cycle a fuel is burned within the system boundary. • In an external combustion (EC) cycle thermal energy is supplied to the system from an

external source.

It should be noted that some energy resources are absolutely not applicable (marked “n.a.” in Table 3.1) for use in SAPS. These are:

48

• Coal is typically suitable for large-scale thermal power plants (EC-cycles) where high-temperature heat and electric power can be utilized to maximize the overall efficiency (Equation 2.43). However, coal in the form of synfuels can be used in IC-engines.

• Nuclear fission energy is, for the same reasons as coal, typically suitable for large-scale thermal power plants.

• Nuclear fusion energy is infeasible; the theory has yet to be proven in practice. • Biomass is not suitable for the same reasons as coal. However, biomass in the form of

biofuel (methanol or ethanol) or biogas (methane) can be used. • Ocean salt gradient energy theory has still to be proven in practice.

Table 3.1 Overview of the applicability of various energy conversion and energy storage options for SAPS.

Energy Resource Energy Conversion Energy System Type Life-time

years Type Storage Transport Comments

Traditional fuels (Primary)

Traditional

Coal 300 comb–therm–mech–elec n.a. Petroleum 70 comb–therm–mech–elec × × IC Natural gas 80 comb–therm–mech–elec × × IC Nuclear Energy U-235 80 nucl–therm–mech–elec n.a. U-238 (breeding) → ∞ nucl–therm–mech–elec n.a. Fusion → ∞ nucl–therm–mech–elec n.a.

Natural Energy Solar-thermal therm–mech–elec × EC Solar-photon photo–elec × Hydro power dam mech–elec ⊗ Hydro power river mech–elec × Wind mech–elec × Biomass comb–therm–mech–elec n.a. Biofuel and biogas comb–therm–mech–elec × × IC Ocean current mech–elec × Ocean wave mech–elec × Ocean thermal therm–mech–elec ⊗ EC Ocean salt gradient mech–elec n.a. Ocean tidal mech–elec × Geothermal → ∞ therm–mech–elec ⊗ EC

Alternative Fuels (Secondary)

Alternative

Methane chem–elec × × Methanol, ethanol chem–elec × × Hydrogen chem–elec ×

Abbreviations: electrical, photon, mechanical, nuclear, chemical, combustion, and thermal Symbols: → ∞ = limit is far into the future, × = requirement, ⊗ = macroscopic potential energy, IC = Internal Combustion, EC = External Combustion,, n.a. = not applicable.

Chapter 3 Stand-Alone Power Systems

49

3.1.2 General Design Guidelines

The optimal solution for SAPS will ultimately depend on the location in question and the power demand of the user(s) (Figure 1.1), but three fundamental principles on energy, independent of location and demand set the precedence:

• Resources • Conversion • Storage

First, as described in detail in Section 2.4 and summarized in the first two columns of Table 3.1, only the natural energy sources provide viable options for a sustainable development. In other words, it is not sustainable to use finite energy resources such as fossil or nuclear energy to meet future energy demands. This means that a switch away from traditional to alternative fuels inevitably must take place, also for SAPS. In view of the scarcity that inevitably will come, the study of alternative fuels should be given priority.

Second, based on the physical laws of energy conversion, as much as possible of the energy source should be converted directly (Section 2.3.2). Furthermore, since thermal energy thermal conversion is limited by the Carnot efficiency (Equation 2.34). Therefore, the utilization of IC or EC devices should be avoided if possible and alternatives, such as electrochemical conversion, should be sought (Examples 2.1 and 2.2).

Third, energy stored in the form of microscopic potential energy (chemical energy) is favorable in comparison to macroscopic potential energy (physical structures) because it is characterized by higher specific energies (Section 2.3.3). In relation to SAPS, fuels (chemical energy) should be preferred to hydro power dams and basins (physical structures). In theory, all SAPS based on intermittent renewable energy sources (Section 2.5) need some kind of energy storage, a point also illustrated in Table 3.1.

Inefficient production or processing of alternative fuels is unfavorable. This is the case for biofuels (e.g., methane, methanol, or ethanol), due to the low overall conversion efficiency from solar energy to biomass and the inefficiencies associated with the subsequent processing of the biomass (Example 2.3). In theory, this low overall conversion efficiency is a major drawback of biofuel, although in practice, particularly in regions of the world with abundant biomass, this might not be a problem.

Hydrogen has a number of benign features. Veziroglu and Barbir (1992) analyzed and compared conventional and alternative fuel to hydrogen based on the following criteria, or merit factors:

• Motivity (for transportation purposes only, not relevant for SAPS) • Versatility (convertibility for end use) • Utilization efficiency (overall efficiency, Equation 2.43) • Environmental compatibility (at extraction, transportation, processing, and end use) • Safety (toxicity and fire hazard) • Economy (effective societal costs)

The conclusion of this study was that hydrogen has the highest overall merit factor. Besides being the best transportation fuel, hydrogen was found to be the most versatile fuel, the most efficient fuel, the environmentally most compatible fuel, the safest fuel, and the most cost

50

effective fuel to society. Another study performed by Selvam (1992) gave similar results. Here specific attention was drawn to the pros and cons of alcohol fuels, particularly methanol, which was found to have some major drawbacks. Thus, particular attention should be paid to hydrogen energy systems. The general guidelines for selecting viable SAPS for the future are summarized in Table 3.2.

Table 3.2 General design guidelines for SAPS.

Recommended Not Recommended

+ Direct conversion of solar photon, wind, hydro, and ocean current, ocean wave and ocean tidal energy.

÷ Conversion of solar thermal, ocean, and geothermal energy in EC-cycles.

+ Energy storage in fuels (1st priority) or storage in physical systems (2nd priority).

÷ Conversion of alternative fuels in IC-cycles

+ Alternative fuels: Hydrogen (1st priority) or biofuels (2nd priority).

+ Low-temperature electrochemical conversion of fuels

3.1.3 Hydrogen Energy Systems

Hydrogen is one of the most promising alternative fuels for the future because it has the capability of storing energy of high quality, and because it is in accordance with a sustainable development. Hydrogen has therefore been visualized to become the cornerstone of future energy systems based on solar energy and other renewable energy sources.

The concept of using hydrogen as an energy carrier in storage and transport of energy, i.e., the so-called hydrogen economy, has been studied by many scientists from all around the world (e.g., Ohta, 1979; Nitsch and Voigt, 1988; Ogden and Williams, 1989; Winter and Nitsch, 1989; Scott and Häfele, 1990). It is also this author’s belief that particular attention should be paid to hydrogen energy based systems.

Hydrogen can be produced chemically from hydrocarbons (e.g., renewable fuels such as methane, ethanol, or methanol), but this will not be considered here due to the inherent constraints indicated above (Section 3.1.2). A more attractive option is to produce hydrogen from water via water electrolysis, simply because of the abundance of water on earth. The basic chemical reaction for splitting water in hydrogen and oxygen is

H O + energy H O2 2 2→ + 12

3.1

For this reaction to occur, an amount of energy must be added, while the opposite reaction releases energy. The oxygen in water electrolysis (Equation 3.1) is usually released to the atmosphere, but may be stored in an artificial structure as well. Thus, in theory, if hydrogen is produced from natural energy resources, the hydrogen cycle is a 100 percent environmentally benign energy cycle (Figure 3.1). Because solar energy for all practical purposes can be regarded as an infinite source of energy, the hydrogen cycle is one of the best options for a sustainable future.


51

To regard solar energy as an infinite source of energy is of course incorrect. In the hydrogen we (the inhabitants of the earth) simply extract a portion of the solar energy that otherwise would be lost in space. All of the solar energy that is not reflected off the atmosphere is converted, in some way or another, on earth (Figure 2.4), before it finally ends up as thermal energy (lowest form of energy). From an exergy point of view (Section 2.3.1), it is important to capture the solar energy of highest quality before converting and storing it in the form of hydrogen. For instance, the exergy efficiency of a solar–hydrogen system is higher than that of a wind–hydrogen, because wind energy is a derivative of solar energy.

Hydrogenproduction

Transportstorage

distribution

Hydrogenutilization

Naturalenergy End use

H2H2

H2O H2O

O2 O2

Atmospheric transport of oxygen

Water cycle

Figure 3.1 The natural energy hydrogen cycle.

3.2 PRACTICAL SAPS

The discussion up to this point in the thesis has been general, where the main focus has been to put SAPS in a global and fundamental perspective. The purpose of this was to arrive at a set of recommendations for viable SAPS options for the future.

From this point the focus of the thesis will be on practical and technical aspects related to SAPS. Only systems that satisfy the general recommendations listed above (Table 3.2) will be considered. However, since there is a large number of energy technologies that satisfies the criteria in Table 3.2, the discussion will be limited to the most practical and promising systems

3.2.1 Size of Systems

The size of the power demand is one of the most important factors when deciding on what kind of SAPS to select. In Chapter 1 a set of common applications of SAPS was discussed and a classification system based on typical peak power demands, in the range from 10 W to 100,000 W, was presented (Table 1.2).

The most distinct difference between the small and large systems is that the small systems predominantly supply a single user (e.g., a dwelling) directly with power, while the larger systems may have several users (e.g., cluster of dwellings, a village) and require a mini-grid to

52

distribute the power. A characteristic of the multi-user systems is that they have smoother power demand curves than single-user systems, due to non-coinciding user needs.

3.2.2 Mini-grid Systems (Fixed Size)

From a technological point of view, some SAPS should predominantly be used in mini-grids because of their inherent advantage of being built on a large scale. According to the recommendations in Section 3.1, this applies to the following renewable energy sources:

• Hydro power dam • Ocean tidal • Ocean current • Ocean wave

A very important advantage of the hydro dams and ocean tidal based systems are that they are storage systems in themselves. In comparison, ocean current and wave energy do not intrinsically provide any kind of energy storage, and do therefore require some kind of energy storage.

A very severe limitation of mini-grid systems based on one of the four sources above is that they cannot easily be changed to meet possible increases in future power demand. A solution to this problem is to oversize the systems. However, this might be financially risky since the future power demand in rural areas (the target area for decentralized systems) often is quite uncertain (Section 1.1.4). A less risky option is to install flexible systems that are relatively simple to scale up.

3.2.3 Modular Systems (Flexible Size)

A prerequisite for a flexible system is that it is composed of modular parts. On the basis of the recommendations given in Section 3.1, only the following renewables meet these criteria:

• Solar-photon • Wind • Hydro river (micro hydro)1

The attractiveness of solar, wind, and hydro-river energy is the possibility to produce electricity directly. Solar and wind energy is in general fairly evenly distributed around the globe, while hydropower based on river runoff is more dependent on the site. However, because of their intermittent nature, a storage or backup system is always required. The extent to which this is necessary is dependent on the matching (or mismatching) between the source and the demand. Thus, the ideal scenario for a decentralized system is that it is located in an area with high and evenly distributed solar radiation levels (Figure 2.6), high wind power densities (Table 2.9), or high river runoff (Table 2.7).

Based on the recommendations given in Section 3.1, only alternative fuels based on renewables should be used in an energy storage or back-up system:

1 The terminology micro hydro is generally used to define as hydro power plants with capacities less than 100 kW. Micro hydro power is almost always obtained from river runoff (Moreira and Poole, 1993).


53

• Hydrogen • Biofuels (e.g., methane, methanol, or ethanol)

The main attractiveness of hydrogen-storage systems is that they provide the opportunity to produce and store energy on site, thus they completely eliminate the need to transport fuel for backup purposes. In comparison, biofuels generally need to be transported to the site.

3.3 HYDROGEN ENERGY TECHNOLOGY

The utilization of intermittent natural energy sources, such as solar, wind, and hydro energy, requires some form of long-term energy storage. The concept of utilizing hydrogen as a substance for long-term storage of energy is shown in Figure 3.2. In practice, a stand-alone power system based on hydrogen technology (H2–SAPS) must consist of a hydrogen production device, a hydrogen storage unit, and a hydrogen utilization device.

It should be emphasized that the main purpose of the hydrogen storage system is to store energy over long periods of time—from season to season. However, since a SAPS based on intermittent energy sources, such as solar and wind energy, is likely to experience large minutely, hourly, and daily fluctuations in energy input, a short-term storage, such as a secondary battery (Section 3.4.4), must also be included.

Energy source:– Solar-photon– Wind– Micro hydro

Short-termenergy storage

End-use:Electricity

H2production

H2storage

H2utilization

Direct conversion

Long-termenergy storage

Figure 3.2 Concept of a stand-alone power system based on hydrogen technology

(H2–SAPS).

3.3.1 Hydrogen Production (Water Electrolysis)

Hydrogen can be produced from water in several ways. The basic methods for water electrolysis are commonly divided into 8 groups (Sandstede, 1989):

I. Alkaline electrolysis II. Acidic electrolysis

54

III. High temperature electrolysis IV. Thermochemical electrolysis V. Photochemical electrolysis VI. Photoelectrochemical electrolysis VII. Biochemical electrolysis VIII. Electrolysis with hydrogen as a by-product

Alkaline water electrolysis (I) is the most established and dominating technology today, but also acidic water electrolyzers (II) are commercially available. High temperature (700–1000°C) steam electrolysis (III) is relatively far from technical maturity (Wendt and Plzak, 1991). This is also the case with the principle methods IV–VIII, which are more futuristic forms of hydrogen production (Ohta, 1979; Wendt (1988). Methods III–VIII are not studied in detail here. Alkaline electrolyzers (I) with will be the main topic of interest, but also acidic electrolyzers (II) will be discussed.

3.3.1.1 Conventional Alkaline Electrolyzers

The electrolyte used in conventional alkaline water electrolyzers has traditionally been aqueous potassium hydroxide (KOH), mostly with solutions of 20–30 wt.% because of the optimal conductivity and remarkable corrosion resistance of stainless steel in this concentration range (Wendt and Plzak, 1991). The typical operating temperatures and pressures of these electrolyzers are 70–100°C and 1–30 bar, respectively.

Physically an electrolyzer consists of several electrolytic cells, connected in parallel. Two distinct cell designs exist: monopolar and bipolar (Divisek, 1990). In monopolar cells the electrodes are either negative or positive, while bipolar cells have electrodes that are negative on one side and positive on the other side (separated by an electrical insulator) (Figure 3.3).

O2 H2

+–

anode cathodediaphragm

Monopolar cells

O2 H2

+

diaphragm

anode cathode

Bipolar cells

O2

–

H2 H2O2O2 H2

insulator

Figure 3.3 Principle of monopolar and bipolar electrolyzer cell designs.

One advantage of the bipolar electrolyzer stacks is that they can be more compact than the monopolar systems. Another feature of the bipolar electrolyzer is that it can operate at high pressures (up to 30 bar). This is an advantage because it greatly reduces the compression work required to store the hydrogen produced by the electrolyzer. In comparison monopolar systems operate at atmospheric pressure.


55

The advantage of the compactness of the bipolar cell design is that it gives shorter current paths in the electrical wires and electrodes compared to the monopolar cell design. This reduces the losses due to internal ohmic resistance of the electrolyte, and therefore increases the electrolyzer efficiency. However, there are also some disadvantages with bipolar cells. One example is the parasitic currents that can cause corrosion problems. Furthermore, the compactness and high pressures of the bipolar electrolyzers require relatively sophisticated and complex system designs, and consequently the manufacturing costs. The relatively simple and sturdy monopolar electrolyzers systems are in comparison less costly to manufacture. Nevertheless, most alkaline electrolyzers manufactured today are bipolar.

3.3.1.2 Advanced Alkaline Electrolyzers

New designs of advanced alkaline electrolyzers are currently being developed. According to Wendt and Plzak (1991) the overall aim of these advanced electrolyzers is to:

• Reduce the practical cell voltages to reduce the unit cost of electrical power and thereby the operation costs.

• Increase the current density (current per surface of electrode area), and thereby reduce the investment costs.

The problem with this is that there is a conflict of interest because increased current densities yield increased cell voltages due to increased ohmic resistance as well as increased overpotentials at the anodes and cathodes. In practice, three basic improvements of alkaline electrolyzers must be made to reach the two aims stated above. These are:

• New cell configurations to reduce the surface-specific cell resistance despite increased current densities (e.g., zero-gap cells and low-resistance diaphragms).

• Higher process temperatures (up to 160°C) to increase electric conductivity of the electrolyte, i.e., to reduce the electric cell resistance.

• New electrocatalysts to reduce anodic and cathodic overpotentials (e.g., mixed-metal coating containing cobalt oxide at anode and Raney-nickel coatings at cathode).

In the zero-gap cell design (Figure 3.4) the electrode materials are pressed on either side of the diaphragm so that the hydrogen and oxygen gases are forced to leave the electrodes at the rear. Most manufacturers are already adopting this design (Divisek, 1990).

O2 H2

anode cathode

diaphragm

Figure 3.4 Geometry of a zero-gap electrolyzer cell.

56

3.3.1.3 Acidic Electrolyzers

One of the most promising types of acid electrolyzers is the proton-conducting solid polymer electrolyte (SPE), which resembles that of the proton exchange membrane (PEM) fuel cells described below (Section 3.3.3). Actually, if properly designed, the same polymer membrane electrolyte unit can operate both as an electrolyzer to produce hydrogen, as well as a hydrogen driven fuel cell to produce electricity (Ledjeff et al., 1994).

3.3.1.4 Solar Photoproduction of Hydrogen

One of the most promising ways to produce hydrogen is solar photoproduction of hydrogen, because it fits perfectly into the ideal hydrogen cycle described above (Figure 3.1). According to Bolton (1996) such solar energy driven water-splitting systems can be classified into the five main categories:

• Photochemical systems (sunlight is absorbed by isolated molecules in solution). • Semiconductor systems (sunlight is absorbed by a semiconductor, either as a suspended

particle in a liquid or as a macroscopic unit in a photovoltaic or an electrochemical cell). • Photobiological systems (sunlight is absorbed by leaf chloroplast or algae in a

configuration coupled to a hydrogen-generating enzyme) • Hybrid systems (combinations of 1 to 3) and other systems • Thermochemical systems

A survey of the state-of-the-art and a technological assessment of various solar photoproduction options based on potential and ideal system efficiencies has been performed by Bolton (1996). The conclusion of this survey showed that four solar hydrogen systems should be considered for future R&D:

1. Photovoltaic (PV) and electrolyzer (group I or II) systems. 2. Photoelectrochemical (PEC) systems. 3. Photobiological systems. 4. Photodegradation systems

From a practical point of view, the combination of Photovoltaic (PV) and electrolyzers are the systems of most interest. This is due to the relatively mature (alkaline) electrolyzer technology and due to the rapid and promising development of the (silicon) PV technology (Section 3.4.2).

The photoelectrochemical (PEC) systems have the advantage of combining the PV cell and electrolyzer into one system without wires. A hydrogen production efficiency of about 12% has been achieved in a laboratory test of a monolithic PEC/PV device (Khaselev and Turner, 1998). However, these PEC systems have yet to be demonstrated on a pilot-plant scale. The same applies to the photobiological systems.

In a photodegradation system, sunlight is used to couple hydrogen evolution to the photodegradation of organic pollutants. Thus it is a by-product system, and not very applicable for SAPS.


57

3.3.2 Hydrogen Storage

Hydrogen is characterized by a very low boiling point (÷253°C) and a low density at standard state (0.08245 kg m-3). Therefore, at ambient conditions hydrogen only exists as a gas.

Hydrogen can be stored mechanically and/or chemically. Apart from storage in chemical compounds (hydrogen storage in molecules such as methane, ethanol, and methanol is not considered in this study), the four basic hydrogen storage concepts are (Carpetis, 1988):

• Liquid hydrogen (LH2) storage • Adsorber storage (e.g., H2 in superactivated carbon, H2 in carbon nanostructures) • Metal hydride (MH) storage (H2 in metal alloys) • Pressurized hydrogen (PH2) gas storage

The liquefaction of hydrogen can only be achieved cryogenically by mechanical compression and cooling. The total energy required to produce LH2 from H2 at standard state is about 16,000 kJ kg-1, where about 25% is cooling energy and 75% is compression work (Ohta, 1994). The tremendous expansion rate of LH2 makes it mainly suitable for mobile applications, which requires this “explosive” feature (e.g., rockets and large IC-engines).

Hydrogen can also be adsorbed (as molecules in the gaseous state) in adsorbing materials such as active carbon. However, in order to obtain a specific energy comparable to LH2 it is necessary to cool the adsorber to very low temperatures (about ÷200°C). Another, interesting adsorber technique involves the storage of hydrogen in carbon graphite nanostructures, which are nanofibers that possess some crystallinity and have interstices of about 0.335 to 0.750 nm (Rodriguez et al., 1997). The technique is claimed to have the potential to store hydrogen at a very high weight percentage (about 75 wt.%) at near-ambient temperatures, while other scientists believe that this is an impossibility. Nevertheless, the technique is mentioned here because it illustrates the serious research currently going on in the area of near-ambient temperature hydrogen adsorption storage.

One severe disadvantage with cryogenic storage, such as LH2 –and cryo-adsorbing systems, is the need for expensive heat insulating materials (e.g., superinsulation). Secondly, since the heat losses are proportional to the surface area A of the storage, the storage should have as large a volume V as possible, so that the A/V–ratio is small. For these reasons LH2 –and adsorbing systems can be ruled out as options for H2–storage in SAPS.

Metal hydride (MH) storage is another new and promising hydrogen storage concept, particularly because of its high specific energy. The specific mass of some metal hydrides is at ambient-temperature approximately 0.012–0.015 kg H2/kg MH (Table 3.3). With the LHV for hydrogen (1.2 × 105 kJ/kg H2), this yields specific energy values of about 1,440–1,800 kJ/kg MH, which is about 12 to 15 times greater than that of a conventional lead-acid battery (Table 2.3). Furthermore, the absorption- and desorption characteristics of some metal hydrides is such that they match well with the operating conditions of small SAPS (Hagström et al., 1995).

The traditional method to store hydrogen is to compress and store it in small vessels or large tanks. For very large applications it is also possible to store the hydrogen in underground caves, but this is not a conceivable option for SAPS because of the relatively small energy storage requirements.

58

Table 3.3 provides some typical specific data for hydrogen storage systems and shows that MH–storage is more favorable than PH2–storage on a per volume basis, while there is no significant difference between the two on a per mass basis. The density of a LH2–storage is comparable to a MH–storage, but is of course much better on a per mass basis. Cryogenic storage is not considered an option for SAPS (for reasons stated above), but is listed in Table 3.3 for comparative purposes.

Table 3.3 Typical data for hydrogen storage systemsa

Type of hydrogen storage Densityb kg H2 m-3

Mass ratioc kg H2 kg-1

Specific energyd kJ kg-1

Pressurized hydrogen (PH2) 15 0.012 1,440 Metal hydride (MH) 50–53 0.012–0.015 1,440–1,800 Liquefied hydrogen (LH2) 65 0.150–0.500 18,000–60,000 a. Adapted from Carpetis (1988). b. Includes volume of storage structure. c. Includes mass of storage structure. d. Based on LHV for hydrogen (Table 2.3).

3.3.3 Hydrogen Utilization (Fuel Cells)

The conversion of hydrogen into end-use energy, which in this context is electricity, can only be achieved via two basic reactions (Peschka, 1988):

• Fuel cell reactions • Combustion reactions

The advantage of the hydrogen combustion in IC– or EC–cycles is that they involve mature technologies (e.g., IC–engines or gas turbines), as opposed to fuel cells which still are at an early stage in the development. However, one significant advantage of a fuel cell reaction vis-à-vis a combustion reaction is the higher overall conversion efficiencies (Examples 2.1–2.2). Fuel cells will therefore be the topic of interest in this study.

Fuel cells are electrochemical devices that convert chemical energy of a fuel directly into electricity in the form of direct current, and are categorized according to the type of electrolyte used types (Wendt and Rohland, 1991). Hydrogen–oxygen fuel cells are generally divided into five main groups, as listed in Table 3.4. Since the application of fuel cells largely depends on the operation conditions, values for typical operation temperature and efficiencies are also included in Table 3.4.

The solid oxide fuel cell (SOFC) and molten carbonate fuel cell (MCFC) operate at high temperatures (about 650°C and 1000°C, respectively), and are therefore most suitable for large power plants. The phosphoric acid fuel cell (PAFC) is today commercially available and can be used over a fairly large power range (from a few kW to several MW). However, since they operate at medium high temperatures (about 200°C), they are typically most suitable for co-generation (combined heat and power generation).

Only two types of low-temperature fuel cells exist—the alkaline fuel cell (AFC) and the solid polymer fuel cell (SPFC), also called a polymer electrolyte fuel cell (PEFC) or proton


59

exchange membrane fuel cell (PEMFC)2. In theory both the AFC and PEMFC are attractive options for SAPS, due to their low operation temperatures.

The fuel cell technology that is currently being given most attention in terms of R&D, is the promising PEMFC. The reason for this, besides the low operation temperature, is the high current densities (current per unit area of electrode) and low weight of the PEM fuel cell, which makes it particularly apt for use in the mobile applications.

Table 3.4 Hydrogen–oxygen fuel cell systems

Type of fuel cell system Electrolyte Temperature°C

Efficiency %

I AFC Alkaline Fuel Cell 35–50 wt.% Potassium hydroxide (KOH)

60–90 50–60

II PEMFC Proton Exchange Membrane Fuel Cell

Polymer membrane

50–80 50–60

III PAFC Phosphoric Acid Fuel Cell

Concentrated phosphoric acid (H3PO4)

160–220 55

IV MCFC Molten Carbonate Fuel Cell

Molten carbonate melts (Li2CO3/Na2CO3)

620–660 60–65

V SOFC Solid Oxide Fuel Cell Yttrium-stabilized zirkondioxide (ZrO2/Y2O3)

800–1000 55–65

Source: Kordesch and Simader (1996).

3.3.3.1 Other Fuel Cell Systems

Although the focus of this study will be on pure hydrogen energy systems and direct fuel cells which convert hydrogen directly into electricity, a few indirect fuel cell systems that require some kind of reforming should also be mentioned. The advantage of reformer–fuel cell systems is that they can use other alternative fuels than hydrogen. For example, methane can in a reformer–fuel cell system be steam reformed to hydrogen via the reactions:

CH4 + H2O → CO + 3 H2 3.2

CH4 + 2H2O → CO2 + 4 H2 3.3

If the reforming of a fuel such as CH4 or other light hydrocarbons occurs externally to the actual fuel cell in a fuel cell system, the process is called external reforming. On the other hand, when the reforming of the fuel occurs inside the fuel cell itself, the process is called internal reforming. If alternative fuels such as methane, methanol and ethanol are to be used

2 PEMFC or PEM fuel cells are the acronyms used in this thesis.

60

in low- and intermediate temperature AFC, PEMFC, or PAFC–systems, external reforming is required. Internal reforming can only be achieved in high-temperature fuel cell systems, such as SOFC or MCFC systems. In SOFC and MCFC systems, a combination of internal and external reforming can also be used (Verfondern, 1997).

Another, but completely different type of fuel cell, is the direct methanol fuel cell (DMFC). The DMFC converts methanol directly into electricity and does not require any kind of reforming at all (Kordesch and Simader, 1996). However, the DMFC technology is still far from mature.

3.4 ENERGY TECHNOLOGIES FOR SAPS

The conclusion from the discussion above (Sections 3.1–3.3) is that solar-hydrogen systems based on photovoltaics (PV) (solar photon energy), or PV–H2 systems, is one of the most interesting concepts for stand-alone power supply. However, tt should be noted that hydrogen systems based on wind or micro-hydro power, although not studied in detail in this thesis, are possible alternatives to photovoltaics.

An overview of recommended SAPS configurations is given in Table 3.5, while a summary of the typical performance characteristics of individual components is given in Table 3.9. The attractiveness of a system configuration depends of course ultimately on the availability of the solar, wind, and/or hydro energy at the site in question.

Furthermore, as it will be demonstrated later (Part II), secondary batteries (short-term energy storage) and power converters (power conditioning) also play an important role in stand-alone PV–H2 systems. The photovoltaic, battery, and power conditioning technologies are given particular attention in Sections 3.4.2–3.4.5.

3.4.1 Recommended SAPS Configurations

An overview of the recommended configurations for future SAPS are given in Table 3.5. (The configurations of most interest are listed above the thin line, while the configuration studied in detail in Part II of this thesis is highlighted in bold italic text).

Table 3.5 Overview of recommended configurations for future SAPS

Type of Systema Maturity Sizeb

PV–Battery Mature S, M PV–Wind–Battery Mature M PV–Battery–H2 New S, M, L PV–Wind–Battery–H2 New M, L Wind–H2 New L

PV–Battery–Biofuel gen set Mature M, L PV–Wind–Battery–Biofuel gen set Mature M, L Micro-hydro–H2 New L a. PV = Photovoltaic generator, Wind =Wind Energy Conversion System, gen set = IC-engine with generator. b. S = Small, M = Medium, L = Large (refer to Table 1.2 for definition of sizes).


61

3.4.2 Characteristics of SAPS Technology

A summary of the characteristics of some of the key SAPS technologies is provided in Table 3.6. The table gives a rough assessment of the maturity of each technology. Values for the theoretical (maximum) and actual (typical) efficiencies of the power conversion devices are also indicated in the table.

Table 3.6 Characteristics of energy technologies for SAPS.

Name Type Maturity Efficiency, % Theoretical Actual (typical)

AC devices Wind turbine mech–mech new 59a 42d Hydraulic turbine mech–mech mature – 95e Generator mech–elec mature – 96f

DC devices Photovoltaic cell photo–elec new 43b 24g–33h Electrolyzer elec–chem new, mature 83c 70i Fuel cell chem–elec new 83c 55j

Power conditioning DC/DC-converter elec–elec new, mature – 98k DC/AC-inverter elec–elec new, mature – 76–94l

Storage Water dam or basin mech mature Pressurized gas mech mature Secondary battery elec–chem–elec new, mature Metal hydride chem new

a. Maximum power coefficient, also called the Betz limit CP,max = 16/27 (Wilson, 1994). b. An optimally configured two-junction GaAs-based cell (Zweibel 1990). c. Thermodynamic efficiency of splitting (or formation) of H2O at standard state (Tilak et al., 1981). d. Power coefficient of 3-bladed horizontal axis wind turbine with tip-speed ratio λ = 8 (Wilson, 1994). e. Hydraulic efficiency of Francis or propeller turbines (reaction turbines) (Streeter and Wylie, 1985). f. Low-speed (below 500 rpm) synchronous generator (Del Toro, 1986). g. Si (crystalline) cell from UNSW PERL (Green et al., 1997). h. Multi-junction GaAs-based cell (monolithic) from Japan Energy (Green et al., 1997). i. Total LHV-efficiency of an advanced alkaline electrolyzer operating at 5 bar (Hug et al., 1992) j. Efficiency corresponding to typical operating current for a PEM fuel cell (Barbir and Gómez, 1996) k. Maximum power point tracker (MPPT) converter for PV installations (Snyman and Enslin, 1993). l. Low and high values for 50 W and 550 kW inverters, respectively (Wilk and Panhuber, 1995).

3.4.3 Photovoltaic Cells

Photovoltaic (PV) cells, or solar cells, convert solar radiation (photon energy) directly into electrical current (DC power). Although photovoltaics is a fairly new technology, there already exists a number of different types of solar cells on the market today (Green, 1993; Carlson and Wagner, 1993; Zweibel and Barnett, 1993).

62

An update of the rapid progress in R&D of photovoltaics is best found in Green et al. (1997), who currently classify photovoltaic cells in five main groups:

I. Crystalline and polycrystalline silicon cells (c-Si and p-Si) II. III-V cells (e.g., GaAs, InP) III. Polycrystalline thin film cells (e.g., CdTe, CuInGaSe2) IV. Amorphous silicon cells (a-Si) V. Multijunction cells (e.g., GaInP/GaAs, GaAs/ CuInSe2)

A conventional solar cell is based on silicon, and is commonly referred to as CZ silicon (named after the Polish physicist J. Czochralski). The CZ silicon technology is commonly used as a reference, or baseline, for the PV technology. In general, the status of a PV technology is judged according to three basic criteria: (1) Cell efficiency, (2) Manufacturing cost, and (3) Outdoor reliability. Since reliability is not such of an issue anymore, the focus of R&D is primarily on efficiency and cost, where the optimal solution is based on a trade-off between the two.

The maximum conversion efficiency of a solar cell is determined by the material’s ability to absorb photon energy over a wide range, and on the band gap of the material (Section 4.3.1). The band gap, maximum currents, and maximum theoretical efficiencies for a few materials is given in Table 3.7. It shows that materials with band gaps close to the maximum solar radiation (about 1.5 eV) are favorable for solar cells. Gallium arsenide (GaAs) has the highest theoretical efficiency at 30%, but there also exist a number of other materials that have efficiencies greater than 20%.

Table 3.7 Band gap, maximum current, and theoretical efficiency of some materialsa.

Material Band gap eV

Maximum currentb mA cm-2

Maximum efficiencyc %

CuInSe2 0.98 50 25 Si 1.1 43.4 28 GaAs 1.4 31.8 30 CdTe 1.5 28.5 29 a-Sid 1.7 21.7 27 a. Approximate values at room temperature (Zweibel, 1990). b. Assumes 100% quantum efficiency. c. The practical efficiency for a conventional solar spectrum (AM1.5). The theoretical black-body (AM0) limit

is slightly higher (Green, 1982). d. The efficiency of amorphous silicon stabilizes after a few months (Carlson and Wagner, 1993).

Conventional silicon cells need a thickness of about 100 microns (100 µm) of silicon to absorb 95% of photons in solar spectrum. Thus, the cells need to be relatively thick and the silicon must be of a very high quality. This has lead to advanced processing techniques and new innovative designs of silicon cells (Table 3.8).

Crystalline and polycrystalline silicon is the material most commonly used in photovoltaics. The advantage of silicon cells is primarily the abundance of silicon on earth. The p–n junction (Figure 4.2) of a silicon cell is formed by doping Si with phosphorus to produce an n-type material and boron to produce a p-type material.


63

Table 3.8 New photovoltaic (PV) manufacturing techniques and designs.

Low-cost manufacturing techniques High efficiency designs

• Thin crystalline silicon (less than 50 microns thick)

• Surface passivation (reduces recombination and reflection)

• Cast silicon • Light-trapping methods • Ribbon growth • Microgrooved cells • High-speed melt spinning • Point contact cells (both contacts on the

rear of the cell)

In general, independent of the material used, one way to lower the manufacturing costs of PV solar cells is to make thin film cells (about 1 micron thick). The three main reasons for why cost are reduced with thin-film technology are: (1) Less material leads to lower material costs, (2) Thinner layers allows for faster processes and lower capital costs, and (3) Processing of larger-area PV devices reduces the handling costs.

The latest innovation of PV cell design is the multijunction cells. This design is based on using more than one electric field to separate electrons and holes (see Section 4.3.1 for more details). In principle, a multijunction is one cell stacked on top of another, where cells with materials of different band gaps are used. In a properly designed multijunction cell, photons with high-energy are absorbed in the top layer, while photons with lower energy levels are absorbed in the bottom layer or layers. Three layers are currently the practical limit (Zweibel, 1990).

Finally, a note on practical types of PV systems, which essentially can be divided into two main categories: (1) Flat-plate PV cell systems and (2) PV cell concentrator systems.

The flat-plate PV cells capture both the direct and diffuse portion of the sunlight while the PV concentrators only capture the direct solar radiation. The PV concentrators require mirrors to concentrate the sunlight onto a PV cell (with one fifth to one hundredth of the area intercepted by the system) and a tracking system to follow the sun during the course of the day. Flat-plate PV systems with tracking also exist. However, the state-of-the-art design is the stationary flat-plate photovoltaic system, and is the design studied in this thesis.

3.4.4 Secondary Batteries

A secondary battery3, also known as an accumulator or rechargeable battery, is an electrochemical device that can transform electrical energy into stored chemical energy (charge) and by reversing the process, release the energy again (discharge).

A battery consists essentially of electrochemical elements, or cells, connected in series and parallel. The main components of an electrochemical cell are the electrodes, the separator, and the electrolyte. The characteristic of a battery depends on the selection of component materials, the configuration of the individual cells, and on the overall design of the battery. Below follows a brief description of the secondary batteries most pertinent to SAPS.

3 A primary battery is not rechargeable and thus not applicable for SAPS. The term battery refers in this thesis to a secondary battery, unless otherwise stated.

64

A secondary battery that is to be used in a SAPS based on intermittent energy sources such as sun and wind (Figure 3.2) should, in addition to being cost effective, be designed according to the following criteria (Chaurey and Deambi, 1992):

• High cycle life (i.e., many charging-discharging cycles) • High capacity at slow rate of discharge • Good reliability under cyclic discharge conditions • High watt-hour and ampere-hour efficiencies at different levels of state of charge (SOC) • Long life, robust design, and low maintenance requirements • Wide operation temperature range • Low self-discharge

These criteria exclude small batteries (e. g. A, C, and D type), button cells, or other small batteries used in power electronics (e.g., radios, cellular phones, video cameras, and tools). Thus, only larger-sized secondary battery systems for energy storage are applicable for SAPS.

3.4.4.1 Classification of Battery Systems

Secondary batteries can be classified according to their technological maturity or commercial availability. Terminology such as conventional or advanced battery systems is frequently used (Linden, 1995). In this thesis the definition of a conventional type of battery includes the new types of batteries that are improvements of conventional batteries. The three main types of conventional batteries that are suitable for SAPS are:

• Flooded and vented lead-acid (Pb-acid) batteries • Valve regulated lead-acid (VLRA) batteries • Pocket plated nickel-cadmium (Ni-Cd) batteries

There are many advanced types of batteries under development. These are usually based on new materials and designs that are completely different from the conventional batteries, and therefore require further development in order to be commercialized. However, for convenience, the definition of advanced batteries used here also includes batteries that have been used for some time in special applications (e.g., nickel-hydrogen batteries for the aerospace industry), but are not yet commercially competitive. Some advanced batteries that have been proposed as short-term energy storage for SAPS are:

• Nickel-hydrogen batteries (e.g., nickel-metal hydride) • Lithium ambient-temperature batteries (e.g., lithium polymer, lithium-ion) • Aqueous batteries (e.g., zinc/bromide, redox flow batteries) • High-temperature batteries (e.g. sodium/sulfur, lithium/iron sulfide)

The first two types belong to the category of new or recently commercialized battery systems, while the last two belong to the category of developmental battery systems (BCC, 1997). However, the nickel-hydrogen battery based on metal hydrides is the battery system that is commercially closest to the market.

Table 3.9 gives the characteristics of some of the most common types of conventional batteries available for SAPS today and a few examples of some promising advanced batteries for the future.


65

Table 3.9 Characteristics of some conventional and advanced types of batteriesa

Electrode Practical battery Type of battery Anode

(÷) Cathode (+)

Theoretical voltage V/cell

Nominal voltage V/cell


Energy density kJ L-1

Conventional Lead-acid

Flooded Pb PbO2 2.1 2.0 20–28 35–60 VRLA Pb PbO2 2.1 2.0 20–31 45–85

Nickel-cadmium Pocket plated Cd Ni oxide 1.35 1.2 19 36

Silver-zinc Zn AgO 1.85 1.5 90 180

Advanced Nickel-hydrogen

Nickel-metal hydride MH Ni oxide 1.35 1.2 50 175 Ambient temperature

Lithium-polymer Li V6O13 – 3.0 200 350 Lithium-ion C LixCoO2 – 4.0 90 200

Zinc/bromine Zn Br2 1.85 1.6 70 60 Redox flow

Vanadium V3V2 V5V4 1.26 – – – High temperature

Lithium/iron disulfide Li(Al) FeS2 1.73 1.7 180 350 Sodium/sulfur Na S 2.1 2.0 170 250

a. Adapted from Berndt (1997) and Linden (1995).

3.4.4.2 Lead-acid Batteries

A traditional lead-acid (Pb-acid) battery consists of the five basic components: Positive plates with lead dioxide (PbO2), negative plates with sponge lead, separators, an aqueous electrolyte of sulfuric acid (H2SO4), and a container (Berndt, 1997). The plates can be of different design. Four common types of plates for lead-acid batteries exist (Havre et al., 1993):

• Positive Planté plates. These plates are made of pure cast lead. They have a lamellar structure, which yields a high surface area, and the construction is therefore suitable for high current applications. Only low energy throughputs can be achieved due to the use of pure lead only.

• Positive tubular plates. These plates are normally constructed of a highly porous glass fiber or plastic arranged around each rod. The active mass (the lead dioxide) is inserted between the lead and the tube. This gives good mass utilization and large energy throughput. High current loading is restricted due to the limitations on the diameter of the tubes. However, the construction provides high mechanical strength and high resistance to corrosion, and hence a high cycle life.

• Positive rod plates. This is a further development of the positive tubular plates. The plates consist of vertical lead rods, where the active mass is enclosed in the area between the rods. The design gives both good mass utilization and high current performance.

66

• Positive and negative grid plates (Pasted plates). In this design the active mass is pasted into a lead grid. The grid acts as both the electrical conductor and mechanical base for the active material. The resistance to corrosion is low, hence the life cycle is low.

Thus, according to the general design criteria listed above, the most suitable type of lead-acid batteries for SAPS based on intermittent energy are the ones based on the positive tubular plate and the positive rod plate designs. This is mainly due to their relatively high specific energy densities and high cycle life. However, it should be emphasized that these types of batteries are less suitable than the positive Planté plate design if a high maximum charge or discharge current is a requirement.

A general disadvantage with the aqueous electrolyte of the flooded and vented lead-acid batteries is the decomposition of water into hydrogen and oxygen. Thus, in order to prevent dry-out of the electrolyte, water needs to be refilled at regular intervals. Another disadvantage of the flooded and vented lead-acid batteries is the fumes of acid (electrolyte) that escape with the gases produced in the battery. Over time this will dilute the electrolyte and thus reduce the capacity of the battery.

Furthermore, there is also the problem of corrosion on the positive grid electrode, which limits the service life of every lead-acid battery. This problem can be alleviated by either increasing the amount of lead on the positive grid (this increases the weight of the battery) or by using lead alloys with materials such as antimony (Sb), calcium (Ca), or tin (Sn). However, since the positive grid also must have high mechanical strength (for handling during production), high creep strength (to resist growth during service), and suitable electrochemical properties (e.g., hydrogen production at the negative electrode is higher for lead-antimony alloys than for pure lead), the problem is not trivial. Corrosion at open-circuit voltage due to self-discharge of the positive electrode is another severe problem, which limits the shelf life of every lead acid battery (Berndt, 1997).

In a SAPS based on intermittent energy sources such as wind and solar, the battery may receive partial or incomplete charge for long periods of time (weeks). This recharge methodology is in the battery industry referred to as opportunity charging. Opportunity charging causes electrolyte stratification and/or irreversible sulfation in flooded deep-cycle lead-antimony batteries. After prolonged periods of time (months) in partial charge condition, full recovery of battery capacity can only be achieved by adding a high and controlled amount of charge (Hund, 1997)

3.4.4.3 Valve-Regulated Lead-Acid (VRLA) Batteries

A valve-regulated lead-acid (VRLA) battery uses the same electrochemical technology as the flooded and vented lead-acid batteries. However, the difference between the two is that the VRLA battery is closed with a pressure-regulating valve (which only opens periodically). In addition, the acid electrolyte of the VRLA battery is immobilized by using a gel or absorbed glass mat (AGM) material.

The main advantage of the VRLA battery is that the need to refill water during the lifetime of the battery can be eliminated. This is because of the internal oxygen cycle, or recombination, where the oxygen generated at the positive electrode during charging or overcharging is


67

reduced at the negative electrode.4 The created oxygen cycle absorbs the overcharging current that otherwise would decompose water into hydrogen and oxygen. A prerequisite for the internal oxygen cycle is a sealed or valve-regulated container to prevent the escape of gaseous oxygen encapsulates the battery. Furthermore, the oxygen transport from the positive to negative electrode needs to fast enough to carry the overcharging current. This is achieved by the immobilized electrolyte (Berndt, 1997).

The rate of water loss in a VRLA battery can be kept so low that the initial amount of electrolyte is sufficient for a service life of 10 years or more. Thus, VRLA batteries are often termed maintenance-free batteries. Another advantage, besides the reduction in maintenance, is that the VRLA battery, because of the immobilized electrolyte, can be packed tightly. This reduces the footprint and weight of the battery (Butler, 1992). Furthermore, in VLRA batteries the employment of corrosion-resistant alloys and immobilized electrolyte reduces the problem of corrosion on the positive grid, because the mobility of the sulfuric acid is reduced to diffusion only.

One disadvantage with the VRLA batteries is that they are less robust than the flooded lead-acid batteries, but the main disadvantage is the need for sophisticated charge (or voltage) control to achieve a high cycle life. If a VRLA battery is charged at an excessively high voltage, it will dry out prematurely and consequently reduce the cycle life. Thus, excessive over overcharging must be avoided.

3.4.4.4 Nickel-Cadmium Batteries

A nickel-cadmium (Ni-Cd) battery uses an alkaline electrolyte, usually potassium hydroxide (KOH) or occasionally sodium hydroxide (NaOH), which act as an ion conducting medium (Berndt, 1997). The nickel-iron, zinc/silver oxide, nickel/zinc oxide, and zinc/manganese dioxide batteries are other types of secondary alkaline batteries (Linden, 1995). However, only the nickel-cadmium battery are considered here, while hydrogen electrode batteries, which also are alkaline, are discussed below (Section 3.4.4.5).

The nickel-cadmium batteries have many favorable characteristics. One great advantage of using an electrolyte which is not significantly involved in the electrochemical reaction, but mainly functions as an ion conductor, is that the electrodes do not need to be spaced out to provide room for the electrolyte (such as the case is with lead-acid batteries). Thus, the amount of electrolyte needed is reduced, which in turn reduces the weight (i.e., increases the specific energy) and internal resistance of the battery.

Another advantage of the nickel-cadmium is that the changes in concentration of the electrolyte during charging or discharging is negligible. As a result the conductivity of the electrolyte remains fairly constant. Furthermore, no problems with electrolyte stratification occur. This makes it easy to monitor the capacity the battery. Since the electrolyte has a fairly constant low freezing point, the nickel-cadmium battery also has excellent low temperature performance. Under normal operating conditions the corrosion of the current conducting part in the battery is negligible. Finally, one of the most favorable characteristics of the nickel-

4 If all of the oxygen evolved at the positive electrode is counterbalanced at the negative electrode, the oxygen cycle is 100% efficient. Only hermetically sealed batteries can achieve a 100% efficient oxygen cycle.

68

cadmium battery is that its charge/discharge reactions can be repeated frequently, which yields a high cycle life that makes it very suitable for SAPS.

A nickel-cadmium battery can be sealed completely, preventing the electrolyte to be spilled and gases to escape. This design, which is the most common, is only used in the area of small-sized maintenance free batteries for power electronics. However, large-sized vented nickel-cadmium batteries with higher capacities are also available; among these are the two basic designs: (1) Sintered plate and (2) Pocket plate.

In the sintered plate design the electrode support and charge collector consists of steel with porous sintered nickel coating, where the active materials are impregnated into the coating. This gives the battery a low internal resistance and makes it rugged and very suitable for high vibration environments (e.g., airplanes). However, a severe disadvantage with this design is that it is suffers from the so-called memory effect5. This makes the sintered plate nickel-cadmium battery unsuitable for SAPS.

In the pocket-plated design the charge collector consists of perforated steel sheets formed into pockets, where the active material is fed into the pockets, either as pressed briquettes or powder. The advantage of the pocket-plated design is that it does not suffer from the memory effect. In general, the self-discharge rate in nickel-cadmium batteries is very low, which gives them a long shelf life. Occasionally, vented nickel-cadmium batteries are delivered in a dry state (without electrolyte). The electrolyte must in such cases be added to the battery upon commissioning of the system. These types of vented nickel-cadmium batteries are usually referred to as ultra-low maintenance batteries, and are particularly suitable for SAPS located in extremely inaccessible areas.

Cadmium and the environment. Cadmium is a toxic metal. This does not cause problems as long as the battery is in service, but it causes severe disposal problems. It is not possible to prevent rundown batteries to become general garbage. When cadmium batteries are treated in incineration plants, cadmium is vaporized and requires filtering of the gas, and the resulting ash is so contaminated with cadmium that it must be classified as hazardous. If the cadmium batteries are not treated, but merely dumped in waste disposals, cadmium will be released gradually and can spoil the ground water. Therefore, a substitute for cadmium in batteries must be sought.

3.4.4.5 Advanced Battery Systems

An advanced battery system is characterized by: high specific energy, high cycle life, deep depth of discharge (DOD), little maintenance, flat charge/discharge curves, and low self-discharge rate. These are all features that match well with the requirements of a battery for a SAPS. A brief description of the features of some advanced battery systems that have been or

5 If Ni-Cd batteries are recharged before they have been fully discharged, cadmium crystals can form at their negative electrode. This results in an unwanted second discharge stage. The battery stores this stage as a discharge stage for the next cycle in its memory, even though there is more capacity available. During the next discharge process, the battery only remembers the reduced capacity. Any further incomplete discharge cycles which follow will aggravate the situation and the performance of the battery will continue to fall. Ni-Cd cells should therefore be discharged fully at occasional intervals. This prevents the memory effect from occurring and prolongs the service life of the cell or battery. This effect does not occur with Ni-MH batteries. Consequently, Ni-MH batteries can be discharged and recharged without a problem.


69

can be considered for short-term or intermediate-term storage of electrical energy in a SAPS are presented below.

Nickel-hydrogen batteries. A sealed nickel-hydrogen (Ni-H2) secondary battery system is a hybrid combining battery and fuel cell technology. Four basic designs of Ni-H2 batteries exist: (1) Individual pressure vessel (IPV), (2) Common pressure vessel (CPV), (3) Bipolar, and (4) Low pressure metal hydride (MH). The main advantages of Ni-H2 batteries is that they have high specific energy, very long cycle life (e.g., 40,000 cycles at 40% DOD for GEO applications), and long lifetime. Another good feature is that they can tolerate overcharge and reversal. Furthermore, the state of charge (SOC) in a Ni-H2 battery can easily be monitored via the hydrogen pressure (Smithrick and O’Donnell, 1995). One disadvantage with the Ni-H2 battery systems, besides their high initial costs, is their low volumetric energy density. Nevertheless, the nickel Ni-H2 battery system is one of the most promising candidates for SAPS. The Ni-H2 battery systems have predominantly been developed for aerospace applications, such as geosynchronous earth orbit (GEO) and low earth orbit (LEO) satellites, but also R&D programs for terrestrial applications have begun. Examples of this is the development of large sized prismatic Ni-MH batteries for electrical vehicles (EV) and the development of a pressurized Ni-H2 battery for PV-systems (Dunlop, 1995).

Ambient-temperature lithium batteries. Rechargeable lithium batteries, which operate at near-ambient temperature, are attractive because of their high specific energies and excellent charge retention characteristics compared to conventional aqueous batteries. The rechargeable lithium cells that can deliver the highest energy density use metallic lithium at the negative electrode, a solid inorganic material at the positive electrode, and an organic liquid electrolyte. An alternative is to use an SPE, which has an advantage over the liquid electrolyte because of the lower reactivity with lithium and the absence of a volatile and flammable electrolyte. Another approach is to use a lithium-ion cell, where a lithiated carbon material is used instead of metallic lithium. The electrolyte in such a battery can either be a liquid organic solution or a SPE. As no metallic lithium is present in the cell, the lithium-ion cells are chemically less reactive and have a longer cycle life (Linden, 1995).

Zinc-bromide batteries. A zinc-bromide battery uses a flowing aqueous zinc-bromide electrolyte. The main advantage of this battery is its unlimited shelf life and modular construction, and that it repeatedly can be deeply discharged (100%) without performance deterioration. Furthermore, because of the chemical nature of the reactants and near-ambient temperature operation conditions, the casing and components can be constructed from lightweight plastic and carbon materials. The major disadvantage of the zinc-bromide battery is the maintenance requirement, including upkeep of the pumps needed to pump the electrolyte (Butler, 1992).

Vanadium redox flow battery (VRB). A cell in a VRB consists of two half-cells, one positive and one negative, that are separated by a membrane. To enable electric charge transfer in and out of the systems each half-cell contains an inert electrode. In redox flow cells the redox couples are all soluble solution species. One of the most important features of the VRB is that the use of solutions to store the energy makes the system power and the energy storage capacity independent. Another advantage of using solutions is that these have an indefinite life and gives the flexibility to increase the system capacity by simply increasing the volume of solution. The electrodes are made of inert materials. All in all this gives the

70

VRB a very long life. Finally, the coulombic and voltage efficiencies of the VRB is high and it can be fully discharged (100%) without any detrimental effects (Menictas et al. 1994).

High-temperature batteries. High-temperature batteries with non-aqueous electrolytes have operation temperatures around 200–500°C. For instance, the sodium-sulfur battery (300–350°C) and lithium-iron sulfide battery (400–500°C) both have a mode of operation similar to the lead acid battery, except that the active electrode materials are liquids which must be kept hot to maintain their shape and good electrical conductivity. In summary these type of batteries are characterized by long cycle life (1000 cycles), high energy efficiency (85%), high specific energy (3–4 times a lead-acid battery), and very low self-discharge rates (Chaurey and Deambi, 1992). In a SAPS based on intermittent energy sources, such as solar and wind energy, heat is not produced at a constant rate. Since high-temperature batteries require a constant supply of heat, this might be a problem. Thus, high-temperature batteries are among the advanced batteries least suitable for SAPS.

3.4.5 Power Converters (Power Conditioners)

The electricity produced and consumed in a SAPS can be either be direct current (DC) or alternating current (AC), depending on the configuration of the system. In general, power converters may be uni-directional, converting AC power to DC power, or DC power to AC power, or they may be bi-directional, capable of converting power in both directions. They may also be electronic of electromechanical devices (Manwell et al. 1996).

Power-conditioning equipment are defined here as electronic devices that make it possible to transform DC power to AC power (inverters), AC power to DC power (rectifiers), or both (bi-directional power electronic converters). The definition also includes devices that convert DC power at one voltage level to DC power of another power level.

Inverter hardware can be grouped into four categories: (1) Stand-alone, (2) Small grid-tied (not applicable for SAPS), (3) Small hybrid, and (4) Large hybrid. Inverters operating in a stand-alone mode provide AC power from a DC battery. Their range in power capability is from a few hundred watts to a few kilowatts. Due to a quite substantial market this type of inverter technology is mature. Small hybrid inverters have evolved from small stand-alone inverters. They typically have single-phase AC power output up to a few kilowatts. They are hybrid because they can operate in stand-alone, while at the same time having the capability of interacting with a secondary AC source (e.g., a wind generator). Large hybrid inverters range in the size from tens to hundreds of kilowatts and generally have three-phase outputs. This technology is still under development (Ginn et al., 1997).

A rotary converter is an electromechanical device for converting AC to DC, or vice versa. It consists of a synchronous (AC) electrical machine connected directly by a shaft to a DC electrical machine. The AC machine can act as a generator or as a motor. As a generator it supplies power to the AC bus. As a motor it absorbs power from the AC bus, and drives the DC machine via the intervening shaft. The DC machine, too, may act as either a generator or a motor. As a generator it supplies power to the DC bus. That power may be used to supply DC loads or it may be used to charge batteries. As a motor the DC machine is fed from a DC power source. Because of its ability to convert power in either direction a rotary converter is a bi-directional device (Manwell et al. 1996).


71

3.5 RECOMMENDED SAPS FOR THE FUTURE

The purpose of this chapter was to find, in a systematic way, the most optimal SAPS for the future. First, the feasibility various generic SAPS were evaluated on the basis of the fundamental principles and facts about energy conversion, energy storage, and availability of energy resources (Table 3.1). From this it was possible to derive a set of general design guidelines (Section 3.1.2). The natural energy hydrogen cycle (Section 3.1.3) was in this context demonstrated to be one of the most promising options.

A closer look at the practicality of the recommended systems narrowed the options down even further (Section 3.2). One very important observation that could be made was that only solar energy (PV) and wind energy in combination with hydrogen provides a truly flexible system because of their modularity. System modularity is not an absolute requirement for SAPS, but it is clearly a great advantage.

Finally, the energy technologies related to solar-hydrogen were evaluated. The economics of these technologies were deliberately left out, because many of the recommended components are not commercially available today. Instead, a technical assessment of each technology was provided.

3.5.1 Hydrogen Systems

From the discussion in Part I of this thesis it seems logical to perform a detailed study on integrated SAPS based on hydrogen energy technology (H2–SAPS). Therefore, the remainder of this thesis (Part II) will deal with the simulation of PV–H2 systems.

However, it should be noted that a good alternative to hydrogen production from PV, is a wind energy conversion system (WECS) coupled to an (alkaline) electrolyzer (Dienhart et al., 1993; Dutton et al., 1996).

Another alternative could be to couple a hydraulic turbine to an electrolyzer. However, in cases were it is possible to pump water up in a small dam or basin, hydrogen storage is superfluous. Thus, hydro-turbine–electrolyzer systems should only be used in connection with river-flow systems. A review of the major hydrogen projects in the world is given in Table 3.10.

72

Table 3.10 Review of major hydrogen energy projects in the worlda

Project/Organization Description of Activity Reference

Solar–Hydrogen Solar-Wasserstoff-Bayern (SWB) (Neunburg vorm Wald, Germany)

Testing and demonstration of solar–hydrogen energy technology. Szyszka (1992)

HYSOLAR (Germany, Saudi Arabia)

Testing and development of components, demonstrations, and system studies.

Grasse et al. (1992)

PHOEBUS (FZ-Jülich, Germany)

Demonstration of an autonomous PV–H2 system for a building.

Barthels et al. (1996; 1998)

FhG-ISE (Stuttgart, Germany)

Development of an energy self-sufficient solar house.

Voss et al. (1996)

SAPHYS (ENEA, Italy)

Design of a stand-alone PV–H2 system for unattended operation.

Galli et al. (1997)

INTA Energy Laboratory (Madrid, Spain)

Experimentation on various hydrogen energy components.

Rosa et al. (1994)

Scahtz Solar Hydrogen Project (Humboldt State University, USA)

Testing and demonstration of a PV–H2 energy system.

Lehman et al. (1994)

Helsinki University of Technology (Finland)

Development of small-scale self-sufficient PV–H2 systems for seasonal energy storage.

Vanhanen et al. (1998)

Wind–Hydrogen University of Oldenburgb (Germany)

Development of hydrogen storage for autonomous energy systems.

Haas et al. (1991)

College of Wiesbaden (Germany)

Testing of an electrolyzer connected to a wind turbine.

Schulien et al. (1990)

a. Adapted from Trieb (1991), Mørner (1995), and Vanhanen (1996). b. A hybrid photovoltaic–wind–hydrogen system

PART II

STAND-ALONE POWER SYSTEMS

BASED ON

SOLAR–HYDROGEN

ENERGY TECHNOLOGY

—

MODELING & SIMULATION

4 MODELING

This chapter describes the models required to simulate the components and sub-systems of a stand-alone PV–H2 system. A logical modeling philosophy was selected: Each physical component is modeled as a separate component subroutine for a modular system simulation program.

The calculations in the subroutines are attempted, as far as possible, to reflect the physical processes occurring in the actual components. In cases where this is difficult or unpractical, empirical models are used instead. However, the models were developed in a general fashion so that other users can easily change the parameters and use the models to simulate solar-hydrogen systems similar to that presented in this thesis.

A schematic of a possible configuration of a stand-alone power system based on solar-hydrogen energy technology is shown in Figure 4.1. The main components of a this kind of SAPS includes a PV-generator, DC/DC-converters, a DC/AC-inverter (at the user end), an electrolyzer, a compressor, a hydrogen storage (compressed gas), a fuel cell, and a secondary battery. Detailed models for all of these components are presented in this chapter.

AC-grid

Grid independentpower supply

PV–Generator

DC/DCConverter DC/AC

Inverter

DC–Busbar

DC/DCConverters

Electrolyzer

H2Buffer

Fuel Cell

H2–StorageCompressor O2 or Air

SecondaryBattery

Figure 4.1 Schematic of a stand-alone solar-hydrogen system.

76

There exist several alternative system configurations similar to that sketched in Figure 4.1. One alternative could be to replace the hydrogen compressor and gas storage tank system with a hydrogen metal hydride (MH) storage system. Another alternative could be to increase the system power input by including a wind energy converter system (WECS). In the latter case, the PV-generator might even be omitted altogether.

No detailed system simulations with a WECS and/or an MH-storage were performed in this thesis. However, the integration of these components in simulations is a recommendation for future work (Chapter 6). Therefore, a wind generator model that is compatible with the other PV–H2 models is presented in this chapter. A model for a hydrogen MH-storage is also proposed.

4.1 SIMULATION OF PV–H2 SYSTEMS

The main goal of Part II of this thesis is to simulate the operation of a an actual PV–H2 system as accurately as possible so that realistic optimal control strategies can be found. To be able to achieve this a set of relatively detailed models are required. These models should take into account the main dynamic and transient effects taking place in a PV–H2 system.

As always, there is a trade-off between simple and complex models. The simpler models are usually based on idealized processes and require very few parameters. The more complex models are usually more detailed and reflect to a greater extent the actual physical processes occurring, but, at the same time, they also require a much greater number of parameters.

The models developed for this thesis, and presented in this chapter, fall into a category somewhere between simple and complex. The intention was to make the models as general as possible, but at the same time practical to use. Thus, in addition to the electrical, electrochemical, and thermal processes, a number of more or less well-established empirical relationships are required.

A great deal of effort was set inn to make the models convenient and practical to use. Thus, many of the models include different modes, ranging from simple to more detailed. The advantage of the simpler models is that they only require parameters that are readily available from manufacturers. In comparison, the detailed models, which require relatively many parameters, can only be used with access to experimental data.

Since the main of the second part of this thesis is to study the operation of PV–H2 systems in detail (Chapter 6), it is utmost important to properly test and verify the accuracy of the models beforehand. This is done in Chapter 5. The data basis for this evaluation is experimental data taken from an actual reference system.

4.1.1 Simulation Programs

There exist only a few simulation programs that can be used to study PV–H2 systems. The most applicable programs are listed in Table 4.1.

Chapter 4 Modeling

77

Table 4.1 List of major computer simulation programs for simulation of PV–H2 systems.

Name Features Reference

TRNSYS

A TRaNsient SYstem Simulation program. A modular and flexible program that links together FORTRAN subroutines. Several uses (Details below).

Klein et al. (1994)

JULSIM JUelich SIMulation. A computer aided engineering tool for

control systems developed specifically for PHOEBUS. The program has been used to design direct feedback control algorithms and to test the complete control system. The modeling of the system components are written in Turbo Pascal that are compatible with SIMNONa.

Brocke (1993)

H2PHOTO H2–PHOTOvoltaic. A program developed specifically to study

the design of a small-scale PV–H2 system at the University of Helsinki, Finland.

Vanhanen (1992)

INSEL A flexible block diagram computer program originally developed

to simulate hybrid PV–Wind–Battery–Gen Set systems. The program has also been used to simulate the electrolyzer, H2-storage and fuel cell at the University of Oldenburg.

Trieb (1991)

SIMELINT SIMulation of ELectrolyzers in INTermittent operation. A

detailed program that can be used as a tool to optimize the design of electrolyzers and control strategies for intermittent electrolyzer operation. The program was developed specifically to optimize the HYSOLAR electrolyzer.

Hug et al. (1993)

a. SIMNON is an integrated simulation program designed for SIMulation of NON-linear systems.

4.1.2 TRNSYS

The TRNSYS program is a transient system simulation program with a modular structure (Klein et al., 1994). TRNSYS was selected for this study because of its modular nature, which gives the program tremendous flexibility and facilitates the addition to the program mathematical models not included in the standard TRNSYS library.

Over the last two decades (since the original version from 1975) the features of the program (e.g., graphics and user-interface) have steadily improved and the number of library components has increased. Today, the standard TRNSYS library consists of components needed to simulate solar thermal systems, HVAC systems, building zones, and some electrical equipment and controllers.

TRNSYS has also been used to simulate PV–H2 systems. Griesshaber and Sick (1991) used TRNSYS with great success in an energy study of the self-sufficient solar house in Freiburg, Germany (Voss et al. 1996). Mørner (1995) improved and modified the models developed by Griesshaber and Sick. He then used the models in a parametric study to find the best possible

78

design of a completely self-sufficient1 solar-hydrogen system for a dwelling located at a high latitude. A summary of these findings is found in (Ulleberg and Mørner, 1997).

The modeling philosophy behind the TRNSYS component models presented in this study stems from the previous studies performed by Griesshaber and Sick (1991) and Mørner (1995). However, models presented below were written and developed (by the author) to meet the specific requirements of this thesis—to optimize the operation and control strategy of an actual PV–H2 system. Only TYPE64 and TYPE75 (Table 4.2) were rewritten and/or modified from the two previous studies. An overview of the key TRNSYS subroutines, or component TYPEs, used in this thesis is provided Table 4.2.

Table 4.2 The TRNSYS solar-hydrogen components used in the simulations in Chapter 6a.

Name of Subroutine Component Described in

TYPE80 PV–Generator Chapter 4 TYPE85 Pb–Accumulator Chapter 4 TYPE75 Power Conditioner (e.g., MPPT) Chapter 4 TYPE60 Alkaline Electrolyzer Chapter 4 TYPE64 Gas Storage Chapter 4 TYPE67 Compressor Chapter 4 TYPE70 PEM Fuel Cell Chapter 4

TYPE91 Fuel Cell Controller Chapter 6 TYPE92 Electrolyzer Controller Chapter 6 TYPE94 Compressor Controller Chapter 6 a. Two models, one for a wind energy generator and for a MH-storage, is described in Chapter 4, but were not used in the system simulations in Chapter 6.

4.2 SIMULATION INPUT

4.2.1 Solar Radiation

In order to be able to perform detailed studies of solar-hydrogen systems it is important to have access to long-term solar radiation data. This long-term radiation data is usually available in terms of monthly averages. An equation for estimating the monthly average daily radiation on a horizontal surface H has been suggested by Page (1964):

Nnba

HHk +==

0T 4.1

where H0 is the extraterrestrial radiation for the location, averaged over the time period in question, a and b are empirical constants depending on location, n is the monthly average daily hours of bright sunshine, N is the monthly average of the maximum possible daily hours of bright sunshine (i.e., the length of the average day of the month), and KT is the clearness index (Duffie and Beckman, 1991).

1 Both electrical and thermal load was meet by solar energy.

Chapter 4 Modeling

79

The clearness index is a convenient measure when looking at the frequency of occurrence of periods with various radiation levels (i.e., frequency of good and bad days). It can also be used in correlations to determine the monthly average fraction of diffuse radiation to that of monthly average total radiation.

4.2.1.1 Weather Data Generator

One great advantage with TRNSYS is that it has a weather data generator (TYPE54) in the standard library. This weather generator generates hourly weather data from monthly average values of solar radiation, dry bulb temperature, humidity ration, and wind speed (optional) (Klein et al., 1994).

4.2.1.2 Solar Radiation Processor

Another great advantage with TRNSYS is that it also includes a solar radiation processor (TYPE16) in the standard library. This component can estimate radiation at time intervals other than one hour. Furthermore, it interpolates radiation data, calculates several quantities related to the position of the sun, and estimates insolation on up to four surfaces of either fixed or variable orientation (Klein et al., 1994).

4.2.2 User Load

The daily, monthly and yearly user load profiles depends heavily on the type of application (Table 1.2). In general, if the overall goal is to design and perform parametric studies of an energy system, it suffices to use a typical user load2 as input to the simulations. However, before designing an energy self-sufficient solar-hydrogen energy system it is extremely important to minimize the thermal and electrical loads (Ulleberg and Mørner, 1997).

If the overall goal is to study the operation and control strategies of an actual system, as the case in this thesis, a more realistic load profile based on actual data should be used as simulation input. In this thesis an actual user power load profile for a specific year was arbitrarily selected. Details about the size and shape of this load are found in Chapter 6.

In either case, the user load profile can readily be input to the simulation via the TRNSYS data reader (TYPE9).

4.3 PV-GENERATOR

The photovoltaic (PV) generator model presented in this section is referred to below as TYPE80. The model was primarily developed for flat-plate PV–arrays consisting of silicon cells, but can also be used for other types of materials.

4.3.1 General Description

When a photon enters a material it can free an electron from a stable position in the material’s crystal structure and give it enough energy to move freely through the material. The minimum

2 The variations over the day, week, and year should be derived from statistics for the type of application at hand.

80

amount of energy required to free an electron from a fixed site is called the band gap of the material, and is equivalent to energy difference between the conduction band and valence band of the material (Fahrenbruch and Bube, 1983).

A photovoltaic (PV) cell converts photon energy directly into electric energy in the form of direct current (DC). This is possible due to two basic properties of PV cells (Zweibel, 1990; Green 1995):

• Electrons are freed in a semiconductor when photons with sufficient energy are absorbed within them.

• When dissimilar semiconductors are joined at a common boundary, a fixed electric field is usually induced across that boundary.

Physically, a generic solar cell consists of so-called negative-type (n-type) and positive-type (p-type) semiconductors (Figure 4.2). In an n-type material electrons move freely at room temperature, while in a p-type material there are few free electrons, but many electron holes (mobile positive charges), that move freely at room temperature. The p–n junction of these two materials (the common boundary referred to above) operates as a diode. If this diode is exposed to photons with higher energy levels than the band gap of the semiconductor, then the number of free electrons in the p-type material and number of holes in the n-type material is greatly increased. In a solar cell a large fraction of these free electrons and electron holes reach the p-n junction, and an electric field is created. Thus, if the p-type and n-type materials in a solar cell are connected to an external circuit, electrical current can flow. The direction of this current is opposite to the direction of the device when it operates as a diode. In other words, when the diode is illuminated a positive current I travels from n to p.

p-type

n-type

Metal base (rear contact)

Contact grid (front contact)

photon

p-n junction+

_

I

Figure 4.2 Operation principle of a solar cell.

4.3.2 Mathematical Modeling

A model of a photovoltaic device must be based on the electrical characteristics, i.e., the voltage-current relationship, of the cells under various levels of radiation and at various cell temperatures. It turns out that a relatively simple idealized one diode model can be used for system design purposes (Rauschenbach, 1980; Roger and Maguin, 1982; Green, 1982).

Chapter 4 Modeling

81

ILID

Rsh

RsI

RloadU

Figure 4.3 The equivalent circuit for the one-diode PV generator model.

The PV generator model developed for this study (TYPE80) is based on the findings of Rauschenbach (1980), Townsend (1989), and Eckstein (1990) on PV array modeling. Detailed examples and methods on how to apply these models are found in Duffie and Beckman (1991).

The equivalent circuit of the one-diode model (Loferski, 1972) is shown in Figure 4.3, and can be used in the modeling of an individual cell, of a module consisting of several cells, or of an array consisting of several modules. The electrical model described in this context is for a module with a number of cells in series.

In practice, PV arrays often consist of modules in series and parallel. Hence, TYPE80 is configured so that the user must specify the number of cells in series per module, the number of modules in series in the array, and the number of modules in parallel per array.

4.3.2.1 Electrical Model (I–U Characteristic)

The relationship between the current I and voltage U of the equivalent circuit in Figure 4.3 can be found by equating the light current IL, diode current ID, and shunt current Ish to the operation current I (Duffie and Beckman, 1991). That is

I I I I I I U IRa

U IRR

= − − = − +

−

− +L D sh L o

s s

sh

exp 1 4.2

where

IL light current, A Io diode reverse saturation current, A Rs, Rsh series resistance and shunt resistance, respectively, Ω a curve fitting parameter U operation voltage, V I operation current, A

The power P produced by the PV generator is simply given by

P = UI 4.3

The five parameters IL, Io, Rs, Rsh, and a in Equation 4.2 depend on the solar radiation and the cell temperature. However, since the shunt resistance Rsh can be assumed to be infinitely large

82

compared to the series resistance Rs, particularly for monocrystalline solar cells, a four- parameter model which the last term in Equation 4.2 can be used (Rauschenbach, 1980):

I I I U IRa

= − +

−

L osexp 1 4.4

A method to calculate the four parameters IL, Io, Rs, and a in Equation 4.4 is summarized in Duffie and Beckman (1991). Three of the four conditions required to solve Equation 4.4 can be found from manufacturers’ data, who usually provide values for I and U at short circuit, open circuit and the maximum power for a given set of references conditions3 (subscript ref). The fourth condition can be derived from the knowledge of the temperature coefficients of the short circuit current and open circuit voltage, µI,sc and µU,oc, respectively (explained below). The short circuit current Isc (U = 0), open circuit voltage Uoc (I = 0), and maximum power points (subscript mp) are illustrated in Figure 4.4.

0

1

2

3

4

5

0 5 10 15 20 25Voltage, V

Cur

rent

, A

0

20

40

60

80

100

Pow

er, W

I sc

I mp

U mp U oc

Power

Current

P mp

Maximum power point

Figure 4.4 Typical I–U and P–U characteristics for a PV generator.

At short circuit conditions, all of the generated light current IL is passing through the diode. Thus, at reference conditions

IL,ref = Isc,ref 4.5

At open circuit conditions the current is zero and the 1 in Equation 4.4 is small compared to the exponential term so that

( )refrefoc,refL,ref,oc /exp aUII −= 4.6

If an I–U pair at maximum power conditions and Io,ref is substituted into Equation 4.4 (again neglecting the 1 to simplify the algebra), the result is

3 The reference solar radiation and temperature used in this thesis is GT,ref = 1000 W m-2 and Tc,ref = 25°C.

Chapter 4 Modeling

83

( )

Ra I I U U

Is,refref mp,ref L,ref mp,ref oc,ref

mp,ref

=− − +ln /1

4.7

The influence of the temperature is illustrated in Figure 4.5. It shows that at a fixed radiation level, an increasing temperature leads to a decreasing open circuit voltage and a slightly increased short circuit current. Thus, the temperature effects must be incorporated into the model.

0

1

2

3

4

5

0 5 10 15 20 25Voltage, V

Cur

rent

, A

0

20

40

60

80

100

Pow

er, W0°C

25°C

T = 50°C

decreasing T

Maximum power point

G T = fixed

Figure 4.5 I–U curves for a PV generator at temperatures of 0, 25, and 50°C, with

corresponding maximum power points.

The temperature coefficient of the short circuit current can be obtained from measurements at reference irradiance Gref and expressed by

( ) ( )µ I,scsc sc sc= ≅

−−

∆∆IT

I T I TT T2 1

2 1

4.8

where T2 and T1 are two temperatures centered around the solar cell reference temperature Tc,ref. Similarly, again from measurements, the temperature coefficient of the open circuit voltage can be found from

( ) ( )µU,ococ oc oc= ≅

−−

∆∆UT

U T U TT T2 1

2 1

4.9

If the series resistance Rs is assumed independent of temperature, then only the parameters IL, Io, and a need to be functions of temperature. Townsend (1989) showed that the following equations are good approximations for many PV modules:

a a TT

= refc

c,ref

4.10

84

( )[ ]I GG

I T TLT

T,refL,ref I,sc c c,ref= + −µ 4.11

I I TT

e Na

TTo o,ref

c

c,ref

gap s

ref

c,ref

c

=

−

3

1exp 4.12

where

a curve fitting parameter, V GT irradiance, W m-2 Ns number of PV modules in series Tc temperature of PV cell, K egap band gap of material, eV

Hence, from the above it is possible to obtain a fourth condition. Townsend (1989) showed that an additional independent equation can be found by analytically differentiating Uoc in Equation 4.6 with respect to T, using Equations 4.8, 4.10 and 4.12, and setting the result (dUoc/dT) equal to the experimental value µU,oc. At reference conditions, this can on compact form be expressed by the curve fitting parameter

aT U e N

TI

refU,oc c,ref oc,ref gap s

I,sc c,ref

L,ref

=− +

−

µµ

3 4.13

The maximum power point of a PV module depends on the solar radiation GT and the cell temperature Tc, as illustrated in Figure 4.5 and Figure 4.6. For a fixed GT and decreasing Tc the maximum power Pmp and corresponding Ump increases (Figure 4.5). Alternatively, for a fixed Tc and decreasing GT, Pmp decreases while Ump remains fairly constant (Figure 4.6).

0

1

2

3

4

5

0 5 10 15 20 25Voltage, V

Cur

rent

, A

0

20

40

60

80

100

Pow

er, W

T = fixed

G T = 1000 W/m2

800

600

400

200

increasing G T

Figure 4.6 I–U curves for a PV generator at different solar radiation levels, with

corresponding maximum power points.

Chapter 4 Modeling

85

4.3.2.2 Thermal Model

To properly predict the performance of a PV module it is necessary to determine its operating temperature. For simplicity, the temperature of the solar cells can be assumed to be homogenous in the plane of the PV module. In other words, an energy balance over the entire module yields the average temperature of a cell in the module.

The temperature Tc of the PV cell(s) depends mainly on the ambient conditions, but also on the operation of the PV module. In principle, the solar energy that is absorbed by the module is converted partly into thermal energy and partly into electrical energy, which is removed through the external circuit. The thermal energy is dissipated by a combination of convection, conduction, and radiation. The rate at which these heat transfer processes occur depends largely on the design of the PV system. For instance, the cells may be cooled artificially by passing air or water on the backside of the module. If a PV module is mounted directly onto the top of a roof, less natural cooling on the backside occurs compared to when it is mounted on a structure at some distance away from the roof.

The thermal model for the PV generator developed and incorporated into TYPE80 was based on the energy balance proposed by Duffie and Beckman (1991). The advantage of this model, as opposed to more detailed models, is that relatively little information is needed about the design of the PV system. This is because all of the heat losses to the surroundings are lumped together into an overall heat loss coefficient UL.

For simulations with very short time-steps it is important to model the dynamic behavior of the cell temperature. This author therefore proposes a dynamic thermal model (that includes the thermal capacitance Ct of the PV module) which can be used for these cases. Thus, three options (or modes) for calculating the cell temperature Tc were included in TYPE80:

Mode 1: Tc is known and given as input Mode 2: Tc is calculated based on UL (static model) Mode 3: Tc is calculated based on UL and Ct (dynamic model)

On general form, the energy balance on a unit area of a PV module, which is cooled by losses to the surroundings, can be written as

( )C Tt

G G U T Ttc

T c T L c add

= − − −τα η 4.14

where

Ct thermal capacitance of PV module, J K-1 m-2 GT irradiance, W m-2 Ta temperature of ambient, K Tc temperature of PV cells, K UL overall heat loss coefficient, J m-2 ηc efficiency of PV cells τα transmittance-absorptance product of PV cells

The term on the left-hand side of Equation 4.14 is the thermal energy stored in the PV module. The three terms on the right hand side are the heat gains due to absorption of solar

86

radiation, electrical energy produced by the PV module, and heat losses to the ambient, respectively.

Mode 2

In mode 2 no thermal capacitance is included in the energy balance on the PV module. A rearrangement of Equation 4.14 (with Ct = 0) gives the following expression for the PV cell temperature

( )( )T T G Uc a T L c= + −τα η τα/ /1 (mode 2) 4.15

In general, measurements of the cell temperature, ambient temperature, and solar radiation are needed to determine the overall heat loss coefficient UL. However, manufacturers usually provide data on the nominal operating cell temperature (NOCT). The NOCT is defined as the cell or module temperature that is reached when the cell are mounted in their normal way at a solar radiation level of 800 W/m2, a wind speed of 1 m/s, an ambient temperature of 20°C, and no load operation (ηc = 0). If the NOCT is available, then, using Equation 4.15, the overall heat loss coefficient can be estimated by

( )U G T TL T,NOCT c,NOCT a,NOCT= −τα / 4.16

The transmittance-absorptance product τα in Equation 4.16 is generally not known, but an estimate of 0.9 can be used without serious error because the term ηc/τα in Equation 4.15 is small compared to unity (Beckman and Duffie, 1991).

Mode 3

In mode 3 both the thermal capacitance and overall heat loss coefficient is included in the energy balance on the PV module. A closer look at Equation 4.14 reveals that it reduces to a linear, first-order, nonhomogeneous differential equation of the form

ddTt

aT bc + − =c 0 4.17

with solution

( ) ( )T t T ba

at bac c,ini= −

− +exp (mode 3) 4.18

and constants given by

a UC

= =L

t t

1τ

4.19

( )bG U T

C=

− +τα η c T L a

t

4.20

where t time, s

Chapter 4 Modeling

87

Tc,ini temperature of cell at initial conditions, K τt thermal time constant for the PV module, s

The expressions described above (mode 3) were developed specifically for this study. As it will be demonstrated later (Section 5.1.4), Equation 4.18 proves to be a convenient method to describe the thermal dynamic behavior of a PV module. A prerequisite for using the model is that the thermal capacitance Ct and the heat loss coefficient UL are known. Ideally Ct and UL should be derived from experiments, but estimations based on measurements on PV modules in actual operation may also be adequate (Section 5.1.4).

4.3.2.3 Numerical Methods

The non-linear Equations 4.4– 4.13 can be solved for any cell temperature Tc and irradiance GT. In the TYPE80 model this is done numerically by using the Newton-Raphson iteration (Cheney and Kincaid, 1985)—for a given voltage U, the model calculates the current I.

A maximum power point tracker (MPPT) algorithm which finds the maximum power point automatically is also included in TYPE80. Since the P–U curve of a PV generator (Figure 4.4) is a unimodal function, a golden section search algorithm (Mathews, 1992) can be used to find the maximum power point. The voltage interval in which the maximum power Pmp is to be found, will always be between zero (U at Isc) and Uoc on the x-axis in Figure 4.4. Furthermore, the open circuit voltage Uoc can, for a given set of input conditions, always be calculated. Thus, numerically, the MPPT algorithm in TYPE80 is extremely robust.

4.3.3 Other PV Models

This section describes briefly some other commonly used PV models. The two-diode electrical model presented here was not included in TYPE80, but was merely used for comparative purposes (Section 5.1.1). A detailed thermal model, which could be an alternative to the thermal model (mode 2) above, is also presented. A sensitivity analysis on some of the key parameters of this model, revealed that it was quite involved and too detailed for system analysis purposes (Section 5.1.3). It was therefore not included as an option in TYPE80. Nevertheless, a description of the detailed model is relevant because it illustrates several important points related to the calculation of the PV cell temperature.

4.3.3.1 Two-diode Model

The equivalent circuit of the two-diode model is similar to that of the one-diode model (Figure 4.3), where the only difference is the addition of one more diode which is placed in parallel with the first diode (Schumacher-Gröhn, 1991). The relationship between the current I and voltage U in this new equivalent circuit is

sh

s

cB2

s2D,

cB1

s1D,L 1exp1exp

RIRU

TkaIRUI

TkaIRUIII +−

−

+−

−

+−= 4.21

with the light current IL and the two dark currents ID,1 and ID,2 are expressed by

( ) I k G TL 0 T 0 c= + −1 27315β . 4.22

88

−=

cB

gap3c1D,1 exp

Tke

TkI 4.23

−=

cB2

gap2.5c2D,2 exp

Tkae

TkI 4.24

where

a1, a2 parameters for diode 1 and 2, respectively k0 parameter for light current, A W-1 m2 k1, k2 parameter for diode 1 and 2, respectively Rs series resistance, Ω Rsh series resistance, Ω β0 temperature coefficient, °C-1 egap band gap of material, eV kB Boltzmann constant, J K-1 Tc temperature of PV cell, K GT solar radiation, W m-2

The advantage of the two-diode model (Equations 4.21–4.24) is its accuracy, while the disadvantage is that it requires 8 parameters (a1, a2, k0, k1, k2, Rs, Rsh, and β0). Thus, the model is only suitable when detailed PV cell and module experiments can be performed in advance.

4.3.3.2 Detailed Thermal Model

An alternative way to model the thermal behavior of a PV module is to treat the heat transfer mechanisms individually, and not as a lumped heat loss coefficient as in Equation 4.14. The detailed thermal model presented here is based on a synthesis of the models proposed by Griesshaber and Sick (1991) and Mayer (1996), and includes a sky temperature model suggested by Berdahl and Martin (1984). From this a thermal energy balance on a unit area of PV module can be found and expressed on the form

( ) ( ) ( )τα εσ ηG T T h T T h T T GT c4

s4

f c a b c a c T= − + − + − + 4.25

with the sky temperature Ts and the convection heat loss coefficients for the front and back, hf and hb, respectively, are

( )[ ]T a bT cT d ts dp dp2= + + + cos 15

14 4.26

( ) ( )[ ]h a T T b vf c a wind= − +1 1

13cos β 4.27

( ) ( )[ ]h a T T b v Fb c a wind dist= − +1 1

13cos β 4.28

where

a, b, c, d empirical constants (clear sky temperature model)

Chapter 4 Modeling

89

a1, b1 constants (heat loss coefficient) Fdist factor for distance between PV module and surface below

(0 = very small distance, 1 = very large distance) hf, hb convection heat loss coefficients (front and back), W K-1 m-2 t time (number of hours from midnight) α, τ, ε absorptance, transmittance, and emittance factors β slope of PV module σ Stephan-Boltzmann constant, W K-4 m-2 ηc efficiency of PV cells GT solar radiation, W m-2 Tc cell temperature of PV cell, K Ta ambient temperature, K Tdp dew point temperature, °C vwind wind speed, m s-1

The term on the left-hand side of Equation 4.25 is equal to the total solar radiation absorbed in the PV module. The four terms on the right hand side account for the heat losses due to radiation from the ambient (front and back), heat losses due to convection to the ambient, and the electrical energy produced by the PV module, respectively.

The model assumes that there is always an air gap between the bottom of the PV module and the surface below (e.g., the roof). Notice that if the PV module is mounted freely at a large distance away from the surface below (very common PV design), then Fdist in Equation 4.28 is set equal to 1, while it is set equal to zero otherwise. If the module is integrated into a roof or wall, the heat is conducted to the inside room temperature Tr. In that case hb must be replaced by the overall heat transfer coefficient of the roof or wall UL and the third term on the right hand side of Equation 4.25 becomes UL(Tc–Ta).

4.4 WIND ENERGY GENERATOR

The power P from a wind energy conversion system (WECS), or wind energy generator, is in theory proportional to the wind speed v raised to the third power (P ∝ v3) (Warne, 1983). A typical power curve for a medium sized WECS is shown in Figure 4.7.

0

20

40

60

0 5 10 15 20

Wind Speed, m/s

Pow

er, k

W

v cut-in

v cut-out

v rated

P rated

Figure 4.7 Typical power curve for a wind generator.

90

The power curve for a WECS can simply be modeled using the empirical relation:

P = a + bv + cv2 + dv3 for vcut-in ≤ v ≤ vrated 4.29

where

a, b, c, d empirical constants vrated wind speed at rated power, m/s vcut-in wind speed at which the wind generator is switched on, m/s vcut-out wind speed at which the wind generator is switched off, m/s Prated rated power, W v wind speed, m/s P power, W

Furthermore, P = 0 at v < vcut-in and P = Prated at v > vcut-out. These algorithms were included in a TRNSYS wind generator component model written by the author.

4.5 ELECTROCHEMICAL REACTORS

The mechanisms and processes occurring in electrochemical reactors, such as electrolyzers, fuel cells, and secondary batteries, is in theory quite similar. Therefore, before going into detail on the modeling of these individual components, it is useful to give a brief overview of the fundamentals of electrochemical reactors, which basically involves: (1) Thermodynamics, (2) Electrode kinetics, and (3) Transport phenomena.

A complete and detailed treatment of electrochemical reactors based on thermodynamics, electrode kinetics, and transport phenomena, leads to the best description of their behavior, but is at the same time very complex. Since the overall aim of this study is to investigate integrated systems, less detailed models were developed.

The electrolyzer, fuel cell, and, secondary battery models, which are presented individually in the subsequent sections, are based on both fundamental electrochemical theory and empirical parameters derived from phenomenological behavior. The aim of this section is to present the basic theory (e.g., thermodynamics) and show the origin of the empirical parameters (e.g., overvoltage) that are used in the models.

4.5.1 Chemical Reaction Principles

A chemical reaction will take place as long as the reaction system is at non-equilibrium conditions. The law of mass action gives a general description of the equilibrium condition of chemical solutions. For a reaction of the type

j k l mA + B C D → + 4.30

where A, B, C, and D represent chemical species and j, k, l, and m their coefficients in the balanced equation. The equilibrium constant K is given by

( )( )( )( )Ka aa a

Cl

Dl

Al

Bl= 4.31

Chapter 4 Modeling

91

where ai is the activity of species i, which can be calculated from the concentration or pressure (Zumdahl, 1995). For instance, the activity of a species in terms of pressure is ai = pi/pref, where pi is the partial pressure of species i and pref is a reference pressure (usually 1 atm).

A relationship between the cell potential E of an electrochemical device and the reaction quotient Q of the reaction system can be given by the Nernst equation4:

QzFRTEE ln−= o 4.32

The reaction quotient Q is found by inserting the activities at initial conditions into the law of mass action (Equation 4.31). The effect of the reaction quotient Q in Equation 4.32 is dependent on the equilibrium constant K for the reaction. Le Châtelier’s principle states that if a change in conditions is imposed on a system at equilibrium, the equilibrium position will shift in a direction that tends to reduce that change in condition. Thus, the reaction in an electrochemical cell will continue until it reaches equilibrium. At that point (Q = K), there is no longer ability to do work.

4.5.2 Standard State

The standard state (superscript “o”) of a chemical substance is in this thesis defined according to the following rules:

• For a gas the pressure is exactly 1 atm. • For a substance present in a solution the molarity (moles of solute per volume of solution)

is 1 M (mol/liter). • For a pure substance that is in condensed state (liquid or solid), the standards state is the

pure liquid or solid. • For an element the standard state is the form in which the elements exist under a pressure

of 1 atm and a temperature of 25°C (unless otherwise stated).

Note that the thermochemical data a “old” standard state pressure of 1 atm (101.325 kPa) does not differ significantly from the “new” standard state pressure of 1 bar (100 kPa) (Aylward and Findlay, 1994). Therefore, in cases where it the most convenient, these can be used interchangeably.

4.5.3 Thermodynamics

Thermodynamics provides a framework for describing reaction equilibria and thermal effects in electrochemical reactors. It also gives a basis for the definition of the driving forces for transport phenomena in electrolytes and leads to the description of the properties of the electrolyte solutions (Roušar, 1989). Below is a description of the thermodynamics of typical low-temperature hydrogen–oxygen electrochemical reactions.

The basic chemical reactions for splitting water into hydrogen and oxygen and the formation of water from hydrogen and oxygen is identical, except that the two reactions are in opposite

4 See Section 2.2.6.1 for more details.

92

directions. Therefore, the thermodynamic expressions for water electrolysis presented in Equations 4.34–4.39 below are the same for a hydrogen–oxygen fuel cell reaction, apart from the sign convention which is exactly opposite.

The electrolysis of water into hydrogen and oxygen is given by

H O( ) + energy H O2 2l g g → +( ) ( )12 2 4.33

The following assumptions can be made about this reaction:

• Hydrogen and oxygen are assumed to be ideal gases • Water is assumed to be an incompressible fluid • The gas and liquid phases are separate

Based on these assumptions the change in enthalpy, entropy, and Gibbs energy of the above reaction can be calculated with reference to pure hydrogen (H2), oxygen (O2), and water (H2O) at a standard pressure and temperature, respectively pref and Tref..

The total change in enthalpy ∆H for splitting water (Equation 4.33) is the enthalpy difference between the products (H2 and O2) and the reactants (H2O), expressed by

∆ ∆ ∆ ∆H H H H= + −H O H O2 2 2

12

4.34

where

( )∆ ∆H C T T Hx p,x ref f,xo= − + ; x = H2, O2, or H2O 4.35

Similarly, the total change in entropy is

∆ ∆ ∆ ∆S S S S= + −H O H O2 2 2

12

4.36

where

( ) ( ) oxf,refrefxp,x /ln/ln SppRTTCS +−=∆ ; x = H2 or O2 4.37

( )∆S C T T SH O p,H O ref f,H Oo

2 2 2= +ln / 4.38

From the definition of Gibbs energy (Equation 2.30), the change in Gibbs energy in terms of enthalpy, entropy, and absolute temperature can be found from

∆G = ∆H – T∆S 4.39

where Cp,x standard specific heat, J K-1 mol-1 ∆Hx change in enthalpy, J mol-1 ∆Hf,x

o standard enthalpy of formation, J mol-1

Chapter 4 Modeling

93

P pressure, bar R universal gas constant, J K-1 mol-1 ∆Sx change in entropy, J mol-1 Sf,x

o standard entropy of formation, J mol-1 T temperature, K

At standard conditions the splitting of water (Equation 4.33) is a non-spontaneous reaction which means that the change in Gibbs energy is positive. The standard Gibbs energy for water splitting∆Gs,H O

o2

can be found by substituting T = 25° and p = 1 bar and all the other necessary data (at standard conditions) into Equations 4.34–4.39. This yields ∆Gs,H O

o2

= 237 kJ mol-1.

The formation of water from hydrogen and oxygen (the opposite reaction of Equation 4.33) is spontaneous which means that the change in Gibbs energy is negative. Hence, the standard Gibbs energy for the formation of water is ∆Gf,H O

o2

= – 237 kJ mol-1.

For a electrochemical process operating at constant pressure and temperature the maximum possible useful work (i.e., the reversible work) is equal to the change in Gibbs energy ∆G. In an ideal electrochemical cell all of this reversible work is electrical work. Hence, Wel = ∆G. Since work is viewed from the point of view of the chemical reaction system, the electrical work is positive for an electrolyzer and negative for a fuel cell.

The total amount of energy needed in water electrolysis is equivalent to the change in enthalpy ∆H. From Equation 4.39 it is seen that ∆H includes the thermal irreversibilities T∆S, which for a reversible process is equal to the heat demand. The standard enthalpy for splitting water∆Hs,H O

o2

= 286 kJ mol-1, and for the formation of water∆Hf,H Oo

2 = –286 kJ mol-1.

Figure 4.8 shows the thermodynamics of water splitting at 1 atm pressure at low temperatures. The phase change from liquid water to water vapor is included for clarity. Note that the heat of vaporization for water ∆Hvap = 41 kJ mol-1.

0

50

100

150

200

250

300

350

25 50 75 100 125Temperature, °C

Spec

ific

ener

gy, k

J/m

ol H

2O

T ∆S (heat demand)

∆G (electrical energy demand)

∆H (total energy demand)P = 1 bar

water vapor

liquid water

Figure 4.8 Thermodynamics of water splitting.

94

The operation temperature of the electrolyzer and fuel cells modeled in this thesis is always below 100°C. A similar set of energy curves as shown in Figure 4.8 could have been generated for a hydrogen–oxygen fuel cell. The absolute values for ∆H, ∆G, and T∆S would then have been the same, but the signs would have been opposite since negative values in this context indicate that work is being done by the system.

A plot of the influence of pressure on the thermodynamics of water splitting in the temperature range 25 to 100°C is given in Figure 4.9. It shows that the total energy demand (∆H), in the given low-temperature regime, is independent of pressure. The comparison also illustrates how the electrical energy demand (∆G) increases with increasing pressure.

0

50

100

150

200

250

300

350

0 25 50 75 100Temperature, °C

Spec

ific

ener

gy, k

J/m

ol H

2O

∆H (total energy demand)

∆G (electrical energy demand)

T ∆S (heat demand)

1 and 100 bar

1 bar100 bar

1 bar100 bar

Figure 4.9 Thermodynamics of water splitting at various temperatures and pressures.

4.5.4 Electrode kinetics

Electrode kinetics deals with electrode reaction rates in the equilibrium states. These can be expressed as functions of overpotential and can be regarded as the driving force. The rate of an electrode reaction can also be influenced by the structure and composition of the electrode-electrolyte interface (Roušar, 1989).

The losses in galvanic cells under operation conditions at charging current (e.g., electrolyzer) or discharging current (e.g., fuel cell) are determined by the electrode kinetics, by the physical structure and geometry of the cell, and by the type of electrolyte used. These losses are usually termed as polarization, overpotential, or overvoltage (Kordesch and Simader, 1996).

The open circuit voltage or equilibrium voltage of a cell describes the voltage, which can be measured at the terminals of an idling cell. This value is usually different from the theoretical open circuit voltage or electromotive force (emf) calculated on the basis of thermodynamics. In addition to this deviation, the potential of a cell will also be decreased (during discharging) or increased (during charging) from its equilibrium due to other irreversibilities such as:

• Activation-overvoltage is an expression for the voltage loss caused by the fact that the charge transfer in any material has a limited speed. An activation catalyst and temperature can influence this limitation.

Chapter 4 Modeling

95

• Concentration-overvoltage is due to voltage differences caused by diffusion processes (pressure gradients, changes in the usage rates of gases and liquids). The delay in reaching steady-state conditions, or the absence of equilibrium conditions, are sources of concentration differences. Other parameters are, for example, the porosity of materials (affects gas or liquid flow), or permeability of membranes (affects the ionic flow).

• Reaction-overvoltage is a term for the voltage difference when an earlier or simultaneous chemical reaction produces another compound which changes the operation conditions. For example, the production of water in a hydrogen–oxygen fuel cell dilutes the electrolyte and causes a change in the concentration of the electrolyte at the electrode surface.

• Transfer-overvoltage is quite complex and deals with the relationship between the current delivered by an electrode and its change in potential under load conditions. In other words, it is the overvoltage U needed to cause a certain current i to flow to or from an electrode. This behavior is generally explained by the Tafel equation:

U = a + blog(i) 4.40

where the constants a and b are determined experimentally. Thus, the transfer-overvoltage is a measure of the thermodynamic irreversibility of the electrode reaction. Electrochemical theory confirms the Tafel equation and shows that if the transfer-overvoltage is negative, then the electrons flow into the solution (de-electronation). If the overvoltage is positive then charges are transferred from the solution (electronation).

• Resistance-overvoltage has no correlation with any chemical processes at the electrodes, but is simply the voltage drop across the resistive components of the cell. The ohmic resistance of electron-conductors (metals, carbon) and the resistance of the ionic conductors (electrolytes) show the same linear dependence (Ohm’s law). However, the speed of electron charge transfer is about 100 times that of ionic charge transfer. This is an important fact because electrode reactions always occur at the interface between conductors and electrolytes.

In the electrolyzer, fuel cell, and battery models presented in the sections below, the overpotentials are accounted for by using relationships for the current-voltage characteristics, where the empirical parameters can be derived from experimental and operational data.

4.5.5 Transport Phenomena

Transport of heat, mass and charge in electrolyte solutions is responsible for bulk effects associated with irreversible energy losses. Additional losses of energy occur at the surface of the electrodes if the electrode process is not rapid enough (Roušar, 1989).

The transport phenomena in the electrolyzer, fuel cell, and battery models presented in the sections below are non-spatial. For convenience, the electrochemical cells are treated as bulks or lumped masses. In other words, the conservation laws of heat, mass, and charge balance are not applied to internal nodes of cells, but rather to individual cells or entire units consisting of several cells. The transient thermal behavior (time-dependent thermal effects) is, when appropriate, accounted for by a lumped thermal capacitance model.

96

4.6 ELECTROLYZER

This section describes in detail the model for a typical advanced alkaline water electrolyzer. The TRNSYS model is referred to below as TYPE60. A general description of electrolyzers with acid electrolytes is also presented.


The decomposition of water into hydrogen and oxygen can be achieved by passing an electric current (DC) between two electrodes separated by an aqueous electrolyte with good ionic conductivity (Divisek, 1990). The total reaction for splitting water is

H O( ) + electrical energy H O2 2l g g → +( ) ( )12 2 4.41

For the reaction in Equation 4.41 to occur a minimum electric voltage must be applied to the two electrodes. This minimum voltage, or reversible voltage, can be determined from Gibbs energy for water splitting (Equation 4.43).

The electrolyte used in water electrolysis can either be alkaline, such as aqueous potassium hydroxide (KOH) solutions, or acidic, such as solid polymer electrolytes (SPE). Table 4.3 shows the anodic and cathodic reactions taking place in alkaline and acid electrolytes. In an alkaline electrolyte, such as KOH, the potassium ion K+ and hydroxide ion OH− take care of the ionic transport, while in an acidic SPE this is taken care of by the hydronium ion5 H3O+ or H+ (compare Figure 4.10 and Figure 4.13).

Table 4.3 Electrochemical reactions of water electrolyzers.

Electrolyte Anode reaction (+ electrode) Cathode reaction (÷ electrode)

Alkaline (KOH)

2 2 2OH 12

O H O( ) + 2− − → +( ) ( )aq g l e 2 22 2H O( ) + 2 H OHl e g aq− − → +( ) ( )

Acidic (SPE) H O( ) O H+

2 212

2 2l g aq e → + + −( ) ( ) 2 2H ( ) + 2 H+ aq e g− → ( )

A schematic of the operation principle of a water electrolysis cell using an alkaline electrolyte is shown in Figure 4.10. The chemical reactions at the electrodes take place in a three-phase boundary, since the simultaneous presence of an electrolyte, an electrocatalyst, and a gas is needed. For instance, the formation of hydrogen (gas) at the cathode can only occur in the presence of a catalyst (solid) and an electrolyte (liquid).

The main components of the cell are the anode, cathode and diaphragm. In an alkaline solution (typically KOH) the electrodes must be resistant to corrosion, and must have good electric conductivity and catalytic properties, as well as good structural integrity, while the diaphragm should have low electrical resistance. This can, among others, be achieved by

5 The hydrated proton H3O+ is abbreviated H+ in this thesis.

Chapter 4 Modeling

97

using anodes based on nickel, cobalt, and iron (Ni, Co, Fe), cathodes based on nickel with a platinum activated carbon catalyst (Ni, C-Pt), and nickel oxide NiO diaphragms (Mergel and Barthels, 1996).

O2 H2

+ _

anode(Ni, Co, Fe)

cathode(Ni, C-Pt)diaphragm

(NiO)

electrolyte(KOH)

2e_2e

_

H2OH2O

2OH_

12

Figure 4.10 Operation principle of a monopolar alkaline water electrolyzer.

The operation principle of a SPE water electrolyzer is not described here because it is similar to the operation of a hydrogen–oxygen proton exchange membrane (PEM) fuel cell, which also consist of a solid polymer electrolyte. A description of a PEM fuel cell is given in Section 4.8 and a schematic of its operation principle is shown in Figure 4.13.

The basic difference between the SPE electrolyzer and PEM fuel cell is that the hydrogen and oxygen reactions on the electrodes are opposite (compare Table 4.3 and Table 4.4). That is, the electrolyzer produces H2 at the cathode (÷) and O2 at the anode (+), while the fuel cell consumes H2 at the anode (÷) and O2 at the cathode (+). Recall that the decomposition of water into H2 and O2 is non-spontaneous and requires a voltage for the reaction to occur, while the opposite fuel cell reaction is spontaneous and produces an electromotive force (emf). In both cases the standard reversible voltage is 1.229 V.


An actual alkaline water electrolyzer consists of several electrolyzer cells connected in series. The electrolyzer model presented here (TYPE60) is based on the characteristics of individual cells. The calculation of the required operation voltage, mass flow production rates of hydrogen and oxygen, and internal heat generation are all done on a per cell basis, while the corresponding values for the whole electrolyzer unit are simply found by multiplying by the number of cells in series. The calculation of the operation temperature is based on an overall heat transfer coefficient and a lumped thermal capacitance for the entire electrolyzer.

4.6.2.1 Relation between Change in Gibbs Energy and Cell Potential

From thermodynamics it can be shown that for a reversible reaction the electrical work Wel needed to split water is equal to the change in Gibbs energy ∆G. That is, Wel = ∆G. The emf E is per definition related to the electrical work by We = qE, where q is the electrical charge

98

transferred in a circuit external to the cell. Faraday’s law relates this electrical work to the chemical conversion rate in molar quantities. Thus, since one mole of water in the water splitting reaction (Equation 4.41) produces a charge q consisting of n moles of electrons, the electrical work added to the system (per cell) can be expressed as

We = ∆G = qE = nFE 4.42

where

n number of moles of electrons transferred per mole of water (n = 2) E emf or voltage difference across the electrodes of a single cell, V F Faraday constant, F = 96,485 C mol-1 or As mol-1

The emf E for a reversible electrochemical process is called the reversible voltage. From Equation 4.42 it is seen that the reversible voltage Urev for a single electrolyzer cell can be expressed as

nF

GU ∆=rev 4.43

Analogously, the total energy demand ∆H is related to the thermoneutral voltage by the expression

nFHU ∆=tn 4.44

Therefore, Urev and Utn is simply the voltaic notation for the energy values ∆G and ∆H, respectively. At standard conditions Urev = 1.229 V and Utn = 1.482, but these will change with temperature and pressure, analogously with ∆G and ∆H (Figure 4.8 and Figure 4.9).

4.6.2.2 I–U Characteristics

The electrode kinetics of an electrolyzer cell can be modeled using empirical current–voltage (I–U) relationships. Empirical I–U models for electrolyzers have been suggested by Griesshaber and Sick (1991), Hug et al. (1992), Havre et al. (1995), and Vanhanen (1996), to mention a few. The basic form of the I–U curve used in this study is based on the one suggested by Griesshaber and Sick (1991), which for a known operation temperature is

+++= 1logrev I

AtsI

ArUU 4.45

where

U operation cell voltage, V Urev reversible cell voltage, V r ohmic resistance of electrolyte, Ω s, t coefficients for overvoltage on electrodes A area of electrode, m2 I current through cell, A

Chapter 4 Modeling

99

A plot of the voltage U for an alkaline water electrolyzer cell versus the current density I/A (current per electrode area) at a high and low operation temperature is shown in Figure 4.11. The difference between the two I–U curves is mainly due to the temperature dependence of the overvoltages (Section 4.5.4).

1.0

1.2

1.4

1.6

1.8

2.0

2.2

0 50 100 150 200 250 300 350Current densisty, mA cm-2

Volta

ge p

er c

ell,

V

T = 20°C

T = 80°C

P = 7 bar

U rev,T=20°C

U rev,T=80°C

overvoltage

Figure 4.11 Typical I–U curves for an electrolyzer cell at high and low temperatures.

In order to properly model the temperature dependence of the overvoltages, Equation 4.45 can be modified into a more detailed I–U model which takes into account the temperature dependence of the ohmic resistance r and the overvoltage coefficients s and t. The following temperature dependent I–U model has been proposed by this author (Ulleberg, 1997):

( )U U r r TA

I s s T s T t t T t TA

I= + + + + + + + +

rev

1 21 2 3

2 1 2 32

1log / / 4.46

where

ri parameters for ohmic resistance of electrolyte, (i = 1…2) si, ti parameters for overvoltage on electrodes (i = 1…3) A area of electrode, m2 T temperature of electrolyte, °C

The empirical parameters (ri, si, and ti) used in Equation 4.46 can be found numerically using non-linear regression techniques (Appendix). Because of the highly nonlinear I–U relationship, a systematic strategy for obtaining a good curve fit is needed (Section 5.2.1).

4.6.2.3 Hydrogen Production (Faraday Efficiency)

According to Faraday’s law, the production rate of hydrogen in an electrolyzer cell is directly proportional to the transfer rate of electrons at the electrodes, which in turn is equivalent to the electrical current in the external circuit (Figure 4.10). Hence, the total hydrogen production rate in an electrolyzer, which consists of several cells connected in series, can be expressed as

&n n InFH F

c2

= η 4.47

100

where

&nH2 hydrogen production rate, mol s-1

ηF Faraday efficiency nc number of cells in series n number of moles of electrons per moles of water, n = 2 F Faraday constant, F = 96,485 As mol-1

In this context the Faraday efficiency ηF in Equation 4.47 is defined as the ratio between the actual and theoretical maximum amount of hydrogen produced in the electrolyzer. Since the Faraday efficiency is caused by parasitic current losses along the gas ducts, it is often called the current efficiency.

The parasitic currents increase with decreasing current densities due to an increasing share of electrolyte and therefore also a lower electrical resistance (Hug et al., 1992). Furthermore, the parasitic current in a cell is linear to the cell potential (Equation 4.46). Hence, the fraction of parasitic currents to total current increases with decreasing current densities. An increase in temperature leads to a lower resistance, more parasitic currents losses, and lower Faraday efficiencies (Figure 4.12). An empirical expression that accurately depicts these phenomena is the non-linear relationship:

( )

η F = + + + + +

a a a T a T

I Aa a T a T

I A12 3 4

25 6 7

2

2exp/ /

4.48

where

ηF Faraday efficiency ai parameters (i = 1…7) A area of electrode, m2 I current, A

0

20

40

60

80

100

0 50 100 150 200Current density, mA cm-2

Fara

day

effic

ienc

y, %

low T

high T

T = 40, 60, and 80°C

Figure 4.12 Typical Faraday efficiency curves for an electrolyzer cell.

Chapter 4 Modeling

101

The water consumption rate &nH O2and oxygen production rate &nO2

are simply found from the stoichiometry of Equation 4.41, which on a molar basis simply is

222 OHOH 2nnn &&& == 4.49.

4.6.2.4 Energy Efficiency

The generation of heat in an electrolyzer is mainly due to electrical inefficiencies. The energy efficiency of a cell is defined as

η etn= U

U 4.50

where Utn is the thermoneutral voltage (Equation 4.44) and U is the actual cell voltage (Equation 4.46). From Equation 4.50 it is seen that an increase in the hydrogen production rate of a cell (i.e., an increase in current density) increases the overvoltage, hence also the cell voltage, and thus decreases the energy efficiency.

In theory, an energy efficiency greater than 100% can be achieved by keeping the cell voltage U in the region between the reversible voltage Urev and the thermoneutral voltage Utn. In practice, this is done by adding thermal energy to the system. However, in the case of low-temperature electrolysis, such as the case in this study, U will always be above Utn.


The temperature of the electrolyte of the electrolyzer, which affects both the I–U curve (Figure 4.11) and the Faraday efficiency (Figure 4.12), can be determined using simple or complex thermal models (the complex model was developed by this author), depending on the need for accuracy. Three options for calculating the temperature T were included in TYPE60:

Mode 1: T is known and therefore given as input Mode 2: T is calculated from a quasi-static thermal model (simple) Mode 3: T is calculated from a lumped thermal capacitance model (complex)

The thermal energy generated internally due to inefficiencies in the cells is partly stored in the surrounding mass and partly transferred to the ambient, either by natural processes or by auxiliary cooling. Thus, from basic heat transfer theory (Incropera and DeWitt., 1990), the overall energy balance on rate form (the forms used in modes 2 to 4) can be expressed as

& & & &Q Q Q Qgen store loss cool= + + 4.51

and

( ) ( )&Q n U U I n UIgen c tn c e= − = −1 η (internal heat generation) 4.52

&Q C Ttstore t

dd

= (thermal energy storage) 4.53

( )&QR

T Tlosst

a= −1 (heat losses to ambient) 4.54

102

( )&Q C T T UA LMTDcool cw cw,i cw,o HX= − = (auxiliary cooling) 4.55

where

nc number of cells in series U operation voltage, V Utn thermoneutral voltage, V I operation current, A ηe energy efficiency Ct heat capacity of electrolyte, J K-1 T temperature of electrolyte, °C Rt thermal resistance, K W-1 Ta ambient temperature, °C Ccw heat capacity of cooling water, J K-1 Tcw,i ,Tcw,o temperature of cooling water (inlet and outlet), °C UAHX overall heat transfer coefficient–area product for heat exchanger, W-1 K LMTD log mean temperature difference, °C

Mode 2

In mode 2 the electrolyzer temperature is simply calculated by assuming constant heat generation and heat transfer rates for a given time interval. Thus, Equation 4.51 can be rewritten as

( )coollossgent

ini QQQC

tTT &&& −−∆+= (mode 2) 4.56

where

∆t time interval, s Tini temperature of cell at initial conditions, °C

Mode 3

The energy generation term (Equation 4.52) is a function of temperature T since both the voltage U (Equation 4.46) and energy efficiency ηe (Equation 4.50) are functions of T. From the definition of the log mean temperature

( ) ( )( ) ( )[ ]LMTDT T T T

T T T T=

− − −

− −cw,i cw,o

cw,i cw,oln / 4.57

and Equation 4.55, assuming constant T (see Section 4.6.2.7 for more details), it can be shown that the temperature of the cooling water out of the heat exchanger is

( )T T T T UACcw,o cw,i cw,i

HX

cw

= + − − −

1 exp 4.58

Chapter 4 Modeling

103

By rearranging Equation 4.51 and inserting the Equations 4.52–4.58 it can be demonstrated that the overall thermal energy balance on the electrolyzer can be expressed by the linear, first-order, nonhomogeneous differential equation

ddTt

aT b+ − = 0 4.59

with solution

( ) ( )T t T ba

at ba

= −

− +ini exp (mode 3) 4.60

and

a CC

UAC

= + − −

1 1τ t

cw

t

HX

cw

exp 4.61

( )bn UI

CT C T

CUAC

=−

+ + − −

c e

t

a

t

cw cw,i

t

HX

cw

11

ητ

exp 4.62

where

t time, s Tini temperature of cell at initial conditions, °C τt thermal time constant for the electrolyzer (τt = RtCt), s

4.6.2.6 Overall Heat Transfer Coefficient–Area Product

The overall heat transfer coefficient–area product for the heat exchanger that cools down the electrolyzer, referred to above (mode 2 and 3) as UAHX, can be modeled as a function of the electrical current passed through the electrolyzer (Section 5.2.3.1). The following empirical expression is proposed:

UAHX = acond + bconvI (mode 2 and 3) 4.63

where

acond constant (value close to the reciprocal of the thermal resistance Rt), W K-1 bconv constant (related to convection heat transfer), W K-1 A-1 I current through electrolyzer, A

The physical explanation for this behavior is that since the electrolyte is stationary, and no pump is being used, the convection heat transfer increases as a result of more mixing of the electrolyte. An increase in mixing occurs because the volume of the gas bubbles in the electrolyte increases with increasing current density. Similarly, the ohmic resistance in the electrolyte increases with increasing currents due to increasing gas bubbling. Hence, this behavior is accounted for in Equation 4.63 and in the ohmic resistance term (2nd term on the right-hand side) of Equation 4.46.

104

4.6.2.7 Numerical Methods

In TYPE60 (mode 2 and 3) the temperature T of the electrolyte is calculated using successive substitution. However, in order to avoid numerical divergence a partial substitution method recommended by Stoecker (1989) was used to calculate T. The temperature used in the other calculations (e.g., I–U curve) is the average of initial temperature Tini (from the previous simulation time step) and the final temperature Tfinal (from the current simulation time step).

4.7 HYDROGEN STORAGE AND AUXILIARY EQUIPMENT

The most practical method to store hydrogen in a SAPS is to store it in a pressure vessel or in a metal hydride (MH). In cases were a high-pressure gas storage vessel is used and the hydrogen is produced in a low-pressure electrolyzer, a compressor is required to compress the hydrogen into the pressure vessel. If a metal hydride is used no compressor is required (Section 3.3.2). This section describes the compressor and pressure vessel models used in this thesis. However, a metal hydride model is also proposed. Only descriptions of the mathematical models are presented here.

4.7.1 Gas Storage (Pressure Vessel)

The pressure gas storage model described below, referred to as TYPE64, was originally developed by Griesshaber and Sick (1991). However, the model used in this thesis was modified to include van der Waals equation for real gases. Thus, two options for calculating the pressure are included in TYPE64:

Mode 1: Ideal gas Mode 2: Real gas (van der Waals equation)

Mode 1

According to the ideal gas law, the pressure p of a gas storage tank can be calculated from

V

nRTp = 4.64

Mode 2

According to the van der Waals equation of state, the pressure p of a real gas in a storage tank can be calculated from

2

2

Vna

nbVnRTp −−

= 4.65

and

cr

2cr

2

6427

pTRa = and

cr

cr

8pRTb = 4.66

where

Chapter 4 Modeling

105

p pressure, Pa n number of moles, mol R universal gas constant, 8.314 J K-1 mol-1 T temperature, K V volume of storage tank, m3 Tcr critical temperature, K pcr critical pressure, Pa

The last term in Equation 4.65 (involving a) accounts for the intermolecular attraction forces, while b accounts for the volume occupied by the gas molecules. Notice that setting the constants a and b to zero gives the ideal gas law (Equation 4.64).

4.7.2 Compressor

The compressor model (TYPE67), written by the author and described below, is mainly based on Equations 4.67 and 4.68. The model is based on a two-stage polytropic compression process with intercooling (Çengel and Boles, 1989). The total compressor work Wcomp required for this process is

( ) compIIIgascomp /ηwwnW += & 4.67

and

−

−=

−

nn

pp

nnRTw

1

1

x1I 1

1 and

−

−=

−

nn

pp

nnRTw

1

x

21II 1

1 4.68

where

W total compressor work, W gasn& gas flow, mol s-1

wI, wII polytropic work, J mol-1 ηcomp efficiency compressor n polytropic coefficient (1 < n < k, where k is the specific heat ratio) R universal gas constant, 8.314 J K-1 mol-1 T1 temperature of inlet gas, K pi pressures (i = 1–2, where 1 = low, x = intermediate, and 2 = high), Pa

A few remarks about this process can be made. Intercooling means that the gas at the intermediate pressure (after the first compression stage) is cooled to the initial temperature T1 before it is passed on to the second compression stage. It should also be noted that the sign convention used in Equation 4.67 is such that the required compressor work (work added to the system) is negative.

4.7.3 Metal Hydride

A hydrogen metal hydride is a substance where a chemical reaction between hydrogen and a metal has occurred. The interaction is loose and can easily be removed from the metal. The

106

reaction, which is exothermic during charging (H2 absorption) and endothermic during discharging (H2 desorption), can be expressed as:

βα →∆+⇔+ Hxx2 MHH

2M 4.69

where M is the metal, MH is the metal hydride, x is ratio of the number of H atoms to the number of M atoms, x = [H]/[M], and ∆Hα→β is the enthalpy of formation of the hydride (Fukai, 1993).

The equilibrium concentration of hydrogen in a MH is a unique function of the temperature T and pressure p of the surrounding gas. Thus, the metal hydride reaction (Equation 4.69) is best described by the p-x-T characteristics, i.e., the pressure-concentration isotherms6. At a given temperature the solubility of hydrogen in a metal increases with increasing pressure of H2 gas. The charging process of a MH at constant temperature can in simple terms be described by three distinct stages.

First, hydrogen intrudes the metal (α-phase). At low hydrogen concentrations x (the first stage) all isotherms have a common slope, and the increase in pressure p is proportional to the concentration x by the relation:

xKp s= 4.70

where Ks is the Sieverts constant. Then, as the concentration increases, hydrogen starts to react with the metal (β-phase). The metal hydride is then at a plateau, where adding more hydrogen (increasing x) will not increase the pressure p, even though the relative amounts of the α and β phase changes (second stage). Once the concentration x reaches a certain upper limit, the pressure will increase (third stage). An equation that relates the temperature and pressure in the second and third stages is:

bTap +=)ln( and

xRHa

βα →∆= 4.71

where R is the universal gas constant and b is an empirical constant (Reilly, 1977). Mørner (1995) developed a TRNSYS simulation model using Equation 4.71.

The thermal characteristics of a metal hydride container operating under steady-state condition were studied in detail by Vanhanen et al. (1996). They proposed to use a lumped thermal capacitance method to model the time-dependent behavior of the MH container. It is recommended that this thermal model be added to the TRNSYS simulation model.

66 Sometimes abbreviated PCI, where P is the pressure in bar, C is the concentration of H2 on a wt.% basis, and I is the isotherm in °C (GfE, 1995). The abbreviation P-C-T is also frequently used (Hagström et al. 1995).

Chapter 4 Modeling

107

4.8 FUEL CELL

This section describes the in detail the models for a hydrogen–oxygen proton exchange membrane fuel cell (PEMFC). The TRNSYS component fuel cell model (TYPE70) described below was developed entirely by this author.


A fuel cell is an electrochemical device that converts the chemical energy of a fuel and an oxidant to electrical current (DC). In the case of a hydrogen–oxygen fuel cell, hydrogen (H2) is the fuel and oxygen (O2) is the oxidant (Kordesch and Simader, 1996). The only product is pure water (H2O), and the total fuel cell reaction is

H O H O( ) + electrical energy2 2( ) ( )g g l+ →12 2 4.72

The maximum possible theoretical voltage (emf) that can be produced across the electrodes of a fuel cell is called the reversible voltage. The reversible voltage for the H2/O2 fuel cell reaction (Equation 4.72) can be determined from the Gibbs energy for water formation, where the thermodynamic relations and the relation between Gibbs energy and cell potential are similar to that of water electrolysis (Section 4.6.2.1).

The electrolytes used in low-temperature H2/O2 fuel cells are, similarly to electrolytes in water electrolyzers (Section 4.6.1), either alkaline or acidic. A KOH solution (alkaline) can be used as an electrolyte in an alkaline fuel cell (AFC), while a solid polymer (acidic) can be used in a proton exchange membrane fuel cell (PEMFC). Table 4.4 shows the anodic and cathodic reactions taking place in an alkaline and PEM fuel cells.

Table 4.4 Electrochemical reactions in fuel cells

Type Anode reaction (÷ electrode) Cathode reaction (+ electrode)

Alkaline Fuel Cell H OH H O( ) + 22 22 2( ) ( )g aq l e+ →− −

12

O H O( ) + 2 OH2 2 2( ) ( )g l e aq+ →− −

PEM Fuel Cell H H ( ) + 2+

2 2( )g aq e → − 12

2 22 2O H H O( )+( ) ( )g aq e l+ + →−

A schematic of the operation principle of a hydrogen–oxygen PEM fuel cell is shown in Figure 4.13. The main components of a single cell is the membrane electrode assembly (MEA)—consisting of a anode, membrane, and cathode—which is pressed between two bipolar current collector plates.

The current collector plates have a manifold of grooves to distribute the reactant gases (H2 and O2) to the electrodes. The plates, which need to be sufficiently electrically conductive to pass the generated electrical current to the adjacent cell, are commonly made of graphite.

The passage of the gaseous reactants to the anode and cathode side is made possible by the porous gas diffusion electrodes. The actual surface area of the porous electrodes is much

108

larger than their geometric area. This gives a large reaction zone. The structure of the electrodes in a PEM fuel cell is hydrophobic, which means that they are based on carbon (C). Hydrophobic gas diffusion electrodes can be made of carbon powder bonded with a plastic material such as polytetrafluorethylene (PTFE) (Wendt and Rohland, 1991).

Two layers can be distinguished in PTFE bonded electrodes: (1) a porous gas diffusion layer, and (2) an electrolyte-wettable thin layer. The electrochemical reactions take place at the interface of these two layers, where a catalytically active material also must be present for the reaction to occur (three-phase reaction zone). The hydrophobicity of the diffusion layer prevents the electrolyte from penetrating deeper into the electrodes, thereby keeping the pores free and facilitating gas access to the reaction sites.

The electrocatalyst material accelerates the reaction on the electrodes, but is not consumed in the overall reaction. In a PEM fuel cell the catalyst, commonly platinum (Pt), is deposited on the inner surface of the porous electrodes to create a large accessible surface, which is the main requirement for high catalytic activity. In order for the reaction to occur at reasonable rates, the catalyst must have access to the reactant gas and must be in contact with the both the proton conductor (polymer membrane) and the electrical conductor (graphite collector). In practice, this can be achieved by impregnating a supported-catalyst electrode with a proton conducting material.

The polymer membrane is an electronic insulator, but at the same time an excellent conductor of hydrogen ions (H+), or protons. It consists of a fluorocarbon backbone to which sulfonic acid groups have been chemically bonded (e.g., Nafion®). The acid molecules are fixed to the polymer and cannot be leached out, but the protons in the acid groups are free to migrate through the electrolyte. The conductive property of a polymer membrane is similar to that of a typical dilute aqueous acid. The thickness of the membrane is about 50–175 µm.

anode(C-Pt)

cathode(C-Pt)

+_

2e_

2e_

O212

H2

H2O

membrane(Nafion®)

current collector(graphite)

current collector(graphite)

2e_

2e_

2H+

Figure 4.13 Operation principle of a hydrogen–oxygen PEM fuel cell.

The operation principle of an AFC is similar to that of an alkaline water electrolyzer. A description of an alkaline water electrolyzer is given in Section 4.6.1 and a schematic of its operation principle is given in Figure 4.10.

Chapter 4 Modeling

109


This section presents a model for a PEM fuel cell stack (TYPE70) using hydrogen and oxygen (H2/O2) or hydrogen and air (H2/air) as reactants. The characteristic data required for the model is mainly the current–voltage curve for a single fuel cell, while the total stack voltage can be found by multiplying by the number of cells in series. A thermal model similar to the one used in the electrolyzer (Section 4.6.2.5) is also proposed.

4.8.2.1 I–U Characteristics

The current–voltage (I–U) characteristics of a PEM fuel cell can be modeled using an empirical equation that takes into account overpotentials due to the Tafel equation, resistances in the proton exchange membrane, and mass–transport limitations. Chamberlin et al. (1995) have proposed the following equation:

U = U0 – blogi – Ri – cexp(di) (full current density range) 4.73

where

U voltage per cell, mV U0 open-circuit voltage per cell, mV i current density, (i = I/A, where I = current and A = electrode area), mA cm-2 b Tafel slope, mV dec-1 R resistance, Ω cm2 c parameter for overpotential due to mass–transport limitation, mV d parameter for overpotential due to mass–transport limitation, cm2 mA-1

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 250 500 750 1000 1250 1500Current density, mA cm-2

Volta

ge p

er c

ell,

V

∆U

U rev

slope = R

U 0

without 4th term in I –U equation

with 4th term in I –U equation

Fixed operation conditions

Figure 4.14 Current–voltage curve (Equation 4.73) for a typical PEM fuel cell.

Figure 4.14 shows the I–U characteristic for a typical H2/O2 PEM fuel cell operating at fixed temperature, pressure, and reaction conditions. The first term on the right hand side of Equation 4.73 is the open-circuit voltage, which can be measured, or calculated from

U0 ≅ Urev + blogi0 4.74

110

where Urev is the reversible voltage and b and i0 are the Tafel parameters. The second term is the Tafel equation at current densities greater than zero. The third term R is predominantly due to the ohmic resistance of the proton exchange membrane, while the other contributions to R are the charge-transfer resistance of the hydrogen-oxygen reaction, the electronic resistance of the single-cell text fixtures, and the mass-transport resistance in the intermediate current density region.

The fourth, and last, overvoltage term is included to account for the experimentally observed departure from linearity at high current densities due for the mass-transport limitation. This term, which includes the parameters c and d, is indicated by ∆U in Figure 4.14. A theoretical evaluation of these parameters reveal that c affects both the slope of the linear region of the I–U curve and the current density at which there is departure from linearity, while d has a major affect on the on the I–U curve after the linear region.

This behavior—the departure from linearity at high current densities—has been demonstrated experimentally by Chamberlin et al. (1995). For instance, by looking at different mixtures of oxygen and inert gases (e.g., O2/He, O2/Ar, and O2/N2) and varying the O2 concentration of these mixture (with all other conditions fixed), they showed how the overpotential ∆U increased with decreasing O2 concentrations. However, no apparent dependence of the parameters c and/or d on the physiochemical parameters such as temperature and pressure was observed.

The overall performance of the PEM fuel cell can be improved by increasing one (or all) of the following conditions (with typical values in parenthesis): (1) Temperature of the PEM (20–80°C), (2) Hydrogen and/or oxygen pressure (1–5 bar), (3) Flow rates of hydrogen and oxygen (1.1–1.2 times stoichiometry), and (4) Oxygen concentration in oxygen-mixtures (80% in air) (Anand et al., 1994; Chamberlin et al., 1995). This is illustrated in Figure 4.15.

0.0

0.2

0.4

0.6

0.8

1.0

1.2


Volta

ge p

er c

ell,

V

Increasing values for(one of the conditions):• temperature of PEM• pressure of H2 or O2

• stoichiometry of H2 or O2

• concentration of O2

in mixture of O2/inert gas

Figure 4.15 The influence of increasing values for temperature, pressure, and reaction

conditions (varied one at a time) on the I–U curve for a typical H2/O2 PEM fuel cell.

The influence of temperature, pressure, and reaction conditions on the performance of a PEMFC is difficult to model, particularly the drop-off from linearity at high currents. However, if the overall goal is not to describe the I–U curve in complete detail, but rather to

Chapter 4 Modeling

111

have an accurate prediction from zero to medium high currents, which is the operating range of an actual PEMFC, then Equation 4.73 can be simplified to

U = U0 – blogi – Ri (limited current density range) 4.75

As it will be demonstrated in Section 5.3, this simplified equation is more than accurate enough for system simulation purposes. One of the main reasons for this is that, for a given set of operation conditions, there exists a maximum power point (Figure 4.16), and operating the fuel cell beyond this optimal point does not make sense. It should also be noted that the basic form of this simplified I–U fuel cell equation (Equation 4.75) resembles that of the electrolyzer (Equation 4.45).

0.0

0.2

0.4

0.6

0.8

1.0

1.2


Volta

ge p

er c

ell,

V

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Pow

er d

ensi

ty p

er c

ell,

W c

m-2

Fixed operation conditions

P mp

I mp

U mp

Operating range

Figure 4.16 Maximum power point for a typical PEMFC operating at fixed conditions.

The ability of Equation 4.75 to predict the I–U curve is best for the H2/O2 PEMFCs, which have a longer linear region of the I–U curve than H2/Air PEMFCs. However, even for H2/Air fuel cells the voltage prediction can be quite good. This is particularly true if the flow of air on the cathode side is higher than the stoichiometric flow. In that case the linear portion of the I–U curve is increased.

The hydrogen and oxygen pressures in a H2/O2 PEMFCs are during operation kept fairly constant. In an H2/Air PEMFC, a fan is usually used to force atmospheric air across the cathode side. Thus the need to model the influence of pressure on the I–U curve is limited.

This leaves only temperature as a variable that needs to be modeled. The parameters U0, b, and R in Equation 4.75 can be linearized with respect to temperature in a similar fashion as the I–U curve of the electrolyzer (Equation 4.46). The results of such a linearization is described in Section 5.3.1.

4.8.2.2 Faraday Efficiency

The stoichiometric flow rates of hydrogen and oxygen supplied to a fuel cell can be calculated from:

112

& &n n n InFH O

c2 2

= =2 (stoichiometric) 4.76

where

&nH2, &nO2

hydrogen and oxygen flow rates, mol s-1 nc number of cells in series n number of moles of electrons per moles of water, n = 2 F Faraday constant, F = 96,485 As mol-1 I current, A

The flow rate of hydrogen on the fuel side and oxygen on the oxidant side affects the performance of the PEM fuel cell. For instance, if the H2 flow is kept fixed and the O2 stoichiometry is increased, the overall performance of the fuel cell also increases (Figure 4.15). In H2/Air fuel cells, which have lower concentrations of O2 on the cathode side than H2/O2 fuel cells, the air flow rates are typically kept about twice stoichiometry.

In an actual PEM fuel cell hydrogen is usually supplied at flow rates slightly higher than stoichiometry. In such instances, the excess hydrogen not consumed in the reaction (Equation 4.72) must be vented out. These hydrogen losses reduce the current efficiency, or Faraday efficiency, of the fuel cell, which can be calculated from:

η FH stoich

H actual

=&

&,

,

nn

2

2

4.77

where

& ,nH stoich2 stoichiometric hydrogen flow rate, mol s-1

& ,nH actual2 actual hydrogen flow rate, mol s-1

The shape of the faraday efficiency curve for the fuel cell is similar to that of the electrolyzer (Figure 4.12).

4.8.2.3 Energy Efficiency

The practical efficiency, or energy efficiency, of a fuel cell is defined as:

η eU

U=

tn

4.78

where

U voltage across a single cell, V Utn thermoneutral voltage (Equation 4.44), V

The shape of the energy efficiency curve is similar to the fuel cell I–U curve (Figure 4.14).

Chapter 4 Modeling

113


A thermal model similar to the one developed for the alkaline electrolyzer can be adopted for the PEM fuel cell stack. Thus, the overall thermal energy balance on a fuel cell stack can be expressed as

& & & &Q Q Q Qgen store loss cool= + + 4.79

where the three terms on the right hand side of the equation—thermal storage, natural heat losses, and auxiliary cooling—are identical to the respective equations for the electrolyzer (Equations 4.53–4.55), while the term for internal heat generation is slightly different (Equation 4.80).

The four basic ways to regulate the temperature of a PEMFC stack is by (1) process air cooling, (2) separate air cooling, (3) liquid cooling, and/or (4) evaporative cooling. For a compact PEMFC stack operating at high current densities, liquid cooling is essential (Anand et al., 1994). In practice, liquid cooling can be implemented by circulating cooling water through cooling cells placed in series with the fuel cells. The number of cooling cells required per fuel cell depends on the design of the stack (e.g., compactness), but about one cooling cell for every 5 fuel cells is common.

The internal heat generation in a fuel cell stack is

( )&Q n U U Igen c tn= − 4.80

where

nc number of fuel cells in series U voltage, V Utn thermoneutral voltage, V I current, A

A rearrangement of the overall energy balance on the fuel cell stack (Equation 4.79), with pertinent sub-equations, yields a differential equation with the same general form as the that of the electrolyzer (Equation 4.59). Solving this differential equation gives an expression for the fuel cell temperature as a function of time

( ) ( )T t T ba

at ba

= −

− +ini exp 4.81

and

a CC

UAC

= + − −

1 1τ t

cw

t

HX

cw

exp 4.82

( )bn U U I

CT C T

CUAC

=−

+ + − −

c tn

t

a

t

cw cw,i

t

HX

cwτ1 exp 4.83

114

The nomenclature used in Equations 4.79–4.83 is the same as the one used for the electrolyzer (Section 4.6.2.5). It should be noted that the only difference between the calculations of the temperature of the fuel cell (Equation 4.81) and electrolyzer (Equation 4.60) is due to the different heat generation terms (Equations 4.80 and 4.52)—a difference reflected in parameter b (first term of Equations 4.83 and 4.62).

Finally, since the electrolyte of the PEMFC is a solid polymer, the overall heat transfer area product of the cooling cell and the neighboring fuel cells UAHX, can be assumed constant. For an alkaline fuel cell, with a liquid electrolyte, the UAHX relation suggested by Equation 4.63 is recommended.

The thermal model presented in this section was not included as an option in TYPE70. The main reason for this was that no exact information about the thermal capacitance Ct, thermal resistance Rt, or heat transfer coefficient UAHX for the PEMFC stack analyzed in this study was available and the thermal model could not be tested and verified properly (Section 5.3.4).

4.9 SECONDARY BATTERY

The battery model presented in this section is referred to below as TYPE85. The model was developed for a lead-acid solar battery, a battery specially designed for PV-applications, but can be used to estimate the performance of any kind of battery with a known characteristic.


A secondary lead-acid battery, or Pb-accumulator, is an electrochemical device that can transform electrical energy into stored chemical energy (charge) and by reversing the process, release the energy again (discharge). In a lead-acid battery this is mainly possible due to the transfer of lead ions to and from the electrodes.

At discharge (the direction of the chemical reactions described below are for discharge, unless stated otherwise), the total reaction for the lead-acid battery is (Berndt, 1997):

Pb + PbO H SO 2PbSO H O2 2 4discharge

4 2+ → +2 2 4.84

In reality, this discharge reaction (Equation 4.84) is the sum of the reactions occurring at the negative and positive electrodes. The basic charge transfer reactions and the complete reactions taking place at the electrodes during discharging of a lead battery with sulfuric acid (H2SO4) as electrolyte, is given in Table 4.5 and further illustrated in Figure 4.17.

Table 4.5 Reactions taking place at the electrode of a lead-acid battery during discharge.

Type of reaction

Negative electrode reaction (÷) (Anode)

Positive electrode reaction (+) (Cathode)

Basic Pb Pb2+→ + −2e Pb + 2 Pb4+ 2+e− →

Complete Pb + HSO PbSO H4 4+− −→ + +2e PbO + HSO H PbSO H O2 4

+4 2

− −+ + → +3 2 2e

Chapter 4 Modeling

115

During discharging, lead ions (Pb2+) are dissolved at the negative electrode, and a corresponding number of electrons (2e–) are removed from the electrode as negative charge. Due to the limited solubility of Pb2+ ions in sulfuric acid (H2SO4), the dissolved ions form lead sulfates (PbSO4) on the electrode. This occurs immediately after the dissolution process.

The discharging process at the positive electrode proceeds in a similar manner. That is, Pb2+ ions are formed by Pb4+ ions by adding a negative charge (2e–). These lead ions are dissolve immediately to form lead sulfate (PbSO4). In addition, water (H2O) is formed at the positive electrode during discharging, because oxygen ions (O2-) are released from the lead dioxide (PbO2) that combine with the protons (H+) of the sulfuric acid.

An illustration of the reaction steps (kinetics) during discharge of a lead-acid battery is given in Figure 4.17, where the direction of the discharge reactions is indicated by the arrows. The charging reactions are exactly the same, but in opposite direction.

+÷

PbSO4 PbSO4

Pb2+ Pb2+

2e_

2e_

2e– + Pb2+Pb Pb4+ + 2e–Pb2+

PbO2

2H2O 4H+ + 2O2–

Pb-electrode PbO2-electrode(porous )

H2SO4 -electrolyte

SO4-

Dissolution

Diffusion

Discharge reaction step(s)

Figure 4.17 Reaction steps in the lead-acid battery with illustration of solution

mechanisms. Arrows mark the discharging reaction(s).

In addition to the kinetic effects taking place, there is also the migration of ions from the electrodes. For instance, during discharging, H+ ions migrate from the negative electrode and HSO4

− ions from the positive electrode. However, these migration effects are usually not noticed, because they are equalized when the battery is discharged and charged again.

Finally, there are the effects of self-discharge and other secondary reactions. The self-discharge reactions can be caused by electronic short-circuits resulting from growth of the positive electrode due to corrosion. Impurities dissolved in the electrolyte may also cause self-discharge.

The self-discharge in lead-acid batteries can essentially be determined by the H2–evolution at the negative electrode. For stationary batteries the self-discharge is about 1–4 mA/100Ah, or about 1–3% loss of nominal capacity per month. In comparison, the self-discharge due to corrosion of the positive grid is equivalent to about 1mA/100 Ah.

116

In summary, according to thermodynamics, the secondary reactions that can take place at the electrodes in a lead-acid battery7 are: H2–evolution at the negative electrode, O2–evolution at the positive electrode, O2–reduction at the negative electrode, H2–oxidation at the positive electrode, and corrosion at the electrodes. Thus, the Pb-battery is unstable in two respects:

1. Water is decomposed into oxygen and hydrogen above 1.229 V/cell (Equation 4.41) which is considerably lower than the open-circuit voltage of about 2 V/cell in an actual lead-acid battery. Hence, water decomposition cannot be avoided.

2. Lead corrosion to lead dioxide (PbO2) occurs at all conducting elements connected to the positive electrodes.


Mathematical modeling of lead-acid batteries is complex due to the many mechanisms involved (Section 4.9.1). Several types of battery models have been proposed. Some of these are described below (Section 4.9.2.1).

4.9.2.1 Literature Survey

One common technique is to evaluate the performance of a Pb-battery by estimating the state of charge SOC in Ah or %. Shepherd (1965) made one of the first attempts on a SOC-model. This model that was later improved by Zimmerman and Peterson (1978) and Hyman et al. (1986). Mørner (1995) gives a description of such a phenomenological battery model for TRNSYS. Another type of steady-state SOC-model is the one developed by Saupe (1993). This is described in more detail below (Sections 4.9.2.2–4.9.2.5).

A fairly different approach is to model the chemical kinetics. Manwell et al. (1993, 1995) have proposed a so-called kinetic battery model that fairly accurately predicts the battery steady-state conditions during charging and discharging.

Since the state of charge (SOC) is not a clearly defined quantity, Protogeropoulos et al. (1994) introduced the concept of state of voltage (SOV). This model takes into account all possible battery conditions during real operation and is therefore suitable for modeling of dynamic battery operation.

In a SAPS based solar and/or wind energy, the charging conditions of the battery varies considerably due to the variable energy source(s). In addition, the discharging conditions might also vary significantly because of a varying power demand. Thus, ideally, a battery model that tackles dynamic effects should be used when simulating integrated energy systems. From this point of view, the SOV-model is probably the most suitable model for simulation of SAPS.

However, the problem with all of the battery models mentioned above is that they require accurate determination of the parameters involved. These parameters depend heavily on the type of battery used. Moreover, some of the parameters may change their value with time as batteries are affected by complex ageing mechanisms (Protogeropoulos, 1996).

7 The standard electrode potentials are –0.36 V for the Pb/PbSO4 reaction (÷ electrode) and 1.69 V for the PbO2/PbSO4 reaction (+ electrode).

Chapter 4 Modeling

117

The battery model technique used in this thesis is based on the work of Saupe (1993), who proposed a quasi-static SOC-model that uses several empirical parameters. One reason for why this particular model was selected was that the parameters could be determined relatively easily from experimental data available from a reference case. Another reason, as experienced by Brocke (1996), was that a very accurate dynamic battery model requires extraordinary many sets of battery parameters, compared to a simpler steady-state model.

The philosophy used here was therefore to select the most practical battery model for the problem at hand. Although the model is general, and can be used on many types of lead-acid batteries, it is by no means the ultimate model. However, it is very important to understand that the selection of a battery model will largely depend on the user’s access to experimental battery data. Since, this kind of data usually is not easily obtained, a relatively simple model with a reasonable number of parameters should be selected for use in simulation of SAPS.

4.9.2.2 Equivalent Circuit

The equivalent circuit for the quasi-static battery model proposed by Saupe (1993) is given in Figure 4.1, where the electrical currents I, voltages U, resistance R (related to the concentration-overvoltage), and capacity C (the symbol Q is used below) are indicated. The three main features of this model are: (1) the gassing current losses Igas, (2) the polarization or overvoltage Upol during charging and discharging, and (3) the equilibrium voltage Uequ at various states of charge. The expressions used in the calculation of these variables are given in Equations 4.85–4.92.

Ibat

Igas

R

UpolUbat

Iq

C Uequ

Iq

Figure 4.18 Equivalent circuit for the quasi-static secondary lead-acid battery model.

4.9.2.3 Current Model

The main reaction current Iq is simply the difference between the current at the battery terminal Ibat and the gassing current Igas. The battery current8 is an input and the gassing current can be found by the following expression proposed by Schöner (1988):

−=

bat

2

1

cell010gas exp

Tg

gUgII 4.85

where

8 In a battery where the cells are placed in series the battery current is equal to the cell current.

118

g0, g1, g2 gassing current parameters Tbat battery temperature, K

The main reaction current is then normalized with respect to the 10-hour discharge current of the battery I10, where I10 = Qbat,nom/10 h and Qbat,nom is the nominal battery capacity in Ah. Since the charging current is positive and the discharge current is negative, the absolute value of the normalized current is used in the calculations:

10

gasbat

10

qnormq, I

IIII

I−

== 4.86

4.9.2.4 Voltage Model

In a battery that consists of several cells in series the individual cell Ucell voltage is simply the terminal voltage Ubat = ncellsUcell, where ncells is the number of cells in series. The cell voltage Ucell is found by adding the equilibrium voltage Uequ and the polarization voltage Upol:

polequcell UUU += 4.87

The equilibrium voltage is defined as the resting voltage (across the terminals) after no current has passed in/out of the battery for a substantial period of time (several hours). This voltage can be assumed to be a linear function of the state of charge SOC of the battery:

100/equ,1equ,0equ SOCUUU += 4.88

where

Uequ,0 equilibrium cell voltage at SOC = 0, V Uequ,1 equilibrium cell voltage gradient at SOC > 0, V/dec SOC state of charge, %

The polarization, or overvoltage, depends heavily on whether the battery is being charged or discharged. These effects can be estimated by non-linear expressions using empirically derived battery parameters. The polarization during charging (subscript ch) can be expressed by:

+

−−= normq,ch

ch

normq,chchpol,ch exp1 Ic

bI

aUU (Ibat > 0) 4.89

where Uch is a constant, ach, bch, and cch are coefficients that are dependent on SOC, and Iq,norm is described in Equation 4.86. (Note that the Equations 4.89 and 4.90 both are functions of the normalized main reaction current Iq,norm and the SOC). Saupe (1993) found a set of empirical expressions for ach, bch, and cch based on battery experiments performed on a solar battery. The expressions for these SOC-dependent coefficients are plotted in Figure 5.22.

The polarization, or overvoltage, during discharging (subscript dch), which is dependent on the main current Iq,norm and the state of charge SOC, can be calculated from:

Upol = Udch fdch gdch (Ibat < 0) 4.90

Chapter 4 Modeling

119

where Udch is a constant, while fdch and gdch are dimensionless coefficients dependent on Iq,norm and SOC, respectively. The two dimensionless coefficients can be approximated by:

normq,dchdch

normq,dch exp1 Ic

bI

f +

−−= 4.91

( )

−−+=100

100dch100exp11

kSOCgg 4.92

where

bdch, cdch parameters for current dependent overvoltage g100 parameter for overvoltage at SOC = 100% (dimensionless height parameter) k100 parameter for overvoltage at SOC = 100% (slope parameter)

It should be noted that Equation 4.92 is only valid for SOC in the range 20–100%.

4.9.2.5 Battery Capacity

The battery capacity Qbat,i for a given time ti can simply be found from the main current Iq and the battery capacity Qbat,i–1 from the previous time ti–1. Alternatively, Qbat,i–1 can be derived from the state of charge for the previous time step SOCi–1 and the nominal battery capacity Qbat,nom (given in Ah). That is,

( ) ( )1iiq1inombat,1iiq1-bat,ibat,i 100/+ −−− −+=−= ttISOCQttIQQ 4.93


In general, the performance of a battery goes down with decreasing temperature. Since no thermal model was included in TYPE85, the model must be used with caution. The battery model described above is only valid for environments with relatively constant temperatures, for instance, indoors.

4.10 POWER CONDITIONING EQUIPMENT

The power converter model presented in this section, referred to below as TYPE75, can be used to model any type of power conditioning equipment, provided its empirical parameters can be determined.


Power conditioners are devices that can invert DC power to AC power, and/or vice versa, or they function as DC/DC-converters (Section 3.4.5). In a SAPS consisting of both DC power producing and DC power consuming components the use of DC/DC-converters are sometimes needed to transfer DC power from one voltage to another. This is particularly true if there is a large mismatch between the I–U characteristics of the various components.

In a SAPS based on a natural energy source, such as solar or wind energy, the system input power varies continuously with time. The output characteristics of a PV array, wind turbine,

120

or hydro turbine have peak power points that depend on solar insolation and cell temperature, wind speeds, and water flow rates, respectively. Therefore, it may be advantageous to use a maximum power point tracker (MPPT) to utilize the input power source to its fullest capability (Snyman and Enslin, 1993).

4.10.2 Mathematical Description

The power loss Ploss for a power conditioner is mainly dependent on the electrical current running through it. Laukamp (1988) proposed a three-parameter expression to describe the power loss for a power conditioner:

2out2

out

iout

out

s0outinloss P

URP

UUPPPP ++=−= 4.94

where

P0 power loss when there is a voltage across inverter or converter, W Us set point voltage, V Ri internal resistance, Ω Pout power output, W Uout voltage output, V

A convenient relationship between the input power Pin and output power Pout can be derived by normalizing Equation 4.94 with respect to the nominal (maximum) power Pnom of the power conditioner:

2

nom

outnomi

nom

out

out

s

nom

0

nom

in 1

+

++=

PPPR

PP

UU

PP

PP 4.95

In TYPE75 either the input power Pin or the output power Pout can be specified as inputs. If Pout is input, then Equation 4.95 is used directly. However, if Pin is input, then an expression analytically derived from Equation 4.95 is used. This makes the model numerically very robust.

The efficiency of the power conditioner is simply:

inout / PP=η 4.96

4.11 SUMMARY

This chapter described in detail the individual component models required to simulate a PV–H2 system. The models are mainly based on electrical, electrochemical, thermodynamics, and heat and mass transfer theory. However, a number of empirical relationships, particularly for the current-voltage characteristics, are also used. The PV-generator and electrolyzer are the most detailed among the major models, but the Pb-battery and fuel cell models are also quite involved. However, all of the models can run in simple modes if necessary.

5 TESTING & VERIFICATION OF MODELS

This chapter describes the testing and verification of the major PV–H2 system component models that were developed in Chapter 4 and are required for the system simulations in Chapter 6. The following TRNSYS models are evaluated: PV-generator (TYPE80), battery (TYPE85), electrolyzer (TYPE60), fuel cell (TYPE70), and power conditioner (TYPE75).

The evaluation of these models is, unless otherwise stated, based on measured data from the PHOEBUS plant operation in 1996. This is the reference system used in this thesis. A detailed description of the PHOEBUS project is found in Barthels et al. (1996; 1998). A schematic of the PHOEBUS demonstration plant is shown in Figure 5.1.

120 bar26.8 m3

LPStorage

HP Storage

DC–Busbar200–260 V

230 V AC

30 kW(PV maximum)

DC/DCConverters

SW 40° SE 40°

SE 90°SW 90°

70 bar20 m3

Photovoltaic cells

Grid independentpower supply

Pb–Battery

DC/ACInverter

DC/DCConverters

26 kW 30–40 VElectrolyzer Fuel Cell

6 kW 45–60 V

Compressors

300 kWh 220 V

11.4 kWp 12.2 kWp

11.4 kWp 7.3 kWp

7 bar

84 m2

84 m2 54 m2

90 m2

260–400 V

7 bar5.5 m3

7 bar25 m3

H2

O2

O2 H2

15 kVA

Figure 5.1 The PHOEBUS demonstration plant at FZ Jülich (Barthels et al., 1996).

122

A number of inputs and outputs (about 85 in all) to and from PHOEBUS was (and still is per 1998) logged continuously and stored in ASCII-files at one-minute intervals. A single file was generated for each day throughout the year. A total of 366 files (i.e., the number of days in a leap year) were available. Each file consisted of 1440 rows of data (i.e., the number of minutes in a day).

Several comparisons between simulated and measured data were made for days with different operating conditions, although only a few illustrative examples are provided in this chapter. The simulation time steps are in these examples very short. Most of the time a simulation time step ∆t of one minute is used, but there are a few exceptions where ∆t was more than one minute, due to the lack of data.

In the cases where simulated and measured data are compared directly, both the date and time step ∆t is indicated in the top-right corner of the plots. Furthermore, the error between the simulated and measured data are summarized in form of the root mean square (RMS) error and the mean error ε (in percent). The formulas for these calculations are given in the Appendix.

The numerical values for the parameters of component models derived from the analyses in this chapter are listed in the Appendix. These parameters were the ones used in the integrated system simulations described in Chapter 6.

5.1 PV–GENERATOR

This section evaluates the electrical and thermal models in the PV-generator (TYPE80), which also includes a maximum power point tracker (MPPT) algorithm (Section 4.3.2). The models are tested and compared to experimental and operational data at one-minute time intervals. A discussion on the alternative thermal models for a PV-generator presented in Section 4.3.3 is also provided here.

5.1.1 Verification of I–U Characteristic

A few steps were needed to verify the I–U characteristics of the one-diode model. First the I–U curve for the one-diode model was compared to that of a two-diode model. Then the performance of the one-diode model was compared to operational data via short-term simulations. The maximum power point tracker was also tested and compared to operational data.

5.1.1.1 Comparison between One-Diode and Two-Diode Model

A two-diode model, such as the 8 parameter model in Equation 4.21, is generally known to depict the I–U characteristics of a PV cell more accurately than a one-diode model, such as the 4 parameter model in Equation 4.2. A comparison between the two models is therefore appropriate.

Extensive experiments, over a wide range of operating conditions, were performed by Groehn (1995) to determine the 8 parameters required for the two-diode model. The PV module analyzed consisted of 150 monocrystalline silicon cells in series, and was oriented to the south-west at a slope of 40°. The 13 experiments were performed in outdoor conditions

Chapter 5 Testing & Verification of Models

123

during the months August (1994) to February (1995). For each experiment the parameters required for the two-diode model were accurately determined. Then the 8 parameters for an average I–U characteristics was found. Based on this average I–U curve, and by following the procedure described in Section 4.3.2.1, it was possible to determine the 4 parameters needed for the one-diode model.

A comparison between the one-diode and two-diode model at three different conditions shows that there is good agreement between the two models (Figure 5.2). This is particularly true for operation voltages less than or equal to the maximum power point voltages (Ulleberg, 1997). The curves in Figure 5.2 show that the one-diode model is practically horizontal on the flat portion of the curves, while the two-diode model is slightly downwards sloped.

The flatness of the curves in Figure 5.2 is interrelated to the shunt resistance Rsh of the solar cell. For very large values for Rsh, the flat portion of the curve becomes a horizontal line. Thus, solar cells that have high values for Rsh (the case with most modern silicon solar cells), small errors are associated with the one-diode model which assumes that Rsh is infinite.

0

1

2

3

0 20 40 60 80 100Voltage, V

Cur

rent

, A

G T = 800 W m-2, T c = 25 °C

G T = 1000 W m-2, T c = 25 °C

G T = 1000 W m-2, T c = 50 °C

maximum power points

Figure 5.2 Comparison of I–U curves for one-diode (thick lines) and two-diode (thin

lines) PV generator models.

5.1.1.2 Comparison with Operational Data

The next step was to test the PV model by comparing it to operational data. A PV array (with the I–U curve given in Figure 5.2) consisting of 56 modules (4 modules in series and 14 modules in parallel) oriented to the southwest at a slope of 40° was analyzed. This particular PV array will be referred to as PV1.

Short-term simulations of several arbitrarily selected days were made at one-minute time intervals. The results showed that there was excellent agreement between simulated and measured data. Figure 5.3 shows the result for PV1 on a day with very variable solar radiation levels (May 17, 1996). In this case the irradiance GT was the only input allowed to change while the other two inputs, cell temperature Tc and voltage U, were set equal to actual operation data. Figure 5.3 also shows that the error between the simulated and measured power output was very small. For the 12-hour time period (720 minute samples) shown in

124

Figure 5.3, the RMS error was 226 W and the mean error was 11.6%. The accumulated energy production from PV1 for this time period was 35.35 kWh, both for the simulated and measured case.

-2

0

2

4

6

8

10

12

6 8 10 12 14 16 18Time, hour

Pow

er, k

W

-2

0

2

4

6

8

10

12

Erro

r, kW

Error = sim – meas (RMS = 226 W)

Power (sim) May 17, 1996

∆t =1 minSimulation inputs:• Measured temperature• Measured voltage

Total energy production:• sim = 35.37 kWh• meas = 35.37 kWh

Figure 5.3 Simulated and measured power for PV1, May 17, 1996

From results above it can be concluded that the one-diode model accurately depicts the I–U curve of a PV module. The low RMS error (226 W) compared to the peak power (about 10,000 W) suggests that the relative errors are very low at high insolation levels. Conversely, the relative errors are higher at low insolation levels. For the day above (May 17, 1996) the average insolation level was medium high, which resulted in small overall errors.

5.1.2 Maximum Power Point Tracker

If a DC/DC-converter is connected directly to a PV array with the purpose of finding the maximum operation power, it is called a maximum power point tracker (MPPT). In an actual system, the MPPT is a device external to the PV array. However, in TYPE80 the search for the maximum power point (Figure 4.4) is for convenience included (as an option) within the PV model itself, while losses in the MPPT due to inefficiencies are accounted for by the power conditioner model (TYPE75) (Section 5.5).

5.1.2.1 Performance of MPPT

A few simulations where performed to test the robustness of the MPPT algorithm in TYPE80. Simulations similar to the ones above (Figure 5.3) revealed that the MPPT model slightly overestimates the power (Figure 5.4). The mean error between simulated and measured data during the hours 6 to 18 in Figure 5.4 (720 minute samples) was 12.4% while the RMS error was 250 W. The simulated total energy production from the MPPT for PV1 for this time period was 36.73 kWh, which was slightly higher than the measured total energy of 35.37 kWh.


125

-2

0

2

4

6

8

10

12

6 8 10 12 14 16 18Time, hour

Pow

er, k

W

-2

0

2

4

6

8

10

12

Erro

r, kW

Error = sim – meas (RMS = 250 W)

Power (sim)May 17, 1996

∆t =1 minSimulation inputs:• Measured temperature• MPPT mode

Total energy production:• sim = 36.73 kWh• meas = 35.37 kWh

Figure 5.4 Simulated (MPPT mode) and measured power for PV1, May 17, 1996.

Numerically, the MPPT model will always find the maximum power point of the I–U curve (verified in separate control calculations, but not shown here). Therefore, measurement error set aside, the discrepancies between simulated and measured power (Figure 5.4) are either due to constraints associated with the one-diode model or an indication that the actual MPPT installed is operating slightly off the maximum power point (MPP).

Since the discrepancies are almost within the margin of measurement error (about 2–3%), no definite conclusion about the result can be made. However, the MPPT model should be accurate enough to detect malfunctioning of an actual MPPT (Figure 5.4), and more than accurate enough for system simulation purposes. The results from other simulations, in addition to the one described here (May 17, 1996), indicate that the actual MPPT installed in the PHOEBUS plant is operating properly.

5.1.2.2 Temperature Dependence of the MPP

The I–U curve of a PV module is dependent on the temperature of the cells (Figure 4.5). A few calculations of the maximum power Pmp for one of the 56 modules in PV1 (Figure 5.2) were performed at various solar radiation levels GT and PV cell temperatures Tc. Figure 5.5 shows that the negative slope of the linear relationships between Pmp and Tc increases with increasing GT. For example, the maximum power at GT = 1000 W/m2 varies 8.4 W per 10 °C for one module and 470 W (56 × 8.4) for the entire array. This illustrates the importance of modeling Tc correctly, particularly at high insolation levels.

5.1.3 Analysis of a Detailed Thermal Model

A sensitivity analysis the key parameters in the detailed PV thermal model presented in Section 4.3.3.2 was performed. In this model (Equation 4.25) the main energy losses are due to radiation and convection to the ambient. The main factor influencing the radiation is the sky temperature (Equation 4.26), which is a function of the dew point temperature Tdp which in turn is a function of the relative humidity of the air φair. The main factor influencing the convection heat transfer coefficients (Equations 4.27 and 4.28) is the wind speed vwind.

126

0

50

100

150

200

250

-20 -10 0 10 20 30 40 50 60 70Temperature, °C

Max

imum

Pow

er, W

G T = 1000 W/m2

G T = 500 W/m2

G T = 100 W/m2

10

10

8.4

4.4

Figure 5.5 Maximum power of a single PV module in PV1 as a function of cell

temperature and irradiance.

First, a few calculations to find the temperature of the PV cell Tc at standard solar radiation, ambient temperature, and wind speed (GT = 800 W/m2, Ta = 20°C, and vwind = 1 m/s) were carried out to determine the sensitivity with respect to the relative humidity φair. The results from these calculations (Figure 5.6) show that φair has relatively little influence on Tc.

0

10

20

30

40

50

60

70

0.0 1.0 2.0 3.0 4.0 5.0Wind speed, m/s

Tem

pera

ture

, °C

Temperature withTemperature with

G T = 800 W/m2

T a = 20°C

0Relative humidity, %

20 40 60 80 100

v wind = 1 m/sφair = 20%

Figure 5.6 Temperature of a PV cell as a function of wind speed and relative humidity.

Next, similar calculations were carried out, but this time the relative humidity of the ambient air was fixed (φair = 20%) while the wind speed was varied. The results (Figure 5.6) show that the wind speed does have a significant influence on the temperature of the PV cell. From a modeling point of view, this is rather unfortunate because the wind, due to its stochastic nature (Equation 2.48), is likely to vary quite a bit.


127

Furthermore, the convection heat loss coefficient, which depends on the air flow across the surface of the PV array, is in reality largely dependent on the direction of the wind. To model this phenomenon requires very detailed information about the characteristics of the wind. Thus, the results from this analysis suggest that a more stable, and not so detailed, thermal model needs to be developed. Such a model should not include the wind speed as input.

5.1.4 Verification of Thermal Models

The two thermal models included as options in TYPE80 (Equations 4.15 and 4.18) are both based on a lumped heat loss coefficient UL, where the heat loss calculations are only dependent on the ambient temperature Ta, and are not dependent on either sky temperature Ts nor the wind speed vwind. The static thermal model (Equation 4.15) uses only the heat loss coefficient UL, while the dynamic thermal model (Equation 4.18) includes also the thermal capacitance Ct of the PV array.

Approximate or average values for UL and Ct can be found experimentally. By running simulations for days with very different insolation levels and ambient temperatures and then comparing the results to operational data, the following values were derived: UL = 30 W K-1 m-2 and Ct = 50,000 J K-1 m-2.

A simple calculation shows that the thermal time constant τt was about 28 minutes (τt = Ct/UL). For UL = 30 W K-1 m-2 it can be shown from Equation 4.16 that Tc,NOCT = 44°C. This is comparable to values provided by manufacturers for freestanding PV modules tested at NOCT conditions. The thermal capacitance corresponds to a medium weight PV structure (framing included).

The PV array investigated in these simulations (PV1) was installed on top of a roof with a medium weight framing system. This PV design make it possible for air to pass on the back side of the array, but only when the wind is blowing from behind or from the sides, as there exists no gap for air to pass underneath the PV array when the wind comes from the front.

The results below (Figure 5.7–Figure 5.10) are based on minutely measurements of insolation and ambient temperature for two days with very different insolation levels. Note that the temperature of the PV cells at night was set equal to the ambient temperature and that all of the simulations were run in the MPPT mode.

The first simulations showed that the prediction of the cell temperature for a day with variable insolation using the static thermal model (Figure 5.7) is not as accurate as the calculations based on the dynamic model (Figure 5.8). In other words, the inclusion of thermal capacitance Ct in the dynamic model (mode 3) makes the model more stable.

A second set of simulations show that the prediction of the cell temperature for a day with fairly even levels of solar radiation is about the same for the two thermal models (Figure 5.9 and Figure 5.10). Thus, in such instances the use of a static thermal model (mode 2) is justified.

In conclusion, for short-term simulations with short time steps the dynamic model (mode 3) should be used. This is particularly important for days with very variable or stochastic solar radiation. However, from an energy point of view, both of the two thermal models are accurate enough for long-term system simulations (Table 5.1).

128

Integrated system simulations are typically run with one-hour time steps. Thus, in the system simulations in Chapter 6 is is not necessary to use the dynamic model because of the relatively low thermal time constant for the PV arrays (e.g., for PV1 the thermal time constant τt = 28 minutes).

0

10

20

30

40

50

60

6 8 10 12 14 16 18Time, hour

Tem

pera

ture

, °C

sim (mode 2)measambient

May 17, 1996∆t =1 min

Simulation inputs:• Ambient temperature• MPPT mode

Figure 5.7 Temperature of PV using static thermal model (mode 2), May 17, 1996.

0

10

20

30

40

50

60

6 8 10 12 14 16 18Time, hour

Tem

pera

ture

, °C


May 17, 1996∆t =1 min


Figure 5.8 Temperature of PV using dynamic thermal model (mode 3), May 17, 1996.


129

0

10

20

30

40

50

60

6 8 10 12 14 16 18 20 22Time, hour

Tem

pera

ture

, °C


June 5, 1996∆t =1 min


Figure 5.9 Temperature of PV using static thermal model (mode 2), June 5, 1996.

0

10

20

30

40

50

60

6 8 10 12 14 16 18 20 22Time, hour

Tem

pera

ture

, °C


June 5, 1996∆t =1 min


Figure 5.10 Temperature of PV using dynamic thermal model (mode 3), June 5, 1996.

Table 5.1 Total energy production from PV1 for two days with very different insolation.

Total energy production, kWh Measurement/Simulation

May 17, 1996 June 5, 1996

Measurement 35.37 68.82 Simulation with temperature mode 2 36.23 68.33 Simulation with temperature mode 3 35.37 68.57

130

5.2 ELECTROLYZER

The alkaline electrolyzer analyzed in this section is the one installed at the PHOEBUS plant in Jülich. It is a so-called advanced alkaline electrolyzer that operates at a pressure of 7 bar and at temperatures up to about 80°C. The cells are circular, bipolar (Figure 3.3), they have a zero spacing geometry (Figure 3.4), and they consist of NiO diaphragms and activated electrodes (Figure 4.10) which make them highly efficient. The electrolyte is a 30 wt.% KOH solution. Each cell has an electrode area of 0.25 m2 and there are 21 cells connected in series. This gives an operation voltage in the range 30–40 V.

The hydrogen production and water cooling flow rates for the PHOEBUS electrolyzer was not logged and collected on a regular basis, along with the minutely collected operational data. However, an experiment, where this and other pertinent data was sampled every 5 minutes, was performed on June 17, 1996 (Mergel, 1996). It is this one-day experiment that forms the basis for the comparisons between simulated and measured data in Sections 5.2.2–5.2.3.

5.2.1 I–U Characteristic

The current–voltage characteristics, or I–U curve, for an electrolyzer operating at a constant temperature can be described by Equation 4.45, while the temperature dependency can be described by Equation 4.46.

In order to find the 8 parameters needed in the proposed I–U relationship (Equation 4.46), a systematic strategy for obtaining the best possible curve fit was developed. The following steps are recommended:

1. Collect experimental or operational data for current I, voltage U, and temperature T. 2. Organize the measured values for I and U in sets with respect to constant values for T. 3. For a fixed T, fit the three coefficients r, s, and t in Equation 4.45 to the measured data. 4. Repeat step 3 for a few other temperatures (e.g., T = 20, 30, 40,…,80°C). 5. Perform an intermediate curve fit of the three coefficients r, s, and t as a function of T. 6. Verify that the temperature dependent coefficients in Equation 4.46 behave according to

the expressions: r(T) = r1+r2T, s(T) = s1+s2T+ s3T2, and t1+t2/T+ t3/T2. 7. If step 6 is true, then proceed to step 8. If step 6 is false, then modify r(T), s(T), or t(T) and

afterwards proceed to step 8. 8. Perform an overall curve fit on the entire data set, using the values for the parameters ri, si,

and ti found from steps 1–7 as initial values for the regression.

The systematic procedure described above is illustrated graphically in Figure 5.11, which shows the results of individual curve fits at fixed temperatures (data points), intermediate curve fits of these data points (dotted lines), and finally the overall curve fit (solid line). A comparison between simulated and measured values for current and voltage for various operation temperatures are presented in Figure 5.12. The current, voltage, and temperature data base (317 data points) used in Figure 5.11 and Figure 5.12 was derived from 3 months (May–July 1996) of operational data for the PHOEBUS electrolyzer.

The results show to which degree the ohmic resistance r of the electrolyte is linearly dependent on temperature. Furthermore, the results show that the coefficient s in the


131

overpotential term can be assumed constant, while the proposed expression for the coefficient t can be used. That is, only 6 parameters are actually needed to model the I–U curve. Figure 5.12 demonstrates that the predictability of the proposed I–U model in Equation 4.46 is excellent; the RMS error is about 2.5 mV/cell. The numerical values for the parameters are given in the Appendix.

0.00

2.00

4.00

6.00

8.00

10.00

20 40 60 80 100Temperature, °C

Ohm

ic re

sist

ance

r, 1

0-5 Ω

m2

0

0.2

0.4

0.6

0.8

1

Ove

rvol

tage

s,V

Ove

rvol

tage

t, Ω

m2

r step 3

r " 5

r " 8

s step 3

s " 5

s " 8

t step 3

t " 5

t " 8

Figure 5.11 Results from the curve fit of coefficients r, s, and t in Equation 4.45 for a

fixed temperature (step3), the intermediate curve fit of points resulting from step 3 (step 5), and the overall curve fit of parameters ri, si, and ti in Equation 4.46 (step 8).

1.2

1.4

1.6

1.8

2.0

2.2

0 50 100 150 200 250 300 350Current densisty, mA cm-2

Volta

ge, V

/cel

l

T=20°CT=30°CT=40°CT=50°CT=60°CT=70°CT=80°C

Operating conditions:• Variable current densities• Pressure = 7 bar

RMS error = 2.5 mV/cell

• Measured at fixed temperatures (T=30...80°C)

Predicted:

Figure 5.12 Predicted versus measured values for the I–U characteristics of an alkaline

electrolyzer cell.

The strategy for finding the 8 unknown parameters in Equation 4.46 described above proves to be very robust. This indicates that the approach is not only limited to the curve fitting of the I–U characteristics of an electrolyzer cell, but can also be used in other situations where coefficients in a model are sensitive to inputs such as temperature, pressure, or other governing conditions.

132

5.2.2 Hydrogen Production

5.2.2.1 Faraday Efficiency

Measurements of the actual hydrogen production at various current densities for the PHOEBUS electrolyzer (26 kW, 7 bar) was only available for an operation temperature of 80°C (Mergel and Barthels, 1996). However, detailed experiments on the temperature sensitivity of the Faraday efficiency were performed on a very similar electrolyzer (10 kW, 5 bar) installed at the HYSOLAR test and research facility for solar hydrogen production in Stuttgart, Germany (Hug et al., 1992). The parameters for the Faraday efficiency (Equation 4.48) for the PHOEBUS electrolyzer could therefore be derived from experimental data from the HYSOLAR electrolyzer.

Figure 5.13 shows the data points from the HYSOLAR experiments, performed at temperatures of 40, 60, and 80°C, and the corresponding curve fits (lower three curves). It turns out that the parameters a4 and a7 in Equation 4.48 can be assumed to be zero (i.e., only 5 parameters are needed to model the Faraday efficiency). This means that the two terms in the exponential in Equation 4.48 both are linearly dependent on temperature.

The PHOEBUS electrolyzer has higher faraday efficiency than the HYSOLAR electrolyzer. A comparison of the faraday efficiency curves at a temperature 80°C for the two electrolyzers prove this (Figure 5.13). A numerical analysis of the data reveal that if the parameters a2 to a7 (in Equation 4.48) for the PHOEBUS electrolyzer are multiplied by a constant, then the efficiency curves (at 80°) in Figure 5.13 overlap. The high Faraday efficiency of the PHOEBUS electrolyzer is explained by the fact that it is a newer design that includes technical improvements based on the earlier developments of the HYSOLAR electrolyzer.

0

20

40

60

80

100


Fara

day

effic

ienc

y, %

meas 80°C PHOEBUS pred 80°C "meas 40°C HYSOLAR pred 40°C "meas 60°C "pred 60°C "meas 80°C "pred 80°C "

Figure 5.13 Predicted versus measured Faraday efficiency for two advanced alkaline

electrolyzers: (1) HYSOLAR (10 kW, 5 bar) and (2) PHOEBUS (26 kW, 7 bar).


133

5.2.2.2 Comparison between Simulated and Experimental Data

A comparison between simulated (TYPE60) and measured (PHOEBUS) values for hydrogen production is shown in Figure 5.14. Two simulations, using the updated parameters for the Faraday efficiency (Figure 5.13), were performed. In the first simulation (sim 1), no correction factor was used, while in the second simulation (sim 2), the Faraday efficiency curve (Equation 4.48) was multiplied by a correction factor f equal to 0.88.

An analysis of the results revealed that the error between the simulated and measured values is quite large if no correction factor is used. Calculations of the mean error ε and RMS error in hydrogen production for the time period 0500–1900 (168 samples), showed that for the first simulation (sim 1) ε = 16.65% and RMS error = 0.305 Nm3 h-1, while for the second simulation (sim 2) ε = 3.84% and RMS error = 0.066 Nm3 h-1. The total production of hydrogen for the whole day (0400–1900) was about 28 Nm3.

-1

0

1

2

3

4

4 8 12 16 20Time, h

Hyd

roge

n pr

oduc

tion,

Nm

3 h-1

-1

0

1

2

3

4

Erro

r, N

m3 h

-1sim 1sim 2measerror 1error 2

June 17, 1996∆t = 5 min

error = sim – meas

Simulation inputs:• Measured current• Measured temperature

Total hydrogenproduction (meas) = 27.73 Nm3

Figure 5.14 Simulated versus measured hydrogen production, June 17, 1996. The first

simulation (sim 1) includes no correction factor (f = 1) while the second simulation (sim 2) includes a correction factor (f = 0.88).

Measured values for the electrical current and temperature was used as input in the simulations in Figure 5.14. Thus, the systematic error observed between the simulated and measured values is either caused by a deficiency of the Faraday efficiency model (Equation 4.48) or by a measurement error of the hydrogen flow.

A plot of the Faraday efficiency based on the measured values for hydrogen flow and electrical current shows that the efficiency, for the given operation conditions (temperature T = 52–75°C and current densities i = 50–150 mA cm-2), is never above 85% (Figure 5.15). This is not in agreement with the expected behavior, which indicate that the Faraday efficiency of the PHOEBUS electrolyzer, under very unfavorable operation conditions (T = 80°C and i = 50–150 mA cm-2), never should be lower than about 95% (Figure 5.13).

From the above it can be concluded that the difference between the simulated and measured data in Figure 5.14, is most likely due an error in the hydrogen flow measurements. Consequently, no correction factor will be used in the system simulations in Chapter 6.

134

0

20

40

60

80

100

0 50 100 150 200Current, mA cm-2

Fara

day

effc

ienc

y, %

meas

51.7°C < T < 74.7°C

Figure 5.15 Faraday efficiency based on measurements, June 17, 1996.

5.2.3 Thermal Model

5.2.3.1 Overall Heat Transfer Coefficient–Area Product

The cooling of the electrolyzer is crucial to prevent overheating. At FZ Jülich the PHOEBUS electrolyzer is cooled by a constant flow of tap water. On June 17 the average tap water flow rate was about 0.6 Nm3 h-1 and the average input temperature was about 14.5°C.

A model for the overall heat transfer coefficient–area product for the heat exchanger used to cool the electrolyzer UAHX was proposed in Equation 4.63. A plot of the measured and predicted values for UAHX as a function of the electrical current I indicate that there exist a linear relationship between the two (Figure 5.16).

0

5

10

15

20

0 100 200 300 400 500Current, A

Hea

t tra

nsfe

r coe

ffici

ent ×

are

a, W

K-1

measpred

June 17, 1996∆t = 5 min

UA HX = a cond + b conv*I

Inputs (measured):• Temperature of electrolyte• Temperatures of cooling water • Cooling water flow rate• Current

RMS error = 1.64 W K-1

Figure 5.16 Measured and predicted values for the heat transfer coefficient UAHX as a

function of current, June 17, 1996.


135

The linear relationship described in Figure 5.16 is seen more clearly when the results are plotted as a function of time, as in Figure 5.17. Thus, the proposed UAHX-expression is adopted for the integrated system simulations in Chapter 6. Note that the electrical current input and the corresponding voltage and power is shown in Figure 5.19.

0

5

10

15

20

0 4 8 12 16 20 24Time, h

Hea

t tra

nsfe

r coe

ffici

ent,

W K

-1

measpred

June 17, 1996∆t = 5 min

UA HX = a cond + b conv*I

Inputs (measured):• Temperature of electrolyte• Temperature of cooling water (in/out)• Cooling water flow rate• Current

Figure 5.17 Measured and predicted values for the heat transfer coefficient UAHX as a

function of time, June 17, 1996.

5.2.3.2 Comparison between Simulated and Measured Data

The purpose of this section is to test the accuracy of the thermal model of the electrolyzer (Section 4.6.2.5) and to demonstrate their influence on the overall electrical power and energy demand of the electrolyzer. All the simulations below (Figure 5.18–Figure 5.19) were performed using temperature mode 3 in TYPE60, but very similar results were obtained with temperature mode 2.

The heat transfer processes in the electrolyzer with the resulting temperature development is depicted in Figure 5.18. The initial temperature (at midnight) was 56.4°C and the temperature at start-up of the electrolyzer (0400) was 51.7°C. This initial decrease in temperature is only due to natural cooling to the ambient, which was assumed to have a temperature of 20°C (bottom curve in Figure 5.18). The values for the thermal capacitance and for the overall thermal resistance were found by investigating the cooling pattern for electrolyzer for a number of different days. In this case, Ct = 625 kJ/°C and Rt = 0.167 °C/W (equal to τt = 29 h). The heat generation was calculated from the energy efficiency (Equation 4.50), where the electrical current input was based on measurements (Figure 5.19), and the auxiliary cooling was based on measured tap water conditions (14.5 °C and 0.6 Nm3 h-1).

The result of this one-day simulation shows that the model underpredicts the temperature. There are several possibilities for this. One possible reason is measurement error, where the main source of uncertainty is the measured temperature of the electrolyte. Another possible reason is simply the lack of detail in the thermal model, where the main deficiency of the model is that the temperature of the electrolyte is assumed to be homogeneous. However, the general dynamic behavior of the temperature is predicted quite accurately.

136

0.0

0.5

1.0

1.5

2.0

2.5

0 4 8 12 16 20 24Time, h

Hea

t tra

nsfe

r, kW

0

20

40

60

80

100

Tem

pera

ture

, °C

Heat generation (sim)Auxiliary cooling (sim)Heat loss to ambient (sim)Temperature (sim)Temperature (meas)

June 17, 1996∆t = 5 min

Simulation inputs:• Measured current• Temperature mode 3

Figure 5.18 Heat transfer and temperature in electrolyzer, June 17, 1996.

0

10

20

30

40

50

0 4 8 12 16 20 24Time, hr

Volta

ge, V

0

200

400

600

800

Cur

rent

, AVoltage (sim)Voltage (meas)Current (meas)

June 17, 1996∆t = 5 min


0

5

10

15

0 4 8 12 16 20 24Time, h

Pow

er, k

W

Power (sim)Power (meas)

June 17, 1996∆t = 5 min

Energy (sim) = 120.9 kWhEnergy (meas) = 118.8 kWh


Figure 5.19 Simulated and measure voltage (top graph) and power (bottom graph) for

electrolyzer, June 17, 1996. Note that the measured current was used as input for the simulation.


137

The importance of modeling the electrolyzer temperature accurately depends on the purpose of the models. A comparison between simulated and measured electrolyzer voltage and the corresponding power (Figure 5.19) shows that the underprediction of the temperature has relatively little significance. This is particularly true from an energy point of view. For the case of June 17, 1996, the error between the total simulated and measured energy demand was less than 2%.

5.3 FUEL CELL

A 6 kW alkaline fuel cell (AFC) stack was originally integrated into the PHOEBUS plant. Due to various technical problems with this AFC, a “dummy” fuel cell (grid electricity) has been required to assure proper operation of the plant (Brocke, 1996). However, concurrent to the regular operation of PHOEBUS, separate testing and experimentation of two 2.5 kW proton exchange membrane fuel cell (PEMFC) stacks has been performed at FZ Jülich. These two stacks are planned integrated into the PHOEBUS plant in 1998.

The results presented in this section are based on separate experiments performed on one of the two (identical) 2.5 kW PEMFC stacks that will be installed at PHOEBUS (Mergel, 1996). The membrane electrode assembly (MEA) of the PEM fuel cells used in this stack (produced by AF Sammer Corporation), consists of a Nafion® membrane (Nafion 117) and two carbon based platinum coated electrodes (anode: 1.7 mg Pt/cm2, cathode: 4.3 mg Pt/cm2).


An empirical relationship to describe the current–voltage (I–U) characteristic for a PEMFC was presented in Section 4.8.2.1. The simplified I–U curve (Equation 4.75) was fitted to measured data collected at three different temperatures. All of the other operation conditions were fixed: the hydrogen pressure was about 3.77 bar (40 psig), the oxygen pressure was about 4.46 bar (50 psig), and the hydrogen supply was about 1.02 times stoichiometric flow (the oxygen supply was always greater than or equal to stoichiometric flow).

Because the I–U curves of the electrolyzer (Equation 4.45) and the fuel cell (Equation and 4.75) have the same basic form, the same procedure as the one used to find the electrolyzer parameters (Section 5.2.1) can be used to find the fuel cell parameters. However, since the experiments on the fuel cell were performed in a controlled manner, the open-circuit voltage U0 could be found directly from the experimental data. Thus, only the Tafel parameter b and the resistance R needed to be found numerically.

A comparison between measured and predicted data is given in Figure 5.20, where parameters U0, b, and R in Equation 4.75 were linearized with respect to temperature. The results show that there is excellent agreement between the measured and predicted values. The maximum power points, i.e., the maximum practical operation limits, are also indicated. At maximum operation temperature (70°C) the maximum power occurs at 910 mA cm-2 and 0.429 V, while at minimum operation temperature (20°C) the maximum occurs at 800 mA cm-2 and 0.374 V. This illustrates that there is a relatively small difference between the ideal operation voltage at high and low operation temperatures; the RMS error was 5.2 mV/cell. The numerical values for the parameters at 35 and 70°C are given in the Appendix.

138

0.0

0.2

0.4

0.6

0.8

1.0

1.2


Volta

ge p

er c

ell,

V

T=70°CT=65°CT=50°CT=35°CT=20°C

Maximum power points

Test conditions:• H2 pressure = 3.77 bar• O2 pressure = 4.46 bar• H2 supply = 1.02 stoich• O2 supply > 1.0 stoich

Measurements at T =35, 65, 70°C

Predicted curves at:

RMS = 5.2 mV/cell

Figure 5.20 Predicted and measured values for I–U characteristics of a PEM fuel cell.

5.3.2 PEMFC Stack Performance

Each of the fuel cells (Figure 5.20) in the PEMFC stack at Jülich has an electrode area of 300 cm2. There are 26 cells connected in series per stack. This gives a maximum (open circuit) voltage of about 28 V per stack. The voltage at an operating temperature of 70°C and a stack power of 1.75 kW is about 18 V per stack. A plot of the energy efficiency and power curves (at constant operating conditions) of the stack is provided in Figure 5.21. Two stacks (with identical characteristics) placed in series were used in the simulations in Chapter 6.

0.0

0.2

0.4

0.6

0.8

1.0

0 75 150 225 300Current, A

Ener

gy e

ffici

ency

, 0–1

0.00

1.00

2.00

3.00

4.00

Pow

er, k

W

energy efficiencypower

T = 70°C

One stack with 26 cells

Figure 5.21 Energy efficiency and power for a PEMFC stack.

5.3.3 Hydrogen Consumption

No experimental data on the hydrogen consumption for the PEMFC stack at FZ Jülich was available. A characteristic for the faraday efficiency could therefore not be found. However, according to experiments with PEMFC show that a H2 supply of about 1.02 times stoichiometry during regular operation (70°C and 1.75 kW per stack) gives good results


139

Mergel (1997). The overall hydrogen utility factor is about 95%. Thus, it can be deducted that the average faraday efficiency is about 97%.

5.3.4 Thermal Model

No exact experimental data about the thermal behavior of the PEMFC stack at FZ Jülich was available either. However, it is expected that the PEMFC stack, due to its light structure, has a relatively low thermal time constant τt. This is reflected by the thermal behavior observed during testing of the stack (Mergel, 1996). Therefore, it can be assumed, without too much error, that the fuel cell is brought up to its normal operation temperature (~70°C) relatively quickly. Hence, a detailed model, which includes the thermal capacitance Ct, might not be required.

The PEMFC stack is in this case cooled by water and the operating temperature can be therefore quite easily (because of the low τt) be controlled to keep a fixed level (~70°C). The total required cooling demand can be calculated from Equation 4.79. Since, no detailed information about the thermal behavior was available, the thermal resistance Rt and thermal capacitance Ct of the fuel cell could not be calculated. However, with sufficient data, a procedure similar to the one described for the electrolyzer could have been used.

5.4 SECONDARY BATTERY

The secondary battery analyzed in this section is the large Pb-accumulator integrated into the PHOEBUS plant in Jülich. This battery bank consists of 110 cells placed in series, which gives a nominal battery capacity of 1380 Ah (at 10 A) or 303 kWh (at 10 A and 220 V).

The battery cells used at the PHOEBUS plant are of the conventional lead-acid type for stationary applications. They utilize an aqueous electrolyte and the electrode grids (with copper) are of the pasted plate design. The construction around is closed, but excess gases are allowed to escape through vent caps.

The main purpose of this section is to test the secondary battery model (TYPE85) presented in Section 4.9. Most of the testing and verification here was based on the data from PHOEBUS, as this is the system analyzed in detail in Chapter 6.

In addition, a few comparisons were made with battery data from a SAPS located at Lyklingholmen in Norway (Ulleberg and Tallhaug, 1997). The purpose of this was to illustrate how the parameters in the battery model can be adjusted to fit the performance of an operational battery. The problem here is usually that it is not possible to perform separate battery experiments, and the battery parameters therefore need to be retrofitted. Furthermore, the experiments performed at Lyklingholmen illustrate the limitation of the battery model.

5.4.1 Voltage Model

The parameters for the battery model (TYPE85) will vary slightly from one battery system to the other. The parameters for an individual battery cell similar to the one integrated into PHOEBUS were derived from separate experiments performed by Heuts (1995).

140

The function for the coefficients ach, bch, and cch, the coefficients used in the expression for overvoltage during charging (Equation 4.89), are shown in Figure 5.22. The experiments performed by Heuts (1995) showed that the overvoltage at high SOC was slightly lower for the PHOEBUS battery than for the solar battery used in the original study by Saupe (1993). This was accounted for by lowering ach and increasing cch at SOC > 85.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

50 60 70 80 90 100SOC, %

Coe

ffici

ents

for O

verv

olta

gedu

ring

Cha

rgin

g

1.0

3.0

0.114

2.8

1.0a ch

b ch

c ch

Figure 5.22 Coefficients for the overvoltage during charging of a battery as a function of

SOC. The values for SOC in the range 0–50% are equal to those at 50%.


The I–U characteristics of the Pb-accumulator installed at PHOEBUS is given in Figure 5.23. Notice that in this figure the equilibrium voltages are found on the y-axis (at zero current), the voltages during discharging are found on the left hand side of the y-axis, while the charging voltages are found on the right hand side of the y-axis.

210.0

220.0

230.0

240.0

250.0

260.0

270.0

-80 -60 -40 -20 0 20 40 60 80Current, A

Volta

ge, V

SOC = 0, 10, 20 … 100%

100

0

(Discharge) (Charge) Figure 5.23 I–U characteristics of a lead-acid battery for SOC in the range 0–100%

(Discharging currents are indicated by a negative sign).


141

5.4.2.1 Comparison with Operational Data from the SAPS at Lyklingholmen

A study of the performance of a battery in a hybrid PV, wind – diesel system was made for a SAPS located at Lyklingholmen, a small island located on the west coast of Norway (Ulleberg and Tallhaug, 1997). A schematic of the Lyklingholmen system is given in Figure 5.24.

In the period February 6-12, 1996 a test of the capacity of the battery of a SAPS at Lyklingholmen was performed. The experiments began after the system had attained a high and stable battery voltage, i.e., the SOC was equal to about 100%. Figure 5.25 shows the charging/discharging of the battery on February 7-10 that followed after a 20-hour period (on February 6) with relatively constant charging.

The battery voltage resulting from the charging/discharging in Figure 5.25 is depicted in Figure 5.26. An initial SOC of 90% (hour 0) was assumed for the simulations. The battery was then discharged for 24 hours at relatively constant currents (discharge 1, Figure 5.25) until it was nearly empty, i.e., the SOC was about 10%. It was then allowed to rest for about 12 hours. Afterwards the battery was charged for about 10 hours (charge 1), mainly with excess power from the diesel generator. At this point in time (hour 44), the SOC was about 60%. A second discharge period, which lasted for about 14 hours (discharge 2), reduced the SOC to about 20% (hour 60). Finally, the battery was charged with excess wind energy (charge 2), until it reached a SOC of 100%.

Battery900 Ah, 24 V DC

Wind turbine

PV-array

South 75°

3 kWr

Diesel generator

5.5 kWr

DC-Busbar24 V DC

User Load (1 person)

Voltage inverter

DC/AC-inverter

24 V AC3-phase

PV- regulator

220 V AC50 Hz

24 V DC0.5 kWp

Figure 5.24 Schematic of the PV, wind – diesel system at Lyklingholmen, Norway.

142

The original motivation for running the experiment at Lyklingholmen was to check the capacity of the battery installed. The purpose of the short-term simulations presented in Figure 5.25 and Figure 5.26 was to take this experimental data and test the model’s ability to accurately depict deep cycling of a battery. Unfortunately, the battery was not completely empty after the first discharge period (discharge 1), nor completely charged after the second charging period (charge 2). This is clearly seen by calculating the change in battery capacity ∆Qbat (Figure 5.25).

-100

-50

0

50

100

0 12 24 36 48 60 72 84 96Time, h

Cur

rent

, A

0

25

50

75

100

SOC

, %

currentSOC

∆Q bat= -742 Ah 0 Ah + 544 - 454 Ah + 735 Ah

February 7–10, 1996∆t =10 min

44

Figure 5.25 The charging/discharging current and resulting SOC for the battery in the

SAPS at Lyklingholmen, February 7-10, 1996.

18

20

22

24

26

28

30

0 12 24 36 48 60 72 84 96Time, h

Volta

ge, V

meassim 1sim 2

discharge 1 resting charge 2

February 7–10, 1996∆t =10 min

charge 1 discharge 2

44

testEquilibrium voltage

at SOC = 10%

Figure 5.26 Comparison between measured and simulated battery voltages,

Lyklingholmen, February 7-10, 1996 (sim 1 = simulations with manufacturer’s battery parameters, sim 2 = simulations with adjusted battery parameters).

Ideally, battery experiments should be performed in a controlled environment. In this case, that would have ensured that the battery had been completely discharged and recharged.


143

Nevertheless, it is possible to find fairly good estimates for the battery parameters Uequ,0 and Uequ,1 in Equation 4.88 based on in situ experiments such as the one described above. The following two-step procedure is recommended:

1. Find the the equilibrium voltage Uequ,0 at minimum SOC by discharging the battery completely and letting it rest with no current going in/out of the battery. The Uequ,0 is the voltage after the battery voltage has stabilized (e.g., hour 36, Figure 5.26).

2. Find the voltage gradient term Uequ,1 by deriving it from Uequ,0 at maximum and minimum SOC. These voltages must both be stabilized (e.g., hour 0 and 36, Figure 5.26).

A comparison between simulations based on the battery manufacturer’s data (sim 1) and a set of adjusted battery parameters (sim 2) are also shown in Figure 5.26. This comparison illustrates the importance of properly estimating Uequ,0 and Uequ,1. Figure 5.26 also illustrates that the model is only reasonably accurate during discharging for SOC in the range 40–100%. However, the battery model is quite accurate in predicting the voltage during charging.

5.4.2.2 Comparison with Operational Data from PHOEBUS

Several comparisons between simulated and measured voltages of the PHOEBUS battery were also performed. Figure 5.27 shows the results for a day with variable solar radiation (May 17, 1996). For the 12-hour charging period 0600–1800 (720 minute samples) the RMS error was 1.7 V and the mean error was 0.6%. This indicates that the model is reasonably accurate in predicting the voltage during charging SOC in the intermediate range, even during variable battery charging.

220

225

230

235

240

245

0 4 8 12 16 20 24Time, h

Volta

ge, V

-20

0

20

40

60

80

SOC

, %Er

ror,

V simmeasSOCerror

error = sim – meas

May 17, 1996∆t =1 min

Simulation input:• Measured current

Figure 5.27 Comparison between simulated and measured voltage, PHOEBUS, May 17,

1996. The SOC shown were based values from the simulation.

In conclusion, the battery model is sufficiently accurate to be used in system simulations, provided that the battery parameters have been properly adjusted. However, the model is not very accurate for deep cycle operation. The battery parameters for the PHOEBUS lead-acid battery system are given in the Appendix.

144

5.5 POWER CONDITIONING EQUIPMENT

The main purpose of this section is to verify the power-conditioning model (TYPE75) presented in Section 4.10 and to find the characteristics of the units integrated into the PHOEBUS plant. Seven power conditioners were installed at PHOEBUS: four maximum power point trackers, one for each PV array; one DC/DC-converter for down-converting the voltage on the DC-busbar to that of the electrolyzer; one DC/DC-converter for up-converting the voltage of the fuel cell to that of the DC-busbar; and one DC/AC-inverter for supplying the AC-grid (user load) with power from the DC-busbar (Figure 5.1).

5.5.1 Efficiency Curves

The characteristic efficiency curves for a power-conditioning unit can be obtained by curve fitting Equation 4.95 to measured data. The measured data used in this particular analysis was based on operational data from PHOEBUS during the period January–September 1996. Figure 5.28 gives the efficiency curves for the MPPT for the PV1 array (Section 5.1.1.2), the DC/DC-converter for the fuel cell, and the DC/AC-inverter for the user load.

In general, a power-conditioning unit reaches its maximum efficiency of about 90% at relatively small power outputs. However, as illustrated by Figure 5.28, the characteristics at low power outputs differ significantly from unit to unit. For instance, the fuel cell converter (a DC/DC device) reaches the maximum efficiency much faster than the user load inverter (a DC/AC device).

A study of the MPPT characteristics (the curves for PV2, PV3, and PV4 are not shown here, but are similar to PV1) reveal that they all operate at about 90% efficiency for input powers greater than about 10% of the nominal power. Furthermore, the electrolyzer converter has about the same characteristic as the fuel cell converter.

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.1 0.2 0.3 0.4Output Power/Nominal Power

Effic

ienc

y Fuel cell converter (meas)Fuel cell converter (calc)MPPT for PV1 (meas)MPPT for PV1 (calc)User load inverter (meas)User load inverter (calc)

0.90

Figure 5.28 Efficiency curves for three different power conditioners installed at

PHOEBUS.


145

A comparison between measured and calculated data (Figure 5.28) shows that there is good to excellent agreement between the two. (Note that, for clarity, not all of the measured data points are included in the figure). The parameters (Equation 4.95) for the seven power conditioning units used in the system simulations in Chapter 6 are given in the Appendix.

5.6 CONCLUSIONS & RECOMMENDATIONS

In this chapter the key PV–H2 component models that are to be used in the integrated system simulations to come in Chapter 6 were evaluated. Below is a summary of the main conclusions and recommendations from the testing and verification of these models.

5.6.1 PV–Generator

The I–U characteristic of a relatively simple one-diode model was more than accurate enough for the simulation purposes of this thesis. No significant difference between the one-diode (few parameters) and a two-diode model (many parameters) was found. Thus, the simpler one-diode model is recommended for the simulations.

Several thermal models were evaluated. In cases where it is important to simulate the short-term dynamics of a system (e.g., 24-hour simulations with time steps less than about 20 minutes), a dynamic thermal model is recommended. However, for long-term simulations (e.g., one-year simulations with time steps greater or equal to one hour) a simpler and more straightforward static thermal model is recommended. In any case, a detailed model that includes the wind speed in the calculations is not recommended.

Finally, the MPPT algorithm included in the PV-generator model was tested. The accuracy of this was excellent and it could be established that the actual MPPTs of the reference system were operating properly.

5.6.2 Electrolyzer

An empirical relationship describing the I–U characteristic of the electrolyzer as a function of temperature (proposed in Chapter 4) was evaluated. A systematic analysis of the parameters of this I–U curve demonstrated that the number of proposes parameters could be reduced from 8 to 6, due to linearity in the expression. By following the steps of a systematic method (proposed in this chapter), an excellent curve-fit between calculated and measured data should always be found.

The faraday efficiency for the electrolyzer of the reference system studied in this thesis was expected to be high (above 95% at regular operation). However, measured data from the actual electrolyzer operation showed the opposite. The short-term simulations performed in this chapter indicated that the expected H2 production should be about 10% higher than what was actually measured at PHOEBUS. It was therefore concluded that the discrepancy between measured and simulated data was due to an error in the H2 flow measurements.

A special lumped capacitance dynamic thermal model for the electrolyzer was evaluated. Comparisons between simulated and measured data (at 5-minute time steps) showed that such a model can only be used with reasonable accuracy if an empirical relationship for the overall heat transfer is used. This overall heat transfer area product (of the cooling heat exchanger)

146

needs to be a function of the electrical current demand. However, for long-term simulations (with one-hour time steps), such as those in Chapter 6, a constant overall heat transfer area product can be assumed.

5.6.3 Fuel Cell

An empirical relationship describing the I–U characteristics of the fuel cell at constant temperatures (proposed in Chapter 4) was evaluated. Most fuel cell I–U curves show a drop-off at high current densities. However, for an H2/O2-fuel cell similar to the one investigated in this study, this drop-off will have little or no influence on overall accuracy of the long-term system simulations. The reason for this is that the PEM fuel cell never should operate at too high current densities.

The inclusion of a lumped capacitance thermal model, similar to the one for the electrolyzer, is recommended for future work. However, since the PEMFC stack heats up relatively quickly, such a model would probably have little influence on the overall results in Chapter 6.

5.6.4 Battery

To model the dynamic behavior of Pb-batteries is extremely complicated, and is a topic in itself. The testing and evaluation of a relatively simple steady-state (quasi-static) model showed that this model could be used to simulate the charging and discharging of a battery reasonably accurate for SOC in the range 40–100%. A very important aspect of this battery model was that its key parameters, such as the equilibrium voltage, easily could be estimated. The parameters for an actual battery in a system in full operation can be estimated by using a simple two-step procedure outlined in this chapter.

5.6.5 Power Conditioning Equipment

The empirical relationship describing the efficiency curves for a power conditioner was evaluated. The results show that the accuracy of the model is good, particularly at powers above 10% of the nominal power. At lower power (less than 10% of nominal power) the DC/DC-converters were more efficient than the DC/AC-inverters. However, at higher power both the inverters and converter operated at efficiencies of about 90%.

6 SIMULATION OF STAND-ALONE PV–H2 SYSTEMS

The overall aim of this chapter is to simulate stand-alone power systems (SAPS) that use solar radiation as the primary energy input and hydrogen as a seasonal energy storage. The SAPS models that have been developed, tested and verified in the previous two chapters, are used to simulate an stand-alone PV–H2 system as realistically as possible.

The main objective of this chapter is to present a method on how to optimize the operation and control strategies of a typical PV–H2 system. An existing solar hydrogen system, with a known load and solar input, was therefore selected as a reference system.

It will be demonstrated how the simulation models presented earlier in Chapter 4, along with a few other simulation model presented in this chapter, can be used to find optimal operation and control strategies for stand-alone PV–H2 systems. A number of control strategies for systems similar to the reference system are recommended, along with a few improvements.

The simulation tools are very flexible and could therefore also be used to find alternative and/or new and improved system designs. Detailed simulations to find new designs were not performed in this study, but a set of possible system improvements are recommended.

6.1 SIMULATION SETUP

6.1.1 Reference System

The PHOEBUS plant at FZ–Jülich in Germany was used as the reference system for the simulations presented in this chapter. The main components of this plant are: four differently oriented PV arrays (South West and South East with tilt angles of 40° and 90°), a Pb-accumulator, and a hydrogen system consisting of an alkaline electrolyzer, a hydrogen storage, an oxygen storage, and an alkaline fuel cell (AFC) stack (Barthels et al., 1996). A schematic of the reference system is provided in Figure 5.1.

The state of charge of the Pb-accumulator (300 kWh at 220 V) determines the voltage on the DC-busbar (200–260 V). All of the other plant components are connected to the DC-busbar via DC/DC-converters, while a DC/AC-inverter provides the consumer with alternating current at 230 V.

In the actual system the user load is similar to that of an office building. The maximum peak is 15 kW, the daily average power (during working hours) is 4.5 kW in the winter and 3.6 kW in the summer, and the base load (outside working hours) is 1.8 kW. The additional requirement for auxiliary power for the electrolyzer, the compressors, the converters, the inverter, and the computer data acquisition and control system DACS), a total of 0.5 kW, is taken from the grid.

148

6.1.2 Simulated System

In the system simulations performed in this chapter two 2.5 kW PEMFC stacks placed in series (i.e., a total of 52 cells in series) was used instead of the original 6 kW alkaline fuel cell stack of the reference system. This was done partly because the AFC stack in reality was going to be replaced by these two PEMFC stacks, and partly because of the authors desire to study the behavior of a PEMFC in an stand-alone PV–H2 system. The operation range for the PEMFC stack used in the simulations is about 30–50 V (Figure 5.20).

The solar radiation and the user load that was used as simulation input was derived from actual measurements made at the reference site (FZ–Jülich) in 1996. That is, hourly average values for solar radiation and user load were produced from minutely values (original data). As a result the simulation input is much less stochastic than the original data. The maximum and minimum power levels in an actual system will vary much more than in the simulations. However, it is important to remember that no short-term dynamic effects are modeled in the simulations presented in this chapter. Therefore, the use of hourly average input values is probably not a bad approximation.

An overview of the TRNSYS components (TYPEs) required to run the simulation of the reference system is provided in Figure 6.1. This figure does not describe the entire information flow in the simulations, but merely indicates the main flow of information between the component models.

All of the TRNSYS simulation TYPEs used in this chapter are described in Chapter 4, except TYPE77, TYPE91, TYPE92, and TYPE94. The first of these (TYPE77) takes care of the current balance on the busbar. The next three include the algorithms and logical statements required to control a stand-alone PV–H2 system. Two of these models (TYPE91 and TYPE92) are described in some detail later in this chapter.

6.1.3 Assumptions & Simplifications

Below is a description of some of the assumptions and simplifications that were made in the simulations of the reference system.

6.1.3.1 Oxygen Handling System

No oxygen handling system was included in the system simulations. In other words, it was assumed that the oxygen required by the O2/H2 PEM fuel cell always could be supplied.

In an actual PV–H2 system provisioned with an O2/H2-fuel cell, the oxygen can either be produced by an electrolyzer, for so to be stored in a high pressure tank (Figure 5.1), or it can be purified from air. In an Air/H2 fuel cell stack no oxygen purification system is required.

In the simulations the I–U characteristic for an O2/H2 PEMFC (Equation 4.75) was used, but could easily have been replaced by the characteristic of an Air/H2 PEMFC. In general, the O2/H2 PEMFC has a better performance than the Air/H2 PEMFC (Figure 4.15), but requires an O2-storage or a purification system. Thus, a tradeoff analysis is required to find the optimal fuel cell system design. Such a tradeoff analysis is not performed in this study, but is left as a recommendation for future work.

Chapter 6 Simulation of Stand-Alone PV–H2 Systems

149

UNIT 1 TYPE 9

Data Reader: Solar Rad. & User Load

UNIT 56 TYPE 76

DC/DC-Converter

UNIT 20 TYPE 60

Electrolyzer

UNIT 22 TYPE 64

Hydrogen Buffer

UNIT 24 TYPE 67 Hydrogen

Compressor

UNIT 26 TYPE 64

Hydrogen Storage (high pressure)

UNIT 28 TYPE 70 Fuel Cell

UNIT 57 TYPE 75

DC/DC-Converter

UNIT 55 TYPE 85

Pb-Accumulator

UNIT 5 TYPE 75

DC/AC-Inverter

UNIT 41 TYPE 80

PV1

UNIT 51 TYPE 75 MPPT1

UNIT 42 TYPE 80

PV2


UNIT 43 TYPE 80

PV3


UNIT 44 TYPE 80

PV4A


UNIT 45 TYPE 80

PV4B

UNIT 12 TYPE 92

Electrolyzer Controller

UNIT 14 TYPE 94

Compressor Controller

UNIT 11 TYPE 91 Fuel Cell

Controller

UNIT 50 TYPE 77 Busbar

Figure 6.1 Overview of the TRNSYS component models (TYPEs) used in the

simulations of the reference system.

150

6.1.3.2 Hydrogen Losses

The following hydrogen losses are expected, but were not included in the simulations:

• H2 losses in the electrolyzer during startup & shutdown • H2 losses in the compressor • H2 losses in the gas storage • H2 losses in the fuel cell during startup & shutdown • H2 losses in the fuel cell during operation

The losses due to flushing of hydrogen during startup and shutdown of the electrolyzer typically amount to about 4%. Furthermore, major leakage due to the wear of the piston rings in the high-pressure stage of a H2 compressor have also been observed (Barthels et al., 1998). In a high-pressure gas storage a small amount of hydrogen will inevitably leak through the valves. Thus, a combined hydrogen loss of 5% in the compression and storage process can be expected.

During startup of a PEMFC a small amount of hydrogen needs to be supplied to the fuel cell while it still operates at a low voltage. This is to ensure that the membrane has been completely humidified (H2 + ½ O2 → H2O) before it is switched to normal operation (BCS, 1998). During operation of a PEMFC it is necessary to purge some hydrogen (at regular intervals) to remove excess water in the membrane. Intermittent venting of hydrogen should typically occur every 15 minutes (Galli et al. 1997). The overall hydrogen utility factor of the O2/H2-PEMFC which is being integrated into PHOEBUS is about 95% (Section 5.3.3).

Although the inclusion of the H2 losses in the PEMFC would make the simulations more accurate, it would probably not affect the overall results significantly as long as very short fuel cell run times are avoided.

6.1.3.3 Parasitic Loads

In the reference system many of the parasitic loads were handled by an auxiliary power supply (the grid). Below is a list of the components whose parasitic powers were omitted from the simulation of the reference system:

• Compressor • Water cooling pump for the electrolyzer • Protective current for the electrolyzer during standby operation • Water rinsing and gas (H2, and O2) purification systems • Water cooling pump for the fuel cell • MPPTs, DC/DC-converters, and DC/AC-inverter • Data acquisition and control system (DACS)1

The main objective of this chapter is to investigate the operation and control of an existing system. Separate simulations (not included in this chapter) proved that the addition of the parasitic powers (listed above) to the measured user load would require a redesign of the reference system, but did not give any new information on the how to operate the system

1 Often also referred to as SCADA (Supervisory control and data acquisition).


151

optimally. The principle of the optimization method described in this study is therefore not dependent on whether the parasitic loads are included or not. However, the inclusion of the parasitic loads would of course give different numerical values than those found in this study.

It should also be noted that if the goal had been to redesign the existing reference system or to design a new and more optimal system, many of the parasitic loads listed above could have been omitted or reduced by using more energy efficient solutions. A more detailed discussion on possible improved system designs is provided in Section 6.6.

6.1.3.4 Protective Current for the Electrolyzer

In an actual system the electrolyzer requires auxiliary power to maintain a protective current during standby operation. This protective current can be obtained by maintaining a minimum voltage across the electrolyzer. For the HYSOLAR electrolyzer, which is similar to the PHOEBUS electrolyzer (Section 5.2.2.1), it was found that a stable single cell voltage of about 1.4 V was sufficient for the standby mode (Hug et al. 1992). In PHOEBUS the standby energy was about 3% of the total electrolyzer energy (Barthels et al., 1998).

The power needed to maintain this voltage depends on the temperature of the electrolyzer. In the simulations, the temperature of the electrolyzer varied from 20–80°C over the year (Figure 6.2). In this particular simulation the electrolyzer operated 4,469 hours in the standby mode, at an average temperature of 34.8°C (Table 6.2).

0

20

40

60

80

100

0 1 2 3 4 5 6 7 8 9 10 11 12Time, month

Tem

pera

ture

, °C

electrolyzer temperature Sim 6

Figure 6.2 The temperature of the electrolyzer over a year. The plot is based on a one-

year simulation of the reference system (Sim 6, Table 6.3). Detailed results for Sim 6 are found in Section 6.4.2.

From the single cell I–U characteristic for the PHOEBUS electrolyzer (Equation 4.46), it can be shown how the power for standby operation varies (nonlinearly) with temperature. The power requirement for a single cell resting voltage of 1.4 V is in the range 13–441 W (in the temperature range 20–80°C), which for the entire stack (21 cells in series) is equivalent to 273–9,261 W.

In the simulations performed in this chapter, the standby power was not included in the calculations of the total load. However, minimizing the number of standby operation hours (Table 6.5) will minimize the standby operation energy, and is therefore an important simulation result that can be used (indirectly) to optimize the overall system performance.

152

6.2 CONTROL STRATEGIES FOR PV–H2 SYSTEMS

This section describes a set of control strategies for PV–H2 systems similar to the reference system described above. Definitions of the key control parameters referred to in this chapter are for convenience summarized in Table 6.1.

Table 6.1 Definition of the parameters in the fuel cell controller (TYPE91), the electrolyzer controller (TYPE92), and the compressor controller (TYPE94).

Parameter Description

Fuel cell TYPE91 FClow Battery SOC at which fuel cell is switched on, % FCup Battery SOC at which fuel cell is switched off, % tsummer Time at which FClow and FCup is switched to summer settings, h twinter Time at which FClow and FCup is switched to winter settings, h VH2,FC Hydrogen flow supply rate set point, Nm3hr-1 γFC Fuel cell switch variable (0 = Off, 1 = On)

Electrolyzer TYPE92 ELlow Battery SOC at which electrolyzer is switched off, % ELup Battery SOC at which electrolyzer is switched on, % Elymode Electrical mode of operation for the electrolyzer

1 = fixed power input, W 2 = fixed current input, A 3 = variable current input, A

Pely,sp Power set point (for Elymode = 1), W Iely,sp Current set point (for Elymode = 2), A Iidle Idling current at low insolation (for SOC > ELlow), A tsummer Time at which the electrolyzer is switched on for the summer, h twinter Time at which the electrolyzer is switched off for the winter, h STARTCLK Time at which the electrolyzer is switched to the idling mode, h STOPCLK Time at which the electrolyzer is switched to the standby mode, h γEL Electrolyzer switch variable (0 = Off, 1 = On)

Compressor TYPE94 pup Pressure in H2-buffer at which compressor is switched on, bar plow Pressure in H2-buffer at which compressor is switched off, bar

6.2.1 Basic Control Strategy

The on/off-switching of the electrolyzer and fuel cell in a PV–H2 hydrogen system that uses a secondary battery as an energy buffer, can be based on the SOC of the battery. The basic control scheme adopted in this thesis is illustrated in Figure 6.3. This is similar to the so-called five-step charge controller adopted at the reference plant (Brocke et al., 1996).

Figure 6.3 shows the on/off-switching set points (or thresholds) for the electrolyzer and fuel cell, ELup ELlow, FClow, and FCup, respectively. It also shows the control signals for the electrolyzer and fuel cell, γEL and γFC, which are discrete variables that can only attain the values 0 (off) or 1 (on).


153

In addition to the on/off-switching of the fuel cell and electrolyzer, the battery needs to be protected from overcharging (at high SOC) or undercharging (at low SOC). Thus, a pair of battery protection thresholds for high and low SOC is also included in the basic control strategy.

100%

0%

BatterySOC

Battery protection (upper)

Battery protection (lower)

ELup

ELlow

FCup

FClow

Inactive control zone

ONγFC = 1γEL = 1

OFFγFC = 0γEL = 0

Electrolyzer ON

Electrolyzer OFF

Fuel Cell OFF

Fuel Cell ON

Figure 6.3 The basic control scheme for the fuel cell and electrolyzer in a PV–H2

system, with the battery SOC thresholds and the logical variables indicated.

6.2.2 Electrolyzer Controller

The electrolyzer controller model (TYPE92) includes the basic on/off-switching scheme described in Figure 6.3, along with a set of other smart control strategies. A flow diagram of the decision-making in TYPE92 is shown Figure 6.4, while a more complete description of the electrolyzer control actions are described below (Sections 6.2.2.1–6.2.2.3).

The input variables to the electrolyzer controller (TYPE92) are shown in Figure 6.4. As indicated in Figure 6.1 the battery SOC comes from TYPE85, the solar radiation G comes from the data reader (TYPE9), the fuel cell control signal γFC from TYPE91, while power P or currents I come from the electrolyzer converter (TYPE76). The special feature of the electrolyzer control signal γEL is described below (Section 6.2.2.4). Note also that the power set point PEL,sp (Elymode = 1) and IEL,sp (Elymode = 2) are fixed inputs, while the current Iexcess or Iidle (Elymode = 3) are variable inputs. A more detailed description of Elymode is also given below (Section 6.2.2.1).

6.2.2.1 Mode of Operation

When the electrolyzer is switched on it can be operated in three distinct electrical modes2:

Mode 1: Fixed electrolyzer power mode (Elymode = 1) Mode 2: Fixed electrolyzer current mode (Elymode = 2) Mode 3: Variable electrolyzer current mode (Elymode = 3)

2 All of the current balance calculations (Equations 6.1–6.3) are taken care of by TYPE77.

154

Start (call TYPE92)

Standby?

γ_FC = 0

γ_EL_old = 1

Yes

γ_EL_new = 0Continue

No

SOC > EL_up

Daytime?

No

γ_EL_new = 1

SOC > EL_low

Yes

G > G_min

Yes

Yes

γ_EL_new = 0

Idle

No

No

Yes

Yes

Yes

No

No

No

Stop (End TYPE92)

Set Outputs: • γ_EL • P_EL_sp (Ely_mode = 1) • I_EL_sp (Ely_mode = 2, 3)

Read Inputs: • SOC, G, γ_FC, γ_EL • P_EL_sp (fixed) (Ely_mode = 1) • I_EL_sp (fixed) (Ely_mode = 2) • I_excess or I_idle (Ely_mode = 3)

Figure 6.4 Information flow diagram of the electrolyzer controller model (TYPE92).


155

Mode 1

In this mode (Elymode = 1) the electrolyzer operates at a fixed power. This means that if the power from the MPPTs minus the power to the user load inverter is less than the power required by the electrolyzer inverter, the battery must cover the power deficit. In the opposite case, the excess power is used to charge the battery.

Mode 2

In this mode (Elymode = 2) the electrolyzer operates at a fixed current, which means that the electrolyzer requires an almost fixed amount of power. During operation in Elymode = 2, the electrolyzer power is not completely constant (Figure 6.7b). This is because the I–U characteristic for the electrolyzer is temperature dependent (Figure 5.12). Nevertheless, the difference between mode 1 and 2 is quite small. The current balance on the busbar (subscript b) in Elymode = 2 is:

bload,bely,MPPTbat IIII −−= 6.1

where

Ibat net battery current (Ibat > 0 is a charging current), A IMPPT total current from all of the MPPTs, A Iely,b current to electrolyzer converter (fixed), A Iload,b current to the user load converter, A

A fixed electrolyzer current set point Iely,sp yields a fixed converter current Iely,b. Thus, the charging or discharging of the battery depends only on IMPPT and Iload,b. It should also be noticed that no current is supplied to the busbar from the fuel cell converter when the electrolyzer is switched on (Section 6.2.2.3).

Mode 3

In this mode (Elymode = 3) the electrolyzer utilizes only the excess power available on the busbar, which means that no current passes in/out of the battery during operation (Equation 6.2). However, if Iexcess is lower than a lower critical current Iidle,b the current deficit must be drawn from the battery (Equation 6.3). If Iexcess,b is above a specified maximum current, the simulation is stopped.

The current balance on the busbar in Elymode = 3 is based on the following calculations:

If Iexcess,b > Iidle,b then bload,MPPTbexcess, III −= and Iely,b = Iexcess,b 6.2

else

If Iexcess,b ≤ Iidle,b then bidle,bload,MPPTbat IIII −−= and Iely,b = Iidle,b 6.3

Where

Iexcess excess current on the busbar, A Iidle,b idling current drawn by the electrolyzer converter (not the same as Iidle the

idling current drawn by the electrolyzer), A

156

6.2.2.2 Standby Mode & Seasonal On/Off-Switching

First of all, once the electrolyzer has been installed in an actual system it can never be completely switched off, as this will damage the electrodes (Section 6.1.3.4). Therefore, in the simulations performed here, switching off the electrolyzer actually means that the electrolyzer is switched to the standby mode.

An actual electrolyzer operating in the standby mode requires, in addition to the power required to maintain an electrode protective current, parasitic power to run miscellaneous auxiliary equipment (e.g., DACS, water rinsing and gas purification systems). A method on how to minimize the parasitic power required in the standby mode should be adopted. Hence, a seasonal on/off-switching scheme is proposed in this thesis.

In TYPE92 the seasonal on/off-switching of the electrolyzer can be specified by the two parameters tsummer and twinter. That is, during the summer (tsummer < time < twinter) the electrolyzer is in the standby mode all the time, while it is shut down (but maintains a protective voltage across the electrodes) during the winter.

6.2.2.3 Additional Controls

In addition to the basic control scheme described in Figure 6.3 and the seasonal on/off-switching scheme described above, there is also a need for additional controls. In summary, the additional logical control statements included in TYPE92 (Figure 6.4) are:

• If the fuel cell is switched on (γFC = 1), then the electrolyzer is switched off (γEL = 0). • The electrolyzer can only operate during the day (between STARTCLK and STOPCLK). • If the solar radiation during daytime is less than a minimum value close to zero (G < Gmin),

then the electrolyzer is switched to the idling mode. (The idling mode is used together with STARTCLK and STOPCLK to avoid abrupt startups and shutdowns).

It should be reemphasized that the above statements relate to the daily on/off-switching of the electrolyzer during the summertime. Thus, switching off the electrolyzer during this period, really means switching it to the standby mode.

Two operation hour set points are proposed in this thesis:

STARTCLK hour of the day at which the electrolyzer is switched to the idling mode STOPCLK hour of the day at which the electrolyzer is switched to the standby mode

The purpose of this feature is to avoid abrupt startups and shutdowns (Figure 5.19). Ideally, STARTCLK and STOPCLK should be the actual sunrise and sunset hours, respectively. However, the STARTCLK parameter can only be fully utilized in connection with a weather forecasting system. That is, if the weather forecast predicts a sunny day, the electrolyzer should be switched on to its idling mode at STARTCLK, otherwise it should remain in the standby mode.

In TYPE92 the length of the daytime operation mode can be specified by the two parameters STARTCLK and STOPCLK. Since a weather forecasting system was not integrated into the simulations presented in this chapter, the use of these parameters was somewhat different than what they would be in an actual system. Actually, as it will be demonstrated below in Scenario 1 and 2 (Section 6.3.1), only STOPCLK is really needed in the simulations.


157

The main purpose of the idling mode included in TYPE92 is to prevent the electrolyzer to be switched to the standby mode when a short disruptions of solar radiation (G < Gmin) during the middle of the day occurs (provided that SOC > ELlow). Instead, the user can specify an idling current Iidle at which the electrolyzer is to operate when this situation (G < Gmin) occurs. However, as the case in an actual system, Iidle should always be greater than the minimum electrode protective current.

Furthermore, when the electrolyzer operates on the excess power on the busbar (Elymode = 3), another check must also be performed (not drawn in Figure 6.4): If the excess power on the busbar (at some point during the course of the day) is less than the minimum power required in the standby mode, the electrolyzer must operate in the idling mode (Equation 6.3).

6.2.2.4 Numerical Solutions in TRNSYS

A Special Note on the On/Off-switching TYPEs

In TYPE92 the electrolyzer control signal γEL goes through a special loop, where the handling of the discrete control variable γEL is taken care of by the ICNTRL array in TRNSYS. This is to ensure proper on/off-switching of TYPE92. The number of calls to TYPE92 depends on the number of iterations needed to reach convergence. Figure 6.4 shows a single call to TYPE92. A similar on/off-switching scheme (with the ICNTRL array) was used in the fuel cell controller model (TYPE91) and compressor controller model (TYPE 94).

A Special Note on Equation Solving

The electrolyzer model (TYPE60) was configured so that the current was an input variable and power was an output variable. Therefore, if Elymode = 1, the power output from TYPE60 must be found implicitly. Since the equations in TYPE60 are highly non-linear, the new solver in TRNSYS (a non-linear equation solver) should be used to handle this backward solution problem. However, if Elymode = 2 or 3, the simulations can be performed using the old solver in TRNSYS (a successive substitution computational scheme).

Several simulations were performed using both the new and the old solver in TRNSYS. An analysis of the results showed that the old solver was to be preferred. The main reason for this was that the old solver gave better numerical stability during on/off-switching of the electrolyzer (TYPE60), fuel cell (TYPE70), and the compressor (TYPE67). In particular, the on/off-switching of TYPE60 and TYPE67, which often ran concurrently, caused problems when the new solver was used. The new solver gives the user more flexibility in his or her modeling work. For future work, it is therefore recommended that the problem is fixed so that the new solver can be used.

6.2.3 Fuel Cell Controller

The fuel cell controller model (TYPE91) includes the basic on/off-switching scheme described in Figure 6.3. A flow diagram of the decision-making in TYPE91 is shown Figure 6.5, and described below (Sections 6.2.3.1–6.2.3.2).

The input variables to the fuel cell controller (TYPE91) are shown in Figure 6.3. The battery SOC comes from TYPE85, the fuel cell control signal γFC comes from TYPE91 itself (see Section 6.2.2.4 for more details), and the hydrogen flow set point VH2,FC is a fixed value.

158

Summer time?

γ_FC_old = 1

Yes

γ_FC_new = 0Continue

SOC < FC_low

No

γ_FC_new = 1

SOC < FC_upYes

γ_FC_new = 0

Use winter time settings for:

FC_low & FC_up

No

Use summer time settings for:

FC_low & FC_up

Yes

Yes

No

Stop (End TYPE91)

Set Outputs: • γ_FC • V_H2_FC

Start (call TYPE91)

Read Inputs: • SOC • γ_FC • V_H2_FC (fixed)

No

Figure 6.5 Information flow diagram for the fuel cell controller (TYPE91).


159

6.2.3.1 Mode of Operation

When the fuel cell is switched on it can only be operated in a constant current mode. This is achieved by maintaining a constant hydrogen supply flow rate VH2,FC. Since the I–U characteristics for the fuel cell is temperature dependent (Figure 5.20), a constant VH2,FC will yield a variable power output. However, because the fuel cell has a fairly low thermal capacity, it will reach its maximum operation temperature relatively fast. Thus, the assumption that the fuel cell operates at a constant VH2,FC, and consequently at a constant power, is not a bad one. This is particularly true if the fuel cell is switched on for several hours at a time.

6.2.3.2 Seasonal Switching

The fuel cell has no seasonal on/off-switching, but can be operated all-year-round. However, two different pairs of on/off-switching thresholds FCup and FClow can be used—one pair for the winter and another pair for the summer. The time period for which these thresholds are valid are set by the parameters tsummer and twinter.

6.2.4 Compressor Controller

A compressor is included in the simulations (as in the reference system) to compress hydrogen from a short-term low-pressure H2-buffer (after the electrolyzer) up to a long-term high-pressure H2-storage (Figure 5.1). The compressor controller unit (TYPE94) uses a simple on/off-switching strategy based on the two parameters pup and plow.

6.3 TYPICAL CONTROL ACTIONS

This section provides a few examples of the control actions implemented in the simulation of the reference system. The purpose is to illustrate the on/off-switching of the electrolyzer, fuel cell, and hydrogen compressor. The simulated scenarios presented here are extracted from a one-year (1996) simulations performed at one-hour time steps. The parameter settings for the simulations are given in Table 6.3, while the main results are found in Table 6.5.

6.3.1 Electrolyzer

6.3.1.1 March 10–12

Three arbitrarily selected days (March 10–12) with different insolation and user load profiles (Figure 6.6) were selected for the two scenarios described below (Figure 6.7 and Figure 6.8). Sunday March 10 was a day with high insolation, while the user load was at a constant low. On Monday the insolation level was lower and more irregular, while the user load was higher, compared to the Sunday. On Tuesday the insolation was quite high, except for a drop around noon, while the user load was about the same as on the Monday.

160

-10

0

10

20

30

1656 1680 1704 1728Time, hr

Pow

er, k

Wpower from MPPTsuser load

Sunday Tuesday

Figure 6.6 Power from MPPTs and power to user load inverter, March 10–12.

The electrolyzer control actions depend on the mode of operation. This can be illustrated by looking at two different scenarios. In both of these two scenarios (Sim 2 and Sim 5) the SOC thresholds (Figure 6.3) were the same (ELup = 90% and ELlow = 80%), while the electrolyzer day time operation period was 5 a.m. – 9 p.m. (STARTCLK = 5 h and STOPCLK = 21 h).

6.3.1.2 Scenario 1

In this scenario the electrolyzer was operated in the fixed current mode (Elymode = 2). Hence, a significant amount of current passed in/out of the battery (Figure 6.7a). The power required by the electrolyzer was almost constant (Figure 6.7b). On Sunday the electrolyzer was switched on at 11 a.m. as the battery SOC passed 90%, while it was switched off at 6 p.m. because the battery SOC at that time dropped below 80%.

On Monday the SOC never reached 90%, hence the electrolyzer was never switched on. On Tuesday there was less power available from the MPPTs than on Sunday, and the electrolyzer was not switched on before 12 p.m., while it was switched off at 4 p.m. (Figure 6.7b).

6.3.1.3 Scenario 2

In this scenario the electrolyzer was operated in the variable current mode (Elymode = 3). Hence, practically no current passed in/out of the battery (Figure 6.8a). The power required by the electrolyzer varied, depending on the excess power available on the busbar (Figure 6.8b). On Sunday the electrolyzer was switched on at 11 a.m. as the battery SOC passed 90%, but it was not switched off until 9 p.m. because the SOC was still greater than 80% (it was switched off at 6 p.m. in Scenario 1). However, at 9 p.m. STOPCLK was reached, and the electrolyzer was switched off. In the hours 6–9 p.m. on Sunday, the excess power on the busbar dropped below a minimum, and the electrolyzer was switched to the idling mode (Figure 6.8b).

On Monday the SOC never reached 90%, hence the electrolyzer was never switched on. On Tuesday there was less power available from the MPPTs, and the electrolyzer was not switched on before 12 p.m. This is similar to that observed in Scenario 1. However, since the electrolyzer in Scenario 2 only operated on the excess power on the busbar (Elymode = 3), the battery SOC did not drop below 80 %. Thus, the electrolyzer did not need to be switched to the idling mode before 6 p.m. The electrolyzer was switched off at 9 p.m. (STOPCLK) on Tuesday (as on Sunday) (Figure 6.8b).


161

-100

-50

0

50

100

1656 1680 1704 1728Time, hr

Cur

rent

, Anet battery currentelectrolyzer converter current

Sunday Tuesday

Sim 2(a)

0

20

40

60

80

100

1656 1680 1704 1728Time, hr

Batte

ry S

tate

of C

harg

e, %

0

5

10

15

20

25

Pow

er, k

W

battery SOCelectrolyzer power

Sunday Tuesday

Sim 2(b)

Figure 6.7 Fixed electrolyzer current mode (Elymode = 2), Scenario 1, March 10–12.

-100

-50

0

50

100

1656 1680 1704 1728Time, hr

Cur

rent

, A

net battery currentelectrolyzer converter current

Sunday Tuesday

Sim 5(a)

0

20

40

60

80

100

1656 1680 1704 1728Time, hr

Batte

ry S

tate

of C

harg

e, %

0

5

10

15

20

25

Pow

er, k

W


Sunday Tuesday

Sim 5(b)

Figure 6.8 Variable electrolyzer current mode (Elymode = 3), Scenario 2, March 10–12.

162

6.3.1.4 June 7

This day (June 7) had a brief disruption in insolation during the middle of the day (Figure 6.9). The electrolyzer control actions on days like this depend heavily on the mode of operation, as illustrated in Scenario 3 (Figure 6.10) and Scenario 4 (Figure 6.11) below.

-10

0

10

20

30

3792 3798 3804 3810 3816Time, hr

Pow

er, k

W

power from MPPTsuser load

Figure 6.9 A day with a temporary disruption in insolation during the middle of the

day, June 7.

6.3.1.5 Scenario 3

In this scenario the electrolyzer was operated in the fixed current mode (Elymode = 2). On June 7 the electrolyzer was switched on at 10 a.m. and off at 12 p.m., due to the disruption in insolation (i.e., power from the MPPTs) which caused the battery SOC to drop below 80%.

At 2 p.m. the insolation increased, and as a result the SOC rose again. At 4 p.m. the SOC was above 90% and the electrolyzer was switched on for a second time that day. It was switched off at 6 p.m. (Figure 6.10b). One disadvantage with the control scheme chosen in this scenario is the increased charging/discharging activity in the battery (Figure 6.10a). However, the main drawback is that the battery SOC temporarily drops below ELlow during the middle of the day, which causes the electrolyzer to be switched off for several sunshine hours. As a result, no hydrogen is produced, even though the sun is shining.

6.3.1.6 Scenario 4

In this scenario the electrolyzer operated in the variable current mode (Elymode = 3). The electrolyzer was switched on at 10 a.m. and off at 9 p.m. In other words, it operated continuously for 11 hours (Figure 6.11b). In comparison, the electrolyzer run time was only 5 hours in Scenario 3 (Figure 6.10b). Another advantage with Elymode = 3 was that only a small amount of current was drawn from the battery in (Figure 6.11a).

At 1 p.m. the electrolyzer was switched to the idling mode, due to the temporary disruption in insolation, and some current needed to be drawn from the battery. A closer look at the battery conditions at 12 p.m. reveal that the final SOC is higher in Scenario 4 than in Scenario 3. As a consequence, the battery SOC in Scenario 4 will reach Elup earlier in the morning of the next day (not plotted in Figure 6.10b or Figure 6.11b) than in Scenario 3.


163

-100

-50

0

50

100

3792 3798 3804 3810 3816Time, hr

Cur

rent

, Anet battery currentelectrolyzer converter current

Sim 2(a)

0

20

40

60

80

100

3792 3798 3804 3810 3816Time, hr

Batte

ry S

tate

of C

harg

e, %

0

5

10

15

20

25

Pow

er, k

W


Sim 2(b)

Figure 6.10 Fixed electrolyzer current mode (Elymode = 2), Scenario 3, June 7.

-100

-50

0

50

100

3792 3798 3804 3810 3816Time, hr

Cur

rent

, A

net battery currentelectrolyzer converter current

Sim 5(a)

0

20

40

60

80

100

3792 3798 3804 3810 3816Time, hr

Batte

ry S

tate

of C

harg

e, %

0

5

10

15

20

25

Pow

er, k

W


Sim 5(b)

Figure 6.11 Variable electrolyzer current mode (Elymode = 3), Scenario 4, June 7.

164

6.3.2 Compressor

6.3.2.1 Scenario 5

In this scenario the control actions of the compressor that compresses the hydrogen gas from the low-pressure H2-buffer up to the high-pressure H2-storage is illustrated. Two days (March 9–10) were arbitrarily selected (Figure 6.12). In Scenario 5 the compressor was switched on when the pressure p was greater than 5 bar (p > pup), while it was switched off when the pressure dropped below 3 bar (p < plow).

0

2

4

6

8

1632 1656 1680Time, hr

Hyd

roge

n Fl

ow, N

m3 h

r-1

0.0

2.0

4.0

6.0

8.0

Pres

sure

Hyd

roge

n Bu

ffer,

bar

hydrogen flow through compressorhydrogen flow from electrolyzerpressure in hydrogen buffer

Saturday Sunday

Sim 5

Figure 6.12 Hydrogen flow from the electrolyzer (input to H2–buffer), hydrogen flow

through the compressor (output from H2–buffer), and pressure in the H2–buffer, Scenario 5, March 9–10.

6.3.3 Fuel Cell

6.3.3.1 January 1–4

An example of a 4-day period during the winter (January 1–4) with low insolation (Figure 6.13) was selected to illustrate the on/off switching of the fuel cell. Two different fuel cells modes of operation were investigated below in Scenario 6 and 7. In both of these two scenarios the battery SOC threshold for the on/off switching of the fuel cell were the same (FClow = 45% and FCup = 55%).

-10

0

10

20

30

0 24 48 72 96Time, hr

Pow

er, k

W


ThursdayMonday

Figure 6.13 Power from the MPPTs and user load for a 4-day period with low insolation, January 1–4.


165

6.3.3.2 Scenario 6

In this scenario a relatively high hydrogen flow rate set point (VH2,FC = 4 Nm3h-1) was chosen. The average fuel cell power at this setting was about 5.3 kW. The fuel cell was switched on three times. Each time the fuel cell was switched off, a current was drawn from the battery to supply the user, and, hence, the battery SOC slowly dropped below 45% (Figure 6.14a).

In Scenario 6 the fuel cell needed to be switched on/off three times, due to the low insolation the first three days of the period (Figure 6.14b). The fuel cell run time (number of operations hours) each time was 9, 12, and 15 h. Hence, the total hydrogen consumption for the period was 4 × 36 = 144 Nm3.

-100

-50

0

50

100

0 24 48 72 96Time, hr

Cur

rent

, A

fuel cell converter currentnet battery current

(a) Sim 11

Monday Thursday

0

20

40

60

80

100

0 24 48 72 96Time, hr

Batte

ry S

tate

of C

harg

e, %

0

2

4

6

8

10

Pow

er, k

W

battery SOCfuel cell power

Monday Thursday

(b) Sim 11

Figure 6.14 High fuel cell H2 supply (VH2,FC = 4 Nm3h-1), Scenario 6 , January 1–4.

6.3.3.3 Scenario 7

In this scenario a quite low hydrogen flow rate set point (VH2,FC = 1.5 Nm3h-1) was chosen. This gave an average fuel cell power of about 2.6 kW and resulted in only one single on/off-switching of the fuel cell (Figure 6.15b). The fuel cell run time in this scenario was 80 h, which is about twice that of the total run time in Scenario 6.

Hence, the total hydrogen consumption in Scenario 7 was 1.5 × 80 = 120 Nm3. This is not directly comparable to Scenario 6 (144 Nm3) because the final battery SOC in Scenario 6 was slightly higher than in Scenario 7 (compare Figure 6.14b and Figure 6.15b). However, the results indicate that, for a given set of FClow and FCup, there should exist an optimal VH2,FC.

166

-100

-50

0

50

100

0 24 48 72 96Time, hr

Cur

rent

, Afuel cell converter currentnet battery current

(a) Sim 13

Monday Thursday

0

20

40

60

80

100

0 24 48 72 96Time, hr

Batte

ry S

tate

of C

harg

e, %

0

2

4

6

8

10

Pow

er, k

W

battery SOCfuel cell power

Monday Thursday

(b) Sim 13

Figure 6.15 Low fuel cell H2 supply (VH2,FC = 1.5 Nm3h-1), Scenario 7, January 1–4.

6.4 SYSTEM SIMULATIONS

This section gives an overview of the results from a typical simulation (Sim 6) of the reference system. However, first the result for a typical week of the reference year (1996) is presented. The parameter settings for Sim 6 are given in Table 6.3.

6.4.1 Typical Week

The week (March 4–10) selected here was a week with a typical user load profile (Figure 6.16). Typically, the load for the reference system is lower during nighttime than daytime, while it remains constant during the weekend. Furthermore, the load profile has a small peak in the morning, before it settles at a relatively constant level later in the day.

The solar radiation varies independently of the load. Hence, the power from the PV-arrays (conditioned in the MPPTs) will vary stochastically with time. The insolation during the week (March 4–10) varied from medium high (Monday), to low (Tuesday–Thursday), and back to high (Friday–Sunday) (Figure 6.16).

During the period with low insolation the battery SOC dropped below 45% (FClow), and the fuel cell was switched on. About 8 hours later, on Thursday afternoon, the SOC was greater than 55% (FCup), and the fuel cell was switched off (Figure 6.17c). The SOC did not reach 90% (ELup) until Saturday morning. At that time the electrolyzer was switched on.


167

-10

0

10

20

30

1512 1536 1560 1584 1608 1632 1656 1680Time, hr

Pow

er, k

Wpower from MPPTsuser load

SunMon Figure 6.16 Total power from MPPTs and power to user load inverter, March 4–10.

0

20

40

60

80

100

1512 1536 1560 1584 1608 1632 1656 1680

Batte

ry S

tate

of C

harg

e, %

220

240

260

280

300

320

Volta

ge a

cros

s Ba

ttery

, Vbattery SOCbattery voltage

(a) Sim 6

-100

-50

0

50

100

1512 1536 1560 1584 1608 1632 1656 1680

Cur

rent

, A

net battery currentelectrolyzer converter currentfuel cell converter current

(b) Sim 6

0

20

40

60

80

100

1512 1536 1560 1584 1608 1632 1656 1680Time, hr

Batte

ry S

tate

of C

harg

e, %

0

5

10

15

20

25

Pow

er, k

W

battery SOCelectrolyzer powerfuel cell power

Mon Sun

Sim 6(c)

Figure 6.17 Control actions for the fuel cell and electrolyzer (variable current mode),

March 4–10. (a) Battery SOC and voltage; (b) Net battery current (+ = charging), current to electrolyzer converter, and current from fuel cell converter; and (c) Battery SOC, electrolyzer power, and fuel cell power.

168

During the weekend, when the user load was at a constant low, the insolation was high. Since the electrolyzer in this case (Sim 6) operated in the variable current mode (Elymode = 3), practically all of the power from the MPPTs could be used to run the electrolyzer (Figure 6.17b). This gave an ideal situation for high hydrogen production.

An analysis of the battery SOC and voltage (Figure 6.17a) and charging/discharging current (Figure 6.17b) shows that battery in essence experiences one complete cycle (from high to low to high SOC) at relatively moderate currents.

The advantage of operating the electrolyzer in the variable current mode (Elymode = 3) is that a high (and constant) battery SOC is maintained during the daytime, even when the electrolyzer is switched on. This fact is clearly illustrated by the shaved peaks of the SOC-curve on Saturday and Sunday (Figure 6.17a).

The depth of the battery cycle depends mainly on FClow and VH2,FC. From a battery SOC point of view, the specific fuel cell settings chosen in Sim 6 seem to be acceptable (Figure 6.17c).

6.4.2 Typical Year

A summary of the annual results for a typical simulation (Sim 6, Table 6.3) is given in Figure 6.19 and Table 6.2. The simulation of the reference system was performed at one-hour time steps, which for the reference year 1996 (leap year) gave a total of 8,784 hours.

6.4.2.1 Solar Radiation & User Load

As indicated by the power output from the maximum power point trackers (MPPTs) for the PV–arrays, the periods with most stable solar radiation input occurred during the months April–September, where April was a particularly good month (Figure 6.18).

The same solar radiation was used as input in all of the simulations presented in this chapter (Sim 1–16, Table 6.3). This means that the total power from the total MPPTs to the busbar was approximately the same in all of the simulations. Any differences in this regard are therefore due to small differences in the voltage on the busbar (i.e., the battery voltage), as these have an affect on the efficiency of the MPPTs and, hence, on the power output.

-10

0

10

20

30

0 1 2 3 4 5 6 7 8 9 10 11 12Time, month

Pow

er, k

W


Figure 6.18 Total power from the MPPTs (upper curve) and power to the user load

inverter in the simulations of the reference system, January–December, 1996.


169

The user load (i.e., the user power demand on the DC-busbar) had a slight seasonal variation, with an annual average of 2.13 kW and a maximum of 8.3 kW (Figure 6.18). The slight increase in the user load occurred during five winter months January–February and October–December. It should also be noted that the same user load was used as input in all of the simulations (Sim 1–16) presented in this chapter.

6.4.2.2 Battery Conditions

A plot of the seasonal variation of the battery SOC and voltage shows how these generally are at a higher level during the summer than during the winter (Figure 6.19a). However, on a few occasions (in February and December) the SOC rose to unacceptable high levels, and some energy (0.16 MWh) needed to be dumped to an external source. However, this situation occurred only when the electrolyzer was switched off for the season. In this case (Sim 6) that meant before March 1 (tsummer = 1,441 h) and after October 31 (twinter = 7,320 h).

A closer look at the battery conditions revealed that the SOC in Sim 6 was in the range 80–90% about 52% of the time (Table 6.2). The battery SOC operating range was 44–99%, while the average SOC was 75%. The corresponding battery voltages were 225–260 V, and 233 V. Finally, it should be noted that the battery had about 7 deep discharge cycles (SOC < 50%) during the period March 1–October 31 (Figure 6.19a), but operated in this range only 9% of the time (Table 6.2).

6.4.2.3 Fuel Cell and Electrolyzer Operation

A plot of the power produced by the fuel cell (input to the converter) and the power consumed by the electrolyzer (output from the converter) show that electrolyzer operates much more often than the fuel cell (Figure 6.19b). In fact, in this case (Sim 6) the electrolyzer had 156 starts versus the 61 starts for the fuel cell (Table 6.2). Another interesting note is that the fuel cell only needed to be switched on four times during the period March 1–October 31.

The fuel cell operating power was fixed at 6 kW, while the electrolyzer, which operated in the power range 0.8–21.7 kW, had an average power of 7.5 kW. The total electrolyzer run time for the season (March 1–October 31) was 1,411 hours, while the total standby time was 4,469 hours. The average run time was 9 hours (Table 6.2). In other words, when the electrolyzer was switched on, it remained switched on for several hours. This was a direct result of the fact that the electrolyzer was operated in the variable current mode (Elymode = 3).

6.4.2.4 Hydrogen Storage

The fluctuations in the pressure of the high-pressure hydrogen storage (H2-storage) varies with the hydrogen produced by the electrolyzer and the hydrogen consumed by the fuel cell. In the simulations the hydrogen produced by the electrolyzer is first feed to the low-pressure hydrogen storage (H2-buffer) for so to be compressed into the high-pressure H2-storage (Figure 5.1). The purpose of the H2-storage in the reference system is to use it as a seasonal energy storage, where hydrogen is produced during summer and consumed during winter.

In Sim 6 the pressure in the H2-storage was lowest (7 bar) around March 1 and at highest (114 bar) around October 31 (Figure 6.19c). Thus, the utilization of the H2-storage capacity was good, as the maximum pressure was rated to 120 bar. The pressure in the H2-buffer varied between 3 to 5 bar.

170

In the simulations, as in an actual system, the final pressure of the H2-storage at the end of the year pH2,final should equal to the initial pressure at the beginning of the year pH2,ini. For a given system (in this case the reference system in Section 6.1.1) with a known user load and solar radiation input, the only way to a make pH2,final = pH2,ini is to adjust the control strategy. Thus, the difference between pH2,final and pH2,ini can be used as a measure in the optimization of the control strategy. Optimal control is the topic of Section 6.5.

0

20

40

60

80

100

0 1 2 3 4 5 6 7 8 9 10 11 12

Stat

e of

Cha

rge

of B

atte

ry, %

220

240

260

280

300

320

Volta

ge a

cros

s Ba

ttery

, V

battery SOCbattery voltage

Sim 6(a)

-25

-20

-15

-10

-5

0

5

10

0 1 2 3 4 5 6 7 8 9 10 11 12

Pow

er, k

W

fuel cell powerelectrolyzer power

Sim 6(b)

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4 5 6 7 8 9 10 11 12Time, month

Pres

sure

Lev

el, 0

–1

high pressure hydrogen storagehydrogen buffer

(c) Sim 6

Figure 6.19 Typical annual results for a simulation (Sim 6); (a) Battery SOC (upper

curve) and battery voltage; (b) Fuel cell power (upper curve) and electrolyzer power; and (c) Pressure levels in high pressure H2–storage (solid curve) and H2–buffer.

6.4.2.5 Total System

A summary of the annual energy consumption/production and efficiencies of the various components and subsystems of the simulation scenario discussed above (Sim 6) are given Table 6.2. The results show that about one third of the energy produced by the PV-arrays


171

went to the production of hydrogen in the electrolyzer, one-third went to battery charging, and one-third directly went to cover the user load. The overall system efficiency was about 58%.

The hydrogen system efficiency in Sim 6 was about 21%, which is somewhat low. The reason for this is that the fuel cell was operated at a high hydrogen flow set point VH2,FC, which gave a high power supply, but a low energy efficiency. The optimal setting of VH2,FC is investigated later (Section 6.5).

Table 6.2 Summary of the results from a one-year (1996) simulation (Sim 6, Table 6.3) of the reference system.

Component/System Miscellaneous

Energy Electrolyzer Solar 304.47 MWh Number of starts 156 PV1…PV4 31.52 " H2 production 2,719 Nm3 MPPTs 28.53 " Run time 1,411 h Electrolyzer converter 11.84 " Standby time 4,469 h Electrolyzer 10.56 " Average run time 9.0 h Fuel Cell 3.39 " Average power 7.5 kW Fuel Cell converter 3.06 " Average operation temp. 51.5 °C Battery (charging) 9.74 " Average standby temp. 34.8 °C Battery (discharging) 8.90 " Fuel Cell User Load (inverter) 18.74 " Number of starts 61

Auxiliary Energiesa) H2 consumption 3,366 Nm3 Dumped 0.16 MWh Run time 561 h Compressor 0.28 " Average run time 9.2 h Inverters & converters 1.55 " Average power 6.0 kW DACS 2.02 " Compressor

Efficienciesb) Number of starts 45 PV-arrays 10.4 % H2 compressed 2,740 Nm3 MPPTs 90.5 " Battery Electrolyzer converter 89.2 " Distribution of SOC Electrolyzerc) 81.8 " (on a per time basis) Fuel celld) 31.3 " 0…40 0 % Fuel cell converter 90.4 40…50 9 " Battery (energy) 91.3 " 50…60 15 " Battery (current) 97.0 " 60…70 10 "

System Efficiencies 70…80 11 " Hydrogen subsysteme) 20.7 " 80…90 52 " Overall systemf) 57.7 " 90…100 2 " Total systemg) 6.0 "

a. Auxiliary loads are calculated in the simulations, but not added to the user load. b. Average component efficiencies. c. Total efficiency, i.e., the product of the Faraday and energy efficiency (Equations 4.48 and 4.50). d. Energy efficiency (Equation 4.78). e. Combined electrolyzer–compressor–H2-storage–fuel cell efficiency. f. From PV power output to user load (on the DC-busbar side) g. From solar radiation input to user load (on the DC-busbar side)

172

The battery had the capacity (300 kWh at 220 V) to supply the user continuously with power for about 4–5 days (average user load was about 50 kWh per day) without receiving any power from the PV-arrays or fuel cell. This explains why such a large amount of energy passed through the battery. The average energy efficiency of the battery was about 91%.

The total volume of the high-pressure H2-storage tanks was 26.8 m3, which gave a maximum capacity of about 2,900 Nm3 (at T = 25 °C and p = 120 bar). In Sim 6 the total annual H2 production in the electrolyzer was 2,700 Nm3, while the H2 consumption in the fuel cell was about 3,350 Nm3. In other words, there was a hydrogen deficit of about 650 Nm3 over the year. However, as it will be demonstrated below (Section 6.5) this deficit can be turned into a surplus by carefully choosing an optimal control strategy.

6.5 OPTIMAL CONTROL STRATEGIES

In this section the optimal control strategies for PV–H2 systems similar to the reference system are investigated. The results from 16 key simulations based on different electrolyzer and fuel cell controller set points are analyzed and discussed. A summary of these results is found in Table 6.5.

6.5.1 Controller Set Points

The controller set points for 16 different simulations are listed in Table 6.3. The first ten simulations (Sim 1–10) are related to the electrolyzer controller (TYPE92), while the last six simulations (Sim 11–16) are related to the fuel cell controller (TYPE91).

Table 6.3 The controller set points (defined in Table 6.1) for 16 different simulationsa).

Electrolyzer (EL) EL & FC Fuel Cell (FC) Sim no.

Elymode –

Iely A

Iidle A

ELup%

ELlow%

tsummerh

twinter h

VH2,FCNm3h-1

FCup summer

%

FClow summer

%

FCup winter %

FClow winter %

Sim 1 2 550 100 90 80 1441 7320 6 55 45 55 45 Sim 2 2 450 100 90 80 1441 7320 6 55 45 55 45 Sim 3 2 350 100 90 80 1441 7320 6 55 45 55 45 Sim 4 2 350 100 90 85 1441 7320 6 55 45 55 45 Sim 5 3 – 100 90 80 1441 7320 6 55 45 55 45 Sim 6 3 – 25 90 80 1441 7320 6 55 45 55 45 Sim 7 3 – 25 90 85 1441 7320 6 55 45 55 45 Sim 8 3 – 25 80 70 1441 7320 6 55 45 55 45 Sim 9 3 – 25 90 80 1 8784 6 55 45 55 45 Sim 10 3 – 25 90 80 2185 6576 6 55 45 55 45 Sim 11 3 – 25 90 80 1441 7320 4 55 45 55 45 Sim 12 3 – 25 90 80 1441 7320 3 55 45 55 45 Sim 13 3 – 25 90 80 1441 7320 1.5 55 45 55 45 Sim 14 3 – 25 90 80 1441 7320 3 45 35 45 35 Sim 15 3 – 25 90 80 1441 7320 3 50 45 50 45 Sim 16 3 – 25 90 80 1441 7320 3 40 35 50 45 a. A shaded area indicates a change in a set point from one simulation to the next.


173

6.5.1.1 Electrolyzer Mode of Operation

The difference between operating the electrolyzer in the fixed current mode (Elymode = 2) as opposed to the variable current mode (Elymode = 3) was illustrated in Figure 6.7 and Figure 6.8. In Sim 1–3 the electrolyzer was operated at three different fixed current levels (high, medium, and low), while in Sim 5 it was operated in the variable current mode. (Sim 4 is discussed in Section 6.5.1.2).

The average electrolyzer operation powers in Sim 1–3 were 21, 17 and 13 kW, respectively, while the total energy consumption remained about the same (10 MWh). With an increase in the average power from a low (13 kW) to a high (21 kW), the number of electrolyzer starts doubled, from 273 to 135, while average electrolyzer run time was reduced by more than a third, from 6.0 to 1.7 h.

One consequence of the above was that more energy passed in/out of the batter. The battery charging energy was, for instance, increased by 16%. At the same time, the battery operated more frequently at a high SOC. In fact, the battery operated 48% of the time in the SOC range 80–90% in Sim 1, compared to 38% of the time in Sim 3 (Table 6.5).

The problem with running the electrolyzer at a high power (Sim 1) is that not enough hydrogen is produced over the year. This is best seen by comparing the final pressures in the H2-storage (Figure 6.21a) from one simulation to the next. Thus, if the electrolyzer is operated in the fixed current mode (Elymode = 2), a relatively low current set point (Sim 3) is recommended.

Finally, the variable current mode was analyzed (Sim 5). In this mode of operation a large fraction of the total energy from the PV–arrays was used directly to run the electrolyzer. As a consequence the use of the battery was minimized. A comparison between Sim 5 and Sim 3 shows that the battery charging energy decreased by 18% and that the battery operated more frequently at a high state of charge (SOC > 80%) in Sim 5 (Table 6.5).

In addition the hydrogen production that was greater in Sim 5 than in Sim 3 (Figure 6.21a). Hence, it can be concluded that the variable current mode is a more optimal mode of operation than the fixed current mode.

6.5.1.2 Basic Control Strategy for the Electrolyzer

An analysis of the basic control strategy for the electrolyzer shows that the overall system performance depend on the setting of the battery SOC thresholds ELup and ELlow and on the electrolyzer mode of operation Elymode.

A comparison between a wide and a narrow electrolyzer hysteresis (∆EL = ELup – ELlow) for the fixed current mode (Elymode = 2) was performed in Sim 3 (∆EL = 10%) and Sim 4 (∆EL = 5%). The results show how a reduction in ∆EL gave an increase in the number of electrolyzer starts from 135 to 238, but decreased the average run time from 6.0 to 3.4 h (Table 6.5).

The other result remained about unchanged (Table 6.5 and Figure 6.21a). However, in an actual system the best solution is to minimize the number of starts and to maximize the average run time of the electrolyzer. Thus, a fairly large ∆EL is recommended for an electrolyzer operating at a fixed power level.

174

An investigation of the hysteresis ∆EL for the variable current mode (Elymode = 3) was performed in Sim 6 (∆EL = 10%) and Sim 7 (∆EL = 5%), and showed that a reduction in ∆EL had no significant effect on the results (Table 6.5 and Figure 6.21b). The reason for this was simply that the battery SOC seldom reached ELlow when the electrolyzer was switched on. Instead it was the STOPCLK parameter that decided when to switch off the electrolyzer.

Finally, a comparison between a high and a low upper electrolyzer threshold ELup was tested. In both cases (Sim 6 and Sim 8) the hysteresis was the same (∆EL = 10%). The result showed that a reduction in ELup from 90 to 80% had some effect on the overall system performance. The hydrogen production was about the same, but there was a slight increase in hydrogen consumption due to a slight increase in the number of fuel cell starts. Hence, a high ELup is recommended.

6.5.1.3 Additional Controls

In all of the simulations in Table 6.3 the electrolyzer was allowed to operate between 5 a.m. and 9 p.m. (STARTCLK = 5 h and STOPCLK = 21 h). However, the STARTCLK parameter was really not needed as no weather forecasting system was implemented (Section 6.2.2.3), while the STOPCLK parameter was only needed when the electrolyzer was operated in the variable current mode (Figure 6.8). In this mode (Elymode = 3) some of the energy required for idling occurred during the middle of the day, but most of it occurred towards the end of the day, before STOPCLK was reached (Figure 6.11).

A comparison between a high and a low idling current Iidle for Elymode = 3 (Sim 5 and Sim 6) show that the overall system performance is improved when a low Iidle is assumed. The main difference between Sim 5 and Sim 6 is the increase in number of electrolyzer starts from 143 to 156, along with the 9% reduction in battery charging energy (Table 6.5).

One conclusion from the above was of course that Iidle must be kept as low as possible. Setting Iidle to a value close to zero in the simulations (recall that in an actual system Iidle must be greater than the minimum protection current) essentially means that the electrolyzer is switched off at sunset.

If one assumes that very little energy is required for idling due to temporary disruptions in insolation during the day (Figure 6.9), then the total energy required for idling is mainly due to the idling in the end of the day before STOPCLK is reached (Figure 6.11). Hence, the comparison between Sim 5 and 6 also indicates the improvement of the system performance when a solar clock (that tells the system to switch off the electrolyzer exactly at the sunset hour) is included.

6.5.1.4 Seasonal On/Off-Switching for the Electrolyzer

The optimal seasonal on/off-switching of the electrolyzer was investigated by running simulations with different tsummer and twinter parameters settings (Figure 6.20). Three scenarios were selected:

1. The electrolyzer was in the standby mode all-year-round (Sim 9) 2. The electrolyzer was in the standby mode in the period March 1–October 31 (Sim 6) 3. The electrolyzer was in the standby mode in the period April 1–September 30 (Sim 10).


175

0

25

50

75

100

0 1 2 3 4 5 6 7 8 9 10 11 12

Batte

ry S

OC

, %

-25

0

25

50

75

Pow

er, k

W

battery SOCfuel cell powerelectrolyzer power

Sim 9(a)

0

25

50

75

100

0 1 2 3 4 5 6 7 8 9 10 11 12

Batte

ry S

OC

, %

-25

0

25

50

75

Pow

er, k

W


Sim 6(b)

0

25

50

75

100

0 1 2 3 4 5 6 7 8 9 10 11 12Time, month

Batte

ry S

OC

, %

-25

0

25

50

75

Pow

er, k

W


Sim 10(c)

Figure 6.20 Three simulations with different electrolyzer standby periods:

(a) January 1–December 31, (b) March 1–October 31, and (c) April 1–September 30.

The results show for the first scenario (Sim 9) show that there is not much to gain by having the electrolyzer operating in a standby mode all-year-round (Figure 6.20a). For instance, the electrolyzer was only started 5 times during the four winter months January, February, November, and December. In fact, the additional annual H2 production compared to the second scenario (Sim 6) was only 63 Nm3 (Table 6.5).

The energy required to operate the electrolyzer in the standby mode was not included in the simulations, but a simple calculation shows that a hydrogen quantity of 63 Nm3 can produce about 84 kWh of electric energy in the fuel cell. (At a flow rate of 4 Nm3 h-1 the fuel cell power is about 5.25 kW). This energy from the fuel cell is not sufficient to cover the energy that would have been required to operate the electrolyzer four months in the standby mode.

176

The results from the second scenario (Sim 6) seem to be more reasonable than the first scenario (Sim 9), as the number of electrolyzer standby hours was reduced from 7,372 h in Sim 9 to 4,469 h in Sim 6. However, the problem with having the electrolyzer shut down for four months of the year (Sim 6) is that some energy (0.16 MWh) occasionally need to be dumped because of a too high battery SOC (Figure 6.20b). However, this dumped energy is significantly smaller than the energy that would have been required to operate the electrolyzer four months in the standby mode.

In the third scenario (Sim 10) the electrolyzer operation period was narrowed down to only six months (April–September). This reduced the number of standby hours to 3,188 h, which is an additional reduction of 1,281 h compared to the second scenario (Sim 6). However, in Sim 10 an unacceptable amount of energy (1.43 MWh) needed to be dumped from the battery (Figure 6.20c).

Based on the trade-off analysis above, the seasonal set points selected in the second scenario (Sim 6) seem to be the most optimal. An exact optimization is recommended, but this can only be performed if the electrolyzer standby energy and all the other parasitic loads (Section 6.1.3.3) are included in the simulations.

6.5.1.5 Hydrogen Supply Flow Set Point for the Fuel Cell

The difference between a high and a low hydrogen supply flow set point VH2,FC was illustrated in Figure 6.14 and Figure 6.15. The overall system performance for three different values for VH2,FC is presented in Sim 11–13. The results show that a low VH2,FC, i.e., a low fuel cell power output PFC, gives relatively few fuel cell starts and a long average fuel cell run time (Table 6.5). The opposite is true for a high VH2,FC. Furthermore, a reduction in VH2,FC also reduces the annual hydrogen consumption in the fuel cell. Since the hydrogen production in the electrolyzer in Sim 11–13 were about the same, the final pressure in the H2-storage was bound to be greater in Sim 13 than in Sim 11 (Figure 6.21c).

An analysis of the above results is best explained by performing an overall energy balance on the busbar:

EMPPT + EFC – EEly + Ebat,ch – Ebat,dch – Eload – Edumped = 0 6.4

where E is the annual energy flow and the subscripts symbolize the maximum power point trackers, the fuel cell, the electrolyzer, the battery charging and discharging, the user load, and the dumped energy, respectively. The annual energy flows for Sim 11–13 are given in Table 6.4.

Table 6.4 Annual energy flow in three simulations (Sim 11–13) with different fuel cell hydrogen flow set points, power outputs, and efficiencies.

Fuel Cell Annual Energy Flow, MWh Sim no VH2,FC

Nm3h-1 PFCkW

ηFCa)

% EMPPT EFC EEly Ebat,ch

g Ebat,dchg Eload

Edumpe

d Sim 11 4.0 5.3 41 28.53 3.05 11.83 9.69 8.85 18.74 0.15 Sim 12 3.0 4.5 46 28.53 3.06 11.83 9.65 8.82 18.74 0.17 Sim 13 1.5 2.6 54 28.53 3.00 11.82 9.29 8.47 18.74 0.13 a. Energy efficiency (Equation 4.78).


177

From Table 6.4 it is clearly seen that the energy flows in/out of the various components is about the same in all of the three simulations. The exception is the battery charging and discharging energy. However, the battery energy losses (Ebat,losses = Ebat,ch – Ebat,dch) are also about the same in all three simulations. It can therefore be concluded that the pressure difference in the H2-storage observed in Figure 6.21c is mainly related to the fuel cell hydrogen flow set point VH2,FC. The explanation is simply that the fuel cell energy efficiency ηFC decreases with an increasing hydrogen flow VH2,FC (and fuel cell power PFC).

Hence, the optimal solution is to operate the fuel cell at the lowest VH2,FC possible. In an actual system there is of course a practical minimum, due to the faraday efficiency which drops dramatically at very low VH2,FC. Another constraint is the battery capacity. At too low VH2,FC the average fuel cell power will be so low that the battery SOC drops below a critical minimum. This trend is already beginning to show in Sim 13, where the battery SOC was below 40% about 3% of the time (Table 6.5). Thus, a medium high VH2,FC, which both gives a sufficiently high fuel cell power and at the same time a relatively good energy efficiency is recommended. In this study VH2,FC = 3.0 Nm3h-1 (Sim 12) satisfy these criteria3.

6.5.1.6 Basic Control Strategy for the Fuel Cell

An analysis of the basic control strategy for the fuel cell shows that the overall system performance may depend significantly on the settings of the battery SOC thresholds FCup and FClow, as illustrated by the three scenarios Sim 12, 14 and 15. The optimal setting of FCup and FClow depends essentially on the three important questions:

• Is an acceptable battery recharging strategy satisfied? • Is the fuel cell on/off-switching scheme acceptable? • Is the annual fuel cell H2 consumption acceptable?

The lowest acceptable SOC for a battery, such as the Pb-accumulator of the reference system, can be assumed to be about 30–40%. (A deeper discharging can be accepted in other types of batteries, as described in Section 3.4.4). The FClow in this case should therefore not be much lower than 40%. A closer look the three scenarios shows that the battery SOC was in the range 0–40% about 9% of the time in Sim 14, which may be unacceptable. The SOC in the other simulations was acceptable (Table 6.5). Thus, from a battery SOC point of view, Sim 12 was more optimal than Sim 14 and 15, as the SOC in this scenario was less than 50% only 10% of the time, compared to 23 and 18% of the time in the other two scenarios.

The number of on/off-switches for the fuel cell is closely related to the average fuel cell run time, and vice versa. That is, once the fuel cell is switched on it should remain on for a certain number of hours so that the losses during startup and shutdown are minimized (Section 6.1.3.2). The time needed to get a PEMFC stack up to normal operating conditions is about one hour, while about 30 minutes is needed for a secure shutdown. Therefore, in an actual system, a minimum fuel cell run time of about 2 hours is acceptable (Galli et al. 1997). A separate analysis of Sim 12, 14 and 15 showed that the minimum fuel cell run time in was always above a minimum of 2 hours. The average fuel cell run times are given in Table 6.5.

3 The theoretical maximum hydrogen supply flow for the PEMFC stack simulated in this study was 6.0 Nm3h-1.

178

Another criterion of the optimal settings of FCup and FClow is the total annual hydrogen consumption in the fuel cell, which should be minimized. A comparison between Sim 12 and Sim 14 show that, for a fixed fuel cell hysteresis (∆FC = FCup–FClow) of 10%, a decrease in FCup and FClow gives a slight reduction in the H2 consumption (Table 6.5). Another comparison (between Sim 12 and Sim 15) shows that for a ∆FC = 5%, a decrease in the FCup does not affect the H2 consumption significantly (but the average fuel cell run time did of course decrease).

Finally, it should be recalled that altering FCup and FClow will affect the battery SOC, which in turn will affect the electrolyzer on/off-switching, and ultimately the H2 production in the electrolyzer. Thus, a more complete picture of the three scenarios can be found by looking at the development of the pressure in the H2-storage over the year. Plots of this pressure show that there are relatively small differences between the scenarios (Figure 6.21c and d).

In summary, it can be concluded that, although setting FClow = 45% and ∆FC = 5% gave the best results in this particular case (Sim 15), changing the fuel cell thresholds and/or the hysteresis will in general have little influence on the overall system performance. However, care must be taken so that no system component operation limits are violated. Operation close to these limits should also be avoided.

6.5.1.7 Seasonal Settings of Fuel Cell Thresholds

In all of the simulations in this chapter, except the last one (Sim 16), the same fuel cell thresholds FCup and FClow were used for the summer and winter. This seems to be a quite logical choice, since the fuel cell typically only starts a few times during the summer (Figure 6.19b).

On a day during the summer when the insolation is low and the battery SOC drops below FClow, the probability that the sun will soon return is much greater than on a day during the winter. At the same time the user load is typically slightly lower during the summer than during the winter. Thus, in order to reduce the fuel cell run time during the summer, it might therefore be beneficial to set FCup and FClow slightly lower during the summer than during the winter.

A different pair of settings for the fuel cell thresholds FCup and FClow for the period March 1–October 31 was selected in Sim 16. A comparison between Sim 15 and 16 show that there is a slight improvement in the overall system performance if the FCup and FClow set points are lowered during the summer (Table 6.5 and Figure 6.21d). However, the improvement is marginal, and, similarly to above, care must be taken so that no system component operation limits are violated.

6.5.2 Discussion of Results

In an optimally designed and operated system the capacity of the H2-storage must be fully utilized. The simulations performed in this thesis showed that the fluctuation in the H2-storage was very sensitive to the total load assumed. Another important issue was the setting of the initial pressure of the H2-storage. These two issues (load and initial pressure) are discussed in some more detail below (Sections 6.5.2.1 and 6.5.2.2).


179

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4 5 6 7 8 9 10 11 12

Pres

sure

Lev

el, 0

–1

Sim 5Sim 3Sim 2Sim 1

(a)

Note: Curve for Sim 4 (not drawn)has a similar shape to Sim 3.

0.45

0.240.200.160.11

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4 5 6 7 8 9 10 11 12

Pres

sure

Lev

el, 0

–1

Sim 6Sim 8Sim 10

(b)

Note: Curves for Sim 5, Sim 7 & Sim 9(not drawn) have similar shape as Sim 6.

0.45

0.240.200.14

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4 5 6 7 8 9 10 11 12

Pres

sure

Lev

el, 0

–1

Sim 13Sim 12Sim 11

(c)

0.30 Note: Different initial pressure than in (a) and (b)

0.570.450.35

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4 5 6 7 8 9 10 11 12Time, month

Pres

sure

Lev

el, 0

–1

Sim 16Sim 14Sim 15

(d)

0.30 Note: Initial pressure as in (c). Curve for Sim 12(not drawn) is slightly lower than Sim 15.

0.490.480.46

Figure 6.21 Pressure level in the high-pressure H2-storage for the 16 simulations

described in Table 6.3. Testing of: (a) Electrolyzer fixed current mode (Sim 1–4) and variable current mode (Sim 5); (b) Electrolyzer SOC thresholds (Sim 6–8) and seasonal set points (Sim 9–10); (c) Fuel cell H2 supply flow set point (Sim 11–13); and (d) Fuel cell SOC thresholds (Sim 14–15) and seasonal set points (Sim 16).

180

Table 6.5 Results from 16 simulations with different electrolyzer and fuel cell controller set points (key results are indicated by a shaded area).

Simulation Number Component 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Electrolyzer No. of starts 273 185 135 238 143 156 153 162 161 137 151 152 152 160 152 149 Standby time, h 5,407 5,278 5,057 5,074 4,620 4,469 4,482 4,412 7,372 3,188 4,484 4,480 4,475 4,479 4,480 4,506 Avg. run time, h 1.7 3.3 6.0 3.4 8.8 9.0 9.1 9.1 8.8 9.0 9.2 9.2 9.2 8.8 9.2 9.2 H2 prod.,Nm3 2,473 2,571 2,664 2,669 2,727 2,719 2,717 2,788 2,782 2,394 2,719 2,719 2,716 2,687 2,709 2,689 Energy, MWh 9.94 10.18 10.39 10.41 10.52 10.56 10.55 10.83 10.81 9.27 10.55 10.55 10.55 10.43 10.52 10.44 Avg. power, kW 21.01 16.91 12.89 12.92 8.35 7.48 7.54 7.37 7.66 7.55 7.56 7.54 7.51 7.45 7.51 7.60 Fuel Cell No. of starts 61 60 62 62 60 61 60 64 64 59 56 50 27 44 81 76 Avg. run time, h 9.2 9.4 9.1 9.1 9.3 9.2 9.3 9.3 8.9 9.4 11.3 15.2 47.0 16.1 9.1 9.4 H2 cons., Nm3 3,378 3,366 3,384 3,372 3,354 3,366 3,354 3,558 3,432 3,330 2,540 2,274 1,904 2,127 2,217 2,145 Energy, MWh 3.40 3.39 3.41 3.39 3.38 3.39 3.38 3.58 3.45 3.35 3.37 3.37 3.29 3.16 3.29 3.18 Avg. power, kW 6.04 6.04 6.04 6.04 6.04 6.04 6.04 6.04 6.04 6.04 5.31 4.45 2.59 4.45 4.45 4.45 Battery Energy in, MWh 15.09 13.56 12.97 12.17 10.70 9.74 9.72 9.54 9.67 9.70 9.69 9.65 9.29 9.71 9.47 9.49 Energy out MWh 13.68 12.36 11.86 11.09 9.79 8.90 8.88 8.85 8.90 8.83 8.85 8.82 8.47 8.90 8.65 8.67 Dumped, MWh 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0 1.43 0.15 0.17 0.13 0.11 0.14 0.14 SOC distribution (on a per time basis):

0…40 0 0 0 0 0 0 0 0 0 0 0 0 3 9 0 1 40…50 10 9 9 9 9 9 9 10 9 9 10 10 12 14 18 18 50…60 15 15 15 14 15 15 14 18 15 14 14 15 9 7 7 7 60…70 10 11 11 11 11 10 10 13 12 8 10 10 10 8 10 10 70…80 14 16 22 11 15 11 11 53 12 12 12 11 11 11 11 12 80…90 48 46 38 51 47 52 52 3 52 46 52 52 52 49 51 50 90…100 % 2 2 4 4 2 2 2 2 0 11 2 2 2 2 2 2

181

6.5.2.1 Sensitivity Analysis

Separate simulations (not included in this thesis) showed that if all of the parasitic loads (Section 6.1.3.3) were added to the user load used, the result was that the fuel cell ran more frequently, the electrolyzer less frequently, and, consequently, the H2-storage was tapped prematurely.

One way to fix the above problem is to produce more hydrogen by increasing the area of the PV-arrays and the size of the electrolyzer. Since the main objective with the simulations presented in this thesis was to find the optimal control strategy for an actual system, a redesign of the system was not performed. However, a combined optimization of the design and operation is recommended (Section 6.6.5).

In the first set of simulation (Sim 1–10) the initial pressure level in the H2-storage at the beginning of the year was fH2,ini = 0.45, while the final pressure level fH2,final was in the range 0.11–0.24 (Figure 6.21a and b)1. Thus, none of the selected control strategies satisfy the criterion fH2,final ≥ fH2,ini.

In the next set of simulations (Sim 11–16) fH2,ini = 0.30 and fH2,final was in the range 0.35–0.57 (Figure 6.21c and d). In the most optimal (and at the same time most realistic) of these simulations (Sim 16) fH2,final = 0.49. Thus, it was demonstrated that the reference system can be operated in such a way that fH2,final ≥ fH2,ini.

6.5.2.2 Two Extreme Scenarios

In relation to the simulation presented above (Sim 1–16) there are two extremely important scenarios that have not been discussed so far, but are mentioned separately here.

Scenario F (Full Storage)

In this scenario the H2-storage and the battery are both almost full (99%) and the power from the PV-arrays exceeds the total load. If Scenario F occurs when the electrolyzer and compressor are running the following control actions must be taken:

1. H2 in the high-pressure storage is vented out through a safety valve. 2. The PV-arrays are disconnected. 3. The electrolyzer is switched off. 4. The compressor is switched off.

If Scenario F occurs during a period when the electrolyzer is shut down for the season (i.e., only a protective current is maintained), it is sufficient to disconnect the PV-arrays until the battery SOC drops to an acceptable level. The hysteresis of the upper battery protection is illustrated in Figure 6.3.

In the simulations the control actions needed in Scenario F were simplified compared to those needed in an actual system. In the first case (the electrolyzer is running) only control action number 1 was taken (H2 is vented out). This occurred at fH2 = 0.99. In the second case

1The pressure level in the H2-storage is defined as: fH2= pH2/pH2,max where pH2,max = 120 bar

182

(electrolyzer switched off for the season) the excess power was simply dumped from the busbar (to an imagined resistive load). This occurred at SOC = 99%.

Scenario E (Empty Storage)

In this scenario the H2-storage and the battery are both almost empty and the total load exceeds the power from the PV-arrays. With the assumption that the fuel cell is allowed to operate all-year-round, Scenario E will always occur when the fuel cell is running. Thus, if Scenario E occurs the following control actions must be taken:

1. The load is disconnected (blackout). 2. The fuel cell is switched off.

In the simulations a no advanced control scheme was followed if Scenario E occurred. Instead, the simulation was simply stopped. Scenario E usually occurred when the initial pressure level in the H2-storage fH2,ini was set too low. A quick fix to this problem was therefore to simply reset fH2,ini to at a higher value. The simulation was then rerun.

A criterion for a successful simulation was that there were no or very few occurrences of Scenario F (full storage). The above process was therefore repeated until a satisfactory simulation result was found (fH2,final ≥ fH2,ini). Usually, only 2–3 iterations were needed.

6.5.3 Conclusions & Recommendations

The main conclusions and recommendations that can be drawn from the above simulations (Sim 1–16) are:

• It is more optimal to operate the electrolyzer in a variable power mode (where it runs on the excess power on the busbar) than in a fixed power or fixed current mode (where it uses battery power if needed).

• If the electrolyzer must operate in a fixed current or fixed power mode it should run at a moderate power and not at full power. This will significantly reduce the use and, hence, the wear of the battery.

• The upper electrolyzer threshold ELup should be set relatively high (e.g., 90%) and the hysteresis ∆EL should be quite small (e.g., 5%). However, the setting of ∆EL is most crucial if the electrolyzer is operating in a fixed power or fixed current mode.

• A smart control strategy for on/off-switching of the electrolyzer is recommended. A weather forecasting system should be included. This system could “tell” the electrolyzer to go from the standby mode to the idling mode (needed for warm-up) only on days that are expected to give high insolation. A solar clock that tells the system to switch back to the standby mode at sunset is also recommended.

• A seasonal on/off-switching scheme for the electrolyzer is recommended. The decision about when the electrolyzer should to be switched on (to the standby mode) in the spring and shut down (to the protective current mode) in the fall is dependent on the seasonal variation in the insolation and user load. Thus, long-term solar radiation data and information from past operating experience can be used to determine what these seasonal

183

on/off-switching set points should be. In an actual system the seasonal set points can be determined by a human operator or by a sophisticated predictive controller.

• It is recommended that the fuel cell operate at the highest energy efficiency possible (i.e., at the lowest H2 supply flow feasible). In a system that does not permit frequent operation at low battery SOC, the H2 supply should be fixed so that the fuel cell operates at a medium high power (i.e., at a medium high efficiency).

• For a fixed fuel cell hydrogen supply flow (and fixed power) the lower fuel cell threshold FClow should be relatively low, but always higher than the lowest allowable battery SOC (e.g., 45%), while the hysteresis ∆FC should be quite small (e.g., 5%). However, care must be taken so that the fuel cell run time does not drop below a minimum number of hours (e.g., 2 h), or that no other system component limits are violated.

• Setting the fuel cell thresholds FClow and FCup at a lower level in the summer than in the winter reduces the total fuel cell hydrogen consumption slightly, but does not improve the overall system performance significantly.

6.6 OPTIMAL SYSTEM DESIGNS

The design of a PV–H2 system for a given location with a known insolation2 is extremely dependent on the load. The minimization of the load before dimensioning a PV–H2 system is one of the main criteria for an optimally designed system (Ulleberg and Mørner, 1997). After having minimized the load, new and improved designs may be considered. Some of the most viable alternative designs are:

• Direct coupling of the PV-arrays, the electrolyzer, and/or the fuel cell to the DC-busbar. • Replacement of the low-pressure electrolyzer with a high-pressure electrolyzer • Replacement of the compressed hydrogen gas storage with a low-pressure ambient

temperature metal hydride (MH) storage instead of • Inclusion of a wind turbine

6.6.1 Direct Coupling of Components

The advantage of coupling the components directly to the DC-busbar is that the energy losses associated with the inverters and converters are avoided. However, system simulations similar to the ones performed in this study have shown that a maximum power point tracker should be included (Ulleberg and Mørner, 1997).

Vanhanen (1996) and others have studied in detail the issues related to direct coupling of a PV-array, electrolyzer, fuel cell, and battery. This approach seems to be appropriate for small to medium sized (Table 1.2) solar-hydrogen system.

The advantage of including DC/DC-converters (e.g., one by the electrolyzer and one by the fuel cell) is that it gives the system a more robust and flexible design. This is particularly important for large systems, such as the reference system analyzed in this study, where the

2 Determined statistically from long-term solar radiation data.

184

safety measures and costs for retrofitting and/or redesign usually are much greater than for smaller systems.

6.6.2 High-pressure Electrolyzer

A new and improved high-pressure electrolyzer design could eliminate the need to compress hydrogen into a high-pressure storage. This is the idea behind the high-pressure electrolyzer for solar-hydrogen energy system that is under development at FZ–Jülich in Germany (Barthels et al. 1998). This electrolyzer will operate at a pressure of about 100 bar.

The energy demand for a high-pressure electrolyzer is related to the thermodynamics of water electrolysis (Figure 4.9). Theoretically, the energy demand in a 100 bar electrolyzer system will increase by about 8% compared to a 1 bar system. This energy increase is less than or equal to the energy required compressing the hydrogen from 1 to 100 bar (typically about 10% of the total electrolyzer energy demand). However, a very important advantage of the high-pressure electrolyzer is that the hydrogen losses due to leakage in the compressor are completely eliminated.

6.6.3 Metal Hydride Storage

An alternative design is to store the hydrogen in a near-ambient temperature and atmospheric metal hydride (MH) storage. One advantage of the MH-storage is that is requires less space than a 120 bar pressure vessel with the same capacity (Table 3.3). However, the greatest advantage of the MH-storage is that it can be coupled directly to a low-pressure electrolyzer, thus eliminating the need for a compressor.

Since the charging MH reaction is exothermic it requires cooling during the hydrogen absorption process (charging) and heating during the hydrogen desorption process (discharging). A typical3 charging process for a 40°C isotherm takes place at a pressure of 6–10 bar, while a discharging process at 40°C takes place at a pressure of 4–7 bar (Gfe, 1995).

The cooling and heating requirements of the MH-storage depend on the ambient temperature. These thermal energy loads are therefore directly dependent on the location (cold or warm climate) of the system and on the local placement (indoors or outdoors) of the MH-storage. For instance, the waste heat from the fuel cell could be used to heat up the MH during discharging (H2-desorption). Studies show that this may be a particularly suitable solution for PV–MH systems located in cold climates (Mørner, 1995). The cooling required during charging (H2-absorption) is typically quite low, and is therefore relatively easy to handle (e.g., tap water cooling).

3 This is the expected behavior of the metal hydride alloy Hydralloy ® (C15 Ti0.85Zr0.15Mn1.45V0.45Fe0.1Ni0.05) which will be tested at the PV–H2 laboratory at Institute for Energy Technology (IFE) in Norway (Eriksen, 1998).

185

6.6.4 PV–Wind–H2 System

For a system with known wind regime4 and load, a wind energy conversion system (WECS) will influence the system design in two basic ways:

1. It will reduce the required PV-array area. 2. It will reduce the required H2-storage volume.

The interplay between size of the WECS on one side and the PV-array area and H2-storage volume on the other side was illustrated in a simulation study performed by Mørner (1995). The system analyzed in that study was located at a high latitude (with great seasonal variation in the insolation) and in a region with a very favorable wind regime.

6.6.5 Recommendations

In order to design the most practical and energy efficient solar-hydrogen system the following step are recommended:

1. The expected solar radiation and wind energy for the site in question should be determined from long-term data5.

2. The user load should be determined and great measures to reduce the load to a minimum should be taken.

3. A system configuration based on the recommendations given in Chapter 3 should be selected.

4. Once a viable system configuration has been established a detailed analysis of the operation of the system should be performed.

5. A systematic methodology on modeling, testing & verification of the models, and simulation similar to that described in Chapters 4–6 should be performed.

6. If step 5 shows that it is possible to reduce the sizes of the initially selected components, a redesign of the system configuration should be performed.

7. A combined optimization of the design and operation (steps 4–6) is recommended

It must be emphasized that for a true combined optimization of the design and operation (step 7) to be realistic, the objective function should include models for component wear and deterioration.

In order to design the most economical solar-hydrogen system the following step are needed:

1. Go through steps 1–6 above. 2. Define the cost function for several alternatives. 3. Perform a combined optimization of the design and operation for each alternative (step 7) 4. Compare and evaluate each (optimized) alternative.

4 Determined statistically from long-term wind data.

5 Chapter 2 can be used as a quick reference to determine the general availability of a resource for a region. However, more detailed statistical methods are required to develop short-term data (e.g., hourly data) from long-term data (e.g., monthly means).

186

However, an extensive economical optimization is not recommended at this stage, since solar-hydrogen energy technology still is at an early stage in the development. Instead, it is recommended that a combined optimization (step 7) be performed for a few carefully selected alternative designs. These alternatives should be selected on the basis of the needs and requirements of the user and on the availability of the resource.

6.7 SUMMARY

The purpose of this chapter has been to simulate integrated stand-alone solar-hydrogen systems. An actual system based on PV–H2 energy technology was selected as a reference system and a control strategy was presented. The simulations of the reference system showed that it is possible to perform detailed studies on the operation of PV–H2 systems by using the model that were developed, tested, and verified in Chapters 4–5.

A systematic method on how to optimize the operation of PV–H2 systems was presented and an optimal solution was found. A method on how to perform a combined optimization of the system design and operation was outlined and recommended for future work. Finally, the most viable alternative designs are discussed. A combined optimization of the design and operation of these alternatives are also recommended.

7 CONCLUSIONS & RECOMMENDATIONS

The overall goal of this thesis was to investigate and study the most optimal and viable long-term solutions that satisfy the requirements of stand-alone power systems (SAPS) for the future. The work was twofold. Thus, the thesis was organized into two separate parts: one fundamental Part I and one technical Part II. The first part was primarily meant as a guide for politicians and other energy decision-makers, while the second part, the crux of the matter, was meant as a supplement for students and researchers working in the field of energy. The main conclusions and recommendations that can be drawn from these two, somewhat different, discussions are summarized below.

7.1 SUSTAINABLE STAND-ALONE POWER SYSTEM (SAPS) FOR THE FUTURE (PART I)

The main conclusion from the fundamental discussions in Chapters 2 and 3 is that there are few generic types of SAPS that satisfy the requirement for sustainable development. In the long run, all energy systems, including SAPS, must be based on natural energy sources.

A systematic assessment of the availability of the natural energy sources show that solar, wind, and hydro energy are generically the best options for stand alone power applications, while ocean, ocean tidal, and geothermal energy are less suitable. This conclusion is based on several aspects.

First, there is a trade-off between natural energy resource availability on one side and user energy demand on the other side. The energy resources that are available to most people should therefore be given first priority.

Second, there is the issue of efficient energy conversion. For stand-alone systems that require electrical power, conversion via thermal energy should be avoided. Direct conversion from solar (radiation) energy to electrical energy is a more optimal solution. However, solar derivatives such as wind power or hydropower may also be suitable options for SAPS. The advantage of hydropower is, of course, that it also provides a means for storage of gravitational energy.

Third, there is the issue of efficient energy storage. Several options were considered. Among these was biofuel from photosynthesis. In a SAPS the biofuel could be converted to electrical energy in regular IC-engine generators (gen sets). However, the overall conversion efficiency from solar energy to biomass to biofuel to electrical energy is very low. Furthermore, the cultivation of energy crops can in the future come in conflict with the cultivation of food crops. Thus, this option is not recommended. Instead, an alternative fuel derived from solar, wind, or hydropower is recommended. In this context, one of the most logical and promising options is hydrogen derived from solar energy, a concept commonly referred to as solar-hydrogen energy.

188

From a practical point of view, most of the solar-hydrogen energy technologies are quite new and immature. However, an assessment of both the available and the more innovative solar-hydrogen energy concepts, illustrated that a few technologies clearly distinguish themselves from the rest: Photovoltaic–hydrogen systems, or simply PV–H2 systems.

7.2 SIMULATION OF STAND-ALONE PV–H2 SYSTEMS (PART II)

In the second part of this thesis (Chapters 4–6) PV–H2 systems were studied in detail via modeling and simulation tools developed specifically for this thesis. This was done after having evaluated several simulation programs beforehand.

A transient system simulation program (TRNSYS) particularly designed for simulating solar energy systems was selected because of its modular structure and tremendous flexibility. The possibility of adding user-written mathematical models not included in the standard library is a particularly attractive feature of this program. Another important feature of TRNSYS was that it includes several convenient component models that can be used for solar radiation calculations. Thus, the PV–H2 component models that were developed and used to simulate the reference system in this thesis, could easily have been used to simulate another system located at a completely different site.

The reference PV–H2 system selected in this thesis, the PHOEBUS demonstration plant at FZ–Jülich, Germany, had a configuration that is suitable for medium to large sized SAPS. Hence, any knowledge acquired about the operation of this specific system would be directly transferable to many kinds of solar-hydrogen energy systems with similar configurations. This was the main reason for why the PHOEBUS plant was selected as the reference system. Another reason was of course that this was one of the few PV–H2 plants in the world with such an enormous amount of operational data available. In addition, the research center at FZ–Jülich had conducted several separate experiments on individual PV–H2 components such as the PV-array, the lead-acid battery, and the PEM fuel cell. Thus, the premises for modeling the individual components accurately were excellent.

7.2.1 Modeling of PV–H2 Components

Detailed descriptions of the individual component models required to simulate a PV–H2 system were presented. These models were mainly based on electrical, electrochemical, thermodynamics, and heat and mass transfer theory. However, a number of empirical relationships, particularly for the current-voltage (I–U) characteristics, were also used. The PV-generator and electrolyzer were the most detailed among the major models, but the Pb-battery and fuel cell models were also quite involved. All of the models could, if lack of data was a problem, be run in simpler modes.

The modeling, testing, and verification of the component models showed that the agreement between simulated and measured data was very good. Several short-term simulations were performed so that the I–U characteristics, dynamic thermal behavior, hydrogen production and consumption rates, and other physical processes of the individual component models could be properly evaluated. Below is a list of the main conclusions that could be drawn from the evaluation of the key PV–H2 component models:

Chapter 7 Conclusions & Recommendations

189

PV–Generator

• A one-diode model is more than accurate enough for both long-term and short-term simulation purposes, as long as the PV operating range is limited to voltages less than or equal to the maximum power point. A two-diode model is not recommended.

• A detailed thermal model that accounts for dynamic behavior of the temperature of a PV-array is only required for short-term simulations with time steps less than 30 minutes. The inclusion of wind speed in the calculations is not recommended.

• Comparisons between the simulated MPPT power (included in the PV-model) and the measured power from the MPPTs of the reference system showed that the actual MPPTs were operating properly.

Electrolyzer

• A new and improved form of the empirical relationship describing the I–U characteristic of an alkaline electrolyzer as a function of temperature was proposed. This I–U curve gave a remarkably good curve-fit between calculated and measured data. A systematic method on how this, and similar I–U curve fits, best can be performed was also proposed.

• A comparison between simulated and measured data showed that there most likely was an error in the H2 flow measurements in the reference system.

• The thermal behavior of an electrolyzer (with a stationary electrolyte) was modeled using a lumped capacitance model. A comparison between simulated and measured data showed that this thermal model was only accurate if a special empirical relationship for the overall heat transfer in the heat exchanger (water-cooling) was included. This relationship took into account the mixing of the stationary electrolyte at high electrical current densities.

Fuel Cell

• A simplified empirical relationship describing the I–U fuel cell characteristics for constant temperatures can be used without much error for fuel cells with little voltage drop-off at high current densities. The voltage drop-off is relatively small for H2/O2-PEMFCs, but much more pronounced in H2/Air-PEMFCs. Hence, a more detailed I–U relationship is recommended for air-breathing PEMFCs.

Battery

• To model the dynamic behavior of Pb-batteries is extremely complicated. However, a relatively simple steady-state (quasi-static) model can be used to simulate the battery charging/discharging with reasonable accuracy for SOC in the range 40–100%.

• The advantage of a simple battery model is that the parameters easily can be retrofitted to an actual battery of a system in full operation. A straightforward two-step procedure on how to find the most crucial battery parameters was proposed.

190

7.2.2 Optimization of the Operation of PV-H2 Systems

The main conclusions and recommendations about the operation of a PV–H2 systems that could be drawn from the integrated system simulations were:

• An electrolyzer that is to be used in a PV–H2 system, or any other kind of system based on intermittent energy, should be designed to operate in a variable power mode.

• An electrolyzer that is designed to operate in a fixed power mode only, should always run at moderate power and not at full power, as this will reduce wear of the battery.

• The upper battery SOC threshold for switching on the electrolyzer should be set as high as possible (e.g., 90%) while the hysteresis should be quite small (e.g., 5%). The setting of the hysteresis is most crucial if the electrolyzer is operating in a fixed power mode.

• A smart control strategy for on/off-switching of the electrolyzer is recommended. A weather forecasting system should be included.

• A seasonal on/off-switching scheme for the electrolyzer is recommended. The decision about when the electrolyzer should to be switched on in the spring and shut down in the fall is dependent on the seasonal variation in the insolation and user load. Thus, long-term solar radiation data and information from past operating experience should be used to determine what these seasonal on/off-switching set points should be.

• It is recommended that the fuel cell operate at the highest energy efficiency possible. In a system that does not permit frequent operation at low battery SOC, the H2 supply should be fixed so that the fuel cell operates at a medium high power.

• The lower battery SOC threshold for switching on the fuel cell should be relatively low, but always higher than the lowest allowable battery SOC (e.g., 45%), while the hysteresis should be quite small (e.g., 5%). However, care must be taken so that the fuel cell run time never drops below a minimum

• Setting the battery SOC thresholds for the on/off-switching of the fuel cell at a lower level in the summer than in the winter does not improve the overall system performance significantly.

7.2.3 Recommendations for Improved Designs

The design of a PV–H2 system for a given location with a known insolation is extremely dependent on the load. The minimization of the load before dimensioning a PV–H2 system is one of the main criteria for an optimally designed system. After having minimized the load, new and improved designs may be considered. Some of the most promising alternative designs are:

1. Direct coupling of the PV-arrays, the electrolyzer, and/or the fuel cell to the DC-busbar.

2. Replacement of the low-pressure electrolyzer with a high-pressure electrolyzer.

3. Replacement of the high-pressure hydrogen gas storage with a low-pressure ambient temperature metal hydride (MH) storage.

4. Inclusion of a wind turbine.

Chapter 7 Conclusions & Recommendations

191

The inclusion of power conditioning equipment gives the overall system a robust and flexible design. This is particularly important for large SAPS. However, coupling the system PV-arrays, the electrolyzer, and/or the fuel cell directly to the DC-busbar may be a good alternative for smaller SAPS.

The second and third alternative in the list above represents two fundamentally very different concepts for hydrogen storage. One is based on storage of H2 at a high pressure in a pressure vessel, while the other is based on storage of H2 at a low-pressure in a metal hydride. It is important to note that it is not possible to give an absolute recommendation about which of these two concepts to chose. Instead, the decision should be based on the type of application at hand. For applications with quite small power requirements, hydrogen storage in low-pressure near-ambient temperature metal hydrides seems to be a favorable option. In comparison, applications with relatively large power demands probably favor the high-pressure hydrogen storage concepts.

The inclusion of a wind turbine will reduce the size of the PV-array, and may even eliminate the need for PV entirely. A trade-off analysis between PV-area and wind generator size is an interesting option for systems located at sites with high average wind speeds.

REFERENCES

Anand N. K., Appleby A. J., Dhar H. P., Ferreira A. C., Kim J., Mukerjee S., Nandi A., Parthasarathy A., Rho Y. W., Somasandaran S., Srinivasan S., Velev O. A., and Wakizoe M. (1994) Recent progress in proton exchange membrane fuel cells at Texas A&M University. In Proceedings of the 10th World Hydrogen Energy Conference, Block D. L. and Veziroglu T. N.(Eds), pp. 1669–1679, June 20–24, Cocoa Beach, Florida.

Anderson E. E. (1982) Introduction to Modern Physics. Saunders College Publishing, London.

Aylward G. and Findlay T. (1994) SI Chemical Data. 3rd edn. John Wiley & Sons, New York.

Asbjørnsen O. A. (1992) Systems Engineering Principle and Practices. SKARPODD Co., Arnold, Maryland.

Asbjørnsen O. A. (1989) System Modeling and Simulation. SKARPODD Co., Arnold, Maryland.

Barbir F. and Gómez T. (1996) Efficiency and economics of proton exchange membrane (PEM) fuel cells. Int. J. Hydrogen Energy, 21 (10), 891–901.

Barthels H., Brocke W. A., Bonhoff K., Groehn H. G., Heuts G., Lennartz M., Mai H., Mergel J., Schmid L., and Ritzenhoff P. (1998) PHOEBUS-Jülich: An autonomous energy supply system comprising photovoltaics, electrolytic hydrogen, fuel cell. Int. J. Hydrogen Energy 23 (4), 295–301.

Barthels H. (Ed), Brocke W. A., Groehn H. G., Heuts G., Hinßen H., Mai H., Mergel J., Lennartz M., Moll M., Schmid L., Wilhelm H., Bonhoff K., Ritzenhoff P., and Bischkopf W. (1996) Status Report for the first Project Phase 1992–1995 (in German). FZ Jülich, Germany.

BCC (1997). Large and Advanced Battery Technology Markets. Report GB–197. Business Communications Company, Inc., Norwalk, Connecticut.

BCS (1998) Guidelines for Operation of Air-Breathing Fuel Cell Stack. BCS Technology, Inc., Bryan, Texas.

Berdahl P. and Martin M. (1984) Emissivity of Clear Skies. Solar Energy, 32 (5).

Berndt D. (1997) Maintenance-Free Batteries: Lead-acid, Nickel/Cadmium, Nickel/Metal Hydride—A Handbook of Battery Technology. 2nd edn. Research Studies Press Ltd., Somerset, UK.

References

193

Bockris J. O’M., and Reddy A. K. N. (1998) Modern Electrochemistry: ionics. Vol. 1, 2nd edn. Plenum Press, London.

Bolton J. R. (1996) Solar photoproduction of hydrogen: a review. Solar Energy 57 (1), 37–50.

Brocke W. A., Ritzenhoff P., and Barthels H. (1996) Systematic design of the PHOEBUS Jülich energy management system. In Proceedings of the 11th World Hydrogen Energy Conference, Veziroglu T. N., Winter C.-J., Baselt J. P., and Kreysa G (Eds), pp.1191–1196 (Vol. 2), June 23–28, Stuttgart, Germany.

Brocke W. A. (1993) Presentation of JULSIM and solar applications. An unpublished paper presented at an IEA meeting, March 8–9, 1993, FZ-Jülich.

Brocke W. A. (1996) FZ Jülich, personal communication (in situ).

Butler P. (1997) Battery storage for supplementing renewable energy systems. In Renewable Energy Technology Characterizations, Galdo J. F. and DeMeo E. A. (Project managers), Electrical Power Research Institute, Inc., Palo Alto, California.

Cavallo A. J., Hock S. M., and Smith D. R. (1993) Wind energy: technology and economics. In Renewable Energy—Sources for Fuels and Electricity, Johansson T. B., Kelly H., Reddy K. A. N., Williams R. H. , and Burnham L. (Eds), pp. 121–156. Earthscan Publications Ltd., London.

Carlson D. E. and Wagner S. (1993) Amorphous silicon photovoltaic systems. In Renewable Energy—Sources for Fuels and Electricity, Johansson T. B., Kelly H., Reddy K. A. N., Williams R. H. , and Burnham L. (Eds), pp. 404–435. Earthscan Publications Ltd., London.

Carpetis C. (1988) Storage, transport and distribution of hydrogen. In Hydrogen as an energy carrier—Technologies, Systems, Economy, Winter C.-J. and Nitsch J. (Eds), pp. 249–289. Springer-Verlag, London.

Cavanagh J. E. , Clarke J. H., and Price R. (1993) Ocean energy systems. In Renewable Energy—Sources for Fuels and Electricity, Johansson T. B., Kelly H., Reddy K. A. N., Williams R. H. , and Burnham L. (Eds), pp. 513–547. Earthscan Publications Ltd., London.

Çengel Y. A. and Boles M. A. (1989) Thermodynamics—An Engineering Approach. McGraw-Hill, Inc., London.

Chamberlin C. E., Kim J., Lee S.-M., and Srinivasan S. (1995) Modeling of proton exchange membrane fuel cell performance with an empirical equation. J. Electrochem. Soc., 142 (8), 2670–2674.

Chaurey A. and Deambi S. (1992) Battery storage for PV power systems: an overview. Renewable Energy. 2 (3), 227–235.

Cheney W. and Kincaid D. (1985) Numerical Mathematics and Computing, 2nd edn. Brooks/Cole Publishing Co., Monterey, California.

Culp A. W. (1991) Principles of Energy Conversion, 2nd edn. McGraw-Hill, Inc., London.

194

Del Toro V. (1986) Electrical Engineering Fundamentals, 2nd edn. Prentice Hall International (UK) Limited, London.

Dessus B., Devin B., and Pharabod F. (1992) Le potential mondial des energies renouvelables. La Houile Blanche No. 1.

Dienhart H., Hille G. Hug W., Kürsten T., and Steinborn. F (1993) Hydrogen storage in isolated grids with wind energy–electrolyzer technology and economics. In Proceedings of 1993 European Community Wind Energy Conference, pp. 334–338, March 8–12, Lübeck, H. S. Stephens & Associates, Bedford, UK.

Divisek J. (1990) Water electrolysis in low– and medium temperature regime. In Electrochemical Hydrogen Technologies—Electrochemical Production and Combustion of Hydrogen, Wendt H. (Ed), pp. 137–212, Elsevier Science Publishing Co., Inc., Oxford.

Duffie J. A. and Bechman W. A. (1991) Solar Engineering of Thermal Processes, 2nd edn. John Wiley & Sons, Inc., New York.

Dunlop J. D. (1995) Nickel-hydrogen batteries. In Handbook of Batteries, Linden D. (Ed), pp. 32.1–32.30, 2nd edn. McGraw-Hill, Inc., London.

Dutton A. G., Rudell A. J., Dienhart H., Hug W., Seeger W., and Bleijs J. A. M. (1996) Electrolyzer and system operation in wind/hydrogen electrolyzer systems. In Proceedings of 1996 European Community Wind Energy Conference, pp. 357–360, May 20–24, Göteborg, H. S. Stephens & Associates, Bedford, UK.

Eckstein J. H. (1990) Detailed Modelling of Photovoltaic System Components, M.Sc. thesis, University of Wisconsin–Madison, U.S.A.

El-Wakil M. M. (1984) Powerplant Technology. McGraw-Hill Publishing Co., London.

Eriksen J. (1998) Development of a data acquisition and control system for a small-scale PV–H2 system. In Proceedings of the 12th World Hydrogen Energy Conference, Bolcich J. C. and Veziroglu T. N.(Eds), pp.195–203 (Vol. 1), June 21–26, Buenos Aires, Argentina.

Fahrenbruch A. L. and Bube R. H. (1983) Fundamentals of Solar Cells—Photovoltaic Solar Energy Conversion. Academic Press Ltd., London.

Flavin C. and O’Meara M. (1997) Financing solar electricity—the off-the-grid revolution goes global. World Watch, 10 (3), 28–36.

Fukai Y. (1993) The Metal-Hydrogen Systems: Basic Bulk Properties. Springer-Verlag, Berlin.

Galli S. (project leader), Stefanoni M., Borg P., Brocke W. A., and Mergel J. (1997) Development and Testing of a Stand-Alone Small-Size Solar Photovoltaic–Hydrogen Power System (SAPHYS), Report no. JOU2-CT94-0428, JOULE II–Programme, Directorate General XII: Science, Research and Development, European Commission, Brussels, Belgium.

Gfe (1995) Operational and Maintenance Guide for Metal Hydride Storage Container SW1-C15. Gesellschaft für Elektrometallurgie mbH, Nürnberg, Germany.

References

195

Ginn J. W., Bonn R. H., and Sittler G. (1997) Inverter testing at Sandia National Laboratories. In Proceedings of the 14th NREL/SNL Photovoltaic Program Review Meeting, 394 (1), pp. 335–345, November 18-22, 1996, Lakewood, Colorado, AIP Press, New York.

Grasse W., Oster F., and Aba-Oud H. (1992) HYSOLAR: the German–Saudia Arabian program on solar hydrogen—5 years of experience. Int. J. Hydrogen Energy 17 (1), 1–7.

Green M. A., Emery K, Bücher K, King D. L., and Igari S (Eds) (1997) Solar cell efficiency tables (version 9). Progress in Photovoltaics: Research and Applications, 5, 51–54.

Green M. A. (1995) Silicon Solar Cells—Advanced Principles & Practices. Bridge Printery Pty. Ltd., Rosebery, New South Wales, Australia.

Green M. A. (1993) Crystalline- and polycrystalline-silicon solar cells. In Renewable Energy—Sources for Fuels and Electricity, Johansson T. B., Kelly H., Reddy K. A. N., Williams R. H. , and Burnham L. (Eds), pp. 337–360. Earthscan Publications Ltd., London.

Green M. A. (1982) Solar Cells—Operating Principles, Technology, and System Applications. Prentice Hall, New Jersey.

Groehn H. G. (1995) Determination of Cell Parameters for the I–U Characteristic ‘IEV102…IEV115’ for the Two-Diode Model (in German). Report no. IB-3-96, IEV-95-Gh. FZ Jülich, Germany.

Griesshaber W. and Sick F. (1991) Simulation of Hydrogen-Oxygen–Systems with PV for the Self-Sufficient Solar House (in German). FhG–ISE, Freiburg im Breisgau, Germany.

Grubb M. J. and Meyer N. I. (1993) Wind energy: resources, systems, and regional strategies. In Renewable Energy—Sources for Fuels and Electricity, Johansson T. B., Kelly H., Reddy K. A. N., Williams R. H. , and Burnham L. (Eds), pp. 157–212. Earthscan Publications Ltd., London.

Haas A., Luther J., and Trieb F. (1991) Hydrogen energy storage for an autonomous renewable energy system—Analysis of experimental results. In Proceedings of the ISES 1991 Solar World Congress, pp. 723–728, Denver, Colorado.

Hagström M. T., Lund P. D., and Vanhanen J. P. (1995) Metal hydride hydrogen storage for near-ambient temperature and atmospheric applications, a PDSC study. Int. J. Hydrogen Energy 20 (11), 897–909.

Hall D. O., Rosillo-Calle F., Williams R. H., and Woods J. (1993) Biomass for energy: supply prospects. In Renewable Energy—Sources for Fuels and Electricity, Johansson T. B., Kelly H., Reddy K. A. N., Williams R. H. , and Burnham L. (Eds), pp. 594–651. Earthscan Publications Ltd., London.

Harvey A. (1995) Renewable energy technologies in developing countries. In The World directory of Renewable Energy Suppliers and Services 1995, Cross B. (Ed), pp. 23–25. James & James Science Publishers Ltd., London.

Havre K., Borg P. Tømmerberg K (1995) Modeling and control of pressurized electrolyzer for operation in stand alone power systems. In: Proceedings of the 2nd Nordic Symposium on

196

Hydrogen and Fuel Cells for Energy Storage, Lund P. D. (Ed), pp. 63–78, January 19–20, Helsinki.

Havre K., Gaudernack B., Alm L. K., Nygaard T. A. (1993) Stand-Alone Power Systems based on renewable energy sources. Report no. IFE/KR/F-93/141, Institute for Energy Technology, Kjeller, Norway.

Herrmann J. (1992) The nature of our planet. In: The Great World Atlas, Benson V. (Ed). American Map Corporation, New York.

Heuts G. (1995) Results from battery experiments (Communicated by Brocke, 1996), FZ Jülich.

Hug W., Divisek J., Mergel J., Seeger W., and Steeb H. (1992) Highly efficient advanced alkaline electrolyzer for solar operation. Int. J. Hydrogen Energy, 17 (9), 699–705.

Hug W., Bussmann H., and Brinner A. (1993) Intermittent operation and operation modeling of an alkaline electrolyzer. Int. J. Hydrogen Energy, 18 (12), 973–977.

Hund T. (1997) Battery testing for photovoltaic applications. In Proceedings of the 14th NREL/SNL Photovoltaic Program Review Meeting, 394 (1), pp. 379–393, November 18-22, 1996, Lakewood, Colorado, AIP Press, New York.

Hyman E., Spindler W. C., and Fatula J. F. (1986) Phenomenological discharge voltage model for lead-acid batteries. In Proceedings of AIChe Meeting—Mathematical Modeling of Batteries. November 1986.

IPCC (1995) Climate Change 1995: The Science of Climate Change Contribution of Working Group I to the Second Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, New York.

Imamura M. S., Helm P., and Palz W. (1992) Photovoltaic System Technology—A European handbook. H S Stephens & Associates, Bedford, UK.

Incropera F. P. and DeWitt D. P. (1990) Fundamentals of Heat and Mass Transfer. 3rd edn. John Wiley & Sons, New York.

Jenkins B. M. (1989) Physical properties of biomass. In: Biomass Handbook, Kitani O and Hall C. W. (Eds). Gordon and Breach, New York.

Khaselev O. and Turner J. A. (1998) A monolithic photovoltaic-photoelectrochemical device for hydrogen production via water splitting. Science, 280 (April 17), 425–427.

Klein S. A., Beckman W. A. and Duffie J. A. (1994) TRNSYS—A Transient System Simulation Program. Program Manual, Version 14.1. Solar Energy Laboratory, University of Wisconsin.

Kordesch K. and Simader G. (1996) Fuel Cells and their Applications. VCH Publishers, Inc., Cambridge.

References

197

Koryta J., Dvorák J. and Kavan L. (1993) Principles of Electrochemistry, 2nd edn. John Wiley & Sons Ltd., Chichester.

Lasdon L. and Waren A. (1995) The GRG2 Solver Algorithm. User Manual for Microsoft Excel for Windows 95. Version 7.0a. Microsoft Corporation.

Laukamp H. (1988) Inverter for Photovoltaic systems (in German). User-written TRNSYS source code. Fraunhofer Institut für Solare Energiesysteme, Freiburg im Breisgau, Germany.

Ledjeff K., Heinzel A., Peinecke V., and Mahlendorf F. (1994) Development of pressure electrolyzer and fuel cell with polymer electrolyte. Int. J. Hydrogen Energy, 19 (5), 453–455.

Lehman P. A., Chamberlin C. E., Pauletto G., and Rocheleau M. A. (1994) Operating experience with a photovoltaic hydrogen energy system. In Proceedings of the 10th World Hydrogen Energy Conference, Block D. L. and Veziroglu T. N., pp. 411–420, June 20–24, Cocoa Beach, Florida.

Linden D. (Ed.) (1995) Handbook of Batteries. 2nd edn. McGraw-Hill, Inc., London.

Loferski J. J. (1972) An introduction to the physics of solar cells. In Solar Cells—Outlook for Improved Efficiency, pp. 47–53, National Academy of Sciences–Space Science Board, Washington, DC.

Manwell J. F. et al. (1996) Hybrid2 : Theory Manual. Renewable Energy Research Laboratory, University of Massachusetts, Amherst, U.S.A.

Manwell J. F., McGowan J. G., Baring-Gould I., and Stein W. (1995) Recent progress in battery models for hybrid wind power systems. In Proceedings of 1995 AWEA Annual Conference, Palm Springs, California.

Manwell J. F. and McGowan J. G. (1993) Lead acid battery storage model for hybrid energy systems. Solar Energy, 50 (5), 399–405.

Mathews J. H. (1992) Numerical Methods for Mathematics, Science, and Engineering, 2nd edn. Prentice-Hall, New Jersey.

Mayer O. (1996) DASTPVPS Simulation Tool Manual, Universität der Bundeswehr München, Neubiberg, Germany.

Menictas C., Hong D. R., Yan Z. H., Wilson J., Kazacos M., and Skyllas- Kazacos M. (1994) Status of the vanadium redox battery development program. In Proceedings of Electrical Engineering Congress '94, pp. 299–306, Sydney, Australia.

Mergel J. (1996) FZ Jülich, personal communication (in situ).

Mergel J. (1997) FZ Jülich, personal communication (telephone).

Mergel J. and Barthels H. (1996) Design, Construction and Commissioning of an Advanced 26 kW Water Electrolyser. Information sheet. FZ Jülich.

198

Moreira J. R. and Poole A. D. (1993) Hydropower and its constraints. In Renewable Energy—Sources for Fuels and Electricity, Johansson T. B., Kelly H., Reddy K. A. N., Williams R. H. , and Burnham L. (Eds), pp. 73–119. Earthscan Publications Ltd., London.

Murray R. L. (1993) Nuclear Energy: An introduction to the Concepts, Systems, and Applications of Nuclear Processes. 4th edn. Pergamon Press, Oxford.

Mørner S. O. (1995) Seasonal Storage of Solar Energy for Self-Sufficient Buildings with Focus on Hydrogen Systems. Ph.D. thesis. Norwegian University of Science and Technology, Trondheim.

NAS (1969) Resources and Man: A study and recommendations by the Committee on Resources and Man of the Division of Earth Sciences, National Academy of Sciences. Freeman, San Francisco.

Nitsch J. and Voigt C. (1988) Design of a future hydrogen energy economy. In Hydrogen as an energy carrier—Technologies, Systems, Economy, Winter C.-J. and Nitsch J. (Eds), pp. 291–267. Springer-Verlag, London.

Ogden J. M. and Williams R. H. (1989) Solar Hydrogen—Moving Beyond Fossil Fuels. World Resources Institute, Washington, District of Columbia.

Ohta T. (1994) Energy Technology—Sources, Systems, and Frontier Conversion. Elsevier Science Ltd., Oxford.

Ohta T. (Ed) (1979) Solar-Hydrogen Energy Systems—An Authoritative Review of Water-Splitting Systems by Solar Beam and Solar Heat, Hydrogen Production, Storage and Utilisation, Pergamon, Oxford.

Oldham H. B. and Myland J. C. (1994) Fundamentals of Electrochemical Science. Academic Press Ltd., London.

Page J. K. (1964) The estimation of monthly mean values of daily total short-wave radiation of vertical and inclined surfaces from sunshine records for latitudes 40°N–40°S. Proceedings of the UN conference on new sources of energy, 4, p378.

Palmerini C. G (1993) Geothermal energy. In Renewable Energy—Sources for Fuels and Electricity Johansson T. B., Kelly H., Reddy K. A. N., Williams R. H., and Burnham L. (Eds), pp. 549–591. Earthscan Publications Ltd., London.

Peschka W. (1988) Hydrogen energy applications engineering. In Hydrogen as an energy carrier—Technologies, Systems, Economy, Winter C.-J. and Nitsch J. (Eds), pp. 30–55. Springer-Verlag, London.

Pleym H. (1992) Global Environmental Problems and Atmospheric Connections. Lecture notes in Fag 62023–Energy Technology, Norwegian University of Science and Technology, Trondheim.

Protogeropoulos C. (1996) Center for Renewable Energy Sources, Pikermi, Greece, personal communication (letter).

References

199

Protogeropoulos C., Marshall R. H., and Brinkworth B. J. (1994) Battery state of voltage modelling and an algorithm describing dynamic conditions for long-term storage simulation in a renewable system. Solar Energy, 53 (6), 517–527.

Rauschenbach H. S. (1980) Solar Cell Array Design Handbook: the Principles and Technology of Photovoltaic Energy Conversion, Van Nostrand Reinhold, New York.

Reilly J. J. (1977) Metal hydrides as hydrogen energy storage media and their application. In Hydrogen: Its Technology and Implications, Cox K. E. and Wiliamson K. D. (Eds), Vol. II, pp. 13–48, CRC Press, Cleveland.

Rodriguez N. M., Terry R., and Baker K. (1997) Storage of Hydrogen in Layered Nanostructures. United States Patent No. 5,653,951 (August 5, 1997).

Roger J. A. and Maguin C. (1982) Photovoltaic solar panels including dynamic thermal effects, Solar Energy 29, 245–256.

Rosa F. Lopéz E., García-Conde A. G. Luque R., and del Pozo F. (1994) Intermittent operation of a solar hydrogen production facility: yearly evaluation. In Proceedings of the 10th World Hydrogen Energy Conference, Block D. L. and Veziroglu T. N.(Eds), pp. 421–430, June 20–24, Cocoa Beach, Florida.

Roušar I. (1989) Fundamentals of electrochemical reactors. In Electrochemical Reactors: Their Science and Technology Part A, Ismail M. I. (Ed), Chapter 2, Elsevier Science Publishers B. V., Amsterdam.

Sandstede G. (1989) Moderne elektrolyseverfahren für die wasserstoff-technologie. Chem. Ing. Tech. 61, 349–361.

Saupe G. (1993) Photovoltaic Power Supply System with Lead-Acid Battery Storage: Analysis of the Main Problem, System Improvements, Development of a Simulation Model for a Battery (in German). Ph.D. Thesis, University of Stuttgart, Germany.

Selvam P. (1992) Alcohol fuels—the question of their introduction: a comparison with conventional vehicular fuels and hydrogen. Int. J. Hydrogen Energy 17 (3), 237–242.

Serway R. A. (1990) Physics for Scientists and Engineers. 3rd edn. Saunders College Publishing, London.

Schulien S. and Steinmetz M. (1990) Optimierung eienes energiversorgungssystem auf der basis von windenergie und wasserstoff, Tagungsbericht Internationales Sonnenforum, 2, 1464–1469, Frankfurt, Germany.

Schumacher-Gröhn J. (1991) Digital Simulation of Regenerative Electrical Energy Supply Systems (in German). Ph.D. thesis, University of Oldenburg, Germany.

Schöner H. P. (1988) Evaluation of the Electrical Behavior of Lead-Batteries during Discharging and Charging (in German). Ph.D. thesis, Technical University of Aachen, Germany.

200

Scott D. S. and Häfele W. (1990) The coming hydrogen age: preventing world climatic disruption. Int. J. Hydrogen Energy 15, 727–737.

Shepherd C. M. (1965) Design of primary and secondary cells—An equation describing battery discharge. J. Electroch. Society 112 (7), 657–664.

Smithrick J. J. and O’Donnell P. (1995) A review of nickel hydrogen battery technology. In Proceedings of 30th Intersociety Energy Conversion Engineering Conference, pp. 123–130, Orlando, Florida, ASME, New York.

Snyman D. B. and Enslin J. H. R. (1993) An experimental evaluation of MPPT converter topologies for PV installations. Renewable Energy 3 (8), 841–848.

Stoecker W. F. (1989) Design of Thermal Systems, 3rd edn. McGraw-Hill Book Co., London.

Streeter V. L. and Wylie E. B. (1985) Fluid Mechanics. 8th edn. McGraw-Hill Book Co., London.

Szyszka A. (1992) Demonstration plant, Nurnburg Vorm Wald, Germany, to investigate and test solar-hydrogen technology. Int. J. Hydrogen Energy 17 (7), 485–498.

Tilak B. V., Yeo R. S., and Srinivasan S. (1981) Electrochemical energy conversion—principles. In Comprehensive Treatise of Electrochemistry. Volume 3: Electrochemical Energy Conversion and Storage, Bockris J. O’M., Conway B. E., Yeager E., and White R. E. (Eds), pp. 39–122. Plenum Press, New York.

Townsend T. U. (1989) A Method for Estimating the Long-term Performance of Direct-Coupled Photovoltaic Systems, M.Sc. thesis, University of Wisconsin–Madison, U.S.A.

Trieb F. X. (1991) Hydrogen–Energy Storage for an Autonomous Electrical Energy Supply Systems based on Renewable Sources (in German). Ph.D. thesis, University of Oldenburg, Germany.

Twidell J. W. and Weir A. D. (1986) Renewable Energy Resources. E. & F. N. Spon Ltd., London.

Ulleberg Ø. (1997) Simulation of autonomous PV–H2 systems: analysis of the PHOEBUS plant design, operation and energy management. In Proceedings of ISES 1997 Solar World Congress, August 24–29, Taejon, Korea.

Ulleberg Ø. and Mørner S. O. (1997) TRNSYS simulation models for solar-hydrogen systems. Solar Energy 59 (4–6), 271–279.

Ulleberg Ø. and Tallhaug L. (1997) Simulation of stand alone power systems: case study of a small scale hybrid PV, wind – diesel system located on the west coast of Norway. In Proceedings of the 7th International Conference on Solar Energy at High Latitudes, Konttinen P. and Lund P. D. (Eds), Vol. 1, pp. 242–249, June 9–11, Espoo-Otaniemi, Finland.

UNESCO (1977) Atlas of World Water Balance. Explanatory text, UNESCO, Paris.

References

201

Vanhanen J. P., Lund P. D., and Tolonen J. S. (1998) Electrolyzer–metal hydride–fuel cell system for seasonal energy storage. Int. J. Hydrogen Energy 23 (4), 267–271.

Vanhanen J. (1992) H2 – design Tool 1.0 for Solar-Hydrogen Energy Systems. Report TKK-F-A701. Helsinki University of Technology, Otaniemi, Finland.

Vanhanen J. (1996) On the Performance Improvements of Small-Scale Photovoltaic–Hydrogen Energy Systems. Ph.D. thesis. Helsinki University of Technology, Espoo, Finland.

Vanhanen J., Lund P. D., and Hagström M. T. (1996) Feasibility study of a metal hydride store for a self-sufficient solar hydrogen energy system. Int. J. Hydrogen Energy 21 (3), 213–221.

Verfondern K. (1997) Considerations on Hydrogen as a Future Energy Carrier and its Production by Nuclear Power. Report no. FZJ-ISR-IB-9/97, FZ Jülich.

Veziroglu T. N. and F. Barbir (1992) Hydrogen: the wonder fuel. Int. J. Hydrogen Energy 17 (6), 391–404.

Voss K., Goetzberger A., Boop G., Häberle A., Heinzel A., and Lehmberg H. (1996) The self-sufficient solar house in Freiburg—Results of 3 years of operation. Solar Energy 58 (1–3), 17–23.

Warne D. F. (1983) Wind Power Equipment. E. & F. N. Spon Ltd., London.

Wendt H. and Plzak H. (1991) Hydrogen production by water electrolysis. Kerntechnik 56 (1), 22–28.

Wendt H. and Rohland B. (1991) Electricity generation by fuel cells. Kerntechnik 56 (3), 161–166.

Wendt H. (1988) Water–splitting methods. In Hydrogen as an Energy Carrier—Technologies, Systems, Economy, Winter C.-J. and Nitsch J. (Eds), pp. 166–208. Springer-Verlag, London.

Wilk H. and Panhuber C. (1995) Power conditioners for grid interactive PV systems. What is the optimal size: 50 W or 500 kW? In Proceedings of the 13th European Photovoltaic Solar Energy Conference, 23–27 October, Nice, France.

Wilson R. E. (1994) Aerodynamic behavior of wind turbines. In Wind Turbine Technology—Fundamental Concepts of Wind Turbine Engineering, Spera D. A. (Ed), pp. 215–282. ASME Press, New York.

Winter C. J. and Nitsch J. (1989) Hydrogen energy—a 'sustainable development' towards a world energy supply system for future decades. Int. J. Hydrogen Energy 14, 785–796.

WCED (1987) Our Common Future. Oxford University Press, Oxford.

WMO (1985) Solar Radiation and Radiation Balance Data (The World Network). (Annual data compilations, 1964–1985), World Radiation Data Centre, A. I. Voeikov Main Geophysical Observatory, St. Petersburg.

202

Zimmerman H. G. and Peterson R. G. (1978) An electrochemical cell equivalent circuit for storage battery/power systems calculations by digital computer. In Proceedings of the 13th Intersociety Energy Conversion, pp. 33–38.

Zumdahl S. S. (1995) Chemical Principles. 2nd edn. D. C. Heath and Company, Toronto.

Zweibel K. and Barnett A. M. (1993) Polycrystalline thin-film photovoltaics. In Renewable Energy—Sources for Fuels and Electricity Johansson T. B., Kelly H., Reddy K. A. N., Williams R. H., and Burnham L. (Eds), pp. 437–481. Earthscan Publications Ltd., London.

Zweibel K. (1990) Harnessing Solar Power—The Photovoltaic Challenge. Plenum Press, New York.

APPENDIX

ELEMENTS

Table of elements referred to in the thesis.

Element Symbol Atomic Number

Atomic Weight

Aluminum Al 13 26.98 Antimony Sb 51 121.8 Arsenic As 33 74.92 Bromine Br 35 79.90 Cadmium Cd 48 112.4 Calcium Ca 20 40.08 Carbon C 6 12.01 Cerium Ce 58 140.1 Chlorine Cl 17 35.45 Cobalt Co 27 58.93 Copper Cu 29 63.55 Gallium Ga 31 69.72 Helium He 2 4.003 Hydrogen H 1 1.008 Indium In 49 114.8 Iron Fe 26 55.85 Lead Pb 82 207.2 Lithium Li 3 6.941 Nickel Ni 28 58.69 Nitrogen N 7 14.01 Oxygen O 8 16.00 Platinum Pt 78 195.1 Plutonium Pu 94 (239.1) Selenium Se 34 78.96 Silicon Si 14 28.09 Silver Ag 47 107.9 Sodium Na 11 22.99 Sulfur S 16 32.07 Tellurium Te 52 127.6 Thorium Th 90 232.0 Tin Sn 50 118.7 Uranium U 92 238.0 Vanadium V 23 50.94 Zinc Zn 30 65.39 Zirconium Zr 40 91.22

204

SUBSTANCES

Table of some of the substances referred to in the thesis.

Substance Symbol State at standard conditions*

Cadmium telluride CdTe s Carbon dioxide CO2 g Carbon monoxide CO g Ethane C2H6 g Ethanol CH3CH2OH l Gallium arsenide GaAs s Hydrogen H2 g Methane CH4 g Methanol CH3OH l Nitrogen N2 g Nitrous oxide N2O g n-Butane C4H10 g Oxygen O2 g Ozone O3 g Potassium hydroxide KOH l Propane C3H8 g Sodium hydroxide NaOH l Sulfuric acid H2SO4 l Water H2O l * Standard conditions: T = 25°C, p = 1 atm l = liquid, g = gas, s = solid

FUNDAMENTAL CONSTANTS

Table of fundamental constants used in thesis.

Description Symbol Value

Avogadro constant NA 6.022 137 × 1023 mol-1 Boltzmann constant kB = R/NA 1.380 658 × 10-23 J K-1 Faraday constant F 96,485.309 C mol-1 Permeability of a vacuum µ0 4π × 10-7 kg m s-2 A-2 Permittivity of a vacuum ε0 8.854 188 × 10-12 kg-1 m-3 s4

A2 Planck constant h 6.626 076 × 10-34 J s Speed of light in vacuum c0 2.997 925 × 108 m s-1 Standard acceleration of gravity g 9.806 65 m s-2 Stefan-Boltzmann constant σ 5.6697 × 10-8 W K-4 m-2 Universal gas constant R 8.314 510 J K-1 mol-1

Appendix

205

UNIT CONVERSION FACTORS

Table of some useful unit conversion factors used in thesis. Energy Pressure 1 eV = 1.602 × 10-

19 J 1 atm = 1.01325 × 105 Pa

1 kWh = 3.60 × 106 J 1 atm = 10.34 m H2O 1 cal = 4.1868 J 1 bar = 1 × 105 Pa Mass Area 1 t = 1000 kg 1 hectare = 1 × 104 m2

FORMULAS

The formulas for the root mean square (RMS), absolute error, and mean error are given below in Equations A.1–A.3.

Root mean square (RMS):

( )

RMS =-1

i i=1

$y y

ni

n

−∑ 2

A.1

Absolute error (in percent):

ε = i i

i

$y yy− ×100 A.2

Mean error:

ε ε=n

A.3

where

$yi predicted value of sample i yi measured value of sample i n total number of samples

For nonlinear curve fits, the RMS method is used in connection with a generalized reduced gradient (GRG) nonlinear optimization algorithm developed by Lasdon and Waren (1995).

206

PARAMETERS

Below is a list of the parameters of the equations of the main component models developed in Chapter 4, verified in Chapter 5, and used in the system simulations in Chapter 6.

PV-model

The PV parameters below are for a single PV module (150 cells in series) of the PV1-array in PHOEBUS.

One-diode model (Equation 4.2)

Tc,ref 25 °C GT,ref 1000 W m-2 Isc,ref 2.664 A Uoc,ref 87.720 V Imp 2.448 A Ump 70.731 V µI,sc 0.00148 A K-1 µU,oc -0.3318 V K-1 Ta,NOC

T 20 °C

Tc,NOC

T 44 °C

GT,NO

CT 800 W m-2

Thermal constants (Equation 4.14)

Cc 30 J K-1 m-2 UL 50,000 J m-2

Two-diode model (Equation 4.21)

a1 1 V J-1 a2 2 V J-1 k0 0.002631 A W-1 m2 k1 690 k2 0.014 β0 5.59e-4 °C-1 Rs 0.0145 Ω Rp 10 Ω egap 1.17 eV

Detailed thermal model (Equation 4.25)

a 0.711 °C b 0.0056 c 0.000073 °C-1 d 0.013 °C a1 1.247 W K-1 m-2

b1 3.81 s m-1

Electrolyzer

The electrolyzer I–U parameters below are for a single cell (of the 21 cells connected in series) in the electrolyzer at PHOEBUS. The thermal parameters are for the electrolyzer as a whole.

I–U curve (Equation 4.46)

r1 7.331e-5 Ω m2 r2 -1.107e-7 Ω m2 °C-1 r3 0 s1 1.586e-1 V s2 1.378e-3 V °C-1 s3 -1.606e-5 V C-2 t1 1.599e-2 m2 A-1 t2 -1.302 m2 A-1 °C-1 t3 4.213e2 m2 A-1 °C-2 A 0.25 m2

Faraday efficiency (Equation 4.48)

a1 99.5 % a2 -9.5788 m2 A-1 a3 -0.0555 m2 A-1 °C-1 a4 0 a5 1502.7083 m4 A-1 a6 -70.8005 m4 A-1 C-1 a7 0

Thermal model (Equation 4.51)

Rt 0.167 K W-1 τt 29 h aconv 3.0 W K-1 acond 0.0350 W K-1 A-1

Fuel Cell

The fuel cell parameters below are for a single fuel cell (of the 26 cells placed in series per stack) in the PEMFC-stack at PHOEBUS. The parameters given here are for a high and low temperature. A linear interpolation to find the parameters for

Appendix

207

operation between these temperatures can be used (Equation 4.75).

T = 70°C

Uo 1065 mV b 80 mV dec-1 R 0.438 Ω cm2

T = 35°C

Uo 1049 mV b 108 mV dec-1 R 0.412 Ω cm2 A 300 cm2

Battery

The battery parameters below are for a single cell (of the 110 cells placed in series) in the Pb-accumulator at PHOEBUS (Equations 4.85–4.93). g0 1.6e-6 g1 0.0812 V g2 6000 K Uequ,0 1.997 V Uequ,0 0.1464 V dec-1 Udch -0.02703 bdch 0.4085 cdch 0.5610 g100 2.36 k100 53 Qbat,no

m 1,380 Ah

Power Conditioning Equipment

The curve fitting of the parameters in the equation for the power conditioning equipment used in PHOEBUS was based on fixed output voltages Uout. Specifically, Uout = 230 V was assumed for the MPPTs, the DC/DC-converter for the fuel cell, and the DC/AC-inverter for the user load, while a Uout = 35 V was assumed for the

DC/DC-converter for the electrolyzer (Equation 4.95).

MPPT for PV1

Po 2.489e-3 W Us 18.72 V Ri 1316.89 Ω Pnom 10 kW

MPPT for PV2

Po 2.773e-3 W

Us 19.29 V Ri 950.86 Ω Pnom 10 kW

MPPT for PV3


MPPT for PV4

Po 3.736e-3 W

Us 18.71 V Ri 1392.86 Ω Pnom 12 kW

DC/DC-converter for Electrolyzer


DC/DC-converter for Fuel Cell

Po 1.474e-3 W Us 19.25 V Ri 1362.76 Ω Pnom 6.5 kW

DC/DC-inverter for Auxiliary Load


208

NOMENCLATURE

Most of the symbols used in the thesis are defined locally. This Table of Nomenclature lists for clarity all of the symbols used in the thesis, and should be used if there is confusion about the significance of any of the symbols. A area (m2) a photovoltaic model curve fitting parameter, wave amplitude (m), activity,

empirical parameter, constant B magnetic flux density (T = Wb m-2 = Vs m-2 = kg A-1 s-2) b empirical parameter, constant, Tafel slope (V dec-1), Weibull parameter C electrical capacitance (F = C V-1), battery capacity (Ah) Cp specific heat (J K-1 mol-1) Cp,max Betz limit Ct thermal capacitance (J K-1) c molar concentration (mol m-3), speed of light, empirical parameter, constant d empirical parameter, constant E energy (J), electric field strength (N C-1 = V m-1), electromotive force (V) Elymode electrolyzer mode egap energy band gap of material (eV) F force (N), Helmholtz function (J), Faraday constant (C mol-1) f pressure level (0–1), empirical coefficient, function G Gibbs energy (J), irradiance (W m-2) GT instantaneous solar radiation (irradiance) on a tilted surface (W m-2) g gravitational acceleration (m s-2), empirical parameter H enthalpy (J), magnetic field strength (A m-1), daily solar radiation (J m-2) H0 daily extraterrestrial solar radiation (J m-2) h height (m), molar enthalpy (J mol-1), heat transfer coefficient (W m-2 K-1) HHV higher heating value (kJ -1

fuelkg ) I electric current (A), moment of inertia (kg m2) i current density (A m-2), instantaneous current (A) i0 Tafel parameter K chemical equilibrium constant Ks Sieverts constant k spring constant (N m3), Boltzmann constant, proportionality factor, parameter kT clearness index (hourly average) KE kinetic energy (J) L inductance (H = Vs A-1 = Wb A-1 = kg m2 s-2 A-2) LHV lower heating value (kJ -1

fuelkg ) LMTD log mean temperature difference (K) M molecular weight (g mol-1), molarity of solute m mass (kg) ME mechanical energy (J) Ns number of photovoltaic cells in series n amount of substance (mol), polytropic coefficient, neutron nc number of electrolyzer cells in series n& molar flow (mol s-1)

Appendix

209

P power (W) P average power (W) p pressure (Pa = N m-2 = kg m-1 s-2) PE potential energy (J) Q thermal energy (J), electrical charge (C = As), reaction quotient Q& heat transfer rate (W) Qbat battery capacity (Ah) q electric charge (C = As) R electrical resistance (Ω), tidal range (m), universal gas constant, Rt thermal resistance (K W-1) r empirical coefficient or parameter for ohmic resistance, radius (m) S entropy (J K-1) SOC battery state of charge (%) s empirical coefficient T temperature (K), periodic time (s) t time (s), empirical coefficient U electrical potential or voltage (V), internal energy (J) Urev reversible voltage (thermodynamic constant) (V) UL overall heat loss coefficient (W m-2 K-1) UAHX overall heat transfer coefficient area product in heat exchanger (W K-1) V volume (m3), voltage (V), v velocity (m s-1), frequency (Hz = s-1) vc characteristic wind speed (m s-1) W work (J), energy density (J m-3) w specific work (J kg-1), molar energy (J mol-3) x molar ratio or concentration, displacement (m) z electrical charge number, relative elevation (m) Greek Letters

α absorptance, empirical constant β slope of surface β0 temperature coefficient γ switch variable (0 or 1), specific weight (kg m-2 s-2) ∆ difference, hysteresis ε error (%), emittance η efficiency (0–1) λ wavelength (m), tip-speed ratio µ chemical potential (J mol-1), permeability (H m-1), temperature coefficient Π osmotic pressure (Pa) ρ density (kg m-3) τ transmittance, intertidal period (s) τt thermal time constant (s) φ relative humidity (%) ω angular velocity (rad s-1) Ω number of microstates

210

Subscripts

a ambient, atomic B Boltzmann b back, busbar, boundary,

black body, binding bat battery c cell ch charging chem chemical cond conduction comp compression conv convection cr critical cw cooling water D dark dch discharge dp dew point e energy, electrical EL, ely electrolyzer equ equilibrium F Faraday, final, factor f front, formation, final fg fluid to gas FC fuel cell g gravitational gas gassing gen generated H high HX heat exchanger I current, initial i input, initial, internal,

species, ignition idle idling in input ini initial L light, low, loss low lower m magnetic min minimum mp maximum power MPPT maximum power point

tracker n number, neutron nom nominal norm normalized NOCT nominal operating cell

temperature o output, open circuit, overall,

extraterrestrial oc open circuit out output P products p pressure, peak, proton pol polarization q charging R reactants r rated, rotational ref reference conditions rev reversible process s series, sky, splitting, spring,

set point, sc short circuit sh shunt sp set point stoich stoichiometric surr surroundings sys system T tilted t thermal, translating therm thermal tn thermoneutral U voltage up upper x substance, molar

concentration 0 0 % state of charge,

ambient 10 10-hour discharge 100 100 % state of charge

Superscript

° standard state

Appendix

211

END OF DOCUMENT

stand-alone power systems for the future: s3. · pdf filethe work of this thesis is divided...

Documents