Photovoltaic Modeling Handbook

This book provides the reader with a solid understanding of the fundamental modeling of photovoltaic devices. After the material independent limit of photovoltaic conversion, the readers are introduced to the most well-known theory of "classical" silicon modeling. Based on this, for each of the most important PV materials, their performance under different conditions is modeled. This book also covers different modeling approaches, from very fundamental theoretic investigations to applied numeric simulations based on experimental values. The book concludes wth a chapter on the influence of spectral variations. The information is supported by providing the names of simulation software and basic literature to the field.

The information in the book gives the user specific application with a solid background in hand, to judge which materials could be appropriate as well as realistic expectations of the performance the devices could achieve.

Monika Freunek (Müller), studied Mechatronic and Product Engineering at the Universities of Applied Sciences of Bielefeld and Furtwangen, Germany from 2002-2006. After graduation and postdoctoral research at IBM Research Zurich, she worked as a researcher and co-founder of a start-up. Monika Freunek is now at BKW, Switzerland, as an energy specialist. Her main focus in research is modeling of energy and photovoltaic systems under different application conditions. She is an expert in indoor photovoltaics.

Preface xiii

1 Introduction 1
Monika Freunek Müller

2 Fundamental Limits of Solar Energy Conversion 7
Thorsten Trupke and Peter Würfel

2.1 Introduction 8

2.2 The Carnot Efficiency – A Realistic Limit for PV Conversion? 8

2.3 Solar Cell Absorbers – Converting Heat into Chemical Energy 10

2.4 No Junction Required – The IV Curve of a Uniform Absorber 12

2.5 Limiting Efficiency Calculations 15

2.6 Real Solar Cell Structures 19

2.7 Beyond the Shockley Queisser Limit 20

2.8 Summary and Conclusions 22

Acknowledgement 23

References 24

3 Optical Modeling of Photovoltaic Modules with Ray Tracing Simulations 27
Carsten Schinke, Malte R.Vogt and Karsten Bothe

3.1 Introduction 28

3.1.1 Terminology 30

3.2 Basics of Optical Ray Tracing Simulations 32

3.2.1 Ray Optics 32

3.2.1.1 Basic Assumptions 33

3.2.1.2 Absorption of Light 33

3.2.1.3 Refraction of Light at Interfaces 34

3.2.1.4 Modeling of Thin Films 35

3.2.2 Ray Tracing 37

3.2.3 Monte-Carlo Particle Tracing 38

3.2.4 Statistical Uncertainty of Monte-Carlo Results 40

3.2.5 Generating Random Numbers with Non-Uniform Distributions 42

3.3 Modeling Illumination 46

3.3.1 Basic Light Sources 46

3.3.2 Modeling Realistic Illumination Conditions 48

3.3.2.1 Preprocessing of Irradiance Data 49

3.3.2.2 Implementation for Ray Tracing 50

3.3.2.3 Application Example 52

3.4 Specific Issues for Ray Tracing of Photovoltaic Modules 53

3.4.1 Geometries and Symmetries in PV Devices 55

3.4.2 Multi-Domain Approach 57

3.4.2.1 Module domain 59

3.4.2.2 Front Finger Domain 60

3.4.2.3 Front Texture Domain 60

3.4.2.4 Rear Side Domains 61

3.4.3 Post processing of Simulation Results 61

3.4.4 Ray Tracing Application Examples 64

3.4.4.1 Validation of Simulation Results 64

3.4.4.2 Optical Loss Analysis: From Cell to Module 66

3.4.4.3 Bifacial Solar Cells and Modules 68

3.5 From Optics to Power Output 69

3.5.1 Calculation Chain: From Ray Tracing to Module Power Output 70

3.5.1.1 Inclusion of the Irradiation Spectrum 73

3.5.1.2 Calculation of Module Output Power 75

3.5.1.3 Outlook: Energy Yield Calculation 75

3.5.2 Application Examples 76

3.5.2.1 Calculation of Short Circuit Current and Power Output 77

3.5.2.2 Current Loss Analysis: Standard Testing Conditions vs. Field Conditions 79

3.6 Overview of Optical Simulation Tools for PV Devices 80

3.6.1 Analysis of Solar Cells 82

3.6.2 Analysis of PV Modules and Their Surrounding 82

3.6.3 Further Tools Which are not Publicly Available 85

Acknowledgments 85

References 86

4 Optical Modelling and Simulations of Thin-Film Silicon Solar Cells 93
Janez Krc, Martin Sever, Benjamin Lipovsek, Andrej Campa and Marko Topic

4.1 Introduction 94

4.2 Approaches of Optical Modelling 95

4.2.1 One-Dimensional Optical Modelling 96

4.2.2 Two- and Three-Dimensional Rigorous Optical Modelling 97

4.2.3 Challenges in Optical Modelling 97

4.3 Selected Methods and Approaches 98

4.3.1 Finite Element Method 98

4.3.2 Coupled Modelling Approach 100

4.4 Examples of Optical Modelling and Simulations 102

4.4.1 Texture Optimization Applying Spatial Fourier Analysis 103

4.4.2 Model of Non-Conformal Layer Growth 110

4.4.3 Optical Simulations of Tandem Thin-Film Silicon Solar Cell 118

4.5 The Role of Illumination Spectrum 129

4.6 Conclusion 133

Acknowledgement 134

References 135

5 Modelling of Organic Photovoltaics 141
Ian R. Thompson

5.1 Introduction to Organic Photovoltaics 141

5.2 Performance of Organic Photovoltaics 143

5.3 Charge Transport in Organic Semiconductors 145

5.4 Energetic Disorder in Organic Semiconductors 150

5.5 Morphology of Organic Materials 153

5.6 Considerations for Photovoltaics 155

5.6.1 Excitons in Organic Semiconductors 155

5.6.2 Optical Absorption in Organic Photovoltaics 160

5.6.3 Carrier Harvesting in Organic Photovoltaics 161

5.7 Simulation Methods of Organic Photovoltaics 163

5.7.1 Lattice Morphologies and Device Geometry 163

5.7.2 Gaussian Disorder Model 164

5.7.3 Kinetic Monte Carlo Methods 164

5.7.4 Electrostatic Interactions 168

5.7.5 Neighbour Lists 169

5.8 Considerations When Modelling Organic Photovoltaics 169

5.8.1 The Next Steps for OPV Modelling 171

Acknowledgements 172

References 172

6 Modeling the Device Physics of Chalcogenide Thin Film Solar Cells 177
Nima E. Gorji and Lindsay Kuhn

6.1 Introduction 177

6.2 Kosyachenko’s Approach: Carrier Transport 178

6.3 Demtsu-Sites Approach: Double-Diode Model 181

6.4 Kosyachenko’s Approach: Optical Loss Modeling 184

6.5 Karpov’s Approach 186

6.6 Conclusion 187

Acknowledgements 188

References 188

7 Temperature and Irradiance Dependent Efficiency Model for GaInP-GaInAs-Ge Multijunction Solar Cells 191
Monika Freunek Mueller, Bruno Michel and Harold J. Hovel

7.1 Motivation 191

7.2 Efficiency Model 196

7.3 Results and Discussion 209

7.4 Conclusions 211

7.5 Acknowledgments 211

References 212

Appendix: Shockley-Queisser-Modell Calculations 213

8 Variation of Output with Environmental Factors 217
Youichi Hirata, Yuzuru Ueda, Shinichiro Oke and Naotoshi Sekiguchi

8.1 Conversion Efficiency and Standard Test Conditions (STC) 218

8.2 Variation of I-V curve with Each Environmental Factor 218

8.2.1 Irradiance 219

8.2.2 Cell Temperature 221

8.2.3 Spectral Response 222

8.3 Example of Measurement of Spectral Distribution of Solar Radiation 222

8.3.1 Example of Changes with Weather 223

8.3.2 Spectral Variation with Season 225

8.3.3 Effect of Variation in Spectral Solar Radiation 226

8.4 Irradiance 227

8.5 Effects on Performance of PV Modules/Cells 229

8.5.1 System Configurations and Measurements 229

8.5.2 Evaluation Methods 231

8.5.2.1 Performance Ratio 231

8.5.2.2 Effective Array Peak Power of PV Systems 233

8.5.3 Measurement Results 233

8.5.3.1 Performance Ratios 233

8.5.3.2 Degradation Rates 234

8.6 Cell Temperature 236

8.6.1 Output Energy by Temperature Coefficient 236

8.6.2 Output Energy with Different Installation Method 237

8.7 Results for Concentrated Photovoltaics 239

8.7.1 Introduction 239

8.7.2 Field Test of a CPV Module 239

8.7.3 Decline of Efficiency of the Early-Type CPV Module 239

8.7.4 Influences of the Degradation 241

Acknowledgments 243

References 244

9 Modeling of Indoor Photovoltaic Devices 245
Monika Freunek Müller

9.1 Introduction 245

9.1.1 Brief History of IPV 246

9.1.2 Characteristics of IPV Modeling 247

9.2 Indoor Radiation 248

9.2.1 Modeling Indoor Spectral Irradiance 250

9.3 Maximum Efficiencies 252

9.3.1 Intensity effects 255

9.4 Demonstrated Efficiencies and Further Optimization 257

9.5 Characterization and Measured Efficiencies 261

9.5.1 Irradiance Measurements 261

9.6 Outlook 262

9.7 Acknowledgement 264

References 264

10 Modelling Hysteresis in Perovskite Solar Cells 267
James M. Cave and Alison B. Walker

10.1 Introduction to Perovskite Solar Cells 267

Acknowledgements 277

References 277

Index 279

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