Cable System Transients

Akihiro Ametani, Doshisha University, JapanTeruo Ohno, Tokyo Electric Power Company, JapanNaoto Nagaoka, Doshisha University, Japan

• About the Authors xiPreface xiiiAcknowledgements xv1 Various Cables Used in Practice 1Teruo Ohno1.1 Introduction 11.2 Land Cables 31.2.1 Introduction 31.2.2 XLPE Cables 41.2.3 SCOF Cables 91.2.4 HPOF Cables 101.3 Submarine Cables 111.3.1 Introduction 111.3.2 HVAC Submarine Cables 111.3.3 HVDC Submarine Cables 121.4 Laying Configurations 131.4.1 Burial Condition 131.4.2 Sheath Bonding 14References 192 Impedance and Admittance Formulas 21Akihiro Ametani2.1 Single-core Coaxial Cable (SC Cable) 222.1.1 Impedance 222.1.2 Potential Coefficient 252.2 Pipe-enclosed Type Cable (PT Cable) 272.2.1 Impedance 272.2.2 Potential Coefficient 292.3 Arbitrary Cross-section Conductor 312.3.1 Equivalent Cylindrical Conductor 312.3.2 Examples 322.4 Semiconducting Layer Impedance 352.4.1 Derivation of Impedance 352.4.2 Impedance of Two-layered Conductor 382.4.3 Discussion of the Impedance Formula 382.4.4 Admittance of Semiconducting Layer 402.4.5 Wave Propagation Characteristic of Cable with Core Outer Semiconducting Layer 402.4.6 Concluding Remarks 472.5 Discussion of the Formulation 472.5.1 Discussion of the Formulas 472.5.2 Parameters Influencing Cable Impedance and Admittance 492.6 EMTP Subroutines “Cable Constants” and “Cable Parameters” 522.6.1 Overhead Line 522.6.2 Underground/Overhead Cable 52Appendix 2.A Impedance of an SC Cable Consisting of a Core, a Sheath and an Armor 54Appendix 2.B Potential Coefficient 56Appendix 2.C Internal Impedances of Arbitrary Cross-section Conductor 57Appendix 2.D Derivation of Semiconducting Layer Impedance 58References 613 Theory of Wave Propagation in Cables 63Akihiro Ametani3.1 Modal Theory 633.1.1 Eigenvalues and Vectors 633.1.2 Calculation of a Matrix Function by Eigenvalues/Vectors 653.1.3 Direct Application of Eigenvalue Theory to a Multi-conductor System 663.1.4 Modal Theory 673.1.5 Formulation of Multi-conductor Voltages and Currents 693.1.6 Boundary Conditions and Two-port Theory 713.1.7 Problems 773.2 Basic Characteristics of Wave Propagation on Single-phase SC Cables 783.2.1 Basic Propagation Characteristics for a Transient 783.2.2 Frequency-dependent Characteristics 813.2.3 Time Response of Wave Deformation 843.3 Three-phase Underground SC Cables 843.3.1 Mutual Coupling between Phases 843.3.2 Transformation Matrix 863.3.3 Attenuation and Velocity 873.3.4 Characteristic Impedance 883.4 Effect of Various Parameters of an SC Cable 903.4.1 Buried Depth h 913.4.2 Earth Resistivity ρ e 913.4.3 Sheath Thickness d 913.4.4 Sheath Resistivity ρ s 913.4.5 Arrangement of a Three-phase SC Cable 933.5 Cross-bonded Cable 943.5.1 Introduction of Cross-bonded Cable 943.5.2 Theoretical Formulation of a Cross-bonded Cable 953.5.3 Homogeneous Model of a Cross-bonded Cable 1023.5.4 Difference between Tunnel-installed and Buried Cables 1053.6 PT Cable 1143.6.1 Introduction of PT Cable 1143.6.2 PT Cable with Finite-pipe Thickness 1153.6.3 Effect of Eccentricity of Inner Conductor 1283.6.4 Effect of the Permittivity of the Pipe Inner Insulator 1333.6.5 Overhead PT Cable 1333.7 Propagation Characteristics of Intersheath Modes 1343.7.1 Theoretical Analysis of Intersheath Modes 1343.7.2 Transients on a Cross-bonded Cable 1443.7.3 Earth-return Mode 1593.7.4 Concluding Remarks 160References 1604 Cable Modeling for Transient Simulations 163Teruo Ohno and Akihiro Ametani4.1 Sequence Impedances Using a Lumped PI-circuit Model 1634.1.1 Solidly Bonded Cables 1634.1.2 Cross-bonded Cables 1674.1.3 Derivation of Sequence Impedance Formulas 1684.2 Electromagnetic Transients Program (EMTP) Cable Models for Transient Simulations 1744.3 Dommel Model 1754.4 Semlyen Frequency-dependent Model 1764.4.1 Semlyen Model 1774.4.2 Linear Model 1784.5 Marti Model 1784.6 Latest Frequency-dependent Models 1794.6.1 Vector Fitting 1794.6.2 Frequency Region Partitioning Algorithm 181References 1825 Basic Characteristics of Transients on Single-phase Cables 185Akihiro Ametani5.1 Single-core Coaxial (SC) Cable 1855.1.1 Experimental Observations 1855.1.2 EMTP Simulations 1875.1.3 Theoretical Analysis 1925.1.4 Analytical Evaluation of Parameters 2035.1.5 Analytical Calculation of Transient Voltages 2045.1.6 Concluding Remarks 2115.2 Pipe-enclosed Type (PT) Cable–Effect of Eccentricity 2125.2.1 Model Circuit for the EMTP Simulation 2125.2.2 Simulation Results for Step-function Voltage Source 2145.2.3 FDTD Simulation 2185.2.4 Theoretical Analysis 2185.2.5 Concluding Remarks 2245.3 Effect of a Semiconducting Layer on a Transient 2255.3.1 StepFunctionVoltageAppliedtoa2kmCable 2255.3.2 5 × 70 μs Impulse Voltage Applied to a 40 km Cable 226References 2276 Transient on Three-phase Cables in a Real System 229Akihiro Ametani6.1 Cross-bonded Cable 2296.1.1 Field Test on an 110 kV Oil-filled (OF) Cable 2296.1.2 Effect of Cross-bonding 2296.1.3 Effect of Various Parameters 2326.1.4 Homogeneous Model (See Section 3.5.3) 2376.1.5 PAI-circuit Model 2396.2 Tunnel-installed 275 kV Cable 2406.2.1 Cable Configuration 2406.2.2 Effect of Geometrical Parameters on Wave Propagation 2416.2.3 Field Test on 275 kV XLPE Cable 2436.2.4 Concluding Remarks 2496.3 Cable Installed Underneath a Bridge 2526.3.1 Model System 2526.3.2 Effect of an Overhead Cable and a Bridge 2536.3.3 Effect of Overhead Lines on a Cable Transient 2576.4 Cable Modeling in EMTP Simulations 2626.4.1 Marti’s and Dommel’s Cable Models 2626.4.2 Homogeneous Cable Model (See Section 3.5.3) 2656.4.3 Effect of Tunnel-installed Cable 2656.5 Pipe-enclosed Type (PT) Cable 2666.5.1 Field Test on a 275 kV Pressure Oil-filled (POF) Cable 2666.5.2 Measured Results 2676.5.3 FTP Simulation 2696.6 Gas-insulated Substation (GIS) – Overhead Cables 2746.6.1 Basic Characteristic of an Overhead Cable 2746.6.2 Effect of Spacer in a Bus 2756.6.3 Three-phase Underground Gas-insulated Line 2816.6.4 Switching Surges in a 500 kV GIS 2826.6.5 Basic Characteristics of Switching Surges Induced to a Control Cable 284Appendix 6.A 293Appendix 6.B 295References 2957 Examples of Cable System Transients 297Teruo Ohno7.1 Reactive Power Compensation 2977.2 Temporary Overvoltages 2987.2.1 Series Resonance Overvoltage 2987.2.2 Parallel Resonance Overvoltage 3107.2.3 Overvoltage Caused by System Islanding 3147.3 Slow-front Overvoltages 3177.3.1 Line Energization Overvoltages from a Lumped Source 3177.3.2 Line Energization Overvoltages from a Complex Source 3297.3.3 Analysis of Statistical Distribution of Energization Overvoltages 3327.4 Leading Current Interruption 3417.5 Zero-missing Phenomenon 3427.5.1 Zero-missing Phenomenon and Countermeasures 3427.5.2 Sequential Switching 3447.6 Cable Discharge 346References 3478 Cable Transient in Distributed Generation System 351Naoto Nagaoka8.1 Transient Simulation of Wind Farm 3518.1.1 Circuit Diagram 3518.1.2 Cable Model and Dominant Frequency 3528.1.3 Data for Cable Parameters 3548.1.4 EMTP Data Structure 3598.1.5 Results of Pre-calculation 3638.1.6 Cable Energization 3648.2 Transients in a Solar Plant 3748.2.1 Modeling of Solar Plant 3748.2.2 Simulated Results 379References 388Index 391

“Because the authors have included fundamental background theory, and much practical information, this book will be considered a reference standard on power cable transients for many years.”  (IEEE Electrical Engineering magazine, 1 January 2016)