Fundamental Elements of Applied Superconductivity€¦ · Fundamental elements of applied superconductivity in electrical engineering / Yinshun Wang. pages cm Includes bibliographical

Fundamental Elements of

AppliedSuperconductivity

in Electrical Engineering

Yinshun Wang

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FUNDAMENTALELEMENTS OF APPLIEDSUPERCONDUCTIVITYIN ELECTRICALENGINEERING



FUNDAMENTALELEMENTS OF APPLIEDSUPERCONDUCTIVITYIN ELECTRICALENGINEERING

Yinshun WangNorth China Electric Power University, China


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Library of Congress Cataloging-in-Publication Data

Wang, Yinshun.Fundamental elements of applied superconductivity in electrical engineering / Yinshun Wang.

pages cmIncludes bibliographical references and index.ISBN 978-1-118-45114-4 (cloth)

1. Superconductors. 2. Electric power. 3. Superconductivity. 4. Electrical engineering. I. Title.TK454.4.S93W26 2013621.3′5–dc23

2012049085

A catalogue record for this book is available from the British Library.

ISBN: 9781118451144

Typeset in 9/11pt Times by Aptara Inc., New Delhi, India

http://www.wiley.com

mailto:[email protected]


Contents

Preface xiii

Acknowledgments xv

Abbreviations and Symbols xvii

1 Introduction 1References 3

2 Superconductivity 52.1 The Basic Properties of Superconductors 5

2.1.1 Zero-Resistance Characteristic 52.1.2 Complete Diamagnetism – Meissner Effect 112.1.3 Josephson Effects 15

2.2 Critical Parameters 172.2.1 Critical Temperature Tc 182.2.2 Critical Field Hc 182.2.3 Critical Current Density Jc 18

2.3 Classification and Magnetization 192.3.1 Coherence Length 192.3.2 Classifications 212.3.3 Type I Superconductor and Magnetization 222.3.4 Type II Superconductor and Magnetization 22

2.4 Measurement Technologies of Critical Parameters 272.4.1 Cryogenic Thermometers 272.4.2 Measurement of Critical Temperature 272.4.3 Measurement of Critical Current Ic 332.4.4 Measurement of Critical Magnetic Field 40References 43

3 Mechanical Properties and Anisotropy of Superconducting Materials 453.1 Mechanical Properties 45

3.1.1 General Description of Mechanical Properties 453.1.2 Tensile Properties 463.1.3 Bending Properties 47

3.2 Electromagnetic Anisotropy 483.2.1 Anisotropy of Critical Current in HTS Materials 493.2.2 Anisotropy of Critical Current in 1G HTS Tape 50


vi Contents

3.2.3 Anisotropy of Critical Current in 2G HTS Tape 533.2.4 Anisotropy of Critical Current in Bi-2212 Wire 553.2.5 Anisotropy of n Value for HTS Tape 553.2.6 Anisotropy of Critical Current Density in HTS Bulk 56

3.3 Critical Current Characteristics of LTS Materials 573.3.1 Dependence of Critical Current Density of NbTi on Magnetic Field 583.3.2 Dependence of Critical Current Density of NbTi on Magnetic Field

and Temperature 583.3.3 Dependence of Critical Current Density of Nb3Sn on Magnetic Field 59

3.4 Irreversible Fields of Superconducting Materials 603.5 Critical Temperature of Several Kinds of HTS Materials 613.6 Thermodynamic Properties of Practical Superconducting Materials 62

3.6.1 Thermal and Mechanical Characteristics of PracticalSuperconducting Materials 62

3.6.2 Thermal Contraction of Superconducting Materials 65References 67

4 Stability of Superconductors 714.1 Critical States 724.2 Adiabatic Stabilization 724.3 Adiabatic Stability with Flux Jump 754.4 Self-Field Stability 794.5 Dynamic Stability 82

4.5.1 Stability of Composite Superconducting Slab with Cooled Side 834.5.2 Stability of Composite Superconducting Slab with Cooled Edge 874.5.3 Dynamic Stability of Current-Carrying Composite Superconductor Slab 894.5.4 Dynamic Stability of Current-Carrying Composite Superconductor

with Circular Cross-Section 914.6 Cryostability 95

4.6.1 Stekly Parameter 964.6.2 One–Dimensional Normal Zone Propagation 1004.6.3 Three-Dimensional Normal Propagation Zone and Minimum Quench Energy 101

4.7 NPZ Velocity in Adiabatic Composite Superconductors 1054.7.1 Longitudinal Propagation Velocity 1054.7.2 Transverse Propagation Velocity 107

4.8 Stability of HTS Bulks 1094.8.1 Evolution of Super-Current Density 1094.8.2 Magnetic Relaxation 110

4.9 Mechanical Stability of Superconducting Magnets 1124.10 Degradation and Training Effect of Superconducting Magnets 113

4.10.1 Degradation of Superconducting Magnets 1134.10.2 Training Effects of Superconducting Magnets 114

4.11 Quench and Protection of Superconducting Magnets 1144.11.1 Resistance Increase and Current Decay in Quench Processes 1154.11.2 Factors Causing Quench 1224.11.3 Active Protection 1244.11.4 Passive Protection 1284.11.5 Numerical Simulation on Quench 134


Contents vii

4.12 Tests of Stability 1354.12.1 Flux Jump Experiments 1354.12.2 Measurement of Quench Parameters 138References 139

5 AC Losses 1415.1 AC Losses of Slab 142

5.1.1 Slab in Parallel AC Magnetic Field 1425.1.2 Slab in Perpendicular AC Magnetic Field 1445.1.3 Self-Field Losses 1445.1.4 Slab-Carrying DC and AC Currents Located in Parallel DC/AC Magnetic

Fields 1465.1.5 Slab-Carrying AC and DC Currents 1475.1.6 Slab with AC Transport Current in Perpendicular AC Magnetic Field 1485.1.7 Slab in AC and DC Magnetic Fields 1505.1.8 Flux-Flow Loss of Slab with Combinations of AC and DC Transport Currents

in Perpendicular and Parallel AC and DC Magnetic Fields 1515.1.9 Total AC Losses of Slab with any AC/DC Current and AC/DC

Magnetic Field 1555.2 AC Losses of Concentric Cylinder 156

5.2.1 Rod in Longitudinal AC Magnetic Field 1565.2.2 Rod in Transverse AC Magnetic Field 1575.2.3 Rod in Transverse AC Magnetic Field and Carrying DC Transport Current 1605.2.4 Rod in Self-Magnetic Field 1615.2.5 Rod-Carrying AC Transport Current in AC Transverse Magnetic Field

with Same Phase 1635.2.6 Flux-Flow Losses of Rod-Carrying AC/DC Transport Currents Subjected

to AC/DC Magnetic Field 1655.3 AC Losses of Hybrid Concentric Cylinder 1655.4 AC Losses of Concentric Hollow Cylinder in Longitudinal Field 1675.5 AC Losses for Large Transverse Rotating Field 1675.6 AC Losses with Different Phases between AC Field and AC Current 168

5.6.1 Slab-Carrying Current Exposed to AC Magnetic Field Parallel to its WideSurface with Different Phases 169

5.6.2 Slab-Carrying Current Exposed to Parallel AC Magnetic Field at One Sidewith Different Phases 170

5.6.3 AC Losses of Slab-Carrying AC Current and Exposed to SymmetricalParallel AC Magnetic Field with Different Phases 172

5.7 AC Losses for other Waves of AC Excitation Fields 1755.8 AC Losses for other Critical State Models 177

5.8.1 Kim Model 1775.8.2 Kim–Anderson Model 1785.8.3 Voltage-Current Power-Law Model – Nonlinear Conductor Model 1795.8.4 Combination of Kim-Anderson Model and Voltage-Current

Power-Law Model 1815.9 Other AC Losses 182

5.9.1 Eddy Current Losses 1825.9.2 Penetration Loss in Transverse AC Magnetic Field 184


viii Contents

5.9.3 Twist Pitch 1865.9.4 AC Losses in Longitudinal AC Magnetic Field 1875.9.5 Coupling Losses 1895.9.6 Measures for Reducing AC Losses 193

5.10 Measurements of AC Loss 1945.10.1 Magnetic Method 1945.10.2 Electrical Method 1965.10.3 Thermal Method 2005.10.4 Comparison of Electrical with Calorimetric Measuring Method 204

5.11 AC Losses Introduction of Superconducting Electrical Apparatus 204References 206

6 Brief Introduction to Fabricating Technologies of PracticalSuperconducting Materials 209

6.1 NbTi Wire 2116.2 Nb3Sn Wire 213

6.2.1 Internal Diffusion Process 2136.2.2 External Diffusion Process 214

6.3 Nb3Al Wire 2156.4 MgB2 Wire 2166.5 BSCCO Tape/Wire 2166.6 YBCO Tape 221

6.6.1 Substrate and Textured Insulated Layer 2226.6.2 Deposition of Superconducting Layer with High Critical

Current Density 2226.7 HTS Bulk 223

6.7.1 Melt-Texture-Growth (MTG) Process 2246.7.2 Quench-Melt-Growth (MTG) Process/Melt-Powder-Melt-Growth

(MPMG) Process 2246.7.3 Powder-Melting-Process (PMP) 2246.7.4 Melt Cast Process (MCP) 225References 226

7 Principles and Methods for Contact-Free Measurements of HTS Critical Currentand n Values 229

7.1 Measurement Introduction of Critical Current and n Values 2297.2 Critical Current Measurements of HTS Tape by Contact-Free Methods 230

7.2.1 Remanent Field Method 2307.2.2 AC Magnetic Field-Induced Method 2327.2.3 Mechanical Force Method 233

7.3 n Value Measurements of HTS Tape by Contact-Free Methods 2357.3.1 Hysteretic Loss Component – Varying Amplitude Method 2357.3.2 Fundamental Component Method – Varying Frequency 2367.3.3 Third Harmonic Component Voltage Method 237

7.4 Analysis on Uniformity of Critical Current and n Values in Practical Long HTS Tape 2387.4.1 Gauss Statistical Method 2387.4.2 Weibull Statistical Method 239

7.5 Next Measurements of Critical Currents and n Values by Contact-Free Methods 240References 240


Contents ix

8 Cryogenic Insulating Materials and Performances 2438.1 Insulating Properties of Cryogenic Gas 243

8.1.1 Insulating Properties of Common Cryogenic Gas 2448.1.2 Insulating Properties of Other Gases 248

8.2 Insulating Characteristics of Cryogenic Liquid 2488.2.1 Comparison of Cryogens 2488.2.2 Electrical Properties of Cryogens 248

8.3 Insulating Properties of Organic Insulating Films 2568.3.1 Thermodynamic Properties of Organic Films 2588.3.2 Resistivity of Organic Films 2608.3.3 Permittivity of Organic Films 2608.3.4 Dielectric Loss 2608.3.5 Breakdown Voltage 2638.3.6 Electrical Ageing Characteristics 267

8.4 Cryogenic Insulating Paints and Cryogenic Adhesive 2698.4.1 Epoxy Resin 2698.4.2 GE7031 Varnish 2718.4.3 Polyvinyl Acetal Adhesive and other Cryogenic Adhesives 271

8.5 Structural Materials for Cryogenic Insulation 2718.5.1 Polymer Materials 2718.5.2 Epoxy Resin Composites 272

8.6 Inorganic Insulating Materials 2738.6.1 Thermodynamic Properties of Glasses 2738.6.2 Electrical Properties of Ceramics 2748.6.3 Thermodynamic and Electrical Properties of Mica Glass 276References 278

9 Refrigeration and Cryostats 2799.1 Cryogens 2809.2 Cryostat 281

9.2.1 Cryogenic Thermal Insulation 2829.2.2 Basic Classification and Structure of Cryogenic Thermal Insulation 2909.2.3 Structure Design of Cryostats 3049.2.4 Cryogenic Transfer Lines and Flexible Pipes 3079.2.5 Ultra-Cryogenic Cryostat with Dual-Cryostat Structure 309

9.3 Refrigeration 3109.3.1 Principle of Refrigeration and Performance of Refrigerators 3109.3.2 Choice of Refrigerator Suitable for Superconducting Power Apparatus 317

9.4 Cooling Technologies of Superconducting Electric Apparatus 3179.4.1 Open-Cycle Cooling 3189.4.2 Closed-Cycle Cooling by Reducing Pressure 3199.4.3 Closed-Cycle Cooling by Refrigerator 3199.4.4 Forced-Flow Circulation Cooling 3209.4.5 Direct Cooling by Refrigerator 322References 323

10 Power Supplying Technology in Superconducting Electrical Apparatus 32510.1 Current Leads 326

10.1.1 Conduction-Cooled Current Leads 32610.1.2 Approximate Design of Conduction-Cooled Current Lead 329


x Contents

10.1.3 Demountable Current Leads 33510.1.4 Gas-Cooled Current Leads 33610.1.5 HTS Current Leads 34010.1.6 Peltier Thermoelectric (TE) Effect 34310.1.7 Gas-Cooled Peltier Current Leads (PCL) 345

10.2 Superconducting Switch 35210.2.1 Design of LTS Switch 35310.2.2 Design of HTS Switch 35410.2.3 Fabrication of Superconducting Switches 355

10.3 Flux Pump 35710.3.1 Principle of Superconducting Flux Pump 35710.3.2 Transformer-Type Superconducting Magnetic Flux Pump 35810.3.3 HTS Permanent Magnetic Flux Pump 359References 361

11 Basic Structure and Principle of Superconducting Apparatus in Power System 36311.1 Cable 36311.2 Fault Current Limiter 366

11.2.1 Classifications 36711.2.2 Resistive Type 36711.2.3 Saturated Iron Core Type 36811.2.4 Transformer Type 37011.2.5 Shielded Iron Core Type 37011.2.6 Bridge Type 37111.2.7 Hybrid Type 37211.2.8 Three-Phase Reactance Type 373

11.3 Transformer 37411.3.1 Configuration 37411.3.2 Advantages 37511.3.3 Further Key Technology 375

11.4 Rotating Machine-Generator/Motor 37611.4.1 Configuration 37611.4.2 Advantages 37711.4.3 Electric Machine with HTS Bulk 37811.4.4 Applications 378

11.5 Superconducting Magnetic Energy Storage (SMES) 37911.5.1 Principle and Basic Topology 37911.5.2 Application in Grid System 381

11.6 Superconducting Flywheel Energy Storage (SFES) 38211.6.1 Principle and Structure 38211.6.2 Application in Grid System 383

11.7 Other Industrial Applications 38411.7.1 High Magnetic Field 38411.7.2 Low Magnetic Field 38511.7.3 Maglev Transportation 387References 387

12 Case Study of Superconductivity Applications in Power System-HTS Cable 38912.1 Design of AC/CD HTS Cable Conductor 389

12.1.1 Former Size 38912.1.2 Number of Tapes 391


Contents xi

12.1.3 Number of Layers 39112.1.4 Number of Tapes on Layer 39212.1.5 Insulation 39312.1.6 Shielding and Protection Layers 395

12.2 Electromagnetic Design of AC/CD Cable Conductor 39512.2.1 Range of Winding Angle (Pitch) 39512.2.2 Design of CD Cable Conductor 396

12.3 Analysis on AC Losses of DC HTS Cable 39912.3.1 Magnetic Field Analysis 39912.3.2 AC Losses of HTS CD Cable Conductor 400

12.4 Design of AC WD HTS Cable Conductor 40412.4.1 Eddy Current Loss in Cryostat 40512.4.2 Dielectric Loss 405

12.5 Design of DC HTS Cable Conductor 40512.6 Design of Cryostat 40812.7 Manufacture of CD HTS Cable Conductor 41012.8 Bending of HTS Cable 41212.9 Termination and Joint 412

12.9.1 Termination 41212.9.2 Joint 414

12.10 Circulating Cooling System and Monitoring System 41512.10.1 Cooling System 41512.10.2 Monitoring System 418References 419

Appendix 421A.1 Calculations of Volumetric Heat Capacity, Thermal Conductivity and Resistivity of

Composite Conductor 421A.2 Eddy Current Loss of Practical HTS Coated Conductor (YBCO CC) 422

A.2.1 Eddy Current Loss with Transporting Alternating Current 423A.2.2 Eddy Current Loss of YBCO CC Exposed to Perpendicular AC Magnetic

Field 423A.2.3 Eddy Current Loss Exposed to Parallel AC Magnetic Field 424A.2.4 Iron Losses of Substrate 424

A.3 Calculation of Geometrical Factor G 425A.4 Derivation of Self and Mutual Inductances of CD Cable 426

A.4.1 Self Inductance of Layer 426A.4.2 Mutual Inductances amongst Layers 428

A.5 Other Models for Hysteresis Loss Calculations of HTS Cable 429A.6 Cooling Arrangements 430

A.6.1 Counter-Flow Cooling 430A.6.2 Counter-Flow Cooling with Sub-Cooled Station 434A.6.3 Parallel-Flow Cooling 435References 438

Index 439


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Preface

Since its discovery, superconductivity and its applications have become one of the most active frontiers inmodern science and technology. With the progress in exploration and research of superconductivity overnearly half a century, the practical NbTi and Nb3Sn superconducting wires were successfully fabricatedin the 1960s. Superconducting technology, especially superconducting magnet technology, was then putinto applications. However, it is difficult for superconductors to be extensively used since they must workat a liquid helium temperature of 4.2 K.

Although the alternating current (AC) losses of superconducting windings is much lower than thoseof conventional copper windings, the effect of 1 W power consumption generated at a liquid heliumtemperature is at least equivalent to 500 W consumption of cooling power at room temperature. There-fore, the AC loss is not fully compensated for by reduction in AC losses, and the operating cost ofsuperconducting electrical equipment is expensive, except in direct current (DC) applications. Until the1980s, the AC application of the Low Temperature Superconductors (LTS) in a power system had notmade substantial progress.

Since the High Temperature Superconductor (HTS) was discovered in 1986, the application of HTSelectrical equipment operating at the liquid nitrogen temperature of 77 K came into being, and super-conducting power technology was hoped to be applied in electrical power systems.

Great progress was made in development of HTS materials in the late 1990s, and practical HTS tapeswere commercially realized. Research on superconducting power technology has made important andsignificant progress in many countries. At present, many superconducting equipment prototypes, suchas superconducting cable, superconducting transformer, superconducting Fault Current Limiter (FCL),superconducting motor/generator, superconducting magnetic energy storage and other superconductingequipment, have been developed and demonstrated. At present, several groups of HTS cable prototypesoperate in live grids. Superconducting technology has also found important applications in informationtechnology, traffic transportation, scientific instrument, medical technology, national defence, largescientific projects and other fields besides the energy field.

Superconducting power technology is highly comprehensive and interdisciplinary, and related tosuperconducting technology, electric power technology, cryogenic insulation, cryogenic refrigeration,materials science and technology, etc. At the present, it is a promising research field of new scienceand high technology, with important scientific significance and application prospects in power systems.At the same time, superconducting power technology will be one of the key technologies in the futureSmart Grid. It is predicted that this technology will become a practical technology of extensive scaleand play an important role in energy saving, emission reduction, low carbon economy, renewable energyresources, and in other fields.

This book briefly introduces the basic theory of superconductivity. According to the knowledge struc-ture and the order required in application of superconducting technology, electromagnetic properties ofpractical superconducting materials, stability, AC losses, processing technology, measurement of criticalcurrent and n values by contact-free methods, cryogenic insulation, cryostat and refrigeration, current

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xiv Preface

leads and flux pump, are presented respectively. The principles and structures of various superconductingequipment are also described. Finally, high-Tc superconducting (HTS) cables, and superconductivity ap-plications in power systems, are systematically described to show how the basic technologies describedelsewhere in the book fit together. The content of the book focuses on the fundamental elements of ap-plied superconductivity in electrical engineering. A feature of this book is that experimental technologyis added to related chapters together with the introduction of fundamental theoretical and technologicalprinciples.

There are 12 chapters in the book. The first chapter briefly introduces applications of superconductingpower technology with several superconducting apparatus used in power systems. Chapter 2 presentsthe basic theories and critical parameters of superconductors. Chapter 3 describes mechanical and elec-tromagnetic properties of superconducting materials. Chapter 4 introduces the stability and quenchcharacteristics of superconducting materials and magnets, and protection technology of superconduct-ing magnets. Chapter 5 systematically describes various AC losses of superconducting in commercialfrequency power, which includes hysteresis loss, magnetic flux flow loss, coupling and eddy currentlosses, and methods of measuring AC loss. Chapter 6 briefly lists the preparation techniques of practicalsuperconducting materials. Chapter 7 presents theory and measurements of critical current and n valuesin practical HTS tapes by contact-free methods, and their evaluation and calculation of non-uniformityare also included. Chapter 8 concerns the insulation characteristics of some cryogenic gas, cryogenicliquid, organic insulation film materials, inorganic insulating materials and cryogenic adhesive. Chapter9 mainly shows the heat-conduction theory, cryogenic device design and cryogenic refrigeration tech-nology. Chapter 10 systematically introduces the design principles and methods of various current leads,including conductor-cooled current leads, gas-cooled lead, Peltier current lead (PCL) and the hybridcurrent lead, the applications of superconducting persistent current switch (PCS) and superconductingflux pump technology. Chapter 11 presents basic structures of several superconducting apparatus inpower systems. As in the case of the application of superconductivity in a power system, Chapter 12systematically describes the design of HTS cable.

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Acknowledgments

The author would like to thank Science Press for kindly granting permissions for all the figures and tablesobtained from the Chinese title: Bases of applied superconductivity in Electrical Engineering, ISBN:9787030315632, by Yinshun Wang, published by Science Press in June 2011.

When writing this book, the author referenced many worldwide research articles and books, so hewould like to express his cordial thanks and respect to these copyright owners. The author is alsoindebted to undergraduates and graduates for suggesting a book based on their several years of coursework. Thanks also go to Prof. Shen Guoliu for his detailed proofreading of the book and for providingvaluable suggestions. Specifically, the author thanks his wife Ms. Yang Haiyan, who did almost all thehousework by herself in order to support his writing.

Because of my limited knowledge, it is very hard to avoid some omissions and even mistakes, so it ismy pleasure to receive your criticisms and corrections.

Yinshun WangState Key Laboratory for Alternate Electrical Power System with Renewable Energy Sources

Key Laboratory of HV and EMC BeijingNorth China Electric Power University

Beijing, ChinaOctober 2012

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Abbreviations and Symbols

Abbreviations

Abbreviations Meanings

1D One-dimensional3D Three-dimensional2D Two-dimensional1G BSCCO-2223 conductors made by PIT process2G YBCO-123 coated conductorsAC Alternating currentACSR Aluminium Cable Steel ReinforcedAMSC American Superconductor Corporation, MA, USAASTM American Society for Testing and MaterialsAVR automatic voltage regulatorBCS Barden Cooper SchriefferBSCCO-2212 Bi2Sr2CaCu2O8

BSCC0-2223 (Bi,Pb)2Sr2Ca2Cu3O10

CAES Compressed air energy storageCB Circuit breakerCC Coated conductorCCl4 Carbon tetrachlorideCD Cold dielectricCH4 Liquid MethaneCICC cable-in-conduit conductorCO Carbon monoxideCOV Coefficient of varianceCSC Current source converterCSM Critical state modelCTC Continuously transposed cableCVD Chemical vapor depositionDC Direct currentDP Double pancakeDSC Dynamic synchronous condenserEC Equivalent circuit


xviii Abbreviations and Symbols


EM ElectromagneticEMF Electromagnetic fieldEMS Maglev Electromagnetic SystemFACTS Flexible alternating current transmission systemFC Field coolingFCL Fault current limiterFDM Finite difference methodFEM Finite element methodFES Flywheel energy storageFRP Fiber reinforced plasticsGFRP Glass fiber reinforced plasticsG-M Gilford–McMahonGHe Gas – heliumGN2 Gas – nitrogenGNe Gas – neonH2 HydrogenHe HeliumHc Critical magnetic fieldHM Hysteresis machineHTS High temperature superconductorHV High voltageHVDC High voltage direct currentIBAD Ion beam assisted depositionIEC International Electrotechnical CommissionInnoST Innova Superconductor Technology, Beijing, ChinaINSTEC International Superconductivity Technology Center, Tokyo, JapanISD Inclined substrate depositionITER International Thermonuclear Experimental ReactorJJ Josephson junctionkA · m Kilo-ampere current carried in 1 m length of a wireLHe Liquid heliumLN2 Liquid nitrogenLNe Liquid neonLO2 Liquid oxygenLTS Low temperature superconductorL-type Transformer typeLV Low voltagemol Molemaglev Magnetic levitationMAJ model Majoros modelMB Mono-blockMCG Magneto-cardiogramMCP Melt cast processMEG Magneto-encephalogramMFC Multi-filamentary composite


Abbreviations and Symbols xix


MgB2 Magnesium DiborideMHD Magneto-hydrodynamicMJR Modified jelly rollMLI Multi-layer super-thermal insulationMOCVD Metal-organic chemical vapourMOD Metal organic depositionMPMG Melt-powder-melt-growthMPZ Minimum propagation zoneMQE Minimum quench energyMRI Magnetic Resonance ImagingMTG Melt-textured growthN2 NitrogenNb3Al Niobium – aluminumNb3Sn Niobium – tinNbTi Niobium – titaniumNe NeonNMR Nuclear magnetic resonanceNS model Norris modelNu Nusselt numberNZP Normal zone propagationOF Oxygen-free

Oil-filledPCL Peltier current leadPCS Persistent current switchPD Partial dischargePIT Powder-in-tubePLD Pulse laser depositionPSF PolysulfonePM Permanent magnetPMP Powder melt processPPLP Laminated Polypropylene PaperPSS Power system stabilizerPr Prandtl numberPVC PolyvinylchloridePVD Physical vapour depositionPWM Pulse width modulationQMG Quench-melt growthRABiTS Rolling-assisted biaxially textured substrateRe Reynolds numberRF Radio frequencyRM Reluctance machineRMS Root mean squareR-type Resistive typeRT Room temperatureRRR Residual resistivity ratio


xx Abbreviations and Symbols


SC Superconducting cableSF6 Sulphur hexafluorideSFCL Superconducting fault current limiterSFES Superconducting flywheel energy storageSI Super-insulationSIS Superconducting insulator superconductorSMES Superconducting magnetic energy storageSNS Short section of non-superconductingSQUID Superconducting quantum interference deviceTE ThermoelectricTeflon/PTFE PolytetrafluoroethyleneUPS Uninterrupted power supplyVSC Voltage source converterVSM Vibrating sample magnetometerWD Warm dielectricXLPE Cross linked polyethyleneYBCO-123 YBa2Cu3O7

YSZ Yttria – stabilized zirconiaZFC Zero-field cooling

Symbols

Symbols Nomenclature Units

A Magnetic vector potential Wb/mA Area m2

Current unita Half thickness maf Size of filament mB, B Magnetic field strength TBc Critical magnetic field strength TBc1 Lower magnetic field strength TBc2 Upper critical magnetic field strength TBdc DC magnetic field strength TBf Characteristic magnetic field strength TBirr(T) Irreversible magnetic field TBm Amplitude and peak-to-peak value of AC magnetic field strength TBp Full penetration magnetic field strength Tb Normalized magnetic field strength

Thickness of sheath mbac Normalized AC magnetic field strengthbc1 Normalized lower critical magnetic field strengthbc2 Normalized upper critical magnetic field strengthbdc Normalized DC magnetic field strengthC Effective cross-sectional factor


Abbreviations and Symbols xxi


Specific heat capacity J/(kg · K)Capacity FElectron charger unitFitted constant

CL Latent heat J/kgCp Specific heat capacity with constant pressure J/(kg · K)Cv Specific heat capacity with constant volume J/(kg · K)c Wall thickness m

Velocity of light in vacuum (3.0 × 108) m/sD Diameter m

Outermost radius of shielding layer of CD cable conductor mdiffusivity

De Hydraulic diameter mDm Magnetic diffusivity m2/sDT Thermal diffusivity m2/sd Thickness mE Electric field V/m

Energy JYoung’s modulus N/m2

Emax The maximum breakdown field V/me Electron charge (1.6 × 10−19) C

Ratio of ellipse axesF force N

Capacity unitFL Lorenz force NFp Pinning force Nf Frictional factor

Frequency HzVolumetric ratioThe efficiency of convective heat transferCooling efficiency

f c Critical frequency HzfL Lorenz force density N/m3

fp Pinning force density N/m3

G Geometrical factorGiga (109)Ohmic heat generation per unit volume of conductor W/m3

Gc Heat generation at critical temperature Tc W/m3

g Gap between tapes mAcceleration of gravity kg · m/s2

H Magnetic filed A/mH Inductance unitHc Critical magnetic field A/mHc1 Lower critical magnetic field A/mHc2 Upper critical magnetic field A/mHf Characteristic magnetic field A/mHm Amplitude of AC magnetic field A/mHp Full penetration magnetic field A/m


xxii Abbreviations and Symbols


Hz Frequency unith Normalized magnetic field

Heat transfer coefficient W/(m2 · K)ParameterPlanck’s constant (6.63 × 10−34) J · sHeight m

hac Normalized AC magnetic fieldhc1 Normalized lower critical magnetic fieldhc2 Normalized upper critical magnetic fieldI Current A

Bessel functionIc Critical current AIm Amplitude of AC current AIn n-order Bessel functioni Normalized AC current

Subscript indexImaginary number unit i2 = √−1

iac Normalized AC currentic Normalized critical currentidc Normal DC critical currentJ Current density A/m2

Energy unit N · mJc Critical current density A/m2

Je Engineering current density A/m2

Jt Transport current density A/m2

j Subscript indexImaginary number unit

K Effective thermal conductivity W/(m · K)Kelvin-temperature unitConstant

k Thermal conductivity W/(m · K)Wave vector m−1

Coupling coefficientkB Boltzmann constant (1.38 × 10−23) J/KL Length m

Self inductance HL0 Lorentz number W·�/K2

Lc Critical length mLp Twist pitch mlp Perimeter length mM Magnetization A/m

Mutual inductance HMega (106)Mass kgMolar mass kg/mol.Mass flow rate kg/s


Abbreviations and Symbols xxiii


m Magnetic moment A · m2

MassLength unit

mol Unit of measurement used in chemistry toexpress amounts of a chemical substance

N NumbersForce unit

NF Density of statesn Number of shielding layers

Numbersn n value

Density of Cooper pairP Power W

Pressure PaCooling circumference m

Pa Stress and pressure unitPc Coupling loss per unit length W/mPd Dielectric loss per unit length W/mPe Eddy current loss per unit length W/mPh Hysteresis loss per unit length W/mPpump Pumping fluid loss Wp Momentum kg · m/sQ Heat per unit length W/m

Strain energy J/m3

Heat conduction Wq Heat conduction per unit length W/m

Heat leakage per unit lengthHeat per unit area W/m2

R Resistance �

Universal gas constant (8.3145) J/(mol · K)Radius m

Rg Radius of generation normal zone mr Radius mradian Angle unit rad.S Cross-sectional area m2

s Time unitT Temperature K

Tesla-magnetic field unitPeriod of time s

T0 Base temperature – typically the cryogenbath

K

Tc Critical temperature KTg Temperature at which power generation

starts in composite conductorK

Tm Time of field ramp sTsh Sharing temperature K


xxiv Abbreviations and Symbols


Tp Peak of temperature Kt Time s

Normalized critical temperaturetc Thickness of normal metal mtgδ Dielectric loss angle tangenttQ Quench time for unbalanced normal zone sU Voltage V

Potential VProtection function

u Velocity of gas molecules m/sV Voltage V

Volume m3

Potential difference Vv Velocity m/sW Power W

Energy unitWb Magnetic flux unit T · m2

w Half width mx Distance m

CoordinateFitted parameter

Y Yield strength MPay CoordinateZ Impedance �

Figure of merit Z = η2/(kρ) 1/Kz CoordinateGreekα Thermal accommodation coefficient

Defined parameterStekly parameter

β Specific heat ratio (Cp/Cv)Stability parameter

χ Susceptibilityχ ′ Real part of complex susceptibilityχ ′′ Imaginary part of complex susceptibilityδ Skin depth m

Magnetic penetration depth mDielectric loss angle rad

ε Relative permittivityStrainEmissivity/blackness

εb Bending strainε0 Vacuum permittivity (8.85 × 10−12) F/mε′ Real part of complex permittivity F/mε′ ′ Imaginary part of complex permittivity F/mφ Angle radianγ Solid density kg/m3


Abbreviations and Symbols xxv


η EfficiencyViscosity Pa · sSeebeck coefficient V/KCharacteristic rate for tunneling 1/sCurrent margin of HTS cable

τ Characteristic time constant sCoupling time constant

ϕ Phase angle radianκ Ginsburg-Landau parameter (= λ/ξ )λ Penetration depth m

Wave length mFilling factor

μ Relative permeabilityμ0 Vacuum permeability (4π × 10−7) H/mμ′ Real part of complex permeability H/mμ′ ′ Imaginary part of complex permeability H/mν Poission ratio

Heat transfer stability factorθ Angle radianρ Fluid (liquid and gas) density kg/m3

Resistivity � · mσ Stress Pa

Stefan-Boltzmann constant (5.67 × 10−8) W/(m2 · K4)τ Characteristic time constant s

Decay time constant sω Angular frequency (2π f ) Radian/s

order parameterξ Coherent length m� Wave function� Magnetic flux Wb�0 Magnetic flux quantum (2.07 × 10−15) Wb� � function� Temperature of cooling gas K� Resistance unit� h/(2π ) J · s// Parallel orientation⊥ Perpendicular orientation


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1Introduction

In 1911, the physicist H.K. Onnes, of Leiden Laboratory in the Netherlands, was measuring the resistivityof metals at low temperatures. He discovered that the resistance of mercury completely disappearedwhen the temperature dropped to that of liquid helium (4.2 K). This phenomenon became known assuperconductivity. In 1933, German scientists W. Meissner and R. Ochsenfeld found that the magneticflux completely disappeared from the interior of materials with zero resistance when cooled to 4.2 K inthe magnetic field. This zero magnetic field inside a material became known as perfect diamagnetismand is now called the Meissner effect.

In 1962, B.D. Josephson theoretically predicted the superconducting quantum tunneling effect, knownas the Josephson effect. This is where a current flows for an indefinitely long time, without any voltageapplied, across a device known as a Josephson junction (JJ) consisting of two superconductors coupledby a weak link. The weak link can consist of a thin insulating barrier (known as a superconductor-insulator-superconductor, or S-I-S) junction, and a short section of non-superconducting (S-N-S) metal.Subsequently, P.W. Anderson and J.M. Rowell experimentally confirmed Josephson’s prediction.

Since its discovery, the superconductor and its applications have been one of the most active researchfields in modern science and technology, due to its unique physical properties of zero resistance, perfectdiamagnetism and the quantum tunneling effect. Superconducting technology is mainly applied inelectrical engineering and electronics, and these applications and characteristics are listed in Table 1.1.

Table 1.1 shows that superconducting technology is of great value in the fields of energy resources,transportation, scientific instruments, medical care, national defence and large scientific project. Sinceits discovery, widespread application of the superconductor has become the pursuit of scientists andengineers. Before the 1960s, practical NbTi and Nb3Sn superconducting wires were not manufactureduntil nearly half of a century after the discovery of superconductivity. Since then, superconductingtechnology and application of superconducting magnets are used for laboratory and practical applications.However, the conventional superconductors have not been widely used in power systems, particularly inalternating current (AC) applications, because of their need to operate at 4.2 K.

With the development of NbTi wires, the Magnetic Resonance Imaging (MRI) system has beenincreasingly used in hospitals for clinical diagnosis since the 1980s. In 1986, a true breakthrough wasmade in the field of superconductivity by A. Muller and G. Bednorz, researchers at the IBM ResearchLaboratory in Ruschlikon, Switzerland. They created a brittle copper oxide ceramic compound, the so-called high temperature superconductor (HTS), which presents superconductivity at temperatures above40 K. Since then, several kinds of HTS have been discovered and the transition temperature from thenormal to superconducting state has reached more than 90 K, which is higher than the liquid nitrogentemperature of 77 K.

Fundamental Elements of Applied Superconductivity in Electrical Engineering, First Edition. Yinshun Wang.© 2013 Science Press. Published 2013 by John Wiley & Sons Singapore Pte. Ltd.

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2 Fundamental Elements of Applied Superconductivity in Electrical Engineering

Table 1.1 Main applications and characteristics of superconducting technology in electrical engineering

Applications Characteristics

Superconductingpowertechnology

Transmission power cable Power transmission with low loss and large capacityFault current limiter (FCL) Safety and stability of gridSuperconducting Magnetic Energy

Storage (SMES)Regulation of power quality and stability of the grid

Transformer Energy saving and small sizeMotor Higher efficiency and small sizeGenerator Higher specific power, higher efficiency and increased

grid stabilityCurrent leads High current density and low heat leakage

Superconductingmagnettechnology

Magnet with high field strength Large scientific project in particle and nuclear physics,Nuclear magnetic resonance (NMR), scientificinstruments, magnetic separation, materialpreparation, biological and medical science

Magnetic levitation (maglev) Maglev train, maglev propulsion, flywheel bearing andhigh precision gyroscope

Therefore, superconducting apparatus working at temperatures of 77 K made the widespread use ofsuperconducting technology possible. With the great progress in development of HTS materials in the late1990s, practical HTS tapes were manufactured and commercialized. The application of superconductingpower technology was developed on a large scale, with the support of governments and multinationalcompanies. Many prototypes of superconducting power apparatus, such as cable, transformer, FCL,motor/generator and SMES, were developed and demonstrated. At present, commercial superconductingapparatus, particularly the HTSs, are continuing to be developed with increasing investment from gov-ernments and companies. It is believed that a major breakthrough in superconducting technology willcontinue well into the future.

Applications of superconductors in electrical engineering primarily involve superconducting powertechnology and superconducting magnet technology. With their transition from normal state to super-conducting state and then the largely increased current carrying capacity at high current density andzero resistance, superconducting power technology has developed further [1–3]. Table 1.2 lists the mainadvantages of superconducting apparatus and their influence on the electrical power industry. Other appli-cations include the dynamic synchronous condensers (DSC), magneto-hydrodynamic (MHD) generationof power, cryogenic capacitors, gyrotrons, and superconducting induction heaters [4–14].

Table 1.2 shows that utilization of superconducting power technology cannot only improve powerquality, enhance safety, stability and reliability of the grid system, reduce voltage level, and make a superlarge-scale power grid possible, but also greatly increases apparatus capacity and transmission capacity,and simultaneously reduces loss of power to the grid. Furthermore, the quality of power from renewableenergy resources can be improved by using SMES to which a large grid can be effectively connected.

In comparison with a conventional magnet, a superconducting magnet has many unique advantages,such as no energy consumption, small volume, light weight, greater efficiency, greater thermal stability,longer magnetic field life and easier cooling, and also the ability to generate a high magnetic fieldin a relatively large space. Superconducting magnet technology has been extensively applied in largescience projects, scientific instruments, inductive heating, magnetic separation, traffic, biomedicine andthe defence industry [15–17].

Because superconductivity appears only at low temperatures, cryogenic technology is an essentialprerequisite for any superconducting apparatus. Maintaining the cryogenic temperature consumes moreenergy and, in particular, maintaining the helium temperature will consume even more energy, which is amajor impediment to the commercialization of low temperature superconductor (LTS) technology in ACoperation. However, the cooling technology greatly influences customer perception of the superconductor

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Fundamental Elements of Applied Superconductivity€¦ · Fundamental elements of applied superconductivity in electrical engineering / Yinshun Wang. pages cm Includes bibliographical