TRANSIENTS POWER SYSTEM. Theory and Applications TERUO OHNO AKIH1RO AMETANI NAOTO NAGAOKA YOSHIHIRO BABA. CRC Press. Taylor & Francis Croup

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1 POWER SYSTEM TRANSIENTS Theory and Applications AKIH1RO AMETANI NAOTO NAGAOKA YOSHIHIRO BABA TERUO OHNO CRC Press Taylor & Francis Croup Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business

2 Contents Introduction List of Symbols List of Acronyms International Standards xv xix xxi xxiii 1. Theory of Distributed-Parameter Circuits and the Impedance/Admittance Formulas Introduction Impedance and Admittance Formula Conductor Internal Impedance Z, Derivation of an Approximate Formula Accurate Formula by Schelkunoff Outer-Media Impedance Z Outer-Media Impedance Overhead Conductor Pollaczek's General Formula for Overhead, Underground, and Overhead/Underground Conductor Systems Problems Basic Theory of Distributed-Parameter Circuit Partial Differential Equations of Voltages and Currents General Solutions of Voltages and Currents Sinusoidal Excitation Lossless Line 21 and Currents on a Semi-Infinite Line Voltages Solutions of Voltages and Currents Waveforms of Voltages and Currents Phase Velocity Traveling Wave Wave Length Propagation Constants and Characteristic Impedance Propagation Constants Characteristic Impedance Voltages and Currents on a Finite Line Short-Circuited Line Open-Circuited Line Problems 38 v

3 vi Contents 1.4 Multiconductor System Steady-State Solutions Modal Theory Eigenvalue Theory Modal Theory Current Mode Parameters in Modal Domain Two-Port Circuit Theory and Boundary Conditions Four-Terminal Parameter Impedance/Admittance Parameters Modal Distribution of Multiphase Voltages and Currents Transformation Matrix Modal Distribution Problems Frequency-Dependent Effect Frequency Dependence of Impedance Frequency-Dependent Parameters Frequency-Dependent Effect Propagation Constant Characteristic Impedance Transformation Matrix Line Parameters in the Extreme Case Time Response Time-Dependent Responses Propagation Constant: Step Response Characteristic Impedance Transformation Matrix Problems Traveling Wave Reflection and Refraction Coefficients Thevenin's Theorem Equivalent Circuit of a Semi-Infinite Line Voltage and Current Sources at the End 79 Sending Boundary Condition at the Receiving End Thevenin's Theorem Multiple Reflection Multiconductors Reflection and Refraction Coefficients Lossless Two Conductors Consideration of Modal Propagation Consideration of Losses in a Velocities 91 Two-Conductor System Three-Conductor System 99

4 Contents vii Cascaded System Composed of the Different Numbers of Conductors Problems Nonuniform Conductors Characteristic of Nonuniform Conductors Nonuniform Conductor Difference from Uniform Conductors Impedance and Admittance Formulas Finite-Length Horizontal Conductor Vertical Conductor Line Parameters Finite Horizontal Conductor Vertical Conductor Nonparallel Conductor Problems Introduction of EMTP Introduction History of a Transient Analysis Background of EMTP EMTP Development Basic Theory of EMTP Representation of a Circuit Element by a Current Source and a Resistance Composition of Nodal Conductance Other Circuit Elements Solutions of the Problems 131 References Transients on Overhead Lines Introduction Switching Surge on Overhead Line Basic Mechanism of Switching Surge Basic Parameters Influencing Switching Surge Source Circuit Switch Transformer Transmission Line Switching Surges in Practice Classification of Switching Surges Basic Characteristic of Closing Surge: Field Test Results Closing Surge on a Single-Phase Line Closing Surges on a Multiphase Effect of Various Parameters on Line 153 Closing Surge 162

5 viii Contents 2.3 Fault Surge Fault Initiation Surge Characteristic of a Fault Initiation Surge Effect of Line Transposition Overvoltage Distribution Fault-Clearing Surge Lightning Surge Mechanism of Lightning Surge Modeling Lightning Generation 177 of Circuit Elements 179 Current Tower and Gantry Tower Footing Impedance Arc Horn Transmission Line Substation Lightning Surge Overvoltage Model Circuit Lightning Surge Overvoltage Effect of Various Parameters Theoretical Analysis of Transients: Hand Calculations Switching Surge on an Overhead Line Traveling Wave Theory Lumped-Parameter Equivalent with Laplace Transform Fault Surge Lightning Surge Tower Top Voltage Two-Phase Model No Back Flashover Case of a Back Flashover Consideration of Substation Frequency-Domain Method of Transient Simulations Introduction Numerical Fourier/Laplace Transform Finite Fourier Transform Shift of Integral Path: Laplace Transform Numerical Laplace Transform: Discrete Transform 218 Laplace Odd-Number Sampling: Accuracy Improvement Application of FFT: Fast Laplace Transform (FLT) Transient Simulation Definition of Variables 228

6 Contents ix Subroutine to Prepare F(co) Subroutine FLT Remarks of the Frequency-Domain Method 230 References Transients on Cable Systems Introduction Impedance and Admittance of Cable Systems Single-Phase Cable Cable Structure Impedance and Admittance Sheath Bonding 235 Model of a Cross-Bonded Cable Homogeneous Homogeneous Impedance and Admittance Reduction of Sheath Theoretical Formula of Sequence Currents Cross-Bonded Cable Solidly Bonded Cable Wave Propagation and Overvoltages Single-Phase Cable Propagation Constant Example of Transient Analysis Wave Propagation Characteristic Impedance: R, L Capacitance: C Transformation Matrix Attenuation Constant and Propagation Velocity Transient Voltage Limitation of the Sheath Voltage Installation of SVLs Studies on Recent and Planned EHV AC Cable Projects Recent Cable Projects Planned Cable Projects Cable System Design and Equipment Selection Study Flow 277 Phenomenon Zero-Missing Sequential Switching Leading Current Interruption Cable Discharge EMTP Simulation Test Cases 285 References 287

7 X Contents 4. Transient and Dynamic Characteristics of New Energy Systems Wind Farm Model Circuit of Wind Farm Steady-State Analysis Cable Model Charging Current Load-Flow Calculation Transient Calculation Power-Electronics Simulation by EMTP Simple-Switching Circuit Switching-Transistor Model Simple-Switch Model Switch with Delay Model MOSFET Simple Model Modified Switching Device Model Simulation Circuit and Results Thermal Calculation Voltage Regulation Equipment Using Battery in a DC Railway System Introduction Feeding Circuit Measured and Calculated Results Measured Results Calculated Results of Conventional System Calculated Results with Power Compensator Concluding Remarks 343 References Numerical Electromagnetic Analysis Methods and Their Applications to Transient Analyses Fundamentals Maxwell's Equations Finite-Difference Time-Domain Method Method of Moments Applications Grounding Electrodes Transmission Towers Distribution Lines: Lightning-Induced Surges Transmission Lines: Propagation of Lightning Surges in the Presence of Corona Power Cables: Propagation of Power Line Communication Signals 379

8 Contents xi Air-Insulated Substations Wind Turbine Generator Towers 387 References Electromagnetic Disturbances in Power Systems and Customers Introduction Disturbances in Power Stations and Substations Statistical Data of Disturbances Overall Data Disturbed Equipments Surge Incoming Route Characteristics of Disturbances Characteristics of Lightning Surge Disturbances Characteristics of Switching Surge Disturbances Switching Surge in DC Circuits Influence, Countermeasures, and Costs of Disturbances Influence of Disturbances on Power System Operation Countermeasures Carried Out Cost of Countermeasures Case Studies Case No Case No Case No Concluding Remarks Disturbances in Customers and Home Appliances Statistical Data of Disturbances Breakdown Voltage of Home Appliances Testing Voltage Breakdown Test Surge Voltages and Currents into Customers due to Nearby Lightning Introduction Model Circuits for Experiments and EMTP Simulations Experimental and Simulation Results Concluding Remarks Lightning Surge Incoming from a Communication Line Introduction 429

9 xii Contents Protective Device Lightning Surge Concluding 6.4 Analytical Method of Solving Induced Remarks 433 Voltages and Currents Introduction F-Parameter Formulation for Induced and Currents 439 Voltages Formulation of F-Parameter Approximation of F-Parameters Cascaded Connection of Pipelines Application Examples Single Section Terminated by R, and R Two-Cascaded Sections of a Pipeline (Problem 6.1) Three-Cascaded Sections of a Pipeline Comparison with a Field-Test Result Comparison with EMTP Simulations Field-Test Result Concluding Remarks 459 Solution of Problem Appendix 6.A.1 Test Voltage for Low-Voltage Control Circuits in Power Stations and Substations (JEC ) A.2 Traveling Wave Solution A.3 Boundary Conditions and Solutions of a Voltage and a Current A.4 Approximate Formulas for Impedance and Admittance A.5 Accurate Solutions for Two-Cascaded Sections 466 References Problems and Application Limits of Numerical Simulations Problems of Existing Impedance Formulas Used in Circuit Theory-Based Approaches Earth-Return Impedance Carson's Impedance Basic Assumption of the Impedance Nonparallel Conductor Stratified Earth Earth Resistivity and Permittivity Internal Impedance Schelkunoff's Impedance Arbitrary Cross-Section Conductor 473

10 Contents xiii Semiconducting Layer of Cable Proximity Effect Earth-Return Admittance Existing Problems in Circuit Theory-Based Numerical Analysis Reliability of a Simulation Tool Assumption and Limit of a Simulation Tool Input Data 476 for Power 7.3 Numerical Electromagnetic Analysis System Transients 476 References 477 Index 481

Comparison of Transient Simulations on Overhead Cables by EMTP and FDTD

Comparison of Transient Simulations on Overhead Cables by EMTP and FDTD H. Xue, M. Natsui, A. Ametani, J. Mahseredjian, H. Tanaka, Y. Baba 1 Abstract--Transient simulations on an overhead cable are performed