The Theory of Fault Travel Waves and Its Application

Foreword by Jiali He
Foreword by Yaozhong Ge
Foreword by Qixun Yang
Preamble
Contents
1 Introduction
1.1 Power Systems and Faults
1.2 Power System Failure Analysis
1.2.1 Kirchhoff’s Law
1.2.2 Nodal Voltage and Loop Current Methods
1.2.3 Symmetric Component Method
1.2.4 Laplace Transform Method
1.2.5 Shortcomings of Existing Power System Fault Analysis
1.3 Challenges to Traditional Protective Relaying and Fault Detection Techniques
1.3.1 Transmission Line Split-Phase Current Differential Protection
1.3.2 Flexible DC Grid Protection
1.3.3 Single-Phase Grounding Protection for Distribution Lines in Neutral Point Noneffective Grounding Systems
1.3.4 Power Line Fault Location
2 Fundamentals of Electromagnetic Waves
2.1 Time-Varying Electromagnetic Fields
2.1.1 Maxwell’s Equations
2.1.2 Poynting’s Theorem
2.2 Wave Equations and Their D’Alembert Solutions
2.2.1 Wave Equations for the Electromagnetic Field
2.2.2 Dynamic Potentials
2.2.3 D’Alembert Solutions of the Wave Equation
2.3 Planar Electromagnetic Waves
2.3.1 Uniform Plane Waves in an Ideal Medium
2.3.2 Uniform Plane Waves in a Conductive Medium
2.3.3 Reflection of Electromagnetic Waves at the Interface of Different Media
2.4 Guided Electromagnetic Waves in Homogeneous Transmission Lines
2.4.1 Basic Equations for a Homogeneous Transmission Line
2.4.2 Sinusoidal Steady-State Solutions of the Uniform Transmission Line Equation
2.4.3 Equivalent Circuits and Operating States for Uniform Transmission Lines
2.5 Guided Electromagnetic Waves in Parallel Multiconductor Lines
2.5.1 Wave Equations for Parallel Multiconductor Lines
2.5.2 Phase-Modal Transformation of Parallel Multiconductor Lines
2.5.3 Wave Impedance and Wave Velocity on a Parallel Multiconductor Line Modulus
3 Fault Traveling Wave Theory
3.1 Fault Traveling Waves in Single-Phase Uniform Lossless Lines
3.1.1 Generation of Fault Traveling Waves
3.1.2 Fluctuation Equation for a Single Conductor Line
3.2 Fault Traveling Waves in Three-Phase Transmission Lines
3.2.1 Phase Mode Transformation
3.2.2 Composite Modulus Network
3.3 Traveling Wave Phenomena at Nominal Frequency
3.3.1 Line Wave Decomposition
3.3.2 Folded Reflection Phenomena of Traveling Waves
3.4 Status of Research on the Fault Traveling Wave Problem
3.5 Transient Solutions for Fault Traveling Waves Without Considering the Parameter-Dependent Frequency Characteristics
3.5.1 Basic Idea of the Grid Method for Solving Fault Traveling Waves [17]
3.5.2 Analysis of Faulted Traveling Wave Sources
3.5.3 Initial Traveling Waves for Different Traveling Wave Source Moduli
3.5.4 Representation of Power Networks
3.5.5 Reflection of Traveling Waves at Each Node
3.5.6 Fault Traveling Wave Resolution Calculation Method—Frequency Domain Method
3.6 Faulted Traveling Wave Transient Solutions Considering Parametric-Dependent Frequency Characteristics [17]
3.6.1 Complex Frequency Domain Solutions of the Fluctuation Equations for Parallel Multiconductor Lines
3.6.2 Selection of the Fitting Function for Traveling Waves Under Frequency-Dependent Characteristics
3.6.3 Acquisition of Parameters
3.7 Fault Steady-State Calculations
3.8 Computer Implementation of Fault Traveling Wave Transient Solutions
3.8.1 Representation and Storage of Power Networks
3.8.2 Network Changes After a Failure
3.8.3 Generation Method for Traveling Wave Propagation Paths
3.8.4 Calculation of Fault Traveling Waves
3.8.5 Analysis of Algorithms
3.9 Instantaneous Reactive Power Theory and Fault Direction Characteristics
3.9.1 Overview of Instantaneous Reactive Power Theory
3.9.2 Definition of Instantaneous Reactive Power Based on the Hilbert Transform
3.9.3 Fault Direction Characteristics of Reactive Power Under the Hilbert Transform [16]
3.10 Faulty Traveling Wave Characteristics for Various Fault Types
4 Wavelet Transform and Its Application to Fault Traveling Wave Analysis
4.1 Basic Concepts
4.1.1 History of Wavelet Analysis and Overview of Its Applications
4.1.2 Time–Frequency Localized Representation of the Signal
4.1.3 Continuous Wavelet Transform
4.1.4 Time–Frequency Localization Performance of Wavelet Transform
4.1.5 Two Important Types of Wavelet Transforms
4.1.6 Wavelet Representation of the Signal
4.2 Discrete Wavelet Transform
4.2.1 Discrete Wavelets and Discrete Wavelet Transforms
4.2.2 Multiresolution Analysis with Scale Functions
4.2.3 Mallat Algorithm
4.2.4 Coefficient Characteristics of the R-Wavelet
4.2.5 Applications of the Discrete Wavelet Transform
4.3 Dyadic Wavelet Transform and Singularity Detection of the Signal
4.3.1 Dyadic Wavelet and Dyadic Wavelet Transform
4.3.2 B-Sample-Based Dyadic Wavelet Function with a Scale Function
4.3.3 Decomposition and Reconstruction Algorithm for Dyadic Wavelet Transform
4.3.4 Wavelet Transform Modal Maxima Representation of Signals and Singularity Detection Theory
4.3.5 Reconstructing the Original Signal Using Wavelet Transform Modal Maxima [51]
4.3.6 Applications of the Dyadic Wavelet Transform [57]
4.4 Wavelet Representation of Fault Traveling Waves
4.4.1 Introduction
4.4.2 Fault Characteristics of Traveling Waves
4.4.3 Wavelet Transform Mode Maxima Representation of Various Traveling Waves
4.4.4 Comparison of Voltage Traveling Waves, Current Traveling Waves, and Directional Traveling Waves
5 Fault Traveling Wave Transmission Characteristics of Transformers and Secondary Cables
5.1 Current Transformer Model and Its Dynamic Transfer Characteristics
5.1.1 Operating Principle of Current Transformers and Their Electromagnetic Transient Model
5.1.2 Operating Frequency Transfer Characteristics of Current Transformers
5.1.3 Transient Traveling Wave Transfer Characteristics of Current Transformers
5.2 Voltage Transformer Model and Its Dynamic Transfer Characteristics
5.2.1 Operating Principle of Voltage Transformers and Their Corresponding Electromagnetic Transient Models
5.2.2 Operating Frequency Transfer Characteristics of Capacitance-Divided Voltage Transformers
5.2.3 Transient Traveling Wave Transfer Characteristics of Capacitive Voltage Transformers Under a Simplified Model [69]
5.2.4 Transient Traveling Wave Transfer Characteristics of Capacitive Voltage Transformers Under a Detailed Model
5.3 Fault Traveling Wave Transmission Characteristics of Secondary Cables
5.3.1 Equivalence Analysis Between the Centralized and Distributed Parameter Models for the Secondary-Side Cable
5.3.2 Equivalent Modeling of Secondary-Side Cables
5.4 Traveling Wave Transmission Characteristics of the Secondary Current Transmission Channel
5.4.1 Joint Modeling of Secondary Current Loops [89]
5.4.2 Analysis of the Secondary-Side Circuit Transmission Characteristics [89]
6 Transmission Line Longitudinal Traveling Wave Direction Protection
6.1 Wave Impedance Relays
6.1.1 Basic Principles of Wave Impedance Relays
6.1.2 Algorithmic Study of Wave Impedance Relays
6.1.3 Performance Analysis of Wave Impedance Relays
6.1.4 Use of Wave Impedance Relays to Form Longitudinal Directional Protection
6.2 Uniform Traveling Wave Direction Relay
6.2.1 Fundamentals of the Unified Traveling Wave Direction Relay
6.2.2 Uniform Traveling Wave Direction Relay Action Criterion
6.2.3 Modeling and Simulation
6.2.4 Motion Characteristics Analysis
6.2.5 Longitudinal Directional Protection of Transmission Lines Based on Unified Traveling Wave Directional Relays
6.3 Polarization Current Traveling Wave Direction Relay
6.3.1 Consistency of Line Wave Polarity for Voltage Faults at Different Frequency Bands
6.3.2 Polarization Current Traveling Wave Direction Relay Principle and Algorithm
6.3.3 Performance Analysis of Polarization Current Traveling Wave Direction Relay Operation
6.3.4 TP-01 Ultrahigh-Speed Traveling Wave Protection Device
7 Transmission Line Longitudinal Traveling Wave Differential Protection
7.1 Traveling Wave Differential Protection
7.1.1 Basic Principle of Traveling Wave Differential Protection
7.1.2 Traveling Wave Differential Current and Traveling Wave Braking Current Components [112]
7.1.3 Unbalanced Traveling Differential Current Analysis During Out-of-Area Disturbances or Faults
7.1.4 Comparison of Traveling Wave Differential Currents During in- and Out-of-Zone Faults
7.1.5 Action Criteria
7.1.6 Protection Algorithms
7.1.7 Modeling Simulation and Performance Evaluation
7.1.8 PT Disconnection Handling
7.1.9 TP-02 Traveling Wave Differential Protection Device
7.2 Reconfiguration of Current Traveling Wave Differential Protection
7.2.1 Reconstructing the Current Traveling Wave
7.2.2 Characterization of Reconstructed Current Traveling Waves
7.2.3 Principle of Reconfiguration of Current Traveling Wave Differential Protection
7.2.4 Reconfigured Current Traveling Wave Differential Protection Algorithm
7.2.5 Reconfiguration of Current Traveling Wave Differential Protection Performance Evaluation
7.3 Traveling Wave Differential Protection Based on Wavelet Transform Modulus Maxima
7.3.1 Ideas for Constructing Traveling Wave Differential Protection Using Initial Traveling Wave Modulus Maxima
7.3.2 Traveling Wave Differential Protection Algorithm Based on Wavelet Transform Modulus Maxima
7.3.3 Communication Volume Analysis
7.3.4 Impact Factor Analysis and Performance Evaluation
7.4 Modulus Traveling Wave Differential Protection
7.4.1 Distributed Capacitor Current Time Domain Compensation Algorithm and Error Analysis
7.4.2 Modulus Traveling Wave Differential Protection Principle
7.4.3 Operating Characteristics of Modulus Traveling Wave Differential Protection
7.4.4 Lines with Shunt Reactors
7.4.5 Lines with Series Capacitor Compensation Devices
8 DC Line Traveling Wave Protection
8.1 DC Transmission System Protection and Control
8.1.1 DC Transmission Systems
8.1.2 DC Control and Protection Systems
8.2 Analysis of DC Transmission Line Faults
8.2.1 Equivalent Circuit of a DC System
8.2.2 DC Line Fault Traveling Wave Characteristics
8.2.3 LCC DC Line Fault Transient Characteristics
8.2.4 LCC DC Line Fault Steady-State Characteristics
8.2.5 VSC DC Line Fault Traveling Wave Analysis [132]
8.2.6 Approximate Calculation of Short-Circuit Fault Current for MMC DC Transmission Grid Lines
8.3 Single-Ended Ultrahigh-Speed Traveling Wave Protection for DC Lines
8.3.1 Principle of Single-Ended Traveling Wave Protection
8.3.2 Single-Ended Traveling Wave Protection Implementation Scheme
8.3.3 Modeling Simulation and Performance Evaluation
8.3.4 Ultra-PSL3000 Flexible DC Line Protection Device
8.4 Single-Ended DC Line Protection Based on the Rate of Change of the Current
8.4.1 Characterization of the Rate of Change of Line Current Under Different Fault and Operating Conditions
8.4.2 Single-Terminal Quantity Current Rate of Change Protection Scheme
8.5 DC Line Longitudinal Traveling Wave Differential Protection
8.5.1 Principle of DC Line Traveling Wave Differential Protection
8.5.2 Time Domain Calculation Method for Fault Differential Flow
8.5.3 DC Line Traveling Wave Differential Protection Algorithm
8.5.4 Modeling Simulation and Performance Evaluation
8.5.5 TP-03 Traveling Wave Differential Protection Device for EHV DC Lines
9 Transmission Line Transient Traveling Wave Fault Location
9.1 Wavelet Transform-Based Traveling Wave Fault Distance Characterization
9.1.1 Traveling Wave Fault Location Method
9.1.2 Wavelet Transform-Based Traveling Wave Fault Distance Characterization
9.2 Single-End Volume Traveling Wave Fault Location on Transmission Lines
9.2.1 Characteristic Traveling Waves
9.2.2 Fault Location Using Modal Directional Traveling Waves as Characteristic Traveling Waves
9.2.3 Fault Location Using Nonfault Line Currents and Fault Line Currents to Form a Directional Traveling Wave as a Characteristic Traveling Wave
9.2.4 Waveform Comparison Method
9.2.5 Wavelet Transform Method for Single-Ended Electrical Volume Traveling Wave Fault Location [189]
9.2.6 Traveling Waveform Comparison Method Considering the Transient Characteristics of the Secondary Circuit
9.2.7 Fault Point Reflection Wave Criterion Construction
9.2.8 Adjacent Bus Reflection Wave Criterion Construction
9.2.9 Flow Chart of the Waveform Comparison Method Considering the Transient Characteristics of the Secondary Circuit
9.3 Transmission Line Single-Ended Volume Combined Fault Location
9.3.1 Formulation of the Problem
9.3.2 Single-Ended Electrical Volume Impedance Fault Location Methods with Robustness
9.3.3 Combined Single-Ended Fault Location Methods
9.3.4 Improved Combined Fault Location Algorithm
9.4 Transmission Line Double-Ended Volume Traveling Wave Fault Location
9.4.1 Principle of Electrical Volume Traveling Wave Ranging at Both Ends
9.4.2 GPS Timing Principle
9.4.3 Analysis of the Performance of the GPS-Based Two-End Electrical Volume Traveling Wave Ranging
9.5 Fault Location Implementation Scheme for High-Voltage Transmission Lines Using Transient Current Traveling Waves
9.5.1 Ranging System Components and Main Functions
9.5.2 Ranging Program
9.5.3 XC-11 Transmission Line Traveling Wave Fault Location Device
10 Single-Phase Grounding Selection Line Wave Protection for Noneffectively Grounded Distribution Networks at Neutral Points
10.1 Traveling Wave Analysis of Faults in Noneffectively Grounded Distribution Networks at the Neutral Point
10.1.1 Physical Characteristics of the Traveling Wave of a Single-Phase Ground Fault [181]
10.1.2 Wavelet Analysis of the Three-Phase Initial Current Traveling Wave
10.1.3 Wavelet Analysis of the Initial Current Traveling Wave Modal
10.2 Single-Phase Grounding Traveling Wave Line Selection in Neutral Noneffectively Grounded Distribution Networks
10.2.1 The Basic Idea of Traveling Wave Line Selection
10.2.2 Ground Line Selection Method Based on Three-Phase Traveling Waves
10.2.3 Line Selection Method Based on the Initial Current Traveling Wave Modal
10.2.4 Analysis of Factors Affecting Traveling Wave Routing
10.2.5 Implementation of the SL-01 Traveling Wave Routing Device
10.3 Adaptive Time–Frequency Window Distribution Line Traveling Wave Routing
10.3.1 Adaptive Time–Frequency Window Selection Method
10.3.2 Initial Wavehead Calibration Method [175]
10.3.3 Traveling Wave Routing Method for Distribution Lines with Adaptive Time–Frequency Windows
10.4 Single-Phase Grounding Traveling Wave Protection for Distribution Networks with Noneffective Neutral Grounding
10.4.1 Traveling Wave Direction Criterion
10.4.2 Wavelet Representation of the Initial Traveling Wave of a Ground Fault
10.4.3 Selection of the Signal Sampling Rate and Wavelet Scale
10.4.4 Effect of High-Frequency Noise on the Traveling Wave Direction Criterion
10.4.5 Analysis of the Transformer Transmission Characteristics for Traveling Wave Signals
10.4.6 Implementation of Single-Phase Grounding Protection for Noneffectively Grounded Lines at Neutral Points
11 Power Line Travelling Wave Protection Test Systems
11.1 Power Line Travelling Wave Protection Test System Implementation Scheme
11.1.1 Functionality and System Design
11.1.2 Software and Hardware Implementation of the Power Line Travelling Wave Protection Test System [215]
11.2 Testing of the Traveling Wave Protection Tester
11.2.1 Amplitude and Frequency Accuracy Tests of the Output Waveform [14, 17, 210]
11.2.2 Output Waveform Synchronization Test
11.2.3 Switching Inputs Test
11.2.4 Comparison of Whole Group Tests
11.3 TP-01 Test System Test Example
11.3.1 Performance Test Program for Dual-Ended Traveling Wave Fault Location Devices
11.3.2 Testing of Power Line Travelling Wave Direction Comparison Pilot Protection Devices
Appendix A Cross-Reference Table of Symbols
Appendix B Vector Identity
Appendix C Simulation Model of a Four-Terminal Bipolar MMC Flexible DC Transmission Grid
Bibliography