Elsevier S & T

Fundamentals of Thermophotovoltaic Energy Conversion

Chubb, Donald

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Table of contents
  • Cover
  • Acknowledgementsv
  • Prefacevii
  • Table of Contentsix
  • Chapter 1 – Introduction1
  • 1.1 Symbols1
  • 1.2 Thermphotovoltaic (TPV) Energy Conversion Concept3
  • 1.3 A Short History of TPV Energy Conversion3
  • 1.4 TPV Applications5
  • 1.5 Propagation of Electromagnetic Waves6
  • 1.5.1 Plane Wave Solution to Maxwell’s Equations6
  • 1.5.2 Energy Flux for Plane Electromagnetic Waves14
  • 1.5.3 Boundary Conditions at an Interface17
  • 1.5.4 The Law of Reflection and Snell’s Law of Refraction20
  • 1.5.5 Reflectivity and Transmissivity at an Interface25
  • 1.5.6 Connections between Electromagnetic Theory and Radiation Transfer Theory34
  • 1.6 Introduction to Radiation Transfer35
  • 1.6.1 Radiation Intensity35
  • 1.6.2 Blackbody38
  • 1.6.3 Blackbody Spectral Emissive Power39
  • 1.6.4 Blackbody Total Emissive Power42
  • 1.6.5 Equations for Radiation Energy Transfer44
  • 1.6.6 Energy Conservation Including Radiation47
  • 1.7 Optical Properties50
  • 1.7.1 Emittance and Absorptance51
  • 1.7.2 Hemispherical Spectral and Hemispherical Total Reflectivity55
  • 1.7.3 Independence of Emitted (Absorbed), Reflected, and Transmitted Radiation57
  • 1.8 Radiation Energy Balance for One Dimensional Model63
  • 1.9 Emittance of a Metal into a Dielectric66
  • 1.10 Summary70
  • References71
  • Problems72
  • Chapter 2 – Maximum Efficiency and Power Density for TPV Energy Conversion77
  • 2.1 Symbols77
  • 2.2 Maximum TPV Efficiency79
  • 2.3 Maximum TPV Efficiency for Constant Emitter Emittance and PV Cell Reflectance83
  • 2.4 Ideal TPV System84
  • 2.5 Approximation of Selective Emitter and Filter TPV Systems86
  • 2.6 Power Output89
  • 2.7 Summary91
  • References92
  • Problems92
  • Chapter 3 – Emitter Performances95
  • 3.1 Symbols95
  • 3.2 Gray Body Emitters97
  • 3.3 Selective Emitters98
  • 3.3.1 Rare Earth Selective Emitters99
  • 3.3.2 Other Selective Emitters102
  • 3.4 Extinction Coefficient and Optical Depth104
  • 3.5 Extinction Coefficients of Rare Earth Selective Emitters105
  • 3.6 Coupled Energy Equation and Radiation Transfer Equation for a Solid Material108
  • 3.7 One Dimensional Radiation Transfer Equations108
  • 3.7.1 One Dimensional Source Function Equation112
  • 3.7.2 One Dimensional Radiation Flux113
  • 3.7.3 No Scattering Medium114
  • 3.8 Spectral Emittance for Planar Emitter115
  • 3.8.1 No Scattering Spectral Emittance128
  • 3.8.2 No Scattering, Linear Temperature Variation Spectral Emittance131
  • 3.8.3 Importance of Temperature Change Across Planar Emitter140
  • 3.8.4 Effect of Scattering on Spectral Emittance of a Planar Emitter142
  • 3.9 Cylindrical Emitter146
  • 3.10 Emitter Performance153
  • 3.10.1 Gray Body Emitter Performance154
  • 3.10.2 Selective Emitter Performance157
  • 3.10.3 Cylindrical Selective Emitter Performance157
  • 3.10.4 Planar Selective Emitter Performance164
  • 3.11 Comparison of Selective Emitters and Gray Body Emitters170
  • 3.12 Summary172
  • References174
  • Problems175
  • Chapter 4 – Optical Filters for Thermophotovoltaics179
  • 4.1 Symbols179
  • 4.2 Filter Performance Parameters181
  • 4.3 Interference Filters183
  • 4.3.1 Introduction183
  • 4.3.2 Interference183
  • 4.3.3 Interference Filter Model185
  • 4.3.4 Reflectance, Transmittance, and Absorptance193
  • 4.3.5 Single Film System198
  • 4.3.6 Many Layer System for phii = Npi or phii = Npi/2 and N is an Odd Integer210
  • 4.3.7 Equivalent Layer Procedure214
  • 4.3.8 Interference Filter with Embedded Metallic Layer222
  • 4.3.9 Interference Filter Performance for Angles of Incidence Greater than Zero229
  • 4.4 Plasma Filters232
  • 4.4.1 Drude Model232
  • 4.4.2 Reflectance, Transmittance, and Absorptance of a Plasma Filter244
  • 4.4.3 Efficiency and Total Transmittance, Reflectance, and Absorptance of a Plasma Filter249
  • 4.5 Combined Interference-Plasma Filter253
  • 4.6 Resonant Array Filters260
  • 4.6.1 Transmission Line Theory261
  • 4.6.2 Transmission Line Equivalent Circuit for Resonant Array Filter266
  • 4.6.3 Metallic Mesh Filter270
  • 4.7 Spectral Control Using a Back Surface Reflector (BSR)277
  • 4.7.1 Efficiency of a Back Surface Reflector (BSR) for Spectral Control277
  • 4.8 Summary283
  • References284
  • Problems286
  • Chapter 5 – Photovoltaic Cells291
  • 5.1 Symbols291
  • 5.2 Energy Bands (Kronig-Penney Model) and Current in Semiconductors294
  • 5.3 Density of Electrons and Holes and Mass Action Law302
  • 5.4 Transport Equations310
  • 5.5 Generation and Recombination of Electrons and Holes313
  • 5.5.1 Generation of Electrons and Holes313
  • 5.5.2 Recombination of Electrons and Holes316
  • 5.6 p-n Junction320
  • 5.7 Current-Voltage Relation for an Ideal Junction in the Dark323
  • 5.7.1 Assumptions for Ideal p-n Junction324
  • 5.7.2 Current-Voltage Relation for Infinite Neutral Regions326
  • 5.7.3 Current-Voltage Relation for Finite Neutral Regions330
  • 5.7.4 Depletion Region Contribution to Current and High-Injection Effects336
  • 5.8 Ideality Factor and Empirical Current-Voltage Relation of p-n Junction in the Dark338
  • 5.9 Current-Voltage Relation for an Ideal p-n Junction Under Illumination339
  • 5.9.1 Electron Current Density in p Region340
  • 5.9.2 Hole Current Density in n Region349
  • 5.9.3 Current Generation in Depletion Region357
  • 5.9.4 Current-Voltage Relation359
  • 5.10 Quantum Efficiency and Spectral Response362
  • 5.11 Equivalent Circuit for PV Cells368
  • 5.12 PV Cell Efficiency and Power Output374
  • 5.13 Summary388
  • References391
  • Problems392
  • Chapter 6 – Governing Equations for Radiation Fluxes in Optical Cavity395
  • 6.1 Symbols395
  • 6.2 Radiation Transfer Theory397
  • 6.2.1 Radiation Transfer for Uniform Intensity397
  • 6.2.2 View-Factors for TPV Systems399
  • 6.2.3 Optical Properties of Components405
  • 6.2.4 Energy Balance on a Component of a TPV System410
  • 6.3 Radiation Energy Transfer in Planar TPV System413
  • 6.4 Radiation Energy Transfer in Cylindrical TPV System417
  • 6.5 Efficiency of TPV Systems422
  • 6.5.1 Overall Efficiency422
  • 6.5.2 Thermal Efficiency422
  • 6.5.3 Cavity Efficiency422
  • 6.5.4 Photovoltaic Efficiency423
  • 6.6 Summary423
  • References424
  • Problems424
  • Chapter 7 – Radiation Losses in Optical Cavity427
  • 7.1 Symbols427
  • 7.2 Cavity Efficiency for Planar Filter and Selective Emitter TPV Systems without a Window428
  • 7.3 Cavity Efficiency for Cylindrical Filter and Selective Emitter TPV Systems without a Window440
  • 7.4 Cavity Efficiency for TPV Systems with Reflectivity End Caps446
  • 7.4.1 Development of Radiation Transfer Equations446
  • 7.4.2 Radiation Transfer Equations for TPV Systems with Close Coupled Emitter-Window and Filter-PV C450
  • 7.4.3 Cavity Efficiency454
  • 7.5 Summary457
  • Problems458
  • Chapter 8 – TPV System Performance461
  • 8.1 Symbols461
  • 8.2 TPV System Model462
  • 8.3 Radiation Transfer Equations463
  • 8.4 Solution Method for TPV System Model468
  • 8.5 Results of TPV System Model for Hypothetical System472
  • 8.5.1 Importance of Radiation Leakage474
  • 8.5.2 Importance of Filter Absorptance474
  • 8.6 TPV System with Selective Emitter and Back Surface Reflector (BSR)476
  • 8.6.1 Dependence of TPV Performance upon Input Power479
  • 8.7 Importance of PV Array Temperature on TPV Performance483
  • 8.8 Review of Radiation Transfer Method484
  • 8.9 Summary485
  • Problems485
  • Appendices491
  • Appendix A – Exponential Integrals491
  • Appendix B – Coupled Energy and Radiation Transfer Equations495
  • Appendix C – 2 x 2 Matrix Algebra499
  • Appendix D – Mathematica Program for Multi-layer Interference Filter501
  • Appendix E – Quantum Mechanics503
  • Appendix F – Mathematica Program for Planar Geometry TPV Model509
  • Index513
Book details
  • Vendor Elsevier S & T
  • SKU 9780444527219
  • ISBN-13 9780080560687
  • Author Chubb, Donald
  • Category Technology & Engineering
  • Subject Materials Science

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This is a text book presenting the fundamentals of thermophotovoltaic(TPV) energy conversion suitable for an upper undergraduate or first year graduate course. In addition it can serve as a reference or design aid for engineers developing TPV systems. Mathematica design programs for interference filters and a planar TPV system are included on a CD-Rom disk. Each chapter includes a summary and concludes with a set of problems.

The first chapter presents the electromagnetic theory and radiation transfer theory necessary to calculate the optical properties of the components in a TPV optical cavity. Using a simplified model, Chapter 2 develops expressions for the maximum efficiency and power density for an ideal TPV system. The next three chapters consider the three major components in a TPV system; the emitter, filter and photovoltaic(PV) array. Chapter 3 applies the electromagnetic theory and radiation transfer theory presented in Chapter 1 in the calculation of spectral emittance. From the spectral emittance the emitter efficiency is calculated. Chapter 4 discusses interference, plasma and resonant array filters plus an interference filter with an imbedded metallic layer, a combined interference-plasma filter and spectral control using a back surface reflector(BSR) on the PV array. The theory necessary to calculate the optical properties of these filters is presented. Chapter 5 presents the fundamentals of semiconductor PV cells. Using transport equations calculation of the current-voltage relation for a PV cell is carried out. Quantum efficiency, spectral response and the electrical equivalent circuit for a PV cell are introduced so that the PV cell efficiency and power output can be calculated.

The final three chapters of the book consider the combination of the emitter, filter and PV array that make up the optical cavity of a TPV system. Chapter 6 applies radiation transfer theory to calculate the cavity efficiency of planar and cylindrical optical cavities. Also introduced in Chapter 6 are the overall TPV efficiency, thermal efficiency and PV efficiency. Leakage of radiation out of the optical cavity results in a significant loss in TPV efficiency. Chapter 7 considers that topic. The final chapter presents a model for a planar TPV system.

Six appendices present background information necessary to carry out theoretical developments in the text. Two of the appendices include Mathematica programs for the spectral optical properties of multi-layer interference filters and a planar TPV system. These programs are contained on a CD-Rom disk included with the book.

· First text written on thermophotovoltaic(TPV) energy conversion
· Includes all the necessary theory to calculate TPV system performance
· Author has been doing TPV energy conversion research since 1980's
· Emphasizes the fundamentals of TPV energy conversion
· Includes a summary and problem set at the end of each chapter
· Mathematica programs for calculating optical properties of interference filters and planar TPV system performance included on CD-Rom