About the Authors xi -- Preface xiii -- Acknowledgements xv -- 1 Various Cables Used in Practice 1 /Teruo Ohno -- 1.1 Introduction 1 -- 1.2 Land Cables 3 -- 1.2.1 Introduction 3 -- 1.2.2 XLPE Cables 4 -- 1.2.3 SCOF Cables 9 -- 1.2.4 HPOF Cables 10 -- 1.3 Submarine Cables 11 -- 1.3.1 Introduction 11 -- 1.3.2 HVAC Submarine Cables 11 -- 1.3.3 HVDC Submarine Cables 12 -- 1.4 Laying Configurations 13 -- 1.4.1 Burial Condition 13 -- 1.4.2 Sheath Bonding 14 -- References 19 -- 2 Impedance and Admittance Formulas 21 /Akihiro Ametani -- 2.1 Single-core Coaxial Cable (SC Cable) 22 -- 2.1.1 Impedance 22 -- 2.1.2 Potential Coefficient 25 -- 2.2 Pipe-enclosed Type Cable (PT Cable) 27 -- 2.2.1 Impedance 27 -- 2.2.2 Potential Coefficient 29 -- 2.3 Arbitrary Cross-section Conductor 31 -- 2.3.1 Equivalent Cylindrical Conductor 31 -- 2.3.2 Examples 32 -- 2.4 Semiconducting Layer Impedance 35 -- 2.4.1 Derivation of Impedance 35 -- 2.4.2 Impedance of Two-layered Conductor 38 -- 2.4.3 Discussion of the Impedance Formula 38 -- 2.4.4 Admittance of Semiconducting Layer 40 -- 2.4.5 Wave Propagation Characteristic of Cable with Core Outer Semiconducting Layer 40 -- 2.4.6 Concluding Remarks 47 -- 2.5 Discussion of the Formulation 47 -- 2.5.1 Discussion of the Formulas 47 -- 2.5.2 Parameters Influencing Cable Impedance and Admittance 49 -- 2.6 EMTP Subroutines “Cable Constants” and “Cable Parameters” 52 -- 2.6.1 Overhead Line 52 -- 2.6.2 Underground/Overhead Cable 52 -- Appendix 2.A Impedance of an SC Cable Consisting of a Core, a Sheath and an Armor 54 -- Appendix 2.B Potential Coefficient 56 -- Appendix 2.C Internal Impedances of Arbitrary Cross-section Conductor 57 -- Appendix 2.D Derivation of Semiconducting Layer Impedance 58 -- References 61 -- 3 Theory ofWave Propagation in Cables 63 /Akihiro Ametani -- 3.1 Modal Theory 63 -- 3.1.1 Eigenvalues and Vectors 63 -- 3.1.2 Calculation of a Matrix Function by Eigenvalues/Vectors 65 -- 3.1.3 Direct Application of Eigenvalue Theory to a Multi-conductor System 66.

3.1.4 Modal Theory 67 -- 3.1.5 Formulation of Multi-conductor Voltages and Currents 69 -- 3.1.6 Boundary Conditions and Two-port Theory 71 -- 3.1.7 Problems 77 -- 3.2 Basic Characteristics of Wave Propagation on Single-phase SC Cables 78 -- 3.2.1 Basic Propagation Characteristics for a Transient 78 -- 3.2.2 Frequency-dependent Characteristics 81 -- 3.2.3 Time Response of Wave Deformation 84 -- 3.3 Three-phase Underground SC Cables 84 -- 3.3.1 Mutual Coupling between Phases 84 -- 3.3.2 Transformation Matrix 86 -- 3.3.3 Attenuation and Velocity 87 -- 3.3.4 Characteristic Impedance 88 -- 3.4 Effect of Various Parameters of an SC Cable 90 -- 3.4.1 Buried Depth h 91 -- 3.4.2 Earth Resistivity ��e 91 -- 3.4.3 Sheath Thickness d 91 -- 3.4.4 Sheath Resistivity ��s 91 -- 3.4.5 Arrangement of a Three-phase SC Cable 93 -- 3.5 Cross-bonded Cable 94 -- 3.5.1 Introduction of Cross-bonded Cable 94 -- 3.5.2 Theoretical Formulation of a Cross-bonded Cable 95 -- 3.5.3 Homogeneous Model of a Cross-bonded Cable 102 -- 3.5.4 Difference between Tunnel-installed and Buried Cables 105 -- 3.6 PT Cable 114 -- 3.6.1 Introduction of PT Cable 114 -- 3.6.2 PT Cable with Finite-pipe Thickness 115 -- 3.6.3 Effect of Eccentricity of Inner Conductor 128 -- 3.6.4 Effect of the Permittivity of the Pipe Inner Insulator 133 -- 3.6.5 Overhead PT Cable 133 -- 3.7 Propagation Characteristics of Intersheath Modes 134 -- 3.7.1 Theoretical Analysis of Intersheath Modes 134 -- 3.7.2 Transients on a Cross-bonded Cable 144 -- 3.7.3 Earth-return Mode 159 -- 3.7.4 Concluding Remarks 160 -- References 160 -- 4 Cable Modeling for Transient Simulations 163 /Teruo Ohno and Akihiro Ametani -- 4.1 Sequence Impedances Using a Lumped PI-circuit Model 163 -- 4.1.1 Solidly Bonded Cables 163 -- 4.1.2 Cross-bonded Cables 167 -- 4.1.3 Derivation of Sequence Impedance Formulas 168 -- 4.2 Electromagnetic Transients Program (EMTP) Cable Models for Transient Simulations 174 -- 4.3 Dommel Model 175 -- 4.4 Semlyen Frequency-dependent Model 176.

4.4.1 Semlyen Model 177 -- 4.4.2 Linear Model 178 -- 4.5 Marti Model 178 -- 4.6 Latest Frequency-dependent Models 179 -- 4.6.1 Vector Fitting 179 -- 4.6.2 Frequency Region Partitioning Algorithm 181 -- References 182 -- 5 Basic Characteristics of Transients on Single-phase Cables 185 /Akihiro Ametani -- 5.1 Single-core Coaxial (SC) Cable 185 -- 5.1.1 Experimental Observations 185 -- 5.1.2 EMTP Simulations 187 -- 5.1.3 Theoretical Analysis 192 -- 5.1.4 Analytical Evaluation of Parameters 203 -- 5.1.5 Analytical Calculation of Transient Voltages 204 -- 5.1.6 Concluding Remarks 211 -- 5.2 Pipe-enclosed Type (PT) Cable-Effect of Eccentricity 212 -- 5.2.1 Model Circuit for the EMTP Simulation 212 -- 5.2.2 Simulation Results for Step-function Voltage Source 214 -- 5.2.3 FDTD Simulation 218 -- 5.2.4 Theoretical Analysis 218 -- 5.2.5 Concluding Remarks 224 -- 5.3 Effect of a Semiconducting Layer on a Transient 225 -- 5.3.1 Step Function Voltage Applied to a 2 km Cable 225 -- 5.3.2 5 x 70 μs Impulse Voltage Applied to a 40 km Cable 226 -- References 227 -- 6 Transient on Three-phase Cables in a Real System 229 /Akihiro Ametani -- 6.1 Cross-bonded Cable 229 -- 6.1.1 Field Test on an 110 kV Oil-filled (OF) Cable 229 -- 6.1.2 Effect of Cross-bonding 229 -- 6.1.3 Effect of Various Parameters 232 -- 6.1.4 Homogeneous Model (See Section 3.5.3) 237 -- 6.1.5 PAI-circuit Model 239 -- 6.2 Tunnel-installed 275 kV Cable 240 -- 6.2.1 Cable Configuration 240 -- 6.2.2 Effect of Geometrical Parameters on Wave Propagation 241 -- 6.2.3 Field Test on 275 kV XLPE Cable 243 -- 6.2.4 Concluding Remarks 249 -- 6.3 Cable Installed Underneath a Bridge 252 -- 6.3.1 Model System 252 -- 6.3.2 Effect of an Overhead Cable and a Bridge 253 -- 6.3.3 Effect of Overhead Lines on a Cable Transient 257 -- 6.4 Cable Modeling in EMTP Simulations 262 -- 6.4.1 Marti's and Dommel's Cable Models 262 -- 6.4.2 Homogeneous Cable Model (See Section 3.5.3) 265 -- 6.4.3 Effect of Tunnel-installed Cable 265 -- 6.5 Pipe-enclosed Type (PT) Cable 266.

6.5.1 Field Test on a 275 kV Pressure Oil-filled (POF) Cable 266 -- 6.5.2 Measured Results 267 -- 6.5.3 FTP Simulation 269 -- 6.6 Gas-insulated Substation (GIS) - Overhead Cables 274 -- 6.6.1 Basic Characteristic of an Overhead Cable 274 -- 6.6.2 Effect of Spacer in a Bus 275 -- 6.6.3 Three-phase Underground Gas-insulated Line 281 -- 6.6.4 Switching Surges in a 500 kV GIS 282 -- 6.6.5 Basic Characteristics of Switching Surges Induced to a Control Cable 284 -- Appendix 6.A 293 -- Appendix 6.B 295 -- References 295 -- 7 Examples of Cable System Transients 297 /Teruo Ohno -- 7.1 Reactive Power Compensation 297 -- 7.2 Temporary Overvoltages 298 -- 7.2.1 Series Resonance Overvoltage 298 -- 7.2.2 Parallel Resonance Overvoltage 310 -- 7.2.3 Overvoltage Caused by System Islanding 314 -- 7.3 Slow-front Overvoltages 317 -- 7.3.1 Line Energization Overvoltages from a Lumped Source 317 -- 7.3.2 Line Energization Overvoltages from a Complex Source 329 -- 7.3.3 Analysis of Statistical Distribution of Energization Overvoltages 332 -- 7.4 Leading Current Interruption 341 -- 7.5 Zero-missing Phenomenon 342 -- 7.5.1 Zero-missing Phenomenon and Countermeasures 342 -- 7.5.2 Sequential Switching 344 -- 7.6 Cable Discharge 346 -- References 347 -- 8 Cable Transient in Distributed Generation System 351 /Naoto Nagaoka -- 8.1 Transient Simulation of Wind Farm 351 -- 8.1.1 Circuit Diagram 351 -- 8.1.2 Cable Model and Dominant Frequency 352 -- 8.1.3 Data for Cable Parameters 354 -- 8.1.4 EMTP Data Structure 359 -- 8.1.5 Results of Pre-calculation 363 -- 8.1.6 Cable Energization 364 -- 8.2 Transients in a Solar Plant 374 -- 8.2.1 Modeling of Solar Plant 374 -- 8.2.2 Simulated Results 379 -- References 388 -- Index 391.